Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
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, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.2091141441.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.1 | ||
Root | \(0.199732 - 1.72050i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.l.337.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.58986 | + | 0.687275i | −0.917906 | + | 0.396799i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.300268 | − | 0.520080i | −0.134284 | − | 0.232587i | 0.791040 | − | 0.611765i | \(-0.209540\pi\) |
−0.925324 | + | 0.379178i | \(0.876207\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.05531 | − | 2.18534i | 0.685102 | − | 0.728447i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.800268 | + | 1.38611i | −0.241290 | + | 0.417926i | −0.961082 | − | 0.276263i | \(-0.910904\pi\) |
0.719792 | + | 0.694190i | \(0.244237\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.165178 | − | 0.286096i | −0.0458120 | − | 0.0793487i | 0.842210 | − | 0.539149i | \(-0.181254\pi\) |
−0.888022 | + | 0.459801i | \(0.847921\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.834822 | + | 0.620487i | 0.215550 | + | 0.160209i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.44990 | −0.351652 | −0.175826 | − | 0.984421i | \(-0.556260\pi\) | ||||
−0.175826 | + | 0.984421i | \(0.556260\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.57918 | −0.591705 | −0.295852 | − | 0.955234i | \(-0.595604\pi\) | ||||
−0.295852 | + | 0.955234i | \(0.595604\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.199732 | − | 1.72050i | 0.0435850 | − | 0.375443i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.924682 | + | 1.60160i | 0.192809 | + | 0.333956i | 0.946180 | − | 0.323640i | \(-0.104907\pi\) |
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.31968 | − | 4.01780i | 0.463936 | − | 0.803560i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.76571 | + | 4.88695i | −0.339812 | + | 0.940493i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.75950 | + | 3.04755i | −0.326732 | + | 0.565916i | −0.981861 | − | 0.189601i | \(-0.939281\pi\) |
0.655130 | + | 0.755517i | \(0.272614\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.81034 | − | 8.33176i | −0.863963 | − | 1.49643i | −0.868073 | − | 0.496436i | \(-0.834642\pi\) |
0.00411031 | − | 0.999992i | \(-0.498692\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.319678 | − | 2.75372i | 0.0556488 | − | 0.479361i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.600537 | 0.101509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.600537 | 0.0987276 | 0.0493638 | − | 0.998781i | \(-0.484281\pi\) | ||||
0.0493638 | + | 0.998781i | \(0.484281\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.459236 | + | 0.341330i | 0.0735366 | + | 0.0546565i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.31034 | − | 5.73368i | −0.516989 | − | 0.895450i | −0.999805 | − | 0.0197291i | \(-0.993720\pi\) |
0.482817 | − | 0.875721i | \(-0.339614\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.81481 | − | 3.14334i | 0.276756 | − | 0.479355i | −0.693821 | − | 0.720148i | \(-0.744074\pi\) |
0.970577 | + | 0.240793i | \(0.0774074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.75370 | − | 0.412734i | −0.261425 | − | 0.0615267i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.95477 | − | 3.38576i | 0.285132 | − | 0.493864i | −0.687509 | − | 0.726176i | \(-0.741296\pi\) |
0.972641 | + | 0.232312i | \(0.0746291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.30514 | − | 0.996481i | 0.322784 | − | 0.139535i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.27166 | −1.27356 | −0.636780 | − | 0.771046i | \(-0.719734\pi\) | ||||
−0.636780 | + | 0.771046i | \(0.719734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.961181 | 0.129606 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.10054 | − | 1.77261i | 0.543129 | − | 0.234788i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.93476 | − | 12.0113i | −0.902828 | − | 1.56374i | −0.823806 | − | 0.566872i | \(-0.808154\pi\) |
−0.0790221 | − | 0.996873i | \(-0.525180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.59433 | − | 4.49351i | 0.332169 | − | 0.575334i | −0.650768 | − | 0.759277i | \(-0.725553\pi\) |
0.982937 | + | 0.183943i | \(0.0588861\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.864909 | + | 2.87262i | 0.108968 | + | 0.361916i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0991952 | + | 0.171811i | −0.0123036 | + | 0.0213105i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.90467 | − | 10.2272i | −0.721370 | − | 1.24945i | −0.960451 | − | 0.278450i | \(-0.910179\pi\) |
0.239081 | − | 0.971000i | \(-0.423154\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.57085 | − | 1.91080i | −0.309494 | − | 0.230033i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.17972 | 0.496041 | 0.248021 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248021 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.13969 | 0.484514 | 0.242257 | − | 0.970212i | \(-0.422112\pi\) | ||||
0.242257 | + | 0.970212i | \(0.422112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.926627 | + | 7.98199i | −0.106998 | + | 0.921681i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.800268 | − | 1.38611i | −0.0911990 | − | 0.157961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.06538 | − | 7.04144i | 0.457391 | − | 0.792224i | −0.541431 | − | 0.840745i | \(-0.682117\pi\) |
0.998822 | + | 0.0485208i | \(0.0154507\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.551441 | − | 8.98309i | −0.0612713 | − | 0.998121i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.78959 | + | 4.83171i | −0.306197 | + | 0.530349i | −0.977527 | − | 0.210809i | \(-0.932390\pi\) |
0.671330 | + | 0.741159i | \(0.265723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.435359 | + | 0.754064i | 0.0472213 | + | 0.0817897i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.702858 | − | 6.05444i | 0.0753542 | − | 0.649104i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.83069 | −0.406053 | −0.203026 | − | 0.979173i | \(-0.565078\pi\) | ||||
−0.203026 | + | 0.979173i | \(0.565078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.330355 | 0.0346306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.3740 | + | 9.94029i | 1.38682 | + | 1.03076i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.774447 | + | 1.34138i | 0.0794565 | + | 0.137623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.974782 | − | 1.68837i | 0.0989741 | − | 0.171428i | −0.812286 | − | 0.583259i | \(-0.801777\pi\) |
0.911260 | + | 0.411831i | \(0.135111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.38432 | + | 4.59773i | 0.139129 | + | 0.462089i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.79520 | + | 15.2337i | −0.875155 | + | 1.51581i | −0.0185572 | + | 0.999828i | \(0.505907\pi\) |
−0.856598 | + | 0.515985i | \(0.827426\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.30547 | − | 9.18935i | −0.522764 | − | 0.905454i | −0.999649 | − | 0.0264880i | \(-0.991568\pi\) |
0.476885 | − | 0.878966i | \(-0.341766\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.954769 | + | 0.412734i | −0.0931759 | + | 0.0402787i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.43949 | 0.332508 | 0.166254 | − | 0.986083i | \(-0.446833\pi\) | ||||
0.166254 | + | 0.986083i | \(0.446833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.55010 | −0.531603 | −0.265802 | − | 0.964028i | \(-0.585637\pi\) | ||||
−0.265802 | + | 0.964028i | \(0.585637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.954769 | + | 0.412734i | −0.0906226 | + | 0.0391750i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.38079 | − | 7.58775i | −0.412110 | − | 0.713796i | 0.583010 | − | 0.812465i | \(-0.301875\pi\) |
