Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(241,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 241.2 | ||
Root | \(0.403374 - 1.68443i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.241 |
Dual form | 720.2.q.j.481.2 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0.403374 | + | 1.68443i | 0.232888 | + | 0.972504i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.596626 | + | 1.03339i | −0.225504 | + | 0.390584i | −0.956470 | − | 0.291829i | \(-0.905736\pi\) |
0.730967 | + | 0.682413i | \(0.239069\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.67458 | + | 1.35891i | −0.891526 | + | 0.452969i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.66044 | + | 2.87597i | −0.500642 | + | 0.867138i | 0.499358 | + | 0.866396i | \(0.333569\pi\) |
−1.00000 | 0.000741679i | \(0.999764\pi\) | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.853695 | − | 1.47864i | −0.236772 | − | 0.410102i | 0.723014 | − | 0.690833i | \(-0.242756\pi\) |
−0.959786 | + | 0.280732i | \(0.909423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.25707 | − | 1.19154i | 0.324574 | − | 0.307656i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.34916 | −1.53990 | −0.769949 | − | 0.638106i | \(-0.779718\pi\) | ||||
−0.769949 | + | 0.638106i | \(0.779718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.32088 | −0.303032 | −0.151516 | − | 0.988455i | \(-0.548415\pi\) | ||||
−0.151516 | + | 0.988455i | \(0.548415\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.98133 | − | 0.588131i | −0.432361 | − | 0.128341i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.43165 | + | 5.94379i | 0.715548 | + | 1.23937i | 0.962748 | + | 0.270401i | \(0.0871563\pi\) |
−0.247200 | + | 0.968965i | \(0.579510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.36783 | − | 3.95698i | −0.648139 | − | 0.761522i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.01414 | + | 1.75654i | −0.188321 | + | 0.326181i | −0.944690 | − | 0.327963i | \(-0.893638\pi\) |
0.756370 | + | 0.654144i | \(0.226971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.33956 | − | 2.32018i | −0.240592 | − | 0.416717i | 0.720291 | − | 0.693672i | \(-0.244008\pi\) |
−0.960883 | + | 0.276955i | \(0.910675\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.51414 | − | 1.63680i | −0.959888 | − | 0.284930i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.19325 | 0.201696 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.32088 | 0.545950 | 0.272975 | − | 0.962021i | \(-0.411992\pi\) | ||||
0.272975 | + | 0.962021i | \(0.411992\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.14631 | − | 2.03443i | 0.343684 | − | 0.325770i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.16044 | − | 2.00994i | −0.181231 | − | 0.313901i | 0.761069 | − | 0.648671i | \(-0.224675\pi\) |
−0.942300 | + | 0.334770i | \(0.891341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.17458 | + | 5.49853i | −0.484119 | + | 0.838518i | −0.999834 | − | 0.0182420i | \(-0.994193\pi\) |
0.515715 | + | 0.856760i | \(0.327526\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.51414 | + | 1.63680i | 0.374785 | + | 0.244000i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.38470 | + | 11.0586i | −0.931304 | + | 1.61307i | −0.150209 | + | 0.988654i | \(0.547995\pi\) |
−0.781095 | + | 0.624412i | \(0.785339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.78807 | + | 4.82909i | 0.398296 | + | 0.689869i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.56108 | − | 10.6947i | −0.358623 | − | 1.49756i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.02827 | 0.141244 | 0.0706221 | − | 0.997503i | \(-0.477502\pi\) | ||||
0.0706221 | + | 0.997503i | \(0.477502\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.32088 | 0.447788 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.532810 | − | 2.22493i | −0.0705724 | − | 0.294699i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.83502 | − | 10.1066i | −0.759655 | − | 1.31576i | −0.943027 | − | 0.332718i | \(-0.892034\pi\) |
0.183371 | − | 0.983044i | \(-0.441299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.86783 | − | 8.43133i | 0.623262 | − | 1.07952i | −0.365612 | − | 0.930767i | \(-0.619140\pi\) |
0.988874 | − | 0.148754i | \(-0.0475263\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.191448 | − | 3.57463i | 0.0241202 | − | 0.450362i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.853695 | + | 1.47864i | −0.105888 | + | 0.183403i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.28534 | − | 9.15448i | −0.645707 | − | 1.11840i | −0.984138 | − | 0.177406i | \(-0.943229\pi\) |
0.338430 | − | 0.940991i | \(-0.390104\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.62763 | + | 8.17792i | −1.03864 | + | 0.984506i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.06562 | 0.126466 | 0.0632329 | − | 0.997999i | \(-0.479859\pi\) | ||||
0.0632329 | + | 0.997999i | \(0.479859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0565 | 1.64519 | 0.822597 | − | 0.568624i | \(-0.192524\pi\) | ||||
0.822597 | + | 0.568624i | \(0.192524\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.66044 | − | 0.492881i | −0.191731 | − | 0.0569130i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.98133 | − | 3.43176i | −0.225793 | − | 0.391085i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.707389 | − | 1.22523i | 0.0795875 | − | 0.137850i | −0.823485 | − | 0.567339i | \(-0.807973\pi\) |
0.903072 | + | 0.429489i | \(0.141306\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.30675 | − | 7.26900i | 0.589639 | − | 0.807667i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.91751 | + | 10.2494i | −0.649531 | + | 1.12502i | 0.333704 | + | 0.942678i | \(0.391701\pi\) |
−0.983235 | + | 0.182343i | \(0.941632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.17458 | + | 5.49853i | 0.344331 | + | 0.596400i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.36783 | − | 0.999697i | −0.361069 | − | 0.107179i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0000 | −1.16600 | −0.582999 | − | 0.812473i | \(-0.698121\pi\) | ||||
−0.582999 | + | 0.812473i | \(0.698121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.03735 | 0.213572 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.36783 | − | 3.19229i | 0.349228 | − | 0.331025i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.660442 | + | 1.14392i | 0.0677599 | + | 0.117364i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.12763 | + | 14.0775i | −0.825236 | + | 1.42935i | 0.0765028 | + | 0.997069i | \(0.475625\pi\) |
−0.901739 | + | 0.432281i | \(0.857709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.532810 | − | 9.94840i | 0.0535494 | − | 0.999851i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.19325 | − | 2.06677i | 0.118733 | − | 0.205652i | −0.800533 | − | 0.599289i | \(-0.795450\pi\) |
0.919266 | + | 0.393637i | \(0.128783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.88197 | + | 8.45582i | 0.481035 | + | 0.833176i | 0.999763 | − | 0.0217626i | \(-0.00692779\pi\) |
−0.518729 | + | 0.854939i | \(0.673594\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.481327 | + | 2.00994i | 0.0469727 | + | 0.196151i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.57976 | 0.732763 | 0.366381 | − | 0.930465i | \(-0.380597\pi\) | ||||
0.366381 | + | 0.930465i | \(0.380597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.5761 | 1.58771 | 0.793854 | − | 0.608109i | \(-0.208072\pi\) | ||||
0.793854 | + | 0.608109i | \(0.208072\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.33956 | + | 5.59378i | 0.127145 | + | 0.530938i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5424 | + | 18.2600i | 0.991747 | + | 1.71776i | 0.606909 | + | 0.794771i | \(0.292409\pi\) |
