Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (of order \(3\), 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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1801.2 | ||
Root | \(-2.19149i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.1801 |
Dual form | 2520.2.bi.s.361.2 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.780339 | + | 2.52806i | −0.294941 | + | 0.955516i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.39788 | + | 4.15326i | 0.722989 | + | 1.25225i | 0.959796 | + | 0.280697i | \(0.0905657\pi\) |
−0.236807 | + | 0.971557i | \(0.576101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.94151 | 1.64788 | 0.823939 | − | 0.566678i | \(-0.191772\pi\) | ||||
0.823939 | + | 0.566678i | \(0.191772\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.41674 | − | 5.91796i | −0.828680 | − | 1.43532i | −0.899074 | − | 0.437797i | \(-0.855759\pi\) |
0.0703939 | − | 0.997519i | \(-0.477574\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.26995 | + | 7.39577i | −0.979593 | + | 1.69671i | −0.315733 | + | 0.948848i | \(0.602250\pi\) |
−0.663860 | + | 0.747857i | \(0.731083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.48961 | + | 7.77623i | −0.936148 | + | 1.62146i | −0.163574 | + | 0.986531i | \(0.552302\pi\) |
−0.772574 | + | 0.634925i | \(0.781031\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.414934 | −0.0770514 | −0.0385257 | − | 0.999258i | \(-0.512266\pi\) | ||||
−0.0385257 | + | 0.999258i | \(0.512266\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.80796 | − | 4.86353i | −0.504325 | − | 0.873516i | −0.999987 | − | 0.00500080i | \(-0.998408\pi\) |
0.495663 | − | 0.868515i | \(-0.334925\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.79919 | + | 1.93982i | 0.304119 | + | 0.327890i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.79919 | + | 4.84834i | −0.460184 | + | 0.797063i | −0.998970 | − | 0.0453805i | \(-0.985550\pi\) |
0.538786 | + | 0.842443i | \(0.318883\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.325591 | −0.0508487 | −0.0254244 | − | 0.999677i | \(-0.508094\pi\) | ||||
−0.0254244 | + | 0.999677i | \(0.508094\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.90381 | 0.595325 | 0.297663 | − | 0.954671i | \(-0.403793\pi\) | ||||
0.297663 | + | 0.954671i | \(0.403793\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.86864 | − | 8.43273i | 0.710164 | − | 1.23004i | −0.254631 | − | 0.967038i | \(-0.581954\pi\) |
0.964795 | − | 0.263002i | \(-0.0847126\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.78214 | − | 3.94548i | −0.826020 | − | 0.563641i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.927128 | + | 1.60583i | 0.127351 | + | 0.220578i | 0.922649 | − | 0.385640i | \(-0.126019\pi\) |
−0.795299 | + | 0.606218i | \(0.792686\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.79577 | 0.646661 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.58830 | − | 7.94717i | −0.597346 | − | 1.03463i | −0.993211 | − | 0.116325i | \(-0.962889\pi\) |
0.395865 | − | 0.918309i | \(-0.370445\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.33063 | + | 10.9650i | −0.810554 | + | 1.40392i | 0.101923 | + | 0.994792i | \(0.467500\pi\) |
−0.912477 | + | 0.409128i | \(0.865833\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.97076 | − | 5.14550i | 0.368477 | − | 0.638221i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.34102 | + | 2.32271i | 0.163831 | + | 0.283764i | 0.936240 | − | 0.351362i | \(-0.114281\pi\) |
−0.772408 | + | 0.635126i | \(0.780948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.17660 | −0.614349 | −0.307175 | − | 0.951653i | \(-0.599384\pi\) | ||||
−0.307175 | + | 0.951653i | \(0.599384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.40454 | + | 7.62889i | 0.515513 | + | 0.892894i | 0.999838 | + | 0.0180061i | \(0.00573183\pi\) |
−0.484325 | + | 0.874888i | \(0.660935\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.3708 | + | 2.82104i | −1.40979 | + | 0.321487i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.81624 | + | 3.14582i | −0.204343 | + | 0.353933i | −0.949923 | − | 0.312483i | \(-0.898839\pi\) |
0.745580 | + | 0.666416i | \(0.232173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.07619 | 0.996241 | 0.498120 | − | 0.867108i | \(-0.334024\pi\) | ||||
0.498120 | + | 0.867108i | \(0.334024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.83347 | −0.741194 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.646788 | − | 1.12027i | 0.0685594 | − | 0.118748i | −0.829708 | − | 0.558198i | \(-0.811493\pi\) |
0.898267 | + | 0.439449i | \(0.144826\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.63640 | + | 15.0205i | −0.486026 | + | 1.57457i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.26995 | + | 7.39577i | 0.438087 | + | 0.758790i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0101 | −1.01637 | −0.508184 | − | 0.861248i | \(-0.669683\pi\) | ||||
−0.508184 | + | 0.861248i | \(0.669683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.570762 | − | 0.988589i | −0.0567930 | − | 0.0983683i | 0.836231 | − | 0.548377i | \(-0.184754\pi\) |
−0.893024 | + | 0.450009i | \(0.851421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.58799 | + | 11.4107i | −0.649134 | + | 1.12433i | 0.334196 | + | 0.942504i | \(0.391535\pi\) |
−0.983330 | + | 0.181830i | \(0.941798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.41674 | + | 7.65001i | −0.426982 | + | 0.739554i | −0.996603 | − | 0.0823529i | \(-0.973757\pi\) |
0.569621 | + | 0.821907i | \(0.307090\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.75775 | + | 9.97272i | 0.551493 | + | 0.955214i | 0.998167 | + | 0.0605170i | \(0.0192749\pi\) |
