Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,4,Mod(28,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.28");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.e (of order \(9\), degree \(6\), 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: | \(14.3374641314\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 109.7 | ||
Character | \(\chi\) | \(=\) | 243.109 |
Dual form | 243.4.e.b.136.7 |
$q$-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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{7}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.61428 | − | 2.19364i | 0.924286 | − | 0.775568i | −0.0504967 | − | 0.998724i | \(-0.516080\pi\) |
0.974783 | + | 0.223156i | \(0.0716360\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.633205 | − | 3.59108i | 0.0791506 | − | 0.448886i | ||||
\(5\) | −10.3200 | + | 3.75618i | −0.923051 | + | 0.335963i | −0.759452 | − | 0.650564i | \(-0.774533\pi\) |
−0.163599 | + | 0.986527i | \(0.552310\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.765086 | − | 4.33902i | −0.0413108 | − | 0.234285i | 0.957161 | − | 0.289558i | \(-0.0935082\pi\) |
−0.998471 | + | 0.0552729i | \(0.982397\pi\) | |||||||
\(8\) | 7.42861 | + | 12.8667i | 0.328301 | + | 0.568635i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −18.7397 | + | 32.4581i | −0.592601 | + | 1.02641i | ||||
\(11\) | 54.1997 | + | 19.7271i | 1.48562 | + | 0.540722i | 0.952292 | − | 0.305187i | \(-0.0987190\pi\) |
0.533328 | + | 0.845909i | \(0.320941\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 30.0290 | + | 25.1973i | 0.640657 | + | 0.537575i | 0.904220 | − | 0.427067i | \(-0.140453\pi\) |
−0.263563 | + | 0.964642i | \(0.584898\pi\) | |||||||
\(14\) | −11.5184 | − | 9.66507i | −0.219887 | − | 0.184507i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 75.0580 | + | 27.3189i | 1.17278 | + | 0.426857i | ||||
\(17\) | 44.7356 | − | 77.4844i | 0.638235 | − | 1.10545i | −0.347585 | − | 0.937648i | \(-0.612998\pi\) |
0.985820 | − | 0.167806i | \(-0.0536683\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.6770 | + | 51.4022i | 0.358336 | + | 0.620656i | 0.987683 | − | 0.156468i | \(-0.0500109\pi\) |
−0.629347 | + | 0.777124i | \(0.716678\pi\) | |||||||
\(20\) | 6.95407 | + | 39.4385i | 0.0777489 | + | 0.440936i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 184.967 | − | 67.3225i | 1.79250 | − | 0.652418i | ||||
\(23\) | 3.97027 | − | 22.5165i | 0.0359939 | − | 0.204131i | −0.961507 | − | 0.274779i | \(-0.911395\pi\) |
0.997501 | + | 0.0706474i | \(0.0225065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.36157 | + | 2.82069i | −0.0268925 | + | 0.0225655i | ||||
\(26\) | 133.778 | 1.00908 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.0662 | −0.108437 | ||||||||
\(29\) | 45.1257 | − | 37.8649i | 0.288953 | − | 0.242460i | −0.486776 | − | 0.873527i | \(-0.661827\pi\) |
0.775728 | + | 0.631067i | \(0.217383\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −57.9966 | + | 328.915i | −0.336016 | + | 1.90564i | 0.0809453 | + | 0.996719i | \(0.474206\pi\) |
−0.416962 | + | 0.908924i | \(0.636905\pi\) | |||||||
\(32\) | 144.460 | − | 52.5792i | 0.798037 | − | 0.290462i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −53.0214 | − | 300.699i | −0.267444 | − | 1.51675i | ||||
\(35\) | 24.1938 | + | 41.9050i | 0.116843 | + | 0.202378i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −47.4944 | + | 82.2627i | −0.211028 | + | 0.365511i | −0.952036 | − | 0.305985i | \(-0.901014\pi\) |
0.741009 | + | 0.671495i | \(0.234348\pi\) | |||||||
\(38\) | 190.342 | + | 69.2787i | 0.812566 | + | 0.295750i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −124.993 | − | 104.882i | −0.494079 | − | 0.414582i | ||||
\(41\) | 277.092 | + | 232.508i | 1.05547 | + | 0.885649i | 0.993659 | − | 0.112439i | \(-0.0358663\pi\) |
0.0618163 | + | 0.998088i | \(0.480311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −443.174 | − | 161.302i | −1.57171 | − | 0.572054i | −0.598326 | − | 0.801252i | \(-0.704167\pi\) |
−0.973380 | + | 0.229198i | \(0.926390\pi\) | |||||||
\(44\) | 105.161 | − | 182.144i | 0.360310 | − | 0.624075i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −39.0137 | − | 67.5738i | −0.125049 | − | 0.216591i | ||||
\(47\) | −41.1310 | − | 233.266i | −0.127651 | − | 0.723943i | −0.979698 | − | 0.200478i | \(-0.935750\pi\) |
0.852048 | − | 0.523464i | \(-0.175361\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 304.073 | − | 110.673i | 0.886510 | − | 0.322663i | ||||
\(50\) | −2.60049 | + | 14.7481i | −0.00735530 | + | 0.0417140i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 109.500 | − | 91.8815i | 0.292018 | − | 0.245032i | ||||
\(53\) | −391.866 | −1.01560 | −0.507802 | − | 0.861474i | \(-0.669542\pi\) | ||||
−0.507802 | + | 0.861474i | \(0.669542\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −633.441 | −1.55297 | ||||||||
\(56\) | 50.1455 | − | 42.0770i | 0.119660 | − | 0.100407i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 34.9090 | − | 197.979i | 0.0790306 | − | 0.448205i | ||||
\(59\) | 526.804 | − | 191.741i | 1.16244 | − | 0.423094i | 0.312473 | − | 0.949927i | \(-0.398843\pi\) |
0.849969 | + | 0.526833i | \(0.176621\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29.3061 | + | 166.203i | 0.0615126 | + | 0.348855i | 0.999994 | + | 0.00352488i | \(0.00112200\pi\) |
−0.938481 | + | 0.345330i | \(0.887767\pi\) | |||||||
\(62\) | 569.902 | + | 987.099i | 1.16738 | + | 2.02196i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −57.1812 | + | 99.0407i | −0.111682 | + | 0.193439i | ||||
\(65\) | −404.545 | − | 147.242i | −0.771964 | − | 0.280972i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −416.993 | − | 349.898i | −0.760354 | − | 0.638013i | 0.177865 | − | 0.984055i | \(-0.443081\pi\) |
−0.938219 | + | 0.346042i | \(0.887526\pi\) | |||||||
\(68\) | −249.926 | − | 209.713i | −0.445706 | − | 0.373992i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 155.174 | + | 56.4786i | 0.264954 | + | 0.0964355i | ||||
\(71\) | 97.0579 | − | 168.109i | 0.162235 | − | 0.280998i | −0.773435 | − | 0.633875i | \(-0.781463\pi\) |
0.935670 | + | 0.352877i | \(0.114797\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −80.6653 | − | 139.716i | −0.129331 | − | 0.224008i | 0.794087 | − | 0.607805i | \(-0.207950\pi\) |
−0.923418 | + | 0.383797i | \(0.874616\pi\) | |||||||
\(74\) | 56.2911 | + | 319.243i | 0.0884285 | + | 0.501503i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 203.381 | − | 74.0247i | 0.306966 | − | 0.111726i | ||||
\(77\) | 44.1287 | − | 250.266i | 0.0653108 | − | 0.370396i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 278.476 | − | 233.669i | 0.396595 | − | 0.332783i | −0.422581 | − | 0.906325i | \(-0.638876\pi\) |
0.819176 | + | 0.573542i | \(0.194431\pi\) | |||||||
\(80\) | −877.215 | −1.22594 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1234.43 | 1.66244 | ||||||||
\(83\) | 432.830 | − | 363.187i | 0.572400 | − | 0.480301i | −0.310041 | − | 0.950723i | \(-0.600343\pi\) |
0.882441 | + | 0.470422i | \(0.155898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −170.627 | + | 967.676i | −0.217731 | + | 1.23481i | ||||
\(86\) | −1512.42 | + | 550.475i | −1.89637 | + | 0.690223i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 148.805 | + | 843.918i | 0.180258 | + | 1.02229i | ||||
\(89\) | −187.611 | − | 324.952i | −0.223446 | − | 0.387021i | 0.732406 | − | 0.680868i | \(-0.238397\pi\) |
−0.955852 | + | 0.293848i | \(0.905064\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 86.3568 | − | 149.574i | 0.0994797 | − | 0.172304i | ||||
\(92\) | −78.3448 | − | 28.5152i | −0.0887827 | − | 0.0323143i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −619.228 | − | 519.594i | −0.679452 | − | 0.570128i | ||||
\(95\) | −499.344 | − | 418.999i | −0.539280 | − | 0.452509i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 548.136 | + | 199.505i | 0.573760 | + | 0.208832i | 0.612572 | − | 0.790415i | \(-0.290135\pi\) |
−0.0388115 | + | 0.999247i | \(0.512357\pi\) | |||||||
\(98\) | 552.153 | − | 956.357i | 0.569141 | − | 0.985782i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.00078 | + | 13.8578i | 0.00800078 | + | 0.0138578i | ||||
\(101\) | −8.55984 | − | 48.5453i | −0.00843303 | − | 0.0478261i | 0.980301 | − | 0.197510i | \(-0.0632855\pi\) |
−0.988734 | + | 0.149684i | \(0.952174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −339.056 | + | 123.406i | −0.324352 | + | 0.118054i | −0.499064 | − | 0.866565i | \(-0.666323\pi\) |
0.174712 | + | 0.984620i | \(0.444100\pi\) | |||||||
\(104\) | −101.133 | + | 573.556i | −0.0953552 | + | 0.540786i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1024.45 | + | 859.613i | −0.938708 | + | 0.787670i | ||||
\(107\) | −1057.66 | −0.955583 | −0.477792 | − | 0.878473i | \(-0.658563\pi\) | ||||
−0.477792 | + | 0.878473i | \(0.658563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.04341 | 0.00794680 | 0.00397340 | − | 0.999992i | \(-0.498735\pi\) | ||||
