Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1081,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3240.1081");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.8715302549\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2161.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.2161 |
Dual form | 3240.2.q.n.1081.1 |
$q$-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 \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).
\(n\) | \(1297\) | \(1621\) | \(2431\) | \(3161\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 3.46410i | −0.554700 | − | 0.960769i | −0.997927 | − | 0.0643593i | \(-0.979500\pi\) |
0.443227 | − | 0.896410i | \(-0.353834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | − | 6.92820i | −0.834058 | − | 1.44463i | −0.894795 | − | 0.446476i | \(-0.852679\pi\) |
0.0607377 | − | 0.998154i | \(-0.480655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.00000 | − | 8.66025i | 0.928477 | − | 1.60817i | 0.142605 | − | 0.989780i | \(-0.454452\pi\) |
0.785872 | − | 0.618389i | \(-0.212214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | − | 6.92820i | 0.609994 | − | 1.05654i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) |
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | + | 6.92820i | −0.583460 | + | 1.01058i | 0.411606 | + | 0.911362i | \(0.364968\pi\) |
−0.995066 | + | 0.0992202i | \(0.968365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.00000 | + | 12.1244i | 0.911322 | + | 1.57846i | 0.812198 | + | 0.583382i | \(0.198271\pi\) |
0.0991242 | + | 0.995075i | \(0.468396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | − | 12.1244i | 0.896258 | − | 1.55236i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
0.832240 | − | 0.554416i | \(-0.187058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | − | 3.46410i | 0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | + | 3.46410i | 0.244339 | + | 0.423207i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | − | 3.46410i | −0.227921 | − | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | − | 10.3923i | 0.675053 | − | 1.16923i | −0.301401 | − | 0.953498i | \(-0.597454\pi\) |
0.976453 | − | 0.215728i | \(-0.0692125\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.00000 | + | 3.46410i | −0.219529 | + | 0.380235i | −0.954664 | − | 0.297686i | \(-0.903785\pi\) |
0.735135 | + | 0.677920i | \(0.237119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | − | 1.73205i | −0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | + | 3.46410i | 0.205196 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | − | 12.1244i | 0.710742 | − | 1.23104i | −0.253837 | − | 0.967247i | \(-0.581693\pi\) |
0.964579 | − | 0.263795i | \(-0.0849741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.00000 | − | 15.5885i | −0.846649 | − | 1.46644i | −0.884182 | − | 0.467143i | \(-0.845283\pi\) |
0.0375328 | − | 0.999295i | \(-0.488050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | − | 6.92820i | 0.373002 | − | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | − | 3.46410i | 0.183340 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000 | 1.59724 | 0.798621 | − | 0.601834i | \(-0.205563\pi\) | ||||
0.798621 | + | 0.601834i | \(0.205563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 6.92820i | −0.346844 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00000 | + | 1.73205i | −0.0854358 | + | 0.147979i | −0.905577 | − | 0.424182i | \(-0.860562\pi\) |
0.820141 | + | 0.572161i | \(0.193895\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | − | 10.3923i | −0.508913 | − | 0.881464i | −0.999947 | − | 0.0103230i | \(-0.996714\pi\) |
0.491033 | − | 0.871141i | \(-0.336619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | − | 8.66025i | −0.409616 | − | 0.709476i | 0.585231 | − | 0.810867i | \(-0.301004\pi\) |
−0.994847 | + | 0.101391i | \(0.967671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | − | 3.46410i | 0.160644 | − | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | − | 3.46410i | −0.159617 | − | 0.276465i | 0.775113 | − | 0.631822i | \(-0.217693\pi\) |
