Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.11 | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.d.215.11 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.555155 | + | 0.320519i | −0.196277 | + | 0.113320i | −0.594918 | − | 0.803787i | \(-0.702815\pi\) |
0.398641 | + | 0.917107i | \(0.369482\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.79454 | + | 6.57233i | −0.474317 | + | 0.821541i | ||||
\(5\) | −6.03646 | − | 10.4555i | −0.539918 | − | 0.935165i | −0.998908 | − | 0.0467235i | \(-0.985122\pi\) |
0.458990 | − | 0.888441i | \(-0.348211\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 9.99318i | − | 0.441640i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.70234 | + | 3.86960i | 0.211947 | + | 0.122367i | ||||
\(11\) | −38.0525 | − | 21.9696i | −1.04302 | − | 0.602190i | −0.122336 | − | 0.992489i | \(-0.539038\pi\) |
−0.920688 | + | 0.390298i | \(0.872372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 66.9783i | 1.42896i | 0.699657 | + | 0.714479i | \(0.253336\pi\) | ||||
−0.699657 | + | 0.714479i | \(0.746664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −27.1533 | − | 47.0309i | −0.424270 | − | 0.734857i | ||||
\(17\) | −19.7155 | + | 34.1482i | −0.281277 | + | 0.487186i | −0.971700 | − | 0.236220i | \(-0.924091\pi\) |
0.690423 | + | 0.723406i | \(0.257425\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 50.1554 | − | 28.9572i | 0.605601 | − | 0.349644i | −0.165641 | − | 0.986186i | \(-0.552969\pi\) |
0.771242 | + | 0.636542i | \(0.219636\pi\) | |||||||
\(20\) | 91.6223 | 1.02437 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 28.1667 | 0.272962 | ||||||||
\(23\) | 39.9687 | − | 23.0759i | 0.362350 | − | 0.209203i | −0.307761 | − | 0.951464i | \(-0.599580\pi\) |
0.670111 | + | 0.742261i | \(0.266246\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.3778 | + | 17.9748i | −0.0830221 | + | 0.143799i | ||||
\(26\) | −21.4678 | − | 37.1833i | −0.161930 | − | 0.280471i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 201.623i | − | 1.29105i | −0.763738 | − | 0.645526i | \(-0.776638\pi\) | ||
0.763738 | − | 0.645526i | \(-0.223362\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −160.666 | − | 92.7605i | −0.930853 | − | 0.537428i | −0.0437720 | − | 0.999042i | \(-0.513938\pi\) |
−0.887081 | + | 0.461613i | \(0.847271\pi\) | |||||||
\(32\) | 99.3833 | + | 57.3790i | 0.549020 | + | 0.316977i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 25.2767i | − | 0.127498i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 205.402 | + | 355.767i | 0.912647 | + | 1.58075i | 0.810310 | + | 0.586002i | \(0.199299\pi\) |
0.102338 | + | 0.994750i | \(0.467368\pi\) | |||||||
\(38\) | −18.5626 | + | 32.1515i | −0.0792437 | + | 0.137254i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −104.483 | + | 60.3234i | −0.413006 | + | 0.238449i | ||||
\(41\) | 408.886 | 1.55749 | 0.778746 | − | 0.627339i | \(-0.215856\pi\) | ||||
0.778746 | + | 0.627339i | \(0.215856\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 129.530 | 0.459377 | 0.229688 | − | 0.973264i | \(-0.426229\pi\) | ||||
0.229688 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(44\) | 288.783 | − | 166.729i | 0.989448 | − | 0.571258i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.7925 | + | 25.6214i | −0.0474139 | + | 0.0821234i | ||||
\(47\) | 257.340 | + | 445.726i | 0.798658 | + | 1.38332i | 0.920490 | + | 0.390766i | \(0.127790\pi\) |
−0.121832 | + | 0.992551i | \(0.538877\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 13.3051i | − | 0.0376324i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −440.204 | − | 254.152i | −1.17395 | − | 0.677779i | ||||
\(53\) | 378.958 | + | 218.792i | 0.982150 | + | 0.567045i | 0.902919 | − | 0.429812i | \(-0.141420\pi\) |
0.0792314 | + | 0.996856i | \(0.474753\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 530.475i | 1.30053i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 64.6241 | + | 111.932i | 0.146303 | + | 0.253404i | ||||
\(59\) | −303.953 | + | 526.462i | −0.670701 | + | 1.16169i | 0.307005 | + | 0.951708i | \(0.400673\pi\) |
−0.977706 | + | 0.209980i | \(0.932660\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21.2342 | + | 12.2596i | −0.0445699 | + | 0.0257324i | −0.522119 | − | 0.852872i | \(-0.674858\pi\) |
0.477549 | + | 0.878605i | \(0.341525\pi\) | |||||||
\(62\) | 118.926 | 0.243607 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 360.888 | 0.704860 | ||||||||
\(65\) | 700.289 | − | 404.312i | 1.33631 | − | 0.771519i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −220.750 | + | 382.350i | −0.402520 | + | 0.697186i | −0.994029 | − | 0.109113i | \(-0.965199\pi\) |
0.591509 | + | 0.806298i | \(0.298532\pi\) | |||||||
\(68\) | −149.622 | − | 259.153i | −0.266829 | − | 0.462161i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1150.89i | − | 1.92373i | −0.273518 | − | 0.961867i | \(-0.588187\pi\) | ||
0.273518 | − | 0.961867i | \(-0.411813\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 454.730 | + | 262.539i | 0.729070 | + | 0.420929i | 0.818082 | − | 0.575102i | \(-0.195038\pi\) |
−0.0890117 | + | 0.996031i | \(0.528371\pi\) | |||||||
\(74\) | −228.060 | − | 131.671i | −0.358263 | − | 0.206843i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 439.517i | 0.663369i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 75.9251 | + | 131.506i | 0.108130 | + | 0.187286i | 0.915013 | − | 0.403425i | \(-0.132181\pi\) |
−0.806883 | + | 0.590711i | \(0.798847\pi\) | |||||||
\(80\) | −327.820 | + | 567.800i | −0.458142 | + | 0.793525i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −226.995 | + | 131.055i | −0.305700 | + | 0.176496i | ||||
\(83\) | 1302.05 | 1.72191 | 0.860956 | − | 0.508680i | \(-0.169866\pi\) | ||||
0.860956 | + | 0.508680i | \(0.169866\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 476.047 | 0.607466 | ||||||||
\(86\) | −71.9094 | + | 41.5169i | −0.0901650 | + | 0.0520568i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −219.546 | + | 380.266i | −0.265951 | + | 0.460641i | ||||
\(89\) | −291.595 | − | 505.057i | −0.347292 | − | 0.601528i | 0.638475 | − | 0.769642i | \(-0.279565\pi\) |
−0.985767 | + | 0.168115i | \(0.946232\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 350.250i | 0.396914i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −285.727 | − | 164.965i | −0.313516 | − | 0.181009i | ||||
\(95\) | −605.522 | − | 349.598i | −0.653950 | − | 0.377558i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1091.84i | 1.14288i | 0.820643 | + | 0.571441i | \(0.193616\pi\) | ||||
−0.820643 | + | 0.571441i | \(0.806384\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −78.7576 | − | 136.412i | −0.0787576 | − | 0.136412i | ||||
\(101\) | −78.3866 | + | 135.770i | −0.0772254 | + | 0.133758i | −0.902052 | − | 0.431628i | \(-0.857939\pi\) |
0.824826 | + | 0.565386i | \(0.191273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 208.779 | − | 120.539i | 0.199725 | − | 0.115311i | −0.396802 | − | 0.917904i | \(-0.629880\pi\) |
0.596527 | + | 0.802593i | \(0.296547\pi\) | |||||||
\(104\) | 669.326 | 0.631085 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −280.507 | −0.257031 | ||||||||
\(107\) | 11.1175 | − | 6.41871i | 0.0100446 | − | 0.00579926i | −0.494969 | − | 0.868910i | \(-0.664821\pi\) |
0.505014 | + | 0.863111i | \(0.331487\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1033.20 | − | 1789.56i | 0.907915 | − | 1.57256i | 0.0909595 | − | 0.995855i | \(-0.471007\pi\) |
0.816956 | − | 0.576701i | \(-0.195660\pi\) | |||||||
\(110\) | −170.027 | − | 294.496i | −0.147377 | − | 0.255264i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 87.2159i | − | 0.0726069i | −0.999341 | − | 0.0363035i | \(-0.988442\pi\) | ||
