Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.10 | ||
Character | \(\chi\) | \(=\) | 1008.529 |
Dual form | 1008.2.q.l.625.10 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.69989 | + | 0.332219i | 0.981433 | + | 0.191807i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.59750 | + | 2.76695i | −0.714423 | + | 1.23742i | 0.248759 | + | 0.968566i | \(0.419977\pi\) |
−0.963182 | + | 0.268851i | \(0.913356\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.66645 | + | 2.05498i | 0.629857 | + | 0.776711i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.77926 | + | 1.12947i | 0.926420 | + | 0.376491i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.14139 | − | 1.97695i | −0.344143 | − | 0.596073i | 0.641055 | − | 0.767495i | \(-0.278497\pi\) |
−0.985198 | + | 0.171422i | \(0.945164\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.675051 | − | 1.16922i | −0.187225 | − | 0.324284i | 0.757099 | − | 0.653300i | \(-0.226616\pi\) |
−0.944324 | + | 0.329017i | \(0.893283\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.63481 | + | 4.17279i | −0.938503 | + | 1.07741i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.21425 | − | 3.83519i | 0.537033 | − | 0.930169i | −0.462028 | − | 0.886865i | \(-0.652878\pi\) |
0.999062 | − | 0.0433042i | \(-0.0137885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.69214 | + | 6.39497i | 0.847034 | + | 1.46711i | 0.883843 | + | 0.467784i | \(0.154948\pi\) |
−0.0368084 | + | 0.999322i | \(0.511719\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.15007 | + | 4.04687i | 0.469184 | + | 0.883100i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.23479 | + | 5.60283i | −0.674501 | + | 1.16827i | 0.302113 | + | 0.953272i | \(0.402308\pi\) |
−0.976614 | + | 0.214999i | \(0.931025\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.60400 | − | 4.51026i | −0.520800 | − | 0.902053i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.34921 | + | 2.84330i | 0.837006 | + | 0.547194i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.06167 | + | 1.83887i | −0.197148 | + | 0.341470i | −0.947602 | − | 0.319452i | \(-0.896501\pi\) |
0.750455 | + | 0.660922i | \(0.229834\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.632308 | 0.113566 | 0.0567830 | − | 0.998387i | \(-0.481916\pi\) | ||||
0.0567830 | + | 0.998387i | \(0.481916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.28346 | − | 3.73979i | −0.223422 | − | 0.651014i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.34818 | + | 1.32814i | −1.41110 | + | 0.224496i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.92885 | + | 3.34087i | 0.317102 | + | 0.549236i | 0.979882 | − | 0.199578i | \(-0.0639570\pi\) |
−0.662780 | + | 0.748814i | \(0.730624\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.759075 | − | 2.21182i | −0.121549 | − | 0.354174i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.05124 | − | 8.74900i | −0.788871 | − | 1.36636i | −0.926659 | − | 0.375903i | \(-0.877333\pi\) |
0.137788 | − | 0.990462i | \(-0.456001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24701 | + | 7.35603i | −0.647663 | + | 1.12178i | 0.336017 | + | 0.941856i | \(0.390920\pi\) |
−0.983680 | + | 0.179929i | \(0.942413\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.56506 | + | 5.88574i | −1.12773 | + | 0.877395i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.53173 | −0.952751 | −0.476375 | − | 0.879242i | \(-0.658050\pi\) | ||||
−0.476375 | + | 0.879242i | \(0.658050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.44591 | + | 6.84904i | −0.206559 | + | 0.978434i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.03810 | − | 5.78379i | 0.705475 | − | 0.809892i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.39950 | − | 4.15606i | 0.329597 | − | 0.570879i | −0.652835 | − | 0.757500i | \(-0.726420\pi\) |
0.982432 | + | 0.186621i | \(0.0597538\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.29349 | 0.983454 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.15170 | + | 12.0974i | 0.549906 | + | 1.60233i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.20383 | −0.807670 | −0.403835 | − | 0.914832i | \(-0.632323\pi\) | ||||
−0.403835 | + | 0.914832i | \(0.632323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.91093 | −1.14093 | −0.570464 | − | 0.821323i | \(-0.693236\pi\) | ||||
−0.570464 | + | 0.821323i | \(0.693236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.31044 | + | 7.59354i | 0.291088 | + | 0.956696i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.31357 | 0.535033 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.01570 | 0.368426 | 0.184213 | − | 0.982886i | \(-0.441026\pi\) | ||||
0.184213 | + | 0.982886i | \(0.441026\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.36017 | + | 8.44954i | −0.886060 | + | 1.01721i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.3791 | 1.82516 | 0.912580 | − | 0.408899i | \(-0.134087\pi\) | ||||
0.912580 | + | 0.408899i | \(0.134087\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.36577 | − | 7.56173i | 0.510974 | − | 0.885033i | −0.488945 | − | 0.872315i | \(-0.662618\pi\) |
0.999919 | − | 0.0127186i | \(-0.00404857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.92813 | − | 8.53206i | −0.338111 | − | 0.985197i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.16053 | − | 5.64002i | 0.246215 | − | 0.642740i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.87610 | 0.211078 | 0.105539 | − | 0.994415i | \(-0.466343\pi\) | ||||
0.105539 | + | 0.994415i | \(0.466343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.44859 | + | 6.27819i | 0.716510 | + | 0.697577i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00140 | − | 5.19857i | 0.329446 | − | 0.570617i | −0.652956 | − | 0.757396i | \(-0.726471\pi\) |
0.982402 | + | 0.186779i | \(0.0598047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.07451 | + | 12.2534i | 0.767338 | + | 1.32907i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.41563 | + | 2.77317i | −0.258983 | + | 0.297315i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.65390 | + | 4.59668i | 0.281313 | + | 0.487248i | 0.971708 | − | 0.236184i | \(-0.0758969\pi\) |
−0.690396 | + | 0.723432i | \(0.742564\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.27780 | − | 3.33566i | 0.133949 | − | 0.349673i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.07486 | + | 0.210065i | 0.111457 | + | 0.0217827i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −23.5927 | −2.42056 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.44539 | − | 12.8958i | 0.755965 | − | 1.30937i | −0.188929 | − | 0.981991i | \(-0.560502\pi\) |
0.944893 | − | 0.327378i | \(-0.106165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.939319 | − | 6.78363i | −0.0944051 | − | 0.681781i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.00299 | + | 12.1295i | 0.696824 | + | 1.20693i | 0.969562 | + | 0.244846i | \(0.0787374\pi\) |
−0.272738 | + | 0.962088i | \(0.587929\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.03055 | − | 13.9093i | 0.791274 | − | 1.37053i | −0.133905 | − | 0.990994i | \(-0.542752\pi\) |
0.925179 | − | 0.379532i | \(-0.123915\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.6322 | − | 0.515732i | −1.42796 | − | 0.0503303i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.26820 | − | 2.19658i | −0.122601 | − | 0.212352i | 0.798191 | − | 0.602404i | \(-0.205790\pi\) |
−0.920793 | + | 0.390052i | \(0.872457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.10946 | − | 14.0460i | 0.776746 | − | 1.34536i | −0.157062 | − | 0.987589i | \(-0.550202\pi\) |
0.933808 | − | 0.357775i | \(-0.116464\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.16894 | + | 6.31992i | 0.205867 | + | 0.599860i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.61499 | + | 2.79725i | 0.151926 | + | 0.263143i | 0.931935 | − | 0.362625i | \(-0.118119\pi\) |
