Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(323,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("324.323");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.b (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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.9 | ||
Character | \(\chi\) | \(=\) | 324.323 |
Dual form | 324.4.b.c.323.10 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16011 | − | 2.57956i | −0.410161 | − | 0.912013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.30829 | + | 5.98515i | −0.663536 | + | 0.748144i | ||||
\(5\) | 16.7343i | 1.49677i | 0.663267 | + | 0.748383i | \(0.269169\pi\) | ||||
−0.663267 | + | 0.748383i | \(0.730831\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 19.3037i | 1.04230i | 0.853464 | + | 0.521152i | \(0.174497\pi\) | ||||
−0.853464 | + | 0.521152i | \(0.825503\pi\) | |||||||
\(8\) | 21.5973 | + | 6.74964i | 0.954474 | + | 0.298295i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 43.1673 | − | 19.4137i | 1.36507 | − | 0.613915i | ||||
\(11\) | 4.88184 | 0.133812 | 0.0669059 | − | 0.997759i | \(-0.478687\pi\) | ||||
0.0669059 | + | 0.997759i | \(0.478687\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.0770 | −0.257657 | −0.128829 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(14\) | 49.7952 | − | 22.3944i | 0.950594 | − | 0.427512i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.64410 | − | 63.5419i | −0.119439 | − | 0.992842i | ||||
\(17\) | 71.2528i | 1.01655i | 0.861195 | + | 0.508275i | \(0.169717\pi\) | ||||
−0.861195 | + | 0.508275i | \(0.830283\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 68.3003i | − | 0.824693i | −0.911027 | − | 0.412347i | \(-0.864709\pi\) | ||
0.911027 | − | 0.412347i | \(-0.135291\pi\) | |||||||
\(20\) | −100.158 | − | 88.8308i | −1.11980 | − | 0.993158i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.66347 | − | 12.5930i | −0.0548844 | − | 0.122038i | ||||
\(23\) | −136.098 | −1.23385 | −0.616923 | − | 0.787024i | \(-0.711621\pi\) | ||||
−0.616923 | + | 0.787024i | \(0.711621\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −155.038 | −1.24031 | ||||||||
\(26\) | 14.0106 | + | 31.1533i | 0.105681 | + | 0.234987i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −115.536 | − | 102.470i | −0.779793 | − | 0.691606i | ||||
\(29\) | 219.667i | 1.40659i | 0.710899 | + | 0.703295i | \(0.248288\pi\) | ||||
−0.710899 | + | 0.703295i | \(0.751712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 329.345i | − | 1.90813i | −0.299600 | − | 0.954065i | \(-0.596853\pi\) | ||
0.299600 | − | 0.954065i | \(-0.403147\pi\) | |||||||
\(32\) | −155.042 | + | 93.4340i | −0.856495 | + | 0.516155i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 183.801 | − | 82.6611i | 0.927107 | − | 0.416949i | ||||
\(35\) | −323.035 | −1.56008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −133.618 | −0.593693 | −0.296847 | − | 0.954925i | \(-0.595935\pi\) | ||||
−0.296847 | + | 0.954925i | \(0.595935\pi\) | |||||||
\(38\) | −176.185 | + | 79.2359i | −0.752131 | + | 0.338257i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −112.951 | + | 361.416i | −0.446477 | + | 1.42862i | ||||
\(41\) | 34.1013i | 0.129896i | 0.997889 | + | 0.0649480i | \(0.0206881\pi\) | ||||
−0.997889 | + | 0.0649480i | \(0.979312\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.644564i | 0.00228593i | 0.999999 | + | 0.00114297i | \(0.000363817\pi\) | ||||
−0.999999 | + | 0.00114297i | \(0.999636\pi\) | |||||||
\(44\) | −25.9142 | + | 29.2186i | −0.0887890 | + | 0.100111i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 157.889 | + | 351.074i | 0.506075 | + | 1.12528i | ||||
\(47\) | 186.951 | 0.580203 | 0.290102 | − | 0.956996i | \(-0.406311\pi\) | ||||
0.290102 | + | 0.956996i | \(0.406311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −29.6338 | −0.0863958 | ||||||||
\(50\) | 179.862 | + | 399.931i | 0.508725 | + | 1.13118i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 64.1080 | − | 72.2825i | 0.170965 | − | 0.192765i | ||||
\(53\) | − | 266.453i | − | 0.690569i | −0.938498 | − | 0.345284i | \(-0.887782\pi\) | ||
0.938498 | − | 0.345284i | \(-0.112218\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 81.6944i | 0.200285i | ||||||||
\(56\) | −130.293 | + | 416.908i | −0.310913 | + | 0.994851i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 566.644 | − | 254.838i | 1.28283 | − | 0.576928i | ||||
\(59\) | −208.694 | −0.460501 | −0.230251 | − | 0.973131i | \(-0.573955\pi\) | ||||
−0.230251 | + | 0.973131i | \(0.573955\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.60377 | −0.00336626 | −0.00168313 | − | 0.999999i | \(-0.500536\pi\) | ||||
−0.00168313 | + | 0.999999i | \(0.500536\pi\) | |||||||
\(62\) | −849.565 | + | 382.076i | −1.74024 | + | 0.782640i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 420.885 | + | 291.548i | 0.822041 | + | 0.569429i | ||||
\(65\) | − | 202.100i | − | 0.385653i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 428.864i | 0.782001i | 0.920390 | + | 0.391001i | \(0.127871\pi\) | ||||
−0.920390 | + | 0.391001i | \(0.872129\pi\) | |||||||
\(68\) | −426.459 | − | 378.231i | −0.760526 | − | 0.674518i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 374.756 | + | 833.290i | 0.639885 | + | 1.42282i | ||||
\(71\) | 386.365 | 0.645817 | 0.322909 | − | 0.946430i | \(-0.395339\pi\) | ||||
0.322909 | + | 0.946430i | \(0.395339\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −776.832 | −1.24550 | −0.622749 | − | 0.782422i | \(-0.713984\pi\) | ||||
−0.622749 | + | 0.782422i | \(0.713984\pi\) | |||||||
\(74\) | 155.011 | + | 344.676i | 0.243510 | + | 0.541456i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 408.788 | + | 362.558i | 0.616989 | + | 0.547214i | ||||
\(77\) | 94.2377i | 0.139472i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 79.0970i | − | 0.112647i | −0.998413 | − | 0.0563235i | \(-0.982062\pi\) | ||
0.998413 | − | 0.0563235i | \(-0.0179378\pi\) | |||||||
\(80\) | 1063.33 | − | 127.919i | 1.48605 | − | 0.178772i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 87.9665 | − | 39.5613i | 0.118467 | − | 0.0532782i | ||||
\(83\) | −925.337 | −1.22372 | −0.611861 | − | 0.790965i | \(-0.709579\pi\) | ||||
−0.611861 | + | 0.790965i | \(0.709579\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1192.37 | −1.52154 | ||||||||
\(86\) | 1.66269 | − | 0.747765i | 0.00208480 | − | 0.000937599i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 105.434 | + | 32.9506i | 0.127720 | + | 0.0399154i | ||||
\(89\) | 1044.26i | 1.24372i | 0.783128 | + | 0.621861i | \(0.213623\pi\) | ||||
−0.783128 | + | 0.621861i | \(0.786377\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 233.130i | − | 0.268557i | ||||||
\(92\) | 722.449 | − | 814.569i | 0.818701 | − | 0.923094i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −216.883 | − | 482.251i | −0.237977 | − | 0.529153i | ||||
\(95\) | 1142.96 | 1.23437 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1466.37 | −1.53492 | −0.767460 | − | 0.641097i | \(-0.778479\pi\) | ||||
−0.767460 | + | 0.641097i | \(0.778479\pi\) | |||||||
\(98\) | 34.3784 | + | 76.4422i | 0.0354362 | + | 0.0787941i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 822.989 | − | 927.929i | 0.822989 | − | 0.927929i | ||||
\(101\) | − | 362.925i | − | 0.357548i | −0.983890 | − | 0.178774i | \(-0.942787\pi\) | ||
0.983890 | − | 0.178774i | \(-0.0572131\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 538.238i | 0.514895i | 0.966292 | + | 0.257447i | \(0.0828814\pi\) | ||||
−0.966292 | + | 0.257447i | \(0.917119\pi\) | |||||||
\(104\) | −260.830 | − | 81.5151i | −0.245927 | − | 0.0768578i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −687.333 | + | 309.115i | −0.629808 | + | 0.283244i | ||||
\(107\) | 430.456 | 0.388914 | 0.194457 | − | 0.980911i | \(-0.437706\pi\) | ||||
0.194457 | + | 0.980911i | \(0.437706\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 899.324 | 0.790272 | 0.395136 | − | 0.918623i | \(-0.370697\pi\) | ||||
0.395136 | + | 0.918623i | \(0.370697\pi\) | |||||||
