Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 33.2 | ||
Character | \(\chi\) | \(=\) | 76.33 |
Dual form | 76.5.j.a.53.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −7.79937 | − | 1.37524i | −0.866597 | − | 0.152804i | −0.277361 | − | 0.960766i | \(-0.589460\pi\) |
−0.589235 | + | 0.807961i | \(0.700571\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.638039 | + | 0.535378i | 0.0255216 | + | 0.0214151i | 0.655459 | − | 0.755231i | \(-0.272475\pi\) |
−0.629938 | + | 0.776646i | \(0.716920\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.1636 | + | 40.1206i | 0.472728 | + | 0.818788i | 0.999513 | − | 0.0312103i | \(-0.00993616\pi\) |
−0.526785 | + | 0.849998i | \(0.676603\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −17.1762 | − | 6.25164i | −0.212052 | − | 0.0771807i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 95.5660 | − | 165.525i | 0.789802 | − | 1.36798i | −0.136286 | − | 0.990669i | \(-0.543517\pi\) |
0.926088 | − | 0.377307i | \(-0.123150\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 208.358 | − | 36.7391i | 1.23289 | − | 0.217391i | 0.481021 | − | 0.876709i | \(-0.340266\pi\) |
0.751864 | + | 0.659318i | \(0.229155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.24003 | − | 5.05307i | −0.0188446 | − | 0.0224581i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 504.579 | − | 183.652i | 1.74595 | − | 0.635473i | 0.746399 | − | 0.665499i | \(-0.231781\pi\) |
0.999549 | + | 0.0300258i | \(0.00955895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 130.825 | + | 336.461i | 0.362397 | + | 0.932024i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −125.486 | − | 344.771i | −0.284550 | − | 0.781794i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −238.506 | + | 200.131i | −0.450863 | + | 0.378319i | −0.839756 | − | 0.542964i | \(-0.817302\pi\) |
0.388893 | + | 0.921283i | \(0.372858\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −108.410 | − | 614.822i | −0.173455 | − | 0.983715i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 680.917 | + | 393.128i | 0.934042 | + | 0.539270i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 67.5830 | − | 185.683i | 0.0803603 | − | 0.220788i | −0.893005 | − | 0.450046i | \(-0.851408\pi\) |
0.973366 | + | 0.229258i | \(0.0736299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −677.986 | + | 391.435i | −0.705500 | + | 0.407321i | −0.809393 | − | 0.587268i | \(-0.800204\pi\) |
0.103892 | + | 0.994589i | \(0.466870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −972.991 | + | 1159.57i | −0.893472 | + | 1.06480i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.70040 | + | 37.9998i | −0.00546971 | + | 0.0310203i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1109.80i | − | 0.810665i | −0.914169 | − | 0.405332i | \(-0.867156\pi\) | ||
0.914169 | − | 0.405332i | \(-0.132844\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1675.58 | −1.10163 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1014.78 | + | 178.934i | 0.603679 | + | 0.106445i | 0.467130 | − | 0.884188i | \(-0.345288\pi\) |
0.136549 | + | 0.990633i | \(0.456399\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 867.530 | + | 727.944i | 0.469189 | + | 0.393696i | 0.846498 | − | 0.532391i | \(-0.178706\pi\) |
−0.377310 | + | 0.926087i | \(0.623151\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.61212 | − | 13.1846i | −0.00375907 | − | 0.00651090i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1488.89 | − | 541.910i | −0.674009 | − | 0.245319i | −0.0177359 | − | 0.999843i | \(-0.505646\pi\) |
−0.656273 | + | 0.754524i | \(0.727868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 127.391 | − | 220.647i | 0.0530574 | − | 0.0918981i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4187.96 | + | 738.451i | −1.61014 | + | 0.283910i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 623.443 | + | 742.990i | 0.221945 | + | 0.264504i | 0.865514 | − | 0.500884i | \(-0.166992\pi\) |
−0.643570 | + | 0.765388i | \(0.722547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 149.593 | − | 54.4476i | 0.0494524 | − | 0.0179992i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −557.642 | − | 2804.10i | −0.171635 | − | 0.863064i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1659.58 | + | 4559.66i | 0.476754 | + | 1.30987i | 0.912233 | + | 0.409671i | \(0.134357\pi\) |
−0.435480 | + | 0.900199i | \(0.643421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3868.03 | + | 3245.67i | −1.03951 | + | 0.872257i | −0.991952 | − | 0.126612i | \(-0.959590\pi\) |
−0.0475625 | + | 0.998868i | \(0.515145\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −147.045 | − | 833.932i | −0.0370483 | − | 0.210111i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 152.610 | + | 88.1093i | 0.0361206 | + | 0.0208543i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −70.2062 | + | 192.890i | −0.0156396 | + | 0.0429695i | −0.947267 | − | 0.320446i | \(-0.896167\pi\) |
0.931627 | + | 0.363415i | \(0.118389\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2135.43 | − | 1232.89i | 0.448525 | − | 0.258956i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3442.94 | − | 4103.13i | 0.682987 | − | 0.813953i | −0.307501 | − | 0.951548i | \(-0.599493\pi\) |
0.990489 | + | 0.137595i | \(0.0439373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1418.98 | − | 8047.43i | 0.266275 | − | 1.51012i | −0.499106 | − | 0.866541i | \(-0.666338\pi\) |
0.765380 | − | 0.643578i | \(-0.222551\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4944.31i | 0.878988i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8854.63 | 1.49344 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5647.18 | + | 995.751i | 0.904852 | + | 0.159550i | 0.606665 | − | 0.794957i | \(-0.292507\pi\) |
0.298187 | + | 0.954507i | \(0.403618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3635.90 | − | 3050.88i | −0.554169 | − | 0.465003i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2389.76 | − | 4139.18i | −0.346894 | − | 0.600839i | 0.638802 | − | 0.769371i | \(-0.279430\pi\) |
−0.985696 | + | 0.168533i | \(0.946097\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 420.264 | + | 152.964i | 0.0581681 | + | 0.0211714i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −782.463 | + | 1355.27i | −0.103377 | + | 0.179055i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11031.2 | − | 1945.10i | 1.39265 | − | 0.245562i | 0.573532 | − | 0.819183i | \(-0.305573\pi\) |
0.819121 | + | 0.573621i | \(0.194462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6300.32 | + | 7508.43i | 0.760816 | + | 0.906705i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5826.18 | − | 2120.56i | 0.673624 | − | 0.245179i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −96.6620 | + | 284.716i | −0.0107105 | + | 0.0315475i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 613.294 | + | 1685.01i | 0.0651816 | + | 0.179085i | 0.968007 | − | 0.250921i | \(-0.0807335\pi\) |
−0.902826 | + | 0.430006i | \(0.858511\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2676.27 | + | 2245.66i | −0.273061 | + | 0.229125i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2527.79 | − | 14335.8i | −0.247798 | − | 1.40533i | −0.813903 | − | 0.581000i | \(-0.802661\pi\) |
0.566105 | − | 0.824333i | \(-0.308450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16876.4 | − | 9743.57i | −1.59076 | − | 0.918425i | −0.993177 | − | 0.116618i | \(-0.962795\pi\) |
−0.597582 | − | 0.801808i | \(-0.703872\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 104.518 | − | 287.160i | 0.00948007 | − | 0.0260463i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3946.18 | + | 2278.33i | −0.344675 | + | 0.198998i | −0.662337 | − | 0.749206i | \(-0.730435\pi\) |
0.317663 | + | 0.948204i | \(0.397102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8297.49 | + | 9888.56i | −0.698383 | + | 0.832300i | −0.992342 | − | 0.123517i | \(-0.960582\pi\) |
0.293959 | + | 0.955818i | \(0.405027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1526.24 | + | 8655.74i | −0.123873 | + | 0.702519i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17919.3i | 1.40334i | 0.712500 | + | 0.701672i | \(0.247563\pi\) | ||||
