Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(269,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.t (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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.20 | ||
Character | \(\chi\) | \(=\) | 1620.269 |
Dual form | 1620.3.t.f.1349.20 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | 4.45514 | + | 2.26973i | 0.891029 | + | 0.453947i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.97789 | − | 1.71928i | −0.425412 | − | 0.245612i | 0.271978 | − | 0.962303i | \(-0.412322\pi\) |
−0.697390 | + | 0.716692i | \(0.745656\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.1039 | + | 6.41086i | 1.00945 | + | 0.582806i | 0.911030 | − | 0.412339i | \(-0.135288\pi\) |
0.0984188 | + | 0.995145i | \(0.468622\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.55354 | − | 0.896938i | 0.119503 | − | 0.0689952i | −0.439057 | − | 0.898459i | \(-0.644687\pi\) |
0.558560 | + | 0.829464i | \(0.311354\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 30.9523 | 1.82073 | 0.910363 | − | 0.413811i | \(-0.135803\pi\) | ||||
0.910363 | + | 0.413811i | \(0.135803\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.2201 | −1.01158 | −0.505792 | − | 0.862656i | \(-0.668800\pi\) | ||||
−0.505792 | + | 0.862656i | \(0.668800\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.19201 | + | 2.06461i | 0.0518263 | + | 0.0897659i | 0.890775 | − | 0.454445i | \(-0.150162\pi\) |
−0.838948 | + | 0.544211i | \(0.816829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.6966 | + | 20.2240i | 0.587865 | + | 0.808959i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −31.0770 | − | 17.9423i | −1.07162 | − | 0.618701i | −0.142998 | − | 0.989723i | \(-0.545674\pi\) |
−0.928624 | + | 0.371022i | \(0.879007\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.4538 | + | 35.4270i | 0.659800 | + | 1.14281i | 0.980667 | + | 0.195683i | \(0.0626924\pi\) |
−0.320867 | + | 0.947124i | \(0.603974\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.36459 | − | 14.4187i | −0.267560 | − | 0.411962i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 53.6302i | − | 1.44947i | −0.689030 | − | 0.724733i | \(-0.741963\pi\) | ||
0.689030 | − | 0.724733i | \(-0.258037\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.14983 | − | 1.24120i | 0.0524348 | − | 0.0302732i | −0.473553 | − | 0.880765i | \(-0.657029\pi\) |
0.525988 | + | 0.850492i | \(0.323696\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 47.7611 | + | 27.5749i | 1.11072 | + | 0.641276i | 0.939016 | − | 0.343873i | \(-0.111739\pi\) |
0.171706 | + | 0.985148i | \(0.445072\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −28.5250 | + | 49.4067i | −0.606914 | + | 1.05121i | 0.384831 | + | 0.922987i | \(0.374260\pi\) |
−0.991746 | + | 0.128220i | \(0.959074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.5881 | − | 32.1956i | −0.379350 | − | 0.657053i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19.4030 | 0.366094 | 0.183047 | − | 0.983104i | \(-0.441404\pi\) | ||||
0.183047 | + | 0.983104i | \(0.441404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 34.9187 | + | 53.7643i | 0.634886 | + | 0.977533i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 59.8830 | − | 34.5735i | 1.01497 | − | 0.585991i | 0.102324 | − | 0.994751i | \(-0.467372\pi\) |
0.912642 | + | 0.408760i | \(0.134039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.80471 | + | 15.2502i | −0.144340 | + | 0.250003i | −0.929126 | − | 0.369762i | \(-0.879439\pi\) |
0.784787 | + | 0.619766i | \(0.212772\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.95707 | − | 0.469861i | 0.137801 | − | 0.00722864i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.3133 | − | 25.5843i | 0.661393 | − | 0.381855i | −0.131415 | − | 0.991327i | \(-0.541952\pi\) |
0.792807 | + | 0.609472i | \(0.208619\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53.9194i | 0.759428i | 0.925104 | + | 0.379714i | \(0.123978\pi\) | ||||
−0.925104 | + | 0.379714i | \(0.876022\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 42.7832i | 0.586072i | 0.956101 | + | 0.293036i | \(0.0946655\pi\) | ||||
−0.956101 | + | 0.293036i | \(0.905334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22.0442 | − | 38.1816i | −0.286288 | − | 0.495865i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −44.4228 | + | 76.9425i | −0.562314 | + | 0.973956i | 0.434980 | + | 0.900440i | \(0.356755\pi\) |
−0.997294 | + | 0.0735161i | \(0.976578\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.0472 | + | 24.3305i | −0.169243 | + | 0.293138i | −0.938154 | − | 0.346218i | \(-0.887466\pi\) |
0.768911 | + | 0.639356i | \(0.220799\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 137.897 | + | 70.2536i | 1.62232 | + | 0.826512i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 68.3114i | 0.767544i | 0.923428 | + | 0.383772i | \(0.125375\pi\) | ||||
−0.923428 | + | 0.383772i | \(0.874625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.16836 | −0.0677842 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −85.6282 | − | 43.6245i | −0.901350 | − | 0.459205i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 135.186 | + | 78.0498i | 1.39367 | + | 0.804637i | 0.993720 | − | 0.111899i | \(-0.0356933\pi\) |
0.399952 | + | 0.916536i | \(0.369027\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −60.5918 | − | 34.9827i | −0.599919 | − | 0.346364i | 0.169091 | − | 0.985601i | \(-0.445917\pi\) |
−0.769010 | + | 0.639237i | \(0.779250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 166.405 | − | 96.0740i | 1.61558 | − | 0.932757i | 0.627539 | − | 0.778585i | \(-0.284062\pi\) |
0.988044 | − | 0.154172i | \(-0.0492710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 78.5826 | 0.734417 | 0.367209 | − | 0.930139i | \(-0.380314\pi\) | ||||
0.367209 | + | 0.930139i | \(0.380314\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.54619 | 0.0325339 | 0.0162669 | − | 0.999868i | \(-0.494822\pi\) | ||||
