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 | 323.11 | ||
Character | \(\chi\) | \(=\) | 324.323 |
Dual form | 324.4.b.c.323.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.513200 | − | 2.78148i | −0.181444 | − | 0.983401i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.47325 | + | 2.85491i | −0.934156 | + | 0.356864i | ||||
\(5\) | 2.40947i | 0.215510i | 0.994177 | + | 0.107755i | \(0.0343662\pi\) | ||||
−0.994177 | + | 0.107755i | \(0.965634\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.66000i | − | 0.143626i | −0.997418 | − | 0.0718131i | \(-0.977121\pi\) | ||
0.997418 | − | 0.0718131i | \(-0.0228785\pi\) | |||||||
\(8\) | 11.7761 | + | 19.3216i | 0.520437 | + | 0.853900i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.70190 | − | 1.23654i | 0.211933 | − | 0.0391029i | ||||
\(11\) | −48.2857 | −1.32352 | −0.661758 | − | 0.749717i | \(-0.730190\pi\) | ||||
−0.661758 | + | 0.749717i | \(0.730190\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.7140 | 0.868618 | 0.434309 | − | 0.900764i | \(-0.356993\pi\) | ||||
0.434309 | + | 0.900764i | \(0.356993\pi\) | |||||||
\(14\) | −7.39872 | + | 1.36511i | −0.141242 | + | 0.0260601i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 47.6990 | − | 42.6709i | 0.745297 | − | 0.666733i | ||||
\(17\) | − | 36.3729i | − | 0.518925i | −0.965753 | − | 0.259463i | \(-0.916455\pi\) | ||
0.965753 | − | 0.259463i | \(-0.0835455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 125.173i | 1.51141i | 0.654914 | + | 0.755703i | \(0.272705\pi\) | ||||
−0.654914 | + | 0.755703i | \(0.727295\pi\) | |||||||
\(20\) | −6.87883 | − | 18.0066i | −0.0769076 | − | 0.201320i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 24.7802 | + | 134.306i | 0.240144 | + | 1.30155i | ||||
\(23\) | 194.112 | 1.75979 | 0.879894 | − | 0.475169i | \(-0.157613\pi\) | ||||
0.879894 | + | 0.475169i | \(0.157613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 119.194 | 0.953556 | ||||||||
\(26\) | −20.8944 | − | 113.245i | −0.157605 | − | 0.854200i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.59405 | + | 19.8788i | 0.0512550 | + | 0.134169i | ||||
\(29\) | − | 177.354i | − | 1.13565i | −0.823149 | − | 0.567826i | \(-0.807785\pi\) | ||
0.823149 | − | 0.567826i | \(-0.192215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 175.582i | − | 1.01727i | −0.860982 | − | 0.508636i | \(-0.830150\pi\) | ||
0.860982 | − | 0.508636i | \(-0.169850\pi\) | |||||||
\(32\) | −143.167 | − | 110.775i | −0.790895 | − | 0.611951i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −101.171 | + | 18.6666i | −0.510312 | + | 0.0941557i | ||||
\(35\) | 6.40918 | 0.0309529 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 199.364 | 0.885818 | 0.442909 | − | 0.896566i | \(-0.353946\pi\) | ||||
0.442909 | + | 0.896566i | \(0.353946\pi\) | |||||||
\(38\) | 348.167 | − | 64.2389i | 1.48632 | − | 0.274235i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −46.5547 | + | 28.3743i | −0.184024 | + | 0.112159i | ||||
\(41\) | − | 233.037i | − | 0.887665i | −0.896110 | − | 0.443832i | \(-0.853619\pi\) | ||
0.896110 | − | 0.443832i | \(-0.146381\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 291.623i | 1.03424i | 0.855914 | + | 0.517118i | \(0.172995\pi\) | ||||
−0.855914 | + | 0.517118i | \(0.827005\pi\) | |||||||
\(44\) | 360.851 | − | 137.851i | 1.23637 | − | 0.472315i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −99.6182 | − | 539.918i | −0.319302 | − | 1.73058i | ||||
\(47\) | 61.8953 | 0.192093 | 0.0960463 | − | 0.995377i | \(-0.469380\pi\) | ||||
0.0960463 | + | 0.995377i | \(0.469380\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 335.924 | 0.979372 | ||||||||
\(50\) | −61.1706 | − | 331.537i | −0.173017 | − | 0.937728i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −304.266 | + | 116.235i | −0.811425 | + | 0.309978i | ||||
\(53\) | − | 352.175i | − | 0.912735i | −0.889791 | − | 0.456367i | \(-0.849150\pi\) | ||
0.889791 | − | 0.456367i | \(-0.150850\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 116.343i | − | 0.285231i | ||||||
\(56\) | 51.3952 | − | 31.3245i | 0.122642 | − | 0.0747484i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −493.308 | + | 91.0183i | −1.11680 | + | 0.206057i | ||||
\(59\) | −141.582 | −0.312414 | −0.156207 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156207 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.4304 | 0.0323878 | 0.0161939 | − | 0.999869i | \(-0.494845\pi\) | ||||
0.0161939 | + | 0.999869i | \(0.494845\pi\) | |||||||
\(62\) | −488.377 | + | 90.1086i | −1.00039 | + | 0.184577i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −234.645 | + | 455.067i | −0.458291 | + | 0.888802i | ||||
\(65\) | 98.0993i | 0.187196i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 152.024i | 0.277204i | 0.990348 | + | 0.138602i | \(0.0442609\pi\) | ||||
−0.990348 | + | 0.138602i | \(0.955739\pi\) | |||||||
\(68\) | 103.841 | + | 271.824i | 0.185186 | + | 0.484758i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.28919 | − | 17.8270i | −0.00561620 | − | 0.0304391i | ||||
\(71\) | 28.0331 | 0.0468580 | 0.0234290 | − | 0.999726i | \(-0.492542\pi\) | ||||
0.0234290 | + | 0.999726i | \(0.492542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 124.499 | 0.199609 | 0.0998047 | − | 0.995007i | \(-0.468178\pi\) | ||||
0.0998047 | + | 0.995007i | \(0.468178\pi\) | |||||||
\(74\) | −102.314 | − | 554.527i | −0.160726 | − | 0.871115i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −357.358 | − | 935.451i | −0.539366 | − | 1.41189i | ||||
\(77\) | 128.440i | 0.190092i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 748.721i | − | 1.06630i | −0.846021 | − | 0.533150i | \(-0.821008\pi\) | ||
0.846021 | − | 0.533150i | \(-0.178992\pi\) | |||||||
\(80\) | 102.814 | + | 114.929i | 0.143687 | + | 0.160619i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −648.187 | + | 119.595i | −0.872931 | + | 0.161061i | ||||
\(83\) | 348.888 | 0.461390 | 0.230695 | − | 0.973026i | \(-0.425900\pi\) | ||||
0.230695 | + | 0.973026i | \(0.425900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 87.6396 | 0.111833 | ||||||||
\(86\) | 811.144 | − | 149.661i | 1.01707 | − | 0.187655i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −568.619 | − | 932.955i | −0.688807 | − | 1.13015i | ||||
\(89\) | 416.864i | 0.496488i | 0.968698 | + | 0.248244i | \(0.0798535\pi\) | ||||
−0.968698 | + | 0.248244i | \(0.920146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 108.299i | − | 0.124756i | ||||||
\(92\) | −1450.65 | + | 554.172i | −1.64392 | + | 0.628005i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −31.7647 | − | 172.160i | −0.0348540 | − | 0.188904i | ||||
\(95\) | −301.601 | −0.325723 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1505.13 | 1.57549 | 0.787747 | − | 0.615999i | \(-0.211248\pi\) | ||||
0.787747 | + | 0.615999i | \(0.211248\pi\) | |||||||
\(98\) | −172.396 | − | 934.367i | −0.177701 | − | 0.963115i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −890.770 | + | 340.289i | −0.890770 | + | 0.340289i | ||||
\(101\) | − | 435.424i | − | 0.428973i | −0.976727 | − | 0.214487i | \(-0.931192\pi\) | ||
0.976727 | − | 0.214487i | \(-0.0688078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1745.36i | 1.66966i | 0.550506 | + | 0.834831i | \(0.314435\pi\) | ||||
−0.550506 | + | 0.834831i | \(0.685565\pi\) | |||||||
\(104\) | 479.454 | + | 786.658i | 0.452061 | + | 0.741713i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −979.567 | + | 180.736i | −0.897585 | + | 0.165610i | ||||
\(107\) | 783.805 | 0.708161 | 0.354081 | − | 0.935215i | \(-0.384794\pi\) | ||||
0.354081 | + | 0.935215i | \(0.384794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1581.89 | 1.39007 | 0.695035 | − | 0.718976i | \(-0.255389\pi\) | ||||
0.695035 | + | 0.718976i | \(0.255389\pi\) | |||||||
\(110\) | −323.606 | + | 59.7072i | −0.280496 | + | 0.0517533i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −113.504 | − | 126.879i | −0.0957604 | − | 0.107044i | ||||
\(113\) | − | 443.829i | − | 0.369486i | −0.982787 | − | 0.184743i | \(-0.940855\pi\) | ||