−0.712500 | + | 0.701672i | \(0.752437\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −259.322 | −0.0196085 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3808.48 | − | 671.538i | −0.278215 | − | 0.0490567i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19056.1 | + | 15990.0i | 1.34568 | + | 1.12916i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10945.2 | − | 18957.7i | −0.747574 | − | 1.29484i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7668.60 | − | 2791.14i | −0.506881 | − | 0.184490i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 520.274 | − | 901.141i | 0.0332976 | − | 0.0576731i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −29312.4 | + | 5168.57i | −1.81737 | + | 0.320452i | −0.975629 | − | 0.219424i | \(-0.929582\pi\) |
−0.841744 | + | 0.539876i | \(0.818471\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5765.09 | − | 6870.56i | −0.346439 | − | 0.412870i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16507.9 | − | 6008.38i | 0.961942 | − | 0.350118i | 0.187148 | − | 0.982332i | \(-0.440076\pi\) |
0.774794 | + | 0.632213i | \(0.217853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10468.6 | + | 13042.5i | −0.591815 | + | 0.737320i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 223.980 | + | 615.379i | 0.0122897 | + | 0.0337657i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5277.66 | + | 4428.48i | −0.281190 | + | 0.235947i | −0.772464 | − | 0.635059i | \(-0.780976\pi\) |
0.491274 | + | 0.871005i | \(0.336531\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −390.360 | − | 2213.84i | −0.0202039 | − | 0.114582i | 0.973038 | − | 0.230645i | \(-0.0740836\pi\) |
−0.993242 | + | 0.116063i | \(0.962973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10867.1 | + | 6274.13i | 0.546608 | + | 0.315584i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13830.7 | − | 37999.5i | 0.676349 | − | 1.85825i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 142.531 | − | 82.2904i | 0.00677913 | − | 0.00391393i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1297.01 | + | 1545.72i | −0.0600218 | + | 0.0715312i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3144.64 | + | 17834.2i | −0.141644 | + | 0.803304i | 0.828356 | + | 0.560201i | \(0.189276\pi\) |
−0.970001 | + | 0.243103i | \(0.921835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12669.8i | 0.555668i | 0.960629 | + | 0.277834i | \(0.0896166\pi\) | ||||
−0.960629 | + | 0.277834i | \(0.910383\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9814.89 | −0.419278 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −642.148 | − | 113.228i | −0.0267283 | − | 0.00471292i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12674.1 | + | 10634.8i | 0.514183 | + | 0.431451i | 0.862598 | − | 0.505889i | \(-0.168836\pi\) |
−0.348415 | + | 0.937340i | \(0.613280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3840.67 | − | 6652.24i | −0.151919 | − | 0.263132i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13554.0 | − | 4933.27i | −0.522898 | − | 0.190319i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5938.09 | + | 10285.1i | −0.223497 | + | 0.387108i | −0.955867 | − | 0.293798i | \(-0.905081\pi\) |
0.732370 | + | 0.680906i | \(0.238414\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1241.61 | + | 218.930i | −0.0456056 | + | 0.00804150i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9815.28 | − | 11697.4i | −0.351941 | − | 0.419427i | 0.560809 | − | 0.827945i | \(-0.310490\pi\) |
−0.912750 | + | 0.408518i | \(0.866046\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15224.6 | − | 5541.30i | 0.533056 | − | 0.194016i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −143.659 | − | 6597.00i | −0.00491292 | − | 0.225608i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11914.5 | + | 32734.8i | 0.398092 | + | 1.09375i | 0.963212 | + | 0.268741i | \(0.0866076\pi\) |
−0.565120 | + | 0.825009i | \(0.691170\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22155.9 | − | 18591.0i | 0.723457 | − | 0.607052i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6673.05 | − | 37844.8i | −0.212999 | − | 1.20798i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 27682.7 | + | 15982.6i | 0.863978 | + | 0.498818i | 0.865342 | − | 0.501181i | \(-0.167101\pi\) |
−0.00136433 | + | 0.999999i | \(0.500434\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19495.0 | + | 53562.1i | −0.595068 | + | 1.63494i | 0.165897 | + | 0.986143i | \(0.446948\pi\) |
−0.760965 | + | 0.648793i | \(0.775274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 34631.8 | − | 19994.7i | 1.03412 | − | 0.597052i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 594.163 | − | 708.096i | 0.0173605 | − | 0.0206894i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17821.6 | − | 101071.i | 0.509640 | − | 2.89031i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 36425.1i | 1.01971i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 50921.9 | 1.39585 | 0.697924 | − | 0.716172i | \(-0.254107\pi\) | ||||
0.697924 | + | 0.716172i | \(0.254107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7155.09 | + | 1261.64i | 0.192088 | + | 0.0338703i | 0.268864 | − | 0.963178i | \(-0.413352\pi\) |
−0.0767763 | + | 0.997048i | \(0.524463\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1069.09 | − | 897.071i | −0.0281154 | − | 0.0235916i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6657.78 | − | 11531.6i | −0.171552 | − | 0.297137i | 0.767410 | − | 0.641156i | \(-0.221545\pi\) |
−0.938963 | + | 0.344019i | \(0.888212\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27819.3 | − | 10125.4i | −0.702491 | − | 0.255686i | −0.0340168 | − | 0.999421i | \(-0.510830\pi\) |
−0.668474 | + | 0.743736i | \(0.733052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 812.834 | − | 1407.87i | 0.0201191 | − | 0.0348474i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9015.18 | − | 1589.62i | 0.218767 | − | 0.0385746i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 551.675 | + | 657.461i | 0.0131273 | + | 0.0156445i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5347.78 | − | 1946.43i | 0.124805 | − | 0.0454254i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 68195.2 | + | 10499.3i | 1.56121 | + | 0.240363i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0715 | − | 44.1560i | −0.000360986 | − | 0.000991801i | 0.939512 | − | 0.342516i | \(-0.111279\pi\) |
−0.939873 | + | 0.341524i | \(0.889057\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −32495.5 | + | 27267.0i | −0.716250 | + | 0.601005i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 163.792 | + | 928.913i | 0.00354337 | + | 0.0200955i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31409.2 | − | 18134.1i | −0.667019 | − | 0.385103i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22134.3 | + | 60813.4i | −0.461506 | + | 1.26798i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 98385.7 | − | 56803.0i | 2.01441 | − | 1.16302i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15121.7 | + | 18021.4i | −0.304082 | + | 0.362391i | −0.896348 | − | 0.443352i | \(-0.853789\pi\) |
0.592265 | + | 0.805743i | \(0.298234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1981.57 | + | 11238.1i | −0.0391422 | + | 0.221986i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9051.77i | − | 0.175664i | −0.996135 | − | 0.0878318i | \(-0.972006\pi\) | ||
0.996135 | − | 0.0878318i | \(-0.0279938\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17379.0 | −0.331401 | −0.165700 | − | 0.986176i | \(-0.552988\pi\) | ||||
−0.165700 | + | 0.986176i | \(0.552988\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −69060.5 | − | 12177.2i | −1.29421 | − | 0.228205i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −52913.9 | − | 44400.0i | −0.974670 | − | 0.817845i | 0.00860682 | − | 0.999963i | \(-0.497260\pi\) |
−0.983277 | + | 0.182118i | \(0.941705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −659.840 | − | 1142.88i | −0.0119482 | − | 0.0206949i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −42675.1 | − | 15532.5i | −0.759762 | − | 0.276531i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −47309.5 | + | 81942.5i | −0.828233 | + | 1.43454i | 0.0711902 | + | 0.997463i | \(0.477320\pi\) |