−0.780010 | + | 0.625767i | \(0.784786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.3352 | − | 17.9010i | −0.963759 | − | 1.66928i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.555539 | − | 4.01203i | −0.0513596 | − | 0.370912i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.5712 | − | 1.84089i | 1.06073 | − | 0.168754i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.89445 | − | 5.01333i | 0.263131 | − | 0.455757i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.67997 | − | 16.5505i | −0.512146 | − | 1.49231i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.664575 | 0.0594414 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6429 | 1.12187 | 0.560936 | − | 0.827859i | \(-0.310441\pi\) | ||||
0.560936 | + | 0.827859i | \(0.310441\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.66326 | + | 11.0935i | −0.850803 | + | 0.976730i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.53430 | − | 16.5139i | 0.833015 | − | 1.44282i | −0.0626210 | − | 0.998037i | \(-0.519946\pi\) |
0.895636 | − | 0.444787i | \(-0.146721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.98881 | + | 18.2442i | −0.606007 | + | 1.58197i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.8151 | + | 7.49187i | −1.27508 | + | 0.644797i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.38236 | − | 5.85842i | −0.288975 | − | 0.500519i | 0.684591 | − | 0.728928i | \(-0.259981\pi\) |
−0.973565 | + | 0.228409i | \(0.926648\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.57218 | + | 11.3834i | 0.557445 | + | 0.965524i | 0.997709 | + | 0.0676550i | \(0.0215517\pi\) |
−0.440263 | + | 0.897869i | \(0.645115\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.1032 | − | 2.16996i | −0.935061 | − | 0.182744i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.54100 | + | 2.66908i | −0.128865 | + | 0.223200i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.39204 | − | 5.87518i | −0.281693 | − | 0.487907i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.73328 | + | 11.1623i | −0.390394 | + | 0.920648i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.140257 | + | 0.242932i | −0.0114903 | + | 0.0199018i | −0.871713 | − | 0.490016i | \(-0.836991\pi\) |
0.860223 | + | 0.509918i | \(0.170324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.42899 | + | 7.67123i | 0.360426 | + | 0.624276i | 0.988031 | − | 0.154256i | \(-0.0492980\pi\) |
−0.627605 | + | 0.778532i | \(0.715965\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.4857 | − | 8.15806i | 0.847719 | − | 0.659540i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.01011 | + | 1.74956i | −0.0811341 | + | 0.140528i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.92894 | −0.153946 | −0.0769731 | − | 0.997033i | \(-0.524526\pi\) | ||||
−0.0769731 | + | 0.997033i | \(0.524526\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.45962 | − | 6.26769i | 0.432976 | − | 0.497060i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.9043 | + | 2.68936i | −1.33225 | + | 0.211952i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1983 | + | 21.1281i | 0.955446 | + | 1.65488i | 0.733345 | + | 0.679856i | \(0.237958\pi\) |
0.222100 | + | 0.975024i | \(0.428709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.3981 | + | 2.42304i | 0.965194 | + | 0.188633i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.75658 | − | 4.77453i | −0.213310 | − | 0.369464i | 0.739438 | − | 0.673224i | \(-0.235091\pi\) |
−0.952749 | + | 0.303760i | \(0.901758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.58861 | − | 9.67976i | 0.429893 | − | 0.744597i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.03848 | + | 21.9435i | 0.232358 | + | 1.67806i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6052 | 0.958355 | 0.479178 | − | 0.877718i | \(-0.340935\pi\) | ||||
0.479178 | + | 0.877718i | \(0.340935\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.92909 | − | 12.8673i | 0.372604 | − | 0.972676i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.5458 | − | 2.06103i | −0.792674 | − | 0.154916i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.10472 | + | 8.84164i | −0.381545 | + | 0.660855i | −0.991283 | − | 0.131747i | \(-0.957941\pi\) |
0.609738 | + | 0.792603i | \(0.291275\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.2398 | −1.20710 | −0.603548 | − | 0.797327i | \(-0.706247\pi\) | ||||
−0.603548 | + | 0.797327i | \(0.706247\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.1476 | − | 2.96038i | −1.11974 | − | 0.218837i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.3254 | −0.906179 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.1093 | −0.739265 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.40479 | + | 13.6758i | 0.102183 | + | 0.994766i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.94120 | 0.285175 | 0.142587 | − | 0.989782i | \(-0.454458\pi\) | ||||
0.142587 | + | 0.989782i | \(0.454458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.74112 | −0.413255 | −0.206627 | − | 0.978420i | \(-0.566249\pi\) | ||||
−0.206627 | + | 0.978420i | \(0.566249\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.33260 | + | 1.43305i | 0.525098 | + | 0.102623i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.67480 | −0.546807 | −0.273403 | − | 0.961899i | \(-0.588149\pi\) | ||||
−0.273403 | + | 0.961899i | \(0.588149\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.26928 | − | 3.93050i | 0.160865 | − | 0.278626i | −0.774314 | − | 0.632801i | \(-0.781905\pi\) |
0.935179 | + | 0.354175i | \(0.115238\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.12636 | + | 1.00187i | 0.361586 | + | 0.0706666i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.54807 | + | 0.882659i | −0.389398 | + | 0.0619505i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.2774 | 2.25435 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.3186 | + | 11.9181i | −1.06471 | + | 0.828366i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.42836 | − | 14.5983i | 0.583002 | − | 1.00979i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.84097 | − | 17.0451i | −0.677480 | − | 1.17343i | −0.975737 | − | 0.218944i | \(-0.929739\pi\) |
0.298257 | − | 0.954486i | \(-0.403595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.1427 | + | 5.10922i | 1.79127 | + | 0.350078i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.5692 | − | 23.5025i | −0.925410 | − | 1.60286i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.05371 | + | 1.29938i | 0.0715304 | + | 0.0882079i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.93348 | − | 11.4037i | 0.671242 | − | 0.770592i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.97891 | −0.402185 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.63518 | + | 11.4925i | −0.444324 | + | 0.769592i | −0.998005 | − | 0.0631368i | \(-0.979890\pi\) |
0.553681 | + | 0.832729i | \(0.313223\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.14299 | − | 15.4764i | −0.142866 | − | 1.03176i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0305 | + | 19.1053i | 0.732118 | + | 1.26807i | 0.955976 | + | 0.293445i | \(0.0948016\pi\) |
−0.223858 | + | 0.974622i | \(0.571865\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.92359 | − | 15.4561i | 0.589688 | − | 1.02137i | −0.404585 | − | 0.914500i | \(-0.632584\pi\) |
0.994273 | − | 0.106869i | \(-0.0340825\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.54639 | − | 8.86966i | 0.364926 | − | 0.583581i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.84409 | − | 13.5864i | −0.513883 | − | 0.890072i | −0.999870 | − | 0.0161061i | \(-0.994873\pi\) |
0.485987 | − | 0.873966i | \(-0.338460\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4344 | − | 18.0730i | 0.680667 | − | 1.17895i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.18917 | + | 0.623276i | 0.207159 | + | 0.0404861i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.0639656 | + | 0.110792i | 0.00413759 | + | 0.00716652i | 0.868087 | − | 0.496412i | \(-0.165350\pi\) |
−0.863949 | + | 0.503579i | \(0.832016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.54343 | − | 13.0656i | −0.485915 | − | 0.841630i | 0.513954 | − | 0.857818i | \(-0.328180\pi\) |
