Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 3781.1 | ||
Character | \(\chi\) | \(=\) | 4020.3781 |
Dual form | 4020.2.q.l.841.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.18326 | − | 3.78152i | −0.825196 | − | 1.42928i | −0.901770 | − | 0.432217i | \(-0.857732\pi\) |
0.0765741 | − | 0.997064i | \(-0.475602\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.774215 | − | 1.34098i | −0.233435 | − | 0.404321i | 0.725382 | − | 0.688347i | \(-0.241663\pi\) |
−0.958817 | + | 0.284026i | \(0.908330\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.02478 | − | 3.50702i | 0.561573 | − | 0.972673i | −0.435786 | − | 0.900050i | \(-0.643530\pi\) |
0.997359 | − | 0.0726231i | \(-0.0231370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.99263 | − | 3.45134i | 0.483284 | − | 0.837072i | −0.516532 | − | 0.856268i | \(-0.672777\pi\) |
0.999816 | + | 0.0191959i | \(0.00611063\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00975 | − | 3.48099i | 0.461069 | − | 0.798595i | −0.537946 | − | 0.842980i | \(-0.680799\pi\) |
0.999015 | + | 0.0443849i | \(0.0141328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.18326 | + | 3.78152i | 0.476427 | + | 0.825196i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.40559 | − | 4.16660i | 0.501599 | − | 0.868796i | −0.498399 | − | 0.866948i | \(-0.666078\pi\) |
0.999998 | − | 0.00184784i | \(-0.000588185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.387293 | + | 0.670812i | 0.0719186 | + | 0.124567i | 0.899742 | − | 0.436422i | \(-0.143754\pi\) |
−0.827824 | + | 0.560989i | \(0.810421\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.951794 | − | 1.64856i | −0.170947 | − | 0.296089i | 0.767804 | − | 0.640685i | \(-0.221349\pi\) |
−0.938751 | + | 0.344595i | \(0.888016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.774215 | + | 1.34098i | 0.134774 | + | 0.233435i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.18326 | + | 3.78152i | 0.369039 | + | 0.639194i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51829 | − | 4.36181i | 0.414005 | − | 0.717077i | −0.581319 | − | 0.813676i | \(-0.697463\pi\) |
0.995323 | + | 0.0965986i | \(0.0307963\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.02478 | + | 3.50702i | −0.324224 | + | 0.561573i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.44093 | + | 4.22781i | 0.381209 | + | 0.660273i | 0.991235 | − | 0.132108i | \(-0.0421746\pi\) |
−0.610027 | + | 0.792381i | \(0.708841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.63465 | 0.554278 | 0.277139 | − | 0.960830i | \(-0.410614\pi\) | ||||
0.277139 | + | 0.960830i | \(0.410614\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.40947 | + | 5.90538i | 0.497323 | + | 0.861388i | 0.999995 | − | 0.00308877i | \(-0.000983187\pi\) |
−0.502673 | + | 0.864477i | \(0.667650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.03327 | + | 10.4499i | −0.861896 | + | 1.49285i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.99263 | + | 3.45134i | −0.279024 | + | 0.483284i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.93977 | 0.403808 | 0.201904 | − | 0.979405i | \(-0.435287\pi\) | ||||
0.201904 | + | 0.979405i | \(0.435287\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.774215 | + | 1.34098i | 0.104395 | + | 0.180818i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00975 | + | 3.48099i | −0.266198 | + | 0.461069i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.02740 | −1.17527 | −0.587633 | − | 0.809127i | \(-0.699940\pi\) | ||||
−0.587633 | + | 0.809127i | \(0.699940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.44868 | − | 4.24123i | 0.313521 | − | 0.543034i | −0.665601 | − | 0.746308i | \(-0.731825\pi\) |
0.979122 | + | 0.203274i | \(0.0651581\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.18326 | − | 3.78152i | −0.275065 | − | 0.476427i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.02478 | + | 3.50702i | −0.251143 | + | 0.434993i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.16914 | + | 0.514996i | 0.998019 | + | 0.0629168i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.40559 | + | 4.16660i | −0.289599 | + | 0.501599i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.16336 | − | 8.94320i | −0.612778 | − | 1.06136i | −0.990770 | − | 0.135554i | \(-0.956719\pi\) |
0.377992 | − | 0.925809i | \(-0.376615\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.95853 | − | 3.39227i | 0.229228 | − | 0.397035i | −0.728351 | − | 0.685204i | \(-0.759713\pi\) |
0.957580 | + | 0.288169i | \(0.0930464\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.38063 | + | 5.85542i | −0.385259 | + | 0.667287i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.84670 | − | 10.1268i | −0.657805 | − | 1.13935i | −0.981183 | − | 0.193082i | \(-0.938152\pi\) |
0.323377 | − | 0.946270i | \(-0.395182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.02913 | − | 8.71071i | 0.552019 | − | 0.956124i | −0.446110 | − | 0.894978i | \(-0.647191\pi\) |
0.998129 | − | 0.0611463i | \(-0.0194756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.99263 | + | 3.45134i | −0.216131 | + | 0.374350i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.387293 | − | 0.670812i | −0.0415222 | − | 0.0719186i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9973 | 1.27172 | 0.635858 | − | 0.771806i | \(-0.280646\pi\) | ||||
0.635858 | + | 0.771806i | \(0.280646\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.6825 | −1.85363 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.951794 | + | 1.64856i | 0.0986965 | + | 0.170947i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00975 | + | 3.48099i | −0.206196 | + | 0.357142i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0931549 | − | 0.161349i | 0.00945845 | − | 0.0163825i | −0.861257 | − | 0.508169i | \(-0.830323\pi\) |
0.870716 | + | 0.491786i | \(0.163656\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.774215 | − | 1.34098i | −0.0778116 | − | 0.134774i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.32909 | + | 5.76615i | 0.331257 | + | 0.573753i | 0.982759 | − | 0.184894i | \(-0.0591941\pi\) |
−0.651502 | + | 0.758647i | \(0.725861\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.77624 | − | 4.80859i | −0.273551 | − | 0.473805i | 0.696217 | − | 0.717831i | \(-0.254865\pi\) |
−0.969769 | + | 0.244026i | \(0.921532\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.18326 | − | 3.78152i | −0.213065 | − | 0.369039i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.51834 | −0.630151 | −0.315076 | − | 0.949067i | \(-0.602030\pi\) | ||||
−0.315076 | + | 0.949067i | \(0.602030\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1705 | −1.45307 | −0.726533 | − | 0.687132i | \(-0.758870\pi\) | ||||
−0.726533 | + | 0.687132i | \(0.758870\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.51829 | + | 4.36181i | −0.239026 | + | 0.414005i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.43521 | + | 12.8782i | 0.699446 | + | 1.21148i | 0.968659 | + | 0.248395i | \(0.0799032\pi\) |
−0.269213 | + | 0.963081i | \(0.586763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.40559 | + | 4.16660i | −0.224322 | + | 0.388537i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.02478 | − | 3.50702i | 0.187191 | − | 0.324224i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.4017 | −1.59521 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.30118 | − | 7.44986i | 0.391016 | − | 0.677260i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.44093 | − | 4.22781i | −0.220091 | − | 0.381209i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.37459 | + | 4.11291i | 0.210711 | + | 0.364962i | 0.951937 | − | 0.306293i | \(-0.0990888\pi\) |
