Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(13,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.s (of order \(4\), degree \(2\), 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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40282095616.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 8x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 13.3 | ||
Root | \(1.03179 - 1.39119i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.13 |
Dual form | 280.2.s.a.237.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | ||||
\(3\) | 0.359404 | + | 0.359404i | 0.207502 | + | 0.207502i | 0.803205 | − | 0.595703i | \(-0.203126\pi\) |
−0.595703 | + | 0.803205i | \(0.703126\pi\) | |||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | −1.39119 | − | 1.75060i | −0.622160 | − | 0.782890i | ||||
\(6\) | −0.718808 | −0.293452 | ||||||||
\(7\) | −1.87083 | + | 1.87083i | −0.707107 | + | 0.707107i | ||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | − | 2.74166i | − | 0.913886i | ||||||
\(10\) | 3.14179 | + | 0.359404i | 0.993520 | + | 0.113654i | ||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0.718808 | − | 0.718808i | 0.207502 | − | 0.207502i | ||||
\(13\) | −4.48655 | − | 4.48655i | −1.24435 | − | 1.24435i | −0.958180 | − | 0.286166i | \(-0.907619\pi\) |
−0.286166 | − | 0.958180i | \(-0.592381\pi\) | |||||||
\(14\) | − | 3.74166i | − | 1.00000i | ||||||
\(15\) | 0.129171 | − | 1.12917i | 0.0333519 | − | 0.291551i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | 2.74166 | + | 2.74166i | 0.646215 | + | 0.646215i | ||||
\(19\) | − | 7.62834i | − | 1.75006i | −0.484067 | − | 0.875031i | \(-0.660841\pi\) | ||
0.484067 | − | 0.875031i | \(-0.339159\pi\) | |||||||
\(20\) | −3.50119 | + | 2.78238i | −0.782890 | + | 0.622160i | ||||
\(21\) | −1.34477 | −0.293452 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.741657 | + | 0.741657i | 0.154646 | + | 0.154646i | 0.780189 | − | 0.625543i | \(-0.215123\pi\) |
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 1.43762i | 0.293452i | ||||||||
\(25\) | −1.12917 | + | 4.87083i | −0.225834 | + | 0.974166i | ||||
\(26\) | 8.97311 | 1.75977 | ||||||||
\(27\) | 2.06358 | − | 2.06358i | 0.397135 | − | 0.397135i | ||||
\(28\) | 3.74166 | + | 3.74166i | 0.707107 | + | 0.707107i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 1.00000 | + | 1.25834i | 0.182574 | + | 0.229741i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 4.00000 | − | 4.00000i | 0.707107 | − | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.87775 | + | 0.672384i | 0.993520 | + | 0.113654i | ||||
\(36\) | −5.48331 | −0.913886 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 7.62834 | + | 7.62834i | 1.23748 | + | 1.23748i | ||||
\(39\) | − | 3.22497i | − | 0.516409i | ||||||
\(40\) | 0.718808 | − | 6.28357i | 0.113654 | − | 0.993520i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 1.34477 | − | 1.34477i | 0.207502 | − | 0.207502i | ||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.79953 | + | 3.81417i | −0.715472 | + | 0.568583i | ||||
\(46\) | −1.48331 | −0.218703 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | −1.43762 | − | 1.43762i | −0.207502 | − | 0.207502i | ||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | −3.74166 | − | 6.00000i | −0.529150 | − | 0.848528i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.97311 | + | 8.97311i | −1.24435 | + | 1.24435i | ||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 4.12715i | 0.561634i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.48331 | −1.00000 | ||||||||
\(57\) | 2.74166 | − | 2.74166i | 0.363141 | − | 0.363141i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.3495i | 1.99834i | 0.0407464 | + | 0.999170i | \(0.487026\pi\) | ||||
−0.0407464 | + | 0.999170i | \(0.512974\pi\) | |||||||
\(60\) | −2.25834 | − | 0.258343i | −0.291551 | − | 0.0333519i | ||||
\(61\) | −14.6307 | −1.87327 | −0.936636 | − | 0.350304i | \(-0.886078\pi\) | ||||
−0.936636 | + | 0.350304i | \(0.886078\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.12917 | + | 5.12917i | 0.646215 | + | 0.646215i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −1.61249 | + | 14.0958i | −0.200004 | + | 1.74837i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.533109i | 0.0641788i | ||||||||
\(70\) | −6.55013 | + | 5.20536i | −0.782890 | + | 0.622160i | ||||
\(71\) | 7.22497 | 0.857446 | 0.428723 | − | 0.903436i | \(-0.358964\pi\) | ||||
0.428723 | + | 0.903436i | \(0.358964\pi\) | |||||||
\(72\) | 5.48331 | − | 5.48331i | 0.646215 | − | 0.646215i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.15642 | + | 1.34477i | −0.249002 | + | 0.155280i | ||||
\(76\) | −15.2567 | −1.75006 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.22497 | + | 3.22497i | 0.365156 | + | 0.365156i | ||||
\(79\) | − | 15.7417i | − | 1.77107i | −0.464568 | − | 0.885537i | \(-0.653790\pi\) | ||
0.464568 | − | 0.885537i | \(-0.346210\pi\) | |||||||
\(80\) | 5.56477 | + | 7.00238i | 0.622160 | + | 0.782890i | ||||
\(81\) | −6.74166 | −0.749073 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.83132 | + | 5.83132i | 0.640071 | + | 0.640071i | 0.950573 | − | 0.310502i | \(-0.100497\pi\) |
−0.310502 | + | 0.950573i | \(0.600497\pi\) | |||||||
\(84\) | 2.68953i | 0.293452i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0.985363 | − | 8.61370i | 0.103866 | − | 0.907964i | ||||
\(91\) | 16.7871 | 1.75977 | ||||||||
\(92\) | 1.48331 | − | 1.48331i | 0.154646 | − | 0.154646i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.3541 | + | 10.6125i | −1.37011 | + | 1.08882i | ||||
\(96\) | 2.87523 | 0.293452 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 7.00000 | + | 7.00000i | 0.707107 | + | 0.707107i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.74166 | + | 2.25834i | 0.974166 | + | 0.225834i | ||||
\(101\) | 13.1931 | 1.31276 | 0.656382 | − | 0.754429i | \(-0.272086\pi\) | ||||
