Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(367,1008)]
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([3, 0, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cz (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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 367.4 | ||
Character | \(\chi\) | \(=\) | 1008.367 |
Dual form | 1008.2.cz.g.607.4 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.42297 | + | 0.987503i | −0.821551 | + | 0.570135i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.679706 | − | 0.392428i | −0.303974 | − | 0.175499i | 0.340253 | − | 0.940334i | \(-0.389487\pi\) |
−0.644227 | + | 0.764835i | \(0.722821\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.49091 | − | 0.891831i | −0.941476 | − | 0.337081i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.04968 | − | 2.81037i | 0.349892 | − | 0.936790i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.22712 | + | 0.708477i | −0.369990 | + | 0.213614i | −0.673454 | − | 0.739229i | \(-0.735190\pi\) |
0.303464 | + | 0.952843i | \(0.401857\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50450 | + | 0.868623i | −0.417273 | + | 0.240913i | −0.693910 | − | 0.720062i | \(-0.744113\pi\) |
0.276637 | + | 0.960975i | \(0.410780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.35472 | − | 0.112799i | 0.349788 | − | 0.0291245i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.43701 | + | 3.13906i | 1.31867 | + | 0.761334i | 0.983514 | − | 0.180829i | \(-0.0578782\pi\) |
0.335154 | + | 0.942163i | \(0.391212\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.736632 | + | 1.27588i | 0.168995 | + | 0.292708i | 0.938067 | − | 0.346455i | \(-0.112615\pi\) |
−0.769072 | + | 0.639162i | \(0.779281\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.42517 | − | 1.19073i | 0.965652 | − | 0.259840i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.85720 | − | 2.80431i | −1.01280 | − | 0.584739i | −0.100787 | − | 0.994908i | \(-0.532136\pi\) |
−0.912009 | + | 0.410169i | \(0.865470\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.19200 | − | 3.79666i | −0.438400 | − | 0.759331i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.28159 | + | 5.03562i | 0.246643 | + | 0.969106i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.95678 | − | 6.85335i | 0.734756 | − | 1.27263i | −0.220075 | − | 0.975483i | \(-0.570630\pi\) |
0.954830 | − | 0.297151i | \(-0.0960366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.41859 | 1.51202 | 0.756011 | − | 0.654559i | \(-0.227145\pi\) | ||||
0.756011 | + | 0.654559i | \(0.227145\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.04653 | − | 2.21992i | 0.182177 | − | 0.386439i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.34311 | + | 1.58369i | 0.227026 | + | 0.267692i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.74187 | + | 6.48111i | 0.615160 | + | 1.06549i | 0.990356 | + | 0.138543i | \(0.0442420\pi\) |
−0.375196 | + | 0.926945i | \(0.622425\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.28309 | − | 2.72172i | 0.205458 | − | 0.435824i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.19180 | − | 4.15219i | 1.12317 | − | 0.648463i | 0.180962 | − | 0.983490i | \(-0.442079\pi\) |
0.942208 | + | 0.335027i | \(0.108746\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.85087 | + | 4.53270i | 1.19725 | + | 0.691230i | 0.959940 | − | 0.280205i | \(-0.0904023\pi\) |
0.237306 | + | 0.971435i | \(0.423736\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.81634 | + | 1.49830i | −0.270764 | + | 0.223354i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.110085 | −0.0160576 | −0.00802880 | − | 0.999968i | \(-0.502556\pi\) | ||||
−0.00802880 | + | 0.999968i | \(0.502556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.40927 | + | 4.44294i | 0.772753 | + | 0.634706i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.8365 | + | 0.902283i | −1.51742 | + | 0.126345i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.28575 | + | 7.42313i | −0.588693 | + | 1.01965i | 0.405711 | + | 0.914001i | \(0.367024\pi\) |
−0.994404 | + | 0.105644i | \(0.966309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.11211 | 0.149956 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.30814 | − | 1.08812i | −0.305721 | − | 0.144124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0736173 | −0.00958415 | −0.00479208 | − | 0.999989i | \(-0.501525\pi\) | ||||
−0.00479208 | + | 0.999989i | \(0.501525\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.23776i | − | 0.158479i | −0.996856 | − | 0.0792394i | \(-0.974751\pi\) | ||
0.996856 | − | 0.0792394i | \(-0.0252492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.12102 | + | 6.06425i | −0.645188 | + | 0.764023i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.36349 | 0.169120 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.8735i | 1.45058i | 0.688442 | + | 0.725291i | \(0.258295\pi\) | ||||
−0.688442 | + | 0.725291i | \(0.741705\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.68091 | − | 0.806063i | 1.16544 | − | 0.0970386i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.390149i | − | 0.0463021i | −0.999732 | − | 0.0231511i | \(-0.992630\pi\) | ||
0.999732 | − | 0.0231511i | \(-0.00736987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.70538 | + | 2.13930i | 0.433682 | + | 0.250386i | 0.700914 | − | 0.713246i | \(-0.252776\pi\) |
−0.267232 | + | 0.963632i | \(0.586109\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.86835 | + | 3.23791i | 0.793089 | + | 0.373882i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.68848 | − | 0.670370i | 0.420342 | − | 0.0763958i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00205i | 0.675283i | 0.941275 | + | 0.337642i | \(0.109629\pi\) | ||||
−0.941275 | + | 0.337642i | \(0.890371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.79636 | − | 5.89995i | −0.755151 | − | 0.655551i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.88696 | − | 13.6606i | 0.865706 | − | 1.49945i | −0.000637973 | − | 1.00000i | \(-0.500203\pi\) |
0.866344 | − | 0.499447i | \(-0.166464\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.46371 | − | 4.26727i | −0.267227 | − | 0.462851i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.13733 | + | 13.6594i | 0.121934 | + | 1.46444i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.15579 | − | 3.55405i | 0.652513 | − | 0.376729i | −0.136905 | − | 0.990584i | \(-0.543716\pi\) |
0.789418 | + | 0.613856i | \(0.210382\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.52224 | − | 0.821903i | 0.474060 | − | 0.0861589i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.9794 | + | 8.31338i | −1.24220 | + | 0.862057i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1.15630i | − | 0.118634i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.89647 | + | 3.40433i | 0.598695 | + | 0.345657i | 0.768528 | − | 0.639816i | \(-0.220989\pi\) |
−0.169833 | + | 0.985473i | \(0.554323\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.703006 | + | 4.19233i | 0.0706548 | + | 0.421345i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.82630 | + | 1.63176i | −0.281227 | + | 0.162366i | −0.633979 | − | 0.773350i | \(-0.718579\pi\) |
0.352752 | + | 0.935717i | \(0.385246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.39149 | − | 14.5345i | 0.826838 | − | 1.43212i | −0.0736690 | − | 0.997283i | \(-0.523471\pi\) |
0.900507 | − | 0.434842i | \(-0.143196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.47509 | − | 0.927214i | −0.339134 | − | 0.0904868i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.07017 | − | 4.65932i | 0.780173 | − | 0.450433i | −0.0563185 | − | 0.998413i | \(-0.517936\pi\) |
0.836492 | + | 0.547980i | \(0.184603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.10094 | − | 1.90688i | 0.105451 | − | 0.182646i | −0.808471 | − | 0.588535i | \(-0.799705\pi\) |
0.913922 | + | 0.405889i | \(0.133038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.7247 | − | 5.52731i | −1.11286 | − | 0.524629i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.33634 | − | 5.77872i | −0.313857 | − | 0.543616i | 0.665337 | − | 0.746543i | \(-0.268288\pi\) |
