Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(127,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(-0.385731i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.127 |
Dual form | 1728.3.o.f.1279.2 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.454613 | − | 0.787412i | −0.0909226 | − | 0.157482i | 0.816977 | − | 0.576670i | \(-0.195648\pi\) |
−0.907900 | + | 0.419188i | \(0.862315\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.10709 | − | 3.52593i | −0.872442 | − | 0.503704i | −0.00428285 | − | 0.999991i | \(-0.501363\pi\) |
−0.868159 | + | 0.496286i | \(0.834697\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.96661 | − | 4.02218i | −0.633329 | − | 0.365652i | 0.148711 | − | 0.988881i | \(-0.452487\pi\) |
−0.782040 | + | 0.623228i | \(0.785821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.35952 | − | 5.81886i | −0.258425 | − | 0.447605i | 0.707395 | − | 0.706818i | \(-0.249870\pi\) |
−0.965820 | + | 0.259213i | \(0.916537\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.3462 | 1.54978 | 0.774889 | − | 0.632097i | \(-0.217806\pi\) | ||||
0.774889 | + | 0.632097i | \(0.217806\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.5603i | 1.08212i | 0.840984 | + | 0.541059i | \(0.181977\pi\) | ||||
−0.840984 | + | 0.541059i | \(0.818023\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.8305 | − | 12.6038i | 0.949150 | − | 0.547992i | 0.0563333 | − | 0.998412i | \(-0.482059\pi\) |
0.892817 | + | 0.450420i | \(0.148726\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0867 | − | 20.9347i | 0.483466 | − | 0.837388i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.1693 | − | 26.2741i | 0.523081 | − | 0.906002i | −0.476558 | − | 0.879143i | \(-0.658116\pi\) |
0.999639 | − | 0.0268597i | \(-0.00855072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.120040 | + | 0.0693050i | −0.00387225 | + | 0.00223565i | −0.501935 | − | 0.864905i | \(-0.667378\pi\) |
0.498063 | + | 0.867141i | \(0.334045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.41173i | 0.183192i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −69.7588 | −1.88537 | −0.942687 | − | 0.333679i | \(-0.891710\pi\) | ||||
−0.942687 | + | 0.333679i | \(0.891710\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 29.3794 | + | 50.8866i | 0.716571 | + | 1.24114i | 0.962351 | + | 0.271811i | \(0.0876227\pi\) |
−0.245780 | + | 0.969326i | \(0.579044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.45853 | − | 1.41943i | −0.0571751 | − | 0.0330100i | 0.471140 | − | 0.882058i | \(-0.343843\pi\) |
−0.528315 | + | 0.849048i | \(0.677176\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −70.7583 | − | 40.8523i | −1.50550 | − | 0.869198i | −0.999980 | − | 0.00638063i | \(-0.997969\pi\) |
−0.505516 | − | 0.862817i | \(-0.668698\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.364383 | + | 0.631130i | 0.00743639 | + | 0.0128802i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −30.0259 | −0.566526 | −0.283263 | − | 0.959042i | \(-0.591417\pi\) | ||||
−0.283263 | + | 0.959042i | \(0.591417\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.31413i | 0.132984i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −77.1442 | + | 44.5392i | −1.30753 | + | 0.754902i | −0.981683 | − | 0.190520i | \(-0.938983\pi\) |
−0.325846 | + | 0.945423i | \(0.605649\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24.0688 | + | 41.6885i | −0.394571 | + | 0.683417i | −0.993046 | − | 0.117724i | \(-0.962440\pi\) |
0.598475 | + | 0.801141i | \(0.295774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.05456 | + | 5.29066i | −0.0469933 | + | 0.0813948i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −44.0829 | + | 25.4513i | −0.657953 | + | 0.379870i | −0.791497 | − | 0.611173i | \(-0.790698\pi\) |
0.133543 | + | 0.991043i | \(0.457364\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 68.4355i | 0.963881i | 0.876204 | + | 0.481940i | \(0.160068\pi\) | ||||
−0.876204 | + | 0.481940i | \(0.839932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −22.1474 | −0.303389 | −0.151695 | − | 0.988427i | \(-0.548473\pi\) | ||||
−0.151695 | + | 0.988427i | \(0.548473\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 28.3638 | + | 49.1276i | 0.368362 | + | 0.638021i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −34.4343 | − | 19.8807i | −0.435877 | − | 0.251654i | 0.265970 | − | 0.963981i | \(-0.414308\pi\) |
−0.701847 | + | 0.712327i | \(0.747641\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −23.0801 | − | 13.3253i | −0.278073 | − | 0.160546i | 0.354478 | − | 0.935065i | \(-0.384659\pi\) |
−0.632551 | + | 0.774519i | \(0.717992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.9773 | − | 20.7453i | −0.140910 | − | 0.244063i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 25.7926 | 0.289804 | 0.144902 | − | 0.989446i | \(-0.453713\pi\) | ||||
0.144902 | + | 0.989446i | \(0.453713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 47.3818i | 0.520679i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.1894 | − | 9.34695i | 0.170415 | − | 0.0983890i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.3697 | + | 90.7070i | −0.539894 | + | 0.935123i | 0.459016 | + | 0.888428i | \(0.348202\pi\) |
−0.998909 | + | 0.0466950i | \(0.985131\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 20.4790 | − | 35.4707i | 0.202763 | − | 0.351195i | −0.746655 | − | 0.665212i | \(-0.768341\pi\) |
0.949418 | + | 0.314016i | \(0.101675\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −125.278 | + | 72.3293i | −1.21629 | + | 0.702227i | −0.964123 | − | 0.265456i | \(-0.914477\pi\) |
−0.252169 | + | 0.967683i | \(0.581144\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 177.858i | − | 1.66222i | −0.556105 | − | 0.831112i | \(-0.687705\pi\) | ||
0.556105 | − | 0.831112i | \(-0.312295\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 142.616 | 1.30840 | 0.654200 | − | 0.756322i | \(-0.273006\pi\) | ||||