0.656382 | + | 0.754429i | \(0.272086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | − | 17.9462i | − | 1.75977i | ||||||
\(105\) | 1.87083 | + | 2.35414i | 0.182574 | + | 0.229741i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | −4.12715 | − | 4.12715i | −0.397135 | − | 0.397135i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.48331 | − | 7.48331i | 0.707107 | − | 0.707107i | ||||
\(113\) | −11.2250 | − | 11.2250i | −1.05596 | − | 1.05596i | −0.998339 | − | 0.0576178i | \(-0.981650\pi\) |
−0.0576178 | − | 0.998339i | \(-0.518350\pi\) | |||||||
\(114\) | 5.48331i | 0.513559i | ||||||||
\(115\) | 0.266555 | − | 2.33013i | 0.0248564 | − | 0.217286i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.3006 | + | 12.3006i | −1.13719 | + | 1.13719i | ||||
\(118\) | −15.3495 | − | 15.3495i | −1.41304 | − | 1.41304i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.51669 | − | 2.00000i | 0.229741 | − | 0.182574i | ||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 14.6307 | − | 14.6307i | 1.32460 | − | 1.32460i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0977 | − | 4.79953i | 0.903170 | − | 0.429283i | ||||
\(126\) | −10.2583 | −0.913886 | ||||||||
\(127\) | −12.2250 | + | 12.2250i | −1.08479 | + | 1.08479i | −0.0887357 | + | 0.996055i | \(0.528283\pi\) |
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.4833 | − | 15.7083i | −1.09486 | − | 1.37771i | ||||
\(131\) | −4.93881 | −0.431506 | −0.215753 | − | 0.976448i | \(-0.569221\pi\) | ||||
−0.215753 | + | 0.976448i | \(0.569221\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.2713 | + | 14.2713i | 1.23748 | + | 1.23748i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.48331 | − | 0.741657i | −0.557995 | − | 0.0638317i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4833 | − | 16.4833i | 1.40826 | − | 1.40826i | 0.639343 | − | 0.768922i | \(-0.279207\pi\) |
0.768922 | − | 0.639343i | \(-0.220793\pi\) | |||||||
\(138\) | −0.533109 | − | 0.533109i | −0.0453813 | − | 0.0453813i | ||||
\(139\) | − | 12.4743i | − | 1.05806i | −0.848604 | − | 0.529028i | \(-0.822557\pi\) | ||
0.848604 | − | 0.529028i | \(-0.177443\pi\) | |||||||
\(140\) | 1.34477 | − | 11.7555i | 0.113654 | − | 0.993520i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.22497 | + | 7.22497i | −0.606306 | + | 0.606306i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.9666i | 0.913886i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.51583 | − | 2.51583i | 0.207502 | − | 0.207502i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0.811658 | − | 3.50119i | 0.0662716 | − | 0.285871i | ||||
\(151\) | 22.4499 | 1.82695 | 0.913475 | − | 0.406894i | \(-0.133388\pi\) | ||||
0.913475 | + | 0.406894i | \(0.133388\pi\) | |||||||
\(152\) | 15.2567 | − | 15.2567i | 1.23748 | − | 1.23748i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.44994 | −0.516409 | ||||||||
\(157\) | 16.4277 | − | 16.4277i | 1.31108 | − | 1.31108i | 0.390455 | − | 0.920622i | \(-0.372318\pi\) |
0.920622 | − | 0.390455i | \(-0.127682\pi\) | |||||||
\(158\) | 15.7417 | + | 15.7417i | 1.25234 | + | 1.25234i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.5671 | − | 1.43762i | −0.993520 | − | 0.113654i | ||||
\(161\) | −2.77503 | −0.218703 | ||||||||
\(162\) | 6.74166 | − | 6.74166i | 0.529675 | − | 0.529675i | ||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.6626 | −0.905197 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | −2.68953 | − | 2.68953i | −0.207502 | − | 0.207502i | ||||
\(169\) | 27.2583i | 2.09680i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.9143 | −1.59936 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.5525 | − | 13.5525i | −1.03038 | − | 1.03038i | −0.999524 | − | 0.0308546i | \(-0.990177\pi\) |
−0.0308546 | − | 0.999524i | \(-0.509823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.00000 | − | 11.2250i | −0.529150 | − | 0.848528i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.51669 | + | 5.51669i | −0.414659 | + | 0.414659i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 7.62834 | + | 9.59907i | 0.568583 | + | 0.715472i | ||||
\(181\) | 19.2910 | 1.43389 | 0.716944 | − | 0.697131i | \(-0.245540\pi\) | ||||
0.716944 | + | 0.697131i | \(0.245540\pi\) | |||||||
\(182\) | −16.7871 | + | 16.7871i | −1.24435 | + | 1.24435i | ||||
\(183\) | −5.25834 | − | 5.25834i | −0.388708 | − | 0.388708i | ||||
\(184\) | 2.96663i | 0.218703i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.72119i | 0.561634i | ||||||||
\(190\) | 2.74166 | − | 23.9666i | 0.198901 | − | 1.73872i | ||||
\(191\) | 27.2250 | 1.96993 | 0.984965 | − | 0.172754i | \(-0.0552667\pi\) | ||||
0.984965 | + | 0.172754i | \(0.0552667\pi\) | |||||||
\(192\) | −2.87523 | + | 2.87523i | −0.207502 | + | 0.207502i | ||||
\(193\) | −6.00000 | − | 6.00000i | −0.431889 | − | 0.431889i | 0.457381 | − | 0.889271i | \(-0.348787\pi\) |
−0.889271 | + | 0.457381i | \(0.848787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.64562 | + | 4.48655i | −0.404291 | + | 0.321289i | ||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −12.0000 | + | 7.48331i | −0.848528 | + | 0.529150i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.1931 | + | 13.1931i | −0.928264 | + | 0.928264i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.03337 | − | 2.03337i | 0.141329 | − | 0.141329i | ||||
\(208\) | 17.9462 | + | 17.9462i | 1.24435 | + | 1.24435i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.22497 | − | 0.483315i | −0.291551 | − | 0.0333519i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.59668 | + | 2.59668i | 0.177922 | + | 0.177922i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.25430 | 0.561634 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 14.9666i | 1.00000i | ||||||||
\(225\) | 13.3541 | + | 3.09580i | 0.890276 | + | 0.206387i | ||||
\(226\) | 22.4499 | 1.49335 | ||||||||
\(227\) | −21.0880 | + | 21.0880i | −1.39966 | + | 1.39966i | −0.598647 | + | 0.801013i | \(0.704295\pi\) |