−0.995120 | + | 0.0986691i | \(0.968541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.555305 | − | 0.961817i | 0.0517825 | − | 0.0896899i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.964708 | − | 0.227045i | −0.0891873 | − | 0.0209903i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.724950 | − | 1.25565i | 0.0664561 | − | 0.115105i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.21914 | + | 7.30777i | 0.383558 | + | 0.664342i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.20360 | + | 6.84063i | 0.829860 | + | 0.616799i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.78879 | −0.517765 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.1521 | 0.989590 | 0.494795 | − | 0.869010i | \(-0.335243\pi\) | ||||
0.494795 | + | 0.869010i | \(0.335243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.724950 | + | 6.24474i | −0.0638283 | + | 0.549819i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59993 | − | 4.50322i | −0.227157 | − | 0.393448i | 0.729807 | − | 0.683653i | \(-0.239610\pi\) |
−0.956964 | + | 0.290205i | \(0.906276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.28959 | − | 2.23364i | 0.111822 | − | 0.193681i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.07179 | − | 0.549083i | 0.264378 | − | 0.0472575i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.39399 | + | 7.61062i | −0.375404 | + | 0.650219i | −0.990387 | − | 0.138321i | \(-0.955829\pi\) |
0.614983 | + | 0.788540i | \(0.289163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.50934 | − | 7.81040i | −0.382477 | − | 0.662469i | 0.608939 | − | 0.793217i | \(-0.291596\pi\) |
−0.991416 | + | 0.130748i | \(0.958262\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.780859 | + | 6.72634i | −0.0657602 | + | 0.566460i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.528746 | 0.0442159 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.11329 | 0.175499 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.39013 | + | 1.03322i | 0.114656 | + | 0.0852186i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.525620 | + | 0.910400i | 0.0430604 | + | 0.0745829i | 0.886752 | − | 0.462245i | \(-0.152956\pi\) |
−0.843692 | + | 0.536828i | \(0.819623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.48932 | + | 11.2398i | −0.528094 | + | 0.914685i | 0.471370 | + | 0.881936i | \(0.343760\pi\) |
−0.999464 | + | 0.0327494i | \(0.989574\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.97999 | + | 3.16853i | −0.240918 | + | 0.256160i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.88879 | + | 5.00352i | −0.232033 | + | 0.401893i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.86699 | + | 17.0901i | 0.787471 | + | 1.36394i | 0.927511 | + | 0.373795i | \(0.121944\pi\) |
−0.140040 | + | 0.990146i | \(0.544723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.7406 | − | 6.37218i | 1.16901 | − | 0.505347i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.84936 | −0.145750 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.9214 | 1.79534 | 0.897672 | − | 0.440664i | \(-0.145257\pi\) | ||||
0.897672 | + | 0.440664i | \(0.145257\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.52814 | + | 0.660596i | −0.118966 | + | 0.0514273i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.61508 | + | 2.79740i | 0.124978 | + | 0.216469i | 0.921725 | − | 0.387845i | \(-0.126780\pi\) |
−0.796746 | + | 0.604314i | \(0.793447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.44543 | − | 11.1638i | 0.495803 | − | 0.858755i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.30101 | + | 5.63640i | −0.405378 | + | 0.431026i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.08052 | + | 12.2638i | −0.538322 | + | 0.932401i | 0.460672 | + | 0.887570i | \(0.347608\pi\) |
−0.998995 | + | 0.0448312i | \(0.985725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.31968 | + | 4.01780i | 0.175351 | + | 0.303717i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.2804 | + | 14.3303i | 1.44920 | + | 1.07713i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.06790 | −0.528280 | −0.264140 | − | 0.964484i | \(-0.585088\pi\) | ||||
−0.264140 | + | 0.964484i | \(0.585088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6207 | −1.45839 | −0.729197 | − | 0.684304i | \(-0.760106\pi\) | ||||
−0.729197 | + | 0.684304i | \(0.760106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.03634 | + | 8.92706i | −0.0766084 | + | 0.659907i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.180322 | − | 0.312327i | −0.0132575 | − | 0.0229627i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.16031 | − | 2.00971i | 0.0848502 | − | 0.146965i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.34936 | − | 3.97263i | −0.243630 | − | 0.288966i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1096 | + | 17.5104i | −0.731505 | + | 1.26700i | 0.224734 | + | 0.974420i | \(0.427849\pi\) |
−0.956240 | + | 0.292584i | \(0.905485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.89473 | − | 15.4061i | −0.640257 | − | 1.10896i | −0.985375 | − | 0.170398i | \(-0.945495\pi\) |
0.345119 | − | 0.938559i | \(-0.387839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0396248 | − | 0.341330i | 0.00283759 | − | 0.0244431i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.04150 | 0.572933 | 0.286467 | − | 0.958090i | \(-0.407519\pi\) | ||||
0.286467 | + | 0.958090i | \(0.407519\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0332 | −0.994790 | −0.497395 | − | 0.867524i | \(-0.665710\pi\) | ||||
−0.497395 | + | 0.867524i | \(0.665710\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.4165 | + | 12.2017i | 1.15793 | + | 0.860638i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.75950 | − | 3.04755i | −0.123493 | − | 0.213896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.98798 | + | 3.44328i | −0.138847 | + | 0.240489i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.40054 | + | 1.27102i | 0.375363 | + | 0.0883421i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.06404 | − | 3.57502i | 0.142772 | − | 0.247289i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.32622 | + | 12.6894i | 0.504358 | + | 0.873574i | 0.999987 | + | 0.00503962i | \(0.00160417\pi\) |
−0.495629 | + | 0.868534i | \(0.665062\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.64516 | + | 2.87262i | −0.455319 | + | 0.196829i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.17972 | −0.148656 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.62068 | 0.653095 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.58153 | + | 2.84511i | −0.444738 | + | 0.192255i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.239491 | + | 0.414811i | 0.0161099 | + | 0.0279032i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.02696 | + | 12.1711i | −0.470560 | + | 0.815034i | −0.999433 | − | 0.0336670i | \(-0.989281\pi\) |
0.528873 | + | 0.848701i | \(0.322615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.01262 | − | 13.3271i | −0.267508 | − | 0.888473i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.40601 | − | 4.16733i | 0.159692 | − | 0.276596i | −0.775065 | − | 0.631881i | \(-0.782283\pi\) |
0.934758 | + | 0.355286i | \(0.115616\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.68419 | − | 2.91710i | −0.111294 | − | 0.192767i | 0.804998 | − | 0.593277i | \(-0.202166\pi\) |
−0.916292 | + | 0.400510i | \(0.868833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.22495 | + | 1.65371i | 0.146391 | + | 0.108806i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.9137 | 1.37010 | 0.685051 | − | 0.728495i | \(-0.259780\pi\) | ||||
0.685051 | + | 0.728495i | \(0.259780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.34782 | −0.153155 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.62397 | + | 13.9889i | −0.105488 | + | 0.908679i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.60614 | + | 16.6383i | 0.621370 | + | 1.07624i | 0.989231 | + | 0.146363i | \(0.0467568\pi\) |
