Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\), 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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.11 | ||
Character | \(\chi\) | \(=\) | 336.17 |
Dual form | 336.4.bc.f.257.11 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.919514 | − | 5.11415i | −0.176960 | − | 0.984218i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.04693 | − | 10.4736i | −0.540854 | − | 0.936786i | −0.998855 | − | 0.0478345i | \(-0.984768\pi\) |
0.458002 | − | 0.888951i | \(-0.348565\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.9632 | − | 9.39028i | −0.861930 | − | 0.507027i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.3090 | + | 9.40505i | −0.937370 | + | 0.348335i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.2732 | − | 17.4782i | −0.829791 | − | 0.479080i | 0.0239903 | − | 0.999712i | \(-0.492363\pi\) |
−0.853781 | + | 0.520632i | \(0.825696\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 81.1032i | 1.73031i | 0.501507 | + | 0.865154i | \(0.332779\pi\) | ||||
−0.501507 | + | 0.865154i | \(0.667221\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −48.0032 | + | 40.5555i | −0.826292 | + | 0.698092i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.14503 | + | 7.17941i | −0.0591364 | + | 0.102427i | −0.894078 | − | 0.447911i | \(-0.852168\pi\) |
0.834942 | + | 0.550339i | \(0.185501\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 52.7556 | − | 30.4585i | 0.636998 | − | 0.367771i | −0.146459 | − | 0.989217i | \(-0.546788\pi\) |
0.783457 | + | 0.621446i | \(0.213454\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33.3449 | + | 90.2725i | −0.346498 | + | 0.938051i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 157.219 | − | 90.7706i | 1.42533 | − | 0.822912i | 0.428579 | − | 0.903504i | \(-0.359014\pi\) |
0.996747 | + | 0.0805920i | \(0.0256811\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.6306 | + | 18.4128i | −0.0850451 | + | 0.147302i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 71.3708 | + | 120.786i | 0.508715 | + | 0.860935i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 75.6434i | 0.484366i | 0.970231 | + | 0.242183i | \(0.0778635\pi\) | ||||
−0.970231 | + | 0.242183i | \(0.922137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −77.3344 | − | 44.6491i | −0.448054 | − | 0.258684i | 0.258954 | − | 0.965890i | \(-0.416622\pi\) |
−0.707008 | + | 0.707206i | \(0.749956\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −61.5496 | + | 170.893i | −0.324679 | + | 0.901473i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.82179 | + | 223.974i | −0.00879825 | + | 1.08167i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −58.4106 | − | 101.170i | −0.259531 | − | 0.449521i | 0.706585 | − | 0.707628i | \(-0.250235\pi\) |
−0.966116 | + | 0.258107i | \(0.916901\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 414.774 | − | 74.5755i | 1.70300 | − | 0.306196i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 147.344 | 0.561249 | 0.280625 | − | 0.959818i | \(-0.409458\pi\) | ||||
0.280625 | + | 0.959818i | \(0.409458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −389.121 | −1.38001 | −0.690005 | − | 0.723804i | \(-0.742392\pi\) | ||||
−0.690005 | + | 0.723804i | \(0.742392\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 251.546 | + | 208.204i | 0.833295 | + | 0.689716i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −99.8765 | − | 172.991i | −0.309968 | − | 0.536880i | 0.668387 | − | 0.743814i | \(-0.266985\pi\) |
−0.978355 | + | 0.206934i | \(0.933652\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 166.645 | + | 299.797i | 0.485846 | + | 0.874044i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 40.5279 | + | 14.5967i | 0.111275 | + | 0.0400775i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 578.226 | + | 333.839i | 1.49859 | + | 0.865214i | 0.999999 | − | 0.00162105i | \(-0.000515997\pi\) |
0.498595 | + | 0.866835i | \(0.333849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 422.758i | 1.03645i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −204.278 | − | 241.793i | −0.474690 | − | 0.561864i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.54890 | + | 14.8071i | −0.0188639 | + | 0.0326733i | −0.875303 | − | 0.483574i | \(-0.839338\pi\) |
0.856439 | + | 0.516248i | \(0.172672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −661.389 | + | 381.853i | −1.38823 | + | 0.801497i | −0.993116 | − | 0.117134i | \(-0.962629\pi\) |
−0.395117 | + | 0.918631i | \(0.629296\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 492.328 | + | 87.5240i | 0.984563 | + | 0.175032i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 849.442 | − | 490.425i | 1.62093 | − | 0.935843i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −428.169 | + | 741.610i | −0.780733 | + | 1.35227i | 0.150782 | + | 0.988567i | \(0.451821\pi\) |
−0.931515 | + | 0.363703i | \(0.881512\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −608.780 | − | 720.578i | −1.06215 | − | 1.25721i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 700.045i | 1.17014i | 0.810982 | + | 0.585070i | \(0.198933\pi\) | ||||
−0.810982 | + | 0.585070i | \(0.801067\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −748.329 | − | 432.048i | −1.19980 | − | 0.692704i | −0.239288 | − | 0.970949i | \(-0.576914\pi\) |
−0.960510 | + | 0.278245i | \(0.910247\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 103.941 | + | 37.4358i | 0.160027 | + | 0.0576362i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 319.130 | + | 563.281i | 0.472315 | + | 0.833660i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 463.245 | + | 802.364i | 0.659736 | + | 1.14270i | 0.980684 | + | 0.195600i | \(0.0626654\pi\) |
−0.320947 | + | 0.947097i | \(0.604001\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 552.090 | − | 476.065i | 0.757325 | − | 0.653038i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1053.69 | −1.39347 | −0.696734 | − | 0.717329i | \(-0.745364\pi\) | ||||
−0.696734 | + | 0.717329i | \(0.745364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 100.259 | 0.127936 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 386.851 | − | 69.5551i | 0.476722 | − | 0.0857137i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −224.645 | − | 389.097i | −0.267554 | − | 0.463418i | 0.700675 | − | 0.713480i | \(-0.252882\pi\) |
−0.968230 | + | 0.250063i | \(0.919549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 761.582 | − | 1294.66i | 0.877313 | − | 1.49140i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −157.232 | + | 436.555i | −0.175314 | + | 0.486760i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −638.018 | − | 368.360i | −0.689045 | − | 0.397820i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 213.360i | 0.223334i | 0.993746 | + | 0.111667i | \(0.0356190\pi\) | ||||
−0.993746 | + | 0.111667i | \(0.964381\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 930.566 | + | 157.635i | 0.944701 | + | 0.160030i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −404.582 | + | 700.756i | −0.398588 | + | 0.690375i | −0.993552 | − | 0.113378i | \(-0.963833\pi\) |
0.594964 | + | 0.803752i | \(0.297166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −855.486 | + | 493.915i | −0.818384 | + | 0.472494i | −0.849859 | − | 0.527010i | \(-0.823313\pi\) |
0.0314750 | + | 0.999505i | \(0.489980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1147.11 | − | 196.630i | 1.06616 | − | 0.182754i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −502.297 | + | 290.002i | −0.453822 | + | 0.262014i | −0.709443 | − | 0.704763i | \(-0.751053\pi\) |
0.255621 | + | 0.966777i | \(0.417720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 121.714 | − | 210.814i | 0.106955 | − | 0.185251i | −0.807580 | − | 0.589757i | \(-0.799223\pi\) |
0.914535 | + | 0.404507i | \(0.132557\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −463.689 | + | 391.748i | −0.396499 | + | 0.334982i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 176.852i | 0.147229i | 0.997287 | + | 0.0736143i | \(0.0234534\pi\) | ||||