−0.801013 | + | 0.598647i | \(0.795705\pi\) | |||||||
\(228\) | −5.48331 | − | 5.48331i | −0.363141 | − | 0.363141i | ||||
\(229\) | 18.9436i | 1.25183i | 0.779893 | + | 0.625913i | \(0.215274\pi\) | ||||
−0.779893 | + | 0.625913i | \(0.784726\pi\) | |||||||
\(230\) | 2.06358 | + | 2.59668i | 0.136068 | + | 0.171220i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.9666 | − | 17.9666i | −1.17703 | − | 1.17703i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) |
−0.196537 | − | 0.980497i | \(-0.562969\pi\) | |||||||
\(234\) | − | 24.6012i | − | 1.60823i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 30.6991 | 1.99834 | ||||||||
\(237\) | 5.65762 | − | 5.65762i | 0.367502 | − | 0.367502i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.48331i | − | 0.484055i | −0.970269 | − | 0.242028i | \(-0.922188\pi\) | ||
0.970269 | − | 0.242028i | \(-0.0778125\pi\) | |||||||
\(240\) | −0.516685 | + | 4.51669i | −0.0333519 | + | 0.291551i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −11.0000 | + | 11.0000i | −0.707107 | + | 0.707107i | ||||
\(243\) | −8.61370 | − | 8.61370i | −0.552569 | − | 0.552569i | ||||
\(244\) | 29.2615i | 1.87327i | ||||||||
\(245\) | −12.2542 | + | 9.73834i | −0.782890 | + | 0.622160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −34.2250 | + | 34.2250i | −2.17768 | + | 2.17768i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.19160i | 0.265632i | ||||||||
\(250\) | −5.29821 | + | 14.8973i | −0.335088 | + | 0.942187i | ||||
\(251\) | −11.0367 | −0.696629 | −0.348315 | − | 0.937378i | \(-0.613246\pi\) | ||||
−0.348315 | + | 0.937378i | \(0.613246\pi\) | |||||||
\(252\) | 10.2583 | − | 10.2583i | 0.646215 | − | 0.646215i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 24.4499i | − | 1.53413i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 28.1916 | + | 3.22497i | 1.74837 | + | 0.200004i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.93881 | − | 4.93881i | 0.305121 | − | 0.305121i | ||||
\(263\) | −11.2250 | − | 11.2250i | −0.692161 | − | 0.692161i | 0.270546 | − | 0.962707i | \(-0.412796\pi\) |
−0.962707 | + | 0.270546i | \(0.912796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −28.5426 | −1.75006 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 31.8581i | − | 1.94242i | −0.238215 | − | 0.971212i | \(-0.576562\pi\) | ||
0.238215 | − | 0.971212i | \(-0.423438\pi\) | |||||||
\(270\) | 7.22497 | − | 5.74166i | 0.439698 | − | 0.349426i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.03337 | + | 6.03337i | 0.365156 | + | 0.365156i | ||||
\(274\) | 32.9666i | 1.99159i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.06622 | 0.0641788 | ||||||||
\(277\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(278\) | 12.4743 | + | 12.4743i | 0.748159 | + | 0.748159i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.4107 | + | 13.1003i | 0.622160 | + | 0.782890i | ||||
\(281\) | −14.9666 | −0.892834 | −0.446417 | − | 0.894825i | \(-0.647300\pi\) | ||||
−0.446417 | + | 0.894825i | \(0.647300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3985 | − | 18.3985i | −1.09368 | − | 1.09368i | −0.995133 | − | 0.0985428i | \(-0.968582\pi\) |
−0.0985428 | − | 0.995133i | \(-0.531418\pi\) | |||||||
\(284\) | − | 14.4499i | − | 0.857446i | ||||||
\(285\) | −8.61370 | − | 0.985363i | −0.510232 | − | 0.0583679i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −10.9666 | − | 10.9666i | −0.646215 | − | 0.646215i | ||||
\(289\) | − | 17.0000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.8654 | + | 17.8654i | 1.04371 | + | 1.04371i | 0.999000 | + | 0.0447054i | \(0.0142349\pi\) |
0.0447054 | + | 0.999000i | \(0.485765\pi\) | |||||||
\(294\) | 5.03166i | 0.293452i | ||||||||
\(295\) | 26.8708 | − | 21.3541i | 1.56448 | − | 1.24329i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 6.65497i | − | 0.384867i | ||||||
\(300\) | 2.68953 | + | 4.31285i | 0.155280 | + | 0.249002i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.4499 | + | 22.4499i | −1.29185 | + | 1.29185i | ||||
\(303\) | 4.74166 | + | 4.74166i | 0.272401 | + | 0.272401i | ||||
\(304\) | 30.5134i | 1.75006i | ||||||||
\(305\) | 20.3541 | + | 25.6125i | 1.16547 | + | 1.46657i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.452253 | + | 0.452253i | −0.0258115 | + | 0.0258115i | −0.719895 | − | 0.694083i | \(-0.755810\pi\) |
0.694083 | + | 0.719895i | \(0.255810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 6.44994 | − | 6.44994i | 0.365156 | − | 0.365156i | ||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 32.8555i | 1.85414i | ||||||||
\(315\) | 1.84345 | − | 16.1148i | 0.103866 | − | 0.907964i | ||||
\(316\) | −31.4833 | −1.77107 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 14.0048 | − | 11.1295i | 0.782890 | − | 0.622160i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.77503 | − | 2.77503i | 0.154646 | − | 0.154646i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 13.4833i | 0.749073i | ||||||||
\(325\) | 26.9193 | − | 16.7871i | 1.49322 | − | 0.931184i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 11.6626 | − | 11.6626i | 0.640071 | − | 0.640071i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.37907 | 0.293452 | ||||||||
\(337\) | 18.0000 | − | 18.0000i | 0.980522 | − | 0.980522i | −0.0192914 | − | 0.999814i | \(-0.506141\pi\) |
0.999814 | + | 0.0192914i | \(0.00614103\pi\) | |||||||
\(338\) | −27.2583 | − | 27.2583i | −1.48266 | − | 1.48266i | ||||
\(339\) | − | 8.06860i | − | 0.438226i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 20.9143 | − | 20.9143i | 1.13092 | − | 1.13092i | ||||
\(343\) | 13.0958 | + | 13.0958i | 0.707107 | + | 0.707107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.933259 | − | 0.741657i | 0.0502450 | − | 0.0399295i | ||||
\(346\) | 27.1050 | 1.45718 | ||||||||
\(347\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11.2224i | − | 0.600720i | −0.953826 | − | 0.300360i | \(-0.902893\pi\) | ||