−0.367861 | + | 0.929881i | \(0.619910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.88912 | − | 15.3964i | 0.572599 | − | 0.991770i | −0.423699 | − | 0.905803i | \(-0.639269\pi\) |
0.996298 | − | 0.0859672i | \(-0.0273980\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.05057 | + | 13.9029i | 0.452294 | + | 0.891869i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.300268 | + | 0.520080i | −0.0191834 | + | 0.0332267i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.426023 | + | 0.737894i | 0.0271072 | + | 0.0469510i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.11434 | − | 9.59896i | 0.0706184 | − | 0.608309i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5531 | −1.29730 | −0.648649 | − | 0.761088i | \(-0.724665\pi\) | ||||
−0.648649 | + | 0.761088i | \(0.724665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.95997 | −0.186092 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.21041 | − | 0.899644i | −0.0757988 | − | 0.0563379i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.6943 | + | 21.9871i | 0.791846 | + | 1.37152i | 0.924823 | + | 0.380399i | \(0.124213\pi\) |
−0.132976 | + | 0.991119i | \(0.542453\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.300268 | + | 0.520080i | −0.0186578 | + | 0.0323162i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.04362 | + | 10.1088i | 0.188396 | + | 0.625717i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.3557 | + | 26.5969i | −0.946874 | + | 1.64003i | −0.194918 | + | 0.980820i | \(0.562444\pi\) |
−0.751956 | + | 0.659213i | \(0.770889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.78398 | + | 4.82200i | 0.171019 | + | 0.296213i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.09026 | − | 2.63274i | 0.372718 | − | 0.161121i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.7402 | 0.837757 | 0.418878 | − | 0.908042i | \(-0.362423\pi\) | ||||
0.418878 | + | 0.908042i | \(0.362423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.64977 | −0.464690 | −0.232345 | − | 0.972633i | \(-0.574640\pi\) | ||||
−0.232345 | + | 0.972633i | \(0.574640\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.525218 | + | 0.227045i | −0.0317877 | + | 0.0137414i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.71273 | + | 6.43064i | 0.223886 | + | 0.387782i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.19174 | − | 7.26030i | 0.251857 | − | 0.436229i | −0.712180 | − | 0.701997i | \(-0.752292\pi\) |
0.964037 | + | 0.265768i | \(0.0856254\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.0945 | − | 6.61206i | −1.68197 | − | 0.395854i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7786 | − | 22.1333i | 0.762310 | − | 1.32036i | −0.179347 | − | 0.983786i | \(-0.557398\pi\) |
0.941657 | − | 0.336574i | \(-0.109268\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.46132 | + | 9.45928i | 0.324641 | + | 0.562296i | 0.981440 | − | 0.191771i | \(-0.0614230\pi\) |
−0.656798 | + | 0.754066i | \(0.728090\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.15316 | − | 1.60035i | −0.127542 | − | 0.0947965i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.62068 | 0.390807 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8978 | −0.876341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.389390 | + | 3.35422i | −0.0228264 | + | 0.196628i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.9994 | − | 24.2477i | −0.817853 | − | 1.41656i | −0.907261 | − | 0.420569i | \(-0.861831\pi\) |
0.0894073 | − | 0.995995i | \(-0.471503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.16457 | + | 7.21325i | −0.242471 | + | 0.419972i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.36078 | − | 6.35833i | −0.311064 | − | 0.368948i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.305473 | − | 0.529095i | 0.0176660 | − | 0.0305984i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.81481 | + | 3.14334i | 0.104604 | + | 0.181179i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.51336 | − | 30.2642i | 0.201837 | − | 1.73863i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.11598 | −0.178420 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.0259 | 1.88489 | 0.942443 | − | 0.334367i | \(-0.108523\pi\) | ||||
0.942443 | + | 0.334367i | \(0.108523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.7506 | + | 10.9635i | 0.839131 | + | 0.623689i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0143 | − | 22.5415i | −0.737975 | − | 1.27821i | −0.953406 | − | 0.301692i | \(-0.902449\pi\) |
0.215430 | − | 0.976519i | \(-0.430885\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.46618 | − | 9.46771i | 0.308967 | − | 0.535146i | −0.669170 | − | 0.743110i | \(-0.733350\pi\) |
0.978137 | + | 0.207963i | \(0.0666834\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.23429 | − | 1.31238i | 0.0695441 | − | 0.0739441i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.98593 | − | 10.3679i | 0.336203 | − | 0.582321i | −0.647512 | − | 0.762055i | \(-0.724190\pi\) |
0.983715 | + | 0.179734i | \(0.0575237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.81615 | − | 4.87772i | −0.157674 | − | 0.273100i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.46830 | + | 2.36388i | −0.305211 | + | 0.131939i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.73956 | 0.208074 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.53264 | −0.0850153 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.82388 | − | 3.81445i | 0.487962 | − | 0.210939i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.95477 | + | 3.38576i | 0.107770 | + | 0.186663i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6176 | − | 20.1223i | 0.638561 | − | 1.10602i | −0.347188 | − | 0.937796i | \(-0.612863\pi\) |
0.985749 | − | 0.168224i | \(-0.0538034\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.23429 | − | 1.31238i | 0.0676384 | − | 0.0719179i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.54597 | + | 6.14180i | −0.193737 | + | 0.335562i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.89594 | − | 6.74796i | −0.212225 | − | 0.367585i | 0.740185 | − | 0.672403i | \(-0.234738\pi\) |
−0.952411 | + | 0.304818i | \(0.901404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.1797 | + | 9.05265i | 0.661512 | + | 0.491672i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.3983 | 0.833862 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.221824 | + | 1.91080i | −0.0119426 | + | 0.102874i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.26198 | − | 16.0422i | −0.497209 | − | 0.861192i | 0.502785 | − | 0.864411i | \(-0.332309\pi\) |
−0.999995 | + | 0.00321932i | \(0.998975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.958498 | − | 1.66017i | 0.0513072 | − | 0.0888667i | −0.839231 | − | 0.543775i | \(-0.816995\pi\) |
0.890538 | + | 0.454908i | \(0.150328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.68979 | − | 0.302050i | 0.0901944 | − | 0.0161223i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.869778 | − | 1.50650i | 0.0462936 | − | 0.0801829i | −0.841950 | − | 0.539555i | \(-0.818592\pi\) |
0.888244 | + | 0.459372i | \(0.151926\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.25504 | − | 2.17379i | −0.0666104 | − | 0.115373i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.289591 | + | 2.49455i | −0.0153268 | + | 0.132025i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.07616 | 0.162354 | 0.0811768 | − | 0.996700i | \(-0.474132\pi\) | ||||
0.0811768 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3478 | −0.649885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.7303 | − | 8.71861i | −0.615681 | − | 0.457608i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.24302 | − | 2.15297i | −0.0650625 | − | 0.112692i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.17871 | + | 10.7018i | −0.322526 | + | 0.558632i | −0.981009 | − | 0.193964i | \(-0.937865\pi\) |
