Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 143.6 | ||
Character | \(\chi\) | \(=\) | 1152.143 |
Dual form | 1152.2.w.b.1007.6 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
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 | ||||||||
\(5\) | 0.366958 | − | 0.885915i | 0.164109 | − | 0.396193i | −0.820338 | − | 0.571880i | \(-0.806214\pi\) |
0.984446 | + | 0.175686i | \(0.0562144\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.21471 | + | 1.21471i | −0.459117 | + | 0.459117i | −0.898366 | − | 0.439249i | \(-0.855245\pi\) |
0.439249 | + | 0.898366i | \(0.355245\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.545272 | + | 1.31640i | −0.164406 | + | 0.396910i | −0.984516 | − | 0.175295i | \(-0.943912\pi\) |
0.820110 | + | 0.572206i | \(0.193912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0270492 | − | 0.0112041i | 0.00750210 | − | 0.00310747i | −0.378929 | − | 0.925426i | \(-0.623708\pi\) |
0.386431 | + | 0.922318i | \(0.373708\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.32687 | 0.321814 | 0.160907 | − | 0.986970i | \(-0.448558\pi\) | ||||
0.160907 | + | 0.986970i | \(0.448558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73653 | + | 4.19236i | 0.398388 | + | 0.961793i | 0.988049 | + | 0.154142i | \(0.0492614\pi\) |
−0.589661 | + | 0.807651i | \(0.700739\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.934512 | + | 0.934512i | −0.194859 | + | 0.194859i | −0.797792 | − | 0.602933i | \(-0.793999\pi\) |
0.602933 | + | 0.797792i | \(0.293999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.88535 | + | 2.88535i | 0.577069 | + | 0.577069i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.35195 | − | 3.87371i | 1.73661 | − | 0.719329i | 0.737586 | − | 0.675253i | \(-0.235966\pi\) |
0.999028 | − | 0.0440761i | \(-0.0140344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.74390i | 1.75006i | 0.484072 | + | 0.875028i | \(0.339157\pi\) | ||||
−0.484072 | + | 0.875028i | \(0.660843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.630382 | + | 1.52188i | 0.106554 | + | 0.257244i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.28278 | − | 2.60241i | −1.03288 | − | 0.427834i | −0.199131 | − | 0.979973i | \(-0.563812\pi\) |
−0.833752 | + | 0.552139i | \(0.813812\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.42377 | + | 3.42377i | 0.534703 | + | 0.534703i | 0.921968 | − | 0.387266i | \(-0.126580\pi\) |
−0.387266 | + | 0.921968i | \(0.626580\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.997463 | − | 0.413163i | −0.152112 | − | 0.0630067i | 0.305329 | − | 0.952247i | \(-0.401234\pi\) |
−0.457440 | + | 0.889240i | \(0.651234\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.21143i | − | 0.906031i | −0.891503 | − | 0.453015i | \(-0.850348\pi\) | ||
0.891503 | − | 0.453015i | \(-0.149652\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.04896i | 0.578423i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.94741 | + | 1.22086i | 0.404858 | + | 0.167698i | 0.575814 | − | 0.817581i | \(-0.304685\pi\) |
−0.170955 | + | 0.985279i | \(0.554685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.966130 | + | 0.966130i | 0.130273 | + | 0.130273i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.4533 | + | 4.32990i | 1.36090 | + | 0.563704i | 0.939306 | − | 0.343079i | \(-0.111470\pi\) |
0.421596 | + | 0.906784i | \(0.361470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.76809 | + | 6.68277i | 0.354418 | + | 0.855641i | 0.996064 | + | 0.0886397i | \(0.0282520\pi\) |
−0.641646 | + | 0.767001i | \(0.721748\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.0280747i | − | 0.00348224i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1069 | − | 4.18640i | 1.23475 | − | 0.511450i | 0.332680 | − | 0.943040i | \(-0.392047\pi\) |
0.902070 | + | 0.431590i | \(0.142047\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.38725 | − | 7.38725i | −0.876705 | − | 0.876705i | 0.116487 | − | 0.993192i | \(-0.462837\pi\) |
−0.993192 | + | 0.116487i | \(0.962837\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.30156 | + | 8.30156i | −0.971625 | + | 0.971625i | −0.999608 | − | 0.0279838i | \(-0.991091\pi\) |
0.0279838 | + | 0.999608i | \(0.491091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.936700 | − | 2.26139i | −0.106747 | − | 0.257710i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.54363 | −0.623707 | −0.311853 | − | 0.950130i | \(-0.600950\pi\) | ||||
−0.311853 | + | 0.950130i | \(0.600950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.4571 | − | 4.74570i | 1.25758 | − | 0.520909i | 0.348417 | − | 0.937340i | \(-0.386719\pi\) |
0.909167 | + | 0.416431i | \(0.136719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.486907 | − | 1.17550i | 0.0528125 | − | 0.127501i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.93127 | + | 7.93127i | −0.840713 | + | 0.840713i | −0.988952 | − | 0.148238i | \(-0.952640\pi\) |
0.148238 | + | 0.988952i | \(0.452640\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0192471 | + | 0.0464667i | −0.00201765 | + | 0.00487103i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.35131 | 0.446435 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.5582 | 1.27509 | 0.637545 | − | 0.770413i | \(-0.279950\pi\) | ||||
0.637545 | + | 0.770413i | \(0.279950\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.67080 | − | 4.03367i | 0.166251 | − | 0.401365i | −0.818695 | − | 0.574229i | \(-0.805302\pi\) |
0.984946 | + | 0.172864i | \(0.0553020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.18742 | − | 2.18742i | 0.215533 | − | 0.215533i | −0.591080 | − | 0.806613i | \(-0.701298\pi\) |
