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 | 383.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.383 |
Dual form | 576.2.s.d.191.1 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 | 0.987048 | − | 0.160424i | \(-0.0512862\pi\) |
0.354593 | + | 0.935021i | \(0.384620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | + | 1.73205i | −1.13389 | + | 0.654654i | −0.944911 | − | 0.327327i | \(-0.893852\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 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 | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00000 | 1.54919 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205i | 0.420084i | 0.977692 | + | 0.210042i | \(0.0673601\pi\) | ||||
−0.977692 | + | 0.210042i | \(0.932640\pi\) | |||||||
\(18\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 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 | −0.194889 | − | 0.980825i | \(-0.562435\pi\) |
0.751975 | + | 0.659192i | \(0.229101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 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 | 0.105601 | − | 0.994409i | \(-0.466323\pi\) |
−0.808383 | + | 0.588657i | \(0.799657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.50000 | + | 2.59808i | −0.686244 | + | 0.396203i | −0.802203 | − | 0.597051i | \(-0.796339\pi\) |
0.115960 | + | 0.993254i | \(0.463006\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.00000 | − | 5.19615i | 1.34164 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | − | 10.3923i | −0.875190 | − | 1.51587i | −0.856560 | − | 0.516047i | \(-0.827403\pi\) |
−0.0186297 | − | 0.999826i | \(-0.505930\pi\) | |||||||
\(48\) | 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 | 0.301239 | − | 0.953549i | \(-0.402600\pi\) |
0.675178 | − | 0.737655i | \(-0.264067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | + | 6.92820i | 0.512148 | + | 0.887066i | 0.999901 | + | 0.0140840i | \(0.00448323\pi\) |
−0.487753 | + | 0.872982i | \(0.662183\pi\) | |||||||
\(62\) | 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 | \(-0.155897\pi\) |
0.0338274 | + | 0.999428i | \(0.489230\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 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 | \(-0.604238\pi\) |
0.659178 | + | 0.751987i | \(0.270905\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | − | 10.3923i | −0.658586 | − | 1.14070i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.322396 | − | 0.946605i | \(-0.395512\pi\) | |||||||
\(84\) | 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 | \(0.262531\pi\) | ||||
−0.678730 | + | 0.734388i | \(0.737469\pi\) | |||||||
\(90\) | 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 | −0.980622 | − | 0.195911i | \(-0.937234\pi\) |
0.320647 | − | 0.947199i | \(-0.396100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.00000 | 0.904534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | + | 5.19615i | −0.895533 | + | 0.517036i | −0.875748 | − | 0.482768i | \(-0.839632\pi\) |
−0.0197851 | + | 0.999804i | \(0.506298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0000 | + | 6.92820i | 1.18240 | + | 0.682656i | 0.956567 | − | 0.291511i | \(-0.0941580\pi\) |
0.225828 | + | 0.974167i | \(0.427491\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.0000 | + | 10.3923i | −1.75662 | + | 1.01419i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | −0.290021 | −0.145010 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(108\) | 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 | 0.190490 | − | 0.981689i | \(-0.438992\pi\) |
−0.754923 | + | 0.655814i | \(0.772326\pi\) | |||||||
\(114\) | 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 | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 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 | −0.562706 | − | 0.826657i | \(-0.690240\pi\) |
0.434553 | + | 0.900646i | \(0.356906\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5000 | − | 9.52628i | −1.39951 | − | 0.808008i | −0.405170 | − | 0.914241i | \(-0.632788\pi\) |
−0.994341 | + | 0.106233i | \(0.966121\pi\) | |||||||
