Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,2,Mod(575,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.l (of order \(4\), degree \(2\), 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: | \(18.3975326257\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1727.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1727 |
Dual form | 2304.2.l.f.575.1 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.93185 | − | 1.93185i | −0.863950 | − | 0.863950i | 0.127844 | − | 0.991794i | \(-0.459194\pi\) |
−0.991794 | + | 0.127844i | \(0.959194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | 0.534522 | 0.267261 | − | 0.963624i | \(-0.413881\pi\) | ||||
0.267261 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.732051 | + | 0.732051i | −0.220722 | + | 0.220722i | −0.808802 | − | 0.588081i | \(-0.799884\pi\) |
0.588081 | + | 0.808802i | \(0.299884\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.73205 | − | 1.73205i | −0.480384 | − | 0.480384i | 0.424870 | − | 0.905254i | \(-0.360320\pi\) |
−0.905254 | + | 0.424870i | \(0.860320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.27792i | 1.28008i | 0.768340 | + | 0.640041i | \(0.221083\pi\) | ||||
−0.768340 | + | 0.640041i | \(0.778917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.27792 | − | 5.27792i | 1.21084 | − | 1.21084i | 0.240085 | − | 0.970752i | \(-0.422825\pi\) |
0.970752 | − | 0.240085i | \(-0.0771754\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410i | 0.722315i | 0.932505 | + | 0.361158i | \(0.117618\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.46410i | 0.492820i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.31079 | − | 2.31079i | 0.429103 | − | 0.429103i | −0.459220 | − | 0.888323i | \(-0.651871\pi\) |
0.888323 | + | 0.459220i | \(0.151871\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.14162i | − | 1.64188i | −0.571012 | − | 0.820942i | \(-0.693449\pi\) | ||
0.571012 | − | 0.820942i | \(-0.306551\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.73205 | − | 2.73205i | −0.461801 | − | 0.461801i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.46410 | − | 2.46410i | 0.405096 | − | 0.405096i | −0.474929 | − | 0.880024i | \(-0.657526\pi\) |
0.880024 | + | 0.474929i | \(0.157526\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.52004 | 0.705912 | 0.352956 | − | 0.935640i | \(-0.385177\pi\) | ||||
0.352956 | + | 0.935640i | \(0.385177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.48477 | − | 3.48477i | −0.531422 | − | 0.531422i | 0.389574 | − | 0.920995i | \(-0.372622\pi\) |
−0.920995 | + | 0.389574i | \(0.872622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.3923 | −1.51587 | −0.757937 | − | 0.652328i | \(-0.773792\pi\) | ||||
−0.757937 | + | 0.652328i | \(0.773792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.24504 | − | 8.24504i | −1.13254 | − | 1.13254i | −0.989753 | − | 0.142791i | \(-0.954392\pi\) |
−0.142791 | − | 0.989753i | \(-0.545608\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.82843 | 0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.92820 | + | 8.92820i | −1.16235 | + | 1.16235i | −0.178394 | + | 0.983959i | \(0.557090\pi\) |
−0.983959 | + | 0.178394i | \(0.942910\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 3.00000i | 0.384111 | + | 0.384111i | 0.872581 | − | 0.488470i | \(-0.162445\pi\) |
−0.488470 | + | 0.872581i | \(0.662445\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.69213i | 0.830057i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.86370 | + | 3.86370i | −0.472026 | + | 0.472026i | −0.902570 | − | 0.430543i | \(-0.858322\pi\) |
0.430543 | + | 0.902570i | \(0.358322\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.0000i | − | 1.66149i | −0.556650 | − | 0.830747i | \(-0.687914\pi\) | ||
0.556650 | − | 0.830747i | \(-0.312086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.92820i | 0.576803i | 0.957510 | + | 0.288401i | \(0.0931237\pi\) | ||||
−0.957510 | + | 0.288401i | \(0.906876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.03528 | + | 1.03528i | −0.117981 | + | 0.117981i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.17209i | 0.244379i | 0.992507 | + | 0.122190i | \(0.0389916\pi\) | ||||
−0.992507 | + | 0.122190i | \(0.961008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.7321 | − | 10.7321i | −1.17800 | − | 1.17800i | −0.980254 | − | 0.197741i | \(-0.936639\pi\) |
−0.197741 | − | 0.980254i | \(-0.563361\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.1962 | − | 10.1962i | 1.10593 | − | 1.10593i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.1112 | 1.70778 | 0.853889 | − | 0.520455i | \(-0.174237\pi\) | ||||
0.853889 | + | 0.520455i | \(0.174237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.44949 | − | 2.44949i | −0.256776 | − | 0.256776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.3923 | −2.09221 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.3923 | −1.86746 | −0.933728 | − | 0.357984i | \(-0.883464\pi\) | ||||
−0.933728 | + | 0.357984i | \(0.883464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.58819 | − | 2.58819i | −0.257535 | − | 0.257535i | 0.566516 | − | 0.824051i | \(-0.308291\pi\) |
−0.824051 | + | 0.566516i | \(0.808291\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4543 | −1.03009 | −0.515046 | − | 0.857162i | \(-0.672225\pi\) | ||||
−0.515046 | + | 0.857162i | \(0.672225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.53590 | − | 6.53590i | 0.631849 | − | 0.631849i | −0.316682 | − | 0.948532i | \(-0.602569\pi\) |
0.948532 | + | 0.316682i | \(0.102569\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.73205 | + | 7.73205i | 0.740596 | + | 0.740596i | 0.972693 | − | 0.232097i | \(-0.0745585\pi\) |