−0.999869 | + | 0.0161883i | \(0.994847\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.87616 | + | 12.8146i | 0.569406 | + | 0.822056i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.6411 | − | 14.9421i | −1.06316 | − | 0.954616i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.98476 | − | 8.63386i | 0.317173 | − | 0.549359i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.82911 | − | 7.83989i | 0.432777 | − | 0.496833i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3738 | −0.781030 | −0.390515 | − | 0.920596i | \(-0.627703\pi\) | ||||
−0.390515 | + | 0.920596i | \(0.627703\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7687 | 0.928499 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.95508 | + | 23.1797i | 0.498167 | + | 1.45157i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.0433 | + | 19.1276i | −0.688865 | + | 1.19315i | 0.283340 | + | 0.959019i | \(0.408557\pi\) |
−0.972205 | + | 0.234130i | \(0.924776\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.65111 | + | 9.53115i | −0.226869 | + | 0.592237i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.02762 | + | 3.91157i | −0.311202 | + | 0.242120i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.89678 | − | 6.74943i | −0.240286 | − | 0.416187i | 0.720510 | − | 0.693445i | \(-0.243908\pi\) |
−0.960796 | + | 0.277257i | \(0.910575\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.66641 | + | 13.2786i | 0.470944 | + | 0.815698i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.98423 | + | 8.69554i | 0.182632 | + | 0.532158i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.85738 | + | 6.68119i | −0.235189 | + | 0.407359i | −0.959328 | − | 0.282295i | \(-0.908904\pi\) |
0.724139 | + | 0.689654i | \(0.242238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5744 | − | 21.7795i | −0.763839 | − | 1.32301i | −0.940858 | − | 0.338801i | \(-0.889979\pi\) |
0.177019 | − | 0.984207i | \(-0.443355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.28029 | − | 5.24576i | 0.198532 | − | 0.317488i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.94438 | + | 10.2960i | −0.358460 | + | 0.620870i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.98137 | + | 6.89593i | 0.239217 | + | 0.414336i | 0.960490 | − | 0.278315i | \(-0.0897759\pi\) |
−0.721273 | + | 0.692651i | \(0.756443\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.75735 | + | 0.714175i | 0.105210 | + | 0.0427565i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3385 | − | 23.1030i | 0.795710 | − | 1.37821i | −0.126678 | − | 0.991944i | \(-0.540431\pi\) |
0.922388 | − | 0.386266i | \(-0.126235\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.4399 | −0.858364 | −0.429182 | − | 0.903218i | \(-0.641198\pi\) | ||||
−0.429182 | + | 0.903218i | \(0.641198\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −40.1051 | − | 7.83795i | −2.37562 | − | 0.464280i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.56144 | − | 24.9600i | 0.564394 | − | 1.47334i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.30577 | − | 2.26166i | −0.0768099 | − | 0.133039i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.9406 | − | 19.4479i | 0.993074 | − | 1.14006i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.27703 | − | 14.3362i | −0.483549 | − | 0.837532i | 0.516272 | − | 0.856424i | \(-0.327319\pi\) |
−0.999822 | + | 0.0188927i | \(0.993986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.91061 | − | 17.1657i | 0.577018 | − | 0.999424i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.656910 | − | 11.8435i | 0.0381178 | − | 0.687229i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.73460 | 0.505135 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.1939 | + | 3.53090i | −1.27924 | + | 0.203518i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.87467 | + | 22.9454i | 0.452388 | + | 1.31818i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.2352 | − | 24.6561i | 0.815105 | − | 1.41180i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.9233 | −0.623425 | −0.311713 | − | 0.950176i | \(-0.600903\pi\) | ||||
−0.311713 | + | 0.950176i | \(0.600903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.2720 | − | 20.9764i | 1.03946 | − | 1.19331i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.25360 | 0.297904 | 0.148952 | − | 0.988844i | \(-0.452410\pi\) | ||||
0.148952 | + | 0.988844i | \(0.452410\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.5184 | 1.21629 | 0.608145 | − | 0.793826i | \(-0.291914\pi\) | ||||
0.608145 | + | 0.793826i | \(0.291914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.7019 | − | 5.73779i | −1.39179 | − | 0.323288i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.5323 | −0.984710 | −0.492355 | − | 0.870394i | \(-0.663864\pi\) | ||||
−0.492355 | + | 0.870394i | \(0.663864\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.84714 | 0.271388 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.42605 | − | 4.15527i | −0.0795945 | − | 0.231925i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.7012 | 1.81954 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.51567 | + | 6.08932i | −0.195014 | + | 0.337774i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.4516 | − | 21.1826i | 1.02037 | − | 1.17140i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.8848 | − | 13.4226i | −0.600097 | − | 0.740012i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.27589 | −0.344954 | −0.172477 | − | 0.985014i | \(-0.555177\pi\) | ||||
−0.172477 | + | 0.985014i | \(0.555177\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.58737 | + | 11.4637i | 0.0869872 | + | 0.628209i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.81757 | + | 8.34428i | −0.263212 | + | 0.455897i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5924 | + | 23.5427i | 0.740426 | + | 1.28246i | 0.952302 | + | 0.305159i | \(0.0987095\pi\) |
−0.211876 | + | 0.977297i | \(0.567957\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.81601 | + | 5.29155i | 0.0986322 | + | 0.287397i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.721712 | − | 1.25004i | −0.0390829 | − | 0.0676936i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4842 | + | 8.44222i | −0.890063 | + | 0.455837i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.6216 | − | 33.8633i | −0.625685 | − | 1.82314i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.1808 | 1.02968 | 0.514840 | − | 0.857286i | \(-0.327851\pi\) | ||||
0.514840 | + | 0.857286i | \(0.327851\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1028 | − | 17.4985i | 0.540789 | − | 0.936675i | −0.458069 | − | 0.888916i | \(-0.651459\pi\) |
0.998859 | − | 0.0477584i | \(-0.0152078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.388515 | − | 7.00457i | 0.0207374 | − | 0.373876i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.2499 | + | 24.6816i | 0.758448 | + | 1.31367i | 0.943642 | + | 0.330969i | \(0.107376\pi\) |
−0.185193 | + | 0.982702i | \(0.559291\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.5680 | + | 42.5531i | −1.30394 | + | 2.25848i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.2813 | + | 0.714841i | 1.07340 | + | 0.0378334i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.4572 | − | 26.7727i | −0.815802 | − | 1.41301i | −0.908751 | − | 0.417339i | \(-0.862963\pi\) |
0.0929489 | − | 0.995671i | \(-0.470371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7638 | + | 30.7677i | −0.934934 | + | 1.61935i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.58576 | − | 7.56052i | 0.345663 | − | 0.396824i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.9486 | + | 24.1597i | 0.730103 | + | 1.26458i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.41547 | − | 5.91577i | −0.178286 | − | 0.308801i | 0.763007 | − | 0.646390i | \(-0.223722\pi\) |