0.654200 | + | 0.756322i | \(0.273006\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −100.147 | − | 173.459i | −0.886254 | − | 1.53504i | −0.844270 | − | 0.535918i | \(-0.819966\pi\) |
−0.0419835 | − | 0.999118i | \(-0.513368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.8488 | − | 11.4597i | −0.172598 | − | 0.0996497i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −160.899 | − | 92.8950i | −1.35209 | − | 0.780630i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −28.1442 | − | 48.7472i | −0.232597 | − | 0.402869i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −44.7096 | −0.357677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 181.723i | 1.43089i | 0.698670 | + | 0.715445i | \(0.253776\pi\) | ||||
−0.698670 | + | 0.715445i | \(0.746224\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −52.9361 | + | 30.5627i | −0.404092 | + | 0.233303i | −0.688248 | − | 0.725475i | \(-0.741620\pi\) |
0.284156 | + | 0.958778i | \(0.408287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 72.4940 | − | 125.563i | 0.545068 | − | 0.944085i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.1131 | + | 31.3729i | −0.132213 | + | 0.228999i | −0.924529 | − | 0.381111i | \(-0.875542\pi\) |
0.792317 | + | 0.610110i | \(0.208875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −154.652 | + | 89.2885i | −1.11261 | + | 0.642363i | −0.939503 | − | 0.342541i | \(-0.888713\pi\) |
−0.173103 | + | 0.984904i | \(0.555379\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 54.0504i | 0.377975i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −27.5847 | −0.190239 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 120.043 | + | 207.921i | 0.805660 | + | 1.39544i | 0.915845 | + | 0.401533i | \(0.131522\pi\) |
−0.110185 | + | 0.993911i | \(0.535144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 98.1393 | + | 56.6607i | 0.649929 | + | 0.375237i | 0.788429 | − | 0.615126i | \(-0.210895\pi\) |
−0.138500 | + | 0.990362i | \(0.544228\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.109143 | + | 0.0630139i | 0.000704150 | + | 0.000406541i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60.3604 | + | 104.547i | 0.384461 | + | 0.665907i | 0.991694 | − | 0.128617i | \(-0.0410538\pi\) |
−0.607233 | + | 0.794524i | \(0.707720\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −177.761 | −1.10410 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.3498i | 0.124845i | 0.998050 | + | 0.0624226i | \(0.0198827\pi\) | ||||
−0.998050 | + | 0.0624226i | \(0.980117\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −151.530 | + | 87.4858i | −0.907365 | + | 0.523867i | −0.879582 | − | 0.475747i | \(-0.842178\pi\) |
−0.0277823 | + | 0.999614i | \(0.508845\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 61.9272 | − | 107.261i | 0.366433 | − | 0.634681i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 55.9175 | − | 96.8520i | 0.323223 | − | 0.559838i | −0.657928 | − | 0.753080i | \(-0.728567\pi\) |
0.981151 | + | 0.193243i | \(0.0619004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −147.629 | + | 85.2334i | −0.843592 | + | 0.487048i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.6939i | − | 0.104435i | −0.998636 | − | 0.0522176i | \(-0.983371\pi\) | ||
0.998636 | − | 0.0522176i | \(-0.0166289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 98.0536 | 0.541733 | 0.270866 | − | 0.962617i | \(-0.412690\pi\) | ||||
0.270866 | + | 0.962617i | \(0.412690\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.7132 | + | 54.9290i | 0.171423 | + | 0.296913i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −183.544 | − | 105.969i | −0.981519 | − | 0.566680i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −240.713 | − | 138.976i | −1.26028 | − | 0.727621i | −0.287149 | − | 0.957886i | \(-0.592707\pi\) |
−0.973128 | + | 0.230265i | \(0.926041\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 81.1285 | + | 140.519i | 0.420355 | + | 0.728076i | 0.995974 | − | 0.0896419i | \(-0.0285722\pi\) |
−0.575619 | + | 0.817718i | \(0.695239\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −106.182 | −0.538993 | −0.269496 | − | 0.963001i | \(-0.586857\pi\) | ||||
−0.269496 | + | 0.963001i | \(0.586857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 63.3880i | 0.318532i | 0.987236 | + | 0.159266i | \(0.0509128\pi\) | ||||
−0.987236 | + | 0.159266i | \(0.949087\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −185.281 | + | 106.972i | −0.912715 | + | 0.526956i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.7125 | − | 46.2674i | 0.130305 | − | 0.225695i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 82.6970 | − | 143.235i | 0.395679 | − | 0.685337i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.98019 | − | 2.87531i | 0.0236028 | − | 0.0136271i | −0.488152 | − | 0.872759i | \(-0.662329\pi\) |
0.511755 | + | 0.859131i | \(0.328996\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.58117i | 0.0120054i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.977459 | 0.00450442 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −88.5107 | − | 153.305i | −0.400501 | − | 0.693688i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −179.786 | − | 103.799i | −0.806215 | − | 0.465469i | 0.0394246 | − | 0.999223i | \(-0.487448\pi\) |
−0.845640 | + | 0.533754i | \(0.820781\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −78.8889 | − | 45.5465i | −0.347528 | − | 0.200646i | 0.316068 | − | 0.948737i | \(-0.397637\pi\) |
−0.663596 | + | 0.748091i | \(0.730971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.04945 | − | 3.54974i | −0.00894954 | − | 0.0155011i | 0.861516 | − | 0.507731i | \(-0.169515\pi\) |
−0.870465 | + | 0.492229i | \(0.836182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −171.761 | −0.737170 | −0.368585 | − | 0.929594i | \(-0.620158\pi\) | ||||
−0.368585 | + | 0.929594i | \(0.620158\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 74.2879i | 0.316119i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 78.9068 | − | 45.5569i | 0.330154 | − | 0.190614i | −0.325755 | − | 0.945454i | \(-0.605619\pi\) |