0.806613 | + | 0.591080i | \(0.201298\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.09671 | + | 7.47611i | −0.299370 | + | 0.722743i | 0.700588 | + | 0.713566i | \(0.252921\pi\) |
−0.999958 | + | 0.00917704i | \(0.997079\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.499988 | + | 0.207102i | −0.0478902 | + | 0.0198368i | −0.406500 | − | 0.913651i | \(-0.633251\pi\) |
0.358610 | + | 0.933488i | \(0.383251\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.7112 | −1.85427 | −0.927137 | − | 0.374722i | \(-0.877738\pi\) | ||||
−0.927137 | + | 0.374722i | \(0.877738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.484972 | + | 1.17083i | 0.0452239 | + | 0.109180i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.61177 | + | 1.61177i | −0.147750 | + | 0.147750i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.34258 | + | 6.34258i | 0.576598 | + | 0.576598i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.04455 | − | 3.33216i | 0.719526 | − | 0.298038i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.1620i | 1.07920i | 0.841920 | + | 0.539602i | \(0.181425\pi\) | ||||
−0.841920 | + | 0.539602i | \(0.818575\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.68416 | + | 4.06591i | 0.147145 | + | 0.355240i | 0.980217 | − | 0.197924i | \(-0.0634200\pi\) |
−0.833072 | + | 0.553165i | \(0.813420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.20188 | − | 2.98312i | −0.624482 | − | 0.258669i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.05217 | + | 7.05217i | 0.602508 | + | 0.602508i | 0.940977 | − | 0.338470i | \(-0.109909\pi\) |
−0.338470 | + | 0.940977i | \(0.609909\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.5567 | − | 5.61536i | −1.14986 | − | 0.476288i | −0.275374 | − | 0.961337i | \(-0.588802\pi\) |
−0.874487 | + | 0.485049i | \(0.838802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0417169i | 0.00348855i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.70653i | − | 0.806083i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.14803 | − | 3.37503i | −0.667513 | − | 0.276493i | 0.0230832 | − | 0.999734i | \(-0.492652\pi\) |
−0.690596 | + | 0.723241i | \(0.742652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4470 | − | 13.4470i | −1.09430 | − | 1.09430i | −0.995064 | − | 0.0992395i | \(-0.968359\pi\) |
−0.0992395 | − | 0.995064i | \(-0.531641\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.63227 | + | 3.57560i | 0.693361 | + | 0.287199i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.17205 | + | 2.82959i | 0.0935400 | + | 0.225826i | 0.963724 | − | 0.266902i | \(-0.0860000\pi\) |
−0.870184 | + | 0.492727i | \(0.836000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.27032i | − | 0.178926i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.7015 | − | 6.08955i | 1.15151 | − | 0.476970i | 0.276469 | − | 0.961023i | \(-0.410836\pi\) |
0.875039 | + | 0.484052i | \(0.160836\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.30270 | − | 8.30270i | −0.642482 | − | 0.642482i | 0.308683 | − | 0.951165i | \(-0.400112\pi\) |
−0.951165 | + | 0.308683i | \(0.900112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.19178 | + | 9.19178i | −0.707060 | + | 0.707060i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.16308 | − | 12.4648i | −0.392542 | − | 0.947680i | −0.989384 | − | 0.145322i | \(-0.953578\pi\) |
0.596843 | − | 0.802358i | \(-0.296422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.00971 | −0.529885 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.43728 | + | 0.595340i | −0.107427 | + | 0.0444978i | −0.435750 | − | 0.900068i | \(-0.643517\pi\) |
0.328323 | + | 0.944566i | \(0.393517\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.57818 | − | 13.4669i | 0.414623 | − | 1.00099i | −0.569258 | − | 0.822159i | \(-0.692769\pi\) |
0.983880 | − | 0.178828i | \(-0.0572307\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.61104 | + | 4.61104i | −0.339010 | + | 0.339010i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.723507 | + | 1.74670i | −0.0529081 | + | 0.127731i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.01680 | 0.507718 | 0.253859 | − | 0.967241i | \(-0.418300\pi\) | ||||
0.253859 | + | 0.967241i | \(0.418300\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.3761 | 1.53868 | 0.769342 | − | 0.638837i | \(-0.220584\pi\) | ||||
0.769342 | + | 0.638837i | \(0.220584\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.34168 | + | 10.4817i | −0.309332 | + | 0.746793i | 0.690395 | + | 0.723432i | \(0.257437\pi\) |
−0.999727 | + | 0.0233605i | \(0.992563\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.04307 | − | 9.04307i | 0.641047 | − | 0.641047i | −0.309766 | − | 0.950813i | \(-0.600251\pi\) |
0.950813 | + | 0.309766i | \(0.100251\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.65448 | + | 16.0653i | −0.467053 | + | 1.12757i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.28955 | − | 1.77679i | 0.299595 | − | 0.124096i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.46572 | −0.447243 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.73872 | − | 13.8545i | −0.395070 | − | 0.953783i | −0.988817 | − | 0.149132i | \(-0.952352\pi\) |
0.593747 | − | 0.804652i | \(-0.297648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.732055 | + | 0.732055i | −0.0499257 | + | 0.0499257i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.8360 | − | 11.8360i | −0.803480 | − | 0.803480i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0358909 | − | 0.0148665i | 0.00241428 | − | 0.00100003i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.0857822i | − | 0.00574440i | −0.999996 | − | 0.00287220i | \(-0.999086\pi\) | ||
