Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,4,Mod(314,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.314");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.g (of order \(2\), degree \(1\), 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: | \(18.5856016518\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 314.30 | ||
Character | \(\chi\) | \(=\) | 315.314 |
Dual form | 315.4.g.a.314.31 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41590 | 0.500595 | 0.250298 | − | 0.968169i | \(-0.419472\pi\) | ||||
0.250298 | + | 0.968169i | \(0.419472\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.99524 | −0.749405 | ||||||||
\(5\) | −2.48890 | − | 10.8998i | −0.222614 | − | 0.974907i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.69164 | + | 17.6240i | 0.307320 | + | 0.951606i | ||||
\(8\) | −19.8158 | −0.875743 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.52402 | − | 15.4330i | −0.111439 | − | 0.488034i | ||||
\(11\) | − | 30.5871i | − | 0.838397i | −0.907895 | − | 0.419198i | \(-0.862311\pi\) | ||
0.907895 | − | 0.419198i | \(-0.137689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.5994 | 0.354142 | 0.177071 | − | 0.984198i | \(-0.443338\pi\) | ||||
0.177071 | + | 0.984198i | \(0.443338\pi\) | |||||||
\(14\) | 8.05877 | + | 24.9538i | 0.153843 | + | 0.476369i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 19.9047 | 0.311012 | ||||||||
\(17\) | 81.3047i | 1.15996i | 0.814632 | + | 0.579979i | \(0.196939\pi\) | ||||
−0.814632 | + | 0.579979i | \(0.803061\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 87.9721i | 1.06222i | 0.847303 | + | 0.531110i | \(0.178225\pi\) | ||||
−0.847303 | + | 0.531110i | \(0.821775\pi\) | |||||||
\(20\) | 14.9215 | + | 65.3468i | 0.166828 | + | 0.730600i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 43.3082i | − | 0.419697i | ||||||
\(23\) | −51.9402 | −0.470882 | −0.235441 | − | 0.971889i | \(-0.575653\pi\) | ||||
−0.235441 | + | 0.971889i | \(0.575653\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −112.611 | + | 54.2569i | −0.900886 | + | 0.434055i | ||||
\(26\) | 23.5030 | 0.177282 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −34.1227 | − | 105.660i | −0.230307 | − | 0.713138i | ||||
\(29\) | 160.205i | 1.02584i | 0.858437 | + | 0.512919i | \(0.171436\pi\) | ||||
−0.858437 | + | 0.512919i | \(0.828564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 306.111i | 1.77352i | 0.462226 | + | 0.886762i | \(0.347051\pi\) | ||||
−0.462226 | + | 0.886762i | \(0.652949\pi\) | |||||||
\(32\) | 186.710 | 1.03143 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 115.119i | 0.580669i | ||||||||
\(35\) | 177.932 | − | 105.902i | 0.859314 | − | 0.511449i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 104.929i | − | 0.466221i | −0.972450 | − | 0.233111i | \(-0.925110\pi\) | ||
0.972450 | − | 0.233111i | \(-0.0748904\pi\) | |||||||
\(38\) | 124.559i | 0.531742i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 49.3195 | + | 215.988i | 0.194952 | + | 0.853768i | ||||
\(41\) | 477.920 | 1.82045 | 0.910227 | − | 0.414110i | \(-0.135907\pi\) | ||||
0.910227 | + | 0.414110i | \(0.135907\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 265.819i | 0.942720i | 0.881941 | + | 0.471360i | \(0.156237\pi\) | ||||
−0.881941 | + | 0.471360i | \(0.843763\pi\) | |||||||
\(44\) | 183.377i | 0.628298i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −73.5419 | −0.235721 | ||||||||
\(47\) | − | 140.739i | − | 0.436785i | −0.975861 | − | 0.218393i | \(-0.929919\pi\) | ||
0.975861 | − | 0.218393i | \(-0.0700813\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −278.210 | + | 200.619i | −0.811109 | + | 0.584895i | ||||
\(50\) | −159.445 | + | 76.8222i | −0.450979 | + | 0.217286i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −99.5173 | −0.265396 | ||||||||
\(53\) | −305.963 | −0.792966 | −0.396483 | − | 0.918042i | \(-0.629769\pi\) | ||||
−0.396483 | + | 0.918042i | \(0.629769\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −333.393 | + | 76.1282i | −0.817358 | + | 0.186639i | ||||
\(56\) | −112.784 | − | 349.234i | −0.269133 | − | 0.833363i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 226.833i | 0.513529i | ||||||||
\(59\) | 134.064 | 0.295825 | 0.147912 | − | 0.989000i | \(-0.452745\pi\) | ||||
0.147912 | + | 0.989000i | \(0.452745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 303.805i | 0.637676i | 0.947809 | + | 0.318838i | \(0.103293\pi\) | ||||
−0.947809 | + | 0.318838i | \(0.896707\pi\) | |||||||
\(62\) | 433.422i | 0.887817i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 105.123 | 0.205319 | ||||||||
\(65\) | −41.3142 | − | 180.930i | −0.0788368 | − | 0.345255i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 671.592i | − | 1.22460i | −0.790626 | − | 0.612299i | \(-0.790245\pi\) | ||
0.790626 | − | 0.612299i | \(-0.209755\pi\) | |||||||
\(68\) | − | 487.441i | − | 0.869277i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 251.933 | − | 149.946i | 0.430168 | − | 0.256029i | ||||
\(71\) | 616.486i | 1.03047i | 0.857049 | + | 0.515236i | \(0.172296\pi\) | ||||
−0.857049 | + | 0.515236i | \(0.827704\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1021.48 | −1.63774 | −0.818871 | − | 0.573977i | \(-0.805400\pi\) | ||||
−0.818871 | + | 0.573977i | \(0.805400\pi\) | |||||||
\(74\) | − | 148.568i | − | 0.233388i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 527.413i | − | 0.796033i | ||||||
\(77\) | 539.067 | − | 174.091i | 0.797823 | − | 0.257656i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −558.731 | −0.795723 | −0.397862 | − | 0.917445i | \(-0.630248\pi\) | ||||
−0.397862 | + | 0.917445i | \(0.630248\pi\) | |||||||
\(80\) | −49.5409 | − | 216.958i | −0.0692355 | − | 0.303207i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 676.686 | 0.911310 | ||||||||
\(83\) | − | 335.471i | − | 0.443648i | −0.975087 | − | 0.221824i | \(-0.928799\pi\) | ||
0.975087 | − | 0.221824i | \(-0.0712010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 886.204 | − | 202.359i | 1.13085 | − | 0.258222i | ||||
\(86\) | 376.372i | 0.471921i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 606.108i | 0.734220i | ||||||||
\(89\) | 931.364 | 1.10926 | 0.554632 | − | 0.832096i | \(-0.312859\pi\) | ||||
0.554632 | + | 0.832096i | \(0.312859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 94.4778 | + | 292.548i | 0.108835 | + | 0.337004i | ||||
\(92\) | 311.394 | 0.352881 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 199.272i | − | 0.218653i | ||||||
\(95\) | 958.877 | − | 218.953i | 1.03557 | − | 0.236465i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −772.248 | −0.808350 | −0.404175 | − | 0.914682i | \(-0.632441\pi\) | ||||
−0.404175 | + | 0.914682i | \(0.632441\pi\) | |||||||
\(98\) | −393.917 | + | 284.056i | −0.406037 | + | 0.292795i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 675.128 | − | 325.283i | 0.675128 | − | 0.325283i | ||||
\(101\) | −889.653 | −0.876473 | −0.438237 | − | 0.898860i | \(-0.644397\pi\) | ||||
−0.438237 | + | 0.898860i | \(0.644397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1586.47 | 1.51766 | 0.758831 | − | 0.651288i | \(-0.225771\pi\) | ||||
0.758831 | + | 0.651288i | \(0.225771\pi\) | |||||||
\(104\) | −328.931 | −0.310137 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −433.211 | −0.396955 | ||||||||
\(107\) | 767.328 | 0.693275 | 0.346638 | − | 0.937999i | \(-0.387323\pi\) | ||||
0.346638 | + | 0.937999i | \(0.387323\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −814.720 | −0.715927 | −0.357963 | − | 0.933736i | \(-0.616529\pi\) | ||||
−0.357963 | + | 0.933736i | \(0.616529\pi\) | |||||||
