Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(49,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bi (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Character | \(\chi\) | \(=\) | 360.49 |
Dual form | 360.2.bi.b.169.1 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −1.72704 | + | 0.131617i | −0.997109 | + | 0.0759891i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23514 | − | 0.0643013i | 0.999586 | − | 0.0287564i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.19102 | + | 0.687633i | −0.450161 | + | 0.259901i | −0.707898 | − | 0.706314i | \(-0.750357\pi\) |
0.257737 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.96535 | − | 0.454616i | 0.988451 | − | 0.151539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.00579778 | − | 0.0100420i | −0.00174810 | − | 0.00302779i | 0.865150 | − | 0.501513i | \(-0.167223\pi\) |
−0.866898 | + | 0.498485i | \(0.833890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.919334 | + | 0.530778i | 0.254977 | + | 0.147211i | 0.622041 | − | 0.782984i | \(-0.286304\pi\) |
−0.367064 | + | 0.930196i | \(0.619637\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.85173 | + | 0.405234i | −0.994511 | + | 0.104631i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.57910i | 0.382987i | 0.981494 | + | 0.191494i | \(0.0613331\pi\) | ||||
−0.981494 | + | 0.191494i | \(0.938667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.38234 | 1.46421 | 0.732105 | − | 0.681192i | \(-0.238538\pi\) | ||||
0.732105 | + | 0.681192i | \(0.238538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.96643 | − | 1.34433i | 0.429110 | − | 0.293357i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.37844 | + | 3.68260i | 1.33000 | + | 0.767874i | 0.985299 | − | 0.170839i | \(-0.0546479\pi\) |
0.344698 | + | 0.938714i | \(0.387981\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99173 | − | 0.287445i | 0.998346 | − | 0.0574891i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.06146 | + | 1.17543i | −0.974078 | + | 0.226212i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.66231 | + | 4.61126i | 0.494379 | + | 0.856289i | 0.999979 | − | 0.00647886i | \(-0.00206230\pi\) |
−0.505600 | + | 0.862768i | \(0.668729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.15651 | − | 2.00314i | 0.207716 | − | 0.359774i | −0.743279 | − | 0.668982i | \(-0.766730\pi\) |
0.950995 | + | 0.309207i | \(0.100064\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0113347 | + | 0.0165800i | 0.00197312 | + | 0.00288620i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.61787 | + | 1.61354i | −0.442501 | + | 0.272738i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.8828i | − | 1.78912i | −0.446948 | − | 0.894560i | \(-0.647489\pi\) | ||
0.446948 | − | 0.894560i | \(-0.352511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.65759 | − | 0.795676i | −0.265427 | − | 0.127410i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.09133 | + | 7.08638i | −0.638958 | + | 1.10671i | 0.346704 | + | 0.937975i | \(0.387301\pi\) |
−0.985662 | + | 0.168733i | \(0.946033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.93252 | − | 1.69309i | 0.447204 | − | 0.258194i | −0.259444 | − | 0.965758i | \(-0.583539\pi\) |
0.706649 | + | 0.707564i | \(0.250206\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.59876 | − | 1.20681i | 0.983685 | − | 0.179900i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.60966 | + | 2.66139i | −0.672388 | + | 0.388203i | −0.796981 | − | 0.604005i | \(-0.793571\pi\) |
0.124593 | + | 0.992208i | \(0.460237\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.55432 | + | 4.42422i | −0.364903 | + | 0.632031i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.207836 | − | 2.72717i | −0.0291028 | − | 0.381880i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.27370i | 0.174956i | 0.996166 | + | 0.0874782i | \(0.0278808\pi\) | ||||
−0.996166 | + | 0.0874782i | \(0.972119\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0136046 | − | 0.0220726i | −0.00183444 | − | 0.00297627i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.0226 | + | 0.840025i | −1.45998 | + | 0.111264i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.39712 | − | 5.88399i | 0.442268 | − | 0.766031i | −0.555589 | − | 0.831457i | \(-0.687507\pi\) |
0.997857 | + | 0.0654262i | \(0.0208407\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.29148 | − | 7.43306i | −0.549468 | − | 0.951706i | −0.998311 | − | 0.0580954i | \(-0.981497\pi\) |
0.448843 | − | 0.893610i | \(-0.351836\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.21917 | + | 2.58053i | −0.405578 | + | 0.325116i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.08897 | + | 1.12725i | 0.259105 | + | 0.139818i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.16967 | − | 4.71676i | −0.998084 | − | 0.576244i | −0.0904031 | − | 0.995905i | \(-0.528816\pi\) |
−0.907681 | + | 0.419661i | \(0.862149\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.5005 | − | 5.52049i | −1.38450 | − | 0.664589i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.4442 | −1.95157 | −0.975786 | − | 0.218727i | \(-0.929809\pi\) | ||||
−0.975786 | + | 0.218727i | \(0.929809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.32462i | − | 0.974323i | −0.873312 | − | 0.487162i | \(-0.838032\pi\) | ||
0.873312 | − | 0.487162i | \(-0.161968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.58310 | + | 1.15343i | −0.991091 | + | 0.133186i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0138105 | + | 0.00797348i | 0.00157385 | + | 0.000908663i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.86663 | + | 6.69719i | 0.435030 | + | 0.753493i | 0.997298 | − | 0.0734615i | \(-0.0234046\pi\) |
−0.562269 | + | 0.826955i | \(0.690071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.58665 | − | 2.69620i | 0.954072 | − | 0.299577i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.67610 | − | 2.69975i | 0.513269 | − | 0.296336i | −0.220907 | − | 0.975295i | \(-0.570902\pi\) |
0.734176 | + | 0.678959i | \(0.237569\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.101538 | + | 3.52951i | 0.0110133 | + | 0.382829i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.20484 | − | 7.61343i | −0.558018 | − | 0.816246i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.6835 | −1.34445 | −0.672223 | − | 0.740349i | \(-0.734660\pi\) | ||||
−0.672223 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.45992 | −0.153041 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.73370 | + | 3.61172i | −0.179776 | + | 0.374518i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.2655 | − | 0.410393i | 1.46360 | − | 0.0421055i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0741723 | + | 0.0428234i | −0.00753106 | + | 0.00434806i | −0.503761 | − | 0.863843i | \(-0.668051\pi\) |
0.496230 | + | 0.868191i | \(0.334717\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0217577 | − | 0.0271425i | −0.00218673 | − | 0.00272792i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.22526 | + | 12.5145i | 0.718940 | + | 1.24524i | 0.961420 | + | 0.275085i | \(0.0887058\pi\) |
−0.242480 | + | 0.970156i | \(0.577961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.27682 | + | 2.46922i | 0.421407 | + | 0.243300i | 0.695679 | − | 0.718353i | \(-0.255103\pi\) |
−0.274272 | + | 0.961652i | \(0.588437\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.30881 | − | 3.13121i | 0.420497 | − | 0.305575i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.5968i | − | 1.31445i | −0.753693 | − | 0.657227i | \(-0.771729\pi\) | ||
0.753693 | − | 0.657227i | \(-0.228271\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.92265 | −0.950417 | −0.475209 | − | 0.879873i | \(-0.657627\pi\) | ||||
−0.475209 | + | 0.879873i | \(0.657627\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.43236 | + | 18.7951i | 0.135954 | + | 1.78395i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.19397 | + | 1.26669i | 0.206391 | + | 0.119160i | 0.599633 | − | 0.800275i | \(-0.295313\pi\) |