−0.934731 | + | 0.355357i | \(0.884359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0000 | 1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.00000 | − | 1.73205i | 0.0760286 | − | 0.131685i | −0.825505 | − | 0.564396i | \(-0.809109\pi\) |
0.901533 | + | 0.432710i | \(0.142443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −0.0755929 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.0000 | −1.04641 | −0.523205 | − | 0.852207i | \(-0.675264\pi\) | ||||
−0.523205 | + | 0.852207i | \(0.675264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | − | 3.46410i | 0.146254 | − | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | − | 19.0526i | −0.791797 | − | 1.37143i | −0.924853 | − | 0.380325i | \(-0.875812\pi\) |
0.133056 | − | 0.991109i | \(-0.457521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.0000 | + | 17.3205i | 0.701862 | + | 1.21566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | + | 6.92820i | −0.276686 | + | 0.479234i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | − | 17.3205i | −0.688428 | − | 1.19239i | −0.972346 | − | 0.233544i | \(-0.924968\pi\) |
0.283918 | − | 0.958849i | \(-0.408366\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | + | 6.92820i | 0.269069 | + | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.0000 | − | 19.0526i | 0.736614 | − | 1.27585i | −0.217397 | − | 0.976083i | \(-0.569757\pi\) |
0.954011 | − | 0.299770i | \(-0.0969101\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.73205i | 0.0660819 | + | 0.114457i | 0.897173 | − | 0.441679i | \(-0.145617\pi\) |
−0.831092 | + | 0.556136i | \(0.812283\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | − | 10.3923i | −0.388108 | − | 0.672222i | 0.604087 | − | 0.796918i | \(-0.293538\pi\) |
−0.992195 | + | 0.124696i | \(0.960204\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.50000 | + | 2.59808i | −0.0958315 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.00000 | − | 13.8564i | −0.509028 | − | 0.881662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.00000 | 0.378717 | 0.189358 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189358 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | + | 5.19615i | 0.184289 | + | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00000 | −0.121942 | −0.0609711 | − | 0.998140i | \(-0.519420\pi\) | ||||
−0.0609711 | + | 0.998140i | \(0.519420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | − | 1.73205i | −0.0603023 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.00000 | − | 13.8564i | 0.480673 | − | 0.832551i | −0.519081 | − | 0.854725i | \(-0.673726\pi\) |
0.999754 | + | 0.0221745i | \(0.00705893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0000 | − | 24.2487i | 0.835170 | − | 1.44656i | −0.0587220 | − | 0.998274i | \(-0.518703\pi\) |
0.893892 | − | 0.448282i | \(-0.147964\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00000 | − | 1.73205i | −0.0584206 | − | 0.101187i | 0.835336 | − | 0.549740i | \(-0.185273\pi\) |
−0.893757 | + | 0.448552i | \(0.851940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.00000 | + | 12.1244i | −0.407556 | + | 0.705907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.0000 | + | 27.7128i | −0.925304 | + | 1.60267i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 13.8564i | 0.461112 | + | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.0000 | 0.801638 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.0000 | −1.82634 | −0.913168 | − | 0.407583i | \(-0.866372\pi\) | ||||
−0.913168 | + | 0.407583i | \(0.866372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000 | + | 17.3205i | 0.567048 | + | 0.982156i | 0.996856 | + | 0.0792356i | \(0.0252479\pi\) |
−0.429808 | + | 0.902920i | \(0.641419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | − | 8.66025i | 0.282617 | − | 0.489506i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
0.972028 | + | 0.234863i | \(0.0754642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0000 | − | 25.9808i | 0.842484 | − | 1.45922i | −0.0453045 | − | 0.998973i | \(-0.514426\pi\) |
0.887788 | − | 0.460252i | \(-0.152241\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0000 | + | 17.3205i | 0.559893 | + | 0.969762i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | − | 13.8564i | −0.441054 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000 | − | 10.3923i | 0.329790 | − | 0.571213i | −0.652680 | − | 0.757634i | \(-0.726355\pi\) |