\(110\) | −472.050 | + | 107.790i | −0.409166 | + | 0.0934303i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 113.291 | + | 350.801i | 0.0955800 | + | 0.295961i | ||||
\(113\) | −1649.68 | −1.37335 | −0.686676 | − | 0.726964i | \(-0.740931\pi\) | ||||
−0.686676 | + | 0.726964i | \(0.740931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 129.274 | + | 566.137i | 0.104825 | + | 0.459066i | ||||
\(116\) | − | 960.466i | − | 0.768767i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 189.821 | 0.148088 | ||||||||
\(119\) | −1432.91 | + | 462.757i | −1.10382 | + | 0.356478i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 395.428 | 0.297091 | ||||||||
\(122\) | 430.156i | 0.319217i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 1835.21i | − | 1.32909i | ||||||
\(125\) | 871.665 | + | 1092.39i | 0.623713 | + | 0.781654i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 173.846i | − | 0.121467i | −0.998154 | − | 0.0607337i | \(-0.980656\pi\) | ||
0.998154 | − | 0.0607337i | \(-0.0193440\pi\) | |||||||
\(128\) | −1344.83 | −0.928652 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −58.4966 | − | 256.178i | −0.0394653 | − | 0.172833i | ||||
\(131\) | 468.800 | 0.312666 | 0.156333 | − | 0.987704i | \(-0.450033\pi\) | ||||
0.156333 | + | 0.987704i | \(0.450033\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1550.42 | + | 500.705i | −1.01082 | + | 0.326441i | ||||
\(134\) | − | 950.906i | − | 0.613028i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 1611.12i | − | 1.01583i | ||||||
\(137\) | −1374.98 | −0.857463 | −0.428731 | − | 0.903432i | \(-0.641039\pi\) | ||||
−0.428731 | + | 0.903432i | \(0.641039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1723.01i | − | 1.05140i | −0.850671 | − | 0.525698i | \(-0.823804\pi\) | ||
0.850671 | − | 0.525698i | \(-0.176196\pi\) | |||||||
\(140\) | −1066.74 | + | 634.907i | −0.643974 | + | 0.383282i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 872.881i | 0.515849i | ||||||||
\(143\) | − | 507.728i | − | 0.296911i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1746.20 | − | 398.733i | 1.00010 | − | 0.228365i | ||||
\(146\) | −1446.31 | −0.819846 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 629.073i | 0.349388i | ||||||||
\(149\) | − | 621.643i | − | 0.341792i | −0.985289 | − | 0.170896i | \(-0.945334\pi\) | ||
0.985289 | − | 0.170896i | \(-0.0546662\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2791.64 | 1.50451 | 0.752253 | − | 0.658874i | \(-0.228967\pi\) | ||||
0.752253 | + | 0.658874i | \(0.228967\pi\) | |||||||
\(152\) | − | 1743.24i | − | 0.930232i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 763.263 | − | 246.495i | 0.399387 | − | 0.128981i | ||||
\(155\) | 3336.55 | − | 761.880i | 1.72902 | − | 0.394811i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1735.14 | 0.882034 | 0.441017 | − | 0.897499i | \(-0.354618\pi\) | ||||
0.441017 | + | 0.897499i | \(0.354618\pi\) | |||||||
\(158\) | −791.105 | −0.398335 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −464.701 | − | 2035.09i | −0.229611 | − | 1.00555i | ||||
\(161\) | −295.625 | − | 915.393i | −0.144711 | − | 0.448094i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 995.750i | 0.478486i | 0.970960 | + | 0.239243i | \(0.0768992\pi\) | ||||
−0.970960 | + | 0.239243i | \(0.923101\pi\) | |||||||
\(164\) | −2865.25 | −1.36426 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 474.993i | − | 0.222088i | ||||||
\(167\) | 1877.32i | 0.869888i | 0.900457 | + | 0.434944i | \(0.143232\pi\) | ||||
−0.900457 | + | 0.434944i | \(0.856768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1921.46 | −0.874584 | ||||||||
\(170\) | 1254.77 | − | 286.519i | 0.566098 | − | 0.129265i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1593.64i | − | 0.706478i | ||||||
\(173\) | − | 2654.34i | − | 1.16651i | −0.812291 | − | 0.583253i | \(-0.801780\pi\) | ||
0.812291 | − | 0.583253i | \(-0.198220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1597.16 | − | 1675.84i | −0.689910 | − | 0.723895i | ||||
\(176\) | − | 608.829i | − | 0.260751i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1318.72 | 0.555292 | ||||||||
\(179\) | 4472.92i | 1.86772i | 0.357642 | + | 0.933859i | \(0.383581\pi\) | ||||
−0.357642 | + | 0.933859i | \(0.616419\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 396.033i | − | 0.162635i | −0.996688 | − | 0.0813173i | \(-0.974087\pi\) | ||
0.996688 | − | 0.0813173i | \(-0.0259127\pi\) | |||||||
\(182\) | 133.771 | + | 414.217i | 0.0544821 | + | 0.168702i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1029.24 | 0.412371 | ||||||||
\(185\) | −1143.70 | + | 261.157i | −0.454522 | + | 0.103787i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2486.87 | 0.972504 | ||||||||
\(188\) | 843.764i | 0.327329i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1357.67 | − | 310.015i | 0.518399 | − | 0.118373i | ||||
\(191\) | − | 1297.93i | − | 0.491702i | −0.969308 | − | 0.245851i | \(-0.920933\pi\) | ||
0.969308 | − | 0.245851i | \(-0.0790673\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4471.94i | 1.66786i | 0.551868 | + | 0.833931i | \(0.313915\pi\) | ||||
−0.551868 | + | 0.833931i | \(0.686085\pi\) | |||||||
\(194\) | −1093.42 | −0.404656 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1667.94 | − | 1202.76i | 0.607849 | − | 0.438323i | ||||
\(197\) | −21.6839 | −0.00784220 | −0.00392110 | − | 0.999992i | \(-0.501248\pi\) | ||||
−0.00392110 | + | 0.999992i | \(0.501248\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1699.27i | 0.605316i | 0.953099 | + | 0.302658i | \(0.0978740\pi\) | ||||
−0.953099 | + | 0.302658i | \(0.902126\pi\) | |||||||
\(200\) | 2231.47 | − | 1075.14i | 0.788945 | − | 0.380121i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1259.66 | −0.438758 | ||||||||
\(203\) | −2823.45 | + | 911.828i | −0.976193 | + | 0.315260i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1189.49 | − | 5209.23i | −0.405258 | − | 1.77477i | ||||
\(206\) | 2246.27 | 0.759734 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 330.407 | 0.110142 | ||||||||
\(209\) | 2690.81 | 0.890562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1882.71 | −0.614269 | −0.307135 | − | 0.951666i | \(-0.599370\pi\) | ||||
−0.307135 | + | 0.951666i | \(0.599370\pi\) | |||||||
\(212\) | 1834.32 | 0.594252 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1086.46 | 0.347050 | ||||||||
\(215\) | 2897.37 | − | 661.595i | 0.919064 | − | 0.209862i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5394.91 | + | 1742.28i | −1.68770 | + | 0.545039i | ||||
\(218\) | −1153.56 | −0.358389 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1998.77 | − | 456.406i | 0.612532 | − | 0.139868i | ||||
\(221\) | 1349.61i | 0.410790i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5818.27 | −1.74717 | −0.873587 | − | 0.486668i | \(-0.838212\pi\) | ||||
−0.873587 | + | 0.486668i | \(0.838212\pi\) | |||||||
\(224\) | 1062.68 | + | 3290.57i | 0.316980 | + | 0.981519i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2335.77 | −0.687493 | ||||||||
\(227\) | − | 2706.94i | − | 0.791480i | −0.918363 | − | 0.395740i | \(-0.870488\pi\) | ||
0.918363 | − | 0.395740i | \(-0.129512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6228.53i | 1.79735i | 0.438616 | + | 0.898674i | \(0.355469\pi\) | ||||
−0.438616 | + | 0.898674i | \(0.644531\pi\) | |||||||
\(230\) | 183.038 | + | 801.592i | 0.0524747 | + | 0.229806i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 3174.59i | − | 0.898370i | ||||||
\(233\) | −4128.59 | −1.16083 | −0.580414 | − | 0.814322i | \(-0.697109\pi\) | ||||
−0.580414 | + | 0.814322i | \(0.697109\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1534.03 | + | 350.285i | −0.425825 | + | 0.0972344i | ||||