0.00397340 | + | 0.999992i | \(0.498735\pi\) | |||||||
\(110\) | −1655.99 | + | 1389.54i | −1.43538 | + | 1.20443i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 61.1113 | − | 346.579i | 0.0515578 | − | 0.292399i | ||||
\(113\) | −189.066 | + | 68.8143i | −0.157397 | + | 0.0572877i | −0.419517 | − | 0.907748i | \(-0.637801\pi\) |
0.262120 | + | 0.965035i | \(0.415578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 43.6029 | + | 247.284i | 0.0353564 | + | 0.200516i | ||||
\(116\) | −107.402 | − | 186.026i | −0.0859660 | − | 0.148898i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 956.601 | − | 1656.88i | 0.746290 | − | 1.29261i | ||||
\(119\) | −370.433 | − | 134.827i | −0.285357 | − | 0.103862i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1528.84 | + | 1282.85i | 1.14864 | + | 0.963826i | ||||
\(122\) | 441.204 | + | 370.214i | 0.327416 | + | 0.274735i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1144.44 | + | 416.542i | 0.828820 | + | 0.301666i | ||||
\(125\) | 710.493 | − | 1230.61i | 0.508387 | − | 0.880552i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 619.475 | + | 1072.96i | 0.432831 | + | 0.749685i | 0.997116 | − | 0.0758949i | \(-0.0241813\pi\) |
−0.564285 | + | 0.825580i | \(0.690848\pi\) | |||||||
\(128\) | 281.333 | + | 1595.52i | 0.194270 | + | 1.10176i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1380.59 | + | 502.494i | −0.931429 | + | 0.339012i | ||||
\(131\) | −113.960 | + | 646.297i | −0.0760053 | + | 0.431048i | 0.922932 | + | 0.384963i | \(0.125786\pi\) |
−0.998938 | + | 0.0460851i | \(0.985325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 200.329 | − | 168.096i | 0.130607 | − | 0.109592i | ||||
\(134\) | −1857.68 | −1.19761 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1329.29 | 0.838133 | ||||||||
\(137\) | 37.9244 | − | 31.8223i | 0.0236504 | − | 0.0198450i | −0.630886 | − | 0.775876i | \(-0.717308\pi\) |
0.654536 | + | 0.756031i | \(0.272864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 347.687 | − | 1971.83i | 0.212161 | − | 1.20323i | −0.673604 | − | 0.739093i | \(-0.735254\pi\) |
0.885765 | − | 0.464134i | \(-0.153634\pi\) | |||||||
\(140\) | 165.804 | − | 60.3477i | 0.100093 | − | 0.0364308i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −115.035 | − | 652.393i | −0.0679823 | − | 0.385547i | ||||
\(143\) | 1130.49 | + | 1958.07i | 0.661094 | + | 1.14505i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −323.470 | + | 560.267i | −0.185260 | + | 0.320880i | ||||
\(146\) | −517.368 | − | 188.307i | −0.293272 | − | 0.106742i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 265.339 | + | 222.645i | 0.147370 | + | 0.123658i | ||||
\(149\) | −2032.19 | − | 1705.21i | −1.11734 | − | 0.937559i | −0.118872 | − | 0.992910i | \(-0.537928\pi\) |
−0.998467 | + | 0.0553509i | \(0.982372\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −394.116 | − | 143.447i | −0.212402 | − | 0.0773080i | 0.233628 | − | 0.972326i | \(-0.424940\pi\) |
−0.446030 | + | 0.895018i | \(0.647162\pi\) | |||||||
\(152\) | −440.919 | + | 763.693i | −0.235284 | + | 0.407524i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −433.629 | − | 751.068i | −0.226901 | − | 0.393005i | ||||
\(155\) | −636.939 | − | 3612.26i | −0.330065 | − | 1.87189i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2326.88 | + | 846.913i | −1.18283 | + | 0.430516i | −0.857202 | − | 0.514980i | \(-0.827799\pi\) |
−0.325632 | + | 0.945497i | \(0.605577\pi\) | |||||||
\(158\) | 215.428 | − | 1221.75i | 0.108472 | − | 0.615173i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1293.34 | + | 1085.24i | −0.639044 | + | 0.536222i | ||||
\(161\) | −100.737 | −0.0493118 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2583.99 | −1.24168 | −0.620840 | − | 0.783938i | \(-0.713208\pi\) | ||||
−0.620840 | + | 0.783938i | \(0.713208\pi\) | |||||||
\(164\) | 1010.41 | − | 847.835i | 0.481096 | − | 0.403688i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 334.835 | − | 1898.94i | 0.156556 | − | 0.887871i | ||||
\(167\) | 596.104 | − | 216.964i | 0.276215 | − | 0.100534i | −0.200198 | − | 0.979755i | \(-0.564159\pi\) |
0.476414 | + | 0.879221i | \(0.341936\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −114.670 | − | 650.324i | −0.0521938 | − | 0.296006i | ||||
\(170\) | 1676.66 | + | 2904.07i | 0.756437 | + | 1.31019i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −859.869 | + | 1489.34i | −0.381188 | + | 0.660238i | ||||
\(173\) | 1596.36 | + | 581.026i | 0.701553 | + | 0.255345i | 0.668074 | − | 0.744095i | \(-0.267119\pi\) |
0.0334794 | + | 0.999439i | \(0.489341\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.8109 | + | 12.4278i | 0.00639771 | + | 0.00536832i | ||||
\(176\) | 3529.20 | + | 2961.35i | 1.51150 | + | 1.26830i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1203.29 | − | 437.963i | −0.506689 | − | 0.184420i | ||||
\(179\) | 324.339 | − | 561.772i | 0.135432 | − | 0.234574i | −0.790331 | − | 0.612681i | \(-0.790091\pi\) |
0.925762 | + | 0.378106i | \(0.123425\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1836.50 | − | 3180.92i | −0.754178 | − | 1.30627i | −0.945782 | − | 0.324802i | \(-0.894702\pi\) |
0.191605 | − | 0.981472i | \(-0.438631\pi\) | |||||||
\(182\) | −102.351 | − | 580.464i | −0.0416857 | − | 0.236411i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 319.208 | − | 116.182i | 0.127893 | − | 0.0465493i | ||||
\(185\) | 181.150 | − | 1027.35i | 0.0719912 | − | 0.408283i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3953.20 | − | 3317.13i | 1.54592 | − | 1.29718i | ||||
\(188\) | −863.721 | −0.335071 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2224.55 | −0.849401 | ||||||||
\(191\) | 1323.99 | − | 1110.96i | 0.501575 | − | 0.420871i | −0.356578 | − | 0.934266i | \(-0.616057\pi\) |
0.858153 | + | 0.513394i | \(0.171612\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 188.684 | − | 1070.08i | 0.0703718 | − | 0.399099i | −0.929193 | − | 0.369595i | \(-0.879496\pi\) |
0.999565 | − | 0.0295033i | \(-0.00939254\pi\) | |||||||
\(194\) | 1870.62 | − | 680.850i | 0.692282 | − | 0.251970i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −204.897 | − | 1162.03i | −0.0746710 | − | 0.423480i | ||||
\(197\) | −1804.76 | − | 3125.94i | −0.652711 | − | 1.13053i | −0.982462 | − | 0.186461i | \(-0.940298\pi\) |
0.329751 | − | 0.944068i | \(-0.393035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −726.376 | + | 1258.12i | −0.258751 | + | 0.448169i | −0.965908 | − | 0.258887i | \(-0.916644\pi\) |
0.707157 | + | 0.707057i | \(0.249977\pi\) | |||||||
\(200\) | −61.2648 | − | 22.2986i | −0.0216604 | − | 0.00788374i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −128.869 | − | 108.134i | −0.0448869 | − | 0.0376646i | ||||
\(203\) | −198.822 | − | 166.831i | −0.0687416 | − | 0.0576810i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3732.94 | − | 1358.68i | −1.27180 | − | 0.462898i | ||||
\(206\) | −615.678 | + | 1066.39i | −0.208235 | + | 0.360673i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1565.55 | + | 2711.62i | 0.521882 | + | 0.903927i | ||||
\(209\) | 594.473 | + | 3371.42i | 0.196749 | + | 1.11582i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3037.97 | − | 1105.73i | 0.991197 | − | 0.360766i | 0.205013 | − | 0.978759i | \(-0.434276\pi\) |
0.786184 | + | 0.617993i | \(0.212054\pi\) | |||||||
\(212\) | −248.132 | + | 1407.23i | −0.0803857 | + | 0.455890i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2765.00 | + | 2320.11i | −0.883232 | + | 0.741120i | ||||
\(215\) | 5179.44 | 1.64295 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1471.54 | 0.460344 | ||||||||
\(218\) | 23.6420 | − | 19.8380i | 0.00734512 | − | 0.00616329i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −401.098 | + | 2274.74i | −0.122918 | + | 0.697104i | ||||
\(221\) | 3295.76 | − | 1199.56i | 1.00315 | − | 0.365118i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 342.826 | + | 1944.26i | 0.102948 | + | 0.583845i | 0.992020 | + | 0.126079i | \(0.0402392\pi\) |
−0.889073 | + | 0.457766i | \(0.848650\pi\) | |||||||
\(224\) | −338.666 | − | 586.587i | −0.101018 | − | 0.174969i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −343.317 | + | 594.642i | −0.101049 | + | 0.175022i | ||||
\(227\) | 1481.41 | + | 539.188i | 0.433147 | + | 0.157653i | 0.549386 | − | 0.835569i | \(-0.314862\pi\) |
−0.116239 | + | 0.993221i | \(0.537084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4956.09 | + | 4158.65i | 1.43016 | + | 1.20005i | 0.945616 | + | 0.325285i | \(0.105460\pi\) |
0.484548 | + | 0.874765i | \(0.338984\pi\) | |||||||
\(230\) | 656.442 | + | 550.820i | 0.188193 | + | 0.157913i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 822.419 | + | 299.336i | 0.232735 | + | 0.0847085i | ||||
\(233\) | 1287.98 | − | 2230.85i | 0.362139 | − | 0.627244i | −0.626173 | − | 0.779684i | \(-0.715380\pi\) |
0.988313 | + | 0.152440i | \(0.0487131\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1300.66 | + | 2252.81i | 0.361046 | + | 0.625350i | ||||
