Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(557,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.s (of order \(6\), 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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 863.1 | ||
Root | \(-1.00781 + 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.863 |
Dual form | 882.3.s.e.557.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | −5.25600 | − | 3.03455i | −1.05120 | − | 0.606910i | −0.128214 | − | 0.991746i | \(-0.540925\pi\) |
−0.922985 | + | 0.384836i | \(0.874258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.29150 | + | 7.43310i | 0.429150 | + | 0.743310i | ||||
\(11\) | 10.5120 | − | 6.06910i | 0.955636 | − | 0.551736i | 0.0608086 | − | 0.998149i | \(-0.480632\pi\) |
0.894827 | + | 0.446413i | \(0.147299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.5830 | −1.42946 | −0.714731 | − | 0.699399i | \(-0.753451\pi\) | ||||
−0.714731 | + | 0.699399i | \(0.753451\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 9.44094 | − | 5.45073i | 0.555350 | − | 0.320631i | −0.195927 | − | 0.980618i | \(-0.562772\pi\) |
0.751277 | + | 0.659987i | \(0.229438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.0000 | + | 17.3205i | −0.526316 | + | 0.911606i | 0.473214 | + | 0.880947i | \(0.343094\pi\) |
−0.999530 | + | 0.0306583i | \(0.990240\pi\) | |||||||
\(20\) | − | 12.1382i | − | 0.606910i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17.1660 | −0.780273 | ||||||||
\(23\) | −10.5120 | − | 6.06910i | −0.457043 | − | 0.263874i | 0.253757 | − | 0.967268i | \(-0.418334\pi\) |
−0.710800 | + | 0.703394i | \(0.751667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.91699 | + | 10.2485i | 0.236680 | + | 0.409941i | ||||
\(26\) | 22.7594 | + | 13.1402i | 0.875363 | + | 0.505391i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 41.8367i | − | 1.44264i | −0.692600 | − | 0.721322i | \(-0.743535\pi\) | ||
0.692600 | − | 0.721322i | \(-0.256465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.5830 | − | 21.7944i | −0.405903 | − | 0.703045i | 0.588523 | − | 0.808481i | \(-0.299710\pi\) |
−0.994426 | + | 0.105435i | \(0.966376\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −15.4170 | −0.453441 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.0000 | + | 32.9090i | −0.513514 | + | 0.889431i | 0.486364 | + | 0.873757i | \(0.338323\pi\) |
−0.999877 | + | 0.0156750i | \(0.995010\pi\) | |||||||
\(38\) | 24.4949 | − | 14.1421i | 0.644603 | − | 0.372161i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.58301 | + | 14.8662i | −0.214575 | + | 0.371655i | ||||
\(41\) | 60.6337i | 1.47887i | 0.673227 | + | 0.739435i | \(0.264908\pi\) | ||||
−0.673227 | + | 0.739435i | \(0.735092\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 83.4980 | 1.94181 | 0.970907 | − | 0.239455i | \(-0.0769689\pi\) | ||||
0.970907 | + | 0.239455i | \(0.0769689\pi\) | |||||||
\(44\) | 21.0240 | + | 12.1382i | 0.477818 | + | 0.275868i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.58301 | + | 14.8662i | 0.186587 | + | 0.323178i | ||||
\(47\) | −14.6969 | − | 8.48528i | −0.312701 | − | 0.180538i | 0.335434 | − | 0.942064i | \(-0.391117\pi\) |
−0.648134 | + | 0.761526i | \(0.724451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 16.7358i | − | 0.334716i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −18.5830 | − | 32.1867i | −0.357365 | − | 0.618975i | ||||
\(53\) | −81.4431 | + | 47.0212i | −1.53666 | + | 0.887193i | −0.537632 | + | 0.843180i | \(0.680681\pi\) |
−0.999031 | + | 0.0440129i | \(0.985986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −73.6680 | −1.33942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −29.5830 | + | 51.2393i | −0.510052 | + | 0.883436i | ||||
\(59\) | 50.4179 | − | 29.1088i | 0.854540 | − | 0.493369i | −0.00764008 | − | 0.999971i | \(-0.502432\pi\) |
0.862180 | + | 0.506602i | \(0.169099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.83399 | + | 13.5689i | −0.128426 | + | 0.222440i | −0.923067 | − | 0.384639i | \(-0.874326\pi\) |
0.794641 | + | 0.607080i | \(0.207659\pi\) | |||||||
\(62\) | 35.5901i | 0.574034i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 97.6722 | + | 56.3911i | 1.50265 | + | 0.867555i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66.3320 | + | 114.890i | 0.990030 | + | 1.71478i | 0.617000 | + | 0.786964i | \(0.288348\pi\) |
0.373031 | + | 0.927819i | \(0.378319\pi\) | |||||||
\(68\) | 18.8819 | + | 10.9015i | 0.277675 | + | 0.160316i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1382i | 0.170961i | 0.996340 | + | 0.0854803i | \(0.0272425\pi\) | ||||
−0.996340 | + | 0.0854803i | \(0.972758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 38.4575 | + | 66.6104i | 0.526815 | + | 0.912471i | 0.999512 | + | 0.0312455i | \(0.00994736\pi\) |
−0.472696 | + | 0.881225i | \(0.656719\pi\) | |||||||
\(74\) | 46.5403 | − | 26.8701i | 0.628923 | − | 0.363109i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40.0000 | −0.526316 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.8340 | + | 29.1573i | −0.213088 | + | 0.369080i | −0.952680 | − | 0.303976i | \(-0.901686\pi\) |
0.739591 | + | 0.673056i | \(0.235019\pi\) | |||||||
\(80\) | 21.0240 | − | 12.1382i | 0.262800 | − | 0.151728i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 42.8745 | − | 74.2608i | 0.522860 | − | 0.905620i | ||||
\(83\) | 60.5764i | 0.729836i | 0.931040 | + | 0.364918i | \(0.118903\pi\) | ||||
−0.931040 | + | 0.364918i | \(0.881097\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −66.1621 | −0.778377 | ||||||||
\(86\) | −102.264 | − | 59.0420i | −1.18911 | − | 0.686535i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −17.1660 | − | 29.7324i | −0.195068 | − | 0.337868i | ||||
\(89\) | −4.13532 | − | 2.38753i | −0.0464643 | − | 0.0268262i | 0.476588 | − | 0.879127i | \(-0.341873\pi\) |
−0.523052 | + | 0.852301i | \(0.675207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 24.2764i | − | 0.263874i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.0000 | + | 20.7846i | 0.127660 | + | 0.221113i | ||||
\(95\) | 105.120 | − | 60.6910i | 1.10653 | − | 0.638853i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −188.413 | −1.94240 | −0.971201 | − | 0.238260i | \(-0.923423\pi\) | ||||
−0.971201 | + | 0.238260i | \(0.923423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.8340 | + | 20.4971i | −0.118340 | + | 0.204971i | ||||
\(101\) | −92.4162 | + | 53.3565i | −0.915012 | + | 0.528282i | −0.882040 | − | 0.471174i | \(-0.843830\pi\) |
−0.0329716 | + | 0.999456i | \(0.510497\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −65.7490 | + | 113.881i | −0.638340 | + | 1.10564i | 0.347457 | + | 0.937696i | \(0.387045\pi\) |
−0.985797 | + | 0.167941i | \(0.946288\pi\) | |||||||
\(104\) | 52.5607i | 0.505391i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 132.996 | 1.25468 | ||||||||
\(107\) | 71.3426 | + | 41.1897i | 0.666753 | + | 0.384950i | 0.794845 | − | 0.606812i | \(-0.207552\pi\) |
−0.128092 | + | 0.991762i | \(0.540885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.9150 | − | 29.2977i | −0.155184 | − | 0.268786i | 0.777942 | − | 0.628336i | \(-0.216264\pi\) |
−0.933126 | + | 0.359550i | \(0.882930\pi\) | |||||||
\(110\) | 90.2245 | + | 52.0911i | 0.820223 | + | 0.473556i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 28.5190i | 0.252381i | 0.992006 | + | 0.126190i | \(0.0402750\pi\) | ||||
−0.992006 | + | 0.126190i | \(0.959725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 36.8340 | + | 63.7983i | 0.320296 | + | 0.554768i | ||||
\(116\) | 72.4633 | − | 41.8367i | 0.624683 | − | 0.360661i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −82.3320 | −0.697729 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.1680 | − | 22.8076i | 0.108826 | − | 0.188493i | ||||