0.0162669 | + | 0.999868i | \(0.494822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −106.243 | − | 184.018i | −0.940201 | − | 1.62848i | −0.765086 | − | 0.643928i | \(-0.777304\pi\) |
−0.175115 | − | 0.984548i | \(-0.556030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.624433 | + | 11.9037i | 0.00542985 | + | 0.103510i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −92.1725 | − | 53.2158i | −0.774559 | − | 0.447192i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.6983 | + | 37.5826i | 0.179325 | + | 0.310600i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 19.5725 | + | 123.458i | 0.156580 | + | 0.987665i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 183.486i | 1.44477i | 0.691489 | + | 0.722387i | \(0.256955\pi\) | ||||
−0.691489 | + | 0.722387i | \(0.743045\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 52.5451 | − | 30.3369i | 0.401107 | − | 0.231579i | −0.285854 | − | 0.958273i | \(-0.592277\pi\) |
0.686962 | + | 0.726694i | \(0.258944\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 57.2352 | + | 33.0448i | 0.430340 | + | 0.248457i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.23685 | − | 10.8025i | 0.0455244 | − | 0.0788506i | −0.842365 | − | 0.538907i | \(-0.818837\pi\) |
0.887890 | + | 0.460056i | \(0.152171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 36.8400 | + | 63.8088i | 0.265036 | + | 0.459056i | 0.967573 | − | 0.252591i | \(-0.0812828\pi\) |
−0.702537 | + | 0.711647i | \(0.747949\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.0006 | 0.160843 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −97.7283 | − | 150.472i | −0.673989 | − | 1.03774i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.02350 | + | 2.32297i | −0.0270033 | + | 0.0155904i | −0.513441 | − | 0.858125i | \(-0.671629\pi\) |
0.486438 | + | 0.873715i | \(0.338296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −118.510 | + | 205.265i | −0.784835 | + | 1.35937i | 0.144263 | + | 0.989539i | \(0.453919\pi\) |
−0.929098 | + | 0.369835i | \(0.879414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.7147 | + | 204.257i | 0.0691273 | + | 1.31779i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 136.484 | − | 78.7991i | 0.869325 | − | 0.501905i | 0.00220122 | − | 0.999998i | \(-0.499299\pi\) |
0.867124 | + | 0.498092i | \(0.165966\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 8.19758i | − | 0.0509166i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 82.9389i | − | 0.508828i | −0.967095 | − | 0.254414i | \(-0.918117\pi\) | ||
0.967095 | − | 0.254414i | \(-0.0818826\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 45.2172 | + | 78.3185i | 0.270762 | + | 0.468973i | 0.969057 | − | 0.246837i | \(-0.0793911\pi\) |
−0.698295 | + | 0.715810i | \(0.746058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −82.8910 | + | 143.571i | −0.490479 | + | 0.849535i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −129.905 | + | 225.003i | −0.750898 | + | 1.30059i | 0.196490 | + | 0.980506i | \(0.437046\pi\) |
−0.947388 | + | 0.320088i | \(0.896288\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.99411 | − | 85.4923i | −0.0513949 | − | 0.488528i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 228.604i | − | 1.27712i | −0.769573 | − | 0.638559i | \(-0.779531\pi\) | ||
0.769573 | − | 0.638559i | \(-0.220469\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 30.8901 | 0.170664 | 0.0853318 | − | 0.996353i | \(-0.472805\pi\) | ||||
0.0853318 | + | 0.996353i | \(0.472805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 121.726 | − | 238.930i | 0.657980 | − | 1.29152i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 343.693 | + | 198.431i | 1.83793 | + | 1.06113i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.27714 | − | 1.31471i | −0.0119222 | − | 0.00688330i | 0.494027 | − | 0.869447i | \(-0.335524\pi\) |
−0.505949 | + | 0.862563i | \(0.668858\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9076 | − | 10.9163i | 0.0979666 | − | 0.0565610i | −0.450216 | − | 0.892920i | \(-0.648653\pi\) |
0.548183 | + | 0.836359i | \(0.315320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 68.8358 | 0.349421 | 0.174710 | − | 0.984620i | \(-0.444101\pi\) | ||||
0.174710 | + | 0.984620i | \(0.444101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 116.185 | 0.583846 | 0.291923 | − | 0.956442i | \(-0.405705\pi\) | ||||
0.291923 | + | 0.956442i | \(0.405705\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 61.6959 | + | 106.860i | 0.303921 | + | 0.526406i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3950 | − | 0.650205i | 0.0604633 | − | 0.00317173i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −213.419 | − | 123.217i | −1.02114 | − | 0.589557i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 112.307 | + | 194.521i | 0.532258 | + | 0.921898i | 0.999291 | + | 0.0376582i | \(0.0119898\pi\) |
−0.467032 | + | 0.884240i | \(0.654677\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 150.195 | + | 231.255i | 0.698580 | + | 1.07560i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 140.664i | − | 0.648219i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 48.0858 | − | 27.7623i | 0.217583 | − | 0.125621i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 219.753 | + | 126.874i | 0.985439 | + | 0.568944i | 0.903908 | − | 0.427727i | \(-0.140686\pi\) |
0.0815313 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.7996 | + | 48.1503i | −0.122465 | + | 0.212116i | −0.920739 | − | 0.390179i | \(-0.872413\pi\) |
0.798274 | + | 0.602294i | \(0.205747\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 111.391 | + | 192.935i | 0.486423 | + | 0.842509i | 0.999878 | − | 0.0156074i | \(-0.00496819\pi\) |
−0.513456 | + | 0.858116i | \(0.671635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 399.458 | 1.71441 | 0.857207 | − | 0.514972i | \(-0.172198\pi\) | ||||
0.857207 | + | 0.514972i | \(0.172198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −239.223 | + | 155.370i | −1.01797 | + | 0.661149i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.4959 | + | 10.1013i | −0.0732046 | + | 0.0422647i | −0.536156 | − | 0.844119i | \(-0.680124\pi\) |