0.982787 | − | 0.184743i | \(-0.0591453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 467.707i | 0.379252i | ||||||||
\(116\) | 506.331 | + | 1325.41i | 0.405273 | + | 1.06088i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 72.6600 | + | 393.808i | 0.0566855 | + | 0.307228i | ||||
\(119\) | −96.7518 | −0.0745313 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1000.51 | 0.751697 | ||||||||
\(122\) | −7.91886 | − | 42.9192i | −0.00587656 | − | 0.0318502i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 501.270 | + | 1312.17i | 0.363027 | + | 0.950291i | ||||
\(125\) | 588.380i | 0.421010i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 425.829i | − | 0.297529i | −0.988873 | − | 0.148765i | \(-0.952470\pi\) | ||
0.988873 | − | 0.148765i | \(-0.0475297\pi\) | |||||||
\(128\) | 1386.18 | + | 419.120i | 0.957203 | + | 0.289416i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 272.861 | − | 50.3445i | 0.184088 | − | 0.0339654i | ||||
\(131\) | −1743.67 | −1.16294 | −0.581471 | − | 0.813567i | \(-0.697522\pi\) | ||||
−0.581471 | + | 0.813567i | \(0.697522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 332.960 | 0.217078 | ||||||||
\(134\) | 422.851 | − | 78.0187i | 0.272603 | − | 0.0502969i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 702.782 | − | 428.333i | 0.443110 | − | 0.270068i | ||||
\(137\) | 1471.46i | 0.917632i | 0.888531 | + | 0.458816i | \(0.151726\pi\) | ||||
−0.888531 | + | 0.458816i | \(0.848274\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1278.30i | − | 0.780030i | −0.920809 | − | 0.390015i | \(-0.872470\pi\) | ||
0.920809 | − | 0.390015i | \(-0.127530\pi\) | |||||||
\(140\) | −47.8974 | + | 18.2976i | −0.0289148 | + | 0.0110459i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.3866 | − | 77.9735i | −0.00850209 | − | 0.0460802i | ||||
\(143\) | −1965.90 | −1.14963 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 427.331 | 0.244744 | ||||||||
\(146\) | −63.8928 | − | 346.291i | −0.0362179 | − | 0.196296i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1489.90 | + | 569.167i | −0.827493 | + | 0.316116i | ||||
\(149\) | 2149.07i | 1.18160i | 0.806818 | + | 0.590800i | \(0.201188\pi\) | ||||
−0.806818 | + | 0.590800i | \(0.798812\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 956.815i | 0.515659i | 0.966190 | + | 0.257829i | \(0.0830073\pi\) | ||||
−0.966190 | + | 0.257829i | \(0.916993\pi\) | |||||||
\(152\) | −2418.54 | + | 1474.06i | −1.29059 | + | 0.786592i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 357.252 | − | 65.9152i | 0.186936 | − | 0.0344909i | ||||
\(155\) | 423.059 | 0.219232 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2093.20 | 1.06405 | 0.532024 | − | 0.846729i | \(-0.321431\pi\) | ||||
0.532024 | + | 0.846729i | \(0.321431\pi\) | |||||||
\(158\) | −2082.55 | + | 384.243i | −1.04860 | + | 0.193473i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 266.909 | − | 344.958i | 0.131881 | − | 0.170446i | ||||
\(161\) | − | 516.337i | − | 0.252752i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1468.60i | 0.705703i | 0.935679 | + | 0.352851i | \(0.114788\pi\) | ||||
−0.935679 | + | 0.352851i | \(0.885212\pi\) | |||||||
\(164\) | 665.299 | + | 1741.54i | 0.316775 | + | 0.829218i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −179.049 | − | 970.424i | −0.0837163 | − | 0.453732i | ||||
\(167\) | 3048.38 | 1.41252 | 0.706261 | − | 0.707952i | \(-0.250381\pi\) | ||||
0.706261 | + | 0.707952i | \(0.250381\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −539.369 | −0.245503 | ||||||||
\(170\) | −44.9766 | − | 243.768i | −0.0202915 | − | 0.109977i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −832.558 | − | 2179.37i | −0.369081 | − | 0.966137i | ||||
\(173\) | 2775.57i | 1.21978i | 0.792484 | + | 0.609892i | \(0.208787\pi\) | ||||
−0.792484 | + | 0.609892i | \(0.791213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 317.057i | − | 0.136956i | ||||||
\(176\) | −2303.18 | + | 2060.39i | −0.986413 | + | 0.882432i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1159.50 | − | 213.934i | 0.488247 | − | 0.0900846i | ||||
\(179\) | 477.618 | 0.199435 | 0.0997174 | − | 0.995016i | \(-0.468206\pi\) | ||||
0.0997174 | + | 0.995016i | \(0.468206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −732.350 | −0.300747 | −0.150373 | − | 0.988629i | \(-0.548048\pi\) | ||||
−0.150373 | + | 0.988629i | \(0.548048\pi\) | |||||||
\(182\) | −301.232 | + | 55.5791i | −0.122686 | + | 0.0226362i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2285.89 | + | 3750.54i | 0.915859 | + | 1.50268i | ||||
\(185\) | 480.363i | 0.190902i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1756.29i | 0.686807i | ||||||||
\(188\) | −462.559 | + | 176.705i | −0.179445 | + | 0.0685509i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 154.782 | + | 838.898i | 0.0591003 | + | 0.320316i | ||||
\(191\) | −3086.00 | −1.16908 | −0.584542 | − | 0.811364i | \(-0.698726\pi\) | ||||
−0.584542 | + | 0.811364i | \(0.698726\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1634.32 | −0.609539 | −0.304769 | − | 0.952426i | \(-0.598579\pi\) | ||||
−0.304769 | + | 0.952426i | \(0.598579\pi\) | |||||||
\(194\) | −772.433 | − | 4186.49i | −0.285863 | − | 1.54934i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2510.45 | + | 959.034i | −0.914886 | + | 0.349502i | ||||
\(197\) | 3350.67i | 1.21181i | 0.795539 | + | 0.605903i | \(0.207188\pi\) | ||||
−0.795539 | + | 0.605903i | \(0.792812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1046.61i | 0.372826i | 0.982471 | + | 0.186413i | \(0.0596863\pi\) | ||||
−0.982471 | + | 0.186413i | \(0.940314\pi\) | |||||||
\(200\) | 1403.65 | + | 2303.02i | 0.496266 | + | 0.814241i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1211.12 | + | 223.459i | −0.421853 | + | 0.0778344i | ||||
\(203\) | −471.762 | −0.163109 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 561.496 | 0.191300 | ||||||||
\(206\) | 4854.68 | − | 895.718i | 1.64195 | − | 0.302950i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1942.02 | − | 1737.30i | 0.647378 | − | 0.579136i | ||||
\(209\) | − | 6044.08i | − | 2.00037i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5277.87i | − | 1.72201i | −0.508598 | − | 0.861004i | \(-0.669836\pi\) | ||
0.508598 | − | 0.861004i | \(-0.330164\pi\) | |||||||
\(212\) | 1005.43 | + | 2631.89i | 0.325722 | + | 0.852637i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −402.249 | − | 2180.14i | −0.128491 | − | 0.696407i | ||||
\(215\) | −702.658 | −0.222888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −467.047 | −0.146107 | ||||||||
\(218\) | −811.826 | − | 4400.00i | −0.252219 | − | 1.36700i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 332.149 | + | 869.461i | 0.101789 | + | 0.266450i | ||||
\(221\) | − | 1480.89i | − | 0.450748i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4759.70i | − | 1.42930i | −0.699484 | − | 0.714648i | \(-0.746587\pi\) | ||
0.699484 | − | 0.714648i | \(-0.253413\pi\) | |||||||
\(224\) | −294.661 | + | 380.824i | −0.0878923 | + | 0.113593i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1234.50 | + | 227.773i | −0.363353 | + | 0.0670409i | ||||
\(227\) | −2230.45 | −0.652161 | −0.326080 | − | 0.945342i | \(-0.605728\pi\) | ||||
−0.326080 | + | 0.945342i | \(0.605728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5834.58 | −1.68367 | −0.841833 | − | 0.539737i | \(-0.818524\pi\) | ||||
−0.841833 | + | 0.539737i | \(0.818524\pi\) | |||||||
\(230\) | 1300.92 | − | 240.027i | 0.372957 | − | 0.0688128i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3426.76 | − | 2088.55i | 0.969733 | − | 0.591035i | ||||
\(233\) | − | 3080.09i | − | 0.866022i | −0.901389 | − | 0.433011i | \(-0.857451\pi\) | ||
0.901389 | − | 0.433011i | \(-0.142549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 149.135i | 0.0413978i | ||||||||
\(236\) | 1058.08 | − | 404.204i | 0.291844 | − | 0.111489i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 49.6530 | + | 269.113i | 0.0135232 | + | 0.0732942i | ||||
\(239\) | 5291.45 | 1.43212 | 0.716058 | − | 0.698041i | \(-0.245945\pi\) | ||||
