Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(191,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.s (of order \(6\), 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.191 |
Dual form | 576.2.s.a.383.1 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 1.73205i | 1.34164 | − | 0.774597i | 0.354593 | − | 0.935021i | \(-0.384620\pi\) |
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | + | 1.73205i | 1.13389 | + | 0.654654i | 0.944911 | − | 0.327327i | \(-0.106148\pi\) |
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.46410i | 0.554700 | + | 0.960769i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) |
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.00000 | −1.54919 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.73205i | − | 0.420084i | −0.977692 | − | 0.210042i | \(-0.932640\pi\) | ||
0.977692 | − | 0.210042i | \(-0.0673601\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205i | 0.397360i | 0.980064 | + | 0.198680i | \(0.0636654\pi\) | ||||
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | − | 5.19615i | −0.654654 | − | 1.13389i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.50000 | − | 6.06218i | 0.700000 | − | 1.21244i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 1.73205i | 0.557086 | + | 0.321634i | 0.751975 | − | 0.659192i | \(-0.229101\pi\) |
−0.194889 | + | 0.980825i | \(0.562435\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.50000 | − | 2.59808i | 0.783349 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.0000 | 2.02837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.92820i | − | 1.10940i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | + | 2.59808i | −0.702782 | + | 0.405751i | −0.808383 | − | 0.588657i | \(-0.799657\pi\) |
0.105601 | + | 0.994409i | \(0.466323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50000 | + | 2.59808i | 0.686244 | + | 0.396203i | 0.802203 | − | 0.597051i | \(-0.203661\pi\) |
−0.115960 | + | 0.993254i | \(0.536994\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.00000 | + | 5.19615i | 1.34164 | + | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | − | 10.3923i | 0.875190 | − | 1.51587i | 0.0186297 | − | 0.999826i | \(-0.494070\pi\) |
0.856560 | − | 0.516047i | \(-0.172597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.50000 | + | 4.33013i | 0.357143 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.3923i | 1.40130i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.50000 | − | 2.59808i | 0.198680 | − | 0.344124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.50000 | − | 12.9904i | −0.976417 | − | 1.69120i | −0.675178 | − | 0.737655i | \(-0.735933\pi\) |
−0.301239 | − | 0.953549i | \(-0.597400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.3923i | 1.30931i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | + | 6.92820i | 1.48842 | + | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.50000 | + | 4.33013i | −0.916271 | + | 0.529009i | −0.882443 | − | 0.470418i | \(-0.844103\pi\) |
−0.0338274 | + | 0.999428i | \(0.510770\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0000 | −1.28745 | −0.643726 | − | 0.765256i | \(-0.722612\pi\) | ||||
−0.643726 | + | 0.765256i | \(0.722612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.5000 | + | 6.06218i | −1.21244 | + | 0.700000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.00000 | + | 5.19615i | −1.02565 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00000 | − | 1.73205i | −0.337526 | − | 0.194871i | 0.321651 | − | 0.946858i | \(-0.395762\pi\) |
−0.659178 | + | 0.751987i | \(0.729095\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | − | 10.3923i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | − | 5.19615i | −0.325396 | − | 0.563602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.00000 | − | 5.19615i | −0.321634 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.8564i | − | 1.46878i | −0.678730 | − | 0.734388i | \(-0.737469\pi\) | ||
0.678730 | − | 0.734388i | \(-0.262531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8564i | 1.45255i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | + | 5.19615i | 0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.50000 | + | 11.2583i | −0.659975 | + | 1.14311i | 0.320647 | + | 0.947199i | \(0.396100\pi\) |
−0.980622 | + | 0.195911i | \(0.937234\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.00000 | −0.904534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | − | 5.19615i | −0.895533 | − | 0.517036i | −0.0197851 | − | 0.999804i | \(-0.506298\pi\) |
−0.875748 | + | 0.482768i | \(0.839632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0000 | + | 6.92820i | −1.18240 | + | 0.682656i | −0.956567 | − | 0.291511i | \(-0.905842\pi\) |
−0.225828 | + | 0.974167i | \(0.572509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.0000 | − | 10.3923i | −1.75662 | − | 1.01419i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.00000 | + | 1.73205i | 0.284747 | + | 0.164399i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | + | 3.46410i | −0.564433 | + | 0.325875i | −0.754923 | − | 0.655814i | \(-0.772326\pi\) |
0.190490 | + | 0.981689i | \(0.438992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.00000 | + | 10.3923i | −0.554700 | + | 0.960769i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | − | 5.19615i | 0.275010 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.00000 | 0.811503 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.50000 | − | 7.79423i | −0.396203 | − | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | + | 10.3923i | 0.524222 | + | 0.907980i | 0.999602 | + | 0.0281993i | \(0.00897729\pi\) |
−0.475380 | + | 0.879781i | \(0.657689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 5.19615i | −0.260133 | + | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.00000 | − | 15.5885i | −0.774597 | − | 1.34164i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.50000 | − | 0.866025i | −0.128154 | − | 0.0739895i | 0.434553 | − | 0.900646i | \(-0.356906\pi\) |
−0.562706 | + | 0.826657i | \(0.690240\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.5000 | − | 9.52628i | 1.39951 | − | 0.808008i | 0.405170 | − | 0.914241i | \(-0.367212\pi\) |
0.994341 | + | 0.106233i | \(0.0338788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0000 | + | 10.3923i | −1.51587 | + | 0.875190i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 8.66025i | − | 0.714286i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0000 | + | 6.92820i | −0.983078 | + | 0.567581i | −0.903198 | − | 0.429224i | \(-0.858787\pi\) |
