Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(577,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.s (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: | \(21.8470699930\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1873 |
Dual form | 2736.2.s.e.577.1 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.00000 | 1.80907 | 0.904534 | − | 0.426401i | \(-0.140219\pi\) | ||||
0.904534 | + | 0.426401i | \(0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | 0.0898027 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898027 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | − | 5.19615i | 0.507093 | − | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | − | 3.46410i | −0.274721 | − | 0.475831i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
−0.970065 | + | 0.242846i | \(0.921919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | + | 10.3923i | −0.809040 | + | 1.40130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50000 | + | 9.52628i | 0.704203 | + | 1.21972i | 0.966978 | + | 0.254858i | \(0.0820288\pi\) |
−0.262776 | + | 0.964857i | \(0.584638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.50000 | + | 12.9904i | 0.916271 | + | 1.58703i | 0.805030 | + | 0.593234i | \(0.202149\pi\) |
0.111241 | + | 0.993793i | \(0.464517\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.50000 | + | 7.79423i | −0.526685 | + | 0.912245i | 0.472831 | + | 0.881153i | \(0.343232\pi\) |
−0.999517 | + | 0.0310925i | \(0.990101\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.0000 | −2.05129 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.50000 | + | 11.2583i | −0.731307 | + | 1.26666i | 0.225018 | + | 0.974355i | \(0.427756\pi\) |
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.0000 | 1.53670 | 0.768350 | − | 0.640030i | \(-0.221078\pi\) | ||||
0.768350 | + | 0.640030i | \(0.221078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | − | 3.46410i | −0.216930 | − | 0.375735i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | + | 10.3923i | 0.635999 | + | 1.10158i | 0.986303 | + | 0.164946i | \(0.0527450\pi\) |
−0.350304 | + | 0.936636i | \(0.613922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50000 | − | 2.59808i | −0.157243 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | + | 8.66025i | −0.102598 | + | 0.888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | + | 8.66025i | −0.507673 | + | 0.879316i | 0.492287 | + | 0.870433i | \(0.336161\pi\) |
−0.999961 | + | 0.00888289i | \(0.997172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.00000 | 0.492665 | 0.246332 | − | 0.969185i | \(-0.420775\pi\) | ||||
0.246332 | + | 0.969185i | \(0.420775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0000 | −0.966736 | −0.483368 | − | 0.875417i | \(-0.660587\pi\) | ||||
−0.483368 | + | 0.875417i | \(0.660587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.00000 | + | 15.5885i | −0.862044 | + | 1.49310i | 0.00790932 | + | 0.999969i | \(0.497482\pi\) |
−0.869953 | + | 0.493135i | \(0.835851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.0000 | −1.50515 | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | − | 5.19615i | 0.275010 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | + | 5.19615i | −1.04053 | + | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | + | 15.5885i | 0.768922 | + | 1.33181i | 0.938148 | + | 0.346235i | \(0.112540\pi\) |
−0.169226 | + | 0.985577i | \(0.554127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | + | 5.19615i | 0.250873 | + | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | 0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.00000 | + | 1.73205i | −0.0819232 | + | 0.141895i | −0.904076 | − | 0.427372i | \(-0.859440\pi\) |
0.822153 | + | 0.569267i | \(0.192773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | + | 1.73205i | −0.0803219 | + | 0.139122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.50000 | + | 4.33013i | −0.199522 | + | 0.345582i | −0.948373 | − | 0.317156i | \(-0.897272\pi\) |
0.748852 | + | 0.662738i | \(0.230606\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0000 | −1.48819 | −0.744097 | − | 0.668071i | \(-0.767120\pi\) | ||||
−0.744097 | + | 0.668071i | \(0.767120\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.00000 | − | 6.92820i | −0.309529 | − | 0.536120i | 0.668730 | − | 0.743505i | \(-0.266838\pi\) |