−0.393242 | + | 0.919435i | \(0.628646\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4935 | + | 7.82099i | 1.35153 | + | 0.729311i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.96745 | + | 1.15600i | 0.274341 | + | 0.106872i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.08584 | − | 1.88073i | −0.0995387 | − | 0.172406i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.49993 | − | 9.52616i | 0.499994 | − | 0.866015i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.13321 | − | 12.7770i | 0.553013 | − | 1.15206i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1388 | − | 0.963456i | 0.996280 | − | 0.0861742i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2790i | 1.62200i | 0.585046 | + | 0.811000i | \(0.301076\pi\) | ||||
−0.585046 | + | 0.811000i | \(0.698924\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.84174 | + | 3.31000i | −0.426291 | + | 0.291430i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.64613 | − | 2.85119i | 0.143823 | − | 0.249109i | −0.785110 | − | 0.619356i | \(-0.787394\pi\) |
0.928933 | + | 0.370247i | \(0.120727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.60147 | + | 4.38871i | −0.659131 | + | 0.380549i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.2375 | + | 2.95272i | −0.967170 | + | 0.254129i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.56464 | + | 4.36744i | −0.646290 | + | 0.373136i | −0.787034 | − | 0.616910i | \(-0.788384\pi\) |
0.140743 | + | 0.990046i | \(0.455051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.30750 | − | 5.72876i | 0.280539 | − | 0.485908i | −0.690979 | − | 0.722875i | \(-0.742820\pi\) |
0.971518 | + | 0.236968i | \(0.0761535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.61079 | − | 5.20304i | 0.640944 | − | 0.438175i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.0123093i | − | 0.00102936i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.24716 | + | 10.1356i | 0.518798 | + | 0.841718i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.82912 | − | 7.97700i | 0.315821 | − | 0.657932i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.11139 | − | 5.38909i | 0.254895 | − | 0.441491i | −0.709972 | − | 0.704230i | \(-0.751292\pi\) |
0.964867 | + | 0.262739i | \(0.0846257\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.46299 | − | 4.26602i | −0.200435 | − | 0.347164i | 0.748233 | − | 0.663436i | \(-0.230902\pi\) |
−0.948669 | + | 0.316271i | \(0.897569\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.717883 | + | 4.68258i | 0.0580374 | + | 0.378564i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.45617 | − | 4.55167i | 0.197284 | − | 0.365599i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.14939 | − | 4.70505i | −0.650392 | − | 0.375504i | 0.138214 | − | 0.990402i | \(-0.455864\pi\) |
−0.788606 | + | 0.614898i | \(0.789197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.167641 | − | 2.19974i | −0.0132948 | − | 0.174450i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.1291 | −0.798285 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.333348i | − | 0.0261098i | −0.999915 | − | 0.0130549i | \(-0.995844\pi\) | ||
0.999915 | − | 0.0130549i | \(-0.00415562\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0264008 | + | 0.0363297i | 0.00205530 | + | 0.00282827i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.75260 | − | 3.32126i | −0.445150 | − | 0.257007i | 0.260630 | − | 0.965439i | \(-0.416070\pi\) |
−0.705780 | + | 0.708432i | \(0.749403\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.93655 | − | 10.2824i | −0.456658 | − | 0.790954i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.9259 | − | 2.90152i | 1.44730 | − | 0.221885i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.7457 | + | 10.2455i | −1.34918 | + | 0.778952i | −0.988134 | − | 0.153595i | \(-0.950915\pi\) |
−0.361050 | + | 0.932546i | \(0.617582\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.74757 | + | 3.77483i | −0.434475 | + | 0.285350i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.09255 | + | 10.6090i | −0.382779 | + | 0.797423i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.0795 | 1.20184 | 0.600919 | − | 0.799310i | \(-0.294802\pi\) | ||||
0.600919 | + | 0.799310i | \(0.294802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6942 | −0.794891 | −0.397445 | − | 0.917626i | \(-0.630103\pi\) | ||||
−0.397445 | + | 0.917626i | \(0.630103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.38989 | + | 12.2724i | 0.620198 | + | 0.907201i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.699778 | − | 24.3246i | −0.0514487 | − | 1.78838i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0158574 | − | 0.00915525i | 0.00115960 | − | 0.000669498i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.22001 | − | 4.88038i | 0.379700 | − | 0.354996i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.16174 | + | 14.1366i | 0.590563 | + | 1.02289i | 0.994157 | + | 0.107947i | \(0.0344277\pi\) |
−0.403594 | + | 0.914938i | \(0.632239\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0526 | + | 10.4227i | 1.29945 | + | 0.750240i | 0.980310 | − | 0.197466i | \(-0.0632714\pi\) |
0.319144 | + | 0.947706i | \(0.396605\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.75611 | − | 1.67187i | −0.268981 | − | 0.119725i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.80666i | 0.342460i | 0.985231 | + | 0.171230i | \(0.0547742\pi\) | ||||
−0.985231 | + | 0.171230i | \(0.945226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.79500 | 0.552573 | 0.276286 | − | 0.961075i | \(-0.410896\pi\) | ||||
0.276286 | + | 0.961075i | \(0.410896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.7302 | + | 7.07078i | 1.03899 | + | 0.498734i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.34170 | − | 3.66138i | −0.445100 | − | 0.256979i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.68903 | + | 16.1022i | −0.606868 | + | 1.12462i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.5885 | + | 8.02046i | 1.43100 | + | 0.557460i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0370034 | − | 0.0640918i | −0.00255958 | − | 0.00443332i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.8034 | − | 18.7121i | 0.743740 | − | 1.28820i | −0.207041 | − | 0.978332i | \(-0.566383\pi\) |
0.950781 | − | 0.309863i | \(-0.100283\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 28.3999 | − | 2.16434i | 1.94593 | − | 0.148298i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.44572 | − | 3.97286i | 0.439595 | − | 0.270947i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.18102i | 0.215942i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.09566 | + | 14.3770i | 0.0740379 | + | 0.971506i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.838149 | + | 1.45172i | −0.0563800 | + | 0.0976531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.59672 | + | 4.96332i | −0.575679 | + | 0.332368i | −0.759414 | − | 0.650607i | \(-0.774514\pi\) |
0.183735 | + | 0.982976i | \(0.441181\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.6716 | − | 3.12170i | 0.978105 | − | 0.208113i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.23057 | + | 0.710467i | −0.0816755 | + | 0.0471554i | −0.540282 | − | 0.841484i | \(-0.681682\pi\) |
0.458606 | + | 0.888640i | \(0.348349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.7536 | + | 23.8220i | −0.908866 | + | 1.57420i | −0.0932237 | + | 0.995645i | \(0.529717\pi\) |
−0.815642 | + | 0.578557i | \(0.803616\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0249007 | − | 0.0119529i | −0.00163835 | − | 0.000786440i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 27.1509i | − | 1.77871i | −0.457213 | − | 0.889357i | \(-0.651152\pi\) | ||
0.457213 | − | 0.889357i | \(-0.348848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1321 | + | 6.24499i | −0.660946 | + | 0.407378i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.55929 | − | 11.0574i | −0.491029 | − | 0.718257i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.9142 | − | 20.6361i | 0.770668 | − | 1.33484i | −0.166530 | − | 0.986036i | \(-0.553256\pi\) |
0.937197 | − | 0.348799i | \(-0.113411\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.1551 | − | 21.0533i | −0.782979 | − | 1.35616i | −0.930199 | − | 0.367056i | \(-0.880366\pi\) |
