Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(863,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1727.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.1727 |
Dual form | 2592.2.s.c.863.1 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | −3.34607 | + | 1.93185i | −1.49641 | + | 0.863950i | −0.999991 | − | 0.00413535i | \(-0.998684\pi\) |
−0.496414 | + | 0.868086i | \(0.665350\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.23205 | − | 1.86603i | −1.22160 | − | 0.705291i | −0.256341 | − | 0.966586i | \(-0.582517\pi\) |
−0.965259 | + | 0.261295i | \(0.915850\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.517638 | + | 0.896575i | −0.156074 | + | 0.270328i | −0.933449 | − | 0.358709i | \(-0.883217\pi\) |
0.777376 | + | 0.629037i | \(0.216550\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.23205 | − | 3.86603i | −0.619060 | − | 1.07224i | −0.989658 | − | 0.143449i | \(-0.954181\pi\) |
0.370598 | − | 0.928793i | \(-0.379153\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.79315i | 0.434903i | 0.976071 | + | 0.217451i | \(0.0697744\pi\) | ||||
−0.976071 | + | 0.217451i | \(0.930226\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.73205i | − | 0.397360i | −0.980064 | − | 0.198680i | \(-0.936335\pi\) | ||
0.980064 | − | 0.198680i | \(-0.0636654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.38134 | − | 7.58871i | −0.913573 | − | 1.58235i | −0.808977 | − | 0.587840i | \(-0.799979\pi\) |
−0.104595 | − | 0.994515i | \(-0.533355\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.96410 | − | 8.59808i | 0.992820 | − | 1.71962i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.69213 | + | 3.86370i | 1.24270 | + | 0.717472i | 0.969643 | − | 0.244527i | \(-0.0786326\pi\) |
0.273055 | + | 0.961998i | \(0.411966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.46410 | + | 3.73205i | −1.16099 | + | 0.670296i | −0.951540 | − | 0.307524i | \(-0.900500\pi\) |
−0.209447 | + | 0.977820i | \(0.567166\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.4195 | 2.43735 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.464102 | 0.0762978 | 0.0381489 | − | 0.999272i | \(-0.487854\pi\) | ||||
0.0381489 | + | 0.999272i | \(0.487854\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.69213 | + | 3.86370i | −1.04514 | + | 0.603409i | −0.921283 | − | 0.388892i | \(-0.872858\pi\) |
−0.123852 | + | 0.992301i | \(0.539525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.464102 | + | 0.267949i | 0.0707748 | + | 0.0408619i | 0.534970 | − | 0.844871i | \(-0.320323\pi\) |
−0.464195 | + | 0.885733i | \(0.653656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.31079 | − | 4.00240i | 0.337063 | − | 0.583811i | −0.646816 | − | 0.762646i | \(-0.723900\pi\) |
0.983879 | + | 0.178836i | \(0.0572331\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.46410 | + | 6.00000i | 0.494872 | + | 0.857143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.58630i | 0.492616i | 0.969192 | + | 0.246308i | \(0.0792175\pi\) | ||||
−0.969192 | + | 0.246308i | \(0.920782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.17449 | + | 10.6945i | 0.803850 | + | 1.39231i | 0.917064 | + | 0.398739i | \(0.130552\pi\) |
−0.113214 | + | 0.993571i | \(0.536115\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.69615 | + | 9.86603i | −0.729318 | + | 1.26322i | 0.227854 | + | 0.973695i | \(0.426829\pi\) |
−0.957172 | + | 0.289520i | \(0.906504\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.9372 | + | 8.62398i | 1.85273 | + | 1.06967i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.42820 | − | 3.13397i | 0.663161 | − | 0.382876i | −0.130320 | − | 0.991472i | \(-0.541600\pi\) |
0.793480 | + | 0.608596i | \(0.208267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.92820 | −0.459761 | −0.229881 | − | 0.973219i | \(-0.573834\pi\) | ||||
−0.229881 | + | 0.973219i | \(0.573834\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.34607 | − | 1.93185i | 0.381320 | − | 0.220155i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.16025 | − | 2.40192i | −0.468065 | − | 0.270238i | 0.247364 | − | 0.968923i | \(-0.420436\pi\) |
−0.715429 | + | 0.698685i | \(0.753769\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.03528 | + | 1.79315i | −0.113636 | + | 0.196824i | −0.917234 | − | 0.398349i | \(-0.869583\pi\) |
0.803597 | + | 0.595173i | \(0.202917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46410 | − | 6.00000i | −0.375735 | − | 0.650791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.79315i | 0.190074i | 0.995474 | + | 0.0950368i | \(0.0302969\pi\) | ||||
−0.995474 | + | 0.0950368i | \(0.969703\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.6603i | 1.74647i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.34607 | + | 5.79555i | 0.343299 | + | 0.594611i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50000 | + | 6.06218i | −0.355371 | + | 0.615521i | −0.987181 | − | 0.159602i | \(-0.948979\pi\) |
0.631810 | + | 0.775123i | \(0.282312\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.58630 | − | 2.07055i | −0.356850 | − | 0.206028i | 0.310848 | − | 0.950460i | \(-0.399387\pi\) |
−0.667698 | + | 0.744432i | \(0.732720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.7679 | − | 6.79423i | 1.15953 | − | 0.669455i | 0.208339 | − | 0.978057i | \(-0.433194\pi\) |
0.951191 | + | 0.308601i | \(0.0998609\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2784 | 0.993654 | 0.496827 | − | 0.867850i | \(-0.334498\pi\) | ||||
0.496827 | + | 0.867850i | \(0.334498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9282 | 1.23830 | 0.619149 | − | 0.785274i | \(-0.287478\pi\) | ||||
0.619149 | + | 0.785274i | \(0.287478\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.13922 | − | 2.96713i | 0.483457 | − | 0.279124i | −0.238399 | − | 0.971167i | \(-0.576623\pi\) |