0.982470 | + | 0.186421i | \(0.0596888\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | + | 3.46410i | −0.109272 | + | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | + | 1.73205i | 0.0544735 | + | 0.0943508i | 0.891976 | − | 0.452082i | \(-0.149319\pi\) |
−0.837503 | + | 0.546433i | \(0.815985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.00000 | − | 13.8564i | −0.429463 | − | 0.743851i | 0.567363 | − | 0.823468i | \(-0.307964\pi\) |
−0.996826 | + | 0.0796169i | \(0.974630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.00000 | − | 5.19615i | 0.160586 | − | 0.278144i | −0.774493 | − | 0.632583i | \(-0.781995\pi\) |
0.935079 | + | 0.354439i | \(0.115328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0000 | − | 22.5167i | 0.691920 | − | 1.19844i | −0.279288 | − | 0.960207i | \(-0.590098\pi\) |
0.971208 | − | 0.238233i | \(-0.0765683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.00000 | + | 5.19615i | 0.157027 | + | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0000 | + | 22.5167i | −0.678594 | + | 1.17536i | 0.296810 | + | 0.954937i | \(0.404077\pi\) |
−0.975404 | + | 0.220423i | \(0.929256\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.0000 | −2.06010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | + | 20.7846i | 0.613171 | + | 1.06204i | 0.990702 | + | 0.136047i | \(0.0434398\pi\) |
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | − | 3.46410i | 0.101929 | − | 0.176547i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.00000 | + | 15.5885i | −0.456318 | + | 0.790366i | −0.998763 | − | 0.0497253i | \(-0.984165\pi\) |
0.542445 | + | 0.840091i | \(0.317499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | + | 13.8564i | 0.404577 | + | 0.700749i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0000 | 0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.00000 | −0.401508 | −0.200754 | − | 0.979642i | \(-0.564339\pi\) | ||||
−0.200754 | + | 0.979642i | \(0.564339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | + | 10.3923i | 0.299626 | + | 0.518967i | 0.976050 | − | 0.217545i | \(-0.0698049\pi\) |
−0.676425 | + | 0.736512i | \(0.736472\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | + | 13.8564i | −0.398508 | + | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | − | 8.66025i | −0.247234 | − | 0.428222i | 0.715523 | − | 0.698589i | \(-0.246188\pi\) |
−0.962757 | + | 0.270367i | \(0.912855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.0000 | −1.37779 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0000 | − | 25.9808i | −0.732798 | − | 1.26924i | −0.955683 | − | 0.294398i | \(-0.904881\pi\) |
0.222885 | − | 0.974845i | \(-0.428453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.0000 | + | 25.9808i | −0.731055 | + | 1.26622i | 0.225377 | + | 0.974272i | \(0.427639\pi\) |
−0.956433 | + | 0.291953i | \(0.905695\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.0000 | + | 24.2487i | 0.677507 | + | 1.17348i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | − | 27.7128i | −0.765384 | − | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | − | 27.7128i | 0.763638 | − | 1.32266i | −0.177325 | − | 0.984152i | \(-0.556744\pi\) |
0.940963 | − | 0.338508i | \(-0.109922\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0000 | + | 20.7846i | −0.570137 | + | 0.987507i | 0.426414 | + | 0.904528i | \(0.359777\pi\) |
−0.996551 | + | 0.0829786i | \(0.973557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | − | 10.3923i | −0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.00000 | + | 6.92820i | 0.187523 | + | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.00000 | + | 8.66025i | −0.233890 | + | 0.405110i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | − | 25.9808i | 0.698620 | − | 1.21004i | −0.270326 | − | 0.962769i | \(-0.587131\pi\) |
0.968945 | − | 0.247276i | \(-0.0795353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0000 | − | 25.9808i | −0.697109 | − | 1.20743i | −0.969465 | − | 0.245232i | \(-0.921136\pi\) |