−0.232097 | + | 0.972693i | \(0.574559\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24264i | 0.399114i | 0.979886 | + | 0.199557i | \(0.0639503\pi\) | ||||
−0.979886 | + | 0.199557i | \(0.936050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.69213 | − | 6.69213i | 0.624044 | − | 0.624044i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.46410i | 0.684233i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.92820i | 0.902564i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.89898 | + | 4.89898i | −0.438178 | + | 0.438178i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.0406i | − | 1.24590i | −0.782261 | − | 0.622951i | \(-0.785934\pi\) | ||
0.782261 | − | 0.622951i | \(-0.214066\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.92820 | − | 6.92820i | −0.605320 | − | 0.605320i | 0.336399 | − | 0.941719i | \(-0.390791\pi\) |
−0.941719 | + | 0.336399i | \(0.890791\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.46410 | − | 7.46410i | 0.647220 | − | 0.647220i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.20736 | −0.274024 | −0.137012 | − | 0.990569i | \(-0.543750\pi\) | ||||
−0.137012 | + | 0.990569i | \(0.543750\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.93426 | − | 5.93426i | −0.503337 | − | 0.503337i | 0.409136 | − | 0.912473i | \(-0.365830\pi\) |
−0.912473 | + | 0.409136i | \(0.865830\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.53590 | 0.212062 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.92820 | −0.741447 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.79555 | − | 5.79555i | −0.474790 | − | 0.474790i | 0.428671 | − | 0.903461i | \(-0.358982\pi\) |
−0.903461 | + | 0.428671i | \(0.858982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.656339 | 0.0534121 | 0.0267060 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267060 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.6603 | + | 17.6603i | −1.41851 | + | 1.41851i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.92820 | − | 3.92820i | −0.313505 | − | 0.313505i | 0.532761 | − | 0.846266i | \(-0.321154\pi\) |
−0.846266 | + | 0.532761i | \(0.821154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.89898i | 0.386094i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.656339 | − | 0.656339i | 0.0514084 | − | 0.0514084i | −0.680935 | − | 0.732344i | \(-0.738426\pi\) |
0.732344 | + | 0.680935i | \(0.238426\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.53590i | − | 0.505763i | −0.967497 | − | 0.252882i | \(-0.918622\pi\) | ||
0.967497 | − | 0.252882i | \(-0.0813783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.00000i | − | 0.538462i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.51815 | − | 5.51815i | 0.419537 | − | 0.419537i | −0.465507 | − | 0.885044i | \(-0.654128\pi\) |
0.885044 | + | 0.465507i | \(0.154128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.48477i | 0.263424i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | − | 6.00000i | −0.448461 | − | 0.448461i | 0.446382 | − | 0.894843i | \(-0.352712\pi\) |
−0.894843 | + | 0.446382i | \(0.852712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.803848 | + | 0.803848i | −0.0597495 | + | 0.0597495i | −0.736350 | − | 0.676601i | \(-0.763452\pi\) |
0.676601 | + | 0.736350i | \(0.263452\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.52056 | −0.699965 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.86370 | − | 3.86370i | −0.282542 | − | 0.282542i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4641 | −0.974228 | −0.487114 | − | 0.873338i | \(-0.661950\pi\) | ||||
−0.487114 | + | 0.873338i | \(0.661950\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.7846 | 1.64007 | 0.820036 | − | 0.572312i | \(-0.193953\pi\) | ||||
0.820036 | + | 0.572312i | \(0.193953\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.7303 | − | 16.7303i | −1.19199 | − | 1.19199i | −0.976509 | − | 0.215478i | \(-0.930869\pi\) |
−0.215478 | − | 0.976509i | \(-0.569131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6975 | 1.39632 | 0.698158 | − | 0.715944i | \(-0.254003\pi\) | ||||
0.698158 | + | 0.715944i | \(0.254003\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.26795 | − | 3.26795i | 0.229365 | − | 0.229365i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.73205 | − | 8.73205i | −0.609873 | − | 0.609873i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.72741i | 0.534516i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2784 | − | 10.2784i | 0.707596 | − | 0.707596i | −0.258433 | − | 0.966029i | \(-0.583206\pi\) |
0.966029 | + | 0.258433i | \(0.0832061\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4641i | 0.918244i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 12.9282i | − | 0.877624i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.14162 | − | 9.14162i | 0.614932 | − | 0.614932i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.7279i | − | 0.852325i | −0.904647 | − | 0.426162i | \(-0.859865\pi\) | ||
0.904647 | − | 0.426162i | \(-0.140135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.7321 | + | 14.7321i | 0.977801 | + | 0.977801i | 0.999759 | − | 0.0219583i | \(-0.00699012\pi\) |
−0.0219583 | + | 0.999759i | \(0.506990\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.19615 | + | 7.19615i | −0.475535 | + | 0.475535i | −0.903700 | − | 0.428165i | \(-0.859160\pi\) |
0.428165 | + | 0.903700i | \(0.359160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.4553 | 1.34007 | 0.670037 | − | 0.742328i | \(-0.266278\pi\) | ||||
0.670037 | + | 0.742328i | \(0.266278\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.0764 | + | 20.0764i | 1.30964 | + | 1.30964i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.4641 | 1.38840 | 0.694199 | − | 0.719783i | \(-0.255759\pi\) | ||||