0.716058 | + | 0.698041i | \(0.245945\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5003.21 | −1.33728 | −0.668642 | − | 0.743585i | \(-0.733124\pi\) | ||||
−0.668642 | + | 0.743585i | \(0.733124\pi\) | |||||||
\(242\) | −513.461 | − | 2782.89i | −0.136391 | − | 0.739220i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −115.315 | + | 44.0523i | −0.0302553 | + | 0.0115580i | ||||
\(245\) | 809.401i | 0.211064i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5096.31i | 1.31283i | ||||||||
\(248\) | 3392.51 | − | 2067.68i | 0.868648 | − | 0.529426i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1636.57 | − | 301.956i | 0.414022 | − | 0.0763896i | ||||
\(251\) | 2577.68 | 0.648215 | 0.324107 | − | 0.946020i | \(-0.394936\pi\) | ||||
0.324107 | + | 0.946020i | \(0.394936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9372.83 | −2.32911 | ||||||||
\(254\) | −1184.43 | + | 218.535i | −0.292591 | + | 0.0539848i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 454.386 | − | 4070.72i | 0.110934 | − | 0.993828i | ||||
\(257\) | − | 870.567i | − | 0.211301i | −0.994403 | − | 0.105651i | \(-0.966307\pi\) | ||
0.994403 | − | 0.105651i | \(-0.0336925\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 530.308i | − | 0.127227i | ||||||
\(260\) | −280.065 | − | 733.121i | −0.0668033 | − | 0.174870i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 894.852 | + | 4849.99i | 0.211008 | + | 1.14364i | ||||
\(263\) | 4310.39 | 1.01061 | 0.505304 | − | 0.862942i | \(-0.331380\pi\) | ||||
0.505304 | + | 0.862942i | \(0.331380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 848.556 | 0.196703 | ||||||||
\(266\) | −170.875 | − | 926.122i | −0.0393873 | − | 0.213474i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −434.015 | − | 1136.11i | −0.0989241 | − | 0.258952i | ||||
\(269\) | − | 5603.52i | − | 1.27008i | −0.772478 | − | 0.635042i | \(-0.780983\pi\) | ||
0.772478 | − | 0.635042i | \(-0.219017\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2149.22i | − | 0.481756i | −0.970555 | − | 0.240878i | \(-0.922565\pi\) | ||
0.970555 | − | 0.240878i | \(-0.0774353\pi\) | |||||||
\(272\) | −1552.07 | − | 1734.95i | −0.345985 | − | 0.386753i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4092.84 | − | 755.155i | 0.902400 | − | 0.166498i | ||||
\(275\) | −5755.39 | −1.26205 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3209.99 | −0.696279 | −0.348140 | − | 0.937443i | \(-0.613186\pi\) | ||||
−0.348140 | + | 0.937443i | \(0.613186\pi\) | |||||||
\(278\) | −3555.57 | + | 656.025i | −0.767083 | + | 0.141531i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 75.4755 | + | 123.835i | 0.0161090 | + | 0.0264306i | ||||
\(281\) | 940.375i | 0.199637i | 0.995006 | + | 0.0998187i | \(0.0318263\pi\) | ||||
−0.995006 | + | 0.0998187i | \(0.968174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2050.10i | − | 0.430621i | −0.976546 | − | 0.215310i | \(-0.930924\pi\) | ||
0.976546 | − | 0.215310i | \(-0.0690763\pi\) | |||||||
\(284\) | −209.499 | + | 80.0320i | −0.0437727 | + | 0.0167219i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1008.90 | + | 5468.12i | 0.208593 | + | 1.13055i | ||||
\(287\) | −619.877 | −0.127492 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3590.01 | 0.730716 | ||||||||
\(290\) | −219.306 | − | 1188.61i | −0.0444072 | − | 0.240682i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −930.411 | + | 355.433i | −0.186466 | + | 0.0712334i | ||||
\(293\) | − | 4436.71i | − | 0.884625i | −0.896861 | − | 0.442312i | \(-0.854158\pi\) | ||
0.896861 | − | 0.442312i | \(-0.145842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 341.138i | − | 0.0673283i | ||||||
\(296\) | 2347.74 | + | 3852.03i | 0.461013 | + | 0.756400i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5977.58 | − | 1102.90i | 1.16199 | − | 0.214394i | ||||
\(299\) | 7903.08 | 1.52858 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 775.716 | 0.148543 | ||||||||
\(302\) | 2661.36 | − | 491.037i | 0.507100 | − | 0.0935630i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5341.26 | + | 5970.64i | 1.00770 | + | 1.12645i | ||||
\(305\) | 37.1790i | 0.00697988i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7392.80i | − | 1.37436i | −0.726486 | − | 0.687181i | \(-0.758848\pi\) | ||
0.726486 | − | 0.687181i | \(-0.241152\pi\) | |||||||
\(308\) | −366.684 | − | 959.862i | −0.0678368 | − | 0.177575i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −217.114 | − | 1176.73i | −0.0397782 | − | 0.215593i | ||||
\(311\) | −4896.50 | −0.892782 | −0.446391 | − | 0.894838i | \(-0.647291\pi\) | ||||
−0.446391 | + | 0.894838i | \(0.647291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 681.722 | 0.123109 | 0.0615546 | − | 0.998104i | \(-0.480394\pi\) | ||||
0.0615546 | + | 0.998104i | \(0.480394\pi\) | |||||||
\(314\) | −1074.23 | − | 5822.20i | −0.193065 | − | 1.04639i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2137.53 | + | 5595.38i | 0.380524 | + | 0.996091i | ||||
\(317\) | − | 1552.07i | − | 0.274993i | −0.990502 | − | 0.137497i | \(-0.956094\pi\) | ||
0.990502 | − | 0.137497i | \(-0.0439056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8563.69i | 1.50305i | ||||||||
\(320\) | −1096.47 | − | 565.370i | −0.191546 | − | 0.0987661i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1436.18 | + | 264.984i | −0.248556 | + | 0.0458602i | ||||
\(323\) | 4552.92 | 0.784307 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4852.88 | 0.828276 | ||||||||
\(326\) | 4084.88 | − | 753.685i | 0.693989 | − | 0.128045i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4502.63 | − | 2744.28i | 0.757977 | − | 0.461973i | ||||
\(329\) | − | 164.641i | − | 0.0275895i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7401.89i | 1.22914i | 0.788863 | + | 0.614569i | \(0.210670\pi\) | ||||
−0.788863 | + | 0.614569i | \(0.789330\pi\) | |||||||
\(332\) | −2607.33 | + | 996.043i | −0.431011 | + | 0.164653i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1564.43 | − | 8479.02i | −0.256293 | − | 1.38908i | ||||
\(335\) | −366.297 | −0.0597402 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9743.17 | −1.57491 | −0.787454 | − | 0.616373i | \(-0.788601\pi\) | ||||
−0.787454 | + | 0.616373i | \(0.788601\pi\) | |||||||
\(338\) | 276.804 | + | 1500.24i | 0.0445449 | + | 0.241428i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −654.953 | + | 250.203i | −0.104470 | + | 0.0399093i | ||||
\(341\) | 8478.09i | 1.34638i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1805.94i | − | 0.284290i | ||||||
\(344\) | −5634.61 | + | 3434.20i | −0.883134 | + | 0.538254i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7720.19 | − | 1424.42i | 1.19954 | − | 0.221322i | ||||
\(347\) | −7047.49 | −1.09029 | −0.545143 | − | 0.838343i | \(-0.683525\pi\) | ||||
−0.545143 | + | 0.838343i | \(0.683525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1207.55 | −0.185210 | −0.0926052 | − | 0.995703i | \(-0.529519\pi\) | ||||
−0.0926052 | + | 0.995703i | \(0.529519\pi\) | |||||||
\(350\) | −881.886 | + | 162.713i | −0.134682 | + | 0.0248497i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6912.94 | + | 5348.85i | 1.04676 | + | 0.809928i | ||||
\(353\) | − | 1520.13i | − | 0.229201i | −0.993412 | − | 0.114601i | \(-0.963441\pi\) | ||
0.993412 | − | 0.114601i | \(-0.0365589\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 67.5450i | 0.0100984i | ||||||||
\(356\) | −1190.11 | − | 3115.33i | −0.177179 | − | 0.463798i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −245.114 | − | 1328.48i | −0.0361862 | − | 0.196125i | ||||
\(359\) | −6515.20 | −0.957825 | −0.478912 | − | 0.877863i | \(-0.658969\pi\) | ||||
−0.478912 | + | 0.877863i | \(0.658969\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8809.35 | −1.28435 | ||||||||
\(362\) | 375.842 | + | 2037.02i | 0.0545686 | + | 0.295755i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 309.184 | + | 809.346i | 0.0445210 | + | 0.116542i | ||||
\(365\) | 299.977i | 0.0430178i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4032.62i | − | 0.573573i | −0.957995 | − | 0.286786i | \(-0.907413\pi\) | ||