0.384837 | + | 0.922985i | \(0.374258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.43165 | − | 5.94379i | 0.320003 | − | 0.554261i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.29261 | + | 2.79466i | 0.396852 | + | 0.258366i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.78807 | − | 6.56114i | 0.347252 | − | 0.601458i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0141369 | − | 0.0244859i | −0.00128518 | − | 0.00222599i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.91751 | − | 2.76544i | 0.263063 | − | 0.249351i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4112 | 1.36752 | 0.683760 | − | 0.729707i | \(-0.260343\pi\) | ||||
0.683760 | + | 0.729707i | \(0.260343\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.5424 | − | 3.12938i | −0.928208 | − | 0.275526i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.67912 | − | 2.90831i | −0.146705 | − | 0.254101i | 0.783303 | − | 0.621640i | \(-0.213533\pi\) |
−0.930008 | + | 0.367540i | \(0.880200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.788074 | − | 1.36498i | 0.0683347 | − | 0.118359i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.74293 | + | 4.89512i | −0.150008 | + | 0.421305i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.80675 | − | 6.59348i | 0.325232 | − | 0.563319i | −0.656327 | − | 0.754477i | \(-0.727891\pi\) |
0.981559 | + | 0.191158i | \(0.0612241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.64177 | + | 11.5039i | 0.563347 | + | 0.975746i | 0.997201 | + | 0.0747632i | \(0.0238201\pi\) |
−0.433854 | + | 0.900983i | \(0.642847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.2029 | − | 6.29379i | −1.78560 | − | 0.530033i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.67004 | 0.474153 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.02827 | 0.168439 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.00960 | + | 6.64423i | −0.578142 | + | 0.548007i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.99546 | + | 15.5806i | 0.736937 | + | 1.27641i | 0.953868 | + | 0.300226i | \(0.0970620\pi\) |
−0.216931 | + | 0.976187i | \(0.569605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.33956 | + | 7.51633i | −0.353148 | + | 0.611671i | −0.986799 | − | 0.161948i | \(-0.948222\pi\) |
0.633651 | + | 0.773619i | \(0.281556\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.9813 | − | 8.62791i | 1.37286 | − | 0.697525i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.33956 | + | 2.32018i | −0.107596 | + | 0.186362i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.44852 | − | 16.3653i | −0.754074 | − | 1.30609i | −0.945834 | − | 0.324652i | \(-0.894753\pi\) |
0.191760 | − | 0.981442i | \(-0.438581\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.414779 | + | 1.73205i | 0.0328941 | + | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.18964 | −0.645434 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.990927 | 0.0776154 | 0.0388077 | − | 0.999247i | \(-0.487644\pi\) | ||||
0.0388077 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.33956 | + | 5.59378i | 0.104284 | + | 0.435475i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.79948 | + | 11.7770i | 0.526160 | + | 0.911335i | 0.999536 | + | 0.0304745i | \(0.00970185\pi\) |
−0.473376 | + | 0.880860i | \(0.656965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.04241 | − | 8.73371i | 0.387878 | − | 0.671824i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.53281 | − | 1.79496i | 0.270161 | − | 0.137264i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0938942 | − | 0.162630i | 0.00713865 | − | 0.0123645i | −0.862434 | − | 0.506170i | \(-0.831061\pi\) |
0.869573 | + | 0.493805i | \(0.164394\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.596626 | − | 1.03339i | −0.0451007 | − | 0.0781167i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.6700 | − | 13.9054i | 1.10267 | − | 1.04519i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.76394 | −0.729791 | −0.364895 | − | 0.931048i | \(-0.618895\pi\) | ||||
−0.364895 | + | 0.931048i | \(0.618895\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0848 | −1.19558 | −0.597788 | − | 0.801654i | \(-0.703953\pi\) | ||||
−0.597788 | + | 0.801654i | \(0.703953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.1655 | + | 4.79852i | 1.19499 | + | 0.354717i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.66044 | − | 2.87597i | −0.122078 | − | 0.211446i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.5424 | − | 18.2600i | 0.770937 | − | 1.33530i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.09843 | − | 1.11943i | 0.443596 | − | 0.0814268i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.53281 | + | 2.65491i | −0.110910 | + | 0.192102i | −0.916138 | − | 0.400864i | \(-0.868710\pi\) |
0.805227 | + | 0.592966i | \(0.202043\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.118031 | − | 0.204436i | −0.00849609 | − | 0.0147157i | 0.861746 | − | 0.507340i | \(-0.169371\pi\) |
−0.870242 | + | 0.492624i | \(0.836038\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.83502 | − | 0.841540i | −0.203020 | − | 0.0602639i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.74474 | −0.124307 | −0.0621536 | − | 0.998067i | \(-0.519797\pi\) | ||||
−0.0621536 | + | 0.998067i | \(0.519797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7922 | 1.61570 | 0.807848 | − | 0.589390i | \(-0.200632\pi\) | ||||
0.807848 | + | 0.589390i | \(0.200632\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.2881 | − | 12.5954i | 0.937268 | − | 0.888414i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.21012 | − | 2.09599i | −0.0849339 | − | 0.147110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.16044 | + | 2.00994i | −0.0810488 | + | 0.140381i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.2553 | − | 11.2338i | −1.19932 | − | 0.780806i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.19325 | − | 3.79882i | 0.151710 | − | 0.262770i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.68872 | − | 11.5852i | −0.460470 | − | 0.797558i | 0.538514 | − | 0.842616i | \(-0.318986\pi\) |
−0.998984 | + | 0.0450587i | \(0.985653\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.429843 | + | 1.79496i | 0.0294524 | + | 0.122989i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.34916 | 0.433009 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.19686 | 0.217017 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.67004 | + | 23.6772i | 0.383146 | + | 1.59996i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.42024 | + | 9.38814i | 0.364605 | + | 0.631514i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.74293 | + | 8.21500i | −0.317610 | + | 0.550117i | −0.979989 | − | 0.199052i | \(-0.936214\pi\) |
0.662379 | + | 0.749169i | \(0.269547\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.160442 | − | 2.99571i | 0.0106961 | − | 0.199714i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.75434 | − | 3.03860i | 0.116439 | − | 0.201679i | −0.801915 | − | 0.597438i | \(-0.796185\pi\) |
0.918354 | + | 0.395759i | \(0.129519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.36330 | − | 16.2177i | −0.618744 | − | 1.07170i | −0.989715 | − | 0.143052i | \(-0.954308\pi\) |
0.370971 | − | 0.928644i | \(-0.379025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.98133 | − | 4.72168i | 0.327747 | − | 0.310664i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.15044 | 0.140880 | 0.0704401 | − | 0.997516i | \(-0.477560\pi\) | ||||
0.0704401 | + | 0.997516i | \(0.477560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7694 | 0.832984 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.34916 | + | 0.697317i | 0.152594 | + | 0.0452956i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.7977 | − | 22.1662i | −0.827813 | − | 1.43381i | −0.899751 | − | 0.436405i | \(-0.856252\pi\) |
0.0719377 | − | 0.997409i | \(-0.477082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.38197 | + | 4.12569i | −0.153436 | + | 0.265759i | −0.932488 | − | 0.361200i | \(-0.882367\pi\) |