\(140\) | 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 | −0.0798802 | − | 0.996804i | \(-0.525454\pi\) |
−0.903198 | + | 0.429224i | \(0.858787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.00000 | + | 3.46410i | −0.488273 | + | 0.281905i | −0.723858 | − | 0.689949i | \(-0.757633\pi\) |
0.235585 | + | 0.971854i | \(0.424299\pi\) | |||||||
\(152\) | 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 | −0.661094 | − | 0.750303i | \(-0.729907\pi\) |
0.980329 | + | 0.197372i | \(0.0632408\pi\) | |||||||
\(158\) | 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 | \(-0.907908\pi\) |
0.726293 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(168\) | 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 | 0.604465 | − | 0.796632i | \(-0.293387\pi\) |
0.992136 | − | 0.125166i | \(-0.0399462\pi\) | |||||||
\(174\) | 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 | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 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 | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5000 | + | 19.9186i | −0.827788 | + | 1.43377i | 0.0719816 | + | 0.997406i | \(0.477068\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | − | 20.7846i | 0.859338 | − | 1.48842i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.8564i | 0.987228i | 0.869681 | + | 0.493614i | \(0.164324\pi\) | ||||
−0.869681 | + | 0.493614i | \(0.835676\pi\) | |||||||
\(198\) | 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 | \(-0.130011\pi\) |
0.114902 | + | 0.993377i | \(0.463345\pi\) | |||||||
\(212\) | 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 | \(-0.911670\pi\) |
−0.243625 | + | 0.969870i | \(0.578337\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.0000 | 1.40000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | + | 2.59808i | 0.0995585 | + | 0.172440i | 0.911502 | − | 0.411296i | \(-0.134924\pi\) |
−0.811943 | + | 0.583736i | \(0.801590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0000 | + | 22.5167i | −0.859064 | + | 1.48794i | 0.0137585 | + | 0.999905i | \(0.495620\pi\) |
−0.872823 | + | 0.488037i | \(0.837713\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.0000 | −1.18431 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 12.1244i | − | 0.794293i | −0.917755 | − | 0.397146i | \(-0.870000\pi\) | ||
0.917755 | − | 0.397146i | \(-0.130000\pi\) | |||||||
\(234\) | 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 | −0.157893 | − | 0.987456i | \(-0.550470\pi\) |
0.934109 | − | 0.356988i | \(-0.116196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50000 | + | 14.7224i | 0.547533 | + | 0.948355i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 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 | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(252\) | 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 | −0.112474 | − | 0.993655i | \(-0.535878\pi\) |
−0.916767 | + | 0.399422i | \(0.869211\pi\) | |||||||
\(258\) | 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 | 0.997906 | + | 0.0646755i | \(0.0206012\pi\) |
−0.442943 | + | 0.896550i | \(0.646065\pi\) | |||||||
\(264\) | 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 | \(0.0677404\pi\) | ||||
−0.977441 | + | 0.211210i | \(0.932260\pi\) | |||||||
\(270\) | 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 | 0.720473 | − | 0.693482i | \(-0.243925\pi\) |
−0.960810 | + | 0.277207i | \(0.910591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | − | 3.46410i | 0.357930 | − | 0.206651i | −0.310242 | − | 0.950657i | \(-0.600410\pi\) |
0.668172 | + | 0.744007i | \(0.267077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.00000 | + | 5.19615i | 0.534994 | + | 0.308879i | 0.743048 | − | 0.669238i | \(-0.233379\pi\) |
−0.208053 | + | 0.978117i | \(0.566713\pi\) | |||||||
\(284\) | 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 | 0.585065 | − | 0.810987i | \(-0.301069\pi\) |
−0.409803 | + | 0.912174i | \(0.634402\pi\) | |||||||