0.655909 | + | 0.754840i | \(0.272285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 37.2352 | − | 64.4933i | 0.154503 | − | 0.267607i | −0.778375 | − | 0.627800i | \(-0.783956\pi\) |
0.932878 | + | 0.360193i | \(0.117289\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.331306 | − | 0.573840i | 0.00135227 | − | 0.00234220i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 119.637 | − | 69.0726i | 0.484362 | − | 0.279646i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 216.868i | − | 0.864014i | −0.901870 | − | 0.432007i | \(-0.857806\pi\) | ||
0.901870 | − | 0.432007i | \(-0.142194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −202.779 | −0.801499 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 143.577 | + | 248.682i | 0.558665 | + | 0.967636i | 0.997608 | + | 0.0691212i | \(0.0220195\pi\) |
−0.438943 | + | 0.898515i | \(0.644647\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 426.023 | + | 245.965i | 1.64488 | + | 0.949671i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 361.740 | + | 208.851i | 1.37544 | + | 0.794108i | 0.991606 | − | 0.129295i | \(-0.0412715\pi\) |
0.383830 | + | 0.923404i | \(0.374605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6502 | + | 23.6428i | 0.0515100 | + | 0.0892180i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −489.868 | −1.82107 | −0.910535 | − | 0.413433i | \(-0.864330\pi\) | ||||
−0.910535 | + | 0.413433i | \(0.864330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 325.133i | − | 1.19975i | −0.800093 | − | 0.599876i | \(-0.795216\pi\) | ||
0.800093 | − | 0.599876i | \(-0.204784\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −168.406 | + | 97.2293i | −0.612386 | + | 0.353561i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −86.0882 | + | 149.109i | −0.310788 | + | 0.538300i | −0.978533 | − | 0.206089i | \(-0.933926\pi\) |
0.667745 | + | 0.744390i | \(0.267260\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 60.1019 | − | 104.100i | 0.213886 | − | 0.370461i | −0.739042 | − | 0.673660i | \(-0.764721\pi\) |
0.952927 | + | 0.303199i | \(0.0980546\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −95.8910 | + | 55.3627i | −0.338837 | + | 0.195628i | −0.659758 | − | 0.751478i | \(-0.729341\pi\) |
0.320920 | + | 0.947106i | \(0.396008\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 414.359i | − | 1.44376i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 405.124 | 1.40181 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 42.3365 | + | 73.3289i | 0.144493 | + | 0.250269i | 0.929184 | − | 0.369618i | \(-0.120512\pi\) |
−0.784691 | + | 0.619888i | \(0.787178\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 70.1415 | + | 40.4962i | 0.237768 | + | 0.137275i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −146.680 | − | 84.6856i | −0.490568 | − | 0.283229i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0096 | + | 17.3372i | 0.0332546 | + | 0.0575987i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.7680 | 0.143502 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 220.477i | 0.718167i | 0.933306 | + | 0.359083i | \(0.116911\pi\) | ||||
−0.933306 | + | 0.359083i | \(0.883089\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −268.968 | + | 155.289i | −0.864849 | + | 0.499321i | −0.865633 | − | 0.500679i | \(-0.833084\pi\) |
0.000784168 | 1.00000i | \(0.499750\pi\) | ||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −65.5787 | + | 113.586i | −0.209516 | + | 0.362893i | −0.951562 | − | 0.307456i | \(-0.900522\pi\) |
0.742046 | + | 0.670349i | \(0.233856\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 169.980 | − | 294.414i | 0.536214 | − | 0.928750i | −0.462889 | − | 0.886416i | \(-0.653187\pi\) |
0.999104 | − | 0.0423342i | \(-0.0134794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −211.358 | + | 122.028i | −0.662564 | + | 0.382532i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 541.685i | 1.67704i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −162.422 | −0.499759 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 288.085 | + | 498.978i | 0.875638 | + | 1.51665i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −394.447 | − | 227.734i | −1.19168 | − | 0.688018i | −0.232994 | − | 0.972478i | \(-0.574852\pi\) |
−0.958688 | + | 0.284460i | \(0.908186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.0813 | + | 23.1409i | 0.119646 | + | 0.0690774i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.9543 | − | 38.0259i | −0.0651462 | − | 0.112837i | 0.831613 | − | 0.555356i | \(-0.187418\pi\) |
−0.896759 | + | 0.442520i | \(0.854085\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.11503 | 0.00326988 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 340.402i | 0.992426i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 340.283 | − | 196.462i | 0.980642 | − | 0.566174i | 0.0781781 | − | 0.996939i | \(-0.475090\pi\) |
0.902464 | + | 0.430766i | \(0.141756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −271.979 | + | 471.082i | −0.779310 | + | 1.34981i | 0.153029 | + | 0.988222i | \(0.451097\pi\) |
−0.932340 | + | 0.361584i | \(0.882236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 63.7961 | − | 110.498i | 0.180725 | − | 0.313026i | −0.761402 | − | 0.648280i | \(-0.775489\pi\) |
0.942128 | + | 0.335254i | \(0.108822\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 53.8870 | − | 31.1117i | 0.151794 | − | 0.0876385i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 285.077i | − | 0.794085i | −0.917800 | − | 0.397043i | \(-0.870037\pi\) | ||
0.917800 | − | 0.397043i | \(-0.129963\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −61.7239 | −0.170980 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0685 | + | 17.4391i | 0.0275849 | + | 0.0477785i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −280.084 | − | 161.706i | −0.763171 | − | 0.440617i | 0.0672623 | − | 0.997735i | \(-0.478574\pi\) |