−0.941294 | + | 0.337589i | \(0.890389\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.15696 | − | 30.0210i | −0.216403 | − | 1.56283i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.5393 | − | 1.99491i | 0.651007 | − | 0.103571i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.38245 | + | 5.85858i | −0.175137 | + | 0.303346i | −0.940209 | − | 0.340599i | \(-0.889370\pi\) |
0.765072 | + | 0.643945i | \(0.222703\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.12970 | + | 0.220784i | 0.0583377 | + | 0.0114012i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.86673 | 0.147644 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.62967 | 0.391910 | 0.195955 | − | 0.980613i | \(-0.437219\pi\) | ||||
0.195955 | + | 0.980613i | \(0.437219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.4915 | + | 4.20019i | 1.10104 | + | 0.215182i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.21132 | + | 5.56217i | −0.164091 | + | 0.284214i | −0.936332 | − | 0.351116i | \(-0.885802\pi\) |
0.772241 | + | 0.635329i | \(0.219136\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.1542 | + | 14.9880i | 0.619436 | + | 0.763860i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.1120 | + | 15.6475i | −1.02235 | + | 0.795405i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.92675 | + | 13.7295i | 0.401902 | + | 0.696115i | 0.993955 | − | 0.109784i | \(-0.0350159\pi\) |
−0.592053 | + | 0.805899i | \(0.701683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3253 | + | 24.8121i | 0.724460 | + | 1.25480i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.6935 | − | 24.9043i | 1.09429 | − | 1.25626i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.99707 | + | 5.19107i | −0.150799 | + | 0.261191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.56287 | − | 14.8313i | −0.429758 | − | 0.744363i | 0.567093 | − | 0.823654i | \(-0.308068\pi\) |
−0.996852 | + | 0.0792903i | \(0.974735\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.9413 | + | 28.6913i | −0.898187 | + | 1.43636i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.8845 | + | 20.5846i | −0.593486 | + | 1.02795i | 0.400273 | + | 0.916396i | \(0.368915\pi\) |
−0.993759 | + | 0.111552i | \(0.964418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.426840 | − | 0.739309i | −0.0212624 | − | 0.0368276i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.6730 | + | 7.81350i | −1.37508 | + | 0.388256i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.40316 | − | 7.62649i | 0.218256 | − | 0.378031i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1189 | 0.747582 | 0.373791 | − | 0.927513i | \(-0.378058\pi\) | ||||
0.373791 | + | 0.927513i | \(0.378058\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.80337 | − | 11.0824i | −0.187606 | − | 0.546653i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3383 | − | 12.7488i | −0.508717 | − | 0.627326i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.58945 | + | 16.6094i | 0.470728 | + | 0.815324i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.39023 | + | 21.5339i | 0.361901 | + | 1.05452i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.82673 | − | 4.89604i | −0.138095 | − | 0.239187i | 0.788681 | − | 0.614803i | \(-0.210764\pi\) |
−0.926775 | + | 0.375616i | \(0.877431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5088 | + | 21.6658i | −0.609640 | + | 1.05593i | 0.381660 | + | 0.924303i | \(0.375353\pi\) |
−0.991300 | + | 0.131625i | \(0.957981\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.1534 | − | 7.37741i | −0.882648 | − | 0.358702i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.0636 | −1.11875 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.8496 | − | 18.3118i | −0.718622 | − | 0.886171i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.50625 | + | 4.02520i | −0.169283 | + | 0.194339i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4514 | + | 18.1024i | −0.503428 | + | 0.871962i | 0.496564 | + | 0.868000i | \(0.334595\pi\) |
−0.999992 | + | 0.00396247i | \(0.998739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.2708 | −1.02221 | −0.511104 | − | 0.859519i | \(-0.670763\pi\) | ||||
−0.511104 | + | 0.859519i | \(0.670763\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.81425 | − | 11.1141i | −0.182879 | − | 0.532879i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −47.7732 | −2.28530 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.1817 | −0.820040 | −0.410020 | − | 0.912077i | \(-0.634478\pi\) | ||||
−0.410020 | + | 0.912077i | \(0.634478\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.7544 | + | 17.4021i | −0.559732 | + | 0.828674i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.7436 | 0.605467 | 0.302734 | − | 0.953075i | \(-0.402101\pi\) | ||||
0.302734 | + | 0.953075i | \(0.402101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.9584 | −0.803905 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.319128 | + | 0.366362i | −0.0150942 | + | 0.0173283i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.5913 | 1.49088 | 0.745442 | − | 0.666570i | \(-0.232238\pi\) | ||||
0.745442 | + | 0.666570i | \(0.232238\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.5309 | + | 19.9721i | −0.542969 | + | 0.940449i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.98027 | + | 14.5117i | 0.233994 | + | 0.681817i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.18833 | + | 8.86432i | 0.336994 | + | 0.415566i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.30486 | −0.341707 | −0.170853 | − | 0.985296i | \(-0.554652\pi\) | ||||
−0.170853 | + | 0.985296i | \(0.554652\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.5348 | − | 10.3843i | 0.958483 | − | 0.484696i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.3651 | + | 23.1491i | −0.622477 | + | 1.07816i | 0.366546 | + | 0.930400i | \(0.380540\pi\) |
−0.989023 | + | 0.147761i | \(0.952793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.75608 | + | 3.04161i | 0.0816117 | + | 0.141356i | 0.903942 | − | 0.427654i | \(-0.140660\pi\) |
−0.822331 | + | 0.569010i | \(0.807327\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.29832 | + | 2.63849i | −0.106582 | + | 0.122357i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.80239 | + | 13.5141i | 0.361052 | + | 0.625360i | 0.988134 | − | 0.153593i | \(-0.0490845\pi\) |
−0.627083 | + | 0.778953i | \(0.715751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.02550 | + | 6.19721i | 0.232056 | + | 0.286161i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.27899 | − | 0.640831i | −0.151088 | − | 0.0295279i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.3900 | 0.891554 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.2287 | − | 33.3050i | 0.882272 | − | 1.52814i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.3630 | − | 8.84061i | 0.520276 | − | 0.404784i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.54444 | − | 14.7994i | −0.390405 | − | 0.676202i | 0.602098 | − | 0.798422i | \(-0.294332\pi\) |
−0.992503 | + | 0.122221i | \(0.960998\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.60415 | − | 4.51052i | 0.118739 | − | 0.205662i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −29.6290 | − | 1.04431i | −1.34817 | − | 0.0475179i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.7880 | + | 41.2020i | 1.08016 | + | 1.87089i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9335 | − | 22.4014i | 0.586072 | − | 1.01511i | −0.408669 | − | 0.912683i | \(-0.634007\pi\) |
0.994741 | − | 0.102423i | \(-0.0326597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.7167 | + | 39.9680i | 0.620289 | + | 1.80741i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.51452 | + | 13.0155i | 0.339126 | + | 0.587383i | 0.984269 | − | 0.176679i | \(-0.0565355\pi\) |
−0.645143 | + | 0.764062i | \(0.723202\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.70160 | + | 8.14342i | 0.211750 | + | 0.366761i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.2705 | + | 8.23779i | 0.911092 | + | 0.370261i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.6284 | + | 31.6037i | 1.14959 | + | 1.41762i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.62094 | − | 13.1999i | 0.341160 | − | 0.590907i | −0.643488 | − | 0.765456i | \(-0.722513\pi\) |