0.462951 | + | 0.886384i | \(0.346791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 168.299 | − | 291.502i | 0.698336 | − | 1.20955i | −0.270707 | − | 0.962662i | \(-0.587257\pi\) |
0.969043 | − | 0.246892i | \(-0.0794092\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.73740 | − | 185.626i | −0.0397445 | − | 0.757658i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.8592 | + | 17.2392i | −0.120887 | + | 0.0697944i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 280.569i | 1.11781i | 0.829233 | + | 0.558903i | \(0.188778\pi\) | ||||
−0.829233 | + | 0.558903i | \(0.811222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.5671i | 0.120819i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −82.1464 | − | 142.282i | −0.319636 | − | 0.553625i | 0.660776 | − | 0.750583i | \(-0.270227\pi\) |
−0.980412 | + | 0.196958i | \(0.936894\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −92.2056 | + | 159.705i | −0.356006 | + | 0.616621i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 147.024 | − | 254.654i | 0.559028 | − | 0.968266i | −0.438550 | − | 0.898707i | \(-0.644508\pi\) |
0.997578 | − | 0.0695585i | \(-0.0221590\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 86.4430 | + | 44.0396i | 0.326200 | + | 0.166187i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 373.214i | − | 1.38741i | −0.720259 | − | 0.693706i | \(-0.755977\pi\) | ||
0.720259 | − | 0.693706i | \(-0.244023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −388.909 | −1.43509 | −0.717543 | − | 0.696514i | \(-0.754733\pi\) | ||||
−0.717543 | + | 0.696514i | \(0.754733\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.5372 | + | 318.784i | 0.121954 | + | 1.15921i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −321.698 | − | 185.732i | −1.16136 | − | 0.670514i | −0.209733 | − | 0.977759i | \(-0.567260\pi\) |
−0.951630 | + | 0.307245i | \(0.900593\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 234.725 | + | 135.519i | 0.835321 | + | 0.482273i | 0.855671 | − | 0.517520i | \(-0.173145\pi\) |
−0.0203504 | + | 0.999793i | \(0.506478\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.8742 | − | 16.6705i | 0.102029 | − | 0.0589065i | −0.448117 | − | 0.893975i | \(-0.647905\pi\) |
0.550146 | + | 0.835068i | \(0.314572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.53591 | −0.0297419 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 669.047 | 2.31504 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 59.5109 | + | 103.076i | 0.203109 | + | 0.351795i | 0.949529 | − | 0.313681i | \(-0.101562\pi\) |
−0.746420 | + | 0.665476i | \(0.768229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 345.260 | − | 18.1113i | 1.17037 | − | 0.0613943i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.70366 | + | 2.13831i | 0.0123868 | + | 0.00715154i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −94.8180 | − | 164.230i | −0.315010 | − | 0.545613i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −73.8402 | + | 47.9575i | −0.242099 | + | 0.157238i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 63.9942i | − | 0.208450i | −0.994554 | − | 0.104225i | \(-0.966764\pi\) | ||
0.994554 | − | 0.104225i | \(-0.0332362\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 92.3321 | − | 53.3079i | 0.296888 | − | 0.171408i | −0.344156 | − | 0.938912i | \(-0.611835\pi\) |
0.641044 | + | 0.767504i | \(0.278502\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −189.421 | − | 109.362i | −0.605179 | − | 0.349401i | 0.165897 | − | 0.986143i | \(-0.446948\pi\) |
−0.771076 | + | 0.636743i | \(0.780281\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −176.345 | + | 305.438i | −0.556292 | + | 0.963526i | 0.441510 | + | 0.897256i | \(0.354443\pi\) |
−0.997802 | + | 0.0662695i | \(0.978890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −230.052 | − | 398.461i | −0.721165 | − | 1.24909i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −594.906 | −1.84182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 40.9715 | + | 18.2369i | 0.126066 | + | 0.0561134i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 169.888 | − | 98.0850i | 0.516378 | − | 0.298131i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.3510 | + | 52.5695i | −0.0916949 | + | 0.158820i | −0.908224 | − | 0.418483i | \(-0.862562\pi\) |
0.816529 | + | 0.577304i | \(0.195895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 255.492 | − | 13.4024i | 0.762662 | − | 0.0400070i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.1598 | − | 11.0619i | 0.0568539 | − | 0.0328246i | −0.471304 | − | 0.881971i | \(-0.656216\pi\) |
0.528158 | + | 0.849146i | \(0.322883\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 524.506i | 1.53814i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 296.323i | 0.863915i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −174.972 | − | 303.060i | −0.504241 | − | 0.873371i | −0.999988 | − | 0.00490371i | \(-0.998439\pi\) |
0.495747 | − | 0.868467i | \(-0.334894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −140.703 | + | 243.705i | −0.403161 | + | 0.698296i | −0.994106 | − | 0.108416i | \(-0.965422\pi\) |
0.590944 | + | 0.806712i | \(0.298755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −79.9931 | + | 138.552i | −0.226609 | + | 0.392499i | −0.956801 | − | 0.290743i | \(-0.906097\pi\) |
0.730192 | + | 0.683242i | \(0.239431\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −122.383 | + | 240.219i | −0.344740 | + | 0.676673i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 643.967i | − | 1.79378i | −0.442254 | − | 0.896890i | \(-0.645821\pi\) | ||
0.442254 | − | 0.896890i | \(-0.354179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.41153 | 0.0233006 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −97.1065 | + | 190.605i | −0.266045 | + | 0.522207i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −536.920 | − | 309.991i | −1.46300 | − | 0.844663i | −0.463850 | − | 0.885914i | \(-0.653532\pi\) |