−0.741226 | + | 0.671255i | \(0.765755\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.63465 | −0.320013 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.249267 | −0.0217785 | −0.0108893 | − | 0.999941i | \(-0.503466\pi\) | ||||
−0.0108893 | + | 0.999941i | \(0.503466\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5513 | −1.52189 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.4329 | −1.40396 | −0.701980 | − | 0.712197i | \(-0.747700\pi\) | ||||
−0.701980 | + | 0.712197i | \(0.747700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.61090 | −0.730367 | −0.365184 | − | 0.930936i | \(-0.618994\pi\) | ||||
−0.365184 | + | 0.930936i | \(0.618994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.40947 | − | 5.90538i | −0.287129 | − | 0.497323i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.27047 | −0.524363 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.387293 | − | 0.670812i | −0.0321630 | − | 0.0557079i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.03327 | − | 10.4499i | 0.497616 | − | 0.861896i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.9091 | 1.05755 | 0.528777 | − | 0.848761i | \(-0.322651\pi\) | ||||
0.528777 | + | 0.848761i | \(0.322651\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.79380 | − | 3.10695i | 0.145977 | − | 0.252840i | −0.783760 | − | 0.621064i | \(-0.786701\pi\) |
0.929737 | + | 0.368224i | \(0.120034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.99263 | − | 3.45134i | 0.161095 | − | 0.279024i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.951794 | + | 1.64856i | 0.0764500 | + | 0.132415i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0871390 | − | 0.150929i | 0.00695445 | − | 0.0120455i | −0.862527 | − | 0.506011i | \(-0.831120\pi\) |
0.869482 | + | 0.493965i | \(0.164453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.93977 | −0.233139 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.0081 | −1.65567 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.82908 | + | 3.16805i | 0.143264 | + | 0.248141i | 0.928724 | − | 0.370772i | \(-0.120907\pi\) |
−0.785460 | + | 0.618913i | \(0.787573\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.774215 | − | 1.34098i | −0.0602726 | − | 0.104395i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.18346 | − | 10.7101i | −0.478491 | − | 0.828770i | 0.521205 | − | 0.853431i | \(-0.325483\pi\) |
−0.999696 | + | 0.0246611i | \(0.992149\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.69948 | − | 2.94358i | −0.130729 | − | 0.226429i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00975 | − | 3.48099i | 0.153690 | − | 0.266198i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.13800 | + | 8.89928i | −0.390635 | + | 0.676600i | −0.992533 | − | 0.121973i | \(-0.961078\pi\) |
0.601898 | + | 0.798573i | \(0.294411\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.18326 | − | 3.78152i | −0.165039 | − | 0.285856i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.02740 | 0.678541 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.67334 | 0.349301 | 0.174651 | − | 0.984630i | \(-0.444120\pi\) | ||||
0.174651 | + | 0.984630i | \(0.444120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.86171 | − | 15.3489i | −0.658685 | − | 1.14088i | −0.980956 | − | 0.194229i | \(-0.937779\pi\) |
0.322271 | − | 0.946648i | \(-0.395554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.44868 | + | 4.24123i | −0.181011 | + | 0.313521i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.51829 | + | 4.36181i | −0.185149 | + | 0.320687i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.17090 | −0.451261 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.18326 | + | 3.78152i | 0.158809 | + | 0.275065i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.71018 | − | 4.69417i | 0.196102 | − | 0.339658i | −0.751159 | − | 0.660121i | \(-0.770505\pi\) |
0.947261 | + | 0.320463i | \(0.103838\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.93928 | 0.715445 | 0.357723 | − | 0.933828i | \(-0.383553\pi\) | ||||
0.357723 | + | 0.933828i | \(0.383553\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.02478 | − | 3.50702i | 0.144998 | − | 0.251143i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.490545 | + | 0.849650i | 0.0349499 | + | 0.0605350i | 0.882971 | − | 0.469427i | \(-0.155539\pi\) |
−0.848021 | + | 0.529962i | \(0.822206\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.34262 | + | 2.32548i | −0.0951756 | + | 0.164849i | −0.909682 | − | 0.415306i | \(-0.863675\pi\) |
0.814506 | + | 0.580155i | \(0.197008\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.16914 | − | 0.514996i | −0.576206 | − | 0.0363250i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.69113 | − | 2.92912i | 0.118694 | − | 0.205584i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.44093 | − | 4.22781i | −0.170482 | − | 0.295283i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.40559 | − | 4.16660i | 0.167200 | − | 0.289599i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.22392 | −0.430518 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.83190 | + | 6.63704i | −0.263799 | + | 0.456913i | −0.967248 | − | 0.253833i | \(-0.918309\pi\) |
0.703450 | + | 0.710745i | \(0.251642\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.16336 | + | 8.94320i | 0.353788 | + | 0.612778i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.63465 | −0.247881 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.15603 | + | 7.19846i | −0.282130 | + | 0.488663i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.95853 | + | 3.39227i | −0.132345 | + | 0.229228i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.06928 | − | 13.9764i | −0.542798 | − | 0.940154i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.2812 | 1.42510 | 0.712549 | − | 0.701623i | \(-0.247541\pi\) | ||||
0.712549 | + | 0.701623i | \(0.247541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.97874 | − | 13.8196i | −0.529567 | − | 0.917238i | −0.999405 | − | 0.0344849i | \(-0.989021\pi\) |
0.469838 | − | 0.882753i | \(-0.344312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.32882 | + | 9.22978i | −0.352138 | + | 0.609921i | −0.986624 | − | 0.163013i | \(-0.947879\pi\) |
0.634486 | + | 0.772935i | \(0.281212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.38063 | − | 5.85542i | 0.222429 | − | 0.385259i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.99402 | + | 5.18580i | 0.196145 | + | 0.339733i | 0.947275 | − | 0.320421i | \(-0.103824\pi\) |
−0.751130 | + | 0.660154i | \(0.770491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.40947 | − | 5.90538i | −0.222409 | − | 0.385224i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.84670 | + | 10.1268i | 0.379784 | + | 0.657805i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.4991 | + | 18.1850i | 0.679131 | + | 1.17629i | 0.975243 | + | 0.221137i | \(0.0709767\pi\) |
−0.296111 | + | 0.955153i | \(0.595690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6890 | −0.881784 | −0.440892 | − | 0.897560i | \(-0.645338\pi\) | ||||