0.999341 | − | 0.0363035i | \(-0.0115583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −482.539 | − | 278.594i | −0.391278 | − | 0.225905i | ||||
\(116\) | 1325.14 | + | 765.067i | 1.06065 | + | 0.612368i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 389.691i | − | 0.304016i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 299.829 | + | 519.320i | 0.225266 | + | 0.390173i | ||||
\(122\) | 7.85885 | − | 13.6119i | 0.00583202 | − | 0.0101014i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1219.31 | − | 703.966i | 0.883039 | − | 0.509823i | ||||
\(125\) | −1258.54 | −0.900535 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1933.38 | 1.35086 | 0.675432 | − | 0.737423i | \(-0.263957\pi\) | ||||
0.675432 | + | 0.737423i | \(0.263957\pi\) | |||||||
\(128\) | −995.415 | + | 574.703i | −0.687368 | + | 0.396852i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −259.179 | + | 448.912i | −0.174858 | + | 0.302863i | ||||
\(131\) | 677.042 | + | 1172.67i | 0.451553 | + | 0.782112i | 0.998483 | − | 0.0550661i | \(-0.0175370\pi\) |
−0.546930 | + | 0.837178i | \(0.684204\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 283.018i | − | 0.182455i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 341.249 | + | 197.020i | 0.215161 | + | 0.124223i | ||||
\(137\) | 53.9293 | + | 31.1361i | 0.0336313 | + | 0.0194171i | 0.516721 | − | 0.856154i | \(-0.327152\pi\) |
−0.483090 | + | 0.875571i | \(0.660486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2355.95i | − | 1.43762i | −0.695208 | − | 0.718808i | \(-0.744688\pi\) | ||
0.695208 | − | 0.718808i | \(-0.255312\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 368.881 | + | 638.920i | 0.217998 | + | 0.377584i | ||||
\(143\) | 1471.49 | − | 2548.69i | 0.860504 | − | 1.49044i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2108.07 | + | 1217.09i | −1.20735 | + | 0.697062i | ||||
\(146\) | −336.594 | −0.190799 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3117.63 | −1.73154 | ||||||||
\(149\) | 310.258 | − | 179.128i | 0.170586 | − | 0.0984881i | −0.412276 | − | 0.911059i | \(-0.635266\pi\) |
0.582862 | + | 0.812571i | \(0.301933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −230.159 | + | 398.648i | −0.124040 | + | 0.214844i | −0.921357 | − | 0.388716i | \(-0.872919\pi\) |
0.797317 | + | 0.603561i | \(0.206252\pi\) | |||||||
\(152\) | −289.374 | − | 501.211i | −0.154417 | − | 0.267458i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2239.78i | 1.16067i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 652.641 | + | 376.803i | 0.331761 | + | 0.191542i | 0.656623 | − | 0.754219i | \(-0.271984\pi\) |
−0.324862 | + | 0.945762i | \(0.605318\pi\) | |||||||
\(158\) | −84.3003 | − | 48.6708i | −0.0424467 | − | 0.0245066i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1385.46i | − | 0.684566i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1206.86 | − | 2090.34i | −0.579929 | − | 1.00447i | −0.995487 | − | 0.0948996i | \(-0.969747\pi\) |
0.415558 | − | 0.909567i | \(-0.363586\pi\) | |||||||
\(164\) | −1551.53 | + | 2687.33i | −0.738745 | + | 1.27954i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −722.839 | + | 417.332i | −0.337971 | + | 0.195128i | ||||
\(167\) | −2912.06 | −1.34935 | −0.674676 | − | 0.738114i | \(-0.735717\pi\) | ||||
−0.674676 | + | 0.738114i | \(0.735717\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2289.10 | −1.04192 | ||||||||
\(170\) | −264.280 | + | 152.582i | −0.119231 | + | 0.0688383i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −491.508 | + | 851.316i | −0.217890 | + | 0.377397i | ||||
\(173\) | 869.770 | + | 1506.49i | 0.382239 | + | 0.662057i | 0.991382 | − | 0.131003i | \(-0.0418198\pi\) |
−0.609143 | + | 0.793060i | \(0.708486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2386.19i | 1.02197i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 323.761 | + | 186.923i | 0.136331 | + | 0.0787106i | ||||
\(179\) | −2283.30 | − | 1318.26i | −0.953418 | − | 0.550456i | −0.0592772 | − | 0.998242i | \(-0.518880\pi\) |
−0.894141 | + | 0.447785i | \(0.852213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 208.975i | 0.0858175i | 0.999079 | + | 0.0429087i | \(0.0136625\pi\) | ||||
−0.999079 | + | 0.0429087i | \(0.986338\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −230.602 | − | 399.414i | −0.0923924 | − | 0.160028i | ||||
\(185\) | 2479.81 | − | 4295.15i | 0.985509 | − | 1.70695i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1500.45 | − | 866.284i | 0.586757 | − | 0.338765i | ||||
\(188\) | −3905.95 | −1.51527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 448.211 | 0.171140 | ||||||||
\(191\) | −667.111 | + | 385.157i | −0.252725 | + | 0.145911i | −0.621011 | − | 0.783802i | \(-0.713278\pi\) |
0.368286 | + | 0.929712i | \(0.379945\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −430.418 | + | 745.506i | −0.160529 | + | 0.278045i | −0.935059 | − | 0.354493i | \(-0.884654\pi\) |
0.774529 | + | 0.632538i | \(0.217987\pi\) | |||||||
\(194\) | −349.955 | − | 606.140i | −0.129512 | − | 0.224321i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1034.13i | − | 0.374003i | −0.982360 | − | 0.187001i | \(-0.940123\pi\) | ||
0.982360 | − | 0.187001i | \(-0.0598769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4469.63 | + | 2580.54i | 1.59218 | + | 0.919246i | 0.992932 | + | 0.118682i | \(0.0378670\pi\) |
0.599248 | + | 0.800564i | \(0.295466\pi\) | |||||||
\(200\) | 179.626 | + | 103.707i | 0.0635072 | + | 0.0366659i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 100.498i | − | 0.0350049i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2468.22 | − | 4275.09i | −0.840918 | − | 1.45651i | ||||
\(206\) | −77.2699 | + | 133.835i | −0.0261342 | + | 0.0452658i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3150.05 | − | 1818.68i | 1.05008 | − | 0.606264i | ||||
\(209\) | −2544.72 | −0.842209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 136.191 | 0.0444349 | 0.0222174 | − | 0.999753i | \(-0.492927\pi\) | ||||
0.0222174 | + | 0.999753i | \(0.492927\pi\) | |||||||
\(212\) | −2875.94 | + | 1660.43i | −0.931701 | + | 0.537918i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.11463 | + | 7.12675i | −0.00131435 | + | 0.00227652i | ||||
\(215\) | −781.906 | − | 1354.30i | −0.248026 | − | 0.429593i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1324.64i | 0.411541i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3486.46 | − | 2012.91i | −1.06844 | − | 0.616865i | ||||
\(221\) | −2287.19 | − | 1320.51i | −0.696168 | − | 0.401933i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2544.16i | − | 0.763989i | −0.924165 | − | 0.381994i | \(-0.875237\pi\) | ||
0.924165 | − | 0.381994i | \(-0.124763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27.9543 | + | 48.4183i | 0.00822785 | + | 0.0142511i | ||||
\(227\) | 2219.10 | − | 3843.59i | 0.648840 | − | 1.12382i | −0.334560 | − | 0.942374i | \(-0.608588\pi\) |
0.983400 | − | 0.181449i | \(-0.0580789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2692.24 | + | 1554.36i | −0.776892 | + | 0.448539i | −0.835328 | − | 0.549753i | \(-0.814722\pi\) |
0.0584360 | + | 0.998291i | \(0.481389\pi\) | |||||||
\(230\) | 357.179 | 0.102398 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2014.86 | −0.570181 | ||||||||
\(233\) | −3973.34 | + | 2294.01i | −1.11718 | + | 0.645002i | −0.940679 | − | 0.339299i | \(-0.889810\pi\) |
−0.176498 | + | 0.984301i | \(0.556477\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3106.85 | − | 5381.22i | 0.862419 | − | 1.49375i | ||||
\(236\) | −2306.72 | − | 3995.36i | −0.636249 | − | 1.10202i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 738.555i | 0.199888i | 0.994993 | + | 0.0999439i | \(0.0318663\pi\) | ||||