0.272355 | − | 0.962197i | \(-0.412197\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.0000 | −0.925490 | −0.462745 | − | 0.886492i | \(-0.653135\pi\) | ||||
−0.462745 | + | 0.886492i | \(0.653135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.00000 | + | 13.8564i | 0.367840 | + | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | + | 3.46410i | −0.0917663 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.00000 | − | 3.46410i | 0.0913823 | − | 0.158279i | −0.816711 | − | 0.577047i | \(-0.804205\pi\) |
0.908093 | + | 0.418769i | \(0.137538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.0000 | 0.635707 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0000 | 0.996915 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.00000 | + | 15.5885i | 0.406164 | + | 0.703497i | 0.994456 | − | 0.105151i | \(-0.0335327\pi\) |
−0.588292 | + | 0.808649i | \(0.700199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | + | 17.3205i | −0.450377 | + | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | + | 20.7846i | −0.538274 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0000 | − | 17.3205i | −0.447661 | − | 0.775372i | 0.550572 | − | 0.834788i | \(-0.314410\pi\) |
−0.998233 | + | 0.0594153i | \(0.981076\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.00000 | − | 12.1244i | −0.310270 | − | 0.537403i | 0.668151 | − | 0.744026i | \(-0.267086\pi\) |
−0.978421 | + | 0.206623i | \(0.933753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | + | 10.3923i | −0.265424 | + | 0.459728i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.00000 | + | 12.1244i | −0.308457 | + | 0.534263i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.00000 | − | 13.8564i | −0.351840 | − | 0.609404i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.0000 | 0.876216 | 0.438108 | − | 0.898922i | \(-0.355649\pi\) | ||||
0.438108 | + | 0.898922i | \(0.355649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.0000 | 1.22435 | 0.612177 | − | 0.790721i | \(-0.290294\pi\) | ||||
0.612177 | + | 0.790721i | \(0.290294\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000 | + | 6.92820i | 0.174243 | + | 0.301797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | − | 10.3923i | −0.259403 | − | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.00000 | −0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.00000 | + | 1.73205i | 0.0428353 | + | 0.0741929i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | + | 6.92820i | −0.171028 | + | 0.296229i | −0.938779 | − | 0.344519i | \(-0.888042\pi\) |
0.767752 | + | 0.640747i | \(0.221375\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.0000 | − | 34.6410i | 0.852029 | − | 1.47576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | + | 20.7846i | 0.510292 | + | 0.883852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.0000 | −1.10166 | −0.550828 | − | 0.834619i | \(-0.685688\pi\) | ||||
−0.550828 | + | 0.834619i | \(0.685688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.0000 | −1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.00000 | − | 6.92820i | −0.168580 | − | 0.291989i | 0.769341 | − | 0.638838i | \(-0.220585\pi\) |
−0.937921 | + | 0.346850i | \(0.887251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | − | 15.5885i | 0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | − | 17.3205i | 0.419222 | − | 0.726113i | −0.576640 | − | 0.816999i | \(-0.695636\pi\) |
0.995861 | + | 0.0908852i | \(0.0289696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | − | 3.46410i | −0.0836974 | − | 0.144968i | 0.821138 | − | 0.570730i | \(-0.193340\pi\) |
−0.904835 | + | 0.425762i | \(0.860006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0000 | 1.08239 | 0.541197 | − | 0.840896i | \(-0.317971\pi\) | ||||
0.541197 | + | 0.840896i | \(0.317971\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | − | 6.92820i | −0.165948 | − | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | + | 10.3923i | −0.248495 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0000 | + | 31.1769i | −0.742940 | + | 1.28681i | 0.208212 | + | 0.978084i | \(0.433236\pi\) |
