Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(81,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.r (of order \(6\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 737.26 | ||
Character | \(\chi\) | \(=\) | 1148.737 |
Dual form | 1148.2.r.a.81.26 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.67190 | − | 1.54262i | 1.54262 | − | 0.890634i | 0.543951 | − | 0.839117i | \(-0.316928\pi\) |
0.998672 | − | 0.0515172i | \(-0.0164057\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.10096 | + | 1.90691i | −0.492363 | + | 0.852797i | −0.999961 | − | 0.00879665i | \(-0.997200\pi\) |
0.507599 | + | 0.861594i | \(0.330533\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60761 | + | 0.447649i | −0.985583 | + | 0.169195i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.25937 | − | 5.64540i | 1.08646 | − | 1.88180i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.16097 | − | 1.82499i | 0.953070 | − | 0.550255i | 0.0590366 | − | 0.998256i | \(-0.481197\pi\) |
0.894033 | + | 0.448001i | \(0.147864\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.353091i | 0.0979297i | 0.998801 | + | 0.0489649i | \(0.0155922\pi\) | ||||
−0.998801 | + | 0.0489649i | \(0.984408\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.79344i | 1.75406i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.88342 | − | 2.24210i | 0.941869 | − | 0.543788i | 0.0513232 | − | 0.998682i | \(-0.483656\pi\) |
0.890546 | + | 0.454894i | \(0.150323\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.86226 | + | 3.38458i | 1.34490 | + | 0.776476i | 0.987521 | − | 0.157486i | \(-0.0503389\pi\) |
0.357374 | + | 0.933961i | \(0.383672\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.27671 | + | 5.21863i | −1.36969 | + | 1.13880i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.07187 | − | 5.32063i | 0.640529 | − | 1.10943i | −0.344786 | − | 0.938681i | \(-0.612048\pi\) |
0.985315 | − | 0.170748i | \(-0.0546182\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0757913 | + | 0.131274i | 0.0151583 | + | 0.0262549i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 10.8562i | − | 2.08928i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.443384i | 0.0823344i | 0.999152 | + | 0.0411672i | \(0.0131076\pi\) | ||||
−0.999152 | + | 0.0411672i | \(0.986892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14434 | − | 3.71411i | −0.385135 | − | 0.667073i | 0.606653 | − | 0.794967i | \(-0.292512\pi\) |
−0.991788 | + | 0.127893i | \(0.959178\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.63054 | − | 9.75239i | 0.980152 | − | 1.69767i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.01723 | − | 5.46532i | 0.340975 | − | 0.923807i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.730118 | − | 1.26460i | 0.120031 | − | 0.207899i | −0.799749 | − | 0.600335i | \(-0.795034\pi\) |
0.919779 | + | 0.392436i | \(0.128367\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.544686 | + | 0.943424i | 0.0872196 | + | 0.151069i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.647886 | − | 6.37026i | −0.101183 | − | 0.994868i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.86200 | −1.04645 | −0.523223 | − | 0.852196i | \(-0.675270\pi\) | ||||
−0.523223 | + | 0.852196i | \(0.675270\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.17685 | + | 12.4307i | 1.06986 | + | 1.85306i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.36060 | + | 3.09494i | 0.781924 | + | 0.451444i | 0.837112 | − | 0.547032i | \(-0.184242\pi\) |
−0.0551878 | + | 0.998476i | \(0.517576\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.59922 | − | 2.33458i | 0.942746 | − | 0.333512i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.91742 | − | 11.9813i | 0.968633 | − | 1.67772i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.66478 | + | 5.57996i | −1.32756 | + | 0.766467i | −0.984922 | − | 0.173001i | \(-0.944654\pi\) |
−0.342638 | + | 0.939468i | \(0.611320\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.03693i | 1.08370i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 20.8845 | 2.76622 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.14222 | + | 8.90659i | 0.669460 | + | 1.15954i | 0.978055 | + | 0.208346i | \(0.0668080\pi\) |
−0.308595 | + | 0.951194i | \(0.599859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.88811 | − | 10.1985i | 0.753896 | − | 1.30579i | −0.192026 | − | 0.981390i | \(-0.561506\pi\) |
0.945921 | − | 0.324396i | \(-0.105161\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.97201 | + | 16.1800i | −0.752402 | + | 2.03849i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.673313 | − | 0.388737i | −0.0835142 | − | 0.0482169i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.36850 | + | 5.40891i | −1.14454 | + | 0.660803i | −0.947552 | − | 0.319602i | \(-0.896451\pi\) |
−0.196993 | + | 0.980405i | \(0.563118\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 18.9550i | − | 2.28191i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5157i | 1.48534i | 0.669660 | + | 0.742668i | \(0.266440\pi\) | ||||
−0.669660 | + | 0.742668i | \(0.733560\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.23009 | − | 2.13058i | −0.143971 | − | 0.249366i | 0.785017 | − | 0.619474i | \(-0.212654\pi\) |
−0.928989 | + | 0.370108i | \(0.879321\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.405014 | + | 0.233835i | 0.0467670 | + | 0.0270009i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.42562 | + | 6.17386i | −0.846228 | + | 0.703577i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.47630 | + | 0.852345i | 0.166097 | + | 0.0958963i | 0.580744 | − | 0.814086i | \(-0.302762\pi\) |
−0.414647 | + | 0.909982i | \(0.636095\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.96891 | − | 12.0705i | −0.774324 | − | 1.34117i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.57776 | −0.173182 | −0.0865908 | − | 0.996244i | \(-0.527597\pi\) | ||||
−0.0865908 | + | 0.996244i | \(0.527597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.87380i | 1.07096i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.683975 | + | 1.18468i | 0.0733298 | + | 0.127011i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.1590 | − | 8.75205i | −1.60685 | − | 0.927716i | −0.990069 | − | 0.140581i | \(-0.955103\pi\) |
−0.616781 | − | 0.787135i | \(-0.711564\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.158061 | − | 0.920722i | −0.0165693 | − | 0.0965178i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.4589 | − | 6.61582i | −1.18824 | − | 0.686029i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.9082 | + | 7.45254i | −1.32435 | + | 0.764615i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0452i | 1.52761i | 0.645450 | + | 0.763803i | \(0.276670\pi\) | ||||
−0.645450 | + | 0.763803i | \(0.723330\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 23.7933i | − | 2.39132i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.65074 | + | 1.53041i | −0.263759 | + | 0.152281i | −0.626048 | − | 0.779785i | \(-0.715329\pi\) |
0.362289 | + | 0.932066i | \(0.381995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.80895 | − | 6.59730i | 0.375307 | − | 0.650051i | −0.615066 | − | 0.788476i | \(-0.710871\pi\) |
0.990373 | + | 0.138425i | \(0.0442039\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.04108 | − | 17.7146i | −0.296779 | − | 1.72877i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.76934 | + | 11.7248i | −0.654416 | + | 1.13348i | 0.327623 | + | 0.944808i | \(0.393752\pi\) |
−0.982040 | + | 0.188674i | \(0.939581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.94788 | − | 2.27931i | 0.378139 | − | 0.218318i | −0.298870 | − | 0.954294i | \(-0.596610\pi\) |