0.953826 | − | 0.300360i | \(-0.0971069\pi\) | |||||||
\(350\) | 18.2250 | + | 4.22497i | 0.974166 | + | 0.225834i | ||||
\(351\) | −18.5167 | −0.988348 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(354\) | − | 11.0334i | − | 0.586417i | ||||||
\(355\) | −10.0513 | − | 12.6480i | −0.533469 | − | 0.671286i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000i | 0.316668i | 0.987386 | + | 0.158334i | \(0.0506123\pi\) | ||||
−0.987386 | + | 0.158334i | \(0.949388\pi\) | |||||||
\(360\) | −17.2274 | − | 1.97073i | −0.907964 | − | 0.103866i | ||||
\(361\) | −39.1916 | −2.06272 | ||||||||
\(362\) | −19.2910 | + | 19.2910i | −1.01391 | + | 1.01391i | ||||
\(363\) | 3.95345 | + | 3.95345i | 0.207502 | + | 0.207502i | ||||
\(364\) | − | 33.5743i | − | 1.75977i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.5167 | 0.549716 | ||||||||
\(367\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(368\) | −2.96663 | − | 2.96663i | −0.154646 | − | 0.154646i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.35414 | + | 1.90420i | 0.276487 | + | 0.0983324i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −7.72119 | − | 7.72119i | −0.397135 | − | 0.397135i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 21.2250 | + | 26.7083i | 1.08882 | + | 1.37011i | ||||
\(381\) | −8.78741 | −0.450193 | ||||||||
\(382\) | −27.2250 | + | 27.2250i | −1.39295 | + | 1.39295i | ||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | − | 5.75047i | − | 0.293452i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.0000 | 0.610784 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 1.15907 | − | 10.1322i | 0.0586917 | − | 0.513063i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 14.0000 | − | 14.0000i | 0.707107 | − | 0.707107i | ||||
\(393\) | −1.77503 | − | 1.77503i | −0.0895383 | − | 0.0895383i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.5573 | + | 21.8997i | −1.38656 | + | 1.10189i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.5842 | + | 18.5842i | −0.932713 | + | 0.932713i | −0.997875 | − | 0.0651619i | \(-0.979244\pi\) |
0.0651619 | + | 0.997875i | \(0.479244\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.2583i | 0.513559i | ||||||||
\(400\) | 4.51669 | − | 19.4833i | 0.225834 | − | 0.974166i | ||||
\(401\) | 37.2250 | 1.85893 | 0.929463 | − | 0.368915i | \(-0.120271\pi\) | ||||
0.929463 | + | 0.368915i | \(0.120271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 26.3862i | − | 1.31276i | ||||||
\(405\) | 9.37894 | + | 11.8019i | 0.466043 | + | 0.586442i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8483 | 0.584436 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.7163 | − | 28.7163i | −1.41304 | − | 1.41304i | ||||
\(414\) | 4.06674i | 0.199869i | ||||||||
\(415\) | 2.09580 | − | 18.3208i | 0.102879 | − | 0.899331i | ||||
\(416\) | −35.8924 | −1.75977 | ||||||||
\(417\) | 4.48331 | − | 4.48331i | 0.219549 | − | 0.219549i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 40.8312i | 1.99474i | 0.0725002 | + | 0.997368i | \(0.476902\pi\) | ||||
−0.0725002 | + | 0.997368i | \(0.523098\pi\) | |||||||
\(420\) | 4.70829 | − | 3.74166i | 0.229741 | − | 0.182574i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.19337 | −0.251620 | ||||||||
\(427\) | 27.3716 | − | 27.3716i | 1.32460 | − | 1.32460i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0000 | −0.867029 | −0.433515 | − | 0.901146i | \(-0.642727\pi\) | ||||
−0.433515 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(432\) | −8.25430 | + | 8.25430i | −0.397135 | + | 0.397135i | ||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.65762 | − | 5.65762i | 0.270640 | − | 0.270640i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.1916 | −0.913886 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.9666 | − | 14.9666i | −0.707107 | − | 0.707107i | ||||
\(449\) | 29.9333i | 1.41264i | 0.707894 | + | 0.706319i | \(0.249646\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | −16.4499 | + | 10.2583i | −0.775458 | + | 0.483583i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −22.4499 | + | 22.4499i | −1.05596 | + | 1.05596i | ||||
\(453\) | 8.06860 | + | 8.06860i | 0.379096 | + | 0.379096i | ||||
\(454\) | − | 42.1760i | − | 1.97942i | ||||||
\(455\) | −23.3541 | − | 29.3875i | −1.09486 | − | 1.37771i | ||||
\(456\) | 10.9666 | 0.513559 | ||||||||
\(457\) | −3.74166 | + | 3.74166i | −0.175027 | + | 0.175027i | −0.789184 | − | 0.614157i | \(-0.789496\pi\) |
0.614157 | + | 0.789184i | \(0.289496\pi\) | |||||||
\(458\) | −18.9436 | − | 18.9436i | −0.885175 | − | 0.885175i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.66026 | − | 0.533109i | −0.217286 | − | 0.0248564i | ||||
\(461\) | −21.9805 | −1.02373 | −0.511867 | − | 0.859064i | \(-0.671046\pi\) | ||||
−0.511867 | + | 0.859064i | \(0.671046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | + | 24.0000i | 1.11537 | + | 1.11537i | 0.992411 | + | 0.122963i | \(0.0392398\pi\) |
0.122963 | + | 0.992411i | \(0.460760\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.9333 | 1.66458 | ||||||||
\(467\) | 30.3397 | − | 30.3397i | 1.40395 | − | 1.40395i | 0.616949 | − | 0.787003i | \(-0.288368\pi\) |
0.787003 | − | 0.616949i | \(-0.211632\pi\) | |||||||
\(468\) | 24.6012 | + | 24.6012i | 1.13719 | + | 1.13719i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8084 | 0.544102 | ||||||||
\(472\) | −30.6991 | + | 30.6991i | −1.41304 | + | 1.41304i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 11.3152i | 0.519726i | ||||||||
\(475\) | 37.1563 | + | 8.61370i | 1.70485 | + | 0.395224i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.48331 | + | 7.48331i | 0.342279 | + | 0.342279i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | −4.00000 | − | 5.03337i | −0.182574 | − | 0.229741i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.997356 | − | 0.997356i | −0.0453813 | − | 0.0453813i | ||||