−0.440892 | + | 0.897560i | \(0.645338\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.03327 | − | 10.4499i | 0.385451 | − | 0.667621i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.13862 | − | 14.0965i | −0.517848 | − | 0.896939i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.02913 | + | 8.71071i | −0.318708 | + | 0.552019i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.93590 | − | 5.08513i | 0.185313 | − | 0.320971i | −0.758369 | − | 0.651825i | \(-0.774004\pi\) |
0.943682 | + | 0.330854i | \(0.107337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.44977 | −0.468363 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.99263 | − | 3.45134i | 0.124783 | − | 0.216131i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.40142 | + | 4.15939i | 0.149797 | + | 0.259456i | 0.931152 | − | 0.364631i | \(-0.118805\pi\) |
−0.781356 | + | 0.624086i | \(0.785471\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.9924 | −1.36654 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.387293 | + | 0.670812i | 0.0239729 | + | 0.0415222i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.03375 | 0.495382 | 0.247691 | − | 0.968839i | \(-0.420328\pi\) | ||||
0.247691 | + | 0.968839i | \(0.420328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.93977 | −0.180588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.9973 | −0.734226 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.5623 | 1.25370 | 0.626851 | − | 0.779139i | \(-0.284343\pi\) | ||||
0.626851 | + | 0.779139i | \(0.284343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.9461 | −1.15089 | −0.575445 | − | 0.817840i | \(-0.695171\pi\) | ||||
−0.575445 | + | 0.817840i | \(0.695171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.6825 | 1.07019 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.774215 | − | 1.34098i | −0.0466869 | − | 0.0808641i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.4595 | −1.10912 | −0.554561 | − | 0.832143i | \(-0.687114\pi\) | ||||
−0.554561 | + | 0.832143i | \(0.687114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.951794 | − | 1.64856i | −0.0569824 | − | 0.0986965i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.81169 | − | 3.13794i | 0.108076 | − | 0.187194i | −0.806915 | − | 0.590668i | \(-0.798864\pi\) |
0.914991 | + | 0.403474i | \(0.132198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.7679 | −1.11564 | −0.557818 | − | 0.829964i | \(-0.688361\pi\) | ||||
−0.557818 | + | 0.829964i | \(0.688361\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00975 | − | 3.48099i | 0.119047 | − | 0.206196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6584 | − | 18.4608i | 0.629143 | − | 1.08971i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.558854 | + | 0.967963i | 0.0328737 | + | 0.0569390i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0931549 | + | 0.161349i | −0.00546084 | + | 0.00945845i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6838 | 0.857839 | 0.428920 | − | 0.903343i | \(-0.358894\pi\) | ||||
0.428920 | + | 0.903343i | \(0.358894\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.02740 | 0.525595 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.774215 | + | 1.34098i | 0.0449245 | + | 0.0778116i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.74157 | − | 16.8729i | −0.563370 | − | 0.975785i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.93538 | − | 13.7445i | −0.457388 | − | 0.792219i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.32909 | − | 5.76615i | −0.191251 | − | 0.331257i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.44868 | + | 4.24123i | −0.140211 | + | 0.242852i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.8768 | + | 20.5711i | −0.677842 | + | 1.17406i | 0.297787 | + | 0.954632i | \(0.403752\pi\) |
−0.975629 | + | 0.219425i | \(0.929582\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.77624 | + | 4.80859i | 0.157935 | + | 0.273551i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.63955 | −0.0929704 | −0.0464852 | − | 0.998919i | \(-0.514802\pi\) | ||||
−0.0464852 | + | 0.998919i | \(0.514802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.62336 | −0.0917576 | −0.0458788 | − | 0.998947i | \(-0.514609\pi\) | ||||
−0.0458788 | + | 0.998947i | \(0.514609\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.18326 | + | 3.78152i | 0.123013 | + | 0.213065i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.96536 | + | 15.5285i | −0.503545 | + | 0.872165i | 0.496447 | + | 0.868067i | \(0.334638\pi\) |
−0.999992 | + | 0.00409784i | \(0.998696\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.599697 | − | 1.03871i | 0.0335766 | − | 0.0581563i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.51834 | 0.363818 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00938 | − | 13.8727i | −0.445654 | − | 0.771896i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.02478 | − | 3.50702i | 0.112315 | − | 0.194535i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.1705 | 0.838928 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.8875 | − | 25.7860i | 0.820777 | − | 1.42163i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.99055 | − | 6.91184i | −0.219341 | − | 0.379909i | 0.735266 | − | 0.677779i | \(-0.237057\pi\) |
−0.954607 | + | 0.297870i | \(0.903724\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.51829 | − | 4.36181i | 0.138002 | − | 0.239026i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.16914 | − | 0.514996i | −0.446328 | − | 0.0281372i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.30931 | − | 10.9280i | 0.343690 | − | 0.595289i | −0.641425 | − | 0.767186i | \(-0.721656\pi\) |
0.985115 | + | 0.171897i | \(0.0549897\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.43521 | − | 12.8782i | −0.403825 | − | 0.699446i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.47379 | + | 2.55267i | −0.0798101 | + | 0.138235i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.1232 | 1.19454 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.40559 | − | 4.16660i | 0.129512 | − | 0.224322i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.59815 | + | 13.1604i | 0.407890 | + | 0.706487i | 0.994653 | − | 0.103272i | \(-0.0329313\pi\) |
−0.586763 | + | 0.809759i | \(0.699598\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.3604 | −1.78574 | −0.892871 | − | 0.450312i | \(-0.851313\pi\) | ||||
−0.892871 | + | 0.450312i | \(0.851313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.02478 | + | 3.50702i | −0.108075 | + | 0.187191i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.95901 | + | 5.12516i | −0.157492 | + | 0.272785i | −0.933964 | − | 0.357368i | \(-0.883674\pi\) |
0.776471 | + | 0.630152i | \(0.217008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.16336 | + | 8.94320i | 0.274043 | + | 0.474656i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.4017 | 0.920997 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.33249 | −0.334216 | −0.167108 | − | 0.985939i | \(-0.553443\pi\) | ||||
−0.167108 | + | 0.985939i | \(0.553443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.42179 | + | 2.46261i | 0.0748311 | + | 0.129611i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.30118 | + | 7.44986i | −0.225753 | + | 0.391016i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.95853 | + | 3.39227i | −0.102514 | + | 0.177560i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.07721 | + | 15.7222i | 0.473826 | + | 0.820691i | 0.999551 | − | 0.0299636i | \(-0.00953913\pi\) |
