Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), degree \(2\), not 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.41342275584.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} + 2x^{5} + 81x^{4} - 8x^{3} + 208x^{2} + 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 608) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(-0.564469 - 0.977689i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.961 |
Dual form | 1216.2.i.o.577.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.20711 | + | 2.09077i | −0.696923 | + | 1.20711i | 0.272605 | + | 0.962126i | \(0.412115\pi\) |
−0.969528 | + | 0.244981i | \(0.921218\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.06447 | + | 1.84371i | −0.476045 | + | 0.824534i | −0.999623 | − | 0.0274433i | \(-0.991263\pi\) |
0.523578 | + | 0.851978i | \(0.324597\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.59656 | 0.603443 | 0.301721 | − | 0.953396i | \(-0.402439\pi\) | ||||
0.301721 | + | 0.953396i | \(0.402439\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.41421 | − | 2.44949i | −0.471405 | − | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.12894 | −0.340388 | −0.170194 | − | 0.985411i | \(-0.554439\pi\) | ||||
−0.170194 | + | 0.985411i | \(0.554439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.27696 | + | 5.67587i | 0.908866 | + | 1.57420i | 0.815642 | + | 0.578557i | \(0.196384\pi\) |
0.0932238 | + | 0.995645i | \(0.470283\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.56986 | − | 4.45112i | −0.663534 | − | 1.14927i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.14802 | + | 3.72049i | −0.520972 | + | 0.902351i | 0.478730 | + | 0.877962i | \(0.341097\pi\) |
−0.999703 | + | 0.0243886i | \(0.992236\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.69341 | − | 3.42718i | −0.617910 | − | 0.786249i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.92722 | + | 3.33804i | −0.420554 | + | 0.728420i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.85513 | + | 4.94523i | 0.595336 | + | 1.03115i | 0.993499 | + | 0.113838i | \(0.0363144\pi\) |
−0.398163 | + | 0.917315i | \(0.630352\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.233811 | + | 0.404972i | 0.0467622 | + | 0.0809944i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.882123 | + | 1.52788i | 0.163806 | + | 0.283720i | 0.936231 | − | 0.351386i | \(-0.114290\pi\) |
−0.772425 | + | 0.635107i | \(0.780956\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.25341 | −0.943541 | −0.471771 | − | 0.881721i | \(-0.656385\pi\) | ||||
−0.471771 | + | 0.881721i | \(0.656385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.36275 | − | 2.36035i | 0.237224 | − | 0.410884i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.69949 | + | 2.94360i | −0.287266 | + | 0.497559i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.23187 | 0.202518 | 0.101259 | − | 0.994860i | \(-0.467713\pi\) | ||||
0.101259 | + | 0.994860i | \(0.467713\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.8226 | −2.53364 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.04315 | − | 7.00294i | 0.631434 | − | 1.09368i | −0.355824 | − | 0.934553i | \(-0.615800\pi\) |
0.987259 | − | 0.159123i | \(-0.0508668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35736 | − | 4.08307i | 0.359494 | − | 0.622663i | −0.628382 | − | 0.777905i | \(-0.716283\pi\) |
0.987876 | + | 0.155242i | \(0.0496158\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.02155 | 0.897639 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.973296 | − | 1.68580i | −0.141970 | − | 0.245899i | 0.786269 | − | 0.617885i | \(-0.212010\pi\) |
−0.928238 | + | 0.371986i | \(0.878677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.45100 | −0.635857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.18579 | − | 8.98205i | −0.726156 | − | 1.25774i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.56224 | + | 7.90203i | 0.626672 | + | 1.08543i | 0.988215 | + | 0.153072i | \(0.0489166\pi\) |
−0.361544 | + | 0.932355i | \(0.617750\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.20172 | − | 2.08144i | 0.162040 | − | 0.280661i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.4167 | − | 1.49433i | 1.37972 | − | 0.197928i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.33605 | + | 2.31410i | −0.173938 | + | 0.301270i | −0.939793 | − | 0.341743i | \(-0.888983\pi\) |
0.765855 | + | 0.643013i | \(0.222316\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.89290 | − | 10.2068i | −0.754508 | − | 1.30685i | −0.945619 | − | 0.325278i | \(-0.894542\pi\) |
0.191110 | − | 0.981569i | \(-0.438791\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.25788 | − | 3.91076i | −0.284466 | − | 0.492709i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.9529 | −1.73064 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.87920 | − | 10.1831i | −0.718258 | − | 1.24406i | −0.961689 | − | 0.274142i | \(-0.911606\pi\) |
0.243431 | − | 0.969918i | \(-0.421727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.7858 | −1.65961 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.71817 | + | 4.70800i | −0.322587 | + | 0.558737i | −0.981021 | − | 0.193901i | \(-0.937886\pi\) |
0.658434 | + | 0.752639i | \(0.271219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.967622 | − | 1.67597i | 0.113252 | − | 0.196157i | −0.803828 | − | 0.594862i | \(-0.797207\pi\) |
0.917079 | + | 0.398704i | \(0.130540\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.12894 | −0.130359 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.80242 | −0.205405 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.49707 | − | 12.9853i | 0.843487 | − | 1.46096i | −0.0434422 | − | 0.999056i | \(-0.513832\pi\) |
0.886929 | − | 0.461906i | \(-0.152834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.74264 | − | 8.21449i | 0.526960 | − | 0.912722i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.06418 | 0.446102 | 0.223051 | − | 0.974807i | \(-0.428398\pi\) | ||||
0.223051 | + | 0.974807i | \(0.428398\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.57301 | − | 7.92069i | −0.496013 | − | 0.859119i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.25927 | −0.456641 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.680403 | + | 1.17849i | 0.0721226 | + | 0.124920i | 0.899831 | − | 0.436238i | \(-0.143689\pi\) |
−0.827709 | + | 0.561158i | \(0.810356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.23187 | + | 9.06186i | 0.548449 | + | 0.949941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.34143 | − | 10.9837i | 0.657576 | − | 1.13895i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.18579 | − | 1.31775i | 0.942442 | − | 0.135198i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.00052 | + | 15.5894i | −0.913864 | + | 1.58286i | −0.105308 | + | 0.994440i | \(0.533583\pi\) |
−0.808556 | + | 0.588419i | \(0.799750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.59656 | + | 2.76532i | 0.160460 | + | 0.277925i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.220806 | + | 0.382447i | 0.0219710 | + | 0.0380549i | 0.876802 | − | 0.480852i | \(-0.159673\pi\) |
−0.854831 | + | 0.518907i | \(0.826339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.39898 | 0.334911 | 0.167456 | − | 0.985880i | \(-0.446445\pi\) | ||||
0.167456 | + | 0.985880i | \(0.446445\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.10293 | − | 7.10648i | −0.400405 | − | 0.693522i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.7089 | −1.90533 | −0.952664 | − | 0.304024i | \(-0.901670\pi\) | ||||
−0.952664 | + | 0.304024i | \(0.901670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.63777 | − | 13.2290i | 0.731566 | − | 1.26711i | −0.224648 | − | 0.974440i | \(-0.572123\pi\) |