0.999996 | − | 0.00287220i | \(-0.000914251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.62555 | − | 23.2381i | −0.638870 | − | 1.54237i | −0.828187 | − | 0.560452i | \(-0.810627\pi\) |
0.189317 | − | 0.981916i | \(-0.439373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.5201 | − | 10.1566i | −1.62034 | − | 0.671165i | −0.626237 | − | 0.779633i | \(-0.715406\pi\) |
−0.994100 | + | 0.108468i | \(0.965406\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.44973 | − | 2.44973i | −0.160487 | − | 0.160487i | 0.622295 | − | 0.782782i | \(-0.286200\pi\) |
−0.782782 | + | 0.622295i | \(0.786200\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.50280 | − | 2.27934i | −0.358963 | − | 0.148687i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3256i | 0.732589i | 0.930499 | + | 0.366295i | \(0.119374\pi\) | ||||
−0.930499 | + | 0.366295i | \(0.880626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 13.4166i | − | 0.864239i | −0.901816 | − | 0.432119i | \(-0.857766\pi\) | ||
0.901816 | − | 0.432119i | \(-0.142234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.58704 | + | 1.48580i | 0.229167 | + | 0.0949243i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0939436 | + | 0.0939436i | 0.00597749 | + | 0.00597749i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2970 | − | 6.33621i | −0.965535 | − | 0.399938i | −0.156487 | − | 0.987680i | \(-0.550017\pi\) |
−0.809048 | + | 0.587742i | \(0.800017\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.720632 | − | 1.73976i | −0.0453057 | − | 0.109378i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.43408i | 0.151833i | 0.997114 | + | 0.0759167i | \(0.0241883\pi\) | ||||
−0.997114 | + | 0.0759167i | \(0.975812\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.7929 | − | 4.47058i | 0.670640 | − | 0.277788i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.2250 | − | 15.2250i | −0.938816 | − | 0.938816i | 0.0594176 | − | 0.998233i | \(-0.481076\pi\) |
−0.998233 | + | 0.0594176i | \(0.981076\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.16316 | − | 2.16316i | 0.132882 | − | 0.132882i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.29849 | + | 5.54904i | 0.140141 | + | 0.338331i | 0.978331 | − | 0.207048i | \(-0.0663857\pi\) |
−0.838190 | + | 0.545379i | \(0.816386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.5866 | 0.643088 | 0.321544 | − | 0.946895i | \(-0.395798\pi\) | ||||
0.321544 | + | 0.946895i | \(0.395798\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.37158 | + | 2.22498i | −0.323918 | + | 0.134171i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.91980 | − | 14.2917i | 0.355686 | − | 0.858702i | −0.640210 | − | 0.768200i | \(-0.721153\pi\) |
0.995896 | − | 0.0905024i | \(-0.0288473\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0206 | − | 12.0206i | 0.717087 | − | 0.717087i | −0.250921 | − | 0.968008i | \(-0.580733\pi\) |
0.968008 | + | 0.250921i | \(0.0807334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.86696 | − | 14.1641i | 0.348754 | − | 0.841968i | −0.648013 | − | 0.761629i | \(-0.724400\pi\) |
0.996768 | − | 0.0803386i | \(-0.0256002\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.31776 | −0.490982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2394 | −0.896436 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.02149 | + | 14.5372i | −0.351779 | + | 0.849270i | 0.644622 | + | 0.764502i | \(0.277015\pi\) |
−0.996401 | + | 0.0847682i | \(0.972985\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.67184 | − | 7.67184i | 0.446672 | − | 0.446672i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0148074 | + | 0.0357482i | −0.000856334 | + | 0.00206737i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.71350 | − | 0.709755i | 0.0987645 | − | 0.0409096i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.93614 | 0.397162 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0677 | + | 24.3055i | 0.574592 | + | 1.38719i | 0.897608 | + | 0.440795i | \(0.145303\pi\) |
−0.323016 | + | 0.946394i | \(0.604697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.5777 | + | 22.5777i | −1.28027 | + | 1.28027i | −0.339751 | + | 0.940516i | \(0.610343\pi\) |
−0.940516 | + | 0.339751i | \(0.889657\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.91862 | − | 9.91862i | −0.560633 | − | 0.560633i | 0.368854 | − | 0.929487i | \(-0.379750\pi\) |
−0.929487 | + | 0.368854i | \(0.879750\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4152 | − | 4.31414i | 0.584979 | − | 0.242306i | −0.0705101 | − | 0.997511i | \(-0.522463\pi\) |
0.655489 | + | 0.755205i | \(0.272463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.4232i | 0.807542i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.30416 | + | 5.56273i | 0.128207 | + | 0.309519i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.110374 | + | 0.0457185i | 0.00612245 | + | 0.00253600i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.54509 | + | 7.54509i | 0.415974 | + | 0.415974i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0127 | − | 5.39006i | −0.715245 | − | 0.296264i | −0.00477208 | − | 0.999989i | \(-0.501519\pi\) |
−0.710473 | + | 0.703724i | \(0.751519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 10.4901i | − | 0.573133i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.7271i | − | 0.911182i | −0.890189 | − | 0.455591i | \(-0.849428\pi\) | ||
0.890189 | − | 0.455591i | \(-0.150572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.8269 | − | 5.31308i | −0.694616 | − | 0.287719i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4213 | − | 13.4213i | −0.724681 | − | 0.724681i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.4060 | − | 7.20981i | −0.934404 | − | 0.387043i | −0.137056 | − | 0.990563i | \(-0.543764\pi\) |