−0.0798802 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.00000 | + | 3.46410i | 0.488273 | + | 0.281905i | 0.723858 | − | 0.689949i | \(-0.242367\pi\) |
−0.235585 | + | 0.971854i | \(0.575701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50000 | − | 2.59808i | 0.363803 | − | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.00000 | + | 6.92820i | 0.319235 | + | 0.552931i | 0.980329 | − | 0.197372i | \(-0.0632408\pi\) |
−0.661094 | + | 0.750303i | \(0.729907\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.46410i | 0.271329i | 0.990755 | + | 0.135665i | \(0.0433170\pi\) | ||||
−0.990755 | + | 0.135665i | \(0.956683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.00000 | − | 15.5885i | 0.700649 | − | 1.21356i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000 | + | 5.19615i | 0.232147 | + | 0.402090i | 0.958440 | − | 0.285295i | \(-0.0920916\pi\) |
−0.726293 | + | 0.687386i | \(0.758758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.50000 | + | 2.59808i | −0.344124 | + | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.0000 | + | 12.1244i | 1.59660 | + | 0.921798i | 0.992136 | + | 0.125166i | \(0.0399462\pi\) |
0.604465 | + | 0.796632i | \(0.293387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.0000 | − | 12.1244i | 1.58745 | − | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.9808i | 1.95283i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0000 | + | 6.92820i | −0.887066 | + | 0.512148i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | + | 3.46410i | −0.441129 | + | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.50000 | + | 2.59808i | 0.329073 | + | 0.189990i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | − | 15.5885i | 0.654654 | − | 1.13389i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5000 | − | 19.9186i | −0.827788 | − | 1.43377i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
0.0719816 | − | 0.997406i | \(-0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0000 | − | 20.7846i | −0.859338 | − | 1.48842i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.8564i | − | 0.987228i | −0.869681 | − | 0.493614i | \(-0.835676\pi\) | ||
0.869681 | − | 0.493614i | \(-0.164324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.46410i | − | 0.245564i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) | ||
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.0000 | 1.05802 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.00000 | + | 10.3923i | 0.421117 | + | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | + | 15.5885i | −0.628587 | + | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.50000 | − | 2.59808i | −0.311272 | − | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0000 | + | 8.66025i | −1.03264 | + | 0.596196i | −0.917741 | − | 0.397180i | \(-0.869989\pi\) |
−0.114902 | + | 0.993377i | \(0.536655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.00000 | − | 5.19615i | −0.616670 | − | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.0000 | 1.22759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.5000 | + | 9.52628i | 1.11497 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 3.46410i | 0.403604 | − | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0000 | + | 10.3923i | 1.20537 | + | 0.695920i | 0.961744 | − | 0.273949i | \(-0.0883300\pi\) |
0.243625 | + | 0.969870i | \(0.421663\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.0000 | 1.40000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | + | 2.59808i | −0.0995585 | + | 0.172440i | −0.911502 | − | 0.411296i | \(-0.865076\pi\) |
0.811943 | + | 0.583736i | \(0.198410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0000 | − | 22.5167i | −0.859064 | − | 1.48794i | −0.872823 | − | 0.488037i | \(-0.837713\pi\) |
0.0137585 | − | 0.999905i | \(-0.495620\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0000 | 1.18431 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.1244i | 0.794293i | 0.917755 | + | 0.397146i | \(0.130000\pi\) | ||||
−0.917755 | + | 0.397146i | \(0.870000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 41.5692i | − | 2.71168i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.00000 | + | 5.19615i | 0.194871 | + | 0.337526i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | − | 20.7846i | −0.776215 | − | 1.34444i | −0.934109 | − | 0.356988i | \(-0.883804\pi\) |
0.157893 | − | 0.987456i | \(-0.449530\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50000 | − | 14.7224i | 0.547533 | − | 0.948355i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) |
0.998443 | − | 0.0557856i | \(-0.0177663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.0000 | + | 8.66025i | 0.958315 | + | 0.553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | + | 3.46410i | −0.381771 | + | 0.220416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.0000 | + | 10.3923i | −1.14070 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0000 | −1.32551 | −0.662754 | − | 0.748837i | \(-0.730613\pi\) | ||||
−0.662754 | + | 0.748837i | \(0.730613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.3923i | 0.650791i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.5000 | + | 9.52628i | −1.02924 | + | 0.594233i | −0.916767 | − | 0.399422i | \(-0.869211\pi\) |
−0.112474 | + | 0.993655i | \(0.535878\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | − | 3.46410i | −0.372822 | − | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3923i | 0.643268i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.00000 | + | 15.5885i | −0.554964 | + | 0.961225i | 0.442943 | + | 0.896550i | \(0.353935\pi\) |
−0.997906 | + | 0.0646755i | \(0.979399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0000 | + | 20.7846i | −0.734388 | + | 1.27200i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.92820i | − | 0.422420i | −0.977441 | − | 0.211210i | \(-0.932260\pi\) | ||
0.977441 | − | 0.211210i | \(-0.0677404\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.92820i | − | 0.420858i | −0.977609 | − | 0.210429i | \(-0.932514\pi\) | ||
0.977609 | − | 0.210429i | \(-0.0674861\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0000 | − | 20.7846i | 0.726273 | − | 1.25794i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.5000 | + | 18.1865i | 0.633174 | + | 1.09669i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | + | 6.92820i | −0.240337 | + | 0.416275i | −0.960810 | − | 0.277207i | \(-0.910591\pi\) |