\(294\) | 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 | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.0000 | + | 31.1769i | −1.01419 | + | 1.75662i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | − | 3.46410i | 0.336994 | − | 0.194563i | −0.321948 | − | 0.946757i | \(-0.604338\pi\) |
0.658942 | + | 0.752194i | \(0.271004\pi\) | |||||||
\(318\) | 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 | \(-0.434495\pi\) |
0.949923 | + | 0.312485i | \(0.101161\pi\) | |||||||
\(332\) | 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 | −0.676441 | − | 0.736497i | \(-0.736479\pi\) |
0.976045 | + | 0.217567i | \(0.0698121\pi\) | |||||||
\(338\) | 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 | −0.234372 | − | 0.972147i | \(-0.575303\pi\) |
0.959090 | − | 0.283101i | \(-0.0913633\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0000 | + | 27.7128i | 0.856460 | + | 1.48343i | 0.875284 | + | 0.483610i | \(0.160675\pi\) |
−0.0188232 | + | 0.999823i | \(0.505992\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0000 | − | 10.3923i | −0.960769 | − | 0.554700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.5000 | − | 12.9904i | 1.19755 | − | 0.691408i | 0.237545 | − | 0.971377i | \(-0.423657\pi\) |
0.960009 | + | 0.279968i | \(0.0903240\pi\) | |||||||
\(354\) | 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 | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(360\) | 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 | \(-0.695485\pi\) |
0.419653 | + | 0.907685i | \(0.362152\pi\) | |||||||
\(368\) | 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 | −0.482006 | − | 0.876168i | \(-0.660092\pi\) |
0.999787 | − | 0.0206542i | \(-0.00657489\pi\) | |||||||
\(374\) | 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 | \(-0.681226\pi\) |
0.998954 | + | 0.0457244i | \(0.0145596\pi\) | |||||||
\(384\) | 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 | −0.254177 | − | 0.967158i | \(-0.581804\pi\) |
0.710495 | + | 0.703702i | \(0.248471\pi\) | |||||||
\(390\) | 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 | 0.300904 | − | 0.953654i | \(-0.402711\pi\) |
−0.675437 | + | 0.737418i | \(0.736045\pi\) | |||||||
\(402\) | 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 | −0.428063 | − | 0.903749i | \(-0.640804\pi\) |
0.996701 | − | 0.0811615i | \(-0.0258630\pi\) | |||||||
\(410\) | 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 | \(-0.738640\pi\) |
0.974546 | + | 0.224189i | \(0.0719734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | 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 | \(-0.357273\pi\) | ||||
0.433515 | + | 0.901146i | \(0.357273\pi\) | |||||||
\(432\) | 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 | \(-0.831864\pi\) |
0.00461537 | + | 0.999989i | \(0.498531\pi\) | |||||||
\(440\) | 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 | \(-0.0980821\pi\) |
−0.739100 | + | 0.673596i | \(0.764749\pi\) | |||||||
\(444\) | 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 | \(0.210059\pi\) | ||||
−0.790041 | + | 0.613054i | \(0.789941\pi\) | |||||||
\(450\) | 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 | 0.965512 | − | 0.260358i | \(-0.0838407\pi\) |
−0.708233 | + | 0.705979i | \(0.750507\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.00000 | 0.420084 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0000 | + | 10.3923i | −0.838344 | + | 0.484018i | −0.856701 | − | 0.515814i | \(-0.827490\pi\) |
0.0183573 | + | 0.999831i | \(0.494156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0000 | − | 8.66025i | −0.697109 | − | 0.402476i | 0.109161 | − | 0.994024i | \(-0.465184\pi\) |
−0.806270 | + | 0.591548i | \(0.798517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.00000 | −0.138823 | −0.0694117 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694117 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(468\) | 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 | 0.973321 | + | 0.229447i | \(0.0736918\pi\) |
−0.287954 | + | 0.957644i | \(0.592975\pi\) | |||||||
\(480\) | 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 | \(-0.943243\pi\) |
0.645675 | + | 0.763612i | \(0.276576\pi\) | |||||||
\(492\) | 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 | \(-0.219883\pi\) |