−0.999149 | + | 0.0412512i | \(0.986866\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −57.7798 | − | 33.3592i | −0.155741 | − | 0.0899169i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −123.864 | + | 71.5129i | −0.332075 | + | 0.191724i | −0.656762 | − | 0.754098i | \(-0.728074\pi\) |
0.324687 | + | 0.945822i | \(0.394741\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −64.3726 | −0.170750 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −57.1486 | −0.150788 | −0.0753940 | − | 0.997154i | \(-0.524021\pi\) | ||||
−0.0753940 | + | 0.997154i | \(0.524021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −145.454 | − | 251.933i | −0.379775 | − | 0.657789i | 0.611254 | − | 0.791434i | \(-0.290665\pi\) |
−0.991029 | + | 0.133645i | \(0.957332\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5479 | − | 220.139i | −0.0299944 | − | 0.571790i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −566.472 | − | 327.053i | −1.45623 | − | 0.840753i | −0.457404 | − | 0.889259i | \(-0.651221\pi\) |
−0.998823 | + | 0.0485060i | \(0.984554\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.8954 | + | 63.9046i | 0.0943615 | + | 0.163439i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −372.549 | + | 241.962i | −0.943162 | + | 0.612563i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 229.991i | − | 0.579323i | −0.957129 | − | 0.289661i | \(-0.906457\pi\) | ||
0.957129 | − | 0.289661i | \(-0.0935427\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −442.493 | + | 255.474i | −1.10347 | + | 0.637091i | −0.937131 | − | 0.348977i | \(-0.886529\pi\) |
−0.166343 | + | 0.986068i | \(0.553196\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 63.5517 | + | 36.6916i | 0.157697 | + | 0.0910461i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 343.816 | − | 595.507i | 0.844757 | − | 1.46316i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −299.632 | − | 518.979i | −0.732598 | − | 1.26890i | −0.955769 | − | 0.294117i | \(-0.904974\pi\) |
0.223172 | − | 0.974779i | \(-0.428359\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −237.766 | −0.575705 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −117.806 | + | 76.5123i | −0.283870 | + | 0.184367i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −525.674 | + | 303.498i | −1.25459 | + | 0.724339i | −0.972018 | − | 0.234906i | \(-0.924522\pi\) |
−0.282574 | + | 0.959245i | \(0.591188\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 226.077 | − | 391.578i | 0.537001 | − | 0.930113i | −0.462062 | − | 0.886847i | \(-0.652890\pi\) |
0.999064 | − | 0.0432659i | \(-0.0137763\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 454.895 | + | 625.979i | 1.07034 | + | 1.47289i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.4389 | − | 30.2756i | 0.122808 | − | 0.0709030i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 684.701i | − | 1.58863i | −0.607505 | − | 0.794316i | \(-0.707829\pi\) | ||
0.607505 | − | 0.794316i | \(-0.292171\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 458.058i | − | 1.05787i | −0.848662 | − | 0.528936i | \(-0.822591\pi\) | ||
0.848662 | − | 0.528936i | \(-0.177409\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.9104 | − | 39.6821i | −0.0524267 | − | 0.0908056i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.07259 | + | 10.5180i | −0.0138328 | + | 0.0239591i | −0.872859 | − | 0.487973i | \(-0.837737\pi\) |
0.859026 | + | 0.511932i | \(0.171070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 237.224 | − | 410.885i | 0.535495 | − | 0.927505i | −0.463644 | − | 0.886022i | \(-0.653458\pi\) |
0.999139 | − | 0.0414836i | \(-0.0132084\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −155.049 | + | 304.337i | −0.348424 | + | 0.683904i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 269.662i | − | 0.600583i | −0.953847 | − | 0.300291i | \(-0.902916\pi\) | ||
0.953847 | − | 0.300291i | \(-0.0970840\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.8287 | 0.0705737 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.4809 | − | 14.0005i | −0.0603977 | − | 0.0307704i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −483.695 | − | 279.261i | −1.05841 | − | 0.611075i | −0.133420 | − | 0.991060i | \(-0.542596\pi\) |
−0.924993 | + | 0.379985i | \(0.875929\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 606.316 | + | 350.056i | 1.31522 | + | 0.759341i | 0.982955 | − | 0.183845i | \(-0.0588546\pi\) |
0.332263 | + | 0.943187i | \(0.392188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −694.612 | + | 401.035i | −1.50024 | + | 0.866165i | −0.500242 | + | 0.865885i | \(0.666756\pi\) |
−1.00000 | 0.000279830i | \(0.999911\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −868.960 | −1.86073 | −0.930364 | − | 0.366636i | \(-0.880509\pi\) | ||||
−0.930364 | + | 0.366636i | \(0.880509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −175.947 | −0.375153 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 353.557 | + | 612.379i | 0.747478 | + | 1.29467i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −282.470 | − | 388.707i | −0.594674 | − | 0.818330i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −610.797 | − | 352.644i | −1.27515 | − | 0.736208i | −0.299197 | − | 0.954191i | \(-0.596719\pi\) |
−0.975953 | + | 0.217983i | \(0.930052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.1030 | − | 83.3169i | −0.100006 | − | 0.173216i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 425.122 | + | 654.560i | 0.876540 | + | 1.34961i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 715.753i | 1.46972i | 0.678220 | + | 0.734859i | \(0.262752\pi\) | ||||
−0.678220 | + | 0.734859i | \(0.737248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −87.8066 | + | 50.6952i | −0.178832 | + | 0.103249i | −0.586744 | − | 0.809773i | \(-0.699590\pi\) |