0.984648 | + | 0.174549i | \(0.0558468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.09969 | − | 9.03197i | −0.138484 | − | 0.403519i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.6284 | −0.830599 | −0.415299 | − | 0.909685i | \(-0.636323\pi\) | ||||
−0.415299 | + | 0.909685i | \(0.636323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.7491 | −1.99131 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.7158 | − | 14.5979i | 0.564730 | − | 0.648316i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.72333 | − | 6.44899i | 0.165034 | − | 0.285847i | −0.771634 | − | 0.636067i | \(-0.780560\pi\) |
0.936667 | + | 0.350221i | \(0.113893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.8145 | − | 3.62964i | 1.00926 | − | 0.160566i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.12495 | + | 38.3109i | −0.0938188 | + | 1.69147i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.6576 | + | 44.4402i | 1.13061 | + | 1.95827i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.45527 | + | 12.9129i | 0.327882 | + | 0.567909i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.4275 | + | 4.18768i | 0.940561 | + | 0.183819i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.3853 | + | 19.7200i | −0.498800 | + | 0.863947i | −0.999999 | − | 0.00138491i | \(-0.999559\pi\) |
0.501199 | + | 0.865332i | \(0.332893\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5092 | − | 28.5949i | −0.721899 | − | 1.25037i | −0.960238 | − | 0.279184i | \(-0.909936\pi\) |
0.238339 | − | 0.971182i | \(-0.423397\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.6537 | − | 20.2355i | 0.552252 | − | 0.883148i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.40009 | − | 2.42502i | 0.0609887 | − | 0.105636i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.42780 | − | 16.3294i | −0.409904 | − | 0.709975i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.2421 | − | 7.00705i | −0.748242 | − | 0.304080i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.81969 | + | 11.8120i | −0.295393 | + | 0.511636i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.10378 | 0.350357 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.6148 | + | 13.3339i | −0.501217 | + | 0.575402i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.1906 | − | 4.95894i | 0.654304 | − | 0.213597i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.53464 | + | 14.7824i | 0.366933 | + | 0.635546i | 0.989084 | − | 0.147351i | \(-0.0470745\pi\) |
−0.622151 | + | 0.782897i | \(0.713741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.6059 | − | 5.39517i | −1.18468 | − | 0.231529i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.9097 | + | 44.8769i | 1.10985 | + | 1.92232i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.3574 | + | 28.3318i | −0.699390 | + | 1.21138i | 0.269288 | + | 0.963060i | \(0.413212\pi\) |
−0.968678 | + | 0.248319i | \(0.920122\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.7658 | − | 10.0646i | −1.05698 | − | 0.429548i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.6794 | −0.667963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.12642 | + | 3.85536i | 0.132949 | + | 0.163946i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.9518 | − | 4.09472i | −0.889353 | − | 0.173811i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.0783 | − | 29.5806i | 0.723633 | − | 1.25337i | −0.235902 | − | 0.971777i | \(-0.575804\pi\) |
0.959534 | − | 0.281592i | \(-0.0908623\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.4678 | 0.485036 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.1847 | − | 3.35850i | −0.725539 | − | 0.141796i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.67074 | 0.407573 | 0.203786 | − | 0.979015i | \(-0.434675\pi\) | ||||
0.203786 | + | 0.979015i | \(0.434675\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.3198 | −0.434157 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.15536 | + | 23.7140i | −0.0905168 | + | 0.995895i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.1274 | 0.466484 | 0.233242 | − | 0.972419i | \(-0.425067\pi\) | ||||
0.233242 | + | 0.972419i | \(0.425067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.729305 | −0.0305205 | −0.0152602 | − | 0.999884i | \(-0.504858\pi\) | ||||
−0.0152602 | + | 0.999884i | \(0.504858\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.69960 | + | 1.30934i | 0.279880 | + | 0.0546984i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.6937 | 1.40512 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.49359 | − | 16.4434i | 0.395223 | − | 0.684547i | −0.597906 | − | 0.801566i | \(-0.704001\pi\) |
0.993130 | + | 0.117019i | \(0.0373338\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.75928 | − | 1.90731i | −0.405582 | − | 0.0792650i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.6846 | − | 2.49532i | 0.650709 | − | 0.103523i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9551 | −0.453714 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.9885 | + | 4.87206i | 0.495665 | + | 0.201435i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.30535 | − | 2.26093i | 0.0538775 | − | 0.0933185i | −0.837829 | − | 0.545933i | \(-0.816175\pi\) |
0.891706 | + | 0.452615i | \(0.149509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.33457 | + | 4.04359i | 0.0961942 | + | 0.166613i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.0463 | − | 2.54971i | −0.536654 | − | 0.104881i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.92622 | − | 13.7286i | −0.325491 | − | 0.563767i | 0.656121 | − | 0.754656i | \(-0.272196\pi\) |
−0.981612 | + | 0.190889i | \(0.938863\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.3913 | + | 34.9576i | −0.548988 | + | 1.43312i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.16331 | − | 5.92753i | 0.211320 | − | 0.242598i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.8610 | −0.648063 | −0.324032 | − | 0.946046i | \(-0.605038\pi\) | ||||
−0.324032 | + | 0.946046i | \(0.605038\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.834141 | − | 1.44477i | 0.0340253 | − | 0.0589336i | −0.848511 | − | 0.529177i | \(-0.822501\pi\) |
0.882537 | + | 0.470244i | \(0.155834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.38142 | + | 3.40615i | 0.341318 | + | 0.138709i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.24774 | + | 16.0176i | 0.375974 | + | 0.651207i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.2555 | + | 31.6194i | −0.740968 | + | 1.28339i | 0.211088 | + | 0.977467i | \(0.432299\pi\) |
−0.952055 | + | 0.305926i | \(0.901034\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.72435 | − | 0.342747i | −0.394050 | − | 0.0138888i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.40925 | + | 7.63705i | 0.178379 | + | 0.308962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.2957 | − | 31.6891i | 0.738958 | − | 1.27991i | −0.214007 | − | 0.976832i | \(-0.568652\pi\) |
0.952965 | − | 0.303080i | \(-0.0980150\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 54.8680 | + | 10.7232i | 2.21249 | + | 0.432399i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.10936 | − | 8.84967i | −0.205695 | − | 0.356274i | 0.744659 | − | 0.667445i | \(-0.232612\pi\) |
−0.950354 | + | 0.311171i | \(0.899279\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.3664 | − | 21.4193i | −0.497049 | − | 0.860914i | 0.502945 | − | 0.864318i | \(-0.332250\pi\) |
−0.999994 | + | 0.00340432i | \(0.998916\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29.9993 | + | 15.1704i | −1.20383 | + | 0.608767i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.02353 | + | 13.1138i | −0.201264 | + | 0.525395i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.9584 | − | 20.7125i | 0.478334 | − | 0.828499i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.1771 | − | 22.0155i | 0.765861 | − | 0.879216i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.0838 | 0.681177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.1420 | −1.67765 | −0.838823 | − | 0.544404i | \(-0.816756\pi\) | ||||