0.658482 | + | 0.752596i | \(0.271199\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.3338 | − | 4.55023i | −1.00648 | − | 0.236876i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.63583 | − | 8.02949i | 0.240680 | − | 0.416870i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3999 | − | 21.4773i | −0.642044 | − | 1.11205i | −0.984976 | − | 0.172693i | \(-0.944753\pi\) |
0.342931 | − | 0.939360i | \(-0.388580\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.20335 | − | 3.97849i | 0.475259 | − | 0.205448i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.16252 | 0.0598730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.9650 | 0.614602 | 0.307301 | − | 0.951612i | \(-0.400574\pi\) | ||||
0.307301 | + | 0.951612i | \(0.400574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.7303 | + | 7.66457i | −0.908350 | + | 0.392668i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.85810 | + | 10.1465i | 0.299335 | + | 0.518463i | 0.975984 | − | 0.217843i | \(-0.0699020\pi\) |
−0.676649 | + | 0.736306i | \(0.736569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.480590 | + | 0.832407i | −0.0244932 | + | 0.0424234i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.13929 | − | 10.4265i | −0.159579 | − | 0.530009i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.1360 | + | 33.1445i | −0.970232 | + | 1.68049i | −0.275384 | + | 0.961334i | \(0.588805\pi\) |
−0.694848 | + | 0.719156i | \(0.744528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.34070 | − | 2.32215i | −0.0678019 | − | 0.117436i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.22848 | + | 5.37261i | 0.364628 | + | 0.271012i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.88282 | −0.245681 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.8396 | 0.644402 | 0.322201 | − | 0.946671i | \(-0.395577\pi\) | ||||
0.322201 | + | 0.946671i | \(0.395577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.515144 | + | 4.43747i | −0.0257895 | + | 0.222152i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.1570 | − | 19.3245i | −0.557155 | − | 0.965021i | −0.997732 | − | 0.0673063i | \(-0.978560\pi\) |
0.440577 | − | 0.897715i | \(-0.354774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.58912 | + | 2.75244i | −0.0791598 | + | 0.137109i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.50634 | + | 2.98413i | −0.223922 | + | 0.148283i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.480590 | + | 0.832407i | −0.0238220 | + | 0.0412609i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.76605 | + | 6.52299i | 0.186219 | + | 0.322541i | 0.943987 | − | 0.329984i | \(-0.107043\pi\) |
−0.757767 | + | 0.652525i | \(0.773710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.75524 | − | 15.1197i | 0.0865796 | − | 0.745799i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.8695 | 0.682474 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.35050 | 0.164470 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.5371 | + | 9.31828i | 0.613945 | + | 0.456318i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1245 | − | 24.4644i | −0.690029 | − | 1.19517i | −0.971828 | − | 0.235692i | \(-0.924264\pi\) |
0.281798 | − | 0.959474i | \(-0.409069\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.53395 | + | 16.5133i | −0.464656 | + | 0.804808i | −0.999186 | − | 0.0403414i | \(-0.987155\pi\) |
0.534530 | + | 0.845150i | \(0.320489\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.38140 | − | 11.2306i | −0.164409 | − | 0.546051i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.36330 | + | 5.82541i | −0.163144 | + | 0.282574i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.59433 | + | 4.49351i | 0.125548 | + | 0.217456i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.840631 | + | 0.363394i | −0.0405860 | + | 0.0175448i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.9786 | 1.10684 | 0.553421 | − | 0.832902i | \(-0.313322\pi\) | ||||
0.553421 | + | 0.832902i | \(0.313322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.0806 | −1.39752 | −0.698762 | − | 0.715354i | \(-0.746265\pi\) | ||||
−0.698762 | + | 0.715354i | \(0.746265\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.35984 | + | 1.45241i | −0.161092 | + | 0.0696379i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.38492 | − | 4.13081i | −0.114086 | − | 0.197603i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.36777 | + | 12.7613i | −0.351644 | + | 0.609066i | −0.986538 | − | 0.163534i | \(-0.947711\pi\) |
0.634893 | + | 0.772600i | \(0.281044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.92021 | − | 0.687275i | −0.139058 | − | 0.0327274i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2548 | + | 29.8861i | −0.819799 | + | 1.41993i | 0.0860314 | + | 0.996292i | \(0.472581\pi\) |
−0.905830 | + | 0.423641i | \(0.860752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.15024 | + | 1.99227i | 0.0545264 | + | 0.0944425i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.46136 | − | 1.08616i | −0.0691198 | − | 0.0513737i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5508 | 0.545115 | 0.272557 | − | 0.962140i | \(-0.412131\pi\) | ||||
0.272557 | + | 0.962140i | \(0.412131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5966 | 0.498977 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.59225 | − | 22.3297i | 0.121794 | − | 1.04914i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0991952 | − | 0.171811i | −0.00465034 | − | 0.00805463i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.6995 | + | 32.3884i | −0.874724 | + | 1.51507i | −0.0176677 | + | 0.999844i | \(0.505624\pi\) |
−0.857056 | + | 0.515223i | \(0.827709\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.56011 | − | 7.08558i | 0.119496 | − | 0.330727i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.13929 | − | 15.8297i | 0.425659 | − | 0.737263i | −0.570823 | − | 0.821073i | \(-0.693376\pi\) |
0.996482 | + | 0.0838101i | \(0.0267089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.24610 | + | 7.35447i | 0.197333 | + | 0.341791i | 0.947663 | − | 0.319273i | \(-0.103439\pi\) |
−0.750330 | + | 0.661064i | \(0.770105\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.15396 | − | 9.94029i | 0.0535138 | − | 0.460970i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.6746 | 0.679060 | 0.339530 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8093 | 0.545305 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.4327 | − | 20.3896i | −1.26403 | − | 0.939501i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.90467 | + | 5.03103i | 0.133557 | + | 0.231327i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.98287 | + | 10.3626i | −0.274513 | + | 0.475470i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.0561 | + | 20.2617i | −0.872518 | + | 0.927722i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.7151 | − | 32.4156i | 0.855117 | − | 1.48111i | −0.0214198 | − | 0.999771i | \(-0.506819\pi\) |
0.876537 | − | 0.481335i | \(-0.159848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0991952 | − | 0.171811i | −0.00452291 | − | 0.00783391i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.94023 | − | 1.27102i | 0.133785 | − | 0.0578335i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.17078 | −0.0531626 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.3216 | −1.50994 | −0.754972 | − | 0.655757i | \(-0.772350\pi\) | ||||
−0.754972 | + | 0.655757i | \(0.772350\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −36.4418 | + | 15.7533i | −1.64796 | + | 0.712390i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.9456 | − | 34.5467i | −0.900131 | − | 1.55907i | −0.827323 | − | 0.561726i | \(-0.810137\pi\) |
−0.0728078 | − | 0.997346i | \(-0.523196\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.55110 | − | 4.41864i | 0.114896 | − | 0.199006i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.97552 | − | 2.10051i | 0.0887930 | − | 0.0944108i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.08986 | + | 3.61974i | −0.0937430 | + | 0.162368i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0370 | + | 19.1167i | 0.494086 | + | 0.855781i | 0.999977 | − | 0.00681602i | \(-0.00216962\pi\) |