\(110\) | 210.736 | − | 94.7745i | 0.182663 | − | 0.0821490i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1226.59 | − | 147.560i | 1.03484 | − | 0.124492i | ||||
\(113\) | 382.044i | 0.318050i | 0.987275 | + | 0.159025i | \(0.0508351\pi\) | ||||
−0.987275 | + | 0.159025i | \(0.949165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2277.52i | − | 1.84678i | ||||||
\(116\) | −1314.74 | − | 1166.05i | −1.05233 | − | 0.933323i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 242.107 | + | 538.338i | 0.188880 | + | 0.419983i | ||||
\(119\) | −1375.44 | −1.05955 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1307.17 | −0.982094 | ||||||||
\(122\) | 1.86055 | + | 4.13703i | 0.00138071 | + | 0.00307008i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1971.18 | + | 1748.26i | 1.42756 | + | 1.26611i | ||||
\(125\) | − | 502.674i | − | 0.359684i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1677.92i | − | 1.17237i | −0.810177 | − | 0.586186i | \(-0.800629\pi\) | ||
0.810177 | − | 0.586186i | \(-0.199371\pi\) | |||||||
\(128\) | 263.793 | − | 1423.93i | 0.182158 | − | 0.983269i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −521.330 | + | 234.458i | −0.351721 | + | 0.158180i | ||||
\(131\) | −1424.84 | −0.950294 | −0.475147 | − | 0.879906i | \(-0.657605\pi\) | ||||
−0.475147 | + | 0.879906i | \(0.657605\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1318.45 | 0.859580 | ||||||||
\(134\) | 1106.28 | − | 497.529i | 0.713196 | − | 0.320746i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −480.931 | + | 1538.87i | −0.303231 | + | 0.970270i | ||||
\(137\) | 26.8231i | 0.0167274i | 0.999965 | + | 0.00836370i | \(0.00266228\pi\) | ||||
−0.999965 | + | 0.00836370i | \(0.997338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1656.50i | − | 1.01081i | −0.862882 | − | 0.505406i | \(-0.831343\pi\) | ||
0.862882 | − | 0.505406i | \(-0.168657\pi\) | |||||||
\(140\) | 1714.77 | − | 1933.42i | 1.03517 | − | 1.16717i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −448.225 | − | 996.652i | −0.264889 | − | 0.588994i | ||||
\(143\) | −58.9578 | −0.0344776 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3675.98 | −2.10533 | ||||||||
\(146\) | 901.211 | + | 2003.89i | 0.510854 | + | 1.13591i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 709.283 | − | 799.724i | 0.393937 | − | 0.444168i | ||||
\(149\) | − | 852.498i | − | 0.468720i | −0.972150 | − | 0.234360i | \(-0.924700\pi\) | ||
0.972150 | − | 0.234360i | \(-0.0752995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1468.84i | 0.791608i | 0.918335 | + | 0.395804i | \(0.129534\pi\) | ||||
−0.918335 | + | 0.395804i | \(0.870466\pi\) | |||||||
\(152\) | 461.002 | − | 1475.10i | 0.246002 | − | 0.787148i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 243.092 | − | 109.326i | 0.127201 | − | 0.0572061i | ||||
\(155\) | 5511.37 | 2.85602 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2689.05 | 1.36694 | 0.683469 | − | 0.729979i | \(-0.260470\pi\) | ||||
0.683469 | + | 0.729979i | \(0.260470\pi\) | |||||||
\(158\) | −204.036 | + | 91.7612i | −0.102736 | + | 0.0462034i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1563.56 | − | 2594.53i | −0.772563 | − | 1.28197i | ||||
\(161\) | − | 2627.20i | − | 1.28604i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2186.50i | 1.05067i | 0.850895 | + | 0.525336i | \(0.176060\pi\) | ||||
−0.850895 | + | 0.525336i | \(0.823940\pi\) | |||||||
\(164\) | −204.102 | − | 181.020i | −0.0971809 | − | 0.0861907i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1073.49 | + | 2386.96i | 0.501923 | + | 1.11605i | ||||
\(167\) | 3581.29 | 1.65945 | 0.829726 | − | 0.558171i | \(-0.188497\pi\) | ||||
0.829726 | + | 0.558171i | \(0.188497\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2051.15 | −0.933613 | ||||||||
\(170\) | 1383.28 | + | 3075.79i | 0.624075 | + | 1.38766i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.85781 | − | 3.42153i | −0.00171021 | − | 0.00151680i | ||||
\(173\) | − | 109.125i | − | 0.0479574i | −0.999712 | − | 0.0239787i | \(-0.992367\pi\) | ||
0.999712 | − | 0.0239787i | \(-0.00763338\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2992.82i | − | 1.29278i | ||||||
\(176\) | −37.3173 | − | 310.201i | −0.0159824 | − | 0.132854i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2693.73 | − | 1211.46i | 1.13429 | − | 0.510126i | ||||
\(179\) | 268.397 | 0.112072 | 0.0560361 | − | 0.998429i | \(-0.482154\pi\) | ||||
0.0560361 | + | 0.998429i | \(0.482154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 898.582 | 0.369011 | 0.184506 | − | 0.982831i | \(-0.440932\pi\) | ||||
0.184506 | + | 0.982831i | \(0.440932\pi\) | |||||||
\(182\) | −601.375 | + | 270.457i | −0.244928 | + | 0.110152i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2939.35 | − | 918.614i | −1.17767 | − | 0.368049i | ||||
\(185\) | − | 2236.01i | − | 0.888620i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 347.845i | 0.136026i | ||||||||
\(188\) | −992.388 | + | 1118.93i | −0.384986 | + | 0.434076i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1325.96 | − | 2948.34i | −0.506291 | − | 1.12576i | ||||
\(191\) | 514.662 | 0.194972 | 0.0974860 | − | 0.995237i | \(-0.468920\pi\) | ||||
0.0974860 | + | 0.995237i | \(0.468920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2459.32 | −0.917232 | −0.458616 | − | 0.888635i | \(-0.651655\pi\) | ||||
−0.458616 | + | 0.888635i | \(0.651655\pi\) | |||||||
\(194\) | 1701.15 | + | 3782.59i | 0.629564 | + | 1.39987i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 157.305 | − | 177.363i | 0.0573268 | − | 0.0646365i | ||||
\(197\) | − | 646.506i | − | 0.233815i | −0.993143 | − | 0.116908i | \(-0.962702\pi\) | ||
0.993143 | − | 0.116908i | \(-0.0372982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1742.98i | − | 0.620886i | −0.950592 | − | 0.310443i | \(-0.899523\pi\) | ||
0.950592 | − | 0.310443i | \(-0.100477\pi\) | |||||||
\(200\) | −3348.41 | − | 1046.45i | −1.18384 | − | 0.369977i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −936.188 | + | 421.033i | −0.326089 | + | 0.146652i | ||||
\(203\) | −4240.39 | −1.46609 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −570.664 | −0.194424 | ||||||||
\(206\) | 1388.42 | − | 624.415i | 0.469591 | − | 0.211190i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 92.3175 | + | 767.393i | 0.0307744 | + | 0.255813i | ||||
\(209\) | − | 333.431i | − | 0.110354i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4212.66i | 1.37446i | 0.726439 | + | 0.687231i | \(0.241174\pi\) | ||||
−0.726439 | + | 0.687231i | \(0.758826\pi\) | |||||||
\(212\) | 1594.76 | + | 1414.41i | 0.516645 | + | 0.458218i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −499.376 | − | 1110.39i | −0.159517 | − | 0.354694i | ||||
\(215\) | −10.7864 | −0.00342150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6357.58 | 1.98885 | ||||||||
\(218\) | −1043.31 | − | 2319.86i | −0.324138 | − | 0.720738i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −488.954 | − | 433.658i | −0.149842 | − | 0.132896i | ||||
\(221\) | − | 860.518i | − | 0.261922i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6418.45i | 1.92741i | 0.266977 | + | 0.963703i | \(0.413975\pi\) | ||||
−0.266977 | + | 0.963703i | \(0.586025\pi\) | |||||||
\(224\) | −1803.62 | − | 2992.89i | −0.537990 | − | 0.892728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 985.507 | − | 443.213i | 0.290066 | − | 0.130452i | ||||
\(227\) | −2249.67 | −0.657778 | −0.328889 | − | 0.944369i | \(-0.606674\pi\) | ||||
−0.328889 | + | 0.944369i | \(0.606674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3470.73 | 1.00154 | 0.500769 | − | 0.865581i | \(-0.333051\pi\) | ||||
0.500769 | + | 0.865581i | \(0.333051\pi\) | |||||||
\(230\) | −5875.00 | + | 2642.17i | −1.68429 | + | 0.757476i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1482.67 | + | 4744.20i | −0.419578 | + | 1.34255i | ||||
\(233\) | 3852.67i | 1.08325i | 0.840621 | + | 0.541624i | \(0.182190\pi\) | ||||
−0.840621 | + | 0.541624i | \(0.817810\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3128.50i | 0.868428i | ||||||||