0.720473 | + | 0.693482i | \(0.243925\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | + | 3.46410i | 0.357930 | + | 0.206651i | 0.668172 | − | 0.744007i | \(-0.267077\pi\) |
−0.310242 | + | 0.950657i | \(0.600410\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.00000 | + | 5.19615i | −0.534994 | + | 0.308879i | −0.743048 | − | 0.669238i | \(-0.766621\pi\) |
0.208053 | + | 0.978117i | \(0.433287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 10.3923i | − | 0.615587i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.0000 | −1.06251 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0000 | 0.823529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.5000 | − | 11.2583i | 1.14311 | − | 0.659975i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.00000 | − | 1.73205i | 0.175262 | − | 0.101187i | −0.409803 | − | 0.912174i | \(-0.634402\pi\) |
0.585065 | + | 0.810987i | \(0.301069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −45.0000 | − | 25.9808i | −2.62000 | − | 1.51266i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | + | 7.79423i | 0.783349 | + | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.00000 | + | 15.5885i | 0.518751 | + | 0.898504i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | + | 15.5885i | 0.517036 | + | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 27.7128i | − | 1.58683i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.9808i | 1.48280i | 0.671063 | + | 0.741400i | \(0.265838\pi\) | ||||
−0.671063 | + | 0.741400i | \(0.734162\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.0000 | 1.36531 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | − | 5.19615i | −0.170114 | − | 0.294647i | 0.768345 | − | 0.640036i | \(-0.221080\pi\) |
−0.938460 | + | 0.345389i | \(0.887747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.0000 | + | 31.1769i | 1.01419 | + | 1.75662i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | + | 3.46410i | 0.336994 | + | 0.194563i | 0.658942 | − | 0.752194i | \(-0.271004\pi\) |
−0.321948 | + | 0.946757i | \(0.604338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | + | 5.19615i | −0.503903 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | − | 2.59808i | −0.251166 | − | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.0000 | 1.55316 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.00000 | + | 3.46410i | 0.331801 | + | 0.191565i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.0000 | − | 20.7846i | 1.98474 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0000 | − | 12.1244i | −1.15426 | − | 0.666415i | −0.204342 | − | 0.978900i | \(-0.565505\pi\) |
−0.949923 | + | 0.312485i | \(0.898839\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | − | 5.19615i | −0.164399 | − | 0.284747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0000 | + | 25.9808i | −0.819538 | + | 1.41948i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.50000 | + | 9.52628i | 0.299604 | + | 0.518930i | 0.976045 | − | 0.217567i | \(-0.0698121\pi\) |
−0.676441 | + | 0.736497i | \(0.736479\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0000 | 0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.92820i | − | 0.374088i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5000 | − | 23.3827i | −0.724718 | − | 1.25525i | −0.959090 | − | 0.283101i | \(-0.908637\pi\) |
0.234372 | − | 0.972147i | \(-0.424697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0000 | − | 27.7128i | 0.856460 | − | 1.48343i | −0.0188232 | − | 0.999823i | \(-0.505992\pi\) |
0.875284 | − | 0.483610i | \(-0.160675\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | − | 10.3923i | 0.960769 | − | 0.554700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.5000 | + | 12.9904i | 1.19755 | + | 0.691408i | 0.960009 | − | 0.279968i | \(-0.0903240\pi\) |
0.237545 | + | 0.971377i | \(0.423657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | − | 10.3923i | 0.955341 | − | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.00000 | + | 5.19615i | −0.476331 | + | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.0000 | 1.58334 | 0.791670 | − | 0.610949i | \(-0.209212\pi\) | ||||
0.791670 | + | 0.610949i | \(0.209212\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.46410i | − | 0.181818i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.0000 | + | 19.0526i | −1.72730 | + | 0.997257i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.00000 | + | 1.73205i | 0.156599 | + | 0.0904123i | 0.576252 | − | 0.817272i | \(-0.304515\pi\) |
−0.419653 | + | 0.907685i | \(0.637848\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.5000 | − | 7.79423i | −0.702782 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | + | 17.3205i | 0.517780 | + | 0.896822i | 0.999787 | + | 0.0206542i | \(0.00657489\pi\) |
−0.482006 | + | 0.876168i | \(0.660092\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | + | 10.3923i | −0.309839 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8564i | 0.713641i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.0526i | − | 0.978664i | −0.872098 | − | 0.489332i | \(-0.837241\pi\) | ||
0.872098 | − | 0.489332i | \(-0.162759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.00000 | − | 15.5885i | −0.459879 | − | 0.796533i | 0.539076 | − | 0.842257i | \(-0.318774\pi\) |
−0.998954 | + | 0.0457244i | \(0.985440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.0000 | + | 31.1769i | −0.917365 | + | 1.58892i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.5885i | 0.792406i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.00000 | + | 5.19615i | 0.456318 | + | 0.263455i | 0.710495 | − | 0.703702i | \(-0.248471\pi\) |
−0.254177 | + | 0.967158i | \(0.581804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.7846i | − | 1.04844i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.00000 | − | 5.19615i | 0.450564 | − | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | + | 4.33013i | −0.374532 | + | 0.216236i | −0.675437 | − | 0.737418i | \(-0.736045\pi\) |
0.300904 | + | 0.953654i | \(0.402711\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.1769i | 1.54919i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000 | − | 5.19615i | 0.148704 | − | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5000 | + | 19.9186i | 0.568638 | + | 0.984911i | 0.996701 | + | 0.0811615i | \(0.0258630\pi\) |