\(236\) | −354.983 | − | 2013.21i | −0.0979129 | − | 0.555291i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1264.17 | + | 460.122i | −0.344303 | + | 0.125316i | ||||
\(239\) | 26.3109 | − | 149.216i | 0.00712096 | − | 0.0403850i | −0.981040 | − | 0.193804i | \(-0.937917\pi\) |
0.988161 | + | 0.153419i | \(0.0490285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4391.96 | − | 3685.29i | 1.17390 | − | 0.985023i | 0.173905 | − | 0.984762i | \(-0.444362\pi\) |
1.00000 | 0.000260554i | \(-8.29368e-5\pi\) | ||||||||
\(242\) | 6810.93 | 1.80919 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 615.407 | 0.161465 | ||||||||
\(245\) | −2722.33 | + | 2284.31i | −0.709891 | + | 0.595669i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −404.024 | + | 2291.34i | −0.104079 | + | 0.590260i | ||||
\(248\) | −4662.90 | + | 1697.16i | −1.19393 | + | 0.434555i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −842.088 | − | 4775.72i | −0.213033 | − | 1.20817i | ||||
\(251\) | 352.490 | + | 610.530i | 0.0886413 | + | 0.153531i | 0.906937 | − | 0.421266i | \(-0.138414\pi\) |
−0.818296 | + | 0.574797i | \(0.805081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 659.373 | − | 1142.07i | 0.163851 | − | 0.283799i | ||||
\(254\) | 3973.17 | + | 1446.12i | 0.981492 | + | 0.357234i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3534.62 | + | 2965.90i | 0.862945 | + | 0.724097i | ||||
\(257\) | −576.896 | − | 484.074i | −0.140023 | − | 0.117493i | 0.570086 | − | 0.821585i | \(-0.306910\pi\) |
−0.710109 | + | 0.704092i | \(0.751354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 393.276 | + | 143.141i | 0.0943514 | + | 0.0343411i | ||||
\(260\) | −784.920 | + | 1359.52i | −0.187226 | + | 0.324285i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1119.82 | + | 1939.58i | 0.264056 | + | 0.457359i | ||||
\(263\) | 1078.57 | + | 6116.85i | 0.252879 | + | 1.43415i | 0.801459 | + | 0.598050i | \(0.204058\pi\) |
−0.548580 | + | 0.836098i | \(0.684831\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4044.07 | − | 1471.92i | 0.937454 | − | 0.341205i | ||||
\(266\) | 154.974 | − | 878.900i | 0.0357220 | − | 0.202590i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1520.56 | + | 1275.90i | −0.346577 | + | 0.290813i | ||||
\(269\) | −3724.81 | −0.844259 | −0.422130 | − | 0.906535i | \(-0.638717\pi\) | ||||
−0.422130 | + | 0.906535i | \(0.638717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5353.13 | 1.19992 | 0.599962 | − | 0.800028i | \(-0.295182\pi\) | ||||
0.599962 | + | 0.800028i | \(0.295182\pi\) | |||||||
\(272\) | 5474.55 | − | 4593.70i | 1.22038 | − | 1.02402i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 29.3381 | − | 166.385i | 0.00646854 | − | 0.0366849i | ||||
\(275\) | −237.840 | + | 86.5667i | −0.0521538 | + | 0.0189824i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 520.822 | + | 2953.73i | 0.112972 | + | 0.640694i | 0.987735 | + | 0.156143i | \(0.0499060\pi\) |
−0.874763 | + | 0.484551i | \(0.838983\pi\) | |||||||
\(278\) | −3416.53 | − | 5917.61i | −0.737086 | − | 1.27667i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −359.453 | + | 622.591i | −0.0767194 | + | 0.132882i | ||||
\(281\) | −6936.81 | − | 2524.79i | −1.47265 | − | 0.536002i | −0.523833 | − | 0.851821i | \(-0.675499\pi\) |
−0.948819 | + | 0.315819i | \(0.897721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6736.75 | − | 5652.80i | −1.41505 | − | 1.18736i | −0.953932 | − | 0.300024i | \(-0.903005\pi\) |
−0.461114 | − | 0.887341i | \(-0.652550\pi\) | |||||||
\(284\) | −542.237 | − | 454.991i | −0.113295 | − | 0.0950659i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7250.71 | + | 2639.04i | 1.49910 | + | 0.545629i | ||||
\(287\) | 796.856 | − | 1380.19i | 0.163892 | − | 0.283869i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1546.06 | − | 2677.85i | −0.314687 | − | 0.545053i | ||||
\(290\) | 383.382 | + | 2174.27i | 0.0776310 | + | 0.440267i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −552.811 | + | 201.207i | −0.110790 | + | 0.0403244i | ||||
\(293\) | −171.495 | + | 972.594i | −0.0341939 | + | 0.193923i | −0.997120 | − | 0.0758428i | \(-0.975835\pi\) |
0.962926 | + | 0.269766i | \(0.0869464\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4716.42 | + | 3957.54i | −0.930849 | + | 0.781075i | ||||
\(296\) | −1411.27 | −0.277123 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9053.32 | −1.75988 | ||||||||
\(299\) | 686.579 | − | 576.108i | 0.132796 | − | 0.111429i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −360.826 | + | 2046.35i | −0.0690953 | + | 0.391859i | ||||
\(302\) | −1345.00 | + | 489.539i | −0.256278 | + | 0.0932775i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 823.250 | + | 4668.88i | 0.155318 | + | 0.880852i | ||||
\(305\) | −926.730 | − | 1605.14i | −0.173982 | − | 0.301345i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 833.402 | − | 1443.49i | 0.154934 | − | 0.268354i | −0.778101 | − | 0.628139i | \(-0.783817\pi\) |
0.933035 | + | 0.359786i | \(0.117150\pi\) | |||||||
\(308\) | −870.785 | − | 316.940i | −0.161096 | − | 0.0586342i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9589.12 | − | 8046.23i | −1.75686 | − | 1.47418i | ||||
\(311\) | −3266.44 | − | 2740.87i | −0.595572 | − | 0.499744i | 0.294447 | − | 0.955668i | \(-0.404865\pi\) |
−0.890019 | + | 0.455924i | \(0.849309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1440.39 | − | 524.260i | −0.260114 | − | 0.0946739i | 0.208671 | − | 0.977986i | \(-0.433086\pi\) |
−0.468786 | + | 0.883312i | \(0.655308\pi\) | |||||||
\(314\) | −4225.27 | + | 7318.39i | −0.759382 | + | 1.31529i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −662.794 | − | 1147.99i | −0.117991 | − | 0.204366i | ||||
\(317\) | −1413.56 | − | 8016.68i | −0.250452 | − | 1.42038i | −0.807482 | − | 0.589892i | \(-0.799170\pi\) |
0.557030 | − | 0.830492i | \(-0.311941\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3192.76 | − | 1162.07i | 0.560377 | − | 0.203961i | ||||
\(320\) | 218.096 | − | 1236.89i | 0.0380999 | − | 0.216075i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −263.355 | + | 220.981i | −0.0455782 | + | 0.0382447i | ||||
\(323\) | 5310.49 | 0.914809 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −172.018 | −0.0293596 | ||||||||
\(326\) | −6755.26 | + | 5668.34i | −1.14767 | + | 0.963007i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −933.206 | + | 5292.48i | −0.157097 | + | 0.890939i | ||||
\(329\) | −980.675 | + | 356.937i | −0.164336 | + | 0.0598132i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −472.291 | − | 2678.49i | −0.0784273 | − | 0.444783i | −0.998582 | − | 0.0532291i | \(-0.983049\pi\) |
0.920155 | − | 0.391554i | \(-0.128062\pi\) | |||||||
\(332\) | −1030.17 | − | 1784.30i | −0.170294 | − | 0.294958i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1082.44 | − | 1874.84i | 0.177331 | − | 0.307146i | ||||
\(335\) | 5617.65 | + | 2044.66i | 0.916195 | + | 0.333468i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5243.78 | − | 4400.06i | −0.847617 | − | 0.711235i | 0.111646 | − | 0.993748i | \(-0.464388\pi\) |
−0.959264 | + | 0.282513i | \(0.908832\pi\) | |||||||
\(338\) | −1726.35 | − | 1448.58i | −0.277814 | − | 0.233114i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3366.96 | + | 1225.48i | 0.537057 | + | 0.195473i | ||||
\(341\) | −9631.94 | + | 16683.0i | −1.52961 | + | 2.64937i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1468.48 | − | 2543.48i | −0.231167 | − | 0.400393i | ||||
\(344\) | −1216.74 | − | 6900.45i | −0.190703 | − | 1.08153i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5447.88 | − | 1982.86i | 0.846473 | − | 0.308091i | ||||
\(347\) | −1684.95 | + | 9555.81i | −0.260671 | + | 1.47834i | 0.520416 | + | 0.853913i | \(0.325777\pi\) |
−0.781086 | + | 0.624423i | \(0.785334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −210.474 | + | 176.609i | −0.0322820 | + | 0.0270878i | −0.658786 | − | 0.752330i | \(-0.728930\pi\) |
0.626504 | + | 0.779418i | \(0.284485\pi\) | |||||||
\(350\) | 65.9820 | 0.0100768 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8866.93 | 1.34264 | ||||||||
\(353\) | −1328.64 | + | 1114.86i | −0.200330 | + | 0.168097i | −0.737434 | − | 0.675419i | \(-0.763963\pi\) |
0.537104 | + | 0.843516i | \(0.319518\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −370.191 | + | 2099.46i | −0.0553456 | + | 0.313881i | ||||
\(356\) | −1285.73 | + | 467.966i | −0.191414 | + | 0.0696690i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −384.412 | − | 2180.11i | −0.0567509 | − | 0.321850i | ||||
\(359\) | −2140.65 | − | 3707.72i | −0.314706 | − | 0.545087i | 0.664669 | − | 0.747138i | \(-0.268573\pi\) |
−0.979375 | + | 0.202051i | \(0.935239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1668.05 | − | 2889.14i | 0.243191 | − | 0.421219i | ||||
\(362\) | −11778.9 | − | 4287.17i | −1.71018 | − | 0.622455i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −482.453 | − | 404.826i | −0.0694708 | − | 0.0582930i | ||||