\(236\) | 1107.81 | − | 1249.06i | 0.305559 | − | 0.344521i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1595.67 | + | 3548.05i | 0.434587 | + | 0.966326i | ||||
\(239\) | 39.8668 | 0.0107898 | 0.00539491 | − | 0.999985i | \(-0.498283\pi\) | ||||
0.00539491 | + | 0.999985i | \(0.498283\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3458.36 | 0.924369 | 0.462184 | − | 0.886784i | \(-0.347066\pi\) | ||||
0.462184 | + | 0.886784i | \(0.347066\pi\) | |||||||
\(242\) | 1516.46 | + | 3371.92i | 0.402817 | + | 0.895683i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.51329 | − | 9.59882i | 0.00223364 | − | 0.00251845i | ||||
\(245\) | − | 495.902i | − | 0.129314i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 824.861i | 0.212488i | ||||||||
\(248\) | 2222.96 | − | 7112.95i | 0.569185 | − | 1.82126i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1296.68 | + | 583.156i | −0.328036 | + | 0.147528i | ||||
\(251\) | −2977.61 | −0.748786 | −0.374393 | − | 0.927270i | \(-0.622149\pi\) | ||||
−0.374393 | + | 0.927270i | \(0.622149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −664.410 | −0.165103 | ||||||||
\(254\) | −4328.30 | + | 1946.57i | −1.06922 | + | 0.480861i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3979.14 | + | 971.441i | −0.971469 | + | 0.237168i | ||||
\(257\) | 6458.56i | 1.56760i | 0.621011 | + | 0.783802i | \(0.286722\pi\) | ||||
−0.621011 | + | 0.783802i | \(0.713278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2579.32i | − | 0.618808i | ||||||
\(260\) | 1209.60 | + | 1072.81i | 0.288524 | + | 0.255895i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1652.97 | + | 3675.46i | 0.389773 | + | 0.866681i | ||||
\(263\) | −5881.98 | −1.37908 | −0.689540 | − | 0.724247i | \(-0.742187\pi\) | ||||
−0.689540 | + | 0.724247i | \(0.742187\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4458.92 | 1.03362 | ||||||||
\(266\) | −1529.55 | − | 3401.03i | −0.352566 | − | 0.783949i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2566.82 | − | 2276.54i | −0.585050 | − | 0.518886i | ||||
\(269\) | 2967.07i | 0.672510i | 0.941771 | + | 0.336255i | \(0.109160\pi\) | ||||
−0.941771 | + | 0.336255i | \(0.890840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1985.78i | 0.445121i | 0.974919 | + | 0.222561i | \(0.0714415\pi\) | ||||
−0.974919 | + | 0.222561i | \(0.928559\pi\) | |||||||
\(272\) | 4527.54 | − | 544.664i | 1.00927 | − | 0.121416i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 69.1919 | − | 31.1178i | 0.0152556 | − | 0.00686092i | ||||
\(275\) | −756.873 | −0.165968 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4342.96 | 0.942034 | 0.471017 | − | 0.882124i | \(-0.343887\pi\) | ||||
0.471017 | + | 0.882124i | \(0.343887\pi\) | |||||||
\(278\) | −4273.05 | + | 1921.73i | −0.921873 | + | 0.414595i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6976.68 | − | 2180.37i | −1.48906 | − | 0.465365i | ||||
\(281\) | 7796.65i | 1.65519i | 0.561323 | + | 0.827597i | \(0.310292\pi\) | ||||
−0.561323 | + | 0.827597i | \(0.689708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2045.51i | 0.429658i | 0.976652 | + | 0.214829i | \(0.0689194\pi\) | ||||
−0.976652 | + | 0.214829i | \(0.931081\pi\) | |||||||
\(284\) | −2050.94 | + | 2312.45i | −0.428523 | + | 0.483165i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 68.3975 | + | 152.085i | 0.0141414 | + | 0.0314440i | ||||
\(287\) | −658.283 | −0.135391 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −163.963 | −0.0333732 | ||||||||
\(290\) | 4264.54 | + | 9482.42i | 0.863525 | + | 1.92009i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4123.65 | − | 4649.46i | 0.826433 | − | 0.931812i | ||||
\(293\) | 2357.43i | 0.470043i | 0.971990 | + | 0.235022i | \(0.0755161\pi\) | ||||
−0.971990 | + | 0.235022i | \(0.924484\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3492.35i | − | 0.689263i | ||||||
\(296\) | −2885.78 | − | 901.873i | −0.566665 | − | 0.177096i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2199.07 | + | 988.991i | −0.427479 | + | 0.192251i | ||||
\(299\) | 1643.65 | 0.317910 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.4425 | −0.00238263 | ||||||||
\(302\) | 3788.98 | − | 1704.02i | 0.721957 | − | 0.324687i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4339.93 | + | 522.095i | −0.818790 | + | 0.0985006i | ||||
\(305\) | − | 26.8381i | − | 0.00503851i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5521.27i | − | 1.02643i | −0.858259 | − | 0.513217i | \(-0.828454\pi\) | ||
0.858259 | − | 0.513217i | \(-0.171546\pi\) | |||||||
\(308\) | −564.027 | − | 500.241i | −0.104346 | − | 0.0925451i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6393.79 | − | 14216.9i | −1.17143 | − | 2.60473i | ||||
\(311\) | −1534.66 | −0.279815 | −0.139908 | − | 0.990165i | \(-0.544681\pi\) | ||||
−0.139908 | + | 0.990165i | \(0.544681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8766.55 | 1.58311 | 0.791557 | − | 0.611095i | \(-0.209271\pi\) | ||||
0.791557 | + | 0.611095i | \(0.209271\pi\) | |||||||
\(314\) | −3119.59 | − | 6936.57i | −0.560664 | − | 1.24667i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 473.408 | + | 419.870i | 0.0842762 | + | 0.0747454i | ||||
\(317\) | − | 7014.17i | − | 1.24276i | −0.783509 | − | 0.621380i | \(-0.786572\pi\) | ||
0.783509 | − | 0.621380i | \(-0.213428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1072.38i | 0.188218i | ||||||||
\(320\) | −4878.86 | + | 7043.23i | −0.852302 | + | 1.23040i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6777.04 | + | 3047.84i | −1.17289 | + | 0.527484i | ||||
\(323\) | 4866.59 | 0.838342 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1872.39 | 0.319574 | ||||||||
\(326\) | 5640.20 | − | 2536.58i | 0.958227 | − | 0.430945i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −230.172 | + | 736.496i | −0.0387473 | + | 0.123982i | ||||
\(329\) | 3608.84i | 0.604748i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 9887.94i | − | 1.64196i | −0.570954 | − | 0.820982i | \(-0.693426\pi\) | ||
0.570954 | − | 0.820982i | \(-0.306574\pi\) | |||||||
\(332\) | 4911.96 | − | 5538.28i | 0.811984 | − | 0.915520i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4154.69 | − | 9238.16i | −0.680642 | − | 1.51344i | ||||
\(335\) | −7176.76 | −1.17047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5008.19 | −0.809536 | −0.404768 | − | 0.914419i | \(-0.632648\pi\) | ||||
−0.404768 | + | 0.914419i | \(0.632648\pi\) | |||||||
\(338\) | 2379.56 | + | 5291.06i | 0.382931 | + | 0.851467i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6329.44 | − | 7136.51i | 1.00959 | − | 1.13833i | ||||
\(341\) | − | 1607.81i | − | 0.255330i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6049.14i | 0.952252i | ||||||||
\(344\) | −4.35057 | + | 13.9208i | −0.000681881 | + | 0.00218186i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −281.495 | + | 126.597i | −0.0437378 | + | 0.0196702i | ||||
\(347\) | 7795.06 | 1.20594 | 0.602969 | − | 0.797764i | \(-0.293984\pi\) | ||||
0.602969 | + | 0.797764i | \(0.293984\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9081.62 | −1.39292 | −0.696458 | − | 0.717597i | \(-0.745242\pi\) | ||||
−0.696458 | + | 0.717597i | \(0.745242\pi\) | |||||||
\(350\) | −7720.17 | + | 3472.00i | −1.17903 | + | 0.530246i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −756.891 | + | 456.130i | −0.114609 | + | 0.0690676i | ||||
\(353\) | 4554.78i | 0.686760i | 0.939197 | + | 0.343380i | \(0.111572\pi\) | ||||
−0.939197 | + | 0.343380i | \(0.888428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6465.56i | 0.966637i | ||||||||
\(356\) | −6250.05 | − | 5543.23i | −0.930483 | − | 0.825255i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −311.370 | − | 692.347i | −0.0459676 | − | 0.102211i | ||||
\(359\) | −5415.10 | −0.796095 | −0.398047 | − | 0.917365i | \(-0.630312\pi\) | ||||
−0.398047 | + | 0.917365i | \(0.630312\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2194.06 | 0.319881 | ||||||||
\(362\) | −1042.45 | − | 2317.95i | −0.151354 | − | 0.336543i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1395.32 | + | 1237.52i | 0.200919 | + | 0.178197i | ||||