0.721856 | + | 0.692043i | \(0.243289\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 29.3205 | + | 16.9282i | 2.73415 | + | 1.57856i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.34607 | − | 5.79555i | 0.306733 | − | 0.531278i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.96410 | + | 8.59808i | 0.451282 | + | 0.781643i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 19.0411i | 1.70309i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.46410i | − | 0.307389i | −0.988118 | − | 0.153695i | \(-0.950883\pi\) | ||
0.988118 | − | 0.153695i | \(-0.0491172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.03528 | + | 1.79315i | 0.0904525 | + | 0.156668i | 0.907702 | − | 0.419616i | \(-0.137835\pi\) |
−0.817249 | + | 0.576285i | \(0.804502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.23205 | + | 5.59808i | −0.280254 | + | 0.485415i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.8313 | − | 6.83083i | −1.01082 | − | 0.583597i | −0.0993885 | − | 0.995049i | \(-0.531689\pi\) |
−0.911432 | + | 0.411451i | \(0.865022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.96410 | − | 4.59808i | 0.675506 | − | 0.390004i | −0.122653 | − | 0.992450i | \(-0.539140\pi\) |
0.798160 | + | 0.602446i | \(0.205807\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.62158 | 0.386476 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −29.8564 | −2.47944 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.79796 | + | 5.65685i | −0.802680 | + | 0.463428i | −0.844407 | − | 0.535701i | \(-0.820047\pi\) |
0.0417274 | + | 0.999129i | \(0.486714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1603 | − | 5.86603i | −0.826830 | − | 0.477370i | 0.0259362 | − | 0.999664i | \(-0.491743\pi\) |
−0.852766 | + | 0.522293i | \(0.825077\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.4195 | − | 24.9754i | 1.15821 | − | 2.00607i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.46410 | + | 14.6603i | 0.675509 | + | 1.17002i | 0.976320 | + | 0.216332i | \(0.0694093\pi\) |
−0.300811 | + | 0.953684i | \(0.597257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.7028i | 2.57734i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.5885i | − | 1.22098i | −0.792023 | − | 0.610491i | \(-0.790972\pi\) | ||
0.792023 | − | 0.610491i | \(-0.209028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0735 | + | 19.1798i | 0.856891 | + | 1.48418i | 0.874880 | + | 0.484341i | \(0.160940\pi\) |
−0.0179886 | + | 0.999838i | \(0.505726\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.46410 | + | 6.00000i | −0.266469 | + | 0.461538i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.4901 | + | 9.52056i | 1.25372 | + | 0.723835i | 0.971846 | − | 0.235617i | \(-0.0757112\pi\) |
0.281872 | + | 0.959452i | \(0.409045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −32.0885 | + | 18.5263i | −2.42566 | + | 1.40046i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.5959 | −1.46467 | −0.732334 | − | 0.680946i | \(-0.761569\pi\) | ||||
−0.732334 | + | 0.680946i | \(0.761569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.464102 | 0.0344964 | 0.0172482 | − | 0.999851i | \(-0.494509\pi\) | ||||
0.0172482 | + | 0.999851i | \(0.494509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.55291 | + | 0.896575i | −0.114173 | + | 0.0659175i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.60770 | − | 0.928203i | −0.117566 | − | 0.0678769i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.41662 | − | 9.38186i | 0.391933 | − | 0.678847i | −0.600772 | − | 0.799421i | \(-0.705140\pi\) |
0.992704 | + | 0.120573i | \(0.0384733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.96410 | − | 12.0622i | −0.501287 | − | 0.868255i | −0.999999 | − | 0.00148674i | \(-0.999527\pi\) |
0.498712 | − | 0.866768i | \(-0.333807\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.277401i | 0.0197640i | 0.999951 | + | 0.00988202i | \(0.00314559\pi\) | ||||
−0.999951 | + | 0.00988202i | \(0.996854\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.58846i | 0.396155i | 0.980186 | + | 0.198078i | \(0.0634698\pi\) | ||||
−0.980186 | + | 0.198078i | \(0.936530\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.4195 | − | 24.9754i | −1.01205 | − | 1.75293i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.9282 | − | 25.8564i | 1.04263 | − | 1.80589i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.55291 | + | 0.896575i | 0.107417 | + | 0.0620174i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8205 | − | 9.13397i | 1.08913 | − | 0.628809i | 0.155784 | − | 0.987791i | \(-0.450210\pi\) |
0.933344 | + | 0.358982i | \(0.116876\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.07055 | −0.141210 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.8564 | 1.89102 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.93237 | − | 4.00240i | 0.466321 | − | 0.269231i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.3205 | − | 8.26795i | −0.958972 | − | 0.553663i | −0.0631156 | − | 0.998006i | \(-0.520104\pi\) |
−0.895857 | + | 0.444343i | \(0.853437\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.72741 | − | 13.3843i | 0.512886 | − | 0.888345i | −0.487002 | − | 0.873401i | \(-0.661910\pi\) |
0.999888 | − | 0.0149439i | \(-0.00475698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.3137i | 0.741186i | 0.928795 | + | 0.370593i | \(0.120845\pi\) | ||||
−0.928795 | + | 0.370593i | \(0.879155\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.8564i | 1.16482i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.07055 | + | 3.58630i | 0.133933 | + | 0.231979i | 0.925189 | − | 0.379506i | \(-0.123906\pi\) |
−0.791256 | + | 0.611484i | \(0.790573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.96410 | − | 6.86603i | 0.255350 | − | 0.442280i | −0.709640 | − | 0.704564i | \(-0.751143\pi\) |