\(365\) | 1357.27 | + | 1138.88i | 0.194637 | + | 0.163320i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3806.51 | − | 1385.46i | −0.541412 | − | 0.197058i | 0.0568146 | − | 0.998385i | \(-0.481906\pi\) |
−0.598227 | + | 0.801327i | \(0.704128\pi\) | |||||||
\(368\) | 913.127 | − | 1581.58i | 0.129348 | − | 0.224037i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1780.06 | − | 3083.15i | −0.250110 | − | 0.433204i | ||||
\(371\) | 299.811 | + | 1700.32i | 0.0419554 | + | 0.237941i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13066.7 | + | 4755.90i | −1.81386 | + | 0.660191i | −0.817406 | + | 0.576062i | \(0.804589\pi\) |
−0.996455 | + | 0.0841290i | \(0.973189\pi\) | |||||||
\(374\) | 3058.18 | − | 17343.8i | 0.422819 | − | 2.39793i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2695.82 | − | 2262.06i | 0.369751 | − | 0.310258i | ||||
\(377\) | 2309.17 | 0.315460 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5487.05 | 0.743669 | 0.371835 | − | 0.928299i | \(-0.378729\pi\) | ||||
0.371835 | + | 0.928299i | \(0.378729\pi\) | |||||||
\(380\) | −1820.85 | + | 1527.87i | −0.245809 | + | 0.206259i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1024.23 | − | 5808.72i | 0.137184 | − | 0.778011i | ||||
\(383\) | 8422.82 | − | 3065.66i | 1.12372 | − | 0.409002i | 0.287714 | − | 0.957716i | \(-0.407105\pi\) |
0.836010 | + | 0.548714i | \(0.184883\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 484.636 | + | 2748.51i | 0.0641542 | + | 0.363836i | ||||
\(386\) | −1854.10 | − | 3211.39i | −0.244484 | − | 0.423459i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1063.52 | − | 1842.07i | 0.139155 | − | 0.241024i | ||||
\(389\) | −5415.31 | − | 1971.01i | −0.705828 | − | 0.256900i | −0.0359310 | − | 0.999354i | \(-0.511440\pi\) |
−0.669897 | + | 0.742454i | \(0.733662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1567.07 | − | 1314.93i | −0.202685 | − | 0.170073i | ||||
\(392\) | 3682.84 | + | 3090.27i | 0.474520 | + | 0.398169i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11575.3 | − | 4213.08i | −1.48009 | − | 0.538710i | ||||
\(395\) | −1996.18 | + | 3457.48i | −0.254275 | + | 0.440417i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 849.799 | + | 1471.89i | 0.107431 | + | 0.186076i | 0.914729 | − | 0.404068i | \(-0.132404\pi\) |
−0.807298 | + | 0.590144i | \(0.799071\pi\) | |||||||
\(398\) | 860.912 | + | 4882.48i | 0.108426 | + | 0.614916i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −329.371 | + | 119.881i | −0.0411713 | + | 0.0149851i | ||||
\(401\) | −1819.64 | + | 10319.7i | −0.226605 | + | 1.28514i | 0.632987 | + | 0.774162i | \(0.281829\pi\) |
−0.859592 | + | 0.510980i | \(0.829283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10029.4 | + | 8415.63i | −1.23970 | + | 1.04023i | ||||
\(404\) | −179.750 | −0.0221359 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −885.741 | −0.108272 | ||||||||
\(407\) | −4196.98 | + | 3521.69i | −0.511147 | + | 0.428903i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −357.046 | + | 2024.91i | −0.0431657 | + | 0.244805i | −0.998754 | − | 0.0498993i | \(-0.984110\pi\) |
0.955589 | + | 0.294704i | \(0.0952211\pi\) | |||||||
\(410\) | −12739.4 | + | 4636.75i | −1.53452 | + | 0.558519i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 228.471 | + | 1295.72i | 0.0273203 | + | 0.154941i | ||||
\(413\) | −1235.02 | − | 2139.11i | −0.147146 | − | 0.254864i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3102.61 | + | 5373.89i | −0.366991 | + | 0.635647i | ||||
\(416\) | 5662.84 | + | 2061.11i | 0.667413 | + | 0.242918i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8949.80 | + | 7509.77i | 1.04725 | + | 0.878744i | ||||
\(419\) | 2008.19 | + | 1685.07i | 0.234145 | + | 0.196471i | 0.752309 | − | 0.658810i | \(-0.228940\pi\) |
−0.518164 | + | 0.855281i | \(0.673384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7645.13 | + | 2782.60i | 0.885038 | + | 0.322128i | 0.744241 | − | 0.667911i | \(-0.232811\pi\) |
0.140797 | + | 0.990038i | \(0.455034\pi\) | |||||||
\(422\) | 5516.52 | − | 9554.90i | 0.636351 | − | 1.10219i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2911.02 | − | 5042.04i | −0.333424 | − | 0.577507i | ||||
\(425\) | 68.1776 | + | 386.655i | 0.00778141 | + | 0.0441306i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 698.738 | − | 254.320i | 0.0791904 | − | 0.0288229i | ||||
\(428\) | −669.713 | + | 3798.13i | −0.0756350 | + | 0.428948i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13540.5 | − | 11361.8i | 1.51856 | − | 1.27422i | ||||
\(431\) | −10524.6 | −1.17622 | −0.588112 | − | 0.808780i | \(-0.700128\pi\) | ||||
−0.588112 | + | 0.808780i | \(0.700128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15556.7 | −1.72658 | −0.863290 | − | 0.504708i | \(-0.831600\pi\) | ||||
−0.863290 | + | 0.504708i | \(0.831600\pi\) | |||||||
\(434\) | 3847.01 | − | 3228.03i | 0.425490 | − | 0.357028i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.72633 | − | 32.4756i | 0.000628995 | − | 0.00356721i | ||||
\(437\) | 1275.22 | − | 464.144i | 0.139593 | − | 0.0508078i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2473.12 | + | 14025.8i | 0.268874 | + | 1.52486i | 0.757773 | + | 0.652518i | \(0.226287\pi\) |
−0.488900 | + | 0.872340i | \(0.662602\pi\) | |||||||
\(440\) | −4705.58 | − | 8150.31i | −0.509841 | − | 0.883070i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5984.63 | − | 10365.7i | 0.644027 | − | 1.11549i | ||||
\(443\) | 9858.79 | + | 3588.31i | 1.05735 | + | 0.384843i | 0.811431 | − | 0.584448i | \(-0.198689\pi\) |
0.245917 | + | 0.969291i | \(0.420911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3156.73 | + | 2648.81i | 0.336277 | + | 0.282170i | ||||
\(446\) | 5161.25 | + | 4330.80i | 0.547964 | + | 0.459797i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 473.488 | + | 172.336i | 0.0499335 | + | 0.0181743i | ||||
\(449\) | 5192.42 | − | 8993.54i | 0.545759 | − | 0.945282i | −0.452800 | − | 0.891612i | \(-0.649575\pi\) |
0.998559 | − | 0.0536697i | \(-0.0170918\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10431.6 | + | 18068.1i | 1.08915 | + | 1.88646i | ||||
\(452\) | 127.401 | + | 722.525i | 0.0132576 | + | 0.0751874i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5055.59 | − | 1840.08i | 0.522622 | − | 0.190219i | ||||
\(455\) | −329.376 | + | 1867.98i | −0.0339371 | + | 0.192467i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 419.782 | − | 352.239i | 0.0429685 | − | 0.0360548i | −0.621051 | − | 0.783771i | \(-0.713294\pi\) |
0.664019 | + | 0.747716i | \(0.268849\pi\) | |||||||
\(458\) | 22079.2 | 2.25260 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 915.628 | 0.0928074 | ||||||||
\(461\) | 8411.57 | − | 7058.15i | 0.849818 | − | 0.713082i | −0.109932 | − | 0.993939i | \(-0.535063\pi\) |
0.959750 | + | 0.280857i | \(0.0906188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1692.97 | − | 9601.33i | 0.169933 | − | 0.963740i | −0.773898 | − | 0.633311i | \(-0.781695\pi\) |
0.943831 | − | 0.330429i | \(-0.107193\pi\) | |||||||
\(464\) | 4421.47 | − | 1609.28i | 0.442374 | − | 0.161011i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1526.54 | − | 8657.42i | −0.151750 | − | 0.860617i | ||||
\(467\) | 7561.18 | + | 13096.3i | 0.749228 | + | 1.29770i | 0.948193 | + | 0.317695i | \(0.102909\pi\) |
−0.198965 | + | 0.980007i | \(0.563758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1199.18 | + | 2077.04i | −0.118066 | + | 0.204496i | ||||
\(470\) | 8342.14 | + | 3036.29i | 0.818711 | + | 0.297987i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6380.50 | + | 5353.88i | 0.622217 | + | 0.522102i | ||||
\(473\) | −20837.9 | − | 17485.0i | −2.02564 | − | 1.69971i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −244.751 | − | 89.0821i | −0.0236420 | − | 0.00860498i | ||||
\(476\) | −718.733 | + | 1244.88i | −0.0692082 | + | 0.119872i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −258.543 | − | 447.809i | −0.0247395 | − | 0.0428500i | ||||
\(479\) | 501.655 | + | 2845.03i | 0.0478522 | + | 0.271383i | 0.999341 | − | 0.0363002i | \(-0.0115573\pi\) |
−0.951489 | + | 0.307684i | \(0.900446\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3499.00 | + | 1273.53i | −0.331686 | + | 0.120724i | ||||
\(482\) | 3397.60 | − | 19268.7i | 0.321071 | − | 1.82089i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5574.91 | − | 4677.90i | 0.523564 | − | 0.439322i | ||||
\(485\) | −6406.15 | −0.599770 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15221.1 | 1.41629 | 0.708146 | − | 0.706066i | \(-0.249532\pi\) | ||||
0.708146 | + | 0.706066i | \(0.249532\pi\) | |||||||
\(488\) | −1920.79 | + | 1611.73i | −0.178176 | + | 0.149508i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2105.98 | + | 11943.6i | −0.194160 | + | 1.10114i | ||||
\(491\) | 2636.65 | − | 959.662i | 0.242343 | − | 0.0882056i | −0.217993 | − | 0.975950i | \(-0.569951\pi\) |