\(365\) | − | 12999.8i | − | 1.86422i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10656.2i | 1.51566i | 0.652452 | + | 0.757830i | \(0.273740\pi\) | ||||
−0.652452 | + | 0.757830i | \(0.726260\pi\) | |||||||
\(368\) | 1040.35 | + | 8647.94i | 0.147369 | + | 1.22501i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5767.93 | + | 2594.02i | −0.810433 | + | 0.364477i | ||||
\(371\) | 5143.54 | 0.719782 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2709.97 | 0.376185 | 0.188093 | − | 0.982151i | \(-0.439769\pi\) | ||||
0.188093 | + | 0.982151i | \(0.439769\pi\) | |||||||
\(374\) | 897.288 | − | 403.538i | 0.124058 | − | 0.0557927i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4037.63 | + | 1261.85i | 0.553789 | + | 0.173072i | ||||
\(377\) | − | 2652.91i | − | 0.362418i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6395.35i | 0.866774i | 0.901208 | + | 0.433387i | \(0.142682\pi\) | ||||
−0.901208 | + | 0.433387i | \(0.857318\pi\) | |||||||
\(380\) | −6067.17 | + | 6840.80i | −0.819051 | + | 0.923489i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −597.065 | − | 1327.60i | −0.0799699 | − | 0.177817i | ||||
\(383\) | −1365.16 | −0.182131 | −0.0910656 | − | 0.995845i | \(-0.529027\pi\) | ||||
−0.0910656 | + | 0.995845i | \(0.529027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1577.01 | −0.208758 | ||||||||
\(386\) | 2853.08 | + | 6343.97i | 0.376212 | + | 0.836528i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7783.91 | − | 8776.44i | 1.01847 | − | 1.14834i | ||||
\(389\) | − | 6213.24i | − | 0.809830i | −0.914354 | − | 0.404915i | \(-0.867301\pi\) | ||
0.914354 | − | 0.404915i | \(-0.132699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9697.38i | − | 1.25427i | ||||||
\(392\) | −640.009 | − | 200.017i | −0.0824626 | − | 0.0257714i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1667.70 | + | 750.018i | −0.213243 | + | 0.0959019i | ||||
\(395\) | 1323.64 | 0.168606 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3291.69 | 0.416134 | 0.208067 | − | 0.978115i | \(-0.433283\pi\) | ||||
0.208067 | + | 0.978115i | \(0.433283\pi\) | |||||||
\(398\) | −4496.11 | + | 2022.04i | −0.566256 | + | 0.254663i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1185.13 | + | 9851.43i | 0.148141 | + | 1.23143i | ||||
\(401\) | − | 4075.53i | − | 0.507536i | −0.967265 | − | 0.253768i | \(-0.918330\pi\) | ||
0.967265 | − | 0.253768i | \(-0.0816700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3977.48i | 0.491644i | ||||||||
\(404\) | 2172.16 | + | 1926.51i | 0.267498 | + | 0.237246i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4919.31 | + | 10938.3i | 0.601333 | + | 1.33710i | ||||
\(407\) | −652.301 | −0.0794432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14109.6 | 1.70580 | 0.852900 | − | 0.522074i | \(-0.174841\pi\) | ||||
0.852900 | + | 0.522074i | \(0.174841\pi\) | |||||||
\(410\) | 662.032 | + | 1472.06i | 0.0797450 | + | 0.177317i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3221.44 | − | 2857.12i | −0.385216 | − | 0.341652i | ||||
\(413\) | − | 4028.56i | − | 0.479982i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15484.9i | − | 1.83162i | ||||||
\(416\) | 1872.44 | − | 1128.40i | 0.220682 | − | 0.132991i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −860.107 | + | 386.817i | −0.100644 | + | 0.0452628i | ||||
\(419\) | −6368.39 | −0.742521 | −0.371261 | − | 0.928529i | \(-0.621074\pi\) | ||||
−0.371261 | + | 0.928529i | \(0.621074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10812.5 | 1.25171 | 0.625853 | − | 0.779941i | \(-0.284751\pi\) | ||||
0.625853 | + | 0.779941i | \(0.284751\pi\) | |||||||
\(422\) | 10866.8 | − | 4887.15i | 1.25353 | − | 0.563750i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1798.46 | − | 5754.66i | 0.205993 | − | 0.659130i | ||||
\(425\) | − | 11046.9i | − | 1.26083i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 30.9588i | − | 0.00350867i | ||||||
\(428\) | −2284.99 | + | 2576.35i | −0.258058 | + | 0.290963i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5134 | + | 27.8241i | 0.00140337 | + | 0.00312046i | ||||
\(431\) | 10968.4 | 1.22583 | 0.612913 | − | 0.790150i | \(-0.289998\pi\) | ||||
0.612913 | + | 0.790150i | \(0.289998\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1491.10 | −0.165491 | −0.0827457 | − | 0.996571i | \(-0.526369\pi\) | ||||
−0.0827457 | + | 0.996571i | \(0.526369\pi\) | |||||||
\(434\) | −7375.49 | − | 16399.8i | −0.815748 | − | 1.81386i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4773.87 | + | 5382.59i | −0.524374 | + | 0.591237i | ||||
\(437\) | 9295.56i | 1.01754i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2225.82i | 0.241988i | 0.992653 | + | 0.120994i | \(0.0386081\pi\) | ||||
−0.992653 | + | 0.120994i | \(0.961392\pi\) | |||||||
\(440\) | −551.408 | + | 1764.38i | −0.0597439 | + | 0.191167i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2219.76 | + | 998.295i | −0.238876 | + | 0.107430i | ||||
\(443\) | 15877.5 | 1.70285 | 0.851425 | − | 0.524477i | \(-0.175739\pi\) | ||||
0.851425 | + | 0.524477i | \(0.175739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17475.0 | −1.86156 | ||||||||
\(446\) | 16556.8 | − | 7446.11i | 1.75782 | − | 0.790546i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5627.95 | + | 8124.64i | −0.593517 | + | 0.856816i | ||||
\(449\) | 11558.7i | 1.21490i | 0.794358 | + | 0.607450i | \(0.207807\pi\) | ||||
−0.794358 | + | 0.607450i | \(0.792193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 166.477i | 0.0173816i | ||||||||
\(452\) | −2286.59 | − | 2028.00i | −0.237947 | − | 0.211038i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2609.86 | + | 5803.16i | 0.269795 | + | 0.599902i | ||||
\(455\) | 3901.29 | 0.401967 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10889.7 | −1.11466 | −0.557329 | − | 0.830292i | \(-0.688174\pi\) | ||||
−0.557329 | + | 0.830292i | \(0.688174\pi\) | |||||||
\(458\) | −4026.43 | − | 8952.96i | −0.410792 | − | 0.913416i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13631.3 | + | 12089.7i | 1.38166 | + | 1.22540i | ||||
\(461\) | 11775.1i | 1.18963i | 0.803862 | + | 0.594816i | \(0.202775\pi\) | ||||
−0.803862 | + | 0.594816i | \(0.797225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2659.94i | 0.266993i | 0.991049 | + | 0.133497i | \(0.0426206\pi\) | ||||
−0.991049 | + | 0.133497i | \(0.957379\pi\) | |||||||
\(464\) | 13958.0 | − | 1679.15i | 1.39652 | − | 0.168002i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9938.21 | − | 4469.52i | 0.987937 | − | 0.444306i | ||||
\(467\) | −32.9750 | −0.00326746 | −0.00163373 | − | 0.999999i | \(-0.500520\pi\) | ||||
−0.00163373 | + | 0.999999i | \(0.500520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8278.68 | −0.815083 | ||||||||
\(470\) | 8070.16 | − | 3629.40i | 0.792018 | − | 0.356195i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4507.21 | − | 1408.61i | −0.439537 | − | 0.137365i | ||||
\(473\) | 3.14666i | 0.000305885i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10589.2i | 1.02287i | ||||||||
\(476\) | 7301.26 | − | 8232.25i | 0.703052 | − | 0.792698i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −46.2499 | − | 102.839i | −0.00442556 | − | 0.00984046i | ||||
\(479\) | 8138.15 | 0.776287 | 0.388144 | − | 0.921599i | \(-0.373116\pi\) | ||||
0.388144 | + | 0.921599i | \(0.373116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1613.70 | 0.152970 | ||||||||
\(482\) | −4012.08 | − | 8921.07i | −0.379140 | − | 0.843036i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6938.83 | − | 7823.60i | 0.651655 | − | 0.734748i | ||||
\(485\) | − | 24538.7i | − | 2.29741i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1992.29i | 0.185378i | 0.995695 | + | 0.0926891i | \(0.0295463\pi\) | ||||
−0.995695 | + | 0.0926891i | \(0.970454\pi\) | |||||||
\(488\) | −34.6371 | − | 10.8249i | −0.00321301 | − | 0.00100414i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1279.21 | + | 575.301i | −0.117936 | + | 0.0530396i | ||||
\(491\) | −8814.69 | −0.810186 | −0.405093 | − | 0.914275i | \(-0.632761\pi\) | ||||