−0.428063 | + | 0.903749i | \(0.640804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.50000 | + | 2.59808i | 0.0739895 | + | 0.128154i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 51.9615i | − | 2.55686i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 41.5692i | − | 2.04055i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.0000 | −1.61602 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | − | 10.3923i | −0.293119 | − | 0.507697i | 0.681426 | − | 0.731887i | \(-0.261360\pi\) |
−0.974546 | + | 0.224189i | \(0.928027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | − | 8.66025i | 0.243685 | − | 0.422075i | −0.718076 | − | 0.695965i | \(-0.754977\pi\) |
0.961761 | + | 0.273890i | \(0.0883103\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 36.0000 | 1.75038 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.5000 | − | 6.06218i | −0.509325 | − | 0.294059i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0000 | − | 13.8564i | 1.16144 | − | 0.670559i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.0000 | + | 10.3923i | 0.869048 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0000 | −0.867029 | −0.433515 | − | 0.901146i | \(-0.642727\pi\) | ||||
−0.433515 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.0000 | −1.48976 | −0.744882 | − | 0.667196i | \(-0.767494\pi\) | ||||
−0.744882 | + | 0.667196i | \(0.767494\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0000 | − | 10.3923i | −0.863034 | − | 0.498273i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0000 | + | 10.3923i | 0.859093 | + | 0.495998i | 0.863708 | − | 0.503992i | \(-0.168136\pi\) |
−0.00461537 | + | 0.999989i | \(0.501469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.50000 | + | 12.9904i | −0.357143 | + | 0.618590i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.50000 | + | 7.79423i | −0.213801 | + | 0.370315i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) |
0.739100 | + | 0.673596i | \(0.235251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0000 | − | 41.5692i | −1.13771 | − | 1.97057i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 24.0000 | 1.13516 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 25.9808i | − | 1.22611i | −0.790041 | − | 0.613054i | \(-0.789941\pi\) | ||
0.790041 | − | 0.613054i | \(-0.210059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.5885i | − | 0.734032i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.00000 | − | 10.3923i | −0.281905 | − | 0.488273i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.0000 | + | 41.5692i | 1.12514 | + | 1.94880i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.50000 | − | 9.52628i | 0.257279 | − | 0.445621i | −0.708233 | − | 0.705979i | \(-0.750507\pi\) |
0.965512 | + | 0.260358i | \(0.0838407\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.00000 | −0.420084 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0000 | − | 10.3923i | −0.838344 | − | 0.484018i | 0.0183573 | − | 0.999831i | \(-0.494156\pi\) |
−0.856701 | + | 0.515814i | \(0.827490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.0000 | − | 8.66025i | 0.697109 | − | 0.402476i | −0.109161 | − | 0.994024i | \(-0.534816\pi\) |
0.806270 | + | 0.591548i | \(0.201483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.00000 | 0.138823 | 0.0694117 | − | 0.997588i | \(-0.477888\pi\) | ||||
0.0694117 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0000 | −1.38527 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 13.8564i | − | 0.638470i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.5000 | + | 7.79423i | −0.620731 | + | 0.358379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.5000 | + | 6.06218i | 0.481773 | + | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.0000 | + | 25.9808i | −0.685367 | + | 1.18709i | 0.287954 | + | 0.957644i | \(0.407025\pi\) |
−0.973321 | + | 0.229447i | \(0.926308\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | − | 6.92820i | −0.182384 | − | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 45.0333i | 2.04486i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3205i | 0.784867i | 0.919780 | + | 0.392434i | \(0.128367\pi\) | ||||
−0.919780 | + | 0.392434i | \(0.871633\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.00000 | − | 5.19615i | 0.135665 | − | 0.234978i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.50000 | + | 12.9904i | 0.338470 | + | 0.586248i | 0.984145 | − | 0.177365i | \(-0.0567572\pi\) |
−0.645675 | + | 0.763612i | \(0.723424\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00000 | − | 5.19615i | 0.135113 | − | 0.234023i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.0000 | + | 15.5885i | −1.21356 | + | 0.700649i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.0000 | + | 10.3923i | 0.807410 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5000 | + | 7.79423i | −0.604343 | + | 0.348918i | −0.770748 | − | 0.637140i | \(-0.780117\pi\) |
0.166405 | + | 0.986057i | \(0.446784\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 10.3923i | − | 0.464294i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.50000 | − | 2.59808i | 0.199852 | − | 0.115385i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.0000 | + | 10.3923i | −0.797836 | + | 0.460631i | −0.842714 | − | 0.538362i | \(-0.819043\pi\) |
0.0448779 | + | 0.998992i | \(0.485710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.0000 | − | 19.0526i | −1.45983 | − | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.00000 | 0.397360 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.0000 | + | 41.5692i | −1.05757 | + | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | + | 31.1769i | 0.791639 | + | 1.37116i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.0000 | − | 36.3731i | −0.921798 | − | 1.59660i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.5885i | 0.682943i | 0.939892 | + | 0.341471i | \(0.110925\pi\) | ||||
−0.939892 | + | 0.341471i | \(0.889075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3205i | 0.757373i | 0.925525 | + | 0.378686i | \(0.123624\pi\) | ||||