−0.997287 | + | 0.0736143i | \(0.976547\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1901.39 | − | 1097.77i | −1.54179 | − | 0.890150i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −762.780 | − | 2052.64i | −0.602727 | − | 1.62194i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 133.584 | − | 75.6830i | 0.102905 | − | 0.0583013i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −54.5242 | − | 94.4387i | −0.0409648 | − | 0.0709532i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −135.485 | − | 753.537i | −0.0993190 | − | 0.552392i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1254.60 | −0.897719 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 709.586 | 0.495792 | 0.247896 | − | 0.968787i | \(-0.420261\pi\) | ||||
0.247896 | + | 0.968787i | \(0.420261\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 357.802 | + | 1990.02i | 0.244207 | + | 1.35823i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −45.5566 | − | 78.9063i | −0.0303839 | − | 0.0526265i | 0.850434 | − | 0.526082i | \(-0.176340\pi\) |
−0.880818 | + | 0.473456i | \(0.843006\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1128.16 | − | 9.17638i | −0.735518 | − | 0.00598266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 833.486 | − | 1477.89i | 0.531371 | − | 0.942197i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −805.981 | − | 465.333i | −0.502625 | − | 0.290191i | 0.227172 | − | 0.973855i | \(-0.427052\pi\) |
−0.729797 | + | 0.683664i | \(0.760385\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1704.57i | − | 1.04014i | −0.854124 | − | 0.520070i | \(-0.825906\pi\) | ||
0.854124 | − | 0.520070i | \(-0.174094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −792.865 | + | 669.851i | −0.473555 | + | 0.400082i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1417.54 | − | 2455.25i | 0.828955 | − | 1.43579i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 792.257 | − | 457.410i | 0.453748 | − | 0.261971i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1379.97 | − | 1127.92i | 0.774274 | − | 0.632850i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2848.50 | − | 1644.58i | 1.56616 | − | 0.904225i | 0.569555 | − | 0.821954i | \(-0.307116\pi\) |
0.996610 | − | 0.0822720i | \(-0.0262176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −995.034 | + | 1723.45i | −0.536256 | + | 0.928823i | 0.462845 | + | 0.886439i | \(0.346829\pi\) |
−0.999101 | + | 0.0423842i | \(0.986505\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 37.3839 | − | 220.688i | 0.0197536 | − | 0.116611i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1079.96i | 0.559641i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3247.22 | + | 1874.78i | 1.65068 | + | 0.953019i | 0.976794 | + | 0.214180i | \(0.0687078\pi\) |
0.673882 | + | 0.738839i | \(0.264626\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1175.62 | − | 3264.10i | 0.586367 | − | 1.62805i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3362.08 | − | 27.3470i | −1.64577 | − | 0.0133866i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −83.7914 | − | 145.131i | −0.0402641 | − | 0.0697395i | 0.845191 | − | 0.534464i | \(-0.179487\pi\) |
−0.885455 | + | 0.464725i | \(0.846153\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2162.05 | − | 388.732i | 1.02009 | − | 0.183410i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 676.970 | 0.313686 | 0.156843 | − | 0.987624i | \(-0.449868\pi\) | ||||
0.156843 | + | 0.987624i | \(0.449868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4380.74 | −1.99396 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1048.73 | + | 1267.04i | −0.468995 | + | 0.566626i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −716.045 | − | 1240.23i | −0.314682 | − | 0.545045i | 0.664688 | − | 0.747121i | \(-0.268564\pi\) |
−0.979370 | + | 0.202076i | \(0.935231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 342.600 | − | 194.102i | 0.147989 | − | 0.0838441i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 83.5867 | + | 30.1050i | 0.0354958 | + | 0.0127843i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2583.90 | − | 1491.82i | −1.07894 | − | 0.622925i | −0.148328 | − | 0.988938i | \(-0.547389\pi\) |
−0.930610 | + | 0.366013i | \(0.880723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 420.728i | 0.172776i | 0.996262 | + | 0.0863880i | \(0.0275325\pi\) | ||||
−0.996262 | + | 0.0863880i | \(0.972468\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2561.01 | + | 3031.32i | 1.03451 | + | 1.22449i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −706.409 | + | 1223.54i | −0.280736 | + | 0.486250i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 250.966 | − | 144.896i | 0.0981416 | − | 0.0566621i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.09124 | − | 2598.32i | −0.00195943 | − | 0.999998i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3537.32 | − | 2042.27i | 1.34006 | − | 0.773684i | 0.353245 | − | 0.935531i | \(-0.385078\pi\) |
0.986816 | + | 0.161847i | \(0.0517450\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 807.596 | − | 1398.80i | 0.301202 | − | 0.521697i | −0.675206 | − | 0.737629i | \(-0.735945\pi\) |
0.976409 | + | 0.215931i | \(0.0692788\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3289.18 | − | 3893.22i | −1.20791 | − | 1.42974i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 596.168i | − | 0.215610i | −0.994172 | − | 0.107805i | \(-0.965618\pi\) | ||
0.994172 | − | 0.107805i | \(-0.0343822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −134.161 | − | 77.4579i | −0.0477910 | − | 0.0275922i | 0.475914 | − | 0.879492i | \(-0.342117\pi\) |
−0.523705 | + | 0.851900i | \(0.675451\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4186.41 | + | 1507.80i | 1.46909 | + | 0.529113i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 710.313 | − | 1207.51i | 0.245587 | − | 0.417490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −890.977 | − | 1543.22i | −0.303554 | − | 0.525770i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3125.36 | + | 3775.97i | −1.04941 | + | 1.26786i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2129.44 | −0.704767 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2328.06 | −0.759576 | −0.379788 | − | 0.925074i | \(-0.624003\pi\) | ||||
−0.379788 | + | 0.925074i | \(0.624003\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3580.13 | − | 643.700i | 1.15167 | − | 0.207069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2352.99 | + | 4075.49i | 0.746383 | + | 1.29277i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 815.235 | + | 1438.93i | 0.255031 | + | 0.450143i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1521.46 | + | 4224.34i | −0.469455 | + | 1.30344i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −582.273 | − | 336.176i | −0.177230 | − | 0.102324i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1385.14i | − | 0.415945i | −0.978135 | − | 0.207973i | \(-0.933314\pi\) | ||
0.978135 | − | 0.207973i | \(-0.0666865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 95.8772 | − | 565.991i | 0.0284081 | − | 0.167701i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −605.053 | + | 1047.98i | −0.176911 | + | 0.306419i | −0.940821 | − | 0.338904i | \(-0.889944\pi\) |
0.763910 | + | 0.645323i | \(0.223277\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5041.96 | + | 2910.98i | −1.45494 | + | 0.840012i | −0.998756 | − | 0.0498722i | \(-0.984119\pi\) |
−0.456187 | + | 0.889884i | \(0.650785\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2587.26 | − | 2150.02i | 0.736922 | − | 0.612386i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1233.80 | − | 712.335i | 0.346905 | − | 0.200286i | −0.316416 | − | 0.948620i | \(-0.602480\pi\) |
0.663321 | + | 0.748335i | \(0.269146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1207.89 | + | 2092.13i | −0.335294 | + | 0.580747i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3677.45 | − | 3106.89i | 1.00792 | − | 0.851537i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1673.51i | 0.452929i | 0.974019 | + | 0.226465i | \(0.0727168\pi\) | ||||