0.407912 | + | 0.913021i | \(0.366257\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −961.907 | − | 555.357i | −1.95113 | − | 1.12648i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 92.7027 | − | 160.566i | 0.186525 | − | 0.323070i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −468.963 | − | 812.267i | −0.939805 | − | 1.62779i | −0.765833 | − | 0.643040i | \(-0.777673\pi\) |
−0.173973 | − | 0.984751i | \(-0.555660\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 766.791 | 1.52444 | 0.762218 | − | 0.647321i | \(-0.224111\pi\) | ||||
0.762218 | + | 0.647321i | \(0.224111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −190.544 | − | 293.380i | −0.377315 | − | 0.580951i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 647.269 | − | 373.701i | 1.27165 | − | 0.734186i | 0.296350 | − | 0.955079i | \(-0.404231\pi\) |
0.975298 | + | 0.220893i | \(0.0708972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 73.5565 | − | 127.404i | 0.143946 | − | 0.249322i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 959.421 | − | 50.3284i | 1.86295 | − | 0.0977251i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −633.479 | + | 365.739i | −1.22530 | + | 0.707426i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.7011i | 0.0762018i | 0.999274 | + | 0.0381009i | \(0.0121308\pi\) | ||||
−0.999274 | + | 0.0381009i | \(0.987869\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 135.722i | 0.259506i | 0.991546 | + | 0.129753i | \(0.0414184\pi\) | ||||
−0.991546 | + | 0.129753i | \(0.958582\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 633.093 | + | 1096.55i | 1.20132 | + | 2.08074i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 261.658 | − | 453.205i | 0.494628 | − | 0.856721i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.22656 | − | 3.85652i | 0.00417742 | − | 0.00723550i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 350.097 | + | 178.362i | 0.654387 | + | 0.333386i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 476.664i | − | 0.884349i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 840.659 | 1.55390 | 0.776949 | − | 0.629563i | \(-0.216766\pi\) | ||||
0.776949 | + | 0.629563i | \(0.216766\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.7988 | + | 8.04892i | 0.0289886 | + | 0.0147687i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 819.259 | + | 472.999i | 1.49773 | + | 0.864715i | 0.999997 | − | 0.00261458i | \(-0.000832248\pi\) |
0.497734 | + | 0.867330i | \(0.334166\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 597.303 | + | 344.853i | 1.08403 | + | 0.625868i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 264.572 | − | 152.751i | 0.478430 | − | 0.276222i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 78.6518 | 0.141206 | 0.0706031 | − | 0.997504i | \(-0.477508\pi\) | ||||
0.0706031 | + | 0.997504i | \(0.477508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 98.9317 | 0.176980 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 139.427 | + | 241.495i | 0.247651 | + | 0.428944i | 0.962874 | − | 0.269953i | \(-0.0870080\pi\) |
−0.715223 | + | 0.698897i | \(0.753675\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −55.6553 | − | 1060.97i | −0.0985049 | − | 1.87782i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −504.075 | − | 291.028i | −0.885895 | − | 0.511472i | −0.0132978 | − | 0.999912i | \(-0.504233\pi\) |
−0.872598 | + | 0.488440i | \(0.837566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 153.625 | + | 266.087i | 0.269046 | + | 0.466001i | 0.968616 | − | 0.248563i | \(-0.0799583\pi\) |
−0.699570 | + | 0.714564i | \(0.746625\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.2363 | + | 54.4500i | −0.0421500 | + | 0.0946956i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.6333i | 0.0426921i | 0.999772 | + | 0.0213460i | \(0.00679517\pi\) | ||||
−0.999772 | + | 0.0213460i | \(0.993205\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 83.6619 | − | 48.3022i | 0.143996 | − | 0.0831363i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 215.449 | + | 124.390i | 0.369553 | + | 0.213362i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.2262 | − | 17.7123i | 0.0174211 | − | 0.0301743i | −0.857183 | − | 0.515011i | \(-0.827788\pi\) |
0.874605 | + | 0.484837i | \(0.161121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −393.124 | − | 680.910i | −0.667443 | − | 1.15604i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −676.813 | −1.14134 | −0.570669 | − | 0.821180i | \(-0.693316\pi\) | ||||
−0.570669 | + | 0.821180i | \(0.693316\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −289.856 | − | 446.291i | −0.487153 | − | 0.750069i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −47.0075 | + | 27.1398i | −0.0784766 | + | 0.0453085i | −0.538725 | − | 0.842482i | \(-0.681094\pi\) |
0.460248 | + | 0.887790i | \(0.347760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 142.651 | − | 247.078i | 0.237355 | − | 0.411111i | −0.722599 | − | 0.691267i | \(-0.757053\pi\) |
0.959955 | + | 0.280156i | \(0.0903861\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.3667 | + | 216.685i | 0.0187879 | + | 0.358158i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −850.741 | + | 491.175i | −1.40155 | + | 0.809185i | −0.994552 | − | 0.104244i | \(-0.966758\pi\) |
−0.406998 | + | 0.913429i | \(0.633424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 102.341i | 0.167497i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 850.701i | − | 1.38777i | −0.720087 | − | 0.693883i | \(-0.755898\pi\) | ||
0.720087 | − | 0.693883i | \(-0.244102\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 64.4265 | + | 111.590i | 0.104419 | + | 0.180859i | 0.913501 | − | 0.406837i | \(-0.133368\pi\) |
−0.809082 | + | 0.587696i | \(0.800035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −452.830 | + | 784.325i | −0.731552 | + | 1.26708i | 0.224668 | + | 0.974435i | \(0.427870\pi\) |
−0.956220 | + | 0.292649i | \(0.905463\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 117.447 | − | 203.424i | 0.188518 | − | 0.326523i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −193.019 | + | 594.448i | −0.308830 | + | 0.951117i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1659.98i | − | 2.63908i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1083.23 | −1.71669 | −0.858345 | − | 0.513073i | \(-0.828507\pi\) | ||||