−0.838823 | + | 0.544404i | \(0.816756\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.0659 | − | 32.2441i | −0.439829 | − | 1.28159i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.1969 | + | 34.9821i | −0.801491 | + | 1.38822i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.98411 | − | 2.93285i | 0.355964 | − | 0.116204i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 42.7424 | + | 17.3702i | 1.69086 | + | 0.687155i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.16519 | + | 2.01817i | 0.0460222 | + | 0.0797128i | 0.888119 | − | 0.459614i | \(-0.152012\pi\) |
−0.842097 | + | 0.539327i | \(0.818679\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5035 | − | 28.5850i | −0.650836 | − | 1.12728i | −0.982920 | − | 0.184031i | \(-0.941085\pi\) |
0.332085 | − | 0.943250i | \(-0.392248\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.2582 | − | 44.4596i | −0.600789 | − | 1.75060i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.4187 | − | 18.0458i | 0.409603 | − | 0.709452i | −0.585243 | − | 0.810858i | \(-0.699001\pi\) |
0.994845 | + | 0.101406i | \(0.0323341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.08101 | + | 12.2647i | 0.277954 | + | 0.481430i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.35951 | + | 2.55887i | 0.0532834 | + | 0.100290i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.4176 | − | 42.2925i | 0.955534 | − | 1.65503i | 0.222391 | − | 0.974958i | \(-0.428614\pi\) |
0.733142 | − | 0.680075i | \(-0.238053\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.4620 | + | 52.7618i | 1.19025 | + | 2.06157i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.6744 | − | 16.0850i | 0.806584 | − | 0.627536i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.272662 | + | 0.472265i | −0.0106214 | + | 0.0183968i | −0.871287 | − | 0.490773i | \(-0.836714\pi\) |
0.860666 | + | 0.509170i | \(0.170048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.4250 | −1.80572 | −0.902861 | − | 0.429933i | \(-0.858537\pi\) | ||||
−0.902861 | + | 0.429933i | \(0.858537\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.1635 | − | 1.98631i | −0.394718 | − | 0.0771418i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −39.3160 | − | 48.4827i | −1.52461 | − | 1.88008i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.86858 | − | 11.8967i | −0.265953 | − | 0.460643i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.0971 | + | 17.3316i | −0.583687 | + | 0.670079i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1709 | + | 17.6165i | 0.392642 | + | 0.680076i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9838 | + | 29.4168i | −0.654677 | + | 1.13393i | 0.327298 | + | 0.944921i | \(0.393862\pi\) |
−0.981975 | + | 0.189013i | \(0.939471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.49869 | − | 27.0201i | 0.0576847 | − | 1.04000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.2851 | 1.20238 | 0.601191 | − | 0.799105i | \(-0.294693\pi\) | ||||
0.601191 | + | 0.799105i | \(0.294693\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.9080 | − | 6.18999i | 1.49315 | − | 0.237550i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.4035 | + | 36.1415i | 0.475301 | + | 1.38495i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.289712 | + | 0.501795i | −0.0110855 | + | 0.0192007i | −0.871515 | − | 0.490369i | \(-0.836862\pi\) |
0.860429 | + | 0.509570i | \(0.170195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.6133 | 0.825801 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.3040 | − | 23.3091i | 0.774644 | − | 0.889299i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.47915 | −0.246836 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.21565 | −0.0842872 | −0.0421436 | − | 0.999112i | \(-0.513419\pi\) | ||||
−0.0421436 | + | 0.999112i | \(0.513419\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.3749 | − | 13.2348i | 0.470085 | − | 0.502750i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.9962 | −1.59301 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.7387 | −1.69460 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.82046 | − | 25.7013i | −0.333620 | − | 0.972112i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.74299 | 0.179140 | 0.0895702 | − | 0.995981i | \(-0.471451\pi\) | ||||
0.0895702 | + | 0.995981i | \(0.471451\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.2432 | + | 24.6699i | −0.537192 | + | 0.930444i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.7416 | − | 27.2556i | 0.894159 | − | 1.02650i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.2559 | + | 34.6043i | −0.498539 | + | 1.30143i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.3765 | −0.877923 | −0.438962 | − | 0.898506i | \(-0.644654\pi\) | ||||
−0.438962 | + | 0.898506i | \(0.644654\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.21417 | + | 2.11900i | 0.195547 | + | 0.0794688i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.04539 | + | 3.54272i | −0.0766004 | + | 0.132676i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.92348 | − | 8.52771i | −0.184128 | − | 0.318918i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.0719275 | + | 0.209584i | 0.00268618 | + | 0.00782707i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.0256 | − | 22.5610i | −0.485772 | − | 0.841382i | 0.514094 | − | 0.857734i | \(-0.328128\pi\) |
−0.999866 | + | 0.0163516i | \(0.994795\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.9659 | − | 6.67649i | 1.56289 | − | 0.248645i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.48237 | − | 24.7162i | −0.315463 | − | 0.919205i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.0584 | 0.410698 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.79712 | + | 10.0409i | −0.215003 | + | 0.372396i | −0.953274 | − | 0.302108i | \(-0.902310\pi\) |
0.738270 | + | 0.674505i | \(0.235643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.8313 | + | 24.7322i | 0.401158 | + | 0.916009i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.8078 | + | 32.5761i | 0.695633 | + | 1.20487i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.6743 | − | 30.6128i | 0.652816 | − | 1.13071i | −0.329620 | − | 0.944114i | \(-0.606921\pi\) |
0.982436 | − | 0.186597i | \(-0.0597459\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −23.3240 | − | 30.9284i | −0.860319 | − | 1.14081i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.44210 | − | 5.96189i | −0.126791 | − | 0.219609i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.66968 | + | 8.08812i | −0.171777 | + | 0.297526i | −0.939041 | − | 0.343805i | \(-0.888284\pi\) |
0.767264 | + | 0.641331i | \(0.221617\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.3419 | − | 13.0206i | 0.416654 | − | 0.478323i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.6308 | + | 25.3412i | 0.536750 | + | 0.929679i | 0.999076 | + | 0.0429687i | \(0.0136816\pi\) |
−0.462326 | + | 0.886710i | \(0.652985\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.448120 | − | 0.776167i | −0.0164179 | − | 0.0284366i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.2133 | − | 11.0582i | 0.520038 | − | 0.404598i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.40056 | − | 6.26662i | 0.0877146 | − | 0.228977i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.3106 | − | 23.0547i | 0.485712 | − | 0.841278i | −0.514153 | − | 0.857699i | \(-0.671894\pi\) |
0.999865 | + | 0.0164202i | \(0.00522696\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.0342 | − | 4.11083i | −0.766529 | − | 0.149807i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.3012 | −1.02999 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.3183 | −1.28367 | −0.641833 | − | 0.766845i | \(-0.721826\pi\) | ||||
−0.641833 | + | 0.766845i | \(0.721826\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.1052 | + | 4.90644i | 0.911260 | + | 0.178092i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.7824 | + | 27.3359i | −0.572112 | + | 0.990927i | 0.424237 | + | 0.905551i | \(0.360542\pi\) |