\(236\) | −803.746 | −0.221692 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2028.86 | + | 655.216i | −0.552568 | + | 0.178451i | ||||
\(239\) | − | 4645.24i | − | 1.25722i | −0.777721 | − | 0.628610i | \(-0.783624\pi\) | ||
0.777721 | − | 0.628610i | \(-0.216376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6926.50i | 1.85135i | 0.378320 | + | 0.925675i | \(0.376502\pi\) | ||||
−0.378320 | + | 0.925675i | \(0.623498\pi\) | |||||||
\(242\) | 559.886 | 0.148722 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1821.38i | − | 0.477877i | ||||||
\(245\) | 2879.14 | + | 2533.12i | 0.750782 | + | 0.660550i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1460.28i | 0.376177i | ||||||||
\(248\) | − | 6065.85i | − | 1.55315i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1234.19 | + | 1546.72i | 0.312228 | + | 0.391292i | ||||
\(251\) | 5572.63 | 1.40136 | 0.700680 | − | 0.713476i | \(-0.252880\pi\) | ||||
0.700680 | + | 0.713476i | \(0.252880\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1588.70i | 0.394785i | ||||||||
\(254\) | − | 246.148i | − | 0.0608060i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2745.13 | −0.670198 | ||||||||
\(257\) | − | 2220.94i | − | 0.539060i | −0.962992 | − | 0.269530i | \(-0.913132\pi\) | ||
0.962992 | − | 0.269530i | \(-0.0868683\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1849.26 | − | 597.217i | 0.443659 | − | 0.143279i | ||||
\(260\) | 247.688 | + | 1084.72i | 0.0590807 | + | 0.258736i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 663.772 | 0.156519 | ||||||||
\(263\) | −4665.04 | −1.09376 | −0.546880 | − | 0.837211i | \(-0.684184\pi\) | ||||
−0.546880 | + | 0.837211i | \(0.684184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 761.509 | + | 3334.93i | 0.176525 | + | 0.773068i | ||||
\(266\) | −2195.23 | + | 708.947i | −0.506009 | + | 0.163415i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4026.36i | 0.917719i | ||||||||
\(269\) | 4373.91 | 0.991384 | 0.495692 | − | 0.868498i | \(-0.334915\pi\) | ||||
0.495692 | + | 0.868498i | \(0.334915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1610.82i | 0.361071i | 0.983568 | + | 0.180535i | \(0.0577830\pi\) | ||||
−0.983568 | + | 0.180535i | \(0.942217\pi\) | |||||||
\(272\) | 1618.35i | 0.360760i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1946.83 | −0.429242 | ||||||||
\(275\) | 1659.56 | + | 3444.44i | 0.363910 | + | 0.755300i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4785.35i | − | 1.03799i | −0.854777 | − | 0.518996i | \(-0.826306\pi\) | ||
0.854777 | − | 0.518996i | \(-0.173694\pi\) | |||||||
\(278\) | − | 2439.61i | − | 0.526324i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3525.87 | + | 2098.53i | −0.752538 | + | 0.447898i | ||||
\(281\) | 4559.34i | 0.967927i | 0.875088 | + | 0.483964i | \(0.160803\pi\) | ||||
−0.875088 | + | 0.483964i | \(0.839197\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3503.70 | 0.735949 | 0.367975 | − | 0.929836i | \(-0.380051\pi\) | ||||
0.367975 | + | 0.929836i | \(0.380051\pi\) | |||||||
\(284\) | − | 3695.98i | − | 0.772240i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 718.890i | − | 0.148632i | ||||||
\(287\) | 2720.15 | + | 8422.87i | 0.559461 | + | 1.73236i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1697.45 | −0.345501 | ||||||||
\(290\) | 2472.44 | − | 564.565i | 0.500643 | − | 0.114319i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6124.02 | 1.22733 | ||||||||
\(293\) | 5727.17i | 1.14193i | 0.820975 | + | 0.570964i | \(0.193431\pi\) | ||||
−0.820975 | + | 0.570964i | \(0.806569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −333.672 | − | 1461.27i | −0.0658546 | − | 0.288401i | ||||
\(296\) | 2079.25i | 0.408290i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 880.182i | − | 0.171099i | ||||||
\(299\) | −862.176 | −0.166759 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4684.78 | + | 1512.94i | −0.897098 | + | 0.289716i | ||||
\(302\) | 3952.67 | 0.753149 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1751.06i | 0.330363i | ||||||||
\(305\) | 3311.41 | − | 756.139i | 0.621674 | − | 0.141955i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1876.50 | −0.348852 | −0.174426 | − | 0.984670i | \(-0.555807\pi\) | ||||
−0.174426 | + | 0.984670i | \(0.555807\pi\) | |||||||
\(308\) | −3231.84 | + | 1043.72i | −0.597893 | + | 0.193088i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4724.21 | − | 1078.74i | 0.865539 | − | 0.197640i | ||||
\(311\) | −4517.34 | −0.823650 | −0.411825 | − | 0.911263i | \(-0.635108\pi\) | ||||
−0.411825 | + | 0.911263i | \(0.635108\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7150.40 | 1.29126 | 0.645630 | − | 0.763650i | \(-0.276595\pi\) | ||||
0.645630 | + | 0.763650i | \(0.276595\pi\) | |||||||
\(314\) | 2456.78 | 0.441542 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3349.72 | 0.596318 | ||||||||
\(317\) | 4062.32 | 0.719756 | 0.359878 | − | 0.932999i | \(-0.382818\pi\) | ||||
0.359878 | + | 0.932999i | \(0.382818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4900.20 | 0.860059 | ||||||||
\(320\) | −261.641 | − | 1145.82i | −0.0457069 | − | 0.200167i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −418.574 | − | 1296.10i | −0.0724417 | − | 0.224314i | ||||
\(323\) | −7152.54 | −1.23213 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1869.27 | + | 900.632i | −0.319042 | + | 0.153717i | ||||
\(326\) | 1409.88i | 0.239528i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9470.38 | −1.59425 | ||||||||
\(329\) | 2480.39 | − | 801.036i | 0.415648 | − | 0.134233i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −868.986 | −0.144301 | −0.0721507 | − | 0.997394i | \(-0.522986\pi\) | ||||
−0.0721507 | + | 0.997394i | \(0.522986\pi\) | |||||||
\(332\) | 2011.23i | 0.332472i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2658.09i | 0.435462i | ||||||||
\(335\) | −7320.22 | + | 1671.52i | −1.19387 | + | 0.272612i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1287.31i | 0.208083i | 0.994573 | + | 0.104042i | \(0.0331775\pi\) | ||||
−0.994573 | + | 0.104042i | \(0.966823\pi\) | |||||||
\(338\) | −2720.59 | −0.437812 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5313.00 | + | 1213.19i | −0.847464 | + | 0.193513i | ||||
\(341\) | 9363.07 | 1.48692 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5119.18 | − | 3761.33i | −0.805859 | − | 0.592107i | ||||
\(344\) | − | 5267.41i | − | 0.825580i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 3758.27i | − | 0.583947i | ||||||
\(347\) | −422.265 | −0.0653268 | −0.0326634 | − | 0.999466i | \(-0.510399\pi\) | ||||
−0.0326634 | + | 0.999466i | \(0.510399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4640.81i | 0.711797i | 0.934525 | + | 0.355898i | \(0.115825\pi\) | ||||
−0.934525 | + | 0.355898i | \(0.884175\pi\) | |||||||
\(350\) | −2261.42 | − | 2372.82i | −0.345365 | − | 0.362379i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 5710.91i | − | 0.864751i | ||||||
\(353\) | − | 1539.01i | − | 0.232048i | −0.993246 | − | 0.116024i | \(-0.962985\pi\) | ||
0.993246 | − | 0.116024i | \(-0.0370150\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6719.57 | − | 1534.37i | 1.00461 | − | 0.229397i | ||||
\(356\) | −5583.75 | −0.831287 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6333.19i | 0.934970i | ||||||||
\(359\) | − | 1035.99i | − | 0.152305i | −0.997096 | − | 0.0761525i | \(-0.975736\pi\) | ||
0.997096 | − | 0.0761525i | \(-0.0242636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −880.088 | −0.128311 | ||||||||