−0.978259 | + | 0.207385i | \(0.933505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.00000 | − | 12.1244i | 0.532200 | − | 0.921798i | −0.467093 | − | 0.884208i | \(-0.654699\pi\) |
0.999293 | − | 0.0375896i | \(-0.0119679\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.50000 | − | 2.59808i | −0.113389 | − | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | + | 8.66025i | 0.371647 | + | 0.643712i | 0.989819 | − | 0.142331i | \(-0.0454598\pi\) |
−0.618172 | + | 0.786043i | \(0.712126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.00000 | − | 12.1244i | 0.514650 | − | 0.891400i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | + | 10.3923i | −0.438763 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | −0.434145 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.50000 | − | 7.79423i | 0.323917 | − | 0.561041i | −0.657376 | − | 0.753563i | \(-0.728333\pi\) |
0.981293 | + | 0.192522i | \(0.0616668\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | + | 2.59808i | 0.106332 | + | 0.184173i | 0.914282 | − | 0.405079i | \(-0.132756\pi\) |
−0.807950 | + | 0.589252i | \(0.799423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000 | + | 5.19615i | 0.210559 | + | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000 | − | 10.3923i | 1.66011 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.50000 | − | 7.79423i | 0.309793 | − | 0.536577i | −0.668524 | − | 0.743690i | \(-0.733074\pi\) |
0.978317 | + | 0.207114i | \(0.0664070\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.00000 | − | 1.73205i | −0.0681994 | − | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | −0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.50000 | + | 4.33013i | −0.167412 | + | 0.289967i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) |
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.0000 | −1.46019 | −0.730096 | − | 0.683345i | \(-0.760525\pi\) | ||||
−0.730096 | + | 0.683345i | \(0.760525\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0000 | −1.12339 | −0.561696 | − | 0.827344i | \(-0.689851\pi\) | ||||
−0.561696 | + | 0.827344i | \(0.689851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.00000 | − | 8.66025i | 0.327561 | − | 0.567352i | −0.654466 | − | 0.756091i | \(-0.727107\pi\) |
0.982027 | + | 0.188739i | \(0.0604400\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.50000 | − | 7.79423i | −0.289870 | − | 0.502070i | 0.683908 | − | 0.729568i | \(-0.260279\pi\) |
−0.973779 | + | 0.227498i | \(0.926946\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.00000 | + | 3.46410i | −0.127775 | + | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.50000 | + | 2.59808i | 0.222700 | + | 0.165312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.00000 | − | 13.8564i | −0.504956 | − | 0.874609i | −0.999984 | − | 0.00573163i | \(-0.998176\pi\) |
0.495028 | − | 0.868877i | \(-0.335158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.00000 | − | 10.3923i | −0.374270 | − | 0.648254i | 0.615948 | − | 0.787787i | \(-0.288773\pi\) |
−0.990217 | + | 0.139533i | \(0.955440\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.0000 | 1.30488 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.00000 | − | 8.66025i | 0.308313 | − | 0.534014i | −0.669680 | − | 0.742650i | \(-0.733569\pi\) |
0.977993 | + | 0.208635i | \(0.0669022\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.0000 | − | 27.7128i | 0.975537 | − | 1.68968i | 0.297386 | − | 0.954757i | \(-0.403885\pi\) |
0.678151 | − | 0.734923i | \(-0.262782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | + | 5.19615i | 0.180907 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.0000 | −1.80253 | −0.901263 | − | 0.433273i | \(-0.857359\pi\) | ||||
−0.901263 | + | 0.433273i | \(0.857359\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.00000 | + | 8.66025i | 0.298275 | + | 0.516627i | 0.975741 | − | 0.218926i | \(-0.0702554\pi\) |
−0.677466 | + | 0.735554i | \(0.736922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.0000 | 1.16841 | 0.584206 | − | 0.811605i | \(-0.301406\pi\) | ||||
0.584206 | + | 0.811605i | \(0.301406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | + | 13.8564i | 0.465778 | + | 0.806751i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.50000 | − | 2.59808i | 0.0864586 | − | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.0000 | −1.25972 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0000 | + | 17.3205i | −0.570730 | + | 0.988534i | 0.425761 | + | 0.904836i | \(0.360006\pi\) |