−0.994993 | + | 0.0999439i | \(0.968134\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 216.280 | + | 124.870i | 0.0578085 | + | 0.0333757i | 0.528626 | − | 0.848855i | \(-0.322708\pi\) |
−0.470817 | + | 0.882231i | \(0.656041\pi\) | |||||||
\(242\) | −332.903 | − | 192.202i | −0.0884291 | − | 0.0510545i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 186.078i | − | 0.0488213i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1939.51 | + | 3359.32i | 0.499627 | + | 0.865379i | ||||
\(248\) | −926.972 | + | 1605.56i | −0.237350 | + | 0.411102i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 698.682 | − | 403.384i | 0.176754 | − | 0.102049i | ||||
\(251\) | 4098.68 | 1.03070 | 0.515351 | − | 0.856979i | \(-0.327662\pi\) | ||||
0.515351 | + | 0.856979i | \(0.327662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2027.88 | −0.503920 | ||||||||
\(254\) | −1073.32 | + | 619.684i | −0.265143 | + | 0.153080i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1075.15 | + | 1862.21i | −0.262487 | + | 0.454641i | ||||
\(257\) | 1337.52 | + | 2316.66i | 0.324640 | + | 0.562293i | 0.981439 | − | 0.191773i | \(-0.0614236\pi\) |
−0.656800 | + | 0.754065i | \(0.728090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6136.71i | 1.46378i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −751.726 | − | 434.009i | −0.177259 | − | 0.102340i | ||||
\(263\) | −1632.27 | − | 942.393i | −0.382700 | − | 0.220952i | 0.296292 | − | 0.955097i | \(-0.404250\pi\) |
−0.678993 | + | 0.734145i | \(0.737583\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5282.91i | − | 1.22463i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1675.28 | − | 2901.68i | −0.381844 | − | 0.661374i | ||||
\(269\) | 603.608 | − | 1045.48i | 0.136813 | − | 0.236967i | −0.789476 | − | 0.613782i | \(-0.789647\pi\) |
0.926289 | + | 0.376815i | \(0.122981\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3938.31 | − | 2273.78i | 0.882786 | − | 0.509677i | 0.0112103 | − | 0.999937i | \(-0.496432\pi\) |
0.871576 | + | 0.490260i | \(0.163098\pi\) | |||||||
\(272\) | 2141.36 | 0.477350 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −39.9188 | −0.00880140 | ||||||||
\(275\) | 789.800 | − | 455.991i | 0.173188 | − | 0.0999903i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2136.36 | − | 3700.29i | 0.463400 | − | 0.802632i | −0.535728 | − | 0.844391i | \(-0.679963\pi\) |
0.999128 | + | 0.0417588i | \(0.0132961\pi\) | |||||||
\(278\) | 755.125 | + | 1307.91i | 0.162911 | + | 0.282171i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8218.49i | − | 1.74475i | −0.488840 | − | 0.872374i | \(-0.662580\pi\) | ||
0.488840 | − | 0.872374i | \(-0.337420\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4172.42 | + | 2408.95i | 0.876411 | + | 0.505996i | 0.869473 | − | 0.493980i | \(-0.164458\pi\) |
0.00693786 | + | 0.999976i | \(0.497792\pi\) | |||||||
\(284\) | 7564.01 | + | 4367.08i | 1.58043 | + | 0.912460i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1886.56i | 0.390051i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1679.10 | + | 2908.28i | 0.341767 | + | 0.591957i | ||||
\(290\) | 780.201 | − | 1351.35i | 0.157983 | − | 0.273634i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3450.98 | + | 1992.42i | −0.691621 | + | 0.399307i | ||||
\(293\) | −6857.68 | −1.36734 | −0.683669 | − | 0.729792i | \(-0.739617\pi\) | ||||
−0.683669 | + | 0.729792i | \(0.739617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7339.21 | 1.44849 | ||||||||
\(296\) | 3555.25 | − | 2052.62i | 0.698123 | − | 0.403062i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −114.828 | + | 198.887i | −0.0223214 | + | 0.0386618i | ||||
\(299\) | 1545.59 | + | 2677.04i | 0.298942 | + | 0.517783i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 295.081i | − | 0.0562253i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2723.77 | − | 1572.57i | −0.513877 | − | 0.296687i | ||||
\(305\) | 256.359 | + | 148.009i | 0.0481281 | + | 0.0277868i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7537.04i | 1.40118i | 0.713565 | + | 0.700589i | \(0.247079\pi\) | ||||
−0.713565 | + | 0.700589i | \(0.752921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −717.892 | − | 1243.43i | −0.131527 | − | 0.227812i | ||||
\(311\) | −2793.76 | + | 4838.93i | −0.509388 | + | 0.882285i | 0.490553 | + | 0.871411i | \(0.336795\pi\) |
−0.999941 | + | 0.0108742i | \(0.996539\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3655.95 | + | 2110.76i | −0.660212 | + | 0.381174i | −0.792358 | − | 0.610057i | \(-0.791147\pi\) |
0.132146 | + | 0.991230i | \(0.457813\pi\) | |||||||
\(314\) | −483.089 | −0.0868226 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1152.40 | −0.205151 | ||||||||
\(317\) | 7158.31 | − | 4132.85i | 1.26830 | − | 0.732252i | 0.293632 | − | 0.955918i | \(-0.405136\pi\) |
0.974666 | + | 0.223666i | \(0.0718025\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4429.59 | + | 7672.28i | −0.777459 | + | 1.34660i | ||||
\(320\) | −2178.49 | − | 3773.25i | −0.380566 | − | 0.659161i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2283.62i | 0.393387i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1203.92 | − | 695.086i | −0.205482 | − | 0.118635i | ||||
\(326\) | 1339.99 | + | 773.641i | 0.227653 | + | 0.131436i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 4086.07i | − | 0.687851i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3654.72 | + | 6330.16i | 0.606893 | + | 1.05117i | 0.991749 | + | 0.128193i | \(0.0409178\pi\) |
−0.384856 | + | 0.922977i | \(0.625749\pi\) | |||||||
\(332\) | −4940.68 | + | 8557.51i | −0.816732 | + | 1.41462i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1616.64 | − | 933.369i | 0.264846 | − | 0.152909i | ||||
\(335\) | 5330.19 | 0.869311 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 127.665 | 0.0206361 | 0.0103180 | − | 0.999947i | \(-0.496716\pi\) | ||||
0.0103180 | + | 0.999947i | \(0.496716\pi\) | |||||||
\(338\) | 1270.80 | − | 733.698i | 0.204505 | − | 0.118071i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1806.38 | + | 3128.74i | −0.288131 | + | 0.499058i | ||||
\(341\) | 4075.83 | + | 7059.54i | 0.647268 | + | 1.12110i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1294.42i | − | 0.202879i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −965.713 | − | 557.555i | −0.150049 | − | 0.0866310i | ||||
\(347\) | −4477.85 | − | 2585.29i | −0.692748 | − | 0.399958i | 0.111893 | − | 0.993720i | \(-0.464309\pi\) |
−0.804641 | + | 0.593762i | \(0.797642\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11271.1i | 1.72874i | 0.502855 | + | 0.864370i | \(0.332283\pi\) | ||||
−0.502855 | + | 0.864370i | \(0.667717\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2521.19 | − | 4366.83i | −0.381761 | − | 0.661229i | ||||
\(353\) | −828.962 | + | 1435.80i | −0.124989 | + | 0.216488i | −0.921729 | − | 0.387835i | \(-0.873223\pi\) |
0.796740 | + | 0.604323i | \(0.206556\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12033.0 | + | 6947.28i | −1.79901 | + | 1.03866i | ||||
\(356\) | 4425.87 | 0.658906 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1690.11 | 0.249512 | ||||||||
\(359\) | −247.512 | + | 142.901i | −0.0363878 | + | 0.0210085i | −0.518084 | − | 0.855330i | \(-0.673354\pi\) |
0.481696 | + | 0.876339i | \(0.340021\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1752.46 | + | 3035.35i | −0.255498 | + | 0.442535i | ||||
\(362\) | −66.9803 | − | 116.013i | −0.00972488 | − | 0.0168440i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6339.22i | − | 0.909068i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3815.77 | + | 2203.04i | 0.542729 | + | 0.313345i | 0.746184 | − | 0.665739i | \(-0.231884\pi\) |