−0.974019 | + | 0.226465i | \(0.927283\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1907.97 | + | 1101.57i | 0.509971 | + | 0.294432i | 0.732822 | − | 0.680421i | \(-0.238203\pi\) |
−0.222851 | + | 0.974853i | \(0.571536\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2942.32 | − | 2385.72i | −0.776749 | − | 0.629811i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2132.26 | − | 3558.22i | 0.556020 | − | 0.927864i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2470.28 | + | 4278.65i | 0.636357 | + | 1.10220i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 968.886 | + | 5388.74i | 0.246589 | + | 1.37148i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6110.91 | −1.53672 | −0.768361 | − | 0.640016i | \(-0.778928\pi\) | ||||
−0.768361 | + | 0.640016i | \(0.778928\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6346.03 | −1.57696 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −92.1893 | − | 512.738i | −0.0226397 | − | 0.125917i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 586.762 | + | 1016.30i | 0.142417 | + | 0.246674i | 0.928406 | − | 0.371567i | \(-0.121179\pi\) |
−0.785989 | + | 0.618240i | \(0.787846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.5977 | + | 2163.49i | −0.00422188 | + | 0.519044i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −711.430 | − | 1914.46i | −0.168722 | − | 0.454030i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2283.56 | + | 1318.41i | 0.535400 | + | 0.309113i | 0.743212 | − | 0.669055i | \(-0.233301\pi\) |
−0.207813 | + | 0.978169i | \(0.566634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8074.80i | − | 1.87182i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1783.33 | + | 1506.65i | −0.408757 | + | 0.345338i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3876.21 | + | 6713.78i | −0.878574 | + | 1.52173i | −0.0256678 | + | 0.999671i | \(0.508171\pi\) |
−0.852906 | + | 0.522064i | \(0.825162\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3512.22 | + | 2027.78i | −0.787277 | + | 0.454535i | −0.839003 | − | 0.544127i | \(-0.816861\pi\) |
0.0517260 | + | 0.998661i | \(0.483528\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7321.39 | − | 2704.38i | −1.62312 | − | 0.599548i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 643.646 | − | 371.609i | 0.141139 | − | 0.0814868i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 576.130 | − | 997.886i | 0.124968 | − | 0.216452i | −0.796752 | − | 0.604306i | \(-0.793450\pi\) |
0.921721 | + | 0.387854i | \(0.126784\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2377.18 | + | 402.688i | 0.510101 | + | 0.0864097i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1042.40i | 0.221296i | 0.993860 | + | 0.110648i | \(0.0352926\pi\) | ||||
−0.993860 | + | 0.110648i | \(0.964707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1873.40 | + | 1081.61i | 0.393506 | + | 0.227191i | 0.683678 | − | 0.729783i | \(-0.260379\pi\) |
−0.290172 | + | 0.956975i | \(0.593712\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1297.18 | + | 3601.63i | −0.269608 | + | 0.748569i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2352.07 | − | 1383.60i | −0.483758 | − | 0.284569i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2422.14 | + | 4195.27i | 0.493006 | + | 0.853911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1091.15 | − | 196.187i | 0.219810 | − | 0.0395213i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5371.61 | −1.07103 | −0.535517 | − | 0.844525i | \(-0.679883\pi\) | ||||
−0.535517 | + | 0.844525i | \(0.679883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 206.778 | 0.0408105 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −49.4987 | − | 4904.00i | −0.00967073 | − | 0.958111i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7361.79 | + | 12751.0i | 1.42389 | + | 2.46625i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6211.61 | + | 3653.96i | 1.18947 | + | 0.699703i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3955.79 | + | 1424.74i | 0.750014 | + | 0.270129i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7998.74 | + | 4618.08i | 1.50166 | + | 0.866985i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3027.33i | 0.562797i | 0.959591 | + | 0.281399i | \(0.0907983\pi\) | ||||
−0.959591 | + | 0.281399i | \(0.909202\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3312.58 | + | 3920.92i | 0.609859 | + | 0.721855i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4481.30 | − | 7761.84i | 0.817078 | − | 1.41522i | −0.0907478 | − | 0.995874i | \(-0.528926\pi\) |
0.907826 | − | 0.419347i | \(-0.137741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1548.33 | − | 893.927i | 0.279606 | − | 0.161431i | −0.353639 | − | 0.935382i | \(-0.615056\pi\) |
0.633245 | + | 0.773951i | \(0.281723\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2060.38 | − | 5685.69i | −0.368537 | − | 1.01699i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5728.18 | − | 3307.17i | 1.01491 | − | 0.585959i | 0.102285 | − | 0.994755i | \(-0.467385\pi\) |
0.912626 | + | 0.408796i | \(0.134051\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1322.11 | − | 2289.96i | 0.232050 | − | 0.401923i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1944.98 | + | 2302.16i | 0.338187 | + | 0.400293i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 505.005i | 0.0869945i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1493.34 | − | 862.179i | −0.254878 | − | 0.147154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1190.05 | − | 428.615i | −0.201254 | − | 0.0724846i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.0903 | + | 3699.36i | −0.00504235 | + | 0.619915i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3731.74 | − | 6463.57i | −0.619684 | − | 1.07332i | −0.989543 | − | 0.144236i | \(-0.953928\pi\) |
0.369860 | − | 0.929088i | \(-0.379406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2429.82 | + | 2011.16i | 0.399860 | + | 0.330963i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10356.4 | 1.68905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 589.545 | 0.0952954 | 0.0476477 | − | 0.998864i | \(-0.484828\pi\) | ||||
0.0476477 | + | 0.998864i | \(0.484828\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 904.447 | − | 162.618i | 0.144905 | − | 0.0260536i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1560.77 | + | 2703.34i | 0.247861 | + | 0.429307i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 154.993 | − | 6350.56i | 0.0243989 | − | 0.999702i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3865.79 | + | 10733.4i | −0.603267 | + | 1.67497i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8535.10 | + | 4927.74i | 1.32043 | + | 0.762349i | 0.983797 | − | 0.179288i | \(-0.0573793\pi\) |
0.336631 | + | 0.941637i | \(0.390713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3853.61i | 0.591057i | 0.955334 | + | 0.295528i | \(0.0954957\pi\) | ||||
−0.955334 | + | 0.295528i | \(0.904504\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9796.12 | + | 5788.40i | −1.48968 | + | 0.880234i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5226.31 | − | 9052.23i | 0.788012 | − | 1.36488i | −0.139171 | − | 0.990268i | \(-0.544444\pi\) |
0.927183 | − | 0.374608i | \(-0.122223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7331.97 | − | 4233.12i | 1.09617 | − | 0.632875i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −509.887 | − | 613.579i | −0.0755912 | − | 0.0909637i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9947.70 | + | 5743.31i | −1.46245 | + | 0.844346i | −0.999124 | − | 0.0418417i | \(-0.986677\pi\) |
−0.463326 | + | 0.886188i | \(0.653344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1574.06 | + | 2726.36i | −0.229489 | + | 0.397487i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −432.838 | + | 365.682i | −0.0625842 | + | 0.0528742i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10450.2i | 1.49861i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1546.71 | − | 892.995i | −0.219994 | − | 0.127014i | 0.385953 | − | 0.922518i | \(-0.373873\pi\) |