−0.525725 | + | 0.850655i | \(0.676206\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.44093 | + | 4.22781i | 0.127070 | + | 0.220091i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.41828 | − | 11.1168i | −0.333221 | − | 0.577155i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.51926 | − | 16.4878i | −0.492889 | − | 0.853708i | 0.507078 | − | 0.861900i | \(-0.330726\pi\) |
−0.999966 | + | 0.00819205i | \(0.997392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.13674 | 0.161550 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.12012 | + | 15.7965i | −0.468469 | + | 0.811413i | −0.999351 | − | 0.0360336i | \(-0.988528\pi\) |
0.530881 | + | 0.847446i | \(0.321861\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.37459 | − | 4.11291i | −0.121654 | − | 0.210711i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.06204 | − | 10.4998i | 0.309756 | − | 0.536513i | −0.668553 | − | 0.743665i | \(-0.733086\pi\) |
0.978309 | + | 0.207152i | \(0.0664193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.38063 | − | 5.85542i | 0.172293 | − | 0.298420i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.63465 | 0.184759 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.09748 | − | 15.7573i | 0.461261 | − | 0.798927i | −0.537763 | − | 0.843096i | \(-0.680731\pi\) |
0.999024 | + | 0.0441689i | \(0.0140640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.58689 | − | 16.6050i | −0.484830 | − | 0.839750i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.249267 | 0.0125739 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.84670 | + | 10.1268i | 0.294179 | + | 0.509534i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.0728 | 0.806670 | 0.403335 | − | 0.915052i | \(-0.367851\pi\) | ||||
0.403335 | + | 0.915052i | \(0.367851\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.5513 | 0.878662 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.4963 | −1.02354 | −0.511769 | − | 0.859123i | \(-0.671010\pi\) | ||||
−0.511769 | + | 0.859123i | \(0.671010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.70870 | −0.383998 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.79880 | −0.386572 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0692 | + | 19.1725i | 0.547338 | + | 0.948017i | 0.998456 | + | 0.0555529i | \(0.0176921\pi\) |
−0.451118 | + | 0.892464i | \(0.648975\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.4329 | 0.810576 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.7092 | + | 34.1373i | 0.969825 | + | 1.67979i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.02913 | + | 8.71071i | −0.246870 | + | 0.427592i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.61090 | 0.421678 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.4101 | − | 28.4232i | 0.801688 | − | 1.38856i | −0.116817 | − | 0.993153i | \(-0.537269\pi\) |
0.918505 | − | 0.395410i | \(-0.129398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.7572 | + | 32.4884i | −0.914169 | + | 1.58339i | −0.106055 | + | 0.994360i | \(0.533822\pi\) |
−0.808114 | + | 0.589027i | \(0.799511\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.40947 | + | 5.90538i | 0.165774 | + | 0.287129i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.99263 | − | 3.45134i | 0.0966567 | − | 0.167414i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.3844 | −1.03486 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.27047 | 0.302741 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.63745 | − | 6.30024i | −0.175210 | − | 0.303472i | 0.765024 | − | 0.644002i | \(-0.222727\pi\) |
−0.940234 | + | 0.340530i | \(0.889394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.2770 | + | 22.9965i | 0.638053 | + | 1.10514i | 0.985859 | + | 0.167574i | \(0.0535934\pi\) |
−0.347806 | + | 0.937567i | \(0.613073\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.387293 | + | 0.670812i | 0.0185693 | + | 0.0321630i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.66927 | − | 16.7477i | −0.462544 | − | 0.801149i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.5882 | − | 26.9995i | 0.743984 | − | 1.28862i | −0.206685 | − | 0.978408i | \(-0.566267\pi\) |
0.950668 | − | 0.310210i | \(-0.100399\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.03327 | + | 10.4499i | −0.287299 | + | 0.497616i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.32988 | + | 10.9637i | 0.300742 | + | 0.520900i | 0.976304 | − | 0.216403i | \(-0.0694325\pi\) |
−0.675563 | + | 0.737303i | \(0.736099\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.9973 | −0.568729 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.9091 | −0.610579 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.2507 | + | 26.4149i | 0.719723 | + | 1.24660i | 0.961110 | + | 0.276167i | \(0.0890644\pi\) |
−0.241387 | + | 0.970429i | \(0.577602\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.77960 | − | 6.54647i | 0.177975 | − | 0.308261i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.79380 | + | 3.10695i | −0.0842799 | + | 0.145977i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.6825 | 0.828969 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.52501 | − | 11.3016i | −0.305227 | − | 0.528669i | 0.672085 | − | 0.740474i | \(-0.265399\pi\) |
−0.977312 | + | 0.211805i | \(0.932066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.99263 | + | 3.45134i | −0.0930080 | + | 0.161095i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.5153 | −1.84041 | −0.920205 | − | 0.391437i | \(-0.871978\pi\) | ||||
−0.920205 | + | 0.391437i | \(0.871978\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.44180 | − | 7.69342i | 0.206428 | − | 0.357543i | −0.744159 | − | 0.668003i | \(-0.767149\pi\) |
0.950587 | + | 0.310459i | \(0.100483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.951794 | − | 1.64856i | −0.0441384 | − | 0.0764500i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.86479 | + | 11.8902i | −0.317664 | + | 0.550211i | −0.980000 | − | 0.198996i | \(-0.936232\pi\) |
0.662336 | + | 0.749207i | \(0.269565\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.8879 | − | 32.0161i | −0.733635 | − | 1.47837i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0871390 | + | 0.150929i | −0.00401515 | + | 0.00695445i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.81400 | − | 4.87399i | −0.129388 | − | 0.224106i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00975 | − | 3.48099i | 0.0922138 | − | 0.159719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.93977 | 0.134603 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.55719 | − | 4.42919i | 0.116841 | − | 0.202375i | −0.801673 | − | 0.597763i | \(-0.796057\pi\) |
0.918514 | + | 0.395388i | \(0.129390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1980 | − | 17.6634i | −0.464988 | − | 0.805383i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.0081 | 0.955902 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0931549 | + | 0.161349i | −0.00422995 | + | 0.00732648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.83885 | − | 4.91703i | 0.128641 | − | 0.222812i | −0.794510 | − | 0.607252i | \(-0.792272\pi\) |
0.923150 | + | 0.384440i | \(0.125605\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.82908 | − | 3.16805i | −0.0827137 | − | 0.143264i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.42882 | 0.0644818 | 0.0322409 | − | 0.999480i | \(-0.489736\pi\) | ||||