−0.996349 | + | 0.0853760i | \(0.972791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.3783 | − | 6.74210i | 1.53420 | − | 0.244080i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.82203 | + | 42.0459i | 0.210496 | + | 1.52017i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.18790 | + | 7.25366i | 0.151216 | + | 0.261914i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.8477 | − | 41.3055i | −0.859972 | − | 1.48951i | −0.871955 | − | 0.489587i | \(-0.837148\pi\) |
0.0119829 | − | 0.999928i | \(-0.496186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.1270 | + | 28.8461i | −0.904928 | + | 1.03887i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.7219 | − | 35.8914i | 0.745314 | − | 1.29092i | −0.204733 | − | 0.978818i | \(-0.565633\pi\) |
0.950048 | − | 0.312105i | \(-0.101034\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.64653 | − | 2.85188i | −0.0591452 | − | 0.102442i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.37291 | + | 14.9889i | −0.336251 | + | 0.537725i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.2997 | − | 64.6050i | 1.33640 | − | 2.31472i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.5536 | − | 30.4036i | −0.628116 | − | 1.08793i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.84590 | + | 4.97898i | −0.351864 | + | 0.177934i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.08148 | − | 5.33728i | 0.109983 | − | 0.190496i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.3177 | 0.938125 | 0.469063 | − | 0.883165i | \(-0.344592\pi\) | ||||
0.469063 | + | 0.883165i | \(0.344592\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.38182 | − | 12.7679i | −0.155997 | − | 0.454548i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.05700 | + | 7.98024i | −0.108694 | + | 0.283745i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.01533 | + | 10.4189i | 0.213611 | + | 0.369984i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.62065 | + | 25.1191i | 0.305743 | + | 0.890883i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.42109 | + | 14.5858i | 0.298290 | + | 0.516654i | 0.975745 | − | 0.218911i | \(-0.0702503\pi\) |
−0.677455 | + | 0.735565i | \(0.736917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.4629 | + | 25.0504i | −0.511659 | + | 0.886220i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.18405 | + | 15.7729i | 0.0771695 | + | 0.557308i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.9322 | −0.703392 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.5633 | − | 51.0697i | 0.689516 | − | 1.79997i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.77675 | + | 10.0758i | −0.308956 | + | 0.354685i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.8734 | + | 20.5653i | −0.417445 | + | 0.723036i | −0.995682 | − | 0.0928330i | \(-0.970408\pi\) |
0.578237 | + | 0.815869i | \(0.303741\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.9596 | −0.771107 | −0.385553 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385553 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.1395 | − | 41.2002i | −0.495895 | − | 1.44495i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −77.9471 | −2.73037 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62.7221 | −2.19437 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.31887 | − | 7.82745i | 0.255742 | − | 0.273513i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.2208 | −0.740610 | −0.370305 | − | 0.928910i | \(-0.620747\pi\) | ||||
−0.370305 | + | 0.928910i | \(0.620747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0785 | −0.455890 | −0.227945 | − | 0.973674i | \(-0.573201\pi\) | ||||
−0.227945 | + | 0.973674i | \(0.573201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.5253 | + | 15.5272i | −0.470891 | + | 0.540587i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.8079 | 0.897427 | 0.448714 | − | 0.893676i | \(-0.351882\pi\) | ||||
0.448714 | + | 0.893676i | \(0.351882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.21392 | + | 10.7628i | −0.215818 | + | 0.373808i | −0.953525 | − | 0.301313i | \(-0.902575\pi\) |
0.737707 | + | 0.675121i | \(0.235909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.47693 | + | 13.0450i | 0.155303 | + | 0.452526i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.0657 | + | 20.7108i | 0.799180 | + | 0.717587i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.6145 | 0.609575 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.75004 | + | 1.79784i | 0.0950554 | + | 0.0621426i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.492155 | + | 0.852437i | −0.0169911 | + | 0.0294294i | −0.874396 | − | 0.485213i | \(-0.838742\pi\) |
0.857405 | + | 0.514643i | \(0.172075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2457 | + | 21.2102i | 0.422266 | + | 0.731386i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.3493 | − | 34.8413i | 1.04529 | − | 1.20000i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.8556 | + | 30.9268i | 0.614251 | + | 1.06391i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.1257 | − | 2.40640i | 0.519727 | − | 0.0826849i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.5463 | − | 4.79721i | −0.842427 | − | 0.164640i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.9578 | −0.855542 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.66990 | + | 8.08850i | −0.159894 | + | 0.276945i | −0.934830 | − | 0.355095i | \(-0.884449\pi\) |
0.774936 | + | 0.632040i | \(0.217782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −65.5704 | − | 26.6473i | −2.24246 | − | 0.911319i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.78991 | + | 10.0284i | 0.197779 | + | 0.342564i | 0.947808 | − | 0.318841i | \(-0.103294\pi\) |
−0.750029 | + | 0.661405i | \(0.769960\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.8214 | + | 46.4560i | −0.915134 | + | 1.58506i | −0.108429 | + | 0.994104i | \(0.534582\pi\) |
−0.806705 | + | 0.590954i | \(0.798751\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.5456 | − | 39.2527i | 0.836511 | − | 1.33773i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.80485 | + | 8.32225i | 0.163559 | + | 0.283293i | 0.936143 | − | 0.351620i | \(-0.114369\pi\) |
−0.772584 | + | 0.634913i | \(0.781036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.1368 | + | 34.8779i | −0.684671 | + | 1.18588i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.46830 | − | 4.27837i | −0.0498661 | − | 0.145301i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.14137 | − | 3.70896i | −0.0726409 | − | 0.125818i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.03575 | − | 3.52602i | −0.0689788 | − | 0.119475i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.2581 | − | 27.4314i | 1.19331 | − | 0.928413i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.10748 | + | 1.36569i | 0.0374396 | + | 0.0461687i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.532415 | − | 0.922170i | 0.0179784 | − | 0.0311395i | −0.856896 | − | 0.515489i | \(-0.827610\pi\) |
0.874875 | + | 0.484349i | \(0.160944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.30728 | − | 27.1198i | −0.313927 | − | 0.914729i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.7526 | −0.699171 | −0.349586 | − | 0.936904i | \(-0.613678\pi\) | ||||
−0.349586 | + | 0.936904i | \(0.613678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.80560 | 0.296332 | 0.148166 | − | 0.988963i | \(-0.452663\pi\) | ||||
0.148166 | + | 0.988963i | \(0.452663\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.5497 | − | 25.8873i | 0.758000 | − | 0.870192i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.0074 | − | 17.3334i | 0.336017 | − | 0.581998i | −0.647663 | − | 0.761927i | \(-0.724254\pi\) |