−0.605947 | + | 0.795505i | \(0.707206\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3729.12 | + | 1385.78i | −0.526098 | + | 0.195503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6095.48 | − | 10758.8i | −0.852996 | − | 1.50558i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5796.80 | + | 10040.4i | 0.804683 | + | 1.39375i | 0.916505 | + | 0.400024i | \(0.130998\pi\) |
−0.111821 | + | 0.993728i | \(0.535668\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1153.62 | + | 6416.21i | 0.158861 | + | 0.883552i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6134.92 | −0.838103 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7025.12 | −0.952128 | −0.476064 | − | 0.879411i | \(-0.657937\pi\) | ||||
−0.476064 | + | 0.879411i | \(0.657937\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −652.474 | − | 3628.93i | −0.0877356 | − | 0.487968i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4735.12 | − | 8201.47i | −0.631732 | − | 1.09419i | −0.987197 | − | 0.159503i | \(-0.949011\pi\) |
0.355465 | − | 0.934689i | \(-0.384322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3969.81 | − | 6748.55i | 0.525508 | − | 0.893346i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9848.27 | − | 3659.71i | 1.29358 | − | 0.480706i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12106.3 | − | 6989.56i | −1.57792 | − | 0.911015i | −0.995149 | − | 0.0983806i | \(-0.968634\pi\) |
−0.582775 | − | 0.812634i | \(-0.698033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1504.99i | 0.194656i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −361.648 | + | 305.538i | −0.0464192 | + | 0.0392172i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5602.42 | − | 9703.68i | 0.713641 | − | 1.23606i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 453.470 | − | 261.811i | 0.0573274 | − | 0.0330980i | −0.471062 | − | 0.882100i | \(-0.656129\pi\) |
0.528390 | + | 0.849002i | \(0.322796\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 990.429 | + | 5778.01i | 0.124269 | + | 0.724968i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4171.52 | − | 2408.43i | 0.519491 | − | 0.299928i | −0.217235 | − | 0.976119i | \(-0.569704\pi\) |
0.736726 | + | 0.676191i | \(0.236371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3621.18 | − | 6272.07i | 0.447603 | − | 0.775271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8324.55 | − | 2903.63i | −1.02136 | − | 0.356253i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4083.65i | 0.497344i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10923.1 | − | 6306.47i | −1.32057 | − | 0.762432i | −0.336751 | − | 0.941594i | \(-0.609328\pi\) |
−0.983820 | + | 0.179161i | \(0.942662\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1638.67 | + | 4549.78i | −0.196666 | + | 0.546045i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 275.511 | − | 156.092i | 0.0328256 | − | 0.0185976i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6371.61 | + | 11036.0i | 0.753663 | + | 1.30538i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8717.40 | + | 1567.37i | −1.02372 | + | 0.184064i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16375.7 | −1.90932 | −0.954659 | − | 0.297701i | \(-0.903780\pi\) | ||||
−0.954659 | + | 0.297701i | \(0.903780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6148.10 | 0.711734 | 0.355867 | − | 0.934537i | \(-0.384186\pi\) | ||||
0.355867 | + | 0.934537i | \(0.384186\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4154.77 | + | 3438.89i | 0.477569 | + | 0.395282i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −88.1286 | − | 152.643i | −0.0100585 | − | 0.0174219i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14143.6 | + | 115.043i | 1.60294 | + | 0.0130382i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13860.0 | − | 4991.87i | −1.55983 | − | 0.561794i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5503.76 | − | 3177.60i | −0.615097 | − | 0.355127i | 0.159861 | − | 0.987140i | \(-0.448896\pi\) |
−0.774958 | + | 0.632013i | \(0.782229\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11089.9i | − | 1.23083i | −0.788204 | − | 0.615414i | \(-0.788989\pi\) | ||
0.788204 | − | 0.615414i | \(-0.211011\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3067.75 | − | 3631.13i | −0.338132 | − | 0.400228i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5529.47 | − | 9577.32i | 0.605287 | − | 1.04839i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 389.043 | − | 224.614i | 0.0422962 | − | 0.0244197i | −0.478703 | − | 0.877977i | \(-0.658893\pi\) |
0.520999 | + | 0.853557i | \(0.325560\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7037.23 | − | 6020.26i | −0.759878 | − | 0.650065i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6182.74 | + | 3569.61i | −0.663094 | + | 0.382838i | −0.793455 | − | 0.608629i | \(-0.791720\pi\) |
0.130361 | + | 0.991467i | \(0.458386\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2716.82 | + | 4705.68i | −0.289415 | + | 0.501282i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11029.9 | − | 13055.4i | −1.16710 | − | 1.38144i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2229.59i | − | 0.234345i | −0.993112 | − | 0.117172i | \(-0.962617\pi\) | ||
0.993112 | − | 0.117172i | \(-0.0373830\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4460.56 | − | 2575.31i | −0.465720 | − | 0.268883i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9728.92 | + | 3504.01i | 1.00906 | + | 0.363428i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18165.0 | − | 147.753i | −1.87162 | − | 0.0152237i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −173.693 | − | 300.845i | −0.0177790 | − | 0.0307942i | 0.856999 | − | 0.515318i | \(-0.172326\pi\) |
−0.874778 | + | 0.484524i | \(0.838993\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1163.00 | + | 11.7388i | −0.118267 | + | 0.00119373i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 499.529 | 0.0504672 | 0.0252336 | − | 0.999682i | \(-0.491967\pi\) | ||||
0.0252336 | + | 0.999682i | \(0.491967\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2521.67 | −0.253114 | −0.126557 | − | 0.991959i | \(-0.540393\pi\) | ||||
−0.126557 | + | 0.991959i | \(0.540393\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5523.06 | − | 993.036i | 0.550809 | − | 0.0990343i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1963.45 | + | 3400.79i | 0.194556 | + | 0.336980i | 0.946755 | − | 0.321956i | \(-0.104340\pi\) |
−0.752199 | + | 0.658936i | \(0.771007\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13798.9 | − | 7817.82i | 1.35858 | − | 0.769709i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6602.05 | − | 18330.6i | 0.645873 | − | 1.79327i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11779.9 | + | 6801.15i | 1.14512 | + | 0.661135i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1295.17i | 0.125108i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17774.1 | − | 3010.88i | −1.70612 | − | 0.289012i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5680.39 | + | 9838.73i | −0.541845 | + | 0.938503i | 0.456953 | + | 0.889491i | \(0.348941\pi\) |
−0.998798 | + | 0.0490121i | \(0.984393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8205.22 | − | 4737.29i | 0.777809 | − | 0.449068i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2951.62 | + | 17219.3i | 0.278061 | + | 1.62217i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2234.64 | − | 1290.17i | 0.209216 | − | 0.120791i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9543.14 | − | 16529.2i | 0.887969 | − | 1.53801i | 0.0456972 | − | 0.998955i | \(-0.485449\pi\) |
0.842272 | − | 0.539053i | \(-0.181218\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −665.174 | + | 561.972i | −0.0615137 | + | 0.0519698i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16255.8i | − | 1.49412i | −0.664756 | − | 0.747060i | \(-0.731465\pi\) | ||