0.460336 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −915.216 | − | 5190.45i | −0.0836090 | − | 0.474170i | ||||
\(494\) | 3970.13 | + | 6876.47i | 0.361588 | + | 0.626289i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13338.7 | + | 23103.3i | −1.20751 | + | 2.09147i | ||||
\(497\) | −803.686 | − | 292.518i | −0.0725357 | − | 0.0264008i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3778.64 | + | 3170.66i | 0.338989 | + | 0.284445i | 0.796350 | − | 0.604835i | \(-0.206761\pi\) |
−0.457362 | + | 0.889281i | \(0.651206\pi\) | |||||||
\(500\) | −3969.34 | − | 3330.67i | −0.355028 | − | 0.297904i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2260.79 | + | 822.859i | 0.201004 | + | 0.0731594i | ||||
\(503\) | −2185.55 | + | 3785.49i | −0.193735 | + | 0.335560i | −0.946485 | − | 0.322747i | \(-0.895394\pi\) |
0.752750 | + | 0.658307i | \(0.228727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 270.683 | + | 468.836i | 0.0238519 | + | 0.0413127i | ||||
\(506\) | −781.500 | − | 4432.10i | −0.0686599 | − | 0.389389i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4245.35 | − | 1545.18i | 0.370782 | − | 0.134954i | ||||
\(509\) | −3169.78 | + | 17976.7i | −0.276027 | + | 1.56543i | 0.459652 | + | 0.888099i | \(0.347974\pi\) |
−0.735679 | + | 0.677330i | \(0.763137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −544.516 | + | 456.903i | −0.0471389 | + | 0.0395542i | ||||
\(512\) | 2785.52 | 0.240437 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2570.05 | −0.220545 | ||||||||
\(515\) | 3035.53 | − | 2547.12i | 0.259731 | − | 0.217940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2372.36 | − | 13454.3i | 0.201811 | − | 1.14453i | ||||
\(518\) | 1342.13 | − | 488.496i | 0.113842 | − | 0.0414349i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1110.68 | − | 6298.98i | −0.0936665 | − | 0.531209i | ||||
\(521\) | 4209.97 | + | 7291.88i | 0.354016 | + | 0.613173i | 0.986949 | − | 0.161033i | \(-0.0514827\pi\) |
−0.632933 | + | 0.774206i | \(0.718149\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1221.04 | + | 2114.91i | −0.102089 | + | 0.176823i | −0.912545 | − | 0.408976i | \(-0.865886\pi\) |
0.810456 | + | 0.585799i | \(0.199219\pi\) | |||||||
\(524\) | 2248.75 | + | 818.477i | 0.187475 | + | 0.0682354i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16237.8 | + | 13625.1i | 1.34601 | + | 1.12944i | ||||
\(527\) | 22891.3 | + | 19208.1i | 1.89214 | + | 1.58770i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10942.0 | + | 3982.57i | 0.899319 | + | 0.327325i | ||||
\(530\) | 7343.45 | − | 12719.2i | 0.601848 | − | 1.04243i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −476.798 | − | 825.839i | −0.0388568 | − | 0.0673020i | ||||
\(533\) | 2462.22 | + | 13963.9i | 0.200095 | + | 1.13479i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10915.0 | − | 3972.75i | 0.882052 | − | 0.321041i | ||||
\(536\) | 1404.37 | − | 7964.59i | 0.113171 | − | 0.641824i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9737.69 | + | 8170.89i | −0.780337 | + | 0.654781i | ||||
\(539\) | 18663.9 | 1.49149 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22321.4 | −1.77389 | −0.886943 | − | 0.461879i | \(-0.847176\pi\) | ||||
−0.886943 | + | 0.461879i | \(0.847176\pi\) | |||||||
\(542\) | 13994.6 | − | 11742.8i | 1.10907 | − | 0.930623i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2388.45 | − | 13545.6i | 0.188243 | − | 1.06758i | ||||
\(545\) | −93.3282 | + | 33.9687i | −0.00733530 | + | 0.00266983i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1549.26 | − | 8786.27i | −0.121100 | − | 0.686789i | −0.983548 | − | 0.180645i | \(-0.942181\pi\) |
0.862449 | − | 0.506144i | \(-0.168930\pi\) | |||||||
\(548\) | −90.2628 | − | 156.340i | −0.00703619 | − | 0.0121870i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −431.883 | + | 748.044i | −0.0334828 | + | 0.0579940i | ||||
\(551\) | 3285.53 | + | 1195.84i | 0.254026 | + | 0.0924580i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1226.95 | − | 1029.54i | −0.0943497 | − | 0.0791688i | ||||
\(554\) | 7840.98 | + | 6579.36i | 0.601320 | + | 0.504567i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6860.86 | − | 2497.15i | −0.523318 | − | 0.190472i | ||||
\(557\) | −268.972 | + | 465.874i | −0.0204609 | + | 0.0354393i | −0.876075 | − | 0.482176i | \(-0.839847\pi\) |
0.855614 | + | 0.517615i | \(0.173180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9243.68 | − | 16010.5i | −0.699402 | − | 1.21140i | ||||
\(560\) | 671.145 | + | 3806.25i | 0.0506447 | + | 0.287220i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23673.2 | + | 8616.35i | −1.77686 | + | 0.646724i | ||||
\(563\) | 1343.84 | − | 7621.32i | 0.100597 | − | 0.570516i | −0.892290 | − | 0.451462i | \(-0.850903\pi\) |
0.992888 | − | 0.119054i | \(-0.0379862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1692.69 | − | 1420.33i | 0.126039 | − | 0.105759i | ||||
\(566\) | −30011.9 | −2.22879 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2884.02 | 0.213047 | ||||||||
\(569\) | −6106.18 | + | 5123.70i | −0.449885 | + | 0.377498i | −0.839393 | − | 0.543525i | \(-0.817089\pi\) |
0.389508 | + | 0.921023i | \(0.372645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1403.64 | − | 7960.43i | 0.102873 | − | 0.583421i | −0.889176 | − | 0.457566i | \(-0.848721\pi\) |
0.992049 | − | 0.125855i | \(-0.0401675\pi\) | |||||||
\(572\) | 7747.43 | − | 2819.83i | 0.566322 | − | 0.206124i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −944.446 | − | 5356.22i | −0.0686767 | − | 0.389485i | ||||
\(575\) | 50.1658 | + | 86.8898i | 0.00363836 | + | 0.00630183i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4242.14 | − | 7347.60i | 0.306070 | − | 0.530130i | −0.671429 | − | 0.741069i | \(-0.734319\pi\) |
0.977499 | + | 0.210940i | \(0.0676524\pi\) | |||||||
\(578\) | −9916.04 | − | 3609.15i | −0.713587 | − | 0.259724i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1807.14 | + | 1516.37i | 0.129375 | + | 0.108559i | ||||
\(581\) | −1907.03 | − | 1600.19i | −0.136174 | − | 0.114263i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21239.0 | − | 7730.38i | −1.50880 | − | 0.549159i | ||||
\(584\) | 1198.46 | − | 2075.80i | 0.0849190 | − | 0.147084i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1685.18 | + | 2918.82i | 0.118796 | + | 0.205760i | ||||
\(587\) | −2873.45 | − | 16296.2i | −0.202044 | − | 1.14585i | −0.902023 | − | 0.431687i | \(-0.857918\pi\) |
0.699979 | − | 0.714163i | \(-0.253193\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18628.1 | + | 6780.08i | −1.30316 | + | 0.474310i | ||||
\(590\) | −3648.60 | + | 20692.2i | −0.254594 | + | 1.44387i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5812.15 | + | 4876.98i | −0.403510 | + | 0.338585i | ||||
\(593\) | −12748.0 | −0.882796 | −0.441398 | − | 0.897311i | \(-0.645517\pi\) | ||||
−0.441398 | + | 0.897311i | \(0.645517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4329.31 | 0.298293 | ||||||||
\(596\) | −7410.35 | + | 6218.02i | −0.509295 | + | 0.427349i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 531.134 | − | 3012.21i | 0.0363206 | − | 0.205984i | ||||
\(599\) | 23393.1 | − | 8514.39i | 1.59569 | − | 0.580783i | 0.617148 | − | 0.786847i | \(-0.288288\pi\) |
0.978538 | + | 0.206064i | \(0.0660656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2949.21 | − | 16725.8i | −0.200167 | − | 1.13521i | −0.904865 | − | 0.425698i | \(-0.860028\pi\) |
0.704698 | − | 0.709508i | \(-0.251083\pi\) | |||||||
\(602\) | 3545.65 | + | 6141.24i | 0.240050 | + | 0.415778i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −764.685 | + | 1324.47i | −0.0515142 | + | 0.0892253i | ||||
\(605\) | −20596.3 | − | 7496.45i | −1.38407 | − | 0.503759i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2424.14 | − | 2034.09i | −0.162097 | − | 0.136015i | 0.558131 | − | 0.829753i | \(-0.311518\pi\) |
−0.720228 | + | 0.693737i | \(0.755963\pi\) | |||||||
\(608\) | 6989.83 | + | 5865.17i | 0.466242 | + | 0.391224i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5943.83 | − | 2163.38i | −0.394523 | − | 0.143594i | ||||
\(611\) | 4642.54 | − | 8041.12i | 0.307393 | − | 0.532421i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3473.88 | + | 6016.94i | 0.228889 | + | 0.396447i | 0.957479 | − | 0.288503i | \(-0.0931575\pi\) |
−0.728590 | + | 0.684950i | \(0.759824\pi\) | |||||||
\(614\) | −987.761 | − | 5601.87i | −0.0649231 | − | 0.368197i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3547.93 | − | 1291.34i | 0.232062 | − | 0.0844635i | ||||
\(617\) | 3318.80 | − | 18821.9i | 0.216548 | − | 1.22810i | −0.661653 | − | 0.749810i | \(-0.730145\pi\) |
0.878201 | − | 0.478293i | \(-0.158744\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9966.32 | + | 8362.73i | −0.647141 | + | 0.543016i | −0.906202 | − | 0.422845i | \(-0.861031\pi\) |
0.259061 | + | 0.965861i | \(0.416587\pi\) | |||||||
\(620\) | −13375.2 | −0.866391 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14551.8 | −0.938064 | ||||||||