−0.979194 | + | 0.202927i | \(0.934955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.20098 | + | 3.81221i | 0.205242 | + | 0.355490i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.861916 | + | 5.13997i | 0.0796842 | + | 0.475191i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.7436 | − | 12.6680i | −0.984864 | − | 1.16127i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.49612 | + | 7.78751i | −0.408738 | + | 0.707955i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.13340 | + | 13.0104i | −0.553030 | + | 1.17310i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.36510i | 0.658754i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.5443i | − | 1.37934i | −0.724125 | − | 0.689669i | \(-0.757756\pi\) | ||
0.724125 | − | 0.689669i | \(-0.242244\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.6476 | + | 1.30287i | −1.37769 | + | 0.114711i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.63094 | + | 4.55693i | −0.229867 | + | 0.398140i | −0.957768 | − | 0.287541i | \(-0.907162\pi\) |
0.727902 | + | 0.685681i | \(0.240496\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.697011 | − | 3.83506i | −0.0604385 | − | 0.332542i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.10501 | − | 3.92568i | 0.0951045 | − | 0.337869i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.84273 | − | 11.8520i | −0.584614 | − | 1.01258i | −0.994923 | − | 0.100635i | \(-0.967913\pi\) |
0.410309 | − | 0.911946i | \(-0.365421\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.61572 | + | 7.99465i | 0.391500 | + | 0.678098i | 0.992648 | − | 0.121040i | \(-0.0386230\pi\) |
−0.601148 | + | 0.799138i | \(0.705290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.156648 | − | 0.108710i | 0.0131921 | − | 0.00915500i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.23080 | − | 2.13181i | 0.102925 | − | 0.178271i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.37889 | + | 3.10551i | −0.446693 | + | 0.257898i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0846 | − | 0.980495i | −0.996725 | − | 0.0808698i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.44849 | − | 16.3653i | 0.774051 | − | 1.34070i | −0.161276 | − | 0.986909i | \(-0.551561\pi\) |
0.935326 | − | 0.353786i | \(-0.115106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.66662 | + | 1.53957i | −0.217006 | + | 0.125289i | −0.604563 | − | 0.796557i | \(-0.706652\pi\) |
0.387557 | + | 0.921846i | \(0.373319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.5290 | − | 11.9850i | 1.17460 | − | 0.968931i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.72216 | − | 3.30369i | −0.459615 | − | 0.265359i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2290i | 1.21541i | 0.794164 | + | 0.607703i | \(0.207909\pi\) | ||||
−0.794164 | + | 0.607703i | \(0.792091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.23188 | − | 14.7951i | −0.0976948 | − | 1.17333i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.59789 | + | 11.3171i | 0.756420 | + | 0.891911i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.96129 | − | 2.86440i | 0.388599 | − | 0.224357i | −0.292954 | − | 0.956126i | \(-0.594638\pi\) |
0.681553 | + | 0.731769i | \(0.261305\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.58249 | + | 1.09821i | −0.123197 | + | 0.0854953i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.28326 | − | 3.95472i | −0.176684 | − | 0.306025i | 0.764059 | − | 0.645147i | \(-0.223204\pi\) |
−0.940743 | + | 0.339121i | \(0.889870\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.99099 | + | 8.64464i | −0.383922 | + | 0.664973i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.35893 | − | 0.730944i | 0.333336 | − | 0.0558967i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.8762i | 1.35910i | 0.733628 | + | 0.679551i | \(0.237826\pi\) | ||||
−0.733628 | + | 0.679551i | \(0.762174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.07410 | + | 11.4120i | 0.156787 | + | 0.862668i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.104755 | − | 0.0726973i | 0.00787387 | − | 0.00546426i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.15176 | − | 3.55172i | −0.459804 | − | 0.265468i | 0.252158 | − | 0.967686i | \(-0.418860\pi\) |
−0.711962 | + | 0.702218i | \(0.752193\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.31771i | − | 0.469591i | −0.972045 | − | 0.234796i | \(-0.924558\pi\) | ||
0.972045 | − | 0.234796i | \(-0.0754421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.22229 | + | 1.76129i | 0.0903544 | + | 0.130198i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.87367i | − | 0.431841i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.89580 | −0.650526 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.29859 | − | 13.6863i | 0.0944586 | − | 0.995529i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 21.6174i | − | 1.56418i | −0.623165 | − | 0.782090i | \(-0.714153\pi\) | ||
0.623165 | − | 0.782090i | \(-0.285847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.11201 | −0.367970 | −0.183985 | − | 0.982929i | \(-0.558900\pi\) | ||||
−0.183985 | + | 0.982929i | \(0.558900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.94020 | + | 1.34645i | −0.138941 | + | 0.0964213i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7051 | −0.905199 | −0.452599 | − | 0.891714i | \(-0.649503\pi\) | ||||
−0.452599 | + | 0.891714i | \(0.649503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.35332 | − | 2.34401i | 0.0959341 | − | 0.166163i | −0.814064 | − | 0.580775i | \(-0.802750\pi\) |
0.909998 | + | 0.414612i | \(0.136083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.7251 | − | 16.8957i | −0.827028 | − | 1.19173i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.9680 | + | 13.5423i | −1.12074 | + | 0.950483i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.51774 | −0.455219 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.9796 | + | 10.7069i | −0.902147 | + | 0.744183i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.80787 | − | 1.04377i | −0.125053 | − | 0.0721993i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.54303 | − | 4.35497i | 0.519284 | − | 0.299809i | −0.217358 | − | 0.976092i | \(-0.569744\pi\) |
0.736641 | + | 0.676283i | \(0.236411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.385273 | + | 0.555169i | 0.0263985 | + | 0.0380396i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.55752 | − | 6.16181i | −0.242621 | − | 0.420232i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.9699 | − | 7.50796i | −1.42353 | − | 0.509673i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.38521 | + | 0.614916i | −0.499046 | + | 0.0415522i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.9066 | −0.733660 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.60457 | − | 7.97535i | 0.308345 | − | 0.534069i | −0.669656 | − | 0.742672i | \(-0.733558\pi\) |
0.978000 | + | 0.208603i | \(0.0668916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.9709 | + | 2.17507i | −0.864726 | + | 0.145005i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.08469 | − | 7.07489i | −0.271110 | − | 0.469577i | 0.698036 | − | 0.716063i | \(-0.254057\pi\) |
−0.969146 | + | 0.246486i | \(0.920724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.76036 | + | 1.01634i | 0.116328 | + | 0.0671618i | 0.557035 | − | 0.830489i | \(-0.311939\pi\) |
−0.440707 | + | 0.897651i | \(0.645272\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.58660 | + | 4.59630i | −0.301776 | + | 0.302415i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.74641 | + | 9.95307i | 0.376460 | + | 0.652047i | 0.990544 | − | 0.137193i | \(-0.0438080\pi\) |
−0.614085 | + | 0.789240i | \(0.710475\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0748256 | + | 0.0432006i | 0.00488109 | + | 0.00281810i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.92704 | − | 8.54072i | −0.385003 | − | 0.554780i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.1651 | − | 8.75560i | 0.980952 | − | 0.566353i | 0.0783945 | − | 0.996922i | \(-0.475021\pi\) |