0.694199 | + | 0.719783i | \(0.255759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.53590 | 0.421014 | 0.210507 | − | 0.977592i | \(-0.432488\pi\) | ||||
0.210507 | + | 0.977592i | \(0.432488\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.65926 | + | 9.65926i | 0.617107 | + | 0.617107i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.2832 | −1.16333 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.66025 | − | 7.66025i | 0.483511 | − | 0.483511i | −0.422740 | − | 0.906251i | \(-0.638932\pi\) |
0.906251 | + | 0.422740i | \(0.138932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.53590 | − | 2.53590i | −0.159431 | − | 0.159431i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.9700i | 0.746671i | 0.927696 | + | 0.373336i | \(0.121786\pi\) | ||||
−0.927696 | + | 0.373336i | \(0.878214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.48477 | − | 3.48477i | 0.216533 | − | 0.216533i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.92820i | 0.180561i | 0.995916 | + | 0.0902804i | \(0.0287763\pi\) | ||||
−0.995916 | + | 0.0902804i | \(0.971224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.8564i | 1.95692i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.93237 | + | 6.93237i | −0.422674 | + | 0.422674i | −0.886123 | − | 0.463449i | \(-0.846612\pi\) |
0.463449 | + | 0.886123i | \(0.346612\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.92996i | 0.177983i | 0.996032 | + | 0.0889913i | \(0.0283643\pi\) | ||||
−0.996032 | + | 0.0889913i | \(0.971636\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.80385 | − | 1.80385i | −0.108776 | − | 0.108776i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1962 | + | 11.1962i | −0.672712 | + | 0.672712i | −0.958340 | − | 0.285629i | \(-0.907798\pi\) |
0.285629 | + | 0.958340i | \(0.407798\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.14162 | −0.545343 | −0.272672 | − | 0.962107i | \(-0.587907\pi\) | ||||
−0.272672 | + | 0.962107i | \(0.587907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.7990 | − | 19.7990i | −1.17693 | − | 1.17693i | −0.980523 | − | 0.196405i | \(-0.937073\pi\) |
−0.196405 | − | 0.980523i | \(-0.562927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.39230 | 0.377326 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8564 | −0.638612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.9019 | + | 13.9019i | 0.812158 | + | 0.812158i | 0.984957 | − | 0.172799i | \(-0.0552812\pi\) |
−0.172799 | + | 0.984957i | \(0.555281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.4959 | 2.00843 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | − | 6.00000i | 0.346989 | − | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.92820 | − | 4.92820i | −0.284057 | − | 0.284057i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 11.5911i | − | 0.663705i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.03528 | − | 1.03528i | 0.0590863 | − | 0.0590863i | −0.676946 | − | 0.736033i | \(-0.736697\pi\) |
0.736033 | + | 0.676946i | \(0.236697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.14359i | 0.121552i | 0.998151 | + | 0.0607760i | \(0.0193575\pi\) | ||||
−0.998151 | + | 0.0607760i | \(0.980642\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.00000i | − | 0.113047i | −0.998401 | − | 0.0565233i | \(-0.981998\pi\) | ||
0.998401 | − | 0.0565233i | \(-0.0180015\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.03339 | + | 2.03339i | −0.114206 | + | 0.114206i | −0.761901 | − | 0.647694i | \(-0.775733\pi\) |
0.647694 | + | 0.761901i | \(0.275733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.38323i | 0.189425i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.8564 | + | 27.8564i | 1.54997 | + | 1.54997i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.26795 | − | 4.26795i | 0.236743 | − | 0.236743i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.6969 | −0.810268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.4901 | + | 16.4901i | 0.906377 | + | 0.906377i | 0.995978 | − | 0.0896005i | \(-0.0285590\pi\) |
−0.0896005 | + | 0.995978i | \(0.528559\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.9282 | 0.815615 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.7846 | 1.24116 | 0.620578 | − | 0.784144i | \(-0.286898\pi\) | ||||
0.620578 | + | 0.784144i | \(0.286898\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.69213 | + | 6.69213i | 0.362399 | + | 0.362399i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.875644 | + | 0.875644i | −0.0470071 | + | 0.0470071i | −0.730220 | − | 0.683213i | \(-0.760582\pi\) |
0.683213 | + | 0.730220i | \(0.260582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.3923 | + | 13.3923i | 0.716874 | + | 0.716874i | 0.967964 | − | 0.251090i | \(-0.0807890\pi\) |
−0.251090 | + | 0.967964i | \(0.580789\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 31.5660i | − | 1.68009i | −0.542519 | − | 0.840043i | \(-0.682529\pi\) | ||
0.542519 | − | 0.840043i | \(-0.317471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.0459 | + | 27.0459i | −1.43545 | + | 1.43545i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.8564i | − | 1.25909i | −0.776963 | − | 0.629546i | \(-0.783241\pi\) | ||
0.776963 | − | 0.629546i | \(-0.216759\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 36.7128i | − | 1.93225i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.52056 | − | 9.52056i | 0.498329 | − | 0.498329i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3848i | 0.959678i | 0.877357 | + | 0.479839i | \(0.159305\pi\) | ||||