\(623\) | −1266.43 | + | 1062.66i | −0.0814424 | + | 0.0683382i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2614.66 | + | 14828.5i | −0.167338 | + | 0.949022i | ||||
\(626\) | −4915.62 | + | 1789.14i | −0.313846 | + | 0.114231i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1567.95 | + | 8892.28i | 0.0996305 | + | 0.565033i | ||||
\(629\) | 4249.38 | + | 7360.15i | 0.269370 | + | 0.466563i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12528.8 | − | 21700.5i | 0.790432 | − | 1.36907i | −0.135268 | − | 0.990809i | \(-0.543189\pi\) |
0.925700 | − | 0.378259i | \(-0.123477\pi\) | |||||||
\(632\) | 5075.25 | + | 1847.24i | 0.319435 | + | 0.116265i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21281.1 | − | 17857.0i | −1.33309 | − | 1.11860i | ||||
\(635\) | −10423.2 | − | 8746.14i | −0.651392 | − | 0.546583i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11919.7 | + | 4338.40i | 0.741404 | + | 0.269849i | ||||
\(638\) | 5797.60 | − | 10041.7i | 0.359763 | − | 0.623129i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8896.43 | − | 15409.1i | −0.549472 | − | 0.951714i | ||||
\(641\) | −1384.86 | − | 7853.93i | −0.0853334 | − | 0.483950i | −0.997284 | − | 0.0736500i | \(-0.976535\pi\) |
0.911951 | − | 0.410300i | \(-0.134576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11197.1 | + | 4075.43i | −0.686737 | + | 0.249952i | −0.661738 | − | 0.749735i | \(-0.730181\pi\) |
−0.0249998 | + | 0.999687i | \(0.507959\pi\) | |||||||
\(644\) | −63.7873 | + | 361.756i | −0.00390306 | + | 0.0221354i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13883.1 | − | 11649.3i | 0.845546 | − | 0.709497i | ||||
\(647\) | −3355.80 | −0.203911 | −0.101955 | − | 0.994789i | \(-0.532510\pi\) | ||||
−0.101955 | + | 0.994789i | \(0.532510\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32335.1 | 1.95572 | ||||||||
\(650\) | −449.703 | + | 377.346i | −0.0271366 | + | 0.0227703i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1636.20 | + | 9279.33i | −0.0982797 | + | 0.557372i | ||||
\(653\) | −26473.9 | + | 9635.72i | −1.58653 | + | 0.577450i | −0.976611 | − | 0.215012i | \(-0.931021\pi\) |
−0.609920 | + | 0.792463i | \(0.708799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1251.54 | − | 7097.85i | −0.0746593 | − | 0.423414i | ||||
\(656\) | 14446.1 | + | 25021.4i | 0.859795 | + | 1.48921i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1780.77 | + | 3084.38i | −0.105504 | + | 0.182738i | ||||
\(659\) | 10183.6 | + | 3706.54i | 0.601970 | + | 0.219099i | 0.624986 | − | 0.780636i | \(-0.285105\pi\) |
−0.0230158 | + | 0.999735i | \(0.507327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19264.9 | + | 16165.2i | 1.13361 | + | 0.951214i | 0.999211 | − | 0.0397130i | \(-0.0126444\pi\) |
0.134401 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(662\) | −7110.34 | − | 5966.28i | −0.417449 | − | 0.350281i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7888.35 | + | 2871.13i | 0.461035 | + | 0.167803i | ||||
\(665\) | −1436.00 | + | 2487.23i | −0.0837381 | + | 0.145039i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −673.426 | − | 1166.41i | −0.0390932 | − | 0.0677114i | ||||
\(668\) | −401.681 | − | 2278.04i | −0.0232657 | − | 0.131946i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19171.3 | − | 6977.80i | 1.10545 | − | 0.402352i | ||||
\(671\) | −1690.32 | + | 9586.30i | −0.0972492 | + | 0.551528i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7274.92 | − | 6104.39i | 0.416683 | − | 0.349639i | −0.410217 | − | 0.911988i | \(-0.634547\pi\) |
0.826900 | + | 0.562350i | \(0.190102\pi\) | |||||||
\(674\) | −23360.8 | −1.33505 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2407.98 | −0.137004 | ||||||||
\(677\) | −2770.73 | + | 2324.92i | −0.157294 | + | 0.131985i | −0.718038 | − | 0.696004i | \(-0.754960\pi\) |
0.560744 | + | 0.827989i | \(0.310515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 446.285 | − | 2531.01i | 0.0252236 | − | 0.143050i | ||||
\(680\) | −13718.4 | + | 4993.07i | −0.773640 | + | 0.281582i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11415.9 | + | 64742.9i | 0.640966 | + | 3.63510i | ||||
\(683\) | −1790.30 | − | 3100.89i | −0.100298 | − | 0.173722i | 0.811509 | − | 0.584340i | \(-0.198646\pi\) |
−0.911808 | + | 0.410618i | \(0.865313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −271.850 | + | 470.858i | −0.0151633 | + | 0.0262636i | ||||
\(686\) | −9418.47 | − | 3428.04i | −0.524197 | − | 0.190792i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28857.1 | − | 24214.0i | −1.59908 | − | 1.34179i | ||||
\(689\) | −11767.3 | − | 9873.98i | −0.650653 | − | 0.545963i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15363.7 | + | 5591.94i | 0.845822 | + | 0.307854i | 0.728336 | − | 0.685220i | \(-0.240294\pi\) |
0.117487 | + | 0.993074i | \(0.462516\pi\) | |||||||
\(692\) | 3097.34 | − | 5364.74i | 0.170149 | − | 0.294706i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16557.1 | + | 28677.7i | 0.905616 | + | 1.56857i | ||||
\(695\) | 3818.42 | + | 21655.3i | 0.208404 | + | 1.18192i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30411.6 | − | 11068.9i | 1.65269 | − | 0.601528i | ||||
\(698\) | −162.822 | + | 923.407i | −0.00882935 | + | 0.0500737i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 54.0077 | − | 45.3179i | 0.00291614 | − | 0.00244694i | ||||
\(701\) | −11210.5 | −0.604015 | −0.302007 | − | 0.953306i | \(-0.597657\pi\) | ||||
−0.302007 | + | 0.953306i | \(0.597657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5637.97 | −0.302475 | ||||||||
\(704\) | −5052.99 | + | 4239.96i | −0.270514 | + | 0.226988i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1027.83 | + | 5829.11i | −0.0547916 | + | 0.310739i | ||||
\(707\) | −204.090 | + | 74.2826i | −0.0108566 | + | 0.00395147i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1416.45 | + | 8033.11i | 0.0750297 | + | 0.425514i | 0.999066 | + | 0.0432098i | \(0.0137584\pi\) |
−0.924036 | + | 0.382305i | \(0.875131\pi\) | |||||||
\(710\) | 3637.67 | + | 6300.63i | 0.192281 | + | 0.333040i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2787.38 | − | 4827.88i | 0.146716 | − | 0.254119i | ||||
\(713\) | 7175.77 | + | 2611.77i | 0.376907 | + | 0.137183i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19021.6 | − | 15961.0i | −0.994918 | − | 0.834835i | ||||
\(716\) | −1812.00 | − | 1520.45i | −0.0945776 | − | 0.0793600i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13729.7 | − | 4997.19i | −0.713630 | − | 0.259740i | ||||
\(719\) | 12784.1 | − | 22142.8i | 0.663099 | − | 1.14852i | −0.316698 | − | 0.948526i | \(-0.602574\pi\) |
0.979797 | − | 0.199994i | \(-0.0640924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 794.870 | + | 1376.76i | 0.0410576 | + | 0.0711138i | ||||
\(722\) | −1976.99 | − | 11212.1i | −0.101906 | − | 0.577938i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12585.8 | + | 4580.86i | −0.646061 | + | 0.235147i | ||||
\(725\) | −44.8877 | + | 254.571i | −0.00229943 | + | 0.0130407i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12418.2 | + | 10420.1i | −0.633515 | + | 0.531582i | −0.902019 | − | 0.431696i | \(-0.857915\pi\) |
0.268504 | + | 0.963279i | \(0.413471\pi\) | |||||||
\(728\) | 2566.04 | 0.130637 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6046.57 | 0.306566 | ||||||||
\(731\) | −32324.1 | + | 27123.1i | −1.63550 | + | 1.37235i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4003.77 | + | 22706.5i | −0.201750 | + | 1.14418i | 0.700723 | + | 0.713434i | \(0.252861\pi\) |
−0.902473 | + | 0.430747i | \(0.858250\pi\) | |||||||
\(734\) | −12990.5 | + | 4728.14i | −0.653252 | + | 0.237764i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −610.355 | − | 3461.50i | −0.0305679 | − | 0.173359i | ||||
\(737\) | −15698.4 | − | 27190.4i | −0.784611 | − | 1.35899i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9222.49 | + | 15973.8i | −0.459073 | + | 0.795137i | −0.998912 | − | 0.0466309i | \(-0.985152\pi\) |
0.539840 | + | 0.841768i | \(0.318485\pi\) | |||||||
\(740\) | −3574.60 | − | 1301.05i | −0.177574 | − | 0.0646317i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4513.67 | + | 3787.42i | 0.223318 | + | 0.187386i | ||||
\(743\) | −8601.48 | − | 7217.49i | −0.424707 | − | 0.356372i | 0.405243 | − | 0.914209i | \(-0.367187\pi\) |
−0.829950 | + | 0.557837i | \(0.811631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27377.3 | + | 9964.53i | 1.34635 | + | 0.490030i | ||||
\(746\) | −23727.3 | + | 41096.9i | −1.16450 | + | 2.01698i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9408.90 | − | 16296.7i | −0.459925 | − | 0.796613i | ||||
\(749\) | 809.197 | + | 4589.19i | 0.0394759 | + | 0.223879i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25956.7 | − | 9447.48i | 1.26122 | − | 0.459046i | 0.377041 | − | 0.926197i | \(-0.376942\pi\) |
0.884178 | + | 0.467151i | \(0.154719\pi\) | |||||||
\(752\) | 3285.34 | − | 18632.1i | 0.159314 | − | 0.903515i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6036.81 | − | 5065.48i | 0.291575 | − | 0.244661i | ||||