−0.858345 | + | 0.513073i | \(0.828507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −416.465 | + | 817.458i | −0.655850 | + | 1.28734i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −57.7549 | − | 33.3448i | −0.0906670 | − | 0.0523466i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −875.815 | − | 505.652i | −1.36633 | − | 0.788848i | −0.375869 | − | 0.926673i | \(-0.622656\pi\) |
−0.990457 | + | 0.137825i | \(0.955989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −984.875 | + | 568.618i | −1.53169 | + | 0.884320i | −0.532403 | + | 0.846491i | \(0.678711\pi\) |
−0.999284 | + | 0.0378292i | \(0.987956\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −273.788 | −0.423166 | −0.211583 | − | 0.977360i | \(-0.567862\pi\) | ||||
−0.211583 | + | 0.977360i | \(0.567862\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 886.583 | 1.36608 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −200.616 | − | 347.478i | −0.307223 | − | 0.532125i | 0.670531 | − | 0.741882i | \(-0.266066\pi\) |
−0.977754 | + | 0.209756i | \(0.932733\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 302.953 | − | 15.8920i | 0.462523 | − | 0.0242626i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −323.745 | − | 186.914i | −0.491267 | − | 0.283633i | 0.233833 | − | 0.972277i | \(-0.424873\pi\) |
−0.725100 | + | 0.688644i | \(0.758206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −65.4788 | − | 113.413i | −0.0990602 | − | 0.171577i | 0.812236 | − | 0.583329i | \(-0.198250\pi\) |
−0.911296 | + | 0.411752i | \(0.864917\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 179.988 | + | 277.128i | 0.270659 | + | 0.416734i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 85.5494i | − | 0.128260i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −195.534 | + | 112.892i | −0.291407 | + | 0.168244i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −603.505 | − | 348.434i | −0.896738 | − | 0.517732i | −0.0205979 | − | 0.999788i | \(-0.506557\pi\) |
−0.876141 | + | 0.482056i | \(0.839890\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 246.437 | − | 426.841i | 0.364013 | − | 0.630489i | −0.624604 | − | 0.780941i | \(-0.714740\pi\) |
0.988617 | + | 0.150453i | \(0.0480731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −268.379 | − | 464.847i | −0.395257 | − | 0.684605i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −628.686 | −0.920477 | −0.460238 | − | 0.887795i | \(-0.652236\pi\) | ||||
−0.460238 | + | 0.887795i | \(0.652236\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 52.3049 | − | 33.9709i | 0.0763576 | − | 0.0495925i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.1433 | − | 17.4033i | 0.0437494 | − | 0.0252587i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 617.313 | − | 1069.22i | 0.893362 | − | 1.54735i | 0.0575441 | − | 0.998343i | \(-0.481673\pi\) |
0.835818 | − | 0.549006i | \(-0.184994\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.2987 | + | 367.894i | 0.0277679 | + | 0.529344i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 66.5421 | − | 38.4181i | 0.0954694 | − | 0.0551193i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 834.094i | 1.18986i | 0.803777 | + | 0.594931i | \(0.202821\pi\) | ||||
−0.803777 | + | 0.594931i | \(0.797179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1030.78i | 1.46626i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 120.290 | + | 208.349i | 0.170142 | + | 0.294695i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −51.1022 | + | 88.5117i | −0.0720765 | + | 0.124840i | −0.899811 | − | 0.436279i | \(-0.856296\pi\) |
0.827735 | + | 0.561120i | \(0.189629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48.7621 | + | 84.4584i | −0.0683901 | + | 0.118455i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 102.471 | + | 52.2052i | 0.143316 | + | 0.0730143i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 593.832i | − | 0.825913i | −0.910751 | − | 0.412957i | \(-0.864496\pi\) | ||
0.910751 | − | 0.412957i | \(-0.135504\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −660.714 | −0.916385 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −93.8619 | − | 892.193i | −0.129465 | − | 1.23061i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −580.916 | − | 335.392i | −0.799059 | − | 0.461337i | 0.0440827 | − | 0.999028i | \(-0.485963\pi\) |
−0.843142 | + | 0.537691i | \(0.819297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1478.32 | + | 853.506i | 2.02232 | + | 1.16759i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 729.510 | − | 421.183i | 0.995239 | − | 0.574602i | 0.0884030 | − | 0.996085i | \(-0.471824\pi\) |
0.906836 | + | 0.421483i | \(0.138490\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 656.070 | 0.890190 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1423.99 | 1.92692 | 0.963460 | − | 0.267853i | \(-0.0863141\pi\) | ||||
0.963460 | + | 0.267853i | \(0.0863141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 275.646 | + | 477.432i | 0.370990 | + | 0.642574i | 0.989718 | − | 0.143032i | \(-0.0456850\pi\) |
−0.618728 | + | 0.785605i | \(0.712352\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.1978 | + | 1.21689i | −0.0311380 | + | 0.00163341i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −234.010 | − | 135.106i | −0.312430 | − | 0.180382i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −142.586 | − | 246.967i | −0.189862 | − | 0.328851i | 0.755342 | − | 0.655331i | \(-0.227471\pi\) |
−0.945204 | + | 0.326480i | \(0.894137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −993.877 | + | 645.501i | −1.31639 | + | 0.854968i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 787.273i | − | 1.03999i | −0.854169 | − | 0.519995i | \(-0.825934\pi\) | ||