−0.446674 | + | 0.894697i | \(0.647392\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.12136 | 0.105488 | 0.0527442 | − | 0.998608i | \(-0.483203\pi\) | ||||
0.0527442 | + | 0.998608i | \(0.483203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.48961 | + | 7.77623i | 0.418658 | + | 0.725137i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.6272 | − | 4.01968i | 1.61588 | − | 0.368484i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.99969 | + | 10.3918i | −0.545426 | + | 0.944706i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.54674 | −0.492194 | −0.246097 | − | 0.969245i | \(-0.579148\pi\) | ||||
−0.246097 | + | 0.969245i | \(0.579148\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.19042 | + | 3.79391i | −0.191378 | + | 0.331476i | −0.945707 | − | 0.325020i | \(-0.894629\pi\) |
0.754329 | + | 0.656496i | \(0.227962\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.3649 | − | 16.5659i | −1.33231 | − | 1.43644i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.75986 | + | 15.1725i | 0.748406 | + | 1.29628i | 0.948587 | + | 0.316518i | \(0.102514\pi\) |
−0.200181 | + | 0.979759i | \(0.564153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.727208 | 0.0616810 | 0.0308405 | − | 0.999524i | \(-0.490182\pi\) | ||||
0.0308405 | + | 0.999524i | \(0.490182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.2471 | + | 24.6766i | 1.19140 | + | 2.06356i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.207467 | + | 0.359344i | −0.0172292 | + | 0.0298419i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5776 | − | 18.3209i | 0.866551 | − | 1.50091i | 0.00105144 | − | 0.999999i | \(-0.499665\pi\) |
0.865499 | − | 0.500910i | \(-0.167001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.02582 | − | 6.97292i | −0.327617 | − | 0.567449i | 0.654422 | − | 0.756130i | \(-0.272912\pi\) |
−0.982038 | + | 0.188681i | \(0.939579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.61592 | −0.451082 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.34948 | + | 16.1938i | 0.746170 | + | 1.29240i | 0.949646 | + | 0.313324i | \(0.101443\pi\) |
−0.203477 | + | 0.979080i | \(0.565224\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.1553 | − | 17.4181i | −1.27322 | − | 1.37274i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.70642 | + | 11.6159i | −0.525288 | + | 0.909825i | 0.474279 | + | 0.880375i | \(0.342709\pi\) |
−0.999566 | + | 0.0294501i | \(0.990624\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.97922 | 0.540068 | 0.270034 | − | 0.962851i | \(-0.412965\pi\) | ||||
0.270034 | + | 0.962851i | \(0.412965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.3016 | 1.71550 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.48781 | − | 4.30901i | 0.189144 | − | 0.327608i | −0.755821 | − | 0.654779i | \(-0.772762\pi\) |
0.944965 | + | 0.327171i | \(0.106095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.57953 | − | 0.588234i | 0.194994 | − | 0.0444663i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.40797 | + | 2.43867i | 0.105236 | + | 0.182275i | 0.913835 | − | 0.406086i | \(-0.133107\pi\) |
−0.808598 | + | 0.588361i | \(0.799773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5922 | 0.861638 | 0.430819 | − | 0.902438i | \(-0.358225\pi\) | ||||
0.430819 | + | 0.902438i | \(0.358225\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.79919 | + | 4.84834i | 0.205801 | + | 0.356457i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.3859 | − | 28.3812i | 1.19825 | − | 2.07544i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.27279 | − | 10.8648i | 0.453883 | − | 0.786149i | −0.544740 | − | 0.838605i | \(-0.683372\pi\) |
0.998623 | + | 0.0524561i | \(0.0167050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.14867 | + | 10.6498i | 0.442591 | + | 0.766590i | 0.997881 | − | 0.0650668i | \(-0.0207261\pi\) |
−0.555290 | + | 0.831657i | \(0.687393\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7518 | −0.908525 | −0.454262 | − | 0.890868i | \(-0.650097\pi\) | ||||
−0.454262 | + | 0.890868i | \(0.650097\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.0635238 | − | 0.110027i | −0.00450309 | − | 0.00779957i | 0.863765 | − | 0.503895i | \(-0.168100\pi\) |
−0.868268 | + | 0.496095i | \(0.834767\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.323790 | − | 1.04898i | 0.0227256 | − | 0.0736238i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.162795 | + | 0.281970i | −0.0113701 | + | 0.0196936i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −40.9553 | −2.83294 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5909 | 1.14217 | 0.571083 | − | 0.820892i | \(-0.306523\pi\) | ||||
0.571083 | + | 0.820892i | \(0.306523\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.95190 | − | 3.38080i | 0.133119 | − | 0.230568i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.4864 | − | 3.30348i | 0.983404 | − | 0.224255i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.3006 | − | 35.1616i | −1.36556 | − | 2.36523i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.00438 | −0.201188 | −0.100594 | − | 0.994928i | \(-0.532074\pi\) | ||||
−0.100594 | + | 0.994928i | \(0.532074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.270991 | + | 0.469370i | 0.0179863 | + | 0.0311532i | 0.874878 | − | 0.484343i | \(-0.160941\pi\) |
−0.856892 | + | 0.515496i | \(0.827608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.33094 | − | 5.76935i | 0.220114 | − | 0.381249i | −0.734728 | − | 0.678362i | \(-0.762690\pi\) |
0.954843 | + | 0.297112i | \(0.0960236\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1383 | + | 22.7562i | −0.860717 | + | 1.49081i | 0.0105206 | + | 0.999945i | \(0.496651\pi\) |
