Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(1343,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1343");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.n (of order \(4\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 800) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1407.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1407 |
Dual form | 1600.2.n.k.1343.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | + | 1.00000i | 0.577350 | + | 0.577350i | 0.934172 | − | 0.356822i | \(-0.116140\pi\) |
−0.356822 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.00000i | −0.377964 | + | 0.377964i | −0.870367 | − | 0.492403i | \(-0.836119\pi\) |
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000i | 1.20605i | 0.797724 | + | 0.603023i | \(0.206037\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | − | 4.00000i | 1.10940 | − | 1.10940i | 0.116171 | − | 0.993229i | \(-0.462938\pi\) |
0.993229 | − | 0.116171i | \(-0.0370621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | + | 4.00000i | 0.970143 | + | 0.970143i | 0.999567 | − | 0.0294245i | \(-0.00936746\pi\) |
−0.0294245 | + | 0.999567i | \(0.509367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.00000 | − | 5.00000i | −1.04257 | − | 1.04257i | −0.999053 | − | 0.0435195i | \(-0.986143\pi\) |
−0.0435195 | − | 0.999053i | \(-0.513857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | − | 4.00000i | 0.769800 | − | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000i | 1.43684i | 0.695608 | + | 0.718421i | \(0.255135\pi\) | ||||
−0.695608 | + | 0.718421i | \(0.744865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | + | 4.00000i | −0.696311 | + | 0.696311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.00000 | 1.28103 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.00000 | + | 7.00000i | 1.06749 | + | 1.06749i | 0.997551 | + | 0.0699387i | \(0.0222804\pi\) |
0.0699387 | + | 0.997551i | \(0.477720\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 3.00000i | −0.437595 | + | 0.437595i | −0.891202 | − | 0.453607i | \(-0.850137\pi\) |
0.453607 | + | 0.891202i | \(0.350137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.00000i | 1.12022i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | − | 4.00000i | 0.549442 | − | 0.549442i | −0.376837 | − | 0.926279i | \(-0.622988\pi\) |
0.926279 | + | 0.376837i | \(0.122988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | + | 4.00000i | 0.529813 | + | 0.529813i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | + | 1.00000i | 0.125988 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | + | 3.00000i | −0.366508 | + | 0.366508i | −0.866202 | − | 0.499694i | \(-0.833446\pi\) |
0.499694 | + | 0.866202i | \(0.333446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 10.0000i | − | 1.20386i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0000i | 1.89885i | 0.313993 | + | 0.949425i | \(0.398333\pi\) | ||||
−0.313993 | + | 0.949425i | \(0.601667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | + | 4.00000i | −0.468165 | + | 0.468165i | −0.901319 | − | 0.433155i | \(-0.857400\pi\) |
0.433155 | + | 0.901319i | \(0.357400\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | − | 4.00000i | −0.455842 | − | 0.455842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.00000 | − | 5.00000i | −0.548821 | − | 0.548821i | 0.377279 | − | 0.926100i | \(-0.376860\pi\) |
−0.926100 | + | 0.377279i | \(0.876860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | + | 2.00000i | −0.214423 | + | 0.214423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.0000i | − | 1.06000i | −0.847998 | − | 0.529999i | \(-0.822192\pi\) | ||
0.847998 | − | 0.529999i | \(-0.177808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000i | 0.838628i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.00000 | + | 8.00000i | −0.829561 | + | 0.829561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | − | 12.0000i | −1.21842 | − | 1.21842i | −0.968187 | − | 0.250229i | \(-0.919494\pi\) |
−0.250229 | − | 0.968187i | \(-0.580506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | − | 3.00000i | −0.295599 | − | 0.295599i | 0.543688 | − | 0.839287i | \(-0.317027\pi\) |
−0.839287 | + | 0.543688i | \(0.817027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | − | 3.00000i | 0.290021 | − | 0.290021i | −0.547068 | − | 0.837088i | \(-0.684256\pi\) |
0.837088 | + | 0.547068i | \(0.184256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0000i | 1.53252i | 0.642529 | + | 0.766261i | \(0.277885\pi\) | ||||