−0.899423 | + | 0.437079i | \(0.856013\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −105764. | + | 18649.1i | −1.82098 | + | 0.321088i | −0.976667 | − | 0.214761i | \(-0.931103\pi\) |
−0.844314 | + | 0.535849i | \(0.819992\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16775.0 | − | 19991.6i | −0.284086 | − | 0.338560i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 199.410 | − | 72.5793i | 0.00332212 | − | 0.00120915i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 39619.7 | + | 65297.7i | 0.649408 | + | 1.07030i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12946.2 | + | 35569.5i | 0.208807 | + | 0.573692i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4024.48 | + | 3376.94i | −0.0638796 | + | 0.0536013i | −0.674168 | − | 0.738578i | \(-0.735498\pi\) |
0.610289 | + | 0.792179i | \(0.291053\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10333.6 | + | 58604.5i | 0.161439 | + | 0.915566i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3067.44 | − | 1770.98i | −0.0471732 | − | 0.0272354i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6106.37 | − | 16777.1i | 0.0924521 | − | 0.254010i | −0.884844 | − | 0.465887i | \(-0.845735\pi\) |
0.977296 | + | 0.211877i | \(0.0679576\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 44525.9 | − | 25707.0i | 0.663763 | − | 0.383224i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2321.64 | + | 2766.83i | −0.0340812 | + | 0.0406164i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −817.509 | + | 4636.32i | −0.0118190 | + | 0.0670289i | −0.990147 | − | 0.140033i | \(-0.955279\pi\) |
0.978328 | + | 0.207062i | \(0.0663902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 807.835i | 0.0115035i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −88711.4 | −1.24439 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7559.50 | + | 1332.94i | 0.104469 | + | 0.0184208i | 0.225638 | − | 0.974211i | \(-0.427553\pi\) |
−0.121169 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 52245.4 | + | 43839.1i | 0.711392 | + | 0.596929i | 0.924989 | − | 0.379993i | \(-0.124074\pi\) |
−0.213597 | + | 0.976922i | \(0.568518\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −38812.6 | − | 67225.4i | −0.520772 | − | 0.902004i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −112129. | − | 40811.5i | −1.48269 | − | 0.539657i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31305.4 | + | 54222.6i | −0.408000 | + | 0.706677i | −0.994666 | − | 0.103153i | \(-0.967107\pi\) |
0.586665 | + | 0.809829i | \(0.300440\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14092.4 | − | 2484.86i | 0.181040 | − | 0.0319223i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −67625.0 | − | 80592.3i | −0.856435 | − | 1.02066i | −0.999521 | − | 0.0309495i | \(-0.990147\pi\) |
0.143086 | − | 0.989710i | \(-0.454298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 125903. | − | 45824.9i | 1.57204 | − | 0.572175i | 0.598584 | − | 0.801060i | \(-0.295730\pi\) |
0.973453 | + | 0.228885i | \(0.0735081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1145.46 | − | 2087.67i | 0.0141022 | − | 0.0257023i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16327.2 | + | 44858.6i | 0.198220 | + | 0.544605i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 156891. | − | 131647.i | 1.87846 | − | 1.57622i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2466.01 | − | 13985.5i | −0.0291212 | − | 0.165155i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 100485. | + | 58014.9i | 1.17048 | + | 0.675779i | 0.953794 | − | 0.300462i | \(-0.0971409\pi\) |
0.216689 | + | 0.976241i | \(0.430474\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1382.27 | + | 3797.74i | −0.0158835 | + | 0.0436397i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 130145. | − | 75139.3i | 1.47542 | − | 0.851832i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −42342.0 | + | 50461.3i | −0.473619 | + | 0.564437i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9110.40 | + | 51667.7i | −0.100555 | + | 0.570277i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 115287.i | 1.25572i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4205.62 | −0.0452095 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −136092. | − | 23996.7i | −1.44396 | − | 0.254610i | −0.603884 | − | 0.797072i | \(-0.706381\pi\) |
−0.840080 | + | 0.542462i | \(0.817492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 118225. | + | 99202.8i | 1.23821 | + | 1.03898i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −57568.9 | − | 99712.2i | −0.595205 | − | 1.03093i | −0.993518 | − | 0.113676i | \(-0.963737\pi\) |
0.398313 | − | 0.917250i | \(-0.369596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −49771.9 | − | 18115.5i | −0.508037 | − | 0.184910i | 0.0752683 | − | 0.997163i | \(-0.476019\pi\) |
−0.583305 | + | 0.812253i | \(0.698241\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 352.649 | − | 610.806i | 0.00355403 | − | 0.00615576i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −46437.0 | + | 8188.09i | −0.462110 | + | 0.0814825i | −0.399856 | − | 0.916578i | \(-0.630940\pi\) |
−0.0622538 | + | 0.998060i | \(0.519829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24276.5 | − | 28931.7i | −0.238564 | − | 0.284310i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33911.0 | − | 12342.6i | 0.329102 | − | 0.119783i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 127803. | + | 145745.i | 1.22500 | + | 1.39697i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −45176.0 | − | 124120.i | −0.427701 | − | 1.17510i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 78314.3 | − | 65713.5i | 0.732395 | − | 0.614553i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12746.3 | − | 72287.6i | −0.117758 | − | 0.667840i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30281.9 | + | 17483.2i | 0.276393 | + | 0.159575i | 0.631789 | − | 0.775140i | \(-0.282321\pi\) |
−0.355396 | + | 0.934716i | \(0.615654\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6938.07 | + | 19062.2i | −0.0625677 | + | 0.171903i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −148.063 | + | 85.4844i | −0.00131934 | + | 0.000761724i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31733.6 | − | 37818.6i | 0.279421 | − | 0.333001i | −0.608020 | − | 0.793921i | \(-0.708036\pi\) |
0.887442 | + | 0.460920i | \(0.152481\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24643.3 | − | 139759.i | 0.214437 | − | 1.21613i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 149632.i | 1.28681i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 123035. | 1.04578 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2022.55 | + | 356.630i | 0.0169926 | + | 0.00299626i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33446.4 | − | 28064.9i | −0.277774 | − | 0.233080i | 0.493248 | − | 0.869889i | \(-0.335810\pi\) |
−0.771022 | + | 0.636809i | \(0.780254\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28848.8 | + | 49967.6i | 0.236852 | + | 0.410239i | 0.959809 | − | 0.280653i | \(-0.0905511\pi\) |
−0.722957 | + | 0.690893i | \(0.757218\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 156317. | + | 56894.9i | 1.26880 | + | 0.461805i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 39122.8 | − | 67762.7i | 0.313965 | − | 0.543803i | −0.665252 | − | 0.746619i | \(-0.731676\pi\) |
0.979217 | + | 0.202816i | \(0.0650093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4393.46 | − | 774.686i | 0.0348618 | − | 0.00614708i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −126636. | − | 150918.i | −0.993618 | − | 1.18415i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −136903. | + | 49828.5i | −1.06224 | + | 0.386624i | −0.813270 | − | 0.581887i | \(-0.802315\pi\) |