\(755\) | 4606.10 | 0.222031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1558.81 | −0.0748425 | −0.0374213 | − | 0.999300i | \(-0.511914\pi\) | ||||
−0.0374213 | + | 0.999300i | \(0.511914\pi\) | |||||||
\(758\) | 14344.7 | − | 12036.6i | 0.687363 | − | 0.576766i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1681.72 | − | 9537.50i | 0.0802663 | − | 0.455213i | ||||
\(761\) | −13156.0 | + | 4788.39i | −0.626681 | + | 0.228093i | −0.635786 | − | 0.771865i | \(-0.719324\pi\) |
0.00910498 | + | 0.999959i | \(0.497102\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.91898 | − | 39.2395i | −0.000328288 | − | 0.00186182i | ||||
\(764\) | −3151.20 | − | 5458.04i | −0.149223 | − | 0.258462i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15294.6 | − | 26491.1i | 0.721433 | − | 1.24956i | ||||
\(767\) | 20650.7 | + | 7516.26i | 0.972171 | + | 0.353841i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6398.15 | − | 5368.68i | −0.300030 | − | 0.251755i | 0.480327 | − | 0.877090i | \(-0.340518\pi\) |
−0.780357 | + | 0.625335i | \(0.784963\pi\) | |||||||
\(770\) | 7296.21 | + | 6122.25i | 0.341477 | + | 0.286533i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3723.27 | − | 1355.16i | −0.173580 | − | 0.0631778i | ||||
\(773\) | 13400.6 | − | 23210.5i | 0.623527 | − | 1.07998i | −0.365297 | − | 0.930891i | \(-0.619033\pi\) |
0.988824 | − | 0.149089i | \(-0.0476341\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −732.808 | − | 1269.26i | −0.0339655 | − | 0.0588300i | ||||
\(776\) | 1504.91 | + | 8534.76i | 0.0696174 | + | 0.394820i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18480.8 | + | 6726.46i | −0.851631 | + | 0.309968i | ||||
\(779\) | −3728.13 | + | 21143.3i | −0.171469 | + | 0.972446i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8576.81 | − | 7196.80i | 0.392961 | − | 0.329733i | ||||
\(782\) | −6981.22 | −0.319243 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25846.6 | 1.17741 | ||||||||
\(785\) | 20832.3 | − | 17480.3i | 0.947178 | − | 0.794777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −183.323 | + | 1039.67i | −0.00830336 | + | 0.0470907i | −0.988678 | − | 0.150053i | \(-0.952056\pi\) |
0.980375 | + | 0.197144i | \(0.0631666\pi\) | |||||||
\(788\) | −12368.3 | + | 4501.70i | −0.559141 | + | 0.203511i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2365.90 | + | 13417.7i | 0.106551 | + | 0.604279i | ||||
\(791\) | 443.238 | + | 767.711i | 0.0199238 | + | 0.0345091i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3307.84 | + | 5729.35i | −0.148127 | + | 0.256564i | ||||
\(794\) | 5450.41 | + | 1983.79i | 0.243612 | + | 0.0886675i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4058.07 | + | 3405.12i | 0.180697 | + | 0.151622i | ||||
\(797\) | −7844.59 | − | 6582.39i | −0.348644 | − | 0.292547i | 0.451601 | − | 0.892220i | \(-0.350853\pi\) |
−0.800245 | + | 0.599673i | \(0.795297\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19914.5 | − | 7248.28i | −0.881757 | − | 0.320933i | ||||
\(800\) | −337.303 | + | 584.226i | −0.0149068 | + | 0.0258194i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17880.7 | + | 30970.2i | 0.787267 | + | 1.36359i | ||||
\(803\) | −1615.84 | − | 9163.87i | −0.0710108 | − | 0.402722i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1039.61 | − | 378.387i | 0.0455173 | − | 0.0165670i | ||||
\(806\) | −7758.66 | + | 44001.5i | −0.339066 | + | 1.92294i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 561.032 | − | 470.761i | 0.0244270 | − | 0.0204967i | ||||
\(809\) | 11391.9 | 0.495077 | 0.247538 | − | 0.968878i | \(-0.420378\pi\) | ||||
0.247538 | + | 0.968878i | \(0.420378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8743.55 | −0.378579 | −0.189289 | − | 0.981921i | \(-0.560618\pi\) | ||||
−0.189289 | + | 0.981921i | \(0.560618\pi\) | |||||||
\(812\) | −724.999 | + | 608.347i | −0.0313331 | + | 0.0262916i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3246.77 | + | 18413.3i | −0.139802 | + | 0.792858i | ||||
\(815\) | 26666.8 | − | 9705.93i | 1.14613 | − | 0.417158i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4860.82 | − | 27567.1i | −0.208150 | − | 1.18048i | ||||
\(818\) | 3508.50 | + | 6076.89i | 0.149965 | + | 0.259748i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7242.84 | + | 12545.0i | −0.308452 | + | 0.534255i | ||||
\(821\) | −32343.5 | − | 11772.1i | −1.37490 | − | 0.500424i | −0.454274 | − | 0.890862i | \(-0.650101\pi\) |
−0.920629 | + | 0.390438i | \(0.872323\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14548.9 | + | 12208.0i | 0.616212 | + | 0.517063i | 0.896610 | − | 0.442821i | \(-0.146022\pi\) |
−0.280399 | + | 0.959884i | \(0.590467\pi\) | |||||||
\(824\) | −4106.56 | − | 3445.81i | −0.173615 | − | 0.145680i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7921.12 | − | 2883.05i | −0.333669 | − | 0.121446i | ||||
\(827\) | 2770.81 | − | 4799.19i | 0.116506 | − | 0.201795i | −0.801875 | − | 0.597492i | \(-0.796164\pi\) |
0.918381 | + | 0.395698i | \(0.129497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21645.5 | − | 37491.1i | −0.906850 | − | 1.57071i | −0.818414 | − | 0.574628i | \(-0.805147\pi\) |
−0.0884355 | − | 0.996082i | \(-0.528187\pi\) | |||||||
\(830\) | 3677.27 | + | 20854.8i | 0.153783 | + | 0.872147i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4212.65 | + | 1533.28i | −0.175538 | + | 0.0638905i | ||||
\(833\) | 5027.43 | − | 28512.0i | 0.209112 | − | 1.18593i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5336.85 | + | 4478.15i | −0.221185 | + | 0.185596i | ||||
\(836\) | 12483.5 | 0.516448 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8946.41 | 0.368793 | ||||||||
\(839\) | 18955.6 | − | 15905.7i | 0.780002 | − | 0.654499i | −0.163247 | − | 0.986585i | \(-0.552197\pi\) |
0.943249 | + | 0.332086i | \(0.107752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3632.53 | + | 20601.1i | −0.148941 | + | 0.844689i | ||||
\(842\) | 26090.5 | − | 9496.17i | 1.06786 | − | 0.388669i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2047.12 | − | 11609.8i | −0.0834889 | − | 0.473489i | ||||
\(845\) | 3626.13 | + | 6280.64i | 0.147624 | + | 0.255693i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4396.62 | − | 7615.18i | 0.178359 | − | 0.308926i | ||||
\(848\) | −29412.7 | − | 10705.3i | −1.19108 | − | 0.433518i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1026.41 | + | 861.264i | 0.0414185 | + | 0.0347543i | ||||
\(851\) | 1663.70 | + | 1396.01i | 0.0670165 | + | 0.0562335i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24373.5 | + | 8871.21i | 0.978349 | + | 0.356090i | 0.781198 | − | 0.624283i | \(-0.214609\pi\) |
0.197151 | + | 0.980373i | \(0.436831\pi\) | |||||||
\(854\) | 1268.81 | − | 2197.64i | 0.0508404 | − | 0.0880582i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7856.91 | − | 13608.6i | −0.313719 | − | 0.543378i | ||||
\(857\) | −1686.17 | − | 9562.75i | −0.0672094 | − | 0.381164i | −0.999796 | − | 0.0202163i | \(-0.993565\pi\) |
0.932586 | − | 0.360947i | \(-0.117547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8650.88 | + | 3148.66i | −0.343614 | + | 0.125065i | −0.508062 | − | 0.861321i | \(-0.669638\pi\) |
0.164448 | + | 0.986386i | \(0.447416\pi\) | |||||||
\(860\) | 3279.65 | − | 18599.8i | 0.130041 | − | 0.737498i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27514.2 | + | 23087.2i | −1.08717 | + | 0.912241i | ||||
\(863\) | −13248.8 | −0.522590 | −0.261295 | − | 0.965259i | \(-0.584150\pi\) | ||||
−0.261295 | + | 0.965259i | \(0.584150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18656.9 | −0.733356 | ||||||||
\(866\) | −40669.6 | + | 34125.9i | −1.59585 | + | 1.33908i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 931.788 | − | 5284.43i | 0.0364366 | − | 0.206642i | ||||
\(869\) | 19702.9 | − | 7171.28i | 0.769133 | − | 0.279941i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3705.37 | − | 21014.2i | −0.144146 | − | 0.817495i | ||||
\(872\) | 67.1800 | + | 116.359i | 0.00260895 | + | 0.00451883i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2315.62 | − | 4010.78i | 0.0896192 | − | 0.155225i | ||||
\(875\) | −5883.22 | − | 2141.32i | −0.227302 | − | 0.0827312i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28936.2 | − | 24280.3i | −1.11415 | − | 0.934879i | −0.115851 | − | 0.993267i | \(-0.536960\pi\) |
−0.998294 | + | 0.0583879i | \(0.981404\pi\) | |||||||
\(878\) | 37232.8 | + | 31242.1i | 1.43115 | + | 1.20088i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −47544.8 | − | 17304.9i | −1.82129 | − | 0.662895i | ||||
\(881\) | −2464.91 | + | 4269.35i | −0.0942622 | + | 0.163267i | −0.909300 | − | 0.416140i | \(-0.863383\pi\) |
0.815038 | + | 0.579407i | \(0.196716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10096.6 | + | 17487.8i | 0.384799 | + | 0.666492i | 0.991741 | − | 0.128254i | \(-0.0409374\pi\) |
−0.606942 | + | 0.794746i | \(0.707604\pi\) | |||||||