−0.203455 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(368\) | −2170.56 | − | 1253.18i | −0.307469 | − | 0.177517i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3179.30i | 0.446713i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6272.53 | + | 10864.3i | 0.870722 | + | 1.50813i | 0.861251 | + | 0.508179i | \(0.169681\pi\) |
0.00947025 | + | 0.999955i | \(0.496985\pi\) | |||||||
\(374\) | −555.320 | + | 961.843i | −0.0767779 | + | 0.132983i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4454.22 | − | 2571.65i | 0.610928 | − | 0.352720i | ||||
\(377\) | 13504.4 | 1.84486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4695.85 | 0.636437 | 0.318219 | − | 0.948017i | \(-0.396915\pi\) | ||||
0.318219 | + | 0.948017i | \(0.396915\pi\) | |||||||
\(380\) | 4595.35 | − | 2653.13i | 0.620359 | − | 0.358164i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 246.900 | − | 427.643i | 0.0330693 | − | 0.0572778i | ||||
\(383\) | −3595.01 | − | 6226.74i | −0.479625 | − | 0.830735i | 0.520102 | − | 0.854104i | \(-0.325894\pi\) |
−0.999727 | + | 0.0233693i | \(0.992561\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 551.828i | − | 0.0727651i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7175.94 | − | 4143.03i | −0.938925 | − | 0.542089i | ||||
\(389\) | 7956.88 | + | 4593.91i | 1.03709 | + | 0.598767i | 0.919009 | − | 0.394237i | \(-0.128991\pi\) |
0.118086 | + | 0.993003i | \(0.462324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1819.81i | 0.235376i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 331.457 | + | 574.101i | 0.0423822 | + | 0.0734080i | ||||
\(395\) | 916.638 | − | 1587.66i | 0.116762 | − | 0.202238i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10350.6 | − | 5975.91i | 1.30851 | − | 0.755471i | 0.326667 | − | 0.945140i | \(-0.394075\pi\) |
0.981848 | + | 0.189668i | \(0.0607412\pi\) | |||||||
\(398\) | −3308.45 | −0.416677 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1127.16 | 0.140895 | ||||||||
\(401\) | 5927.66 | − | 3422.34i | 0.738188 | − | 0.426193i | −0.0832223 | − | 0.996531i | \(-0.526521\pi\) |
0.821410 | + | 0.570338i | \(0.193188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6212.94 | − | 10761.1i | 0.767962 | − | 1.33015i | ||||
\(404\) | −594.882 | − | 1030.37i | −0.0732586 | − | 0.126888i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18050.5i | − | 2.19835i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4474.70 | − | 2583.47i | −0.540977 | − | 0.312333i | 0.204498 | − | 0.978867i | \(-0.434444\pi\) |
−0.745475 | + | 0.666534i | \(0.767777\pi\) | |||||||
\(410\) | 2740.49 | + | 1582.22i | 0.330105 | + | 0.190586i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1829.56i | 0.218776i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7859.78 | − | 13613.5i | −0.929690 | − | 1.61027i | ||||
\(416\) | −3843.15 | + | 6656.53i | −0.452947 | + | 0.784527i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1412.71 | − | 815.629i | 0.165306 | − | 0.0954395i | ||||
\(419\) | 13900.4 | 1.62071 | 0.810356 | − | 0.585938i | \(-0.199274\pi\) | ||||
0.810356 | + | 0.585938i | \(0.199274\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7800.31 | 0.903003 | 0.451501 | − | 0.892270i | \(-0.350889\pi\) | ||||
0.451501 | + | 0.892270i | \(0.350889\pi\) | |||||||
\(422\) | −75.6069 | + | 43.6517i | −0.00872153 | + | 0.00503538i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2186.42 | − | 3787.00i | 0.250430 | − | 0.433757i | ||||
\(425\) | −409.206 | − | 708.765i | −0.0467044 | − | 0.0808945i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 97.4241i | 0.0110027i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 868.157 | + | 501.231i | 0.0973634 | + | 0.0562128i | ||||
\(431\) | −1806.23 | − | 1042.83i | −0.201863 | − | 0.116546i | 0.395661 | − | 0.918397i | \(-0.370515\pi\) |
−0.597524 | + | 0.801851i | \(0.703849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1186.95i | − | 0.131735i | −0.997828 | − | 0.0658674i | \(-0.979019\pi\) | ||
0.997828 | − | 0.0658674i | \(-0.0209814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7841.04 | + | 13581.1i | 0.861279 | + | 1.49178i | ||||
\(437\) | 1336.43 | − | 2314.76i | 0.146293 | − | 0.253387i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7527.93 | − | 4346.25i | 0.818425 | − | 0.472518i | −0.0314484 | − | 0.999505i | \(-0.510012\pi\) |
0.849873 | + | 0.526988i | \(0.176679\pi\) | |||||||
\(440\) | 5301.13 | 0.574367 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1692.99 | 0.182189 | ||||||||
\(443\) | −5853.20 | + | 3379.34i | −0.627751 | + | 0.362432i | −0.779881 | − | 0.625928i | \(-0.784720\pi\) |
0.152130 | + | 0.988361i | \(0.451387\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3520.40 | + | 6097.52i | −0.375018 | + | 0.649551i | ||||
\(446\) | 815.451 | + | 1412.40i | 0.0865756 | + | 0.149953i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6721.89i | 0.706516i | 0.935526 | + | 0.353258i | \(0.114926\pi\) | ||||
−0.935526 | + | 0.353258i | \(0.885074\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15559.1 | − | 8983.06i | −1.62450 | − | 0.937907i | ||||
\(452\) | 573.212 | + | 330.944i | 0.0596496 | + | 0.0344387i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2845.05i | 0.294107i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1650.93 | + | 2859.50i | 0.168988 | + | 0.292695i | 0.938064 | − | 0.346461i | \(-0.112617\pi\) |
−0.769077 | + | 0.639157i | \(0.779284\pi\) | |||||||
\(458\) | 996.406 | − | 1725.83i | 0.101657 | − | 0.176075i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3662.02 | − | 2114.27i | 0.371180 | − | 0.214301i | ||||
\(461\) | 7241.19 | 0.731574 | 0.365787 | − | 0.930699i | \(-0.380800\pi\) | ||||
0.365787 | + | 0.930699i | \(0.380800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7585.65 | −0.761415 | −0.380707 | − | 0.924696i | \(-0.624319\pi\) | ||||
−0.380707 | + | 0.924696i | \(0.624319\pi\) | |||||||
\(464\) | −9482.52 | + | 5474.74i | −0.948739 | + | 0.547755i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1470.54 | − | 2547.06i | 0.146184 | − | 0.253198i | ||||
\(467\) | 1024.28 | + | 1774.11i | 0.101495 | + | 0.175794i | 0.912301 | − | 0.409521i | \(-0.134304\pi\) |
−0.810806 | + | 0.585315i | \(0.800971\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3983.21i | 0.390919i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5261.03 | + | 3037.46i | 0.513048 | + | 0.296208i | ||||
\(473\) | −4928.96 | − | 2845.74i | −0.479141 | − | 0.276632i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1202.04i | 0.116113i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −236.721 | − | 410.012i | −0.0226514 | − | 0.0392333i | ||||
\(479\) | −1648.52 | + | 2855.32i | −0.157250 | + | 0.272365i | −0.933876 | − | 0.357597i | \(-0.883596\pi\) |
0.776626 | + | 0.629962i | \(0.216929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23828.7 | + | 13757.5i | −2.25883 | + | 1.30413i | ||||
\(482\) | −160.092 | −0.0151286 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4550.85 | −0.427390 | ||||||||
\(485\) | 11415.7 | − | 6590.86i | 1.06878 | − | 0.617063i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 589.853 | − | 1021.66i | 0.0548846 | − | 0.0950630i | −0.837278 | − | 0.546778i | \(-0.815854\pi\) |
0.892162 | + | 0.451715i | \(0.149188\pi\) | |||||||
\(488\) | 122.512 | + | 212.197i | 0.0113645 | + | 0.0196839i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7573.80i | − | 0.696132i | −0.937470 | − | 0.348066i | \(-0.886838\pi\) | ||
0.937470 | − | 0.348066i | \(-0.113162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6885.08 | + | 3975.10i | 0.628983 | + | 0.363143i | ||||