0.779052 | + | 0.626959i | \(0.215701\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3847 | + | 6.00670i | 0.922779 | + | 0.385330i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.78807 | − | 4.82909i | 0.178124 | − | 0.308519i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.12763 | + | 1.95312i | 0.0717495 | + | 0.124274i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.6514 | − | 5.83326i | −1.24535 | − | 0.369668i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.76394 | −0.490055 | −0.245028 | − | 0.969516i | \(-0.578797\pi\) | ||||
−0.245028 | + | 0.969516i | \(0.578797\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.7922 | −1.43293 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.98133 | + | 7.56531i | −0.499810 | + | 0.473758i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.64177 | − | 16.7000i | −0.601437 | − | 1.04172i | −0.992604 | − | 0.121400i | \(-0.961262\pi\) |
0.391167 | − | 0.920320i | \(-0.372072\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.98133 | + | 3.43176i | −0.123114 | + | 0.213239i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.325421 | − | 6.07611i | 0.0201430 | − | 0.376102i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.85369 | − | 6.67479i | 0.237629 | − | 0.411585i | −0.722404 | − | 0.691471i | \(-0.756963\pi\) |
0.960033 | + | 0.279885i | \(0.0902964\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.514137 | − | 0.890511i | −0.0315832 | − | 0.0547037i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.43711 | − | 18.5287i | −0.271547 | − | 1.13394i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.1222 | 0.861044 | 0.430522 | − | 0.902580i | \(-0.358330\pi\) | ||||
0.430522 | + | 0.902580i | \(0.358330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.26434 | 0.198294 | 0.0991472 | − | 0.995073i | \(-0.468389\pi\) | ||||
0.0991472 | + | 0.995073i | \(0.468389\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.821812 | + | 3.43176i | 0.0497383 | + | 0.207699i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.66044 | − | 2.87597i | −0.100128 | − | 0.173428i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.2311 | + | 22.9170i | −0.794981 | + | 1.37695i | 0.127870 | + | 0.991791i | \(0.459186\pi\) |
−0.922851 | + | 0.385157i | \(0.874147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.73566 | + | 4.38518i | 0.403254 | + | 0.262534i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.70285 | + | 16.8058i | −0.578824 | + | 1.00255i | 0.416791 | + | 0.909002i | \(0.363155\pi\) |
−0.995615 | + | 0.0935497i | \(0.970179\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.69598 | − | 4.66958i | −0.160260 | − | 0.277578i | 0.774702 | − | 0.632326i | \(-0.217900\pi\) |
−0.934962 | + | 0.354749i | \(0.884566\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.66044 | + | 1.57389i | −0.0983561 | + | 0.0932294i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.76940 | 0.163473 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.3118 | 1.37128 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −26.9909 | − | 8.01191i | −1.58224 | − | 0.469666i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.4581 | + | 28.5063i | 0.961493 | + | 1.66536i | 0.718755 | + | 0.695264i | \(0.244712\pi\) |
0.242739 | + | 0.970092i | \(0.421954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.83502 | + | 10.1066i | −0.339728 | + | 0.588426i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.9723 | − | 3.11544i | 0.984830 | − | 0.180776i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.85916 | − | 10.1484i | 0.338844 | − | 0.586895i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.78807 | − | 6.56114i | −0.218341 | − | 0.378178i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.96265 | + | 1.17626i | 0.227648 | + | 0.0675745i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.73566 | −0.557462 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.27807 | −0.358309 | −0.179154 | − | 0.983821i | \(-0.557336\pi\) | ||||
−0.179154 | + | 0.983821i | \(0.557336\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.2739 | + | 11.6342i | −0.698240 | + | 0.661845i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2311 | − | 17.7208i | −0.580154 | − | 1.00486i | −0.995461 | − | 0.0951747i | \(-0.969659\pi\) |
0.415307 | − | 0.909681i | \(-0.363674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6887 | + | 20.2455i | −0.660685 | + | 1.14434i | 0.319751 | + | 0.947502i | \(0.396401\pi\) |
−0.980436 | + | 0.196839i | \(0.936932\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.19145 | + | 1.62152i | −0.179818 | + | 0.0913622i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.04695 | − | 1.81337i | 0.0588024 | − | 0.101849i | −0.835126 | − | 0.550059i | \(-0.814605\pi\) |
0.893928 | + | 0.448210i | \(0.147938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.36783 | − | 5.83326i | −0.188562 | − | 0.326600i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.05748 | + | 12.7675i | 0.170652 | + | 0.712614i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.38650 | 0.466638 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.70739 | 0.0947089 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.68638 | + | 27.9213i | 0.369758 | + | 1.54405i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.61856 | − | 13.1957i | −0.420025 | − | 0.727504i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1559 | + | 22.7867i | −0.723114 | + | 1.25247i | 0.236632 | + | 0.971599i | \(0.423957\pi\) |
−0.959746 | + | 0.280871i | \(0.909377\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.88197 | + | 4.51277i | −0.486729 | + | 0.247298i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.28534 | + | 9.15448i | −0.288769 | + | 0.500163i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.5333 | + | 19.9763i | 0.628261 | + | 1.08818i | 0.987901 | + | 0.155089i | \(0.0495663\pi\) |
−0.359640 | + | 0.933091i | \(0.617100\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.5051 | + | 25.1235i | −1.43956 | + | 1.36452i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.89703 | 0.481801 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0065 | −0.810276 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.3961 | + | 3.38279i | 0.613546 | + | 0.182123i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.26847 | − | 12.5894i | −0.390192 | − | 0.675833i | 0.602283 | − | 0.798283i | \(-0.294258\pi\) |
−0.992475 | + | 0.122450i | \(0.960925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4909 | − | 19.9029i | 0.615095 | − | 1.06538i | −0.375273 | − | 0.926915i | \(-0.622451\pi\) |
0.990368 | − | 0.138462i | \(-0.0442158\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.97586 | + | 8.35787i | −0.158840 | + | 0.446110i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.6983 | + | 18.5300i | −0.569414 | + | 0.986254i | 0.427210 | + | 0.904152i | \(0.359496\pi\) |
−0.996624 | + | 0.0821015i | \(0.973837\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.532810 | − | 0.922854i | −0.0282786 | − | 0.0489800i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.5798 | + | 3.73414i | 0.665791 | + | 0.197632i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.5935 | −1.19244 | −0.596220 | − | 0.802821i | \(-0.703331\pi\) | ||||
−0.596220 | + | 0.802821i | \(0.703331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2553 | −0.908172 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0355422 | − | 0.0336896i | 0.00186548 | − | 0.00176824i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.02827 | − | 12.1733i | −0.367877 | − | 0.637181i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.14631 | − | 7.18161i | 0.216435 | − | 0.374877i | −0.737280 | − | 0.675587i | \(-0.763890\pi\) |