0.902557 | + | 0.430570i | \(0.141687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.6422 | + | 10.1858i | −1.13644 | + | 0.656122i | −0.945546 | − | 0.325489i | \(-0.894471\pi\) |
−0.190891 | + | 0.981611i | \(0.561138\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4972 | + | 1.68402i | 0.994148 | + | 0.108030i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.93318 | − | 5.14265i | −0.123506 | − | 0.328552i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.21652 | − | 1.27971i | −0.141034 | − | 0.0814260i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.26701 | + | 27.2270i | 0.143666 | + | 1.72544i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.09897 | −0.448083 | −0.224041 | − | 0.974580i | \(-0.571925\pi\) | ||||
−0.224041 | + | 0.974580i | \(0.571925\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.94715 | 0.499633 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.71973 | + | 3.63927i | 0.483428 | + | 0.227900i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.4449 | + | 12.9585i | 1.40007 | + | 0.808332i | 0.994399 | − | 0.105687i | \(-0.0337042\pi\) |
0.405672 | + | 0.914019i | \(0.367037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.54061 | − | 19.4810i | −0.220003 | − | 1.21049i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.1071 | − | 18.3138i | −0.935106 | − | 1.13360i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.18333 | − | 2.41525i | 0.257955 | − | 0.148931i | −0.365446 | − | 0.930832i | \(-0.619084\pi\) |
0.623401 | + | 0.781902i | \(0.285750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.82610 | − | 3.36370i | 0.357894 | − | 0.206630i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.24986 | + | 11.1362i | −0.321286 | + | 0.681522i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.63937 | − | 3.83324i | −0.404809 | − | 0.233717i | 0.283748 | − | 0.958899i | \(-0.408422\pi\) |
−0.688557 | + | 0.725182i | \(0.741756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.53360 | + | 4.38832i | 0.153905 | + | 0.266571i | 0.932660 | − | 0.360757i | \(-0.117482\pi\) |
−0.778755 | + | 0.627328i | \(0.784148\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.62337 | + | 5.63527i | −0.340342 | + | 0.341062i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.37968 | + | 3.10596i | 0.324407 | + | 0.187297i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.9256 | − | 18.9237i | −0.656455 | − | 1.13701i | −0.981527 | − | 0.191325i | \(-0.938722\pi\) |
0.325071 | − | 0.945689i | \(-0.394612\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.83678 | − | 23.6593i | 0.529044 | − | 1.41645i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.09695 | − | 1.89998i | 0.0654388 | − | 0.113343i | −0.831450 | − | 0.555600i | \(-0.812489\pi\) |
0.896889 | + | 0.442257i | \(0.145822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3003 | 0.909509 | 0.454754 | − | 0.890617i | \(-0.349727\pi\) | ||||
0.454754 | + | 0.890617i | \(0.349727\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.14185 | + | 1.64538i | 0.0676374 | + | 0.0974638i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.6172 | + | 3.92886i | −1.27602 | + | 0.231913i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.2074 | + | 19.4118i | 0.659258 | + | 1.14187i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.7523 | + | 0.978531i | −0.688930 | + | 0.0573625i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.07666 | − | 2.93101i | 0.296581 | − | 0.171231i | −0.344325 | − | 0.938851i | \(-0.611892\pi\) |
0.640906 | + | 0.767619i | \(0.278559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0500381 | + | 0.0288895i | 0.00291333 | + | 0.00168201i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.14029 | − | 5.27133i | −0.298270 | − | 0.305873i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.74355 | 0.563484 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.5134 | − | 18.2922i | −0.894178 | − | 1.05435i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.41036 | − | 5.11292i | 0.138471 | − | 0.293730i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.485732 | + | 0.841312i | −0.0278129 | + | 0.0481734i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.38567 | 0.478596 | 0.239298 | − | 0.970946i | \(-0.423083\pi\) | ||||
0.239298 | + | 0.970946i | \(0.423083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.41203 | + | 28.9687i | 0.137215 | + | 1.64797i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.8576 | 1.63636 | 0.818182 | − | 0.574960i | \(-0.194982\pi\) | ||||
0.818182 | + | 0.574960i | \(0.194982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.4132i | 1.60601i | 0.595973 | + | 0.803005i | \(0.296767\pi\) | ||||
−0.595973 | + | 0.803005i | \(0.703233\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.86057 | − | 2.11227i | 0.330206 | − | 0.119013i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.98308 | −0.504540 | −0.252270 | − | 0.967657i | \(-0.581177\pi\) | ||||
−0.252270 | + | 0.967657i | \(0.581177\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.2131i | 0.627816i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.88251 | + | 14.5994i | −0.384144 | + | 0.814858i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.24932i | 0.514646i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.59573 | + | 3.80804i | 0.365865 | + | 0.211232i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.316451 | + | 3.80062i | 0.0174998 | + | 0.210175i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.274213 | + | 0.0981775i | 0.0151178 | + | 0.00541270i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.80699i | 0.374146i | 0.982346 | + | 0.187073i | \(0.0599001\pi\) | ||||
−0.982346 | + | 0.187073i | \(0.940100\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.1421 | − | 3.71298i | 1.21338 | − | 0.203470i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.65951 | − | 8.07051i | 0.254576 | − | 0.440939i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.43310 | + | 14.6066i | 0.459380 | + | 0.795670i | 0.998928 | − | 0.0462849i | \(-0.0147382\pi\) |
−0.539548 | + | 0.841955i | \(0.681405\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.4540 | + | 4.92828i | 0.567784 | + | 0.267667i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.3306 | + | 5.96437i | −0.559433 | + | 0.322989i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.51166 | − | 15.8911i | −0.513581 | − | 0.858041i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.89649 | − | 3.25118i | −0.371295 | − | 0.175037i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.9020i | 1.81995i | 0.414659 | + | 0.909977i | \(0.363901\pi\) | ||||
−0.414659 | + | 0.909977i | \(0.636099\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.57679 | + | 4.95181i | 0.459105 | + | 0.265065i | 0.711668 | − | 0.702516i | \(-0.247940\pi\) |
−0.252563 | + | 0.967581i | \(0.581273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.30222 | − | 6.46287i | −0.336388 | − | 0.344963i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.7683 | + | 14.8774i | −1.37151 | + | 0.791842i | −0.991118 | − | 0.132983i | \(-0.957544\pi\) |
−0.380392 | + | 0.924825i | \(0.624211\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.153105 | + | 0.265186i | −0.00812599 | + | 0.0140746i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.7975 | + | 7.41684i | 1.47120 | + | 0.392541i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.8705 | + | 6.85344i | −0.626502 | + | 0.361711i | −0.779396 | − | 0.626532i | \(-0.784474\pi\) |
0.152894 | + | 0.988243i | \(0.451141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.41475 | − | 14.5748i | 0.442881 | − | 0.767093i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.29235 | − | 15.5213i | −0.0678310 | − | 0.814658i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.67905 | − | 2.90819i | −0.0878853 | − | 0.152222i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.3229 | + | 28.2720i | 0.852047 | + | 1.47579i | 0.879358 | + | 0.476162i | \(0.157972\pi\) |