−0.830433 | + | 0.557119i | \(0.811907\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 183.371 | + | 105.869i | 0.494261 | + | 0.285362i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −257.740 | − | 446.419i | −0.690993 | − | 1.19683i | −0.971513 | − | 0.236987i | \(-0.923840\pi\) |
0.280520 | − | 0.959848i | \(-0.409493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −203.847 | −0.540708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.2535i | − | 0.0560779i | −0.999607 | − | 0.0280389i | \(-0.991074\pi\) | ||
0.999607 | − | 0.0280389i | \(-0.00892624\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 93.4125 | − | 53.9317i | 0.243897 | − | 0.140814i | −0.373070 | − | 0.927803i | \(-0.621695\pi\) |
0.616966 | + | 0.786989i | \(0.288361\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.7891 | − | 44.6681i | 0.0669847 | − | 0.116021i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 75.1474 | − | 130.159i | 0.193181 | − | 0.334599i | −0.753122 | − | 0.657881i | \(-0.771453\pi\) |
0.946303 | + | 0.323282i | \(0.104786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 575.150 | − | 332.063i | 1.47097 | − | 0.849266i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 36.1520i | 0.0915241i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −137.203 | −0.345600 | −0.172800 | − | 0.984957i | \(-0.555281\pi\) | ||||
−0.172800 | + | 0.984957i | \(0.555281\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 133.366 | + | 230.996i | 0.332583 | + | 0.576050i | 0.983017 | − | 0.183512i | \(-0.0587466\pi\) |
−0.650435 | + | 0.759562i | \(0.725413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.806553 | + | 0.465664i | 0.00200137 | + | 0.00115549i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 485.983 | + | 280.582i | 1.19406 | + | 0.689391i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −341.404 | − | 591.329i | −0.834729 | − | 1.44579i | −0.894251 | − | 0.447565i | \(-0.852291\pi\) |
0.0595226 | − | 0.998227i | \(-0.481042\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 628.169 | 1.52099 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.2314i | 0.0583889i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 449.030 | − | 259.248i | 1.07167 | − | 0.618730i | 0.143034 | − | 0.989718i | \(-0.454314\pi\) |
0.928638 | + | 0.370988i | \(0.120981\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 170.758 | − | 295.761i | 0.405601 | − | 0.702521i | −0.588790 | − | 0.808286i | \(-0.700396\pi\) |
0.994391 | + | 0.105765i | \(0.0337290\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 318.438 | − | 551.550i | 0.749265 | − | 1.29777i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 293.981 | − | 169.730i | 0.688481 | − | 0.397495i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 166.603i | 0.386550i | 0.981145 | + | 0.193275i | \(0.0619110\pi\) | ||||
−0.981145 | + | 0.193275i | \(0.938089\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −677.766 | −1.56528 | −0.782640 | − | 0.622475i | \(-0.786127\pi\) | ||||
−0.782640 | + | 0.622475i | \(0.786127\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 259.138 | + | 448.840i | 0.592992 | + | 1.02709i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 427.032 | + | 246.547i | 0.972738 | + | 0.561610i | 0.900070 | − | 0.435746i | \(-0.143515\pi\) |
0.0726678 | + | 0.997356i | \(0.476849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −284.084 | − | 164.016i | −0.641273 | − | 0.370239i | 0.143832 | − | 0.989602i | \(-0.454058\pi\) |
−0.785105 | + | 0.619363i | \(0.787391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7256 | − | 20.3094i | −0.0263497 | − | 0.0456391i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.0862 | −0.0425082 | −0.0212541 | − | 0.999774i | \(-0.506766\pi\) | ||||
−0.0212541 | + | 0.999774i | \(0.506766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 472.677i | − | 1.04806i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 37.3090 | − | 21.5404i | 0.0819978 | − | 0.0473415i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −137.806 | + | 238.686i | −0.301544 | + | 0.522289i | −0.976486 | − | 0.215581i | \(-0.930835\pi\) |
0.674942 | + | 0.737871i | \(0.264169\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −199.467 | + | 345.486i | −0.432683 | + | 0.749428i | −0.997103 | − | 0.0760589i | \(-0.975766\pi\) |
0.564421 | + | 0.825487i | \(0.309100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.7881 | − | 9.11524i | 0.0340995 | − | 0.0196873i | −0.482853 | − | 0.875701i | \(-0.660400\pi\) |
0.516953 | + | 0.856014i | \(0.327066\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 499.275i | 1.06911i | 0.845133 | + | 0.534555i | \(0.179521\pi\) | ||||
−0.845133 | + | 0.534555i | \(0.820479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 358.958 | 0.765368 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.4184 | + | 19.7773i | 0.0241404 | + | 0.0418124i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 430.423 | + | 248.505i | 0.906153 | + | 0.523168i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −52.4473 | − | 30.2805i | −0.109493 | − | 0.0632160i | 0.444253 | − | 0.895901i | \(-0.353469\pi\) |
−0.553747 | + | 0.832685i | \(0.686802\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 234.356 | + | 405.917i | 0.487227 | + | 0.843902i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 95.2317 | 0.196354 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 852.354i | − | 1.75021i | −0.483931 | − | 0.875106i | \(-0.660791\pi\) | ||
0.483931 | − | 0.875106i | \(-0.339209\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 585.457 | − | 338.014i | 1.19238 | − | 0.688419i | 0.233532 | − | 0.972349i | \(-0.424972\pi\) |
0.958845 | + | 0.283930i | \(0.0916382\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 399.655 | − | 692.223i | 0.810659 | − | 1.40410i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 241.299 | − | 417.942i | 0.485511 | − | 0.840930i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 736.084 | − | 424.978i | 1.47512 | − | 0.851660i | 0.475512 | − | 0.879709i | \(-0.342263\pi\) |