\(484\) | − | 22.0000i | − | 1.00000i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 17.2274 | 0.781451 | ||||||||
\(487\) | 7.77503 | − | 7.77503i | 0.352320 | − | 0.352320i | −0.508652 | − | 0.860972i | \(-0.669856\pi\) |
0.860972 | + | 0.508652i | \(0.169856\pi\) | |||||||
\(488\) | −29.2615 | − | 29.2615i | −1.32460 | − | 1.32460i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.51583 | − | 21.9925i | 0.113654 | − | 0.993520i | ||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | − | 68.4499i | − | 3.07971i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.5167 | + | 13.5167i | −0.606306 | + | 0.606306i | ||||
\(498\) | −4.19160 | − | 4.19160i | −0.187830 | − | 0.187830i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −9.59907 | − | 20.1955i | −0.429283 | − | 0.903170i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.0367 | − | 11.0367i | 0.492591 | − | 0.492591i | ||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | 20.5167i | 0.913886i | ||||||||
\(505\) | −18.3541 | − | 23.0958i | −0.816749 | − | 1.02775i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.79676 | + | 9.79676i | −0.435089 | + | 0.435089i | ||||
\(508\) | 24.4499 | + | 24.4499i | 1.08479 | + | 1.08479i | ||||
\(509\) | − | 8.88026i | − | 0.393611i | −0.980443 | − | 0.196805i | \(-0.936943\pi\) | ||
0.980443 | − | 0.196805i | \(-0.0630567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | −15.7417 | − | 15.7417i | −0.695011 | − | 0.695011i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.74166i | − | 0.427611i | ||||||
\(520\) | −31.4166 | + | 24.9666i | −1.37771 | + | 1.09486i | ||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.7773 | + | 31.7773i | 1.38952 | + | 1.38952i | 0.826315 | + | 0.563209i | \(0.190433\pi\) |
0.563209 | + | 0.826315i | \(0.309567\pi\) | |||||||
\(524\) | 9.87762i | 0.431506i | ||||||||
\(525\) | 1.51847 | − | 6.55013i | 0.0662716 | − | 0.285871i | ||||
\(526\) | 22.4499 | 0.978864 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.8999i | − | 0.952169i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 42.0832 | 1.82625 | ||||||||
\(532\) | 28.5426 | − | 28.5426i | 1.23748 | − | 1.23748i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.8581 | + | 31.8581i | 1.37350 | + | 1.37350i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.48331 | + | 12.9666i | −0.0638317 | + | 0.557995i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.93326 | + | 6.93326i | 0.297535 | + | 0.297535i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.0667 | −0.516409 | ||||||||
\(547\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(548\) | −32.9666 | − | 32.9666i | −1.40826 | − | 1.40826i | ||||
\(549\) | 40.1124i | 1.71196i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.06622 | + | 1.06622i | −0.0453813 | + | 0.0453813i | ||||
\(553\) | 29.4499 | + | 29.4499i | 1.25234 | + | 1.25234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.9486 | −1.05806 | ||||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −23.5110 | − | 2.68953i | −0.993520 | − | 0.113654i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.9666 | − | 14.9666i | 0.631329 | − | 0.631329i | ||||
\(563\) | 28.1832 | + | 28.1832i | 1.18778 | + | 1.18778i | 0.977679 | + | 0.210103i | \(0.0673798\pi\) |
0.210103 | + | 0.977679i | \(0.432620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.03430 | + | 35.2665i | −0.169724 | + | 1.48367i | ||||
\(566\) | 36.7969 | 1.54669 | ||||||||
\(567\) | 12.6125 | − | 12.6125i | 0.529675 | − | 0.529675i | ||||
\(568\) | 14.4499 | + | 14.4499i | 0.606306 | + | 0.606306i | ||||
\(569\) | 31.6749i | 1.32788i | 0.747785 | + | 0.663941i | \(0.231117\pi\) | ||||
−0.747785 | + | 0.663941i | \(0.768883\pi\) | |||||||
\(570\) | 9.59907 | − | 7.62834i | 0.402061 | − | 0.319516i | ||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.78477 | + | 9.78477i | 0.408764 | + | 0.408764i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.44994 | + | 2.77503i | −0.185576 | + | 0.115727i | ||||
\(576\) | 21.9333 | 0.913886 | ||||||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | 17.0000 | + | 17.0000i | 0.707107 | + | 0.707107i | ||||
\(579\) | − | 4.31285i | − | 0.179236i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.8188 | −0.905197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 38.6459 | + | 4.42088i | 1.59781 | + | 0.182781i | ||||
\(586\) | −35.7307 | −1.47602 | ||||||||
\(587\) | −32.4961 | + | 32.4961i | −1.34126 | + | 1.34126i | −0.446447 | + | 0.894810i | \(0.647311\pi\) |
−0.894810 | + | 0.446447i | \(0.852689\pi\) | |||||||
\(588\) | −5.03166 | − | 5.03166i | −0.207502 | − | 0.207502i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −5.51669 | + | 48.2250i | −0.227118 | + | 1.98539i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.65497 | + | 6.65497i | 0.272142 | + | 0.272142i | ||||
\(599\) | 41.6749i | 1.70279i | 0.524524 | + | 0.851395i | \(0.324243\pi\) | ||||
−0.524524 | + | 0.851395i | \(0.675757\pi\) | |||||||
\(600\) | −7.00238 | − | 1.62332i | −0.285871 | − | 0.0662716i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 44.8999i | − | 1.82695i | ||||||
\(605\) | −15.3031 | − | 19.2566i | −0.622160 | − | 0.782890i | ||||
\(606\) | −9.48331 | −0.385233 | ||||||||
\(607\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(608\) | −30.5134 | − | 30.5134i | −1.23748 | − | 1.23748i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −45.9666 | − | 5.25834i | −1.86113 | − | 0.212904i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(614\) | − | 0.904507i | − | 0.0365029i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.6749 | − | 33.6749i | 1.35570 | − | 1.35570i | 0.476558 | − | 0.879143i | \(-0.341884\pi\) |
0.879143 | − | 0.476558i | \(-0.158116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.16145i | 0.328036i | 0.986457 | + | 0.164018i | \(0.0524456\pi\) | ||||