0.147220 | − | 0.989104i | \(-0.452968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.4746 | + | 5.78659i | −0.928549 | + | 0.371210i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.42479 | + | 10.0530i | −0.346577 | + | 0.642263i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.86751 | + | 3.38761i | 0.373341 | + | 0.215548i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.72050 | + | 5.27804i | −0.489267 | + | 0.334482i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.1181 | −1.01737 | −0.508683 | − | 0.860954i | \(-0.669868\pi\) | ||||
−0.508683 | + | 0.860954i | \(0.669868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.0854035i | − | 0.00536927i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.639903 | − | 6.08224i | −0.0400723 | − | 0.380885i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3751 | + | 7.14475i | 0.771936 | + | 0.445678i | 0.833565 | − | 0.552422i | \(-0.186296\pi\) |
−0.0616287 | + | 0.998099i | \(0.519629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.48337 | + | 12.9616i | 0.464994 | + | 0.805393i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.99104 | + | 12.4637i | 0.618430 | + | 0.771482i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.56810 | + | 3.21475i | −0.343344 | + | 0.198230i | −0.661750 | − | 0.749725i | \(-0.730186\pi\) |
0.318406 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0819007 | + | 2.84690i | 0.00503112 | + | 0.174884i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.9049 | − | 1.66936i | 1.34056 | − | 0.102163i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.18395 | 0.498984 | 0.249492 | − | 0.968377i | \(-0.419736\pi\) | ||||
0.249492 | + | 0.968377i | \(0.419736\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.8758 | −1.32886 | −0.664430 | − | 0.747350i | \(-0.731326\pi\) | ||||
−0.664430 | + | 0.747350i | \(0.731326\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.52135 | − | 0.192150i | 0.152599 | − | 0.0116295i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0318275 | − | 0.0484606i | −0.00191927 | − | 0.00292229i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6432 | − | 6.14485i | 0.639487 | − | 0.369208i | −0.144930 | − | 0.989442i | \(-0.546296\pi\) |
0.784417 | + | 0.620234i | \(0.212962\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.51881 | − | 6.46578i | 0.150797 | − | 0.387096i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.29349 | − | 12.6327i | −0.435093 | − | 0.753603i | 0.562210 | − | 0.826994i | \(-0.309951\pi\) |
−0.997303 | + | 0.0733910i | \(0.976618\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0885 | − | 5.82460i | −0.599699 | − | 0.346236i | 0.169224 | − | 0.985578i | \(-0.445874\pi\) |
−0.768923 | + | 0.639341i | \(0.779207\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.5830 | + | 2.58634i | −1.45617 | + | 0.153202i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 11.2533i | − | 0.664262i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.5065 | 0.853321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.122462 | − | 0.0837202i | 0.00717888 | − | 0.00490776i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.50023 | − | 2.59821i | −0.262906 | − | 0.151789i | 0.362753 | − | 0.931885i | \(-0.381837\pi\) |
−0.625659 | + | 0.780096i | \(0.715170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.21471 | − | 13.3700i | 0.420057 | − | 0.778432i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.0411489 | + | 0.0440125i | 0.00238770 | + | 0.00255386i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.90928 | + | 6.77107i | 0.226080 | + | 0.391581i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.32845 | + | 4.03299i | −0.134209 | + | 0.232458i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.1255 | − | 20.6621i | −0.811486 | − | 1.18701i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.0700 | − | 16.3380i | −0.576608 | − | 0.935512i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.2676i | 1.78453i | 0.451509 | + | 0.892267i | \(0.350886\pi\) | ||||
−0.451509 | + | 0.892267i | \(0.649114\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.71124 | − | 3.70155i | −0.438677 | − | 0.210574i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5500 | + | 23.4692i | −0.768348 | + | 1.33082i | 0.170110 | + | 0.985425i | \(0.445588\pi\) |
−0.938458 | + | 0.345393i | \(0.887746\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.3115 | + | 17.5004i | −1.71331 | + | 0.989179i | −0.783297 | + | 0.621647i | \(0.786464\pi\) |
−0.930011 | + | 0.367532i | \(0.880203\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.02938 | + | 5.97485i | −0.396061 | + | 0.336645i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.1212 | − | 8.73025i | 0.849293 | − | 0.490339i | −0.0111193 | − | 0.999938i | \(-0.503539\pi\) |
0.860412 | + | 0.509599i | \(0.170206\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0308710 | − | 0.0534701i | 0.00172844 | − | 0.00299375i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.78957 | + | 23.4823i | 0.0998841 | + | 1.31065i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0783i | 0.560774i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.74164 | + | 2.38524i | 0.263019 | + | 0.132309i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.1368 | − | 1.30599i | 0.947669 | − | 0.0722213i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.66011 | − | 6.33950i | 0.201789 | − | 0.349508i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5945 | − | 25.2785i | −0.802189 | − | 1.38943i | −0.918173 | − | 0.396181i | \(-0.870335\pi\) |
0.115984 | − | 0.993251i | \(-0.462998\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.94749 | − | 32.2713i | −0.271121 | − | 1.76846i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.5637 | − | 10.0173i | −1.01424 | − | 0.547304i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5048 | + | 8.37436i | 0.790128 | + | 0.456181i | 0.840008 | − | 0.542575i | \(-0.182550\pi\) |
−0.0498797 | + | 0.998755i | \(0.515884\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.95580 | − | 1.89886i | −0.214850 | − | 0.103132i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0268208 | −0.00145243 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.6526i | − | 0.899156i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.0603 | − | 11.5996i | −1.40304 | − | 0.624501i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.1261 | − | 10.4651i | −0.973062 | − | 0.561798i | −0.0728940 | − | 0.997340i | \(-0.523223\pi\) |
−0.900169 | + | 0.435542i | \(0.856557\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.05625 | + | 10.4897i | 0.324184 | + | 0.561503i | 0.981347 | − | 0.192246i | \(-0.0615771\pi\) |
−0.657163 | + | 0.753748i | \(0.728244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.27707 | − | 1.60589i | −0.281669 | − | 0.0857163i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.1118 | − | 12.7663i | 1.17689 | − | 0.679480i | 0.221600 | − | 0.975138i | \(-0.428872\pi\) |
0.955294 | + | 0.295658i | \(0.0955388\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.7552 | + | 1.05739i | −1.95076 | + | 0.0561202i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.12283 | + | 3.10518i | 0.112352 | + | 0.164344i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.41790 | −0.338724 | −0.169362 | − | 0.985554i | \(-0.554171\pi\) | ||||
−0.169362 | + | 0.985554i | \(0.554171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.7343 | 1.14391 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.24482 | + | 17.1760i | −0.432741 | + | 0.901505i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.535284 | − | 18.6067i | −0.0280181 | − | 0.973920i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.01929 | + | 2.32054i | −0.209805 | + | 0.121131i | −0.601221 | − | 0.799083i | \(-0.705319\pi\) |
0.391416 | + | 0.920214i | \(0.371986\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.91064 | + | 22.8736i | −0.463870 | + | 1.19075i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.875839 | − | 1.51700i | −0.0454713 | − | 0.0787586i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.9009 | + | 10.9124i | 0.978652 | + | 0.565025i | 0.901863 | − | 0.432023i | \(-0.142200\pi\) |