0.664756 | − | 0.747060i | \(-0.268535\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −543.075 | − | 313.544i | −0.0496123 | − | 0.0286437i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3976.06 | − | 10699.6i | −0.361032 | − | 0.971535i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6573.61 | − | 11174.9i | 0.593294 | − | 1.00858i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5281.57 | + | 9147.95i | 0.473819 | + | 0.820679i | 0.999551 | − | 0.0299718i | \(-0.00954176\pi\) |
−0.525732 | + | 0.850650i | \(0.676208\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −622.483 | − | 3462.12i | −0.0555099 | − | 0.308735i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2625.85 | −0.232766 | −0.116383 | − | 0.993204i | \(-0.537130\pi\) | ||||
−0.116383 | + | 0.993204i | \(0.537130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9785.91 | 0.862311 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4028.15 | + | 22403.7i | 0.352853 | + | 1.96249i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3951.26 | − | 6843.79i | −0.344080 | − | 0.595964i | 0.641106 | − | 0.767452i | \(-0.278476\pi\) |
−0.985186 | + | 0.171488i | \(0.945142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7888.65 | + | 13923.9i | 0.682922 | + | 1.20539i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7444.16 | + | 4198.28i | 0.640678 | + | 0.361323i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10346.1 | + | 5973.34i | 0.885252 | + | 0.511100i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6982.65i | 0.593997i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5684.29 | + | 4802.37i | −0.480756 | + | 0.406167i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4428.45 | + | 7670.29i | −0.372387 | + | 0.644993i | −0.989932 | − | 0.141542i | \(-0.954794\pi\) |
0.617545 | + | 0.786535i | \(0.288127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7370.81 | + | 4255.54i | −0.616258 | + | 0.355797i | −0.775411 | − | 0.631457i | \(-0.782457\pi\) |
0.159152 | + | 0.987254i | \(0.449124\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1307.69 | − | 1573.63i | −0.108709 | − | 0.130817i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 641.107 | − | 370.144i | 0.0529926 | − | 0.0305953i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10395.1 | − | 18004.9i | 0.854370 | − | 1.47981i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 77.1022 | − | 455.156i | 0.00630122 | − | 0.0371979i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11950.1i | 0.971134i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6074.71 | + | 3507.24i | 0.490902 | + | 0.283422i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5253.44 | + | 14586.2i | −0.422165 | + | 1.17214i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 195.040 | − | 11988.5i | 0.0155862 | − | 0.958033i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3515.29 | − | 6088.65i | −0.279360 | − | 0.483866i | 0.691866 | − | 0.722026i | \(-0.256789\pi\) |
−0.971226 | + | 0.238160i | \(0.923456\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2151.66 | − | 386.865i | 0.170049 | − | 0.0305745i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2943.97 | −0.231387 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13482.4 | 1.05387 | 0.526935 | − | 0.849905i | \(-0.323341\pi\) | ||||
0.526935 | + | 0.849905i | \(0.323341\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13147.7 | − | 15884.7i | 1.02210 | − | 1.23487i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2303.98 | + | 3990.61i | 0.178136 | + | 0.308540i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 139.564 | − | 17158.3i | 0.0107322 | − | 1.31943i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6906.90 | + | 2487.62i | 0.528255 | + | 0.190259i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1711.26 | − | 987.995i | −0.130177 | − | 0.0751575i | 0.433498 | − | 0.901155i | \(-0.357279\pi\) |
−0.563674 | + | 0.825997i | \(0.690613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31559.0i | − | 2.38784i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −971.784 | − | 1150.25i | −0.0731350 | − | 0.0865658i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3293.90 | + | 5705.20i | −0.246574 | + | 0.427079i | −0.962573 | − | 0.271022i | \(-0.912638\pi\) |
0.715999 | + | 0.698101i | \(0.245972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1852.27 | − | 1069.41i | 0.137922 | − | 0.0796291i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13283.5 | + | 2415.22i | −0.983869 | + | 0.178889i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1886.69 | + | 1089.28i | −0.139006 | + | 0.0802549i | −0.567890 | − | 0.823104i | \(-0.692240\pi\) |
0.428884 | + | 0.903359i | \(0.358907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.0470 | + | 60.7032i | −0.00256860 | + | 0.00444895i | −0.867307 | − | 0.497774i | \(-0.834151\pi\) |
0.864738 | + | 0.502223i | \(0.167484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13697.1 | − | 16212.5i | −0.998612 | − | 1.18200i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3859.80i | 0.279939i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12250.2 | − | 7072.64i | −0.883850 | − | 0.510291i | −0.0119244 | − | 0.999929i | \(-0.503796\pi\) |
−0.871926 | + | 0.489638i | \(0.837129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7896.25 | − | 2843.95i | −0.566765 | − | 0.204129i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16820.3 | + | 9894.48i | 1.20107 | + | 0.706527i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11669.8 | − | 20212.7i | −0.829013 | − | 1.43589i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16886.0 | + | 20401.2i | −1.19342 | + | 1.44186i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8833.09 | 0.621091 | 0.310546 | − | 0.950558i | \(-0.399488\pi\) | ||||
0.310546 | + | 0.950558i | \(0.399488\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5439.77 | −0.380546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3048.89 | + | 548.184i | −0.212207 | + | 0.0381545i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11738.8 | − | 20332.2i | −0.812910 | − | 1.40800i | −0.910819 | − | 0.412806i | \(-0.864549\pi\) |
0.0979090 | − | 0.995195i | \(-0.468785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1600.45 | − | 941.458i | −0.110272 | − | 0.0648673i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −272.768 | + | 757.342i | −0.0186996 | + | 0.0519195i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2426.76 | + | 1401.09i | 0.165534 | + | 0.0955710i | 0.580478 | − | 0.814276i | \(-0.302866\pi\) |
−0.414944 | + | 0.909847i | \(0.636199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24832.3i | 1.68541i | 0.538376 | + | 0.842705i | \(0.319038\pi\) | ||||
−0.538376 | + | 0.842705i | \(0.680962\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3861.64 | − | 22796.4i | 0.260793 | − | 1.53953i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −659.408 | + | 1142.13i | −0.0443120 | + | 0.0767506i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7023.78 | + | 4055.18i | −0.469665 | + | 0.271161i | −0.716099 | − | 0.697998i | \(-0.754074\pi\) |
0.246435 | + | 0.969159i | \(0.420741\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6828.51 | − | 2522.32i | −0.454360 | − | 0.167832i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14030.1 | − | 8100.31i | 0.928967 | − | 0.536340i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7061.93 | + | 12231.6i | −0.465300 | + | 0.805923i | −0.999215 | − | 0.0396154i | \(-0.987387\pi\) |
0.533915 | + | 0.845538i | \(0.320720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7072.97 | + | 5975.59i | −0.463756 | + | 0.391804i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22028.2i | 1.43731i | 0.695364 | + | 0.718657i | \(0.255243\pi\) | ||||
−0.695364 | + | 0.718657i | \(0.744757\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10812.4 | + | 6242.54i | 0.702080 | + | 0.405346i | 0.808121 | − | 0.589016i | \(-0.200484\pi\) |