0.956214 | − | 0.292669i | \(-0.0945433\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.48700 | + | 2.57555i | −0.141139 | + | 0.244461i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1460 | 1.14260 | 0.571301 | − | 0.820741i | \(-0.306439\pi\) | ||||
0.571301 | + | 0.820741i | \(0.306439\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.1568 | −1.13363 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.26865 | − | 16.0538i | 0.856887 | − | 1.48417i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.42945 | + | 5.93998i | −0.314377 | + | 0.544517i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.72550 | −0.884136 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.76103 | + | 16.9066i | 0.880123 | + | 1.52442i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.6402 | −1.04113 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.82498 | + | 8.35712i | 0.428148 | + | 0.741574i | 0.996709 | − | 0.0810672i | \(-0.0258328\pi\) |
−0.568561 | + | 0.822641i | \(0.692499\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.69118 | + | 9.85741i | 0.501080 | + | 0.867896i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.80367 | + | 11.7843i | −0.594439 | + | 1.02960i | 0.399187 | + | 0.916870i | \(0.369293\pi\) |
−0.993626 | + | 0.112729i | \(0.964041\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.30019 | − | 5.47170i | −0.372873 | − | 0.474456i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.440918 | − | 0.763692i | 0.0379481 | − | 0.0657281i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.14608 | + | 7.18122i | 0.354224 | + | 0.613533i | 0.986985 | − | 0.160814i | \(-0.0514118\pi\) |
−0.632761 | + | 0.774347i | \(0.718079\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.464983 | + | 0.805375i | 0.0394394 | + | 0.0683110i | 0.885071 | − | 0.465455i | \(-0.154109\pi\) |
−0.845632 | + | 0.533766i | \(0.820776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.69949 | 0.395768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.69949 | − | 6.40770i | −0.309367 | − | 0.535839i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.75597 | −0.311916 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.37283 | − | 9.30601i | 0.443143 | − | 0.767547i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.90367 | + | 13.6896i | −0.647494 | + | 1.12149i | 0.336226 | + | 0.941781i | \(0.390850\pi\) |
−0.983719 | + | 0.179711i | \(0.942484\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.53180 | −0.206035 | −0.103018 | − | 0.994680i | \(-0.532850\pi\) | ||||
−0.103018 | + | 0.994680i | \(0.532850\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.1511 | 0.982355 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.59210 | − | 9.68580i | 0.449168 | − | 0.777982i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.47593 | + | 4.28844i | −0.197601 | + | 0.342255i | −0.947750 | − | 0.319014i | \(-0.896648\pi\) |
0.750149 | + | 0.661269i | \(0.229982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.0284 | −1.74697 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.55839 | + | 7.89536i | 0.359251 | + | 0.622241i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.66520 | 0.522059 | 0.261030 | − | 0.965331i | \(-0.415938\pi\) | ||||
0.261030 | + | 0.965331i | \(0.415938\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.90121 | + | 5.02504i | 0.225859 | + | 0.391199i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.97158 | + | 15.5392i | 0.694242 | + | 1.20246i | 0.970436 | + | 0.241360i | \(0.0775935\pi\) |
−0.276194 | + | 0.961102i | \(0.589073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.9770 | + | 25.9409i | −1.15207 | + | 1.99545i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.58579 | + | 11.4442i | −0.350684 | + | 0.875163i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.56224 | − | 11.3661i | 0.498918 | − | 0.864151i | −0.501082 | − | 0.865400i | \(-0.667064\pi\) |
0.999999 | + | 0.00124927i | \(0.000397655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.373293 | + | 0.646562i | 0.0282183 | + | 0.0488755i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.22550 | − | 5.58673i | −0.242443 | − | 0.419924i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.7005 | 1.69672 | 0.848358 | − | 0.529422i | \(-0.177591\pi\) | ||||
0.848358 | + | 0.529422i | \(0.177591\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9144 | + | 18.9044i | 0.811264 | + | 1.40515i | 0.911980 | + | 0.410235i | \(0.134553\pi\) |
−0.100715 | + | 0.994915i | \(0.532113\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.4534 | 2.10334 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.31128 | + | 2.27121i | −0.0964076 | + | 0.166983i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.42499 | − | 4.20020i | 0.177333 | − | 0.307149i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.661317 | −0.0481037 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.13725 | − | 8.89798i | 0.369787 | − | 0.640491i | −0.619745 | − | 0.784803i | \(-0.712764\pi\) |
0.989532 | + | 0.144313i | \(0.0460972\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.8426 | − | 29.1723i | 1.20613 | − | 2.08907i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.4250 | −0.885244 | −0.442622 | − | 0.896708i | \(-0.645952\pi\) | ||||
−0.442622 | + | 0.896708i | \(0.645952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.01422 | + | 8.68488i | 0.355448 | + | 0.615655i | 0.987195 | − | 0.159521i | \(-0.0509948\pi\) |
−0.631746 | + | 0.775175i | \(0.717662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 28.3873 | 2.00228 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.40836 | + | 2.43935i | 0.0988476 | + | 0.171209i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.60762 | + | 14.9088i | 0.601182 | + | 1.04128i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.07553 | − | 13.9872i | 0.561288 | − | 0.972180i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.04069 | + | 3.86907i | 0.210329 | + | 0.267629i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.6108 | − | 21.8425i | 0.868162 | − | 1.50370i | 0.00428844 | − | 0.999991i | \(-0.498635\pi\) |
0.863873 | − | 0.503709i | \(-0.168032\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.56224 | − | 11.3661i | −0.449637 | − | 0.778794i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.01868 | + | 8.69261i | 0.342271 | + | 0.592831i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.38739 | −0.569373 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.33605 | + | 4.04615i | 0.157855 | + | 0.273413i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.1560 | −1.89398 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.155642 | + | 0.269580i | −0.0104226 | + | 0.0180524i | −0.871190 | − | 0.490947i | \(-0.836651\pi\) |
0.860767 | + | 0.508999i | \(0.169984\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.661317 | − | 1.14543i | 0.0440878 | − | 0.0763623i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.1073 | −0.936333 | −0.468166 | − | 0.883640i | \(-0.655085\pi\) | ||||
−0.468166 | + | 0.883640i | \(0.655085\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1511 | 0.802965 | 0.401482 | − | 0.915867i | \(-0.368495\pi\) | ||||
0.401482 | + | 0.915867i | \(0.368495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.17571 | − | 3.76844i | 0.143151 | − | 0.247945i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.424470 | + | 0.735203i | −0.0278079 | + | 0.0481648i | −0.879594 | − | 0.475724i | \(-0.842186\pi\) |