0.0767888 | + | 0.997047i | \(0.475533\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.1103 | + | 3.12998i | −0.986851 | + | 0.161631i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.65238i | 0.291112i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.1095 | −1.49526 | −0.747628 | − | 0.664117i | \(-0.768808\pi\) | ||||
−0.747628 | + | 0.664117i | \(0.768808\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.40583 | − | 31.5686i | −0.123254 | − | 1.61731i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.20924 | − | 4.16226i | −0.368375 | − | 0.212681i | 0.304373 | − | 0.952553i | \(-0.401553\pi\) |
−0.672748 | + | 0.739871i | \(0.734886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0313811 | + | 0.0169338i | 0.00159933 | + | 0.000863029i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.92624 | − | 6.35377i | 0.402913 | − | 0.322981i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.42579 | − | 2.46953i | −0.0722902 | − | 0.125210i | 0.827614 | − | 0.561297i | \(-0.189697\pi\) |
−0.899905 | + | 0.436087i | \(0.856364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.81517 | + | 10.0722i | −0.294086 | + | 0.509372i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.46768 | + | 5.14078i | −0.124478 | + | 0.259318i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.07310 | + | 14.7206i | 0.456517 | + | 0.740672i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.4781i | − | 1.47946i | −0.672903 | − | 0.739731i | \(-0.734953\pi\) | ||
0.672903 | − | 0.739731i | \(-0.265047\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.5504 | − | 8.57997i | 0.628308 | − | 0.429536i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.9053 | + | 22.3526i | −0.644460 | + | 1.11624i | 0.339966 | + | 0.940438i | \(0.389584\pi\) |
−0.984426 | + | 0.175799i | \(0.943749\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.12644 | − | 1.22770i | 0.105926 | − | 0.0611562i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.0190 | − | 6.57852i | 0.945063 | − | 0.326889i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.109285 | + | 0.0630960i | −0.00541708 | + | 0.00312755i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5371 | − | 23.4470i | 0.669367 | − | 1.15938i | −0.308714 | − | 0.951155i | \(-0.599899\pi\) |
0.978081 | − | 0.208223i | \(-0.0667679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.4896 | − | 8.53840i | 0.616068 | − | 0.421168i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.34390i | 0.459783i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.2782 | − | 6.33501i | 0.504535 | − | 0.310973i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.95820 | + | 10.3291i | −0.242804 | + | 0.505820i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0092 | + | 20.8005i | −0.586688 | + | 1.01617i | 0.407975 | + | 0.912993i | \(0.366235\pi\) |
−0.994663 | + | 0.103180i | \(0.967098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.09439 | + | 7.09168i | 0.199548 | + | 0.345628i | 0.948382 | − | 0.317130i | \(-0.102719\pi\) |
−0.748834 | + | 0.662758i | \(0.769386\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.4594 | + | 9.98758i | −0.605795 | + | 0.485613i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.453904 | + | 7.88242i | 0.0220176 | + | 0.382354i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.2224 | + | 5.90193i | 0.494698 | + | 0.285614i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.00162012 | + | 0.0212587i | 7.82199e−5 | + | 0.00102638i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.20494 | 0.250713 | 0.125357 | − | 0.992112i | \(-0.459992\pi\) | ||||
0.125357 | + | 0.992112i | \(0.459992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.2500i | − | 1.06927i | −0.845084 | − | 0.534633i | \(-0.820450\pi\) | ||
0.845084 | − | 0.534633i | \(-0.179550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.1231 | − | 16.6824i | −0.581259 | − | 0.799862i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 40.7094 | + | 23.5036i | 1.94740 | + | 1.12433i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.98693 | − | 12.1017i | −0.333468 | − | 0.577583i | 0.649721 | − | 0.760172i | \(-0.274886\pi\) |
−0.983189 | + | 0.182589i | \(0.941552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.56315 | + | 14.2806i | −0.264912 | + | 0.680029i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.57467 | + | 2.64119i | −0.217349 | + | 0.125487i | −0.604722 | − | 0.796436i | \(-0.706716\pi\) |
0.387373 | + | 0.921923i | \(0.373383\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.3494 | + | 0.815565i | −1.34389 | + | 0.0386615i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.66421 | + | 9.71670i | −0.220610 | + | 0.459584i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.87417 | −0.0884474 | −0.0442237 | − | 0.999022i | \(-0.514081\pi\) | ||||
−0.0442237 | + | 0.999022i | \(0.514081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0948824 | 0.00446784 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.81517 | + | 7.04343i | 0.226236 | + | 0.330929i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.26313 | + | 0.0938749i | −0.152978 | + | 0.00440092i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3262 | − | 11.1580i | 0.904040 | − | 0.521948i | 0.0255315 | − | 0.999674i | \(-0.491872\pi\) |
0.878509 | + | 0.477726i | \(0.158539\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.85612 | − | 7.99253i | −0.0866363 | − | 0.373059i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.87818 | − | 10.1813i | −0.273774 | − | 0.474191i | 0.696051 | − | 0.717992i | \(-0.254939\pi\) |
−0.969825 | + | 0.243802i | \(0.921605\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2152 | + | 5.89776i | 0.474741 | + | 0.274092i | 0.718222 | − | 0.695814i | \(-0.244956\pi\) |
−0.243481 | + | 0.969906i | \(0.578289\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.64283 | + | 8.18420i | −0.168932 | + | 0.379533i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.4898i | 0.994431i | 0.867627 | + | 0.497215i | \(0.165644\pi\) | ||||
−0.867627 | + | 0.497215i | \(0.834356\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9736 | 0.599065 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.6936 | + | 7.05323i | 0.677046 | + | 0.324996i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.0340041 | − | 0.0196323i | −0.00156351 | − | 0.000902694i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.8589 | − | 1.83458i | 1.46179 | − | 0.0841761i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.579045 | + | 3.77697i | 0.0265127 | + | 0.172936i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.98546 | + | 3.43891i | 0.0907178 | + | 0.157128i | 0.907813 | − | 0.419374i | \(-0.137751\pi\) |
−0.817096 | + | 0.576502i | \(0.804417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.77635 | − | 10.0049i | 0.263379 | − | 0.456185i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.4934 | − | 1.33316i | 0.795976 | − | 0.0606609i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.163032 | + | 0.100486i | −0.00740291 | + | 0.00456283i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.7847i | − | 0.579329i | −0.957128 | − | 0.289664i | \(-0.906456\pi\) | ||
0.957128 | − | 0.289664i | \(-0.0935437\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.0438742 | + | 0.575705i | 0.00198406 | + | 0.0260343i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.50061 | − | 6.06323i | 0.157980 | − | 0.273630i | −0.776160 | − | 0.630536i | \(-0.782835\pi\) |
0.934140 | + | 0.356906i | \(0.116168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.28162 | + | 4.20404i | −0.327948 | + | 0.189341i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0503770 | − | 0.0592682i | −0.00226428 | − | 0.00266391i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.5853 | − | 11.3076i | 0.878522 | − | 0.507215i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.76235 | + | 9.98068i | −0.257958 | + | 0.446796i | −0.965695 | − | 0.259680i | \(-0.916383\pi\) |