−0.797347 | + | 0.603521i | \(0.793764\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.01279 | + | 19.3446i | 0.428915 | + | 1.03549i | 0.979632 | + | 0.200800i | \(0.0643541\pi\) |
−0.550718 | + | 0.834692i | \(0.685646\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.2201i | − | 1.55523i | −0.628743 | − | 0.777613i | \(-0.716430\pi\) | ||
0.628743 | − | 0.777613i | \(-0.283570\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.25529 | + | 3.83367i | −0.491220 | + | 0.203470i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.8752 | + | 23.8752i | 1.26008 | + | 1.26008i | 0.951052 | + | 0.309032i | \(0.100005\pi\) |
0.309032 | + | 0.951052i | \(0.399995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.12530 | + | 1.12530i | −0.0592262 | + | 0.0592262i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.30816 | + | 10.4008i | 0.225499 | + | 0.544403i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.91904 | 0.413370 | 0.206685 | − | 0.978408i | \(-0.433732\pi\) | ||||
0.206685 | + | 0.978408i | \(0.433732\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.06324 | + | 2.09726i | −0.262870 | + | 0.108884i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.910870 | + | 2.19904i | −0.0471631 | + | 0.113862i | −0.945705 | − | 0.325025i | \(-0.894627\pi\) |
0.898542 | + | 0.438887i | \(0.144627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.209561 | − | 0.209561i | 0.0107930 | − | 0.0107930i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.94487 | + | 21.5948i | −0.459467 | + | 1.10925i | 0.509146 | + | 0.860680i | \(0.329961\pi\) |
−0.968613 | + | 0.248572i | \(0.920039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.41070 | 0.429767 | 0.214883 | − | 0.976640i | \(-0.431063\pi\) | ||||
0.214883 | + | 0.976640i | \(0.431063\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.34713 | −0.119621 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.66887 | + | 11.2717i | −0.236721 | + | 0.571496i | −0.996940 | − | 0.0781715i | \(-0.975092\pi\) |
0.760219 | + | 0.649667i | \(0.225092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.23998 | + | 1.23998i | −0.0627085 | + | 0.0627085i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.03428 | + | 4.91118i | −0.102356 | + | 0.247108i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1886 | − | 5.46289i | 0.661916 | − | 0.274175i | −0.0263285 | − | 0.999653i | \(-0.508382\pi\) |
0.688245 | + | 0.725479i | \(0.258382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.87685 | 0.193601 | 0.0968004 | − | 0.995304i | \(-0.469139\pi\) | ||||
0.0968004 | + | 0.995304i | \(0.469139\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.109172 | + | 0.263565i | 0.00543825 | + | 0.0131291i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.85165 | − | 6.85165i | 0.339624 | − | 0.339624i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.61246 | + | 6.61246i | 0.326965 | + | 0.326965i | 0.851431 | − | 0.524466i | \(-0.175735\pi\) |
−0.524466 | + | 0.851431i | \(0.675735\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.9573 | + | 7.43815i | −0.883620 | + | 0.366007i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.8915i | − | 0.583732i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.69097 | − | 18.5676i | −0.375729 | − | 0.907089i | −0.992756 | − | 0.120147i | \(-0.961663\pi\) |
0.617028 | − | 0.786942i | \(-0.288337\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8875 | + | 6.58080i | 0.774307 | + | 0.320729i | 0.734616 | − | 0.678483i | \(-0.237362\pi\) |
0.0396916 | + | 0.999212i | \(0.487362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.82849 | + | 3.82849i | 0.185709 | + | 0.185709i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.4800 | − | 4.75519i | −0.555558 | − | 0.230120i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.7583i | 0.614548i | 0.951621 | + | 0.307274i | \(0.0994168\pi\) | ||||
−0.951621 | + | 0.307274i | \(0.900583\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.18066i | − | 0.0567390i | −0.999598 | − | 0.0283695i | \(-0.990968\pi\) | ||
0.999598 | − | 0.0283695i | \(-0.00903150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.54062 | − | 2.29500i | −0.265044 | − | 0.109785i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.88783 | + | 8.88783i | 0.424193 | + | 0.424193i | 0.886644 | − | 0.462452i | \(-0.153030\pi\) |
−0.462452 | + | 0.886644i | \(0.653030\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.1498 | + | 5.03262i | 0.577255 | + | 0.239107i | 0.652157 | − | 0.758084i | \(-0.273864\pi\) |
−0.0749018 | + | 0.997191i | \(0.523864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.11599 | + | 9.93688i | 0.195117 | + | 0.471053i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.529631i | 0.0249948i | 0.999922 | + | 0.0124974i | \(0.00397815\pi\) | ||||
−0.999922 | + | 0.0124974i | \(0.996022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.37394 | + | 2.64017i | −0.300137 | + | 0.124321i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0341027 | + | 0.0341027i | 0.00159876 | + | 0.00159876i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.43494 | + | 5.43494i | −0.254236 | + | 0.254236i | −0.822705 | − | 0.568469i | \(-0.807536\pi\) |
0.568469 | + | 0.822705i | \(0.307536\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.55433 | − | 18.2378i | −0.351840 | − | 0.849418i | −0.996393 | − | 0.0848579i | \(-0.972956\pi\) |
0.644553 | − | 0.764560i | \(-0.277044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.63562 | −0.215436 | −0.107718 | − | 0.994182i | \(-0.534354\pi\) | ||||
−0.107718 | + | 0.994182i | \(0.534354\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.9494 | − | 7.84910i | 0.876874 | − | 0.363213i | 0.101590 | − | 0.994826i | \(-0.467607\pi\) |