0.677008 | + | 0.735976i | \(0.263276\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.50519i | − | 0.427613i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.643235 | 0.0605104 | 0.0302552 | − | 0.999542i | \(-0.490368\pi\) | ||||
0.0302552 | + | 0.999542i | \(0.490368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.76399 | + | 11.7156i | 0.630745 | + | 1.09248i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.99334 | + | 1.15085i | 0.184284 | + | 0.106397i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.12277 | + | 7.58492i | −0.836283 | + | 0.695308i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.16118 | − | 2.01121i | 0.105561 | − | 0.182838i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.5580 | − | 16.0213i | −1.04215 | − | 1.44459i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3433 | −1.01458 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6422 | −1.03308 | −0.516539 | − | 0.856264i | \(-0.672780\pi\) | ||||
−0.516539 | + | 0.856264i | \(0.672780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.3346 | + | 10.5855i | −1.61427 | + | 0.932000i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.73254 | + | 3.00085i | −0.151373 | + | 0.262185i | −0.931732 | − | 0.363146i | \(-0.881703\pi\) |
0.780360 | + | 0.625331i | \(0.215036\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.8016 | − | 6.20141i | −1.45688 | − | 0.537731i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.7018 | + | 11.9522i | 1.78173 | + | 1.02868i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.27868 | − | 5.35705i | 0.792731 | − | 0.457683i | −0.0481921 | − | 0.998838i | \(-0.515346\pi\) |
0.840923 | + | 0.541155i | \(0.182013\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.7524 | −0.996824 | −0.498412 | − | 0.866940i | \(-0.666083\pi\) | ||||
−0.498412 | + | 0.866940i | \(0.666083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.0973 | 1.60829 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.644387 | + | 1.11611i | 0.0538863 | + | 0.0933339i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.845495 | − | 0.488147i | −0.0702145 | − | 0.0405384i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.0311 | − | 16.4179i | 1.15726 | − | 1.35413i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.0374 | + | 9.25919i | 1.31383 | + | 0.758542i | 0.982729 | − | 0.185052i | \(-0.0592454\pi\) |
0.331105 | + | 0.943594i | \(0.392579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.70226 | − | 3.86955i | 0.545422 | − | 0.314900i | −0.201851 | − | 0.979416i | \(-0.564696\pi\) |
0.747274 | + | 0.664517i | \(0.231362\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 29.2313i | − | 2.36321i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.44330 | 0.758504 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.88381 | + | 5.70642i | −0.788814 | + | 0.455422i | −0.839545 | − | 0.543290i | \(-0.817178\pi\) |
0.0507309 | + | 0.998712i | \(0.483845\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.2156 | + | 29.8182i | −1.36528 | + | 2.36474i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.62845 | + | 15.2492i | −0.443584 | + | 1.20181i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.26768 | − | 10.8559i | 0.490923 | − | 0.850303i | −0.509023 | − | 0.860753i | \(-0.669993\pi\) |
0.999945 | + | 0.0104499i | \(0.00332635\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.3980 | + | 21.4739i | 0.965180 | + | 1.67174i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.92899i | 0.768328i | 0.923265 | + | 0.384164i | \(0.125510\pi\) | ||||
−0.923265 | + | 0.384164i | \(0.874490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8753 | 0.990410 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 38.2146 | − | 22.0632i | 2.92234 | − | 1.68722i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.419924 | + | 0.727330i | −0.0319263 | + | 0.0552979i | −0.881547 | − | 0.472096i | \(-0.843498\pi\) |
0.849621 | + | 0.527394i | \(0.176831\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.256399 | − | 0.308384i | −0.0193819 | − | 0.0233117i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.4790 | + | 15.8650i | 2.06545 | + | 1.19249i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.3809 | + | 8.88017i | −1.14962 | + | 0.663735i | −0.948795 | − | 0.315892i | \(-0.897696\pi\) |
−0.200827 | + | 0.979627i | \(0.564363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.6515i | − | 0.866049i | −0.901382 | − | 0.433024i | \(-0.857446\pi\) | ||
0.901382 | − | 0.433024i | \(-0.142554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 36.3326i | − | 2.68578i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.60765 | + | 2.78454i | 0.118197 | + | 0.204723i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.18361 | − | 14.1744i | 0.598444 | − | 1.03654i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.85977 | + | 28.3087i | 0.353496 | + | 2.05916i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.32761 | + | 4.23060i | 0.530207 | + | 0.306115i | 0.741101 | − | 0.671394i | \(-0.234304\pi\) |
−0.210894 | + | 0.977509i | \(0.567637\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2408 | − | 5.91251i | 0.737147 | − | 0.425592i | −0.0838843 | − | 0.996476i | \(-0.526733\pi\) |
0.821031 | + | 0.570884i | \(0.193399\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.39870 | −0.171775 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.49928 | −0.106819 | −0.0534097 | − | 0.998573i | \(-0.517009\pi\) | ||||
−0.0534097 | + | 0.998573i | \(0.517009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.85211 | + | 1.64667i | −0.202181 | + | 0.116729i | −0.597672 | − | 0.801740i | \(-0.703908\pi\) |
0.395491 | + | 0.918470i | \(0.370574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.6878 | + | 28.9041i | −1.17707 | + | 2.03874i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.198481 | − | 1.15617i | −0.0139306 | − | 0.0811473i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.8608 | + | 5.77792i | 0.898239 | + | 0.403547i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.0247 | − | 34.6839i | −1.39182 | − | 2.41070i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.7073 | 1.70904 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.28479i | 0.570348i | 0.958476 | + | 0.285174i | \(0.0920514\pi\) | ||||
−0.958476 | + | 0.285174i | \(0.907949\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.3070 | + | 33.4406i | 1.32289 | + | 2.29131i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.55477 | − | 13.0852i | 0.515231 | − | 0.892406i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.25421 | + | 8.72502i | 0.492448 | + | 0.592293i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.57337 | − | 3.79514i | −0.444187 | − | 0.256451i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.791663 | + | 1.37120i | 0.0532530 | + | 0.0922370i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.8726 | −1.26380 | −0.631900 | − | 0.775050i | \(-0.717725\pi\) | ||||
−0.631900 | + | 0.775050i | \(0.717725\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.988129 | 0.0658753 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.20151 | − | 0.693691i | 0.0797469 | − | 0.0460419i | −0.459596 | − | 0.888128i | \(-0.652006\pi\) |
0.539343 | + | 0.842086i | \(0.318673\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.0766 | − | 9.28180i | −1.06237 | − | 0.613359i | −0.136282 | − | 0.990670i | \(-0.543515\pi\) |
−0.926086 | + | 0.377311i | \(0.876849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.3166 | + | 27.9509i | −0.678782 | + | 1.83903i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.33949 | − | 3.08276i | −0.349802 | − | 0.201958i | 0.314796 | − | 0.949159i | \(-0.398064\pi\) |