0.0322409 | + | 0.999480i | \(0.489736\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.08693 | 0.139028 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.774215 | + | 1.34098i | 0.0347984 | + | 0.0602726i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.5459 | + | 39.0507i | −1.01132 | + | 1.75166i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.5307 | + | 26.9000i | −0.695250 | + | 1.20421i | 0.274847 | + | 0.961488i | \(0.411373\pi\) |
−0.970096 | + | 0.242720i | \(0.921960\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.18346 | + | 10.7101i | 0.276257 | + | 0.478491i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.56682 | + | 16.5702i | 0.426563 | + | 0.738830i | 0.996565 | − | 0.0828140i | \(-0.0263908\pi\) |
−0.570002 | + | 0.821644i | \(0.693057\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.32909 | − | 5.76615i | −0.148142 | − | 0.256590i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.69948 | + | 2.94358i | 0.0754763 | + | 0.130729i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.8386 | 1.85446 | 0.927232 | − | 0.374488i | \(-0.122182\pi\) | ||||
0.927232 | + | 0.374488i | \(0.122182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.1039 | −0.756633 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00975 | + | 3.48099i | −0.0887327 | + | 0.153690i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.77624 | + | 4.80859i | 0.122336 | + | 0.211892i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.27933 | − | 9.14407i | 0.232185 | − | 0.402156i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.13800 | − | 8.89928i | 0.225533 | − | 0.390635i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.3936 | 0.849650 | 0.424825 | − | 0.905275i | \(-0.360336\pi\) | ||||
0.424825 | + | 0.905275i | \(0.360336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.9207 | − | 24.1113i | 0.608708 | − | 1.05431i | −0.382746 | − | 0.923854i | \(-0.625021\pi\) |
0.991454 | − | 0.130460i | \(-0.0416453\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.18326 | + | 3.78152i | 0.0952854 | + | 0.165039i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.58629 | −0.330464 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.0736910 | − | 0.127636i | −0.00320395 | − | 0.00554941i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.02740 | −0.391756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.7694 | 0.856306 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.51834 | 0.281812 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.67334 | −0.201669 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.6842 | 0.804785 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.5874 | −1.27206 | −0.636030 | − | 0.771664i | \(-0.719425\pi\) | ||||
−0.636030 | + | 0.771664i | \(0.719425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.86171 | + | 15.3489i | 0.380292 | + | 0.658685i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.1705 | 0.649831 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5832 | − | 23.5268i | −0.580776 | − | 1.00593i | −0.995388 | − | 0.0959353i | \(-0.969416\pi\) |
0.414611 | − | 0.909999i | \(-0.363918\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.44868 | − | 4.24123i | 0.104507 | − | 0.181011i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.11345 | 0.132638 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.5298 | + | 44.2188i | −1.08564 | + | 1.88038i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.51829 | − | 4.36181i | 0.106896 | − | 0.185149i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.4280 | + | 21.5259i | 0.526590 | + | 0.912081i | 0.999520 | + | 0.0309809i | \(0.00986310\pi\) |
−0.472930 | + | 0.881100i | \(0.656804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.35936 | − | 12.7468i | 0.311268 | − | 0.539132i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.17090 | 0.260535 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.20628 | −0.0508386 | −0.0254193 | − | 0.999677i | \(-0.508092\pi\) | ||||
−0.0254193 | + | 0.999677i | \(0.508092\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.43521 | − | 12.8782i | −0.312802 | − | 0.541789i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.18326 | − | 3.78152i | −0.0916884 | − | 0.158809i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.0726 | + | 29.5706i | 0.715721 | + | 1.23967i | 0.962681 | + | 0.270639i | \(0.0872351\pi\) |
−0.246960 | + | 0.969026i | \(0.579432\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5866 | + | 32.1929i | 0.777824 | + | 1.34723i | 0.933194 | + | 0.359374i | \(0.117010\pi\) |
−0.155370 | + | 0.987856i | \(0.549657\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.71018 | + | 4.69417i | −0.113219 | + | 0.196102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.40559 | − | 4.16660i | 0.100320 | − | 0.173759i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.9262 | − | 34.5131i | −0.829537 | − | 1.43680i | −0.898402 | − | 0.439175i | \(-0.855271\pi\) |
0.0688642 | − | 0.997626i | \(-0.478062\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.93928 | −0.413063 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.9196 | −1.82209 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.27601 | − | 3.94217i | −0.0942628 | − | 0.163268i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.02478 | + | 3.50702i | −0.0837144 | + | 0.144998i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0039 | + | 24.2554i | −0.578002 | + | 1.00113i | 0.417706 | + | 0.908582i | \(0.362834\pi\) |
−0.995708 | + | 0.0925471i | \(0.970499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.65148 | −0.315274 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.490545 | − | 0.849650i | −0.0201783 | − | 0.0349499i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.77482 | − | 15.1984i | 0.360339 | − | 0.624125i | −0.627678 | − | 0.778473i | \(-0.715994\pi\) |
0.988016 | + | 0.154348i | \(0.0493278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.4017 | 0.713402 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.34262 | − | 2.32548i | 0.0549497 | − | 0.0951756i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.4607 | + | 19.8505i | 0.468270 | + | 0.811068i | 0.999342 | − | 0.0362589i | \(-0.0115441\pi\) |
−0.531072 | + | 0.847327i | \(0.678211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0783 | + | 38.2408i | −0.900594 | + | 1.55987i | −0.0738696 | + | 0.997268i | \(0.523535\pi\) |
−0.826725 | + | 0.562607i | \(0.809798\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.16914 | + | 0.514996i | 0.332673 | + | 0.0209723i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.30118 | + | 7.44986i | −0.174868 | + | 0.302880i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.48880 | + | 6.04278i | 0.141606 | + | 0.245269i | 0.928102 | − | 0.372327i | \(-0.121440\pi\) |
−0.786496 | + | 0.617596i | \(0.788107\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.69113 | + | 2.92912i | −0.0685279 | + | 0.118694i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.6137 | 1.11713 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.67572 | + | 6.36653i | −0.148461 | + | 0.257142i | −0.930659 | − | 0.365888i | \(-0.880765\pi\) |
0.782198 | + | 0.623030i | \(0.214099\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.44093 | + | 4.22781i | 0.0984276 | + | 0.170482i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.25619 | −0.332382 | −0.166191 | − | 0.986094i | \(-0.553147\pi\) | ||||
−0.166191 | + | 0.986094i | \(0.553147\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.414597 | + | 0.718102i | −0.0166640 | + | 0.0288630i | −0.874237 | − | 0.485499i | \(-0.838638\pi\) |