\(122\) | 19.1893 | − | 11.0789i | 0.157289 | − | 0.0908109i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 25.1660 | − | 43.5888i | 0.202952 | − | 0.351523i | ||||
\(125\) | 79.9059i | 0.639247i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 129.668 | 1.02101 | 0.510504 | − | 0.859875i | \(-0.329459\pi\) | ||||
0.510504 | + | 0.859875i | \(0.329459\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −79.7490 | − | 138.129i | −0.613454 | − | 1.06253i | ||||
\(131\) | −128.187 | − | 74.0087i | −0.978525 | − | 0.564952i | −0.0767004 | − | 0.997054i | \(-0.524438\pi\) |
−0.901824 | + | 0.432103i | \(0.857772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 187.615i | − | 1.40011i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.4170 | − | 26.7030i | −0.113360 | − | 0.196346i | ||||
\(137\) | 66.6469 | − | 38.4786i | 0.486474 | − | 0.280866i | −0.236637 | − | 0.971598i | \(-0.576045\pi\) |
0.723111 | + | 0.690732i | \(0.242712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 217.328 | 1.56351 | 0.781756 | − | 0.623585i | \(-0.214324\pi\) | ||||
0.781756 | + | 0.623585i | \(0.214324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.58301 | − | 14.8662i | 0.0604437 | − | 0.104692i | ||||
\(143\) | −195.344 | + | 112.782i | −1.36604 | + | 0.788686i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −126.956 | + | 219.893i | −0.875555 | + | 1.51651i | ||||
\(146\) | − | 108.774i | − | 0.745029i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −76.0000 | −0.513514 | ||||||||
\(149\) | 140.231 | + | 80.9623i | 0.941147 | + | 0.543371i | 0.890320 | − | 0.455336i | \(-0.150481\pi\) |
0.0508272 | + | 0.998707i | \(0.483814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 46.5830 | + | 80.6841i | 0.308497 | + | 0.534332i | 0.978034 | − | 0.208447i | \(-0.0668408\pi\) |
−0.669537 | + | 0.742779i | \(0.733507\pi\) | |||||||
\(152\) | 48.9898 | + | 28.2843i | 0.322301 | + | 0.186081i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 152.735i | 0.985388i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 92.4980 | + | 160.211i | 0.589159 | + | 1.02045i | 0.994343 | + | 0.106219i | \(0.0338743\pi\) |
−0.405183 | + | 0.914235i | \(0.632792\pi\) | |||||||
\(158\) | 41.2347 | − | 23.8069i | 0.260979 | − | 0.150676i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −34.3320 | −0.214575 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −43.4980 | + | 75.3408i | −0.266859 | + | 0.462214i | −0.968049 | − | 0.250761i | \(-0.919319\pi\) |
0.701190 | + | 0.712975i | \(0.252652\pi\) | |||||||
\(164\) | −105.021 | + | 60.6337i | −0.640370 | + | 0.369718i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 42.8340 | − | 74.1906i | 0.258036 | − | 0.446932i | ||||
\(167\) | − | 60.5764i | − | 0.362733i | −0.983416 | − | 0.181366i | \(-0.941948\pi\) | ||
0.983416 | − | 0.181366i | \(-0.0580520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 176.328 | 1.04336 | ||||||||
\(170\) | 81.0317 | + | 46.7837i | 0.476657 | + | 0.275198i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 83.4980 | + | 144.623i | 0.485454 | + | 0.840830i | ||||
\(173\) | 140.791 | + | 81.2858i | 0.813822 | + | 0.469860i | 0.848281 | − | 0.529546i | \(-0.177638\pi\) |
−0.0344594 | + | 0.999406i | \(0.510971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 48.5528i | 0.275868i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.37648 | + | 5.84823i | 0.0189690 | + | 0.0328552i | ||||
\(179\) | −193.202 | + | 111.545i | −1.07934 | + | 0.623159i | −0.930719 | − | 0.365735i | \(-0.880818\pi\) |
−0.148623 | + | 0.988894i | \(0.547484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 188.915 | 1.04373 | 0.521865 | − | 0.853028i | \(-0.325237\pi\) | ||||
0.521865 | + | 0.853028i | \(0.325237\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.1660 | + | 29.7324i | −0.0932935 | + | 0.161589i | ||||
\(185\) | 199.728 | − | 115.313i | 1.07961 | − | 0.623313i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 66.1621 | − | 114.596i | 0.353808 | − | 0.612813i | ||||
\(188\) | − | 33.9411i | − | 0.180538i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −171.660 | −0.903474 | ||||||||
\(191\) | −197.486 | − | 114.019i | −1.03396 | − | 0.596957i | −0.115844 | − | 0.993267i | \(-0.536957\pi\) |
−0.918117 | + | 0.396310i | \(0.870291\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −67.0000 | − | 116.047i | −0.347150 | − | 0.601282i | 0.638592 | − | 0.769546i | \(-0.279517\pi\) |
−0.985742 | + | 0.168264i | \(0.946184\pi\) | |||||||
\(194\) | 230.758 | + | 133.228i | 1.18947 | + | 0.686743i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 188.560i | 0.957157i | 0.878045 | + | 0.478579i | \(0.158848\pi\) | ||||
−0.878045 | + | 0.478579i | \(0.841152\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −51.2470 | − | 88.7625i | −0.257523 | − | 0.446043i | 0.708055 | − | 0.706157i | \(-0.249573\pi\) |
−0.965578 | + | 0.260115i | \(0.916240\pi\) | |||||||
\(200\) | 28.9872 | − | 16.7358i | 0.144936 | − | 0.0836789i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 150.915 | 0.747104 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 183.996 | − | 318.691i | 0.897542 | − | 1.55459i | ||||
\(206\) | 161.052 | − | 92.9831i | 0.781804 | − | 0.451375i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 37.1660 | − | 64.3734i | 0.178683 | − | 0.309488i | ||||
\(209\) | 242.764i | 1.16155i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −84.5020 | −0.400483 | −0.200242 | − | 0.979747i | \(-0.564173\pi\) | ||||
−0.200242 | + | 0.979747i | \(0.564173\pi\) | |||||||
\(212\) | −162.886 | − | 94.0424i | −0.768331 | − | 0.443596i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −58.2510 | − | 100.894i | −0.272201 | − | 0.471466i | ||||
\(215\) | −438.865 | − | 253.379i | −2.04123 | − | 1.17851i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 47.8429i | 0.219463i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −73.6680 | − | 127.597i | −0.334854 | − | 0.579985i | ||||
\(221\) | −175.441 | + | 101.291i | −0.793851 | + | 0.458330i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −158.494 | −0.710736 | −0.355368 | − | 0.934727i | \(-0.615644\pi\) | ||||
−0.355368 | + | 0.934727i | \(0.615644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.1660 | − | 34.9286i | 0.0892301 | − | 0.154551i | ||||
\(227\) | −88.1816 | + | 50.9117i | −0.388465 | + | 0.224281i | −0.681495 | − | 0.731823i | \(-0.738670\pi\) |
0.293030 | + | 0.956103i | \(0.405337\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 134.458 | − | 232.887i | 0.587151 | − | 1.01697i | −0.407453 | − | 0.913226i | \(-0.633583\pi\) |
0.994604 | − | 0.103749i | \(-0.0330837\pi\) | |||||||
\(230\) | − | 104.182i | − | 0.452966i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −118.332 | −0.510052 | ||||||||
\(233\) | −22.7546 | − | 13.1374i | −0.0976593 | − | 0.0563836i | 0.450375 | − | 0.892840i | \(-0.351290\pi\) |
−0.548034 | + | 0.836456i | \(0.684624\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 51.4980 | + | 89.1972i | 0.219141 | + | 0.379563i | ||||
\(236\) | 100.836 | + | 58.2175i | 0.427270 | + | 0.246684i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 92.2733i | − | 0.386081i | −0.981191 | − | 0.193040i | \(-0.938165\pi\) | ||
0.981191 | − | 0.193040i | \(-0.0618348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −171.624 | − | 297.261i | −0.712131 | − | 1.23345i | −0.964056 | − | 0.265700i | \(-0.914397\pi\) |
0.251925 | − | 0.967747i | \(-0.418936\pi\) | |||||||
\(242\) | −32.2548 | + | 18.6223i | −0.133284 | + | 0.0769518i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −31.3360 | −0.128426 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 185.830 | − | 321.867i | 0.752348 | − | 1.30311i | ||||
\(248\) | −61.6439 | + | 35.5901i | −0.248564 | + | 0.143509i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 56.5020 | − | 97.8643i | 0.226008 | − | 0.391457i | ||||