0.854169 | − | 0.519995i | \(-0.174066\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −87.6204 | + | 50.5876i | −0.115138 | + | 0.0664752i | −0.556463 | − | 0.830872i | \(-0.687842\pi\) |
0.441325 | + | 0.897347i | \(0.354509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.5602 | − | 6.09691i | −0.0138403 | − | 0.00799071i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 62.0205 | − | 107.423i | 0.0808612 | − | 0.140056i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.84498 | + | 3.19561i | 0.00239920 | + | 0.00415554i | 0.867223 | − | 0.497921i | \(-0.165903\pi\) |
−0.864823 | + | 0.502076i | \(0.832570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 504.260 | 0.652341 | 0.326171 | − | 0.945311i | \(-0.394242\pi\) | ||||
0.326171 | + | 0.945311i | \(0.394242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −415.874 | + | 934.315i | −0.536611 | + | 1.20557i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.3198 | + | 23.8560i | −0.0530422 | + | 0.0306239i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −345.670 | + | 598.718i | −0.442599 | + | 0.766604i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 786.909 | − | 41.2789i | 1.00243 | − | 0.0525846i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1223.57 | − | 706.429i | 1.55473 | − | 0.897622i | 0.556981 | − | 0.830525i | \(-0.311960\pi\) |
0.997746 | − | 0.0670969i | \(-0.0213737\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 730.645i | 0.923698i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.5891i | 0.0398350i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −241.383 | − | 418.088i | −0.302865 | − | 0.524577i | 0.673919 | − | 0.738805i | \(-0.264610\pi\) |
−0.976784 | + | 0.214228i | \(0.931276\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −882.915 | + | 1529.25i | −1.10502 | + | 1.91396i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −274.277 | + | 475.063i | −0.341566 | + | 0.591610i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.6063 | − | 36.5214i | 0.0231134 | − | 0.0453682i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 874.774i | − | 1.08130i | −0.841247 | − | 0.540652i | \(-0.818178\pi\) | ||
0.841247 | − | 0.540652i | \(-0.181822\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −568.734 | −0.701275 | −0.350638 | − | 0.936511i | \(-0.614035\pi\) | ||||
−0.350638 | + | 0.936511i | \(0.614035\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 188.249 | − | 369.505i | 0.230981 | − | 0.453380i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −917.971 | − | 529.991i | −1.12359 | − | 0.648704i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 128.787 | + | 74.3550i | 0.156866 | + | 0.0905664i | 0.576378 | − | 0.817183i | \(-0.304466\pi\) |
−0.419512 | + | 0.907750i | \(0.637799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 437.829 | − | 252.780i | 0.531991 | − | 0.307145i | −0.209836 | − | 0.977737i | \(-0.567293\pi\) |
0.741827 | + | 0.670591i | \(0.233960\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 980.267 | 1.18533 | 0.592664 | − | 0.805450i | \(-0.298076\pi\) | ||||
0.592664 | + | 0.805450i | \(0.298076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 190.269 | 0.229516 | 0.114758 | − | 0.993393i | \(-0.463391\pi\) | ||||
0.114758 | + | 0.993393i | \(0.463391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −575.346 | − | 996.529i | −0.690692 | − | 1.19631i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.6871 | + | 451.551i | 0.0283677 | + | 0.540780i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1021.86 | − | 589.969i | −1.21795 | − | 0.703181i | −0.253467 | − | 0.967344i | \(-0.581571\pi\) |
−0.964478 | + | 0.264163i | \(0.914904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 223.354 | + | 386.861i | 0.265582 | + | 0.460002i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −695.160 | + | 451.491i | −0.822675 | + | 0.534309i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 149.222i | − | 0.176177i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 110.726 | − | 63.9276i | 0.130113 | − | 0.0751205i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 970.251 | + | 560.175i | 1.13746 | + | 0.656711i | 0.945800 | − | 0.324751i | \(-0.105280\pi\) |
0.191657 | + | 0.981462i | \(0.438614\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −650.362 | + | 1126.46i | −0.758882 | + | 1.31442i | 0.184540 | + | 0.982825i | \(0.440921\pi\) |
−0.943421 | + | 0.331597i | \(0.892413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 433.951 | + | 751.625i | 0.505182 | + | 0.875000i | 0.999982 | + | 0.00599363i | \(0.00190784\pi\) |
−0.494800 | + | 0.869007i | \(0.664759\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −258.845 | −0.299937 | −0.149968 | − | 0.988691i | \(-0.547917\pi\) | ||||
−0.149968 | + | 0.988691i | \(0.547917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1089.44 | + | 707.569i | −1.25947 | + | 0.817999i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −986.536 | + | 569.577i | −1.13525 | + | 0.655439i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.8951 | − | 79.4926i | 0.0526924 | − | 0.0912659i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 153.975 | − | 401.295i | 0.175971 | − | 0.458623i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.4844 | + | 9.51730i | −0.0187964 | + | 0.0108521i | −0.509369 | − | 0.860548i | \(-0.670121\pi\) |
0.490572 | + | 0.871400i | \(0.336788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1688.86i | 1.91699i | 0.285117 | + | 0.958493i | \(0.407968\pi\) | ||||
−0.285117 | + | 0.958493i | \(0.592032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 373.276i | 0.422736i | 0.977407 | + | 0.211368i | \(0.0677918\pi\) | ||||
−0.977407 | + | 0.211368i | \(0.932208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −598.296 | − | 1036.28i | −0.674516 | − | 1.16830i | −0.976610 | − | 0.215018i | \(-0.931019\pi\) |