0.957995 | − | 0.286786i | \(-0.0925870\pi\) | |||||||
\(368\) | 9258.94 | − | 8282.93i | 1.31156 | − | 1.17331i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1336.12 | − | 246.522i | 0.187734 | − | 0.0346380i | ||||
\(371\) | −936.784 | −0.131093 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2455.35 | 0.340840 | 0.170420 | − | 0.985372i | \(-0.445488\pi\) | ||||
0.170420 | + | 0.985372i | \(0.445488\pi\) | |||||||
\(374\) | 4885.09 | − | 901.329i | 0.675407 | − | 0.124617i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 728.888 | + | 1195.91i | 0.0999721 | + | 0.164028i | ||||
\(377\) | − | 7220.81i | − | 0.986448i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9518.27i | 1.29003i | 0.764171 | + | 0.645014i | \(0.223149\pi\) | ||||
−0.764171 | + | 0.645014i | \(0.776851\pi\) | |||||||
\(380\) | 2253.94 | − | 861.045i | 0.304276 | − | 0.116239i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1583.73 | + | 8583.64i | 0.212123 | + | 1.14968i | ||||
\(383\) | 9455.44 | 1.26149 | 0.630744 | − | 0.775991i | \(-0.282750\pi\) | ||||
0.630744 | + | 0.775991i | \(0.282750\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −309.472 | −0.0409666 | ||||||||
\(386\) | 838.733 | + | 4545.83i | 0.110597 | + | 0.599421i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11248.2 | + | 4297.01i | −1.47176 | + | 0.562236i | ||||
\(389\) | 2966.07i | 0.386596i | 0.981140 | + | 0.193298i | \(0.0619184\pi\) | ||||
−0.981140 | + | 0.193298i | \(0.938082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7060.42i | − | 0.913199i | ||||||
\(392\) | 3955.89 | + | 6490.58i | 0.509701 | + | 0.836285i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9319.83 | − | 1719.57i | 1.19169 | − | 0.219874i | ||||
\(395\) | 1804.02 | 0.229798 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1296.85 | 0.163947 | 0.0819733 | − | 0.996635i | \(-0.473878\pi\) | ||||
0.0819733 | + | 0.996635i | \(0.473878\pi\) | |||||||
\(398\) | 2911.13 | − | 537.122i | 0.366638 | − | 0.0676469i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5685.45 | − | 5086.14i | 0.710682 | − | 0.635767i | ||||
\(401\) | − | 2057.85i | − | 0.256270i | −0.991757 | − | 0.128135i | \(-0.959101\pi\) | ||
0.991757 | − | 0.128135i | \(-0.0408991\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7148.64i | − | 0.883620i | ||||||
\(404\) | 1243.10 | + | 3254.03i | 0.153085 | + | 0.400728i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 242.108 | + | 1312.20i | 0.0295951 | + | 0.160402i | ||||
\(407\) | −9626.44 | −1.17240 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5795.08 | 0.700607 | 0.350304 | − | 0.936636i | \(-0.386078\pi\) | ||||
0.350304 | + | 0.936636i | \(0.386078\pi\) | |||||||
\(410\) | −288.160 | − | 1561.79i | −0.0347102 | − | 0.188125i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4982.84 | − | 13043.5i | −0.595842 | − | 1.55973i | ||||
\(413\) | 376.608i | 0.0448709i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 840.635i | 0.0994341i | ||||||||
\(416\) | −5828.92 | − | 4510.09i | −0.686986 | − | 0.531552i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16811.5 | + | 3101.82i | −1.96717 | + | 0.362955i | ||||
\(419\) | 14105.2 | 1.64460 | 0.822298 | − | 0.569058i | \(-0.192692\pi\) | ||||
0.822298 | + | 0.569058i | \(0.192692\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6420.86 | 0.743310 | 0.371655 | − | 0.928371i | \(-0.378790\pi\) | ||||
0.371655 | + | 0.928371i | \(0.378790\pi\) | |||||||
\(422\) | −14680.3 | + | 2708.60i | −1.69343 | + | 0.312447i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6804.57 | − | 4147.26i | 0.779384 | − | 0.475021i | ||||
\(425\) | − | 4335.45i | − | 0.494824i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 41.0447i | − | 0.00465174i | ||||||
\(428\) | −5857.57 | + | 2237.69i | −0.661534 | + | 0.252717i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 360.604 | + | 1954.43i | 0.0404415 | + | 0.219188i | ||||
\(431\) | 1119.73 | 0.125140 | 0.0625700 | − | 0.998041i | \(-0.480070\pi\) | ||||
0.0625700 | + | 0.998041i | \(0.480070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −299.833 | −0.0332773 | −0.0166387 | − | 0.999862i | \(-0.505296\pi\) | ||||
−0.0166387 | + | 0.999862i | \(0.505296\pi\) | |||||||
\(434\) | 239.688 | + | 1299.08i | 0.0265102 | + | 0.143682i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11821.9 | + | 4516.16i | −1.29854 | + | 0.496066i | ||||
\(437\) | 24297.6i | 2.65976i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2413.35i | − | 0.262375i | −0.991358 | − | 0.131188i | \(-0.958121\pi\) | ||
0.991358 | − | 0.131188i | \(-0.0418791\pi\) | |||||||
\(440\) | 2247.93 | − | 1370.07i | 0.243559 | − | 0.148445i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4119.06 | + | 759.992i | −0.443266 | + | 0.0817853i | ||||
\(443\) | −4818.73 | −0.516805 | −0.258402 | − | 0.966037i | \(-0.583196\pi\) | ||||
−0.258402 | + | 0.966037i | \(0.583196\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1004.42 | −0.106998 | ||||||||
\(446\) | −13239.0 | + | 2442.68i | −1.40557 | + | 0.259337i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1210.48 | + | 624.154i | 0.127655 | + | 0.0658226i | ||||
\(449\) | 8677.13i | 0.912024i | 0.889974 | + | 0.456012i | \(0.150723\pi\) | ||||
−0.889974 | + | 0.456012i | \(0.849277\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11252.3i | 1.17484i | ||||||||
\(452\) | 1267.09 | + | 3316.85i | 0.131856 | + | 0.345158i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1144.67 | + | 6203.96i | 0.118330 | + | 0.641336i | ||||
\(455\) | 260.944 | 0.0268862 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6920.09 | −0.708333 | −0.354166 | − | 0.935182i | \(-0.615235\pi\) | ||||
−0.354166 | + | 0.935182i | \(0.615235\pi\) | |||||||
\(458\) | 2994.30 | + | 16228.8i | 0.305491 | + | 1.65572i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1335.26 | − | 3495.29i | −0.135341 | − | 0.354280i | ||||
\(461\) | 15554.8i | 1.57149i | 0.618548 | + | 0.785747i | \(0.287721\pi\) | ||||
−0.618548 | + | 0.785747i | \(0.712279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11540.5i | − | 1.15839i | −0.815189 | − | 0.579194i | \(-0.803367\pi\) | ||
0.815189 | − | 0.579194i | \(-0.196633\pi\) | |||||||
\(464\) | −7567.88 | − | 8459.63i | −0.757177 | − | 0.846397i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8567.20 | + | 1580.70i | −0.851648 | + | 0.157134i | ||||
\(467\) | 7.01271 | 0.000694881 | 0.000347441 | − | 1.00000i | \(-0.499889\pi\) | ||||
0.000347441 | 1.00000i | \(0.499889\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 404.383 | 0.0398138 | ||||||||
\(470\) | 414.816 | − | 76.5361i | 0.0407107 | − | 0.00751137i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1667.29 | − | 2735.59i | −0.162592 | − | 0.266770i | ||||
\(473\) | − | 14081.2i | − | 1.36883i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14920.0i | 1.44121i | ||||||||
\(476\) | 723.051 | − | 276.218i | 0.0696239 | − | 0.0265975i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2715.57 | − | 14718.1i | −0.259848 | − | 1.40834i | ||||
\(479\) | −5661.41 | −0.540034 | −0.270017 | − | 0.962856i | \(-0.587029\pi\) | ||||
−0.270017 | + | 0.962856i | \(0.587029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8116.92 | 0.769438 | ||||||||
\(482\) | 2567.65 | + | 13916.3i | 0.242641 | + | 1.31509i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7477.05 | + | 2856.36i | −0.702203 | + | 0.268253i | ||||
\(485\) | 3626.57i | 0.339534i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9082.26i | − | 0.845085i | −0.906343 | − | 0.422542i | \(-0.861138\pi\) | ||
0.906343 | − | 0.422542i | \(-0.138862\pi\) | |||||||
\(488\) | 181.710 | + | 298.139i | 0.0168558 | + | 0.0276559i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2251.33 | − | 415.384i | 0.207561 | − | 0.0382962i | ||||
\(491\) | −10197.6 | −0.937291 | −0.468646 | − | 0.883386i | \(-0.655258\pi\) | ||||
−0.468646 | + | 0.883386i | \(0.655258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6450.90 | −0.589319 | ||||||||