−0.664598 | + | 0.747201i | \(0.731397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8036 | + | 6.81479i | −0.769980 | + | 0.444548i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.25939 | 0.341634 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.10642i | 0.136253i | 0.997677 | + | 0.0681265i | \(0.0217022\pi\) | ||||
−0.997677 | + | 0.0681265i | \(0.978298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.58032 | + | 13.1295i | 0.488291 | + | 0.845746i | 0.999909 | − | 0.0134675i | \(-0.00428696\pi\) |
−0.511618 | + | 0.859213i | \(0.670954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.03526 | − | 5.21651i | −0.579612 | − | 0.334639i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.81361 | + | 15.1544i | −0.179755 | + | 0.968180i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.19506 | + | 2.06991i | −0.0760400 | + | 0.131705i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.21562 | + | 2.43389i | −0.267154 | + | 0.154242i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.6633 | −1.17802 | −0.589008 | − | 0.808127i | \(-0.700481\pi\) | ||||
−0.589008 | + | 0.808127i | \(0.700481\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 22.4245i | − | 1.40982i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.2316 | + | 26.3818i | 0.953837 | + | 1.65209i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.499938 | − | 0.288639i | −0.0311853 | − | 0.0180048i | 0.484326 | − | 0.874887i | \(-0.339065\pi\) |
−0.515512 | + | 0.856883i | \(0.672398\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.33776 | + | 3.62442i | −0.0831245 | + | 0.225210i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.50308 | + | 1.44516i | 0.154937 | + | 0.0894529i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0450 | + | 7.53154i | −0.804389 | + | 0.464414i | −0.845004 | − | 0.534760i | \(-0.820402\pi\) |
0.0406143 | + | 0.999175i | \(0.487069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 24.5732i | − | 1.50952i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −54.0045 | −3.30502 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.6509 | − | 23.6441i | −0.832311 | − | 1.44160i | −0.896201 | − | 0.443648i | \(-0.853684\pi\) |
0.0638904 | − | 0.997957i | \(-0.479649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6601 | − | 27.1240i | 0.951281 | − | 1.64767i | 0.208622 | − | 0.977996i | \(-0.433102\pi\) |
0.742658 | − | 0.669670i | \(-0.233565\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.84265 | − | 2.21625i | −0.111522 | − | 0.134134i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.479149 | + | 0.276637i | 0.0288938 | + | 0.0166818i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6452 | − | 25.3663i | −0.879946 | − | 1.52411i | −0.851399 | − | 0.524518i | \(-0.824245\pi\) |
−0.0285468 | − | 0.999592i | \(-0.509088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.9568 | −1.67373 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1121i | 0.603240i | 0.953428 | + | 0.301620i | \(0.0975274\pi\) | ||||
−0.953428 | + | 0.301620i | \(0.902473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.19895 | − | 14.2010i | −0.487377 | − | 0.844161i | 0.512518 | − | 0.858677i | \(-0.328713\pi\) |
−0.999895 | + | 0.0145153i | \(0.995379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.9929 | + | 39.8249i | −1.36198 | + | 2.35903i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.54107 | + | 16.3211i | 0.268051 | + | 0.963405i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.55399 | − | 2.69159i | 0.0914112 | − | 0.158329i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.2090 | + | 40.1992i | 1.36054 | + | 2.35652i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.6413i | 1.55640i | 0.628016 | + | 0.778200i | \(0.283867\pi\) | ||||
−0.628016 | + | 0.778200i | \(0.716133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.6454 | −1.31847 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.8125 | − | 34.3162i | −1.14964 | − | 1.99123i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.87867 | + | 1.08465i | 0.108646 | + | 0.0627268i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.8934 | − | 3.07177i | 1.03136 | − | 0.177054i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.72168 | + | 8.17819i | −0.271254 | + | 0.469825i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.9651 | + | 22.4562i | 0.742380 | + | 1.28584i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.2979 | −1.10139 | −0.550696 | − | 0.834706i | \(-0.685638\pi\) | ||||
−0.550696 | + | 0.834706i | \(0.685638\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 23.5031i | − | 1.33705i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.36240 | − | 1.36393i | 0.133960 | − | 0.0773416i | −0.431523 | − | 0.902102i | \(-0.642023\pi\) |
0.565482 | + | 0.824761i | \(0.308690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.7098 | + | 6.18329i | 0.605353 | + | 0.349500i | 0.771144 | − | 0.636660i | \(-0.219685\pi\) |
−0.165792 | + | 0.986161i | \(0.553018\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.2790 | − | 29.2016i | −1.36797 | − | 1.64532i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.9405 | + | 16.1315i | 1.56930 | + | 0.906034i | 0.996251 | + | 0.0865117i | \(0.0275720\pi\) |
0.573047 | + | 0.819523i | \(0.305761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.809172 | + | 1.40153i | 0.0453049 | + | 0.0784704i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 41.7701i | 2.33138i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.3542 | 1.68895 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0463518 | + | 0.0267612i | −0.00257113 | + | 0.00148445i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.03224 | − | 12.1802i | 0.388884 | − | 0.673566i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.3638 | − | 5.67073i | −0.847033 | − | 0.312637i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.9546 | − | 12.0982i | −1.15177 | − | 0.664975i | −0.202453 | − | 0.979292i | \(-0.564891\pi\) |
−0.949318 | + | 0.314317i | \(0.898225\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.75945 | − | 8.24361i | −0.260816 | − | 0.451747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 23.8199i | − | 1.30142i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.11428 | −0.278593 | −0.139296 | − | 0.990251i | \(-0.544484\pi\) | ||||
−0.139296 | + | 0.990251i | \(0.544484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.71866 | − | 0.992269i | 0.0933448 | − | 0.0538927i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.5564 | − | 7.82680i | −0.734121 | − | 0.423845i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1631 | + | 9.04181i | −0.872725 | + | 0.488212i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 36.1454 | + | 20.8686i | 1.94600 | + | 1.12353i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.2404 | − | 16.3046i | 1.51603 | − | 0.875278i | 0.516203 | − | 0.856466i | \(-0.327345\pi\) |
0.999823 | − | 0.0188119i | \(-0.00598835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.5204 | 1.58019 | 0.790094 | − | 0.612986i | \(-0.210032\pi\) | ||||
0.790094 | + | 0.612986i | \(0.210032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.83322 | 0.204602 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.04235 | − | 12.1977i | −0.374827 | − | 0.649219i | 0.615474 | − | 0.788157i | \(-0.288964\pi\) |
−0.990301 | + | 0.138938i | \(0.955631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.8663 | − | 13.7792i | −1.26669 | − | 0.731324i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.6745 | + | 34.3391i | −0.670805 | + | 1.81742i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.9820 | − | 19.0214i | 0.579610 | − | 1.00391i | −0.415914 | − | 0.909404i | \(-0.636538\pi\) |