−0.871238 | + | 0.490861i | \(0.836682\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.86864 | − | 8.43273i | −0.317595 | − | 0.550091i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1831 | 1.37022 | 0.685109 | − | 0.728440i | \(-0.259754\pi\) | ||||
0.685109 | + | 0.728440i | \(0.259754\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.206732 | + | 0.358071i | 0.0133168 | + | 0.0230654i | 0.872607 | − | 0.488423i | \(-0.162428\pi\) |
−0.859290 | + | 0.511488i | \(0.829094\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.30796 | + | 3.03474i | −0.403001 | + | 0.193882i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.3699 | + | 43.9420i | −1.61425 | + | 2.79596i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.7010 | −1.36976 | −0.684879 | − | 0.728657i | \(-0.740145\pi\) | ||||
−0.684879 | + | 0.728657i | \(0.740145\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −43.0622 | −2.70730 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.14755 | − | 10.6479i | 0.383473 | − | 0.664195i | −0.608083 | − | 0.793874i | \(-0.708061\pi\) |
0.991556 | + | 0.129678i | \(0.0413945\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0726 | − | 10.8599i | −0.625879 | − | 0.674799i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.41915 | − | 4.19010i | −0.149171 | − | 0.258373i | 0.781750 | − | 0.623592i | \(-0.214327\pi\) |
−0.930921 | + | 0.365219i | \(0.880994\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.85426 | 0.113906 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.01754 | + | 5.22653i | 0.183983 | + | 0.318667i | 0.943233 | − | 0.332131i | \(-0.107768\pi\) |
−0.759251 | + | 0.650798i | \(0.774434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0748 | − | 24.3782i | 0.854980 | − | 1.48087i | −0.0216828 | − | 0.999765i | \(-0.506902\pi\) |
0.876663 | − | 0.481105i | \(-0.159764\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.39788 | − | 4.15326i | 0.144598 | − | 0.250451i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.51943 | − | 4.36378i | −0.151378 | − | 0.262194i | 0.780356 | − | 0.625335i | \(-0.215038\pi\) |
−0.931734 | + | 0.363141i | \(0.881704\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.05865 | −0.421084 | −0.210542 | − | 0.977585i | \(-0.567523\pi\) | ||||
−0.210542 | + | 0.977585i | \(0.567523\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.4422 | + | 19.8186i | 0.680171 | + | 1.17809i | 0.974928 | + | 0.222519i | \(0.0714278\pi\) |
−0.294758 | + | 0.955572i | \(0.595239\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.254071 | − | 0.823112i | 0.0149974 | − | 0.0485868i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8482 | + | 25.7178i | −0.873421 | + | 1.51281i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.8308 | 1.10011 | 0.550053 | − | 0.835130i | \(-0.314608\pi\) | ||||
0.550053 | + | 0.835130i | \(0.314608\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.17660 | −0.534282 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −26.6751 | + | 46.2026i | −1.54266 | + | 2.67196i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.04630 | + | 9.86905i | −0.175586 | + | 0.568842i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.33063 | + | 10.9650i | 0.362491 | + | 0.627852i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.1788 | −0.980449 | −0.490224 | − | 0.871596i | \(-0.663085\pi\) | ||||
−0.490224 | + | 0.871596i | \(0.663085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.19415 | + | 5.53243i | 0.181124 | + | 0.313715i | 0.942263 | − | 0.334873i | \(-0.108693\pi\) |
−0.761140 | + | 0.648588i | \(0.775360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.754520 | − | 1.30687i | 0.0426480 | − | 0.0738685i | −0.843913 | − | 0.536479i | \(-0.819754\pi\) |
0.886561 | + | 0.462611i | \(0.153087\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.4093 | − | 23.2255i | 0.753140 | − | 1.30448i | −0.193154 | − | 0.981168i | \(-0.561872\pi\) |
0.946294 | − | 0.323308i | \(-0.104795\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.994965 | − | 1.72333i | −0.0557073 | − | 0.0964879i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 58.3571 | 3.24708 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.97076 | − | 5.14550i | −0.164788 | − | 0.285421i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.5192 | + | 18.8886i | 0.965866 | + | 1.04136i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.780259 | + | 1.35145i | −0.0428869 | + | 0.0742823i | −0.886672 | − | 0.462399i | \(-0.846989\pi\) |
0.843785 | + | 0.536681i | \(0.180322\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.68204 | 0.146535 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.7841 | 1.24113 | 0.620564 | − | 0.784156i | \(-0.286904\pi\) | ||||
0.620564 | + | 0.784156i | \(0.286904\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4663 | − | 23.3244i | 0.729242 | − | 1.26308i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.4864 | − | 11.5388i | 0.782194 | − | 0.623035i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.74622 | − | 3.02453i | −0.0937417 | − | 0.162365i | 0.815341 | − | 0.578981i | \(-0.196549\pi\) |
−0.909083 | + | 0.416616i | \(0.863216\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.192385 | 0.0102981 | 0.00514907 | − | 0.999987i | \(-0.498361\pi\) | ||||
0.00514907 | + | 0.999987i | \(0.498361\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.69716 | + | 11.5998i | 0.356454 | + | 0.617396i | 0.987366 | − | 0.158459i | \(-0.0506524\pi\) |
−0.630912 | + | 0.775854i | \(0.717319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.58830 | + | 4.48307i | −0.137373 | + | 0.237936i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.50465 | + | 16.4625i | −0.501636 | + | 0.868859i | 0.498362 | + | 0.866969i | \(0.333935\pi\) |