−0.951151 | + | 0.308725i | \(0.900098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | − | 13.8564i | −0.329634 | − | 0.570943i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.0000 | 1.72473 | 0.862367 | − | 0.506284i | \(-0.168981\pi\) | ||||
0.862367 | + | 0.506284i | \(0.168981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | 0.163984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | + | 20.7846i | 0.490307 | + | 0.849236i | 0.999938 | − | 0.0111569i | \(-0.00355143\pi\) |
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0000 | + | 19.0526i | −0.448699 | + | 0.777170i | −0.998302 | − | 0.0582563i | \(-0.981446\pi\) |
0.549602 | + | 0.835426i | \(0.314779\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.50000 | + | 6.06218i | −0.142295 | + | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.00000 | − | 5.19615i | −0.121766 | − | 0.210905i | 0.798698 | − | 0.601732i | \(-0.205522\pi\) |
−0.920464 | + | 0.390827i | \(0.872189\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.0000 | 1.29458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −48.0000 | −1.93870 | −0.969351 | − | 0.245680i | \(-0.920989\pi\) | ||||
−0.969351 | + | 0.245680i | \(0.920989\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | − | 5.19615i | −0.120775 | − | 0.209189i | 0.799298 | − | 0.600935i | \(-0.205205\pi\) |
−0.920074 | + | 0.391745i | \(0.871871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.0000 | + | 38.1051i | −0.884255 | + | 1.53157i | −0.0376891 | + | 0.999290i | \(0.512000\pi\) |
−0.846566 | + | 0.532284i | \(0.821334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | − | 20.7846i | 0.480770 | − | 0.832718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.00000 | + | 15.5885i | 0.357154 | + | 0.618609i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000 | − | 10.3923i | 0.237729 | − | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0000 | + | 20.7846i | −0.473972 | + | 0.820943i | −0.999556 | − | 0.0297987i | \(-0.990513\pi\) |
0.525584 | + | 0.850741i | \(0.323847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | − | 10.3923i | −0.236617 | − | 0.409832i | 0.723124 | − | 0.690718i | \(-0.242705\pi\) |
−0.959741 | + | 0.280885i | \(0.909372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.0000 | −1.09910 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.00000 | + | 12.1244i | 0.273931 | + | 0.474463i | 0.969865 | − | 0.243643i | \(-0.0783426\pi\) |
−0.695934 | + | 0.718106i | \(0.745009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.00000 | + | 15.5885i | −0.351659 | + | 0.609091i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.00000 | + | 5.19615i | −0.116863 | + | 0.202413i | −0.918523 | − | 0.395367i | \(-0.870617\pi\) |
0.801660 | + | 0.597781i | \(0.203951\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.00000 | − | 15.5885i | −0.350059 | − | 0.606321i | 0.636200 | − | 0.771524i | \(-0.280505\pi\) |
−0.986260 | + | 0.165203i | \(0.947172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −80.0000 | −3.09761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0000 | + | 24.2487i | 0.540464 | + | 0.936111i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0000 | + | 25.9808i | −0.578208 | + | 1.00148i | 0.417477 | + | 0.908687i | \(0.362914\pi\) |
−0.995685 | + | 0.0927975i | \(0.970419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.0000 | + | 22.5167i | −0.499631 | + | 0.865386i | −1.00000 | 0.000426509i | \(-0.999864\pi\) | |
0.500369 | + | 0.865812i | \(0.333198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0000 | + | 24.2487i | 0.537271 | + | 0.930580i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | − | 20.7846i | −0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0000 | − | 24.2487i | 0.532585 | − | 0.922464i | −0.466691 | − | 0.884420i | \(-0.654554\pi\) |
0.999276 | − | 0.0380440i | \(-0.0121127\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.00000 | − | 10.3923i | 0.227593 | − | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.0000 | 0.830929 | 0.415464 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415464 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | − | 10.3923i | −0.225653 | − | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00000 | + | 12.1244i | −0.262891 | + | 0.455340i | −0.967009 | − | 0.254743i | \(-0.918009\pi\) |