−0.505891 | + | 0.862597i | \(0.668836\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.49033 | − | 3.33746i | −0.200613 | − | 0.149107i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.30820 | 0.415032 | 0.207516 | − | 0.978232i | \(-0.433462\pi\) | ||||
0.207516 | + | 0.978232i | \(0.433462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5637 | 0.470077 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.57471 | + | 22.1787i | −0.114347 | + | 0.984990i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.88466 | + | 4.99637i | 0.127860 | + | 0.221460i | 0.922847 | − | 0.385166i | \(-0.125856\pi\) |
−0.794987 | + | 0.606626i | \(0.792522\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.06985 | + | 3.58508i | −0.0915646 | + | 0.158595i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.55410 | − | 12.6043i | 0.201068 | − | 0.556495i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.18613 | + | 5.51854i | −0.140398 | + | 0.243176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.12868 | + | 5.41903i | 0.137599 | + | 0.238329i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.82841 | − | 24.3640i | 0.124153 | − | 1.06946i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.2989 | −0.582634 | −0.291317 | − | 0.956627i | \(-0.594093\pi\) | ||||
−0.291317 | + | 0.956627i | \(0.594093\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.27523 | −0.186943 | −0.0934713 | − | 0.995622i | \(-0.529796\pi\) | ||||
−0.0934713 | + | 0.995622i | \(0.529796\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.44930 | − | 4.79348i | −0.281470 | − | 0.209205i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.97451 | + | 12.0802i | 0.303815 | + | 0.526222i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.78993 | − | 16.9567i | 0.425649 | − | 0.737246i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −40.5019 | − | 9.53217i | −1.75763 | − | 0.413661i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.09359 | + | 1.89415i | −0.0473686 | + | 0.0820448i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.03277 | − | 1.78881i | −0.0446505 | − | 0.0773370i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.2370 | − | 4.85759i | 0.484911 | − | 0.209621i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.60054 | 0.0689400 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2130 | −0.525076 | −0.262538 | − | 0.964922i | \(-0.584560\pi\) | ||||
−0.262538 | + | 0.964922i | \(0.584560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.1941 | − | 13.4848i | 1.33867 | − | 0.578689i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.66652 | + | 2.88650i | 0.0713858 | + | 0.123644i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0910 | − | 33.0666i | 0.816272 | − | 1.41382i | −0.0921387 | − | 0.995746i | \(-0.529370\pi\) |
0.908411 | − | 0.418079i | \(-0.137296\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.48771 | − | 14.9050i | −0.191531 | − | 0.636131i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.53808 | − | 7.86019i | 0.193329 | − | 0.334855i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.06538 | + | 7.04144i | 0.172877 | + | 0.299433i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.501341 | + | 0.372625i | 0.0212808 | + | 0.0158171i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.8404 | 1.56098 | 0.780490 | − | 0.625169i | \(-0.214970\pi\) | ||||
0.780490 | + | 0.625169i | \(0.214970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.19906 | −0.0507150 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.463501 | + | 3.99261i | −0.0195690 | + | 0.168568i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.56265 | + | 16.5630i | 0.403018 | + | 0.698047i | 0.994089 | − | 0.108572i | \(-0.0346279\pi\) |
−0.591071 | + | 0.806620i | \(0.701295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.63083 | + | 4.55672i | −0.110680 | + | 0.191703i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.05531 | + | 4.01398i | 0.338291 | + | 0.168571i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.9576 | − | 22.4433i | 0.543212 | − | 0.940871i | −0.455505 | − | 0.890233i | \(-0.650541\pi\) |
0.998717 | − | 0.0506376i | \(-0.0161253\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5679 | − | 33.8925i | −0.818889 | − | 1.41836i | −0.906501 | − | 0.422203i | \(-0.861257\pi\) |
0.0876117 | − | 0.996155i | \(-0.472077\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.03842 | − | 34.7871i | 0.168707 | − | 1.45325i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.57985 | 0.357805 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.72008 | 0.404652 | 0.202326 | − | 0.979318i | \(-0.435150\pi\) | ||||
0.202326 | + | 0.979318i | \(0.435150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.7296 | + | 18.3804i | 1.02773 | + | 0.763865i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.78959 | − | 4.83171i | −0.115732 | − | 0.200453i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.41981 | − | 12.8515i | 0.307297 | − | 0.532254i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.171590 | + | 0.569900i | 0.00709436 | + | 0.0235625i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.91088 | − | 11.9700i | 0.285242 | − | 0.494054i | −0.687425 | − | 0.726255i | \(-0.741259\pi\) |
0.972668 | + | 0.232200i | \(0.0745925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4067 | + | 21.4891i | 0.511211 | + | 0.885444i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.7849 | + | 5.52673i | −0.525899 | + | 0.227339i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.1361 | −0.909022 | −0.454511 | − | 0.890741i | \(-0.650186\pi\) | ||||
−0.454511 | + | 0.890741i | \(0.650186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.870718 | −0.0356960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.3109 | − | 9.64470i | 0.913123 | − | 0.394731i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.28059 | + | 3.95010i | 0.0931824 | + | 0.161397i | 0.908849 | − | 0.417126i | \(-0.136963\pi\) |
−0.815666 | + | 0.578523i | \(0.803629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.2116 | + | 17.6870i | −0.416541 | + | 0.721469i | −0.995589 | − | 0.0938238i | \(-0.970091\pi\) |
0.579048 | + | 0.815293i | \(0.303424\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −34.4858 | − | 8.11627i | −1.40437 | − | 0.330520i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.53375 | − | 4.38858i | 0.103012 | − | 0.178421i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.11206 | + | 12.3184i | 0.288670 | + | 0.499990i | 0.973492 | − | 0.228719i | \(-0.0734538\pi\) |
−0.684823 | + | 0.728710i | \(0.740120\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.89187 | + | 3.63591i | 0.198229 | + | 0.147335i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.29154 | −0.0522499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.3892 | −1.26780 | −0.633899 | − | 0.773416i | \(-0.718546\pi\) | ||||
−0.633899 | + | 0.773416i | \(0.718546\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.794126 | − | 6.84063i | 0.0320222 | − | 0.275841i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.51767 | − | 4.36073i | −0.101357 | − | 0.175556i | 0.810887 | − | 0.585203i | \(-0.198985\pi\) |
−0.912244 | + | 0.409647i | \(0.865652\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.1803 | + | 33.2212i | −0.770920 | + | 1.33527i | 0.166140 | + | 0.986102i | \(0.446870\pi\) |
−0.937060 | + | 0.349170i | \(0.886464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.45964 | + | 1.69091i | −0.379602 | + | 0.0678539i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.91535 | − | 3.31748i | 0.0767367 | − | 0.132912i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.86020 | − | 17.0784i | −0.394408 | − | 0.683135i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.824508 | + | 7.10234i | −0.0329277 | + | 0.283640i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.870718 | −0.0347178 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0768 | −0.958480 | −0.479240 | − | 0.877684i | \(-0.659088\pi\) | ||||