−0.405093 | + | 0.914275i | \(0.632761\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15651.9 | −1.42987 | ||||||||
\(494\) | 2127.78 | − | 956.929i | 0.193792 | − | 0.0871544i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20927.2 | + | 2517.54i | −1.89447 | + | 0.227905i | ||||
\(497\) | 7458.28i | 0.673138i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 21076.6i | − | 1.89082i | −0.325886 | − | 0.945409i | \(-0.605662\pi\) | ||
0.325886 | − | 0.945409i | \(-0.394338\pi\) | |||||||
\(500\) | 3008.58 | + | 2668.34i | 0.269095 | + | 0.238663i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3454.36 | + | 7680.94i | 0.307123 | + | 0.682903i | ||||
\(503\) | −19011.6 | −1.68526 | −0.842629 | − | 0.538494i | \(-0.818994\pi\) | ||||
−0.842629 | + | 0.538494i | \(0.818994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6073.31 | 0.535166 | ||||||||
\(506\) | 770.788 | + | 1713.89i | 0.0677188 | + | 0.150576i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10042.6 | + | 8906.88i | 0.877103 | + | 0.777911i | ||||
\(509\) | − | 12812.5i | − | 1.11573i | −0.829932 | − | 0.557865i | \(-0.811621\pi\) | ||
0.829932 | − | 0.557865i | \(-0.188379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14995.8i | − | 1.29819i | ||||||
\(512\) | 7122.13 | + | 9137.45i | 0.614759 | + | 0.788715i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16660.3 | − | 7492.64i | 1.42968 | − | 0.642970i | ||||
\(515\) | −9007.06 | −0.770677 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 912.663 | 0.0776381 | ||||||||
\(518\) | −6653.53 | + | 2992.30i | −0.564361 | + | 0.253811i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1364.10 | − | 4364.81i | 0.115038 | − | 0.368096i | ||||
\(521\) | 14455.7i | 1.21558i | 0.794100 | + | 0.607788i | \(0.207943\pi\) | ||||
−0.794100 | + | 0.607788i | \(0.792057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15232.9i | 1.27359i | 0.771032 | + | 0.636796i | \(0.219741\pi\) | ||||
−0.771032 | + | 0.636796i | \(0.780259\pi\) | |||||||
\(524\) | 7563.45 | − | 8527.86i | 0.630555 | − | 0.710957i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6823.74 | + | 15172.9i | 0.565645 | + | 1.25774i | ||||
\(527\) | 23466.7 | 1.93971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6355.73 | 0.522375 | ||||||||
\(530\) | −5172.84 | − | 11502.1i | −0.423950 | − | 0.942675i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6998.72 | + | 7891.13i | −0.570363 | + | 0.643090i | ||||
\(533\) | − | 411.841i | − | 0.0334687i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7203.40i | 0.582113i | ||||||||
\(536\) | −2894.68 | + | 9262.30i | −0.233267 | + | 0.746400i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7653.73 | − | 3442.12i | 0.613338 | − | 0.275837i | ||||
\(539\) | −144.667 | −0.0115608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23075.7 | −1.83383 | −0.916915 | − | 0.399083i | \(-0.869328\pi\) | ||||
−0.916915 | + | 0.399083i | \(0.869328\pi\) | |||||||
\(542\) | 5122.46 | − | 2303.73i | 0.405956 | − | 0.182571i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6657.43 | − | 11047.2i | −0.524697 | − | 0.870670i | ||||
\(545\) | 15049.6i | 1.18285i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 366.215i | 0.0286256i | 0.999898 | + | 0.0143128i | \(0.00455607\pi\) | ||||
−0.999898 | + | 0.0143128i | \(0.995444\pi\) | |||||||
\(548\) | −160.540 | − | 142.385i | −0.0125145 | − | 0.0110992i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 878.056 | + | 1952.40i | 0.0680735 | + | 0.151365i | ||||
\(551\) | 15003.3 | 1.16000 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1526.87 | 0.117412 | ||||||||
\(554\) | −5038.31 | − | 11202.9i | −0.386385 | − | 0.859147i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9914.42 | + | 8793.20i | 0.756232 | + | 0.670710i | ||||
\(557\) | 3402.66i | 0.258842i | 0.991590 | + | 0.129421i | \(0.0413119\pi\) | ||||
−0.991590 | + | 0.129421i | \(0.958688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.78437i | − | 0.000588987i | ||||||
\(560\) | 2469.31 | + | 20526.3i | 0.186335 | + | 1.54892i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20112.0 | − | 9044.97i | 1.50956 | − | 0.678895i | ||||
\(563\) | −4922.90 | −0.368518 | −0.184259 | − | 0.982878i | \(-0.558989\pi\) | ||||
−0.184259 | + | 0.982878i | \(0.558989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6393.26 | −0.476047 | ||||||||
\(566\) | 5276.53 | − | 2373.02i | 0.391854 | − | 0.176229i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8344.42 | + | 2607.82i | 0.616416 | + | 0.192644i | ||||
\(569\) | 12036.3i | 0.886799i | 0.896324 | + | 0.443399i | \(0.146228\pi\) | ||||
−0.896324 | + | 0.443399i | \(0.853772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 603.568i | 0.0442356i | 0.999755 | + | 0.0221178i | \(0.00704090\pi\) | ||||
−0.999755 | + | 0.0221178i | \(0.992959\pi\) | |||||||
\(572\) | 312.965 | − | 352.871i | 0.0228772 | − | 0.0257942i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 763.680 | + | 1698.08i | 0.0555321 | + | 0.123478i | ||||
\(575\) | 21100.5 | 1.53035 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6971.52 | −0.502995 | −0.251497 | − | 0.967858i | \(-0.580923\pi\) | ||||
−0.251497 | + | 0.967858i | \(0.580923\pi\) | |||||||
\(578\) | 190.215 | + | 422.952i | 0.0136884 | + | 0.0304368i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19513.2 | − | 22001.3i | 1.39697 | − | 1.57509i | ||||
\(581\) | − | 17862.4i | − | 1.27549i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1300.78i | − | 0.0924063i | ||||||
\(584\) | −16777.5 | − | 5243.34i | −1.18880 | − | 0.371525i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6081.15 | − | 2734.88i | 0.428686 | − | 0.192793i | ||||
\(587\) | −20669.8 | −1.45338 | −0.726691 | − | 0.686964i | \(-0.758943\pi\) | ||||
−0.726691 | + | 0.686964i | \(0.758943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22494.3 | −1.57362 | ||||||||
\(590\) | −9008.74 | + | 4051.51i | −0.628617 | + | 0.282709i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1021.39 | + | 8490.33i | 0.0709102 | + | 0.589443i | ||||
\(593\) | − | 2417.22i | − | 0.167392i | −0.996491 | − | 0.0836958i | \(-0.973328\pi\) | ||
0.996491 | − | 0.0836958i | \(-0.0266724\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 23017.2i | − | 1.58590i | ||||||
\(596\) | 5102.33 | + | 4525.31i | 0.350670 | + | 0.311013i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1906.82 | − | 4239.91i | −0.130394 | − | 0.289938i | ||||
\(599\) | −28934.9 | −1.97370 | −0.986852 | − | 0.161628i | \(-0.948326\pi\) | ||||
−0.986852 | + | 0.161628i | \(0.948326\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 636.493 | 0.0431998 | 0.0215999 | − | 0.999767i | \(-0.493124\pi\) | ||||
0.0215999 | + | 0.999767i | \(0.493124\pi\) | |||||||
\(602\) | 14.4346 | + | 32.0962i | 0.000977263 | + | 0.00217299i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8791.25 | − | 7797.05i | −0.592237 | − | 0.525261i | ||||
\(605\) | − | 21874.6i | − | 1.46997i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19186.8i | 1.28298i | 0.767131 | + | 0.641490i | \(0.221683\pi\) | ||||
−0.767131 | + | 0.641490i | \(0.778317\pi\) | |||||||
\(608\) | 6381.57 | + | 10589.4i | 0.425669 | + | 0.706346i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −69.2305 | + | 31.1351i | −0.00459518 | + | 0.00206660i | ||||
\(611\) | −2257.80 | −0.149494 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6429.22 | 0.423612 | 0.211806 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211806 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(614\) | −14242.5 | + | 6405.28i | −0.936122 | + | 0.421003i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −636.070 | + | 2035.28i | −0.0416039 | + | 0.133123i | ||||
\(617\) | 6956.82i | 0.453924i | 0.973904 | + | 0.226962i | \(0.0728794\pi\) | ||||
−0.973904 | + | 0.226962i | \(0.927121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 22202.0i | − | 1.44164i | −0.693123 | − | 0.720819i | \(-0.743766\pi\) | ||
0.693123 | − | 0.720819i | \(-0.256234\pi\) | |||||||
\(620\) | −29255.9 | + | 32986.4i | −1.89508 | + | 2.13672i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1780.37 | + | 3958.75i | 0.114769 | + | 0.255195i | ||||