−0.877357 | + | 0.479839i | \(0.840695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.6603 | − | 11.6603i | −0.605370 | − | 0.605370i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.85641 | + | 4.85641i | −0.251455 | + | 0.251455i | −0.821567 | − | 0.570112i | \(-0.806900\pi\) |
0.570112 | + | 0.821567i | \(0.306900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00481 | −0.412269 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.20736 | − | 3.20736i | −0.164751 | − | 0.164751i | 0.619917 | − | 0.784668i | \(-0.287166\pi\) |
−0.784668 | + | 0.619917i | \(0.787166\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.5359 | −0.947140 | −0.473570 | − | 0.880756i | \(-0.657035\pi\) | ||||
−0.473570 | + | 0.880756i | \(0.657035\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.14351 | + | 8.14351i | 0.412892 | + | 0.412892i | 0.882745 | − | 0.469853i | \(-0.155693\pi\) |
−0.469853 | + | 0.882745i | \(0.655693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.2832 | −0.924623 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.19615 | − | 4.19615i | 0.211131 | − | 0.211131i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3205 | + | 18.3205i | 0.919480 | + | 0.919480i | 0.996991 | − | 0.0775115i | \(-0.0246975\pi\) |
−0.0775115 | + | 0.996991i | \(0.524697\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.2485i | − | 1.11104i | −0.831504 | − | 0.555518i | \(-0.812520\pi\) | ||
0.831504 | − | 0.555518i | \(-0.187480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.8338 | + | 15.8338i | −0.788735 | + | 0.788735i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.60770i | 0.178827i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.39230i | − | 0.316079i | −0.987433 | − | 0.158040i | \(-0.949483\pi\) | ||
0.987433 | − | 0.158040i | \(-0.0505174\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.6264 | + | 12.6264i | −0.621304 | + | 0.621304i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.4655i | 2.03546i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.7321 | + | 10.7321i | 0.524295 | + | 0.524295i | 0.918866 | − | 0.394571i | \(-0.129107\pi\) |
−0.394571 | + | 0.918866i | \(0.629107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.2679 | + | 14.2679i | −0.695377 | + | 0.695377i | −0.963410 | − | 0.268033i | \(-0.913627\pi\) |
0.268033 | + | 0.963410i | \(0.413627\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.0053 | −0.630851 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.24264 | + | 4.24264i | 0.205316 | + | 0.205316i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.3205 | 1.79767 | 0.898833 | − | 0.438292i | \(-0.144416\pi\) | ||||
0.898833 | + | 0.438292i | \(0.144416\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.9282 | −0.717404 | −0.358702 | − | 0.933452i | \(-0.616781\pi\) | ||||
−0.358702 | + | 0.933452i | \(0.616781\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.2832 | + | 18.2832i | 0.874606 | + | 0.874606i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.6985 | −1.41743 | −0.708716 | − | 0.705494i | \(-0.750725\pi\) | ||||
−0.708716 | + | 0.705494i | \(0.750725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.58846 | − | 4.58846i | 0.218004 | − | 0.218004i | −0.589653 | − | 0.807657i | \(-0.700735\pi\) |
0.807657 | + | 0.589653i | \(0.200735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.1244 | − | 31.1244i | −1.47544 | − | 1.47544i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.96524i | − | 0.187131i | −0.995613 | − | 0.0935656i | \(-0.970174\pi\) | ||
0.995613 | − | 0.0935656i | \(-0.0298265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.30890 | + | 3.30890i | −0.155810 | + | 0.155810i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.46410i | 0.443684i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 13.3205i | − | 0.623107i | −0.950229 | − | 0.311554i | \(-0.899151\pi\) | ||
0.950229 | − | 0.311554i | \(-0.100849\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.9682 | + | 12.9682i | −0.603987 | + | 0.603987i | −0.941368 | − | 0.337381i | \(-0.890459\pi\) |
0.337381 | + | 0.941368i | \(0.390459\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.03957i | 0.187735i | 0.995585 | + | 0.0938673i | \(0.0299230\pi\) | ||||
−0.995585 | + | 0.0938673i | \(0.970077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.6603 | − | 21.6603i | −1.00232 | − | 1.00232i | −0.999997 | − | 0.00231971i | \(-0.999262\pi\) |
−0.00231971 | − | 0.999997i | \(-0.500738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.46410 | + | 5.46410i | −0.252309 | + | 0.252309i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.10205 | 0.234593 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.0053 | + | 13.0053i | 0.596725 | + | 0.596725i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7846 | 0.492761 | 0.246381 | − | 0.969173i | \(-0.420759\pi\) | ||||
0.246381 | + | 0.969173i | \(0.420759\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.53590 | −0.389203 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.5312 | + | 35.5312i | 1.61339 | + | 1.61339i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.0807 | 1.04589 | 0.522943 | − | 0.852368i | \(-0.324834\pi\) | ||||
0.522943 | + | 0.852368i | \(0.324834\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.8564 | − | 27.8564i | 1.25714 | − | 1.25714i | 0.304691 | − | 0.952451i | \(-0.401447\pi\) |
0.952451 | − | 0.304691i | \(-0.0985531\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.1962 | + | 12.1962i | 0.549287 | + | 0.549287i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 19.7990i | − | 0.888106i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.6665 | + | 21.6665i | −0.969924 | + | 0.969924i | −0.999561 | − | 0.0296363i | \(-0.990565\pi\) |
