Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(911,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.911");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.cc (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 911.9 | ||
Character | \(\chi\) | \(=\) | 1440.911 |
Dual form | 1440.2.cc.a.1391.9 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.801968 | + | 1.53520i | −0.463017 | + | 0.886350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.07138 | − | 2.35061i | −1.53884 | − | 0.888449i | −0.998907 | − | 0.0467391i | \(-0.985117\pi\) |
−0.539931 | − | 0.841709i | \(-0.681550\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.71369 | − | 2.46237i | −0.571231 | − | 0.820789i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.19675 | + | 1.84565i | 0.963857 | + | 0.556483i | 0.897358 | − | 0.441303i | \(-0.145484\pi\) |
0.0664992 | + | 0.997786i | \(0.478817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.94278 | − | 1.69902i | 0.816181 | − | 0.471222i | −0.0329169 | − | 0.999458i | \(-0.510480\pi\) |
0.849098 | + | 0.528236i | \(0.177146\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73051 | − | 0.0730766i | 0.446815 | − | 0.0188683i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.19988i | 0.776084i | 0.921642 | + | 0.388042i | \(0.126849\pi\) | ||||
−0.921642 | + | 0.388042i | \(0.873151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.184741 | 0.0423826 | 0.0211913 | − | 0.999775i | \(-0.493254\pi\) | ||||
0.0211913 | + | 0.999775i | \(0.493254\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.87379 | − | 4.36528i | 1.49998 | − | 0.952582i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.68941 | − | 2.92615i | −0.352267 | − | 0.610145i | 0.634379 | − | 0.773022i | \(-0.281256\pi\) |
−0.986646 | + | 0.162877i | \(0.947923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.15456 | − | 0.656128i | 0.991996 | − | 0.126272i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.71642 | + | 8.16907i | −0.875817 | + | 1.51696i | −0.0199263 | + | 0.999801i | \(0.506343\pi\) |
−0.855890 | + | 0.517157i | \(0.826990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.31877 | + | 0.761389i | −0.236857 | + | 0.136750i | −0.613731 | − | 0.789515i | \(-0.710332\pi\) |
0.376874 | + | 0.926264i | \(0.376999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.39713 | + | 3.42751i | −0.939521 | + | 0.596654i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.70123i | 0.794653i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.21087i | 0.363465i | 0.983348 | + | 0.181732i | \(0.0581704\pi\) | ||||
−0.983348 | + | 0.181732i | \(0.941830\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.248316 | + | 5.88032i | 0.0397625 | + | 0.941605i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.97131 | − | 4.60224i | 1.24491 | − | 0.718749i | 0.274820 | − | 0.961496i | \(-0.411382\pi\) |
0.970090 | + | 0.242746i | \(0.0780483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.05231 | + | 8.75086i | −0.770470 | + | 1.33449i | 0.166836 | + | 0.985985i | \(0.446645\pi\) |
−0.937306 | + | 0.348509i | \(0.886688\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.27563 | + | 2.71529i | −0.190159 | + | 0.404771i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.20071 | + | 5.54379i | −0.466872 | + | 0.808645i | −0.999284 | − | 0.0378398i | \(-0.987952\pi\) |
0.532412 | + | 0.846485i | \(0.321286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.55077 | + | 13.0783i | 1.07868 | + | 1.86833i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.91246 | − | 2.56620i | −0.687882 | − | 0.359340i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.652400 | 0.0896140 | 0.0448070 | − | 0.998996i | \(-0.485733\pi\) | ||||
0.0448070 | + | 0.998996i | \(0.485733\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.69129i | − | 0.497734i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.148157 | + | 0.283616i | −0.0196238 | + | 0.0375658i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.25989 | + | 4.19150i | −0.945157 | + | 0.545687i | −0.891573 | − | 0.452876i | \(-0.850398\pi\) |
−0.0535842 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.59632 | + | 3.23103i | 0.716535 | + | 0.413692i | 0.813476 | − | 0.581599i | \(-0.197573\pi\) |
−0.0969412 | + | 0.995290i | \(0.530906\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.18903 | + | 14.0535i | 0.149804 | + | 1.77057i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.94278 | − | 1.69902i | −0.365007 | − | 0.210737i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.725538 | + | 1.25667i | 0.0886386 | + | 0.153527i | 0.906936 | − | 0.421269i | \(-0.138415\pi\) |
−0.818297 | + | 0.574795i | \(0.805082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.84709 | − | 0.246913i | 0.703907 | − | 0.0297249i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5995 | 1.37661 | 0.688306 | − | 0.725421i | \(-0.258355\pi\) | ||||
0.688306 | + | 0.725421i | \(0.258355\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.3080 | −1.79166 | −0.895832 | − | 0.444393i | \(-0.853419\pi\) | ||||
−0.895832 | + | 0.444393i | \(0.853419\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.928540 | − | 1.46213i | −0.107219 | − | 0.168832i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.67680 | − | 15.0287i | −0.988813 | − | 1.71268i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.19259 | − | 1.26589i | −0.246686 | − | 0.142424i | 0.371560 | − | 0.928409i | \(-0.378823\pi\) |
−0.618246 | + | 0.785985i | \(0.712156\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.12650 | + | 8.43949i | −0.347389 | + | 0.937721i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.86408 | + | 2.23093i | 0.424138 | + | 0.244876i | 0.696846 | − | 0.717221i | \(-0.254586\pi\) |
−0.272708 | + | 0.962097i | \(0.587919\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.77118 | − | 1.59994i | 0.300576 | − | 0.173538i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.75877 | − | 13.7920i | −0.939038 | − | 1.47866i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.32981i | 0.458959i | 0.973313 | + | 0.229480i | \(0.0737024\pi\) | ||||
−0.973313 | + | 0.229480i | \(0.926298\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.9749 | −1.67463 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.111279 | − | 2.63518i | −0.0115391 | − | 0.273256i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0923707 | − | 0.159991i | −0.00947703 | − | 0.0164147i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.59159 | + | 14.8811i | −0.872344 | + | 1.51094i | −0.0127789 | + | 0.999918i | \(0.504068\pi\) |
−0.859565 | + | 0.511026i | \(0.829266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.933599 | − | 11.0345i | −0.0938302 | − | 1.10900i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.01593 | − | 1.75965i | 0.101089 | − | 0.175091i | −0.811045 | − | 0.584984i | \(-0.801101\pi\) |
0.912134 | + | 0.409893i | \(0.134434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.17647 | + | 0.679237i | −0.115921 | + | 0.0669272i | −0.556840 | − | 0.830620i | \(-0.687986\pi\) |
0.440918 | + | 0.897547i | \(0.354653\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.21734 | − | 3.77023i | −0.704340 | − | 0.367937i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.2120i | − | 0.987227i | −0.869681 | − | 0.493614i | \(-0.835676\pi\) | ||
0.869681 | − | 0.493614i | \(-0.164324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9528i | 1.14487i | 0.819950 | + | 0.572435i | \(0.194001\pi\) | ||||
−0.819950 | + | 0.572435i | \(0.805999\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.39413 | − | 1.77305i | −0.322157 | − | 0.168290i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.07593 | − | 4.66264i | 0.759720 | − | 0.438625i | −0.0694752 | − | 0.997584i | \(-0.522132\pi\) |