−0.479240 | + | 0.877684i | \(0.659088\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.3688 | − | 15.1392i | −0.809586 | − | 0.601730i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.34863 | − | 5.79999i | −0.132886 | − | 0.230166i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.165178 | + | 0.286096i | −0.00654457 | + | 0.0113355i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.59060 | − | 9.13412i | 0.339839 | − | 0.361340i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.7800 | + | 35.9920i | −0.820760 | + | 1.42160i | 0.0843567 | + | 0.996436i | \(0.473116\pi\) |
−0.905117 | + | 0.425163i | \(0.860217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.924345 | − | 1.60101i | −0.0364526 | − | 0.0631378i | 0.847224 | − | 0.531237i | \(-0.178272\pi\) |
−0.883676 | + | 0.468099i | \(0.844939\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.46545 | − | 1.49807i | 0.136452 | − | 0.0589863i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.8480 | 1.52727 | 0.763637 | − | 0.645646i | \(-0.223412\pi\) | ||||
0.763637 | + | 0.645646i | \(0.223412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.1987 | 0.871374 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.2955 | + | 6.61206i | −0.599479 | + | 0.259147i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.3225 | − | 35.1996i | −0.795281 | − | 1.37747i | −0.922661 | − | 0.385613i | \(-0.873990\pi\) |
0.127380 | − | 0.991854i | \(-0.459343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.56135 | + | 2.70435i | −0.0610072 | + | 0.105668i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.50833 | − | 9.04664i | 0.331942 | − | 0.352943i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2140 | − | 33.2796i | 0.748471 | − | 1.29639i | −0.200084 | − | 0.979779i | \(-0.564121\pi\) |
0.948555 | − | 0.316612i | \(-0.102545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.72841 | + | 9.92190i | 0.222809 | + | 0.385917i | 0.955660 | − | 0.294472i | \(-0.0951439\pi\) |
−0.732851 | + | 0.680390i | \(0.761811\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.665846 | − | 0.494894i | −0.0258593 | − | 0.0192201i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.54889 | −0.0600635 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.50793 | −0.251988 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.80701 | − | 24.1797i | 0.108525 | − | 0.934842i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.15231 | + | 7.19202i | 0.160298 | + | 0.277645i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.4933 | + | 40.6916i | −0.905601 | + | 1.56855i | −0.0854925 | + | 0.996339i | \(0.527246\pi\) |
−0.820108 | + | 0.572208i | \(0.806087\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.5389 | + | 18.4304i | 0.598092 | + | 0.709388i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.03942 | − | 13.9247i | 0.308980 | − | 0.535169i | −0.669159 | − | 0.743119i | \(-0.733346\pi\) |
0.978140 | + | 0.207950i | \(0.0666790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.974782 | + | 1.68837i | 0.0374087 | + | 0.0647938i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.961113 | + | 8.27906i | −0.0368299 | + | 0.317254i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.20464 | 0.199150 | 0.0995750 | − | 0.995030i | \(-0.468252\pi\) | ||||
0.0995750 | + | 0.995030i | \(0.468252\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.27750 | 0.201643 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.68247 | + | 3.48027i | 0.178647 | + | 0.132781i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.53147 | + | 2.65258i | 0.0583444 | + | 0.101055i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.783381 | − | 1.35686i | 0.0298012 | − | 0.0516172i | −0.850740 | − | 0.525587i | \(-0.823846\pi\) |
0.880541 | + | 0.473969i | \(0.157179\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.67391 | − | 1.10001i | −0.177547 | − | 0.0417859i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.70802 | + | 4.69043i | −0.102721 | + | 0.177918i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.79966 | + | 8.31326i | 0.181800 | + | 0.314887i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −33.2498 | + | 14.3735i | −1.25762 | + | 0.543654i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.94479 | 0.224532 | 0.112266 | − | 0.993678i | \(-0.464189\pi\) | ||||
0.112266 | + | 0.993678i | \(0.464189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.54889 | −0.0584176 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.73270 | − | 1.61360i | 0.140582 | − | 0.0607716i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.79520 | − | 15.2337i | −0.330777 | − | 0.572923i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.53916 | − | 11.3262i | 0.245583 | − | 0.425362i | −0.716712 | − | 0.697369i | \(-0.754354\pi\) |
0.962295 | + | 0.272007i | \(0.0876872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.03237 | − | 23.3566i | −0.263734 | − | 0.875939i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.89607 | − | 15.4084i | 0.333160 | − | 0.577051i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.158766 | − | 0.274990i | −0.00593749 | − | 0.0102840i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.7075 | − | 19.8505i | −0.997411 | − | 0.741332i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5600 | 0.393821 | 0.196910 | − | 0.980422i | \(-0.436909\pi\) | ||||
0.196910 | + | 0.980422i | \(0.436909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6109 | 0.395172 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.55088 | + | 30.5874i | −0.132059 | + | 1.13756i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.16297 | + | 14.1387i | 0.303165 | + | 0.525097i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.08052 | + | 8.79972i | −0.188426 | + | 0.326364i | −0.944726 | − | 0.327862i | \(-0.893672\pi\) |
0.756300 | + | 0.654226i | \(0.227005\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7645 | − | 17.2579i | −0.769056 | − | 0.639182i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.63129 | + | 4.55753i | −0.0973218 | + | 0.168566i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.2280 | − | 22.9116i | −0.488589 | − | 0.846260i | 0.511325 | − | 0.859387i | \(-0.329155\pi\) |
−0.999914 | + | 0.0131270i | \(0.995821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.119946 | − | 1.03322i | 0.00442428 | − | 0.0381109i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.9013 | 0.696237 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.3880 | −0.897127 | −0.448563 | − | 0.893751i | \(-0.648064\pi\) | ||||
−0.448563 | + | 0.893751i | \(0.648064\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.18445 | − | 0.880352i | −0.0435120 | − | 0.0323405i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.21961 | + | 14.2368i | 0.301548 | + | 0.522297i | 0.976487 | − | 0.215577i | \(-0.0691632\pi\) |
−0.674939 | + | 0.737874i | \(0.735830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.315654 | − | 0.546728i | 0.0115647 | − | 0.0200306i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.82549 | + | 16.0269i | 0.176555 | + | 0.586392i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.71974 | + | 2.97869i | −0.0628381 | + | 0.108839i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0653789 | − | 0.113240i | −0.00238571 | − | 0.00413217i | 0.864830 | − | 0.502065i | \(-0.167426\pi\) |
−0.867216 | + | 0.497932i | \(0.834093\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.6765 | − | 14.1256i | 1.19080 | − | 0.514766i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.79415 | 0.283658 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.1017 | 1.31214 | 0.656069 | − | 0.754701i | \(-0.272218\pi\) | ||||