−0.248971 | + | 0.968511i | \(0.580092\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −96090.4 | + | 88035.2i | −0.737336 | + | 0.675526i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 59294.5 | + | 162910.i | 0.449988 | + | 1.23633i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5213.78 | − | 4374.88i | 0.0391352 | − | 0.0328383i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30340.5 | − | 172069.i | −0.225263 | − | 1.27753i | −0.862181 | − | 0.506600i | \(-0.830902\pi\) |
0.636918 | − | 0.770931i | \(-0.280209\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16311.6 | − | 9417.48i | −0.119796 | − | 0.0691643i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15368.0 | + | 42223.3i | −0.111653 | + | 0.306764i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 193882. | − | 111938.i | 1.39354 | − | 0.804561i | 0.399836 | − | 0.916587i | \(-0.369067\pi\) |
0.993705 | + | 0.112025i | \(0.0357337\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5297.10 | + | 6312.83i | −0.0376682 | + | 0.0448913i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7259.62 | − | 41171.4i | 0.0510777 | − | 0.289676i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 194659.i | 1.35518i | 0.735440 | + | 0.677590i | \(0.236976\pi\) | ||||
−0.735440 | + | 0.677590i | \(0.763024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 235726. | 1.62390 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −223241. | − | 39363.5i | −1.52187 | − | 0.268347i | −0.650702 | − | 0.759333i | \(-0.725525\pi\) |
−0.871167 | + | 0.490987i | \(0.836636\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5649.60 | + | 4740.58i | 0.0381150 | + | 0.0319823i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10350.0 | − | 17926.8i | −0.0691068 | − | 0.119696i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −237179. | − | 86325.9i | −1.56739 | − | 0.570482i | −0.594973 | − | 0.803745i | \(-0.702837\pi\) |
−0.972414 | + | 0.233263i | \(0.925060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −83591.0 | + | 144784.i | −0.546771 | + | 0.947036i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −137014. | + | 24159.3i | −0.887115 | + | 0.156422i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3070.02 | + | 3658.71i | 0.0196765 | + | 0.0234495i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 169678. | − | 61757.6i | 1.07657 | − | 0.391841i | 0.257942 | − | 0.966160i | \(-0.416956\pi\) |
0.818631 | + | 0.574320i | \(0.194733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 99585.0 | − | 87326.0i | 0.625530 | − | 0.548527i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24795.4 | + | 68124.8i | 0.154199 | + | 0.423659i | 0.992605 | − | 0.121387i | \(-0.0387343\pi\) |
−0.838406 | + | 0.545046i | \(0.816512\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −126883. | + | 106467.i | −0.781253 | + | 0.655549i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −686.470 | − | 3893.17i | −0.00418516 | − | 0.0237352i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −183700. | − | 106059.i | −1.10897 | − | 0.640264i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −50355.5 | + | 138351.i | −0.301024 | + | 0.827056i | 0.693299 | + | 0.720650i | \(0.256157\pi\) |
−0.994323 | + | 0.106406i | \(0.966066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 47252.6 | − | 27281.3i | 0.279732 | − | 0.161503i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −144494. | + | 172202.i | −0.847131 | + | 1.00957i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 691.269 | − | 3920.38i | 0.00401376 | − | 0.0227631i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17803.4i | 0.102384i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −118436. | −0.674617 | −0.337309 | − | 0.941394i | \(-0.609517\pi\) | ||||
−0.337309 | + | 0.941394i | \(0.609517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3817.47 | − | 673.122i | −0.0215383 | − | 0.00379778i | 0.162869 | − | 0.986648i | \(-0.447925\pi\) |
−0.184407 | + | 0.982850i | \(0.559036\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22185.6 | + | 18615.9i | 0.123991 | + | 0.104041i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −167614. | − | 290316.i | −0.927968 | − | 1.60729i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −219816. | − | 80006.5i | −1.20560 | − | 0.438803i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −160129. | + | 277351.i | −0.870072 | + | 1.50701i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −52442.0 | + | 9246.94i | −0.282309 | + | 0.0497787i | −0.313010 | − | 0.949750i | \(-0.601337\pi\) |
0.0307006 | + | 0.999529i | \(0.490226\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 168576. | + | 200901.i | 0.899127 | + | 1.07154i | 0.997081 | + | 0.0763465i | \(0.0243255\pi\) |
−0.0979547 | + | 0.995191i | \(0.531230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1224.82 | + | 445.799i | −0.00647284 | + | 0.00235592i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −98538.7 | − | 54065.8i | −0.515993 | − | 0.283113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 47629.2 | + | 130860.i | 0.247141 | + | 0.679014i | 0.999788 | + | 0.0205899i | \(0.00655444\pi\) |
−0.752647 | + | 0.658424i | \(0.771223\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3567.50 | + | 2993.49i | −0.0183437 | + | 0.0153922i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 51518.8 | + | 292178.i | 0.262518 | + | 1.48881i | 0.776012 | + | 0.630718i | \(0.217240\pi\) |
−0.513494 | + | 0.858093i | \(0.671649\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8079.70 | + | 4664.82i | 0.0408014 | + | 0.0235567i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 49052.4 | − | 134770.i | 0.245497 | − | 0.674497i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 95659.2 | − | 55228.9i | 0.474498 | − | 0.273951i | −0.243623 | − | 0.969870i | \(-0.578336\pi\) |
0.718121 | + | 0.695919i | \(0.245003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 126597. | − | 150872.i | 0.622401 | − | 0.741749i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17424.0 | − | 98816.4i | 0.0849085 | − | 0.481540i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8163.73i | 0.0394335i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −197803. | −0.947110 | −0.473555 | − | 0.880764i | \(-0.657030\pi\) | ||||
−0.473555 | + | 0.880764i | \(0.657030\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 415775. | + | 73312.3i | 1.97348 | + | 0.347978i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29644.6 | + | 24874.8i | 0.139490 | + | 0.117046i | 0.709863 | − | 0.704340i | \(-0.248757\pi\) |
−0.570373 | + | 0.821386i | \(0.693201\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −60072.0 | − | 104048.i | −0.280227 | − | 0.485368i | 0.691213 | − | 0.722651i | \(-0.257076\pi\) |
−0.971441 | + | 0.237283i | \(0.923743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4852.63 | + | 1766.21i | 0.0224425 | + | 0.00816840i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 71703.3 | − | 124194.i | 0.328780 | − | 0.569464i | −0.653490 | − | 0.756935i | \(-0.726696\pi\) |
0.982270 | + | 0.187471i | \(0.0600292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9365.09 | + | 1651.32i | −0.0425762 | + | 0.00750732i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −84224.5 | − | 100375.i | −0.379662 | − | 0.452463i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 203399. | − | 74031.3i | 0.909133 | − | 0.330897i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 192680. | − | 116910.i | 0.853986 | − | 0.518160i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6063.49 | − | 16659.3i | −0.0266493 | − | 0.0732184i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −120222. | + | 100878.i | −0.523979 | + | 0.439671i | −0.866016 | − | 0.500016i | \(-0.833328\pi\) |
0.342037 | + | 0.939686i | \(0.388883\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40773.0 | − | 231235.i | −0.176231 | − | 0.999457i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 98928.5 | + | 57116.4i | 0.424060 | + | 0.244831i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −510.813 | + | 1403.45i | −0.00217159 | + | 0.00596641i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 134338. | − | 77560.2i | 0.566424 | − | 0.327025i | −0.189296 | − | 0.981920i | \(-0.560621\pi\) |