0.829195 | + | 0.558959i | \(0.188799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.68941 | + | 2.92615i | −0.157539 | + | 0.272865i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.22663 | − | 4.33462i | −0.853002 | − | 0.400735i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.52168 | − | 13.0279i | 0.689511 | − | 1.19427i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.31282 | + | 2.27387i | 0.119347 | + | 0.206715i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.672632 | + | 15.9284i | 0.0606492 | + | 1.43622i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.88163i | − | 0.344439i | −0.985059 | − | 0.172220i | \(-0.944906\pi\) | ||
0.985059 | − | 0.172220i | \(-0.0550939\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.38255 | − | 14.7742i | −0.826087 | − | 1.30080i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.59245 | − | 5.53820i | 0.838096 | − | 0.483875i | −0.0185204 | − | 0.999828i | \(-0.505896\pi\) |
0.856617 | + | 0.515953i | \(0.172562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.752153 | − | 0.434256i | −0.0652199 | − | 0.0376547i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.14550 | − | 4.13592i | −0.270722 | − | 0.355963i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.98251 | + | 2.29930i | 0.340249 | + | 0.196443i | 0.660382 | − | 0.750930i | \(-0.270394\pi\) |
−0.320133 | + | 0.947373i | \(0.603728\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.91862 | + | 10.2514i | 0.502011 | + | 0.869508i | 0.999997 | + | 0.00232356i | \(0.000739612\pi\) |
−0.497986 | + | 0.867185i | \(0.665927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.94398 | − | 9.35969i | −0.500573 | − | 0.788228i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5431 | 1.04891 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.43283 | 0.783354 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −26.1333 | + | 1.10357i | −2.15544 | + | 0.0910208i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.42256 | + | 5.92805i | 0.280387 | + | 0.485645i | 0.971480 | − | 0.237121i | \(-0.0762038\pi\) |
−0.691093 | + | 0.722766i | \(0.742870\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5652 | + | 8.40923i | 1.18530 | + | 0.684333i | 0.957235 | − | 0.289313i | \(-0.0934268\pi\) |
0.228065 | + | 0.973646i | \(0.426760\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.87927 | − | 5.48361i | 0.637002 | − | 0.443324i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.31877 | + | 0.761389i | 0.105926 | + | 0.0611563i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8050 | + | 7.97033i | −1.10176 | + | 0.636102i | −0.936683 | − | 0.350179i | \(-0.886121\pi\) |
−0.165077 | + | 0.986281i | \(0.552787\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.523204 | + | 1.00157i | −0.0414928 | + | 0.0794293i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.8846i | 1.25189i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.41232 | 0.423925 | 0.211963 | − | 0.977278i | \(-0.432014\pi\) | ||||
0.211963 | + | 0.977278i | \(0.432014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.66688 | + | 2.96030i | 0.441166 | + | 0.230459i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.12519 | + | 1.94888i | 0.0870697 | + | 0.150809i | 0.906271 | − | 0.422697i | \(-0.138916\pi\) |
−0.819202 | + | 0.573506i | \(0.805583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.726690 | + | 1.25866i | −0.0558992 | + | 0.0968203i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.316590 | − | 0.454901i | −0.0242103 | − | 0.0347872i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.58385 | + | 4.47535i | −0.196446 | + | 0.340255i | −0.947374 | − | 0.320130i | \(-0.896273\pi\) |
0.750927 | + | 0.660385i | \(0.229607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.07138 | − | 2.35061i | 0.307768 | − | 0.177690i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.612601 | − | 14.5069i | −0.0460459 | − | 1.09040i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.9037i | 1.18870i | 0.804207 | + | 0.594349i | \(0.202590\pi\) | ||||
−0.804207 | + | 0.594349i | \(0.797410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.1761i | 1.12803i | 0.825763 | + | 0.564017i | \(0.190745\pi\) | ||||
−0.825763 | + | 0.564017i | \(0.809255\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.44836 | + | 6.00029i | −0.698443 | + | 0.443554i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.91467 | − | 1.10543i | 0.140769 | − | 0.0812732i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.90584 | + | 10.2292i | −0.431878 | + | 0.748034i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.5285 | − | 9.44503i | −1.63871 | − | 0.687025i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.74786 | + | 6.49149i | −0.271186 | + | 0.469708i | −0.969166 | − | 0.246410i | \(-0.920749\pi\) |
0.697980 | + | 0.716117i | \(0.254082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.69314 | − | 16.7890i | −0.697728 | − | 1.20850i | −0.969252 | − | 0.246069i | \(-0.920861\pi\) |
0.271525 | − | 0.962431i | \(-0.412472\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.96835 | − | 3.15521i | 0.355791 | − | 0.225949i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.617357 | 0.0439849 | 0.0219924 | − | 0.999758i | \(-0.492999\pi\) | ||||
0.0219924 | + | 0.999758i | \(0.492999\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.851922i | − | 0.0603912i | −0.999544 | − | 0.0301956i | \(-0.990387\pi\) | ||
0.999544 | − | 0.0301956i | \(-0.00961301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.51110 | + | 0.106040i | −0.177119 | + | 0.00747946i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 38.4047 | − | 22.1729i | 2.69548 | − | 1.55624i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.97131 | − | 4.60224i | −0.556741 | − | 0.321434i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.31012 | + | 9.17449i | −0.299574 | + | 0.637671i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.590573 | + | 0.340967i | 0.0408508 | + | 0.0235852i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.16321 | + | 5.47885i | 0.217765 | + | 0.377179i | 0.954124 | − | 0.299411i | \(-0.0967902\pi\) |
−0.736360 | + | 0.676590i | \(0.763457\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.30246 | + | 17.8076i | −0.637394 | + | 1.22016i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.1046 | 0.689129 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.15893 | 0.485980 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.2765 | − | 23.5009i | 0.829570 | − | 1.58804i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.43664 | + | 9.41654i | 0.365708 | + | 0.633425i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4436 | − | 7.18433i | −0.833286 | − | 0.481098i | 0.0216902 | − | 0.999765i | \(-0.493095\pi\) |
−0.854977 | + | 0.518667i | \(0.826429\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.98932 | − | 0.252919i | 0.199288 | − | 0.0168613i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.80058 | + | 5.08102i | 0.584115 | + | 0.337239i | 0.762767 | − | 0.646673i | \(-0.223840\pi\) |
−0.178652 | + | 0.983912i | \(0.557174\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4053 | − | 11.2037i | 1.28234 | − | 0.740359i | 0.305063 | − | 0.952332i | \(-0.401322\pi\) |
0.977275 | + | 0.211974i | \(0.0679891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 30.0306 | − | 1.26814i | 1.97587 | − | 0.0834376i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.15942i | − | 0.206981i | −0.994630 | − | 0.103490i | \(-0.966999\pi\) | ||
0.994630 | − | 0.103490i | \(-0.0330011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.40142 | 0.417583 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.70179 | − | 2.35087i | 0.240457 | − | 0.152705i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.27012 | + | 12.5922i | 0.470265 | + | 0.814523i | 0.999422 | − | 0.0340013i | \(-0.0108250\pi\) |
−0.529157 | + | 0.848524i | \(0.677492\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.13622 | + | 5.43210i | −0.202022 | + | 0.349912i | −0.949180 | − | 0.314734i | \(-0.898085\pi\) |