\(884\) | −2220.83 | − | 12594.9i | −0.0844960 | − | 0.479201i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33645.0 | − | 12245.8i | 1.27576 | − | 0.464340i | ||||
\(887\) | 6549.95 | − | 37146.6i | 0.247943 | − | 1.40616i | −0.565614 | − | 0.824670i | \(-0.691361\pi\) |
0.813557 | − | 0.581486i | \(-0.197528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4181.65 | − | 3508.82i | 0.157759 | − | 0.132376i | ||||
\(890\) | 14063.1 | 0.529658 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7199.09 | 0.270228 | ||||||||
\(893\) | 10769.7 | − | 9036.86i | 0.403578 | − | 0.338642i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1237.07 | + | 7015.78i | −0.0462019 | + | 0.262024i | ||||
\(896\) | 6707.75 | − | 2441.42i | 0.250101 | − | 0.0910292i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6154.15 | − | 34901.9i | −0.228693 | − | 1.29698i | ||||
\(899\) | 9837.21 | + | 17038.6i | 0.364949 | + | 0.632111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17530.4 | + | 30363.5i | −0.648193 | + | 1.12270i | ||||
\(902\) | 66905.8 | + | 24351.7i | 2.46976 | + | 0.898918i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2289.91 | − | 1921.46i | −0.0842493 | − | 0.0706936i | ||||
\(905\) | 30900.8 | + | 25928.9i | 1.13500 | + | 0.952382i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17188.1 | + | 6255.97i | 0.629242 | + | 0.229025i | 0.636902 | − | 0.770945i | \(-0.280216\pi\) |
−0.00765914 | + | 0.999971i | \(0.502438\pi\) | |||||||
\(908\) | 2874.30 | − | 4978.44i | 0.105052 | − | 0.181955i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3236.60 | + | 5605.95i | 0.117903 | + | 0.204215i | ||||
\(911\) | −4666.46 | − | 26464.8i | −0.169711 | − | 0.962478i | −0.944073 | − | 0.329736i | \(-0.893040\pi\) |
0.774362 | − | 0.632742i | \(-0.218071\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30623.9 | − | 11146.2i | 1.11008 | − | 0.404036i | ||||
\(914\) | 324.741 | − | 1841.70i | 0.0117522 | − | 0.0666499i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18072.3 | − | 15164.5i | 0.651883 | − | 0.546995i | ||||
\(917\) | 2891.48 | 0.104128 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12622.5 | −0.453078 | −0.226539 | − | 0.974002i | \(-0.572741\pi\) | ||||
−0.226539 | + | 0.974002i | \(0.572741\pi\) | |||||||
\(920\) | −2857.83 | + | 2398.01i | −0.102413 | + | 0.0859347i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6507.15 | − | 36903.9i | 0.232431 | − | 1.31818i | ||||
\(923\) | 7150.45 | − | 2602.55i | 0.254994 | − | 0.0928104i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −72.3820 | − | 410.498i | −0.00257287 | − | 0.0145915i | ||||
\(926\) | −16635.9 | − | 28814.3i | −0.590379 | − | 1.02257i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4527.95 | − | 7842.64i | 0.160170 | − | 0.277422i | ||||
\(929\) | −10067.6 | − | 3664.31i | −0.355552 | − | 0.129410i | 0.158068 | − | 0.987428i | \(-0.449474\pi\) |
−0.513620 | + | 0.858018i | \(0.671696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14712.8 | + | 12345.5i | 0.517931 | + | 0.434596i | ||||
\(932\) | −7195.61 | − | 6037.84i | −0.252897 | − | 0.212206i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 48495.6 | + | 17651.0i | 1.69896 | + | 0.618370i | ||||
\(935\) | −28337.4 | + | 49081.8i | −0.991156 | + | 1.71673i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8051.62 | − | 13945.8i | −0.280720 | − | 0.486222i | 0.690842 | − | 0.723006i | \(-0.257240\pi\) |
−0.971562 | + | 0.236784i | \(0.923907\pi\) | |||||||
\(938\) | 1421.29 | + | 8060.52i | 0.0494741 | + | 0.280581i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8913.63 | − | 3244.29i | 0.309288 | − | 0.112572i | ||||
\(941\) | −3865.23 | + | 21920.8i | −0.133903 | + | 0.759402i | 0.841714 | + | 0.539923i | \(0.181547\pi\) |
−0.975617 | + | 0.219479i | \(0.929564\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6335.40 | − | 5316.03i | 0.218779 | − | 0.183578i | ||||
\(944\) | 44779.0 | 1.54389 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −92831.8 | −3.19051 | ||||||||
\(947\) | 35997.5 | − | 30205.5i | 1.23523 | − | 1.03648i | 0.237346 | − | 0.971425i | \(-0.423722\pi\) |
0.997882 | − | 0.0650540i | \(-0.0207220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1098.18 | − | 6228.08i | 0.0375642 | − | 0.213037i | ||||
\(950\) | −835.260 | + | 304.010i | −0.0285257 | + | 0.0103825i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1017.02 | − | 5767.83i | −0.0346239 | − | 0.196362i | ||||
\(953\) | −562.035 | − | 973.474i | −0.0191040 | − | 0.0330891i | 0.856315 | − | 0.516453i | \(-0.172748\pi\) |
−0.875419 | + | 0.483364i | \(0.839415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9490.67 | + | 16438.3i | −0.321582 | + | 0.556996i | ||||
\(956\) | −519.188 | − | 188.969i | −0.0175646 | − | 0.00639299i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7552.43 | + | 6337.24i | 0.254705 | + | 0.213723i | ||||
\(959\) | −167.093 | − | 140.208i | −0.00562640 | − | 0.00472111i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −76827.3 | − | 27962.8i | −2.57887 | − | 0.938634i | ||||
\(962\) | −6353.69 | + | 11004.9i | −0.212943 | + | 0.368828i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10453.2 | − | 18105.4i | −0.349247 | − | 0.604914i | ||||
\(965\) | 2072.19 | + | 11752.0i | 0.0691256 | + | 0.392031i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43890.4 | + | 15974.8i | −1.45959 | + | 0.531246i | −0.945251 | − | 0.326344i | \(-0.894183\pi\) |
−0.514335 | + | 0.857590i | \(0.671961\pi\) | |||||||
\(968\) | −5148.93 | + | 29201.0i | −0.170964 | + | 0.969584i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16747.4 | + | 14052.8i | −0.554359 | + | 0.465162i | ||||
\(971\) | 43151.1 | 1.42614 | 0.713071 | − | 0.701091i | \(-0.247304\pi\) | ||||
0.713071 | + | 0.701091i | \(0.247304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8821.82 | −0.290662 | ||||||||
\(974\) | 39792.2 | − | 33389.6i | 1.30906 | − | 1.09843i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2340.83 | + | 13275.5i | −0.0767706 | + | 0.435388i | ||||
\(977\) | −494.587 | + | 180.015i | −0.0161957 | + | 0.00589476i | −0.350105 | − | 0.936710i | \(-0.613854\pi\) |
0.333910 | + | 0.942605i | \(0.391632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3758.11 | − | 21313.3i | −0.122686 | − | 0.695788i | ||||
\(980\) | 6479.34 | + | 11222.5i | 0.211199 | + | 0.365807i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4787.78 | − | 8292.67i | 0.155585 | − | 0.269480i | ||||
\(983\) | 1361.23 | + | 495.447i | 0.0441674 | + | 0.0160756i | 0.364009 | − | 0.931395i | \(-0.381408\pi\) |
−0.319842 | + | 0.947471i | \(0.603630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30366.8 | + | 25480.8i | 0.982302 | + | 0.824249i | ||||
\(986\) | −13778.6 | − | 11561.6i | −0.445030 | − | 0.373425i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7972.55 | + | 2901.77i | 0.256721 | + | 0.0934389i | ||||
\(989\) | −5391.48 | + | 9338.32i | −0.173346 | + | 0.300244i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22811.2 | + | 39510.2i | 0.731203 | + | 1.26648i | 0.956369 | + | 0.292161i | \(0.0943743\pi\) |
−0.225166 | + | 0.974320i | \(0.572292\pi\) | |||||||
\(992\) | 8915.90 | + | 50564.6i | 0.285363 | + | 1.61837i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2742.74 | + | 998.274i | −0.0875194 | + | 0.0318545i | ||||
\(995\) | 2770.49 | − | 15712.2i | 0.0882717 | − | 0.500614i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17564.5 | − | 14738.4i | 0.557948 | − | 0.468174i | −0.319673 | − | 0.947528i | \(-0.603573\pi\) |
0.877622 | + | 0.479353i | \(0.159129\pi\) | |||||||
\(998\) | 16833.7 | 0.533929 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 243.4.e.b.109.7 | 48 | ||
3.2 | odd | 2 | 243.4.e.c.109.2 | 48 | |||
9.2 | odd | 6 | 243.4.e.d.190.7 | 48 | |||
9.4 | even | 3 | 81.4.e.a.10.7 | 48 | |||
9.5 | odd | 6 | 27.4.e.a.13.2 | ✓ | 48 | ||
9.7 | even | 3 | 243.4.e.a.190.2 | 48 | |||
27.2 | odd | 18 | 243.4.e.d.55.7 | 48 | |||
27.4 | even | 9 | 729.4.a.c.1.19 | 24 | |||
27.7 | even | 9 | 81.4.e.a.73.7 | 48 | |||
27.11 | odd | 18 | 243.4.e.c.136.2 | 48 | |||
27.16 | even | 9 | inner | 243.4.e.b.136.7 | 48 | ||
27.20 | odd | 18 | 27.4.e.a.25.2 | yes | 48 | ||
27.23 | odd | 18 | 729.4.a.d.1.6 | 24 | |||
27.25 | even | 9 | 243.4.e.a.55.2 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.4.e.a.13.2 | ✓ | 48 | 9.5 | odd | 6 | ||
27.4.e.a.25.2 | yes | 48 | 27.20 | odd | 18 | ||
81.4.e.a.10.7 | 48 | 9.4 | even | 3 | |||
81.4.e.a.73.7 | 48 | 27.7 | even | 9 | |||
243.4.e.a.55.2 | 48 | 27.25 | even | 9 | |||
243.4.e.a.190.2 | 48 | 9.7 | even | 3 | |||
243.4.e.b.109.7 | 48 | 1.1 | even | 1 | trivial | ||
243.4.e.b.136.7 | 48 | 27.16 | even | 9 | inner | ||
243.4.e.c.109.2 | 48 | 3.2 | odd | 2 | |||
243.4.e.c.136.2 | 48 | 27.11 | odd | 18 | |||
243.4.e.d.55.7 | 48 | 27.2 | odd | 18 | |||
243.4.e.d.190.7 | 48 | 9.2 | odd | 6 | |||
729.4.a.c.1.19 | 24 | 27.4 | even | 9 | |||
729.4.a.d.1.6 | 24 | 27.23 | odd | 18 |