0.857573 | + | 0.514362i | \(0.171971\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.40559 | + | 4.16660i | −0.0965329 | + | 0.167200i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.1934 | − | 45.3682i | −1.04941 | − | 1.81764i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.22392 | 0.248560 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.0361 | − | 17.3830i | −0.400164 | − | 0.693104i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.00462415 | − | 0.00800927i | 0.000184085 | − | 0.000318844i | −0.865933 | − | 0.500159i | \(-0.833275\pi\) |
0.866117 | + | 0.499841i | \(0.166608\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.83190 | − | 6.63704i | 0.152304 | − | 0.263799i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.37459 | − | 4.11291i | −0.0942328 | − | 0.163216i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.4321 | + | 42.3176i | 0.968035 | + | 1.67669i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.16336 | − | 8.94320i | −0.204259 | − | 0.353788i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.80972 | + | 3.13454i | 0.0714798 | + | 0.123807i | 0.899550 | − | 0.436818i | \(-0.143895\pi\) |
−0.828070 | + | 0.560624i | \(0.810561\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.7288 | 1.80337 | 0.901685 | − | 0.432394i | \(-0.142331\pi\) | ||||
0.901685 | + | 0.432394i | \(0.142331\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.63465 | 0.143114 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.666592 | − | 1.15457i | 0.0262064 | − | 0.0453909i | −0.852625 | − | 0.522524i | \(-0.824991\pi\) |
0.878831 | + | 0.477133i | \(0.158324\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.98915 | + | 12.1056i | 0.274348 | + | 0.475185i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.15603 | − | 7.19846i | 0.162888 | − | 0.282130i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.15390 | + | 14.1230i | −0.319087 | + | 0.552674i | −0.980298 | − | 0.197526i | \(-0.936709\pi\) |
0.661211 | + | 0.750200i | \(0.270043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.249267 | 0.00973966 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.95853 | − | 3.39227i | 0.0764094 | − | 0.132345i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.10050 | + | 12.2984i | 0.276596 | + | 0.479079i | 0.970537 | − | 0.240954i | \(-0.0774602\pi\) |
−0.693940 | + | 0.720032i | \(0.744127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.32109 | 0.284757 | 0.142379 | − | 0.989812i | \(-0.454525\pi\) | ||||
0.142379 | + | 0.989812i | \(0.454525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.06928 | + | 13.9764i | 0.313385 | + | 0.542798i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.5513 | 0.680609 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.72667 | 0.144297 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.2812 | −0.822780 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.58321 | −0.292747 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.56848 | 0.176102 | 0.0880511 | − | 0.996116i | \(-0.471936\pi\) | ||||
0.0880511 | + | 0.996116i | \(0.471936\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.3054 | + | 21.3136i | 0.472936 | + | 0.819149i | 0.999520 | − | 0.0309741i | \(-0.00986095\pi\) |
−0.526584 | + | 0.850123i | \(0.676528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.813527 | −0.0312203 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.97874 | + | 13.8196i | 0.305746 | + | 0.529567i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.0513 | + | 19.1414i | −0.422866 | + | 0.732425i | −0.996218 | − | 0.0868835i | \(-0.972309\pi\) |
0.573353 | + | 0.819309i | \(0.305643\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.4329 | 0.627870 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.32882 | − | 9.22978i | 0.203307 | − | 0.352138i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.95238 | − | 10.3098i | 0.226768 | − | 0.392773i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.43911 | + | 4.22466i | 0.0927880 | + | 0.160713i | 0.908683 | − | 0.417486i | \(-0.137089\pi\) |
−0.815895 | + | 0.578200i | \(0.803755\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.38063 | + | 5.85542i | −0.128420 | + | 0.222429i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.61090 | 0.326630 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.4554 | 0.736928 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.99402 | − | 5.18580i | −0.113244 | − | 0.196145i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.87303 | − | 3.24418i | −0.0707433 | − | 0.122531i | 0.828484 | − | 0.560013i | \(-0.189204\pi\) |
−0.899227 | + | 0.437482i | \(0.855870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.1223 | − | 17.5323i | −0.381769 | − | 0.661244i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.40947 | + | 5.90538i | 0.128408 | + | 0.222409i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.5365 | − | 25.1780i | 0.546703 | − | 0.946917i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.3008 | − | 42.0903i | 0.912637 | − | 1.58073i | 0.102312 | − | 0.994752i | \(-0.467376\pi\) |
0.810325 | − | 0.585981i | \(-0.199291\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.84670 | − | 10.1268i | −0.219268 | − | 0.379784i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.15849 | −0.342988 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.27047 | 0.234502 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.4991 | − | 18.1850i | −0.392097 | − | 0.679131i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.0646 | − | 38.2171i | 0.822872 | − | 1.42526i | −0.0806630 | − | 0.996741i | \(-0.525704\pi\) |
0.903535 | − | 0.428514i | \(-0.140963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.1225 | + | 20.9968i | −0.451467 | + | 0.781963i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.6890 | 0.509098 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.387293 | + | 0.670812i | 0.0143837 | + | 0.0249133i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.70643 | − | 8.15177i | 0.174552 | − | 0.302332i | −0.765454 | − | 0.643490i | \(-0.777486\pi\) |
0.940006 | + | 0.341158i | \(0.110819\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.24250 | − | 12.5444i | 0.267874 | − | 0.463971i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.14522 | + | 10.6438i | 0.226979 | + | 0.393139i | 0.956911 | − | 0.290380i | \(-0.0937818\pi\) |
−0.729932 | + | 0.683519i | \(0.760448\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.03327 | + | 10.4499i | −0.222540 | + | 0.385451i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.63407 | − | 11.3534i | −0.207534 | − | 0.418207i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.70943 | + | 13.3531i | −0.283596 | + | 0.491203i | −0.972268 | − | 0.233870i | \(-0.924861\pi\) |
0.688672 | + | 0.725073i | \(0.258194\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.13862 | + | 14.0965i | 0.298980 | + | 0.517848i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.0137 | − | 32.9327i | 0.697545 | − | 1.20818i | −0.271770 | − | 0.962362i | \(-0.587609\pi\) |
0.969315 | − | 0.245821i | \(-0.0790576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.9091 | −0.472952 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.02913 | − | 8.71071i | 0.184006 | − | 0.318708i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.2312 | + | 24.6492i | 0.519998 | + | 0.900663i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.42821 | −0.198078 | −0.0990391 | − | 0.995084i | \(-0.531577\pi\) | ||||