0.704118 | + | 0.710083i | \(0.251342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | + | 27.7128i | −0.599205 | + | 1.03785i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | + | 6.92820i | 0.149592 | + | 0.259100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.0000 | −1.49175 | −0.745874 | − | 0.666087i | \(-0.767968\pi\) | ||||
−0.745874 | + | 0.666087i | \(0.767968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.0000 | −1.04277 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.00000 | + | 8.66025i | 0.185695 | + | 0.321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.0000 | + | 32.9090i | −0.704671 | + | 1.22053i | 0.262139 | + | 0.965030i | \(0.415572\pi\) |
−0.966810 | + | 0.255496i | \(0.917761\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | + | 13.8564i | −0.295891 | + | 0.512498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0000 | + | 20.7846i | 0.443230 | + | 0.767697i | 0.997927 | − | 0.0643554i | \(-0.0204991\pi\) |
−0.554697 | + | 0.832052i | \(0.687166\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.00000 | −0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0000 | 0.441427 | 0.220714 | − | 0.975339i | \(-0.429161\pi\) | ||||
0.220714 | + | 0.975339i | \(0.429161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0000 | − | 20.7846i | −0.440237 | − | 0.762513i | 0.557470 | − | 0.830197i | \(-0.311772\pi\) |
−0.997707 | + | 0.0676840i | \(0.978439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | − | 8.66025i | 0.183186 | − | 0.317287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0000 | − | 20.7846i | 0.438470 | − | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.0000 | + | 31.1769i | 0.656829 | + | 1.13766i | 0.981432 | + | 0.191811i | \(0.0614361\pi\) |
−0.324603 | + | 0.945851i | \(0.605231\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.0000 | 1.16306 | 0.581530 | − | 0.813525i | \(-0.302454\pi\) | ||||
0.581530 | + | 0.813525i | \(0.302454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0000 | + | 31.1769i | 0.652499 | + | 1.13016i | 0.982514 | + | 0.186187i | \(0.0596129\pi\) |
−0.330015 | + | 0.943976i | \(0.607054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | + | 3.46410i | −0.0724049 | + | 0.125409i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.0000 | − | 48.4974i | 1.01102 | − | 1.75114i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0000 | + | 43.3013i | 0.901523 | + | 1.56148i | 0.825518 | + | 0.564376i | \(0.190883\pi\) |
0.0760054 | + | 0.997107i | \(0.475783\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.0000 | 1.51064 | 0.755318 | − | 0.655359i | \(-0.227483\pi\) | ||||
0.755318 | + | 0.655359i | \(0.227483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | + | 20.7846i | −0.429394 | + | 0.743732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.00000 | − | 3.46410i | 0.0713831 | − | 0.123639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0000 | + | 24.2487i | 0.499046 | + | 0.864373i | 0.999999 | − | 0.00110111i | \(-0.000350496\pi\) |
−0.500953 | + | 0.865474i | \(0.667017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0000 | 1.28001 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.0000 | −1.98862 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.0000 | − | 25.9808i | −0.531327 | − | 0.920286i | −0.999331 | − | 0.0365596i | \(-0.988360\pi\) |
0.468004 | − | 0.883726i | \(-0.344973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | − | 13.8564i | 0.283020 | − | 0.490204i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.00000 | + | 10.3923i | −0.211735 | + | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | + | 13.8564i | 0.281963 | + | 0.488374i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.0000 | −0.843795 | −0.421898 | − | 0.906644i | \(-0.638636\pi\) | ||||
−0.421898 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.00000 | + | 3.46410i | 0.0700569 | + | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | − | 27.7128i | 0.559769 | − | 0.969549i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.00000 | + | 12.1244i | −0.244302 | + | 0.423143i | −0.961935 | − | 0.273278i | \(-0.911892\pi\) |