0.707737 | + | 0.706476i | \(0.249716\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3721 | + | 4.97883i | 0.463392 | + | 0.222438i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.38880i | 0.329450i | 0.986340 | + | 0.164725i | \(0.0526737\pi\) | ||||
−0.986340 | + | 0.164725i | \(0.947326\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.9542 | + | 27.5071i | 0.754452 | + | 1.22405i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.6060 | + | 16.9768i | 0.515441 | + | 0.753966i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.11067 | − | 1.92373i | 0.0492294 | − | 0.0852678i | −0.840361 | − | 0.542028i | \(-0.817657\pi\) |
0.889590 | + | 0.456760i | \(0.150990\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.72428 | + | 9.91475i | 0.253227 | + | 0.438603i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.3040 | + | 7.50201i | −1.42626 | + | 0.331222i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.71808 | + | 5.24406i | 0.428230 | + | 0.231081i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0534515 | + | 0.0308603i | 0.00235080 | + | 0.00135723i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.2992 | − | 20.0301i | 1.28609 | − | 0.879223i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.09160 | 0.354499 | 0.177250 | − | 0.984166i | \(-0.443280\pi\) | ||||
0.177250 | + | 0.984166i | \(0.443280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14.4193i | − | 0.630512i | −0.949007 | − | 0.315256i | \(-0.897910\pi\) | ||
0.949007 | − | 0.315256i | \(-0.102090\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.42947 | − | 7.27577i | 0.411536 | − | 0.317541i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.16315 | + | 1.82625i | 0.137789 | + | 0.0795525i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.6230 | + | 27.0599i | 0.679262 | + | 1.17652i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.39872 | − | 18.9925i | 0.321077 | − | 0.824205i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.52259 | + | 4.34317i | −0.325840 | + | 0.188124i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.874293 | − | 30.3908i | −0.0377990 | − | 1.31391i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.7700 | + | 2.11633i | −1.19836 | + | 0.0913265i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0592376 | 0.00255154 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.37804 | 0.231220 | 0.115610 | − | 0.993295i | \(-0.463118\pi\) | ||||
0.115610 | + | 0.993295i | \(0.463118\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.4693 | − | 1.40753i | 0.792593 | − | 0.0604030i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.1785 | + | 0.638039i | −0.950024 | + | 0.0273306i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.1488 | − | 12.7876i | 0.947016 | − | 0.546760i | 0.0548630 | − | 0.998494i | \(-0.482528\pi\) |
0.892153 | + | 0.451734i | \(0.149194\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.1049 | − | 20.0907i | −0.687342 | − | 0.857449i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9918 | + | 29.4306i | 0.723874 | + | 1.25379i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.21042 | − | 5.31764i | −0.391667 | − | 0.226129i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.41008 | + | 41.9175i | 0.187197 | + | 1.77930i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.1519i | 1.53181i | 0.642956 | + | 0.765903i | \(0.277708\pi\) | ||||
−0.642956 | + | 0.765903i | \(0.722292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.59462 | 0.152036 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0261813 | + | 0.0178986i | −0.00110538 | + | 0.000755680i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.3594 | + | 16.9507i | 1.23735 | + | 0.714385i | 0.968552 | − | 0.248811i | \(-0.0800397\pi\) |
0.268800 | + | 0.963196i | \(0.413373\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.98529 | + | 2.69016i | 0.209733 | + | 0.113176i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.37284 | + | 9.11567i | −0.351626 | + | 0.382822i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.0057 | − | 24.2586i | −0.587149 | − | 1.01697i | −0.994604 | − | 0.103747i | \(-0.966917\pi\) |
0.407454 | − | 0.913226i | \(-0.366417\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3040 | − | 29.9714i | 0.724150 | − | 1.25427i | −0.235173 | − | 0.971954i | \(-0.575566\pi\) |
0.959323 | − | 0.282311i | \(-0.0911011\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.9563 | − | 23.3402i | −0.666584 | − | 0.975051i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.8980 | + | 16.5491i | 1.37194 | + | 0.690144i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.88098i | 0.0783062i | 0.999233 | + | 0.0391531i | \(0.0124660\pi\) | ||||
−0.999233 | + | 0.0391531i | \(0.987534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32.5494 | − | 15.6244i | −1.35271 | − | 0.649326i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.71287 | + | 6.43089i | −0.154036 | + | 0.266798i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0127906 | − | 0.00738463i | 0.000529731 | − | 0.000305840i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.70701 | + | 2.39301i | 0.277301 | + | 0.0989390i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.92665 | + | 2.84440i | −0.203345 | + | 0.117401i | −0.598215 | − | 0.801336i | \(-0.704123\pi\) |
0.394870 | + | 0.918737i | \(0.370790\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.38126 | − | 12.7847i | 0.304140 | − | 0.526785i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.632638 | − | 8.30131i | −0.0260232 | − | 0.341470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.6302i | 0.970378i | 0.874409 | + | 0.485189i | \(0.161249\pi\) | ||||
−0.874409 | + | 0.485189i | \(0.838751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.54794 | − | 4.13388i | −0.104455 | − | 0.169472i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.4623 | + | 1.02595i | −0.550975 | + | 0.0419895i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.8923 | + | 20.5981i | −0.485908 | + | 0.841617i | −0.999869 | − | 0.0161965i | \(-0.994844\pi\) |
0.513961 | + | 0.857814i | \(0.328178\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.30901 | + | 7.46343i | 0.175768 | + | 0.304440i | 0.940427 | − | 0.339996i | \(-0.110426\pi\) |
−0.764659 | + | 0.644436i | \(0.777092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.3703 | − | 10.2728i | −1.07388 | − | 0.418341i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.6806 | − | 21.6460i | 0.474884 | − | 0.880035i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.7172 | − | 13.6931i | −0.962652 | − | 0.555787i | −0.0656637 | − | 0.997842i | \(-0.520916\pi\) |
−0.896988 | + | 0.442054i | \(0.854250\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.4343 | + | 5.48869i | 0.463341 | + | 0.222413i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.65042 | −0.228592 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.61637i | 0.0652845i | 0.999467 | + | 0.0326422i | \(0.0103922\pi\) | ||||
−0.999467 | + | 0.0326422i | \(0.989608\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.8870 | − | 28.9527i | 0.519655 | − | 1.16749i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.14521 | + | 4.70264i | 0.327914 | + | 0.189321i | 0.654915 | − | 0.755703i | \(-0.272705\pi\) |
−0.327001 | + | 0.945024i | \(0.606038\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.62429 | + | 2.81336i | 0.0652858 | + | 0.113078i | 0.896821 | − | 0.442394i | \(-0.145871\pi\) |
−0.831535 | + | 0.555472i | \(0.812537\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −36.6129 | − | 11.1419i | −1.46922 | − | 0.447108i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.1062 | − | 8.72158i | 0.605218 | − | 0.349423i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8348 | − | 2.86970i | 0.993390 | − | 0.114788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0723420 | + | 0.105819i | 0.00288906 | + | 0.00422600i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.1850 | 0.685210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0746 | 0.878777 | 0.439389 | − | 0.898297i | \(-0.355195\pi\) | ||||