0.953716 | + | 0.300710i | \(0.0972236\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.83502 | + | 3.79882i | 0.303759 | + | 0.197759i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.613495 | + | 1.06260i | −0.0318511 | + | 0.0551677i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.74113 | − | 16.8721i | −0.504376 | − | 0.873606i | −0.999987 | − | 0.00506088i | \(-0.998389\pi\) |
0.495611 | − | 0.868545i | \(-0.334944\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.403374 | + | 1.68443i | 0.0208301 | + | 0.0869834i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.46305 | 0.178356 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.0000 | −1.13006 | −0.565032 | − | 0.825069i | \(-0.691136\pi\) | ||||
−0.565032 | + | 0.825069i | \(0.691136\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.21646 | + | 25.9590i | 0.318479 | + | 1.32992i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.75980 | + | 9.97627i | 0.294312 | + | 0.509763i | 0.974825 | − | 0.222973i | \(-0.0715762\pi\) |
−0.680513 | + | 0.732736i | \(0.738243\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.98133 | + | 3.43176i | −0.100978 | + | 0.174899i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.01867 | − | 19.0202i | 0.0517821 | − | 0.966852i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.1887 | − | 19.3794i | 0.567290 | − | 0.982576i | −0.429542 | − | 0.903047i | \(-0.641325\pi\) |
0.996833 | − | 0.0795290i | \(-0.0253416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.7881 | − | 37.7381i | −1.10187 | − | 1.90850i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.22153 | − | 4.00148i | 0.212948 | − | 0.201848i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.41478 | −0.0711852 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.34009 | −0.468765 | −0.234383 | − | 0.972144i | \(-0.575307\pi\) | ||||
−0.234383 | + | 0.972144i | \(0.575307\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.61710 | + | 0.776853i | 0.131019 | + | 0.0388913i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.86330 | + | 8.42347i | 0.242861 | + | 0.420648i | 0.961528 | − | 0.274706i | \(-0.0885807\pi\) |
−0.718667 | + | 0.695355i | \(0.755247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.28715 | + | 3.96145i | −0.113931 | + | 0.197334i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.94852 | − | 0.961276i | −0.444655 | − | 0.0477662i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.51414 | + | 9.55077i | −0.273326 | + | 0.473414i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.09389 | − | 8.82288i | −0.251877 | − | 0.436264i | 0.712166 | − | 0.702011i | \(-0.247714\pi\) |
−0.964043 | + | 0.265748i | \(0.914381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.6418 | + | 3.75255i | 0.623572 | + | 0.185099i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.9253 | 0.685220 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.8350 | 0.580958 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.6983 | + | 15.8279i | −0.817720 | + | 0.775097i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00960 | + | 10.4089i | 0.293588 | + | 0.508510i | 0.974655 | − | 0.223711i | \(-0.0718172\pi\) |
−0.681067 | + | 0.732221i | \(0.738484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.73566 | + | 16.8627i | −0.474487 | + | 0.821836i | −0.999573 | − | 0.0292132i | \(-0.990700\pi\) |
0.525086 | + | 0.851049i | \(0.324033\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.04875 | − | 38.2534i | 0.0996137 | − | 1.85994i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.17458 | − | 5.49853i | 0.153990 | − | 0.266718i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.80855 | + | 10.0607i | 0.281096 | + | 0.486872i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.28715 | + | 9.55077i | 0.110424 | + | 0.461115i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.8296 | 0.810651 | 0.405326 | − | 0.914172i | \(-0.367158\pi\) | ||||
0.405326 | + | 0.914172i | \(0.367158\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.40571 | −0.403952 | −0.201976 | − | 0.979390i | \(-0.564736\pi\) | ||||
−0.201976 | + | 0.979390i | \(0.564736\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.818153 | + | 3.41648i | 0.0392274 | + | 0.163808i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.53281 | − | 7.85106i | −0.216834 | − | 0.375567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.5424 | + | 25.1882i | −0.694071 | + | 1.20217i | 0.276421 | + | 0.961037i | \(0.410851\pi\) |
−0.970493 | + | 0.241130i | \(0.922482\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.0192 | − | 9.12704i | −0.667581 | − | 0.434621i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.09209 | − | 12.2839i | 0.336955 | − | 0.583624i | −0.646903 | − | 0.762572i | \(-0.723936\pi\) |
0.983858 | + | 0.178948i | \(0.0572695\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.50000 | + | 9.52628i | 0.260725 | + | 0.451589i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.6158 | + | 21.4370i | −1.06969 | + | 1.01394i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.6874 | −1.25946 | −0.629728 | − | 0.776816i | \(-0.716834\pi\) | ||||
−0.629728 | + | 0.776816i | \(0.716834\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.70739 | 0.362927 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.4112 | − | 4.27777i | −0.677096 | − | 0.200987i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.01867 | − | 1.76439i | −0.0477561 | − | 0.0827161i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.95305 | + | 13.7751i | −0.372028 | + | 0.644372i | −0.989877 | − | 0.141925i | \(-0.954671\pi\) |
0.617849 | + | 0.786297i | \(0.288004\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.3829 | + | 25.1235i | 0.998068 | + | 1.17266i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0333 | − | 32.9667i | 0.886471 | − | 1.53541i | 0.0424525 | − | 0.999098i | \(-0.486483\pi\) |
0.844018 | − | 0.536314i | \(-0.180184\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9723 | − | 31.1289i | −0.835241 | − | 1.44668i | −0.893834 | − | 0.448399i | \(-0.851994\pi\) |
0.0585922 | − | 0.998282i | \(-0.481339\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.44852 | − | 1.32048i | −0.206295 | − | 0.0612360i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.4623 | 1.22453 | 0.612264 | − | 0.790654i | \(-0.290259\pi\) | ||||
0.612264 | + | 0.790654i | \(0.290259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.6135 | 0.582437 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.7549 | − | 22.5167i | 1.09457 | − | 1.03751i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.5424 | − | 18.2600i | −0.484741 | − | 0.839595i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.660442 | − | 1.14392i | 0.0303032 | − | 0.0524866i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.75020 | + | 1.39733i | −0.125923 | + | 0.0639792i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.0565 | − | 33.0069i | 0.870716 | − | 1.50812i | 0.00945845 | − | 0.999955i | \(-0.496989\pi\) |
0.861257 | − | 0.508169i | \(-0.169677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.83502 | − | 4.91040i | −0.129266 | − | 0.223895i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.30349 | − | 13.7948i | −0.150314 | − | 0.627687i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.2553 | 0.738114 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.6610 | −1.75190 | −0.875948 | − | 0.482406i | \(-0.839763\pi\) | ||||
−0.875948 | + | 0.482406i | \(0.839763\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.399714 | + | 1.66914i | 0.0180757 | + | 0.0754813i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8633 | + | 27.4760i | 0.715900 | + | 1.23998i | 0.962611 | + | 0.270887i | \(0.0873169\pi\) |