0.656069 | + | 0.754701i | \(0.272218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.70594 | − | 2.03432i | 0.170815 | − | 0.0738410i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.61027 | + | 7.98523i | 0.167122 | + | 0.289464i | 0.937407 | − | 0.348236i | \(-0.113219\pi\) |
−0.770285 | + | 0.637700i | \(0.779886\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.77505 | − | 4.80653i | 0.100464 | − | 0.174008i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.54268 | + | 0.598423i | 0.0919309 | + | 0.0216360i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.29093 | + | 3.96801i | −0.0827208 | + | 0.143277i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.8660 | + | 39.6050i | 0.824568 | + | 1.42819i | 0.902249 | + | 0.431216i | \(0.141915\pi\) |
−0.0776802 | + | 0.996978i | \(0.524751\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.2933 | − | 26.2319i | −1.27106 | − | 0.944721i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.9709 | 0.934109 | 0.467054 | − | 0.884229i | \(-0.345315\pi\) | ||||
0.467054 | + | 0.884229i | \(0.345315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −44.6338 | −1.60329 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.119946 | − | 1.03322i | 0.00430305 | − | 0.0370666i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.53797 | + | 14.7882i | 0.305905 | + | 0.529842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.34490 | + | 5.79353i | −0.119690 | + | 0.207309i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.7864 | − | 13.9797i | −0.421213 | − | 0.499594i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.92549 | − | 10.2632i | 0.211490 | − | 0.366311i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.3821 | + | 43.9630i | 0.904773 | + | 1.56711i | 0.821222 | + | 0.570609i | \(0.193293\pi\) |
0.0835512 | + | 0.996503i | \(0.473374\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.13404 | − | 52.8389i | 0.218378 | − | 1.88111i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.76158 | 0.311526 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.71410 | −0.0608694 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.74019 | − | 5.75294i | −0.274516 | − | 0.204036i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.2977 | − | 23.0322i | −0.471027 | − | 0.815843i | 0.528424 | − | 0.848981i | \(-0.322783\pi\) |
−0.999451 | + | 0.0331379i | \(0.989450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.83422 | + | 4.90901i | −0.100267 | + | 0.173668i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.87324 | + | 8.37137i | −0.278187 | + | 0.295788i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.31286 | + | 5.73805i | −0.116908 | + | 0.202491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.555305 | + | 0.961817i | 0.0195719 | + | 0.0338996i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.8450 | + | 9.44332i | −0.768981 | + | 0.332421i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.1540 | −0.743735 | −0.371867 | − | 0.928286i | \(-0.621282\pi\) | ||||
−0.371867 | + | 0.928286i | \(0.621282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4615 | 0.542927 | 0.271464 | − | 0.962449i | \(-0.412492\pi\) | ||||
0.271464 | + | 0.962449i | \(0.412492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.1621 | − | 5.25750i | 0.426542 | − | 0.184388i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.88258 | − | 11.9210i | −0.241086 | − | 0.417573i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.68072 | + | 8.10725i | −0.163758 | + | 0.283637i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.678981 | − | 0.721939i | 0.0237255 | − | 0.0252266i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.2843 | + | 23.0091i | −0.463626 | + | 0.803024i | −0.999138 | − | 0.0415036i | \(-0.986785\pi\) |
0.535512 | + | 0.844527i | \(0.320119\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5469 | − | 21.7318i | −0.437357 | − | 0.757524i | 0.560128 | − | 0.828406i | \(-0.310752\pi\) |
−0.997485 | + | 0.0708819i | \(0.977419\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.3223 | − | 7.67214i | −0.359378 | − | 0.267110i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.8156 | −0.445642 | −0.222821 | − | 0.974859i | \(-0.571526\pi\) | ||||
−0.222821 | + | 0.974859i | \(0.571526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.9832 | 1.31921 | 0.659605 | − | 0.751613i | \(-0.270724\pi\) | ||||
0.659605 | + | 0.751613i | \(0.270724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.67445 | + | 14.4237i | −0.0580859 | + | 0.500354i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.724950 | + | 1.25565i | 0.0251180 | + | 0.0435057i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.969913 | − | 1.67994i | 0.0335652 | − | 0.0581367i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.2105 | − | 8.79639i | 1.70097 | − | 0.304048i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.95638 | + | 5.12060i | −0.102065 | + | 0.176783i | −0.912535 | − | 0.408998i | \(-0.865878\pi\) |
0.810470 | + | 0.585780i | \(0.199212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.30829 | + | 14.3904i | 0.286493 | + | 0.496220i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.10460 | + | 43.9712i | −0.175812 | + | 1.51445i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.74144 | −0.266313 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.43828 | −0.289943 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.1838 | − | 11.2855i | −0.521108 | − | 0.387317i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.555305 | + | 0.961817i | 0.0190356 | + | 0.0329707i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.72609 | − | 16.8461i | 0.333015 | − | 0.576799i | −0.650087 | − | 0.759860i | \(-0.725267\pi\) |
0.983101 | + | 0.183061i | \(0.0586007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.52310 | + | 1.06452i | 0.154687 | + | 0.0364057i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.42502 | − | 5.93231i | 0.116996 | − | 0.202644i | −0.801580 | − | 0.597888i | \(-0.796007\pi\) |
0.918576 | + | 0.395244i | \(0.129340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.04742 | + | 5.27828i | 0.103977 | + | 0.180093i | 0.913320 | − | 0.407244i | \(-0.133510\pi\) |
−0.809343 | + | 0.587336i | \(0.800177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.5260 | + | 4.55023i | −0.358724 | + | 0.155072i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.6568 | 1.14569 | 0.572846 | − | 0.819663i | \(-0.305839\pi\) | ||||
0.572846 | + | 0.819663i | \(0.305839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.50423 | 0.289152 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.6854 | − | 10.2389i | 0.804398 | − | 0.347731i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.50679 | + | 11.2701i | 0.220728 | + | 0.382312i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.95064 | + | 3.37860i | −0.0660948 | + | 0.114480i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.68620 | − | 5.60035i | −0.0570691 | − | 0.189543i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.89439 | − | 5.01324i | 0.0978483 | − | 0.169478i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.18905 | − | 14.1839i | −0.276525 | − | 0.478955i | 0.693994 | − | 0.719981i | \(-0.255849\pi\) |
−0.970519 | + | 0.241026i | \(0.922516\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.9219 | + | 28.9289i | 1.31280 | + | 0.975749i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.0864 | 0.744108 | 0.372054 | − | 0.928211i | \(-0.378654\pi\) | ||||
0.372054 | + | 0.928211i | \(0.378654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.1872 | −0.443784 | −0.221892 | − | 0.975071i | \(-0.571223\pi\) | ||||
−0.221892 | + | 0.975071i | \(0.571223\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.66360 | − | 14.3303i | 0.0559211 | − | 0.481707i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.7174 | + | 25.4912i | 0.494160 | + | 0.855911i | 0.999977 | − | 0.00672982i | \(-0.00214218\pi\) |