0.747158 | + | 0.664647i | \(0.231418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.4490 | − | 11.5680i | −0.670302 | − | 0.742089i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.55077 | − | 13.0783i | 0.482401 | − | 0.835543i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.543654 | − | 0.313879i | 0.0345919 | − | 0.0199716i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.52380 | + | 4.14301i | −0.413429 | + | 0.262553i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 18.7861i | − | 1.18577i | −0.805287 | − | 0.592885i | \(-0.797989\pi\) | ||
0.805287 | − | 0.592885i | \(-0.202011\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 12.4722i | − | 0.784123i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.233836 | + | 5.53742i | 0.0146434 | + | 0.346766i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.7852 | − | 13.1551i | 1.42130 | − | 0.820590i | 0.424893 | − | 0.905244i | \(-0.360312\pi\) |
0.996410 | + | 0.0846537i | \(0.0269784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.19690 | − | 9.00129i | 0.322920 | − | 0.559313i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.1978 | − | 2.38574i | 1.74540 | − | 0.147674i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.46251 | − | 5.99725i | 0.213508 | − | 0.369806i | −0.739302 | − | 0.673374i | \(-0.764844\pi\) |
0.952810 | + | 0.303568i | \(0.0981778\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.326200 | − | 0.564995i | −0.0200383 | − | 0.0347073i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.64714 | − | 3.47237i | −0.406798 | − | 0.212506i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.6782 | −1.32174 | −0.660871 | − | 0.750500i | \(-0.729813\pi\) | ||||
−0.660871 | + | 0.750500i | \(0.729813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.04312i | − | 0.124111i | −0.998073 | − | 0.0620554i | \(-0.980234\pi\) | ||
0.998073 | − | 0.0620554i | \(-0.0197656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.8114 | − | 24.5247i | 0.775380 | − | 1.48430i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.19675 | + | 1.84565i | −0.192771 | + | 0.111297i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.0765 | − | 11.0138i | −1.14619 | − | 0.661755i | −0.198237 | − | 0.980154i | \(-0.563521\pi\) |
−0.947957 | + | 0.318399i | \(0.896855\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.13478 | + | 1.94250i | 0.247543 | + | 0.116294i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.10884 | − | 4.10429i | −0.424078 | − | 0.244842i | 0.272743 | − | 0.962087i | \(-0.412069\pi\) |
−0.696821 | + | 0.717246i | \(0.745403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.4458 | + | 18.0927i | 0.620939 | + | 1.07550i | 0.989311 | + | 0.145820i | \(0.0465821\pi\) |
−0.368372 | + | 0.929679i | \(0.620085\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.319697 | − | 0.0135003i | 0.0189372 | − | 0.000799687i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −43.2724 | −2.55429 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.76078 | 0.397693 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.9553 | − | 25.1240i | −0.935315 | − | 1.47279i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.921400 | + | 1.59591i | 0.0538288 | + | 0.0932342i | 0.891684 | − | 0.452658i | \(-0.149524\pi\) |
−0.837855 | + | 0.545892i | \(0.816191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.25989 | + | 4.19150i | 0.422687 | + | 0.244039i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.6888 | + | 7.41602i | 1.02641 | + | 0.430321i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.94316 | − | 5.74068i | −0.575028 | − | 0.331992i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.1398 | − | 23.7521i | 2.37126 | − | 1.36905i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.88667 | + | 2.97084i | 0.108386 | + | 0.170670i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6.46207i | − | 0.370017i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.1957 | 0.581899 | 0.290949 | − | 0.956738i | \(-0.406029\pi\) | ||||
0.290949 | + | 0.956738i | \(0.406029\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0992725 | − | 2.35085i | −0.00564742 | − | 0.133735i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2923 | − | 17.8267i | −0.583621 | − | 1.01086i | −0.995046 | − | 0.0994177i | \(-0.968302\pi\) |
0.411425 | − | 0.911444i | \(-0.365031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.71867 | − | 4.70888i | 0.153668 | − | 0.266161i | −0.778905 | − | 0.627142i | \(-0.784225\pi\) |
0.932573 | + | 0.360981i | \(0.117558\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.5761 | − | 8.05647i | 0.652242 | − | 0.453930i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.98948 | + | 17.3023i | −0.561065 | + | 0.971793i | 0.436339 | + | 0.899782i | \(0.356275\pi\) |
−0.997404 | + | 0.0720107i | \(0.977058\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.1544 | + | 17.4097i | −1.68832 | + | 0.974755i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.6774 | + | 8.18966i | 0.875028 | + | 0.457102i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.591150i | 0.0328925i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.39803i | 0.188489i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.3500 | − | 9.58576i | −1.01475 | − | 0.530094i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.0626 | − | 15.0473i | 1.43688 | − | 0.829583i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.711679 | + | 1.23266i | −0.0391174 | + | 0.0677534i | −0.884921 | − | 0.465741i | \(-0.845788\pi\) |
0.845804 | + | 0.533494i | \(0.179121\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.44397 | − | 3.78875i | 0.298328 | − | 0.207622i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.725538 | − | 1.25667i | 0.0396404 | − | 0.0686592i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3266 | − | 17.8863i | −0.562528 | − | 0.974327i | −0.997275 | − | 0.0737746i | \(-0.976495\pi\) |
0.434747 | − | 0.900553i | \(-0.356838\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.681460 | + | 16.1375i | 0.0370118 | + | 0.876468i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.62102 | −0.304395 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 38.0872i | − | 2.05652i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.13738 | − | 4.94027i | −0.168911 | − | 0.265975i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.00513 | − | 4.04441i | 0.376055 | − | 0.217115i | −0.300046 | − | 0.953925i | \(-0.597002\pi\) |
0.676100 | + | 0.736809i | \(0.263669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.62169 | − | 3.24568i | −0.300922 | − | 0.173737i | 0.341935 | − | 0.939724i | \(-0.388918\pi\) |
−0.642857 | + | 0.765986i | \(0.722251\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.0540 | − | 10.6885i | 0.750146 | − | 0.570511i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.32842 | + | 4.80842i | 0.443277 | + | 0.255926i | 0.704987 | − | 0.709220i | \(-0.250953\pi\) |
−0.261710 | + | 0.965147i | \(0.584286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.79977 | − | 10.0455i | −0.307820 | − | 0.533159i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.9684 | + | 21.9953i | 0.739284 | + | 1.16411i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.0939 | −1.74663 | −0.873314 | − | 0.487157i | \(-0.838034\pi\) | ||||
−0.873314 | + | 0.487157i | \(0.838034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9659 | −0.998204 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.54369 | + | 0.191873i | −0.238482 | + | 0.0100707i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.65399 | + | 13.2571i | 0.400628 | + | 0.693908i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3961 | + | 15.8172i | 1.43007 | + | 0.825649i | 0.997125 | − | 0.0757725i | \(-0.0241423\pi\) |
0.432942 | + | 0.901422i | \(0.357476\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.9928 | − | 11.7415i | −1.30107 | − | 0.611237i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.65617 | − | 1.53354i | −0.137901 | − | 0.0796174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6518 | + | 13.0780i | −1.17287 | + | 0.677155i | −0.954353 | − | 0.298679i | \(-0.903454\pi\) |