−0.246711 | + | 0.969089i | \(0.579350\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.43892 | − | 11.1525i | 0.289994 | − | 0.502285i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.88197 | + | 4.51277i | −0.399215 | + | 0.202834i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.635777 | + | 1.10120i | −0.0285185 | + | 0.0493955i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.2407 | + | 33.3259i | 0.861333 | + | 1.49187i | 0.870642 | + | 0.491916i | \(0.163703\pi\) |
−0.00930924 | + | 0.999957i | \(0.502963\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.0948 | + | 16.2038i | −0.763740 | + | 0.723931i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.0994 | −0.494896 | −0.247448 | − | 0.968901i | \(-0.579592\pi\) | ||||
−0.247448 | + | 0.968901i | \(0.579592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.38650 | −0.106198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.7453 | + | 4.97062i | 0.743683 | + | 0.220753i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.2639 | − | 22.9738i | −0.587914 | − | 1.01830i | −0.994505 | − | 0.104686i | \(-0.966616\pi\) |
0.406592 | − | 0.913610i | \(-0.366717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.38650 | + | 14.5259i | −0.370997 | + | 0.642586i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.44852 | + | 5.22672i | 0.196407 | + | 0.230765i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.88197 | − | 8.45582i | 0.215125 | − | 0.372608i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.2029 | − | 36.7244i | −0.932500 | − | 1.61514i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.311812 | + | 0.0925573i | 0.0136870 | + | 0.00406282i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.89703 | −0.433597 | −0.216798 | − | 0.976216i | \(-0.569561\pi\) | ||||
−0.216798 | + | 0.976216i | \(0.569561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.4394 | −1.24357 | −0.621785 | − | 0.783188i | \(-0.713592\pi\) | ||||
−0.621785 | + | 0.783188i | \(0.713592\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.50000 | − | 1.42181i | 0.0654654 | − | 0.0620530i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.50506 | + | 14.7312i | 0.370486 | + | 0.641701i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.0524 | + | 20.8754i | −0.524018 | + | 0.907626i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.3401 | + | 19.1015i | 1.27325 | + | 0.828936i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.98133 | + | 3.43176i | −0.0858208 | + | 0.148646i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.78988 | − | 6.56426i | −0.163851 | − | 0.283798i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.93852 | − | 16.4466i | −0.169960 | − | 0.709724i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.5177 | −0.797616 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1131 | 0.563776 | 0.281888 | − | 0.959447i | \(-0.409039\pi\) | ||||
0.281888 | + | 0.959447i | \(0.409039\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.48820 | − | 27.0937i | −0.278435 | − | 1.16270i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.28807 | − | 14.3554i | −0.355022 | − | 0.614916i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.3660 | − | 21.4186i | 0.528733 | − | 0.915793i | −0.470705 | − | 0.882290i | \(-0.656001\pi\) |
0.999439 | − | 0.0335023i | \(-0.0106661\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.56201 | + | 29.1652i | −0.0666650 | + | 1.24474i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.33956 | − | 2.32018i | 0.0570671 | − | 0.0988431i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.844094 | + | 1.46201i | 0.0358945 | + | 0.0621712i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.17458 | − | 3.95698i | 0.177201 | − | 0.167965i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.7730 | 0.964923 | 0.482462 | − | 0.875917i | \(-0.339743\pi\) | ||||
0.482462 | + | 0.875917i | \(0.339743\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.8405 | 0.458504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.0101 | + | 10.3923i | 1.47813 | + | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.7056 | + | 25.4708i | 0.619767 | + | 1.07347i | 0.989528 | + | 0.144340i | \(0.0461060\pi\) |
−0.369762 | + | 0.929127i | \(0.620561\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.5424 | − | 18.2600i | 0.443523 | − | 0.768204i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.34555 | + | 9.82080i | 0.182496 | + | 0.412435i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.2835 | − | 31.6680i | 0.766486 | − | 1.32759i | −0.172972 | − | 0.984927i | \(-0.555337\pi\) |
0.939457 | − | 0.342666i | \(-0.111330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.18779 | + | 3.78936i | 0.0915561 | + | 0.158580i | 0.908166 | − | 0.418610i | \(-0.137483\pi\) |
−0.816610 | + | 0.577190i | \(0.804149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.09029 | − | 1.51099i | −0.212650 | − | 0.0631223i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.86330 | −0.286219 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.02827 | 0.375852 | 0.187926 | − | 0.982183i | \(-0.439823\pi\) | ||||
0.187926 | + | 0.982183i | \(0.439823\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.296747 | − | 0.281280i | 0.0123324 | − | 0.0116896i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.06108 | − | 12.2302i | −0.292943 | − | 0.507392i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.70739 | + | 2.95729i | −0.0707128 | + | 0.122478i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.273937 | − | 5.11484i | 0.0113259 | − | 0.211473i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.63397 | + | 2.83012i | −0.0674413 | + | 0.116812i | −0.897774 | − | 0.440456i | \(-0.854817\pi\) |
0.830333 | + | 0.557267i | \(0.188150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.76940 | + | 3.06469i | 0.0729069 | + | 0.126278i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.703781 | − | 2.93888i | −0.0289497 | − | 0.120889i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.39558 | 0.139440 | 0.0697198 | − | 0.997567i | \(-0.477789\pi\) | ||||
0.0697198 | + | 0.997567i | \(0.477789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.57615 | −0.310592 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.19378 | + | 38.3918i | 0.376276 | + | 1.57127i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.301683 | + | 0.522531i | 0.0123264 | + | 0.0213500i | 0.872123 | − | 0.489287i | \(-0.162743\pi\) |
−0.859796 | + | 0.510637i | \(0.829410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.9627 | − | 36.3084i | 0.855084 | − | 1.48105i | −0.0214822 | − | 0.999769i | \(-0.506839\pi\) |
0.876567 | − | 0.481281i | \(-0.159828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.5761 | + | 17.3021i | 1.08226 | + | 0.704596i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0141369 | + | 0.0244859i | −0.000574748 | + | 0.000995493i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.71466 | − | 4.70193i | −0.110185 | − | 0.190845i | 0.805660 | − | 0.592378i | \(-0.201811\pi\) |
−0.915845 | + | 0.401533i | \(0.868478\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.04241 | − | 2.88383i | 0.123285 | − | 0.116859i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.8023 | 0.882028 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.42385 | 0.0978984 | 0.0489492 | − | 0.998801i | \(-0.484413\pi\) | ||||
0.0489492 | + | 0.998801i | \(0.484413\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.85369 | − | 1.14392i | −0.155396 | − | 0.0461273i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.5424 | − | 25.1882i | −0.585455 | − | 1.01404i | −0.994818 | − | 0.101667i | \(-0.967582\pi\) |
0.409363 | − | 0.912372i | \(-0.365751\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.72606 | − | 6.45373i | 0.149763 | − | 0.259397i | −0.781377 | − | 0.624060i | \(-0.785482\pi\) |