\(494\) | 14175.3 | − | 2615.42i | 1.29104 | − | 0.238205i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7492.24 | − | 8375.07i | −0.678249 | − | 0.758169i | ||||
\(497\) | − | 74.5680i | − | 0.00673004i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2717.18i | − | 0.243763i | −0.992545 | − | 0.121881i | \(-0.961107\pi\) | ||
0.992545 | − | 0.121881i | \(-0.0388928\pi\) | |||||||
\(500\) | −1679.77 | − | 4397.11i | −0.150243 | − | 0.393289i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1322.87 | − | 7169.77i | −0.117614 | − | 0.637455i | ||||
\(503\) | −8294.45 | −0.735251 | −0.367626 | − | 0.929974i | \(-0.619829\pi\) | ||||
−0.367626 | + | 0.929974i | \(0.619829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1049.14 | 0.0924479 | ||||||||
\(506\) | 4810.14 | + | 26070.3i | 0.422602 | + | 2.29045i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1215.70 | + | 3182.33i | 0.106177 | + | 0.277939i | ||||
\(509\) | 3310.11i | 0.288247i | 0.989560 | + | 0.144124i | \(0.0460363\pi\) | ||||
−0.989560 | + | 0.144124i | \(0.953964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 331.166i | − | 0.0286692i | ||||||
\(512\) | −11555.8 | + | 825.228i | −0.997460 | + | 0.0712310i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2421.46 | + | 446.775i | −0.207794 | + | 0.0383393i | ||||
\(515\) | −4205.39 | −0.359829 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2988.66 | −0.254238 | ||||||||
\(518\) | −1475.04 | + | 272.154i | −0.125115 | + | 0.0230845i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1895.43 | + | 1155.23i | −0.159846 | + | 0.0974235i | ||||
\(521\) | − | 5030.71i | − | 0.423031i | −0.977375 | − | 0.211516i | \(-0.932160\pi\) | ||
0.977375 | − | 0.211516i | \(-0.0678400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9680.16i | − | 0.809338i | −0.914463 | − | 0.404669i | \(-0.867387\pi\) | ||
0.914463 | − | 0.404669i | \(-0.132613\pi\) | |||||||
\(524\) | 13030.9 | − | 4978.02i | 1.08637 | − | 0.415012i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2212.09 | − | 11989.2i | −0.183368 | − | 0.993833i | ||||
\(527\) | −6386.42 | −0.527888 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25512.4 | 2.09686 | ||||||||
\(530\) | −435.479 | − | 2360.24i | −0.0356905 | − | 0.193438i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2488.30 | + | 950.571i | −0.202784 | + | 0.0774671i | ||||
\(533\) | − | 9487.87i | − | 0.771041i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1888.56i | 0.152616i | ||||||||
\(536\) | −2937.34 | + | 1790.26i | −0.236705 | + | 0.144267i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15586.1 | + | 2875.73i | −1.24900 | + | 0.230449i | ||||
\(539\) | −16220.3 | −1.29621 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18659.8 | 1.48290 | 0.741449 | − | 0.671009i | \(-0.234139\pi\) | ||||
0.741449 | + | 0.671009i | \(0.234139\pi\) | |||||||
\(542\) | −5978.01 | + | 1102.98i | −0.473759 | + | 0.0874115i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4029.21 | + | 5207.42i | −0.317557 | + | 0.410416i | ||||
\(545\) | 3811.52i | 0.299574i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4536.56i | − | 0.354606i | −0.984156 | − | 0.177303i | \(-0.943263\pi\) | ||
0.984156 | − | 0.177303i | \(-0.0567372\pi\) | |||||||
\(548\) | −4200.89 | − | 10996.6i | −0.327469 | − | 0.857212i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2953.66 | + | 16008.5i | 0.228990 | + | 1.24110i | ||||
\(551\) | 22200.0 | 1.71643 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1991.59 | −0.153149 | ||||||||
\(554\) | 1647.36 | + | 8928.51i | 0.126335 | + | 0.684722i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3649.44 | + | 9553.07i | 0.278364 | + | 0.728670i | ||||
\(557\) | 17657.1i | 1.34319i | 0.740918 | + | 0.671596i | \(0.234391\pi\) | ||||
−0.740918 | + | 0.671596i | \(0.765609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11873.1i | 0.898355i | ||||||||
\(560\) | 305.712 | − | 273.486i | 0.0230691 | − | 0.0206373i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2615.63 | − | 482.601i | 0.196324 | − | 0.0362229i | ||||
\(563\) | 9944.94 | 0.744457 | 0.372229 | − | 0.928141i | \(-0.378594\pi\) | ||||
0.372229 | + | 0.928141i | \(0.378594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1069.39 | 0.0796278 | ||||||||
\(566\) | −5702.30 | + | 1052.11i | −0.423473 | + | 0.0781334i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 330.122 | + | 541.643i | 0.0243866 | + | 0.0400121i | ||||
\(569\) | 4715.82i | 0.347447i | 0.984794 | + | 0.173724i | \(0.0555799\pi\) | ||||
−0.984794 | + | 0.173724i | \(0.944420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9229.75i | 0.676450i | 0.941065 | + | 0.338225i | \(0.109827\pi\) | ||||
−0.941065 | + | 0.338225i | \(0.890173\pi\) | |||||||
\(572\) | 14691.7 | − | 5612.48i | 1.07393 | − | 0.410261i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 318.121 | + | 1724.17i | 0.0231326 | + | 0.125376i | ||||
\(575\) | 23137.1 | 1.67806 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4076.34 | 0.294108 | 0.147054 | − | 0.989128i | \(-0.453021\pi\) | ||||
0.147054 | + | 0.989128i | \(0.453021\pi\) | |||||||
\(578\) | −1842.39 | − | 9985.54i | −0.132584 | − | 0.718587i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3193.55 | + | 1219.99i | −0.228629 | + | 0.0873403i | ||||
\(581\) | − | 928.039i | − | 0.0662677i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17005.0i | 1.20802i | ||||||||
\(584\) | 1466.12 | + | 2405.51i | 0.103884 | + | 0.170447i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12340.6 | + | 2276.92i | −0.869941 | + | 0.160509i | ||||
\(587\) | 8635.49 | 0.607197 | 0.303599 | − | 0.952800i | \(-0.401812\pi\) | ||||
0.303599 | + | 0.952800i | \(0.401812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21978.1 | 1.53751 | ||||||||
\(590\) | −948.869 | + | 175.072i | −0.0662107 | + | 0.0122163i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9509.47 | − | 8507.05i | 0.660197 | − | 0.590604i | ||||
\(593\) | − | 24260.9i | − | 1.68006i | −0.542537 | − | 0.840032i | \(-0.682536\pi\) | ||
0.542537 | − | 0.840032i | \(-0.317464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 233.121i | − | 0.0160622i | ||||||
\(596\) | −6135.39 | − | 16060.5i | −0.421670 | − | 1.10380i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4055.86 | − | 21982.2i | −0.277352 | − | 1.50321i | ||||
\(599\) | −15098.0 | −1.02986 | −0.514932 | − | 0.857231i | \(-0.672183\pi\) | ||||
−0.514932 | + | 0.857231i | \(0.672183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5928.26 | 0.402361 | 0.201180 | − | 0.979554i | \(-0.435522\pi\) | ||||
0.201180 | + | 0.979554i | \(0.435522\pi\) | |||||||
\(602\) | −398.097 | − | 2157.64i | −0.0269522 | − | 0.146078i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2731.62 | − | 7150.52i | −0.184020 | − | 0.481706i | ||||
\(605\) | 2410.70i | 0.161998i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18608.4i | 1.24430i | 0.782897 | + | 0.622151i | \(0.213741\pi\) | ||||
−0.782897 | + | 0.622151i | \(0.786259\pi\) | |||||||
\(608\) | 13866.1 | − | 17920.7i | 0.924907 | − | 1.19536i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 103.413 | − | 19.0803i | 0.00686403 | − | 0.00126645i | ||||
\(611\) | 2520.01 | 0.166855 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7939.25 | 0.523105 | 0.261552 | − | 0.965189i | \(-0.415766\pi\) | ||||
0.261552 | + | 0.965189i | \(0.415766\pi\) | |||||||
\(614\) | −20562.9 | + | 3793.98i | −1.35155 | + | 0.249369i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2481.65 | + | 1512.52i | −0.162319 | + | 0.0989308i | ||||
\(617\) | − | 29179.0i | − | 1.90389i | −0.306265 | − | 0.951946i | \(-0.599079\pi\) | ||
0.306265 | − | 0.951946i | \(-0.400921\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16301.7i | − | 1.05851i | −0.848462 | − | 0.529256i | \(-0.822471\pi\) | ||
0.848462 | − | 0.529256i | \(-0.177529\pi\) | |||||||
\(620\) | −3161.63 | + | 1207.80i | −0.204797 | + | 0.0782359i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2512.88 | + | 13619.5i | 0.161990 | + | 0.877963i | ||||