−0.999998 | + | 0.00189015i | \(0.999398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −26.9649 | − | 46.7046i | −1.41921 | − | 2.45814i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.80908 | 0.461089 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.773990 | + | 1.34059i | 0.0404019 | + | 0.0699782i | 0.885519 | − | 0.464603i | \(-0.153803\pi\) |
−0.845117 | + | 0.534581i | \(0.820469\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.78311 | + | 1.09074i | −0.248327 | + | 0.0566282i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0952 | − | 26.1457i | 0.781601 | − | 1.35377i | −0.149408 | − | 0.988776i | \(-0.547737\pi\) |
0.931009 | − | 0.364997i | \(-0.118930\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.46534 | −0.126971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.2959 | −0.939796 | −0.469898 | − | 0.882721i | \(-0.655709\pi\) | ||||
−0.469898 | + | 0.882721i | \(0.655709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.3590 | + | 21.4064i | −0.631514 | + | 1.09382i | 0.355728 | + | 0.934590i | \(0.384233\pi\) |
−0.987242 | + | 0.159226i | \(0.949100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.74233 | + | 12.1240i | −0.190727 | + | 0.617895i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.2496 | − | 19.4848i | −0.570375 | − | 0.987918i | −0.996527 | − | 0.0832670i | \(-0.973465\pi\) |
0.426152 | − | 0.904651i | \(-0.359869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61.3592 | 3.10307 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.81624 | + | 3.14582i | 0.0913851 | + | 0.158284i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.3594 | − | 26.6032i | 0.770865 | − | 1.33518i | −0.166225 | − | 0.986088i | \(-0.553158\pi\) |
0.937090 | − | 0.349089i | \(-0.113509\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.3218 | + | 24.8062i | −0.715199 | + | 1.23876i | 0.247684 | + | 0.968841i | \(0.420331\pi\) |
−0.962883 | + | 0.269920i | \(0.913003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.6835 | − | 28.8967i | −0.831066 | − | 1.43945i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.8485 | −1.33083 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.07506 | − | 8.79027i | −0.250946 | − | 0.434651i | 0.712841 | − | 0.701326i | \(-0.247408\pi\) |
−0.963786 | + | 0.266675i | \(0.914075\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.6713 | − | 5.39799i | 1.16479 | − | 0.265618i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.53809 | − | 7.86021i | 0.222766 | − | 0.385842i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.59691 | −0.126868 | −0.0634338 | − | 0.997986i | \(-0.520205\pi\) | ||||
−0.0634338 | + | 0.997986i | \(0.520205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.28805 | −0.452672 | −0.226336 | − | 0.974049i | \(-0.572675\pi\) | ||||
−0.226336 | + | 0.974049i | \(0.572675\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.41674 | + | 5.91796i | −0.165736 | + | 0.287063i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.7800 | − | 24.5606i | −1.10240 | − | 1.18857i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.8655 | − | 32.6760i | −0.908718 | − | 1.57395i | −0.815847 | − | 0.578268i | \(-0.803729\pi\) |
−0.0928719 | − | 0.995678i | \(-0.529605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.7159 | 1.76445 | 0.882226 | − | 0.470826i | \(-0.156044\pi\) | ||||
0.882226 | + | 0.470826i | \(0.156044\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.3408 | − | 66.4082i | −1.83409 | − | 3.17673i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.66191 | − | 15.0029i | 0.413410 | − | 0.716048i | −0.581850 | − | 0.813296i | \(-0.697671\pi\) |
0.995260 | + | 0.0972486i | \(0.0310042\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.30542 | − | 5.72516i | 0.157045 | − | 0.272011i | −0.776756 | − | 0.629801i | \(-0.783136\pi\) |
0.933802 | + | 0.357790i | \(0.116470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.646788 | − | 1.12027i | −0.0306607 | − | 0.0531059i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.2861 | −0.910168 | −0.455084 | − | 0.890449i | \(-0.650391\pi\) | ||||
−0.455084 | + | 0.890449i | \(0.650391\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.780729 | − | 1.35226i | −0.0367631 | − | 0.0636755i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.6899 | + | 11.5255i | 0.501151 | + | 0.540323i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.51700 | − | 16.4839i | 0.445186 | − | 0.771086i | −0.552879 | − | 0.833262i | \(-0.686471\pi\) |
0.998065 | + | 0.0621761i | \(0.0198041\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.71780 | 0.219730 | 0.109865 | − | 0.993947i | \(-0.464958\pi\) | ||||
0.109865 | + | 0.993947i | \(0.464958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.3128 | 1.17639 | 0.588193 | − | 0.808721i | \(-0.299840\pi\) | ||||
0.588193 | + | 0.808721i | \(0.299840\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.18992 | − | 14.1854i | 0.378984 | − | 0.656420i | −0.611931 | − | 0.790911i | \(-0.709607\pi\) |
0.990915 | + | 0.134492i | \(0.0429401\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.91840 | + | 1.57767i | −0.319462 | + | 0.0728499i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.36088 | + | 16.2135i | 0.430414 | + | 0.745498i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.53989 | 0.391837 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.07541 | − | 8.79086i | −0.231901 | − | 0.401665i | 0.726466 | − | 0.687202i | \(-0.241161\pi\) |
−0.958368 | + | 0.285537i | \(0.907828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.6314 | + | 28.8065i | −0.758328 | + | 1.31346i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.00504 | + | 8.66898i | −0.227267 | + | 0.393638i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.28938 | − | 7.42942i | −0.194370 | − | 0.336659i | 0.752324 | − | 0.658794i | \(-0.228933\pi\) |