\(623\) | −20158.1 | −1.29634 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10967.9 | −0.701945 | ||||||||
\(626\) | −10170.2 | − | 22613.9i | −0.649331 | − | 1.44382i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14274.2 | + | 16094.4i | −0.907013 | + | 1.02267i | ||||
\(629\) | − | 9520.65i | − | 0.603519i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 529.250i | 0.0333901i | 0.999861 | + | 0.0166950i | \(0.00531444\pi\) | ||||
−0.999861 | + | 0.0166950i | \(0.994686\pi\) | |||||||
\(632\) | 533.876 | − | 1708.28i | 0.0336020 | − | 0.107519i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18093.5 | + | 8137.20i | −1.13341 | + | 0.509731i | ||||
\(635\) | 28078.9 | 1.75477 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 357.886 | 0.0222605 | ||||||||
\(638\) | 2766.27 | − | 1244.08i | 0.171658 | − | 0.0771997i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23828.5 | + | 4414.40i | 1.47172 | + | 0.272648i | ||||
\(641\) | − | 22939.6i | − | 1.41351i | −0.707458 | − | 0.706755i | \(-0.750158\pi\) | ||
0.707458 | − | 0.706755i | \(-0.249842\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2519.76i | 0.154540i | 0.997010 | + | 0.0772702i | \(0.0246204\pi\) | ||||
−0.997010 | + | 0.0772702i | \(0.975380\pi\) | |||||||
\(644\) | 15724.2 | + | 13946.0i | 0.962144 | + | 0.853335i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5645.78 | − | 12553.7i | −0.343855 | − | 0.764579i | ||||
\(647\) | −5938.61 | −0.360851 | −0.180426 | − | 0.983589i | \(-0.557748\pi\) | ||||
−0.180426 | + | 0.983589i | \(0.557748\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1018.81 | −0.0616205 | ||||||||
\(650\) | −2172.18 | − | 4829.96i | −0.131077 | − | 0.291456i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13086.5 | − | 11606.6i | −0.786054 | − | 0.697159i | ||||
\(653\) | 26052.5i | 1.56128i | 0.624984 | + | 0.780638i | \(0.285106\pi\) | ||||
−0.624984 | + | 0.780638i | \(0.714894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 23843.7i | − | 1.42237i | ||||||
\(656\) | 2166.86 | − | 260.674i | 0.128966 | − | 0.0155146i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9309.24 | − | 4186.66i | 0.551538 | − | 0.248044i | ||||
\(659\) | −28353.5 | −1.67602 | −0.838008 | − | 0.545659i | \(-0.816280\pi\) | ||||
−0.838008 | + | 0.545659i | \(0.816280\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10336.1 | −0.608210 | −0.304105 | − | 0.952638i | \(-0.598357\pi\) | ||||
−0.304105 | + | 0.952638i | \(0.598357\pi\) | |||||||
\(662\) | −25506.6 | + | 11471.1i | −1.49749 | + | 0.673469i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19984.8 | − | 6245.69i | −1.16801 | − | 0.365030i | ||||
\(665\) | 22063.4i | 1.28659i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29896.3i | − | 1.73551i | ||||||
\(668\) | −19010.5 | + | 21434.6i | −1.10111 | + | 1.24151i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8325.83 | + | 18512.9i | 0.480082 | + | 1.06749i | ||||
\(671\) | −7.82936 | −0.000450446 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15083.9 | −0.863957 | −0.431979 | − | 0.901884i | \(-0.642184\pi\) | ||||
−0.431979 | + | 0.901884i | \(0.642184\pi\) | |||||||
\(674\) | 5810.05 | + | 12918.9i | 0.332040 | + | 0.738307i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10888.1 | − | 12276.4i | 0.619486 | − | 0.698477i | ||||
\(677\) | − | 13710.5i | − | 0.778343i | −0.921165 | − | 0.389172i | \(-0.872761\pi\) | ||
0.921165 | − | 0.389172i | \(-0.127239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 28306.4i | − | 1.59985i | ||||||
\(680\) | −25751.9 | − | 8048.06i | −1.45227 | − | 0.453866i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4147.44 | + | 1865.23i | −0.232865 | + | 0.104726i | ||||
\(683\) | 807.274 | 0.0452262 | 0.0226131 | − | 0.999744i | \(-0.492801\pi\) | ||||
0.0226131 | + | 0.999744i | \(0.492801\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −448.867 | −0.0250370 | ||||||||
\(686\) | 15604.1 | − | 7017.66i | 0.868467 | − | 0.390577i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 40.9568 | − | 4.92711i | 0.00226957 | − | 0.000273030i | ||||
\(689\) | 3217.95i | 0.177930i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21946.7i | 1.20824i | 0.796894 | + | 0.604119i | \(0.206475\pi\) | ||||
−0.796894 | + | 0.604119i | \(0.793525\pi\) | |||||||
\(692\) | 653.130 | + | 579.268i | 0.0358790 | + | 0.0318215i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9043.13 | − | 20107.9i | −0.494629 | − | 1.09983i | ||||
\(695\) | 27720.5 | 1.51295 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2429.82 | −0.132046 | ||||||||
\(698\) | 10535.7 | + | 23426.6i | 0.571320 | + | 1.27036i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17912.5 | + | 15886.8i | 0.967183 | + | 0.857804i | ||||
\(701\) | − | 3170.45i | − | 0.170822i | −0.996346 | − | 0.0854110i | \(-0.972780\pi\) | ||
0.996346 | − | 0.0854110i | \(-0.0272203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9126.15i | 0.489615i | ||||||||
\(704\) | 2054.69 | + | 1423.29i | 0.109999 | + | 0.0761963i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11749.3 | − | 5284.04i | 0.626334 | − | 0.281682i | ||||
\(707\) | 7005.80 | 0.372674 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2826.07 | 0.149697 | 0.0748485 | − | 0.997195i | \(-0.476153\pi\) | ||||
0.0748485 | + | 0.997195i | \(0.476153\pi\) | |||||||
\(710\) | 16678.3 | − | 7500.76i | 0.881586 | − | 0.396477i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7048.37 | + | 22553.2i | −0.370996 | + | 1.18710i | ||||
\(713\) | 44823.2i | 2.35434i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 986.621i | − | 0.0516049i | ||||||
\(716\) | −1424.73 | + | 1606.40i | −0.0743640 | + | 0.0838462i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6282.11 | + | 13968.6i | 0.326527 | + | 0.726049i | ||||
\(719\) | 15469.9 | 0.802408 | 0.401204 | − | 0.915989i | \(-0.368592\pi\) | ||||
0.401204 | + | 0.915989i | \(0.368592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10390.0 | −0.536677 | ||||||||
\(722\) | −2545.35 | − | 5659.73i | −0.131203 | − | 0.291736i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4769.93 | + | 5378.15i | −0.244853 | + | 0.276074i | ||||
\(725\) | − | 34056.8i | − | 1.74460i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7967.56i | − | 0.406465i | −0.979130 | − | 0.203233i | \(-0.934855\pi\) | ||
0.979130 | − | 0.203233i | \(-0.0651448\pi\) | |||||||
\(728\) | 1573.55 | − | 5034.98i | 0.0801092 | − | 0.256331i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −33533.8 | + | 15081.2i | −1.70019 | + | 0.764629i | ||||
\(731\) | −45.9270 | −0.00232376 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24669.3 | 1.24308 | 0.621542 | − | 0.783381i | \(-0.286506\pi\) | ||||
0.621542 | + | 0.783381i | \(0.286506\pi\) | |||||||
\(734\) | 27488.3 | − | 12362.3i | 1.38230 | − | 0.621664i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21101.0 | − | 12716.2i | 1.05678 | − | 0.636855i | ||||
\(737\) | 2093.65i | 0.104641i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1182.09i | 0.0588414i | 0.999567 | + | 0.0294207i | \(0.00936624\pi\) | ||||
−0.999567 | + | 0.0294207i | \(0.990634\pi\) | |||||||
\(740\) | 13382.9 | + | 11869.4i | 0.664816 | + | 0.589632i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5967.07 | − | 13268.1i | −0.295226 | − | 0.656451i | ||||
\(743\) | −27232.9 | −1.34465 | −0.672327 | − | 0.740255i | \(-0.734705\pi\) | ||||
−0.672327 | + | 0.740255i | \(0.734705\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14266.0 | 0.701565 | ||||||||
\(746\) | −3143.87 | − | 6990.55i | −0.154296 | − | 0.343086i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2081.90 | − | 1846.46i | −0.101767 | − | 0.0902584i | ||||
\(749\) | 8309.41i | 0.405366i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14188.0i | 0.689383i | 0.938716 | + | 0.344692i | \(0.112017\pi\) | ||||
−0.938716 | + | 0.344692i | \(0.887983\pi\) | |||||||
\(752\) | −1429.07 | − | 11879.2i | −0.0692989 | − | 0.576050i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6843.34 | + | 3077.66i | −0.330530 | + | 0.148650i | ||||