−0.0990391 | + | 0.995084i | \(0.531577\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.93590 | + | 5.08513i | −0.106990 | + | 0.185313i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.79380 | + | 3.10695i | −0.0652830 | + | 0.113073i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.1748 | − | 31.4796i | −0.660573 | − | 1.14415i | −0.980465 | − | 0.196693i | \(-0.936980\pi\) |
0.319892 | − | 0.947454i | \(-0.396353\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.44977 | 0.270409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.2722 | −0.408617 | −0.204308 | − | 0.978907i | \(-0.565494\pi\) | ||||
−0.204308 | + | 0.978907i | \(0.565494\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.1211 | + | 57.3674i | 1.19906 | + | 2.07684i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.99263 | + | 3.45134i | −0.0720437 | + | 0.124783i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.2785 | + | 31.6593i | −0.659998 | + | 1.14315i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.51281 | + | 14.7446i | 0.306980 | + | 0.531705i | 0.977700 | − | 0.210006i | \(-0.0673482\pi\) |
−0.670720 | + | 0.741710i | \(0.734015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.40142 | − | 4.15939i | −0.0864852 | − | 0.149797i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.99794 | + | 8.65669i | 0.179763 | + | 0.311359i | 0.941799 | − | 0.336175i | \(-0.109133\pi\) |
−0.762036 | + | 0.647535i | \(0.775800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.951794 | − | 1.64856i | −0.0341895 | − | 0.0592179i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.9924 | 0.788972 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.6226 | 0.703054 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.99510 | + | 13.8479i | −0.286087 | + | 0.495518i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.387293 | − | 0.670812i | −0.0138407 | − | 0.0239729i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0871390 | + | 0.150929i | −0.00311012 | + | 0.00538689i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.85915 | − | 10.1483i | 0.208856 | − | 0.361750i | −0.742498 | − | 0.669848i | \(-0.766359\pi\) |
0.951354 | + | 0.308098i | \(0.0996926\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.03375 | −0.286009 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.4660 | − | 56.2328i | 1.15436 | − | 1.99941i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.91607 | − | 17.1751i | −0.352130 | − | 0.609907i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.93977 | 0.104263 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.5711 | + | 32.1661i | 0.657822 | + | 1.13938i | 0.981178 | + | 0.193104i | \(0.0618554\pi\) |
−0.323356 | + | 0.946277i | \(0.604811\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.1753 | 0.961392 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.9973 | 0.423905 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.06529 | −0.214039 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.0081 | 0.740438 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.5623 | −0.723826 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.2583 | 0.501297 | 0.250648 | − | 0.968078i | \(-0.419356\pi\) | ||||
0.250648 | + | 0.968078i | \(0.419356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6411 | − | 27.0911i | −0.549232 | − | 0.951297i | −0.998327 | − | 0.0578135i | \(-0.981587\pi\) |
0.449096 | − | 0.893484i | \(-0.351746\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.9461 | 0.664467 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.82908 | − | 3.16805i | −0.0640698 | − | 0.110972i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.30474 | − | 12.6522i | 0.255560 | − | 0.442644i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.6825 | −0.617877 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.2159 | + | 29.8188i | −0.600839 | + | 1.04068i | 0.391856 | + | 0.920027i | \(0.371833\pi\) |
−0.992694 | + | 0.120656i | \(0.961500\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.04769 | + | 1.81466i | −0.0365202 | + | 0.0632549i | −0.883708 | − | 0.468039i | \(-0.844961\pi\) |
0.847188 | + | 0.531294i | \(0.178294\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.774215 | + | 1.34098i | 0.0269547 | + | 0.0466869i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.42881 | + | 12.8671i | −0.258325 | + | 0.447432i | −0.965793 | − | 0.259313i | \(-0.916504\pi\) |
0.707468 | + | 0.706745i | \(0.249837\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.92380 | 0.344668 | 0.172334 | − | 0.985039i | \(-0.444869\pi\) | ||||
0.172334 | + | 0.985039i | \(0.444869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.4595 | 0.640351 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.0441 | + | 41.6457i | 0.833080 | + | 1.44294i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.18346 | + | 10.7101i | 0.213988 | + | 0.370637i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.951794 | + | 1.64856i | 0.0328988 | + | 0.0569824i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.40743 | − | 9.36595i | −0.186685 | − | 0.323348i | 0.757458 | − | 0.652884i | \(-0.226441\pi\) |
−0.944143 | + | 0.329536i | \(0.893108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2000 | − | 24.5951i | 0.489655 | − | 0.848108i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.81169 | + | 3.13794i | −0.0623980 | + | 0.108076i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.69948 | + | 2.94358i | 0.0584637 | + | 0.101262i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.5624 | −1.29066 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.7679 | 0.644112 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.1159 | − | 20.9854i | −0.415329 | − | 0.719371i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.1733 | + | 21.0848i | −0.416807 | + | 0.721931i | −0.995616 | − | 0.0935320i | \(-0.970184\pi\) |
0.578809 | + | 0.815463i | \(0.303518\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.00975 | + | 3.48099i | −0.0687321 | + | 0.119047i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.9953 | −1.02462 | −0.512311 | − | 0.858800i | \(-0.671210\pi\) | ||||
−0.512311 | + | 0.858800i | \(0.671210\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.21209 | + | 12.4917i | 0.246073 | + | 0.426211i | 0.962433 | − | 0.271520i | \(-0.0875263\pi\) |
−0.716360 | + | 0.697731i | \(0.754193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.6584 | + | 18.4608i | −0.363236 | + | 0.629143i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.8312 | 0.572941 | 0.286470 | − | 0.958089i | \(-0.407518\pi\) | ||||
0.286470 | + | 0.958089i | \(0.407518\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.13800 | − | 8.89928i | 0.174697 | − | 0.302585i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.558854 | − | 0.967963i | −0.0189797 | − | 0.0328737i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.05321 | + | 15.6806i | −0.307109 | + | 0.531929i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.3468 | − | 27.6066i | 0.621658 | − | 0.935414i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0931549 | − | 0.161349i | 0.00315282 | − | 0.00546084i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.18326 | + | 3.78152i | 0.0738077 | + | 0.127839i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.1220 | − | 41.7805i | 0.814542 | − | 1.41083i | −0.0951137 | − | 0.995466i | \(-0.530321\pi\) |