\(494\) | −2153.45 | − | 1243.30i | −0.196130 | − | 0.113236i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10075.0i | 0.912059i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 909.766 | + | 1575.76i | 0.0816167 | + | 0.141364i | 0.903945 | − | 0.427650i | \(-0.140658\pi\) |
−0.822328 | + | 0.569014i | \(0.807325\pi\) | |||||||
\(500\) | 4775.56 | − | 8271.51i | 0.427139 | − | 0.739826i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2275.40 | + | 1313.70i | −0.202303 | + | 0.116800i | ||||
\(503\) | −15635.9 | −1.38602 | −0.693012 | − | 0.720926i | \(-0.743717\pi\) | ||||
−0.693012 | + | 0.720926i | \(0.743717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1892.71 | 0.166781 | ||||||||
\(506\) | 1125.79 | − | 649.973i | 0.0989078 | − | 0.0571044i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7336.28 | + | 12706.8i | −0.640737 | + | 1.10979i | ||||
\(509\) | 1646.90 | + | 2852.51i | 0.143413 | + | 0.248399i | 0.928780 | − | 0.370632i | \(-0.120859\pi\) |
−0.785367 | + | 0.619031i | \(0.787526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 10573.7i | − | 0.912685i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1485.06 | − | 857.403i | −0.127439 | − | 0.0735767i | ||||
\(515\) | −2520.58 | − | 1455.26i | −0.215670 | − | 0.124517i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 22614.7i | − | 1.92378i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4040.36 | − | 6998.11i | −0.340734 | − | 0.590168i | ||||
\(521\) | −1649.02 | + | 2856.19i | −0.138666 | + | 0.240176i | −0.926992 | − | 0.375081i | \(-0.877615\pi\) |
0.788326 | + | 0.615258i | \(0.210948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15438.1 | − | 8913.21i | 1.29075 | − | 0.745215i | 0.311963 | − | 0.950094i | \(-0.399013\pi\) |
0.978787 | + | 0.204879i | \(0.0656801\pi\) | |||||||
\(524\) | −10276.2 | −0.856716 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1208.22 | 0.100154 | ||||||||
\(527\) | 6335.22 | − | 3657.64i | 0.523655 | − | 0.302333i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5018.50 | + | 8692.30i | −0.412468 | + | 0.714416i | ||||
\(530\) | 1693.27 | + | 2932.83i | 0.138776 | + | 0.240366i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27386.5i | 2.22559i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −134.221 | − | 77.4926i | −0.0108465 | − | 0.00626224i | ||||
\(536\) | 3820.89 | + | 2205.99i | 0.307905 | + | 0.177769i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 773.871i | 0.0620148i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5209.12 | − | 9022.46i | −0.413969 | − | 0.717016i | 0.581350 | − | 0.813653i | \(-0.302525\pi\) |
−0.995320 | + | 0.0966374i | \(0.969191\pi\) | |||||||
\(542\) | −1457.58 | + | 2524.60i | −0.115514 | + | 0.200076i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3918.78 | + | 2262.51i | −0.308854 | + | 0.178317i | ||||
\(545\) | −24947.5 | −1.96080 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −996.607 | −0.0779010 | −0.0389505 | − | 0.999241i | \(-0.512401\pi\) | ||||
−0.0389505 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(548\) | −409.274 | + | 236.294i | −0.0319038 | + | 0.0184197i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −292.308 | + | 506.292i | −0.0226619 | + | 0.0392515i | ||||
\(551\) | −5838.45 | − | 10112.5i | −0.451409 | − | 0.781863i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2738.98i | 0.210051i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15484.1 | + | 8939.72i | 1.18106 | + | 0.681886i | ||||
\(557\) | 9645.26 | + | 5568.69i | 0.733722 | + | 0.423614i | 0.819782 | − | 0.572676i | \(-0.194095\pi\) |
−0.0860606 | + | 0.996290i | \(0.527428\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8675.73i | 0.656430i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2634.18 | + | 4562.53i | 0.197716 | + | 0.342453i | ||||
\(563\) | 2095.75 | − | 3629.94i | 0.156883 | − | 0.271730i | −0.776860 | − | 0.629673i | \(-0.783189\pi\) |
0.933743 | + | 0.357944i | \(0.116522\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −911.882 | + | 526.476i | −0.0678994 | + | 0.0392018i | ||||
\(566\) | −3088.45 | −0.229359 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11501.0 | −0.849598 | ||||||||
\(569\) | −2596.22 | + | 1498.93i | −0.191281 | + | 0.110436i | −0.592582 | − | 0.805510i | \(-0.701891\pi\) |
0.401301 | + | 0.915946i | \(0.368558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −881.110 | + | 1526.13i | −0.0645768 | + | 0.111850i | −0.896506 | − | 0.443031i | \(-0.853903\pi\) |
0.831929 | + | 0.554881i | \(0.187236\pi\) | |||||||
\(572\) | 11167.2 | + | 19342.2i | 0.816303 | + | 1.41388i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 957.907i | 0.0694739i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13336.8 | + | 7700.03i | 0.962253 | + | 0.555557i | 0.896866 | − | 0.442303i | \(-0.145838\pi\) |
0.0653874 | + | 0.997860i | \(0.479172\pi\) | |||||||
\(578\) | −1864.32 | − | 1076.36i | −0.134162 | − | 0.0774583i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 18473.2i | − | 1.32251i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9613.55 | − | 16651.2i | −0.682937 | − | 1.18288i | ||||
\(584\) | 2623.59 | − | 4544.20i | 0.185899 | − | 0.321987i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3807.07 | − | 2198.02i | 0.268377 | − | 0.154947i | ||||
\(587\) | −2642.97 | −0.185838 | −0.0929190 | − | 0.995674i | \(-0.529620\pi\) | ||||
−0.0929190 | + | 0.995674i | \(0.529620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10744.3 | −0.751635 | ||||||||
\(590\) | −4074.40 | + | 2352.35i | −0.284305 | + | 0.164144i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11154.7 | − | 19320.5i | 0.774418 | − | 1.34133i | ||||
\(593\) | 600.950 | + | 1040.88i | 0.0416156 | + | 0.0720803i | 0.886083 | − | 0.463527i | \(-0.153416\pi\) |
−0.844467 | + | 0.535607i | \(0.820083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2718.83i | 0.186858i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1716.08 | − | 990.780i | −0.117351 | − | 0.0677525i | ||||
\(599\) | −8533.05 | − | 4926.56i | −0.582055 | − | 0.336049i | 0.179895 | − | 0.983686i | \(-0.442424\pi\) |
−0.761950 | + | 0.647636i | \(0.775758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7573.82i | − | 0.514047i | −0.966405 | − | 0.257024i | \(-0.917258\pi\) | ||
0.966405 | − | 0.257024i | \(-0.0827418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1746.70 | − | 3025.37i | −0.117669 | − | 0.203809i | ||||
\(605\) | 3619.82 | − | 6269.71i | 0.243250 | − | 0.421322i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17144.7 | + | 9898.52i | −1.14643 | + | 0.661892i | −0.948015 | − | 0.318226i | \(-0.896913\pi\) |
−0.198416 | + | 0.980118i | \(0.563580\pi\) | |||||||
\(608\) | 6646.14 | 0.443317 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −189.759 | −0.0125952 | ||||||||
\(611\) | −29854.0 | + | 17236.2i | −1.97670 | + | 1.14125i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5263.87 | − | 9117.28i | 0.346828 | − | 0.600724i | −0.638856 | − | 0.769326i | \(-0.720592\pi\) |
0.985684 | + | 0.168603i | \(0.0539254\pi\) | |||||||
\(614\) | −2415.76 | − | 4184.22i | −0.158782 | − | 0.275019i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23133.1i | 1.50940i | 0.656067 | + | 0.754702i | \(0.272219\pi\) | ||||
−0.656067 | + | 0.754702i | \(0.727781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14154.6 | − | 8172.19i | −0.919101 | − | 0.530643i | −0.0357526 | − | 0.999361i | \(-0.511383\pi\) |
−0.883348 | + | 0.468718i | \(0.844716\pi\) | |||||||
\(620\) | −14720.6 | − | 8498.93i | −0.953537 | − | 0.550525i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 3581.81i | − | 0.230896i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8894.32 | + | 15405.4i | 0.569237 | + | 0.985947i | ||||