0.851787 | + | 0.523889i | \(0.175519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.14417 | 0.270336 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.0995 | + | 31.3493i | 1.17569 | + | 2.03636i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.9352 | −1.22482 | −0.612410 | − | 0.790541i | \(-0.709800\pi\) | ||||
−0.612410 | + | 0.790541i | \(0.709800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.81128 | + | 4.86929i | 0.181091 | + | 0.313658i | 0.942252 | − | 0.334904i | \(-0.108704\pi\) |
−0.761161 | + | 0.648562i | \(0.775371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.8284 | + | 18.7554i | 0.694644 | + | 1.20316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.73795 | − | 8.20637i | 0.302696 | − | 0.524286i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.6260 | − | 26.5182i | 0.676117 | − | 1.68731i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.90590 | + | 8.49727i | −0.310899 | + | 0.538493i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.3537 | + | 19.6652i | 0.716640 | + | 1.24126i | 0.962324 | + | 0.271906i | \(0.0876540\pi\) |
−0.245684 | + | 0.969350i | \(0.579013\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.22327 | − | 5.58286i | −0.202645 | − | 0.350992i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 22.0805 | 1.38273 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.79605 | − | 11.7711i | −0.423926 | − | 0.734261i | 0.572394 | − | 0.819979i | \(-0.306015\pi\) |
−0.996319 | + | 0.0857179i | \(0.972682\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.96675 | 0.122208 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.49502 | − | 4.32150i | 0.154438 | − | 0.267494i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.1993 | + | 22.8619i | −0.813904 | + | 1.40972i | 0.0962075 | + | 0.995361i | \(0.469329\pi\) |
−0.910112 | + | 0.414363i | \(0.864005\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.4254 | −1.19330 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.28528 | −0.201056 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.29851 | + | 10.9093i | −0.384027 | + | 0.665154i | −0.991634 | − | 0.129084i | \(-0.958796\pi\) |
0.607607 | + | 0.794238i | \(0.292130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.65616 | − | 6.33265i | 0.222096 | − | 0.384681i | −0.733348 | − | 0.679853i | \(-0.762044\pi\) |
0.955444 | + | 0.295172i | \(0.0953769\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.2617 | −1.52891 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.263958 | − | 0.457189i | −0.0159173 | − | 0.0275695i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3917 | 1.34539 | 0.672695 | − | 0.739920i | \(-0.265137\pi\) | ||||
0.672695 | + | 0.739920i | \(0.265137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.42945 | + | 12.8682i | 0.444790 | + | 0.770398i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.7971 | − | 27.3614i | −0.942375 | − | 1.63224i | −0.760924 | − | 0.648841i | \(-0.775254\pi\) |
−0.181451 | − | 0.983400i | \(-0.558079\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.8297 | + | 20.4896i | −0.703201 | + | 1.21798i | 0.264136 | + | 0.964486i | \(0.414913\pi\) |
−0.967337 | + | 0.253495i | \(0.918420\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.33312 | + | 20.7960i | −0.493611 | + | 1.23185i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.45513 | − | 11.1806i | 0.381035 | − | 0.659971i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.728017 | − | 1.26096i | −0.0428245 | − | 0.0741743i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.7292 | − | 37.6360i | −1.27379 | − | 2.20626i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.176035 | −0.0102841 | −0.00514205 | − | 0.999987i | \(-0.501637\pi\) | ||||
−0.00514205 | + | 0.999987i | \(0.501637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.84436 | − | 4.92657i | −0.165605 | − | 0.286836i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.467622 | 0.0271342 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.7123 | + | 32.4107i | −1.08216 | + | 1.87436i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.76367 | − | 6.51887i | 0.216934 | − | 0.375741i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.06615 | −0.0612485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.0912 | 1.43672 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5673 | + | 23.4993i | −0.774329 | + | 1.34118i | 0.160842 | + | 0.986980i | \(0.448579\pi\) |
−0.935171 | + | 0.354197i | \(0.884754\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.10293 | + | 7.10648i | −0.233407 | + | 0.404274i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.0829 | 0.968681 | 0.484341 | − | 0.874880i | \(-0.339060\pi\) | ||||
0.484341 | + | 0.874880i | \(0.339060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.61370 | + | 7.99117i | 0.260782 | + | 0.451687i | 0.966450 | − | 0.256855i | \(-0.0826863\pi\) |
−0.705668 | + | 0.708543i | \(0.749353\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.61376 | 0.541674 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.34172 | + | 4.05598i | 0.131524 | + | 0.227806i | 0.924264 | − | 0.381753i | \(-0.124680\pi\) |
−0.792740 | + | 0.609560i | \(0.791346\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.995862 | − | 1.72488i | −0.0557576 | − | 0.0965750i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.7907 | − | 41.2067i | 1.32787 | − | 2.29994i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.5363 | − | 2.65912i | 1.03139 | − | 0.147958i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.53238 | + | 2.65416i | −0.0850011 | + | 0.147226i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.4392 | + | 31.9376i | 1.01969 | + | 1.76616i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.55393 | − | 2.69148i | −0.0856707 | − | 0.148386i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.2279 | 1.66147 | 0.830737 | − | 0.556665i | \(-0.187919\pi\) | ||||
0.830737 | + | 0.556665i | \(0.187919\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.74212 | − | 3.01745i | −0.0954678 | − | 0.165355i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.0329 | 1.36769 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.98286 | − | 6.89851i | 0.216960 | − | 0.375786i | −0.736917 | − | 0.675983i | \(-0.763719\pi\) |
0.953877 | + | 0.300197i | \(0.0970525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.6615 | + | 25.3945i | −0.796306 | + | 1.37924i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.93078 | 0.321170 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2822 | −0.987146 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.6746 | − | 25.4171i | 0.790051 | − | 1.36841i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0889 | − | 19.2066i | 0.595286 | − | 1.03106i | −0.398221 | − | 0.917290i | \(-0.630372\pi\) |
0.993507 | − | 0.113775i | \(-0.0362944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.7509 | −1.21783 | −0.608915 | − | 0.793236i | \(-0.708395\pi\) | ||||
−0.608915 | + | 0.793236i | \(0.708395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.35736 | − | 2.35102i | −0.0724506 | − | 0.125488i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.63919 | 0.300144 | 0.150072 | − | 0.988675i | \(-0.452049\pi\) | ||||
0.150072 | + | 0.988675i | \(0.452049\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.78681 | − | 10.0231i | −0.307132 | − | 0.531968i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.27942 | − | 14.3404i | −0.438194 | − | 0.758974i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.90326 | + | 3.29655i | −0.100450 | + | 0.173985i | −0.911870 | − | 0.410478i | \(-0.865362\pi\) |