\(362\) | − | 560.741i | − | 0.0814141i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −566.417 | − | 1753.89i | −0.0815613 | − | 0.252552i | ||||
\(365\) | 2542.36 | + | 11133.9i | 0.364584 | + | 1.59665i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2278.61 | 0.324094 | 0.162047 | − | 0.986783i | \(-0.448190\pi\) | ||||
0.162047 | + | 0.986783i | \(0.448190\pi\) | |||||||
\(368\) | −1033.86 | −0.146450 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1619.36 | + | 369.771i | −0.227532 | + | 0.0519554i | ||||
\(371\) | −1741.43 | − | 5392.28i | −0.243694 | − | 0.754591i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8610.23i | 1.19523i | 0.801783 | + | 0.597615i | \(0.203885\pi\) | ||||
−0.801783 | + | 0.597615i | \(0.796115\pi\) | |||||||
\(374\) | 3521.16 | 0.486831 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2788.86i | 0.382512i | ||||||||
\(377\) | 2659.30i | 0.363292i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.5038 | −0.00223679 | −0.00111840 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111840 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(380\) | −5748.70 | + | 1312.68i | −0.776057 | + | 0.177208i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 1837.74i | − | 0.246143i | ||||||
\(383\) | − | 9887.59i | − | 1.31914i | −0.751641 | − | 0.659572i | \(-0.770737\pi\) | ||
0.751641 | − | 0.659572i | \(-0.229263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3239.24 | − | 5442.42i | −0.428797 | − | 0.720446i | ||||
\(386\) | 6331.81i | 0.834924i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4629.81 | 0.605781 | ||||||||
\(389\) | − | 279.292i | − | 0.0364028i | −0.999834 | − | 0.0182014i | \(-0.994206\pi\) | ||
0.999834 | − | 0.0182014i | \(-0.00579400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4222.98i | − | 0.546203i | ||||||
\(392\) | 5512.97 | − | 3975.43i | 0.710324 | − | 0.512218i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −30.7021 | −0.00392577 | ||||||||
\(395\) | 1390.62 | + | 6090.05i | 0.177139 | + | 0.775756i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10894.0 | 1.37721 | 0.688607 | − | 0.725135i | \(-0.258223\pi\) | ||||
0.688607 | + | 0.725135i | \(0.258223\pi\) | |||||||
\(398\) | 2405.99i | 0.303018i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2241.49 | + | 1079.97i | −0.280186 | + | 0.134996i | ||||
\(401\) | − | 9631.75i | − | 1.19947i | −0.800200 | − | 0.599734i | \(-0.795273\pi\) | ||
0.800200 | − | 0.599734i | \(-0.204727\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5081.27i | 0.628079i | ||||||||
\(404\) | 5333.68 | 0.656833 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3997.71 | + | 1291.05i | −0.488678 | + | 0.157818i | ||||
\(407\) | −3209.47 | −0.390878 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4082.30i | − | 0.493538i | −0.969074 | − | 0.246769i | \(-0.920631\pi\) | ||
0.969074 | − | 0.246769i | \(-0.0793689\pi\) | |||||||
\(410\) | −1684.20 | − | 7375.73i | −0.202870 | − | 0.888443i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9511.24 | −1.13734 | ||||||||
\(413\) | 763.044 | + | 2362.74i | 0.0909127 | + | 0.281509i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3656.57 | + | 834.953i | −0.432515 | + | 0.0987620i | ||||
\(416\) | 3099.27 | 0.365274 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3809.91 | 0.445811 | ||||||||
\(419\) | −15952.5 | −1.85998 | −0.929988 | − | 0.367589i | \(-0.880183\pi\) | ||||
−0.929988 | + | 0.367589i | \(0.880183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16707.5 | 1.93415 | 0.967073 | − | 0.254499i | \(-0.0819104\pi\) | ||||
0.967073 | + | 0.254499i | \(0.0819104\pi\) | |||||||
\(422\) | −2665.72 | −0.307500 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6062.90 | 0.694435 | ||||||||
\(425\) | −4411.34 | − | 9155.78i | −0.503486 | − | 1.04499i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5354.26 | + | 1729.15i | −0.606816 | + | 0.195970i | ||||
\(428\) | −4600.31 | −0.519543 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4102.37 | − | 936.750i | 0.460079 | − | 0.105056i | ||||
\(431\) | 1021.69i | 0.114183i | 0.998369 | + | 0.0570916i | \(0.0181827\pi\) | ||||
−0.998369 | + | 0.0570916i | \(0.981817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1052.40 | −0.116802 | −0.0584008 | − | 0.998293i | \(-0.518600\pi\) | ||||
−0.0584008 | + | 0.998293i | \(0.518600\pi\) | |||||||
\(434\) | −7638.63 | + | 2466.88i | −0.844853 | + | 0.272844i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4884.44 | 0.536519 | ||||||||
\(437\) | − | 4569.29i | − | 0.500180i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13540.8i | − | 1.47213i | −0.676909 | − | 0.736066i | \(-0.736681\pi\) | ||
0.676909 | − | 0.736066i | \(-0.263319\pi\) | |||||||
\(440\) | 6606.45 | − | 1508.54i | 0.715796 | − | 0.163447i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1910.91i | 0.205639i | ||||||||
\(443\) | 12799.7 | 1.37276 | 0.686380 | − | 0.727243i | \(-0.259199\pi\) | ||||
0.686380 | + | 0.727243i | \(0.259199\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2318.07 | − | 10151.7i | −0.246937 | − | 1.08143i | ||||
\(446\) | −8238.06 | −0.874627 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 598.325 | + | 1852.70i | 0.0630986 | + | 0.195383i | ||||
\(449\) | − | 523.887i | − | 0.0550641i | −0.999621 | − | 0.0275320i | \(-0.991235\pi\) | ||
0.999621 | − | 0.0275320i | \(-0.00876482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 14618.2i | − | 1.52626i | ||||||
\(452\) | 9890.21 | 1.02920 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3832.75i | − | 0.396211i | ||||||
\(455\) | 2953.56 | − | 1757.91i | 0.304319 | − | 0.181125i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 5749.64i | − | 0.588527i | −0.955724 | − | 0.294263i | \(-0.904926\pi\) | ||
0.955724 | − | 0.294263i | \(-0.0950743\pi\) | |||||||
\(458\) | 8818.96i | 0.899744i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −775.027 | − | 3394.12i | −0.0785561 | − | 0.344026i | ||||
\(461\) | −14278.7 | −1.44257 | −0.721284 | − | 0.692640i | \(-0.756448\pi\) | ||||
−0.721284 | + | 0.692640i | \(0.756448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16272.2i | − | 1.63333i | −0.577113 | − | 0.816664i | \(-0.695821\pi\) | ||
0.577113 | − | 0.816664i | \(-0.304179\pi\) | |||||||
\(464\) | 3188.84i | 0.319047i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5845.66 | −0.581105 | ||||||||
\(467\) | − | 15119.6i | − | 1.49819i | −0.662464 | − | 0.749094i | \(-0.730489\pi\) | ||
0.662464 | − | 0.749094i | \(-0.269511\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11836.1 | − | 3822.46i | 1.16534 | − | 0.376343i | ||||
\(470\) | −2172.02 | + | 495.967i | −0.213166 | + | 0.0486751i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2656.59 | −0.259066 | ||||||||
\(473\) | 8130.62 | 0.790373 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4773.09 | − | 9906.61i | −0.461062 | − | 0.956940i | ||||
\(476\) | 8590.65 | − | 2774.34i | 0.827210 | − | 0.267146i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 6577.18i | − | 0.629358i | ||||||
\(479\) | −13040.7 | −1.24394 | −0.621970 | − | 0.783041i | \(-0.713667\pi\) | ||||
−0.621970 | + | 0.783041i | \(0.713667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1741.75i | − | 0.165108i | ||||||
\(482\) | 9807.21i | 0.926777i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2370.69 | −0.222642 | ||||||||
\(485\) | 1922.05 | + | 8417.34i | 0.179950 | + | 0.788066i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12919.7i | 1.20215i | 0.799192 | + | 0.601075i | \(0.205261\pi\) | ||||
−0.799192 | + | 0.601075i | \(0.794739\pi\) | |||||||
\(488\) | − | 6020.14i | − | 0.558440i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4076.57 | + | 3586.63i | 0.375838 | + | 0.330668i | ||||