−0.0273109 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.12013 | − | 24.5701i | −0.214485 | − | 1.27907i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.2956 | − | 14.6682i | 0.897943 | − | 0.761535i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1393 | − | 17.5618i | 0.524995 | − | 0.909317i | −0.474582 | − | 0.880211i | \(-0.657401\pi\) |
0.999576 | − | 0.0291058i | \(-0.00926598\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.27305 | − | 10.4803i | −0.375579 | − | 0.541200i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.7478i | 0.708048i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.3099i | 1.14598i | 0.819561 | + | 0.572992i | \(0.194217\pi\) | ||||
−0.819561 | + | 0.572992i | \(0.805783\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3501 | + | 22.1191i | 0.786409 | + | 1.13320i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.4652 | + | 18.1262i | −0.534746 | + | 0.926207i | 0.464430 | + | 0.885610i | \(0.346259\pi\) |
−0.999176 | + | 0.0405971i | \(0.987074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.77016 | − | 0.991811i | −0.141180 | − | 0.0505474i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.9794 | − | 17.3060i | 1.06644 | − | 0.879712i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.14324 | − | 10.6404i | −0.311475 | − | 0.539490i | 0.667207 | − | 0.744872i | \(-0.267490\pi\) |
−0.978682 | + | 0.205382i | \(0.934156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.6058 | − | 30.4941i | −0.890362 | − | 1.54215i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.756231 | − | 9.08242i | −0.0381468 | − | 0.458148i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.35537 | − | 4.07963i | 0.118512 | − | 0.205268i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.2792 | + | 12.2856i | −1.06797 | + | 0.616594i | −0.927627 | − | 0.373508i | \(-0.878155\pi\) |
−0.140346 | + | 0.990103i | \(0.544821\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.77896 | + | 4.76887i | 0.239247 | + | 0.238742i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.3595 | − | 31.7997i | 0.916832 | − | 1.58800i | 0.112634 | − | 0.993637i | \(-0.464071\pi\) |
0.804197 | − | 0.594362i | \(-0.202595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.6658 | + | 7.31258i | −0.630926 | + | 0.364266i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.30422 | + | 6.67732i | 0.114497 | + | 0.331799i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.18344 | − | 5.30206i | −0.455206 | − | 0.262813i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.40233i | 0.415468i | 0.978185 | + | 0.207734i | \(0.0666089\pi\) | ||||
−0.978185 | + | 0.207734i | \(0.933391\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.4408 | + | 10.1077i | 1.05760 | + | 0.498578i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.183374 | + | 0.0656542i | 0.00902325 | + | 0.00323063i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.7216 | + | 6.19013i | −0.526304 | + | 0.303862i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.4628 | − | 6.81810i | −0.708244 | − | 0.333884i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1563 | − | 24.5195i | −0.691583 | − | 1.19786i | −0.971319 | − | 0.237780i | \(-0.923580\pi\) |
0.279736 | − | 0.960077i | \(-0.409753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.2835 | − | 24.7397i | 0.696133 | − | 1.20574i | −0.273664 | − | 0.961825i | \(-0.588236\pi\) |
0.969797 | − | 0.243912i | \(-0.0784309\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.115554 | + | 0.309380i | −0.00561842 | + | 0.0150426i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 27.5233i | − | 1.33507i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.10387 | + | 3.08315i | −0.0534201 | + | 0.149204i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.353778 | + | 4.24891i | 0.0170805 | + | 0.205139i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.31259 | − | 5.37663i | −0.448572 | − | 0.258983i | 0.258655 | − | 0.965970i | \(-0.416721\pi\) |
−0.707227 | + | 0.706987i | \(0.750054\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.52301i | − | 0.121248i | −0.998161 | − | 0.0606241i | \(-0.980691\pi\) | ||
0.998161 | − | 0.0606241i | \(-0.0193091\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.58730 | − | 9.73071i | 0.219944 | − | 0.466552i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 8.26296i | − | 0.395271i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.12556 | −0.101447 | −0.0507237 | − | 0.998713i | \(-0.516153\pi\) | ||||
−0.0507237 | + | 0.998713i | \(0.516153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.1643 | − | 10.5384i | 0.864967 | − | 0.501829i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.4346i | 1.63604i | 0.575193 | + | 0.818018i | \(0.304927\pi\) | ||||
−0.575193 | + | 0.818018i | \(0.695073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.57884 | −0.264462 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.71585 | + | 32.6177i | 0.128455 | + | 1.54276i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.1970 | 1.18912 | 0.594560 | − | 0.804051i | \(-0.297326\pi\) | ||||
0.594560 | + | 0.804051i | \(0.297326\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.88346 | + | 10.1904i | −0.277041 | + | 0.479849i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.27418 | − | 4.82406i | 0.106850 | − | 0.226654i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.39633 | − | 1.21600i | −0.159222 | − | 0.0570071i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.3416 | 1.79354 | 0.896771 | − | 0.442494i | \(-0.145906\pi\) | ||||
0.896771 | + | 0.442494i | \(0.145906\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.83908 | + | 31.4017i | −0.412573 | + | 1.46571i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.0353 | − | 12.7221i | −1.02629 | − | 0.592527i | −0.110368 | − | 0.993891i | \(-0.535203\pi\) |
−0.915919 | + | 0.401364i | \(0.868536\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.6432 | + | 11.3410i | −0.912897 | + | 0.527061i | −0.881362 | − | 0.472441i | \(-0.843373\pi\) |
−0.0315350 | + | 0.999503i | \(0.510040\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.4049 | − | 0.949605i | 0.528888 | − | 0.0440369i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.19769 | + | 5.53857i | 0.147972 | + | 0.256294i | 0.930478 | − | 0.366349i | \(-0.119392\pi\) |
−0.782506 | + | 0.622643i | \(0.786059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.5892 | − | 29.5759i | 0.488963 | − | 1.36569i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.0387 | − | 21.6704i | −0.692946 | − | 0.998519i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.8453 | −0.590625 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.22939 | − | 5.59347i | 0.148175 | − | 0.256646i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.3631 | + | 19.8364i | 0.749215 | + | 0.908247i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.6853 | + | 28.8999i | 0.762373 | + | 1.32047i | 0.941625 | + | 0.336665i | \(0.109299\pi\) |
−0.179252 | + | 0.983803i | \(0.557368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.2593 | − | 6.50056i | −0.513380 | − | 0.296400i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.8331 | − | 6.62591i | −1.12995 | − | 0.301489i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.67191 | − | 4.62788i | −0.121325 | − | 0.210141i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.8011 | + | 18.9377i | 1.48636 | + | 0.858150i | 0.999879 | − | 0.0155410i | \(-0.00494704\pi\) |
0.486481 | + | 0.873691i | \(0.338280\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.23115 | + | 8.97525i | −0.191339 | + | 0.405875i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.1550 | − | 12.2138i | 0.954711 | − | 0.551203i | 0.0601697 | − | 0.998188i | \(-0.480836\pi\) |
0.894541 | + | 0.446986i | \(0.147502\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.0261 | − | 24.8411i | 1.93780 | − | 1.11879i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.16735 | − | 3.12543i | 0.0524685 | − | 0.140478i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.347947 | + | 0.971826i | −0.0156075 | + | 0.0435923i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.4156 | − | 18.1378i | −1.40636 | − | 0.811961i | −0.411322 | − | 0.911490i | \(-0.634933\pi\) |