0.439389 | + | 0.898297i | \(0.355195\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.1952 | + | 33.7386i | −0.643701 | + | 1.34099i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.17536 | + | 40.8562i | 0.0466429 | + | 1.62133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.69655 | + | 2.71155i | −0.186084 | + | 0.107436i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −48.7630 | + | 7.47582i | −1.92903 | + | 0.295739i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.6150 | − | 37.4382i | −0.853739 | − | 1.47872i | −0.877809 | − | 0.479010i | \(-0.840996\pi\) |
0.0240700 | − | 0.999710i | \(-0.492338\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6233 | + | 7.86544i | 0.537252 | + | 0.310183i | 0.743965 | − | 0.668219i | \(-0.232943\pi\) |
−0.206712 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.6091 | + | 7.70966i | −0.417735 | + | 0.303568i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 25.8513i | − | 1.01632i | −0.861263 | − | 0.508159i | \(-0.830326\pi\) | ||
0.861263 | − | 0.508159i | \(-0.169674\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.0787831 | −0.00309251 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.418677 | − | 5.49377i | −0.0164092 | − | 0.215318i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.9197 | − | 12.6553i | −0.857784 | − | 0.495242i | 0.00548578 | − | 0.999985i | \(-0.498254\pi\) |
−0.863269 | + | 0.504743i | \(0.831587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.49601 | − | 6.47866i | 0.136600 | − | 0.253142i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.78451 | − | 24.6854i | −0.147648 | − | 0.963071i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.6426 | − | 23.6297i | −0.531442 | − | 0.920484i | −0.999327 | − | 0.0366946i | \(-0.988317\pi\) |
0.467885 | − | 0.883789i | \(-0.345016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1277 | + | 19.2737i | −0.432817 | + | 0.749661i | −0.997115 | − | 0.0759103i | \(-0.975814\pi\) |
0.564298 | + | 0.825571i | \(0.309147\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.25645 | − | 2.61749i | 0.0487964 | − | 0.101655i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.7082 | + | 10.2982i | −0.647915 | + | 0.399346i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.2169i | 1.51848i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.1936 | − | 9.70333i | 0.548758 | − | 0.375153i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0497621 | + | 0.0861905i | −0.00192104 | + | 0.00332735i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.9334 | + | 8.62183i | −0.575642 | + | 0.332347i | −0.759400 | − | 0.650625i | \(-0.774507\pi\) |
0.183758 | + | 0.982972i | \(0.441174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.9276 | + | 7.32233i | −0.959462 | + | 0.281837i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.940266 | − | 0.542863i | 0.0361373 | − | 0.0208639i | −0.481822 | − | 0.876269i | \(-0.660025\pi\) |
0.517960 | + | 0.855405i | \(0.326692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0588936 | − | 0.102007i | 0.00226013 | − | 0.00391466i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.03173 | − | 1.38897i | 0.0778560 | − | 0.0532255i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.62926i | − | 0.138870i | −0.997586 | − | 0.0694349i | \(-0.977880\pi\) | ||
0.997586 | − | 0.0694349i | \(-0.0221196\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.6272 | + | 10.2483i | −0.635293 | + | 0.391567i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.6177 | − | 42.9518i | 0.786616 | − | 1.63871i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.676052 | + | 1.17096i | −0.0257555 | + | 0.0446099i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.4867 | + | 25.0916i | 0.551099 | + | 0.954531i | 0.998196 | + | 0.0600453i | \(0.0191245\pi\) |
−0.447097 | + | 0.894485i | \(0.647542\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0445778 | + | 0.0173657i | 0.00169337 | + | 0.000659670i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.02438 | − | 13.0173i | 0.266450 | − | 0.493774i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.1901 | − | 6.46060i | −0.423855 | − | 0.244713i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.57352 | + | 46.8908i | 0.135163 | + | 1.77357i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.4520 | 1.07462 | 0.537309 | − | 0.843385i | \(-0.319441\pi\) | ||||
0.537309 | + | 0.843385i | \(0.319441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 69.4577i | − | 2.61965i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.6766 | − | 12.1189i | 0.628079 | − | 0.456425i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.2108 | − | 9.93665i | −0.647278 | − | 0.373706i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.40582 | − | 16.2914i | −0.353243 | − | 0.611835i | 0.633573 | − | 0.773683i | \(-0.281588\pi\) |
−0.986816 | + | 0.161848i | \(0.948254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.5106 | + | 18.1017i | 0.544189 | + | 0.678868i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.7535 | − | 8.51794i | 0.552523 | − | 0.318999i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.000791506 | − | 0.0275131i | −2.96006e−5 | − | 0.00102893i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.8603 | + | 37.2075i | −0.667007 | + | 1.38954i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.22562 | 0.157589 | 0.0787946 | − | 0.996891i | \(-0.474893\pi\) | ||||
0.0787946 | + | 0.996891i | \(0.474893\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.79167 | −0.252935 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.7634 | + | 34.7601i | 0.883769 | + | 1.29274i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.6150 | + | 22.2529i | 0.542788 | + | 0.826451i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.03048 | + | 2.32700i | −0.149482 | + | 0.0863036i | −0.572876 | − | 0.819642i | \(-0.694172\pi\) |
0.423393 | + | 0.905946i | \(0.360839\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.2367 | − | 11.8988i | 0.897656 | − | 0.440696i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.67355 | + | 4.63072i | 0.0988848 | + | 0.171274i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.6506 | + | 12.5000i | 0.799683 | + | 0.461697i | 0.843360 | − | 0.537348i | \(-0.180574\pi\) |
−0.0436770 | + | 0.999046i | \(0.513907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.04570 | − | 18.0760i | 0.296770 | − | 0.666742i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.109387i | 0.00402932i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.4824 | −0.679887 | −0.339944 | − | 0.940446i | \(-0.610408\pi\) | ||||
−0.339944 | + | 0.940446i | \(0.610408\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.5793 | − | 5.07828i | −0.388640 | − | 0.186555i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.86448 | + | 1.65381i | 0.105088 | + | 0.0606723i | 0.551623 | − | 0.834094i | \(-0.314009\pi\) |
−0.446535 | + | 0.894766i | \(0.647342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.60788 | − | 12.2454i | 0.242094 | − | 0.448639i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.6390 | − | 10.1315i | 0.462435 | − | 0.370694i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.34962 | + | 16.1940i | 0.341628 | + | 0.591716i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.9233 | + | 39.7043i | −0.836483 | + | 1.44883i | 0.0563335 | + | 0.998412i | \(0.482059\pi\) |
−0.892817 | + | 0.450420i | \(0.851274\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.8367 | − | 2.12142i | 1.01443 | − | 0.0773088i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.77945 | − | 9.37680i | −0.210336 | − | 0.341257i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 12.2649i | − | 0.445775i | −0.974844 | − | 0.222888i | \(-0.928452\pi\) | ||
0.974844 | − | 0.222888i | \(-0.0715483\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0112405 | + | 0.147495i | 0.000408006 | + | 0.00535375i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.54420 | + | 16.5310i | −0.345977 | + | 0.599250i | −0.985531 | − | 0.169497i | \(-0.945786\pi\) |