\(251\) | − | 356.382i | − | 1.41985i | −0.704278 | − | 0.709924i | \(-0.748729\pi\) | ||
0.704278 | − | 0.709924i | \(-0.251271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −147.336 | −0.582356 | ||||||||
\(254\) | −158.810 | − | 91.6891i | −0.625237 | − | 0.360981i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −220.603 | − | 127.365i | −0.858377 | − | 0.495584i | 0.00509129 | − | 0.999987i | \(-0.498379\pi\) |
−0.863469 | + | 0.504403i | \(0.831713\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 225.564i | 0.867555i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 104.664 | + | 181.283i | 0.399481 | + | 0.691922i | ||||
\(263\) | −226.880 | + | 130.989i | −0.862663 | + | 0.498059i | −0.864903 | − | 0.501939i | \(-0.832620\pi\) |
0.00224015 | + | 0.999997i | \(0.499287\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 570.753 | 2.15378 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −132.664 | + | 229.781i | −0.495015 | + | 0.857391i | ||||
\(269\) | −81.0813 | + | 46.8123i | −0.301417 | + | 0.174023i | −0.643079 | − | 0.765799i | \(-0.722344\pi\) |
0.341662 | + | 0.939823i | \(0.389010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.583005 | + | 1.00979i | −0.00215131 | + | 0.00372618i | −0.867099 | − | 0.498136i | \(-0.834018\pi\) |
0.864948 | + | 0.501862i | \(0.167351\pi\) | |||||||
\(272\) | 43.6058i | 0.160316i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −108.834 | −0.397204 | ||||||||
\(275\) | 124.399 | + | 71.8217i | 0.452359 | + | 0.261170i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0000 | − | 27.7128i | −0.0577617 | − | 0.100046i | 0.835699 | − | 0.549188i | \(-0.185063\pi\) |
−0.893460 | + | 0.449142i | \(0.851730\pi\) | |||||||
\(278\) | −266.171 | − | 153.674i | −0.957451 | − | 0.552785i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 166.757i | − | 0.593441i | −0.954964 | − | 0.296721i | \(-0.904107\pi\) | ||
0.954964 | − | 0.296721i | \(-0.0958930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.16995 | − | 14.1508i | −0.0288691 | − | 0.0500027i | 0.851230 | − | 0.524793i | \(-0.175857\pi\) |
−0.880099 | + | 0.474790i | \(0.842524\pi\) | |||||||
\(284\) | −21.0240 | + | 12.1382i | −0.0740281 | + | 0.0427401i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 318.996 | 1.11537 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −85.0791 | + | 147.361i | −0.294391 | + | 0.509901i | ||||
\(290\) | 310.976 | − | 179.542i | 1.07233 | − | 0.619111i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −76.9150 | + | 133.221i | −0.263408 | + | 0.456235i | ||||
\(293\) | − | 368.921i | − | 1.25912i | −0.776953 | − | 0.629558i | \(-0.783236\pi\) | ||
0.776953 | − | 0.629558i | \(-0.216764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −353.328 | −1.19772 | ||||||||
\(296\) | 93.0806 | + | 53.7401i | 0.314462 | + | 0.181554i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −114.498 | − | 198.316i | −0.384222 | − | 0.665491i | ||||
\(299\) | 195.344 | + | 112.782i | 0.653326 | + | 0.377198i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 131.757i | − | 0.436280i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −40.0000 | − | 69.2820i | −0.131579 | − | 0.227901i | ||||
\(305\) | 82.3508 | − | 47.5453i | 0.270003 | − | 0.155886i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −192.664 | −0.627570 | −0.313785 | − | 0.949494i | \(-0.601597\pi\) | ||||
−0.313785 | + | 0.949494i | \(0.601597\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 108.000 | − | 187.061i | 0.348387 | − | 0.603424i | ||||
\(311\) | −113.688 | + | 65.6380i | −0.365557 | + | 0.211055i | −0.671516 | − | 0.740990i | \(-0.734356\pi\) |
0.305959 | + | 0.952045i | \(0.401023\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.6640 | + | 37.5232i | −0.0692142 | + | 0.119882i | −0.898556 | − | 0.438860i | \(-0.855383\pi\) |
0.829341 | + | 0.558742i | \(0.188716\pi\) | |||||||
\(314\) | − | 261.624i | − | 0.833197i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −67.3360 | −0.213088 | ||||||||
\(317\) | −218.000 | − | 125.862i | −0.687696 | − | 0.397042i | 0.115052 | − | 0.993359i | \(-0.463297\pi\) |
−0.802748 | + | 0.596318i | \(0.796630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −253.911 | − | 439.787i | −0.795960 | − | 1.37864i | ||||
\(320\) | 42.0480 | + | 24.2764i | 0.131400 | + | 0.0758638i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 218.029i | 0.675013i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −109.956 | − | 190.449i | −0.338325 | − | 0.585996i | ||||
\(326\) | 106.548 | − | 61.5155i | 0.326834 | − | 0.188698i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 171.498 | 0.522860 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −180.745 | + | 313.060i | −0.546058 | + | 0.945800i | 0.452482 | + | 0.891774i | \(0.350539\pi\) |
−0.998540 | + | 0.0540260i | \(0.982795\pi\) | |||||||
\(332\) | −104.921 | + | 60.5764i | −0.316028 | + | 0.182459i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −42.8340 | + | 74.1906i | −0.128245 | + | 0.222128i | ||||
\(335\) | − | 805.151i | − | 2.40344i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −298.834 | −0.886748 | −0.443374 | − | 0.896337i | \(-0.646219\pi\) | ||||
−0.443374 | + | 0.896337i | \(0.646219\pi\) | |||||||
\(338\) | −215.957 | − | 124.683i | −0.638926 | − | 0.368884i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −66.1621 | − | 114.596i | −0.194594 | − | 0.337047i | ||||
\(341\) | −264.545 | − | 152.735i | −0.775791 | − | 0.447903i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 236.168i | − | 0.686535i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −114.956 | − | 199.109i | −0.332241 | − | 0.575459i | ||||
\(347\) | −178.505 | + | 103.060i | −0.514425 | + | 0.297003i | −0.734651 | − | 0.678446i | \(-0.762654\pi\) |
0.220226 | + | 0.975449i | \(0.429321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 434.324 | 1.24448 | 0.622241 | − | 0.782826i | \(-0.286222\pi\) | ||||
0.622241 | + | 0.782826i | \(0.286222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 34.3320 | − | 59.4648i | 0.0975342 | − | 0.168934i | ||||
\(353\) | 160.595 | − | 92.7197i | 0.454944 | − | 0.262662i | −0.254972 | − | 0.966948i | \(-0.582066\pi\) |
0.709916 | + | 0.704286i | \(0.248733\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.8340 | − | 63.7983i | 0.103758 | − | 0.179714i | ||||
\(356\) | − | 9.55012i | − | 0.0268262i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 315.498 | 0.881279 | ||||||||
\(359\) | −447.533 | − | 258.383i | −1.24661 | − | 0.719731i | −0.276178 | − | 0.961106i | \(-0.589068\pi\) |
−0.970432 | + | 0.241376i | \(0.922401\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.5000 | − | 33.7750i | −0.0540166 | − | 0.0935595i | ||||
\(362\) | −231.373 | − | 133.583i | −0.639151 | − | 0.369014i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 466.805i | − | 1.27892i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 58.7451 | + | 101.749i | 0.160068 | + | 0.277246i | 0.934893 | − | 0.354930i | \(-0.115495\pi\) |
−0.774825 | + | 0.632176i | \(0.782162\pi\) | |||||||
\(368\) | 42.0480 | − | 24.2764i | 0.114261 | − | 0.0659685i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −326.154 | −0.881498 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 201.332 | − | 348.717i | 0.539764 | − | 0.934899i | −0.459152 | − | 0.888358i | \(-0.651847\pi\) |
0.998916 | − | 0.0465413i | \(-0.0148199\pi\) | |||||||
\(374\) | −162.063 | + | 93.5673i | −0.433324 | + | 0.250180i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | + | 41.5692i | −0.0638298 | + | 0.110556i | ||||
\(377\) | 777.451i | 2.06221i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 398.834 | 1.05233 | 0.526166 | − | 0.850382i | \(-0.323629\pi\) | ||||
0.526166 | + | 0.850382i | \(0.323629\pi\) | |||||||