0.931140 | + | 0.364662i | \(0.118816\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.9623 | − | 33.5966i | 0.480029 | − | 1.34819i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.56289 | − | 11.3673i | 0.262937 | − | 0.455419i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.28354 | + | 2.16202i | 0.290876 | + | 0.0863429i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0848 | −0.840707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.8013 | 1.10675 | 0.553376 | − | 0.832932i | \(-0.313339\pi\) | ||||
0.553376 | + | 0.832932i | \(0.313339\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.8163 | − | 15.9398i | 0.668390 | − | 0.633551i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.70559 | − | 13.3465i | −0.305787 | − | 0.529638i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.76033 | − | 8.24513i | 0.188611 | − | 0.326684i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.85009 | + | 1.44808i | −0.112748 | + | 0.0572851i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0237 | + | 29.4860i | −0.672397 | + | 1.16463i | 0.304825 | + | 0.952408i | \(0.401402\pi\) |
−0.977222 | + | 0.212218i | \(0.931931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.92711 | − | 11.9981i | −0.273179 | − | 0.473159i | 0.696495 | − | 0.717561i | \(-0.254742\pi\) |
−0.969674 | + | 0.244402i | \(0.921408\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.56108 | + | 10.6947i | 0.100843 | + | 0.421103i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.11750 | 0.201190 | 0.100595 | − | 0.994927i | \(-0.467925\pi\) | ||||
0.100595 | + | 0.994927i | \(0.467925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.7549 | 1.52126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.28953 | + | 5.38487i | 0.0505407 | + | 0.211050i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.69779 | + | 6.40476i | 0.144706 | + | 0.250638i | 0.929263 | − | 0.369419i | \(-0.120443\pi\) |
−0.784557 | + | 0.620056i | \(0.787110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.67912 | + | 2.90831i | −0.0656085 | + | 0.113637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −37.5953 | + | 19.1015i | −1.46673 | + | 0.745222i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.54241 | + | 14.7959i | −0.332765 | + | 0.576366i | −0.983053 | − | 0.183322i | \(-0.941315\pi\) |
0.650288 | + | 0.759688i | \(0.274648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.3118 | + | 33.4490i | 0.751142 | + | 1.30102i | 0.947269 | + | 0.320438i | \(0.103830\pi\) |
−0.196127 | + | 0.980579i | \(0.562836\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.6272 | + | 12.9169i | −0.529238 | + | 0.501652i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.57615 | −0.0611204 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.9206 | −0.539009 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.7507 | − | 4.67540i | −0.608958 | − | 0.180761i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.1655 | + | 27.9995i | 0.624062 | + | 1.08091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2649 | + | 22.9754i | −0.511323 | + | 0.885637i | 0.488591 | + | 0.872513i | \(0.337511\pi\) |
−0.999914 | + | 0.0131244i | \(0.995822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.11076 | − | 0.938136i | 0.196713 | − | 0.0361089i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.0096 | + | 32.9256i | −0.730598 | + | 1.26543i | 0.226030 | + | 0.974120i | \(0.427425\pi\) |
−0.956628 | + | 0.291313i | \(0.905908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.69832 | − | 16.7980i | −0.372187 | − | 0.644647i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.82595 | + | 1.72936i | 0.223251 | + | 0.0662691i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.23606 | −0.238616 | −0.119308 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119308 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.61350 | −0.290897 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.5406 | − | 22.3136i | 0.898130 | − | 0.851316i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.877832 | − | 1.52045i | −0.0334427 | − | 0.0579245i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.58522 | − | 2.74568i | 0.0603047 | − | 0.104451i | −0.834297 | − | 0.551315i | \(-0.814126\pi\) |
0.894602 | + | 0.446865i | \(0.147459\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.96265 | + | 6.48607i | 0.378450 | + | 0.246386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.64177 | − | 11.5039i | 0.251937 | − | 0.436367i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.36783 | + | 12.7615i | 0.279077 | + | 0.483375i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.867432 | + | 3.62226i | 0.0328093 | + | 0.137006i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.5863 | 1.94839 | 0.974193 | − | 0.225715i | \(-0.0724718\pi\) | ||||
0.974193 | + | 0.225715i | \(0.0724718\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.38650 | −0.165440 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.15084 | + | 21.5091i | 0.193992 | + | 0.810080i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.42385 | + | 2.46618i | 0.0535494 | + | 0.0927504i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.42892 | + | 11.1352i | −0.241443 | + | 0.418192i | −0.961126 | − | 0.276112i | \(-0.910954\pi\) |
0.719683 | + | 0.694303i | \(0.244287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.226990 | + | 4.23826i | −0.00851280 | + | 0.158947i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.19378 | − | 15.9241i | 0.344310 | − | 0.596362i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.83502 | − | 4.91040i | −0.106024 | − | 0.183639i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.1751 | − | 30.4980i | 1.20160 | − | 1.13897i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.84049 | −0.180520 | −0.0902598 | − | 0.995918i | \(-0.528770\pi\) | ||||
−0.0902598 | + | 0.995918i | \(0.528770\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6508 | −0.433900 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.91024 | − | 2.34805i | −0.294185 | − | 0.0873250i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.01414 | − | 1.75654i | −0.0376641 | − | 0.0652361i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.5351 | + | 35.5679i | −0.761606 | + | 1.31914i | 0.180416 | + | 0.983590i | \(0.442256\pi\) |
−0.942022 | + | 0.335550i | \(0.891078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.31542 | + | 26.6529i | −0.159830 | + | 0.987144i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.1559 | − | 34.9111i | 0.745493 | − | 1.29123i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.6983 | − | 30.6544i | −0.653702 | − | 1.13225i | −0.982217 | − | 0.187747i | \(-0.939882\pi\) |
0.328515 | − | 0.944499i | \(-0.393452\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.25887 | + | 2.74838i | 0.341519 | + | 0.101375i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.1040 | 1.29307 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.4823 | 0.716666 | 0.358333 | − | 0.933594i | \(-0.383345\pi\) | ||||
0.358333 | + | 0.933594i | \(0.383345\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.83502 | + | 2.68725i | −0.104147 | + | 0.0987185i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.10169 | − | 14.0325i | −0.297222 | − | 0.514804i | 0.678277 | − | 0.734806i | \(-0.262727\pi\) |
−0.975499 | + | 0.220002i | \(0.929394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.99546 | − | 15.5806i | 0.329568 | − | 0.570829i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.89884 | − | 35.4543i | 0.0694748 | − | 1.29720i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.52228 | + | 7.83282i | −0.165241 | + | 0.286205i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.17458 | + | 12.4267i | 0.261804 | + | 0.453458i | 0.966721 | − | 0.255832i | \(-0.0823492\pi\) |