\(626\) | 1353.08 | − | 2343.60i | 0.0863896 | − | 0.149631i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4952.94 | + | 2859.58i | −0.314720 | + | 0.181703i | ||||
\(629\) | −16198.4 | −1.02683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11124.2 | −0.701819 | −0.350909 | − | 0.936409i | \(-0.614127\pi\) | ||||
−0.350909 | + | 0.936409i | \(0.614127\pi\) | |||||||
\(632\) | 1314.16 | − | 758.733i | 0.0827130 | − | 0.0477544i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2649.31 | + | 4588.74i | −0.165958 | + | 0.287448i | ||||
\(635\) | −11670.8 | − | 20214.4i | −0.729355 | − | 1.26328i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 5679.07i | − | 0.352408i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12017.6 | + | 6938.35i | 0.742244 | + | 0.428535i | ||||
\(641\) | 3102.69 | + | 1791.34i | 0.191184 | + | 0.110380i | 0.592537 | − | 0.805543i | \(-0.298127\pi\) |
−0.401353 | + | 0.915924i | \(0.631460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14145.6i | − | 0.867570i | −0.901016 | − | 0.433785i | \(-0.857178\pi\) | ||
0.901016 | − | 0.433785i | \(-0.142822\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −731.943 | − | 1267.76i | −0.0445788 | − | 0.0772128i | ||||
\(647\) | 11957.3 | − | 20710.6i | 0.726568 | − | 1.25845i | −0.231758 | − | 0.972773i | \(-0.574448\pi\) |
0.958326 | − | 0.285678i | \(-0.0922189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23132.4 | − | 13355.5i | 1.39911 | − | 0.807779i | ||||
\(650\) | 891.152 | 0.0537751 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18317.9 | 1.10028 | ||||||||
\(653\) | −22006.3 | + | 12705.3i | −1.31879 | + | 0.761406i | −0.983534 | − | 0.180721i | \(-0.942157\pi\) |
−0.335259 | + | 0.942126i | \(0.608824\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8173.87 | − | 14157.6i | 0.487603 | − | 0.844552i | ||||
\(656\) | −11102.6 | − | 19230.2i | −0.660798 | − | 1.14453i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14977.5i | 0.885342i | 0.896684 | + | 0.442671i | \(0.145969\pi\) | ||||
−0.896684 | + | 0.442671i | \(0.854031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −88.5773 | − | 51.1401i | −0.00521219 | − | 0.00300926i | 0.497392 | − | 0.867526i | \(-0.334291\pi\) |
−0.502604 | + | 0.864517i | \(0.667625\pi\) | |||||||
\(662\) | −4057.87 | − | 2342.81i | −0.238238 | − | 0.137547i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 13011.6i | − | 0.760465i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4652.65 | − | 8058.63i | −0.270092 | − | 0.467813i | ||||
\(668\) | 11049.9 | − | 19139.0i | 0.640021 | − | 1.10855i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2959.08 | + | 1708.42i | −0.170626 | + | 0.0985108i | ||||
\(671\) | 1077.35 | 0.0619833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7778.89 | 0.445549 | 0.222774 | − | 0.974870i | \(-0.428489\pi\) | ||||
0.222774 | + | 0.974870i | \(0.428489\pi\) | |||||||
\(674\) | −70.8738 | + | 40.9190i | −0.00405038 | + | 0.00233849i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8686.06 | − | 15044.7i | 0.494200 | − | 0.855979i | ||||
\(677\) | 10208.1 | + | 17680.9i | 0.579510 | + | 1.00374i | 0.995536 | + | 0.0943875i | \(0.0300893\pi\) |
−0.416026 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 4757.22i | − | 0.268281i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4525.43 | − | 2612.76i | −0.254088 | − | 0.146697i | ||||
\(683\) | 23214.1 | + | 13402.7i | 1.30053 | + | 0.750863i | 0.980495 | − | 0.196542i | \(-0.0629711\pi\) |
0.320038 | + | 0.947405i | \(0.396304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 751.808i | − | 0.0419345i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3517.18 | − | 6091.93i | −0.194900 | − | 0.337576i | ||||
\(689\) | −14654.3 | + | 25382.0i | −0.810282 | + | 1.40345i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28328.7 | − | 16355.6i | 1.55959 | − | 0.900429i | 0.562293 | − | 0.826938i | \(-0.309919\pi\) |
0.997296 | − | 0.0734905i | \(-0.0234139\pi\) | |||||||
\(692\) | −13201.5 | −0.725210 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3314.53 | 0.181294 | ||||||||
\(695\) | −24632.5 | + | 14221.6i | −1.34441 | + | 0.776195i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8061.38 | + | 13962.7i | −0.438087 | + | 0.758789i | ||||
\(698\) | −3612.61 | − | 6257.23i | −0.195902 | − | 0.339312i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 503.993i | 0.0271548i | 0.999908 | + | 0.0135774i | \(0.00432196\pi\) | ||||
−0.999908 | + | 0.0135774i | \(0.995678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20604.1 | + | 11895.8i | 1.10540 | + | 0.638204i | ||||
\(704\) | −13732.7 | − | 7928.59i | −0.735186 | − | 0.424460i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1062.79i | − | 0.0566553i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6893.77 | − | 11940.4i | −0.365163 | − | 0.632482i | 0.623639 | − | 0.781713i | \(-0.285654\pi\) |
−0.988802 | + | 0.149231i | \(0.952320\pi\) | |||||||
\(710\) | 4453.47 | − | 7713.63i | 0.235402 | − | 0.407729i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5047.13 | + | 2913.96i | −0.265659 | + | 0.153378i | ||||
\(713\) | −8562.15 | −0.449726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35530.4 | −1.85841 | ||||||||
\(716\) | 17328.1 | − | 10004.4i | 0.904445 | − | 0.522182i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 91.6051 | − | 158.665i | 0.00476138 | − | 0.00824695i | ||||
\(719\) | −16111.5 | − | 27906.0i | −0.835688 | − | 1.44745i | −0.893469 | − | 0.449124i | \(-0.851736\pi\) |
0.0577818 | − | 0.998329i | \(-0.481597\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 2246.78i | − | 0.115813i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1373.45 | − | 792.962i | −0.0705026 | − | 0.0407047i | ||||
\(725\) | 3624.14 | + | 2092.40i | 0.185652 | + | 0.107186i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33807.4i | 1.72469i | 0.506325 | + | 0.862343i | \(0.331004\pi\) | ||||
−0.506325 | + | 0.862343i | \(0.668996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2031.84 | + | 3519.25i | 0.103016 | + | 0.178429i | ||||
\(731\) | −2553.76 | + | 4423.23i | −0.129212 | + | 0.223802i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14239.9 | + | 8221.39i | −0.717546 | + | 0.414275i | −0.813849 | − | 0.581077i | \(-0.802632\pi\) |
0.0963028 | + | 0.995352i | \(0.469298\pi\) | |||||||
\(734\) | −2824.46 | −0.142034 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5296.30 | 0.265250 | ||||||||
\(737\) | 16800.2 | − | 9699.58i | 0.839677 | − | 0.484788i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10102.7 | − | 17498.4i | 0.502888 | − | 0.871028i | −0.497106 | − | 0.867690i | \(-0.665604\pi\) |
0.999994 | − | 0.00333840i | \(-0.00106265\pi\) | |||||||
\(740\) | 18819.4 | + | 32596.2i | 0.934887 | + | 1.61927i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14573.9i | 0.719601i | 0.933029 | + | 0.359800i | \(0.117155\pi\) | ||||
−0.933029 | + | 0.359800i | \(0.882845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3745.73 | − | 2162.60i | −0.184205 | − | 0.106351i | ||||
\(746\) | −6964.45 | − | 4020.92i | −0.341805 | − | 0.197341i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13148.6i | 0.642727i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1344.53 | − | 2328.79i | −0.0653297 | − | 0.113154i | 0.831510 | − | 0.555509i | \(-0.187477\pi\) |
−0.896840 | + | 0.442355i | \(0.854143\pi\) | |||||||
\(752\) | 13975.3 | − | 24205.9i | 0.677694 | − | 1.17380i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7497.03 | + | 4328.41i | −0.362103 | + | 0.209060i | ||||
\(755\) | 5557.39 | 0.267886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11192.8 | 0.537395 | 0.268697 | − | 0.963225i | \(-0.413407\pi\) | ||||