−0.642529 | + | 0.766261i | \(0.722115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | − | 8.00000i | 0.752577 | − | 0.752577i | −0.222383 | − | 0.974959i | \(-0.571383\pi\) |
0.974959 | + | 0.222383i | \(0.0713835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.00000 | − | 4.00000i | −0.369800 | − | 0.369800i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.00000 | −0.733359 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.00000 | − | 4.00000i | −0.360668 | − | 0.360668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.0000 | − | 15.0000i | 1.33103 | − | 1.33103i | 0.426589 | − | 0.904445i | \(-0.359715\pi\) |
0.904445 | − | 0.426589i | \(-0.140285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.0000i | 1.23263i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000i | 1.04844i | 0.851581 | + | 0.524222i | \(0.175644\pi\) | ||||
−0.851581 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 4.00000i | −0.346844 | + | 0.346844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.00000 | − | 8.00000i | −0.683486 | − | 0.683486i | 0.277298 | − | 0.960784i | \(-0.410561\pi\) |
−0.960784 | + | 0.277298i | \(0.910561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.0000 | + | 16.0000i | 1.33799 | + | 1.33799i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.00000 | + | 5.00000i | −0.412393 | + | 0.412393i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 8.00000i | − | 0.655386i | −0.944784 | − | 0.327693i | \(-0.893729\pi\) | ||
0.944784 | − | 0.327693i | \(-0.106271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.00000i | − | 0.651031i | −0.945537 | − | 0.325515i | \(-0.894462\pi\) | ||
0.945537 | − | 0.325515i | \(-0.105538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | − | 4.00000i | 0.323381 | − | 0.323381i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.00000 | + | 8.00000i | 0.638470 | + | 0.638470i | 0.950178 | − | 0.311708i | \(-0.100901\pi\) |
−0.311708 | + | 0.950178i | \(0.600901\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.00000 | 0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0000 | 0.788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.00000 | − | 9.00000i | −0.704934 | − | 0.704934i | 0.260531 | − | 0.965465i | \(-0.416102\pi\) |
−0.965465 | + | 0.260531i | \(0.916102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.00000 | + | 5.00000i | −0.386912 | + | 0.386912i | −0.873584 | − | 0.486673i | \(-0.838210\pi\) |
0.486673 | + | 0.873584i | \(0.338210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 19.0000i | − | 1.46154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 4.00000i | − | 0.305888i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.00000 | + | 8.00000i | −0.608229 | + | 0.608229i | −0.942483 | − | 0.334254i | \(-0.891516\pi\) |
0.334254 | + | 0.942483i | \(0.391516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | + | 4.00000i | 0.300658 | + | 0.300658i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | + | 8.00000i | 0.591377 | + | 0.591377i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.0000 | + | 16.0000i | −1.17004 | + | 1.17004i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000i | 0.581914i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.00000 | − | 4.00000i | 0.287926 | − | 0.287926i | −0.548333 | − | 0.836260i | \(-0.684738\pi\) |
0.836260 | + | 0.548333i | \(0.184738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | + | 4.00000i | 0.284988 | + | 0.284988i | 0.835095 | − | 0.550106i | \(-0.185413\pi\) |
−0.550106 | + | 0.835095i | \(0.685413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | −0.423207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | − | 2.00000i | −0.140372 | − | 0.140372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.00000 | + | 5.00000i | −0.347524 | + | 0.347524i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000i | 1.10674i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 20.0000i | − | 1.37686i | −0.725304 | − | 0.688428i | \(-0.758301\pi\) | ||
0.725304 | − | 0.688428i | \(-0.241699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.0000 | + | 16.0000i | −1.09630 | + | 1.09630i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | − | 8.00000i | −0.543075 | − | 0.543075i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.00000 | −0.540590 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.0000 | 2.15255 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.00000 | − | 9.00000i | −0.602685 | − | 0.602685i | 0.338340 | − | 0.941024i | \(-0.390135\pi\) |