−0.925525 | + | 0.378686i | \(0.876376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −42.0000 | −1.83303 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.5000 | − | 38.9711i | 0.976417 | − | 1.69120i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0000 | − | 10.3923i | −0.779667 | − | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | − | 5.19615i | 0.389104 | − | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0000 | + | 10.3923i | 0.776757 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.0000 | −0.646096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.0000 | − | 6.92820i | −0.514969 | − | 0.297318i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | + | 6.92820i | −0.514024 | + | 0.296772i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.50000 | − | 4.33013i | −0.320677 | − | 0.185143i | 0.331017 | − | 0.943625i | \(-0.392608\pi\) |
−0.651694 | + | 0.758482i | \(0.725941\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.0000 | 1.02430 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | − | 10.3923i | −0.255146 | − | 0.441926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.0000 | 0.509372 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.1051i | 1.61457i | 0.590165 | + | 0.807283i | \(0.299063\pi\) | ||||
−0.590165 | + | 0.807283i | \(0.700937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.7846i | 0.879095i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.50000 | − | 7.79423i | −0.189990 | − | 0.329073i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.50000 | + | 7.79423i | 0.189652 | + | 0.328488i | 0.945134 | − | 0.326682i | \(-0.105931\pi\) |
−0.755482 | + | 0.655169i | \(0.772597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0000 | + | 20.7846i | −0.504844 | + | 0.874415i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.0000 | + | 15.5885i | −1.13389 | + | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.5000 | − | 9.52628i | −0.691716 | − | 0.399362i | 0.112539 | − | 0.993647i | \(-0.464102\pi\) |
−0.804255 | + | 0.594285i | \(0.797435\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5000 | − | 6.06218i | 0.439411 | − | 0.253694i | −0.263937 | − | 0.964540i | \(-0.585021\pi\) |
0.703348 | + | 0.710846i | \(0.251688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.00000 | − | 5.19615i | 0.375980 | − | 0.217072i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.8372i | 1.65558i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0000 | − | 20.7846i | 1.49353 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 41.5692i | 1.71868i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.50000 | + | 2.59808i | −0.0619116 | + | 0.107234i | −0.895320 | − | 0.445424i | \(-0.853053\pi\) |
0.833408 | + | 0.552658i | \(0.186386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0000 | + | 20.7846i | −0.493614 | + | 0.854965i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.92820i | 0.284507i | 0.989830 | + | 0.142254i | \(0.0454349\pi\) | ||||
−0.989830 | + | 0.142254i | \(0.954565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 20.7846i | − | 0.852086i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.00000 | + | 5.19615i | −0.122782 | + | 0.212664i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.00000 | − | 15.5885i | −0.367730 | − | 0.636927i | 0.621480 | − | 0.783430i | \(-0.286532\pi\) |
−0.989210 | + | 0.146503i | \(0.953198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.50000 | − | 6.06218i | 0.142768 | − | 0.247281i | −0.785770 | − | 0.618519i | \(-0.787733\pi\) |
0.928538 | + | 0.371237i | \(0.121066\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.5000 | − | 12.9904i | −0.916271 | − | 0.529009i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.00000 | + | 3.46410i | 0.243935 | + | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0000 | − | 13.8564i | 0.974130 | − | 0.562414i | 0.0736371 | − | 0.997285i | \(-0.476539\pi\) |
0.900493 | + | 0.434871i | \(0.143206\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 20.7846i | − | 0.842235i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.0000 | 1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.0000 | − | 15.5885i | 1.08875 | − | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.5000 | + | 14.7224i | −1.02659 | + | 0.592703i | −0.916006 | − | 0.401164i | \(-0.868606\pi\) |
−0.110585 | + | 0.993867i | \(0.535272\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.5000 | + | 14.7224i | 1.02493 | + | 0.591744i | 0.915529 | − | 0.402253i | \(-0.131773\pi\) |
0.109403 | + | 0.993997i | \(0.465106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.0000 | − | 41.5692i | 0.961540 | − | 1.66544i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.50000 | + | 7.79423i | 0.179713 | + | 0.311272i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.46410i | 0.138123i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.46410i | 0.137904i | 0.997620 | + | 0.0689519i | \(0.0219655\pi\) | ||||
−0.997620 | + | 0.0689519i | \(0.978035\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.0000 | 1.19239 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.0000 | + | 17.3205i | −0.396214 | + | 0.686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.00000 | + | 15.5885i | 0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.5000 | − | 21.6506i | −1.48116 | − | 0.855149i | −0.481389 | − | 0.876507i | \(-0.659868\pi\) |
−0.999772 | + | 0.0213584i | \(0.993201\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.5000 | + | 12.9904i | −0.887313 | + | 0.512291i | −0.873063 | − | 0.487608i | \(-0.837870\pi\) |
−0.0142506 | + | 0.999898i | \(0.504536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.0000 | − | 15.5885i | −1.06312 | − | 0.613795i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.0000 | −1.65119 | −0.825595 | − | 0.564263i | \(-0.809160\pi\) | ||||
−0.825595 | + | 0.564263i | \(0.809160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.0000 | 1.76640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.0000 | − | 15.5885i | 1.05659 | − | 0.610023i | 0.132104 | − | 0.991236i | \(-0.457827\pi\) |
0.924487 | + | 0.381212i | \(0.124493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.0000 | + | 20.7846i | 1.40664 | + | 0.812122i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.5000 | − | 28.5788i | −0.643726 | − | 1.11497i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | − | 20.7846i | 0.467454 | − | 0.809653i | −0.531855 | − | 0.846836i | \(-0.678505\pi\) |
0.999309 | + | 0.0371821i | \(0.0118382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | + | 12.1244i | 0.272268 | + | 0.471583i | 0.969442 | − | 0.245319i | \(-0.0788928\pi\) |