\(491\) | − | 10382.4i | − | 0.954275i | −0.878829 | − | 0.477138i | \(-0.841674\pi\) | ||
0.878829 | − | 0.477138i | \(-0.158326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13025.4 | −1.18993 | ||||||||
\(494\) | 2067.61i | 0.188312i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6093.07i | 0.551587i | ||||||||
\(497\) | −10865.0 | + | 3508.82i | −0.980603 | + | 0.316684i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13113.5 | 1.17643 | 0.588217 | − | 0.808703i | \(-0.299830\pi\) | ||||
0.588217 | + | 0.808703i | \(0.299830\pi\) | |||||||
\(500\) | −5225.84 | − | 6549.16i | −0.467413 | − | 0.585775i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7890.27 | 0.701514 | ||||||||
\(503\) | − | 9544.92i | − | 0.846097i | −0.906107 | − | 0.423049i | \(-0.860960\pi\) | ||
0.906107 | − | 0.423049i | \(-0.139040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2214.25 | + | 9697.03i | 0.195115 | + | 0.854480i | ||||
\(506\) | 2249.44i | 0.197628i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1042.25i | 0.0910282i | ||||||||
\(509\) | 3806.73 | 0.331493 | 0.165747 | − | 0.986168i | \(-0.446997\pi\) | ||||
0.165747 | + | 0.986168i | \(0.446997\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5813.90 | − | 18002.6i | −0.503311 | − | 1.55849i | ||||
\(512\) | 6871.84 | 0.593155 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 3144.62i | − | 0.269851i | ||||||
\(515\) | −3948.55 | − | 17292.2i | −0.337852 | − | 1.47958i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4304.80 | −0.366199 | ||||||||
\(518\) | 2618.37 | − | 845.597i | 0.222094 | − | 0.0717247i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 818.674 | + | 3585.27i | 0.0690408 | + | 0.302355i | ||||
\(521\) | 7738.68 | 0.650744 | 0.325372 | − | 0.945586i | \(-0.394510\pi\) | ||||
0.325372 | + | 0.945586i | \(0.394510\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19441.5 | 1.62547 | 0.812734 | − | 0.582635i | \(-0.197978\pi\) | ||||
0.812734 | + | 0.582635i | \(0.197978\pi\) | |||||||
\(524\) | −2810.57 | −0.234313 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6605.21 | −0.547530 | ||||||||
\(527\) | −24888.3 | −2.05721 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9469.22 | −0.778271 | ||||||||
\(530\) | 1078.22 | + | 4721.91i | 0.0883676 | + | 0.386994i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9295.13 | − | 3001.85i | 0.757510 | − | 0.244636i | ||||
\(533\) | 7933.19 | 0.644699 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1909.80 | − | 8363.72i | −0.154333 | − | 0.675879i | ||||
\(536\) | 13308.1i | 1.07243i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6193.01 | 0.496282 | ||||||||
\(539\) | 6136.35 | + | 8509.66i | 0.490374 | + | 0.680031i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10379.0 | −0.824817 | −0.412409 | − | 0.910999i | \(-0.635312\pi\) | ||||
−0.412409 | + | 0.910999i | \(0.635312\pi\) | |||||||
\(542\) | 2280.75i | 0.180750i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15180.4i | 1.19642i | ||||||||
\(545\) | 2027.75 | + | 8880.28i | 0.159375 | + | 0.697962i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16009.6i | 1.25141i | 0.780061 | + | 0.625703i | \(0.215188\pi\) | ||||
−0.780061 | + | 0.625703i | \(0.784812\pi\) | |||||||
\(548\) | 8243.33 | 0.642587 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2349.77 | + | 4876.97i | 0.182172 | + | 0.378099i | ||||
\(551\) | −14093.6 | −1.08967 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3180.09 | − | 9847.07i | −0.244541 | − | 0.757215i | ||||
\(554\) | − | 6775.56i | − | 0.519614i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10329.9i | 0.787921i | ||||||||
\(557\) | −11746.0 | −0.893526 | −0.446763 | − | 0.894652i | \(-0.647423\pi\) | ||||
−0.446763 | + | 0.894652i | \(0.647423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4412.43i | 0.333857i | ||||||||
\(560\) | 3541.69 | − | 2107.95i | 0.267257 | − | 0.159066i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6455.56i | 0.484540i | ||||||||
\(563\) | 9594.88i | 0.718252i | 0.933289 | + | 0.359126i | \(0.116925\pi\) | ||||
−0.933289 | + | 0.359126i | \(0.883075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4105.88 | + | 17981.1i | 0.305727 | + | 1.33889i | ||||
\(566\) | 4960.88 | 0.368412 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 12216.2i | − | 0.902428i | ||||||
\(569\) | − | 8438.18i | − | 0.621700i | −0.950459 | − | 0.310850i | \(-0.899386\pi\) | ||
0.950459 | − | 0.310850i | \(-0.100614\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18415.6 | 1.34968 | 0.674841 | − | 0.737963i | \(-0.264212\pi\) | ||||
0.674841 | + | 0.737963i | \(0.264212\pi\) | |||||||
\(572\) | 3043.95i | 0.222507i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3851.45 | + | 11925.9i | 0.280064 | + | 0.867209i | ||||
\(575\) | 5849.02 | − | 2818.11i | 0.424211 | − | 0.204389i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5724.61 | −0.413030 | −0.206515 | − | 0.978443i | \(-0.566212\pi\) | ||||
−0.206515 | + | 0.978443i | \(0.566212\pi\) | |||||||
\(578\) | −2403.41 | −0.172956 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10468.9 | + | 2390.50i | −0.749476 | + | 0.171138i | ||||
\(581\) | 5912.35 | − | 1909.38i | 0.422178 | − | 0.136342i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9358.51i | 0.664820i | ||||||||
\(584\) | 20241.5 | 1.43424 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8109.09i | 0.571644i | ||||||||
\(587\) | − | 20033.2i | − | 1.40862i | −0.709894 | − | 0.704309i | \(-0.751257\pi\) | ||
0.709894 | − | 0.704309i | \(-0.248743\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26929.3 | −1.88387 | ||||||||
\(590\) | −472.444 | − | 2069.01i | −0.0329665 | − | 0.144372i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 2088.58i | − | 0.145000i | ||||||
\(593\) | 10763.1i | 0.745341i | 0.927964 | + | 0.372670i | \(0.121558\pi\) | ||||
−0.927964 | + | 0.372670i | \(0.878442\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8610.32 | + | 14466.7i | 0.593259 | + | 0.996768i | ||||
\(596\) | 3726.90i | 0.256140i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1220.75 | −0.0834787 | ||||||||
\(599\) | 12751.4i | 0.869799i | 0.900479 | + | 0.434899i | \(0.143216\pi\) | ||||
−0.900479 | + | 0.434899i | \(0.856784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8319.06i | 0.564628i | 0.959322 | + | 0.282314i | \(0.0911020\pi\) | ||||
−0.959322 | + | 0.282314i | \(0.908898\pi\) | |||||||
\(602\) | −6633.17 | + | 2142.17i | −0.449083 | + | 0.145031i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16736.5 | −1.12748 | ||||||||
\(605\) | −984.181 | − | 4310.09i | −0.0661366 | − | 0.289636i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12259.8 | −0.819786 | −0.409893 | − | 0.912134i | \(-0.634434\pi\) | ||||
−0.409893 | + | 0.912134i | \(0.634434\pi\) | |||||||
\(608\) | 16425.2i | 1.09561i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4688.61 | − | 1070.61i | 0.311207 | − | 0.0710622i | ||||
\(611\) | − | 2336.18i | − | 0.154684i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23691.3i | − | 1.56098i | −0.625167 | − | 0.780491i | \(-0.714969\pi\) | ||
0.625167 | − | 0.780491i | \(-0.285031\pi\) | |||||||
\(614\) | −2656.93 | −0.174634 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10682.1 | + | 3449.75i | −0.698689 | + | 0.225640i | ||||
\(617\) | −8805.60 | −0.574554 | −0.287277 | − | 0.957848i | \(-0.592750\pi\) | ||||
−0.287277 | + | 0.957848i | \(0.592750\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1540.85i | − | 0.100051i | −0.998748 | − | 0.0500257i | \(-0.984070\pi\) | ||