0.811420 | + | 0.584464i | \(0.198695\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.49111 | + | 18.4616i | −0.236374 | + | 0.971662i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.7397 | − | 20.3338i | 0.616175 | − | 1.06725i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.06001 | + | 3.56804i | 0.107826 | + | 0.186760i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.49879 | + | 4.32803i | 0.130436 | + | 0.225921i | 0.923845 | − | 0.382768i | \(-0.125029\pi\) |
−0.793409 | + | 0.608689i | \(0.791696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.8715 | −1.19064 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.28389 | + | 12.6161i | 0.378161 | + | 0.654993i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.76470 | 0.350263 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.0510 | − | 24.3370i | 0.725590 | − | 1.25676i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.78137 | + | 10.0136i | −0.297756 | + | 0.515728i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.1509 | 1.39465 | 0.697325 | − | 0.716755i | \(-0.254373\pi\) | ||||
0.697325 | + | 0.716755i | \(0.254373\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.2971 | −1.19355 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.04883 | + | 5.28072i | −0.155788 | + | 0.269832i | −0.933346 | − | 0.358979i | \(-0.883125\pi\) |
0.777558 | + | 0.628811i | \(0.216458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.91862 | − | 3.32314i | 0.0977818 | − | 0.169363i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.3353 | −0.677869 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.45931 | + | 14.6520i | 0.428904 | + | 0.742884i | 0.996776 | − | 0.0802333i | \(-0.0255665\pi\) |
−0.567872 | + | 0.823117i | \(0.692233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.5316 | −1.24061 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.4255 | − | 28.4498i | −0.828557 | − | 1.43510i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.9608 | + | 27.6449i | 0.803075 | + | 1.39097i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4086 | − | 19.7604i | 0.572584 | − | 0.991744i | −0.423716 | − | 0.905795i | \(-0.639274\pi\) |
0.996300 | − | 0.0859489i | \(-0.0273922\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.6308 | − | 2.38578i | 0.832584 | − | 0.119438i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.1128 | − | 31.3723i | 0.904512 | − | 1.56666i | 0.0829401 | − | 0.996555i | \(-0.473569\pi\) |
0.821571 | − | 0.570106i | \(-0.193098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.2152 | − | 29.8177i | −0.857552 | − | 1.48532i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0968 | + | 17.4882i | 0.501714 | + | 0.868993i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.39070 | −0.0689345 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.46125 | − | 16.3874i | −0.467829 | − | 0.810303i | 0.531495 | − | 0.847061i | \(-0.321630\pi\) |
−0.999324 | + | 0.0367579i | \(0.988297\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.0190 | −0.987467 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.13308 | + | 3.69460i | −0.104962 | + | 0.181799i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.32620 | + | 7.49319i | −0.212365 | + | 0.367826i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.24514 | −0.109945 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0862 | 1.37210 | 0.686050 | − | 0.727554i | \(-0.259343\pi\) | ||||
0.686050 | + | 0.727554i | \(0.259343\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6610 | − | 23.6616i | 0.665798 | − | 1.15320i | −0.313271 | − | 0.949664i | \(-0.601425\pi\) |
0.979068 | − | 0.203532i | \(-0.0652420\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.75290 | + | 4.76816i | −0.133850 | + | 0.231836i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00893 | −0.0974472 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.40836 | − | 16.2958i | −0.455303 | − | 0.788607i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.8627 | 0.862420 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.6534 | + | 27.1125i | 0.753998 | + | 1.30596i | 0.945871 | + | 0.324543i | \(0.105211\pi\) |
−0.191873 | + | 0.981420i | \(0.561456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8201 | + | 20.4730i | 0.568038 | + | 0.983871i | 0.996760 | + | 0.0804347i | \(0.0256309\pi\) |
−0.428721 | + | 0.903437i | \(0.641036\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.53386 | − | 7.85287i | 0.217382 | − | 0.376516i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.25816 | − | 23.1046i | 0.442878 | − | 1.10524i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.59725 | + | 14.8909i | −0.410325 | + | 0.710703i | −0.994925 | − | 0.100618i | \(-0.967918\pi\) |
0.584601 | + | 0.811321i | \(0.301251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.29466 | + | 10.9027i | 0.299746 | + | 0.519175i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.46052 | + | 2.52970i | 0.0693914 | + | 0.120190i | 0.898634 | − | 0.438700i | \(-0.144561\pi\) |
−0.829242 | + | 0.558890i | \(0.811228\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.89707 | −0.137334 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.0811 | − | 33.0495i | −0.902507 | − | 1.56319i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.5108 | −0.826387 | −0.413194 | − | 0.910643i | \(-0.635587\pi\) | ||||
−0.413194 | + | 0.910643i | \(0.635587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.56447 | + | 7.90589i | −0.214932 | + | 0.372274i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.05616 | − | 5.29342i | 0.143591 | − | 0.248706i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.2766 | −1.04435 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.52460 | −0.445542 | −0.222771 | − | 0.974871i | \(-0.571510\pi\) | ||||
−0.222771 | + | 0.974871i | \(0.571510\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.889741 | − | 1.54108i | 0.0415295 | − | 0.0719313i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.8956 | + | 29.2641i | −0.786909 | + | 1.36297i | 0.140944 | + | 0.990018i | \(0.454986\pi\) |
−0.927852 | + | 0.372948i | \(0.878347\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.0226 | −1.34879 | −0.674397 | − | 0.738369i | \(-0.735596\pi\) | ||||
−0.674397 | + | 0.738369i | \(0.735596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.5005 | + | 23.3836i | 0.626072 | + | 1.08439i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.8583 | 0.826385 | 0.413192 | − | 0.910644i | \(-0.364414\pi\) | ||||
0.413192 | + | 0.910644i | \(0.364414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.38649 | − | 16.2579i | −0.433428 | − | 0.750719i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.97743 | − | 10.3532i | −0.275426 | − | 0.477051i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.66132 | + | 4.60954i | −0.122367 | + | 0.211947i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.758164 | − | 1.89207i | 0.0347870 | − | 0.0868140i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.9040 | − | 22.3503i | 0.590832 | − | 1.02335i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.121608 | + | 0.210631i | 0.00555641 | + | 0.00962399i | 0.868790 | − | 0.495180i | \(-0.164898\pi\) |
−0.863234 | + | 0.504804i | \(0.831565\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.03678 | + | 6.99191i | 0.184061 | + | 0.318804i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.0098 | −1.00148 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.1615 | − | 33.1888i | −0.870081 | − | 1.50702i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.6545 | −1.66097 | −0.830486 | − | 0.557039i | \(-0.811937\pi\) | ||||
−0.830486 | + | 0.557039i | \(0.811937\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.04561 | + | 13.9354i | −0.363835 | + | 0.630181i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.0465 | + | 22.5973i | −0.588782 | + | 1.01980i | 0.405610 | + | 0.914046i | \(0.367059\pi\) |