−0.946694 | + | 0.322134i | \(0.895600\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.2669 | 1.41106 | 0.705528 | − | 0.708682i | \(-0.250710\pi\) | ||||
0.705528 | + | 0.708682i | \(0.250710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.41772 | + | 2.45557i | 0.0638510 | + | 0.110593i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.03951 | − | 13.0867i | 0.181197 | − | 0.587020i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.76279 | − | 6.51734i | 0.168446 | − | 0.291756i | −0.769428 | − | 0.638734i | \(-0.779459\pi\) |
0.937874 | + | 0.346977i | \(0.112792\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.11292 | 0.317149 | 0.158575 | − | 0.987347i | \(-0.449310\pi\) | ||||
0.158575 | + | 0.987347i | \(0.449310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.14152 | −0.0507972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.57400 | − | 13.1185i | 0.335711 | − | 0.581469i | −0.647910 | − | 0.761717i | \(-0.724357\pi\) |
0.983621 | + | 0.180248i | \(0.0576899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.7233 | + | 5.18181i | −1.00522 | + | 0.229230i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.58799 | + | 11.4107i | 0.290302 | + | 0.502817i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.6977 | 2.05376 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.76801 | − | 11.7225i | −0.296512 | − | 0.513574i | 0.678823 | − | 0.734302i | \(-0.262490\pi\) |
−0.975336 | + | 0.220728i | \(0.929157\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.3787 | − | 19.7085i | 0.497557 | − | 0.861794i | −0.502439 | − | 0.864613i | \(-0.667564\pi\) |
0.999996 | + | 0.00281888i | \(0.000897277\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.1881 | + | 33.2348i | −0.835847 | + | 1.44773i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.8132 | − | 49.9059i | −1.25275 | − | 2.16982i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.93450 | −0.0837926 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.41674 | + | 7.65001i | 0.190952 | + | 0.330739i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.52171 | − | 33.4755i | 0.108618 | − | 1.44189i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.8916 | + | 18.8648i | −0.468267 | + | 0.811062i | −0.999342 | − | 0.0362623i | \(-0.988455\pi\) |
0.531075 | + | 0.847325i | \(0.321788\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.5155 | 0.493270 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.26935 | −0.182544 | −0.0912721 | − | 0.995826i | \(-0.529093\pi\) | ||||
−0.0912721 | + | 0.995826i | \(0.529093\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.77175 | − | 3.06876i | 0.0754790 | − | 0.130733i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.53554 | − | 7.04637i | −0.277919 | − | 0.299642i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3255 | + | 24.8125i | 0.606991 | + | 1.05134i | 0.991733 | + | 0.128315i | \(0.0409569\pi\) |
−0.384743 | + | 0.923024i | \(0.625710\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.1945 | 0.981024 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.0489 | + | 17.4053i | 0.423512 | + | 0.733544i | 0.996280 | − | 0.0861730i | \(-0.0274638\pi\) |
−0.572768 | + | 0.819717i | \(0.694130\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.560679 | − | 0.971124i | 0.0235879 | − | 0.0408555i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.32186 | + | 9.21773i | −0.223104 | + | 0.386427i | −0.955749 | − | 0.294184i | \(-0.904952\pi\) |
0.732645 | + | 0.680611i | \(0.238286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.75837 | − | 8.24174i | −0.199132 | − | 0.344906i | 0.749115 | − | 0.662439i | \(-0.230479\pi\) |
−0.948247 | + | 0.317533i | \(0.897145\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.97922 | 0.374459 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.84321 | − | 15.3169i | −0.368148 | − | 0.637650i | 0.621128 | − | 0.783709i | \(-0.286675\pi\) |
−0.989276 | + | 0.146058i | \(0.953341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.08251 | + | 22.9451i | −0.293832 | + | 0.951924i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.44629 | + | 7.70120i | −0.184146 | + | 0.318951i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.4738 | 0.679946 | 0.339973 | − | 0.940435i | \(-0.389582\pi\) | ||||
0.339973 | + | 0.940435i | \(0.389582\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.9594 | 1.97613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.41612 | + | 9.38099i | −0.222413 | + | 0.385231i | −0.955540 | − | 0.294861i | \(-0.904727\pi\) |
0.733127 | + | 0.680092i | \(0.238060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.33243 | − | 17.2754i | 0.218608 | − | 0.708222i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.3633 | − | 19.6818i | −0.464292 | − | 0.804177i | 0.534878 | − | 0.844930i | \(-0.320358\pi\) |
−0.999169 | + | 0.0407528i | \(0.987024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.36346 | −0.137198 | −0.0685991 | − | 0.997644i | \(-0.521853\pi\) | ||||
−0.0685991 | + | 0.997644i | \(0.521853\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.99969 | + | 10.3918i | 0.243922 | + | 0.422486i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.6564 | + | 21.9215i | −0.513707 | + | 0.889767i | 0.486166 | + | 0.873866i | \(0.338395\pi\) |
−0.999874 | + | 0.0159007i | \(0.994938\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.9271 | − | 50.1032i | 1.17026 | − | 2.02696i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.97790 | + | 13.8181i | 0.322224 | + | 0.558109i | 0.980947 | − | 0.194277i | \(-0.0622361\pi\) |
−0.658722 | + | 0.752386i | \(0.728903\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.2040 | −1.49778 | −0.748888 | − | 0.662697i | \(-0.769412\pi\) | ||||