0.775284 | + | 0.631613i | \(0.217607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.19164 | + | 17.3622i | −0.332079 | + | 0.801710i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.08778 | − | 1.08778i | 0.0500161 | − | 0.0500161i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.08591 | + | 17.1069i | −0.325124 | + | 0.784918i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.5437 | 1.89818 | 0.949089 | − | 0.315008i | \(-0.102007\pi\) | ||||
0.949089 | + | 0.315008i | \(0.102007\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.199102 | −0.00907827 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.60833 | − | 11.1255i | 0.209253 | − | 0.505182i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.8137 | − | 18.8137i | 0.852529 | − | 0.852529i | −0.137915 | − | 0.990444i | \(-0.544040\pi\) |
0.990444 | + | 0.137915i | \(0.0440400\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.29239 | − | 17.6054i | 0.329101 | − | 0.794520i | −0.669559 | − | 0.742759i | \(-0.733517\pi\) |
0.998660 | − | 0.0517607i | \(-0.0164833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4089 | − | 5.13992i | 0.558867 | − | 0.231490i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.9467 | 0.805020 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.21640 | + | 5.35086i | 0.0992197 | + | 0.239537i | 0.965693 | − | 0.259685i | \(-0.0836189\pi\) |
−0.866474 | + | 0.499223i | \(0.833619\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1494 | − | 13.1494i | 0.586303 | − | 0.586303i | −0.350325 | − | 0.936628i | \(-0.613929\pi\) |
0.936628 | + | 0.350325i | \(0.113929\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.96038 | − | 2.96038i | −0.131735 | − | 0.131735i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.1362 | + | 4.61276i | −0.493603 | + | 0.204457i | −0.615578 | − | 0.788076i | \(-0.711077\pi\) |
0.121975 | + | 0.992533i | \(0.461077\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 20.1680i | − | 0.892179i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.13518 | − | 2.74056i | −0.0500219 | − | 0.120764i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.17675 | + | 3.38692i | 0.359613 | + | 0.148957i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.8812 | − | 12.8812i | −0.564338 | − | 0.564338i | 0.366199 | − | 0.930537i | \(-0.380659\pi\) |
−0.930537 | + | 0.366199i | \(0.880659\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.3454 | + | 5.94206i | 0.627280 | + | 0.259828i | 0.673597 | − | 0.739099i | \(-0.264748\pi\) |
−0.0463167 | + | 0.998927i | \(0.514748\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.9289i | 0.563193i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2534i | 0.924060i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.130971 | + | 0.0542498i | 0.00567296 | + | 0.00234982i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.48684 | + | 5.48684i | 0.237217 | + | 0.237217i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.33007 | − | 2.20779i | −0.229582 | − | 0.0950961i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.53641 | + | 13.3661i | 0.238029 | + | 0.574653i | 0.997079 | − | 0.0763798i | \(-0.0243361\pi\) |
−0.759050 | + | 0.651033i | \(0.774336\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.518945i | 0.0222292i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.8390 | + | 14.4308i | −1.48961 | + | 0.617016i | −0.971232 | − | 0.238137i | \(-0.923463\pi\) |
−0.518376 | + | 0.855153i | \(0.673463\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.4799 | + | 32.4799i | 1.38369 | + | 1.38369i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.73389 | − | 6.73389i | 0.286354 | − | 0.286354i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.6874 | + | 30.6300i | 0.537581 | + | 1.29784i | 0.926407 | + | 0.376524i | \(0.122881\pi\) |
−0.388826 | + | 0.921311i | \(0.627119\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0316097 | −0.00133695 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.8986 | + | 14.8697i | −1.51294 | + | 0.626682i | −0.976163 | − | 0.217040i | \(-0.930360\pi\) |
−0.536781 | + | 0.843722i | \(0.680360\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.23319 | + | 17.4625i | −0.304302 | + | 0.734651i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.9044 | − | 19.9044i | 0.834436 | − | 0.834436i | −0.153684 | − | 0.988120i | \(-0.549114\pi\) |
0.988120 | + | 0.153684i | \(0.0491137\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.51768 | − | 6.07821i | 0.105361 | − | 0.254365i | −0.862403 | − | 0.506223i | \(-0.831041\pi\) |
0.967764 | + | 0.251857i | \(0.0810414\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.39278 | −0.224895 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7117 | −0.778980 | −0.389490 | − | 0.921031i | \(-0.627349\pi\) | ||||
−0.389490 | + | 0.921031i | \(0.627349\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.15244 | + | 19.6817i | −0.338220 | + | 0.816536i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.21428 | + | 3.21428i | −0.133122 | + | 0.133122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.8204 | − | 30.9512i | 0.529155 | − | 1.27749i | −0.402922 | − | 0.915234i | \(-0.632005\pi\) |
0.932077 | − | 0.362260i | \(-0.117995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.8499 | + | 16.9206i | −1.68319 | + | 0.697201i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.7730 | 0.606654 | 0.303327 | − | 0.952887i | \(-0.401903\pi\) | ||||
0.303327 | + | 0.952887i | \(0.401903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.836437 | + | 2.01934i | 0.0342906 | + | 0.0827848i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.9159 | − | 17.9159i | 0.732022 | − | 0.732022i | −0.238998 | − | 0.971020i | \(-0.576819\pi\) |