0.755720 | + | 0.654895i | \(0.227287\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 60457.8 | − | 72050.8i | 0.252833 | − | 0.301315i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27722.8 | − | 157224.i | 0.114994 | − | 0.652163i | −0.871759 | − | 0.489934i | \(-0.837021\pi\) |
0.986753 | − | 0.162228i | \(-0.0518681\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 106103.i | − | 0.436551i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2909.84 | −0.0118757 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 244371. | + | 43089.3i | 0.989322 | + | 0.174444i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 211495. | + | 177466.i | 0.849375 | + | 0.712710i | 0.959652 | − | 0.281190i | \(-0.0907293\pi\) |
−0.110277 | + | 0.993901i | \(0.535174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 60466.2 | + | 104731.i | 0.240900 | + | 0.417252i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −58971.7 | − | 21463.9i | −0.233081 | − | 0.0848347i | 0.222839 | − | 0.974855i | \(-0.428468\pi\) |
−0.455920 | + | 0.890021i | \(0.650690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6062.25 | − | 10500.1i | 0.0237712 | − | 0.0411729i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −126363. | + | 22281.2i | −0.491591 | + | 0.0866807i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 266313. | + | 317380.i | 1.02792 | + | 1.22502i | 0.974017 | + | 0.226476i | \(0.0727205\pi\) |
0.0538991 | + | 0.998546i | \(0.482835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 355736. | − | 129477.i | 1.36234 | − | 0.495852i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −43190.7 | + | 280533.i | −0.164118 | + | 1.06598i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5551.28 | − | 15252.0i | −0.0209305 | − | 0.0575060i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −231987. | + | 194660.i | −0.867924 | + | 0.728275i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −47907.4 | − | 271696.i | −0.177856 | − | 1.00867i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −126272. | − | 72903.2i | −0.465191 | − | 0.268578i | 0.249033 | − | 0.968495i | \(-0.419887\pi\) |
−0.714225 | + | 0.699917i | \(0.753221\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 161926. | − | 444889.i | 0.591990 | − | 1.62648i | −0.174818 | − | 0.984601i | \(-0.555934\pi\) |
0.766807 | − | 0.641877i | \(-0.221844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −198369. | + | 114528.i | −0.719705 | + | 0.415522i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −270210. | + | 322023.i | −0.972925 | + | 1.15949i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31760.9 | + | 180125.i | −0.113496 | + | 0.643668i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 88692.8i | − | 0.314557i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 218012. | 0.767408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3737.59 | − | 659.037i | −0.0130582 | − | 0.00230251i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −193928. | − | 162725.i | −0.672499 | − | 0.564294i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24348.5 | − | 42172.8i | −0.0838096 | − | 0.145163i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 128104. | + | 46625.9i | 0.437690 | + | 0.159306i | 0.551461 | − | 0.834201i | \(-0.314071\pi\) |
−0.113771 | + | 0.993507i | \(0.536293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 225710. | − | 390940.i | 0.765509 | − | 1.32590i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10588.2 | + | 1866.99i | −0.0356477 | + | 0.00628564i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −207771. | − | 247611.i | −0.694400 | − | 0.827554i | 0.297481 | − | 0.954728i | \(-0.403854\pi\) |
−0.991880 | + | 0.127174i | \(0.959409\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 86729.0 | − | 31566.8i | 0.287753 | − | 0.104733i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 71316.5 | − | 1553.02i | 0.234902 | − | 0.00511532i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 90859.2 | + | 249634.i | 0.297111 | + | 0.816306i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5607.90 | + | 4705.59i | −0.0182060 | + | 0.0152766i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −94444.8 | − | 535623.i | −0.304416 | − | 1.72643i | −0.626241 | − | 0.779630i | \(-0.715407\pi\) |
0.321825 | − | 0.946799i | \(-0.395704\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 207500. | + | 119800.i | 0.664042 | + | 0.383385i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −277995. | + | 763784.i | −0.883305 | + | 2.42686i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −364078. | + | 210201.i | −1.14862 | + | 0.663158i | −0.948552 | − | 0.316623i | \(-0.897451\pi\) |
−0.200072 | + | 0.979781i | \(0.564118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9593.61 | + | 11433.2i | −0.0300528 | + | 0.0358155i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 38182.6 | − | 216544.i | 0.118768 | − | 0.673566i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 311903.i | 0.963374i | 0.876343 | + | 0.481687i | \(0.159976\pi\) | ||||
−0.876343 | + | 0.481687i | \(0.840024\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4647.72 | −0.0142550 | −0.00712751 | − | 0.999975i | \(-0.502269\pi\) | ||||
−0.00712751 | + | 0.999975i | \(0.502269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −397159. | − | 70029.8i | −1.20964 | − | 0.213292i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 148901. | + | 124943.i | 0.450362 | + | 0.377899i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 92600.9 | + | 160390.i | 0.278140 | + | 0.481753i | 0.970923 | − | 0.239394i | \(-0.0769487\pi\) |
−0.692782 | + | 0.721147i | \(0.743615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −54070.1 | − | 19679.9i | −0.161287 | − | 0.0587038i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 110711. | − | 191757.i | 0.327973 | − | 0.568066i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 182564. | − | 32190.9i | 0.537127 | − | 0.0947100i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2070.43 | − | 2467.45i | −0.00604992 | − | 0.00721001i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −177355. | + | 64551.9i | −0.514715 | + | 0.187341i | −0.586301 | − | 0.810094i | \(-0.699416\pi\) |
0.0715858 | + | 0.997434i | \(0.477194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −220400. | − | 176906.i | −0.635304 | − | 0.509931i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36067.7 | + | 99095.3i | 0.103263 | + | 0.283712i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 131397. | − | 110255.i | 0.373659 | − | 0.313537i | −0.436548 | − | 0.899681i | \(-0.643799\pi\) |
0.810207 | + | 0.586144i | \(0.199355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3597.86 | + | 20404.5i | 0.0101627 | + | 0.0576357i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 203048. | + | 117230.i | 0.569706 | + | 0.328920i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 136137. | − | 374034.i | 0.379423 | − | 1.04246i | −0.592174 | − | 0.805810i | \(-0.701730\pi\) |
0.971596 | − | 0.236645i | \(-0.0760477\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −376812. | + | 217553.i | −1.04322 | + | 0.602304i | −0.920744 | − | 0.390168i | \(-0.872417\pi\) |
−0.122477 | + | 0.992471i | \(0.539084\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2411.76 | − | 2874.22i | 0.00663283 | − | 0.00790470i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3166.05 | − | 17955.6i | 0.00864983 | − | 0.0490556i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 48561.9i | 0.131801i | 0.997826 | + | 0.0659005i | \(0.0209920\pi\) | ||||
−0.997826 | + | 0.0659005i | \(0.979008\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −72498.8 | −0.195477 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −330130. | − | 58210.8i | −0.884306 | − | 0.155927i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −265441. | − | 222732.i | −0.706395 | − | 0.592736i | 0.217190 | − | 0.976129i | \(-0.430311\pi\) |
−0.923585 | + | 0.383394i | \(0.874755\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3398.55 | − | 5886.47i | −0.00898553 | − | 0.0155634i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 380855. | + | 138620.i | 1.00044 | + | 0.364129i | 0.789753 | − | 0.613426i | \(-0.210209\pi\) |