−0.106042 | + | 0.994362i | \(0.533818\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22184.7 | + | 12511.5i | 1.43356 | + | 0.808485i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −67.6800 | + | 8320.69i | −0.00435240 | + | 0.535091i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8915.31 | + | 15441.8i | 0.570580 | + | 0.988273i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1958.05 | + | 10890.3i | 0.124716 | + | 0.693644i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 968.455 | 0.0613908 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15068.0 | −0.950630 | −0.475315 | − | 0.879816i | \(-0.657666\pi\) | ||||
−0.475315 | + | 0.879816i | \(0.657666\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2140.69 | + | 11906.1i | 0.134415 | + | 0.747588i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4290.82 | − | 7431.91i | −0.268151 | − | 0.464451i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24314.5 | + | 13515.5i | −1.51236 | + | 0.840663i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6583.96 | − | 17717.4i | −0.407601 | − | 1.09685i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23791.9 | − | 13736.2i | −1.46603 | − | 0.846411i | −0.466748 | − | 0.884391i | \(-0.654574\pi\) |
−0.999278 | + | 0.0379800i | \(0.987908\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4302.73i | 0.263893i | 0.991257 | + | 0.131946i | \(0.0421227\pi\) | ||||
−0.991257 | + | 0.131946i | \(0.957877\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18679.1 | − | 15781.0i | 1.14029 | − | 0.963374i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 713.937 | − | 1236.58i | 0.0433814 | − | 0.0751388i | −0.843519 | − | 0.537099i | \(-0.819520\pi\) |
0.886901 | + | 0.461960i | \(0.152854\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 517.604 | − | 298.839i | 0.0313062 | − | 0.0180747i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6609.29 | − | 5492.35i | 0.397909 | − | 0.330664i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6918.20 | − | 3994.22i | 0.414594 | − | 0.239366i | −0.278168 | − | 0.960533i | \(-0.589727\pi\) |
0.692762 | + | 0.721167i | \(0.256394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −550.954 | + | 954.281i | −0.0328665 | + | 0.0569265i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23002.9 | + | 3896.62i | 1.36595 | + | 0.231388i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22182.4i | 1.31123i | 0.755094 | + | 0.655616i | \(0.227591\pi\) | ||||
−0.755094 | + | 0.655616i | \(0.772409\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16557.2 | + | 9559.29i | 0.974280 | + | 0.562501i | 0.900538 | − | 0.434776i | \(-0.143173\pi\) |
0.0737417 | + | 0.997277i | \(0.476506\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1183.84 | + | 3286.95i | −0.0693464 | + | 0.192541i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6725.79 | + | 11871.4i | 0.392203 | + | 0.692258i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6866.20 | + | 11892.6i | 0.398591 | + | 0.690380i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7083.80 | + | 1273.65i | −0.409381 | + | 0.0736058i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26696.4 | 1.53592 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13725.7 | 0.786164 | 0.393082 | − | 0.919503i | \(-0.371409\pi\) | ||||
0.393082 | + | 0.919503i | \(0.371409\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2982.72 | + | 30.1062i | −0.170081 | + | 0.00171672i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14678.4 | − | 25423.8i | −0.833292 | − | 1.44330i | −0.895414 | − | 0.445235i | \(-0.853120\pi\) |
0.0621223 | − | 0.998069i | \(-0.480213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2003.51 | − | 3405.90i | 0.113237 | − | 0.192498i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5915.89 | + | 2130.69i | 0.332889 | + | 0.119895i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18237.7 | + | 10529.5i | 1.02173 | + | 0.589899i | 0.914606 | − | 0.404346i | \(-0.132501\pi\) |
0.107129 | + | 0.994245i | \(0.465834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11255.3i | 0.627802i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19523.3 | + | 23108.6i | 1.08422 | + | 1.28333i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27075.4 | + | 46896.0i | −1.49709 | + | 2.59303i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10470.0 | + | 6044.86i | −0.576408 | + | 0.332789i | −0.759705 | − | 0.650268i | \(-0.774656\pi\) |
0.183297 | + | 0.983058i | \(0.441323\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13374.5 | − | 11254.6i | −0.733127 | − | 0.616924i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17852.9 | + | 10307.4i | −0.974388 | + | 0.562563i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −610.745 | + | 1057.84i | −0.0331902 | + | 0.0574872i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4777.48 | − | 5654.83i | −0.258513 | − | 0.305988i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26152.8i | 1.40910i | 0.709655 | + | 0.704549i | \(0.248851\pi\) | ||||
−0.709655 | + | 0.704549i | \(0.751149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6162.97 | − | 3558.19i | −0.330641 | − | 0.190896i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11810.1 | + | 4253.59i | 0.630915 | + | 0.227233i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13038.7 | − | 7387.15i | 0.693594 | − | 0.392960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7450.21 | + | 12904.1i | 0.394638 | + | 0.683533i | 0.993055 | − | 0.117652i | \(-0.0375367\pi\) |
−0.598417 | + | 0.801185i | \(0.704203\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19270.6 | − | 15950.2i | −1.01646 | − | 0.841320i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16211.3 | −0.851497 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34287.0 | −1.79337 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8558.55 | − | 1538.81i | 0.445781 | − | 0.0801506i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4510.47 | − | 7812.37i | −0.233953 | − | 0.405219i | 0.725015 | − | 0.688733i | \(-0.241833\pi\) |
−0.958968 | + | 0.283515i | \(0.908500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18294.3 | + | 148.804i | 0.944957 | + | 0.00768622i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3879.17 | − | 10770.5i | 0.199540 | − | 0.554025i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1392.81 | − | 804.137i | −0.0713483 | − | 0.0411930i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32781.8i | 1.67236i | 0.548452 | + | 0.836182i | \(0.315217\pi\) | ||||
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9495.42 | + | 17241.2i | −0.482417 | + | 0.875941i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1612.92 | − | 2793.66i | 0.0816088 | − | 0.141351i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16798.2 | + | 9698.47i | −0.846463 | + | 0.488706i | −0.859456 | − | 0.511210i | \(-0.829197\pi\) |
0.0129930 | + | 0.999916i | \(0.495864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20157.9 | − | 7632.85i | −1.01161 | − | 0.383050i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25924.0 | − | 14967.2i | 1.29569 | − | 0.748067i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1168.95 | + | 2024.68i | −0.0581875 | + | 0.100784i | −0.893652 | − | 0.448761i | \(-0.851865\pi\) |
0.835464 | + | 0.549545i | \(0.185199\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19610.2 | − | 16567.6i | 0.972197 | − | 0.821360i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 10849.6i | − | 0.535711i | −0.963459 | − | 0.267856i | \(-0.913685\pi\) | ||
0.963459 | − | 0.267856i | \(-0.0863150\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34449.4 | − | 19889.4i | −1.69413 | − | 0.978107i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26667.9 | − | 9910.05i | 1.30620 | − | 0.485395i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10741.5 | + | 87.3703i | 0.524011 | + | 0.00426227i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 680.252 | + | 1178.23i | 0.0330529 | + | 0.0572494i | 0.882079 | − | 0.471102i | \(-0.156144\pi\) |