0.971020 | + | 0.238998i | \(0.0768189\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.12098 | + | 4.12098i | 0.168098 | + | 0.168098i | 0.786143 | − | 0.618045i | \(-0.212075\pi\) |
−0.618045 | + | 0.786143i | \(0.712075\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.94645 | − | 3.29153i | 0.323069 | − | 0.133820i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.4859i | 1.03444i | 0.855852 | + | 0.517220i | \(0.173033\pi\) | ||||
−0.855852 | + | 0.517220i | \(0.826967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0695938 | − | 0.168014i | −0.00281546 | − | 0.00679713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.2820 | + | 14.6143i | 1.42503 | + | 0.590265i | 0.956118 | − | 0.292982i | \(-0.0946476\pi\) |
0.468908 | + | 0.883247i | \(0.344648\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.7171 | + | 13.7171i | 0.552229 | + | 0.552229i | 0.927084 | − | 0.374855i | \(-0.122307\pi\) |
−0.374855 | + | 0.927084i | \(0.622307\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.5287 | + | 8.91748i | 0.865311 | + | 0.358424i | 0.770782 | − | 0.637099i | \(-0.219866\pi\) |
0.0945288 | + | 0.995522i | \(0.469866\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 19.2684i | − | 0.771971i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.0529i | 0.482117i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.33646 | − | 3.45307i | −0.332396 | − | 0.137683i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8025 | + | 16.8025i | 0.668896 | + | 0.668896i | 0.957460 | − | 0.288565i | \(-0.0931780\pi\) |
−0.288565 | + | 0.957460i | \(0.593178\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7745 | + | 4.46295i | 0.427573 | + | 0.177107i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0453652 | + | 0.109521i | 0.00179743 | + | 0.00433939i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 10.7233i | − | 0.423546i | −0.977319 | − | 0.211773i | \(-0.932076\pi\) | ||
0.977319 | − | 0.211773i | \(-0.0679238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.3018 | − | 12.5514i | 1.19499 | − | 0.494980i | 0.305612 | − | 0.952156i | \(-0.401139\pi\) |
0.889376 | + | 0.457176i | \(0.151139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.94231 | − | 4.94231i | −0.194302 | − | 0.194302i | 0.603250 | − | 0.797552i | \(-0.293872\pi\) |
−0.797552 | + | 0.603250i | \(0.793872\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.3998 | + | 11.3998i | −0.447480 | + | 0.447480i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.01854 | + | 12.1158i | 0.196391 | + | 0.474129i | 0.991142 | − | 0.132806i | \(-0.0423988\pi\) |
−0.794751 | + | 0.606935i | \(0.792399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.22007 | 0.164892 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.1760 | − | 12.0851i | 1.13653 | − | 0.470768i | 0.266537 | − | 0.963825i | \(-0.414121\pi\) |
0.869997 | + | 0.493057i | \(0.164121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.3024 | + | 36.9433i | −0.595196 | + | 1.43693i | 0.283231 | + | 0.959052i | \(0.408594\pi\) |
−0.878426 | + | 0.477877i | \(0.841406\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.28557 | + | 5.28557i | −0.204966 | + | 0.204966i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.11949 | + | 12.3595i | −0.198227 | + | 0.478563i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.3066 | −0.397881 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.49552 | −0.250384 | −0.125192 | − | 0.992133i | \(-0.539955\pi\) | ||||
−0.125192 | + | 0.992133i | \(0.539955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.62635 | + | 6.34057i | −0.100939 | + | 0.243688i | −0.966279 | − | 0.257497i | \(-0.917102\pi\) |
0.865340 | + | 0.501185i | \(0.167102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.2545 | + | 15.2545i | −0.585415 | + | 0.585415i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.22340 | − | 10.1962i | 0.161604 | − | 0.390146i | −0.822248 | − | 0.569129i | \(-0.807281\pi\) |
0.983852 | + | 0.178982i | \(0.0572805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.83548 | − | 3.65978i | 0.337586 | − | 0.139833i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0934039 | 0.00355840 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.10014 | + | 5.07018i | 0.0798931 | + | 0.192879i | 0.958779 | − | 0.284153i | \(-0.0917125\pi\) |
−0.878886 | + | 0.477032i | \(0.841712\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.94946 | + | 9.94946i | −0.377404 | + | 0.377404i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.54291 | + | 4.54291i | 0.172075 | + | 0.172075i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.8651 | + | 16.5127i | −1.50568 | + | 0.623675i | −0.974662 | − | 0.223683i | \(-0.928192\pi\) |
−0.531022 | + | 0.847358i | \(0.678192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 30.8588i | − | 1.16386i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.87020 | + | 6.92928i | 0.107945 | + | 0.260602i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.6775 | + | 5.66541i | 0.513670 | + | 0.212769i | 0.624434 | − | 0.781078i | \(-0.285330\pi\) |
−0.110764 | + | 0.993847i | \(0.535330\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.10580 | − | 9.10580i | −0.341015 | − | 0.341015i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0369577 | + | 0.0153084i | 0.00138214 | + | 0.000572501i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.0055i | 1.41736i | 0.705528 | + | 0.708682i | \(0.250710\pi\) | ||||