−0.166405 | + | 0.986057i | \(0.553216\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3923i | 0.464294i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 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 | 0.0448779 | − | 0.998992i | \(-0.485710\pi\) |
−0.842714 | + | 0.538362i | \(0.819043\pi\) | |||||||
\(510\) | 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 | \(-0.889075\pi\) | ||
0.939892 | − | 0.341471i | \(-0.110925\pi\) | |||||||
\(522\) | 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 | \(-0.607392\pi\) |
0.651694 | + | 0.758482i | \(0.274059\pi\) | |||||||
\(548\) | 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 | \(-0.700937\pi\) | ||
0.590165 | − | 0.807283i | \(-0.299063\pi\) | |||||||
\(558\) | 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 | \(-0.894069\pi\) |
0.755482 | + | 0.655169i | \(0.227403\pi\) | |||||||
\(564\) | 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 | −0.804255 | − | 0.594285i | \(-0.797435\pi\) |
0.112539 | + | 0.993647i | \(0.464102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5000 | − | 6.06218i | −0.439411 | − | 0.253694i | 0.263937 | − | 0.964540i | \(-0.414979\pi\) |
−0.703348 | + | 0.710846i | \(0.748312\pi\) | |||||||
\(572\) | 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 | \(-0.146947\pi\) |
−0.833408 | + | 0.552658i | \(0.813614\pi\) | |||||||
\(588\) | 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 | \(-0.954565\pi\) | ||
0.989830 | − | 0.142254i | \(-0.0454349\pi\) | |||||||
\(594\) | 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 | \(-0.713468\pi\) |
0.989210 | + | 0.146503i | \(0.0468017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.50000 | + | 6.06218i | 0.142768 | + | 0.247281i | 0.928538 | − | 0.371237i | \(-0.121066\pi\) |
−0.785770 | + | 0.618519i | \(0.787733\pi\) | |||||||
\(602\) | 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 | \(-0.523461\pi\) |
−0.900493 | + | 0.434871i | \(0.856794\pi\) | |||||||
\(608\) | 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 | −0.110585 | − | 0.993867i | \(-0.535272\pi\) |
−0.916006 | + | 0.401164i | \(0.868606\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5000 | + | 14.7224i | −1.02493 | + | 0.591744i | −0.915529 | − | 0.402253i | \(-0.868227\pi\) |
−0.109403 | + | 0.993997i | \(0.534894\pi\) | |||||||
\(620\) | 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 | −0.999772 | − | 0.0213584i | \(-0.993201\pi\) |
−0.481389 | + | 0.876507i | \(0.659868\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.5000 | + | 12.9904i | 0.887313 | + | 0.512291i | 0.873063 | − | 0.487608i | \(-0.162130\pi\) |
0.0142506 | + | 0.999898i | \(0.495464\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.0000 | + | 15.5885i | −1.06312 | + | 0.613795i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.0000 | 1.65119 | 0.825595 | − | 0.564263i | \(-0.190840\pi\) | ||||
0.825595 | + | 0.564263i | \(0.190840\pi\) | |||||||
\(648\) | 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 | 0.924487 | − | 0.381212i | \(-0.124493\pi\) |
0.132104 | + | 0.991236i | \(0.457827\pi\) | |||||||
\(654\) | 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 | \(-0.321495\pi\) |
−0.999309 | + | 0.0371821i | \(0.988162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | − | 12.1244i | 0.272268 | − | 0.471583i | −0.697174 | − | 0.716902i | \(-0.745559\pi\) |
0.969442 | + | 0.245319i | \(0.0788928\pi\) | |||||||
\(662\) | 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 | 0.843886 | + | 0.536522i | \(0.180262\pi\) |
0.0426985 | + | 0.999088i | \(0.486405\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 31.5000 | − | 18.1865i | 1.21244 | − | 0.700000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0000 | + | 10.3923i | −0.691796 | + | 0.399409i | −0.804285 | − | 0.594244i | \(-0.797451\pi\) |
0.112488 | + | 0.993653i | \(0.464118\pi\) | |||||||
\(678\) | 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 | \(-0.407349\pi\) | ||||
0.286980 | + | 0.957937i | \(0.407349\pi\) | |||||||