0.268697 | + | 0.963225i | \(0.413407\pi\) | |||||||
\(758\) | −2606.92 | + | 1505.11i | −0.124918 | + | 0.0721214i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3493.60 | + | 6051.09i | −0.166745 | + | 0.288810i | ||||
\(761\) | 14531.7 | + | 25169.6i | 0.692212 | + | 1.19895i | 0.971112 | + | 0.238626i | \(0.0766970\pi\) |
−0.278900 | + | 0.960320i | \(0.589970\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 5845.96i | − | 0.276832i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3991.57 | + | 2304.54i | 0.188279 | + | 0.108703i | ||||
\(767\) | −35261.6 | − | 20358.3i | −1.66000 | − | 0.958403i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 40870.3i | − | 1.91654i | −0.285861 | − | 0.958271i | \(-0.592280\pi\) | ||
0.285861 | − | 0.958271i | \(-0.407720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3266.48 | − | 5657.70i | −0.152284 | − | 0.263763i | ||||
\(773\) | −20145.8 | + | 34893.5i | −0.937378 | + | 1.62359i | −0.167042 | + | 0.985950i | \(0.553421\pi\) |
−0.770337 | + | 0.637637i | \(0.779912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3334.71 | − | 1925.29i | 0.154563 | − | 0.0892369i | ||||
\(776\) | 10911.0 | 0.504743 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5889.73 | −0.271410 | ||||||||
\(779\) | 20507.8 | − | 11840.2i | 0.943220 | − | 0.544568i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25284.6 | + | 43794.1i | −1.15845 | + | 2.00650i | ||||
\(782\) | −583.284 | − | 1010.28i | −0.0266729 | − | 0.0461988i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 9098.22i | − | 0.413668i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4331.01 | + | 2500.51i | 0.196167 | + | 0.113257i | 0.594867 | − | 0.803824i | \(-0.297205\pi\) |
−0.398699 | + | 0.917082i | \(0.630538\pi\) | |||||||
\(788\) | 6796.62 | + | 3924.03i | 0.307259 | + | 0.177396i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1175.20i | 0.0529262i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −821.126 | − | 1422.23i | −0.0367706 | − | 0.0636885i | ||||
\(794\) | −3830.78 | + | 6635.10i | −0.171221 | + | 0.296563i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33920.4 | + | 19583.9i | −1.51040 | + | 0.872028i | ||||
\(797\) | −8762.59 | −0.389444 | −0.194722 | − | 0.980858i | \(-0.562380\pi\) | ||||
−0.194722 | + | 0.980858i | \(0.562380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20294.4 | −0.898577 | ||||||||
\(800\) | −2062.75 | + | 1190.93i | −0.0911617 | + | 0.0526322i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2193.85 | + | 3799.85i | −0.0965927 | + | 0.167304i | ||||
\(803\) | −11535.8 | − | 19980.5i | −0.506959 | − | 0.878078i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7965.46i | 0.348103i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1356.77 | + | 783.331i | 0.0590730 | + | 0.0341058i | ||||
\(809\) | 33466.5 | + | 19321.9i | 1.45441 | + | 0.839705i | 0.998727 | − | 0.0504366i | \(-0.0160613\pi\) |
0.455684 | + | 0.890141i | \(0.349395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3577.67i | 0.154906i | 0.996996 | + | 0.0774530i | \(0.0246788\pi\) | ||||
−0.996996 | + | 0.0774530i | \(0.975321\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5785.51 | + | 10020.8i | 0.249118 | + | 0.431485i | ||||
\(815\) | −14570.3 | + | 25236.5i | −0.626228 | + | 1.08466i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6496.64 | − | 3750.84i | 0.278199 | − | 0.160618i | ||||
\(818\) | 3312.20 | 0.141575 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 37463.0 | 1.59545 | ||||||||
\(821\) | 18194.3 | − | 10504.5i | 0.773431 | − | 0.446541i | −0.0606661 | − | 0.998158i | \(-0.519322\pi\) |
0.834097 | + | 0.551617i | \(0.185989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15654.6 | + | 27114.6i | −0.663044 | + | 1.14843i | 0.316767 | + | 0.948503i | \(0.397403\pi\) |
−0.979812 | + | 0.199923i | \(0.935931\pi\) | |||||||
\(824\) | −1204.57 | − | 2086.37i | −0.0509260 | − | 0.0882065i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27813.3i | − | 1.16949i | −0.811219 | − | 0.584743i | \(-0.801195\pi\) | ||
0.811219 | − | 0.584743i | \(-0.198805\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30364.1 | − | 17530.7i | −1.27212 | − | 0.734460i | −0.296735 | − | 0.954960i | \(-0.595898\pi\) |
−0.975387 | + | 0.220500i | \(0.929231\pi\) | |||||||
\(830\) | 8726.79 | + | 5038.41i | 0.364953 | + | 0.210706i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24171.7i | 1.00722i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17578.5 | + | 30446.9i | 0.728539 | + | 1.26187i | ||||
\(836\) | 9656.02 | − | 16724.7i | 0.399474 | − | 0.691909i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7716.86 | + | 4455.33i | −0.318108 | + | 0.183660i | ||||
\(839\) | 4808.56 | 0.197866 | 0.0989332 | − | 0.995094i | \(-0.468457\pi\) | ||||
0.0989332 | + | 0.995094i | \(0.468457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16263.0 | −0.666816 | ||||||||
\(842\) | −4330.38 | + | 2500.15i | −0.177238 | + | 0.102329i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −516.780 | + | 895.090i | −0.0210762 | + | 0.0365051i | ||||
\(845\) | 13818.0 | + | 23933.6i | 0.562550 | + | 0.974366i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 23763.7i | − | 0.962320i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 454.345 | + | 262.316i | 0.0183340 | + | 0.0105851i | ||||
\(851\) | 16419.3 | + | 9479.71i | 0.661396 | + | 0.381857i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9486.81i | 0.380800i | 0.981707 | + | 0.190400i | \(0.0609784\pi\) | ||||
−0.981707 | + | 0.190400i | \(0.939022\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −64.1433 | − | 111.099i | −0.00256118 | − | 0.00443610i | ||||
\(857\) | 11262.4 | − | 19507.0i | 0.448909 | − | 0.777533i | −0.549406 | − | 0.835555i | \(-0.685146\pi\) |
0.998315 | + | 0.0580220i | \(0.0184793\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23940.7 | − | 13822.2i | 0.950927 | − | 0.549018i | 0.0575581 | − | 0.998342i | \(-0.481669\pi\) |
0.893369 | + | 0.449324i | \(0.148335\pi\) | |||||||
\(860\) | 11867.9 | 0.470571 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1336.98 | 0.0528280 | ||||||||
\(863\) | 17457.3 | − | 10079.0i | 0.688591 | − | 0.397558i | −0.114493 | − | 0.993424i | \(-0.536524\pi\) |
0.803084 | + | 0.595866i | \(0.203191\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10500.7 | − | 18187.7i | 0.412755 | − | 0.714913i | ||||
\(866\) | 380.439 | + | 658.940i | 0.0149282 | + | 0.0258565i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6672.18i | − | 0.260458i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25609.1 | − | 14785.4i | −0.996249 | − | 0.575184i | ||||
\(872\) | −17883.4 | − | 10325.0i | −0.694503 | − | 0.400972i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1713.40i | 0.0663120i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15486.6 | + | 26823.5i | 0.596288 | + | 1.03280i | 0.993364 | + | 0.115015i | \(0.0366916\pi\) |
−0.397076 | + | 0.917786i | \(0.629975\pi\) | |||||||
\(878\) | −2786.11 | + | 4825.68i | −0.107092 | + | 0.185488i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 24948.7 | − | 14404.2i | 0.955706 | − | 0.551777i | ||||
\(881\) | 10973.0 | 0.419626 | 0.209813 | − | 0.977741i | \(-0.432714\pi\) | ||||
0.209813 | + | 0.977741i | \(0.432714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42025.5 | 1.60167 | 0.800833 | − | 0.598888i | \(-0.204390\pi\) | ||||
0.800833 | + | 0.598888i | \(0.204390\pi\) | |||||||
\(884\) | 17357.7 | − | 10021.4i | 0.660409 | − | 0.381287i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2166.29 | − | 3752.12i | 0.0821420 | − | 0.142274i | ||||
