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.r.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 | \(-0.909434\pi\) |
0.236807 | − | 0.971557i | \(-0.423899\pi\) | |||||||
\(12\) | 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 | \(0.144241\pi\) |
−0.0703939 | + | 0.997519i | \(0.522426\pi\) | |||||||
\(18\) | 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 | \(-0.447698\pi\) |
0.772574 | − | 0.634925i | \(-0.218969\pi\) | |||||||
\(24\) | 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 | \(-0.487734\pi\) | ||||
0.0385257 | + | 0.999258i | \(0.487734\pi\) | |||||||
\(30\) | 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 | \(-0.491906\pi\) | ||||
0.0254244 | + | 0.999677i | \(0.491906\pi\) | |||||||
\(42\) | 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 | \(0.418046\pi\) |
−0.964795 | + | 0.263002i | \(0.915287\pi\) | |||||||
\(48\) | 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 | 0.795299 | − | 0.606218i | \(-0.207314\pi\) |
−0.922649 | + | 0.385640i | \(0.873981\pi\) | |||||||
\(54\) | 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 | \(0.0371113\pi\) |
−0.395865 | + | 0.918309i | \(0.629555\pi\) | |||||||
\(60\) | 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 | \(-0.400616\pi\) | ||||
0.307175 | + | 0.951653i | \(0.400616\pi\) | |||||||
\(72\) | 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 | \(-0.665976\pi\) | ||||
−0.498120 | + | 0.867108i | \(0.665976\pi\) | |||||||
\(84\) | 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 | −0.898267 | − | 0.439449i | \(-0.855174\pi\) |
0.829708 | + | 0.558198i | \(0.188507\pi\) | |||||||
\(90\) | 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 | 0.893024 | − | 0.450009i | \(-0.148579\pi\) |
−0.836231 | + | 0.548377i | \(0.815246\pi\) | |||||||
\(102\) | 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 | −0.569621 | − | 0.821907i | \(-0.692910\pi\) |
0.996603 | + | 0.0823529i | \(0.0262435\pi\) | |||||||
\(108\) | 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 | \(-0.516797\pi\) | ||||
−0.0527442 | + | 0.998608i | \(0.516797\pi\) | |||||||
\(114\) | 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 | −0.754329 | − | 0.656496i | \(-0.772038\pi\) |
0.945707 | + | 0.325020i | \(0.105371\pi\) | |||||||
\(132\) | 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 | \(-0.897486\pi\) |
0.200181 | − | 0.979759i | \(-0.435847\pi\) | |||||||
\(138\) | 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 | \(0.500335\pi\) |
−0.865499 | + | 0.500910i | \(0.832999\pi\) | |||||||
\(150\) | 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 | \(-0.587035\pi\) | ||||
−0.270034 | + | 0.962851i | \(0.587035\pi\) | |||||||
\(168\) | 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 | −0.944965 | − | 0.327171i | \(-0.893905\pi\) |
0.755821 | + | 0.654779i | \(0.227238\pi\) | |||||||
\(174\) | 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 | 0.808598 | − | 0.588361i | \(-0.200227\pi\) |
−0.913835 | + | 0.406086i | \(0.866893\pi\) | |||||||
\(180\) | 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 | −0.998623 | − | 0.0524561i | \(-0.983295\pi\) |
0.544740 | + | 0.838605i | \(0.316628\pi\) | |||||||
\(192\) | 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 | \(-0.349903\pi\) | ||||
0.454262 | + | 0.890868i | \(0.349903\pi\) | |||||||
\(198\) | 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 | 0.856892 | − | 0.515496i | \(-0.172392\pi\) |
−0.874878 | + | 0.484343i | \(0.839059\pi\) | |||||||
\(228\) | 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 | \(-0.503349\pi\) |
0.871238 | − | 0.490861i | \(-0.163318\pi\) | |||||||
\(234\) | 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 | \(-0.740246\pi\) | ||||
−0.685109 | + | 0.728440i | \(0.740246\pi\) | |||||||
\(240\) | 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 | \(-0.259855\pi\) | ||||
0.684879 | + | 0.728657i | \(0.259855\pi\) | |||||||
\(252\) | 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 | −0.991556 | − | 0.129678i | \(-0.958606\pi\) |
0.608083 | + | 0.793874i | \(0.291939\pi\) | |||||||
\(258\) | 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 | 0.930921 | − | 0.365219i | \(-0.119006\pi\) |
−0.781750 | + | 0.623592i | \(0.785673\pi\) | |||||||
\(264\) | 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 | 0.759251 | − | 0.650798i | \(-0.225566\pi\) |
−0.943233 | + | 0.332131i | \(0.892232\pi\) | |||||||
\(270\) | 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 | \(-0.432477\pi\) | ||||