0.995524 | − | 0.0945096i | \(-0.0301283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.4107 | + | 23.2281i | 0.705829 | + | 1.22253i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.16502i | − | 0.376066i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.41711 | 0.283544 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.32376 | + | 10.9531i | 0.330097 | + | 0.571745i | 0.982531 | − | 0.186101i | \(-0.0595851\pi\) |
−0.652433 | + | 0.757846i | \(0.726252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −38.0744 | − | 17.1055i | −1.98207 | − | 0.890476i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.7041 | − | 18.8768i | 1.17874 | − | 0.980033i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.728596 | − | 1.26197i | 0.0377253 | − | 0.0653421i | −0.846546 | − | 0.532315i | \(-0.821322\pi\) |
0.884272 | + | 0.466973i | \(0.154655\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −30.3083 | + | 17.4985i | −1.56511 | + | 0.903618i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.156555 | −0.00806299 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.4850 | −0.795410 | −0.397705 | − | 0.917513i | \(-0.630193\pi\) | ||||
−0.397705 | + | 0.917513i | \(0.630193\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.1068 | + | 17.9595i | −1.59365 | + | 0.920095i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5637 | − | 8.40835i | −0.744170 | − | 0.429647i | 0.0794136 | − | 0.996842i | \(-0.474695\pi\) |
−0.823583 | + | 0.567195i | \(0.808029\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.59773 | − | 20.9572i | −0.183357 | − | 1.06808i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.3658 | + | 38.7388i | −1.13692 | + | 1.96920i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.4452 | + | 28.4839i | 0.833803 | + | 1.44419i | 0.895001 | + | 0.446063i | \(0.147174\pi\) |
−0.0611984 | + | 0.998126i | \(0.519492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 27.5497i | − | 1.39325i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.6906i | 0.539271i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.25069 | + | 1.87679i | −0.163560 | + | 0.0944315i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.1591 | + | 10.4842i | 0.911380 | + | 0.526185i | 0.880875 | − | 0.473349i | \(-0.156955\pi\) |
0.0305048 | + | 0.999535i | \(0.490289\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −54.4586 | + | 9.34893i | −2.72634 | + | 0.468032i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.1720 | + | 31.4748i | −0.907466 | + | 1.57178i | −0.0898942 | + | 0.995951i | \(0.528653\pi\) |
−0.817572 | + | 0.575826i | \(0.804680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.31142 | − | 0.757147i | 0.0653263 | − | 0.0377162i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.6899 | 1.52499 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.32983i | − | 0.264190i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.8339 | − | 23.9611i | −0.684043 | − | 1.18480i | −0.973736 | − | 0.227678i | \(-0.926887\pi\) |
0.289693 | − | 0.957120i | \(-0.406447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.5278 | − | 28.6270i | 0.815257 | − | 1.41207i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.3959 | − | 20.9230i | −0.855997 | − | 1.02955i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.73704 | − | 3.00865i | 0.0852682 | − | 0.147689i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.4012 | + | 18.1295i | −1.53772 | + | 0.887806i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.83932 | 0.285270 | 0.142635 | − | 0.989775i | \(-0.454443\pi\) | ||||
0.142635 | + | 0.989775i | \(0.454443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3691i | 0.895254i | 0.894220 | + | 0.447627i | \(0.147731\pi\) | ||||
−0.894220 | + | 0.447627i | \(0.852269\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.9444 | − | 20.1752i | 1.69905 | − | 0.980950i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.588660 | + | 0.339863i | 0.0285542 | + | 0.0164858i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.7885 | + | 29.2295i | −0.522093 | + | 1.41452i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.44348 | + | 1.98809i | 0.166253 | + | 0.0959860i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.62032 | − | 8.00263i | −0.222553 | − | 0.385473i | 0.733029 | − | 0.680197i | \(-0.238106\pi\) |
−0.955583 | + | 0.294724i | \(0.904772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.1993 | −1.59545 | −0.797727 | − | 0.603019i | \(-0.793964\pi\) | ||||
−0.797727 | + | 0.603019i | \(0.793964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.01211 | −0.144419 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.0162 | − | 20.7940i | 1.72289 | − | 0.994710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.49173 | + | 3.74800i | 0.309833 | + | 0.178882i | 0.646852 | − | 0.762616i | \(-0.276085\pi\) |
−0.337019 | + | 0.941498i | \(0.609419\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.32966 | − | 44.8645i | 0.396651 | − | 2.13641i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.5961 | + | 27.0133i | −0.740995 | + | 1.28344i | 0.211047 | + | 0.977476i | \(0.432313\pi\) |
−0.952043 | + | 0.305966i | \(0.901021\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.3788 | − | 19.2712i | 1.58231 | − | 0.913545i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 57.1337 | 2.70233 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.7738 | −0.744409 | −0.372205 | − | 0.928151i | \(-0.621398\pi\) | ||||
−0.372205 | + | 0.928151i | \(0.621398\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6736 | − | 18.9539i | −0.643865 | − | 0.892502i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.9385 | − | 20.6781i | 0.560921 | − | 0.971543i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.92975 | + | 0.712266i | 0.0904682 | + | 0.0333916i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.1813 | + | 14.5384i | 1.17793 | + | 0.680078i | 0.955535 | − | 0.294878i | \(-0.0952791\pi\) |
0.222395 | + | 0.974957i | \(0.428612\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.3407 | − | 42.1593i | −1.13612 | − | 1.96783i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.50886 | 0.256573 | 0.128286 | − | 0.991737i | \(-0.459052\pi\) | ||||
0.128286 | + | 0.991737i | \(0.459052\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.43337i | 0.159562i | 0.996812 | + | 0.0797810i | \(0.0254221\pi\) | ||||
−0.996812 | + | 0.0797810i | \(0.974578\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.2316 | − | 14.5675i | 1.17009 | − | 0.675550i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.28786 | + | 3.96269i | −0.105870 | + | 0.183372i | −0.914093 | − | 0.405504i | \(-0.867096\pi\) |
0.808224 | + | 0.588876i | \(0.200429\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.0081 | − | 18.2981i | 1.01624 | − | 0.844928i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.6057 | + | 30.4940i | −0.811229 | + | 1.40509i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.6906 | + | 12.5231i | −0.997336 | + | 0.575812i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.02609i | 0.0470801i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 72.7487i | 3.33094i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.67862 | + | 3.27856i | −0.259463 | + | 0.149801i | −0.624090 | − | 0.781353i | \(-0.714530\pi\) |
0.364627 | + | 0.931154i | \(0.381197\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.446519 | + | 0.257798i | 0.0203595 | + | 0.0117546i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.48516 | + | 49.4271i | 0.386088 | + | 2.24901i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.6898 | − | 16.5641i | −1.30274 | − | 0.752136i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.6579 | + | 28.8523i | 0.754842 | + | 1.30742i | 0.945453 | + | 0.325759i | \(0.105620\pi\) |