0.964991 | + | 0.262285i | \(0.0844759\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −23.1822 | − | 13.3843i | −1.48106 | − | 0.855089i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.69615 | + | 3.86603i | −0.426066 | + | 0.245989i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3843 | −0.844807 | −0.422404 | − | 0.906408i | \(-0.638813\pi\) | ||||
−0.422404 | + | 0.906408i | \(0.638813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.07180 | 0.570339 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.69213 | − | 3.86370i | 0.417444 | − | 0.241011i | −0.276539 | − | 0.961003i | \(-0.589188\pi\) |
0.693983 | + | 0.719991i | \(0.255854\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.50000 | − | 0.866025i | −0.0932055 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.07055 | + | 3.58630i | −0.127676 | + | 0.221141i | −0.922776 | − | 0.385338i | \(-0.874085\pi\) |
0.795100 | + | 0.606478i | \(0.207418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.92820 | − | 12.0000i | −0.425596 | − | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.5911i | 0.706722i | 0.935487 | + | 0.353361i | \(0.114961\pi\) | ||||
−0.935487 | + | 0.353361i | \(0.885039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 25.0526i | − | 1.52183i | −0.648849 | − | 0.760917i | \(-0.724749\pi\) | ||
0.648849 | − | 0.760917i | \(-0.275251\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.13922 | + | 8.90138i | 0.309906 | + | 0.536774i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.53590 | + | 6.12436i | −0.212452 | + | 0.367977i | −0.952481 | − | 0.304597i | \(-0.901478\pi\) |
0.740030 | + | 0.672574i | \(0.234811\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2784 | − | 5.93426i | −0.613160 | − | 0.354008i | 0.161041 | − | 0.986948i | \(-0.448515\pi\) |
−0.774201 | + | 0.632940i | \(0.781848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.46410 | − | 3.73205i | 0.384251 | − | 0.221847i | −0.295415 | − | 0.955369i | \(-0.595458\pi\) |
0.679666 | + | 0.733522i | \(0.262125\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.8391 | 1.70232 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7846 | 0.810859 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.86559 | − | 1.65445i | 0.167410 | − | 0.0966540i | −0.413954 | − | 0.910298i | \(-0.635853\pi\) |
0.581364 | + | 0.813644i | \(0.302519\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.3205 | − | 23.8564i | −2.40577 | − | 1.38897i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.5588 | + | 33.8768i | −1.13111 | + | 1.95914i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | − | 1.73205i | −0.0576390 | − | 0.0998337i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 44.0165i | − | 2.52038i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.60770i | 0.0917560i | 0.998947 | + | 0.0458780i | \(0.0146086\pi\) | ||||
−0.998947 | + | 0.0458780i | \(0.985391\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1087 | + | 20.9730i | 0.686624 | + | 1.18927i | 0.972923 | + | 0.231128i | \(0.0742415\pi\) |
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.03590 | − | 5.25833i | 0.171599 | − | 0.297218i | −0.767380 | − | 0.641193i | \(-0.778440\pi\) |
0.938979 | + | 0.343974i | \(0.111773\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.69213 | + | 3.86370i | 0.375867 | + | 0.217007i | 0.676019 | − | 0.736884i | \(-0.263704\pi\) |
−0.300151 | + | 0.953892i | \(0.597037\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.92820 | + | 4.00000i | −0.387905 | + | 0.223957i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.10583 | 0.172813 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −44.3205 | −2.45846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.9372 | + | 8.62398i | −0.823513 | + | 0.475456i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8205 | + | 7.40192i | 0.704679 | + | 0.406847i | 0.809088 | − | 0.587688i | \(-0.199962\pi\) |
−0.104409 | + | 0.994534i | \(0.533295\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.1087 | + | 20.9730i | −0.661572 | + | 1.14588i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.42820 | − | 11.1340i | −0.350167 | − | 0.606506i | 0.636112 | − | 0.771597i | \(-0.280542\pi\) |
−0.986278 | + | 0.165091i | \(0.947208\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7.72741i | − | 0.418463i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.267949i | 0.0144679i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.07055 | + | 3.58630i | 0.111153 | + | 0.192523i | 0.916235 | − | 0.400640i | \(-0.131212\pi\) |
−0.805082 | + | 0.593163i | \(0.797879\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.1603 | − | 21.0622i | 0.650923 | − | 1.12743i | −0.331976 | − | 0.943288i | \(-0.607715\pi\) |
0.982899 | − | 0.184145i | \(-0.0589515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.5569 | + | 11.8685i | 1.09413 | + | 0.631697i | 0.934673 | − | 0.355508i | \(-0.115692\pi\) |
0.159458 | + | 0.987205i | \(0.449025\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.8564 | + | 21.8564i | −2.00921 | + | 1.16002i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.2490 | −1.43815 | −0.719073 | − | 0.694934i | \(-0.755434\pi\) | ||||
−0.719073 | + | 0.694934i | \(0.755434\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.1440 | − | 7.58871i | 0.687990 | − | 0.397211i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2321 | + | 10.5263i | 0.951705 | + | 0.549467i | 0.893610 | − | 0.448844i | \(-0.148164\pi\) |
0.0580950 | + | 0.998311i | \(0.481497\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.69213 | − | 11.5911i | 0.347438 | − | 0.601780i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6244 | + | 30.5263i | 0.912555 | + | 1.58059i | 0.810443 | + | 0.585818i | \(0.199227\pi\) |