−0.697174 | + | 0.716902i | \(0.745559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.0000 | −0.466041 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.7846i | 0.805993i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.0000 | − | 31.1769i | −0.695920 | − | 1.20537i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | + | 20.7846i | 0.463255 | + | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.0000 | − | 39.8372i | 0.886585 | − | 1.53561i | 0.0426985 | − | 0.999088i | \(-0.486405\pi\) |
0.843886 | − | 0.536522i | \(-0.180262\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −31.5000 | − | 18.1865i | −1.21244 | − | 0.700000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0000 | − | 10.3923i | −0.691796 | − | 0.399409i | 0.112488 | − | 0.993653i | \(-0.464118\pi\) |
−0.804285 | + | 0.594244i | \(0.797451\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.0000 | + | 22.5167i | −1.49668 | + | 0.864110i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.50000 | − | 2.59808i | 0.172440 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0000 | −0.573959 | −0.286980 | − | 0.957937i | \(-0.592651\pi\) | ||||
−0.286980 | + | 0.957937i | \(0.592651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.0333i | 1.71813i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0000 | − | 15.5885i | −1.02713 | − | 0.593013i | −0.110968 | − | 0.993824i | \(-0.535395\pi\) |
−0.916161 | + | 0.400811i | \(0.868728\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −27.0000 | − | 15.5885i | −1.02565 | − | 0.592157i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.0000 | − | 57.1577i | 1.25176 | − | 2.16811i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.50000 | + | 7.79423i | 0.170450 | + | 0.295227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5000 | − | 18.1865i | 0.397146 | − | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.7128i | − | 1.04670i | −0.852118 | − | 0.523349i | \(-0.824682\pi\) | ||
0.852118 | − | 0.523349i | \(-0.175318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.46410i | − | 0.130651i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −36.0000 | + | 62.3538i | −1.35584 | + | 2.34838i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.0000 | − | 31.1769i | −0.676960 | − | 1.17253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000 | − | 24.2487i | 0.525781 | − | 0.910679i | −0.473768 | − | 0.880650i | \(-0.657106\pi\) |
0.999549 | − | 0.0300298i | \(-0.00956021\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 10.3923i | − | 0.389742i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0000 | + | 20.7846i | −1.34632 | + | 0.777300i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.5692i | 1.55243i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.0000 | 1.56634 | 0.783168 | − | 0.621810i | \(-0.213603\pi\) | ||||
0.783168 | + | 0.621810i | \(0.213603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.0000 | −1.78761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.5000 | + | 14.7224i | −0.948355 | + | 0.547533i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.0000 | − | 12.1244i | 0.779920 | − | 0.450287i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.0000 | + | 20.7846i | 1.33517 | + | 0.770859i | 0.986086 | − | 0.166234i | \(-0.0531609\pi\) |
0.349080 | + | 0.937093i | \(0.386494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.50000 | − | 7.79423i | 0.166439 | − | 0.288280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | + | 19.0526i | 0.406294 | + | 0.703722i | 0.994471 | − | 0.105010i | \(-0.0334875\pi\) |
−0.588177 | + | 0.808732i | \(0.700154\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.0000 | − | 25.9808i | −0.553283 | − | 0.958315i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 25.9808i | − | 0.957014i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9808i | 0.955718i | 0.878437 | + | 0.477859i | \(0.158587\pi\) | ||||
−0.878437 | + | 0.477859i | \(0.841413\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | 0.440831 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.00000 | + | 15.5885i | 0.330178 | + | 0.571885i | 0.982547 | − | 0.186017i | \(-0.0595579\pi\) |
−0.652369 | + | 0.757902i | \(0.726225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.0000 | + | 41.5692i | −0.879292 | + | 1.52298i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.0000 | 1.31717 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.00000 | + | 5.19615i | 0.328853 | + | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.0000 | + | 19.0526i | −1.20419 | + | 0.695238i | −0.961483 | − | 0.274863i | \(-0.911368\pi\) |
−0.242704 | + | 0.970100i | \(0.578034\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.5000 | + | 18.1865i | 1.14792 | + | 0.662754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000 | − | 24.2487i | 1.52250 | − | 0.879015i | 0.522852 | − | 0.852423i | \(-0.324868\pi\) |
0.999646 | − | 0.0265919i | \(-0.00846546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.0000 | − | 6.92820i | −0.434429 | − | 0.250818i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.00000 | − | 15.5885i | 0.325396 | − | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.0000 | − | 51.9615i | 1.08324 | − | 1.87622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.00000 | − | 12.1244i | −0.252426 | − | 0.437215i | 0.711767 | − | 0.702416i | \(-0.247895\pi\) |
−0.964193 | + | 0.265200i | \(0.914562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.0000 | 1.18847 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.92820i | 0.249190i | 0.992208 | + | 0.124595i | \(0.0397632\pi\) | ||||
−0.992208 | + | 0.124595i | \(0.960237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.00000 | + | 10.3923i | 0.215249 | + | 0.372822i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.50000 | − | 7.79423i | −0.161229 | − | 0.279257i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | + | 15.5885i | −0.322045 | + | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.00000 | − | 15.5885i | 0.321634 | − | 0.557086i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.0000 | + | 13.8564i | 0.856597 | + | 0.494556i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | − | 8.66025i | 0.534692 | − | 0.308705i | −0.208233 | − | 0.978079i | \(-0.566771\pi\) |