−0.218513 | + | 0.975834i | \(0.570121\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.801968 | + | 1.53520i | −0.0414135 | + | 0.0792775i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.0531i | 1.65082i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.6890 | −1.62776 | −0.813878 | − | 0.581036i | \(-0.802647\pi\) | ||||
−0.813878 | + | 0.581036i | \(0.802647\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.95909 | + | 3.11295i | 0.305294 | + | 0.159481i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.82550 | + | 6.62596i | 0.195474 | + | 0.338571i | 0.947056 | − | 0.321069i | \(-0.104042\pi\) |
−0.751582 | + | 0.659640i | \(0.770709\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.67680 | + | 15.0287i | −0.442211 | + | 0.765932i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.2059 | − | 2.55565i | 1.53545 | − | 0.129911i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.7167 | − | 23.7581i | 0.695466 | − | 1.20458i | −0.274558 | − | 0.961571i | \(-0.588531\pi\) |
0.970023 | − | 0.243011i | \(-0.0781352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.36333 | − | 5.40592i | 0.473524 | − | 0.273389i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.809426 | + | 19.1678i | 0.0408301 | + | 0.966889i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.53179i | 0.127388i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.681061i | − | 0.0341815i | −0.999854 | − | 0.0170907i | \(-0.994560\pi\) | ||
0.999854 | − | 0.0170907i | \(-0.00544042\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.26987 | − | 0.806448i | 0.0635732 | − | 0.0403729i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.45372 | − | 5.45811i | 0.472096 | − | 0.272565i | −0.245020 | − | 0.969518i | \(-0.578795\pi\) |
0.717117 | + | 0.696953i | \(0.245461\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.58723 | + | 4.48121i | −0.128879 | + | 0.223225i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.87206 | − | 1.51211i | 0.440856 | − | 0.0751375i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.08048 | + | 7.06760i | −0.202262 | + | 0.350328i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9762 | + | 25.9395i | 0.740525 | + | 1.28263i | 0.952256 | + | 0.305299i | \(0.0987565\pi\) |
−0.211731 | + | 0.977328i | \(0.567910\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.72374 | + | 4.26999i | −0.331658 | + | 0.210623i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 39.4104 | 1.93926 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.46186i | − | 0.219024i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.4844 | + | 0.865025i | −1.00313 | + | 0.0423605i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.3390 | − | 14.0521i | 1.18904 | − | 0.686492i | 0.230950 | − | 0.972966i | \(-0.425816\pi\) |
0.958088 | + | 0.286474i | \(0.0924831\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.81125 | + | 2.20043i | 0.185749 | + | 0.107242i | 0.589991 | − | 0.807410i | \(-0.299131\pi\) |
−0.404242 | + | 0.914652i | \(0.632465\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.1359 | − | 1.61904i | 0.930419 | − | 0.0787205i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.77118 | − | 1.59994i | −0.134422 | − | 0.0776084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.1898 | − | 26.3096i | −0.735087 | − | 1.27321i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.0592 | + | 19.2562i | −0.485662 | + | 0.929700i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.9022 | −0.814149 | −0.407074 | − | 0.913395i | \(-0.633451\pi\) | ||||
−0.407074 | + | 0.913395i | \(0.633451\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.10526 | 0.101172 | 0.0505862 | − | 0.998720i | \(-0.483891\pi\) | ||||
0.0505862 | + | 0.998720i | \(0.483891\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.56483 | + | 14.4813i | −0.362706 | + | 0.694326i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.312105 | − | 0.540581i | −0.0149300 | − | 0.0258595i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4910 | − | 8.94370i | −0.739343 | − | 0.426860i | 0.0824875 | − | 0.996592i | \(-0.473714\pi\) |
−0.821830 | + | 0.569732i | \(0.807047\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.2639 | − | 41.0050i | 0.917329 | − | 1.95262i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.8821 | − | 17.2525i | −1.41974 | − | 0.819689i | −0.423468 | − | 0.905911i | \(-0.639187\pi\) |
−0.996276 | + | 0.0862217i | \(0.972521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.74973 | − | 2.16491i | 0.177754 | − | 0.102626i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.8455 | + | 0.500218i | −0.560275 | + | 0.0236595i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 39.3197i | − | 1.85561i | −0.373063 | − | 0.927806i | \(-0.621692\pi\) | ||
0.373063 | − | 0.927806i | \(-0.378308\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.9764 | 1.59989 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.5907 | + | 15.6166i | −1.15537 | + | 0.733732i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.98746 | + | 13.8347i | 0.374458 | + | 0.648580i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.25936 | − | 5.64538i | 0.152467 | − | 0.264080i | −0.779667 | − | 0.626194i | \(-0.784612\pi\) |
0.932134 | + | 0.362114i | \(0.117945\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.09953 | + | 16.4940i | 0.0979976 | + | 0.769872i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.23638 | − | 3.87352i | 0.104158 | − | 0.180408i | −0.809236 | − | 0.587484i | \(-0.800118\pi\) |
0.913394 | + | 0.407077i | \(0.133452\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.0244 | + | 17.3346i | −1.39535 | + | 0.805608i | −0.993901 | − | 0.110273i | \(-0.964828\pi\) |
−0.401452 | + | 0.915880i | \(0.631494\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.22649 | + | 1.41396i | −0.103251 | + | 0.0655709i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4074i | 0.527874i | 0.964540 | + | 0.263937i | \(0.0850211\pi\) | ||||
−0.964540 | + | 0.263937i | \(0.914979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.82184i | − | 0.315003i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.16489 | − | 27.5854i | −0.0536752 | − | 1.27107i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.3020 | + | 18.6496i | −1.48525 | + | 0.857507i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0923707 | + | 0.159991i | −0.00423826 | + | 0.00734088i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.11801 | − | 1.60645i | −0.0511903 | − | 0.0735542i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.73970 | + | 9.94145i | −0.262254 | + | 0.454237i | −0.966840 | − | 0.255381i | \(-0.917799\pi\) |
0.704587 | + | 0.709618i | \(0.251132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.75630 | + | 6.50610i | 0.171273 | + | 0.296653i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.3862 | − | 12.7390i | −1.10961 | − | 0.579644i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.1832 | 0.780248 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.6160i | 1.61391i | 0.590610 | + | 0.806957i | \(0.298887\pi\) | ||||
−0.590610 | + | 0.806957i | \(0.701113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.34050 | + | 8.30900i | −0.196284 | + | 0.375746i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.58796 | + | 2.64886i | −0.207052 | + | 0.119541i | −0.599940 | − | 0.800045i | \(-0.704809\pi\) |
0.392889 | + | 0.919586i | \(0.371476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.1400 | − | 15.0920i | −1.17729 | − | 0.679708i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.08932 | + | 6.32575i | −0.408534 | + | 0.284321i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −47.2262 | − | 27.2660i | −2.11838 | − | 1.22305i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.4386 | − | 31.9366i | −0.825426 | − | 1.42968i | −0.901593 | − | 0.432585i | \(-0.857601\pi\) |