−0.941024 | + | 0.338340i | \(0.890135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.00000 | − | 7.00000i | 0.464606 | − | 0.464606i | −0.435556 | − | 0.900162i | \(-0.643448\pi\) |
0.900162 | + | 0.435556i | \(0.143448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.0000i | − | 1.71813i | −0.511868 | − | 0.859064i | \(-0.671046\pi\) | ||
0.511868 | − | 0.859064i | \(-0.328954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.00000i | − | 0.526361i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0000 | − | 12.0000i | 0.786146 | − | 0.786146i | −0.194714 | − | 0.980860i | \(-0.562378\pi\) |
0.980860 | + | 0.194714i | \(0.0623778\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.00000 | + | 8.00000i | 0.519656 | + | 0.519656i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.00000 | − | 7.00000i | −0.449050 | − | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0000 | − | 16.0000i | 1.01806 | − | 1.01806i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 10.0000i | − | 0.633724i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.0000i | − | 0.757433i | −0.925513 | − | 0.378717i | \(-0.876365\pi\) | ||
0.925513 | − | 0.378717i | \(-0.123635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.0000 | − | 20.0000i | 1.25739 | − | 1.25739i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.0000 | + | 16.0000i | 0.998053 | + | 0.998053i | 0.999998 | − | 0.00194553i | \(-0.000619281\pi\) |
−0.00194553 | + | 0.999998i | \(0.500619\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.00000 | + | 9.00000i | 0.554964 | + | 0.554964i | 0.927869 | − | 0.372906i | \(-0.121638\pi\) |
−0.372906 | + | 0.927869i | \(0.621638\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000 | − | 10.0000i | 0.611990 | − | 0.611990i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.0000i | 1.46331i | 0.681677 | + | 0.731653i | \(0.261251\pi\) | ||||
−0.681677 | + | 0.731653i | \(0.738749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.00000i | − | 0.485965i | −0.970031 | − | 0.242983i | \(-0.921874\pi\) | ||
0.970031 | − | 0.242983i | \(-0.0781258\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.00000 | + | 8.00000i | −0.484182 | + | 0.484182i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0000 | + | 16.0000i | 0.961347 | + | 0.961347i | 0.999280 | − | 0.0379334i | \(-0.0120775\pi\) |
−0.0379334 | + | 0.999280i | \(0.512077\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0000 | −1.19310 | −0.596550 | − | 0.802576i | \(-0.703462\pi\) | ||||
−0.596550 | + | 0.802576i | \(0.703462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00000 | + | 5.00000i | 0.297219 | + | 0.297219i | 0.839924 | − | 0.542705i | \(-0.182600\pi\) |
−0.542705 | + | 0.839924i | \(0.682600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | − | 4.00000i | 0.236113 | − | 0.236113i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000i | 0.882353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 24.0000i | − | 1.40690i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.00000 | − | 8.00000i | 0.467365 | − | 0.467365i | −0.433695 | − | 0.901060i | \(-0.642790\pi\) |
0.901060 | + | 0.433695i | \(0.142790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.0000 | + | 16.0000i | 0.928414 | + | 0.928414i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −40.0000 | −2.31326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0000 | −0.806947 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.00000 | − | 6.00000i | −0.344691 | − | 0.344691i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.00000 | + | 3.00000i | −0.171219 | + | 0.171219i | −0.787515 | − | 0.616296i | \(-0.788633\pi\) |
0.616296 | + | 0.787515i | \(0.288633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.00000i | − | 0.341328i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.00000i | − | 0.453638i | −0.973937 | − | 0.226819i | \(-0.927167\pi\) | ||
0.973937 | − | 0.226819i | \(-0.0728326\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.0000 | − | 20.0000i | −1.12331 | − | 1.12331i | −0.991240 | − | 0.132072i | \(-0.957837\pi\) |
−0.132072 | − | 0.991240i | \(-0.542163\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0000 | + | 16.0000i | 0.890264 | + | 0.890264i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.0000 | + | 16.0000i | −0.884802 | + | 0.884802i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.00000i | − | 0.330791i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 12.0000i | − | 0.659580i | −0.944054 | − | 0.329790i | \(-0.893022\pi\) | ||