0.210542 | + | 0.977585i | \(0.432477\pi\) | |||||||
\(282\) | 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 | \(-0.685392\pi\) | ||||
−0.550053 | + | 0.835130i | \(0.685392\pi\) | |||||||
\(294\) | 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 | 0.761140 | − | 0.648588i | \(-0.224640\pi\) |
−0.942263 | + | 0.334873i | \(0.891307\pi\) | |||||||
\(312\) | 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 | \(0.438128\pi\) |
−0.946294 | + | 0.323308i | \(0.895205\pi\) | |||||||
\(318\) | 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 | 0.909083 | − | 0.416616i | \(-0.136784\pi\) |
−0.815341 | + | 0.578981i | \(0.803451\pi\) | |||||||
\(348\) | 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 | 0.630912 | − | 0.775854i | \(-0.282681\pi\) |
−0.987366 | + | 0.158459i | \(0.949348\pi\) | |||||||
\(354\) | 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 | \(-0.666065\pi\) |
0.999998 | − | 0.00189015i | \(-0.000601655\pi\) | |||||||
\(360\) | 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 | \(-0.615767\pi\) |
0.987242 | − | 0.159226i | \(-0.0508997\pi\) | |||||||
\(384\) | 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 | \(0.0265354\pi\) |
−0.426152 | + | 0.904651i | \(0.640131\pi\) | |||||||
\(390\) | 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 | \(-0.579669\pi\) |
0.962883 | − | 0.269920i | \(-0.0869972\pi\) | |||||||
\(402\) | 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 | \(-0.479795\pi\) | ||||
0.0634338 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(420\) | 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 | \(0.196271\pi\) |
0.0928719 | + | 0.995678i | \(0.470395\pi\) | |||||||
\(432\) | 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 | −0.933802 | − | 0.357790i | \(-0.883530\pi\) |
0.776756 | + | 0.629801i | \(0.216864\pi\) | |||||||
\(444\) | 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 | \(-0.349609\pi\) | ||||
0.455084 | + | 0.890449i | \(0.349609\pi\) | |||||||
\(450\) | 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 | \(-0.535042\pi\) | ||||
−0.109865 | + | 0.993947i | \(0.535042\pi\) | |||||||
\(462\) | 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 | −0.990915 | − | 0.134492i | \(-0.957060\pi\) |
0.611931 | + | 0.790911i | \(0.290393\pi\) | |||||||
\(468\) | 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 | 0.958368 | − | 0.285537i | \(-0.0921720\pi\) |
−0.726466 | + | 0.687202i | \(0.758839\pi\) | |||||||
\(480\) | 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 | \(-0.749290\pi\) | ||||
−0.705528 | + | 0.708682i | \(0.749290\pi\) | |||||||
\(492\) | 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 | \(-0.550690\pi\) | ||||
−0.158575 | + | 0.987347i | \(0.550690\pi\) | |||||||
\(504\) | 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 | −0.983621 | − | 0.180248i | \(-0.942310\pi\) |
0.647910 | + | 0.761717i | \(0.275643\pi\) | |||||||
\(510\) | 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 | 0.975336 | − | 0.220728i | \(-0.0708432\pi\) |
−0.678823 | + | 0.734302i | \(0.737510\pi\) | |||||||
\(522\) | 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 | \(-0.959043\pi\) |
0.384743 | − | 0.923024i | \(-0.374290\pi\) | |||||||
\(558\) | 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 | 0.572768 | − | 0.819717i | \(-0.305870\pi\) |
−0.996280 | + | 0.0861730i | \(0.972536\pi\) | |||||||
\(564\) | 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 | −0.732645 | − | 0.680611i | \(-0.761714\pi\) |
0.955749 | + | 0.294184i | \(0.0950478\pi\) | |||||||
\(570\) | 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 | \(-0.610418\pi\) | ||||
−0.339973 | + | 0.940435i | \(0.610418\pi\) | |||||||
\(588\) | 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 | −0.733127 | − | 0.680092i | \(-0.761940\pi\) |
0.955540 | + | 0.294861i | \(0.0952732\pi\) | |||||||
\(594\) | 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 | 0.999169 | − | 0.0407528i | \(-0.0129756\pi\) |
−0.534878 | + | 0.844930i | \(0.679642\pi\) | |||||||
\(600\) | 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 | \(-0.230588\pi\) | ||||
0.748888 | + | 0.662697i | \(0.230588\pi\) | |||||||
\(618\) | 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 | \(-0.967872\pi\) |
0.410192 | − | 0.911999i | \(-0.365462\pi\) | |||||||
\(642\) | 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 | 0.584196 | − | 0.811613i | \(-0.301410\pi\) |