0.999607 | + | 0.0280487i | \(0.00892936\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 945.179i | 1.87908i | 0.342433 | + | 0.939542i | \(0.388749\pi\) | ||||
−0.342433 | + | 0.939542i | \(0.611251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.2401 | −0.0737428 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 125.931 | + | 218.119i | 0.247409 | + | 0.428524i | 0.962806 | − | 0.270194i | \(-0.0870877\pi\) |
−0.715397 | + | 0.698718i | \(0.753754\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 135.256 | + | 78.0903i | 0.264689 | + | 0.152819i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 113.906 | + | 65.7637i | 0.221177 | + | 0.127696i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 328.630 | + | 569.205i | 0.635649 | + | 1.10098i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −856.423 | −1.64381 | −0.821903 | − | 0.569628i | \(-0.807087\pi\) | ||||
−0.821903 | + | 0.569628i | \(0.807087\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 741.634i | − | 1.41804i | −0.705189 | − | 0.709019i | \(-0.749138\pi\) | ||
0.705189 | − | 0.709019i | \(-0.250862\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.16260 | + | 1.82593i | −0.00600113 | + | 0.00346475i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.2125 | − | 92.1667i | 0.100591 | − | 0.174228i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 197.402 | − | 341.910i | 0.370359 | − | 0.641481i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −140.048 | + | 80.8565i | −0.261771 | + | 0.151134i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.86245i | − | 0.0108765i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 434.157 | 0.802509 | 0.401254 | − | 0.915967i | \(-0.368574\pi\) | ||||
0.401254 | + | 0.915967i | \(0.368574\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −64.8349 | − | 112.297i | −0.118963 | − | 0.206050i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −235.269 | − | 135.832i | −0.430107 | − | 0.248323i | 0.269285 | − | 0.963061i | \(-0.413213\pi\) |
−0.699392 | + | 0.714738i | \(0.746546\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 540.201 | + | 311.885i | 0.980402 | + | 0.566035i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 140.196 | + | 242.826i | 0.253518 | + | 0.439107i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.7759 | 0.0750016 | 0.0375008 | − | 0.999297i | \(-0.488060\pi\) | ||||
0.0375008 | + | 0.999297i | \(0.488060\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.0744i | 0.0341224i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 388.403 | − | 224.245i | 0.689882 | − | 0.398303i | −0.113686 | − | 0.993517i | \(-0.536266\pi\) |
0.803568 | + | 0.595213i | \(0.202932\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −91.0559 | + | 157.713i | −0.161161 | + | 0.279139i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 180.208 | − | 312.130i | 0.316710 | − | 0.548559i | −0.663089 | − | 0.748540i | \(-0.730755\pi\) |
0.979800 | + | 0.199982i | \(0.0640883\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −665.784 | + | 384.391i | −1.16600 | + | 0.673189i | −0.952734 | − | 0.303806i | \(-0.901743\pi\) |
−0.213263 | + | 0.976995i | \(0.568409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 609.352i | − | 1.05974i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −413.359 | −0.716394 | −0.358197 | − | 0.933646i | \(-0.616608\pi\) | ||||
−0.358197 | + | 0.933646i | \(0.616608\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 93.9682 | + | 162.758i | 0.161735 | + | 0.280134i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 209.179 | + | 120.769i | 0.358797 | + | 0.207152i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.41240 | + | 0.815451i | 0.00240614 | + | 0.00138918i | 0.501203 | − | 0.865330i | \(-0.332891\pi\) |
−0.498796 | + | 0.866719i | \(0.666224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.42493 | − | 2.46805i | −0.00241923 | − | 0.00419024i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −652.407 | −1.10018 | −0.550091 | − | 0.835105i | \(-0.685407\pi\) | ||||
−0.550091 | + | 0.835105i | \(0.685407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 168.925i | 0.283908i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 148.315 | − | 85.6298i | 0.247605 | − | 0.142955i | −0.371062 | − | 0.928608i | \(-0.621006\pi\) |
0.618667 | + | 0.785653i | \(0.287673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −65.9875 | + | 114.294i | −0.109796 | + | 0.190173i | −0.915688 | − | 0.401891i | \(-0.868353\pi\) |
0.805891 | + | 0.592063i | \(0.201686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.5894 | + | 44.3222i | −0.0422966 | + | 0.0732598i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 514.763 | − | 297.199i | 0.848045 | − | 0.489619i | −0.0119458 | − | 0.999929i | \(-0.503803\pi\) |
0.859991 | + | 0.510310i | \(0.170469\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 548.977i | 0.898489i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −367.632 | −0.599727 | −0.299863 | − | 0.953982i | \(-0.596941\pi\) | ||||
−0.299863 | + | 0.953982i | \(0.596941\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.0806 | − | 36.5126i | −0.0341662 | − | 0.0591776i | 0.848437 | − | 0.529297i | \(-0.177544\pi\) |
−0.882603 | + | 0.470119i | \(0.844211\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −214.298 | − | 123.725i | −0.346200 | − | 0.199879i | 0.316810 | − | 0.948489i | \(-0.397388\pi\) |
−0.663010 | + | 0.748610i | \(0.730721\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −157.518 | − | 90.9428i | −0.252837 | − | 0.145976i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −281.841 | − | 488.163i | −0.450945 | − | 0.781060i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1837.88 | −2.92191 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 725.556i | 1.14985i | 0.818206 | + | 0.574926i | \(0.194969\pi\) | ||||