0.0296363 | + | 0.999561i | \(0.490565\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.9282i | 1.11149i | 0.831352 | + | 0.555747i | \(0.187568\pi\) | ||||
−0.831352 | + | 0.555747i | \(0.812432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000i | 0.444994i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.5235 | + | 18.5235i | −0.821039 | + | 0.821039i | −0.986257 | − | 0.165218i | \(-0.947167\pi\) |
0.165218 | + | 0.986257i | \(0.447167\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.96953i | 0.308314i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.1962 | + | 20.1962i | 0.889949 | + | 0.889949i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.60770 | − | 7.60770i | 0.334586 | − | 0.334586i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.6012 | −1.42829 | −0.714143 | − | 0.700000i | \(-0.753183\pi\) | ||||
−0.714143 | + | 0.700000i | \(0.753183\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.8338 | + | 15.8338i | 0.692362 | + | 0.692362i | 0.962751 | − | 0.270389i | \(-0.0871525\pi\) |
−0.270389 | + | 0.962751i | \(0.587152\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 48.2487 | 2.10175 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.82894 | − | 7.82894i | −0.339109 | − | 0.339109i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.2528 | −1.09177 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.66025 | − | 3.66025i | 0.157658 | − | 0.157658i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.0526 | + | 27.0526i | 1.16308 | + | 1.16308i | 0.983798 | + | 0.179283i | \(0.0573777\pi\) |
0.179283 | + | 0.983798i | \(0.442622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 29.8744i | − | 1.27968i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.2827 | − | 13.2827i | 0.567928 | − | 0.567928i | −0.363619 | − | 0.931548i | \(-0.618459\pi\) |
0.931548 | + | 0.363619i | \(0.118459\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24.3923i | − | 1.03915i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.07180i | 0.130626i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.2151 | − | 20.2151i | 0.856541 | − | 0.856541i | −0.134388 | − | 0.990929i | \(-0.542907\pi\) |
0.990929 | + | 0.134388i | \(0.0429068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0716i | 0.510574i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.0526 | + | 20.0526i | 0.845115 | + | 0.845115i | 0.989519 | − | 0.144404i | \(-0.0461265\pi\) |
−0.144404 | + | 0.989519i | \(0.546127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.19615 | − | 8.19615i | 0.344815 | − | 0.344815i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.41902 | −0.394866 | −0.197433 | − | 0.980316i | \(-0.563260\pi\) | ||||
−0.197433 | + | 0.980316i | \(0.563260\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7990 | − | 19.7990i | −0.828562 | − | 0.828562i | 0.158756 | − | 0.987318i | \(-0.449252\pi\) |
−0.987318 | + | 0.158756i | \(0.949252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.53590 | −0.355972 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0718 | 1.04375 | 0.521876 | − | 0.853021i | \(-0.325232\pi\) | ||||
0.521876 | + | 0.853021i | \(0.325232\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.1774 | − | 15.1774i | −0.629665 | − | 0.629665i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0716 | 0.499954 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.9282 | − | 16.9282i | 0.698702 | − | 0.698702i | −0.265429 | − | 0.964130i | \(-0.585514\pi\) |
0.964130 | + | 0.265429i | \(0.0855135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.2487 | − | 48.2487i | −1.98805 | − | 1.98805i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.86800i | − | 0.282035i | −0.990007 | − | 0.141017i | \(-0.954963\pi\) | ||
0.990007 | − | 0.141017i | \(-0.0450373\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.4195 | − | 14.4195i | 0.591143 | − | 0.591143i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.32051i | − | 0.0539545i | −0.999636 | − | 0.0269772i | \(-0.991412\pi\) | ||
0.999636 | − | 0.0269772i | \(-0.00858817\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.7846i | − | 1.17415i | −0.809533 | − | 0.587074i | \(-0.800280\pi\) | ||
0.809533 | − | 0.587074i | \(-0.199720\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.1798 | − | 19.1798i | 0.779770 | − | 0.779770i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.82894i | − | 0.317767i | −0.987297 | − | 0.158883i | \(-0.949211\pi\) | ||
0.987297 | − | 0.158883i | \(-0.0507894\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | + | 18.0000i | 0.728202 | + | 0.728202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.3923 | + | 33.3923i | −1.34870 | + | 1.34870i | −0.461630 | + | 0.887073i | \(0.652735\pi\) |
−0.887073 | + | 0.461630i | \(0.847265\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.07107 | 0.284670 | 0.142335 | − | 0.989819i | \(-0.454539\pi\) | ||||
0.142335 | + | 0.989819i | \(0.454539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.04008 | + | 9.04008i | 0.363352 | + | 0.363352i | 0.865045 | − | 0.501694i | \(-0.167290\pi\) |
−0.501694 | + | 0.865045i | \(0.667290\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.7846 | 0.912846 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.2487 | 1.24995 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.0053 | + | 13.0053i | 0.518556 | + | 0.518556i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.0913 | 1.95430 | 0.977148 | − | 0.212562i | \(-0.0681809\pi\) | ||||