\(755\) | −24580.1 | −1.18485 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30482.1 | 1.46353 | 0.731764 | − | 0.681559i | \(-0.238698\pi\) | ||||
0.731764 | + | 0.681559i | \(0.238698\pi\) | |||||||
\(758\) | 16497.2 | − | 7419.31i | 0.790509 | − | 0.355517i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24684.9 | + | 7714.58i | 1.17818 | + | 0.368207i | ||||
\(761\) | 23077.5i | 1.09929i | 0.835398 | + | 0.549645i | \(0.185237\pi\) | ||||
−0.835398 | + | 0.549645i | \(0.814763\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17360.3i | 0.823703i | ||||||||
\(764\) | −2731.98 | + | 3080.33i | −0.129371 | + | 0.145867i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1583.73 | + | 3521.51i | 0.0747031 | + | 0.166106i | ||||
\(767\) | 2520.38 | 0.118652 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2070.62 | 0.0970982 | 0.0485491 | − | 0.998821i | \(-0.484540\pi\) | ||||
0.0485491 | + | 0.998821i | \(0.484540\pi\) | |||||||
\(770\) | 1829.50 | + | 4067.99i | 0.0856242 | + | 0.190390i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13054.8 | − | 14719.4i | 0.608617 | − | 0.686222i | ||||
\(773\) | 35103.0i | 1.63333i | 0.577110 | + | 0.816666i | \(0.304180\pi\) | ||||
−0.577110 | + | 0.816666i | \(0.695820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51061.1i | 2.36667i | ||||||||
\(776\) | −31669.6 | − | 9897.45i | −1.46504 | − | 0.457858i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16027.5 | + | 7208.04i | −0.738576 | + | 0.332161i | ||||
\(779\) | 2329.13 | 0.107124 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1886.17 | 0.0864180 | ||||||||
\(782\) | −25015.0 | + | 11250.0i | −1.14391 | + | 0.514450i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 226.523 | + | 1882.98i | 0.0103190 | + | 0.0857774i | ||||
\(785\) | 44999.4i | 2.04599i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23811.0i | 1.07849i | 0.842149 | + | 0.539245i | \(0.181290\pi\) | ||||
−0.842149 | + | 0.539245i | \(0.818710\pi\) | |||||||
\(788\) | 3869.43 | + | 3431.84i | 0.174928 | + | 0.155145i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1535.56 | − | 3414.41i | −0.0691556 | − | 0.153771i | ||||
\(791\) | −7374.87 | −0.331505 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.3687 | 0.000867343 | ||||||||
\(794\) | −3818.72 | − | 8491.13i | −0.170682 | − | 0.379520i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10432.0 | + | 9252.22i | 0.464512 | + | 0.411980i | ||||
\(797\) | 2401.17i | 0.106718i | 0.998575 | + | 0.0533588i | \(0.0169927\pi\) | ||||
−0.998575 | + | 0.0533588i | \(0.983007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13320.8i | 0.589805i | ||||||||
\(800\) | 24037.5 | − | 14485.9i | 1.06232 | − | 0.640190i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10513.1 | + | 4728.06i | −0.462880 | + | 0.208171i | ||||
\(803\) | −3792.37 | −0.166662 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43964.5 | 1.92490 | ||||||||
\(806\) | 10260.2 | − | 4614.32i | 0.448386 | − | 0.201653i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2449.61 | − | 7838.19i | 0.106655 | − | 0.341270i | ||||
\(809\) | − | 29338.0i | − | 1.27499i | −0.770453 | − | 0.637497i | \(-0.779970\pi\) | ||
0.770453 | − | 0.637497i | \(-0.220030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30884.9i | 1.33726i | 0.743597 | + | 0.668629i | \(0.233118\pi\) | ||||
−0.743597 | + | 0.668629i | \(0.766882\pi\) | |||||||
\(812\) | 22509.2 | − | 25379.4i | 0.972806 | − | 1.09685i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 756.741 | + | 1682.65i | 0.0325845 | + | 0.0724532i | ||||
\(815\) | −36589.6 | −1.57261 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.0239 | 0.00188519 | ||||||||
\(818\) | −16368.6 | − | 36396.5i | −0.699653 | − | 1.55571i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3029.25 | − | 3415.51i | 0.129007 | − | 0.145457i | ||||
\(821\) | − | 20041.8i | − | 0.851965i | −0.904731 | − | 0.425983i | \(-0.859928\pi\) | ||
0.904731 | − | 0.425983i | \(-0.140072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 6233.57i | − | 0.264020i | −0.991248 | − | 0.132010i | \(-0.957857\pi\) | ||
0.991248 | − | 0.132010i | \(-0.0421431\pi\) | |||||||
\(824\) | −3632.91 | + | 11624.5i | −0.153590 | + | 0.491454i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10391.9 | + | 4673.57i | −0.437750 | + | 0.196870i | ||||
\(827\) | −43288.8 | −1.82019 | −0.910096 | − | 0.414397i | \(-0.863993\pi\) | ||||
−0.910096 | + | 0.414397i | \(0.863993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15655.6 | −0.655902 | −0.327951 | − | 0.944695i | \(-0.606358\pi\) | ||||
−0.327951 | + | 0.944695i | \(0.606358\pi\) | |||||||
\(830\) | −39944.3 | + | 17964.2i | −1.67047 | + | 0.751261i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5083.01 | − | 3521.01i | −0.211805 | − | 0.146718i | ||||
\(833\) | − | 2111.49i | − | 0.0878256i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 59930.6i | 2.48381i | ||||||||
\(836\) | 1995.64 | + | 1769.95i | 0.0825605 | + | 0.0732237i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7388.04 | + | 16427.7i | 0.304553 | + | 0.677189i | ||||
\(839\) | 45586.9 | 1.87585 | 0.937924 | − | 0.346842i | \(-0.112746\pi\) | ||||
0.937924 | + | 0.346842i | \(0.112746\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23864.5 | −0.978493 | ||||||||
\(842\) | −12543.7 | − | 27891.5i | −0.513401 | − | 1.14157i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25213.4 | − | 22362.0i | −1.02830 | − | 0.912006i | ||||
\(845\) | − | 34324.6i | − | 1.39740i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 25233.2i | − | 1.02364i | ||||||
\(848\) | −16930.9 | + | 2036.79i | −0.685626 | + | 0.0824809i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −28496.2 | + | 12815.6i | −1.14990 | + | 0.517145i | ||||
\(851\) | 18185.2 | 0.732526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2637.97 | 0.105888 | 0.0529439 | − | 0.998597i | \(-0.483140\pi\) | ||||
0.0529439 | + | 0.998597i | \(0.483140\pi\) | |||||||
\(854\) | −79.8601 | + | 35.9156i | −0.00319995 | + | 0.00143912i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9296.68 | + | 2905.42i | 0.371208 | + | 0.116011i | ||||
\(857\) | − | 24327.4i | − | 0.969670i | −0.874606 | − | 0.484835i | \(-0.838880\pi\) | ||
0.874606 | − | 0.484835i | \(-0.161120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44905.2i | − | 1.78364i | −0.452391 | − | 0.891819i | \(-0.649429\pi\) | ||
0.452391 | − | 0.891819i | \(-0.350571\pi\) | |||||||
\(860\) | 57.2571 | − | 64.5580i | 0.00227029 | − | 0.00255978i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12724.6 | − | 28293.8i | −0.502786 | − | 1.11797i | ||||
\(863\) | −3830.25 | −0.151081 | −0.0755406 | − | 0.997143i | \(-0.524068\pi\) | ||||
−0.0755406 | + | 0.997143i | \(0.524068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1826.14 | 0.0717809 | ||||||||
\(866\) | 1729.84 | + | 3846.39i | 0.0678781 | + | 0.150930i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33747.9 | + | 38051.1i | −1.31967 | + | 1.48795i | ||||
\(869\) | − | 386.139i | − | 0.0150735i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 5179.38i | − | 0.201489i | ||||||
\(872\) | 19423.0 | + | 6070.11i | 0.754294 | + | 0.235734i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23978.5 | − | 10783.9i | 0.928014 | − | 0.417357i | ||||
\(875\) | 9703.47 | 0.374900 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25099.3 | 0.966412 | 0.483206 | − | 0.875507i | \(-0.339472\pi\) | ||||
0.483206 | + | 0.875507i | \(0.339472\pi\) | |||||||
\(878\) | 5741.64 | − | 2582.19i | 0.220696 | − | 0.0992538i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5191.02 | − | 624.480i | 0.198851 | − | 0.0239218i | ||||
\(881\) | 3336.88i | 0.127608i | 0.997962 | + | 0.0638038i | \(0.0203232\pi\) | ||||
−0.997962 | + | 0.0638038i | \(0.979677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26792.8i | − | 1.02112i | −0.859841 | − | 0.510561i | \(-0.829438\pi\) | ||
0.859841 | − | 0.510561i | \(-0.170562\pi\) | |||||||