0.102112 | + | 0.994773i | \(0.467440\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 34.4959i | − | 1.77663i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.19615i | 0.0614422i | 0.999528 | + | 0.0307211i | \(0.00978037\pi\) | ||||
−0.999528 | + | 0.0307211i | \(0.990220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.8685 | − | 20.5569i | −0.606453 | − | 1.05041i | −0.991820 | − | 0.127644i | \(-0.959259\pi\) |
0.385368 | − | 0.922763i | \(-0.374075\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.46410 | + | 12.9282i | −0.380406 | + | 0.658882i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.240237 | + | 0.138701i | 0.0121805 | + | 0.00703241i | 0.506078 | − | 0.862488i | \(-0.331095\pi\) |
−0.493897 | + | 0.869520i | \(0.664428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.6077 | − | 7.85641i | 0.688171 | − | 0.397316i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.5606 | 0.933887 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.7846 | −0.742018 | −0.371009 | − | 0.928629i | \(-0.620988\pi\) | ||||
−0.371009 | + | 0.928629i | \(0.620988\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5959 | − | 11.3137i | 0.978573 | − | 0.564980i | 0.0767343 | − | 0.997052i | \(-0.475551\pi\) |
0.901839 | + | 0.432072i | \(0.142217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.8564 | + | 16.6603i | 1.43744 | + | 0.829906i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.240237 | + | 0.416102i | −0.0119081 | + | 0.0206254i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.50000 | + | 11.2583i | 0.321404 | + | 0.556689i | 0.980778 | − | 0.195127i | \(-0.0625118\pi\) |
−0.659374 | + | 0.751815i | \(0.729178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 46.0870i | − | 2.26779i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.00000i | − | 0.392705i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.28032 | − | 16.0740i | −0.453373 | − | 0.785266i | 0.545220 | − | 0.838293i | \(-0.316446\pi\) |
−0.998593 | + | 0.0530275i | \(0.983113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.23205 | + | 14.2583i | −0.401206 | + | 0.694908i | −0.993872 | − | 0.110540i | \(-0.964742\pi\) |
0.592666 | + | 0.805448i | \(0.298075\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.4176 | + | 8.90138i | 0.747866 | + | 0.431781i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.8205 | − | 21.2583i | 1.78187 | − | 1.02876i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.0764 | −0.967046 | −0.483523 | − | 0.875332i | \(-0.660643\pi\) | ||||
−0.483523 | + | 0.875332i | \(0.660643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.7846 | 0.710503 | 0.355251 | − | 0.934771i | \(-0.384395\pi\) | ||||
0.355251 | + | 0.934771i | \(0.384395\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.1440 | + | 7.58871i | −0.628764 | + | 0.363017i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.5359 | + | 6.66025i | 0.550578 | + | 0.317877i | 0.749355 | − | 0.662168i | \(-0.230364\pi\) |
−0.198777 | + | 0.980045i | \(0.563697\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8332 | + | 18.7637i | −0.514703 | + | 0.891491i | 0.485152 | + | 0.874430i | \(0.338764\pi\) |
−0.999854 | + | 0.0170611i | \(0.994569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.46410 | − | 6.00000i | −0.164214 | − | 0.284427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.3891i | 1.00941i | 0.863291 | + | 0.504706i | \(0.168399\pi\) | ||||
−0.863291 | + | 0.504706i | \(0.831601\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8.00000i | − | 0.376705i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.1851 | − | 55.7463i | −1.50886 | − | 2.61343i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.39230 | + | 5.87564i | −0.158685 | + | 0.274851i | −0.934395 | − | 0.356239i | \(-0.884059\pi\) |
0.775710 | + | 0.631090i | \(0.217392\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.55772 | − | 5.51815i | −0.445148 | − | 0.257006i | 0.260631 | − | 0.965438i | \(-0.416069\pi\) |
−0.705779 | + | 0.708432i | \(0.749403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0167 | − | 10.4019i | 0.837305 | − | 0.483418i | −0.0190421 | − | 0.999819i | \(-0.506062\pi\) |
0.856347 | + | 0.516400i | \(0.172728\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.06678 | −0.188188 | −0.0940940 | − | 0.995563i | \(-0.529995\pi\) | ||||
−0.0940940 | + | 0.995563i | \(0.529995\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.3923 | −1.08016 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.480473 | + | 0.277401i | −0.0220922 | + | 0.0127549i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.8923 | − | 8.59808i | −0.683306 | − | 0.394507i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.3490 | + | 21.3891i | −0.564240 | + | 0.977292i | 0.432880 | + | 0.901451i | \(0.357497\pi\) |
−0.997120 | + | 0.0758402i | \(0.975836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.03590 | − | 1.79423i | −0.0472329 | − | 0.0818098i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 27.0459i | − | 1.22809i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.4449i | 1.60616i | 0.595871 | + | 0.803080i | \(0.296807\pi\) | ||||
−0.595871 | + | 0.803080i | \(0.703193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.28032 | + | 16.0740i | 0.418815 | + | 0.725409i | 0.995821 | − | 0.0913313i | \(-0.0291122\pi\) |
−0.577006 | + | 0.816740i | \(0.695779\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.92820 | + | 12.0000i | −0.312031 | + | 0.540453i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.5665 | − | 21.1117i | −1.64023 | − | 0.946988i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8564 | − | 9.73205i | 0.754596 | − | 0.435666i | −0.0727559 | − | 0.997350i | \(-0.523179\pi\) |
0.827352 | + | 0.561683i | \(0.189846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.9743 | 0.667673 | 0.333836 | − | 0.942631i | \(-0.391657\pi\) | ||||