0.977148 | + | 0.212562i | \(0.0681809\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.1244 | + | 27.1244i | −1.07640 | + | 1.07640i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.66025 | + | 8.66025i | 0.343132 | + | 0.343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.8033i | 0.900676i | 0.892858 | + | 0.450338i | \(0.148696\pi\) | ||||
−0.892858 | + | 0.450338i | \(0.851304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.0807 | + | 23.0807i | −0.910213 | + | 0.910213i | −0.996289 | − | 0.0860753i | \(-0.972567\pi\) |
0.0860753 | + | 0.996289i | \(0.472567\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.39230i | − | 0.0940512i | −0.998894 | − | 0.0470256i | \(-0.985026\pi\) | ||
0.998894 | − | 0.0470256i | \(-0.0149742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13.0718i | − | 0.513113i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.2867 | + | 32.2867i | −1.26348 | + | 1.26348i | −0.314078 | + | 0.949397i | \(0.601695\pi\) |
−0.949397 | + | 0.314078i | \(0.898305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.7685i | 1.04593i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.3923 | + | 14.3923i | 0.560645 | + | 0.560645i | 0.929491 | − | 0.368846i | \(-0.120247\pi\) |
−0.368846 | + | 0.929491i | \(0.620247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.7846 | + | 19.7846i | −0.769532 | + | 0.769532i | −0.978024 | − | 0.208492i | \(-0.933144\pi\) |
0.208492 | + | 0.978024i | \(0.433144\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28.8391 | −1.11833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00481 | + | 8.00481i | 0.309947 | + | 0.309947i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.39230 | −0.169563 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.7846 | 1.26375 | 0.631877 | − | 0.775069i | \(-0.282285\pi\) | ||||
0.631877 | + | 0.775069i | \(0.282285\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.7613 | + | 14.7613i | 0.567323 | + | 0.567323i | 0.931378 | − | 0.364054i | \(-0.118608\pi\) |
−0.364054 | + | 0.931378i | \(0.618608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.0106 | −0.998197 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.7321 | + | 14.7321i | −0.563706 | + | 0.563706i | −0.930358 | − | 0.366652i | \(-0.880504\pi\) |
0.366652 | + | 0.930358i | \(0.380504\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.19615 | + | 6.19615i | 0.236743 | + | 0.236743i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.5617i | 1.08811i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3533 | − | 15.3533i | 0.584066 | − | 0.584066i | −0.351952 | − | 0.936018i | \(-0.614482\pi\) |
0.936018 | + | 0.351952i | \(0.114482\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.9282i | 0.869716i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.8564i | 0.903626i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.6341 | − | 29.6341i | 1.11927 | − | 1.11927i | 0.127416 | − | 0.991849i | \(-0.459332\pi\) |
0.991849 | − | 0.127416i | \(-0.0406682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 26.0106i | − | 0.981010i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.66025 | − | 3.66025i | −0.137658 | − | 0.137658i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.19615 | + | 5.19615i | −0.195146 | + | 0.195146i | −0.797915 | − | 0.602770i | \(-0.794064\pi\) |
0.602770 | + | 0.797915i | \(0.294064\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.6675 | 1.18596 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.89898 | − | 4.89898i | −0.183211 | − | 0.183211i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.7128 | −1.10810 | −0.554050 | − | 0.832483i | \(-0.686919\pi\) | ||||
−0.554050 | + | 0.832483i | \(0.686919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.7846 | −0.550608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.69402 | + | 5.69402i | 0.211471 | + | 0.211471i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.4543 | 0.387728 | 0.193864 | − | 0.981028i | \(-0.437898\pi\) | ||||
0.193864 | + | 0.981028i | \(0.437898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.3923 | − | 18.3923i | 0.680264 | − | 0.680264i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.4449 | − | 21.4449i | −0.792084 | − | 0.792084i | 0.189749 | − | 0.981833i | \(-0.439233\pi\) |
−0.981833 | + | 0.189749i | \(0.939233\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 5.65685i | − | 0.208373i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.96953 | − | 6.96953i | 0.256378 | − | 0.256378i | −0.567201 | − | 0.823579i | \(-0.691974\pi\) |
0.823579 | + | 0.567201i | \(0.191974\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.1051i | 1.32457i | 0.749253 | + | 0.662284i | \(0.230413\pi\) | ||||
−0.749253 | + | 0.662284i | \(0.769587\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.3923i | 0.820391i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.24316 | − | 9.24316i | 0.337738 | − | 0.337738i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5.00052i | − | 0.182471i | −0.995829 | − | 0.0912357i | \(-0.970918\pi\) | ||
0.995829 | − | 0.0912357i | \(-0.0290817\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.26795 | − | 1.26795i | −0.0461454 | − | 0.0461454i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3397 | + | 17.3397i | −0.630224 | + | 0.630224i | −0.948124 | − | 0.317900i | \(-0.897022\pi\) |
0.317900 | + | 0.948124i | \(0.397022\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.1464 | 0.621558 | 0.310779 | − | 0.950482i | \(-0.399410\pi\) | ||||
0.310779 | + | 0.950482i | \(0.399410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.9348 | + | 10.9348i | 0.395865 | + | 0.395865i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.9282 | 1.11675 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.71281 | 0.350253 | 0.175126 | − | 0.984546i | \(-0.443967\pi\) | ||||