−0.748888 | + | 0.662697i | \(0.769412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6698 | + | 34.0690i | 0.790594 | + | 1.36935i | 0.925600 | + | 0.378504i | \(0.123561\pi\) |
−0.135006 | + | 0.990845i | \(0.543105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.32739 | + | 2.50931i | 0.0932450 | + | 0.100533i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.2564 | 1.52538 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.331822 | 0.0132096 | 0.00660481 | − | 0.999978i | \(-0.497898\pi\) | ||||
0.00660481 | + | 0.999978i | \(0.497898\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.77337 | + | 4.80362i | −0.110058 | + | 0.190626i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.3547 | − | 23.4421i | −1.36118 | − | 0.928812i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.8039 | + | 25.6411i | 0.584718 | + | 1.01276i | 0.994911 | + | 0.100763i | \(0.0321282\pi\) |
−0.410192 | + | 0.911999i | \(0.634538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.27639 | −0.129208 | −0.0646042 | − | 0.997911i | \(-0.520578\pi\) | ||||
−0.0646042 | + | 0.997911i | \(0.520578\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.4487 | + | 18.0976i | 0.410779 | + | 0.711490i | 0.994975 | − | 0.100122i | \(-0.0319234\pi\) |
−0.584196 | + | 0.811613i | \(0.698590\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.0044 | − | 38.1128i | 0.863749 | − | 1.49606i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.93656 | − | 10.2824i | 0.232315 | − | 0.402382i | −0.726174 | − | 0.687511i | \(-0.758703\pi\) |
0.958489 | + | 0.285129i | \(0.0920365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.19042 | + | 3.79391i | 0.0855866 | + | 0.148240i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5722 | −0.567653 | −0.283827 | − | 0.958876i | \(-0.591604\pi\) | ||||
−0.283827 | + | 0.958876i | \(0.591604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.37367 | − | 14.5036i | −0.325698 | − | 0.564126i | 0.655955 | − | 0.754800i | \(-0.272266\pi\) |
−0.981653 | + | 0.190674i | \(0.938933\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.0289 | + | 5.02346i | −0.854245 | + | 0.194801i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.86289 | − | 3.22663i | 0.0721315 | − | 0.124935i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.7204 | −2.34409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.7595 | 1.60971 | 0.804855 | − | 0.593471i | \(-0.202243\pi\) | ||||
0.804855 | + | 0.593471i | \(0.202243\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5380 | + | 23.4485i | −0.520308 | + | 0.901199i | 0.479414 | + | 0.877589i | \(0.340849\pi\) |
−0.999721 | + | 0.0236102i | \(0.992484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.81125 | − | 25.3060i | 0.299768 | − | 0.971156i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5859 | + | 26.9955i | 0.596377 | + | 1.03295i | 0.993351 | + | 0.115125i | \(0.0367269\pi\) |
−0.396974 | + | 0.917830i | \(0.629940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.5197 | 0.669394 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.50854 | + | 9.54107i | 0.209859 | + | 0.363486i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.16704 | − | 14.1457i | 0.310689 | − | 0.538129i | −0.667823 | − | 0.744320i | \(-0.732774\pi\) |
0.978512 | + | 0.206192i | \(0.0661070\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.363604 | − | 0.629780i | 0.0137923 | − | 0.0238889i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.11246 | + | 1.92683i | 0.0421373 | + | 0.0729840i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.6205 | −1.87414 | −0.937070 | − | 0.349143i | \(-0.886473\pi\) | ||||
−0.937070 | + | 0.349143i | \(0.886473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.9048 | − | 41.4043i | −0.901587 | − | 1.56159i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.94460 | − | 0.671484i | 0.110743 | − | 0.0252538i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.48953 | + | 16.4363i | −0.356387 | + | 0.617280i | −0.987354 | − | 0.158529i | \(-0.949325\pi\) |
0.630968 | + | 0.775809i | \(0.282658\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.4266 | 1.88849 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.4941 | 1.06562 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.13828 | − | 15.8280i | 0.340800 | − | 0.590283i | −0.643781 | − | 0.765210i | \(-0.722635\pi\) |
0.984582 | + | 0.174926i | \(0.0559687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.7061 | − | 25.5591i | −0.882862 | − | 0.951869i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.207467 | + | 0.359344i | 0.00770514 | + | 0.0133457i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.2878 | −1.01205 | −0.506024 | − | 0.862519i | \(-0.668885\pi\) | ||||
−0.506024 | + | 0.862519i | \(0.668885\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.3383 | − | 23.1026i | −0.493334 | − | 0.854480i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.8175 | − | 30.8609i | 0.658106 | − | 1.13987i | −0.322999 | − | 0.946399i | \(-0.604691\pi\) |
0.981105 | − | 0.193474i | \(-0.0619755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.43121 | + | 11.1392i | −0.236897 | + | 0.410317i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.37114 | + | 11.0351i | 0.234366 | + | 0.405934i | 0.959088 | − | 0.283107i | \(-0.0913652\pi\) |
−0.724722 | + | 0.689041i | \(0.758032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.5025 | −0.458674 | −0.229337 | − | 0.973347i | \(-0.573656\pi\) | ||||