−0.994392 | + | 0.105754i | \(0.966274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.57929 | −0.341354 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.79796 | −0.305545 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.33972 | + | 7.51661i | −0.194663 | + | 0.337166i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.486530 | + | 0.842695i | −0.0217801 | + | 0.0377242i | −0.876710 | − | 0.481019i | \(-0.840267\pi\) |
0.854930 | + | 0.518744i | \(0.173600\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −43.3186 | −1.93533 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.77432 | + | 16.9296i | 0.435816 | + | 0.754855i | 0.997362 | − | 0.0725906i | \(-0.0231267\pi\) |
−0.561546 | + | 0.827445i | \(0.689793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.940165 | −0.0418368 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −36.1576 | − | 62.6268i | −1.60582 | − | 2.78135i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.76224 | − | 4.78435i | −0.122434 | − | 0.212062i | 0.798293 | − | 0.602270i | \(-0.205737\pi\) |
−0.920727 | + | 0.390207i | \(0.872403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.54487 | − | 2.67579i | 0.0683408 | − | 0.118370i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.11565 | + | 1.41958i | 0.0492570 | + | 0.0626762i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.61811 | + | 6.26674i | −0.159433 | + | 0.276146i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.09879 | + | 1.90316i | 0.0483248 | + | 0.0837010i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.8426 | + | 27.4403i | 0.695415 | + | 1.20449i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.4177 | 0.982136 | 0.491068 | − | 0.871121i | \(-0.336607\pi\) | ||||
0.491068 | + | 0.871121i | \(0.336607\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.5034 | − | 19.9244i | −0.503008 | − | 0.871235i | −0.999994 | − | 0.00347673i | \(-0.998893\pi\) |
0.496986 | − | 0.867759i | \(-0.334440\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.80242 | −0.0786640 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.2845 | − | 19.5453i | 0.491559 | − | 0.851405i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.80355 | + | 8.31999i | −0.208850 | + | 0.361739i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.55781 | 0.327981 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.9970 | 2.29556 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.9795 | − | 36.3375i | 0.907022 | − | 1.57101i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.4020 | + | 47.4616i | −1.18248 | + | 2.04812i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.02490 | 0.216438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0495580 | − | 0.0858369i | −0.00213066 | − | 0.00369042i | 0.864958 | − | 0.501844i | \(-0.167345\pi\) |
−0.867089 | + | 0.498154i | \(0.834012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −52.6996 | −2.26156 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.2603 | + | 28.1637i | 0.696516 | + | 1.20640i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.7710 | + | 20.3880i | 0.503292 | + | 0.871727i | 0.999993 | + | 0.00380504i | \(0.00121118\pi\) |
−0.496701 | + | 0.867922i | \(0.665455\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.6676 | + | 28.8692i | −0.711357 | + | 1.23211i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.86041 | − | 7.13840i | 0.121857 | − | 0.304106i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.9695 | − | 20.7318i | 0.508996 | − | 0.881607i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.16572 | − | 5.48319i | −0.134377 | − | 0.232748i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.54458 | + | 7.87144i | 0.192560 | + | 0.333524i | 0.946098 | − | 0.323881i | \(-0.104988\pi\) |
−0.753538 | + | 0.657404i | \(0.771654\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.9000 | 1.30693 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.85444 | + | 10.1402i | 0.247175 | + | 0.428119i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.1682 | −1.27144 | −0.635719 | − | 0.771920i | \(-0.719296\pi\) | ||||
−0.635719 | + | 0.771920i | \(0.719296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.9291 | + | 22.3938i | −0.543930 | + | 0.942114i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.57191 | − | 13.1149i | 0.317990 | − | 0.550775i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.75590 | −0.157455 | −0.0787277 | − | 0.996896i | \(-0.525086\pi\) | ||||
−0.0787277 | + | 0.996896i | \(0.525086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.5858 | −1.65661 | −0.828307 | − | 0.560274i | \(-0.810696\pi\) | ||||
−0.828307 | + | 0.560274i | \(0.810696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.65685 | − | 16.7262i | 0.403421 | − | 0.698745i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.33512 | + | 2.31250i | −0.0556784 | + | 0.0964378i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.4854 | −0.644664 | −0.322332 | − | 0.946627i | \(-0.604467\pi\) | ||||
−0.322332 | + | 0.946627i | \(0.604467\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.4024 | + | 21.4816i | 0.515427 | + | 0.892746i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.48871 | 0.269197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.15049 | − | 8.92090i | −0.213311 | − | 0.369466i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.7324 | + | 34.1775i | 0.815834 | + | 1.41307i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.10441 | − | 10.5731i | 0.251956 | − | 0.436400i | −0.712108 | − | 0.702070i | \(-0.752260\pi\) |
0.964064 | + | 0.265669i | \(0.0855929\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.1496 | + | 18.0044i | 0.583023 | + | 0.741858i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.9983 | − | 25.9778i | 0.616947 | − | 1.06858i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.0813 | − | 24.3896i | −0.578251 | − | 1.00156i | −0.995680 | − | 0.0928502i | \(-0.970402\pi\) |
0.417429 | − | 0.908709i | \(-0.362931\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.30109 | − | 12.6459i | −0.299315 | − | 0.518429i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.2108 | −0.990881 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.63461 | − | 14.9556i | −0.352801 | − | 0.611069i | 0.633938 | − | 0.773384i | \(-0.281437\pi\) |
−0.986739 | + | 0.162315i | \(0.948104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.73546 | 0.233954 | 0.116977 | − | 0.993135i | \(-0.462680\pi\) | ||||
0.116977 | + | 0.993135i | \(0.462680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.6289 | + | 28.8021i | −0.677180 | + | 1.17291i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3525 | − | 17.9310i | 0.420889 | − | 0.729001i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00331 | 0.0407232 | 0.0203616 | − | 0.999793i | \(-0.493518\pi\) | ||||
0.0203616 | + | 0.999793i | \(0.493518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.80017 | −0.275557 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.37891 | − | 11.0486i | 0.258063 | − | 0.446978i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.17015 | − | 12.4191i | 0.289599 | − | 0.501601i | −0.684115 | − | 0.729374i | \(-0.739811\pi\) |
0.973714 | + | 0.227773i | \(0.0731446\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −41.5613 | −1.67591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.10345 | + | 7.10738i | 0.165199 | + | 0.286132i | 0.936726 | − | 0.350064i | \(-0.113840\pi\) |
−0.771527 | + | 0.636196i | \(0.780507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1500 | 0.448157 | 0.224079 | − | 0.974571i | \(-0.428063\pi\) | ||||