0.639554 | + | 0.768746i | \(0.279119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.8180 | − | 6.82314i | 0.427841 | − | 0.247014i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.90567 | + | 10.4201i | 0.0688995 | + | 0.376739i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.24619 | − | 3.60624i | 0.225537 | − | 0.130214i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.60033 | + | 6.23595i | −0.129831 | + | 0.224874i | −0.923611 | − | 0.383331i | \(-0.874777\pi\) |
0.793780 | + | 0.608205i | \(0.208110\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.3127 | − | 10.7105i | −0.803571 | − | 0.385730i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.69028i | 0.0607950i | 0.999538 | + | 0.0303975i | \(0.00967732\pi\) | ||||
−0.999538 | + | 0.0303975i | \(0.990323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.19721 | − | 10.3316i | 0.186689 | − | 0.371121i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.6301 | − | 21.4003i | −0.524850 | − | 0.767730i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.1122 | + | 45.2277i | −0.935568 | + | 1.62045i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0953400 | + | 0.165134i | 0.00341153 | + | 0.00590895i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.8954 | − | 20.2103i | −0.675266 | − | 0.722258i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.5176 | − | 9.99245i | −0.660921 | − | 0.356646i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.7876 | − | 16.6205i | −1.02617 | − | 0.592457i | −0.110282 | − | 0.993900i | \(-0.535175\pi\) |
−0.915884 | + | 0.401443i | \(0.868509\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.19324 | − | 6.28486i | 0.327288 | − | 0.223747i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.48407 | −0.123879 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9.11129i | − | 0.323551i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.516147 | − | 4.90595i | −0.0183058 | − | 0.173996i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.4748 | − | 21.6361i | −1.32743 | − | 0.766390i | −0.342525 | − | 0.939509i | \(-0.611282\pi\) |
−0.984901 | + | 0.173119i | \(0.944615\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.20259 | − | 7.27909i | −0.148677 | − | 0.257516i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.6110 | + | 5.76611i | −1.32892 | + | 0.203736i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.0835962 | + | 0.0482643i | −0.00295005 | + | 0.00170321i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.6400 | + | 0.651314i | −0.797954 | + | 0.0229558i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.1340 | + | 1.07715i | −0.497541 | + | 0.0379173i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4664 | −0.367981 | −0.183990 | − | 0.982928i | \(-0.558902\pi\) | ||||
−0.183990 | + | 0.982928i | \(0.558902\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.4200 | −0.752158 | −0.376079 | − | 0.926588i | \(-0.622728\pi\) | ||||
−0.376079 | + | 0.926588i | \(0.622728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.7805 | − | 2.87923i | 1.32502 | − | 0.100979i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0214347 | − | 0.745079i | −0.000750824 | − | 0.0260990i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.7163 | − | 10.8059i | 0.654801 | − | 0.378050i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.32918 | + | 0.663704i | −0.151274 | + | 0.0231917i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.02464 | − | 6.97089i | −0.140461 | − | 0.243286i | 0.787209 | − | 0.616686i | \(-0.211525\pi\) |
−0.927670 | + | 0.373400i | \(0.878192\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.6630 | + | 18.2806i | 1.10370 | + | 0.637223i | 0.937191 | − | 0.348816i | \(-0.113416\pi\) |
0.166512 | + | 0.986039i | \(0.446750\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0613457 | + | 0.0795046i | 0.00213578 | + | 0.00276799i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7.52915i | − | 0.261814i | −0.991395 | − | 0.130907i | \(-0.958211\pi\) | ||
0.991395 | − | 0.130907i | \(-0.0417890\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.188646 | −0.00655195 | −0.00327597 | − | 0.999995i | \(-0.501043\pi\) | ||||
−0.00327597 | + | 0.999995i | \(0.501043\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5725 | + | 12.0132i | −0.609582 | + | 0.416735i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.98626 | − | 4.03352i | −0.242060 | − | 0.139753i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.0714 | − | 7.05360i | −0.452356 | − | 0.244100i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.49909 | + | 11.4982i | −0.120946 | + | 0.397436i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.22498 | − | 14.2461i | −0.283958 | − | 0.491830i | 0.688398 | − | 0.725333i | \(-0.258314\pi\) |
−0.972356 | + | 0.233504i | \(0.924981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.324206 | − | 0.561541i | 0.0111795 | − | 0.0193635i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.2588 | + | 20.8573i | 0.491101 | + | 0.718362i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.9302 | − | 22.6009i | −0.479214 | − | 0.777495i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.1277i | 0.519795i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.1899 | + | 8.73151i | 0.624275 | + | 0.299665i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0769 | − | 69.4153i | 1.37382 | − | 2.37953i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.3132 | + | 11.7278i | −0.695509 | + | 0.401552i | −0.805673 | − | 0.592361i | \(-0.798196\pi\) |
0.110163 | + | 0.993913i | \(0.464863\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 42.1156 | − | 7.70227i | 1.44032 | − | 0.263412i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.4722 | + | 9.51024i | −0.562680 | + | 0.324864i | −0.754221 | − | 0.656621i | \(-0.771985\pi\) |
0.191540 | + | 0.981485i | \(0.438652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.90912 | − | 13.6990i | 0.269856 | − | 0.467404i | −0.698969 | − | 0.715152i | \(-0.746357\pi\) |
0.968824 | + | 0.247749i | \(0.0796907\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.48113 | + | 19.4350i | 0.0504767 | + | 0.662342i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.81226i | 0.265933i | 0.991121 | + | 0.132966i | \(0.0424502\pi\) | ||||
−0.991121 | + | 0.132966i | \(0.957550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.0055 | + | 24.0413i | −1.32623 | + | 0.817427i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.0533 | + | 1.90929i | −0.850854 | + | 0.0648431i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0448357 | − | 0.0776577i | 0.00152095 | − | 0.00263436i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.00710 | − | 8.67256i | −0.169659 | − | 0.293858i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.200479 | + | 0.160706i | −0.00678518 | + | 0.00543909i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.6039 | + | 8.80686i | −0.426090 | + | 0.297726i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.5193 | − | 27.4353i | −1.60461 | − | 0.926424i | −0.990548 | − | 0.137168i | \(-0.956200\pi\) |
−0.614065 | − | 0.789255i | \(-0.710467\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.11405 | + | 3.89491i | 0.273680 | + | 0.131372i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1017 | 1.04784 | 0.523922 | − | 0.851766i | \(-0.324468\pi\) | ||||
0.523922 | + | 0.851766i | \(0.324468\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.5411i | 0.691264i | 0.938370 | + | 0.345632i | \(0.112335\pi\) | ||||
−0.938370 | + | 0.345632i | \(0.887665\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.7004 | + | 24.0401i | −0.359690 | + | 0.808101i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.1925 | − | 26.0919i | −1.51742 | − | 0.876081i | −0.999790 | − | 0.0204736i | \(-0.993483\pi\) |
−0.517626 | − | 0.855607i | \(-0.673184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5693 | − | 21.7706i | −0.421559 | − | 0.730162i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.0768588 | − | 0.0705956i | −0.00257487 | − | 0.00236504i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.4204 | + | 16.9859i | −0.984517 | + | 0.568411i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.9400 | − | 1.03393i | 1.20134 | − | 0.0345605i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.64268 | − | 11.1794i | −0.255182 | − | 0.373269i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.3160 | 0.410761 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.01130 | −0.0670060 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.49052 | − | 7.27161i | 0.116157 | − | 0.241984i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.9030 | + | 0.687649i | −0.794562 | + | 0.0228582i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.1672 | + | 12.7983i | −0.736051 | + | 0.424959i | −0.820632 | − | 0.571457i | \(-0.806378\pi\) |