0.717633 | + | 0.696421i | \(0.245225\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.00000 | + | 1.73205i | 0.0348578 | + | 0.0603755i | 0.882928 | − | 0.469508i | \(-0.155569\pi\) |
−0.848070 | + | 0.529884i | \(0.822235\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.0000 | −0.834562 | −0.417281 | − | 0.908778i | \(-0.637017\pi\) | ||||
−0.417281 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.00000 | − | 5.19615i | −0.103944 | − | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.0000 | − | 27.7128i | 0.552381 | − | 0.956753i | −0.445721 | − | 0.895172i | \(-0.647053\pi\) |
0.998102 | − | 0.0615805i | \(-0.0196141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.5000 | − | 61.4878i | −1.22414 | − | 2.12027i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0000 | −0.481046 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.00000 | − | 13.8564i | 0.273915 | − | 0.474434i | −0.695946 | − | 0.718094i | \(-0.745015\pi\) |
0.969861 | + | 0.243660i | \(0.0783480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | − | 15.5885i | 0.307434 | − | 0.532492i | −0.670366 | − | 0.742030i | \(-0.733863\pi\) |
0.977800 | + | 0.209539i | \(0.0671963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | + | 3.46410i | 0.0682391 | + | 0.118194i | 0.898126 | − | 0.439738i | \(-0.144929\pi\) |
−0.829887 | + | 0.557931i | \(0.811595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.0000 | 1.63394 | 0.816970 | − | 0.576681i | \(-0.195652\pi\) | ||||
0.816970 | + | 0.576681i | \(0.195652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0000 | + | 20.7846i | 0.407072 | + | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | − | 13.8564i | 0.271070 | − | 0.469506i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | − | 1.73205i | 0.0338062 | − | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0000 | + | 17.3205i | 0.337676 | + | 0.584872i | 0.983995 | − | 0.178195i | \(-0.0570259\pi\) |
−0.646319 | + | 0.763067i | \(0.723693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.0000 | 1.21287 | 0.606435 | − | 0.795133i | \(-0.292599\pi\) | ||||
0.606435 | + | 0.795133i | \(0.292599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.0000 | − | 48.4974i | −0.940148 | − | 1.62838i | −0.765186 | − | 0.643809i | \(-0.777353\pi\) |
−0.174962 | − | 0.984575i | \(-0.555980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | + | 31.1769i | −0.603701 | + | 1.04564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0000 | + | 27.7128i | −0.535420 | + | 0.927374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.00000 | − | 12.1244i | −0.233984 | − | 0.405273i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.0000 | −1.33407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.00000 | + | 1.73205i | 0.0332411 | + | 0.0575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.0000 | + | 20.7846i | −0.398453 | + | 0.690142i | −0.993535 | − | 0.113523i | \(-0.963786\pi\) |
0.595082 | + | 0.803665i | \(0.297120\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | − | 13.8564i | 0.265052 | − | 0.459083i | −0.702525 | − | 0.711659i | \(-0.747944\pi\) |
0.967577 | + | 0.252575i | \(0.0812776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.00000 | − | 6.92820i | −0.132381 | − | 0.229290i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.0000 | −1.18882 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.0000 | − | 41.5692i | −0.789970 | − | 1.36827i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.00000 | − | 3.46410i | 0.0656179 | − | 0.113653i | −0.831350 | − | 0.555749i | \(-0.812431\pi\) |
0.896968 | + | 0.442096i | \(0.145765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | + | 10.3923i | 0.196642 | + | 0.340594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0000 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.0000 | + | 19.0526i | 0.358590 | + | 0.621096i | 0.987725 | − | 0.156200i | \(-0.0499244\pi\) |
−0.629136 | + | 0.777295i | \(0.716591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.0000 | + | 48.4974i | −0.909878 | + | 1.57595i | −0.0956453 | + | 0.995415i | \(0.530491\pi\) |