\(623\) | 1108.85 | 0.0713087 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13481.6 | 0.862824 | ||||||||
\(626\) | −349.860 | − | 1896.19i | −0.0223374 | − | 0.121066i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15643.0 | + | 5975.90i | −0.993988 | + | 0.379720i | ||||
\(629\) | − | 7251.46i | − | 0.459674i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2517.83i | 0.158848i | 0.996841 | + | 0.0794242i | \(0.0253082\pi\) | ||||
−0.996841 | + | 0.0794242i | \(0.974692\pi\) | |||||||
\(632\) | 14466.4 | − | 8817.04i | 0.910513 | − | 0.554942i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4317.05 | + | 796.521i | −0.270429 | + | 0.0498958i | ||||
\(635\) | 1026.02 | 0.0641205 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13676.8 | 0.850700 | ||||||||
\(638\) | 23819.7 | − | 4394.88i | 1.47811 | − | 0.272720i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1009.86 | + | 3339.96i | −0.0623720 | + | 0.206287i | ||||
\(641\) | − | 16826.3i | − | 1.03681i | −0.855134 | − | 0.518407i | \(-0.826525\pi\) | ||
0.855134 | − | 0.518407i | \(-0.173475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20423.8i | 1.25263i | 0.779572 | + | 0.626313i | \(0.215437\pi\) | ||||
−0.779572 | + | 0.626313i | \(0.784563\pi\) | |||||||
\(644\) | 1474.09 | + | 3858.71i | 0.0901979 | + | 0.236110i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2336.56 | − | 12663.8i | −0.142307 | − | 0.771289i | ||||
\(647\) | 21477.2 | 1.30503 | 0.652515 | − | 0.757776i | \(-0.273714\pi\) | ||||
0.652515 | + | 0.757776i | \(0.273714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6836.40 | 0.413485 | ||||||||
\(650\) | −2490.50 | − | 13498.2i | −0.150285 | − | 0.814527i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4192.72 | − | 10975.2i | −0.251840 | − | 0.659237i | ||||
\(653\) | 25214.7i | 1.51107i | 0.655111 | + | 0.755533i | \(0.272622\pi\) | ||||
−0.655111 | + | 0.755533i | \(0.727378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4201.33i | − | 0.250625i | ||||||
\(656\) | −9943.90 | − | 11115.6i | −0.591835 | − | 0.661573i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −457.946 | + | 84.4938i | −0.0271316 | + | 0.00500595i | ||||
\(659\) | −13730.1 | −0.811605 | −0.405802 | − | 0.913961i | \(-0.633008\pi\) | ||||
−0.405802 | + | 0.913961i | \(0.633008\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1544.08 | 0.0908588 | 0.0454294 | − | 0.998968i | \(-0.485534\pi\) | ||||
0.0454294 | + | 0.998968i | \(0.485534\pi\) | |||||||
\(662\) | 20588.2 | − | 3798.65i | 1.20874 | − | 0.223019i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4108.55 | + | 6741.05i | 0.240125 | + | 0.393981i | ||||
\(665\) | 802.258i | 0.0467823i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34426.6i | − | 1.99851i | ||||||
\(668\) | −22781.3 | + | 8702.86i | −1.31952 | + | 0.504078i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 187.984 | + | 1018.85i | 0.0108395 | + | 0.0587486i | ||||
\(671\) | −745.066 | −0.0428658 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5368.23 | −0.307474 | −0.153737 | − | 0.988112i | \(-0.549131\pi\) | ||||
−0.153737 | + | 0.988112i | \(0.549131\pi\) | |||||||
\(674\) | 5000.19 | + | 27100.4i | 0.285757 | + | 1.54877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4030.84 | − | 1539.85i | 0.229338 | − | 0.0876110i | ||||
\(677\) | 19299.4i | 1.09562i | 0.836602 | + | 0.547812i | \(0.184539\pi\) | ||||
−0.836602 | + | 0.547812i | \(0.815461\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4003.64i | − | 0.226282i | ||||||
\(680\) | 1032.06 | + | 1693.33i | 0.0582023 | + | 0.0954946i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23581.6 | − | 4350.95i | 1.32403 | − | 0.244291i | ||||
\(683\) | −7466.11 | −0.418276 | −0.209138 | − | 0.977886i | \(-0.567066\pi\) | ||||
−0.209138 | + | 0.977886i | \(0.567066\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3545.45 | −0.197759 | ||||||||
\(686\) | −5023.17 | + | 926.806i | −0.279571 | + | 0.0515825i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12443.8 | + | 13910.1i | 0.689559 | + | 0.770812i | ||||
\(689\) | − | 14338.5i | − | 0.792818i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 23772.0i | − | 1.30873i | −0.756180 | − | 0.654364i | \(-0.772937\pi\) | ||
0.756180 | − | 0.654364i | \(-0.227063\pi\) | |||||||
\(692\) | −7924.00 | − | 20742.5i | −0.435297 | − | 1.13947i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3616.77 | + | 19602.5i | 0.197825 | + | 1.07219i | ||||
\(695\) | 3080.03 | 0.168104 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8476.24 | −0.460632 | ||||||||
\(698\) | 619.713 | + | 3358.76i | 0.0336052 | + | 0.182136i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 905.168 | + | 2369.44i | 0.0488745 | + | 0.127938i | ||||
\(701\) | 3501.89i | 0.188680i | 0.995540 | + | 0.0943399i | \(0.0300740\pi\) | ||||
−0.995540 | + | 0.0943399i | \(0.969926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24955.1i | 1.33883i | ||||||||
\(704\) | 11330.0 | − | 21973.2i | 0.606556 | − | 1.17634i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4228.20 | + | 780.128i | −0.225397 | + | 0.0415871i | ||||
\(707\) | −1158.23 | −0.0616118 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4158.76 | 0.220290 | 0.110145 | − | 0.993916i | \(-0.464869\pi\) | ||||
0.110145 | + | 0.993916i | \(0.464869\pi\) | |||||||
\(710\) | 187.875 | − | 34.6641i | 0.00993074 | − | 0.00183228i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8054.45 | + | 4909.04i | −0.423951 | + | 0.258391i | ||||
\(713\) | − | 34082.5i | − | 1.79018i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4736.79i | − | 0.247757i | ||||||
\(716\) | −3569.36 | + | 1363.56i | −0.186303 | + | 0.0711711i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3343.60 | + | 18121.9i | 0.173791 | + | 0.941926i | ||||
\(719\) | −20077.1 | −1.04137 | −0.520687 | − | 0.853748i | \(-0.674324\pi\) | ||||
−0.520687 | + | 0.853748i | \(0.674324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4642.64 | 0.239807 | ||||||||
\(722\) | 4520.96 | + | 24503.0i | 0.233037 | + | 1.26303i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5473.04 | − | 2090.79i | 0.280945 | − | 0.107326i | ||||
\(725\) | − | 21139.7i | − | 1.08291i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36050.8i | 1.83913i | 0.392935 | + | 0.919566i | \(0.371460\pi\) | ||||
−0.392935 | + | 0.919566i | \(0.628540\pi\) | |||||||
\(728\) | 2092.51 | − | 1275.35i | 0.106529 | − | 0.0649278i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 834.378 | − | 153.948i | 0.0423037 | − | 0.00780530i | ||||
\(731\) | 10607.2 | 0.536691 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21701.9 | −1.09356 | −0.546779 | − | 0.837277i | \(-0.684146\pi\) | ||||
−0.546779 | + | 0.837277i | \(0.684146\pi\) | |||||||
\(734\) | −11216.7 | + | 2069.54i | −0.564052 | + | 0.104071i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27790.5 | − | 21502.8i | −1.39181 | − | 1.07690i | ||||
\(737\) | − | 7340.58i | − | 0.366884i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26112.0i | 1.29979i | 0.760024 | + | 0.649895i | \(0.225187\pi\) | ||||
−0.760024 | + | 0.649895i | \(0.774813\pi\) | |||||||
\(740\) | −1371.39 | − | 3589.87i | −0.0681262 | − | 0.178333i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 480.757 | + | 2605.64i | 0.0237859 | + | 0.128917i | ||||
\(743\) | −5612.86 | −0.277141 | −0.138570 | − | 0.990353i | \(-0.544251\pi\) | ||||
−0.138570 | + | 0.990353i | \(0.544251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5178.11 | −0.254646 | ||||||||
\(746\) | −1260.09 | − | 6829.51i | −0.0618432 | − | 0.335182i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5014.06 | − | 13125.2i | −0.245096 | − | 0.641585i | ||||
\(749\) | − | 2084.92i | − | 0.101711i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 27745.1i | − | 1.34811i | −0.738681 | − | 0.674056i | \(-0.764551\pi\) | ||
0.738681 | − | 0.674056i | \(-0.235449\pi\) | |||||||
\(752\) | 2952.34 | − | 2641.13i | 0.143166 | − | 0.128075i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20084.5 | + | 3705.72i | −0.970074 | + | 0.178985i | ||||