−0.229337 | + | 0.973347i | \(0.573656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5776 | − | 18.3209i | −0.387533 | − | 0.671227i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.8931 | − | 17.1354i | −0.580721 | − | 0.626113i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.50331 | − | 7.79997i | 0.164328 | − | 0.284625i | −0.772088 | − | 0.635515i | \(-0.780788\pi\) |
0.936417 | + | 0.350890i | \(0.114121\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.05164 | −0.293029 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.1180 | 1.67619 | 0.838094 | − | 0.545526i | \(-0.183670\pi\) | ||||
0.838094 | + | 0.545526i | \(0.183670\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.70540 | − | 4.68588i | 0.0980705 | − | 0.169863i | −0.812815 | − | 0.582521i | \(-0.802066\pi\) |
0.910886 | + | 0.412658i | \(0.135400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.7046 | + | 6.77382i | −1.07538 | + | 0.245229i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.2614 | − | 47.2182i | −0.984353 | − | 1.70495i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.36121 | 0.157269 | 0.0786346 | − | 0.996904i | \(-0.474944\pi\) | ||||
0.0786346 | + | 0.996904i | \(0.474944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.38010 | − | 7.58655i | −0.157541 | − | 0.272869i | 0.776440 | − | 0.630191i | \(-0.217023\pi\) |
−0.933981 | + | 0.357322i | \(0.883690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.80796 | + | 4.86353i | −0.100865 | + | 0.174703i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.39026 | − | 2.40799i | 0.0498111 | − | 0.0862753i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4129 | − | 21.4997i | −0.444168 | − | 0.769321i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.6990 | 0.667394 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0341019 | + | 0.0590662i | 0.00121560 | + | 0.00210548i | 0.866633 | − | 0.498947i | \(-0.166280\pi\) |
−0.865417 | + | 0.501052i | \(0.832946\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.875040 | + | 2.83486i | −0.0311128 | + | 0.100796i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.6135 | + | 65.1485i | −1.33569 | + | 2.31349i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.0302 | 1.34710 | 0.673550 | − | 0.739142i | \(-0.264769\pi\) | ||||
0.673550 | + | 0.739142i | \(0.264769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −66.5394 | −2.35400 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.1232 | + | 36.5864i | −0.745420 | + | 1.29111i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.1622 | + | 5.28188i | −0.816359 | + | 0.186162i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.5293 | + | 23.4335i | 0.475666 | + | 0.823877i | 0.999611 | − | 0.0278745i | \(-0.00887387\pi\) |
−0.523946 | + | 0.851752i | \(0.675541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.7345 | 1.00901 | 0.504503 | − | 0.863410i | \(-0.331676\pi\) | ||||
0.504503 | + | 0.863410i | \(0.331676\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.70642 | + | 11.6159i | 0.234916 | + | 0.406886i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.6691 | + | 28.8716i | −0.583176 | + | 1.01009i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.4671 | − | 45.8424i | 0.923708 | − | 1.59991i | 0.130083 | − | 0.991503i | \(-0.458476\pi\) |
0.793626 | − | 0.608406i | \(-0.208191\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.1683 | − | 41.8608i | −0.842455 | − | 1.45917i | −0.887814 | − | 0.460203i | \(-0.847776\pi\) |
0.0453589 | − | 0.998971i | \(-0.485557\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.1524 | −0.978954 | −0.489477 | − | 0.872016i | \(-0.662812\pi\) | ||||
−0.489477 | + | 0.872016i | \(0.662812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.27573 | + | 3.94168i | 0.0790394 | + | 0.136900i | 0.902836 | − | 0.429986i | \(-0.141481\pi\) |
−0.823796 | + | 0.566886i | \(0.808148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.59317 | + | 47.6992i | −0.124496 | + | 1.65268i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.48961 | − | 6.04418i | 0.120763 | − | 0.209167i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.9914 | 1.20804 | 0.604019 | − | 0.796970i | \(-0.293565\pi\) | ||||
0.604019 | + | 0.796970i | \(0.293565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8278 | −0.994063 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.1508 | − | 19.3137i | 0.383598 | − | 0.664412i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.5892 | − | 23.2767i | −0.741813 | − | 0.799796i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.1345 | − | 43.5343i | −0.861601 | − | 1.49234i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.20800 | −0.212558 | −0.106279 | − | 0.994336i | \(-0.533894\pi\) | ||||
−0.106279 | + | 0.994336i | \(0.533894\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.49652 | + | 12.9844i | 0.256076 | + | 0.443537i | 0.965187 | − | 0.261560i | \(-0.0842368\pi\) |
−0.709111 | + | 0.705097i | \(0.750903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.66191 | + | 15.0029i | −0.295540 | + | 0.511891i | −0.975110 | − | 0.221720i | \(-0.928833\pi\) |
0.679570 | + | 0.733611i | \(0.262166\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.09626 | − | 15.7552i | 0.309640 | − | 0.536313i | −0.668643 | − | 0.743583i | \(-0.733125\pi\) |
0.978284 | + | 0.207271i | \(0.0664580\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.48781 | − | 4.30901i | −0.0845880 | − | 0.146511i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.4206 | −0.590952 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.96768 | + | 13.8004i | 0.269974 | + | 0.467609i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.780339 | − | 2.52806i | 0.0263803 | − | 0.0854639i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.1168 | + | 33.1113i | −0.645530 | + | 1.11809i | 0.338649 | + | 0.940913i | \(0.390030\pi\) |