0.944054 | − | 0.329790i | \(-0.106978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0000 | − | 16.0000i | −0.871576 | − | 0.871576i | 0.121069 | − | 0.992644i | \(-0.461368\pi\) |
−0.992644 | + | 0.121069i | \(0.961368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0000 | 0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.0000 | −1.73290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.00000 | − | 1.00000i | 0.0536828 | − | 0.0536828i | −0.679756 | − | 0.733439i | \(-0.737914\pi\) |
0.733439 | + | 0.679756i | \(0.237914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.00000i | − | 0.107058i | −0.998566 | − | 0.0535288i | \(-0.982953\pi\) | ||
0.998566 | − | 0.0535288i | \(-0.0170469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 32.0000i | − | 1.70803i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.00000 | − | 8.00000i | −0.423405 | − | 0.423405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.00000 | − | 5.00000i | −0.262432 | − | 0.262432i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.0000 | + | 23.0000i | −1.20059 | + | 1.20059i | −0.226603 | + | 0.973987i | \(0.572762\pi\) |
−0.973987 | + | 0.226603i | \(0.927238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.00000i | 0.208232i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.00000i | 0.415339i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.0000 | − | 24.0000i | 1.24267 | − | 1.24267i | 0.283785 | − | 0.958888i | \(-0.408410\pi\) |
0.958888 | − | 0.283785i | \(-0.0915902\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000 | + | 8.00000i | 0.412021 | + | 0.412021i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.0000 | 1.53695 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.0000 | − | 17.0000i | −0.868659 | − | 0.868659i | 0.123665 | − | 0.992324i | \(-0.460535\pi\) |
−0.992324 | + | 0.123665i | \(0.960535\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.00000 | − | 7.00000i | 0.355830 | − | 0.355830i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 8.00000i | − | 0.405616i | −0.979219 | − | 0.202808i | \(-0.934993\pi\) | ||
0.979219 | − | 0.202808i | \(-0.0650067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 40.0000i | − | 2.02289i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | + | 12.0000i | −0.605320 | + | 0.605320i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000 | + | 4.00000i | 0.200754 | + | 0.200754i | 0.800323 | − | 0.599569i | \(-0.204661\pi\) |
−0.599569 | + | 0.800323i | \(0.704661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.0000 | + | 32.0000i | 1.59403 | + | 1.59403i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.0000i | − | 0.988936i | −0.869196 | − | 0.494468i | \(-0.835363\pi\) | ||
0.869196 | − | 0.494468i | \(-0.164637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 16.0000i | − | 0.789222i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | + | 4.00000i | −0.196827 | + | 0.196827i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000 | + | 12.0000i | 0.587643 | + | 0.587643i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | + | 3.00000i | 0.145865 | + | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.00000 | + | 8.00000i | −0.387147 | + | 0.387147i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.0000i | 1.54497i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000i | 0.385346i | 0.981263 | + | 0.192673i | \(0.0617157\pi\) | ||||
−0.981263 | + | 0.192673i | \(0.938284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0000 | + | 20.0000i | −0.961139 | + | 0.961139i | −0.999273 | − | 0.0381340i | \(-0.987859\pi\) |
0.0381340 | + | 0.999273i | \(0.487859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.0000 | − | 20.0000i | −0.956730 | − | 0.956730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.0000 | − | 13.0000i | −0.617649 | − | 0.617649i | 0.327279 | − | 0.944928i | \(-0.393868\pi\) |
−0.944928 | + | 0.327279i | \(0.893868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.00000 | − | 8.00000i | 0.378387 | − | 0.378387i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.00000i | 0.188772i | 0.995536 | + | 0.0943858i | \(0.0300887\pi\) | ||||
−0.995536 | + | 0.0943858i | \(0.969911\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.0000i | − | 0.753411i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.00000 | − | 8.00000i | 0.375873 | − | 0.375873i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32.0000 | 1.49363 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.00000 | − | 3.00000i | −0.139422 | − | 0.139422i | 0.633951 | − | 0.773373i | \(-0.281432\pi\) |