0.210683 | + | 0.977554i | \(0.432431\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −163814. | + | 283734.i | −0.427533 | + | 0.740508i | −0.996653 | − | 0.0817457i | \(-0.973950\pi\) |
0.569120 | + | 0.822254i | \(0.307284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −241080. | + | 42508.9i | −0.625141 | + | 0.110229i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 333561. | + | 397523.i | 0.859409 | + | 1.02420i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −365846. | + | 133157.i | −0.936565 | + | 0.340882i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −517440. | − | 175672.i | −1.31621 | − | 0.446857i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −203817. | − | 559982.i | −0.515156 | − | 1.41538i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −270104. | + | 226644.i | −0.678379 | + | 0.569228i | −0.915532 | − | 0.402244i | \(-0.868230\pi\) |
0.237153 | + | 0.971472i | \(0.423786\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 64.6222 | + | 366.491i | 0.000161278 | + | 0.000914652i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21469.6 | − | 12395.5i | −0.0532448 | − | 0.0307409i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18436.5 | − | 50653.8i | 0.0454359 | − | 0.124834i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −84788.0 | + | 48952.4i | −0.207650 | + | 0.119887i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 284607. | − | 339181.i | 0.692675 | − | 0.825498i | −0.299002 | − | 0.954253i | \(-0.596654\pi\) |
0.991676 | + | 0.128755i | \(0.0410981\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −68762.6 | + | 389972.i | −0.166315 | + | 0.943217i | 0.781384 | + | 0.624050i | \(0.214514\pi\) |
−0.947699 | + | 0.319166i | \(0.896597\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7470.19i | − | 0.0179561i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −129762. | −0.309983 | −0.154992 | − | 0.987916i | \(-0.549535\pi\) | ||||
−0.154992 | + | 0.987916i | \(0.549535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 913338. | + | 161046.i | 2.16841 | + | 0.382350i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 220034. | + | 184630.i | 0.519191 | + | 0.435653i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 126553. | + | 219197.i | 0.296788 | + | 0.514052i | 0.975399 | − | 0.220445i | \(-0.0707511\pi\) |
−0.678611 | + | 0.734498i | \(0.737418\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13749.4 | + | 5004.39i | 0.0320481 | + | 0.0116646i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −74682.3 | + | 129354.i | −0.173016 | + | 0.299673i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 156021. | − | 27510.7i | 0.359263 | − | 0.0633477i | 0.00889634 | − | 0.999960i | \(-0.497168\pi\) |
0.350366 | + | 0.936613i | \(0.386057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −434961. | − | 518366.i | −0.995513 | − | 1.18641i | −0.982456 | − | 0.186492i | \(-0.940288\pi\) |
−0.0130570 | − | 0.999915i | \(-0.504156\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −845464. | + | 307724.i | −1.92339 | + | 0.700058i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13662.0 | + | 2716.93i | −0.0308938 | + | 0.00614377i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21041.8 | + | 57812.0i | 0.0472968 | + | 0.129947i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 142723. | − | 119759.i | 0.318892 | − | 0.267582i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 167587. | + | 950433.i | 0.372216 | + | 2.11094i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −706065. | − | 407647.i | −1.55889 | − | 0.900024i | −0.997364 | − | 0.0725630i | \(-0.976882\pi\) |
−0.561523 | − | 0.827461i | \(-0.689785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 167885. | − | 461261.i | 0.368473 | − | 1.01237i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 316533. | − | 182751.i | 0.690624 | − | 0.398732i | −0.113221 | − | 0.993570i | \(-0.536117\pi\) |
0.803846 | + | 0.594838i | \(0.202784\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −53397.6 | + | 63636.8i | −0.115820 | + | 0.138028i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12448.3 | + | 70598.1i | −0.0268422 | + | 0.152229i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 125776.i | − | 0.269623i | −0.990871 | − | 0.134811i | \(-0.956957\pi\) | ||
0.990871 | − | 0.134811i | \(-0.0430428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5738.27 | −0.0122292 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 135545. | + | 23900.3i | 0.287191 | + | 0.0506395i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 157196. | + | 131903.i | 0.331133 | + | 0.277854i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −289348. | − | 501166.i | −0.605989 | − | 1.04960i | −0.991894 | − | 0.127065i | \(-0.959444\pi\) |
0.385905 | − | 0.922538i | \(-0.373889\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −152089. | − | 55355.9i | −0.316688 | − | 0.115265i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 936.177 | − | 1621.51i | 0.00193815 | − | 0.00335698i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 544901. | − | 96080.7i | 1.12164 | − | 0.197775i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 351634. | + | 419061.i | 0.719675 | + | 0.857676i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 733783. | − | 267075.i | 1.49325 | − | 0.543498i | 0.538945 | − | 0.842341i | \(-0.318823\pi\) |
0.954302 | + | 0.298843i | \(0.0966007\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 373404. | − | 145190.i | 0.755559 | − | 0.293783i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3574.61 | + | 9821.16i | 0.00719201 | + | 0.0197599i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 516609. | − | 433486.i | 1.03353 | − | 0.867234i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 157506. | + | 893259.i | 0.313331 | + | 1.77699i | 0.581427 | + | 0.813598i | \(0.302494\pi\) |
−0.268096 | + | 0.963392i | \(0.586394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −90772.3 | − | 52407.4i | −0.179562 | − | 0.103670i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 83365.7 | − | 229045.i | 0.163987 | − | 0.450550i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29168.6 | − | 16840.5i | 0.0570563 | − | 0.0329415i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 481675. | − | 574038.i | 0.936948 | − | 1.11661i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36072.2 | + | 204576.i | −0.0697775 | + | 0.395728i | 0.929837 | + | 0.367971i | \(0.119947\pi\) |
−0.999615 | + | 0.0277566i | \(0.991164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 902787.i | − | 1.73666i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 850542. | 1.62712 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −121488. | − | 21421.7i | −0.231131 | − | 0.0407547i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −505469. | − | 424139.i | −0.956370 | − | 0.802489i | 0.0239891 | − | 0.999712i | \(-0.492363\pi\) |
−0.980359 | + | 0.197223i | \(0.936808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 295567. | + | 511938.i | 0.556162 | + | 0.963301i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 571425. | + | 207982.i | 1.06936 | + | 0.389216i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 235776. | − | 408377.i | 0.438826 | − | 0.760069i | −0.558773 | − | 0.829321i | \(-0.688728\pi\) |
0.997599 | + | 0.0692514i | \(0.0220611\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1655.09 | + | 291.836i | −0.00306370 | + | 0.000540213i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25218.8 | + | 30054.6i | 0.0464290 | + | 0.0553320i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −559014. | + | 203465.i | −1.02361 | + | 0.372563i | −0.798644 | − | 0.601804i | \(-0.794449\pi\) |
−0.224965 | + | 0.974367i | \(0.572227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −219209. | − | 563768.i | −0.399229 | − | 1.02675i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −115197. | − | 316500.i | −0.208671 | − | 0.573319i | 0.790566 | − | 0.612377i | \(-0.209787\pi\) |