−0.818206 | + | 0.574926i | \(0.805031\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 143.091 | − | 82.6136i | 0.225340 | − | 0.130100i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.44831 | − | 4.24059i | 0.00384349 | − | 0.00665713i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −458.006 | + | 793.290i | −0.714518 | + | 1.23758i | 0.248626 | + | 0.968599i | \(0.420021\pi\) |
−0.963145 | + | 0.268983i | \(0.913312\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 686.803 | − | 396.526i | 1.06812 | − | 0.616681i | 0.140455 | − | 0.990087i | \(-0.455143\pi\) |
0.927668 | + | 0.373406i | \(0.121810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 78.3837i | 0.121150i | 0.998164 | + | 0.0605748i | \(0.0192934\pi\) | ||||
−0.998164 | + | 0.0605748i | \(0.980707\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 716.579 | 1.10413 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 131.250 | + | 227.332i | 0.200996 | + | 0.348135i | 0.948850 | − | 0.315728i | \(-0.102249\pi\) |
−0.747854 | + | 0.663864i | \(0.768915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.1308 | + | 27.7883i | 0.0734822 | + | 0.0424250i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1116.03 | + | 644.339i | 1.69352 | + | 0.977753i | 0.951638 | + | 0.307221i | \(0.0993990\pi\) |
0.741880 | + | 0.670533i | \(0.233934\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 184.429 | + | 319.441i | 0.279016 | + | 0.483270i | 0.971140 | − | 0.238508i | \(-0.0766585\pi\) |
−0.692125 | + | 0.721778i | \(0.743325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −131.827 | −0.198236 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 764.766i | − | 1.14658i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 335.357 | − | 193.618i | 0.499787 | − | 0.288552i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 127.862 | − | 221.463i | 0.189988 | − | 0.329069i | −0.755258 | − | 0.655428i | \(-0.772488\pi\) |
0.945246 | + | 0.326359i | \(0.105822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 566.571 | − | 981.330i | 0.836885 | − | 1.44953i | −0.0556014 | − | 0.998453i | \(-0.517708\pi\) |
0.892486 | − | 0.451074i | \(-0.148959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 639.653 | − | 369.304i | 0.942052 | − | 0.543894i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 941.046i | − | 1.37781i | −0.724850 | − | 0.688907i | \(-0.758091\pi\) | ||
0.724850 | − | 0.688907i | \(-0.241909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.9379 | 0.0480845 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 100.873 | + | 174.717i | 0.146404 | + | 0.253580i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1163.81 | + | 671.923i | 1.68423 | + | 0.972393i | 0.958792 | + | 0.284109i | \(0.0916976\pi\) |
0.725441 | + | 0.688284i | \(0.241636\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 140.614 | + | 81.1834i | 0.202322 | + | 0.116811i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 774.036 | + | 1340.67i | 1.11053 | + | 1.92349i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.1783 | −0.0401973 | −0.0200986 | − | 0.999798i | \(-0.506398\pi\) | ||||
−0.0200986 | + | 0.999798i | \(0.506398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1434.26i | − | 2.04020i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −250.135 | + | 144.415i | −0.353797 | + | 0.204265i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −624.660 | + | 1081.94i | −0.881043 | + | 1.52601i | −0.0308605 | + | 0.999524i | \(0.509825\pi\) |
−0.850183 | + | 0.526488i | \(0.823509\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.74702 | + | 3.02592i | −0.00245023 | + | 0.00424393i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.5599 | − | 24.5720i | 0.0595244 | − | 0.0343664i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 738.132i | − | 1.02661i | −0.858206 | − | 0.513305i | \(-0.828421\pi\) | ||
0.858206 | − | 0.513305i | \(-0.171579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1020.11 | 1.41486 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −366.693 | − | 635.131i | −0.505784 | − | 0.876043i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 326.676 | + | 188.606i | 0.449348 | + | 0.259431i | 0.707555 | − | 0.706659i | \(-0.249798\pi\) |
−0.258207 | + | 0.966090i | \(0.583132\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −64.7729 | − | 37.3967i | −0.0886087 | − | 0.0511582i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −280.849 | − | 486.445i | −0.383150 | − | 0.663635i | 0.608361 | − | 0.793661i | \(-0.291827\pi\) |
−0.991511 | + | 0.130025i | \(0.958494\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 409.478 | 0.555601 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 912.732i | 1.23509i | 0.786535 | + | 0.617545i | \(0.211873\pi\) | ||||
−0.786535 | + | 0.617545i | \(0.788127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 913.005 | − | 527.123i | 1.22881 | − | 0.709453i | 0.262028 | − | 0.965060i | \(-0.415609\pi\) |
0.966781 | + | 0.255608i | \(0.0822755\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 109.146 | − | 189.047i | 0.146505 | − | 0.253755i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −627.115 | + | 1086.20i | −0.837270 | + | 1.45019i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −916.482 | + | 529.131i | −1.22035 | + | 0.704569i | −0.964992 | − | 0.262278i | \(-0.915526\pi\) |
−0.255357 | + | 0.966847i | \(0.582193\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 103.035i | − | 0.136470i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 359.804 | 0.475302 | 0.237651 | − | 0.971351i | \(-0.423623\pi\) | ||||
0.237651 | + | 0.971351i | \(0.423623\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 311.474 | + | 539.489i | 0.409296 | + | 0.708921i | 0.994811 | − | 0.101740i | \(-0.0324411\pi\) |
−0.585515 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −870.966 | − | 502.853i | −1.14150 | − | 0.659047i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 518.336 | + | 299.261i | 0.675796 | + | 0.390171i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −534.453 | − | 925.699i | −0.694997 | − | 1.20377i | −0.970182 | − | 0.242379i | \(-0.922072\pi\) |