−0.986457 | + | 0.164018i | \(0.947554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.06093 | 0.122831 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 12.8999i | 0.516409i | ||||||||
\(625\) | −22.4499 | − | 11.0000i | −0.897998 | − | 0.440000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.8555 | − | 32.8555i | −1.31108 | − | 1.31108i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 14.2713 | + | 17.9582i | 0.568583 | + | 0.715472i | ||||
\(631\) | −50.1916 | −1.99810 | −0.999048 | − | 0.0436231i | \(-0.986110\pi\) | ||||
−0.999048 | + | 0.0436231i | \(0.986110\pi\) | |||||||
\(632\) | 31.4833 | − | 31.4833i | 1.25234 | − | 1.25234i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 38.4083 | + | 4.39371i | 1.52419 | + | 0.174359i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.4059 | + | 31.4059i | −1.24435 | + | 1.24435i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 19.8084i | − | 0.783608i | ||||||
\(640\) | −2.87523 | + | 25.1343i | −0.113654 | + | 0.993520i | ||||
\(641\) | −22.7750 | −0.899560 | −0.449780 | − | 0.893140i | \(-0.648498\pi\) | ||||
−0.449780 | + | 0.893140i | \(0.648498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.4644 | − | 27.4644i | −1.08309 | − | 1.08309i | −0.996219 | − | 0.0868719i | \(-0.972313\pi\) |
−0.0868719 | − | 0.996219i | \(-0.527687\pi\) | |||||||
\(644\) | 5.55006i | 0.218703i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | −13.4833 | − | 13.4833i | −0.529675 | − | 0.529675i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −10.1322 | + | 43.7065i | −0.397417 | + | 1.71431i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.87083 | + | 8.64586i | 0.268465 | + | 0.337822i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4791 | 1.02992 | 0.514958 | − | 0.857215i | \(-0.327807\pi\) | ||||
0.514958 | + | 0.857215i | \(0.327807\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.3253i | 0.905197i | ||||||||
\(665\) | 5.12917 | − | 44.8375i | 0.198901 | − | 1.73872i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −5.37907 | + | 5.37907i | −0.207502 | + | 0.207502i | ||||
\(673\) | 9.44994 | + | 9.44994i | 0.364269 | + | 0.364269i | 0.865382 | − | 0.501113i | \(-0.167076\pi\) |
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | 36.0000i | 1.38667i | ||||||||
\(675\) | 7.72119 | + | 12.3815i | 0.297189 | + | 0.476562i | ||||
\(676\) | 54.5167 | 2.09680 | ||||||||
\(677\) | 20.0218 | − | 20.0218i | 0.769500 | − | 0.769500i | −0.208519 | − | 0.978018i | \(-0.566864\pi\) |
0.978018 | + | 0.208519i | \(0.0668642\pi\) | |||||||
\(678\) | 8.06860 | + | 8.06860i | 0.309873 | + | 0.309873i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.1582 | −0.580865 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(684\) | 41.8286i | 1.59936i | ||||||||
\(685\) | −51.7871 | − | 5.92417i | −1.97868 | − | 0.226351i | ||||
\(686\) | −26.1916 | −1.00000 | ||||||||
\(687\) | −6.80840 | + | 6.80840i | −0.259757 | + | 0.259757i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.191602 | + | 1.67492i | −0.00729415 | + | 0.0637630i | ||||
\(691\) | 15.6969 | 0.597140 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(692\) | −27.1050 | + | 27.1050i | −1.03038 | + | 1.03038i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.8375 | + | 17.3541i | −0.828342 | + | 0.658280i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 11.2224 | + | 11.2224i | 0.424773 | + | 0.424773i | ||||
\(699\) | − | 12.9146i | − | 0.488474i | ||||||
\(700\) | −22.4499 | + | 14.0000i | −0.848528 | + | 0.529150i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 18.5167 | − | 18.5167i | 0.698867 | − | 0.698867i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.6820 | + | 24.6820i | −0.928264 | + | 0.928264i | ||||
\(708\) | 11.0334 | + | 11.0334i | 0.414659 | + | 0.414659i | ||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 22.6993 | + | 2.59668i | 0.851891 | + | 0.0974518i | ||||
\(711\) | −43.1582 | −1.61856 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.68953 | − | 2.68953i | 0.100442 | − | 0.100442i | ||||
\(718\) | −6.00000 | − | 6.00000i | −0.223918 | − | 0.223918i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 19.1981 | − | 15.2567i | 0.715472 | − | 0.568583i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 39.1916 | − | 39.1916i | 1.45856 | − | 1.45856i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 38.5820i | − | 1.43389i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.90689 | −0.293452 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 33.5743 | + | 33.5743i | 1.24435 | + | 1.24435i | ||||
\(729\) | 14.0334i | 0.519754i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −10.5167 | + | 10.5167i | −0.388708 | + | 0.388708i | ||||
\(733\) | −9.95847 | − | 9.95847i | −0.367825 | − | 0.367825i | 0.498859 | − | 0.866683i | \(-0.333753\pi\) |
−0.866683 | + | 0.498859i | \(0.833753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.90420 | − | 0.904199i | −0.291551 | − | 0.0333519i | ||||
\(736\) | 5.93326 | 0.218703 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.6012 | −0.903747 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.7417 | + | 30.7417i | 1.12780 | + | 1.12780i | 0.990534 | + | 0.137268i | \(0.0438322\pi\) |
0.137268 | + | 0.990534i | \(0.456168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.9875 | − | 15.9875i | 0.584952 | − | 0.584952i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.25834 | + | 3.44994i | −0.265037 | + | 0.125974i | ||||
\(751\) | 22.4499 | 0.819210 | 0.409605 | − | 0.912263i | \(-0.365667\pi\) | ||||
0.409605 | + | 0.912263i | \(0.365667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.96663 | − | 3.96663i | −0.144552 | − | 0.144552i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.2322 | − | 39.3008i | −1.13666 | − | 1.43030i | ||||