\(884\) | 5150.33 | + | 4567.88i | 0.195955 | + | 0.173795i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18419.6 | − | 40957.0i | −0.698442 | − | 1.55302i | ||||
\(887\) | 26009.8 | 0.984580 | 0.492290 | − | 0.870431i | \(-0.336160\pi\) | ||||
0.492290 | + | 0.870431i | \(0.336160\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32390.1 | 1.22197 | ||||||||
\(890\) | 20272.9 | + | 45077.9i | 0.763539 | + | 1.69777i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −38415.4 | − | 34071.0i | −1.44198 | − | 1.27890i | ||||
\(893\) | − | 12768.8i | − | 0.478490i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4491.45i | 0.167746i | ||||||||
\(896\) | 27487.1 | + | 5092.18i | 1.02486 | + | 0.189864i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29816.5 | − | 13409.4i | 1.10800 | − | 0.498304i | ||||
\(899\) | 72346.0 | 2.68395 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18985.5 | 0.701998 | ||||||||
\(902\) | 429.439 | − | 193.132i | 0.0158523 | − | 0.00712926i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2578.66 | + | 8251.11i | −0.0948727 | + | 0.303571i | ||||
\(905\) | 15037.2i | 0.552324i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 27354.8i | − | 1.00144i | −0.865610 | − | 0.500718i | \(-0.833069\pi\) | ||
0.865610 | − | 0.500718i | \(-0.166931\pi\) | |||||||
\(908\) | 11941.9 | − | 13464.6i | 0.436460 | − | 0.492113i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4525.92 | − | 10063.6i | −0.164871 | − | 0.366599i | ||||
\(911\) | 5323.87 | 0.193620 | 0.0968100 | − | 0.995303i | \(-0.469136\pi\) | ||||
0.0968100 | + | 0.995303i | \(0.469136\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4517.35 | −0.163748 | ||||||||
\(914\) | 12633.2 | + | 28090.7i | 0.457189 | + | 1.01658i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18423.6 | + | 20772.8i | −0.664557 | + | 0.749295i | ||||
\(917\) | − | 27504.7i | − | 0.990495i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3951.52i | − | 0.141837i | −0.997482 | − | 0.0709187i | \(-0.977407\pi\) | ||
0.997482 | − | 0.0709187i | \(-0.0225931\pi\) | |||||||
\(920\) | 15372.4 | − | 49188.1i | 0.550884 | − | 1.76270i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30374.6 | − | 13660.4i | 1.08496 | − | 0.487940i | ||||
\(923\) | −4666.11 | −0.166400 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20715.9 | 0.736362 | ||||||||
\(926\) | 6861.49 | − | 3085.82i | 0.243502 | − | 0.109510i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20524.3 | − | 34057.6i | −0.726017 | − | 1.20474i | ||||
\(929\) | 3123.74i | 0.110319i | 0.998478 | + | 0.0551597i | \(0.0175668\pi\) | ||||
−0.998478 | + | 0.0551597i | \(0.982433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2024.00i | 0.0712501i | ||||||||
\(932\) | −23058.8 | − | 20451.1i | −0.810426 | − | 0.718775i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38.2547 | + | 85.0612i | 0.00134018 | + | 0.00297996i | ||||
\(935\) | −5820.96 | −0.203600 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24002.2 | 0.836838 | 0.418419 | − | 0.908254i | \(-0.362584\pi\) | ||||
0.418419 | + | 0.908254i | \(0.362584\pi\) | |||||||
\(938\) | 9604.17 | + | 21355.4i | 0.334315 | + | 0.743366i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18724.5 | − | 16607.0i | −0.649710 | − | 0.576234i | ||||
\(941\) | − | 48617.9i | − | 1.68427i | −0.539267 | − | 0.842135i | \(-0.681299\pi\) | ||
0.539267 | − | 0.842135i | \(-0.318701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4641.13i | − | 0.160272i | ||||||
\(944\) | 1595.27 | + | 13260.8i | 0.0550019 | + | 0.457205i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.11700 | − | 3.65047i | 0.000278971 | − | 0.000125462i | ||||
\(947\) | −19740.7 | −0.677388 | −0.338694 | − | 0.940897i | \(-0.609985\pi\) | ||||
−0.338694 | + | 0.940897i | \(0.609985\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9381.78 | 0.320912 | ||||||||
\(950\) | 27315.5 | − | 12284.6i | 0.932874 | − | 0.419542i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29705.9 | − | 9283.75i | −1.01132 | − | 0.316059i | ||||
\(953\) | 47895.5i | 1.62800i | 0.580863 | + | 0.814002i | \(0.302715\pi\) | ||||
−0.580863 | + | 0.814002i | \(0.697285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8612.54i | 0.291827i | ||||||||
\(956\) | −211.625 | + | 238.609i | −0.00715944 | + | 0.00807234i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9441.15 | − | 20992.9i | −0.318403 | − | 0.707984i | ||||
\(959\) | −517.786 | −0.0174350 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −78676.8 | −2.64096 | ||||||||
\(962\) | −1872.07 | − | 4162.64i | −0.0627421 | − | 0.139510i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18358.0 | + | 20698.8i | −0.613352 | + | 0.691561i | ||||
\(965\) | − | 41155.1i | − | 1.37288i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46121.5i | 1.53378i | 0.641776 | + | 0.766892i | \(0.278198\pi\) | ||||
−0.641776 | + | 0.766892i | \(0.721802\pi\) | |||||||
\(968\) | −28231.3 | − | 8822.91i | −0.937383 | − | 0.292953i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −63299.2 | + | 28467.6i | −2.09527 | + | 0.942309i | ||||
\(971\) | 51058.5 | 1.68748 | 0.843741 | − | 0.536751i | \(-0.180349\pi\) | ||||
0.843741 | + | 0.536751i | \(0.180349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31976.7 | 1.05357 | ||||||||
\(974\) | 5139.23 | − | 2311.27i | 0.169067 | − | 0.0760349i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.2594 | + | 101.907i | 0.000402063 | + | 0.00334216i | ||||
\(977\) | − | 22394.9i | − | 0.733342i | −0.930351 | − | 0.366671i | \(-0.880498\pi\) | ||
0.930351 | − | 0.366671i | \(-0.119502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5097.91i | 0.166425i | ||||||||
\(980\) | 2968.05 | + | 2632.39i | 0.0967457 | + | 0.0858047i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10226.0 | + | 22738.0i | 0.332307 | + | 0.738900i | ||||
\(983\) | −13397.6 | −0.434706 | −0.217353 | − | 0.976093i | \(-0.569742\pi\) | ||||
−0.217353 | + | 0.976093i | \(0.569742\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10818.9 | 0.349967 | ||||||||
\(986\) | 18157.9 | + | 40375.0i | 0.586476 | + | 1.30406i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4936.92 | − | 4378.60i | −0.158972 | − | 0.140994i | ||||
\(989\) | − | 87.7240i | − | 0.00282049i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24672.3i | − | 0.790858i | −0.918496 | − | 0.395429i | \(-0.870596\pi\) | ||
0.918496 | − | 0.395429i | \(-0.129404\pi\) | |||||||
\(992\) | 30772.0 | + | 51062.3i | 0.984890 | + | 1.63430i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19239.1 | − | 8652.42i | 0.613910 | − | 0.276095i | ||||
\(995\) | 29167.6 | 0.929320 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58064.2 | 1.84445 | 0.922223 | − | 0.386659i | \(-0.126371\pi\) | ||||
0.922223 | + | 0.386659i | \(0.126371\pi\) | |||||||
\(998\) | −54368.4 | + | 24451.2i | −1.72445 | + | 0.775539i | ||||
\(999\) | 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 | 324.4.b.c.323.9 | 24 | ||
3.2 | odd | 2 | inner | 324.4.b.c.323.16 | 24 | ||
4.3 | odd | 2 | inner | 324.4.b.c.323.15 | 24 | ||
9.2 | odd | 6 | 108.4.h.b.71.9 | 24 | |||
9.4 | even | 3 | 108.4.h.b.35.12 | 24 | |||
9.5 | odd | 6 | 36.4.h.b.11.1 | ✓ | 24 | ||
9.7 | even | 3 | 36.4.h.b.23.4 | yes | 24 | ||
12.11 | even | 2 | inner | 324.4.b.c.323.10 | 24 | ||
36.7 | odd | 6 | 36.4.h.b.23.1 | yes | 24 | ||
36.11 | even | 6 | 108.4.h.b.71.12 | 24 | |||
36.23 | even | 6 | 36.4.h.b.11.4 | yes | 24 | ||
36.31 | odd | 6 | 108.4.h.b.35.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.1 | ✓ | 24 | 9.5 | odd | 6 | ||
36.4.h.b.11.4 | yes | 24 | 36.23 | even | 6 | ||
36.4.h.b.23.1 | yes | 24 | 36.7 | odd | 6 | ||
36.4.h.b.23.4 | yes | 24 | 9.7 | even | 3 | ||
108.4.h.b.35.9 | 24 | 36.31 | odd | 6 | |||
108.4.h.b.35.12 | 24 | 9.4 | even | 3 | |||
108.4.h.b.71.9 | 24 | 9.2 | odd | 6 | |||
108.4.h.b.71.12 | 24 | 36.11 | even | 6 | |||
324.4.b.c.323.9 | 24 | 1.1 | even | 1 | trivial | ||
324.4.b.c.323.10 | 24 | 12.11 | even | 2 | inner | ||
324.4.b.c.323.15 | 24 | 4.3 | odd | 2 | inner | ||
324.4.b.c.323.16 | 24 | 3.2 | odd | 2 | inner |