0.224079 | + | 0.974571i | \(0.428063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.18263 | − | 2.04838i | −0.0474575 | − | 0.0821987i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.08630 | + | 1.88153i | 0.0435218 | + | 0.0753820i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.2216 | − | 19.4364i | 0.448864 | − | 0.777456i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.7598 | + | 1.68700i | −0.469641 | + | 0.0673723i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.64608 | + | 4.58315i | −0.105506 | + | 0.182742i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.19828 | + | 14.1998i | 0.326368 | + | 0.565286i | 0.981788 | − | 0.189978i | \(-0.0608417\pi\) |
−0.655420 | + | 0.755265i | \(0.727508\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.4451 | + | 52.7325i | 1.21008 | + | 2.09593i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.5442 | −0.815271 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.5857 | − | 25.2633i | −0.577908 | − | 1.00097i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.3763 | 0.608276 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.52155 | + | 2.63540i | −0.0600975 | + | 0.104092i | −0.894509 | − | 0.447050i | \(-0.852474\pi\) |
0.834411 | + | 0.551142i | \(0.185808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4611 | + | 21.5833i | −0.491418 | + | 0.851160i | −0.999951 | − | 0.00988183i | \(-0.996854\pi\) |
0.508534 | + | 0.861042i | \(0.330188\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.2323 | −0.954147 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.65801 | −0.301067 | −0.150534 | − | 0.988605i | \(-0.548099\pi\) | ||||
−0.150534 | + | 0.988605i | \(0.548099\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.50831 | − | 2.61247i | 0.0592064 | − | 0.102549i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.1245 | − | 17.5361i | 0.396809 | − | 0.687294i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.8941 | 1.01331 | 0.506657 | − | 0.862148i | \(-0.330881\pi\) | ||||
0.506657 | + | 0.862148i | \(0.330881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.4846 | − | 25.0880i | −0.565960 | − | 0.980271i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.47369 | −0.213549 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.78624 | − | 16.9503i | −0.381218 | − | 0.660288i | 0.610019 | − | 0.792387i | \(-0.291162\pi\) |
−0.991237 | + | 0.132098i | \(0.957828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2163 | + | 22.8914i | 0.514056 | + | 0.890371i | 0.999867 | + | 0.0163075i | \(0.00519106\pi\) |
−0.485811 | + | 0.874064i | \(0.661476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33.9873 | − | 58.8677i | 1.31996 | − | 2.28623i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.6657 | − | 2.10386i | 0.568710 | − | 0.0815844i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.03715 | + | 8.72460i | −0.195039 | + | 0.337818i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.375754 | − | 0.650825i | −0.0145275 | − | 0.0251623i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.65272 | + | 11.5228i | 0.256825 | + | 0.444834i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.3668 | 1.17055 | 0.585276 | − | 0.810834i | \(-0.300986\pi\) | ||||
0.585276 | + | 0.810834i | \(0.300986\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0968476 | − | 0.167745i | −0.00372767 | − | 0.00645651i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.38843 | 0.207094 | 0.103547 | − | 0.994625i | \(-0.466981\pi\) | ||||
0.103547 | + | 0.994625i | \(0.466981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.3699 | + | 24.8893i | −0.551465 | + | 0.955165i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.0290 | − | 29.4951i | 0.652552 | − | 1.13025i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.762636 | 0.0291814 | 0.0145907 | − | 0.999894i | \(-0.495355\pi\) | ||||
0.0145907 | + | 0.999894i | \(0.495355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.6535 | −0.674506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.6676 | + | 25.4051i | −0.559605 | + | 0.969264i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.9006 | + | 51.7893i | −1.13912 | + | 1.97302i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.65685 | −0.367364 | −0.183682 | − | 0.982986i | \(-0.558802\pi\) | ||||
−0.183682 | + | 0.982986i | \(0.558802\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.54900 | + | 4.41500i | 0.0968286 | + | 0.167712i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.97984 | −0.0750997 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3696 | + | 30.0850i | 0.657920 | + | 1.13955i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.02476 | − | 1.77494i | −0.0387600 | − | 0.0671343i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.64191 | + | 13.2362i | −0.288631 | + | 0.499923i | −0.973483 | − | 0.228759i | \(-0.926533\pi\) |
0.684852 | + | 0.728682i | \(0.259867\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.31792 | − | 4.22183i | −0.125138 | − | 0.159229i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.00246 | + | 8.66452i | −0.188404 | + | 0.326325i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.352530 | + | 0.610600i | 0.0132583 | + | 0.0229640i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.02241 | + | 5.23497i | 0.113509 | + | 0.196603i | 0.917183 | − | 0.398467i | \(-0.130458\pi\) |
−0.803674 | + | 0.595070i | \(0.797124\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −42.4099 | −1.59049 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.9992 | − | 25.9794i | −0.561724 | − | 0.972934i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.7520 | 0.589090 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.8569 | − | 39.5892i | 0.853605 | − | 1.47849i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.8947 | + | 30.9945i | −0.667358 | + | 1.15590i | 0.311282 | + | 0.950318i | \(0.399242\pi\) |
−0.978640 | + | 0.205581i | \(0.934092\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.42667 | 0.202100 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.5741 | −0.504826 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.412500 | + | 0.714470i | −0.0153199 | + | 0.0265348i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.07736 | + | 3.59810i | −0.0770451 | + | 0.133446i | −0.901974 | − | 0.431791i | \(-0.857882\pi\) |
0.824929 | + | 0.565237i | \(0.191215\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1273 | + | 17.5411i | 0.374573 | + | 0.648780i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.2024 | −0.376835 | −0.188418 | − | 0.982089i | \(-0.560336\pi\) | ||||
−0.188418 | + | 0.982089i | \(0.560336\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.4384 | + | 19.8119i | 0.421912 | + | 0.730774i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.63725 | + | 11.4961i | 0.244486 | + | 0.423463i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.6542 | + | 34.0421i | −0.722992 | + | 1.25226i | 0.236803 | + | 0.971558i | \(0.423900\pi\) |
−0.959795 | + | 0.280701i | \(0.909433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.6166 | + | 54.2268i | 1.56556 | + | 1.99207i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.7748 | + | 42.9112i | −0.908899 | + | 1.57426i | −0.0933020 | + | 0.995638i | \(0.529742\pi\) |
−0.815597 | + | 0.578621i | \(0.803591\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.8264 | − | 29.1442i | −0.616473 | − | 1.06776i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.74762 | − | 9.95517i | −0.210294 | − | 0.364241i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.4664 | −1.14976 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.28872 | + | 5.69623i | 0.120007 | + | 0.207858i | 0.919770 | − | 0.392457i | \(-0.128375\pi\) |