0.0845808 | + | 0.996417i | \(0.473045\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.1148 | + | 33.8253i | 0.899340 | + | 1.12191i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5975 | − | 35.6760i | −0.682426 | − | 1.18200i | −0.974238 | − | 0.225521i | \(-0.927591\pi\) |
0.291812 | − | 0.956476i | \(-0.405742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0542220 | − | 0.0313051i | −0.00179449 | − | 0.00103605i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.5417 | + | 26.8911i | 0.646030 | + | 0.888991i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.52774i | 0.149519i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.84011 | −0.159661 | −0.0798303 | − | 0.996808i | \(-0.525438\pi\) | ||||
−0.0798303 | + | 0.996808i | \(0.525438\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.11534 | − | 54.0004i | −0.135605 | − | 1.77937i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.1178 | − | 8.72824i | −0.497607 | − | 0.287293i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.12821 | − | 54.3240i | −0.102855 | − | 1.78616i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.8048 | + | 5.37781i | 0.453410 | + | 0.176630i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.9319 | + | 34.5231i | 0.653945 | + | 1.13267i | 0.982157 | + | 0.188063i | \(0.0602208\pi\) |
−0.328212 | + | 0.944604i | \(0.606446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3026 | + | 28.2369i | −0.534295 | + | 0.925426i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.3124 | − | 42.3158i | 0.664999 | − | 1.38536i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0348548 | − | 0.0214829i | 0.00113987 | − | 0.000702567i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.03028i | − | 0.164332i | −0.996619 | − | 0.0821661i | \(-0.973816\pi\) | ||
0.996619 | − | 0.0821661i | \(-0.0261838\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 50.0459 | − | 34.2134i | 1.63319 | − | 1.11651i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.4374 | + | 18.0781i | −0.340250 | + | 0.589330i | −0.984479 | − | 0.175503i | \(-0.943845\pi\) |
0.644229 | + | 0.764832i | \(0.277178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −52.1926 | + | 30.1334i | −1.69962 | + | 0.981278i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.3536 | − | 11.2440i | 0.369334 | − | 0.365768i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.0653614 | + | 0.0377364i | −0.00212396 | + | 0.00122627i | −0.501062 | − | 0.865412i | \(-0.667057\pi\) |
0.498938 | + | 0.866638i | \(0.333724\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.41852 | − | 7.65311i | 0.143431 | − | 0.248430i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.9660 | + | 17.0677i | −0.809577 | + | 0.553459i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.6892i | − | 0.767370i | −0.923464 | − | 0.383685i | \(-0.874655\pi\) | ||
0.923464 | − | 0.383685i | \(-0.125345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.1517 | + | 31.0724i | 0.619733 | + | 1.00548i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0462779 | + | 0.0964083i | −0.00149595 | + | 0.00311644i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00640 | − | 10.4034i | 0.193957 | − | 0.335943i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.8250 | + | 22.2135i | 0.413708 | + | 0.716564i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.18133 | − | 40.3194i | −0.199191 | − | 1.29927i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.0203 | + | 22.1353i | 1.32049 | + | 0.712562i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.2206 | + | 22.6440i | 1.26125 | + | 0.728183i | 0.973316 | − | 0.229467i | \(-0.0736983\pi\) |
0.287934 | + | 0.957650i | \(0.407032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.32648 | − | 17.4057i | −0.0426127 | − | 0.559152i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.4586 | 0.817004 | 0.408502 | − | 0.912757i | \(-0.366051\pi\) | ||||
0.408502 | + | 0.912757i | \(0.366051\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.09739i | 0.291649i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.50295 | − | 3.49533i | −0.272312 | − | 0.111940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.09127 | − | 4.09415i | −0.226870 | − | 0.130983i | 0.382257 | − | 0.924056i | \(-0.375147\pi\) |
−0.609127 | + | 0.793073i | \(0.708480\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0735360 | + | 0.127368i | 0.00235022 | + | 0.00407070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.4242 | + | 4.51100i | −0.939441 | + | 0.144025i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.6001 | − | 6.11998i | 0.338091 | − | 0.195197i | −0.321336 | − | 0.946965i | \(-0.604132\pi\) |
0.659428 | + | 0.751768i | \(0.270799\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.309075 | + | 10.7436i | 0.00984794 | + | 0.342319i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.48679 | + | 11.4303i | −0.174646 | + | 0.363831i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.9398 | 0.793041 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0040 | 1.52490 | 0.762448 | − | 0.647049i | \(-0.223997\pi\) | ||||
0.762448 | + | 0.647049i | \(0.223997\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.5325 | + | 41.7362i | 0.905451 | + | 1.32446i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4229 | − | 0.501229i | 0.552344 | − | 0.0158900i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.36574 | + | 3.09791i | −0.169935 | + | 0.0981118i | −0.582555 | − | 0.812791i | \(-0.697947\pi\) |
0.412620 | + | 0.910903i | \(0.364614\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.7920 | + | 55.0828i | 0.404721 | + | 1.74274i |
(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 | 360.2.bi.b.49.1 | ✓ | 32 | |
3.2 | odd | 2 | 1080.2.bi.b.1009.1 | 32 | |||
4.3 | odd | 2 | 720.2.by.f.49.16 | 32 | |||
5.4 | even | 2 | inner | 360.2.bi.b.49.16 | yes | 32 | |
9.2 | odd | 6 | 1080.2.bi.b.289.11 | 32 | |||
9.4 | even | 3 | 3240.2.f.k.649.5 | 16 | |||
9.5 | odd | 6 | 3240.2.f.i.649.12 | 16 | |||
9.7 | even | 3 | inner | 360.2.bi.b.169.16 | yes | 32 | |
12.11 | even | 2 | 2160.2.by.f.1009.1 | 32 | |||
15.14 | odd | 2 | 1080.2.bi.b.1009.11 | 32 | |||
20.19 | odd | 2 | 720.2.by.f.49.1 | 32 | |||
36.7 | odd | 6 | 720.2.by.f.529.1 | 32 | |||
36.11 | even | 6 | 2160.2.by.f.289.11 | 32 | |||
45.4 | even | 6 | 3240.2.f.k.649.6 | 16 | |||
45.14 | odd | 6 | 3240.2.f.i.649.11 | 16 | |||
45.29 | odd | 6 | 1080.2.bi.b.289.1 | 32 | |||
45.34 | even | 6 | inner | 360.2.bi.b.169.1 | yes | 32 | |
60.59 | even | 2 | 2160.2.by.f.1009.11 | 32 | |||
180.79 | odd | 6 | 720.2.by.f.529.16 | 32 | |||
180.119 | even | 6 | 2160.2.by.f.289.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bi.b.49.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
360.2.bi.b.49.16 | yes | 32 | 5.4 | even | 2 | inner | |
360.2.bi.b.169.1 | yes | 32 | 45.34 | even | 6 | inner | |
360.2.bi.b.169.16 | yes | 32 | 9.7 | even | 3 | inner | |
720.2.by.f.49.1 | 32 | 20.19 | odd | 2 | |||
720.2.by.f.49.16 | 32 | 4.3 | odd | 2 | |||
720.2.by.f.529.1 | 32 | 36.7 | odd | 6 | |||
720.2.by.f.529.16 | 32 | 180.79 | odd | 6 | |||
1080.2.bi.b.289.1 | 32 | 45.29 | odd | 6 | |||
1080.2.bi.b.289.11 | 32 | 9.2 | odd | 6 | |||
1080.2.bi.b.1009.1 | 32 | 3.2 | odd | 2 | |||
1080.2.bi.b.1009.11 | 32 | 15.14 | odd | 2 | |||
2160.2.by.f.289.1 | 32 | 180.119 | even | 6 | |||
2160.2.by.f.289.11 | 32 | 36.11 | even | 6 | |||
2160.2.by.f.1009.1 | 32 | 12.11 | even | 2 | |||
2160.2.by.f.1009.11 | 32 | 60.59 | even | 2 | |||
3240.2.f.i.649.11 | 16 | 45.14 | odd | 6 | |||
3240.2.f.i.649.12 | 16 | 9.5 | odd | 6 | |||
3240.2.f.k.649.5 | 16 | 9.4 | even | 3 | |||
3240.2.f.k.649.6 | 16 | 45.4 | even | 6 |