−0.773373 | + | 0.633951i | \(0.781432\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.0000 | − | 25.0000i | 1.15686 | − | 1.15686i | 0.171715 | − | 0.985147i | \(-0.445069\pi\) |
0.985147 | − | 0.171715i | \(-0.0549310\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.00000i | − | 0.277054i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0000i | 0.737241i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.0000 | + | 28.0000i | −1.28744 | + | 1.28744i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.00000 | − | 4.00000i | −0.183147 | − | 0.183147i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0000 | −0.731059 | −0.365529 | − | 0.930800i | \(-0.619112\pi\) | ||||
−0.365529 | + | 0.930800i | \(0.619112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0000 | + | 10.0000i | 0.455016 | + | 0.455016i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.0000 | − | 25.0000i | 1.13286 | − | 1.13286i | 0.143158 | − | 0.989700i | \(-0.454274\pi\) |
0.989700 | − | 0.143158i | \(-0.0457258\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 18.0000i | − | 0.813988i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000i | 0.541552i | 0.962642 | + | 0.270776i | \(0.0872803\pi\) | ||||
−0.962642 | + | 0.270776i | \(0.912720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | + | 8.00000i | −0.360302 | + | 0.360302i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | − | 16.0000i | −0.717698 | − | 0.717698i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0000 | −0.446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.0000 | − | 11.0000i | −0.490466 | − | 0.490466i | 0.417987 | − | 0.908453i | \(-0.362736\pi\) |
−0.908453 | + | 0.417987i | \(0.862736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.0000 | − | 19.0000i | 0.843820 | − | 0.843820i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 30.0000i | − | 1.32973i | −0.746965 | − | 0.664863i | \(-0.768490\pi\) | ||
0.746965 | − | 0.664863i | \(-0.231510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.00000i | − | 0.353899i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.0000 | − | 16.0000i | 0.706417 | − | 0.706417i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 12.0000i | −0.527759 | − | 0.527759i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0000 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.00000 | + | 5.00000i | 0.218635 | + | 0.218635i | 0.807923 | − | 0.589288i | \(-0.200592\pi\) |
−0.589288 | + | 0.807923i | \(0.700592\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.0000 | + | 32.0000i | −1.39394 | + | 1.39394i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.0000i | 1.17391i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.00000i | − | 0.173585i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.0000 | + | 16.0000i | −0.693037 | + | 0.693037i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | − | 12.0000i | −0.517838 | − | 0.517838i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.0000 | −0.861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.0000 | − | 10.0000i | −0.429141 | − | 0.429141i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.0000 | + | 17.0000i | −0.726868 | + | 0.726868i | −0.969994 | − | 0.243127i | \(-0.921827\pi\) |
0.243127 | + | 0.969994i | \(0.421827\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 8.00000i | − | 0.341432i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.00000i | 0.340811i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | + | 8.00000i | −0.340195 | + | 0.340195i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 56.0000 | 2.36855 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.0000 | −1.35104 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0000 | − | 15.0000i | −0.632175 | − | 0.632175i | 0.316438 | − | 0.948613i | \(-0.397513\pi\) |
−0.948613 | + | 0.316438i | \(0.897513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.00000 | + | 5.00000i | −0.209980 | + | 0.209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0000i | 0.838444i | 0.907884 | + | 0.419222i | \(0.137697\pi\) | ||||
−0.907884 | + | 0.419222i | \(0.862303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.00000i | − | 0.167395i | −0.996491 | − | 0.0836974i | \(-0.973327\pi\) | ||
0.996491 | − | 0.0836974i | \(-0.0266729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.00000 | + | 8.00000i | 0.333044 | + | 0.333044i | 0.853741 | − | 0.520697i | \(-0.174328\pi\) |