−0.190611 | + | 0.981666i | \(0.561047\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 38.6747i | − | 1.74893i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.7108 | 0.618760 | 0.309380 | − | 0.950939i | \(-0.399879\pi\) | ||||
0.309380 | + | 0.950939i | \(0.399879\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.994110 | + | 1.72185i | 0.0447725 | + | 0.0775482i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 45.3717 | + | 26.1954i | 2.03931 | + | 1.17739i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.60262 | − | 32.6359i | −0.251312 | − | 1.46392i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.6743 | − | 15.9778i | −1.23887 | − | 0.715264i | −0.270009 | − | 0.962858i | \(-0.587027\pi\) |
−0.968864 | + | 0.247594i | \(0.920360\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.3167 | + | 26.5293i | 0.684299 | + | 1.18524i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.02693i | − | 0.313315i | −0.987653 | − | 0.156658i | \(-0.949928\pi\) | ||
0.987653 | − | 0.156658i | \(-0.0500719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6.73964i | − | 0.299910i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.4016 | − | 19.8618i | 1.52783 | − | 0.882093i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.6836 | + | 17.7152i | 1.36003 | + | 0.785213i | 0.989627 | − | 0.143659i | \(-0.0458868\pi\) |
0.370402 | + | 0.928872i | \(0.379220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.16135 | + | 5.00507i | 0.184087 | + | 0.221411i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.7437 | − | 63.6419i | 1.62227 | − | 2.80986i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.38698 | + | 14.5267i | 0.369574 | + | 0.640122i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.5930 | 0.993637 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.59114i | 0.113738i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.3229 | − | 15.7749i | 1.19704 | − | 0.691109i | 0.237143 | − | 0.971475i | \(-0.423789\pi\) |
0.959893 | + | 0.280365i | \(0.0904556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.13477 | + | 8.89368i | −0.224528 | + | 0.388893i | −0.956178 | − | 0.292787i | \(-0.905417\pi\) |
0.731650 | + | 0.681681i | \(0.238751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.16079 | − | 0.428445i | −0.0506612 | − | 0.0186989i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.6548 | − | 9.61564i | −0.725493 | − | 0.418864i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.37277 | − | 12.7700i | −0.320555 | − | 0.555218i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 67.0417 | 2.90936 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.24928 | − | 0.228763i | 0.0974272 | − | 0.00990881i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.9055 | − | 25.8171i | −0.644420 | − | 1.11617i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.3975 | + | 47.4539i | −1.18229 | + | 2.04779i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5994 | − | 19.4231i | 0.714986 | − | 0.836611i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.45504 | + | 4.25226i | −0.105551 | + | 0.182819i | −0.913963 | − | 0.405798i | \(-0.866994\pi\) |
0.808412 | + | 0.588616i | \(0.200327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.9739 | − | 31.1316i | −0.771332 | − | 1.33599i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0377i | 0.429967i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.8764i | 0.721584i | 0.932646 | + | 0.360792i | \(0.117493\pi\) | ||||
−0.932646 | + | 0.360792i | \(0.882507\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −38.3831 | − | 66.4815i | −1.63815 | − | 2.83736i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.50067 | + | 2.59923i | −0.0639306 | + | 0.110731i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.23117 | − | 1.56171i | −0.179928 | − | 0.0664108i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.59099 | + | 4.96001i | 0.364667 | + | 0.210541i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00870 | + | 3.46912i | −0.254597 | + | 0.146991i | −0.621867 | − | 0.783123i | \(-0.713626\pi\) |
0.367271 | + | 0.930114i | \(0.380292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.42291i | − | 0.102478i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 50.4969i | − | 2.13198i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.54394 | + | 2.04610i | −0.149359 | + | 0.0862326i | −0.572817 | − | 0.819683i | \(-0.694150\pi\) |
0.423458 | + | 0.905916i | \(0.360816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.708173 | + | 1.22659i | −0.0297931 | + | 0.0516031i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.5755 | + | 28.3555i | 0.990079 | + | 1.19082i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.3866 | + | 17.9902i | −0.435431 | + | 0.754188i | −0.997331 | − | 0.0730169i | \(-0.976737\pi\) |
0.561900 | + | 0.827205i | \(0.310071\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.8882 | − | 14.3692i | 1.04154 | − | 0.601333i | 0.121270 | − | 0.992620i | \(-0.461303\pi\) |
0.920269 | + | 0.391287i | \(0.127970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.1049 | 1.09055 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.931285 | 0.0388372 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.33918 | − | 4.81463i | 0.347165 | − | 0.200436i | −0.316271 | − | 0.948669i | \(-0.602431\pi\) |
0.663436 | + | 0.748233i | \(0.269098\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.2416 | − | 31.5953i | 0.758093 | − | 1.31306i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.11418 | − | 0.706283i | 0.170685 | − | 0.0293015i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.3667 | + | 35.2762i | −0.843505 | + | 1.46099i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.38916 | + | 2.53408i | −0.181469 | + | 0.104771i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.3233i | 0.508637i | 0.967120 | + | 0.254319i | \(0.0818512\pi\) | ||||
−0.967120 | + | 0.254319i | \(0.918149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 29.0308i | − | 1.19619i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.00593 | + | 2.31283i | −0.164782 | + | 0.0951370i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.787934 | + | 0.454914i | 0.0323566 | + | 0.0186811i | 0.516091 | − | 0.856534i | \(-0.327387\pi\) |
−0.483734 | + | 0.875215i | \(0.660720\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.42000 | − | 25.7470i | −0.181202 | − | 1.05552i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.08037 | + | 8.79947i | −0.207926 | + | 0.360138i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.72441 | − | 13.3791i | −0.315611 | − | 0.546654i | 0.663956 | − | 0.747771i | \(-0.268876\pi\) |
−0.979567 | + | 0.201117i | \(0.935543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 37.8156i | − | 1.54253i | −0.636514 | − | 0.771265i | \(-0.719624\pi\) | ||
0.636514 | − | 0.771265i | \(-0.280376\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 70.5186i | 2.87174i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.55681 | + | 4.42852i | 0.103949 | + | 0.180045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.581403 | + | 1.00702i | −0.0235984 | + | 0.0408737i | −0.877583 | − | 0.479424i | \(-0.840846\pi\) |
0.853985 | + | 0.520298i | \(0.174179\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.31386 | − | 2.78300i | −0.0937623 | − | 0.112773i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.09280 | + | 1.89278i | −0.0442098 | + | 0.0765736i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.63135 | − | 11.4858i | −0.267838 | − | 0.463908i | 0.700465 | − | 0.713686i | \(-0.252976\pi\) |
−0.968303 | + | 0.249778i | \(0.919642\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 43.2760 | − | 4.40138i | 1.74506 | − | 0.177481i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.9252 | 0.802158 | 0.401079 | − | 0.916044i | \(-0.368635\pi\) | ||||