−0.999237 | + | 0.0390578i | \(0.987564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11554.4 | + | 9695.31i | −0.0208178 | + | 0.0174682i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15170.4 | + | 86035.4i | 0.0271866 | + | 0.154183i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −182816. | − | 105549.i | −0.325874 | − | 0.188144i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −163368. | + | 448849.i | −0.289659 | + | 0.795831i | 0.706455 | + | 0.707758i | \(0.250293\pi\) |
−0.996114 | + | 0.0880731i | \(0.971929\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36032.5 | − | 20803.4i | 0.0635483 | − | 0.0366896i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6783.13 | + | 8083.82i | −0.0118997 | + | 0.0141815i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −126507. | + | 717459.i | −0.220762 | + | 1.25200i | 0.649861 | + | 0.760053i | \(0.274827\pi\) |
−0.870623 | + | 0.491950i | \(0.836284\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 471289.i | − | 0.818095i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −307163. | −0.530396 | −0.265198 | − | 0.964194i | \(-0.585437\pi\) | ||||
−0.265198 | + | 0.964194i | \(0.585437\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −588935. | − | 103845.i | −1.01162 | − | 0.178376i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6262.28 | − | 5254.68i | −0.0107006 | − | 0.00897891i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 513304. | + | 889068.i | 0.872537 | + | 1.51128i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 968775. | + | 352605.i | 1.63821 | + | 0.596261i | 0.986725 | − | 0.162398i | \(-0.0519229\pi\) |
0.651488 | + | 0.758659i | \(0.274145\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −70698.3 | + | 122453.i | −0.118932 | + | 0.205997i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.03440e6 | − | 182393.i | 1.73113 | − | 0.305245i | 0.782740 | − | 0.622348i | \(-0.213821\pi\) |
0.948391 | + | 0.317103i | \(0.102710\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 314163. | + | 374405.i | 0.523060 | + | 0.623359i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −382627. | + | 139265.i | −0.633773 | + | 0.230674i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 72555.5 | + | 364844.i | 0.119563 | + | 0.601219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −350144. | − | 962013.i | −0.574044 | − | 1.57717i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 119015. | − | 99865.8i | 0.194124 | − | 0.162890i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2392.91 | + | 13570.9i | 0.00388318 | + | 0.0220226i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −152033. | − | 87776.2i | −0.245464 | − | 0.141719i | 0.372221 | − | 0.928144i | \(-0.378596\pi\) |
−0.617686 | + | 0.786425i | \(0.711930\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12752.1 | − | 35036.1i | 0.0204846 | − | 0.0562810i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −718933. | + | 415076.i | −1.14904 | + | 0.663399i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −686692. | + | 818368.i | −1.09198 | + | 1.30137i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1110.97 | − | 6300.60i | 0.00175779 | − | 0.00996891i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 616704.i | − | 0.970868i | −0.874273 | − | 0.485434i | \(-0.838662\pi\) | ||
0.874273 | − | 0.485434i | \(-0.161338\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −850783. | −1.33268 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −201635. | − | 35553.6i | −0.314268 | − | 0.0554139i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.19645e6 | − | 1.00394e6i | −1.85550 | − | 1.55695i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6006.84 | − | 10404.2i | −0.00926946 | − | 0.0160552i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −57126.2 | − | 20792.2i | −0.0877180 | − | 0.0319267i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −51993.1 | + | 90054.7i | −0.0794417 | + | 0.137597i | −0.903009 | − | 0.429621i | \(-0.858647\pi\) |
0.823567 | + | 0.567218i | \(0.191980\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 773819. | − | 136445.i | 1.17652 | − | 0.207452i | 0.448993 | − | 0.893535i | \(-0.351783\pi\) |
0.727523 | + | 0.686084i | \(0.240672\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −347192. | − | 413767.i | −0.525277 | − | 0.626000i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9295.14 | + | 3383.16i | −0.0139940 | + | 0.00509339i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −131429. | + | 387123.i | −0.196901 | + | 0.579969i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −61275.8 | − | 168354.i | −0.0913526 | − | 0.250989i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −712467. | + | 597831.i | −1.05701 | + | 0.886936i | −0.993813 | − | 0.111065i | \(-0.964574\pi\) |
−0.0631958 | + | 0.998001i | \(0.520129\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24772.4 | + | 140491.i | 0.0365736 | + | 0.207419i | 0.997619 | − | 0.0689730i | \(-0.0219722\pi\) |
−0.961045 | + | 0.276392i | \(0.910861\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 818408. | + | 472508.i | 1.20244 | + | 0.694227i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −225103. | + | 618464.i | −0.329131 | + | 0.904281i | 0.659201 | + | 0.751967i | \(0.270895\pi\) |
−0.988332 | + | 0.152314i | \(0.951327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −416484. | + | 240457.i | −0.606024 | + | 0.349888i | −0.771408 | − | 0.636341i | \(-0.780447\pi\) |
0.165384 | + | 0.986229i | \(0.447114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 318732. | − | 379850.i | 0.461555 | − | 0.550060i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23756.4 | − | 134730.i | 0.0342367 | − | 0.194166i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 12718.3i | − | 0.0182413i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −615536. | −0.878623 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −162087. | − | 28580.4i | −0.230264 | − | 0.0406017i | 0.0573256 | − | 0.998356i | \(-0.481743\pi\) |
−0.287589 | + | 0.957754i | \(0.592854\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 511898. | + | 429533.i | 0.723755 | + | 0.607302i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 416598. | + | 721570.i | 0.586223 | + | 1.01537i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12680.6 | + | 4615.36i | 0.0177593 | + | 0.00646386i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 507063. | − | 878258.i | 0.706797 | − | 1.22421i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.04498e6 | + | 184259.i | −1.44975 | + | 0.255631i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 222105. | + | 264694.i | 0.306690 | + | 0.365498i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −989647. | + | 360202.i | −1.36014 | + | 0.495049i | −0.916096 | − | 0.400959i | \(-0.868677\pi\) |
−0.444039 | + | 0.896007i | \(0.646455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3440.23 | − | 4286.06i | 0.00470604 | − | 0.00586308i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −101250. | − | 278182.i | −0.137858 | − | 0.378762i | 0.851482 | − | 0.524383i | \(-0.175704\pi\) |
−0.989340 | + | 0.145621i | \(0.953482\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 620070. | − | 520301.i | 0.840339 | − | 0.705128i | −0.117301 | − | 0.993096i | \(-0.537424\pi\) |
0.957640 | + | 0.287968i | \(0.0929797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −65650.5 | − | 372322.i | −0.0885587 | − | 0.502242i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 966368. | + | 557933.i | 1.29754 | + | 0.749135i | 0.979979 | − | 0.199102i | \(-0.0638027\pi\) |
0.317562 | + | 0.948238i | \(0.397136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9923.60 | + | 27264.9i | −0.0132629 | + | 0.0364394i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.40470e6 | + | 811003.i | −1.86872 | + | 1.07891i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 704501. | − | 839591.i | 0.932915 | − | 1.11180i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7541.40 | + | 42769.4i | −0.00994067 | + | 0.0563763i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 32776.2i | − | 0.0430062i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 48205.8 | 0.0629627 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 453527. | + | 79969.1i | 0.589664 | + | 0.103974i | 0.460515 | − | 0.887652i | \(-0.347665\pi\) |