\(887\) | −2340.56 | − | 4053.97i | −0.0886002 | − | 0.153460i | 0.818319 | − | 0.574764i | \(-0.194906\pi\) |
−0.906920 | + | 0.421304i | \(0.861573\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 4513.42i | − | 0.169989i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16721.1 | + | 9653.90i | 0.627648 | + | 0.362373i | ||||
\(893\) | 25814.0 | + | 14903.7i | 0.967337 | + | 0.558492i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31830.6i | 1.18880i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2154.49 | − | 3731.69i | −0.0800627 | − | 0.138673i | ||||
\(899\) | −18702.7 | + | 32394.0i | −0.693848 | + | 1.20178i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14942.7 | + | 8627.17i | −0.552512 | + | 0.318993i | ||||
\(902\) | 11517.0 | 0.425136 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −871.564 | −0.0320661 | ||||||||
\(905\) | 2184.93 | − | 1261.47i | 0.0802535 | − | 0.0463344i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24203.3 | − | 41921.3i | 0.886060 | − | 1.53470i | 0.0415653 | − | 0.999136i | \(-0.486766\pi\) |
0.844494 | − | 0.535564i | \(-0.179901\pi\) | |||||||
\(908\) | 16840.9 | + | 29169.3i | 0.615512 | + | 1.06610i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20920.5i | 0.760842i | 0.924813 | + | 0.380421i | \(0.124221\pi\) | ||||
−0.924813 | + | 0.380421i | \(0.875779\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49546.3 | − | 28605.6i | −1.79600 | − | 1.03692i | ||||
\(914\) | −1833.05 | − | 1058.31i | −0.0663367 | − | 0.0382995i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 23592.4i | − | 0.850998i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16735.7 | − | 28987.1i | −0.600717 | − | 1.04047i | −0.992713 | − | 0.120506i | \(-0.961548\pi\) |
0.391995 | − | 0.919967i | \(-0.371785\pi\) | |||||||
\(920\) | −2784.04 | + | 4822.10i | −0.0997686 | + | 0.172804i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4019.98 | + | 2320.94i | −0.143591 | + | 0.0829023i | ||||
\(923\) | 77084.5 | 2.74893 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8526.48 | −0.303080 | ||||||||
\(926\) | 4211.21 | − | 2431.34i | 0.149448 | − | 0.0862838i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11568.9 | − | 20038.0i | 0.409234 | − | 0.708814i | ||||
\(929\) | −4685.49 | − | 8115.50i | −0.165475 | − | 0.286610i | 0.771349 | − | 0.636412i | \(-0.219582\pi\) |
−0.936824 | + | 0.349802i | \(0.886249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 34818.8i | − | 1.22374i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1137.27 | − | 656.602i | −0.0398421 | − | 0.0230029i | ||||
\(935\) | −18114.8 | − | 10458.6i | −0.633601 | − | 0.365810i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29702.0i | 1.03556i | 0.855513 | + | 0.517781i | \(0.173242\pi\) | ||||
−0.855513 | + | 0.517781i | \(0.826758\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23578.1 | + | 40838.5i | 0.818120 | + | 1.41703i | ||||
\(941\) | 2451.67 | − | 4246.41i | 0.0849331 | − | 0.147108i | −0.820430 | − | 0.571748i | \(-0.806266\pi\) |
0.905363 | + | 0.424639i | \(0.139599\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16342.6 | − | 9435.42i | 0.564358 | − | 0.325832i | ||||
\(944\) | 33013.3 | 1.13823 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3648.44 | 0.125392 | ||||||||
\(947\) | −18190.4 | + | 10502.3i | −0.624192 | + | 0.360378i | −0.778499 | − | 0.627645i | \(-0.784019\pi\) |
0.154307 | + | 0.988023i | \(0.450685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17584.4 | + | 30457.1i | −0.601489 | + | 1.04181i | ||||
\(950\) | −385.278 | − | 667.321i | −0.0131580 | − | 0.0227903i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4598.25i | 0.156298i | 0.996942 | + | 0.0781489i | \(0.0249010\pi\) | ||||
−0.996942 | + | 0.0781489i | \(0.975099\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8053.98 | + | 4649.97i | 0.272901 | + | 0.157560i | ||||
\(956\) | −4854.03 | − | 2802.47i | −0.164216 | − | 0.0948102i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 2113.52i | − | 0.0712785i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2313.53 | + | 4007.15i | 0.0776587 | + | 0.134509i | ||||
\(962\) | 8819.08 | − | 15275.1i | 0.295570 | − | 0.511942i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1641.37 | + | 947.644i | −0.0548391 | + | 0.0316614i | ||||
\(965\) | 10392.8 | 0.346691 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52408.6 | 1.74286 | 0.871431 | − | 0.490518i | \(-0.163192\pi\) | ||||
0.871431 | + | 0.490518i | \(0.163192\pi\) | |||||||
\(968\) | 5189.65 | − | 2996.25i | 0.172316 | − | 0.0994866i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4224.98 | + | 7317.89i | −0.139852 | + | 0.242230i | ||||
\(971\) | −24356.2 | − | 42186.1i | −0.804971 | − | 1.39425i | −0.916311 | − | 0.400468i | \(-0.868847\pi\) |
0.111339 | − | 0.993782i | \(-0.464486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 756.236i | 0.0248782i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1153.16 | + | 665.776i | 0.0378193 | + | 0.0218350i | ||||
\(977\) | 10094.1 | + | 5827.83i | 0.330541 | + | 0.190838i | 0.656081 | − | 0.754690i | \(-0.272213\pi\) |
−0.325540 | + | 0.945528i | \(0.605546\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25624.9i | 0.836544i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2427.54 | + | 4204.63i | 0.0788860 | + | 0.136635i | ||||
\(983\) | −20228.6 | + | 35036.9i | −0.656350 | + | 1.13683i | 0.325204 | + | 0.945644i | \(0.394567\pi\) |
−0.981554 | + | 0.191187i | \(0.938766\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10812.3 | + | 6242.47i | −0.349754 | + | 0.201931i | ||||
\(986\) | −5096.38 | −0.164606 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29438.1 | −0.947925 | ||||||||
\(989\) | 5177.16 | − | 2989.04i | 0.166455 | − | 0.0961030i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4830.44 | + | 8366.57i | −0.154838 | + | 0.268187i | −0.933000 | − | 0.359877i | \(-0.882819\pi\) |
0.778162 | + | 0.628063i | \(0.216152\pi\) | |||||||
\(992\) | −10645.0 | − | 18437.7i | −0.340705 | − | 0.590118i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 62309.4i | − | 1.98527i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4327.53 | − | 2498.50i | −0.137467 | − | 0.0793665i | 0.429689 | − | 0.902977i | \(-0.358623\pi\) |
−0.567156 | + | 0.823610i | \(0.691956\pi\) | |||||||
\(998\) | −1010.12 | − | 583.194i | −0.0320389 | − | 0.0184977i | ||||
\(999\) | 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 | 441.4.p.d.80.11 | 48 | ||
3.2 | odd | 2 | inner | 441.4.p.d.80.14 | 48 | ||
7.2 | even | 3 | inner | 441.4.p.d.215.13 | 48 | ||
7.3 | odd | 6 | 441.4.c.b.440.5 | ✓ | 24 | ||
7.4 | even | 3 | 441.4.c.b.440.19 | yes | 24 | ||
7.5 | odd | 6 | inner | 441.4.p.d.215.14 | 48 | ||
7.6 | odd | 2 | inner | 441.4.p.d.80.12 | 48 | ||
21.2 | odd | 6 | inner | 441.4.p.d.215.12 | 48 | ||
21.5 | even | 6 | inner | 441.4.p.d.215.11 | 48 | ||
21.11 | odd | 6 | 441.4.c.b.440.6 | yes | 24 | ||
21.17 | even | 6 | 441.4.c.b.440.20 | yes | 24 | ||
21.20 | even | 2 | inner | 441.4.p.d.80.13 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.c.b.440.5 | ✓ | 24 | 7.3 | odd | 6 | ||
441.4.c.b.440.6 | yes | 24 | 21.11 | odd | 6 | ||
441.4.c.b.440.19 | yes | 24 | 7.4 | even | 3 | ||
441.4.c.b.440.20 | yes | 24 | 21.17 | even | 6 | ||
441.4.p.d.80.11 | 48 | 1.1 | even | 1 | trivial | ||
441.4.p.d.80.12 | 48 | 7.6 | odd | 2 | inner | ||
441.4.p.d.80.13 | 48 | 21.20 | even | 2 | inner | ||
441.4.p.d.80.14 | 48 | 3.2 | odd | 2 | inner | ||
441.4.p.d.215.11 | 48 | 21.5 | even | 6 | inner | ||
441.4.p.d.215.12 | 48 | 21.2 | odd | 6 | inner | ||
441.4.p.d.215.13 | 48 | 7.2 | even | 3 | inner | ||
441.4.p.d.215.14 | 48 | 7.5 | odd | 6 | inner |