0.401079 | + | 0.916044i | \(0.368635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.3345 | + | 35.2203i | 0.817311 | + | 1.41562i | 0.907657 | + | 0.419713i | \(0.137869\pi\) |
−0.0903459 | + | 0.995910i | \(0.528797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −57.7619 | − | 33.3488i | −2.31790 | − | 1.33824i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 43.4465 | + | 16.0360i | 1.74065 | + | 0.642469i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1096 | − | 20.9744i | 0.484382 | − | 0.838975i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 66.0154 | − | 38.1140i | 2.63640 | − | 1.52213i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.54797i | − | 0.261085i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.4244 | 0.693655 | 0.346828 | − | 0.937929i | \(-0.387259\pi\) | ||||
0.346828 | + | 0.937929i | \(0.387259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.7803 | + | 22.1361i | 0.507972 | + | 0.879833i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.8176 | − | 22.2007i | 0.508649 | − | 0.881006i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.824320 | + | 2.33012i | 0.0326608 | + | 0.0923229i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 70.6559 | + | 40.7932i | 2.79511 | + | 1.61375i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.01731 | + | 0.587342i | −0.0401812 | + | 0.0231986i | −0.519956 | − | 0.854193i | \(-0.674052\pi\) |
0.479775 | + | 0.877392i | \(0.340718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.7130i | 1.52669i | 0.645989 | + | 0.763347i | \(0.276445\pi\) | ||||
−0.645989 | + | 0.763347i | \(0.723555\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 46.6166i | − | 1.83553i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.2559 | + | 21.2278i | 0.481828 | + | 0.834551i | 0.999782 | − | 0.0208572i | \(-0.00663952\pi\) |
−0.517954 | + | 0.855408i | \(0.673306\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.5089 | + | 18.7690i | 1.27608 | + | 0.736748i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.8420 | + | 12.1219i | 1.28718 | + | 0.475094i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.37942 | − | 1.95111i | −0.132247 | − | 0.0763527i | 0.432417 | − | 0.901674i | \(-0.357661\pi\) |
−0.564664 | + | 0.825321i | \(0.690994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.81490 | − | 6.60761i | −0.149061 | − | 0.258181i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.0373 | −0.625675 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 0.994257i | − | 0.0387308i | −0.999812 | − | 0.0193654i | \(-0.993835\pi\) | ||
0.999812 | − | 0.0193654i | \(-0.00616458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.9645 | − | 39.7757i | −0.893217 | − | 1.54710i | −0.835996 | − | 0.548735i | \(-0.815109\pi\) |
−0.0572208 | − | 0.998362i | \(-0.518224\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.23049 | + | 2.44248i | 0.164299 | + | 0.0948579i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.3233 | − | 25.2116i | 1.17589 | − | 0.977665i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.35909 | + | 1.36202i | 0.0913442 | + | 0.0527376i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −50.4256 | + | 29.1132i | −1.94957 | + | 1.12558i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 42.9830i | − | 1.65934i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 42.9532i | − | 1.65573i | −0.560930 | − | 0.827863i | \(-0.689556\pi\) | ||
0.560930 | − | 0.827863i | \(-0.310444\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.42514 | − | 0.822806i | 0.0548538 | − | 0.0316698i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.4167 | − | 31.8987i | 0.707813 | − | 1.22597i | −0.257854 | − | 0.966184i | \(-0.583015\pi\) |
0.965667 | − | 0.259784i | \(-0.0836515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.73496 | − | 39.2319i | −0.258464 | − | 1.50558i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.14021 | − | 3.70695i | 0.0820130 | − | 0.142051i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.4639 | + | 17.5883i | −1.16567 | + | 0.672999i | −0.952656 | − | 0.304051i | \(-0.901661\pi\) |
−0.213012 | + | 0.977049i | \(0.568327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.5915i | 0.901385i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −57.2733 | −2.18511 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.97023 | − | 3.41254i | −0.0750599 | − | 0.130008i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.36680 | + | 1.94382i | 0.128079 | + | 0.0739466i | 0.562671 | − | 0.826681i | \(-0.309774\pi\) |
−0.434591 | + | 0.900628i | \(0.643107\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.6510 | + | 62.0435i | 0.404600 | + | 2.35684i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9389 | − | 22.4108i | 0.490799 | − | 0.850089i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.7988 | − | 23.2858i | −0.636298 | − | 0.882013i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.0221 | −0.719483 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.09568 | −0.116922 | −0.0584611 | − | 0.998290i | \(-0.518619\pi\) | ||||
−0.0584611 | + | 0.998290i | \(0.518619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.56028 | − | 4.94228i | 0.322857 | − | 0.186402i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.0253 | + | 36.4169i | −0.791860 | + | 1.37154i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.22701 | − | 5.17730i | 0.234191 | − | 0.194712i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.1444 | − | 12.7851i | −0.831650 | − | 0.480153i | 0.0227676 | − | 0.999741i | \(-0.492752\pi\) |
−0.854417 | + | 0.519588i | \(0.826086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.62366 | − | 5.55622i | 0.360915 | − | 0.208375i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.3485 | −0.986761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.83777 | −0.106126 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.24942 | + | 5.62815i | 0.121352 | + | 0.210187i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.2466 | − | 7.07060i | −0.456723 | − | 0.263689i | 0.253943 | − | 0.967219i | \(-0.418273\pi\) |
−0.710665 | + | 0.703530i | \(0.751606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.97897 | + | 18.9082i | −0.259911 | + | 0.704179i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.5078 | + | 23.3872i | 1.50650 | + | 0.869778i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0582050 | + | 0.0336047i | −0.00216168 | + | 0.00124805i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 45.4858i | − | 1.68697i | −0.537149 | − | 0.843487i | \(-0.680499\pi\) | ||
0.537149 | − | 0.843487i | \(-0.319501\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.62503 | 0.356483 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.6481 | + | 15.3853i | −0.985615 | + | 0.569045i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.14908 | − | 10.6505i | 0.227121 | − | 0.393386i | −0.729832 | − | 0.683626i | \(-0.760402\pi\) |
0.956954 | + | 0.290240i | \(0.0937352\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.8599 | + | 44.8314i | 0.585000 | + | 1.65363i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.7424 | + | 34.1948i | −0.727221 | + | 1.25958i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.97466 | + | 8.61637i | 0.182996 | + | 0.316958i | 0.942899 | − | 0.333078i | \(-0.108087\pi\) |
−0.759903 | + | 0.650036i | \(0.774754\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.37413i | 0.270895i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.5550 | −1.26770 | −0.633849 | − | 0.773456i | \(-0.718526\pi\) | ||||