\(756\) | 15.4424 | 0.561634 | ||||||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −47.9333 | − | 5.48331i | −1.73872 | − | 0.198901i | ||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 8.78741 | − | 8.78741i | 0.318334 | − | 0.318334i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 54.4499i | − | 1.96993i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 68.8665 | − | 68.8665i | 2.48663 | − | 2.48663i | ||||
\(768\) | 5.75047 | + | 5.75047i | 0.207502 | + | 0.207502i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.0000 | + | 12.0000i | −0.431889 | + | 0.431889i | ||||
\(773\) | −25.1223 | − | 25.1223i | −0.903587 | − | 0.903587i | 0.0921578 | − | 0.995744i | \(-0.470624\pi\) |
−0.995744 | + | 0.0921578i | \(0.970624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 8.97311 | + | 11.2912i | 0.321289 | + | 0.404291i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000i | 1.00000i | ||||||||
\(785\) | −51.6125 | − | 5.90420i | −1.84213 | − | 0.210730i | ||||
\(786\) | 3.55006 | 0.126626 | ||||||||
\(787\) | 33.9337 | − | 33.9337i | 1.20961 | − | 1.20961i | 0.238451 | − | 0.971154i | \(-0.423360\pi\) |
0.971154 | − | 0.238451i | \(-0.0766398\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 8.06860i | − | 0.287250i | ||||||
\(790\) | 5.65762 | − | 49.4569i | 0.201289 | − | 1.75960i | ||||
\(791\) | 42.0000 | 1.49335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 65.6415 | + | 65.6415i | 2.33100 | + | 2.33100i | ||||
\(794\) | − | 37.1683i | − | 1.31906i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.86562 | − | 9.86562i | 0.349458 | − | 0.349458i | −0.510449 | − | 0.859908i | \(-0.670521\pi\) |
0.859908 | + | 0.510449i | \(0.170521\pi\) | |||||||
\(798\) | −10.2583 | − | 10.2583i | −0.363141 | − | 0.363141i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 14.9666 | + | 24.0000i | 0.529150 | + | 0.848528i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −37.2250 | + | 37.2250i | −1.31446 | + | 1.31446i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.86060 | + | 4.85795i | 0.136068 | + | 0.171220i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.4499 | − | 11.4499i | 0.403057 | − | 0.403057i | ||||
\(808\) | 26.3862 | + | 26.3862i | 0.928264 | + | 0.928264i | ||||
\(809\) | 11.6749i | 0.410468i | 0.978713 | + | 0.205234i | \(0.0657956\pi\) | ||||
−0.978713 | + | 0.205234i | \(0.934204\pi\) | |||||||
\(810\) | −21.1809 | − | 2.42298i | −0.744219 | − | 0.0851348i | ||||
\(811\) | −46.2103 | −1.62266 | −0.811332 | − | 0.584586i | \(-0.801257\pi\) | ||||
−0.811332 | + | 0.584586i | \(0.801257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 46.0246i | − | 1.60823i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | −11.8483 | + | 11.8483i | −0.413258 | + | 0.413258i | ||||
\(823\) | −36.0000 | − | 36.0000i | −1.25488 | − | 1.25488i | −0.953506 | − | 0.301376i | \(-0.902554\pi\) |
−0.301376 | − | 0.953506i | \(-0.597446\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 57.4327 | 1.99834 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | −4.06674 | − | 4.06674i | −0.141329 | − | 0.141329i | ||||
\(829\) | − | 23.2564i | − | 0.807729i | −0.914819 | − | 0.403864i | \(-0.867667\pi\) | ||
0.914819 | − | 0.403864i | \(-0.132333\pi\) | |||||||
\(830\) | 16.2250 | + | 20.4166i | 0.563177 | + | 0.708670i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 35.8924 | − | 35.8924i | 1.24435 | − | 1.24435i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.96663i | 0.310489i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −40.8312 | − | 40.8312i | −1.41049 | − | 1.41049i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | −0.966630 | + | 8.44994i | −0.0333519 | + | 0.291551i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.37907 | − | 5.37907i | −0.185265 | − | 0.185265i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.7183 | − | 37.9216i | 1.64156 | − | 1.30454i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.5791 | + | 20.5791i | −0.707107 | + | 0.707107i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 13.2250i | − | 0.453880i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 5.19337 | − | 5.19337i | 0.177922 | − | 0.177922i | ||||
\(853\) | −20.7406 | − | 20.7406i | −0.710144 | − | 0.710144i | 0.256421 | − | 0.966565i | \(-0.417457\pi\) |
−0.966565 | + | 0.256421i | \(0.917457\pi\) | |||||||
\(854\) | 54.7432i | 1.87327i | ||||||||
\(855\) | 29.0958 | + | 36.6125i | 0.995055 | + | 1.25212i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 0.440260i | − | 0.0150215i | −0.999972 | − | 0.00751074i | \(-0.997609\pi\) | ||
0.999972 | − | 0.00751074i | \(-0.00239076\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | − | 18.0000i | 0.613082 | − | 0.613082i | ||||
\(863\) | −11.2250 | − | 11.2250i | −0.382102 | − | 0.382102i | 0.489757 | − | 0.871859i | \(-0.337086\pi\) |
−0.871859 | + | 0.489757i | \(0.837086\pi\) | |||||||
\(864\) | − | 16.5086i | − | 0.561634i | ||||||
\(865\) | −4.87083 | + | 42.5791i | −0.165613 | + | 1.44773i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.10987 | − | 6.10987i | 0.207502 | − | 0.207502i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.3152i | 0.382743i | ||||||||
\(875\) | −9.91205 | + | 27.8703i | −0.335088 | + | 0.942187i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.8418i | 0.433142i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 19.1916 | − | 19.1916i | 0.646215 | − | 0.646215i | ||||
\(883\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.3323 | + | 1.98272i | 0.582617 | + | 0.0666484i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 45.7417i | − | 1.53413i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333 | 1.00000 | ||||||||
\(897\) | 2.39182 | − | 2.39182i | 0.0798607 | − | 0.0798607i | ||||
\(898\) | −29.9333 | − | 29.9333i | −0.998886 | − | 0.998886i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 6.19160 | − | 26.7083i | 0.206387 | − | 0.890276i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 44.8999i | − | 1.49335i | ||||||