−0.994975 | + | 0.100122i | \(0.968077\pi\) | |||||||
\(648\) | 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 | −0.958489 | − | 0.285129i | \(-0.907963\pi\) |
0.726174 | + | 0.687511i | \(0.241297\pi\) | |||||||
\(654\) | 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 | \(-0.408396\pi\) | ||||
0.283827 | + | 0.958876i | \(0.408396\pi\) | |||||||
\(660\) | 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 | \(-0.659151\pi\) |
0.999721 | − | 0.0236102i | \(-0.00751605\pi\) | |||||||
\(678\) | 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 | \(-0.963273\pi\) |
0.396974 | − | 0.917830i | \(-0.370060\pi\) | |||||||
\(684\) | 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 | \(-0.113527\pi\) | ||||
0.937070 | + | 0.349143i | \(0.113527\pi\) | |||||||
\(702\) | 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 | −0.984582 | − | 0.174926i | \(-0.944031\pi\) |
0.643781 | + | 0.765210i | \(0.277365\pi\) | |||||||
\(720\) | 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 | \(-0.426344\pi\) | ||||
0.229337 | + | 0.973347i | \(0.426344\pi\) | |||||||
\(744\) | 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 | −0.910886 | − | 0.412658i | \(-0.864600\pi\) |
0.812815 | + | 0.582521i | \(0.197934\pi\) | |||||||
\(762\) | 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 | 0.933981 | − | 0.357322i | \(-0.116310\pi\) |
−0.776440 | + | 0.630191i | \(0.782977\pi\) | |||||||
\(774\) | 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 | \(-0.735231\pi\) | ||||
−0.673550 | + | 0.739142i | \(0.735231\pi\) | |||||||
\(798\) | 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 | 0.523946 | − | 0.851752i | \(-0.324459\pi\) |
−0.999611 | + | 0.0278745i | \(0.991126\pi\) | |||||||
\(810\) | 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 | \(0.541524\pi\) |
−0.793626 | + | 0.608406i | \(0.791809\pi\) | |||||||
\(822\) | 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 | \(-0.337188\pi\) | ||||
0.489477 | + | 0.872016i | \(0.337188\pi\) | |||||||
\(828\) | 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 | \(-0.706435\pi\) | ||||
−0.604019 | + | 0.796970i | \(0.706435\pi\) | |||||||
\(840\) | 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 | 0.709111 | − | 0.705097i | \(-0.249097\pi\) |
−0.965187 | + | 0.261560i | \(0.915763\pi\) | |||||||
\(858\) | 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 | −0.978284 | − | 0.207271i | \(-0.933542\pi\) |
0.668643 | + | 0.743583i | \(0.266875\pi\) | |||||||
\(864\) | 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 | \(-0.318308\pi\) | ||||
0.540307 | + | 0.841468i | \(0.318308\pi\) | |||||||
\(882\) | 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 | \(0.337437\pi\) |
−0.999917 | + | 0.0128929i | \(0.995896\pi\) | |||||||
\(888\) | 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 | \(-0.377847\pi\) | ||||
0.374405 | + | 0.927265i | \(0.377847\pi\) | |||||||
\(912\) | 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 | \(0.349731\pi\) |
−0.998673 | + | 0.0514914i | \(0.983603\pi\) | |||||||
\(930\) | 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 | 0.756576 | − | 0.653906i | \(-0.226871\pi\) |
−0.944587 | + | 0.328261i | \(0.893537\pi\) | |||||||
\(942\) | 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 | −0.950213 | − | 0.311600i | \(-0.899135\pi\) |
0.744960 | + | 0.667109i | \(0.232468\pi\) | |||||||
\(948\) | 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 | \(-0.435926\pi\) | ||||
0.199938 | + | 0.979809i | \(0.435926\pi\) | |||||||
\(954\) | 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 | −0.625985 | − | 0.779835i | \(-0.715303\pi\) |
0.988350 | + | 0.152201i | \(0.0486361\pi\) | |||||||
\(972\) | 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 | \(-0.982863\pi\) |
0.452672 | − | 0.891677i | \(-0.350471\pi\) | |||||||
\(978\) | 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 | 0.823550 | − | 0.567244i | \(-0.191990\pi\) |
−0.903023 | + | 0.429593i | \(0.858657\pi\) | |||||||
\(984\) | 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.r.1801.2 | yes | 10 | |
3.2 | odd | 2 | 2520.2.bi.s.1801.2 | yes | 10 | ||
7.4 | even | 3 | inner | 2520.2.bi.r.361.2 | ✓ | 10 | |
21.11 | odd | 6 | 2520.2.bi.s.361.2 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2520.2.bi.r.361.2 | ✓ | 10 | 7.4 | even | 3 | inner | |
2520.2.bi.r.1801.2 | yes | 10 | 1.1 | even | 1 | trivial | |
2520.2.bi.s.361.2 | yes | 10 | 21.11 | odd | 6 | ||
2520.2.bi.s.1801.2 | yes | 10 | 3.2 | odd | 2 |