−0.705528 | + | 0.708682i | \(0.749290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.31416i | 0.197910i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.1606 | + | 15.8066i | 1.41725 | + | 0.587044i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.50408 | + | 3.50408i | 0.129959 | + | 0.129959i | 0.769094 | − | 0.639135i | \(-0.220708\pi\) |
−0.639135 | + | 0.769094i | \(0.720708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.32351 | − | 0.548215i | −0.0489517 | − | 0.0202765i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0521 | − | 43.5817i | −0.666771 | − | 1.60973i | −0.786980 | − | 0.616978i | \(-0.788357\pi\) |
0.120210 | − | 0.992749i | \(-0.461643\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.5874i | 0.574170i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.4444 | + | 16.3384i | −1.45098 | + | 0.601018i | −0.962433 | − | 0.271518i | \(-0.912474\pi\) |
−0.488551 | + | 0.872535i | \(0.662474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.7638 | + | 10.7638i | 0.394884 | + | 0.394884i | 0.876424 | − | 0.481540i | \(-0.159922\pi\) |
−0.481540 | + | 0.876424i | \(0.659922\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.97997 | + | 5.97997i | −0.219089 | + | 0.219089i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.31970 | − | 12.8429i | −0.194378 | − | 0.469269i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.8234 | 0.759856 | 0.379928 | − | 0.925016i | \(-0.375949\pi\) | ||||
0.379928 | + | 0.925016i | \(0.375949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.8474 | + | 6.97843i | −0.613140 | + | 0.253971i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.51339 | − | 10.8963i | 0.164042 | − | 0.396032i | −0.820389 | − | 0.571806i | \(-0.806243\pi\) |
0.984431 | + | 0.175774i | \(0.0562428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8159 | − | 13.8159i | 0.500826 | − | 0.500826i | −0.410868 | − | 0.911695i | \(-0.634774\pi\) |
0.911695 | + | 0.410868i | \(0.134774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.355772 | − | 0.858909i | 0.0128798 | − | 0.0310946i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.331266 | 0.0119613 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.2754 | 0.370539 | 0.185270 | − | 0.982688i | \(-0.440684\pi\) | ||||
0.185270 | + | 0.982688i | \(0.440684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.3918 | − | 49.2302i | 0.733442 | − | 1.77069i | 0.102674 | − | 0.994715i | \(-0.467260\pi\) |
0.630769 | − | 0.775971i | \(-0.282740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.1145 | + | 28.1145i | −1.00990 | + | 1.00990i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.40818 | + | 20.2991i | −0.301254 | + | 0.727292i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.7527 | − | 5.69654i | 0.492109 | − | 0.203838i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.93687 | 0.104821 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.3657 | − | 29.8534i | −0.440789 | − | 1.06416i | −0.975672 | − | 0.219233i | \(-0.929644\pi\) |
0.534883 | − | 0.844926i | \(-0.320356\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.9434 | − | 23.9434i | 0.851329 | − | 0.851329i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.149749 | + | 0.149749i | 0.00531776 | + | 0.00531776i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.74523 | + | 1.55133i | −0.132663 | + | 0.0549508i | −0.448027 | − | 0.894020i | \(-0.647873\pi\) |
0.315364 | + | 0.948971i | \(0.397873\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.24179i | − | 0.291574i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.40159 | − | 15.4548i | −0.225907 | − | 0.545389i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.01131 | − | 0.833113i | −0.0708895 | − | 0.0293634i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.1580 | − | 20.1580i | −0.708716 | − | 0.708716i | 0.257549 | − | 0.966265i | \(-0.417085\pi\) |
−0.966265 | + | 0.257549i | \(0.917085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3626 | + | 10.0913i | 0.855487 | + | 0.354354i | 0.766941 | − | 0.641718i | \(-0.221778\pi\) |
0.0885462 | + | 0.996072i | \(0.471778\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15.2589i | − | 0.534495i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.89919i | − | 0.171401i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.0897 | + | 5.42194i | 0.456834 | + | 0.189227i | 0.599220 | − | 0.800584i | \(-0.295477\pi\) |
−0.142386 | + | 0.989811i | \(0.545477\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.7815 | + | 25.7815i | 0.898685 | + | 0.898685i | 0.995320 | − | 0.0966346i | \(-0.0308078\pi\) |
−0.0966346 | + | 0.995320i | \(0.530808\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.7610 | − | 16.0553i | −1.34785 | − | 0.558299i | −0.412159 | − | 0.911112i | \(-0.635225\pi\) |
−0.935694 | + | 0.352813i | \(0.885225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.355576 | + | 0.858437i | 0.0123497 | + | 0.0298148i | 0.929934 | − | 0.367726i | \(-0.119864\pi\) |
−0.917584 | + | 0.397541i | \(0.869864\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.37246i | 0.186145i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.4022 | + | 4.30875i | −0.359984 | + | 0.149110i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.1750 | − | 17.1750i | −0.592947 | − | 0.592947i | 0.345479 | − | 0.938426i | \(-0.387716\pi\) |
−0.938426 | + | 0.345479i | \(0.887716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.9474 | − | 51.9474i | 1.79129 | − | 1.79129i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.77014 | + | 11.5161i | 0.164098 | + | 0.396167i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.4088 | −0.529452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.30333 | − | 3.43935i | 0.284634 | − | 0.117899i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4371 | − | 39.6827i | 0.562797 | − | 1.35871i | −0.344724 | − | 0.938704i | \(-0.612028\pi\) |