\(755\) | −2305.42 | −0.111129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22792.6 | −1.09433 | −0.547167 | − | 0.837023i | \(-0.684294\pi\) | ||||
−0.547167 | + | 0.837023i | \(0.684294\pi\) | |||||||
\(758\) | 26474.9 | − | 4884.78i | 1.26862 | − | 0.234067i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3551.70 | − | 5827.41i | −0.169518 | − | 0.278135i | ||||
\(761\) | 32307.4i | 1.53895i | 0.638675 | + | 0.769477i | \(0.279483\pi\) | ||||
−0.638675 | + | 0.769477i | \(0.720517\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4207.82i | − | 0.199651i | ||||||
\(764\) | 23062.4 | − | 8810.24i | 1.09211 | − | 0.417203i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4852.53 | − | 26300.1i | −0.228889 | − | 1.24055i | ||||
\(767\) | −5764.38 | −0.271369 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2401.94 | −0.112635 | −0.0563174 | − | 0.998413i | \(-0.517936\pi\) | ||||
−0.0563174 | + | 0.998413i | \(0.517936\pi\) | |||||||
\(770\) | 158.821 | + | 860.790i | 0.00743313 | + | 0.0402866i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12213.7 | − | 4665.84i | 0.569404 | − | 0.217522i | ||||
\(773\) | 21135.4i | 0.983424i | 0.870758 | + | 0.491712i | \(0.163629\pi\) | ||||
−0.870758 | + | 0.491712i | \(0.836371\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20928.4i | − | 0.970025i | ||||||
\(776\) | 17724.6 | + | 29081.5i | 0.819945 | + | 1.34531i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8250.07 | − | 1522.19i | 0.380179 | − | 0.0701454i | ||||
\(779\) | 29170.0 | 1.34162 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1353.60 | −0.0620174 | ||||||||
\(782\) | −19638.4 | + | 3623.41i | −0.898041 | + | 0.165694i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16023.3 | − | 14334.2i | 0.729922 | − | 0.652979i | ||||
\(785\) | 5043.51i | 0.229313i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4360.74i | 0.197514i | 0.995112 | + | 0.0987570i | \(0.0314867\pi\) | ||||
−0.995112 | + | 0.0987570i | \(0.968513\pi\) | |||||||
\(788\) | −9565.87 | − | 25040.4i | −0.432449 | − | 1.13202i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −925.824 | − | 5017.85i | −0.0416954 | − | 0.225984i | ||||
\(791\) | −1180.58 | −0.0530679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 628.232 | 0.0281326 | ||||||||
\(794\) | −665.541 | − | 3607.15i | −0.0297471 | − | 0.161225i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2987.99 | − | 7821.60i | −0.133048 | − | 0.348278i | ||||
\(797\) | − | 20501.8i | − | 0.911181i | −0.890190 | − | 0.455590i | \(-0.849428\pi\) | ||
0.890190 | − | 0.455590i | \(-0.150572\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2251.31i | − | 0.0996818i | ||||||
\(800\) | −17064.8 | − | 13203.8i | −0.754163 | − | 0.583530i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5723.88 | + | 1056.09i | −0.252016 | + | 0.0464985i | ||||
\(803\) | −6011.51 | −0.264186 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1244.10 | 0.0544705 | ||||||||
\(806\) | −19883.8 | + | 3668.68i | −0.868954 | + | 0.160327i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8413.07 | − | 5127.61i | 0.366300 | − | 0.223253i | ||||
\(809\) | − | 34550.7i | − | 1.50153i | −0.660568 | − | 0.750766i | \(-0.729685\pi\) | ||
0.660568 | − | 0.750766i | \(-0.270315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19709.5i | − | 0.853384i | −0.904397 | − | 0.426692i | \(-0.859679\pi\) | ||
0.904397 | − | 0.426692i | \(-0.140321\pi\) | |||||||
\(812\) | 3525.60 | − | 1346.84i | 0.152370 | − | 0.0582078i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4940.29 | + | 26775.7i | 0.212724 | + | 1.15294i | ||||
\(815\) | −3538.55 | −0.152086 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36503.4 | −1.56315 | ||||||||
\(818\) | −2974.03 | − | 16118.9i | −0.127121 | − | 0.688978i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4196.20 | + | 1603.02i | −0.178704 | + | 0.0682682i | ||||
\(821\) | 33361.4i | 1.41817i | 0.705122 | + | 0.709086i | \(0.250892\pi\) | ||||
−0.705122 | + | 0.709086i | \(0.749108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 42193.2i | − | 1.78707i | −0.448990 | − | 0.893537i | \(-0.648216\pi\) | ||
0.448990 | − | 0.893537i | \(-0.351784\pi\) | |||||||
\(824\) | −33723.0 | + | 20553.6i | −1.42572 | + | 0.868954i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1047.53 | − | 193.275i | 0.0441261 | − | 0.00814153i | ||||
\(827\) | 13992.0 | 0.588329 | 0.294165 | − | 0.955755i | \(-0.404959\pi\) | ||||
0.294165 | + | 0.955755i | \(0.404959\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23454.8 | −0.982653 | −0.491327 | − | 0.870975i | \(-0.663488\pi\) | ||||
−0.491327 | + | 0.870975i | \(0.663488\pi\) | |||||||
\(830\) | 2338.21 | − | 431.414i | 0.0977836 | − | 0.0180417i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9553.33 | + | 18527.6i | −0.398080 | + | 0.772030i | ||||
\(833\) | − | 12218.6i | − | 0.508221i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7345.00i | 0.304412i | ||||||||
\(836\) | 17255.3 | + | 45168.9i | 0.713860 | + | 1.86866i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7238.80 | − | 39233.4i | −0.298401 | − | 1.61730i | ||||
\(839\) | 9159.10 | 0.376886 | 0.188443 | − | 0.982084i | \(-0.439656\pi\) | ||||
0.188443 | + | 0.982084i | \(0.439656\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7065.62 | −0.289705 | ||||||||
\(842\) | −3295.19 | − | 17859.5i | −0.134869 | − | 0.730973i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15067.8 | + | 39442.9i | 0.614522 | + | 1.60863i | ||||
\(845\) | − | 1299.60i | − | 0.0529082i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2661.35i | − | 0.107963i | ||||||
\(848\) | −15027.6 | − | 16798.4i | −0.608550 | − | 0.680258i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12059.0 | + | 2224.95i | −0.486611 | + | 0.0897827i | ||||
\(851\) | 38699.0 | 1.55885 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33480.6 | −1.34391 | −0.671955 | − | 0.740592i | \(-0.734545\pi\) | ||||
−0.671955 | + | 0.740592i | \(0.734545\pi\) | |||||||
\(854\) | −114.165 | + | 21.0641i | −0.00457452 | + | 0.000844028i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9230.20 | + | 15144.3i | 0.368553 | + | 0.604699i | ||||
\(857\) | − | 30949.5i | − | 1.23362i | −0.787111 | − | 0.616811i | \(-0.788424\pi\) | ||
0.787111 | − | 0.616811i | \(-0.211576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 6145.24i | − | 0.244089i | −0.992525 | − | 0.122045i | \(-0.961055\pi\) | ||
0.992525 | − | 0.122045i | \(-0.0389451\pi\) | |||||||
\(860\) | 5251.14 | − | 2006.02i | 0.208212 | − | 0.0795405i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −574.644 | − | 3114.50i | −0.0227059 | − | 0.123063i | ||||
\(863\) | 13685.9 | 0.539830 | 0.269915 | − | 0.962884i | \(-0.413004\pi\) | ||||
0.269915 | + | 0.962884i | \(0.413004\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6687.66 | −0.262875 | ||||||||
\(866\) | 153.874 | + | 833.980i | 0.00603795 | + | 0.0327249i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3490.36 | − | 1333.38i | 0.136487 | − | 0.0521402i | ||||
\(869\) | 36152.5i | 1.41127i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6189.50i | 0.240785i | ||||||||
\(872\) | 18628.6 | + | 30564.6i | 0.723444 | + | 1.18698i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 67583.3 | − | 12469.5i | 2.61561 | − | 0.482595i | ||||
\(875\) | 1565.09 | 0.0604681 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5149.46 | −0.198272 | −0.0991361 | − | 0.995074i | \(-0.531608\pi\) | ||||
−0.0991361 | + | 0.995074i | \(0.531608\pi\) | |||||||
\(878\) | −6712.68 | + | 1238.53i | −0.258020 | + | 0.0476063i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4964.46 | − | 5549.44i | −0.190173 | − | 0.212582i | ||||
\(881\) | 26936.4i | 1.03009i | 0.857162 | + | 0.515046i | \(0.172225\pi\) | ||||
−0.857162 | + | 0.515046i | \(0.827775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37301.8i | 1.42164i | 0.703376 | + | 0.710818i | \(0.251675\pi\) | ||||
−0.703376 | + | 0.710818i | \(0.748325\pi\) | |||||||