−0.995035 | + | 0.0995293i | \(0.968266\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.15430 | + | 3.37271i | 0.319631 | + | 0.150682i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.84762 | 0.349908 | 0.174954 | − | 0.984577i | \(-0.444022\pi\) | ||||
0.174954 | + | 0.984577i | \(0.444022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.56140 | 0.113981 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.43460 | − | 17.2297i | −0.0637127 | − | 0.765196i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.4820 | + | 19.3308i | 1.48406 | + | 0.856824i | 0.999836 | − | 0.0181176i | \(-0.00576731\pi\) |
0.484228 | + | 0.874942i | \(0.339101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.32188 | − | 8.63339i | −0.323901 | − | 0.381919i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.48081 | + | 5.34456i | −0.241984 | + | 0.235968i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.4075 | + | 6.58611i | −0.502674 | + | 0.290219i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.135088 | − | 0.0779929i | 0.00594115 | − | 0.00343012i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.6528 | − | 25.4373i | −0.774872 | − | 1.11657i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.3950 | + | 12.3524i | 0.937332 | + | 0.541169i | 0.889123 | − | 0.457668i | \(-0.151315\pi\) |
0.0482092 | + | 0.998837i | \(0.484649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0144 | − | 34.6660i | −0.875168 | − | 1.51584i | −0.856583 | − | 0.516009i | \(-0.827417\pi\) |
−0.0185852 | − | 0.999827i | \(-0.505916\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.2208 | − | 14.1908i | −0.620646 | − | 0.619336i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 45.7719 | + | 26.4264i | 1.99386 | + | 1.15115i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.22828 | + | 7.32359i | 0.183838 | + | 0.318417i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0772742 | + | 0.206892i | −0.00335342 | + | 0.00897834i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.21337 | + | 12.4939i | −0.312446 | + | 0.541172i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.31379 | −0.316203 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.2611 | − | 1.02090i | 0.529105 | − | 0.0440550i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.78554 | − | 1.61967i | −0.421493 | − | 0.0697642i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0341 | + | 17.3795i | 0.431399 | + | 0.747205i | 0.996994 | − | 0.0774780i | \(-0.0246868\pi\) |
−0.565595 | + | 0.824683i | \(0.691353\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.23875 | + | 8.98989i | 0.267731 | + | 0.385793i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.49663 | + | 0.864081i | −0.0641086 | + | 0.0370131i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.60776 | − | 3.81499i | −0.282528 | − | 0.163117i | 0.352040 | − | 0.935985i | \(-0.385488\pi\) |
−0.634567 | + | 0.772868i | \(0.718822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.47856 | − | 1.29925i | −0.148461 | − | 0.0554505i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.6588 | 0.496680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.35282 | − | 14.9506i | 0.227625 | − | 0.635763i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.80027 | + | 8.35804i | 0.246208 | + | 0.354779i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0488 | + | 26.0653i | −0.637638 | + | 1.10442i | 0.348312 | + | 0.937379i | \(0.386755\pi\) |
−0.985950 | + | 0.167042i | \(0.946578\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7488 | −0.666105 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.6584 | − | 8.78463i | 0.534440 | − | 0.370887i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.89980 | −0.0800669 | −0.0400335 | − | 0.999198i | \(-0.512746\pi\) | ||||
−0.0400335 | + | 0.999198i | \(0.512746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.23710i | 0.220327i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.6674 | + | 20.7575i | 0.489983 | + | 0.871732i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.9733 | 0.460024 | 0.230012 | − | 0.973188i | \(-0.426124\pi\) | ||||
0.230012 | + | 0.973188i | \(0.426124\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 13.1336i | − | 0.549625i | −0.961498 | − | 0.274813i | \(-0.911384\pi\) | ||
0.961498 | − | 0.274813i | \(-0.0886159\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.3473 | + | 30.7609i | 0.891794 | + | 1.28505i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.5882i | 1.02540i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.2132 | − | 13.9795i | −1.00801 | − | 0.581973i | −0.0973997 | − | 0.995245i | \(-0.531053\pi\) |
−0.910608 | + | 0.413272i | \(0.864386\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.27422 | − | 5.04812i | 0.302306 | − | 0.209793i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.8287 | + | 26.9935i | −1.32048 | + | 1.11988i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 12.1454i | − | 0.503011i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.43122 | − | 3.83191i | 0.0591737 | − | 0.158430i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.27205 | + | 12.5956i | −0.300150 | + | 0.519875i | −0.976170 | − | 0.217009i | \(-0.930370\pi\) |
0.676020 | + | 0.736883i | \(0.263703\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.20140 | + | 10.7411i | 0.255524 | + | 0.442581i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0789 | − | 12.5463i | 0.743667 | − | 0.516086i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.9941 | − | 21.9359i | 1.56023 | − | 0.900800i | 0.562998 | − | 0.826458i | \(-0.309648\pi\) |
0.997233 | − | 0.0743413i | \(-0.0236854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.33120 | + | 12.8266i | 0.0955698 | + | 0.525840i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.388994 | + | 4.67186i | 0.0159205 | + | 0.191207i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.1395i | − | 0.496008i | −0.968759 | − | 0.248004i | \(-0.920225\pi\) | ||
0.968759 | − | 0.248004i | \(-0.0797745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.5034 | − | 19.9205i | −1.40742 | − | 0.812576i | −0.412284 | − | 0.911055i | \(-0.635269\pi\) |
−0.995139 | + | 0.0984793i | \(0.968602\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.3690 | + | 12.4634i | 1.35889 | + | 0.507547i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.11208 | − | 3.52881i | 0.248491 | − | 0.143467i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.03387 | + | 13.9151i | −0.326085 | + | 0.564795i | −0.981731 | − | 0.190273i | \(-0.939063\pi\) |
0.655647 | + | 0.755068i | \(0.272396\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.34892 | − | 35.0387i | 0.378838 | − | 1.41984i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.165623 | − | 0.0956227i | 0.00670040 | − | 0.00386848i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.8831 | − | 30.9744i | 0.722290 | − | 1.25104i | −0.237789 | − | 0.971317i | \(-0.576423\pi\) |
0.960080 | − | 0.279727i | \(-0.0902439\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.27454 | − | 6.43629i | 0.373986 | − | 0.259536i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.64049 | + | 11.5017i | 0.267336 | + | 0.463040i | 0.968173 | − | 0.250282i | \(-0.0805232\pi\) |
−0.700837 | + | 0.713322i | \(0.747190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.9291 | − | 22.3939i | −0.519666 | − | 0.900088i | −0.999739 | − | 0.0228592i | \(-0.992723\pi\) |
0.480073 | − | 0.877229i | \(-0.340610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.89648 | − | 28.0530i | 0.316875 | − | 1.12573i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.5031 | + | 3.36289i | −0.741313 | + | 0.134731i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.06973 | + | 13.9772i | −0.322789 | + | 0.559087i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.60327 | − | 0.300019i | 0.143901 | − | 0.0119816i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 46.9839i | 1.87337i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8684i | 1.42790i | 0.700198 | + | 0.713948i | \(0.253095\pi\) | ||||