−0.984179 | + | 0.177177i | \(0.943303\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.0744 | −1.08061 | −0.540307 | − | 0.841468i | \(-0.681692\pi\) | ||||
−0.540307 | + | 0.841468i | \(0.681692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.85786 | 0.163480 | 0.0817400 | − | 0.996654i | \(-0.473952\pi\) | ||||
0.0817400 | + | 0.996654i | \(0.473952\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.2226 | − | 26.3663i | 0.511124 | − | 0.885293i | −0.488793 | − | 0.872400i | \(-0.662563\pi\) |
0.999917 | − | 0.0128929i | \(-0.00410404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.32834 | − | 14.0225i | 0.145168 | − | 0.470299i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.5777 | + | 72.0146i | 1.39134 | + | 2.40988i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.81593 | 0.0941263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.16512 | + | 2.01805i | 0.0388589 | + | 0.0673056i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.33550 | − | 10.9734i | 0.211066 | − | 0.365577i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.79608 | − | 10.0391i | 0.192668 | − | 0.333711i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.8008 | + | 30.8319i | 0.591067 | + | 1.02376i | 0.994089 | + | 0.108567i | \(0.0346263\pi\) |
−0.403022 | + | 0.915190i | \(0.632040\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6011 | −0.748809 | −0.374405 | − | 0.927265i | \(-0.622153\pi\) | ||||
−0.374405 | + | 0.927265i | \(0.622153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.7636 | + | 37.6957i | 0.720271 | + | 1.24755i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.88196 | − | 8.49804i | −0.260285 | − | 0.280630i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.17126 | + | 7.22483i | −0.137597 | + | 0.238325i | −0.926587 | − | 0.376082i | \(-0.877271\pi\) |
0.788990 | + | 0.614407i | \(0.210605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.7568 | −1.01237 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.59838 | 0.184074 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.5787 | − | 28.7152i | 0.543930 | − | 0.942114i | −0.454744 | − | 0.890622i | \(-0.650269\pi\) |
0.998673 | − | 0.0514914i | \(-0.0163975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 53.8693 | − | 25.9163i | 1.76550 | − | 0.849374i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.3859 | − | 28.3812i | −0.535875 | − | 0.928163i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.2176 | 1.15051 | 0.575254 | − | 0.817975i | \(-0.304903\pi\) | ||||
0.575254 | + | 0.817975i | \(0.304903\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.76737 | + | 9.98937i | 0.188011 | + | 0.325644i | 0.944587 | − | 0.328261i | \(-0.106463\pi\) |
−0.756576 | + | 0.653906i | \(0.773129\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.46178 | − | 2.53187i | 0.0476020 | − | 0.0824490i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.31632 | − | 10.9402i | 0.205253 | − | 0.355508i | −0.744960 | − | 0.667109i | \(-0.767532\pi\) |
0.950213 | + | 0.311600i | \(0.100865\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.1696 | + | 45.3271i | 0.849502 | + | 1.47138i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.3444 | −0.399876 | −0.199938 | − | 0.979809i | \(-0.564074\pi\) | ||||
−0.199938 | + | 0.979809i | \(0.564074\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.27279 | − | 10.8648i | −0.202983 | − | 0.351577i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.1927 | + | 10.3057i | −1.45935 | + | 0.332789i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.269283 | + | 0.466411i | −0.00868654 | + | 0.0150455i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.2973 | 0.395865 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5901 | 0.726448 | 0.363224 | − | 0.931702i | \(-0.381676\pi\) | ||||
0.363224 | + | 0.931702i | \(0.381676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.2916 | + | 19.5576i | −0.362365 | + | 0.627634i | −0.988350 | − | 0.152201i | \(-0.951364\pi\) |
0.625985 | + | 0.779835i | \(0.284697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.567469 | + | 1.83842i | −0.0181922 | + | 0.0589371i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.0625 | + | 29.5532i | 0.545879 | + | 0.945490i | 0.998551 | + | 0.0538130i | \(0.0171375\pi\) |
−0.452672 | + | 0.891677i | \(0.649529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.20369 | 0.198271 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.49170 | + | 4.31574i | 0.0794727 | + | 0.137651i | 0.903023 | − | 0.429593i | \(-0.141343\pi\) |
−0.823550 | + | 0.567244i | \(0.808010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.37588 | + | 11.0433i | −0.203152 | + | 0.351870i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.5266 | + | 30.3569i | −0.557312 | + | 0.965293i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5672 | + | 47.7478i | 0.875701 | + | 1.51676i | 0.856014 | + | 0.516952i | \(0.172933\pi\) |
0.0196864 | + | 0.999806i | \(0.493733\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.127048 | −0.00402768 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.84386 | − | 6.65777i | −0.121736 | − | 0.210854i | 0.798716 | − | 0.601708i | \(-0.205513\pi\) |
−0.920452 | + | 0.390854i | \(0.872180\pi\) | |||||||
\(998\) | 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 | 2520.2.bi.s.1801.2 | yes | 10 | |
3.2 | odd | 2 | 2520.2.bi.r.1801.2 | yes | 10 | ||
7.4 | even | 3 | inner | 2520.2.bi.s.361.2 | yes | 10 | |
21.11 | odd | 6 | 2520.2.bi.r.361.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2520.2.bi.r.361.2 | ✓ | 10 | 21.11 | odd | 6 | ||
2520.2.bi.r.1801.2 | yes | 10 | 3.2 | odd | 2 | ||
2520.2.bi.s.361.2 | yes | 10 | 7.4 | even | 3 | inner | |
2520.2.bi.s.1801.2 | yes | 10 | 1.1 | even | 1 | trivial |