−0.996491 | + | 0.0836980i | \(0.973327\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0000 | 1.13410 | 0.567048 | − | 0.823685i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823685i | \(0.308085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | + | 8.66025i | 0.282617 | + | 0.489506i | 0.972028 | − | 0.234863i | \(-0.0754642\pi\) |
−0.689412 | + | 0.724370i | \(0.742131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0000 | + | 25.9808i | 0.842484 | + | 1.45922i | 0.887788 | + | 0.460252i | \(0.152241\pi\) |
−0.0453045 | + | 0.998973i | \(0.514426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | − | 10.3923i | −0.335936 | − | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00000 | + | 8.66025i | −0.0556415 | + | 0.481869i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.500000 | + | 0.866025i | −0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | −0.384755 | −0.192377 | − | 0.981321i | \(-0.561620\pi\) | ||||
−0.192377 | + | 0.981321i | \(0.561620\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.0000 | −1.63908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.50000 | − | 12.9904i | 0.408551 | − | 0.707631i | −0.586177 | − | 0.810183i | \(-0.699368\pi\) |
0.994728 | + | 0.102552i | \(0.0327009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00000 | + | 15.5885i | −0.483145 | + | 0.836832i | −0.999813 | − | 0.0193540i | \(-0.993839\pi\) |
0.516667 | + | 0.856186i | \(0.327172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.00000 | 0.267644 | 0.133822 | − | 0.991005i | \(-0.457275\pi\) | ||||
0.133822 | + | 0.991005i | \(0.457275\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0000 | 0.745145 | 0.372572 | − | 0.928003i | \(-0.378476\pi\) | ||||
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0000 | + | 17.3205i | −0.527780 | + | 0.914141i | 0.471696 | + | 0.881761i | \(0.343642\pi\) |
−0.999476 | + | 0.0323801i | \(0.989691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.00000 | − | 15.5885i | −0.471082 | − | 0.815937i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.5000 | − | 30.3109i | −0.913493 | − | 1.58222i | −0.809093 | − | 0.587680i | \(-0.800041\pi\) |
−0.104399 | − | 0.994535i | \(-0.533292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | + | 10.3923i | 0.311504 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00000 | − | 1.73205i | 0.0515026 | − | 0.0892052i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.0000 | −1.38690 | −0.693448 | − | 0.720506i | \(-0.743909\pi\) | ||||
−0.693448 | + | 0.720506i | \(0.743909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.00000 | + | 12.1244i | −0.357683 | + | 0.619526i | −0.987573 | − | 0.157159i | \(-0.949767\pi\) |
0.629890 | + | 0.776684i | \(0.283100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | − | 31.1769i | 0.917365 | − | 1.58892i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.0000 | + | 27.7128i | 0.811232 | + | 1.40510i | 0.912002 | + | 0.410186i | \(0.134536\pi\) |
−0.100770 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0000 | − | 22.5167i | −0.654101 | − | 1.13294i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5000 | + | 21.6506i | −0.627357 | + | 1.08661i | 0.360723 | + | 0.932673i | \(0.382530\pi\) |
−0.988080 | + | 0.153941i | \(0.950803\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | − | 20.7846i | 0.599251 | − | 1.03793i | −0.393680 | − | 0.919247i | \(-0.628798\pi\) |
0.992932 | − | 0.118686i | \(-0.0378683\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.500000 | + | 0.866025i | 0.0249068 | + | 0.0431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −42.0000 | −2.08186 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0000 | + | 32.9090i | 0.939490 | + | 1.62724i | 0.766426 | + | 0.642333i | \(0.222033\pi\) |
0.173064 | + | 0.984911i | \(0.444633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | + | 20.7846i | −0.590481 | + | 1.02274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0000 | + | 24.2487i | −0.687233 | + | 1.19032i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | 0.879358 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | + | 22.5167i | −0.633581 | + | 1.09739i | 0.353233 | + | 0.935536i | \(0.385082\pi\) |