−0.814232 | + | 0.580539i | \(0.802842\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | − | 20.7846i | −0.389536 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.0000 | −1.74923 | −0.874616 | − | 0.484817i | \(-0.838886\pi\) | ||||
−0.874616 | + | 0.484817i | \(0.838886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | −0.129437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.00000 | − | 3.46410i | −0.0645834 | − | 0.111862i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0000 | − | 19.0526i | 0.354103 | − | 0.613324i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.00000 | − | 15.5885i | −0.289420 | − | 0.501291i | 0.684251 | − | 0.729247i | \(-0.260129\pi\) |
−0.973672 | + | 0.227956i | \(0.926796\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.00000 | −0.0641831 | −0.0320915 | − | 0.999485i | \(-0.510217\pi\) | ||||
−0.0320915 | + | 0.999485i | \(0.510217\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.0000 | 0.769405 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.00000 | + | 1.73205i | 0.0319928 | + | 0.0554132i | 0.881579 | − | 0.472037i | \(-0.156481\pi\) |
−0.849586 | + | 0.527451i | \(0.823148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | − | 20.7846i | 0.383522 | − | 0.664279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0000 | − | 20.7846i | 0.382741 | − | 0.662926i | −0.608712 | − | 0.793391i | \(-0.708314\pi\) |
0.991453 | + | 0.130465i | \(0.0416470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00000 | + | 1.73205i | 0.0318626 | + | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −64.0000 | −2.03508 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.00000 | + | 6.92820i | 0.126809 | + | 0.219639i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.0000 | + | 31.1769i | −0.570066 | + | 0.987383i | 0.426493 | + | 0.904491i | \(0.359749\pi\) |
−0.996559 | + | 0.0828918i | \(0.973584\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3240.2.q.n.2161.1 | 2 | ||
3.2 | odd | 2 | 3240.2.q.d.2161.1 | 2 | |||
9.2 | odd | 6 | 360.2.a.d.1.1 | yes | 1 | ||
9.4 | even | 3 | inner | 3240.2.q.n.1081.1 | 2 | ||
9.5 | odd | 6 | 3240.2.q.d.1081.1 | 2 | |||
9.7 | even | 3 | 360.2.a.c.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 720.2.a.a.1.1 | 1 | |||
36.11 | even | 6 | 720.2.a.i.1.1 | 1 | |||
45.2 | even | 12 | 1800.2.f.d.649.2 | 2 | |||
45.7 | odd | 12 | 1800.2.f.h.649.2 | 2 | |||
45.29 | odd | 6 | 1800.2.a.f.1.1 | 1 | |||
45.34 | even | 6 | 1800.2.a.i.1.1 | 1 | |||
45.38 | even | 12 | 1800.2.f.d.649.1 | 2 | |||
45.43 | odd | 12 | 1800.2.f.h.649.1 | 2 | |||
72.11 | even | 6 | 2880.2.a.e.1.1 | 1 | |||
72.29 | odd | 6 | 2880.2.a.n.1.1 | 1 | |||
72.43 | odd | 6 | 2880.2.a.w.1.1 | 1 | |||
72.61 | even | 6 | 2880.2.a.bd.1.1 | 1 | |||
180.7 | even | 12 | 3600.2.f.g.2449.1 | 2 | |||
180.43 | even | 12 | 3600.2.f.g.2449.2 | 2 | |||
180.47 | odd | 12 | 3600.2.f.q.2449.1 | 2 | |||
180.79 | odd | 6 | 3600.2.a.bd.1.1 | 1 | |||
180.83 | odd | 12 | 3600.2.f.q.2449.2 | 2 | |||
180.119 | even | 6 | 3600.2.a.bh.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.a.c.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
360.2.a.d.1.1 | yes | 1 | 9.2 | odd | 6 | ||
720.2.a.a.1.1 | 1 | 36.7 | odd | 6 | |||
720.2.a.i.1.1 | 1 | 36.11 | even | 6 | |||
1800.2.a.f.1.1 | 1 | 45.29 | odd | 6 | |||
1800.2.a.i.1.1 | 1 | 45.34 | even | 6 | |||
1800.2.f.d.649.1 | 2 | 45.38 | even | 12 | |||
1800.2.f.d.649.2 | 2 | 45.2 | even | 12 | |||
1800.2.f.h.649.1 | 2 | 45.43 | odd | 12 | |||
1800.2.f.h.649.2 | 2 | 45.7 | odd | 12 | |||
2880.2.a.e.1.1 | 1 | 72.11 | even | 6 | |||
2880.2.a.n.1.1 | 1 | 72.29 | odd | 6 | |||
2880.2.a.w.1.1 | 1 | 72.43 | odd | 6 | |||
2880.2.a.bd.1.1 | 1 | 72.61 | even | 6 | |||
3240.2.q.d.1081.1 | 2 | 9.5 | odd | 6 | |||
3240.2.q.d.2161.1 | 2 | 3.2 | odd | 2 | |||
3240.2.q.n.1081.1 | 2 | 9.4 | even | 3 | inner | ||
3240.2.q.n.2161.1 | 2 | 1.1 | even | 1 | trivial | ||
3600.2.a.bd.1.1 | 1 | 180.79 | odd | 6 | |||
3600.2.a.bh.1.1 | 1 | 180.119 | even | 6 | |||
3600.2.f.g.2449.1 | 2 | 180.7 | even | 12 | |||
3600.2.f.g.2449.2 | 2 | 180.43 | even | 12 | |||
3600.2.f.q.2449.1 | 2 | 180.47 | odd | 12 | |||
3600.2.f.q.2449.2 | 2 | 180.83 | odd | 12 |