0.333836 | + | 0.942631i | \(0.391657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | 0.711991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.6245 | + | 7.86611i | −0.603895 | + | 0.348659i | −0.770572 | − | 0.637352i | \(-0.780030\pi\) |
0.166677 | + | 0.986012i | \(0.446696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6962 | + | 7.33013i | 0.561645 | + | 0.324266i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.2509 | + | 45.4679i | −1.15675 | + | 2.00355i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.39230 | + | 4.14359i | 0.105213 | + | 0.182235i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.48906i | 0.284291i | 0.989846 | + | 0.142145i | \(0.0454001\pi\) | ||||
−0.989846 | + | 0.142145i | \(0.954600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1962i | 0.926843i | 0.886138 | + | 0.463422i | \(0.153378\pi\) | ||||
−0.886138 | + | 0.463422i | \(0.846622\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.69213 | − | 11.5911i | −0.291514 | − | 0.504917i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −26.8923 | + | 46.5788i | −1.16923 | + | 2.02517i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.8744 | + | 17.2480i | 1.29400 | + | 0.747092i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.3923 | + | 19.8564i | −1.48691 | + | 0.858467i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.17260 | −0.308946 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.3923 | 1.52163 | 0.760817 | − | 0.648966i | \(-0.224798\pi\) | ||||
0.760817 | + | 0.648966i | \(0.224798\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −43.2586 | + | 24.9754i | −1.85300 | + | 1.06983i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.96410 | − | 1.13397i | −0.0839789 | − | 0.0484853i | 0.457422 | − | 0.889249i | \(-0.348773\pi\) |
−0.541401 | + | 0.840764i | \(0.682106\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.69213 | − | 11.5911i | 0.285094 | − | 0.493798i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.96410 | + | 15.5263i | 0.381192 | + | 0.660245i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15.1774i | − | 0.643088i | −0.946895 | − | 0.321544i | \(-0.895798\pi\) | ||
0.946895 | − | 0.321544i | \(-0.104202\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.39230i | − | 0.101184i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.62158 | − | 8.00481i | −0.194776 | − | 0.337362i | 0.752051 | − | 0.659105i | \(-0.229065\pi\) |
−0.946827 | + | 0.321743i | \(0.895731\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.4641 | + | 19.8564i | −0.482298 | + | 0.835365i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.6389 | − | 21.7308i | −1.57791 | − | 0.911004i | −0.995151 | − | 0.0983559i | \(-0.968642\pi\) |
−0.582754 | − | 0.812648i | \(-0.698025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0359 | − | 7.52628i | 0.545535 | − | 0.314965i | −0.201784 | − | 0.979430i | \(-0.564674\pi\) |
0.747319 | + | 0.664465i | \(0.231341\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −86.9977 | −3.62805 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.9282 | −1.66223 | −0.831116 | − | 0.556098i | \(-0.812298\pi\) | ||||
−0.831116 | + | 0.556098i | \(0.812298\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.69213 | − | 3.86370i | 0.277636 | − | 0.160293i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.21539 | − | 1.85641i | −0.133168 | − | 0.0768845i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.20977 | − | 12.4877i | 0.297579 | − | 0.515422i | −0.678003 | − | 0.735060i | \(-0.737154\pi\) |
0.975582 | + | 0.219638i | \(0.0704875\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.46410 | + | 11.1962i | 0.266349 | + | 0.461329i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 42.7781i | − | 1.75669i | −0.478029 | − | 0.878344i | \(-0.658649\pi\) | ||
0.478029 | − | 0.878344i | \(-0.341351\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.8564i | 1.06001i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.76268 | − | 15.1774i | −0.358034 | − | 0.620132i | 0.629599 | − | 0.776920i | \(-0.283219\pi\) |
−0.987632 | + | 0.156788i | \(0.949886\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.3923 | − | 30.1244i | 0.709447 | − | 1.22880i | −0.255616 | − | 0.966778i | \(-0.582278\pi\) |
0.965063 | − | 0.262020i | \(-0.0843885\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33.2204 | − | 19.1798i | −1.35060 | − | 0.779770i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.76795 | − | 3.33013i | 0.234114 | − | 0.135166i | −0.378355 | − | 0.925661i | \(-0.623510\pi\) |
0.612468 | + | 0.790495i | \(0.290177\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.6312 | −0.834649 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.6077 | −0.670778 | −0.335389 | − | 0.942080i | \(-0.608868\pi\) | ||||
−0.335389 | + | 0.942080i | \(0.608868\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.1194 | − | 22.0082i | 1.53463 | − | 0.886018i | 0.535490 | − | 0.844542i | \(-0.320127\pi\) |
0.999139 | − | 0.0414767i | \(-0.0132062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.4282 | + | 8.33013i | 0.579918 | + | 0.334816i | 0.761101 | − | 0.648633i | \(-0.224659\pi\) |
−0.181183 | + | 0.983449i | \(0.557992\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.34607 | − | 5.79555i | 0.134057 | − | 0.232194i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.9641 | − | 20.7224i | −0.478564 | − | 0.828897i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.832204i | 0.0331822i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.9808i | − | 1.27313i | −0.771221 | − | 0.636567i | \(-0.780354\pi\) | ||