0.909656 | − | 0.415362i | \(-0.136345\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.6838 | −0.495274 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.65905 | − | 6.33765i | 0.123276 | − | 0.213521i | −0.797781 | − | 0.602947i | \(-0.793993\pi\) |
0.921058 | + | 0.389426i | \(0.127326\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.97113 | − | 8.61025i | −0.167292 | − | 0.289758i | 0.770175 | − | 0.637833i | \(-0.220169\pi\) |
−0.937467 | + | 0.348075i | \(0.886836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.02740 | −0.303453 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.0074 | − | 39.8500i | 0.772513 | − | 1.33803i | −0.163669 | − | 0.986515i | \(-0.552333\pi\) |
0.936182 | − | 0.351516i | \(-0.114334\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3687 | − | 17.9591i | 0.347755 | − | 0.602330i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.774215 | − | 1.34098i | −0.0259372 | − | 0.0449245i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.4088 | 0.917200 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.67334 | −0.156212 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.74157 | + | 16.8729i | 0.325262 | + | 0.563370i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.737247 | − | 1.27695i | 0.0245886 | − | 0.0425886i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.85787 | − | 10.1461i | 0.195154 | − | 0.338016i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.93538 | + | 13.7445i | 0.264073 | + | 0.457388i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.86171 | + | 15.3489i | 0.294573 | + | 0.510216i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.90469 | − | 10.2272i | −0.196062 | − | 0.339590i | 0.751186 | − | 0.660091i | \(-0.229482\pi\) |
−0.947248 | + | 0.320501i | \(0.896149\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.32909 | + | 5.76615i | 0.110419 | + | 0.191251i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.6124 | −1.17989 | −0.589946 | − | 0.807443i | \(-0.700851\pi\) | ||||
−0.589946 | + | 0.807443i | \(0.700851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.5745 | −0.515441 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.44868 | − | 4.24123i | 0.0809508 | − | 0.140211i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.544215 | + | 0.942608i | 0.0179716 | + | 0.0311277i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.6492 | − | 21.9091i | 0.417260 | − | 0.722716i | −0.578403 | − | 0.815751i | \(-0.696324\pi\) |
0.995663 | + | 0.0930358i | \(0.0296571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.8768 | − | 20.5711i | 0.391353 | − | 0.677842i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41.8187 | −1.37648 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.51829 | − | 4.36181i | 0.0828010 | − | 0.143415i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.77624 | − | 4.80859i | −0.0911838 | − | 0.157935i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.73268 | −0.319319 | −0.159659 | − | 0.987172i | \(-0.551040\pi\) | ||||
−0.159659 | + | 0.987172i | \(0.551040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.2508 | + | 42.0035i | 0.794786 | + | 1.37661i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.63955 | 0.0536765 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.17090 | 0.201810 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.31111 | 0.140838 | 0.0704189 | − | 0.997518i | \(-0.477566\pi\) | ||||
0.0704189 | + | 0.997518i | \(0.477566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.62336 | 0.0529762 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.9298 | 1.23648 | 0.618239 | − | 0.785990i | \(-0.287846\pi\) | ||||
0.618239 | + | 0.785990i | \(0.287846\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.4874 | 0.764856 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.18326 | − | 3.78152i | −0.0710215 | − | 0.123013i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.9093 | 0.419496 | 0.209748 | − | 0.977755i | \(-0.432736\pi\) | ||||
0.209748 | + | 0.977755i | \(0.432736\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.93118 | − | 13.7372i | −0.257457 | − | 0.445929i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.96536 | − | 15.5285i | 0.290722 | − | 0.503545i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.3493 | 1.66337 | 0.831684 | − | 0.555249i | \(-0.187377\pi\) | ||||
0.831684 | + | 0.555249i | \(0.187377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.71018 | + | 4.69417i | −0.0876994 | + | 0.151900i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.599697 | + | 1.03871i | −0.0193854 | + | 0.0335766i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.8774 | + | 62.1415i | 1.15854 | + | 2.00665i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6882 | − | 23.7086i | 0.441554 | − | 0.764794i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.51834 | −0.210050 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.93928 | −0.319957 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.96302 | − | 5.13210i | −0.0952842 | − | 0.165037i | 0.814443 | − | 0.580244i | \(-0.197043\pi\) |
−0.909727 | + | 0.415206i | \(0.863709\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.00938 | + | 13.8727i | 0.257299 | + | 0.445654i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.63899 | + | 2.83881i | 0.0525976 | + | 0.0911017i | 0.891125 | − | 0.453757i | \(-0.149917\pi\) |
−0.838528 | + | 0.544859i | \(0.816583\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.7999 | + | 32.5623i | 0.602696 | + | 1.04390i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.02478 | + | 3.50702i | −0.0648449 | + | 0.112315i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.20100 | − | 10.7405i | 0.198388 | − | 0.343617i | −0.749618 | − | 0.661871i | \(-0.769763\pi\) |
0.948006 | + | 0.318253i | \(0.103096\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.28853 | − | 16.0882i | −0.296863 | − | 0.514181i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.1705 | −0.484355 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.768429 | 0.0245091 | 0.0122545 | − | 0.999925i | \(-0.496099\pi\) | ||||
0.0122545 | + | 0.999925i | \(0.496099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.490545 | − | 0.849650i | −0.0156301 | − | 0.0270721i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.8875 | + | 25.7860i | −0.473876 | + | 0.820777i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.74345 | − | 15.1441i | 0.278026 | − | 0.481554i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.87346 | −0.281875 | −0.140937 | − | 0.990019i | \(-0.545012\pi\) | ||||
−0.140937 | + | 0.990019i | \(0.545012\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.99055 | + | 6.91184i | 0.126636 | + | 0.219341i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.34262 | − | 2.32548i | 0.0425638 | − | 0.0737227i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.4055 | 1.37467 | 0.687333 | − | 0.726342i | \(-0.258781\pi\) | ||||
0.687333 | + | 0.726342i | \(0.258781\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.51829 | + | 4.36181i | −0.0796753 | + | 0.138002i |
(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 | 4020.2.q.l.3781.1 | yes | 22 | |
67.37 | even | 3 | inner | 4020.2.q.l.841.1 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.l.841.1 | ✓ | 22 | 67.37 | even | 3 | inner | |
4020.2.q.l.3781.1 | yes | 22 | 1.1 | even | 1 | trivial |