−0.520697 | + | 0.853741i | \(0.674328\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.00000 | 0.332469 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0000 | 0.414870 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.0000 | + | 16.0000i | 0.662652 | + | 0.662652i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.0000 | + | 25.0000i | −1.03186 | + | 1.03186i | −0.0323850 | + | 0.999475i | \(0.510310\pi\) |
−0.999475 | + | 0.0323850i | \(0.989690\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0000i | 1.31854i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.00000i | 0.329076i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.00000 | − | 8.00000i | 0.328521 | − | 0.328521i | −0.523503 | − | 0.852024i | \(-0.675375\pi\) |
0.852024 | + | 0.523503i | \(0.175375\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.00000 | 0.163163 | 0.0815817 | − | 0.996667i | \(-0.474003\pi\) | ||||
0.0815817 | + | 0.996667i | \(0.474003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.00000 | + | 3.00000i | 0.122169 | + | 0.122169i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.00000 | − | 5.00000i | 0.202944 | − | 0.202944i | −0.598316 | − | 0.801260i | \(-0.704163\pi\) |
0.801260 | + | 0.598316i | \(0.204163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 4.00000i | − | 0.162088i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000i | 0.970936i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0000 | + | 12.0000i | −0.484675 | + | 0.484675i | −0.906621 | − | 0.421946i | \(-0.861347\pi\) |
0.421946 | + | 0.906621i | \(0.361347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.00000 | − | 4.00000i | −0.161034 | − | 0.161034i | 0.621991 | − | 0.783025i | \(-0.286324\pi\) |
−0.783025 | + | 0.621991i | \(0.786324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000 | 0.482321 | 0.241160 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.0000 | −1.60514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.0000 | + | 10.0000i | 0.400642 | + | 0.400642i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0000 | + | 16.0000i | −0.638978 | + | 0.638978i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000i | 1.59237i | 0.605050 | + | 0.796187i | \(0.293153\pi\) | ||||
−0.605050 | + | 0.796187i | \(0.706847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.0000 | − | 20.0000i | 0.794929 | − | 0.794929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.0000 | + | 20.0000i | 0.792429 | + | 0.792429i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.0000 | 0.632950 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0000 | 0.473972 | 0.236986 | − | 0.971513i | \(-0.423841\pi\) | ||||
0.236986 | + | 0.971513i | \(0.423841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.0000 | − | 11.0000i | −0.433798 | − | 0.433798i | 0.456120 | − | 0.889918i | \(-0.349239\pi\) |
−0.889918 | + | 0.456120i | \(0.849239\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.00000 | − | 1.00000i | 0.0393141 | − | 0.0393141i | −0.687176 | − | 0.726491i | \(-0.741150\pi\) |
0.726491 | + | 0.687176i | \(0.241150\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000i | 0.628055i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 16.0000i | − | 0.627089i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.0000 | − | 20.0000i | 0.782660 | − | 0.782660i | −0.197619 | − | 0.980279i | \(-0.563321\pi\) |
0.980279 | + | 0.197619i | \(0.0633207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | + | 4.00000i | 0.156055 | + | 0.156055i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.00000 | 0.155818 | 0.0779089 | − | 0.996960i | \(-0.475176\pi\) | ||||
0.0779089 | + | 0.996960i | \(0.475176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 32.0000 | + | 32.0000i | 1.24278 | + | 1.24278i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000 | − | 10.0000i | 0.387202 | − | 0.387202i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 18.0000i | − | 0.695920i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.0000i | 1.23535i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.00000 | + | 4.00000i | −0.154189 | + | 0.154189i | −0.779986 | − | 0.625797i | \(-0.784774\pi\) |
0.625797 | + | 0.779986i | \(0.284774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.0000 | + | 20.0000i | 0.768662 | + | 0.768662i | 0.977871 | − | 0.209209i | \(-0.0670888\pi\) |
−0.209209 | + | 0.977871i | \(0.567089\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000 | 0.921035 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0000 | 0.536481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.0000 | − | 17.0000i | −0.650487 | − | 0.650487i | 0.302623 | − | 0.953110i | \(-0.402138\pi\) |