\(380\) | 210.240 | + | 121.382i | 0.553263 | + | 0.319426i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 161.247 | + | 279.288i | 0.422113 | + | 0.731121i | ||||
\(383\) | 645.019 | + | 372.402i | 1.68412 | + | 0.972329i | 0.958869 | + | 0.283849i | \(0.0916114\pi\) |
0.725255 | + | 0.688481i | \(0.241722\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 189.505i | 0.490945i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −188.413 | − | 326.341i | −0.485601 | − | 0.841085i | ||||
\(389\) | 463.464 | − | 267.581i | 1.19142 | − | 0.687869i | 0.232795 | − | 0.972526i | \(-0.425213\pi\) |
0.958630 | + | 0.284656i | \(0.0918795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −132.324 | −0.338425 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 133.332 | − | 230.938i | 0.338406 | − | 0.586137i | ||||
\(395\) | 176.959 | − | 102.167i | 0.447997 | − | 0.258651i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 47.1621 | − | 81.6871i | 0.118796 | − | 0.205761i | −0.800495 | − | 0.599340i | \(-0.795430\pi\) |
0.919291 | + | 0.393579i | \(0.128763\pi\) | |||||||
\(398\) | 144.949i | 0.364192i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −47.3360 | −0.118340 | ||||||||
\(401\) | −89.7138 | − | 51.7963i | −0.223725 | − | 0.129168i | 0.383949 | − | 0.923354i | \(-0.374564\pi\) |
−0.607674 | + | 0.794187i | \(0.707897\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 233.830 | + | 405.006i | 0.580223 | + | 1.00498i | ||||
\(404\) | −184.832 | − | 106.713i | −0.457506 | − | 0.264141i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 461.252i | 1.13330i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.87844 | + | 8.44971i | 0.0119277 | + | 0.0206594i | 0.871928 | − | 0.489635i | \(-0.162870\pi\) |
−0.860000 | + | 0.510294i | \(0.829537\pi\) | |||||||
\(410\) | −450.696 | + | 260.210i | −1.09926 | + | 0.634658i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −262.996 | −0.638340 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 183.822 | − | 318.389i | 0.442945 | − | 0.767203i | ||||
\(416\) | −91.0378 | + | 52.5607i | −0.218841 | + | 0.126348i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 171.660 | − | 297.324i | 0.410670 | − | 0.711301i | ||||
\(419\) | − | 339.411i | − | 0.810051i | −0.914305 | − | 0.405025i | \(-0.867263\pi\) | ||
0.914305 | − | 0.405025i | \(-0.132737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −599.320 | −1.42356 | −0.711782 | − | 0.702401i | \(-0.752111\pi\) | ||||
−0.711782 | + | 0.702401i | \(0.752111\pi\) | |||||||
\(422\) | 103.493 | + | 59.7519i | 0.245245 | + | 0.141592i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 132.996 | + | 230.356i | 0.313670 | + | 0.543292i | ||||
\(425\) | 111.724 | + | 64.5039i | 0.262880 | + | 0.151774i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 164.759i | 0.384950i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 358.332 | + | 620.649i | 0.833330 | + | 1.44337i | ||||
\(431\) | −615.725 | + | 355.489i | −1.42860 | + | 0.824800i | −0.997010 | − | 0.0772717i | \(-0.975379\pi\) |
−0.431586 | + | 0.902072i | \(0.642046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 377.984 | 0.872943 | 0.436471 | − | 0.899718i | \(-0.356228\pi\) | ||||
0.436471 | + | 0.899718i | \(0.356228\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.8301 | − | 58.5954i | 0.0775919 | − | 0.134393i | ||||
\(437\) | 210.240 | − | 121.382i | 0.481098 | − | 0.277762i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −264.073 | + | 457.388i | −0.601533 | + | 1.04189i | 0.391056 | + | 0.920367i | \(0.372110\pi\) |
−0.992589 | + | 0.121519i | \(0.961223\pi\) | |||||||
\(440\) | 208.365i | 0.473556i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 286.494 | 0.648177 | ||||||||
\(443\) | 31.7345 | + | 18.3219i | 0.0716354 | + | 0.0413587i | 0.535390 | − | 0.844605i | \(-0.320165\pi\) |
−0.463754 | + | 0.885964i | \(0.653498\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.4902 | + | 25.0977i | 0.0325622 | + | 0.0563993i | ||||
\(446\) | 194.115 | + | 112.072i | 0.435235 | + | 0.251283i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 397.612i | 0.885550i | 0.896633 | + | 0.442775i | \(0.146006\pi\) | ||||
−0.896633 | + | 0.442775i | \(0.853994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 367.992 | + | 637.381i | 0.815947 | + | 1.41326i | ||||
\(452\) | −49.3964 | + | 28.5190i | −0.109284 | + | 0.0630952i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 144.000 | 0.317181 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −172.162 | + | 298.193i | −0.376722 | + | 0.652502i | −0.990583 | − | 0.136912i | \(-0.956282\pi\) |
0.613861 | + | 0.789414i | \(0.289616\pi\) | |||||||
\(458\) | −329.352 | + | 190.152i | −0.719110 | + | 0.415178i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −73.6680 | + | 127.597i | −0.160148 | + | 0.277384i | ||||
\(461\) | 370.936i | 0.804634i | 0.915500 | + | 0.402317i | \(0.131795\pi\) | ||||
−0.915500 | + | 0.402317i | \(0.868205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 78.3320 | 0.169184 | 0.0845918 | − | 0.996416i | \(-0.473041\pi\) | ||||
0.0845918 | + | 0.996416i | \(0.473041\pi\) | |||||||
\(464\) | 144.927 | + | 83.6734i | 0.312342 | + | 0.180331i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.5791 | + | 32.1799i | 0.0398692 | + | 0.0690556i | ||||
\(467\) | −346.201 | − | 199.879i | −0.741330 | − | 0.428007i | 0.0812229 | − | 0.996696i | \(-0.474117\pi\) |
−0.822553 | + | 0.568689i | \(0.807451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 145.658i | − | 0.309912i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −82.3320 | − | 142.603i | −0.174432 | − | 0.302126i | ||||
\(473\) | 877.731 | − | 506.758i | 1.85567 | − | 1.07137i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −236.680 | −0.498273 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −65.2470 | + | 113.011i | −0.136500 | + | 0.236425i | ||||
\(479\) | 609.100 | − | 351.664i | 1.27161 | − | 0.734163i | 0.296317 | − | 0.955090i | \(-0.404241\pi\) |
0.975290 | + | 0.220927i | \(0.0709081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 353.077 | − | 611.547i | 0.734048 | − | 1.27141i | ||||
\(482\) | 485.425i | 1.00711i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 52.6719 | 0.108826 | ||||||||
\(485\) | 990.298 | + | 571.749i | 2.04185 | + | 1.17886i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.2549 | + | 71.4556i | 0.0847124 | + | 0.146726i | 0.905269 | − | 0.424840i | \(-0.139670\pi\) |
−0.820556 | + | 0.571566i | \(0.806336\pi\) | |||||||
\(488\) | 38.3786 | + | 22.1579i | 0.0786446 | + | 0.0454055i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 184.203i | 0.375158i | 0.982249 | + | 0.187579i | \(0.0600641\pi\) | ||||
−0.982249 | + | 0.187579i | \(0.939936\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −228.041 | − | 394.978i | −0.462557 | − | 0.801172i | ||||
\(494\) | −455.189 | + | 262.803i | −0.921435 | + | 0.531991i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 100.664 | 0.202952 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −376.405 | + | 651.953i | −0.754319 | + | 1.30652i | 0.191393 | + | 0.981513i | \(0.438699\pi\) |
−0.945712 | + | 0.325005i | \(0.894634\pi\) | |||||||
\(500\) | −138.401 | + | 79.9059i | −0.276802 | + | 0.159812i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −252.000 | + | 436.477i | −0.501992 | + | 0.869476i | ||||
\(503\) | 662.540i | 1.31718i | 0.752504 | + | 0.658588i | \(0.228846\pi\) | ||||
−0.752504 | + | 0.658588i | \(0.771154\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 647.652 | 1.28248 | ||||||||
\(506\) | 180.449 | + | 104.182i | 0.356618 | + | 0.205894i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 129.668 | + | 224.592i | 0.255252 | + | 0.442109i | ||||
\(509\) | 821.958 | + | 474.557i | 1.61485 | + | 0.932333i | 0.988225 | + | 0.153010i | \(0.0488968\pi\) |