−0.986814 | + | 0.161859i | \(0.948251\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.5000 | − | 28.5788i | −0.798491 | − | 1.38303i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0000 | + | 31.1769i | 0.867029 | + | 1.50174i | 0.865018 | + | 0.501741i | \(0.167307\pi\) |
0.00201168 | + | 0.999998i | \(0.499360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.50000 | − | 16.4545i | −0.456541 | − | 0.790752i | 0.542234 | − | 0.840227i | \(-0.317578\pi\) |
−0.998775 | + | 0.0494752i | \(0.984245\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.50000 | − | 11.2583i | 0.310228 | − | 0.537331i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) |
0.978412 | + | 0.206666i | \(0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.00000 | + | 8.66025i | 0.237557 | + | 0.411461i | 0.960013 | − | 0.279956i | \(-0.0903200\pi\) |
−0.722456 | + | 0.691417i | \(0.756987\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0000 | −1.13771 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | 0.281284 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0000 | 1.16945 | 0.584725 | − | 0.811231i | \(-0.301202\pi\) | ||||
0.584725 | + | 0.811231i | \(0.301202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | − | 31.1769i | 0.838344 | − | 1.45205i | −0.0529352 | − | 0.998598i | \(-0.516858\pi\) |
0.891279 | − | 0.453456i | \(-0.149809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.0000 | 1.44069 | 0.720346 | − | 0.693615i | \(-0.243983\pi\) | ||||
0.720346 | + | 0.693615i | \(0.243983\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.5000 | − | 38.9711i | −1.03895 | − | 1.79952i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00000 | + | 5.19615i | −0.137940 | + | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.50000 | + | 2.59808i | 0.160591 | + | 0.119208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.0000 | − | 19.0526i | −0.502603 | − | 0.870534i | −0.999995 | − | 0.00300810i | \(-0.999042\pi\) |
0.497393 | − | 0.867526i | \(-0.334291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.50000 | − | 6.06218i | −0.159586 | − | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0000 | − | 17.3205i | −0.454077 | − | 0.786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | 0.362515 | 0.181257 | − | 0.983436i | \(-0.441983\pi\) | ||||
0.181257 | + | 0.983436i | \(0.441983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.0000 | − | 29.4449i | 0.767199 | − | 1.32883i | −0.171877 | − | 0.985118i | \(-0.554983\pi\) |
0.939076 | − | 0.343710i | \(-0.111684\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | 0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.00000 | + | 15.5885i | −0.403705 | + | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5000 | − | 21.6506i | 0.559577 | − | 0.969216i | −0.437955 | − | 0.898997i | \(-0.644297\pi\) |
0.997532 | − | 0.0702185i | \(-0.0223697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.0000 | − | 25.9808i | −0.668817 | − | 1.15842i | −0.978235 | − | 0.207499i | \(-0.933468\pi\) |
0.309418 | − | 0.950926i | \(-0.399866\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.0000 | + | 17.3205i | 0.443242 | + | 0.767718i | 0.997928 | − | 0.0643419i | \(-0.0204948\pi\) |
−0.554686 | + | 0.832060i | \(0.687161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5000 | − | 23.3827i | 0.597205 | − | 1.03439i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.00000 | + | 8.66025i | −0.220326 | + | 0.381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.0000 | −0.613351 | −0.306676 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306676 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5000 | − | 26.8468i | −0.677768 | − | 1.17393i | −0.975652 | − | 0.219326i | \(-0.929614\pi\) |
0.297884 | − | 0.954602i | \(-0.403719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.00000 | + | 1.73205i | −0.0435607 | + | 0.0754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0000 | − | 17.3205i | 0.432338 | − | 0.748831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0000 | 0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5000 | − | 26.8468i | −0.666397 | − | 1.15423i | −0.978905 | − | 0.204318i | \(-0.934502\pi\) |