−0.505817 | + | 0.862641i | \(0.668809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.57606 | + | 9.65801i | −0.187015 | + | 0.323919i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.8928 | + | 6.42453i | 0.431925 | + | 0.215230i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.04170 | + | 8.73249i | −0.168714 | + | 0.292222i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.12227 | + | 3.67587i | 0.0709395 | + | 0.122871i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.122025 | + | 1.05113i | −0.00407431 | + | 0.0350963i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.8553 | 1.12914 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.4430 | 0.447850 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.04563 | − | 3.75020i | −0.167908 | − | 0.124799i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.89147 | + | 10.2043i | 0.195839 | + | 0.339203i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.03916 | − | 15.6563i | 0.300140 | − | 0.519858i | −0.676027 | − | 0.736877i | \(-0.736300\pi\) |
0.976167 | + | 0.217018i | \(0.0696332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.2141 | + | 50.5305i | 0.504620 | + | 1.67599i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24050 | − | 7.34475i | 0.140494 | − | 0.243343i | −0.787189 | − | 0.616712i | \(-0.788464\pi\) |
0.927683 | + | 0.373369i | \(0.121798\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.46484 | − | 7.73333i | −0.147765 | − | 0.255936i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.95396 | − | 2.14153i | 0.163773 | − | 0.0707969i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.19987 | 0.171715 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.0092 | −0.726017 | −0.363008 | − | 0.931786i | \(-0.618250\pi\) | ||||
−0.363008 | + | 0.931786i | \(0.618250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −52.5065 | + | 22.6979i | −1.73015 | + | 0.747920i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.690396 | − | 1.19580i | −0.0227247 | − | 0.0393603i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.39305 | − | 2.41284i | 0.0458032 | − | 0.0793336i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.9862 | − | 7.29264i | −1.01772 | − | 0.239522i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.4107 | + | 37.0845i | −0.702464 | + | 1.21670i | 0.265135 | + | 0.964211i | \(0.414583\pi\) |
−0.967599 | + | 0.252492i | \(0.918750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.28959 | + | 2.23364i | 0.0422646 | + | 0.0732045i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.1832 | + | 26.8934i | 1.18458 | + | 0.880450i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39362 | −0.0455761 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.65749 | 0.282828 | 0.141414 | − | 0.989951i | \(-0.454835\pi\) | ||||
0.141414 | + | 0.989951i | \(0.454835\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.18354 | + | 18.8091i | −0.0712572 | + | 0.613812i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.9474 | − | 44.9421i | −0.845859 | − | 1.46507i | −0.884873 | − | 0.465833i | \(-0.845755\pi\) |
0.0390132 | − | 0.999239i | \(-0.487579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.12203 | − | 10.6037i | 0.199361 | − | 0.345303i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.06038 | + | 2.93479i | −0.0344940 | + | 0.0954687i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5394 | + | 19.9869i | −0.374981 | + | 0.649486i | −0.990324 | − | 0.138773i | \(-0.955684\pi\) |
0.615343 | + | 0.788259i | \(0.289017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.683784 | − | 1.18435i | −0.0221966 | − | 0.0384456i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.39116 | + | 20.5975i | −0.0775387 | + | 0.667921i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.9656 | −0.743927 | −0.371964 | − | 0.928247i | \(-0.621315\pi\) | ||||
−0.371964 | + | 0.928247i | \(0.621315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.1424 | 0.392918 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.82962 | + | 5.81941i | 0.253096 | + | 0.188115i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.39399 | − | 7.61062i | −0.141889 | − | 0.245760i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7788 | + | 53.3104i | −0.992864 | + | 1.71969i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.06920 | − | 7.51646i | 0.227802 | − | 0.242215i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.34161 | + | 9.25194i | −0.171953 | + | 0.297830i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.4696 | + | 51.0429i | 0.947680 | + | 1.64143i | 0.750294 | + | 0.661104i | \(0.229912\pi\) |
0.197386 | + | 0.980326i | \(0.436755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.94537 | + | 2.57010i | −0.190993 | + | 0.0825637i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.8074 | −0.828198 | −0.414099 | − | 0.910232i | \(-0.635903\pi\) | ||||
−0.414099 | + | 0.910232i | \(0.635903\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.01867 | 0.289125 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.43667 | − | 1.05334i | 0.0780360 | − | 0.0337340i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.4774 | + | 38.9321i | 0.719117 | + | 1.24555i | 0.961350 | + | 0.275329i | \(0.0887868\pi\) |
−0.242233 | + | 0.970218i | \(0.577880\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.06558 | − | 5.30974i | 0.0979764 | − | 0.169700i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.4071 | + | 12.1289i | −0.364202 | + | 0.387245i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.33576 | + | 7.50976i | −0.138289 | + | 0.239524i | −0.926849 | − | 0.375434i | \(-0.877494\pi\) |
0.788560 | + | 0.614958i | \(0.210827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.41461 | − | 4.18222i | −0.0769358 | − | 0.133257i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.43476 | − | 4.03942i | −0.172990 | − | 0.128576i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.71248 | 0.213445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.39241 | 0.107763 | 0.0538817 | − | 0.998547i | \(-0.482841\pi\) | ||||
0.0538817 | + | 0.998547i | \(0.482841\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.64081 | + | 39.9761i | −0.147272 | + | 1.26860i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.21374 | + | 7.29841i | 0.133584 | + | 0.231375i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0201 | + | 24.2836i | −0.444023 | + | 0.769070i | −0.997984 | − | 0.0634730i | \(-0.979782\pi\) |
0.553961 | + | 0.832543i | \(0.313116\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.06038 | + | 2.93479i | −0.0335488 | + | 0.0928527i |
(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.r.l.673.1 | 8 | ||
3.2 | odd | 2 | 3024.2.r.m.2017.3 | 8 | |||
4.3 | odd | 2 | 504.2.r.e.169.4 | ✓ | 8 | ||
9.2 | odd | 6 | 9072.2.a.cg.1.2 | 4 | |||
9.4 | even | 3 | inner | 1008.2.r.l.337.1 | 8 | ||
9.5 | odd | 6 | 3024.2.r.m.1009.3 | 8 | |||
9.7 | even | 3 | 9072.2.a.cj.1.3 | 4 | |||
12.11 | even | 2 | 1512.2.r.e.505.3 | 8 | |||
36.7 | odd | 6 | 4536.2.a.z.1.3 | 4 | |||
36.11 | even | 6 | 4536.2.a.y.1.2 | 4 | |||
36.23 | even | 6 | 1512.2.r.e.1009.3 | 8 | |||
36.31 | odd | 6 | 504.2.r.e.337.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.e.169.4 | ✓ | 8 | 4.3 | odd | 2 | ||
504.2.r.e.337.4 | yes | 8 | 36.31 | odd | 6 | ||
1008.2.r.l.337.1 | 8 | 9.4 | even | 3 | inner | ||
1008.2.r.l.673.1 | 8 | 1.1 | even | 1 | trivial | ||
1512.2.r.e.505.3 | 8 | 12.11 | even | 2 | |||
1512.2.r.e.1009.3 | 8 | 36.23 | even | 6 | |||
3024.2.r.m.1009.3 | 8 | 9.5 | odd | 6 | |||
3024.2.r.m.2017.3 | 8 | 3.2 | odd | 2 | |||
4536.2.a.y.1.2 | 4 | 36.11 | even | 6 | |||
4536.2.a.z.1.3 | 4 | 36.7 | odd | 6 | |||
9072.2.a.cg.1.2 | 4 | 9.2 | odd | 6 | |||
9072.2.a.cj.1.3 | 4 | 9.7 | even | 3 |