\(684\) | 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 | \(-0.464605\pi\) |
0.916161 | + | 0.400811i | \(0.131272\pi\) | |||||||
\(692\) | 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 | \(0.175318\pi\) | ||||
−0.852118 | + | 0.523349i | \(0.824682\pi\) | |||||||
\(702\) | 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 | 0.999549 | + | 0.0300298i | \(0.00956021\pi\) |
−0.473768 | + | 0.880650i | \(0.657106\pi\) | |||||||
\(710\) | 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 | \(-0.786397\pi\) | ||||
−0.783168 | + | 0.621810i | \(0.786397\pi\) | |||||||
\(720\) | 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 | \(-0.946839\pi\) |
−0.349080 | + | 0.937093i | \(0.613506\pi\) | |||||||
\(728\) | 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 | −0.588177 | − | 0.808732i | \(-0.700154\pi\) |
0.994471 | + | 0.105010i | \(0.0334875\pi\) | |||||||
\(734\) | 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 | \(-0.940442\pi\) |
0.652369 | + | 0.757902i | \(0.273775\pi\) | |||||||
\(744\) | 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 | \(-0.0886324\pi\) |
0.242704 | + | 0.970100i | \(0.421966\pi\) | |||||||
\(752\) | 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 | 0.999646 | + | 0.0265919i | \(0.00846546\pi\) |
0.522852 | + | 0.852423i | \(0.324868\pi\) | |||||||
\(762\) | 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 | −0.964193 | − | 0.265200i | \(-0.914562\pi\) |
0.711767 | + | 0.702416i | \(0.247895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.0000 | −1.18847 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 6.92820i | − | 0.249190i | −0.992208 | − | 0.124595i | \(-0.960237\pi\) | ||
0.992208 | − | 0.124595i | \(-0.0397632\pi\) | |||||||
\(774\) | 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 | \(-0.433229\pi\) |
−0.742925 | + | 0.669375i | \(0.766562\pi\) | |||||||
\(788\) | 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 | 0.445925 | − | 0.895070i | \(-0.352875\pi\) |
−0.552191 | + | 0.833718i | \(0.686208\pi\) | |||||||
\(798\) | 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 | \(0.108711\pi\) | ||||
−0.942244 | + | 0.334926i | \(0.891289\pi\) | |||||||
\(810\) | 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 | −0.551436 | − | 0.834217i | \(-0.685920\pi\) |
0.446735 | + | 0.894666i | \(0.352587\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0000 | − | 12.1244i | −0.732014 | − | 0.422628i | 0.0871445 | − | 0.996196i | \(-0.472226\pi\) |
−0.819159 | + | 0.573567i | \(0.805559\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 36.3731i | 1.26635i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 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 | 0.989220 | + | 0.146438i | \(0.0467809\pi\) |
−0.367791 | + | 0.929909i | \(0.619886\pi\) | |||||||
\(840\) | 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 | 0.998423 | + | 0.0561393i | \(0.0178791\pi\) |
−0.450593 | + | 0.892729i | \(0.648788\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.00000 | + | 15.5885i | 0.307794 | + | 0.533114i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.0000 | − | 17.3205i | 1.02478 | − | 0.591657i | 0.109295 | − | 0.994009i | \(-0.465141\pi\) |
0.915485 | + | 0.402352i | \(0.131807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.5000 | − | 14.7224i | −0.870049 | − | 0.502323i | −0.00268433 | − | 0.999996i | \(-0.500854\pi\) |
−0.867364 | + | 0.497674i | \(0.834188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.0000 | − | 15.5885i | 0.920158 | − | 0.531253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.0000 | −1.02121 | −0.510606 | − | 0.859815i | \(-0.670579\pi\) | ||||
−0.510606 | + | 0.859815i | \(0.670579\pi\) | |||||||
\(864\) | 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 | 0.301014 | + | 0.953620i | \(0.402675\pi\) |
−0.976366 | + | 0.216124i | \(0.930658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.7846i | − | 0.700251i | −0.936703 | − | 0.350126i | \(-0.886139\pi\) | ||
0.936703 | − | 0.350126i | \(-0.113861\pi\) | |||||||
\(882\) | 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 | −0.261540 | − | 0.965193i | \(-0.584230\pi\) |