−0.849026 | + | 0.528351i | \(0.822810\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5619.07 | + | 31252.1i | 0.271939 | + | 1.51247i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24067.6 | 1.16014 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30917.4 | −1.48443 | −0.742214 | − | 0.670163i | \(-0.766224\pi\) | ||||
−0.742214 | + | 0.670163i | \(0.766224\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5835.26 | + | 32454.5i | 0.279060 | + | 1.55208i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5386.71 | − | 9330.06i | −0.256594 | − | 0.444434i | 0.708733 | − | 0.705477i | \(-0.249267\pi\) |
−0.965327 | + | 0.261043i | \(0.915934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3922.54 | + | 2222.34i | −0.186115 | + | 0.105444i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2537.45 | + | 942.940i | −0.119924 | + | 0.0445648i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1200.91 | − | 693.344i | −0.0565348 | − | 0.0326404i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5088.61i | − | 0.238621i | −0.992857 | − | 0.119311i | \(-0.961932\pi\) | ||
0.992857 | − | 0.119311i | \(-0.0380685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4657.98 | − | 3935.29i | 0.217578 | − | 0.183821i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16560.6 | − | 28683.9i | 0.770562 | − | 1.33465i | −0.166693 | − | 0.986009i | \(-0.553309\pi\) |
0.937255 | − | 0.348644i | \(-0.113358\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1644.23 | − | 949.296i | 0.0762096 | − | 0.0439996i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11080.6 | − | 1899.36i | 0.511600 | − | 0.0876951i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7773.21 | − | 4487.86i | 0.357515 | − | 0.206411i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12235.5 | − | 21192.6i | 0.560591 | − | 0.970972i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9136.65 | + | 5398.73i | −0.417008 | + | 0.246405i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 45346.7i | − | 2.06177i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12144.6 | + | 7011.70i | 0.550075 | + | 0.317586i | 0.749152 | − | 0.662398i | \(-0.230461\pi\) |
−0.199077 | + | 0.979984i | \(0.563794\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4642.79 | − | 12890.7i | 0.209490 | − | 0.581651i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1660.69 | − | 2823.12i | 0.0746489 | − | 0.126901i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30969.5 | − | 53640.8i | −1.38684 | − | 2.40207i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −41295.7 | + | 7424.89i | −1.84227 | + | 0.331237i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5707.05 | 0.253644 | 0.126822 | − | 0.991926i | \(-0.459522\pi\) | ||||
0.126822 | + | 0.991926i | \(0.459522\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1655.97 | 0.0733215 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9345.02 | + | 7734.84i | 0.412222 | + | 0.341195i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15102.9 | + | 26158.9i | 0.663721 | + | 1.14960i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20043.8 | + | 35378.4i | 0.877580 | + | 1.54897i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37899.5 | + | 13650.1i | 1.65319 | + | 0.595421i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15291.3 | + | 8828.45i | 0.664542 | + | 0.383674i | 0.794005 | − | 0.607911i | \(-0.207992\pi\) |
−0.129463 | + | 0.991584i | \(0.541325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23363.4i | 1.01159i | 0.862654 | + | 0.505794i | \(0.168801\pi\) | ||||
−0.862654 | + | 0.505794i | \(0.831199\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13599.9 | + | 16097.4i | 0.586678 | + | 0.694418i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1013.36 | + | 1755.19i | −0.0435540 | + | 0.0754377i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20528.3 | + | 11852.0i | −0.879064 | + | 0.507528i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7098.48 | + | 39929.4i | −0.302858 | + | 1.70360i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21621.7 | + | 12483.3i | −0.919124 | + | 0.530657i | −0.883356 | − | 0.468704i | \(-0.844721\pi\) |
−0.0357685 | + | 0.999360i | \(0.511388\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1873.90 | + | 3245.69i | −0.0793683 | + | 0.137470i | −0.902978 | − | 0.429688i | \(-0.858624\pi\) |
0.823609 | + | 0.567158i | \(0.191957\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2492.30 | − | 2950.00i | −0.105177 | − | 0.124492i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 21381.4i | − | 0.899037i | −0.893271 | − | 0.449519i | \(-0.851596\pi\) | ||
0.893271 | − | 0.449519i | \(-0.148404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21555.1 | − | 12444.8i | −0.903062 | − | 0.521383i | −0.0248698 | − | 0.999691i | \(-0.507917\pi\) |
−0.878192 | + | 0.478307i | \(0.841250\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5633.09 | − | 2028.84i | −0.235150 | − | 0.0846928i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2843.12 | − | 46.2545i | −0.118257 | − | 0.00192392i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4093.59 | − | 7090.30i | −0.169658 | − | 0.293856i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −126.447 | − | 12527.5i | −0.00522181 | − | 0.517342i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8042.30 | −0.330931 | −0.165466 | − | 0.986216i | \(-0.552913\pi\) | ||||
−0.165466 | + | 0.986216i | \(0.552913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18667.1 | 0.765389 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5330.96 | − | 958.497i | 0.217803 | − | 0.0391606i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26490.0 | + | 45882.0i | 1.07844 | + | 1.86792i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.4268 | + | 2019.54i | −0.000666389 | + | 0.0819270i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3808.89 | − | 10575.4i | 0.153970 | − | 0.427500i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18366.5 | − | 10603.9i | −0.739832 | − | 0.427142i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6230.54i | − | 0.250093i | −0.992151 | − | 0.125047i | \(-0.960092\pi\) | ||
0.992151 | − | 0.125047i | \(-0.0399080\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19612.0 | + | 3322.22i | 0.784465 | + | 0.132886i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −259.511 | + | 449.486i | −0.0103439 | + | 0.0179162i | −0.871151 | − | 0.491015i | \(-0.836626\pi\) |
0.860807 | + | 0.508931i | \(0.169959\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2239.34 | − | 1292.89i | 0.0889469 | − | 0.0513535i | −0.454867 | − | 0.890559i | \(-0.650313\pi\) |
0.543814 | + | 0.839206i | \(0.316980\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4913.16 | + | 13301.1i | −0.194472 | + | 0.526480i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22261.6 | + | 12852.7i | −0.878091 | + | 0.506966i | −0.870029 | − | 0.493001i | \(-0.835900\pi\) |
−0.00806261 | + | 0.999967i | \(0.502566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8659.75 | + | 14999.1i | −0.340393 | + | 0.589578i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19228.0 | − | 16244.8i | 0.753192 | − | 0.636334i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 32386.8i | − | 1.26427i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60147.0 | − | 34725.9i | −2.33984 | − | 1.35091i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2006.66 | − | 5399.93i | −0.0777952 | − | 0.209347i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20027.4 | + | 11781.1i | 0.773771 | + | 0.455168i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7737.34 | + | 13401.5i | 0.297915 | + | 0.516004i | 0.975659 | − | 0.219294i | \(-0.0703755\pi\) |
−0.677744 | + | 0.735298i | \(0.737042\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4939.27 | + | 27471.2i | 0.189531 | + | 1.05413i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21804.4 | 0.833836 | 0.416918 | − | 0.908944i | \(-0.363110\pi\) | ||||