0.983680 | + | 0.179929i | \(0.0575869\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.0686 | + | 25.9809i | 0.706619 | + | 0.871370i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.05131 | − | 19.9144i | 0.169225 | − | 0.667158i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.1160 | − | 41.7702i | −0.807013 | − | 1.39779i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.3096 | − | 28.2490i | −0.545169 | − | 0.944260i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.8479 | + | 2.90180i | 0.495756 | + | 0.0968883i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.671304 | + | 1.16273i | −0.0223892 | + | 0.0387793i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.6262 | − | 18.4051i | −0.354009 | − | 0.613162i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −38.9003 | − | 1.37109i | −1.29452 | − | 0.0456271i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.9431 | − | 44.9347i | 0.862377 | − | 1.49368i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.5307 | + | 21.7039i | 0.416076 | + | 0.720665i | 0.995541 | − | 0.0943323i | \(-0.0300716\pi\) |
−0.579465 | + | 0.814997i | \(0.696738\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.76317 | + | 41.6208i | 0.191152 | + | 1.38048i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.86265 | + | 8.42236i | −0.161107 | + | 0.279045i | −0.935266 | − | 0.353946i | \(-0.884840\pi\) |
0.774159 | + | 0.632991i | \(0.218173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7031 | −0.453506 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.3895 | − | 37.1835i | 1.07076 | − | 1.22925i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49.8241 | − | 7.92668i | 1.64534 | − | 0.261762i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2582 | + | 40.2844i | 0.767217 | + | 1.32886i | 0.939066 | + | 0.343736i | \(0.111692\pi\) |
−0.171849 | + | 0.985123i | \(0.554974\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.5684 | − | 3.62892i | −0.611850 | − | 0.119577i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.3817 | − | 17.9815i | −0.341716 | − | 0.591870i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0455 | − | 17.3993i | 0.330293 | − | 0.572085i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.0292 | − | 29.5874i | 1.24904 | − | 0.971776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.4680 | 1.13086 | 0.565429 | − | 0.824797i | \(-0.308711\pi\) | ||||
0.565429 | + | 0.824797i | \(0.308711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49.1379 | + | 16.0410i | −1.61043 | + | 0.525723i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.93054 | + | 1.74534i | 0.292373 | + | 0.0571400i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.1496 | − | 27.9719i | 0.528148 | − | 0.914779i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.1376 | 0.886547 | 0.443274 | − | 0.896386i | \(-0.353817\pi\) | ||||
0.443274 | + | 0.896386i | \(0.353817\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.5789 | + | 7.14880i | 1.19371 | + | 0.233292i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0390 | −0.327262 | −0.163631 | − | 0.986522i | \(-0.552321\pi\) | ||||
−0.163631 | + | 0.986522i | \(0.552321\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 65.3589 | 2.12838 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −40.0843 | − | 17.9600i | −1.30394 | − | 0.584240i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0977 | 0.555599 | 0.277800 | − | 0.960639i | \(-0.410395\pi\) | ||||
0.277800 | + | 0.960639i | \(0.410395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.7885 | −0.382669 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.8029 | − | 5.82455i | −0.966427 | − | 0.188874i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.79843 | −0.0906500 | −0.0453250 | − | 0.998972i | \(-0.514432\pi\) | ||||
−0.0453250 | + | 0.998972i | \(0.514432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.29605 | + | 10.9051i | −0.203736 | + | 0.352880i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.23961 | + | 1.61031i | 0.266349 | + | 0.0520539i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.40244 | − | 16.7134i | 0.206746 | − | 0.539705i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6002 | −0.987103 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.04368 | − | 7.53728i | −0.0336320 | − | 0.242885i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.17143 | − | 15.8854i | 0.295239 | − | 0.511369i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.97799 | − | 8.62213i | −0.160081 | − | 0.277269i | 0.774816 | − | 0.632186i | \(-0.217842\pi\) |
−0.934898 | + | 0.354917i | \(0.884509\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 55.5885 | + | 10.8640i | 1.78576 | + | 0.349000i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.13634 | + | 1.96819i | 0.0364668 | + | 0.0631623i | 0.883683 | − | 0.468086i | \(-0.155056\pi\) |
−0.847216 | + | 0.531249i | \(0.821723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.4404 | + | 32.4755i | −0.398822 | + | 1.04112i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.99924 | + | 9.18320i | −0.256181 | + | 0.294098i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.8466 | 0.538971 | 0.269485 | − | 0.963004i | \(-0.413146\pi\) | ||||
0.269485 | + | 0.963004i | \(0.413146\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.05828 | − | 10.4932i | 0.193623 | − | 0.335366i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.4029 | − | 29.8781i | 1.22611 | − | 0.953934i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.7661 | − | 18.6475i | −0.343386 | − | 0.594762i | 0.641673 | − | 0.766978i | \(-0.278241\pi\) |
−0.985059 | + | 0.172216i | \(0.944907\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.2605 | − | 21.2358i | 0.390651 | − | 0.676628i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.0437 | − | 26.4331i | −0.447016 | − | 0.841374i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.4764 | − | 47.5905i | −0.873699 | − | 1.51329i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8227 | − | 29.1378i | 0.534392 | − | 0.925594i | −0.464801 | − | 0.885415i | \(-0.653874\pi\) |
0.999193 | − | 0.0401785i | \(-0.0127927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.6683 | − | 2.08497i | −0.338549 | − | 0.0661645i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.25033 | + | 12.5579i | 0.229851 | + | 0.398113i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.99406 | − | 12.1141i | −0.221504 | − | 0.383656i | 0.733761 | − | 0.679408i | \(-0.237763\pi\) |
−0.955265 | + | 0.295752i | \(0.904430\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.11012 | + | 20.0145i | −0.0351227 | + | 0.633230i |
(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 | 1008.2.q.l.529.10 | 22 | ||
3.2 | odd | 2 | 3024.2.q.l.2881.10 | 22 | |||
4.3 | odd | 2 | 504.2.q.c.25.2 | ✓ | 22 | ||
7.2 | even | 3 | 1008.2.t.l.961.3 | 22 | |||
9.4 | even | 3 | 1008.2.t.l.193.3 | 22 | |||
9.5 | odd | 6 | 3024.2.t.k.1873.2 | 22 | |||
12.11 | even | 2 | 1512.2.q.d.1369.10 | 22 | |||
21.2 | odd | 6 | 3024.2.t.k.289.2 | 22 | |||
28.23 | odd | 6 | 504.2.t.c.457.9 | yes | 22 | ||
36.23 | even | 6 | 1512.2.t.c.361.2 | 22 | |||
36.31 | odd | 6 | 504.2.t.c.193.9 | yes | 22 | ||
63.23 | odd | 6 | 3024.2.q.l.2305.10 | 22 | |||
63.58 | even | 3 | inner | 1008.2.q.l.625.10 | 22 | ||
84.23 | even | 6 | 1512.2.t.c.289.2 | 22 | |||
252.23 | even | 6 | 1512.2.q.d.793.10 | 22 | |||
252.247 | odd | 6 | 504.2.q.c.121.2 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.2 | ✓ | 22 | 4.3 | odd | 2 | ||
504.2.q.c.121.2 | yes | 22 | 252.247 | odd | 6 | ||
504.2.t.c.193.9 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.c.457.9 | yes | 22 | 28.23 | odd | 6 | ||
1008.2.q.l.529.10 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.q.l.625.10 | 22 | 63.58 | even | 3 | inner | ||
1008.2.t.l.193.3 | 22 | 9.4 | even | 3 | |||
1008.2.t.l.961.3 | 22 | 7.2 | even | 3 | |||
1512.2.q.d.793.10 | 22 | 252.23 | even | 6 | |||
1512.2.q.d.1369.10 | 22 | 12.11 | even | 2 | |||
1512.2.t.c.289.2 | 22 | 84.23 | even | 6 | |||
1512.2.t.c.361.2 | 22 | 36.23 | even | 6 | |||
3024.2.q.l.2305.10 | 22 | 63.23 | odd | 6 | |||
3024.2.q.l.2881.10 | 22 | 3.2 | odd | 2 | |||
3024.2.t.k.289.2 | 22 | 21.2 | odd | 6 | |||
3024.2.t.k.1873.2 | 22 | 9.5 | odd | 6 |