0.312507 | − | 0.949915i | \(-0.398831\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.0000 | − | 31.1769i | −0.771035 | − | 1.33547i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.50000 | − | 4.33013i | −0.106892 | − | 0.185143i | 0.807617 | − | 0.589707i | \(-0.200757\pi\) |
−0.914510 | + | 0.404564i | \(0.867423\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.00000 | − | 5.19615i | −0.298210 | − | 0.221364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.5000 | − | 33.7750i | 0.829224 | − | 1.43626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.00000 | + | 8.66025i | 0.211857 | + | 0.366947i | 0.952296 | − | 0.305177i | \(-0.0987156\pi\) |
−0.740439 | + | 0.672124i | \(0.765382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00000 | −0.0422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.0000 | 1.93867 | 0.969334 | − | 0.245745i | \(-0.0790327\pi\) | ||||
0.969334 | + | 0.245745i | \(0.0790327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.0000 | − | 27.7128i | 0.673125 | − | 1.16589i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.0000 | −1.17382 | −0.586911 | − | 0.809652i | \(-0.699656\pi\) | ||||
−0.586911 | + | 0.809652i | \(0.699656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0000 | 0.795125 | 0.397563 | − | 0.917575i | \(-0.369856\pi\) | ||||
0.397563 | + | 0.917575i | \(0.369856\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0000 | −0.416305 | −0.208153 | − | 0.978096i | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.0000 | −1.74245 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | − | 20.7846i | −0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0000 | − | 24.2487i | 0.577842 | − | 1.00085i | −0.417885 | − | 0.908500i | \(-0.637228\pi\) |
0.995726 | − | 0.0923513i | \(-0.0294383\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | − | 1.73205i | 0.164817 | − | 0.0713679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.0000 | + | 31.1769i | 0.739171 | + | 1.28028i | 0.952869 | + | 0.303383i | \(0.0981160\pi\) |
−0.213697 | + | 0.976900i | \(0.568551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | + | 10.3923i | 0.245976 | + | 0.426043i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.00000 | + | 12.1244i | 0.286012 | + | 0.495388i | 0.972854 | − | 0.231419i | \(-0.0743369\pi\) |
−0.686842 | + | 0.726807i | \(0.741004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | −0.0407909 | −0.0203954 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203954 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.0000 | + | 43.3013i | −1.01639 | + | 1.76045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.0000 | −1.09590 | −0.547948 | − | 0.836512i | \(-0.684591\pi\) | ||||
−0.547948 | + | 0.836512i | \(0.684591\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.00000 | + | 12.1244i | −0.282727 | + | 0.489698i | −0.972056 | − | 0.234751i | \(-0.924572\pi\) |
0.689328 | + | 0.724449i | \(0.257906\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0000 | − | 25.9808i | −0.603877 | − | 1.04595i | −0.992228 | − | 0.124434i | \(-0.960288\pi\) |
0.388351 | − | 0.921512i | \(-0.373045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.00000 | −0.0401934 | −0.0200967 | − | 0.999798i | \(-0.506397\pi\) | ||||
−0.0200967 | + | 0.999798i | \(0.506397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.0000 | − | 31.1769i | −0.721155 | − | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.00000 | − | 12.1244i | 0.279108 | − | 0.483430i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5000 | + | 26.8468i | 0.617045 | + | 1.06875i | 0.990022 | + | 0.140913i | \(0.0450038\pi\) |
−0.372977 | + | 0.927841i | \(0.621663\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | + | 1.73205i | 0.0396214 | + | 0.0686264i | ||||
\(638\) | 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 | ||||||||
\(643\) | 2.50000 | − | 4.33013i | 0.0985904 | − | 0.170764i | −0.812511 | − | 0.582946i | \(-0.801900\pi\) |
0.911101 | + | 0.412182i | \(0.135233\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.0000 | 1.49393 | 0.746967 | − | 0.664861i | \(-0.231509\pi\) | ||||
0.746967 | + | 0.664861i | \(0.231509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | − | 41.5692i | 0.942082 | − | 1.63173i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | − | 31.1769i | −0.703318 | − | 1.21818i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.00000 | − | 5.19615i | −0.116863 | − | 0.202413i | 0.801660 | − | 0.597781i | \(-0.203951\pi\) |