0.966651 | − | 0.256096i | \(-0.0824362\pi\) | |||||||
\(888\) | 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 | \(-0.896698\pi\) |
−0.197754 | + | 0.980252i | \(0.563365\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.1769i | 1.03407i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | + | 20.7846i | 0.397578 | + | 0.688625i | 0.993426 | − | 0.114472i | \(-0.0365176\pi\) |
−0.595849 | + | 0.803097i | \(0.703184\pi\) | |||||||
\(912\) | 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 | −0.398333 | − | 0.917241i | \(-0.630411\pi\) |
0.595187 | + | 0.803587i | \(0.297078\pi\) | |||||||
\(930\) | 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 | 0.291486 | − | 0.956575i | \(-0.405850\pi\) |
−0.682675 | + | 0.730722i | \(0.739184\pi\) | |||||||
\(942\) | 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 | \(-0.213381\pi\) |
−0.929831 | + | 0.367986i | \(0.880047\pi\) | |||||||
\(948\) | 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 | \(-0.937084\pi\) | ||
0.980529 | − | 0.196373i | \(-0.0629164\pi\) | |||||||
\(954\) | 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 | \(-0.460821\pi\) |
−0.798087 | + | 0.602542i | \(0.794155\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.50000 | + | 2.59808i | −0.144561 | + | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 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 | 0.268254 | − | 0.963348i | \(-0.413553\pi\) |
−0.700157 | + | 0.713989i | \(0.746887\pi\) | |||||||
\(978\) | 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 | \(-0.197171\pi\) |
−0.909894 | + | 0.414840i | \(0.863838\pi\) | |||||||
\(984\) | 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 | 0.979798 | − | 0.199989i | \(-0.0640908\pi\) |
−0.663095 | + | 0.748535i | \(0.730757\pi\) | |||||||
\(998\) | 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.d.383.1 | 2 | ||
3.2 | odd | 2 | 1728.2.s.a.1151.1 | 2 | |||
4.3 | odd | 2 | 576.2.s.a.383.1 | 2 | |||
8.3 | odd | 2 | 144.2.s.d.95.1 | yes | 2 | ||
8.5 | even | 2 | 144.2.s.a.95.1 | yes | 2 | ||
9.2 | odd | 6 | 576.2.s.a.191.1 | 2 | |||
9.4 | even | 3 | 5184.2.c.a.5183.1 | 2 | |||
9.5 | odd | 6 | 5184.2.c.c.5183.2 | 2 | |||
9.7 | even | 3 | 1728.2.s.b.575.1 | 2 | |||
12.11 | even | 2 | 1728.2.s.b.1151.1 | 2 | |||
24.5 | odd | 2 | 432.2.s.c.287.1 | 2 | |||
24.11 | even | 2 | 432.2.s.d.287.1 | 2 | |||
36.7 | odd | 6 | 1728.2.s.a.575.1 | 2 | |||
36.11 | even | 6 | inner | 576.2.s.d.191.1 | 2 | ||
36.23 | even | 6 | 5184.2.c.a.5183.2 | 2 | |||
36.31 | odd | 6 | 5184.2.c.c.5183.1 | 2 | |||
72.5 | odd | 6 | 1296.2.c.b.1295.1 | 2 | |||
72.11 | even | 6 | 144.2.s.a.47.1 | ✓ | 2 | ||
72.13 | even | 6 | 1296.2.c.d.1295.2 | 2 | |||
72.29 | odd | 6 | 144.2.s.d.47.1 | yes | 2 | ||
72.43 | odd | 6 | 432.2.s.c.143.1 | 2 | |||
72.59 | even | 6 | 1296.2.c.d.1295.1 | 2 | |||
72.61 | even | 6 | 432.2.s.d.143.1 | 2 | |||
72.67 | odd | 6 | 1296.2.c.b.1295.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.s.a.47.1 | ✓ | 2 | 72.11 | even | 6 | ||
144.2.s.a.95.1 | yes | 2 | 8.5 | even | 2 | ||
144.2.s.d.47.1 | yes | 2 | 72.29 | odd | 6 | ||
144.2.s.d.95.1 | yes | 2 | 8.3 | odd | 2 | ||
432.2.s.c.143.1 | 2 | 72.43 | odd | 6 | |||
432.2.s.c.287.1 | 2 | 24.5 | odd | 2 | |||
432.2.s.d.143.1 | 2 | 72.61 | even | 6 | |||
432.2.s.d.287.1 | 2 | 24.11 | even | 2 | |||
576.2.s.a.191.1 | 2 | 9.2 | odd | 6 | |||
576.2.s.a.383.1 | 2 | 4.3 | odd | 2 | |||
576.2.s.d.191.1 | 2 | 36.11 | even | 6 | inner | ||
576.2.s.d.383.1 | 2 | 1.1 | even | 1 | trivial | ||
1296.2.c.b.1295.1 | 2 | 72.5 | odd | 6 | |||
1296.2.c.b.1295.2 | 2 | 72.67 | odd | 6 | |||
1296.2.c.d.1295.1 | 2 | 72.59 | even | 6 | |||
1296.2.c.d.1295.2 | 2 | 72.13 | even | 6 | |||
1728.2.s.a.575.1 | 2 | 36.7 | odd | 6 | |||
1728.2.s.a.1151.1 | 2 | 3.2 | odd | 2 | |||
1728.2.s.b.575.1 | 2 | 9.7 | even | 3 | |||
1728.2.s.b.1151.1 | 2 | 12.11 | even | 2 | |||
5184.2.c.a.5183.1 | 2 | 9.4 | even | 3 | |||
5184.2.c.a.5183.2 | 2 | 36.23 | even | 6 | |||
5184.2.c.c.5183.1 | 2 | 36.31 | odd | 6 | |||
5184.2.c.c.5183.2 | 2 | 9.5 | odd | 6 |