0.626623 | + | 0.779322i | \(0.284437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 180.122 | + | 311.980i | 0.350431 | + | 0.606964i | ||||
\(515\) | 691.153 | − | 399.037i | 1.34204 | − | 0.774830i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −205.992 | −0.398437 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 159.498 | − | 276.259i | 0.306727 | − | 0.531267i | ||||
\(521\) | −618.640 | + | 357.172i | −1.18741 | + | 0.685551i | −0.957717 | − | 0.287712i | \(-0.907105\pi\) |
−0.229692 | + | 0.973263i | \(0.573772\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 116.000 | − | 200.918i | 0.221797 | − | 0.384164i | −0.733556 | − | 0.679629i | \(-0.762141\pi\) |
0.955354 | + | 0.295464i | \(0.0954743\pi\) | |||||||
\(524\) | − | 296.035i | − | 0.564952i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 370.494 | 0.704361 | ||||||||
\(527\) | −237.591 | − | 137.173i | −0.450837 | − | 0.260291i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −190.832 | − | 330.531i | −0.360741 | − | 0.624822i | ||||
\(530\) | −699.027 | − | 403.583i | −1.31892 | − | 0.761478i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1126.76i | − | 2.11399i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −249.984 | − | 432.985i | −0.467260 | − | 0.809319i | ||||
\(536\) | 324.959 | − | 187.615i | 0.606267 | − | 0.350029i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 132.405 | 0.246106 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −82.8340 | + | 143.473i | −0.153113 | + | 0.265199i | −0.932370 | − | 0.361505i | \(-0.882263\pi\) |
0.779257 | + | 0.626704i | \(0.215596\pi\) | |||||||
\(542\) | 1.42807 | − | 0.824494i | 0.00263481 | − | 0.00152121i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 30.8340 | − | 53.4060i | 0.0566801 | − | 0.0981729i | ||||
\(545\) | 205.318i | 0.376730i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 295.676 | 0.540541 | 0.270270 | − | 0.962784i | \(-0.412887\pi\) | ||||
0.270270 | + | 0.962784i | \(0.412887\pi\) | |||||||
\(548\) | 133.294 | + | 76.9573i | 0.243237 | + | 0.140433i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −101.571 | − | 175.926i | −0.184675 | − | 0.319866i | ||||
\(551\) | 724.633 | + | 418.367i | 1.31512 | + | 0.759287i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 45.2548i | 0.0816874i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 217.328 | + | 376.423i | 0.390878 | + | 0.677020i | ||||
\(557\) | −66.5477 | + | 38.4213i | −0.119475 | + | 0.0689790i | −0.558547 | − | 0.829473i | \(-0.688641\pi\) |
0.439071 | + | 0.898452i | \(0.355307\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1551.64 | −2.77575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −117.915 | + | 204.235i | −0.209813 | + | 0.363407i | ||||
\(563\) | −880.170 | + | 508.167i | −1.56336 | + | 0.902605i | −0.566444 | + | 0.824100i | \(0.691681\pi\) |
−0.996914 | + | 0.0785049i | \(0.974985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 86.5425 | − | 149.896i | 0.153173 | − | 0.265303i | ||||
\(566\) | 23.1081i | 0.0408270i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 34.3320 | 0.0604437 | ||||||||
\(569\) | −507.952 | − | 293.266i | −0.892710 | − | 0.515406i | −0.0178822 | − | 0.999840i | \(-0.505692\pi\) |
−0.874828 | + | 0.484434i | \(0.839026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −475.822 | − | 824.148i | −0.833314 | − | 1.44334i | −0.895396 | − | 0.445271i | \(-0.853107\pi\) |
0.0620822 | − | 0.998071i | \(-0.480226\pi\) | |||||||
\(572\) | −390.689 | − | 225.564i | −0.683022 | − | 0.394343i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 143.643i | − | 0.249815i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 74.3360 | + | 128.754i | 0.128832 | + | 0.223143i | 0.923224 | − | 0.384262i | \(-0.125544\pi\) |
−0.794392 | + | 0.607405i | \(0.792211\pi\) | |||||||
\(578\) | 208.400 | − | 120.320i | 0.360554 | − | 0.208166i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −507.822 | −0.875555 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −570.753 | + | 988.573i | −0.978993 | + | 1.69567i | ||||
\(584\) | 188.403 | − | 108.774i | 0.322607 | − | 0.186257i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −260.867 | + | 451.834i | −0.445165 | + | 0.771048i | ||||
\(587\) | − | 332.564i | − | 0.566548i | −0.959039 | − | 0.283274i | \(-0.908579\pi\) | ||
0.959039 | − | 0.283274i | \(-0.0914206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 503.320 | 0.854533 | ||||||||
\(590\) | 432.737 | + | 249.841i | 0.733452 | + | 0.423459i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −76.0000 | − | 131.636i | −0.128378 | − | 0.222358i | ||||
\(593\) | 188.145 | + | 108.625i | 0.317276 | + | 0.183180i | 0.650178 | − | 0.759782i | \(-0.274694\pi\) |
−0.332902 | + | 0.942962i | \(0.608028\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 323.849i | 0.543371i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −159.498 | − | 276.259i | −0.266719 | − | 0.461971i | ||||
\(599\) | 149.111 | − | 86.0896i | 0.248934 | − | 0.143722i | −0.370342 | − | 0.928895i | \(-0.620760\pi\) |
0.619276 | + | 0.785173i | \(0.287426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −418.000 | −0.695507 | −0.347754 | − | 0.937586i | \(-0.613055\pi\) | ||||
−0.347754 | + | 0.937586i | \(0.613055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −93.1660 | + | 161.368i | −0.154248 | + | 0.267166i | ||||
\(605\) | −138.422 | + | 79.9178i | −0.228796 | + | 0.132096i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −313.579 | + | 543.135i | −0.516605 | + | 0.894786i | 0.483209 | + | 0.875505i | \(0.339471\pi\) |
−0.999814 | + | 0.0192808i | \(0.993862\pi\) | |||||||
\(608\) | 113.137i | 0.186081i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −134.478 | −0.220456 | ||||||||
\(611\) | 273.113 | + | 157.682i | 0.446994 | + | 0.258072i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 139.664 | + | 241.905i | 0.227837 | + | 0.394625i | 0.957167 | − | 0.289537i | \(-0.0935014\pi\) |
−0.729330 | + | 0.684162i | \(0.760168\pi\) | |||||||
\(614\) | 235.964 | + | 136.234i | 0.384307 | + | 0.221880i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 358.380i | − | 0.580843i | −0.956899 | − | 0.290422i | \(-0.906204\pi\) | ||
0.956899 | − | 0.290422i | \(-0.0937955\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 491.822 | + | 851.861i | 0.794543 | + | 1.37619i | 0.923129 | + | 0.384491i | \(0.125623\pi\) |
−0.128586 | + | 0.991698i | \(0.541044\pi\) | |||||||
\(620\) | −264.545 | + | 152.735i | −0.426685 | + | 0.246347i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 185.652 | 0.298476 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390.403 | − | 676.198i | 0.624645 | − | 1.08192i | ||||
\(626\) | 53.0658 | − | 30.6376i | 0.0847697 | − | 0.0489418i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −184.996 | + | 320.423i | −0.294580 | + | 0.510227i | ||||
\(629\) | 414.256i | 0.658594i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −298.996 | −0.473845 | −0.236922 | − | 0.971529i | \(-0.576139\pi\) | ||||
−0.236922 | + | 0.971529i | \(0.576139\pi\) | |||||||
\(632\) | 82.4694 | + | 47.6137i | 0.130490 | + | 0.0753382i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 177.996 | + | 308.298i | 0.280751 | + | 0.486275i | ||||
\(635\) | −681.534 | − | 393.484i | −1.07328 | − | 0.619660i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 718.169i | 1.12566i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −34.3320 | − | 59.4648i | −0.0536438 | − | 0.0929138i | ||||
\(641\) | 270.163 | − | 155.979i | 0.421471 | − | 0.243336i | −0.274236 | − | 0.961663i | \(-0.588425\pi\) |
0.695706 | + | 0.718326i | \(0.255091\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −604.000 | −0.939347 | −0.469673 | − | 0.882840i | \(-0.655628\pi\) | ||||