−0.700198 | + | 0.713948i | \(0.746905\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.43294 | + | 13.6457i | −0.255687 | + | 0.542370i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.10004 | + | 10.5656i | −0.242073 | + | 0.419282i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.9975 | − | 1.98579i | −0.475358 | − | 0.0786798i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.09646 | − | 0.409530i | −0.0433754 | − | 0.0162007i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0641 | − | 20.8956i | −0.476502 | − | 0.825325i | 0.523136 | − | 0.852249i | \(-0.324762\pi\) |
−0.999637 | + | 0.0269240i | \(0.991429\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.71638 | − | 13.3652i | −0.304304 | − | 0.527070i | 0.672802 | − | 0.739823i | \(-0.265091\pi\) |
−0.977106 | + | 0.212752i | \(0.931757\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.1470 | + | 5.25499i | 0.438914 | + | 0.206915i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.0842 | + | 34.7869i | −0.789592 | + | 1.36761i | 0.136625 | + | 0.990623i | \(0.456375\pi\) |
−0.926217 | + | 0.376991i | \(0.876959\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0903371 | − | 0.0521561i | 0.00354604 | − | 0.00204731i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.2537 | − | 10.0243i | 1.46009 | − | 0.392883i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.2555 | − | 43.7438i | 0.988324 | − | 1.71183i | 0.362206 | − | 0.932098i | \(-0.382024\pi\) |
0.626117 | − | 0.779729i | \(-0.284643\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.57653 | − | 2.06491i | 0.139747 | − | 0.0806828i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.90168 | − | 8.16792i | 0.386301 | − | 0.318661i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.7746 | + | 9.68482i | 0.653446 | + | 0.377267i | 0.789775 | − | 0.613397i | \(-0.210197\pi\) |
−0.136329 | + | 0.990664i | \(0.543531\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 25.3992i | − | 0.987915i | −0.869486 | − | 0.493957i | \(-0.835550\pi\) | ||
0.869486 | − | 0.493957i | \(-0.164450\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.5198 | − | 10.7703i | 0.602739 | − | 0.418285i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.03123 | + | 2.88024i | −0.0399892 | + | 0.111691i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.4378 | + | 22.1921i | −1.48832 | + | 0.859280i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.32353 | + | 15.8957i | 0.0511705 | + | 0.614563i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.876924 | + | 1.51888i | 0.0338533 | + | 0.0586356i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.47290 | + | 16.4075i | −0.365153 | + | 0.632464i | −0.988801 | − | 0.149242i | \(-0.952317\pi\) |
0.623647 | + | 0.781706i | \(0.285650\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.3093 | − | 15.9039i | 0.627744 | − | 0.612140i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.4853i | 1.86344i | 0.363178 | + | 0.931720i | \(0.381692\pi\) | ||||
−0.363178 | + | 0.931720i | \(0.618308\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.6515 | − | 13.7385i | −0.447143 | − | 0.527236i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.7989 | + | 6.03370i | 0.490453 | + | 0.231212i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.1815 | − | 12.2292i | −0.810489 | − | 0.467936i | 0.0366369 | − | 0.999329i | \(-0.488336\pi\) |
−0.847126 | + | 0.531393i | \(0.821669\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.7411i | 0.410398i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.50857 | + | 0.292135i | −0.133860 | + | 0.0111456i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 14.8908i | − | 0.567294i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.3164 | 1.45763 | 0.728813 | − | 0.684713i | \(-0.240072\pi\) | ||||
0.728813 | + | 0.684713i | \(0.240072\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.98772 | − | 11.0697i | 0.0755073 | − | 0.420502i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.24535i | − | 0.274832i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.1359 | 1.97479 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.0056 | − | 8.48831i | −0.681036 | − | 0.321057i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.3296 | −1.25884 | −0.629421 | − | 0.777064i | \(-0.716708\pi\) | ||||
−0.629421 | + | 0.777064i | \(0.716708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.51276 | + | 9.54839i | −0.207918 | + | 0.360124i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.149135 | + | 0.0124175i | −0.00561676 | + | 0.000467669i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.49531 | − | 1.54400i | 0.319499 | − | 0.0580680i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.43783 | 0.0539990 | 0.0269995 | − | 0.999635i | \(-0.491405\pi\) | ||||
0.0269995 | + | 0.999635i | \(0.491405\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.8680 | + | 6.30021i | 0.632599 | + | 0.236276i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.8908 | − | 23.6083i | −1.53137 | − | 0.884138i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.67316 | + | 0.966001i | −0.0625727 | + | 0.0361264i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.9333 | + | 27.4346i | −0.483004 | + | 1.02456i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0257 | + | 20.8291i | 0.448481 | + | 0.776793i | 0.998287 | − | 0.0584998i | \(-0.0186317\pi\) |
−0.549806 | + | 0.835292i | \(0.685298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.8647 | + | 28.7203i | −1.26119 | + | 1.06960i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.0459 | − | 31.9158i | 0.559563 | − | 1.18696i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.6931 | −1.28847 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.87496 | − | 13.6398i | 0.292066 | − | 0.505873i | −0.682232 | − | 0.731136i | \(-0.738991\pi\) |
0.974298 | + | 0.225262i | \(0.0723239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.7150 | + | 12.9073i | −0.878335 | + | 0.478046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.4568 | + | 49.2887i | 1.05251 | + | 1.82301i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.2669 | − | 20.9387i | −1.33955 | − | 0.773389i | −0.352809 | − | 0.935695i | \(-0.614774\pi\) |
−0.986740 | + | 0.162306i | \(0.948107\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.82923 | + | 5.40881i | 0.288786 | + | 0.199507i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.41212 | − | 14.5702i | −0.309864 | − | 0.536701i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.29085 | + | 0.745272i | 0.0474846 | + | 0.0274153i | 0.523554 | − | 0.851992i | \(-0.324606\pi\) |
−0.476070 | + | 0.879408i | \(0.657939\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.41776 | − | 0.367837i | 0.162290 | − | 0.0135128i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.96436 | − | 4.02088i | 0.255498 | − | 0.147512i | −0.366781 | − | 0.930307i | \(-0.619540\pi\) |
0.622279 | + | 0.782796i | \(0.286207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.8444 | + | 7.41571i | −0.470582 | + | 0.271691i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.1126 | − | 36.5045i | −1.10176 | − | 1.33563i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.2574 | + | 4.40871i | −0.886346 | + | 0.161091i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.4437 | + | 7.76170i | 0.490566 | + | 0.283229i | 0.724809 | − | 0.688949i | \(-0.241928\pi\) |
−0.234243 | + | 0.972178i | \(0.575261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.1016 | − | 7.01025i | 0.368123 | − | 0.255468i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.41669 | 0.0879523 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4868 | 0.708260 | 0.354130 | − | 0.935196i | \(-0.384777\pi\) | ||||
0.354130 | + | 0.935196i | \(0.384777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.3085 | + | 7.84783i | −0.410474 | + | 0.284858i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.0623 | + | 11.5830i | 0.727259 | + | 0.419883i | 0.817419 | − | 0.576044i | \(-0.195404\pi\) |