0.275185 | − | 0.961391i | \(-0.411261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −512.261 | −0.662692 | −0.331346 | − | 0.943509i | \(-0.607503\pi\) | ||||
−0.331346 | + | 0.943509i | \(0.607503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.35066i | 0.00432344i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1046.24 | + | 604.048i | −1.34306 | + | 0.775415i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 275.260 | − | 476.764i | 0.352445 | − | 0.610453i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54.8813 | − | 95.0571i | 0.0699124 | − | 0.121092i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −153.809 | + | 88.8019i | −0.195438 | + | 0.112836i | −0.594526 | − | 0.804077i | \(-0.702660\pi\) |
0.399088 | + | 0.916913i | \(0.369327\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1412.44i | 1.78564i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 323.439 | 0.407868 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −190.381 | − | 329.750i | −0.238872 | − | 0.413739i | 0.721519 | − | 0.692395i | \(-0.243444\pi\) |
−0.960391 | + | 0.278656i | \(0.910111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1864.21 | − | 1076.30i | −2.33318 | − | 1.34706i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 154.292 | + | 89.0808i | 0.192145 | + | 0.110935i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 80.8123 | + | 139.971i | 0.100388 | + | 0.173877i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 720.850 | 0.891039 | 0.445519 | − | 0.895272i | \(-0.353019\pi\) | ||||
0.445519 | + | 0.895272i | \(0.353019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1048.82i | 1.29324i | 0.762813 | + | 0.646619i | \(0.223818\pi\) | ||||
−0.762813 | + | 0.646619i | \(0.776182\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0237 | − | 9.25127i | 0.0196609 | − | 0.0113512i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.1839 | − | 50.5479i | 0.0357208 | − | 0.0618702i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 361.666 | − | 626.424i | 0.440519 | − | 0.763001i | −0.557209 | − | 0.830372i | \(-0.688128\pi\) |
0.997728 | + | 0.0673712i | \(0.0214612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1074.90 | − | 620.596i | 1.30608 | − | 0.754066i | 0.324640 | − | 0.945838i | \(-0.394757\pi\) |
0.981440 | + | 0.191772i | \(0.0614234\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 348.111i | − | 0.420932i | −0.977601 | − | 0.210466i | \(-0.932502\pi\) | ||
0.977601 | − | 0.210466i | \(-0.0674981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −731.151 | −0.881968 | −0.440984 | − | 0.897515i | \(-0.645370\pi\) | ||||
−0.440984 | + | 0.897515i | \(0.645370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.60012 | + | 16.6279i | 0.0115248 | + | 0.0199615i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 137.775 | + | 79.5443i | 0.165000 | + | 0.0952627i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −563.141 | − | 325.130i | −0.671205 | − | 0.387520i | 0.125328 | − | 0.992115i | \(-0.460002\pi\) |
−0.796533 | + | 0.604595i | \(0.793335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.7179 | − | 68.7934i | −0.0472269 | − | 0.0817995i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −112.612 | −0.133268 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 396.938i | 0.468640i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1522.87 | + | 879.227i | −1.78950 | + | 1.03317i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 664.274 | − | 1150.56i | 0.778750 | − | 1.34884i | −0.153912 | − | 0.988085i | \(-0.549187\pi\) |
0.932662 | − | 0.360751i | \(-0.117479\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 323.338 | − | 560.038i | 0.377290 | − | 0.653486i | −0.613377 | − | 0.789791i | \(-0.710189\pi\) |
0.990667 | + | 0.136304i | \(0.0435225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 527.482 | − | 304.542i | 0.614065 | − | 0.354530i | −0.160490 | − | 0.987037i | \(-0.551307\pi\) |
0.774555 | + | 0.632507i | \(0.217974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 93.0849i | 0.107862i | 0.998545 | + | 0.0539310i | \(0.0171751\pi\) | ||||
−0.998545 | + | 0.0539310i | \(0.982825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −101.683 | −0.117553 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 159.927 | + | 277.002i | 0.184036 | + | 0.318759i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 296.195 | + | 171.008i | 0.340063 | + | 0.196335i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 273.046 | + | 157.643i | 0.312052 | + | 0.180164i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −330.684 | − | 572.762i | −0.377063 | − | 0.653092i | 0.613571 | − | 0.789640i | \(-0.289733\pi\) |
−0.990633 | + | 0.136548i | \(0.956399\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 659.388 | 0.748455 | 0.374227 | − | 0.927337i | \(-0.377908\pi\) | ||||
0.374227 | + | 0.927337i | \(0.377908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 776.943i | − | 0.879890i | −0.898025 | − | 0.439945i | \(-0.854998\pi\) | ||
0.898025 | − | 0.439945i | \(-0.145002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −598.849 | + | 345.745i | −0.675139 | + | 0.389792i | −0.798021 | − | 0.602629i | \(-0.794120\pi\) |
0.122882 | + | 0.992421i | \(0.460786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 640.743 | − | 1109.80i | 0.720745 | − | 1.24837i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 839.934 | − | 1454.81i | 0.940575 | − | 1.62912i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.7198 | + | 8.49849i | −0.0164467 | + | 0.00949552i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.20525i | 0.00467769i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −791.069 | −0.877990 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.5764 | − | 77.2087i | −0.0492557 | − | 0.0853134i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 81.4675 | + | 47.0353i | 0.0898209 | + | 0.0518581i | 0.544238 | − | 0.838931i | \(-0.316819\pi\) |