0.0761666 | − | 0.997095i | \(-0.475732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.89430 | + | 0.164450i | −0.173984 | + | 0.00734707i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.6354 | 1.18761 | 0.593807 | − | 0.804608i | \(-0.297624\pi\) | ||||
0.593807 | + | 0.804608i | \(0.297624\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.03186 | −0.0904168 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.34952 | − | 2.12503i | −0.0599344 | − | 0.0943757i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.16205 | − | 5.47683i | −0.140155 | − | 0.242756i | 0.787400 | − | 0.616443i | \(-0.211427\pi\) |
−0.927555 | + | 0.373687i | \(0.878093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 62.3246 | + | 35.9832i | 2.75708 | + | 1.59180i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.952261 | − | 0.121214i | 0.0420433 | − | 0.00535173i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.17647 | + | 0.679237i | 0.0518416 | + | 0.0299307i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4638 | + | 11.8148i | −0.899995 | + | 0.519613i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.79841 | − | 7.55582i | −0.210627 | − | 0.331664i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.86881i | 0.169496i | 0.996402 | + | 0.0847478i | \(0.0270085\pi\) | ||||
−0.996402 | + | 0.0847478i | \(0.972992\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.06854 | −0.309086 | −0.154543 | − | 0.987986i | \(-0.549390\pi\) | ||||
−0.154543 | + | 0.987986i | \(0.549390\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.343550 | + | 8.13551i | 0.0149937 | + | 0.355063i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.43635 | − | 4.21989i | −0.106129 | − | 0.183821i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.79176 | − | 10.0316i | 0.251815 | − | 0.436157i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.7622 | + | 10.6936i | 0.987798 | + | 0.464061i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.6386 | − | 27.0868i | 0.677381 | − | 1.17326i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.84381 | + | 5.10598i | −0.382351 | + | 0.220751i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.4154 | − | 12.7543i | −1.05360 | − | 0.550387i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 55.7442i | 2.40107i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.3091i | 1.08812i | 0.839045 | + | 0.544062i | \(0.183114\pi\) | ||||
−0.839045 | + | 0.544062i | \(0.816886\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.2985 | − | 12.1708i | −0.999832 | − | 0.522298i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.3514 | − | 5.97639i | 0.443406 | − | 0.256001i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.74111 | + | 9.94389i | −0.245472 | + | 0.425170i | −0.962264 | − | 0.272117i | \(-0.912276\pi\) |
0.716792 | + | 0.697287i | \(0.245610\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.63438 | − | 19.3172i | −0.0697537 | − | 0.824437i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.871318 | + | 1.50917i | −0.0371194 | + | 0.0642926i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.95125 | + | 10.3079i | 0.253073 | + | 0.438335i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.161563 | + | 3.82593i | 0.00685795 | + | 0.162402i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.9398 | −0.505907 | −0.252953 | − | 0.967478i | \(-0.581402\pi\) | ||||
−0.252953 | + | 0.967478i | \(0.581402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.3358i | 1.45225i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.9676 | − | 17.2702i | −0.463054 | − | 0.729147i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7893 | + | 12.0027i | −0.876166 | + | 0.505855i | −0.869392 | − | 0.494122i | \(-0.835489\pi\) |
−0.00677354 | + | 0.999977i | \(0.502156\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.07593 | − | 4.66264i | −0.339757 | − | 0.196159i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 32.5672 | − | 27.0112i | 1.36769 | − | 1.13436i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.19323 | − | 1.26626i | −0.0919449 | − | 0.0530844i | 0.453323 | − | 0.891347i | \(-0.350239\pi\) |
−0.545267 | + | 0.838262i | \(0.683572\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.7630 | + | 20.3742i | 0.492267 | + | 0.852632i | 0.999960 | − | 0.00890626i | \(-0.00283499\pi\) |
−0.507693 | + | 0.861538i | \(0.669502\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.96008 | − | 10.9597i | −0.290762 | − | 0.457848i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.37883 | 0.140907 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3679 | 0.723037 | 0.361519 | − | 0.932365i | \(-0.382258\pi\) | ||||
0.361519 | + | 0.932365i | \(0.382258\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.5481 | − | 1.41668i | 1.39421 | − | 0.0588753i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.4881 | − | 18.1659i | −0.435120 | − | 0.753649i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.08556 | + | 1.20410i | 0.0863751 | + | 0.0498687i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.859427 | + | 10.1578i | 0.0355330 | + | 0.419973i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.86272 | + | 2.23014i | 0.159431 | + | 0.0920478i | 0.577593 | − | 0.816325i | \(-0.303992\pi\) |
−0.418162 | + | 0.908373i | \(0.637325\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.243631 | + | 0.140660i | −0.0100386 | + | 0.00579580i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.495101 | + | 0.947768i | −0.0203657 | + | 0.0389860i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.8336i | 1.38938i | 0.719310 | + | 0.694689i | \(0.244458\pi\) | ||||
−0.719310 | + | 0.694689i | \(0.755542\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.0434 | −0.616717 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.30787 | + | 0.683214i | 0.0535277 | + | 0.0279621i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.5171 | − | 30.3406i | −0.715731 | − | 1.23968i | −0.962677 | − | 0.270653i | \(-0.912760\pi\) |
0.246946 | − | 0.969029i | \(-0.420573\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.6687 | − | 30.6032i | 0.720723 | − | 1.24833i | −0.239987 | − | 0.970776i | \(-0.577143\pi\) |
0.960710 | − | 0.277553i | \(-0.0895235\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.85103 | − | 3.94009i | 0.0753798 | − | 0.160453i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.31282 | − | 2.27387i | 0.0533737 | − | 0.0924459i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.95148 | − | 5.74549i | 0.403918 | − | 0.233202i | −0.284255 | − | 0.958749i | \(-0.591746\pi\) |
0.688173 | + | 0.725547i | \(0.258413\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.24065 | + | 76.7410i | 0.131318 | + | 3.10970i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.7522i | 0.880001i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 29.1512i | − | 1.17741i | −0.808349 | − | 0.588704i | \(-0.799638\pi\) | ||
0.808349 | − | 0.588704i | \(-0.200362\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.4581 | − | 8.54673i | 0.542683 | − | 0.344638i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.1438 | − | 7.58860i | 0.529151 | − | 0.305506i | −0.211520 | − | 0.977374i | \(-0.567841\pi\) |
0.740671 | + | 0.671868i | \(0.234508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.6309 | − | 25.3414i | 0.588064 | − | 1.01856i | −0.406421 | − | 0.913686i | \(-0.633223\pi\) |
0.994486 | − | 0.104872i | \(-0.0334432\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.6281 | − | 13.9746i | −0.426492 | − | 0.560780i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.1777 | − | 17.6283i | 0.407762 | − | 0.706264i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.997074 | + | 0.633204i | −0.0398193 | + | 0.0252877i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.07451 | −0.282079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.6089i | − | 0.700998i | −0.936563 | − | 0.350499i | \(-0.886012\pi\) | ||