−0.918523 | + | 0.395367i | \(0.870617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.00000 | − | 25.9808i | 0.116335 | − | 1.00749i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.0000 | + | 57.1577i | 1.27395 | + | 2.20655i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0000 | 0.578208 | 0.289104 | − | 0.957298i | \(-0.406643\pi\) | ||||
0.289104 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.00000 | −0.307465 | −0.153732 | − | 0.988113i | \(-0.549129\pi\) | ||||
−0.153732 | + | 0.988113i | \(0.549129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.0000 | − | 25.9808i | 0.575647 | − | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.0000 | 0.382639 | 0.191320 | − | 0.981528i | \(-0.438723\pi\) | ||||
0.191320 | + | 0.981528i | \(0.438723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.0000 | −1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00000 | − | 3.46410i | 0.0761939 | − | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.0000 | 1.36950 | 0.684752 | − | 0.728776i | \(-0.259910\pi\) | ||||
0.684752 | + | 0.728776i | \(0.259910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.0000 | −0.379322 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.0000 | + | 25.9808i | −0.566542 | + | 0.981280i | 0.430362 | + | 0.902656i | \(0.358386\pi\) |
−0.996904 | + | 0.0786236i | \(0.974947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.0000 | + | 12.1244i | −1.05604 | + | 0.457279i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.00000 | − | 15.5885i | −0.338480 | − | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.5000 | + | 28.5788i | 0.619671 | + | 1.07330i | 0.989546 | + | 0.144219i | \(0.0460671\pi\) |
−0.369875 | + | 0.929081i | \(0.620600\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.00000 | − | 6.92820i | 0.149175 | − | 0.258378i | −0.781748 | − | 0.623595i | \(-0.785672\pi\) |
0.930923 | + | 0.365216i | \(0.119005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0000 | −0.558629 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | − | 1.73205i | 0.0371391 | − | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.50000 | + | 14.7224i | −0.315248 | + | 0.546025i | −0.979490 | − | 0.201492i | \(-0.935421\pi\) |
0.664243 | + | 0.747517i | \(0.268754\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.00000 | − | 1.73205i | −0.0369863 | − | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0000 | −0.517102 | −0.258551 | − | 0.965998i | \(-0.583245\pi\) | ||||
−0.258551 | + | 0.965998i | \(0.583245\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.0000 | + | 77.9423i | 1.65760 | + | 2.87104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.50000 | − | 6.06218i | 0.128750 | − | 0.223001i | −0.794443 | − | 0.607339i | \(-0.792237\pi\) |
0.923192 | + | 0.384338i | \(0.125570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | − | 5.19615i | 0.110059 | − | 0.190628i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) |
0.915794 | + | 0.401648i | \(0.131563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | − | 3.46410i | −0.0732743 | − | 0.126915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.0000 | 1.09618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.50000 | + | 9.52628i | 0.200698 | + | 0.347619i | 0.948753 | − | 0.316017i | \(-0.102346\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.00000 | + | 6.92820i | −0.145575 | + | 0.252143i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.5000 | + | 40.7032i | −0.854122 | + | 1.47938i | 0.0233351 | + | 0.999728i | \(0.492572\pi\) |
−0.877457 | + | 0.479655i | \(0.840762\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.0000 | −1.45000 | −0.724999 | − | 0.688749i | \(-0.758160\pi\) | ||||
−0.724999 | + | 0.688749i | \(0.758160\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.0000 | − | 46.7654i | 0.977466 | − | 1.69302i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.00000 | 0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.50000 | + | 11.2583i | 0.234396 | + | 0.405986i | 0.959097 | − | 0.283078i | \(-0.0913554\pi\) |
−0.724701 | + | 0.689063i | \(0.758022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.0000 | − | 34.6410i | −0.719350 | − | 1.24595i | −0.961258 | − | 0.275651i | \(-0.911106\pi\) |