−0.704917 | + | 0.709290i | \(0.749016\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.13177 | − | 13.0778i | −0.114128 | − | 0.476581i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.67912 | 0.315865 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.7466 | 0.608665 | 0.304333 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304333 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.19378 | − | 38.3918i | −0.333713 | − | 1.39353i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.81542 | + | 17.0008i | 0.355809 | + | 0.616279i | 0.987256 | − | 0.159140i | \(-0.0508721\pi\) |
−0.631447 | + | 0.775419i | \(0.717539\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.88976 | + | 17.1296i | −0.358034 | + | 0.620132i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.9627 | − | 10.3923i | −0.577131 | − | 0.375735i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.96265 | + | 17.2558i | −0.359731 | + | 0.623072i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.4572 | + | 37.1649i | 0.773766 | + | 1.34020i | 0.935485 | + | 0.353365i | \(0.114963\pi\) |
−0.161719 | + | 0.986837i | \(0.551704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.2407 | − | 22.9772i | 0.873008 | − | 0.827504i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.22699 | −0.259937 | −0.129968 | − | 0.991518i | \(-0.541488\pi\) | ||||
−0.129968 | + | 0.991518i | \(0.541488\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.67912 | 0.0962367 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.57976 | − | 1.95312i | −0.236047 | − | 0.0700676i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.53281 | + | 2.65491i | 0.0549186 | + | 0.0951218i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.76940 | + | 3.06469i | −0.0633141 | + | 0.109663i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.3660 | − | 1.90280i | 0.370452 | − | 0.0680004i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.44852 | + | 16.3653i | −0.337232 | + | 0.584103i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.1180 | + | 26.1852i | 0.538900 | + | 0.933402i | 0.998964 | + | 0.0455158i | \(0.0144931\pi\) |
−0.460064 | + | 0.887886i | \(0.652174\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.7977 | + | 3.79882i | 0.455609 | + | 0.135242i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.1595 | −0.894569 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.6226 | −0.590285 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.29261 | − | 1.22523i | 0.0458442 | − | 0.0434546i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.7079 | + | 23.7428i | 0.485559 | + | 0.841013i | 0.999862 | − | 0.0165951i | \(-0.00528264\pi\) |
−0.514303 | + | 0.857609i | \(0.671949\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.5375 | − | 70.2130i | 1.43411 | − | 2.48396i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.4204 | − | 14.9480i | 1.03952 | − | 0.528161i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.3401 | + | 40.4262i | −0.823654 | + | 1.42661i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.09482 | + | 7.09244i | 0.144324 | + | 0.249976i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.69651 | + | 23.7877i | 0.200527 | + | 0.837368i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.1806 | 0.990776 | 0.495388 | − | 0.868672i | \(-0.335026\pi\) | ||||
0.495388 | + | 0.868672i | \(0.335026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.1312 | −0.706903 | −0.353452 | − | 0.935453i | \(-0.614992\pi\) | ||||
−0.353452 | + | 0.935453i | \(0.614992\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.31675 | + | 5.49853i | 0.0461804 | + | 0.192842i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.495464 | − | 0.858168i | −0.0173553 | − | 0.0300603i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.19325 | − | 7.26293i | 0.146703 | − | 0.254098i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.44904 | + | 2.76856i | −0.190405 | + | 0.0967414i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.12310 | + | 10.6055i | −0.213698 | + | 0.370135i | −0.952869 | − | 0.303382i | \(-0.901884\pi\) |
0.739171 | + | 0.673517i | \(0.235217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9645 | − | 24.1872i | −0.486770 | − | 0.843111i | 0.513114 | − | 0.858321i | \(-0.328492\pi\) |
−0.999884 | + | 0.0152094i | \(0.995158\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.17458 | − | 3.95698i | 0.145340 | − | 0.137764i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.57068 | −0.298032 | −0.149016 | − | 0.988835i | \(-0.547611\pi\) | ||||
−0.149016 | + | 0.988835i | \(0.547611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7357 | −0.685448 | −0.342724 | − | 0.939436i | \(-0.611350\pi\) | ||||
−0.342724 | + | 0.939436i | \(0.611350\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.9390 | − | 13.0427i | −1.52423 | − | 0.452448i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.7019 | − | 30.6606i | −0.613335 | − | 1.06233i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.79948 | − | 11.7770i | 0.235306 | − | 0.407561i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.66951 | + | 13.1146i | −0.161402 | + | 0.453307i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.3588 | − | 40.4586i | 0.806434 | − | 1.39678i | −0.108885 | − | 0.994054i | \(-0.534728\pi\) |
0.915319 | − | 0.402730i | \(-0.131939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4431 | + | 21.5520i | 0.429071 | + | 0.743172i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.2221 | − | 9.56470i | −1.10979 | − | 0.329426i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0848 | −0.346928 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0337379 | 0.00115925 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.77807 | − | 6.42477i | 0.232623 | − | 0.220498i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3961 | + | 19.7386i | 0.390653 | + | 0.676632i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.69779 | + | 4.67271i | −0.0923705 | + | 0.159990i | −0.908508 | − | 0.417867i | \(-0.862778\pi\) |
0.816138 | + | 0.577858i | \(0.196111\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.32088 | − | 2.16202i | −0.113572 | − | 0.0739397i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.3359 | + | 24.8306i | −0.489707 | + | 0.848197i | −0.999930 | − | 0.0118452i | \(-0.996229\pi\) |
0.510223 | + | 0.860042i | \(0.329563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.3733 | + | 19.6991i | 0.388052 | + | 0.672125i | 0.992187 | − | 0.124756i | \(-0.0398148\pi\) |
−0.604136 | + | 0.796882i | \(0.706481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.11710 | + | 4.66485i | 0.0380708 | + | 0.158978i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.202325 | 0.00688723 | 0.00344361 | − | 0.999994i | \(-0.498904\pi\) | ||||
0.00344361 | + | 0.999994i | \(0.498904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.187788 | −0.00638500 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.40337 | + | 39.2670i | 0.319355 | + | 1.33358i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.34916 | + | 4.06886i | 0.0796897 | + | 0.138027i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.02414 | + | 15.6303i | −0.305771 | + | 0.529611i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.60803 | − | 48.6960i | 0.0882685 | − | 1.64811i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.596626 | + | 1.03339i | −0.0201696 | + | 0.0349349i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.48639 | − | 11.2348i | −0.219030 | − | 0.379371i | 0.735482 | − | 0.677545i | \(-0.236956\pi\) |
−0.954512 | + | 0.298174i | \(0.903623\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.3780 | + | 39.2212i | −1.39564 | + | 1.32290i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.4905 | 0.555580 | 0.277790 | − | 0.960642i | \(-0.410398\pi\) | ||||
0.277790 | + | 0.960642i | \(0.410398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.38290 | 0.282107 | 0.141053 | − | 0.990002i | \(-0.454951\pi\) | ||||