0.129148 | + | 0.991625i | \(0.458776\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −703934. | − | 590670.i | −0.911074 | − | 0.764482i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 653425. | + | 1.13177e6i | 0.841868 | + | 1.45816i | 0.888313 | + | 0.459238i | \(0.151878\pi\) |
−0.0464448 | + | 0.998921i | \(0.514789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −138215. | − | 50306.2i | −0.177269 | − | 0.0645208i | 0.251861 | − | 0.967764i | \(-0.418958\pi\) |
−0.429130 | + | 0.903243i | \(0.641180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16003.6 | − | 27719.1i | 0.0204330 | − | 0.0353909i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 161952. | − | 28556.5i | 0.205844 | − | 0.0362959i | −0.0697751 | − | 0.997563i | \(-0.522228\pi\) |
0.275619 | + | 0.961267i | \(0.411117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −886349. | − | 1.05631e6i | −1.12150 | − | 1.33656i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −852466. | + | 310272.i | −1.07380 | + | 0.390830i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12452.8 | − | 571847.i | −0.0156157 | − | 0.717095i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9105.91 | + | 25018.3i | 0.0113678 | + | 0.0312328i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 399637. | − | 335336.i | 0.496685 | − | 0.416768i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26862.5 | + | 152345.i | 0.0332374 | + | 0.188498i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 451028. | + | 260401.i | 0.555589 | + | 0.320769i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 142111. | − | 390446.i | 0.174282 | − | 0.478835i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41114.6 | + | 23737.5i | −0.0501994 | + | 0.0289827i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −289245. | + | 344709.i | −0.351602 | + | 0.419023i | −0.912638 | − | 0.408768i | \(-0.865958\pi\) |
0.561036 | + | 0.827791i | \(0.310403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −46204.4 | + | 262038.i | −0.0559185 | + | 0.317129i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.42304e6i | − | 1.71467i | −0.514757 | − | 0.857336i | \(-0.672118\pi\) | ||
0.514757 | − | 0.857336i | \(-0.327882\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −913518. | −1.09591 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32801.2 | + | 5783.73i | 0.0391784 | + | 0.00690822i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 623443. | + | 523131.i | 0.741409 | + | 0.622116i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −92255.4 | − | 159791.i | −0.109235 | − | 0.189200i | 0.806226 | − | 0.591608i | \(-0.201507\pi\) |
−0.915460 | + | 0.402408i | \(0.868173\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.02843e6 | + | 374319.i | 1.21243 | + | 0.441288i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 566617. | − | 981410.i | 0.665099 | − | 1.15199i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −682329. | + | 120313.i | −0.797463 | + | 0.140614i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 228959. | + | 272863.i | 0.266439 | + | 0.317530i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 82033.9 | − | 29857.9i | 0.0950522 | − | 0.0345962i | −0.294056 | − | 0.955788i | \(-0.595005\pi\) |
0.389109 | + | 0.921192i | \(0.372783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 90905.1 | + | 13995.7i | 0.104879 | + | 0.0161471i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 311873. | + | 856863.i | 0.358273 | + | 0.984347i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 65482.3 | − | 54946.2i | 0.0749033 | − | 0.0628513i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 229447. | + | 1.30126e6i | 0.261339 | + | 1.48212i | 0.779262 | + | 0.626698i | \(0.215594\pi\) |
−0.517924 | + | 0.855427i | \(0.673295\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 363276. | + | 209738.i | 0.412008 | + | 0.237873i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −365226. | + | 1.00345e6i | −0.412460 | + | 1.13323i | 0.543418 | + | 0.839462i | \(0.317130\pi\) |
−0.955878 | + | 0.293763i | \(0.905092\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −277843. | + | 160413.i | −0.312447 | + | 0.180391i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −19501.2 | + | 23240.6i | −0.0218372 | + | 0.0260246i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −119571. | + | 678120.i | −0.133329 | + | 0.756148i | 0.842679 | + | 0.538416i | \(0.180977\pi\) |
−0.976009 | + | 0.217732i | \(0.930134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.72888e6i | − | 1.91969i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 373440. | 0.412914 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 929117. | + | 163828.i | 1.02302 | + | 0.180386i | 0.659898 | − | 0.751355i | \(-0.270599\pi\) |
0.363123 | + | 0.931741i | \(0.381711\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32490.2 | + | 27262.5i | 0.0356242 | + | 0.0298923i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 149554. | + | 259035.i | 0.163295 | + | 0.282836i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −299923. | − | 109163.i | −0.326117 | − | 0.118697i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −155317. | + | 269018.i | −0.168180 | + | 0.291296i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 82023.8 | − | 14463.0i | 0.0884479 | − | 0.0155957i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3889.78 | + | 4635.65i | 0.00417705 | + | 0.00497802i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 701607. | − | 255364.i | 0.750310 | − | 0.273091i | 0.0615741 | − | 0.998103i | \(-0.480388\pi\) |
0.688736 | + | 0.725012i | \(0.258166\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −796352. | − | 1.31248e6i | −0.848120 | − | 1.39780i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −422780. | − | 1.16158e6i | −0.448410 | − | 1.23200i | −0.933830 | − | 0.357716i | \(-0.883556\pi\) |
0.485420 | − | 0.874281i | \(-0.338667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 79778.4 | − | 66942.1i | 0.0842675 | − | 0.0707088i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 181649. | + | 1.03019e6i | 0.191084 | + | 1.08369i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.18840e6 | − | 686121.i | −1.24501 | − | 0.718806i | −0.274899 | − | 0.961473i | \(-0.588644\pi\) |
−0.970110 | + | 0.242667i | \(0.921978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 732245. | − | 2.01183e6i | 0.763996 | − | 2.09906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 204339. | − | 117975.i | 0.212331 | − | 0.122589i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29587.7 | − | 35261.2i | 0.0306199 | − | 0.0364914i | −0.750517 | − | 0.660851i | \(-0.770196\pi\) |
0.781137 | + | 0.624360i | \(0.214640\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1925.85 | − | 10922.0i | 0.00198495 | − | 0.0112572i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 581327.i | 0.596741i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −352595. | −0.360482 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 656367. | + | 115735.i | 0.668343 | + | 0.117847i | 0.497517 | − | 0.867454i | \(-0.334245\pi\) |
0.170826 | + | 0.985301i | \(0.445356\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −212136. | − | 178003.i | −0.215137 | − | 0.180522i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12328.9 | − | 21354.3i | −0.0124531 | − | 0.0215694i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.73997e6 | + | 633296.i | 1.75045 | + | 0.637113i | 0.999724 | − | 0.0234964i | \(-0.00747981\pi\) |
0.750730 | + | 0.660609i | \(0.229702\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 436293. | − | 755682.i | 0.437167 | − | 0.757195i |
(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 | 76.5.j.a.33.2 | ✓ | 42 | |
19.15 | odd | 18 | inner | 76.5.j.a.53.2 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.33.2 | ✓ | 42 | 1.1 | even | 1 | trivial | |
76.5.j.a.53.2 | yes | 42 | 19.15 | odd | 18 | inner |