−0.799763 | + | 0.600316i | \(0.795042\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −54.8205 | −1.99777 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.69503 | − | 4.66792i | 0.0980820 | − | 0.169883i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.76810 | − | 4.79448i | 0.100608 | − | 0.174258i | −0.811327 | − | 0.584592i | \(-0.801254\pi\) |
0.911935 | + | 0.410334i | \(0.134588\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.5633 | 0.564912 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.1371 | −1.38247 | −0.691234 | − | 0.722631i | \(-0.742933\pi\) | ||||
−0.691234 | + | 0.722631i | \(0.742933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1942 | − | 21.1209i | 0.441458 | − | 0.764628i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.9344 | + | 22.4031i | −0.467645 | + | 0.809985i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.5127 | −0.632346 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.324873 | + | 0.562697i | 0.0117152 | + | 0.0202914i | 0.871824 | − | 0.489820i | \(-0.162938\pi\) |
−0.860108 | + | 0.510111i | \(0.829604\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.8142 | 1.18178 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.44740 | − | 14.6313i | −0.303832 | − | 0.526252i | 0.673169 | − | 0.739489i | \(-0.264933\pi\) |
−0.977001 | + | 0.213237i | \(0.931599\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.22830 | − | 2.12749i | −0.0441220 | − | 0.0764216i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.37408 | + | 4.11202i | −0.0851695 | + | 0.147518i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34.8902 | + | 5.00518i | −1.25007 | + | 0.179329i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.06864 | − | 5.31505i | 0.109805 | − | 0.190187i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.365387 | − | 0.632869i | −0.0130579 | − | 0.0226169i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.27111 | − | 9.12983i | −0.188134 | − | 0.325858i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.3868 | 0.691065 | 0.345533 | − | 0.938407i | \(-0.387698\pi\) | ||||
0.345533 | + | 0.938407i | \(0.387698\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.8660 | − | 55.1935i | −1.13446 | − | 1.96494i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.3919 | 0.689495 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.6216 | − | 66.8946i | 1.37149 | − | 2.37550i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.4486 | − | 40.6141i | 0.831636 | − | 1.44044i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.3750 | 1.57184 | 0.785922 | − | 0.618325i | \(-0.212189\pi\) | ||||
0.785922 | + | 0.618325i | \(0.212189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.36265 | 0.295849 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.92447 | − | 3.33328i | 0.0679978 | − | 0.117776i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.09239 | + | 1.89207i | −0.0385494 | + | 0.0667696i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.4091 | −0.684079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.2059 | − | 26.3375i | −0.535275 | − | 0.927123i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.0138 | 0.598175 | 0.299088 | − | 0.954226i | \(-0.403318\pi\) | ||||
0.299088 | + | 0.954226i | \(0.403318\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.7397 | − | 20.3338i | −0.412237 | − | 0.714016i | 0.582897 | − | 0.812546i | \(-0.301919\pi\) |
−0.995134 | + | 0.0985305i | \(0.968586\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.82675 | + | 15.2884i | 0.309568 | + | 0.536187i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.09490 | + | 12.2887i | −0.248524 | + | 0.430456i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.3428 | + | 2.91827i | −0.711703 | + | 0.102097i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.7980 | − | 25.6308i | 0.517082 | − | 0.895613i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7074 | + | 20.2779i | 0.408593 | + | 0.707703i | 0.994732 | − | 0.102507i | \(-0.0326863\pi\) |
−0.586140 | + | 0.810210i | \(0.699353\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.46418 | + | 9.46423i | 0.190469 | + | 0.329902i | 0.945406 | − | 0.325895i | \(-0.105666\pi\) |
−0.754937 | + | 0.655798i | \(0.772332\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.27450 | 0.0443725 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2502 | + | 31.6103i | 0.634622 | + | 1.09920i | 0.986595 | + | 0.163187i | \(0.0521774\pi\) |
−0.351974 | + | 0.936010i | \(0.614489\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.9489 | 1.38748 | 0.693741 | − | 0.720224i | \(-0.255961\pi\) | ||||
0.693741 | + | 0.720224i | \(0.255961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.0292 | + | 46.8160i | −0.937633 | + | 1.62403i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.56085 | − | 16.5599i | 0.331264 | − | 0.573766i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.1999 | −1.32196 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.17604 | 0.0752148 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.30752 | − | 16.1211i | 0.321331 | − | 0.556562i | −0.659432 | − | 0.751764i | \(-0.729203\pi\) |
0.980763 | + | 0.195202i | \(0.0625364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9437 | − | 22.4192i | 0.446335 | − | 0.773075i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 76.2751 | 2.62705 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.8850 | − | 55.2265i | −1.09688 | − | 1.89985i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.5273 | −0.533526 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.5594 | − | 49.4663i | −0.980155 | − | 1.69768i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.51714 | + | 6.09187i | 0.120566 | + | 0.208827i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.10458 | + | 10.5734i | −0.209017 | + | 0.362028i | −0.951405 | − | 0.307942i | \(-0.900360\pi\) |
0.742388 | + | 0.669970i | \(0.233693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.2185 | − | 20.6369i | −0.554660 | − | 0.705768i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.4186 | − | 38.8302i | 0.765805 | − | 1.32641i | −0.174014 | − | 0.984743i | \(-0.555674\pi\) |
0.939820 | − | 0.341671i | \(-0.110993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.52285 | − | 4.36971i | −0.0860787 | − | 0.149093i | 0.819772 | − | 0.572690i | \(-0.194100\pi\) |
−0.905850 | + | 0.423598i | \(0.860767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.5841 | + | 26.9924i | 0.531104 | + | 0.919899i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.85825 | 0.301538 | 0.150769 | − | 0.988569i | \(-0.451825\pi\) | ||||
0.150769 | + | 0.988569i | \(0.451825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.9706 | + | 24.1978i | 0.475015 | + | 0.822750i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.51518 | 0.119382 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.46373 | + | 14.6596i | −0.287113 | + | 0.497293i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.5318 | − | 66.7391i | 1.30560 | − | 2.26137i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 50.9146 | 1.72320 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.5843 | −0.628265 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.71386 | − | 11.6287i | 0.226711 | − | 0.392675i | −0.730120 | − | 0.683319i | \(-0.760536\pi\) |
0.956831 | + | 0.290644i | \(0.0938694\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.212494 | − | 0.368050i | 0.00716723 | − | 0.0124140i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.2128 | 1.52326 | 0.761630 | − | 0.648012i | \(-0.224400\pi\) | ||||