0.241908 | − | 0.970299i | \(-0.422227\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.500000 | + | 0.866025i | 0.0179605 | + | 0.0311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | − | 31.1769i | 0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.00000 | − | 8.66025i | −0.178458 | − | 0.309098i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.00000 | −0.178231 | −0.0891154 | − | 0.996021i | \(-0.528404\pi\) | ||||
−0.0891154 | + | 0.996021i | \(0.528404\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.0000 | 1.70668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.50000 | + | 9.52628i | −0.195311 | + | 0.338288i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.0000 | + | 46.7654i | −0.952809 | + | 1.65031i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.0000 | − | 31.1769i | −0.632065 | − | 1.09477i | −0.987129 | − | 0.159927i | \(-0.948874\pi\) |
0.355063 | − | 0.934842i | \(-0.384459\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.0000 | − | 32.9090i | 0.665541 | − | 1.15275i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.500000 | + | 4.33013i | −0.0174928 | + | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0000 | − | 39.8372i | −0.802706 | − | 1.39033i | −0.917829 | − | 0.396976i | \(-0.870060\pi\) |
0.115124 | − | 0.993351i | \(-0.463274\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.00000 | − | 8.66025i | −0.173867 | − | 0.301147i | 0.765902 | − | 0.642958i | \(-0.222293\pi\) |
−0.939769 | + | 0.341811i | \(0.888960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.0000 | 0.520972 | 0.260486 | − | 0.965478i | \(-0.416117\pi\) | ||||
0.260486 | + | 0.965478i | \(0.416117\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | + | 3.46410i | −0.0692959 | + | 0.120024i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | 0.553703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.0000 | − | 25.9808i | 0.517858 | − | 0.896956i | −0.481927 | − | 0.876211i | \(-0.660063\pi\) |
0.999785 | − | 0.0207443i | \(-0.00660359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0000 | + | 20.7846i | 0.412813 | + | 0.715012i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −75.0000 | −2.57703 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.50000 | + | 7.79423i | −0.154077 | + | 0.266869i | −0.932723 | − | 0.360595i | \(-0.882574\pi\) |
0.778646 | + | 0.627464i | \(0.215907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.00000 | − | 6.92820i | 0.136637 | − | 0.236663i | −0.789584 | − | 0.613642i | \(-0.789704\pi\) |
0.926222 | + | 0.376979i | \(0.123037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.50000 | − | 11.2583i | −0.221777 | − | 0.384129i | 0.733571 | − | 0.679613i | \(-0.237852\pi\) |
−0.955348 | + | 0.295484i | \(0.904519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | + | 24.2487i | 0.476014 | + | 0.824481i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.0000 | + | 67.5500i | −1.32298 | + | 2.29148i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.50000 | + | 12.9904i | −0.254128 | + | 0.440162i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.0000 | 1.21702 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.5000 | + | 21.6506i | −0.422095 | + | 0.731090i | −0.996144 | − | 0.0877308i | \(-0.972038\pi\) |
0.574049 | + | 0.818821i | \(0.305372\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.5000 | + | 30.3109i | 0.588922 | + | 1.02004i | 0.994374 | + | 0.105926i | \(0.0337808\pi\) |
−0.405452 | + | 0.914116i | \(0.632886\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.0000 | + | 17.3205i | 0.335767 | + | 0.581566i | 0.983632 | − | 0.180190i | \(-0.0576711\pi\) |
−0.647865 | + | 0.761755i | \(0.724338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | − | 20.7846i | 0.401116 | − | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00000 | − | 1.73205i | −0.0333519 | − | 0.0577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0000 | −0.664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | + | 17.3205i | −0.332045 | + | 0.575118i | −0.982913 | − | 0.184073i | \(-0.941072\pi\) |
0.650868 | + | 0.759191i | \(0.274405\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.0000 | 1.85536 | 0.927681 | − | 0.373373i | \(-0.121799\pi\) | ||||