0.416918 | + | 0.908944i | \(0.363110\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24982.9 | 0.952142 | 0.476071 | − | 0.879407i | \(-0.342060\pi\) | ||||
0.476071 | + | 0.879407i | \(0.342060\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −190.135 | − | 1057.49i | −0.00722185 | − | 0.0401664i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6136.40 | − | 10628.6i | −0.232289 | − | 0.402336i | 0.726193 | − | 0.687491i | \(-0.241288\pi\) |
−0.958481 | + | 0.285156i | \(0.907955\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11327.2 | − | 6663.21i | −0.427338 | − | 0.251380i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25034.3 | + | 4762.44i | −0.941279 | + | 0.179066i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10538.1 | − | 6084.17i | −0.394898 | − | 0.227994i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36083.6i | 1.34765i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 58441.2 | − | 49374.0i | 2.17536 | − | 1.83785i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3377.41 | − | 5849.84i | 0.125298 | − | 0.217022i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4793.53 | + | 2767.55i | −0.177243 | + | 0.102331i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12975.2 | − | 35126.9i | 0.478171 | − | 1.29452i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4406.53 | − | 2544.11i | 0.161854 | − | 0.0934465i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21298.9 | − | 36890.8i | 0.779735 | − | 1.35054i | −0.152360 | − | 0.988325i | \(-0.548687\pi\) |
0.932095 | − | 0.362215i | \(-0.117979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3648.91 | − | 21540.6i | 0.133143 | − | 0.785979i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3752.25i | 0.136463i | 0.997670 | + | 0.0682313i | \(0.0217356\pi\) | ||||
−0.997670 | + | 0.0682313i | \(0.978264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31898.6 | + | 18416.7i | 1.15629 | + | 0.667583i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16262.6 | − | 45153.1i | 0.587567 | − | 1.63138i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.7251 | + | 1687.38i | −0.000494266 | + | 0.0607659i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3227.42 | − | 5590.05i | −0.115846 | − | 0.200651i | 0.802272 | − | 0.596959i | \(-0.203625\pi\) |
−0.918118 | + | 0.396308i | \(0.870291\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15482.2 | − | 2783.67i | 0.553915 | − | 0.0995929i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −56775.9 | −2.02470 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2483.77 | 0.0882873 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17006.2 | − | 20546.4i | 0.602542 | − | 0.727974i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9970.85 | − | 17270.0i | −0.352135 | − | 0.609915i | 0.634489 | − | 0.772932i | \(-0.281211\pi\) |
−0.986623 | + | 0.163017i | \(0.947877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17922.8 | + | 10740.2i | 0.630931 | + | 0.378084i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −43815.8 | − | 15780.9i | −1.53748 | − | 0.553745i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3035.15 | − | 1752.34i | −0.106160 | − | 0.0612918i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20595.3i | 0.718057i | 0.933327 | + | 0.359029i | \(0.116892\pi\) | ||||
−0.933327 | + | 0.359029i | \(0.883108\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5995.38 | − | 7096.40i | −0.208362 | − | 0.246626i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20620.5 | + | 35715.8i | −0.714357 | + | 1.23730i | 0.248850 | + | 0.968542i | \(0.419947\pi\) |
−0.963207 | + | 0.268760i | \(0.913386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23165.3 | − | 13374.5i | 0.799963 | − | 0.461859i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −27182.9 | + | 15765.1i | −0.935724 | + | 0.542688i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32099.0 | + | 18532.4i | −1.10145 | + | 0.635925i | −0.936603 | − | 0.350393i | \(-0.886048\pi\) |
−0.164852 | + | 0.986318i | \(0.552715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35040.5 | − | 60691.9i | 1.19859 | − | 2.07602i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22180.5 | − | 26253.8i | −0.756311 | − | 0.895202i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 32868.6i | − | 1.11723i | −0.829428 | − | 0.558614i | \(-0.811333\pi\) | ||
0.829428 | − | 0.558614i | \(-0.188667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42779.8 | − | 24699.0i | −1.44955 | − | 0.836900i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12926.9 | − | 4655.82i | −0.436643 | − | 0.157264i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8496.40 | + | 14996.6i | 0.286093 | + | 0.504968i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10908.4 | − | 18893.9i | −0.366165 | − | 0.634216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9985.16 | − | 12063.8i | 0.334130 | − | 0.403686i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19533.9 | −0.651625 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30226.5 | 1.00519 | 0.502595 | − | 0.864522i | \(-0.332379\pi\) | ||||
0.502595 | + | 0.864522i | \(0.332379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2582.67 | − | 464.359i | 0.0856216 | − | 0.0153946i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6665.95 | − | 11545.8i | −0.220310 | − | 0.381588i | 0.734592 | − | 0.678509i | \(-0.237373\pi\) |
−0.954902 | + | 0.296921i | \(0.904040\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16006.4 | + | 27210.3i | −0.527379 | + | 0.896528i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3036.16 | + | 8429.93i | −0.0997283 | + | 0.276896i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21717.6 | + | 12538.7i | 0.711166 | + | 0.410592i | 0.811492 | − | 0.584363i | \(-0.198656\pi\) |
−0.100327 | + | 0.994955i | \(0.531989\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15705.6i | 0.512720i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1097.73 | + | 6480.22i | −0.0357266 | + | 0.210905i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13328.7 | − | 23086.0i | 0.432472 | − | 0.749063i | −0.564614 | − | 0.825355i | \(-0.690975\pi\) |
0.997086 | + | 0.0762919i | \(0.0243081\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6244.01 | + | 3604.98i | −0.201980 | + | 0.116613i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18946.7 | − | 3247.72i | 0.611024 | − | 0.104738i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −61177.4 | + | 35320.8i | −1.96696 | + | 1.13563i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10219.7 | − | 17701.0i | 0.327588 | − | 0.567398i | −0.654445 | − | 0.756110i | \(-0.727098\pi\) |
0.982033 | + | 0.188711i | \(0.0604310\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29624.3 | + | 25028.0i | −0.946725 | + | 0.799839i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1873.53i | 0.0596933i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12044.5 | + | 6953.91i | 0.382602 | + | 0.220895i | 0.678950 | − | 0.734185i | \(-0.262435\pi\) |
−0.296348 | + | 0.955080i | \(0.595769\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8051.10 | − | 14275.8i | 0.254981 | − | 0.452117i |
(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 | 336.4.bc.f.17.11 | 48 | ||
3.2 | odd | 2 | inner | 336.4.bc.f.17.4 | 48 | ||
4.3 | odd | 2 | 168.4.u.a.17.14 | ✓ | 48 | ||
7.5 | odd | 6 | inner | 336.4.bc.f.257.4 | 48 | ||
12.11 | even | 2 | 168.4.u.a.17.21 | yes | 48 | ||
21.5 | even | 6 | inner | 336.4.bc.f.257.11 | 48 | ||
28.19 | even | 6 | 168.4.u.a.89.21 | yes | 48 | ||
84.47 | odd | 6 | 168.4.u.a.89.14 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.u.a.17.14 | ✓ | 48 | 4.3 | odd | 2 | ||
168.4.u.a.17.21 | yes | 48 | 12.11 | even | 2 | ||
168.4.u.a.89.14 | yes | 48 | 84.47 | odd | 6 | ||
168.4.u.a.89.21 | yes | 48 | 28.19 | even | 6 | ||
336.4.bc.f.17.4 | 48 | 3.2 | odd | 2 | inner | ||
336.4.bc.f.17.11 | 48 | 1.1 | even | 1 | trivial | ||
336.4.bc.f.257.4 | 48 | 7.5 | odd | 6 | inner | ||
336.4.bc.f.257.11 | 48 | 21.5 | even | 6 | inner |