−0.633849 | + | 0.773456i | \(0.718526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.3129 | + | 20.3879i | −1.29376 | + | 0.746955i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.14251 | + | 8.90709i | −0.188155 | + | 0.325893i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.4032 | − | 33.6040i | 0.453201 | − | 1.22786i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0938 | + | 15.0653i | 0.952176 | + | 0.549739i | 0.893756 | − | 0.448553i | \(-0.148060\pi\) |
0.0584200 | + | 0.998292i | \(0.481394\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −49.8664 | + | 28.7904i | −1.81723 | + | 1.04918i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.0408i | 0.620179i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.4331i | 0.924380i | 0.886781 | + | 0.462190i | \(0.152936\pi\) | ||||
−0.886781 | + | 0.462190i | \(0.847064\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.5926 | − | 59.9161i | −1.25563 | − | 2.17482i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7092 | − | 20.2809i | 0.424457 | − | 0.735181i | −0.571913 | − | 0.820315i | \(-0.693798\pi\) |
0.996370 | + | 0.0851335i | \(0.0271317\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.27419 | + | 7.71081i | −0.335748 | + | 0.279150i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 55.7415 | + | 32.1824i | 2.01534 | + | 1.16356i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.14483 | + | 1.81567i | −0.113553 | + | 0.0655601i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.7089 | −1.03527 | −0.517634 | − | 0.855602i | \(-0.673187\pi\) | ||||
−0.517634 | + | 0.855602i | \(0.673187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.78105 | −0.0641428 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.81317 | − | 2.20153i | 0.137150 | − | 0.0791837i | −0.429855 | − | 0.902898i | \(-0.641435\pi\) |
0.567005 | + | 0.823714i | \(0.308102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.325045 | − | 0.562994i | 0.0116760 | − | 0.0202234i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.01674 | + | 11.7477i | 0.0723502 | + | 0.421448i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.7626 | − | 39.5370i | 0.636410 | − | 1.41656i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.8410 | + | 39.5617i | 0.817314 | + | 1.41563i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.81347 | 0.172019 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 25.1301i | − | 0.896931i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.1731 | − | 29.7448i | −0.612157 | − | 1.06029i | −0.990876 | − | 0.134775i | \(-0.956969\pi\) |
0.378720 | − | 0.925511i | \(-0.376364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.2366 | + | 40.2471i | −0.827247 | + | 1.43283i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.67730 | + | 0.287943i | −0.0596380 | + | 0.0102381i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.60100 | + | 2.07904i | 0.127875 | + | 0.0738288i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −37.9072 | − | 65.6571i | −1.34443 | − | 2.32862i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.9362 | −1.16666 | −0.583330 | − | 0.812235i | \(-0.698251\pi\) | ||||
−0.583330 | + | 0.812235i | \(0.698251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.7566 | 0.981960 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −98.8177 | + | 57.0524i | −3.49155 | + | 2.01585i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.77658 | − | 4.48981i | −0.274429 | − | 0.158442i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.8823 | − | 27.5217i | −0.806494 | − | 0.970012i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −72.9478 | − | 42.1164i | −2.56788 | − | 1.48257i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.4905 | − | 18.7584i | 1.14230 | − | 0.659510i | 0.195304 | − | 0.980743i | \(-0.437431\pi\) |
0.947000 | + | 0.321233i | \(0.104097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3349 | −0.362908 | −0.181454 | − | 0.983399i | \(-0.558080\pi\) | ||||
−0.181454 | + | 0.983399i | \(0.558080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 96.6303i | − | 3.38897i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.8009 | + | 23.9038i | 0.483424 | + | 0.837315i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.2269 | − | 23.2250i | −1.40736 | − | 0.812540i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.71302 | − | 2.10866i | −0.199629 | − | 0.0736825i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.9409 | + | 24.1464i | −0.486541 | + | 0.842714i | −0.999880 | − | 0.0154718i | \(-0.995075\pi\) |
0.513339 | + | 0.858186i | \(0.328408\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.9752 | + | 17.3062i | −1.04487 | + | 0.603255i | −0.921208 | − | 0.389070i | \(-0.872797\pi\) |
−0.123660 | + | 0.992325i | \(0.539463\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.70699 | 0.0594296 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.1260i | 0.491211i | 0.969370 | + | 0.245605i | \(0.0789867\pi\) | ||||
−0.969370 | + | 0.245605i | \(0.921013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1560 | − | 21.0548i | −0.422195 | − | 0.731263i | 0.573959 | − | 0.818884i | \(-0.305407\pi\) |
−0.996154 | + | 0.0876213i | \(0.972073\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −78.2612 | − | 45.1841i | −2.71485 | − | 1.56742i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.3932 | − | 23.8623i | 0.706583 | − | 0.826779i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.9337 | − | 10.9314i | −0.655228 | − | 0.378296i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.3211 | + | 23.2794i | −1.39370 | + | 0.804654i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.5112i | 1.05336i | 0.850063 | + | 0.526682i | \(0.176564\pi\) | ||||
−0.850063 | + | 0.526682i | \(0.823436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8034 | 0.993221 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.5992 | + | 27.0187i | 0.537266 | + | 0.930572i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.1752 | + | 24.5521i | −0.487641 | + | 0.844618i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.12757 | + | 5.76425i | −0.0731042 | + | 0.198062i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.8136 | − | 25.2958i | −1.50368 | − | 0.868149i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.48565 | − | 7.76938i | −0.153766 | − | 0.266331i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.8989 | 1.67427 | 0.837133 | − | 0.547000i | \(-0.184230\pi\) | ||||
0.837133 | + | 0.547000i | \(0.184230\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 97.1625i | 3.32289i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.408558 | − | 0.707642i | −0.0139561 | − | 0.0241726i | 0.858963 | − | 0.512038i | \(-0.171109\pi\) |
−0.872919 | + | 0.487865i | \(0.837776\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.01695 | − | 1.76140i | 0.0346978 | − | 0.0600983i | −0.848155 | − | 0.529748i | \(-0.822286\pi\) |
0.882853 | + | 0.469650i | \(0.155620\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.3106 | + | 36.6032i | 1.27154 | + | 1.24744i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.18418 | − | 3.78310i | 0.0743502 | − | 0.128778i | −0.826453 | − | 0.563005i | \(-0.809645\pi\) |
0.900804 | + | 0.434227i | \(0.142978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.924636 | − | 1.60152i | −0.0314386 | − | 0.0544532i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 9.58889i | − | 0.325656i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.22208 | 0.211070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.90984 | − | 3.30793i | −0.0647123 | − | 0.112085i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 84.9360 | + | 49.0378i | 2.87465 | + | 1.65968i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.5789 | − | 5.07783i | 0.999951 | − | 0.171662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.9397 | − | 43.1969i | 0.842155 | − | 1.45866i | −0.0459133 | − | 0.998945i | \(-0.514620\pi\) |