0.771221 | − | 0.636567i | \(-0.219646\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.69213 | + | 11.5911i | 0.265569 | + | 0.459979i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.4641 | − | 26.7846i | 0.612710 | − | 1.06124i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.62536 | + | 1.51575i | 0.103695 | + | 0.0598685i | 0.550951 | − | 0.834538i | \(-0.314265\pi\) |
−0.447255 | + | 0.894406i | \(0.647599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.2487 | + | 19.1962i | −1.31120 | + | 0.757022i | −0.982295 | − | 0.187340i | \(-0.940013\pi\) |
−0.328906 | + | 0.944363i | \(0.606680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.21166 | −0.244205 | −0.122103 | − | 0.992517i | \(-0.538964\pi\) | ||||
−0.122103 | + | 0.992517i | \(0.538964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.7846 | −0.501840 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.4607 | + | 19.3185i | −1.30942 | + | 0.755992i | −0.981999 | − | 0.188888i | \(-0.939512\pi\) |
−0.327418 | + | 0.944880i | \(0.606178\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.92820 | − | 4.00000i | −0.270707 | − | 0.156293i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.55103 | + | 4.41851i | −0.0993739 | + | 0.172121i | −0.911426 | − | 0.411465i | \(-0.865017\pi\) |
0.812052 | + | 0.583585i | \(0.198351\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.62436 | − | 4.54552i | −0.102076 | − | 0.176800i | 0.810464 | − | 0.585788i | \(-0.199215\pi\) |
−0.912540 | + | 0.408988i | \(0.865882\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 24.9754i | − | 0.968503i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 67.7128i | − | 2.62185i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.89709 | − | 10.2141i | −0.227655 | − | 0.394309i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.42820 | − | 5.93782i | 0.132148 | − | 0.228886i | −0.792357 | − | 0.610058i | \(-0.791146\pi\) |
0.924504 | + | 0.381172i | \(0.124479\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.9420 | − | 13.2456i | −0.881732 | − | 0.509068i | −0.0105029 | − | 0.999945i | \(-0.503343\pi\) |
−0.871229 | + | 0.490877i | \(0.836677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.6244 | − | 13.0622i | 0.868243 | − | 0.501280i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9411 | −1.29872 | −0.649361 | − | 0.760481i | \(-0.724963\pi\) | ||||
−0.649361 | + | 0.760481i | \(0.724963\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 52.7846 | 2.01680 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8647 | − | 8.00481i | 0.528204 | − | 0.304959i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.32051 | − | 4.80385i | −0.316527 | − | 0.182747i | 0.333316 | − | 0.942815i | \(-0.391832\pi\) |
−0.649844 | + | 0.760068i | \(0.725166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.7656 | + | 30.7709i | −0.673888 | + | 1.16721i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.92820 | − | 12.0000i | −0.262424 | − | 0.454532i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.0144i | 0.907012i | 0.891253 | + | 0.453506i | \(0.149827\pi\) | ||||
−0.891253 | + | 0.453506i | \(0.850173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.803848i | − | 0.0303177i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.72741 | + | 13.3843i | 0.290619 | + | 0.503367i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.0885 | − | 43.4545i | 0.942217 | − | 1.63197i | 0.180987 | − | 0.983486i | \(-0.442071\pi\) |
0.761230 | − | 0.648482i | \(-0.224596\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 56.6429 | + | 32.7028i | 2.12129 | + | 1.22473i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.4641 | + | 8.92820i | −0.578325 | + | 0.333896i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3843 | 0.499149 | 0.249574 | − | 0.968356i | \(-0.419709\pi\) | ||||
0.249574 | + | 0.968356i | \(0.419709\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.7128 | −1.88864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 66.4408 | − | 38.3596i | 2.46755 | − | 1.42464i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.5359 | + | 6.66025i | 0.427843 | + | 0.247015i | 0.698427 | − | 0.715681i | \(-0.253884\pi\) |
−0.270584 | + | 0.962696i | \(0.587217\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.480473 | + | 0.832204i | −0.0177709 | + | 0.0307802i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.53590 | + | 16.5167i | 0.352216 | + | 0.610057i | 0.986637 | − | 0.162931i | \(-0.0520948\pi\) |
−0.634421 | + | 0.772988i | \(0.718761\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.48906i | 0.239028i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.39230i | − | 0.235145i | −0.993064 | − | 0.117572i | \(-0.962489\pi\) | ||
0.993064 | − | 0.117572i | \(-0.0375112\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.1793 | + | 24.5593i | 0.520188 | + | 0.900992i | 0.999725 | + | 0.0234702i | \(0.00747149\pi\) |
−0.479536 | + | 0.877522i | \(0.659195\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.8564 | − | 37.8564i | 0.800757 | − | 1.38695i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.2204 | − | 19.1798i | −1.21385 | − | 0.700815i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.23205 | + | 3.59808i | −0.227411 | + | 0.131296i | −0.609377 | − | 0.792881i | \(-0.708580\pi\) |
0.381966 | + | 0.924176i | \(0.375247\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.3292 | 1.64970 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.3923 | 0.559443 | 0.279721 | − | 0.960081i | \(-0.409758\pi\) | ||||
0.279721 | + | 0.960081i | \(0.409758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.6961 | − | 14.8356i | 0.931482 | − | 0.537791i | 0.0442022 | − | 0.999023i | \(-0.485925\pi\) |
0.887280 | + | 0.461231i | \(0.152592\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.7846 | − | 24.1244i | −1.51270 | − | 0.873360i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.5636 | − | 47.7415i | 0.995263 | − | 1.72385i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.42820 | + | 12.8660i | 0.267868 | + | 0.463961i | 0.968311 | − | 0.249747i | \(-0.0803476\pi\) |