0.302094 | − | 0.953278i | \(-0.402314\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 315.465 | − | 546.401i | 0.354854 | − | 0.614624i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 548.252 | − | 949.601i | 0.613944 | − | 1.06338i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 518.870 | − | 1018.46i | 0.579743 | − | 1.13795i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1467.96i | − | 1.63288i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 600.567 | 0.666556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 137.620 | + | 70.1123i | 0.152066 | + | 0.0774722i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 760.118 | + | 438.855i | 0.838058 | + | 0.483853i | 0.856604 | − | 0.515975i | \(-0.172570\pi\) |
−0.0185458 | + | 0.999828i | \(0.505904\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −212.780 | − | 122.849i | −0.233567 | − | 0.134850i | 0.378649 | − | 0.925540i | \(-0.376389\pi\) |
−0.612217 | + | 0.790690i | \(0.709722\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −311.959 | + | 180.109i | −0.341685 | + | 0.197272i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −208.631 | −0.227515 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 66.4769 | 0.0723361 | 0.0361681 | − | 0.999346i | \(-0.488485\pi\) | ||||
0.0361681 | + | 0.999346i | \(0.488485\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.3624 | + | 83.7661i | 0.0523969 | + | 0.0907542i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1084.62 | − | 788.183i | 1.17256 | − | 0.852090i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1179.99 | − | 681.269i | −1.27017 | − | 0.733336i | −0.295154 | − | 0.955450i | \(-0.595371\pi\) |
−0.975021 | + | 0.222114i | \(0.928704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 357.265 | + | 618.802i | 0.383744 | + | 0.664664i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1080.82 | + | 1664.13i | 1.15595 | + | 1.77982i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 750.141i | − | 0.800578i | −0.916389 | − | 0.400289i | \(-0.868910\pi\) | ||
0.916389 | − | 0.400289i | \(-0.131090\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 227.057 | − | 131.091i | 0.241293 | − | 0.139311i | −0.374478 | − | 0.927236i | \(-0.622178\pi\) |
0.615771 | + | 0.787925i | \(0.288845\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.12521 | + | 2.95904i | 0.00543501 | + | 0.00313790i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −329.271 | + | 570.313i | −0.347699 | + | 0.602232i | −0.985840 | − | 0.167687i | \(-0.946370\pi\) |
0.638142 | + | 0.769919i | \(0.279703\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.3739 | + | 66.4656i | 0.0404362 | + | 0.0700375i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 122.390 | 0.128426 | 0.0642131 | − | 0.997936i | \(-0.479546\pi\) | ||||
0.0642131 | + | 0.997936i | \(0.479546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.16096 | − | 11.0257i | −0.00749839 | − | 0.0115453i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.1452 | + | 21.4458i | −0.0387333 | + | 0.0223627i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −356.216 | + | 616.985i | −0.370672 | + | 0.642024i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 109.013 | − | 5.71850i | 0.112967 | − | 0.00592591i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −923.389 | + | 533.119i | −0.954901 | + | 0.551312i | −0.894600 | − | 0.446868i | \(-0.852539\pi\) |
−0.0603010 | + | 0.998180i | \(0.519206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1798.30i | − | 1.85201i | −0.377508 | − | 0.926006i | \(-0.623219\pi\) | ||
0.377508 | − | 0.926006i | \(-0.376781\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 253.354i | − | 0.260384i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −287.036 | − | 497.161i | −0.293794 | − | 0.508865i | 0.680910 | − | 0.732367i | \(-0.261584\pi\) |
−0.974704 | + | 0.223502i | \(0.928251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −437.935 | + | 758.526i | −0.447329 | + | 0.774797i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −382.134 | + | 661.875i | −0.388742 | + | 0.673321i | −0.992281 | − | 0.124013i | \(-0.960424\pi\) |
0.603538 | + | 0.797334i | \(0.293757\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 306.674 | + | 156.239i | 0.311344 | + | 0.158618i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 131.478i | 0.132940i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 398.586 | 0.402206 | 0.201103 | − | 0.979570i | \(-0.435547\pi\) | ||||
0.201103 | + | 0.979570i | \(0.435547\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 517.622 | + | 263.710i | 0.520224 | + | 0.265035i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1278.30 | + | 738.025i | 1.28214 | + | 0.740246i | 0.977240 | − | 0.212138i | \(-0.0680426\pi\) |
0.304903 | + | 0.952383i | \(0.401376\pi\) | |||||||
\(998\) | 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 | 1620.3.t.f.269.20 | 48 | ||
3.2 | odd | 2 | inner | 1620.3.t.f.269.5 | 48 | ||
5.4 | even | 2 | inner | 1620.3.t.f.269.13 | 48 | ||
9.2 | odd | 6 | 1620.3.b.a.809.21 | yes | 24 | ||
9.4 | even | 3 | inner | 1620.3.t.f.1349.12 | 48 | ||
9.5 | odd | 6 | inner | 1620.3.t.f.1349.13 | 48 | ||
9.7 | even | 3 | 1620.3.b.a.809.4 | yes | 24 | ||
15.14 | odd | 2 | inner | 1620.3.t.f.269.12 | 48 | ||
45.4 | even | 6 | inner | 1620.3.t.f.1349.5 | 48 | ||
45.14 | odd | 6 | inner | 1620.3.t.f.1349.20 | 48 | ||
45.29 | odd | 6 | 1620.3.b.a.809.3 | ✓ | 24 | ||
45.34 | even | 6 | 1620.3.b.a.809.22 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.3.b.a.809.3 | ✓ | 24 | 45.29 | odd | 6 | ||
1620.3.b.a.809.4 | yes | 24 | 9.7 | even | 3 | ||
1620.3.b.a.809.21 | yes | 24 | 9.2 | odd | 6 | ||
1620.3.b.a.809.22 | yes | 24 | 45.34 | even | 6 | ||
1620.3.t.f.269.5 | 48 | 3.2 | odd | 2 | inner | ||
1620.3.t.f.269.12 | 48 | 15.14 | odd | 2 | inner | ||
1620.3.t.f.269.13 | 48 | 5.4 | even | 2 | inner | ||
1620.3.t.f.269.20 | 48 | 1.1 | even | 1 | trivial | ||
1620.3.t.f.1349.5 | 48 | 45.4 | even | 6 | inner | ||
1620.3.t.f.1349.12 | 48 | 9.4 | even | 3 | inner | ||
1620.3.t.f.1349.13 | 48 | 9.5 | odd | 6 | inner | ||
1620.3.t.f.1349.20 | 48 | 45.14 | odd | 6 | inner |