\(884\) | 4227.80 | + | 11067.0i | 0.160856 | + | 0.421069i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2472.97 | + | 13403.2i | 0.0937709 | + | 0.508227i | ||||
\(887\) | −34843.5 | −1.31898 | −0.659488 | − | 0.751715i | \(-0.729227\pi\) | ||||
−0.659488 | + | 0.751715i | \(0.729227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1132.70 | −0.0427330 | ||||||||
\(890\) | 515.469 | + | 2793.78i | 0.0194141 | + | 0.105222i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13588.5 | + | 35570.4i | 0.510064 | + | 1.33519i | ||||
\(893\) | 7747.64i | 0.290330i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1150.81i | 0.0429802i | ||||||||
\(896\) | 1114.86 | − | 3687.23i | 0.0415678 | − | 0.137480i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24135.2 | − | 4453.10i | 0.896886 | − | 0.165481i | ||||
\(899\) | −31140.2 | −1.15527 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12809.6 | −0.473641 | ||||||||
\(902\) | 31298.2 | − | 5774.70i | 1.15534 | − | 0.213167i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8575.46 | − | 5226.59i | 0.315504 | − | 0.192294i | ||||
\(905\) | − | 1764.58i | − | 0.0648139i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8883.19i | 0.325206i | 0.986692 | + | 0.162603i | \(0.0519889\pi\) | ||||
−0.986692 | + | 0.162603i | \(0.948011\pi\) | |||||||
\(908\) | 16668.8 | − | 6367.75i | 0.609220 | − | 0.232732i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −133.916 | − | 725.809i | −0.00487833 | − | 0.0264399i | ||||
\(911\) | −44512.1 | −1.61883 | −0.809413 | − | 0.587240i | \(-0.800215\pi\) | ||||
−0.809413 | + | 0.587240i | \(0.800215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16846.3 | −0.610658 | ||||||||
\(914\) | 3551.39 | + | 19248.1i | 0.128522 | + | 0.696575i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43603.3 | − | 16657.2i | 1.57281 | − | 0.600840i | ||||
\(917\) | 4638.16i | 0.167029i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7223.63i | 0.259288i | 0.991561 | + | 0.129644i | \(0.0413834\pi\) | ||||
−0.991561 | + | 0.129644i | \(0.958617\pi\) | |||||||
\(920\) | −9036.83 | + | 5507.79i | −0.323843 | + | 0.197377i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 43265.3 | − | 7982.72i | 1.54541 | − | 0.285137i | ||||
\(923\) | 1141.34 | 0.0407017 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23763.1 | 0.844677 | ||||||||
\(926\) | −32099.7 | + | 5922.60i | −1.13916 | + | 0.210182i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19646.4 | + | 25391.4i | −0.694964 | + | 0.898182i | ||||
\(929\) | 35694.3i | 1.26060i | 0.776353 | + | 0.630298i | \(0.217067\pi\) | ||||
−0.776353 | + | 0.630298i | \(0.782933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42048.8i | 1.48023i | ||||||||
\(932\) | 8793.37 | + | 23018.3i | 0.309052 | + | 0.809000i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.59892 | − | 19.5057i | −0.000126082 | − | 0.000683347i | ||||
\(935\) | −4231.74 | −0.148014 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4657.90 | −0.162398 | −0.0811991 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811991 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(938\) | −207.529 | − | 1124.78i | −0.00722396 | − | 0.0391529i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −425.767 | − | 1114.52i | −0.0147734 | − | 0.0386721i | ||||
\(941\) | 25553.4i | 0.885245i | 0.896708 | + | 0.442623i | \(0.145952\pi\) | ||||
−0.896708 | + | 0.442623i | \(0.854048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 45235.2i | − | 1.56210i | ||||||
\(944\) | −6753.33 | + | 6041.44i | −0.232841 | + | 0.208297i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39166.6 | + | 7226.48i | −1.34611 | + | 0.248365i | ||||
\(947\) | −52939.1 | −1.81657 | −0.908285 | − | 0.418353i | \(-0.862608\pi\) | ||||
−0.908285 | + | 0.418353i | \(0.862608\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5068.85 | 0.173384 | ||||||||
\(950\) | 41499.5 | − | 7656.92i | 1.41729 | − | 0.261498i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1139.36 | − | 1869.40i | −0.0387888 | − | 0.0636423i | ||||
\(953\) | 744.138i | 0.0252938i | 0.999920 | + | 0.0126469i | \(0.00402574\pi\) | ||||
−0.999920 | + | 0.0126469i | \(0.995974\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 7435.63i | − | 0.251949i | ||||||
\(956\) | −39544.4 | + | 15106.6i | −1.33782 | + | 0.511070i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2905.43 | + | 15747.1i | 0.0979857 | + | 0.531070i | ||||
\(959\) | 3914.08 | 0.131796 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1037.96 | −0.0348414 | ||||||||
\(962\) | −4165.60 | − | 22577.0i | −0.139610 | − | 0.756666i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37390.3 | − | 14283.7i | 1.24923 | − | 0.477228i | ||||
\(965\) | − | 3937.85i | − | 0.131361i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16217.2i | − | 0.539308i | −0.962957 | − | 0.269654i | \(-0.913091\pi\) | ||
0.962957 | − | 0.269654i | \(-0.0869093\pi\) | |||||||
\(968\) | 11782.1 | + | 19331.4i | 0.391211 | + | 0.641874i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10087.2 | − | 1861.16i | 0.333898 | − | 0.0616063i | ||||
\(971\) | −33620.7 | −1.11116 | −0.555582 | − | 0.831462i | \(-0.687504\pi\) | ||||
−0.555582 | + | 0.831462i | \(0.687504\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3400.28 | −0.112033 | ||||||||
\(974\) | −25262.1 | + | 4661.01i | −0.831058 | + | 0.153335i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 736.012 | − | 658.428i | 0.0241385 | − | 0.0215940i | ||||
\(977\) | 21219.2i | 0.694843i | 0.937709 | + | 0.347421i | \(0.112943\pi\) | ||||
−0.937709 | + | 0.347421i | \(0.887057\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 20128.5i | − | 0.657110i | ||||||
\(980\) | −2310.77 | − | 6048.85i | −0.0753211 | − | 0.197167i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5233.39 | + | 28364.3i | 0.170065 | + | 0.921733i | ||||
\(983\) | 38298.6 | 1.24266 | 0.621331 | − | 0.783548i | \(-0.286592\pi\) | ||||
0.621331 | + | 0.783548i | \(0.286592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8073.35 | −0.261156 | ||||||||
\(986\) | 3310.60 | + | 17943.1i | 0.106928 | + | 0.579537i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14549.5 | − | 38086.0i | −0.468503 | − | 1.22639i | ||||
\(989\) | 56607.5i | 1.82004i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17803.2i | 0.570674i | 0.958427 | + | 0.285337i | \(0.0921055\pi\) | ||||
−0.958427 | + | 0.285337i | \(0.907894\pi\) | |||||||
\(992\) | −19450.1 | + | 25137.6i | −0.622521 | + | 0.804555i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −207.409 | + | 38.2683i | −0.00661833 | + | 0.00122112i | ||||
\(995\) | −2521.78 | −0.0803477 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9035.77 | 0.287027 | 0.143513 | − | 0.989648i | \(-0.454160\pi\) | ||||
0.143513 | + | 0.989648i | \(0.454160\pi\) | |||||||
\(998\) | −7557.78 | + | 1394.46i | −0.239717 | + | 0.0442292i | ||||
\(999\) | 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.323.11 | 24 | ||
3.2 | odd | 2 | inner | 324.4.b.c.323.14 | 24 | ||
4.3 | odd | 2 | inner | 324.4.b.c.323.13 | 24 | ||
9.2 | odd | 6 | 36.4.h.b.23.10 | yes | 24 | ||
9.4 | even | 3 | 36.4.h.b.11.11 | yes | 24 | ||
9.5 | odd | 6 | 108.4.h.b.35.2 | 24 | |||
9.7 | even | 3 | 108.4.h.b.71.3 | 24 | |||
12.11 | even | 2 | inner | 324.4.b.c.323.12 | 24 | ||
36.7 | odd | 6 | 108.4.h.b.71.2 | 24 | |||
36.11 | even | 6 | 36.4.h.b.23.11 | yes | 24 | ||
36.23 | even | 6 | 108.4.h.b.35.3 | 24 | |||
36.31 | odd | 6 | 36.4.h.b.11.10 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.10 | ✓ | 24 | 36.31 | odd | 6 | ||
36.4.h.b.11.11 | yes | 24 | 9.4 | even | 3 | ||
36.4.h.b.23.10 | yes | 24 | 9.2 | odd | 6 | ||
36.4.h.b.23.11 | yes | 24 | 36.11 | even | 6 | ||
108.4.h.b.35.2 | 24 | 9.5 | odd | 6 | |||
108.4.h.b.35.3 | 24 | 36.23 | even | 6 | |||
108.4.h.b.71.2 | 24 | 36.7 | odd | 6 | |||
108.4.h.b.71.3 | 24 | 9.7 | even | 3 | |||
324.4.b.c.323.11 | 24 | 1.1 | even | 1 | trivial | ||
324.4.b.c.323.12 | 24 | 12.11 | even | 2 | inner | ||
324.4.b.c.323.13 | 24 | 4.3 | odd | 2 | inner | ||
324.4.b.c.323.14 | 24 | 3.2 | odd | 2 | inner |