−0.700443 | + | 0.713708i | \(0.747014\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.3548i | 1.09179i | 0.837855 | + | 0.545894i | \(0.183810\pi\) | ||||
−0.837855 | + | 0.545894i | \(0.816190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 74.1051i | 2.66193i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.69213 | + | 11.5911i | 0.239770 | + | 0.415295i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.85641 | + | 10.1436i | −0.209559 | + | 0.362966i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56.6429 | − | 32.7028i | −2.02167 | − | 1.16721i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.2128 | + | 16.8660i | −1.04132 | + | 0.601209i | −0.920208 | − | 0.391429i | \(-0.871981\pi\) |
−0.121116 | + | 0.992638i | \(0.538647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.1469 | −0.787455 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.8564 | 1.80596 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.5665 | − | 21.1117i | 1.29525 | − | 0.747814i | 0.315671 | − | 0.948869i | \(-0.397770\pi\) |
0.979580 | + | 0.201055i | \(0.0644370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.17691 | + | 4.14359i | 0.253901 | + | 0.146590i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.03339 | − | 3.52193i | 0.0717567 | − | 0.124286i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −63.1769 | − | 109.426i | −2.22669 | − | 3.85675i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5959i | 0.688956i | 0.938794 | + | 0.344478i | \(0.111944\pi\) | ||||
−0.938794 | + | 0.344478i | \(0.888056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.53590i | − | 0.299736i | −0.988706 | − | 0.149868i | \(-0.952115\pi\) | ||
0.988706 | − | 0.149868i | \(-0.0478849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.1146 | + | 52.1600i | 1.05487 | + | 1.82708i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.464102 | − | 0.803848i | 0.0162369 | − | 0.0281231i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.9420 | + | 13.2456i | 0.800681 | + | 0.462273i | 0.843709 | − | 0.536801i | \(-0.180367\pi\) |
−0.0430284 | + | 0.999074i | \(0.513701\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3756 | + | 5.99038i | −0.361672 | + | 0.208812i | −0.669814 | − | 0.742529i | \(-0.733626\pi\) |
0.308142 | + | 0.951340i | \(0.400293\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.9134 | −1.00542 | −0.502709 | − | 0.864456i | \(-0.667663\pi\) | ||||
−0.502709 | + | 0.864456i | \(0.667663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.3205 | 1.74770 | 0.873852 | − | 0.486192i | \(-0.161615\pi\) | ||||
0.873852 | + | 0.486192i | \(0.161615\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.7589 | + | 6.21166i | −0.372774 | + | 0.215221i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −74.1051 | − | 42.7846i | −2.56451 | − | 1.48062i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.5921 | + | 37.3987i | −0.745443 | + | 1.29115i | 0.204544 | + | 0.978857i | \(0.434429\pi\) |
−0.949987 | + | 0.312289i | \(0.898904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3564 | + | 26.5981i | 0.529531 | + | 0.917175i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 26.7685i | − | 0.920865i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 37.0526i | − | 1.27314i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.03339 | − | 3.52193i | −0.0697036 | − | 0.120730i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.6962 | + | 41.0429i | −0.811341 | + | 1.40528i | 0.100585 | + | 0.994928i | \(0.467929\pi\) |
−0.911926 | + | 0.410355i | \(0.865405\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.0096 | + | 9.24316i | 0.546878 | + | 0.315740i | 0.747862 | − | 0.663854i | \(-0.231081\pi\) |
−0.200984 | + | 0.979595i | \(0.564414\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.9641 | + | 13.2583i | −0.783525 | + | 0.452368i | −0.837678 | − | 0.546164i | \(-0.816087\pi\) |
0.0541531 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.0566 | 1.80607 | 0.903033 | − | 0.429570i | \(-0.141335\pi\) | ||||
0.903033 | + | 0.429570i | \(0.141335\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −73.5692 | −2.50143 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.30701 | − | 2.48665i | 0.146105 | − | 0.0843540i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.2321 | − | 13.9904i | −0.821072 | − | 0.474046i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.5312 | − | 61.5419i | 1.20117 | − | 2.08049i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.6244 | + | 20.1340i | 0.392527 | + | 0.679876i | 0.992782 | − | 0.119932i | \(-0.0382678\pi\) |
−0.600255 | + | 0.799808i | \(0.704934\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 21.3891i | − | 0.720616i | −0.932833 | − | 0.360308i | \(-0.882672\pi\) | ||
0.932833 | − | 0.360308i | \(-0.117328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.124356i | 0.00418490i | 0.999998 | + | 0.00209245i | \(0.000666048\pi\) | ||||
−0.999998 | + | 0.00209245i | \(0.999334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.76268 | + | 15.1774i | 0.294222 | + | 0.509608i | 0.974804 | − | 0.223065i | \(-0.0716061\pi\) |
−0.680582 | + | 0.732672i | \(0.738273\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.46410 | + | 11.1962i | −0.216799 | + | 0.375507i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.93237 | − | 4.00240i | −0.231983 | − | 0.133935i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 65.5692 | − | 37.8564i | 2.19174 | − | 1.26540i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.6781 | −1.92367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.43078 | −0.214240 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.55291 | + | 0.896575i | −0.0516206 | + | 0.0298032i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.21281 | − | 4.74167i | −0.272702 | − | 0.157445i | 0.357413 | − | 0.933946i | \(-0.383659\pi\) |