0.761630 | + | 0.648012i | \(0.224400\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.8908 | − | 24.0595i | −0.467462 | − | 0.809668i | 0.531847 | − | 0.846841i | \(-0.321498\pi\) |
−0.999309 | + | 0.0371725i | \(0.988165\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.7338 | 0.461656 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.1931 | − | 41.9037i | −0.812326 | − | 1.40699i | −0.911232 | − | 0.411893i | \(-0.864868\pi\) |
0.0989062 | − | 0.995097i | \(-0.468466\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.70338 | + | 13.3426i | 0.258363 | + | 0.447498i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.35415 | + | 9.27366i | −0.179371 | + | 0.310679i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.15605 | + | 7.87620i | −0.105613 | + | 0.263567i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.1640 | + | 41.8533i | −0.807714 | + | 1.39900i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −45.1755 | − | 78.2463i | −1.50837 | − | 2.61257i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.63416 | − | 8.02659i | −0.154558 | − | 0.267702i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.1992 | −1.30591 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.08630 | + | 15.7379i | 0.302373 | + | 0.523726i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −46.4724 | −1.54479 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0303 | − | 29.4973i | 0.565480 | − | 0.979441i | −0.431524 | − | 0.902101i | \(-0.642024\pi\) |
0.997005 | − | 0.0773396i | \(-0.0246426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.624534 | − | 1.08172i | 0.0207145 | − | 0.0358785i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.88594 | 0.161879 | 0.0809393 | − | 0.996719i | \(-0.474208\pi\) | ||||
0.0809393 | + | 0.996719i | \(0.474208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.58821 | −0.151848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −30.2878 | + | 52.4600i | −1.00128 | + | 1.73427i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.8625 | + | 18.8143i | −0.358710 | + | 0.621304i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.0148 | 1.81477 | 0.907386 | − | 0.420299i | \(-0.138075\pi\) | ||||
0.907386 | + | 0.420299i | \(0.138075\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.7544 | − | 56.7324i | −1.07930 | − | 1.86940i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.6293 | −1.17275 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.288024 | + | 0.498872i | 0.00947017 | + | 0.0164028i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.80688 | − | 8.32576i | −0.157879 | − | 0.273454i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.20395 | − | 2.08530i | 0.0395004 | − | 0.0684166i | −0.845599 | − | 0.533818i | \(-0.820757\pi\) |
0.885100 | + | 0.465401i | \(0.154090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.9883 | + | 15.2544i | 0.392902 | + | 0.499942i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.6209 | + | 35.7164i | −0.675096 | + | 1.16930i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.16265 | + | 8.94197i | 0.168837 | + | 0.292434i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.08821 | − | 7.08099i | −0.133556 | − | 0.231326i | 0.791489 | − | 0.611184i | \(-0.209306\pi\) |
−0.925045 | + | 0.379858i | \(0.875973\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.2769 | −0.726980 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.6309 | − | 32.2696i | −0.607349 | − | 1.05196i | −0.991675 | − | 0.128763i | \(-0.958899\pi\) |
0.384326 | − | 0.923197i | \(-0.374434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.1749 | 1.50366 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.703951 | − | 1.21928i | 0.0228995 | − | 0.0396632i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.5903 | − | 35.6634i | 0.669094 | − | 1.15890i | −0.309064 | − | 0.951041i | \(-0.600016\pi\) |
0.978158 | − | 0.207863i | \(-0.0666509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.6834 | 0.411722 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.3068 | −0.366649 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.81267 | − | 4.87169i | 0.0911114 | − | 0.157810i | −0.816868 | − | 0.576825i | \(-0.804291\pi\) |
0.907979 | + | 0.419016i | \(0.137625\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.51575 | − | 14.7497i | 0.275563 | − | 0.477290i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.80845 | 0.155435 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.61947 | + | 11.4653i | 0.213754 | + | 0.370232i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.40164 | −0.109730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.8726 | + | 48.2767i | 0.898181 | + | 1.55569i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.9369 | + | 18.9432i | 0.352071 | + | 0.609805i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6260 | − | 28.7971i | 0.534657 | − | 0.926052i | −0.464523 | − | 0.885561i | \(-0.653774\pi\) |
0.999180 | − | 0.0404914i | \(-0.0128923\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.8157 | + | 41.9650i | −0.540197 | + | 1.34811i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.9160 | + | 34.4955i | −0.639134 | + | 1.10701i | 0.346489 | + | 0.938054i | \(0.387374\pi\) |
−0.985623 | + | 0.168959i | \(0.945959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.742374 | + | 1.28583i | 0.0237994 | + | 0.0412218i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.69949 | − | 6.40770i | −0.118478 | − | 0.205211i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.54500 | 0.241386 | 0.120693 | − | 0.992690i | \(-0.461488\pi\) | ||||
0.120693 | + | 0.992690i | \(0.461488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.768133 | − | 1.33044i | −0.0245496 | − | 0.0425212i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43.2057 | −1.37945 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.3598 | − | 23.1398i | 0.426111 | − | 0.738046i | −0.570412 | − | 0.821358i | \(-0.693217\pi\) |
0.996523 | + | 0.0833125i | \(0.0265500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2260 | − | 22.9081i | 0.421416 | − | 0.729914i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.50302 | 0.238824 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.9223 | 0.856080 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.753916 | − | 1.30582i | 0.0239489 | − | 0.0414808i | −0.853803 | − | 0.520597i | \(-0.825709\pi\) |
0.877751 | + | 0.479116i | \(0.159043\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.4883 | + | 63.1995i | −1.15792 | + | 2.00558i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.3499 | −0.676838 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.01634 | + | 3.49240i | 0.0638580 | + | 0.110605i | 0.896187 | − | 0.443677i | \(-0.146326\pi\) |
−0.832329 | + | 0.554282i | \(0.812993\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.510256 | −0.0161438 |
(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 | 1216.2.i.o.961.1 | 8 | ||
4.3 | odd | 2 | 1216.2.i.q.961.3 | 8 | |||
8.3 | odd | 2 | 608.2.i.c.353.2 | ✓ | 8 | ||
8.5 | even | 2 | 608.2.i.e.353.4 | yes | 8 | ||
19.7 | even | 3 | inner | 1216.2.i.o.577.1 | 8 | ||
76.7 | odd | 6 | 1216.2.i.q.577.3 | 8 | |||
152.45 | even | 6 | 608.2.i.e.577.4 | yes | 8 | ||
152.83 | odd | 6 | 608.2.i.c.577.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.i.c.353.2 | ✓ | 8 | 8.3 | odd | 2 | ||
608.2.i.c.577.2 | yes | 8 | 152.83 | odd | 6 | ||
608.2.i.e.353.4 | yes | 8 | 8.5 | even | 2 | ||
608.2.i.e.577.4 | yes | 8 | 152.45 | even | 6 | ||
1216.2.i.o.577.1 | 8 | 19.7 | even | 3 | inner | ||
1216.2.i.o.961.1 | 8 | 1.1 | even | 1 | trivial | ||
1216.2.i.q.577.3 | 8 | 76.7 | odd | 6 | |||
1216.2.i.q.961.3 | 8 | 4.3 | odd | 2 |