−0.469673 | + | 0.882840i | \(0.655628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 154.170 | − | 267.030i | 0.238653 | − | 0.413359i | ||||
\(647\) | −155.538 | + | 89.7998i | −0.240398 | + | 0.138794i | −0.615360 | − | 0.788246i | \(-0.710989\pi\) |
0.374961 | + | 0.927040i | \(0.377656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 353.328 | − | 611.982i | 0.544419 | − | 0.942962i | ||||
\(650\) | 311.001i | 0.478463i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −173.992 | −0.266859 | ||||||||
\(653\) | 417.331 | + | 240.946i | 0.639097 | + | 0.368983i | 0.784267 | − | 0.620424i | \(-0.213039\pi\) |
−0.145169 | + | 0.989407i | \(0.546373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 449.166 | + | 777.978i | 0.685750 | + | 1.18775i | ||||
\(656\) | −210.041 | − | 121.267i | −0.320185 | − | 0.184859i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 877.408i | − | 1.33142i | −0.746209 | − | 0.665711i | \(-0.768128\pi\) | ||
0.746209 | − | 0.665711i | \(-0.231872\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 260.822 | + | 451.757i | 0.394587 | + | 0.683445i | 0.993048 | − | 0.117707i | \(-0.0375543\pi\) |
−0.598461 | + | 0.801152i | \(0.704221\pi\) | |||||||
\(662\) | 442.733 | − | 255.612i | 0.668781 | − | 0.386121i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 171.336 | 0.258036 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −253.911 | + | 439.787i | −0.380676 | + | 0.659351i | ||||
\(668\) | 104.921 | − | 60.5764i | 0.157068 | − | 0.0906832i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −569.328 | + | 986.105i | −0.849743 | + | 1.47180i | ||||
\(671\) | 190.181i | 0.283429i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −659.992 | −0.980672 | −0.490336 | − | 0.871534i | \(-0.663126\pi\) | ||||
−0.490336 | + | 0.871534i | \(0.663126\pi\) | |||||||
\(674\) | 365.995 | + | 211.308i | 0.543020 | + | 0.313513i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 176.328 | + | 305.409i | 0.260840 | + | 0.451789i | ||||
\(677\) | 880.121 | + | 508.138i | 1.30003 | + | 0.750573i | 0.980409 | − | 0.196972i | \(-0.0631108\pi\) |
0.319622 | + | 0.947545i | \(0.396444\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 187.135i | 0.275198i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 216.000 | + | 374.123i | 0.316716 | + | 0.548567i | ||||
\(683\) | 203.615 | − | 117.557i | 0.298119 | − | 0.172119i | −0.343479 | − | 0.939160i | \(-0.611605\pi\) |
0.641597 | + | 0.767042i | \(0.278272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −467.061 | −0.681841 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −166.996 | + | 289.246i | −0.242727 | + | 0.420415i | ||||
\(689\) | 1513.46 | − | 873.795i | 2.19660 | − | 1.26821i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4902 | − | 44.1502i | 0.0368888 | − | 0.0638933i | −0.846992 | − | 0.531606i | \(-0.821589\pi\) |
0.883880 | + | 0.467713i | \(0.154922\pi\) | |||||||
\(692\) | 325.143i | 0.469860i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 291.498 | 0.420026 | ||||||||
\(695\) | −1142.28 | − | 659.493i | −1.64356 | − | 0.948911i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 330.498 | + | 572.439i | 0.474172 | + | 0.821290i | ||||
\(698\) | −531.936 | − | 307.114i | −0.762086 | − | 0.439991i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 141.530i | − | 0.201898i | −0.994892 | − | 0.100949i | \(-0.967812\pi\) | ||
0.994892 | − | 0.100949i | \(-0.0321879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −380.000 | − | 658.179i | −0.540541 | − | 0.936244i | ||||
\(704\) | −84.0959 | + | 48.5528i | −0.119454 | + | 0.0689671i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −262.251 | −0.371460 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.7490 | − | 48.0627i | 0.0391382 | − | 0.0677894i | −0.845793 | − | 0.533512i | \(-0.820872\pi\) |
0.884931 | + | 0.465722i | \(0.154205\pi\) | |||||||
\(710\) | −90.2245 | + | 52.0911i | −0.127077 | + | 0.0733678i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.75295 | + | 11.6965i | −0.00948448 | + | 0.0164276i | ||||
\(713\) | 305.470i | 0.428429i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1368.97 | 1.91465 | ||||||||
\(716\) | −386.405 | − | 223.091i | −0.539671 | − | 0.311579i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 365.409 | + | 632.907i | 0.508926 | + | 0.881486i | ||||
\(719\) | −873.843 | − | 504.514i | −1.21536 | − | 0.701688i | −0.251438 | − | 0.967874i | \(-0.580903\pi\) |
−0.963922 | + | 0.266185i | \(0.914237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 55.1543i | 0.0763910i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 188.915 | + | 327.210i | 0.260932 | + | 0.451948i | ||||
\(725\) | 428.765 | − | 247.547i | 0.591400 | − | 0.341445i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −365.182 | −0.502313 | −0.251157 | − | 0.967946i | \(-0.580811\pi\) | ||||
−0.251157 | + | 0.967946i | \(0.580811\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −330.081 | + | 571.717i | −0.452166 | + | 0.783174i | ||||
\(731\) | 788.300 | − | 455.125i | 1.07839 | − | 0.622606i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 176.539 | − | 305.774i | 0.240844 | − | 0.417154i | −0.720111 | − | 0.693859i | \(-0.755909\pi\) |
0.960955 | + | 0.276705i | \(0.0892425\pi\) | |||||||
\(734\) | − | 166.156i | − | 0.226371i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −68.6640 | −0.0932935 | ||||||||
\(737\) | 1394.56 | + | 805.151i | 1.89222 | + | 1.09247i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −164.842 | − | 285.514i | −0.223061 | − | 0.386352i | 0.732675 | − | 0.680579i | \(-0.238271\pi\) |
−0.955736 | + | 0.294226i | \(0.904938\pi\) | |||||||
\(740\) | 399.456 | + | 230.626i | 0.539805 | + | 0.311657i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 112.061i | 0.150822i | 0.997153 | + | 0.0754112i | \(0.0240270\pi\) | ||||
−0.997153 | + | 0.0754112i | \(0.975973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −491.369 | − | 851.075i | −0.659555 | − | 1.14238i | ||||
\(746\) | −493.161 | + | 284.726i | −0.661073 | + | 0.381671i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 264.648 | 0.353808 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 72.4131 | − | 125.423i | 0.0964222 | − | 0.167008i | −0.813779 | − | 0.581174i | \(-0.802593\pi\) |
0.910201 | + | 0.414166i | \(0.135927\pi\) | |||||||
\(752\) | 58.7878 | − | 33.9411i | 0.0781752 | − | 0.0451345i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 549.741 | − | 952.180i | 0.729100 | − | 1.26284i | ||||
\(755\) | − | 565.434i | − | 0.748919i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 78.1699 | 0.103263 | 0.0516314 | − | 0.998666i | \(-0.483558\pi\) | ||||
0.0516314 | + | 0.998666i | \(0.483558\pi\) | |||||||
\(758\) | −488.470 | − | 282.018i | −0.644419 | − | 0.372056i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −171.660 | − | 297.324i | −0.225869 | − | 0.391216i | ||||
\(761\) | 1269.16 | + | 732.752i | 1.66776 | + | 0.962880i | 0.968843 | + | 0.247676i | \(0.0796667\pi\) |
0.698915 | + | 0.715205i | \(0.253667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 456.076i | − | 0.596957i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −526.656 | − | 912.195i | −0.687541 | − | 1.19086i | ||||
\(767\) | −936.915 | + | 540.928i | −1.22153 | + | 0.705252i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 729.320 | 0.948401 | 0.474200 | − | 0.880417i | \(-0.342737\pi\) | ||||
0.474200 | + | 0.880417i | \(0.342737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 134.000 | − | 232.095i | 0.173575 | − | 0.300641i | ||||
\(773\) | 376.339 | − | 217.280i | 0.486855 | − | 0.281086i | −0.236414 | − | 0.971653i | \(-0.575972\pi\) |
0.723269 | + | 0.690566i | \(0.242639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 148.907 | − | 257.915i | 0.192138 | − | 0.332793i | ||||