0.742925 | + | 0.669375i | \(0.233438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.0000 | − | 15.5885i | 0.961225 | − | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.0000 | −0.853342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.0000 | 1.13635 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.00000 | + | 1.73205i | −0.106265 | + | 0.0613524i | −0.552191 | − | 0.833718i | \(-0.686208\pi\) |
0.445925 | + | 0.895070i | \(0.352875\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | − | 10.3923i | −0.636794 | − | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.0000 | − | 20.7846i | 1.27200 | − | 0.734388i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.5000 | − | 28.5788i | 0.582272 | − | 1.00853i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.00000 | + | 10.3923i | −0.211210 | + | 0.365826i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 19.0526i | − | 0.669852i | −0.942244 | − | 0.334926i | \(-0.891289\pi\) | ||
0.942244 | − | 0.334926i | \(-0.108711\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.3731i | 1.27723i | 0.769526 | + | 0.638616i | \(0.220493\pi\) | ||||
−0.769526 | + | 0.638616i | \(0.779507\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.00000 | + | 10.3923i | −0.210429 | + | 0.364474i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | + | 10.3923i | 0.210171 | + | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.50000 | + | 7.79423i | −0.157435 | + | 0.272686i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36.0000 | + | 20.7846i | −1.25794 | + | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00000 | − | 1.73205i | −0.104701 | − | 0.0604490i | 0.446735 | − | 0.894666i | \(-0.352587\pi\) |
−0.551436 | + | 0.834217i | \(0.685920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0000 | − | 12.1244i | 0.732014 | − | 0.422628i | −0.0871445 | − | 0.996196i | \(-0.527774\pi\) |
0.819159 | + | 0.573567i | \(0.194441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 36.3731i | − | 1.26635i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0000 | 0.903017 | 0.451509 | − | 0.892267i | \(-0.350886\pi\) | ||||
0.451509 | + | 0.892267i | \(0.350886\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0000 | − | 6.92820i | 0.416275 | − | 0.240337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.50000 | − | 4.33013i | 0.259860 | − | 0.150030i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | + | 10.3923i | 0.622916 | + | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0000 | + | 31.1769i | −0.621429 | + | 1.07635i | 0.367791 | + | 0.929909i | \(0.380114\pi\) |
−0.989220 | + | 0.146438i | \(0.953219\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.50000 | − | 14.7224i | −0.293103 | − | 0.507670i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.00000 | − | 10.3923i | −0.206651 | − | 0.357930i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.3923i | 0.357506i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.92820i | 0.238056i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.0000 | 0.617758 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0000 | − | 27.7128i | 0.547830 | − | 0.948869i | −0.450593 | − | 0.892729i | \(-0.648788\pi\) |
0.998423 | − | 0.0561393i | \(-0.0178791\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.00000 | + | 15.5885i | −0.307794 | + | 0.533114i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.0000 | + | 17.3205i | 1.02478 | + | 0.591657i | 0.915485 | − | 0.402352i | \(-0.131807\pi\) |
0.109295 | + | 0.994009i | \(0.465141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5000 | − | 14.7224i | 0.870049 | − | 0.502323i | 0.00268433 | − | 0.999996i | \(-0.499146\pi\) |
0.867364 | + | 0.497674i | \(0.165812\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.0000 | + | 15.5885i | 0.920158 | + | 0.531253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.0000 | 1.02121 | 0.510606 | − | 0.859815i | \(-0.329421\pi\) | ||||
0.510606 | + | 0.859815i | \(0.329421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 84.0000 | 2.85609 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.0000 | − | 12.1244i | −0.713197 | − | 0.411765i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.00000 | − | 5.19615i | 0.305304 | − | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.0000 | − | 17.3205i | −1.01651 | − | 0.586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.0000 | −1.31995 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0000 | − | 20.7846i | 0.405674 | − | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0000 | − | 34.6410i | −0.675352 | − | 1.16974i | −0.976366 | − | 0.216124i | \(-0.930658\pi\) |
0.301014 | − | 0.953620i | \(-0.402675\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | −0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.7846i | 0.700251i | 0.936703 | + | 0.350126i | \(0.113861\pi\) | ||||
−0.936703 | + | 0.350126i | \(0.886139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.66025i | 0.291441i | 0.989326 | + | 0.145720i | \(0.0465500\pi\) | ||||
−0.989326 | + | 0.145720i | \(0.953450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 45.0000 | + | 77.9423i | 1.51266 | + | 2.62000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.0000 | − | 36.3731i | −0.705111 | − | 1.22129i | −0.966651 | − | 0.256096i | \(-0.917564\pi\) |
0.261540 | − | 0.965193i | \(-0.415770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | − | 23.3827i | −0.452267 | − | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.0000 | + | 10.3923i | 0.602347 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.0000 | + | 20.7846i | −1.20335 | + | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 31.1769i | − | 1.03750i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.0000 | − | 13.8564i | 0.797787 | − | 0.460603i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.5000 | + | 19.9186i | 1.14555 | + | 0.661386i | 0.947800 | − | 0.318866i | \(-0.103302\pi\) |
0.197754 | + | 0.980252i | \(0.436635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 31.1769i | − | 1.03407i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | + | 20.7846i | −0.397578 | + | 0.688625i | −0.993426 | − | 0.114472i | \(-0.963482\pi\) |
0.595849 | + | 0.803097i | \(0.296816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | + | 31.1769i | 0.595713 | + | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.0000 | + | 41.5692i | −0.793416 | + | 1.37424i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41.5692i | 1.37274i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.5692i | 1.37124i | 0.727959 | + | 0.685621i | \(0.240469\pi\) | ||||