0.175126 | + | 0.984546i | \(0.443967\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.3118 | − | 12.3118i | −0.442825 | − | 0.442825i | 0.450135 | − | 0.892960i | \(-0.351376\pi\) |
−0.892960 | + | 0.450135i | \(0.851376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.5259 | 0.809154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.8564 | − | 23.8564i | 0.854744 | − | 0.854744i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2487 | + | 10.2487i | 0.366728 | + | 0.366728i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.1774i | 0.541705i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.62209 | − | 9.62209i | 0.342991 | − | 0.342991i | −0.514500 | − | 0.857490i | \(-0.672022\pi\) |
0.857490 | + | 0.514500i | \(0.172022\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000i | 0.213335i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.3923i | − | 0.369042i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.1093 | − | 17.1093i | 0.606041 | − | 0.606041i | −0.335868 | − | 0.941909i | \(-0.609030\pi\) |
0.941909 | + | 0.335868i | \(0.109030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 54.8497i | − | 1.94044i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.60770 | − | 3.60770i | −0.127313 | − | 0.127313i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.46410 | − | 9.46410i | 0.333566 | − | 0.333566i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.1475 | −0.954454 | −0.477227 | − | 0.878780i | \(-0.658358\pi\) | ||||
−0.477227 | + | 0.878780i | \(0.658358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.79367 | + | 6.79367i | 0.238558 | + | 0.238558i | 0.816253 | − | 0.577695i | \(-0.196048\pi\) |
−0.577695 | + | 0.816253i | \(0.696048\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.53590 | −0.0888286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.7846 | −1.28693 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.48717 | − | 7.48717i | −0.261304 | − | 0.261304i | 0.564280 | − | 0.825584i | \(-0.309154\pi\) |
−0.825584 | + | 0.564280i | \(0.809154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.5660 | −1.10032 | −0.550160 | − | 0.835059i | \(-0.685433\pi\) | ||||
−0.550160 | + | 0.835059i | \(0.685433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.3923 | + | 16.3923i | −0.570016 | + | 0.570016i | −0.932133 | − | 0.362117i | \(-0.882054\pi\) |
0.362117 | + | 0.932133i | \(0.382054\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.80385 | − | 4.80385i | −0.166845 | − | 0.166845i | 0.618746 | − | 0.785591i | \(-0.287641\pi\) |
−0.785591 | + | 0.618746i | \(0.787641\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 26.3896i | − | 0.914345i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.6264 | + | 12.6264i | −0.436954 | + | 0.436954i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 50.7846i | − | 1.75328i | −0.481147 | − | 0.876640i | \(-0.659780\pi\) | ||
0.481147 | − | 0.876640i | \(-0.340220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.3205i | 0.631742i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.5230 | + | 13.5230i | −0.465204 | + | 0.465204i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0406i | 0.482441i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.53590 | + | 8.53590i | 0.292607 | + | 0.292607i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.7846 | − | 35.7846i | 1.22524 | − | 1.22524i | 0.259498 | − | 0.965744i | \(-0.416443\pi\) |
0.965744 | − | 0.259498i | \(-0.0835571\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.3190 | 0.830722 | 0.415361 | − | 0.909657i | \(-0.363655\pi\) | ||||
0.415361 | + | 0.909657i | \(0.363655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.5660 | − | 31.5660i | −1.07702 | − | 1.07702i | −0.996775 | − | 0.0802414i | \(-0.974431\pi\) |
−0.0802414 | − | 0.996775i | \(-0.525569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.6077 | −0.395131 | −0.197565 | − | 0.980290i | \(-0.563303\pi\) | ||||
−0.197565 | + | 0.980290i | \(0.563303\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.3205 | −0.724919 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.59008 | − | 1.59008i | −0.0539397 | − | 0.0539397i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.3843 | 0.453508 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.92820 | + | 6.92820i | −0.234216 | + | 0.234216i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5359 | + | 11.5359i | 0.389540 | + | 0.389540i | 0.874523 | − | 0.484984i | \(-0.161174\pi\) |
−0.484984 | + | 0.874523i | \(0.661174\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.96902i | 0.0663378i | 0.999450 | + | 0.0331689i | \(0.0105599\pi\) | ||||
−0.999450 | + | 0.0331689i | \(0.989440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.1827 | − | 28.1827i | 0.948425 | − | 0.948425i | −0.0503091 | − | 0.998734i | \(-0.516021\pi\) |
0.998734 | + | 0.0503091i | \(0.0160207\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 46.9282i | − | 1.57569i | −0.615870 | − | 0.787847i | \(-0.711196\pi\) | ||
0.615870 | − | 0.787847i | \(-0.288804\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19.8564i | − | 0.665962i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −54.8497 | + | 54.8497i | −1.83548 | + | 1.83548i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.1822i | 0.774896i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.1244 | − | 21.1244i | −0.704537 | − | 0.704537i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.5167 | − | 43.5167i | 1.44975 | − | 1.44975i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.10583 | 0.103241 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.2122 | − | 11.2122i | −0.372294 | − | 0.372294i | 0.496018 | − | 0.868312i | \(-0.334795\pi\) |