0.998748 | − | 0.0500257i | \(-0.0159303\pi\) | |||||||
\(620\) | −20003.4 | + | 4567.65i | −1.29574 | + | 0.295873i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6396.09 | −0.412315 | ||||||||
\(623\) | 5300.99 | + | 16414.4i | 0.340898 | + | 1.05558i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9737.38 | − | 12219.8i | 0.623192 | − | 0.782069i | ||||
\(626\) | 10124.2 | 0.646399 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10402.6 | −0.661000 | ||||||||
\(629\) | 8531.20 | 0.540797 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4818.83 | 0.304017 | 0.152008 | − | 0.988379i | \(-0.451426\pi\) | ||||
0.152008 | + | 0.988379i | \(0.451426\pi\) | |||||||
\(632\) | 11071.7 | 0.696849 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5751.83 | 0.360306 | ||||||||
\(635\) | −1894.89 | + | 432.685i | −0.118419 | + | 0.0270403i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4618.13 | + | 3330.15i | −0.287248 | + | 0.207136i | ||||
\(638\) | 6938.18 | 0.430541 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3347.15 | + | 14658.4i | 0.206731 | + | 0.905350i | ||||
\(641\) | 18206.7i | 1.12187i | 0.827858 | + | 0.560937i | \(0.189559\pi\) | ||||
−0.827858 | + | 0.560937i | \(0.810441\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18717.3 | 1.14796 | 0.573981 | − | 0.818868i | \(-0.305398\pi\) | ||||
0.573981 | + | 0.818868i | \(0.305398\pi\) | |||||||
\(644\) | 1772.34 | + | 5488.00i | 0.108447 | + | 0.335804i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10127.3 | −0.616798 | ||||||||
\(647\) | 1556.10i | 0.0945542i | 0.998882 | + | 0.0472771i | \(0.0150544\pi\) | ||||
−0.998882 | + | 0.0472771i | \(0.984946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4100.63i | − | 0.248018i | ||||||
\(650\) | −2646.70 | + | 1275.20i | −0.159711 | + | 0.0769500i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 5969.76i | − | 0.358579i | ||||||
\(653\) | 29408.2 | 1.76238 | 0.881189 | − | 0.472765i | \(-0.156744\pi\) | ||||
0.881189 | + | 0.472765i | \(0.156744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1166.79 | − | 5109.82i | −0.0696037 | − | 0.304820i | ||||
\(656\) | 9512.88 | 0.566182 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3511.97 | − | 1134.18i | 0.208071 | − | 0.0671962i | ||||
\(659\) | − | 15993.9i | − | 0.945425i | −0.881217 | − | 0.472713i | \(-0.843275\pi\) | ||
0.881217 | − | 0.472713i | \(-0.156725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17299.8i | 1.01798i | 0.860773 | + | 0.508988i | \(0.169980\pi\) | ||||
−0.860773 | + | 0.508988i | \(0.830020\pi\) | |||||||
\(662\) | −1230.39 | −0.0722366 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6647.64i | 0.388522i | ||||||||
\(665\) | 9316.42 | + | 15653.0i | 0.543271 | + | 0.912780i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8321.07i | − | 0.483048i | ||||||
\(668\) | − | 11255.0i | − | 0.651898i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10364.7 | + | 2366.71i | −0.597645 | + | 0.136468i | ||||
\(671\) | 9292.51 | 0.534625 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 17783.4i | − | 1.01857i | −0.860597 | − | 0.509287i | \(-0.829909\pi\) | ||
0.860597 | − | 0.509287i | \(-0.170091\pi\) | |||||||
\(674\) | 1822.69i | 0.104165i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11519.6 | 0.655417 | ||||||||
\(677\) | 12701.0i | 0.721032i | 0.932753 | + | 0.360516i | \(0.117399\pi\) | ||||
−0.932753 | + | 0.360516i | \(0.882601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4395.36 | − | 13610.1i | −0.248422 | − | 0.769231i | ||||
\(680\) | −17560.8 | + | 4009.91i | −0.990335 | + | 0.226137i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13257.1 | 0.744343 | ||||||||
\(683\) | 27112.0 | 1.51891 | 0.759453 | − | 0.650562i | \(-0.225467\pi\) | ||||
0.759453 | + | 0.650562i | \(0.225467\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3422.18 | + | 14987.0i | 0.190883 | + | 0.835946i | ||||
\(686\) | −7248.23 | − | 5325.66i | −0.403409 | − | 0.296406i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5291.05i | 0.293197i | ||||||||
\(689\) | −5078.80 | −0.280822 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 521.160i | − | 0.0286916i | −0.999897 | − | 0.0143458i | \(-0.995433\pi\) | ||
0.999897 | − | 0.0143458i | \(-0.00456656\pi\) | |||||||
\(692\) | 15913.4i | 0.874185i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −597.884 | −0.0327023 | ||||||||
\(695\) | −18780.5 | + | 4288.40i | −1.02501 | + | 0.234055i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38857.1i | 2.11165i | ||||||||
\(698\) | 6570.91i | 0.356322i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9575.37 | + | 10047.1i | 0.517021 | + | 0.542491i | ||||
\(701\) | 3411.27i | 0.183797i | 0.995768 | + | 0.0918987i | \(0.0292936\pi\) | ||||
−0.995768 | + | 0.0918987i | \(0.970706\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9230.80 | 0.495230 | ||||||||
\(704\) | − | 3215.42i | − | 0.172139i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 2179.07i | − | 0.116162i | ||||||
\(707\) | −5063.58 | − | 15679.2i | −0.269357 | − | 0.834057i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6386.93 | −0.338316 | −0.169158 | − | 0.985589i | \(-0.554105\pi\) | ||||
−0.169158 | + | 0.985589i | \(0.554105\pi\) | |||||||
\(710\) | 9514.22 | − | 2172.51i | 0.502905 | − | 0.114835i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18455.7 | −0.971430 | ||||||||
\(713\) | − | 15899.5i | − | 0.835120i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5534.12 | + | 1263.68i | −0.289461 | + | 0.0660965i | ||||
\(716\) | − | 26816.2i | − | 1.39968i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 1466.86i | − | 0.0762431i | ||||||
\(719\) | 1659.01 | 0.0860510 | 0.0430255 | − | 0.999074i | \(-0.486300\pi\) | ||||
0.0430255 | + | 0.999074i | \(0.486300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9029.60 | + | 27959.9i | 0.466407 | + | 1.44422i | ||||
\(722\) | −1246.11 | −0.0642321 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2374.31i | 0.121879i | ||||||||
\(725\) | −8692.21 | − | 18040.8i | −0.445270 | − | 0.924163i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25833.8 | 1.31791 | 0.658955 | − | 0.752182i | \(-0.270999\pi\) | ||||
0.658955 | + | 0.752182i | \(0.270999\pi\) | |||||||
\(728\) | −1872.15 | − | 5797.07i | −0.0953113 | − | 0.295129i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3599.72 | + | 15764.5i | 0.182509 | + | 0.799273i | ||||
\(731\) | −21612.3 | −1.09351 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17410.3 | −0.877304 | −0.438652 | − | 0.898657i | \(-0.644544\pi\) | ||||
−0.438652 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(734\) | 3226.28 | 0.162240 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9697.73 | −0.485683 | ||||||||
\(737\) | −20542.1 | −1.02670 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26348.6 | −1.31157 | −0.655784 | − | 0.754949i | \(-0.727662\pi\) | ||||
−0.655784 | + | 0.754949i | \(0.727662\pi\) | |||||||
\(740\) | 6856.76 | − | 1565.70i | 0.340621 | − | 0.0777786i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2465.68 | − | 7634.92i | −0.121992 | − | 0.377745i | ||||
\(743\) | 27257.0 | 1.34585 | 0.672923 | − | 0.739713i | \(-0.265039\pi\) | ||||
0.672923 | + | 0.739713i | \(0.265039\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6775.78 | + | 1547.20i | −0.333215 | + | 0.0760875i | ||||
\(746\) | 12191.2i | 0.598326i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14909.4 | −0.728799 | ||||||||
\(749\) | 4367.36 | + | 13523.4i | 0.213057 | + | 0.659725i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12085.2 | 0.587210 | 0.293605 | − | 0.955927i | \(-0.405145\pi\) | ||||