0.936563 | − | 0.350499i | \(-0.113988\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.9479 | + | 0.462313i | −0.435141 | + | 0.0183753i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.36159 | + | 1.94082i | −0.133401 | + | 0.0770190i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 44.4405 | + | 25.6578i | 1.76080 | + | 1.01660i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.8781 | − | 28.5623i | −0.786364 | − | 1.12991i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.78399 | + | 3.33939i | 0.228454 | + | 0.131898i | 0.609859 | − | 0.792510i | \(-0.291226\pi\) |
−0.381405 | + | 0.924408i | \(0.624560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.7601 | + | 30.7613i | 0.700389 | + | 1.21311i | 0.968330 | + | 0.249674i | \(0.0803234\pi\) |
−0.267941 | + | 0.963435i | \(0.586343\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.10358 | + | 15.5126i | −0.319078 | + | 0.610810i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.1567 | 0.831755 | 0.415877 | − | 0.909421i | \(-0.363475\pi\) | ||||
0.415877 | + | 0.909421i | \(0.363475\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.9441 | −1.21466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.74123 | + | 10.9904i | −0.225017 | + | 0.430748i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.9536 | + | 29.3645i | 0.663445 | + | 1.14912i | 0.979705 | + | 0.200447i | \(0.0642395\pi\) |
−0.316260 | + | 0.948673i | \(0.602427\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.59245 | − | 5.53820i | −0.374808 | − | 0.216396i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.2332 | + | 37.6939i | 1.02345 | + | 1.47058i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.53060 | − | 4.34779i | −0.293350 | − | 0.169366i | 0.346101 | − | 0.938197i | \(-0.387505\pi\) |
−0.639452 | + | 0.768831i | \(0.720839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.5930 | + | 15.9308i | −1.07324 | + | 0.619638i | −0.929066 | − | 0.369914i | \(-0.879387\pi\) |
−0.144178 | + | 0.989552i | \(0.546054\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.8163 | + | 0.794582i | −0.730765 | + | 0.0308590i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.868511i | 0.0336794i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.8719 | 1.23409 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.0088 | − | 13.3419i | 0.812247 | − | 0.515827i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9267 | + | 20.6576i | 0.460425 | + | 0.797479i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.39045 | + | 7.60448i | −0.169239 | + | 0.293131i | −0.938153 | − | 0.346222i | \(-0.887464\pi\) |
0.768913 | + | 0.639353i | \(0.220798\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.00906 | + | 4.79204i | −0.0773286 | + | 0.184446i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.38094 | − | 14.5162i | 0.322106 | − | 0.557903i | −0.658817 | − | 0.752304i | \(-0.728943\pi\) |
0.980922 | + | 0.194400i | \(0.0622760\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 69.9593 | − | 40.3910i | 2.68479 | − | 1.55007i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8582 | + | 9.43586i | −0.569366 | + | 0.361583i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.5084i | 1.12911i | 0.825397 | + | 0.564553i | \(0.190952\pi\) | ||||
−0.825397 | + | 0.564553i | \(0.809048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4.59861i | − | 0.175704i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.63745 | + | 38.7761i | 0.0624726 | + | 1.47940i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.91987 | − | 1.10844i | 0.0731412 | − | 0.0422281i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.98412 | − | 5.16864i | 0.113521 | − | 0.196624i | −0.803667 | − | 0.595080i | \(-0.797120\pi\) |
0.917188 | + | 0.398456i | \(0.130454\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.1367 | + | 47.1200i | −0.840904 | + | 1.78994i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.91862 | − | 10.2514i | 0.224506 | − | 0.388856i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7266 | + | 25.5072i | 0.557810 | + | 0.966155i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.85035 | + | 2.53376i | 0.183457 | + | 0.0958354i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9632 | −0.527383 | −0.263692 | − | 0.964607i | \(-0.584940\pi\) | ||||
−0.263692 | + | 0.964607i | \(0.584940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.408439i | 0.0154046i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.13374 | + | 9.82748i | −0.193348 | + | 0.370124i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.27250 | + | 4.77613i | −0.311119 | + | 0.179625i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.0403 | − | 16.1891i | −1.05308 | − | 0.607993i | −0.129566 | − | 0.991571i | \(-0.541359\pi\) |
−0.923509 | + | 0.383578i | \(0.874692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.640338 | + | 7.56832i | 0.0240145 | + | 0.283834i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.45588 | + | 2.57260i | 0.166874 | + | 0.0963448i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.27156 | − | 10.8627i | −0.234543 | − | 0.406241i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.1620 | + | 1.06255i | −0.939692 | + | 0.0396817i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.2991 | 1.57749 | 0.788745 | − | 0.614721i | \(-0.210731\pi\) | ||||
0.788745 | + | 0.614721i | \(0.210731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.38649 | 0.237845 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.82422 | − | 9.17111i | −0.216605 | − | 0.341077i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.71642 | − | 8.16907i | −0.175163 | − | 0.303392i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.2203 | − | 19.1797i | −1.23207 | − | 0.711337i | −0.264610 | − | 0.964355i | \(-0.585243\pi\) |
−0.967461 | + | 0.253019i | \(0.918577\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.1390 | − | 6.76410i | 0.968111 | − | 0.250522i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.0017 | − | 16.1668i | −1.03568 | − | 0.597950i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7323 | − | 7.35097i | 0.470277 | − | 0.271514i | −0.246079 | − | 0.969250i | \(-0.579142\pi\) |
0.716356 | + | 0.697735i | \(0.245809\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.0224 | + | 22.0804i | 0.517224 | + | 0.814446i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.35635i | 0.197304i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.4167 | −1.85461 | −0.927304 | − | 0.374310i | \(-0.877880\pi\) | ||||
−0.927304 | + | 0.374310i | \(0.877880\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0458743 | + | 1.08634i | 0.00168524 | + | 0.0399077i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.23945 | − | 12.5391i | −0.265590 | − | 0.460015i | 0.702128 | − | 0.712051i | \(-0.252233\pi\) |
−0.967718 | + | 0.252036i | \(0.918900\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.42256 | − | 5.92805i | 0.125393 | − | 0.217187i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.12849 | − | 13.3379i | −0.0412893 | − | 0.488009i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.0044 | + | 41.5768i | −0.877101 | + | 1.51918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.0021 | + | 22.5179i | −1.42321 | + | 0.821690i | −0.996572 | − | 0.0827337i | \(-0.973635\pi\) |
−0.426636 | + | 0.904423i | \(0.640302\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.8405 | + | 15.0659i | 1.05101 | + | 0.549031i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 16.8185i | − | 0.612086i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.56940i | 0.202423i | 0.994865 | + | 0.101212i | \(0.0322719\pi\) | ||||
−0.994865 | + | 0.101212i | \(0.967728\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.1474 | + | 10.0023i | 0.695008 | + | 0.363062i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.9383 | + | 20.7490i | −1.30276 | + | 0.752149i | −0.980877 | − | 0.194630i | \(-0.937649\pi\) |