−0.0901595 | + | 0.995927i | \(0.528738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.44296 | + | 3.76803i | −0.160846 | + | 0.136412i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.5787 | + | 2.44469i | −0.527095 | + | 0.0883879i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.110757 | − | 0.0639457i | 0.00399921 | − | 0.00230894i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.2140 | − | 16.2894i | 1.01742 | − | 0.587410i | 0.104067 | − | 0.994570i | \(-0.466814\pi\) |
0.913357 | + | 0.407160i | \(0.133481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.7349 | + | 3.72477i | −1.61109 | + | 0.134144i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.85868 | + | 3.95986i | 0.246690 | + | 0.142426i | 0.618248 | − | 0.785983i | \(-0.287843\pi\) |
−0.371558 | + | 0.928410i | \(0.621176\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.4535 | − | 31.9625i | −0.662871 | − | 1.14813i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.2757 | + | 24.2245i | 0.870887 | + | 0.869048i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.5954 | + | 6.11726i | 0.379620 | + | 0.219174i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.276411 | + | 0.478758i | 0.00989077 | + | 0.0171313i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.5819 | + | 11.1417i | 1.41454 | + | 0.398170i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.97629 | − | 10.3512i | 0.213303 | − | 0.369452i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.2452 | −1.07813 | −0.539063 | − | 0.842266i | \(-0.681221\pi\) | ||||
−0.539063 | + | 0.842266i | \(0.681221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.56768 | + | 7.56787i | −0.127013 | + | 0.269423i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.15689 | + | 17.3697i | 0.112246 | + | 0.617596i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07515 | + | 1.86221i | 0.0381796 | + | 0.0661290i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.96869 | + | 10.5397i | −0.176221 | + | 0.373805i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.9751 | − | 15.5741i | 0.955507 | − | 0.551662i | 0.0607197 | − | 0.998155i | \(-0.480660\pi\) |
0.894787 | + | 0.446493i | \(0.147327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.598535 | − | 0.345564i | −0.0211746 | − | 0.0122252i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.52661 | − | 21.0307i | −0.124607 | − | 0.743082i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.06259 | −0.213944 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.08260 | − | 11.4588i | −0.0734019 | − | 0.403869i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.2329 | − | 1.10182i | 0.465822 | − | 0.0387858i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.0362 | + | 17.3832i | −0.352853 | + | 0.611160i | −0.986748 | − | 0.162259i | \(-0.948122\pi\) |
0.633895 | + | 0.773419i | \(0.281455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.4633 | 0.718564 | 0.359282 | − | 0.933229i | \(-0.383022\pi\) | ||||
0.359282 | + | 0.933229i | \(0.383022\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.93870 | − | 3.74250i | −0.278422 | − | 0.131255i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.49629 | −0.157498 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.3557i | 0.467258i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.43703 | − | 13.5719i | 0.0851568 | − | 0.474241i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.5686 | −1.48566 | −0.742828 | − | 0.669483i | \(-0.766516\pi\) | ||||
−0.742828 | + | 0.669483i | \(0.766516\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.2908i | 0.428432i | 0.976786 | + | 0.214216i | \(0.0687196\pi\) | ||||
−0.976786 | + | 0.214216i | \(0.931280\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.7223 | + | 0.892770i | −0.373301 | + | 0.0310822i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16.1935i | − | 0.563104i | −0.959546 | − | 0.281552i | \(-0.909151\pi\) | ||
0.959546 | − | 0.281552i | \(-0.0908493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.0315654 | + | 0.0182243i | 0.00109631 | + | 0.000632956i | 0.500548 | − | 0.865709i | \(-0.333132\pi\) |
−0.499452 | + | 0.866342i | \(0.666465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.2340 | + | 16.1387i | 1.18756 | + | 0.559847i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.4636 | + | 41.1364i | 0.535782 | + | 1.42529i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.58406i | 0.124032i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.7892 | + | 42.3928i | 0.372930 | + | 1.46531i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.2294 | + | 36.7705i | −0.732921 | + | 1.26946i | 0.222708 | + | 0.974885i | \(0.428510\pi\) |
−0.955629 | + | 0.294572i | \(0.904823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.8122 | − | 29.1196i | −0.579732 | − | 1.00413i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.315306 | + | 3.78686i | 0.0108597 | + | 0.130426i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.78481 | − | 3.91721i | 0.233404 | − | 0.134756i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.1446 | − | 15.3882i | 0.623455 | − | 0.528745i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.7718 | + | 15.1091i | −0.747208 | + | 0.518543i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 41.9735i | − | 1.43883i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.60970 | − | 2.08406i | −0.123594 | − | 0.0713568i | 0.436929 | − | 0.899496i | \(-0.356066\pi\) |
−0.560522 | + | 0.828139i | \(0.689400\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.24963 | − | 1.21374i | −0.111135 | − | 0.0415091i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.96984 | + | 5.75609i | −0.340563 | + | 0.196624i | −0.660521 | − | 0.750808i | \(-0.729665\pi\) |
0.319958 | + | 0.947432i | \(0.396331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.10057 | − | 3.63829i | 0.0716704 | − | 0.124137i | −0.827963 | − | 0.560783i | \(-0.810500\pi\) |
0.899633 | + | 0.436646i | \(0.143834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.8808 | − | 26.9377i | 0.916095 | − | 0.918033i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.9911 | − | 9.23249i | 0.544345 | − | 0.314278i | −0.202493 | − | 0.979284i | \(-0.564904\pi\) |
0.746838 | + | 0.665006i | \(0.231571\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.01513 | − | 12.1506i | 0.238522 | − | 0.413132i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −35.1169 | − | 16.5550i | −1.19263 | − | 0.562237i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.25231 | − | 7.36522i | −0.144250 | − | 0.249848i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3136 | − | 17.8637i | −0.349464 | − | 0.605289i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.7568 | − | 12.9978i | 0.533287 | − | 0.439909i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.56842 | − | 18.3458i | 0.222053 | − | 0.620201i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.77845 | + | 4.81242i | −0.0938217 | + | 0.162504i | −0.909116 | − | 0.416543i | \(-0.863242\pi\) |
0.815295 | + | 0.579046i | \(0.196575\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.32954 | + | 9.18394i | −0.146032 | + | 0.309767i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22.3336i | − | 0.752438i | −0.926531 | − | 0.376219i | \(-0.877224\pi\) | ||
0.926531 | − | 0.376219i | \(-0.122776\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.9024i | − | 1.24186i | −0.783865 | − | 0.620932i | \(-0.786754\pi\) | ||
0.783865 | − | 0.620932i | \(-0.213246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0997311 | + | 0.00830392i | −0.00335242 | + | 0.000279133i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.40494 | + | 5.89752i | −0.114327 | + | 0.198020i | −0.917510 | − | 0.397712i | \(-0.869804\pi\) |