0.888069 | − | 0.459711i | \(-0.152047\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 41.0975 | + | 71.1829i | 1.38618 | + | 2.40094i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.4572 | −0.992437 | −0.496219 | − | 0.868198i | \(-0.665279\pi\) | ||||
−0.496219 | + | 0.868198i | \(0.665279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.0341i | − | 0.943423i | −0.881753 | − | 0.471711i | \(-0.843636\pi\) | ||
0.881753 | − | 0.471711i | \(-0.156364\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −60.5064 | + | 34.9334i | −2.03390 | + | 1.17427i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.0159 | + | 6.36005i | 0.369878 | + | 0.213549i | 0.673405 | − | 0.739273i | \(-0.264831\pi\) |
−0.303527 | + | 0.952823i | \(0.598164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.3583 | − | 5.21162i | 1.01818 | − | 0.174792i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44.0571 | − | 25.4364i | −1.47597 | − | 0.852151i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.9502 | + | 36.2867i | 0.701070 | + | 1.21429i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 39.1067i | − | 1.30719i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.69282 | 0.223467 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.64678 | − | 0.950767i | 0.0549231 | − | 0.0317099i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.0216 | + | 43.3387i | −0.833591 | + | 1.44382i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 43.0708 | − | 35.8102i | 1.43331 | − | 1.19169i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.2184 | + | 12.8278i | 0.738564 | + | 0.426410i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.01389 | + | 5.22021i | 0.100075 | + | 0.173334i | 0.911715 | − | 0.410823i | \(-0.134759\pi\) |
−0.811641 | + | 0.584157i | \(0.801425\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.9527i | 0.661788i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.7915 | 0.755117 | 0.377558 | − | 0.925986i | \(-0.376764\pi\) | ||||
0.377558 | + | 0.925986i | \(0.376764\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.98726 | + | 2.87940i | −0.165054 | + | 0.0952941i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 69.2830 | + | 40.0006i | 2.29043 | + | 1.32238i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.17446 | − | 8.60061i | 0.104830 | − | 0.284017i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.60146 | − | 2.65666i | −0.151788 | − | 0.0876350i | 0.422182 | − | 0.906511i | \(-0.361264\pi\) |
−0.573970 | + | 0.818876i | \(0.694598\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.5622 | + | 29.7695i | −1.69903 | + | 0.980937i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.41916 | −0.145459 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.221346 | 0.00727782 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.8296 | − | 43.0061i | −0.815511 | − | 1.41251i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.1428 | − | 21.4444i | −1.21862 | − | 0.703568i | −0.253994 | − | 0.967206i | \(-0.581744\pi\) |
−0.964622 | + | 0.263637i | \(0.915078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 46.5879 | + | 8.64963i | 1.52686 | + | 0.283480i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.20807 | − | 7.28860i | 0.137766 | − | 0.238618i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.0196 | + | 31.2108i | 0.589303 | + | 1.02070i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.1036i | 1.50614i | 0.657941 | + | 0.753070i | \(0.271428\pi\) | ||||
−0.657941 | + | 0.753070i | \(0.728572\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.1540 | 1.24511 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.6317 | + | 37.4673i | 0.705175 | + | 1.22140i | 0.966628 | + | 0.256182i | \(0.0824648\pi\) |
−0.261454 | + | 0.965216i | \(0.584202\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.8841 | − | 16.1214i | −1.16855 | − | 0.524987i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −59.3326 | − | 21.8995i | −1.93009 | − | 0.712391i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.0965 | + | 24.4158i | −0.458073 | + | 0.793406i | −0.998859 | − | 0.0477542i | \(-0.984794\pi\) |
0.540786 | + | 0.841160i | \(0.318127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.752288 | − | 0.434334i | 0.0244203 | − | 0.0140991i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 99.5392 | 3.22778 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.9250 | −1.45526 | −0.727631 | − | 0.685968i | \(-0.759379\pi\) | ||||
−0.727631 | + | 0.685968i | \(0.759379\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.1348 | + | 9.31541i | −0.522109 | + | 0.301439i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.32406 | + | 2.49649i | 0.139777 | + | 0.0807002i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.7971 | + | 18.1227i | −0.703864 | + | 0.585211i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.30360 | − | 10.9182i | 0.203342 | − | 0.352199i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 44.1276 | + | 76.4312i | 1.42199 | + | 2.46296i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.0377i | 0.838182i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.4158i | 0.560056i | 0.959992 | + | 0.280028i | \(0.0903437\pi\) | ||||
−0.959992 | + | 0.280028i | \(0.909656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 81.1035 | − | 46.8251i | 2.60542 | − | 1.50424i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.489865 | + | 0.282823i | 0.0157205 | + | 0.00907624i | 0.507840 | − | 0.861452i | \(-0.330444\pi\) |
−0.492119 | + | 0.870528i | \(0.663778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.6456 | − | 5.26094i | 0.982453 | − | 0.168658i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0825650 | + | 0.143007i | −0.00264420 | + | 0.00457988i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.9454 | − | 6.31935i | 0.350176 | − | 0.202174i | −0.314587 | − | 0.949229i | \(-0.601866\pi\) |
0.664763 | + | 0.747055i | \(0.268533\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −63.8896 | −2.04192 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 29.7165i | − | 0.948775i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.0513 | + | 17.4094i | 0.320588 | + | 0.555274i | 0.980609 | − | 0.195972i | \(-0.0627862\pi\) |
−0.660022 | + | 0.751247i | \(0.729453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.65064 | − | 2.85900i | 0.0525939 | − | 0.0910953i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.7983 | + | 8.54890i | −1.58510 | + | 0.272115i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.0792 | + | 36.5102i | −0.670279 | + | 1.16096i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5973 | − | 12.4692i | 0.686060 | − | 0.396097i | −0.116074 | − | 0.993241i | \(-0.537031\pi\) |
0.802134 | + | 0.597144i | \(0.203698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −74.6517 | −2.36900 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 7.25163i | − | 0.229892i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.4557 | − | 10.0781i | 0.552828 | − | 0.319175i | −0.197434 | − | 0.980316i | \(-0.563261\pi\) |
0.750262 | + | 0.661141i | \(0.229928\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.7288 | − | 7.92631i | −0.434359 | − | 0.250777i |
(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 | 1148.2.r.a.737.26 | yes | 56 | |
7.4 | even | 3 | inner | 1148.2.r.a.81.3 | ✓ | 56 | |
41.40 | even | 2 | inner | 1148.2.r.a.737.3 | yes | 56 | |
287.81 | even | 6 | inner | 1148.2.r.a.81.26 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.r.a.81.3 | ✓ | 56 | 7.4 | even | 3 | inner | |
1148.2.r.a.81.26 | yes | 56 | 287.81 | even | 6 | inner | |
1148.2.r.a.737.3 | yes | 56 | 41.40 | even | 2 | inner | |
1148.2.r.a.737.26 | yes | 56 | 1.1 | even | 1 | trivial |