0.293605 | + | 0.955927i | \(0.405145\pi\) | |||||||
\(752\) | − | 2801.38i | − | 0.135845i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3765.30i | 0.181862i | ||||||||
\(755\) | −6948.10 | − | 30428.3i | −0.334924 | − | 1.46675i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1931.31i | 0.0927275i | 0.998925 | + | 0.0463638i | \(0.0147633\pi\) | ||||
−0.998925 | + | 0.0463638i | \(0.985237\pi\) | |||||||
\(758\) | −23.3677 | −0.00111973 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19000.9 | + | 4338.74i | −0.906890 | + | 0.207082i | ||||
\(761\) | 26856.6 | 1.27931 | 0.639653 | − | 0.768664i | \(-0.279078\pi\) | ||||
0.639653 | + | 0.768664i | \(0.279078\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4637.09 | − | 14358.6i | −0.220018 | − | 0.681280i | ||||
\(764\) | 7781.40i | 0.368483i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 13999.8i | − | 0.660357i | ||||||
\(767\) | 2225.38 | 0.104764 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2772.05i | − | 0.129990i | −0.997886 | − | 0.0649952i | \(-0.979297\pi\) | ||
0.997886 | − | 0.0649952i | \(-0.0207032\pi\) | |||||||
\(770\) | −4586.42 | − | 7705.91i | −0.214654 | − | 0.360652i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 26810.3i | − | 1.24990i | ||||||
\(773\) | 18591.8i | 0.865071i | 0.901617 | + | 0.432535i | \(0.142381\pi\) | ||||
−0.901617 | + | 0.432535i | \(0.857619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16608.7 | − | 34471.5i | −0.769807 | − | 1.59774i | ||||
\(776\) | 15302.7 | 0.707907 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 395.449i | − | 0.0182230i | ||||||
\(779\) | 42043.6i | 1.93372i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18856.5 | 0.863944 | ||||||||
\(782\) | − | 5979.30i | − | 0.273426i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5537.71 | + | 3993.27i | −0.252264 | + | 0.181909i | ||||
\(785\) | −4318.59 | − | 18912.7i | −0.196353 | − | 0.859901i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10211.2 | −0.462504 | −0.231252 | − | 0.972894i | \(-0.574282\pi\) | ||||
−0.231252 | + | 0.972894i | \(0.574282\pi\) | |||||||
\(788\) | 130.000 | 0.00587698 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1968.98 | + | 8622.88i | 0.0886748 | + | 0.388340i | ||||
\(791\) | −9389.37 | − | 29073.9i | −0.422058 | − | 1.30689i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5042.98i | 0.225828i | ||||||||
\(794\) | 15424.8 | 0.689427 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 10187.5i | − | 0.453627i | ||||||
\(797\) | − | 15129.4i | − | 0.672412i | −0.941788 | − | 0.336206i | \(-0.890856\pi\) | ||
0.941788 | − | 0.336206i | \(-0.109144\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11442.7 | 0.506652 | ||||||||
\(800\) | −21025.5 | + | 10130.3i | −0.929205 | + | 0.447699i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 13637.6i | − | 0.600448i | ||||||
\(803\) | 31244.1i | 1.37308i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9241.82 | + | 5500.57i | −0.404635 | + | 0.240832i | ||||
\(806\) | 7194.55i | 0.314413i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17629.2 | 0.767565 | ||||||||
\(809\) | − | 27312.2i | − | 1.18695i | −0.804851 | − | 0.593477i | \(-0.797755\pi\) | ||
0.804851 | − | 0.593477i | \(-0.202245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 955.054i | − | 0.0413520i | −0.999786 | − | 0.0206760i | \(-0.993418\pi\) | ||
0.999786 | − | 0.0206760i | \(-0.00658184\pi\) | |||||||
\(812\) | 16927.2 | − | 5466.62i | 0.731564 | − | 0.236257i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4544.28 | −0.195672 | ||||||||
\(815\) | 10853.5 | − | 2478.32i | 0.466479 | − | 0.106517i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23384.6 | −1.00138 | ||||||||
\(818\) | − | 5780.12i | − | 0.247063i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7131.30 | + | 31230.6i | 0.303702 | + | 1.33002i | ||||
\(821\) | − | 4863.55i | − | 0.206747i | −0.994643 | − | 0.103373i | \(-0.967036\pi\) | ||
0.994643 | − | 0.103373i | \(-0.0329636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 24899.9i | − | 1.05463i | −0.849671 | − | 0.527313i | \(-0.823200\pi\) | ||
0.849671 | − | 0.527313i | \(-0.176800\pi\) | |||||||
\(824\) | −31437.1 | −1.32908 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1080.39 | + | 3345.40i | 0.0455105 | + | 0.140922i | ||||
\(827\) | −4217.13 | −0.177321 | −0.0886603 | − | 0.996062i | \(-0.528259\pi\) | ||||
−0.0886603 | + | 0.996062i | \(0.528259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15003.0i | 0.628561i | 0.949330 | + | 0.314280i | \(0.101763\pi\) | ||||
−0.949330 | + | 0.314280i | \(0.898237\pi\) | |||||||
\(830\) | −5177.32 | + | 1182.21i | −0.216515 | + | 0.0494398i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1744.99 | 0.0727122 | ||||||||
\(833\) | −16311.2 | − | 22619.8i | −0.678453 | − | 0.940852i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20462.4 | − | 4672.45i | 0.848060 | − | 0.193649i | ||||
\(836\) | −16132.1 | −0.667391 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22587.1 | −0.931095 | ||||||||
\(839\) | 2205.65 | 0.0907597 | 0.0453798 | − | 0.998970i | \(-0.485550\pi\) | ||||
0.0453798 | + | 0.998970i | \(0.485550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1276.58 | −0.0523425 | ||||||||
\(842\) | 23656.1 | 0.968224 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11287.3 | 0.460336 | ||||||||
\(845\) | 4782.32 | + | 20943.5i | 0.194694 | + | 0.852637i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2250.64 | + | 6969.03i | 0.0913020 | + | 0.282714i | ||||
\(848\) | −6090.11 | −0.246622 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6246.00 | − | 12963.6i | −0.252042 | − | 0.523117i | ||||
\(851\) | 5450.02i | 0.219535i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41922.9 | 1.68278 | 0.841391 | − | 0.540426i | \(-0.181737\pi\) | ||||
0.841391 | + | 0.540426i | \(0.181737\pi\) | |||||||
\(854\) | −7581.07 | + | 2448.29i | −0.303769 | + | 0.0981018i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15205.2 | −0.607131 | ||||||||
\(857\) | 5480.18i | 0.218436i | 0.994018 | + | 0.109218i | \(0.0348346\pi\) | ||||
−0.994018 | + | 0.109218i | \(0.965165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13807.4i | − | 0.548431i | −0.961668 | − | 0.274216i | \(-0.911582\pi\) | ||
0.961668 | − | 0.274216i | \(-0.0884182\pi\) | |||||||
\(860\) | −17370.4 | + | 3966.42i | −0.688751 | + | 0.157272i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1446.60i | 0.0571595i | ||||||||
\(863\) | 36042.1 | 1.42165 | 0.710827 | − | 0.703367i | \(-0.248321\pi\) | ||||
0.710827 | + | 0.703367i | \(0.248321\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28931.7 | + | 6606.37i | −1.13723 | + | 0.259680i | ||||
\(866\) | −1490.09 | −0.0584703 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32343.7 | − | 10445.4i | 1.26477 | − | 0.408455i | ||||
\(869\) | 17090.0i | 0.667131i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 11148.0i | − | 0.433681i | ||||||
\(872\) | 16144.3 | 0.626968 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 6469.64i | − | 0.250388i | ||||||
\(875\) | −14291.1 | + | 21579.7i | −0.552147 | + | 0.833747i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25249.1i | 0.972180i | 0.873909 | + | 0.486090i | \(0.161577\pi\) | ||||
−0.873909 | + | 0.486090i | \(0.838423\pi\) | |||||||
\(878\) | − | 19172.4i | − | 0.736943i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6636.11 | + | 1515.31i | −0.254208 | + | 0.0580468i | ||||
\(881\) | −7038.44 | −0.269161 | −0.134581 | − | 0.990903i | \(-0.542969\pi\) | ||||