−0.868312 | + | 0.496018i | \(0.834795\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.1769 | −0.436571 | −0.218285 | − | 0.975885i | \(-0.570046\pi\) | ||||
−0.218285 | + | 0.975885i | \(0.570046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.7128 | 0.520018 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.79796 | − | 9.79796i | −0.323557 | − | 0.323557i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.5259 | 0.743060 | 0.371530 | − | 0.928421i | \(-0.378833\pi\) | ||||
0.371530 | + | 0.928421i | \(0.378833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.2487 | + | 24.2487i | −0.798156 | + | 0.798156i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.07180 | + | 6.07180i | 0.199639 | + | 0.199639i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.1464i | 0.562556i | 0.959626 | + | 0.281278i | \(0.0907583\pi\) | ||||
−0.959626 | + | 0.281278i | \(0.909242\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.3896 | + | 26.3896i | −0.864884 | + | 0.864884i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.9282i | 0.488204i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 30.0000i | − | 0.980057i | −0.871706 | − | 0.490029i | \(-0.836986\pi\) | ||
0.871706 | − | 0.490029i | \(-0.163014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.4582 | − | 29.4582i | 0.960311 | − | 0.960311i | −0.0389305 | − | 0.999242i | \(-0.512395\pi\) |
0.999242 | + | 0.0389305i | \(0.0123951\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.6579i | 0.509891i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.3923 | − | 30.3923i | −0.987617 | − | 0.987617i | 0.0123071 | − | 0.999924i | \(-0.496082\pi\) |
−0.999924 | + | 0.0123071i | \(0.996082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.53590 | − | 8.53590i | 0.277087 | − | 0.277087i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.6307 | 0.506327 | 0.253164 | − | 0.967423i | \(-0.418529\pi\) | ||||
0.253164 | + | 0.967423i | \(0.418529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.0106 | + | 26.0106i | 0.841685 | + | 0.841685i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.53590 | −0.146472 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −52.5692 | −1.69578 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −44.0165 | − | 44.0165i | −1.41694 | − | 1.41694i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.0913 | −1.57867 | −0.789335 | − | 0.613962i | \(-0.789575\pi\) | ||||
−0.789335 | + | 0.613962i | \(0.789575\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.9808 | + | 16.9808i | −0.544939 | + | 0.544939i | −0.924973 | − | 0.380034i | \(-0.875912\pi\) |
0.380034 | + | 0.924973i | \(0.375912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.39230 | − | 8.39230i | −0.269045 | − | 0.269045i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.69161i | 0.0541196i | 0.999634 | + | 0.0270598i | \(0.00861445\pi\) | ||||
−0.999634 | + | 0.0270598i | \(0.991386\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.7942 | + | 11.7942i | −0.376944 | + | 0.376944i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.6410i | 1.23246i | 0.787567 | + | 0.616229i | \(0.211340\pi\) | ||||
−0.787567 | + | 0.616229i | \(0.788660\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 64.6410i | 2.05963i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0716 | − | 12.0716i | 0.383854 | − | 0.383854i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.28169i | − | 0.104246i | −0.998641 | − | 0.0521232i | \(-0.983401\pi\) | ||
0.998641 | − | 0.0521232i | \(-0.0165989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.0526 | − | 38.0526i | −1.20635 | − | 1.20635i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.0000 | + | 21.0000i | −0.665077 | + | 0.665077i | −0.956572 | − | 0.291496i | \(-0.905847\pi\) |
0.291496 | + | 0.956572i | \(0.405847\pi\) | |||||||
\(998\) | 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 | 2304.2.l.f.1727.1 | yes | 8 | |
3.2 | odd | 2 | 2304.2.l.b.1727.4 | yes | 8 | ||
4.3 | odd | 2 | 2304.2.l.b.1727.1 | yes | 8 | ||
8.3 | odd | 2 | 2304.2.l.g.1727.4 | yes | 8 | ||
8.5 | even | 2 | 2304.2.l.c.1727.4 | yes | 8 | ||
12.11 | even | 2 | inner | 2304.2.l.f.1727.4 | yes | 8 | |
16.3 | odd | 4 | 2304.2.l.g.575.1 | yes | 8 | ||
16.5 | even | 4 | inner | 2304.2.l.f.575.4 | yes | 8 | |
16.11 | odd | 4 | 2304.2.l.b.575.4 | yes | 8 | ||
16.13 | even | 4 | 2304.2.l.c.575.1 | yes | 8 | ||
24.5 | odd | 2 | 2304.2.l.g.1727.1 | yes | 8 | ||
24.11 | even | 2 | 2304.2.l.c.1727.1 | yes | 8 | ||
48.5 | odd | 4 | 2304.2.l.b.575.1 | ✓ | 8 | ||
48.11 | even | 4 | inner | 2304.2.l.f.575.1 | yes | 8 | |
48.29 | odd | 4 | 2304.2.l.g.575.4 | yes | 8 | ||
48.35 | even | 4 | 2304.2.l.c.575.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2304.2.l.b.575.1 | ✓ | 8 | 48.5 | odd | 4 | ||
2304.2.l.b.575.4 | yes | 8 | 16.11 | odd | 4 | ||
2304.2.l.b.1727.1 | yes | 8 | 4.3 | odd | 2 | ||
2304.2.l.b.1727.4 | yes | 8 | 3.2 | odd | 2 | ||
2304.2.l.c.575.1 | yes | 8 | 16.13 | even | 4 | ||
2304.2.l.c.575.4 | yes | 8 | 48.35 | even | 4 | ||
2304.2.l.c.1727.1 | yes | 8 | 24.11 | even | 2 | ||
2304.2.l.c.1727.4 | yes | 8 | 8.5 | even | 2 | ||
2304.2.l.f.575.1 | yes | 8 | 48.11 | even | 4 | inner | |
2304.2.l.f.575.4 | yes | 8 | 16.5 | even | 4 | inner | |
2304.2.l.f.1727.1 | yes | 8 | 1.1 | even | 1 | trivial | |
2304.2.l.f.1727.4 | yes | 8 | 12.11 | even | 2 | inner | |
2304.2.l.g.575.1 | yes | 8 | 16.3 | odd | 4 | ||
2304.2.l.g.575.4 | yes | 8 | 48.29 | odd | 4 | ||
2304.2.l.g.1727.1 | yes | 8 | 24.5 | odd | 2 | ||
2304.2.l.g.1727.4 | yes | 8 | 8.3 | odd | 2 |