\(905\) | −26.8375 | − | 33.7707i | −0.892107 | − | 1.12258i | ||||
\(906\) | −16.1372 | −0.536123 | ||||||||
\(907\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(908\) | 42.1760 | + | 42.1760i | 1.39966 | + | 1.39966i | ||||
\(909\) | − | 36.1710i | − | 1.19972i | ||||||
\(910\) | 52.7417 | + | 6.03337i | 1.74837 | + | 0.200004i | ||||
\(911\) | −52.3832 | −1.73553 | −0.867766 | − | 0.496972i | \(-0.834445\pi\) | ||||
−0.867766 | + | 0.496972i | \(0.834445\pi\) | |||||||
\(912\) | −10.9666 | + | 10.9666i | −0.363141 | + | 0.363141i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 7.48331i | − | 0.247526i | ||||||
\(915\) | −1.88987 | + | 16.5206i | −0.0624772 | + | 0.546154i | ||||
\(916\) | 37.8871 | 1.25183 | ||||||||
\(917\) | 9.23966 | − | 9.23966i | 0.305121 | − | 0.305121i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 53.1582i | − | 1.75353i | −0.480921 | − | 0.876764i | \(-0.659697\pi\) | ||
0.480921 | − | 0.876764i | \(-0.340303\pi\) | |||||||
\(920\) | 5.19337 | − | 4.12715i | 0.171220 | − | 0.136068i | ||||
\(921\) | −0.325084 | −0.0107119 | ||||||||
\(922\) | 21.9805 | − | 21.9805i | 0.723890 | − | 0.723890i | ||||
\(923\) | −32.4152 | − | 32.4152i | −1.06696 | − | 1.06696i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −48.0000 | −1.57738 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −53.3984 | −1.75006 | ||||||||
\(932\) | −35.9333 | + | 35.9333i | −1.17703 | + | 1.17703i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 60.6793i | 1.98549i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −49.2024 | −1.60823 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.9267 | 1.30157 | 0.650787 | − | 0.759260i | \(-0.274439\pi\) | ||||
0.650787 | + | 0.759260i | \(0.274439\pi\) | |||||||
\(942\) | −11.8084 | + | 11.8084i | −0.384738 | + | 0.384738i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 61.3981i | − | 1.99834i | ||||||
\(945\) | 13.5167 | − | 10.7417i | 0.439698 | − | 0.349426i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(948\) | −11.3152 | − | 11.3152i | −0.367502 | − | 0.367502i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −45.7701 | + | 28.5426i | −1.48498 | + | 0.926046i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0334 | + | 12.0334i | 0.389799 | + | 0.389799i | 0.874616 | − | 0.484817i | \(-0.161114\pi\) |
−0.484817 | + | 0.874616i | \(0.661114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.8752 | − | 47.6599i | −1.22561 | − | 1.54224i | ||||
\(956\) | −14.9666 | −0.484055 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 61.6749i | 1.99159i | ||||||||
\(960\) | 9.03337 | + | 1.03337i | 0.291551 | + | 0.0333519i | ||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.15642 | + | 18.8507i | −0.0694178 | + | 0.606826i | ||||
\(966\) | 1.99471 | 0.0641788 | ||||||||
\(967\) | 17.7750 | − | 17.7750i | 0.571606 | − | 0.571606i | −0.360971 | − | 0.932577i | \(-0.617555\pi\) |
0.932577 | + | 0.360971i | \(0.117555\pi\) | |||||||
\(968\) | 22.0000 | + | 22.0000i | 0.707107 | + | 0.707107i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.9752 | 0.769402 | 0.384701 | − | 0.923041i | \(-0.374305\pi\) | ||||
0.384701 | + | 0.923041i | \(0.374305\pi\) | |||||||
\(972\) | −17.2274 | + | 17.2274i | −0.552569 | + | 0.552569i | ||||
\(973\) | 23.3373 | + | 23.3373i | 0.748159 | + | 0.748159i | ||||
\(974\) | 15.5501i | 0.498256i | ||||||||
\(975\) | 15.7083 | + | 3.64155i | 0.503068 | + | 0.116623i | ||||
\(976\) | 58.5229 | 1.87327 | ||||||||
\(977\) | −20.9333 | + | 20.9333i | −0.669714 | + | 0.669714i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) |
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 19.4767 | + | 24.5083i | 0.622160 | + | 0.782890i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 68.4499 | + | 68.4499i | 2.17768 | + | 2.17768i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.80840 | 0.311574 | 0.155787 | − | 0.987791i | \(-0.450209\pi\) | ||||
0.155787 | + | 0.987791i | \(0.450209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 27.0334i | − | 0.857446i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.38320 | 0.265632 | ||||||||
\(997\) | −14.3642 | + | 14.3642i | −0.454918 | + | 0.454918i | −0.896983 | − | 0.442065i | \(-0.854246\pi\) |
0.442065 | + | 0.896983i | \(0.354246\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 280.2.s.a.13.3 | yes | 8 | |
4.3 | odd | 2 | 1120.2.w.a.433.2 | 8 | |||
5.2 | odd | 4 | inner | 280.2.s.a.237.3 | yes | 8 | |
7.6 | odd | 2 | inner | 280.2.s.a.13.2 | ✓ | 8 | |
8.3 | odd | 2 | 1120.2.w.a.433.3 | 8 | |||
8.5 | even | 2 | inner | 280.2.s.a.13.2 | ✓ | 8 | |
20.7 | even | 4 | 1120.2.w.a.657.2 | 8 | |||
28.27 | even | 2 | 1120.2.w.a.433.3 | 8 | |||
35.27 | even | 4 | inner | 280.2.s.a.237.2 | yes | 8 | |
40.27 | even | 4 | 1120.2.w.a.657.3 | 8 | |||
40.37 | odd | 4 | inner | 280.2.s.a.237.2 | yes | 8 | |
56.13 | odd | 2 | CM | 280.2.s.a.13.3 | yes | 8 | |
56.27 | even | 2 | 1120.2.w.a.433.2 | 8 | |||
140.27 | odd | 4 | 1120.2.w.a.657.3 | 8 | |||
280.27 | odd | 4 | 1120.2.w.a.657.2 | 8 | |||
280.237 | even | 4 | inner | 280.2.s.a.237.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.s.a.13.2 | ✓ | 8 | 7.6 | odd | 2 | inner | |
280.2.s.a.13.2 | ✓ | 8 | 8.5 | even | 2 | inner | |
280.2.s.a.13.3 | yes | 8 | 1.1 | even | 1 | trivial | |
280.2.s.a.13.3 | yes | 8 | 56.13 | odd | 2 | CM | |
280.2.s.a.237.2 | yes | 8 | 35.27 | even | 4 | inner | |
280.2.s.a.237.2 | yes | 8 | 40.37 | odd | 4 | inner | |
280.2.s.a.237.3 | yes | 8 | 5.2 | odd | 4 | inner | |
280.2.s.a.237.3 | yes | 8 | 280.237 | even | 4 | inner | |
1120.2.w.a.433.2 | 8 | 4.3 | odd | 2 | |||
1120.2.w.a.433.2 | 8 | 56.27 | even | 2 | |||
1120.2.w.a.433.3 | 8 | 8.3 | odd | 2 | |||
1120.2.w.a.433.3 | 8 | 28.27 | even | 2 | |||
1120.2.w.a.657.2 | 8 | 20.7 | even | 4 | |||
1120.2.w.a.657.2 | 8 | 280.27 | odd | 4 | |||
1120.2.w.a.657.3 | 8 | 40.27 | even | 4 | |||
1120.2.w.a.657.3 | 8 | 140.27 | odd | 4 |