−0.727959 | + | 0.685621i | \(0.759531\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.5000 | − | 38.9711i | 0.741400 | − | 1.28414i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | + | 20.7846i | 0.394985 | + | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | + | 12.1244i | −0.230159 | + | 0.398646i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.0000 | − | 20.7846i | −1.18240 | − | 0.682656i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00000 | + | 3.46410i | 0.196854 | + | 0.113653i | 0.595187 | − | 0.803587i | \(-0.297078\pi\) |
−0.398333 | + | 0.917241i | \(0.630411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.50000 | + | 4.33013i | −0.245803 | + | 0.141914i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3923i | 0.340229i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.0000 | 0.588663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.50000 | + | 0.866025i | −0.0489506 | + | 0.0282617i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 6.92820i | −0.391189 | + | 0.225853i | −0.682675 | − | 0.730722i | \(-0.739184\pi\) |
0.291486 | + | 0.956575i | \(0.405850\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 62.3538i | − | 2.02837i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.50000 | − | 7.79423i | 0.146230 | − | 0.253278i | −0.783601 | − | 0.621264i | \(-0.786619\pi\) |
0.929831 | + | 0.367986i | \(0.119953\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.0000 | − | 38.1051i | −0.714150 | − | 1.23694i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | − | 10.3923i | −0.194563 | − | 0.336994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.1244i | 0.392746i | 0.980529 | + | 0.196373i | \(0.0629164\pi\) | ||||
−0.980529 | + | 0.196373i | \(0.937084\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.7846i | 0.672574i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.0000 | 0.581857 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.00000 | − | 5.19615i | −0.0968751 | − | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5000 | + | 26.8468i | −0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.50000 | + | 7.79423i | 0.145010 | + | 0.251166i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −69.0000 | − | 39.8372i | −2.22119 | − | 1.28240i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.0000 | − | 12.1244i | 0.675314 | − | 0.389893i | −0.122773 | − | 0.992435i | \(-0.539179\pi\) |
0.798087 | + | 0.602542i | \(0.205845\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.50000 | − | 2.59808i | −0.144561 | − | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 66.0000 | 2.11586 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −42.0000 | − | 24.2487i | −1.34508 | − | 0.776580i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.5000 | + | 7.79423i | −0.431903 | + | 0.249359i | −0.700157 | − | 0.713989i | \(-0.746887\pi\) |
0.268254 | + | 0.963348i | \(0.413553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.0000 | + | 20.7846i | 1.15056 | + | 0.664279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | − | 10.3923i | −0.191565 | − | 0.331801i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.00000 | − | 5.19615i | 0.0956851 | − | 0.165732i | −0.814209 | − | 0.580572i | \(-0.802829\pi\) |
0.909894 | + | 0.414840i | \(0.136162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0000 | − | 41.5692i | −0.764704 | − | 1.32451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −72.0000 | −2.29179 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.4974i | 1.54057i | 0.637699 | + | 0.770286i | \(0.279886\pi\) | ||||
−0.637699 | + | 0.770286i | \(0.720114\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.0000 | + | 36.3731i | 0.666415 | + | 1.15426i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.00000 | − | 10.3923i | −0.190213 | − | 0.329458i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.0000 | − | 17.3205i | 0.316703 | − | 0.548546i | −0.663095 | − | 0.748535i | \(-0.730757\pi\) |
0.979798 | + | 0.199989i | \(0.0640908\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.3923i | 0.328798i |
(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 | 576.2.s.a.191.1 | 2 | ||
3.2 | odd | 2 | 1728.2.s.b.575.1 | 2 | |||
4.3 | odd | 2 | 576.2.s.d.191.1 | 2 | |||
8.3 | odd | 2 | 144.2.s.a.47.1 | ✓ | 2 | ||
8.5 | even | 2 | 144.2.s.d.47.1 | yes | 2 | ||
9.2 | odd | 6 | 5184.2.c.a.5183.1 | 2 | |||
9.4 | even | 3 | 1728.2.s.a.1151.1 | 2 | |||
9.5 | odd | 6 | 576.2.s.d.383.1 | 2 | |||
9.7 | even | 3 | 5184.2.c.c.5183.2 | 2 | |||
12.11 | even | 2 | 1728.2.s.a.575.1 | 2 | |||
24.5 | odd | 2 | 432.2.s.d.143.1 | 2 | |||
24.11 | even | 2 | 432.2.s.c.143.1 | 2 | |||
36.7 | odd | 6 | 5184.2.c.a.5183.2 | 2 | |||
36.11 | even | 6 | 5184.2.c.c.5183.1 | 2 | |||
36.23 | even | 6 | inner | 576.2.s.a.383.1 | 2 | ||
36.31 | odd | 6 | 1728.2.s.b.1151.1 | 2 | |||
72.5 | odd | 6 | 144.2.s.a.95.1 | yes | 2 | ||
72.11 | even | 6 | 1296.2.c.b.1295.2 | 2 | |||
72.13 | even | 6 | 432.2.s.c.287.1 | 2 | |||
72.29 | odd | 6 | 1296.2.c.d.1295.2 | 2 | |||
72.43 | odd | 6 | 1296.2.c.d.1295.1 | 2 | |||
72.59 | even | 6 | 144.2.s.d.95.1 | yes | 2 | ||
72.61 | even | 6 | 1296.2.c.b.1295.1 | 2 | |||
72.67 | odd | 6 | 432.2.s.d.287.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.s.a.47.1 | ✓ | 2 | 8.3 | odd | 2 | ||
144.2.s.a.95.1 | yes | 2 | 72.5 | odd | 6 | ||
144.2.s.d.47.1 | yes | 2 | 8.5 | even | 2 | ||
144.2.s.d.95.1 | yes | 2 | 72.59 | even | 6 | ||
432.2.s.c.143.1 | 2 | 24.11 | even | 2 | |||
432.2.s.c.287.1 | 2 | 72.13 | even | 6 | |||
432.2.s.d.143.1 | 2 | 24.5 | odd | 2 | |||
432.2.s.d.287.1 | 2 | 72.67 | odd | 6 | |||
576.2.s.a.191.1 | 2 | 1.1 | even | 1 | trivial | ||
576.2.s.a.383.1 | 2 | 36.23 | even | 6 | inner | ||
576.2.s.d.191.1 | 2 | 4.3 | odd | 2 | |||
576.2.s.d.383.1 | 2 | 9.5 | odd | 6 | |||
1296.2.c.b.1295.1 | 2 | 72.61 | even | 6 | |||
1296.2.c.b.1295.2 | 2 | 72.11 | even | 6 | |||
1296.2.c.d.1295.1 | 2 | 72.43 | odd | 6 | |||
1296.2.c.d.1295.2 | 2 | 72.29 | odd | 6 | |||
1728.2.s.a.575.1 | 2 | 12.11 | even | 2 | |||
1728.2.s.a.1151.1 | 2 | 9.4 | even | 3 | |||
1728.2.s.b.575.1 | 2 | 3.2 | odd | 2 | |||
1728.2.s.b.1151.1 | 2 | 36.31 | odd | 6 | |||
5184.2.c.a.5183.1 | 2 | 9.2 | odd | 6 | |||
5184.2.c.a.5183.2 | 2 | 36.7 | odd | 6 | |||
5184.2.c.c.5183.1 | 2 | 36.11 | even | 6 | |||
5184.2.c.c.5183.2 | 2 | 9.7 | even | 3 |