\(776\) | 532.913i | 0.686743i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −756.834 | −0.972794 | ||||||||
\(779\) | −1050.21 | − | 606.337i | −1.34815 | − | 0.778353i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 73.6680 | + | 127.597i | 0.0943252 | + | 0.163376i | ||||
\(782\) | 162.063 | + | 93.5673i | 0.207242 | + | 0.119651i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1122.76i | − | 1.43027i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.67585 | + | 13.2950i | 0.00975331 | + | 0.0168932i | 0.870861 | − | 0.491530i | \(-0.163562\pi\) |
−0.861108 | + | 0.508423i | \(0.830229\pi\) | |||||||
\(788\) | −326.595 | + | 188.560i | −0.414461 | + | 0.239289i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −288.972 | −0.365788 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 145.579 | − | 252.150i | 0.183580 | − | 0.317970i | ||||
\(794\) | −115.523 | + | 66.6972i | −0.145495 | + | 0.0840016i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 102.494 | − | 177.525i | 0.128761 | − | 0.223021i | ||||
\(797\) | 1043.48i | 1.30927i | 0.755947 | + | 0.654633i | \(0.227177\pi\) | ||||
−0.755947 | + | 0.654633i | \(0.772823\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −185.004 | −0.231544 | ||||||||
\(800\) | 57.9745 | + | 33.4716i | 0.0724681 | + | 0.0418395i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 73.2510 | + | 126.874i | 0.0913354 | + | 0.158198i | ||||
\(803\) | 808.530 | + | 466.805i | 1.00689 | + | 0.581326i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 661.371i | − | 0.820560i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 150.915 | + | 261.392i | 0.186776 | + | 0.323506i | ||||
\(809\) | −901.804 | + | 520.657i | −1.11471 | + | 0.643581i | −0.940046 | − | 0.341046i | \(-0.889219\pi\) |
−0.174668 | + | 0.984627i | \(0.555885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 502.316 | 0.619379 | 0.309689 | − | 0.950838i | \(-0.399775\pi\) | ||||
0.309689 | + | 0.950838i | \(0.399775\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 326.154 | − | 564.916i | 0.400681 | − | 0.694000i | ||||
\(815\) | 457.251 | − | 263.994i | 0.561044 | − | 0.323919i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −834.980 | + | 1446.23i | −1.02201 | + | 1.77017i | ||||
\(818\) | − | 13.7983i | − | 0.0168684i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 735.984 | 0.897542 | ||||||||
\(821\) | −20.0170 | − | 11.5568i | −0.0243813 | − | 0.0140765i | 0.487760 | − | 0.872978i | \(-0.337814\pi\) |
−0.512141 | + | 0.858901i | \(0.671148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 300.332 | + | 520.190i | 0.364923 | + | 0.632066i | 0.988764 | − | 0.149486i | \(-0.0477618\pi\) |
−0.623840 | + | 0.781552i | \(0.714428\pi\) | |||||||
\(824\) | 322.103 | + | 185.966i | 0.390902 | + | 0.225687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1309.21i | 1.58308i | 0.611118 | + | 0.791540i | \(0.290720\pi\) | ||||
−0.611118 | + | 0.791540i | \(0.709280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 310.959 | + | 538.598i | 0.375102 | + | 0.649696i | 0.990342 | − | 0.138644i | \(-0.0442744\pi\) |
−0.615240 | + | 0.788340i | \(0.710941\pi\) | |||||||
\(830\) | −450.271 | + | 259.964i | −0.542495 | + | 0.313209i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 148.664 | 0.178683 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −183.822 | + | 318.389i | −0.220146 | + | 0.381305i | ||||
\(836\) | −420.480 | + | 242.764i | −0.502966 | + | 0.290388i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −240.000 | + | 415.692i | −0.286396 | + | 0.496053i | ||||
\(839\) | − | 1190.30i | − | 1.41871i | −0.704851 | − | 0.709355i | \(-0.748986\pi\) | ||
0.704851 | − | 0.709355i | \(-0.251014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −909.308 | −1.08122 | ||||||||
\(842\) | 734.014 | + | 423.783i | 0.871751 | + | 0.503306i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −84.5020 | − | 146.362i | −0.100121 | − | 0.173414i | ||||
\(845\) | −926.780 | − | 535.076i | −1.09678 | − | 0.633227i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 376.170i | − | 0.443596i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −91.2223 | − | 158.002i | −0.107320 | − | 0.185884i | ||||
\(851\) | 399.456 | − | 230.626i | 0.469396 | − | 0.271006i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 137.012 | 0.160623 | 0.0803117 | − | 0.996770i | \(-0.474408\pi\) | ||||
0.0803117 | + | 0.996770i | \(0.474408\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 116.502 | − | 201.787i | 0.136100 | − | 0.235733i | ||||
\(857\) | −403.690 | + | 233.071i | −0.471050 | + | 0.271961i | −0.716679 | − | 0.697403i | \(-0.754339\pi\) |
0.245629 | + | 0.969364i | \(0.421006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.9921 | + | 20.7710i | −0.0139606 | + | 0.0241804i | −0.872921 | − | 0.487861i | \(-0.837777\pi\) |
0.858961 | + | 0.512041i | \(0.171111\pi\) | |||||||
\(860\) | − | 1013.52i | − | 1.17851i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1005.47 | 1.16644 | ||||||||
\(863\) | 0.0992493 | + | 0.0573016i | 0.000115005 | + | 6.63982e-5i | 0.500058 | − | 0.865992i | \(-0.333312\pi\) |
−0.499942 | + | 0.866059i | \(0.666646\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −493.332 | − | 854.476i | −0.570326 | − | 0.987834i | ||||
\(866\) | −462.934 | − | 267.275i | −0.534566 | − | 0.308632i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 408.669i | 0.470275i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1232.65 | − | 2135.01i | −1.41521 | − | 2.45122i | ||||
\(872\) | −82.8664 | + | 47.8429i | −0.0950302 | + | 0.0548657i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −343.320 | −0.392815 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −498.652 | + | 863.691i | −0.568589 | + | 0.984824i | 0.428117 | + | 0.903723i | \(0.359177\pi\) |
−0.996706 | + | 0.0811012i | \(0.974156\pi\) | |||||||
\(878\) | 646.845 | − | 373.456i | 0.736725 | − | 0.425348i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 147.336 | − | 255.193i | 0.167427 | − | 0.289992i | ||||
\(881\) | − | 935.649i | − | 1.06203i | −0.847362 | − | 0.531015i | \(-0.821811\pi\) | ||
0.847362 | − | 0.531015i | \(-0.178189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1549.47 | −1.75478 | −0.877392 | − | 0.479774i | \(-0.840719\pi\) | ||||
−0.877392 | + | 0.479774i | \(0.840719\pi\) | |||||||
\(884\) | −350.882 | − | 202.582i | −0.396926 | − | 0.229165i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.9111 | − | 44.8793i | −0.0292450 | − | 0.0506539i | ||||
\(887\) | −774.654 | − | 447.246i | −0.873341 | − | 0.504224i | −0.00488401 | − | 0.999988i | \(-0.501555\pi\) |
−0.868457 | + | 0.495764i | \(0.834888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 40.9844i | − | 0.0460498i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −158.494 | − | 274.520i | −0.177684 | − | 0.307758i | ||||
\(893\) | 293.939 | − | 169.706i | 0.329159 | − | 0.190040i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1353.96 | 1.51281 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 281.154 | − | 486.973i | 0.313089 | − | 0.542287i | ||||
\(899\) | −911.806 | + | 526.431i | −1.01424 | + | 0.585574i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −512.600 | + | 887.849i | −0.568923 | + | 0.985404i | ||||
\(902\) | − | 1040.84i | − | 1.15392i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 80.6640 | 0.0892301 | ||||||||
\(905\) | −992.937 | − | 573.272i | −1.09717 | − | 0.633450i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 67.9190 | + | 117.639i | 0.0748831 | + | 0.129701i | 0.901035 | − | 0.433746i | \(-0.142808\pi\) |
−0.826152 | + | 0.563447i | \(0.809475\pi\) | |||||||
\(908\) | −176.363 | − | 101.823i | −0.194233 | − | 0.112140i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1242.01i | 1.36335i | 0.731655 | + | 0.681675i | \(0.238748\pi\) | ||||