−0.454417 | + | 0.890789i | \(0.650152\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −818.478 | − | 472.549i | −0.898440 | − | 0.518714i | −0.0217460 | − | 0.999764i | \(-0.506923\pi\) |
−0.876694 | + | 0.481049i | \(0.840256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 107.193 | + | 185.664i | 0.117408 | + | 0.203356i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 431.047 | 0.470062 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.1099i | 0.0316757i | 0.999875 | + | 0.0158378i | \(0.00504155\pi\) | ||||
−0.999875 | + | 0.0158378i | \(0.994958\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 398.217 | − | 229.911i | 0.431438 | − | 0.249091i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −843.151 | + | 1460.38i | −0.911514 | + | 1.57879i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −383.769 | + | 664.707i | −0.413099 | + | 0.715508i | −0.995227 | − | 0.0975893i | \(-0.968887\pi\) |
0.582128 | + | 0.813097i | \(0.302220\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.9762 | + | 7.49181i | −0.0139379 | + | 0.00804705i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 192.700i | 0.206096i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −736.778 | −0.786316 | −0.393158 | − | 0.919471i | \(-0.628617\pi\) | ||||
−0.393158 | + | 0.919471i | \(0.628617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 531.351 | + | 920.327i | 0.564667 | + | 0.978031i | 0.997081 | + | 0.0763560i | \(0.0243285\pi\) |
−0.432414 | + | 0.901675i | \(0.642338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1282.73 | + | 740.585i | 1.36027 | + | 0.785350i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 499.283 | + | 288.261i | 0.527226 | + | 0.304394i | 0.739886 | − | 0.672732i | \(-0.234879\pi\) |
−0.212660 | + | 0.977126i | \(0.568213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 74.4047 | + | 128.873i | 0.0784033 | + | 0.135799i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −677.961 | −0.711397 | −0.355698 | − | 0.934601i | \(-0.615757\pi\) | ||||
−0.355698 | + | 0.934601i | \(0.615757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 252.720i | 0.264629i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 221.237 | − | 127.731i | 0.230696 | − | 0.133192i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −480.490 | + | 832.234i | −0.499990 | + | 0.866008i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 73.7641 | − | 127.763i | 0.0764395 | − | 0.132397i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1153.25 | + | 665.830i | −1.19261 | + | 0.688552i | −0.958897 | − | 0.283755i | \(-0.908420\pi\) |
−0.233710 | + | 0.972306i | \(0.575087\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 385.062i | − | 0.396563i | −0.980145 | − | 0.198281i | \(-0.936464\pi\) | ||
0.980145 | − | 0.198281i | \(-0.0635360\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1259.30 | 1.29424 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −142.550 | − | 246.905i | −0.145906 | − | 0.252717i | 0.783804 | − | 0.621008i | \(-0.213276\pi\) |
−0.929711 | + | 0.368291i | \(0.879943\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −179.687 | − | 103.742i | −0.183541 | − | 0.105968i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1164.42 | − | 672.280i | −1.18456 | − | 0.683907i | −0.227496 | − | 0.973779i | \(-0.573054\pi\) |
−0.957065 | + | 0.289872i | \(0.906387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.2715 | + | 83.6087i | 0.0490066 | + | 0.0848819i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −71.5610 | −0.0723570 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1457.00i | 1.47023i | 0.677944 | + | 0.735114i | \(0.262871\pi\) | ||||
−0.677944 | + | 0.735114i | \(0.737129\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.9125 | − | 28.8170i | 0.0501633 | − | 0.0289618i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −160.689 | + | 278.322i | −0.161173 | + | 0.279160i | −0.935290 | − | 0.353883i | \(-0.884861\pi\) |
0.774117 | + | 0.633043i | \(0.218194\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1728.3.o.f.127.2 | 8 | ||
3.2 | odd | 2 | 576.3.o.f.511.3 | 8 | |||
4.3 | odd | 2 | 1728.3.o.e.127.2 | 8 | |||
8.3 | odd | 2 | 432.3.o.a.127.3 | 8 | |||
8.5 | even | 2 | 432.3.o.b.127.3 | 8 | |||
9.4 | even | 3 | 1728.3.o.e.1279.2 | 8 | |||
9.5 | odd | 6 | 576.3.o.d.319.2 | 8 | |||
12.11 | even | 2 | 576.3.o.d.511.2 | 8 | |||
24.5 | odd | 2 | 144.3.o.a.79.2 | yes | 8 | ||
24.11 | even | 2 | 144.3.o.c.79.3 | yes | 8 | ||
36.23 | even | 6 | 576.3.o.f.319.3 | 8 | |||
36.31 | odd | 6 | inner | 1728.3.o.f.1279.2 | 8 | ||
72.5 | odd | 6 | 144.3.o.c.31.3 | yes | 8 | ||
72.11 | even | 6 | 1296.3.g.j.1135.5 | 8 | |||
72.13 | even | 6 | 432.3.o.a.415.3 | 8 | |||
72.29 | odd | 6 | 1296.3.g.j.1135.6 | 8 | |||
72.43 | odd | 6 | 1296.3.g.k.1135.3 | 8 | |||
72.59 | even | 6 | 144.3.o.a.31.2 | ✓ | 8 | ||
72.61 | even | 6 | 1296.3.g.k.1135.4 | 8 | |||
72.67 | odd | 6 | 432.3.o.b.415.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.o.a.31.2 | ✓ | 8 | 72.59 | even | 6 | ||
144.3.o.a.79.2 | yes | 8 | 24.5 | odd | 2 | ||
144.3.o.c.31.3 | yes | 8 | 72.5 | odd | 6 | ||
144.3.o.c.79.3 | yes | 8 | 24.11 | even | 2 | ||
432.3.o.a.127.3 | 8 | 8.3 | odd | 2 | |||
432.3.o.a.415.3 | 8 | 72.13 | even | 6 | |||
432.3.o.b.127.3 | 8 | 8.5 | even | 2 | |||
432.3.o.b.415.3 | 8 | 72.67 | odd | 6 | |||
576.3.o.d.319.2 | 8 | 9.5 | odd | 6 | |||
576.3.o.d.511.2 | 8 | 12.11 | even | 2 | |||
576.3.o.f.319.3 | 8 | 36.23 | even | 6 | |||
576.3.o.f.511.3 | 8 | 3.2 | odd | 2 | |||
1296.3.g.j.1135.5 | 8 | 72.11 | even | 6 | |||
1296.3.g.j.1135.6 | 8 | 72.29 | odd | 6 | |||
1296.3.g.k.1135.3 | 8 | 72.43 | odd | 6 | |||
1296.3.g.k.1135.4 | 8 | 72.61 | even | 6 | |||
1728.3.o.e.127.2 | 8 | 4.3 | odd | 2 | |||
1728.3.o.e.1279.2 | 8 | 9.4 | even | 3 | |||
1728.3.o.f.127.2 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.o.f.1279.2 | 8 | 36.31 | odd | 6 | inner |