−0.630115 | + | 0.776502i | \(0.716992\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4195 | − | 24.9754i | 0.477741 | − | 0.827471i | −0.521934 | − | 0.852986i | \(-0.674789\pi\) |
0.999674 | + | 0.0255150i | \(0.00812256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.07180 | − | 1.85641i | −0.0354713 | − | 0.0614381i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.72741i | − | 0.255181i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 33.0333i | − | 1.08967i | −0.838544 | − | 0.544834i | \(-0.816593\pi\) | ||
0.838544 | − | 0.544834i | \(-0.183407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.2528 | − | 43.7391i | −0.831205 | − | 1.43969i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.30385 | − | 3.99038i | 0.0757500 | − | 0.131203i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5959 | − | 11.3137i | −0.642921 | − | 0.371191i | 0.142818 | − | 0.989749i | \(-0.454384\pi\) |
−0.785739 | + | 0.618558i | \(0.787717\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3923 | − | 6.00000i | 0.340594 | − | 0.196642i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.17260 | 0.234569 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.7846 | 1.56106 | 0.780528 | − | 0.625121i | \(-0.214951\pi\) | ||||
0.780528 | + | 0.625121i | \(0.214951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5187 | − | 6.07296i | 0.342899 | − | 0.197973i | −0.318654 | − | 0.947871i | \(-0.603231\pi\) |
0.661553 | + | 0.749898i | \(0.269898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.6410 | + | 33.8564i | 1.90961 | + | 1.10252i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.20977 | + | 12.4877i | −0.234286 | + | 0.405795i | −0.959065 | − | 0.283186i | \(-0.908609\pi\) |
0.724779 | + | 0.688981i | \(0.241942\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.76795 | + | 15.1865i | 0.284620 | + | 0.492976i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.3891i | 0.692860i | 0.938076 | + | 0.346430i | \(0.112606\pi\) | ||||
−0.938076 | + | 0.346430i | \(0.887394\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.8564i | 1.35444i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.4930 | + | 44.1552i | 0.823212 | + | 1.42585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3564 | − | 21.4019i | 0.398594 | − | 0.690385i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.6047 | + | 26.9072i | 1.50026 | + | 0.866174i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.16025 | + | 4.13397i | −0.230258 | + | 0.132940i | −0.610691 | − | 0.791869i | \(-0.709108\pi\) |
0.380433 | + | 0.924809i | \(0.375775\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.8429 | −0.861428 | −0.430714 | − | 0.902488i | \(-0.641738\pi\) | ||||
−0.430714 | + | 0.902488i | \(0.641738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.3205 | −1.10026 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.4901 | + | 9.52056i | −0.527565 | + | 0.304590i | −0.740024 | − | 0.672580i | \(-0.765186\pi\) |
0.212459 | + | 0.977170i | \(0.431853\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.60770 | − | 0.928203i | −0.0513822 | − | 0.0296655i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.86181 | − | 8.42091i | 0.155068 | − | 0.268585i | −0.778016 | − | 0.628245i | \(-0.783774\pi\) |
0.933084 | + | 0.359659i | \(0.117107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.535898 | − | 0.928203i | −0.0170751 | − | 0.0295750i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 4.69591i | − | 0.149321i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.5167i | 1.66825i | 0.551578 | + | 0.834123i | \(0.314026\pi\) | ||||
−0.551578 | + | 0.834123i | \(0.685974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.7961 | − | 18.6993i | −0.342258 | − | 0.592809i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.3923 | + | 30.1244i | −0.550820 | + | 0.954048i | 0.447396 | + | 0.894336i | \(0.352352\pi\) |
−0.998216 | + | 0.0597119i | \(0.980982\pi\) | |||||||
\(998\) | 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 | 2592.2.s.c.1727.1 | 8 | ||
3.2 | odd | 2 | inner | 2592.2.s.c.1727.4 | 8 | ||
4.3 | odd | 2 | 2592.2.s.g.1727.1 | 8 | |||
9.2 | odd | 6 | 864.2.c.b.863.8 | yes | 8 | ||
9.4 | even | 3 | 2592.2.s.g.863.4 | 8 | |||
9.5 | odd | 6 | 2592.2.s.g.863.1 | 8 | |||
9.7 | even | 3 | 864.2.c.b.863.2 | yes | 8 | ||
12.11 | even | 2 | 2592.2.s.g.1727.4 | 8 | |||
36.7 | odd | 6 | 864.2.c.b.863.1 | ✓ | 8 | ||
36.11 | even | 6 | 864.2.c.b.863.7 | yes | 8 | ||
36.23 | even | 6 | inner | 2592.2.s.c.863.1 | 8 | ||
36.31 | odd | 6 | inner | 2592.2.s.c.863.4 | 8 | ||
72.11 | even | 6 | 1728.2.c.f.1727.1 | 8 | |||
72.29 | odd | 6 | 1728.2.c.f.1727.2 | 8 | |||
72.43 | odd | 6 | 1728.2.c.f.1727.7 | 8 | |||
72.61 | even | 6 | 1728.2.c.f.1727.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.c.b.863.1 | ✓ | 8 | 36.7 | odd | 6 | ||
864.2.c.b.863.2 | yes | 8 | 9.7 | even | 3 | ||
864.2.c.b.863.7 | yes | 8 | 36.11 | even | 6 | ||
864.2.c.b.863.8 | yes | 8 | 9.2 | odd | 6 | ||
1728.2.c.f.1727.1 | 8 | 72.11 | even | 6 | |||
1728.2.c.f.1727.2 | 8 | 72.29 | odd | 6 | |||
1728.2.c.f.1727.7 | 8 | 72.43 | odd | 6 | |||
1728.2.c.f.1727.8 | 8 | 72.61 | even | 6 | |||
2592.2.s.c.863.1 | 8 | 36.23 | even | 6 | inner | ||
2592.2.s.c.863.4 | 8 | 36.31 | odd | 6 | inner | ||
2592.2.s.c.1727.1 | 8 | 1.1 | even | 1 | trivial | ||
2592.2.s.c.1727.4 | 8 | 3.2 | odd | 2 | inner | ||
2592.2.s.g.863.1 | 8 | 9.5 | odd | 6 | |||
2592.2.s.g.863.4 | 8 | 9.4 | even | 3 | |||
2592.2.s.g.1727.1 | 8 | 4.3 | odd | 2 | |||
2592.2.s.g.1727.4 | 8 | 12.11 | even | 2 |