0.927681 | + | 0.373373i | \(0.121799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 84.0000 | 2.77999 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.0000 | − | 46.7654i | 0.891619 | − | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0000 | −0.824674 | −0.412337 | − | 0.911031i | \(-0.635287\pi\) | ||||
−0.412337 | + | 0.911031i | \(0.635287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.00000 | 0.197492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.50000 | − | 6.06218i | −0.115079 | − | 0.199323i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.0000 | − | 36.3731i | 0.688988 | − | 1.19336i | −0.283178 | − | 0.959067i | \(-0.591389\pi\) |
0.972166 | − | 0.234294i | \(-0.0752779\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00000 | − | 3.46410i | 0.262189 | − | 0.113531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | − | 20.7846i | −0.392442 | − | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.5000 | − | 19.9186i | −0.375689 | − | 0.650712i | 0.614741 | − | 0.788729i | \(-0.289260\pi\) |
−0.990430 | + | 0.138017i | \(0.955927\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.0000 | − | 48.4974i | −0.912774 | − | 1.58097i | −0.810128 | − | 0.586253i | \(-0.800603\pi\) |
−0.102646 | − | 0.994718i | \(-0.532731\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.0000 | − | 43.3013i | 0.812391 | − | 1.40710i | −0.0987955 | − | 0.995108i | \(-0.531499\pi\) |
0.911186 | − | 0.411994i | \(-0.135168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.00000 | −0.292152 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.00000 | + | 8.66025i | −0.161966 | + | 0.280533i | −0.935574 | − | 0.353132i | \(-0.885117\pi\) |
0.773608 | + | 0.633665i | \(0.218450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.00000 | − | 10.3923i | 0.194155 | − | 0.336287i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.0000 | − | 46.7654i | −0.871875 | − | 1.51013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.00000 | + | 15.5885i | 0.289720 | + | 0.501810i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.50000 | + | 12.9904i | −0.241184 | + | 0.417742i | −0.961052 | − | 0.276368i | \(-0.910869\pi\) |
0.719868 | + | 0.694111i | \(0.244202\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.0000 | + | 24.2487i | −0.449281 | + | 0.778178i | −0.998339 | − | 0.0576061i | \(-0.981653\pi\) |
0.549058 | + | 0.835784i | \(0.314987\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.50000 | − | 12.9904i | −0.240439 | − | 0.416452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.0000 | 0.895799 | 0.447900 | − | 0.894084i | \(-0.352172\pi\) | ||||
0.447900 | + | 0.894084i | \(0.352172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.0000 | + | 62.3538i | 1.15056 | + | 1.99284i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.00000 | − | 12.1244i | 0.223265 | − | 0.386707i | −0.732532 | − | 0.680732i | \(-0.761662\pi\) |
0.955798 | + | 0.294025i | \(0.0949950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0000 | + | 20.7846i | −0.382352 | + | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.50000 | − | 4.33013i | 0.0794151 | − | 0.137551i | −0.823583 | − | 0.567196i | \(-0.808028\pi\) |
0.902998 | + | 0.429645i | \(0.141361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.00000 | −0.190213 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.5000 | − | 21.6506i | −0.395879 | − | 0.685682i | 0.597334 | − | 0.801993i | \(-0.296227\pi\) |
−0.993213 | + | 0.116310i | \(0.962893\pi\) | |||||||
\(998\) | 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 | 2736.2.s.e.1873.1 | 2 | ||
3.2 | odd | 2 | 2736.2.s.n.1873.1 | 2 | |||
4.3 | odd | 2 | 1368.2.s.c.505.1 | ✓ | 2 | ||
12.11 | even | 2 | 1368.2.s.f.505.1 | yes | 2 | ||
19.7 | even | 3 | inner | 2736.2.s.e.577.1 | 2 | ||
57.26 | odd | 6 | 2736.2.s.n.577.1 | 2 | |||
76.7 | odd | 6 | 1368.2.s.c.577.1 | yes | 2 | ||
228.83 | even | 6 | 1368.2.s.f.577.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.s.c.505.1 | ✓ | 2 | 4.3 | odd | 2 | ||
1368.2.s.c.577.1 | yes | 2 | 76.7 | odd | 6 | ||
1368.2.s.f.505.1 | yes | 2 | 12.11 | even | 2 | ||
1368.2.s.f.577.1 | yes | 2 | 228.83 | even | 6 | ||
2736.2.s.e.577.1 | 2 | 19.7 | even | 3 | inner | ||
2736.2.s.e.1873.1 | 2 | 1.1 | even | 1 | trivial | ||
2736.2.s.n.577.1 | 2 | 57.26 | odd | 6 | |||
2736.2.s.n.1873.1 | 2 | 3.2 | odd | 2 |