−0.321884 | + | 0.946779i | \(0.604316\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.0964 | − | 48.6644i | 1.01716 | − | 1.76177i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.68858 | − | 4.08185i | −0.314136 | − | 0.147579i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.2429 | + | 24.6693i | −0.514280 | + | 0.890758i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.42654 | − | 14.5952i | −0.303869 | − | 0.526316i | 0.673140 | − | 0.739515i | \(-0.264945\pi\) |
−0.977009 | + | 0.213199i | \(0.931612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.92265 | + | 45.5299i | 0.0692426 | + | 1.63972i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.6992 | 0.708530 | 0.354265 | − | 0.935145i | \(-0.384731\pi\) | ||||
0.354265 | + | 0.935145i | \(0.384731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.52278i | − | 0.0546998i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.65106 | + | 15.1970i | 0.346230 | + | 0.545191i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.47263 | − | 0.850224i | 0.0527625 | − | 0.0304625i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.0809 | + | 21.4086i | 1.32686 | + | 0.766061i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.9511 | + | 45.2026i | −0.677257 | + | 1.61541i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.8050 | + | 7.97033i | 0.492722 | + | 0.284473i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.29184 | + | 9.16574i | 0.188634 | + | 0.326723i | 0.944795 | − | 0.327662i | \(-0.106261\pi\) |
−0.756161 | + | 0.654385i | \(0.772927\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.43017 | + | 10.1253i | 0.228920 | + | 0.360469i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.8403 | −1.55878 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.9583 | 0.779763 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.12898 | − | 0.0476751i | 0.0400409 | − | 0.00169086i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.01916 | + | 12.1575i | 0.248631 | + | 0.430642i | 0.963146 | − | 0.268978i | \(-0.0866859\pi\) |
−0.714515 | + | 0.699620i | \(0.753353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.7395 | − | 10.2419i | −0.627577 | − | 0.362332i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.6616 | − | 7.41997i | 0.376709 | − | 0.262172i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.9358 | − | 28.2531i | −1.72691 | − | 0.997031i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.7565 | − | 7.94232i | 0.484853 | − | 0.279930i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.3852 | − | 33.2804i | 0.611988 | − | 1.17153i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 13.5081i | − | 0.474919i | −0.971397 | − | 0.237459i | \(-0.923685\pi\) | ||
0.971397 | − | 0.237459i | \(-0.0763147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.04752 | −0.0367835 | −0.0183918 | − | 0.999831i | \(-0.505855\pi\) | ||||
−0.0183918 | + | 0.999831i | \(0.505855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.13661 | + | 1.63852i | 0.110006 | + | 0.0574654i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.70616 | − | 4.68720i | −0.0947926 | − | 0.164186i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.933371 | + | 1.61665i | −0.0326545 | + | 0.0565593i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.3761 | + | 39.3361i | 0.956599 | + | 1.37452i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.1991 | + | 38.4500i | −0.774755 | + | 1.34192i | 0.160176 | + | 0.987088i | \(0.448794\pi\) |
−0.934932 | + | 0.354827i | \(0.884540\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.9621 | − | 8.06104i | 0.486689 | − | 0.280990i | −0.236511 | − | 0.971629i | \(-0.576004\pi\) |
0.723200 | + | 0.690639i | \(0.242671\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.269747 | − | 6.38781i | −0.00939138 | − | 0.222395i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.7598i | 0.408930i | 0.978874 | + | 0.204465i | \(0.0655454\pi\) | ||||
−0.978874 | + | 0.204465i | \(0.934455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.9353i | − | 0.379798i | −0.981804 | − | 0.189899i | \(-0.939184\pi\) | ||
0.981804 | − | 0.189899i | \(-0.0608161\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.2071 | − | 20.4535i | 1.11725 | − | 0.709525i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.8490 | + | 24.1615i | −1.44998 | + | 0.837148i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.12519 | − | 1.94888i | 0.0389387 | − | 0.0674439i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.29809 | + | 4.78991i | −0.217694 | + | 0.165563i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.0450 | + | 17.3985i | −0.346793 | + | 0.600663i | −0.985678 | − | 0.168639i | \(-0.946063\pi\) |
0.638885 | + | 0.769302i | \(0.279396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.9892 | − | 51.9428i | −1.03411 | − | 1.79113i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0020 | − | 7.62200i | 0.413370 | − | 0.262516i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.45338 | 0.0499978 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.3437i | − | 0.424135i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −36.1532 | + | 1.52669i | −1.24077 | + | 0.0523958i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.46934 | − | 3.73507i | 0.221766 | − | 0.128037i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.3701 | − | 14.6474i | −0.868654 | − | 0.501518i | −0.00175348 | − | 0.999998i | \(-0.500558\pi\) |
−0.866901 | + | 0.498481i | \(0.833891\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.235661 | + | 0.501626i | −0.00805943 | + | 0.0171552i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.4040 | − | 11.7802i | −0.696987 | − | 0.402406i | 0.109237 | − | 0.994016i | \(-0.465159\pi\) |
−0.806224 | + | 0.591610i | \(0.798493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.37008 | − | 4.10510i | −0.0808660 | − | 0.140064i | 0.822756 | − | 0.568395i | \(-0.192435\pi\) |
−0.903622 | + | 0.428330i | \(0.859102\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.7031 | − | 66.4318i | 1.18268 | − | 2.26399i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.5711 | 0.530046 | 0.265023 | − | 0.964242i | \(-0.414620\pi\) | ||||
0.265023 | + | 0.964242i | \(0.414620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.16769 | 0.175707 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.42193 | + | 10.3792i | −0.184138 | + | 0.352495i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.67278 | − | 8.09350i | −0.158513 | − | 0.274553i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.27020 | + | 2.46540i | 0.144690 | + | 0.0835370i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 51.3660 | − | 4.34596i | 1.73848 | − | 0.147088i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.07138 | − | 2.35061i | −0.137638 | − | 0.0794653i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.1807 | − | 19.7342i | 1.15420 | − | 0.666378i | 0.204293 | − | 0.978910i | \(-0.434511\pi\) |
0.949907 | + | 0.312532i | \(0.101177\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.18898 | + | 0.134666i | −0.107562 | + | 0.00454215i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.8421i | 1.37601i | 0.725708 | + | 0.688003i | \(0.241512\pi\) | ||||
−0.725708 | + | 0.688003i | \(0.758488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.63432 | 0.223263 | 0.111631 | − | 0.993750i | \(-0.464392\pi\) | ||||
0.111631 | + | 0.993750i | \(0.464392\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.2570 | + | 7.78396i | −0.412015 | + | 0.261655i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.69428 | + | 15.0589i | 0.291925 | + | 0.505629i | 0.974265 | − | 0.225406i | \(-0.0723708\pi\) |