−0.134581 | + | 0.990903i | \(0.542969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 17328.3i | − | 0.660413i | −0.943909 | − | 0.330207i | \(-0.892882\pi\) | ||
0.943909 | − | 0.330207i | \(-0.107118\pi\) | |||||||
\(884\) | − | 8091.22i | − | 0.307848i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18123.1 | 0.687197 | ||||||||
\(887\) | 23764.0i | 0.899570i | 0.893137 | + | 0.449785i | \(0.148499\pi\) | ||||
−0.893137 | + | 0.449785i | \(0.851501\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3063.86 | − | 989.470i | 0.115589 | − | 0.0373293i | ||||
\(890\) | −3282.15 | − | 14373.7i | −0.123616 | − | 0.541358i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 34881.9 | 1.30934 | ||||||||
\(893\) | 12381.1 | 0.463962 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48753.8 | − | 11132.6i | 1.82085 | − | 0.415779i | ||||
\(896\) | −7654.30 | − | 23701.3i | −0.285393 | − | 0.883712i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 741.770i | − | 0.0275648i | ||||||
\(899\) | −49040.5 | −1.81935 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 24876.2i | − | 0.919807i | ||||||
\(902\) | − | 20697.9i | − | 0.764039i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32689.7 | 1.20270 | ||||||||
\(905\) | −4316.67 | + | 985.684i | −0.158554 | + | 0.0362047i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 16998.5i | − | 0.622301i | −0.950361 | − | 0.311151i | \(-0.899286\pi\) | ||
0.950361 | − | 0.311151i | \(-0.100714\pi\) | |||||||
\(908\) | 16228.8i | 0.593139i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4181.94 | − | 2489.02i | 0.152341 | − | 0.0906705i | ||||
\(911\) | 40955.7i | 1.48949i | 0.667351 | + | 0.744743i | \(0.267428\pi\) | ||||
−0.667351 | + | 0.744743i | \(0.732572\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10261.1 | −0.371953 | ||||||||
\(914\) | − | 8140.90i | − | 0.294614i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 37341.5i | − | 1.34694i | ||||||
\(917\) | 2668.24 | + | 8262.13i | 0.0960884 | + | 0.297535i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42060.9 | 1.50975 | 0.754876 | − | 0.655867i | \(-0.227697\pi\) | ||||
0.754876 | + | 0.655867i | \(0.227697\pi\) | |||||||
\(920\) | −2561.66 | − | 11218.5i | −0.0917995 | − | 0.402024i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20217.1 | −0.722142 | ||||||||
\(923\) | 10233.3i | 0.364933i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5693.11 | + | 11816.1i | 0.202366 | + | 0.420012i | ||||
\(926\) | − | 23039.7i | − | 0.817636i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29911.8i | 1.05808i | ||||||||
\(929\) | −1206.74 | −0.0426177 | −0.0213088 | − | 0.999773i | \(-0.506783\pi\) | ||||
−0.0213088 | + | 0.999773i | \(0.506783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17648.9 | − | 24474.8i | −0.621287 | − | 0.861577i | ||||
\(932\) | 24751.9 | 0.869930 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 21407.9i | − | 0.749985i | ||||||
\(935\) | −6189.57 | − | 27106.4i | −0.216493 | − | 0.948101i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40024.3 | 1.39545 | 0.697725 | − | 0.716366i | \(-0.254196\pi\) | ||||
0.697725 | + | 0.716366i | \(0.254196\pi\) | |||||||
\(938\) | 16758.8 | − | 5412.21i | 0.583361 | − | 0.188395i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9196.85 | − | 2100.04i | 0.319115 | − | 0.0728679i | ||||
\(941\) | 7112.58 | 0.246401 | 0.123201 | − | 0.992382i | \(-0.460684\pi\) | ||||
0.123201 | + | 0.992382i | \(0.460684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24823.3 | −0.857218 | ||||||||
\(944\) | 2668.51 | 0.0920049 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11512.1 | 0.395657 | ||||||||
\(947\) | −52031.5 | −1.78543 | −0.892713 | − | 0.450626i | \(-0.851201\pi\) | ||||
−0.892713 | + | 0.450626i | \(0.851201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16956.0 | −0.579993 | ||||||||
\(950\) | −6758.21 | − | 14026.7i | −0.230805 | − | 0.479039i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28394.3 | − | 9169.90i | 0.966666 | − | 0.312183i | ||||
\(953\) | −50850.3 | −1.72844 | −0.864220 | − | 0.503114i | \(-0.832188\pi\) | ||||
−0.864220 | + | 0.503114i | \(0.832188\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14147.2 | + | 3230.42i | −0.479363 | + | 0.109459i | ||||
\(956\) | 27849.3i | 0.942166i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18464.3 | −0.622710 | ||||||||
\(959\) | −7825.89 | − | 24232.6i | −0.263515 | − | 0.815967i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −63913.2 | −2.14539 | ||||||||
\(962\) | − | 2466.14i | − | 0.0826525i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 41526.0i | − | 1.38741i | ||||||
\(965\) | 48743.2 | − | 11130.2i | 1.62601 | − | 0.371289i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35434.8i | 1.17839i | 0.807990 | + | 0.589197i | \(0.200556\pi\) | ||||
−0.807990 | + | 0.589197i | \(0.799444\pi\) | |||||||
\(968\) | −7835.74 | −0.260176 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2721.42 | + | 11918.1i | 0.0900820 | + | 0.394502i | ||||
\(971\) | −46207.8 | −1.52717 | −0.763584 | − | 0.645709i | \(-0.776562\pi\) | ||||
−0.763584 | + | 0.645709i | \(0.776562\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30366.4 | − | 9806.77i | 1.00052 | − | 0.323115i | ||||
\(974\) | 18293.0i | 0.601791i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6047.16i | 0.198325i | ||||||||
\(977\) | −14154.5 | −0.463503 | −0.231752 | − | 0.972775i | \(-0.574446\pi\) | ||||
−0.231752 | + | 0.972775i | \(0.574446\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 28487.7i | − | 0.930002i | ||||||
\(980\) | −17261.1 | − | 15186.6i | −0.562639 | − | 0.495019i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 14700.3i | − | 0.477705i | ||||||
\(983\) | − | 12680.8i | − | 0.411451i | −0.978610 | − | 0.205725i | \(-0.934045\pi\) | ||
0.978610 | − | 0.205725i | \(-0.0659554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53.9689 | + | 236.350i | 0.00174578 | + | 0.00764541i | ||||
\(986\) | −18442.6 | −0.595672 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 8754.75i | − | 0.281908i | ||||||
\(989\) | − | 13806.7i | − | 0.443909i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36020.9 | 1.15463 | 0.577317 | − | 0.816520i | \(-0.304100\pi\) | ||||
0.577317 | + | 0.816520i | \(0.304100\pi\) | |||||||
\(992\) | 57153.9i | 1.82927i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15383.7 | + | 4968.12i | −0.490885 | + | 0.158531i | ||||
\(995\) | 18521.7 | − | 4229.30i | 0.590127 | − | 0.134752i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −61180.4 | −1.94343 | −0.971716 | − | 0.236152i | \(-0.924114\pi\) | ||||
−0.971716 | + | 0.236152i | \(0.924114\pi\) | |||||||
\(998\) | 18567.3 | 0.588917 | ||||||||
\(999\) | 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 | 315.4.g.a.314.30 | yes | 48 | |
3.2 | odd | 2 | inner | 315.4.g.a.314.20 | yes | 48 | |
5.4 | even | 2 | inner | 315.4.g.a.314.18 | yes | 48 | |
7.6 | odd | 2 | inner | 315.4.g.a.314.29 | yes | 48 | |
15.14 | odd | 2 | inner | 315.4.g.a.314.32 | yes | 48 | |
21.20 | even | 2 | inner | 315.4.g.a.314.19 | yes | 48 | |
35.34 | odd | 2 | inner | 315.4.g.a.314.17 | ✓ | 48 | |
105.104 | even | 2 | inner | 315.4.g.a.314.31 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.4.g.a.314.17 | ✓ | 48 | 35.34 | odd | 2 | inner | |
315.4.g.a.314.18 | yes | 48 | 5.4 | even | 2 | inner | |
315.4.g.a.314.19 | yes | 48 | 21.20 | even | 2 | inner | |
315.4.g.a.314.20 | yes | 48 | 3.2 | odd | 2 | inner | |
315.4.g.a.314.29 | yes | 48 | 7.6 | odd | 2 | inner | |
315.4.g.a.314.30 | yes | 48 | 1.1 | even | 1 | trivial | |
315.4.g.a.314.31 | yes | 48 | 105.104 | even | 2 | inner | |
315.4.g.a.314.32 | yes | 48 | 15.14 | odd | 2 | inner |