0.803184 | + | 0.595731i | \(0.203138\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.8629 | + | 38.7196i | −0.464948 | + | 1.29861i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.5199 | + | 2.42487i | 0.419433 | + | 0.0812364i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0810923 | − | 0.140456i | −0.00271365 | − | 0.00470018i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.78759 | + | 4.82825i | 0.0931789 | + | 0.161391i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.8648 | + | 9.62178i | −0.462931 | + | 0.321262i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.3105 | − | 57.6955i | 1.11097 | − | 1.92425i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.6033 | + | 26.9064i | −1.55258 | + | 0.896383i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 40.1387 | + | 10.7097i | 1.33573 | + | 0.356396i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.47925 | + | 4.29418i | −0.0824130 | + | 0.142743i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.60190 | + | 2.07956i | −0.119599 | + | 0.0690506i | −0.558606 | − | 0.829433i | \(-0.688664\pi\) |
0.439007 | + | 0.898484i | \(0.355330\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.61916 | + | 9.65576i | 0.0537043 | + | 0.320261i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.80883 | − | 2.77638i | −0.159324 | − | 0.0919856i | 0.418218 | − | 0.908347i | \(-0.362655\pi\) |
−0.577542 | + | 0.816361i | \(0.695988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.3509i | 0.739707i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.139618 | − | 1.67682i | −0.00461561 | − | 0.0554340i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.6175 | − | 9.00454i | 0.350619 | − | 0.297356i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.2582 | + | 13.4281i | −0.767216 | + | 0.442952i | −0.831880 | − | 0.554955i | \(-0.812736\pi\) |
0.0646648 | + | 0.997907i | \(0.479402\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.9325 | + | 8.28088i | −0.393191 | + | 0.272864i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.338892 | + | 0.586979i | 0.0111548 | + | 0.0193206i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.4044 | − | 28.4132i | 0.539372 | − | 0.934220i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32.0389 | − | 38.8397i | −1.05230 | − | 1.27566i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.0523i | 0.920365i | 0.887824 | + | 0.460183i | \(0.152216\pi\) | ||||
−0.887824 | + | 0.460183i | \(0.847784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.68404 | + | 10.1744i | −0.0551921 | + | 0.333453i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −41.0634 | + | 28.4969i | −1.34436 | + | 0.932948i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.04653 | + | 3.49097i | 0.197743 | + | 0.114167i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.2285i | − | 0.497493i | −0.968569 | − | 0.248746i | \(-0.919981\pi\) | ||
0.968569 | − | 0.248746i | \(-0.0800186\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.0581 | − | 40.4311i | −0.915642 | − | 1.31942i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.21460i | − | 0.104793i | −0.998626 | − | 0.0523965i | \(-0.983314\pi\) | ||
0.998626 | − | 0.0523965i | \(-0.0166860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.5760 | −1.51672 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.25354 | + | 8.79303i | −0.203428 | + | 0.286037i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.4308i | 0.663911i | 0.943295 | + | 0.331956i | \(0.107708\pi\) | ||||
−0.943295 | + | 0.331956i | \(0.892292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.43299 | −0.241285 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.7826 | − | 8.87082i | 0.414505 | − | 0.287656i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −57.3984 | −1.85932 | −0.929658 | − | 0.368423i | \(-0.879898\pi\) | ||||
−0.929658 | + | 0.368423i | \(0.879898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.48329 | + | 14.6935i | −0.274513 | + | 0.475470i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.0730 | − | 15.9560i | −0.357940 | − | 0.515783i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.47469 | + | 35.6247i | 0.209079 | + | 1.15038i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.8726 | 1.28621 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.62334 | − | 27.5710i | −0.148985 | − | 0.888461i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.47466 | + | 2.00610i | 0.111853 | + | 0.0645785i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0281 | + | 17.9141i | −0.997797 | + | 0.576078i | −0.907596 | − | 0.419845i | \(-0.862084\pi\) |
−0.0902010 | + | 0.995924i | \(0.528751\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.13373 | − | 13.1615i | −0.293418 | − | 0.422808i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.6346 | − | 47.8645i | −0.886836 | − | 1.53605i | −0.843594 | − | 0.536981i | \(-0.819565\pi\) |
−0.0432421 | − | 0.999065i | \(-0.513769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.36745 | − | 24.0304i | −0.140014 | − | 0.770380i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.1460 | + | 1.09457i | −0.421008 | + | 0.0350544i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.30526 | 0.105745 | 0.0528723 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528723 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.03592 | + | 8.72248i | −0.160949 | + | 0.278772i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.20342 | − | 5.09566i | −0.134205 | − | 0.162692i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.6188 | − | 51.3012i | −0.944692 | − | 1.63626i | −0.756366 | − | 0.654149i | \(-0.773027\pi\) |
−0.188327 | − | 0.982106i | \(-0.560306\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.63571 | + | 4.98583i | 0.275157 | + | 0.158862i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.487147 | + | 0.131082i | −0.0155060 | + | 0.00417240i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.4222 | − | 44.0325i | −0.808378 | − | 1.40015i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.3830 | + | 8.88141i | 0.488659 | + | 0.282127i | 0.724018 | − | 0.689781i | \(-0.242293\pi\) |
−0.235359 | + | 0.971908i | \(0.575627\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.72192 | − | 9.68613i | −0.213314 | − | 0.307380i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.83972 | + | 1.06216i | −0.0583229 | + | 0.0336727i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.4110 | + | 7.16551i | −0.393061 | + | 0.226934i | −0.683486 | − | 0.729964i | \(-0.739537\pi\) |
0.290424 | + | 0.956898i | \(0.406204\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.8409 | + | 27.1488i | −0.880847 | + | 0.858951i |
(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.cz.g.367.4 | yes | 24 | |
3.2 | odd | 2 | 3024.2.cz.h.2719.7 | 24 | |||
4.3 | odd | 2 | 1008.2.cz.h.367.9 | yes | 24 | ||
7.5 | odd | 6 | 1008.2.bf.g.943.7 | yes | 24 | ||
9.4 | even | 3 | 1008.2.bf.h.31.6 | yes | 24 | ||
9.5 | odd | 6 | 3024.2.bf.g.1711.6 | 24 | |||
12.11 | even | 2 | 3024.2.cz.g.2719.7 | 24 | |||
21.5 | even | 6 | 3024.2.bf.h.2287.7 | 24 | |||
28.19 | even | 6 | 1008.2.bf.h.943.6 | yes | 24 | ||
36.23 | even | 6 | 3024.2.bf.h.1711.6 | 24 | |||
36.31 | odd | 6 | 1008.2.bf.g.31.7 | ✓ | 24 | ||
63.5 | even | 6 | 3024.2.cz.g.1279.7 | 24 | |||
63.40 | odd | 6 | 1008.2.cz.h.607.9 | yes | 24 | ||
84.47 | odd | 6 | 3024.2.bf.g.2287.7 | 24 | |||
252.103 | even | 6 | inner | 1008.2.cz.g.607.4 | yes | 24 | |
252.131 | odd | 6 | 3024.2.cz.h.1279.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.bf.g.31.7 | ✓ | 24 | 36.31 | odd | 6 | ||
1008.2.bf.g.943.7 | yes | 24 | 7.5 | odd | 6 | ||
1008.2.bf.h.31.6 | yes | 24 | 9.4 | even | 3 | ||
1008.2.bf.h.943.6 | yes | 24 | 28.19 | even | 6 | ||
1008.2.cz.g.367.4 | yes | 24 | 1.1 | even | 1 | trivial | |
1008.2.cz.g.607.4 | yes | 24 | 252.103 | even | 6 | inner | |
1008.2.cz.h.367.9 | yes | 24 | 4.3 | odd | 2 | ||
1008.2.cz.h.607.9 | yes | 24 | 63.40 | odd | 6 | ||
3024.2.bf.g.1711.6 | 24 | 9.5 | odd | 6 | |||
3024.2.bf.g.2287.7 | 24 | 84.47 | odd | 6 | |||
3024.2.bf.h.1711.6 | 24 | 36.23 | even | 6 | |||
3024.2.bf.h.2287.7 | 24 | 21.5 | even | 6 | |||
3024.2.cz.g.1279.7 | 24 | 63.5 | even | 6 | |||
3024.2.cz.g.2719.7 | 24 | 12.11 | even | 2 | |||
3024.2.cz.h.1279.7 | 24 | 252.131 | odd | 6 | |||
3024.2.cz.h.2719.7 | 24 | 3.2 | odd | 2 |