−0.953110 | + | 0.302623i | \(0.902138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.0000 | − | 26.0000i | 0.991962 | − | 0.991962i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 32.0000i | − | 1.21910i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000i | 0.760836i | 0.924815 | + | 0.380418i | \(0.124220\pi\) | ||||
−0.924815 | + | 0.380418i | \(0.875780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00000 | + | 4.00000i | −0.151947 | + | 0.151947i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0000 | − | 16.0000i | −0.606043 | − | 0.606043i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0000 | 0.907763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.0000 | 1.81293 | 0.906467 | − | 0.422276i | \(-0.138769\pi\) | ||||
0.906467 | + | 0.422276i | \(0.138769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | − | 6.00000i | 0.225653 | − | 0.225653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.00000i | − | 0.225335i | −0.993633 | − | 0.112667i | \(-0.964061\pi\) | ||
0.993633 | − | 0.112667i | \(-0.0359394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.00000i | − | 0.300023i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.0000 | − | 40.0000i | 1.49801 | − | 1.49801i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.0000 | − | 24.0000i | −0.896296 | − | 0.896296i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.00000 | + | 4.00000i | 0.148762 | + | 0.148762i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0000 | − | 15.0000i | 0.556319 | − | 0.556319i | −0.371938 | − | 0.928257i | \(-0.621307\pi\) |
0.928257 | + | 0.371938i | \(0.121307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 56.0000i | 2.07123i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.0000 | + | 24.0000i | −0.886460 | + | 0.886460i | −0.994181 | − | 0.107721i | \(-0.965645\pi\) |
0.107721 | + | 0.994181i | \(0.465645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | − | 12.0000i | −0.442026 | − | 0.442026i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.0000 | 1.91285 | 0.956425 | − | 0.291977i | \(-0.0943129\pi\) | ||||
0.956425 | + | 0.291977i | \(0.0943129\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.0000 | 1.17555 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.00000 | − | 1.00000i | −0.0366864 | − | 0.0366864i | 0.688526 | − | 0.725212i | \(-0.258258\pi\) |
−0.725212 | + | 0.688526i | \(0.758258\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.00000 | + | 5.00000i | −0.182940 | + | 0.182940i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000i | 0.219235i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 16.0000i | − | 0.583848i | −0.956441 | − | 0.291924i | \(-0.905705\pi\) | ||
0.956441 | − | 0.291924i | \(-0.0942955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000 | − | 12.0000i | 0.437304 | − | 0.437304i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0000 | + | 24.0000i | 0.872295 | + | 0.872295i | 0.992722 | − | 0.120427i | \(-0.0384265\pi\) |
−0.120427 | + | 0.992722i | \(0.538426\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 40.0000 | 1.45191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | − | 16.0000i | −0.579239 | − | 0.579239i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.0000 | − | 16.0000i | 0.577727 | − | 0.577727i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00000i | 0.0721218i | 0.999350 | + | 0.0360609i | \(0.0114810\pi\) | ||||
−0.999350 | + | 0.0360609i | \(0.988519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.0000i | 1.15245i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.0000 | + | 20.0000i | −0.719350 | + | 0.719350i | −0.968472 | − | 0.249122i | \(-0.919858\pi\) |
0.249122 | + | 0.968472i | \(0.419858\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.0000 | −0.573259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −64.0000 | −2.29010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000 | + | 8.00000i | 0.285897 | + | 0.285897i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.0000 | − | 11.0000i | 0.392108 | − | 0.392108i | −0.483330 | − | 0.875438i | \(-0.660573\pi\) |
0.875438 | + | 0.483330i | \(0.160573\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.0000i | 0.640817i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.0000i | 0.568895i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.0000 | − | 32.0000i | 1.13635 | − | 1.13635i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 |