−0.731655 | + | 0.681675i | \(0.761252\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 367.644 | + | 636.779i | 0.402677 | + | 0.697458i | ||||
\(914\) | 421.709 | − | 243.474i | 0.461389 | − | 0.266383i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 537.830 | 0.587151 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 194.081 | − | 336.158i | 0.211187 | − | 0.365787i | −0.740899 | − | 0.671616i | \(-0.765600\pi\) |
0.952086 | + | 0.305829i | \(0.0989337\pi\) | |||||||
\(920\) | 180.449 | − | 104.182i | 0.196140 | − | 0.113242i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 262.292 | − | 454.302i | 0.284481 | − | 0.492736i | ||||
\(923\) | − | 225.564i | − | 0.244382i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −449.692 | −0.486153 | ||||||||
\(926\) | −95.9367 | − | 55.3891i | −0.103603 | − | 0.0598154i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −118.332 | − | 204.957i | −0.127513 | − | 0.220859i | ||||
\(929\) | −538.403 | − | 310.847i | −0.579551 | − | 0.334604i | 0.181404 | − | 0.983409i | \(-0.441936\pi\) |
−0.760955 | + | 0.648805i | \(0.775269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 52.5495i | − | 0.0563836i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 282.672 | + | 489.602i | 0.302647 | + | 0.524199i | ||||
\(935\) | −695.495 | + | 401.544i | −0.743845 | + | 0.429459i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1262.00 | 1.34685 | 0.673426 | − | 0.739255i | \(-0.264822\pi\) | ||||
0.673426 | + | 0.739255i | \(0.264822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −102.996 | + | 178.394i | −0.109570 | + | 0.189781i | ||||
\(941\) | −582.324 | + | 336.205i | −0.618835 | + | 0.357285i | −0.776415 | − | 0.630222i | \(-0.782964\pi\) |
0.157580 | + | 0.987506i | \(0.449631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 367.992 | − | 637.381i | 0.390236 | − | 0.675908i | ||||
\(944\) | 232.870i | 0.246684i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1433.33 | −1.51515 | ||||||||
\(947\) | 1004.37 | + | 579.874i | 1.06058 | + | 0.612327i | 0.925593 | − | 0.378520i | \(-0.123567\pi\) |
0.134989 | + | 0.990847i | \(0.456900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −714.656 | − | 1237.82i | −0.753062 | − | 1.30434i | ||||
\(950\) | 289.872 | + | 167.358i | 0.305129 | + | 0.176166i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 163.104i | 0.171148i | 0.996332 | + | 0.0855740i | \(0.0272724\pi\) | ||||
−0.996332 | + | 0.0855740i | \(0.972728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 691.992 | + | 1198.57i | 0.724599 | + | 1.25504i | ||||
\(956\) | 159.822 | − | 92.2733i | 0.167178 | − | 0.0965201i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −994.656 | −1.03826 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 163.836 | − | 283.772i | 0.170485 | − | 0.295288i | ||||
\(962\) | −864.859 | + | 499.326i | −0.899022 | + | 0.519050i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 343.247 | − | 594.521i | 0.356065 | − | 0.616723i | ||||
\(965\) | 813.260i | 0.842756i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 887.012 | 0.917282 | 0.458641 | − | 0.888622i | \(-0.348336\pi\) | ||||
0.458641 | + | 0.888622i | \(0.348336\pi\) | |||||||
\(968\) | −64.5097 | − | 37.2447i | −0.0666422 | − | 0.0384759i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −808.575 | − | 1400.49i | −0.833583 | − | 1.44381i | ||||
\(971\) | −1226.57 | − | 708.160i | −1.26320 | − | 0.729310i | −0.289510 | − | 0.957175i | \(-0.593492\pi\) |
−0.973693 | + | 0.227865i | \(0.926826\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 116.687i | − | 0.119801i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.3360 | − | 54.2755i | −0.0321065 | − | 0.0556101i | ||||
\(977\) | −293.627 | + | 169.525i | −0.300539 | + | 0.173516i | −0.642685 | − | 0.766131i | \(-0.722180\pi\) |
0.342146 | + | 0.939647i | \(0.388846\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57.9606 | −0.0592039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 130.251 | − | 225.601i | 0.132638 | − | 0.229737i | ||||
\(983\) | 422.523 | − | 243.943i | 0.429830 | − | 0.248162i | −0.269444 | − | 0.963016i | \(-0.586840\pi\) |
0.699274 | + | 0.714854i | \(0.253507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 572.195 | − | 991.070i | 0.580908 | − | 1.00616i | ||||
\(986\) | 644.996i | 0.654154i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 743.320 | 0.752348 | ||||||||
\(989\) | −877.731 | − | 506.758i | −0.887493 | − | 0.512394i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 468.737 | + | 811.877i | 0.472994 | + | 0.819250i | 0.999522 | − | 0.0309078i | \(-0.00983984\pi\) |
−0.526528 | + | 0.850158i | \(0.676507\pi\) | |||||||
\(992\) | −123.288 | − | 71.1802i | −0.124282 | − | 0.0717543i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 622.047i | 0.625173i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −230.506 | − | 399.248i | −0.231200 | − | 0.400449i | 0.726962 | − | 0.686678i | \(-0.240932\pi\) |
−0.958161 | + | 0.286229i | \(0.907598\pi\) | |||||||
\(998\) | 922.001 | − | 532.317i | 0.923848 | − | 0.533384i | ||||
\(999\) | 0 | 0 |
(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 | 882.3.s.e.863.1 | 8 | ||
3.2 | odd | 2 | inner | 882.3.s.e.863.4 | 8 | ||
7.2 | even | 3 | 126.3.b.a.71.4 | yes | 4 | ||
7.3 | odd | 6 | 882.3.s.i.557.3 | 8 | |||
7.4 | even | 3 | inner | 882.3.s.e.557.4 | 8 | ||
7.5 | odd | 6 | 882.3.b.f.197.3 | 4 | |||
7.6 | odd | 2 | 882.3.s.i.863.2 | 8 | |||
21.2 | odd | 6 | 126.3.b.a.71.1 | ✓ | 4 | ||
21.5 | even | 6 | 882.3.b.f.197.2 | 4 | |||
21.11 | odd | 6 | inner | 882.3.s.e.557.1 | 8 | ||
21.17 | even | 6 | 882.3.s.i.557.2 | 8 | |||
21.20 | even | 2 | 882.3.s.i.863.3 | 8 | |||
28.23 | odd | 6 | 1008.3.d.a.449.3 | 4 | |||
35.2 | odd | 12 | 3150.3.c.b.449.1 | 8 | |||
35.9 | even | 6 | 3150.3.e.e.701.2 | 4 | |||
35.23 | odd | 12 | 3150.3.c.b.449.7 | 8 | |||
56.37 | even | 6 | 4032.3.d.i.449.2 | 4 | |||
56.51 | odd | 6 | 4032.3.d.j.449.2 | 4 | |||
63.2 | odd | 6 | 1134.3.q.c.701.2 | 8 | |||
63.16 | even | 3 | 1134.3.q.c.701.3 | 8 | |||
63.23 | odd | 6 | 1134.3.q.c.1079.3 | 8 | |||
63.58 | even | 3 | 1134.3.q.c.1079.2 | 8 | |||
84.23 | even | 6 | 1008.3.d.a.449.2 | 4 | |||
105.2 | even | 12 | 3150.3.c.b.449.6 | 8 | |||
105.23 | even | 12 | 3150.3.c.b.449.4 | 8 | |||
105.44 | odd | 6 | 3150.3.e.e.701.4 | 4 | |||
168.107 | even | 6 | 4032.3.d.j.449.3 | 4 | |||
168.149 | odd | 6 | 4032.3.d.i.449.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.b.a.71.1 | ✓ | 4 | 21.2 | odd | 6 | ||
126.3.b.a.71.4 | yes | 4 | 7.2 | even | 3 | ||
882.3.b.f.197.2 | 4 | 21.5 | even | 6 | |||
882.3.b.f.197.3 | 4 | 7.5 | odd | 6 | |||
882.3.s.e.557.1 | 8 | 21.11 | odd | 6 | inner | ||
882.3.s.e.557.4 | 8 | 7.4 | even | 3 | inner | ||
882.3.s.e.863.1 | 8 | 1.1 | even | 1 | trivial | ||
882.3.s.e.863.4 | 8 | 3.2 | odd | 2 | inner | ||
882.3.s.i.557.2 | 8 | 21.17 | even | 6 | |||
882.3.s.i.557.3 | 8 | 7.3 | odd | 6 | |||
882.3.s.i.863.2 | 8 | 7.6 | odd | 2 | |||
882.3.s.i.863.3 | 8 | 21.20 | even | 2 | |||
1008.3.d.a.449.2 | 4 | 84.23 | even | 6 | |||
1008.3.d.a.449.3 | 4 | 28.23 | odd | 6 | |||
1134.3.q.c.701.2 | 8 | 63.2 | odd | 6 | |||
1134.3.q.c.701.3 | 8 | 63.16 | even | 3 | |||
1134.3.q.c.1079.2 | 8 | 63.58 | even | 3 | |||
1134.3.q.c.1079.3 | 8 | 63.23 | odd | 6 | |||
3150.3.c.b.449.1 | 8 | 35.2 | odd | 12 | |||
3150.3.c.b.449.4 | 8 | 105.23 | even | 12 | |||
3150.3.c.b.449.6 | 8 | 105.2 | even | 12 | |||
3150.3.c.b.449.7 | 8 | 35.23 | odd | 12 | |||
3150.3.e.e.701.2 | 4 | 35.9 | even | 6 | |||
3150.3.e.e.701.4 | 4 | 105.44 | odd | 6 | |||
4032.3.d.i.449.2 | 4 | 56.37 | even | 6 | |||
4032.3.d.i.449.3 | 4 | 168.149 | odd | 6 | |||
4032.3.d.j.449.2 | 4 | 56.51 | odd | 6 | |||
4032.3.d.j.449.3 | 4 | 168.107 | even | 6 |