−0.682340 | + | 0.731035i | \(0.739037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.12422 | + | 15.8036i | −0.306017 | + | 0.530036i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.5710 | + | 21.2085i | −0.856660 | + | 0.710513i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.591304 | + | 1.02417i | −0.0197872 | + | 0.0342725i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.7730 | − | 7.95185i | 0.460381 | − | 0.265801i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.7872 | − | 10.6609i | 0.560509 | − | 0.355958i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.3641i | − | 0.479070i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.08760i | 0.0695480i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.47144 | + | 82.2063i | 0.115522 | + | 2.73565i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.1429 | − | 7.58807i | 0.436886 | − | 0.252236i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.1322 | + | 31.4059i | −0.602071 | + | 1.04282i | 0.390436 | + | 0.920630i | \(0.372324\pi\) |
−0.992507 | + | 0.122187i | \(0.961009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.07389 | + | 0.513898i | −0.201458 | + | 0.0170449i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.34808 | + | 7.53110i | −0.144058 | + | 0.249517i | −0.929021 | − | 0.370026i | \(-0.879349\pi\) |
0.784963 | + | 0.619543i | \(0.212682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.23501 | + | 14.2635i | 0.272539 | + | 0.472051i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.92058 | + | 5.18237i | 0.327964 | + | 0.171324i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −52.0727 | −1.71959 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.35467i | 0.275595i | 0.990460 | + | 0.137798i | \(0.0440023\pi\) | ||||
−0.990460 | + | 0.137798i | \(0.955998\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.17662 | + | 15.6524i | −0.269429 | + | 0.515766i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.1349 | − | 19.7078i | 1.12356 | − | 0.648690i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.91467 | − | 1.10543i | −0.0629539 | − | 0.0363465i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.68864 | + | 1.73290i | 0.121151 | + | 0.0569160i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.0492053 | + | 0.0284087i | 0.00161437 | + | 0.000932059i | 0.500807 | − | 0.865559i | \(-0.333037\pi\) |
−0.499193 | + | 0.866491i | \(0.666370\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.39494 | + | 2.41611i | 0.0457173 | + | 0.0791847i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.6217 | − | 1.50425i | 1.16620 | − | 0.0492469i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.8117 | 0.386283 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.91661 | −0.291293 | −0.145646 | − | 0.989337i | \(-0.546526\pi\) | ||||
−0.145646 | + | 0.989337i | \(0.546526\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.04879 | + | 7.95008i | 0.164761 | + | 0.259441i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.9913 | − | 20.7695i | −0.390904 | − | 0.677065i | 0.601665 | − | 0.798748i | \(-0.294504\pi\) |
−0.992569 | + | 0.121683i | \(0.961171\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.9337 | − | 15.5502i | −0.877082 | − | 0.506384i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.08461 | + | 24.2328i | 0.100342 | + | 0.788292i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.8908 | − | 9.17457i | −0.516382 | − | 0.298133i | 0.219071 | − | 0.975709i | \(-0.429697\pi\) |
−0.735453 | + | 0.677576i | \(0.763031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.0480 | + | 26.0085i | −1.46232 | + | 0.844272i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.5513 | − | 29.2118i | −0.601566 | − | 0.947256i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.04509i | 0.195820i | 0.995195 | + | 0.0979099i | \(0.0312157\pi\) | ||||
−0.995195 | + | 0.0979099i | \(0.968784\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.49572 | 0.242556 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.54448 | − | 60.2552i | −0.0822513 | − | 1.94777i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.8095 | − | 18.7227i | −0.349058 | − | 0.604587i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.3406 | + | 24.8386i | −0.462599 | + | 0.801245i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.1456 | + | 17.5002i | −0.810305 | + | 0.563935i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.69314 | + | 16.7890i | −0.312033 | + | 0.540458i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.9898 | + | 16.1599i | −0.900091 | + | 0.519668i | −0.877230 | − | 0.480071i | \(-0.840611\pi\) |
−0.0228612 | + | 0.999739i | \(0.507278\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.907535 | − | 0.474083i | −0.0291542 | − | 0.0152298i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.1694i | 1.64210i | 0.570854 | + | 0.821052i | \(0.306612\pi\) | ||||
−0.570854 | + | 0.821052i | \(0.693388\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 55.6496i | − | 1.78404i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.21667 | − | 2.72511i | −0.167067 | − | 0.0872735i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.6240 | + | 16.5261i | −0.915762 | + | 0.528715i | −0.882281 | − | 0.470724i | \(-0.843993\pi\) |
−0.0334814 | + | 0.999439i | \(0.510659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.99130 | + | 13.8413i | −0.255403 | + | 0.442371i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.4322 | − | 20.4834i | 0.939696 | − | 0.653985i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.80025 | + | 3.11812i | −0.0574189 | + | 0.0994525i | −0.893306 | − | 0.449449i | \(-0.851620\pi\) |
0.835887 | + | 0.548901i | \(0.184954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.308679 | − | 0.534647i | −0.00983532 | − | 0.0170353i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.19921 | + | 52.0789i | 0.0700015 | + | 1.65769i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.1418 | 1.08565 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.89979i | 0.0921149i | 0.998939 | + | 0.0460575i | \(0.0146657\pi\) | ||||
−0.998939 | + | 0.0460575i | \(0.985334\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.32165 | − | 2.08113i | −0.0419412 | − | 0.0660426i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.737786 | + | 0.425961i | −0.0233894 | + | 0.0135039i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.0402 | + | 21.3851i | 1.17307 | + | 0.677274i | 0.954402 | − | 0.298524i | \(-0.0964944\pi\) |
0.218671 | + | 0.975799i | \(0.429828\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.45061 | + | 11.3961i | 0.0458954 | + | 0.360555i |
(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 | 1440.2.cc.a.911.9 | 48 | ||
3.2 | odd | 2 | 4320.2.cc.b.1871.1 | 48 | |||
4.3 | odd | 2 | 360.2.bm.a.11.17 | ✓ | 48 | ||
8.3 | odd | 2 | 1440.2.cc.b.911.9 | 48 | |||
8.5 | even | 2 | 360.2.bm.b.11.9 | yes | 48 | ||
9.4 | even | 3 | 4320.2.cc.a.3311.24 | 48 | |||
9.5 | odd | 6 | 1440.2.cc.b.1391.9 | 48 | |||
12.11 | even | 2 | 1080.2.bm.b.251.8 | 48 | |||
24.5 | odd | 2 | 1080.2.bm.a.251.16 | 48 | |||
24.11 | even | 2 | 4320.2.cc.a.1871.24 | 48 | |||
36.23 | even | 6 | 360.2.bm.b.131.9 | yes | 48 | ||
36.31 | odd | 6 | 1080.2.bm.a.611.16 | 48 | |||
72.5 | odd | 6 | 360.2.bm.a.131.17 | yes | 48 | ||
72.13 | even | 6 | 1080.2.bm.b.611.8 | 48 | |||
72.59 | even | 6 | inner | 1440.2.cc.a.1391.9 | 48 | ||
72.67 | odd | 6 | 4320.2.cc.b.3311.1 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bm.a.11.17 | ✓ | 48 | 4.3 | odd | 2 | ||
360.2.bm.a.131.17 | yes | 48 | 72.5 | odd | 6 | ||
360.2.bm.b.11.9 | yes | 48 | 8.5 | even | 2 | ||
360.2.bm.b.131.9 | yes | 48 | 36.23 | even | 6 | ||
1080.2.bm.a.251.16 | 48 | 24.5 | odd | 2 | |||
1080.2.bm.a.611.16 | 48 | 36.31 | odd | 6 | |||
1080.2.bm.b.251.8 | 48 | 12.11 | even | 2 | |||
1080.2.bm.b.611.8 | 48 | 72.13 | even | 6 | |||
1440.2.cc.a.911.9 | 48 | 1.1 | even | 1 | trivial | ||
1440.2.cc.a.1391.9 | 48 | 72.59 | even | 6 | inner | ||
1440.2.cc.b.911.9 | 48 | 8.3 | odd | 2 | |||
1440.2.cc.b.1391.9 | 48 | 9.5 | odd | 6 | |||
4320.2.cc.a.1871.24 | 48 | 24.11 | even | 2 | |||
4320.2.cc.a.3311.24 | 48 | 9.4 | even | 3 | |||
4320.2.cc.b.1871.1 | 48 | 3.2 | odd | 2 | |||
4320.2.cc.b.3311.1 | 48 | 72.67 | odd | 6 |