0.141053 | + | 0.990002i | \(0.454951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.3774 | − | 5.75194i | −0.651365 | − | 0.193349i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.2311 | − | 50.6298i | −0.981485 | − | 1.69998i | −0.656619 | − | 0.754222i | \(-0.728014\pi\) |
−0.324866 | − | 0.945760i | \(-0.605319\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.19471 | + | 15.9257i | −0.308381 | + | 0.534131i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.0939 | + | 27.3318i | 0.405161 | + | 0.915650i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.43345 | − | 14.6072i | 0.282215 | − | 0.488810i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.88197 | + | 8.45582i | 0.163186 | + | 0.282647i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.4576 | + | 5.77573i | 0.649670 | + | 0.192846i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.43398 | 0.181233 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.52867 | −0.217502 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.52374 | − | 9.02732i | 0.316930 | − | 0.300410i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.04241 | + | 13.9299i | 0.267339 | + | 0.463044i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.3510 | − | 26.5886i | 0.509720 | − | 0.882862i | −0.490216 | − | 0.871601i | \(-0.663082\pi\) |
0.999937 | − | 0.0112607i | \(-0.00358447\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.382896 | + | 7.14927i | −0.0126999 | + | 0.237126i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.1559 | + | 29.7149i | −0.568401 | + | 0.984499i | 0.428324 | + | 0.903625i | \(0.359104\pi\) |
−0.996724 | + | 0.0808733i | \(0.974229\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.6514 | − | 34.0372i | −0.650365 | − | 1.12647i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.92711 | − | 16.3990i | −0.129826 | − | 0.542134i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.00722 | 0.132330 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.8861 | 0.622995 | 0.311498 | − | 0.950247i | \(-0.399169\pi\) | ||||
0.311498 | + | 0.950247i | \(0.399169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.53241 | − | 10.5749i | −0.0834458 | − | 0.348456i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.909714 | − | 1.57567i | −0.0299436 | − | 0.0518639i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.66044 | + | 2.87597i | −0.0545950 | + | 0.0945613i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.5479 | − | 15.9816i | −0.806258 | − | 0.524905i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.04748 | + | 7.01043i | −0.132793 | + | 0.230005i | −0.924752 | − | 0.380569i | \(-0.875728\pi\) |
0.791959 | + | 0.610574i | \(0.209061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.68272 | − | 6.37867i | −0.120696 | − | 0.209052i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.7225 | − | 24.3817i | 0.842115 | − | 0.798221i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.0848 | −0.689547 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.7084 | 0.970533 | 0.485266 | − | 0.874366i | \(-0.338723\pi\) | ||||
0.485266 | + | 0.874366i | \(0.338723\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.8169 | − | 11.5223i | −1.26674 | − | 0.376016i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.24113 | − | 9.07790i | −0.170856 | − | 0.295931i | 0.767863 | − | 0.640614i | \(-0.221320\pi\) |
−0.938719 | + | 0.344682i | \(0.887987\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.96446 | − | 13.7948i | 0.259358 | − | 0.449222i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.01867 | − | 4.72168i | −0.130727 | − | 0.153596i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.32815 | − | 4.03248i | 0.0756548 | − | 0.131038i | −0.825716 | − | 0.564086i | \(-0.809229\pi\) |
0.901371 | + | 0.433048i | \(0.142562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | − | 20.7846i | −0.389536 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.47679 | + | 1.03204i | 0.112743 | + | 0.0334662i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.9445 | −0.710852 | −0.355426 | − | 0.934704i | \(-0.615664\pi\) | ||||
−0.355426 | + | 0.934704i | \(0.615664\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.06562 | 0.0992011 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.46719 | − | 8.02584i | 0.273705 | − | 0.259439i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.54241 | + | 7.86769i | 0.146682 | + | 0.254061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.9112 | − | 20.6308i | 0.384231 | − | 0.665508i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.2727 | + | 10.3002i | −0.653277 | + | 0.331919i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.118031 | + | 0.204436i | −0.00379957 | + | 0.00658104i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3515 | + | 52.5703i | 0.976038 | + | 1.69055i | 0.676466 | + | 0.736474i | \(0.263511\pi\) |
0.299572 | + | 0.954074i | \(0.403156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.38290 | + | 14.1264i | 0.108674 | + | 0.453807i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.9053 | −1.24853 | −0.624265 | − | 0.781212i | \(-0.714602\pi\) | ||||
−0.624265 | + | 0.781212i | \(0.714602\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.8506 | −0.508147 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.688716 | + | 2.87597i | 0.0220566 | + | 0.0921048i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.20832 | + | 12.4852i | 0.230614 | + | 0.399436i | 0.957989 | − | 0.286805i | \(-0.0925930\pi\) |
−0.727375 | + | 0.686241i | \(0.759260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.2649 | − | 31.6357i | 0.583748 | − | 1.01108i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.3342 | + | 22.5254i | −1.41548 | + | 0.719182i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.9512 | − | 22.4322i | 0.413081 | − | 0.715477i | −0.582144 | − | 0.813086i | \(-0.697786\pi\) |
0.995225 | + | 0.0976089i | \(0.0311194\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.872368 | + | 1.51099i | 0.0277960 | + | 0.0481440i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.1541 | − | 18.1557i | 0.609682 | − | 0.577903i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.5761 | −1.38564 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.1987 | 0.832230 | 0.416115 | − | 0.909312i | \(-0.363391\pi\) | ||||
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.6892 | − | 12.9686i | −1.38644 | − | 0.411546i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.3961 | − | 19.7386i | −0.361281 | − | 0.625757i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.3829 | − | 21.4478i | 0.392170 | − | 0.679259i | −0.600565 | − | 0.799576i | \(-0.705058\pi\) |
0.992736 | + | 0.120317i | \(0.0383911\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.1842 | − | 13.1407i | −0.353852 | − | 0.415753i |
(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 | 720.2.q.j.241.2 | 6 | ||
3.2 | odd | 2 | 2160.2.q.j.721.2 | 6 | |||
4.3 | odd | 2 | 360.2.q.d.241.2 | yes | 6 | ||
9.2 | odd | 6 | 6480.2.a.bu.1.2 | 3 | |||
9.4 | even | 3 | inner | 720.2.q.j.481.2 | 6 | ||
9.5 | odd | 6 | 2160.2.q.j.1441.2 | 6 | |||
9.7 | even | 3 | 6480.2.a.bx.1.2 | 3 | |||
12.11 | even | 2 | 1080.2.q.d.721.2 | 6 | |||
36.7 | odd | 6 | 3240.2.a.r.1.2 | 3 | |||
36.11 | even | 6 | 3240.2.a.q.1.2 | 3 | |||
36.23 | even | 6 | 1080.2.q.d.361.2 | 6 | |||
36.31 | odd | 6 | 360.2.q.d.121.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.d.121.2 | ✓ | 6 | 36.31 | odd | 6 | ||
360.2.q.d.241.2 | yes | 6 | 4.3 | odd | 2 | ||
720.2.q.j.241.2 | 6 | 1.1 | even | 1 | trivial | ||
720.2.q.j.481.2 | 6 | 9.4 | even | 3 | inner | ||
1080.2.q.d.361.2 | 6 | 36.23 | even | 6 | |||
1080.2.q.d.721.2 | 6 | 12.11 | even | 2 | |||
2160.2.q.j.721.2 | 6 | 3.2 | odd | 2 | |||
2160.2.q.j.1441.2 | 6 | 9.5 | odd | 6 | |||
3240.2.a.q.1.2 | 3 | 36.11 | even | 6 | |||
3240.2.a.r.1.2 | 3 | 36.7 | odd | 6 | |||
6480.2.a.bu.1.2 | 3 | 9.2 | odd | 6 | |||
6480.2.a.bx.1.2 | 3 | 9.7 | even | 3 |