0.907521 | − | 0.420007i | \(-0.137972\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0099 | − | 18.0099i | 0.615208 | − | 0.615208i | −0.329090 | − | 0.944298i | \(-0.606742\pi\) |
0.944298 | + | 0.329090i | \(0.106742\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.09982 | − | 17.1405i | 0.242243 | − | 0.584826i | −0.755262 | − | 0.655423i | \(-0.772490\pi\) |
0.997505 | + | 0.0705969i | \(0.0224904\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.4875 | −1.92286 | −0.961429 | − | 0.275052i | \(-0.911305\pi\) | ||||
−0.961429 | + | 0.275052i | \(0.911305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.9374 | −0.439884 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.02278 | − | 7.29765i | 0.102541 | − | 0.247556i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.226477 | − | 0.226477i | 0.00767389 | − | 0.00767389i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.72418 | + | 13.8194i | −0.193513 | + | 0.467181i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.8952 | + | 13.2114i | −1.07702 | + | 0.446118i | −0.849464 | − | 0.527646i | \(-0.823075\pi\) |
−0.227560 | + | 0.973764i | \(0.573075\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.8053 | 1.30739 | 0.653693 | − | 0.756760i | \(-0.273219\pi\) | ||||
0.653693 | + | 0.756760i | \(0.273219\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.251252 | − | 0.606576i | −0.00845531 | − | 0.0204129i | 0.919595 | − | 0.392867i | \(-0.128517\pi\) |
−0.928051 | + | 0.372454i | \(0.878517\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.1536 | + | 35.1536i | −1.18034 | + | 1.18034i | −0.200687 | + | 0.979655i | \(0.564317\pi\) |
−0.979655 | + | 0.200687i | \(0.935683\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.7733 | − | 14.7733i | −0.495481 | − | 0.495481i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.0406 | − | 10.7864i | 0.871414 | − | 0.360952i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.49177i | 0.0498644i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.7450 | + | 91.1245i | 1.25887 | + | 3.03917i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.91085 | + | 1.61993i | 0.130289 | + | 0.0539676i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.88358 | − | 9.88358i | −0.328541 | − | 0.328541i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.2246 | + | 10.0341i | 0.804363 | + | 0.333178i | 0.746703 | − | 0.665158i | \(-0.231636\pi\) |
0.0576607 | + | 0.998336i | \(0.481636\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 21.9666i | − | 0.727787i | −0.931441 | − | 0.363894i | \(-0.881447\pi\) | ||
0.931441 | − | 0.363894i | \(-0.118553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6699i | 0.584789i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.98466 | − | 2.89314i | −0.230654 | − | 0.0955399i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.5302 | − | 29.5302i | −0.974110 | − | 0.974110i | 0.0255634 | − | 0.999673i | \(-0.491862\pi\) |
−0.999673 | + | 0.0255634i | \(0.991862\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.282587 | − | 0.117051i | −0.00930146 | − | 0.00385279i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6191 | − | 25.6369i | −0.349155 | − | 0.842935i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.0425i | 1.28094i | 0.767983 | + | 0.640471i | \(0.221261\pi\) | ||||
−0.767983 | + | 0.640471i | \(0.778739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.9747 | + | 7.03115i | −0.556323 | + | 0.230437i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.28193 | + | 1.28193i | 0.0419237 | + | 0.0419237i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.3364 | − | 32.3364i | 1.05638 | − | 1.05638i | 0.0580711 | − | 0.998312i | \(-0.481505\pi\) |
0.998312 | − | 0.0580711i | \(-0.0184950\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.7360 | − | 37.9900i | −0.512979 | − | 1.23844i | −0.942142 | − | 0.335213i | \(-0.891192\pi\) |
0.429164 | − | 0.903227i | \(-0.358808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.39911 | −0.208384 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.4816 | + | 15.9396i | −1.25048 | + | 0.517967i | −0.906976 | − | 0.421182i | \(-0.861615\pi\) |
−0.343508 | + | 0.939150i | \(0.611615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.131539 | + | 0.317563i | −0.00426993 | + | 0.0103085i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.7980 | + | 41.7980i | −1.35397 | + | 1.35397i | −0.472800 | + | 0.881170i | \(0.656757\pi\) |
−0.881170 | + | 0.472800i | \(0.843243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.57487 | − | 6.21629i | 0.0833209 | − | 0.201154i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.1327 | −0.553243 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −63.9436 | −2.06270 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.84413 | − | 18.9374i | 0.252511 | − | 0.609616i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.3866 | + | 31.3866i | −1.00933 | + | 1.00933i | −0.00937024 | + | 0.999956i | \(0.502983\pi\) |
−0.999956 | + | 0.00937024i | \(0.997017\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.4873 | − | 49.4608i | 0.657469 | − | 1.58727i | −0.144230 | − | 0.989544i | \(-0.546071\pi\) |
0.801700 | − | 0.597727i | \(-0.203929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.2884 | − | 9.64638i | 0.746593 | − | 0.309249i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.6979 | −0.502221 | −0.251110 | − | 0.967958i | \(-0.580796\pi\) | ||||
−0.251110 | + | 0.967958i | \(0.580796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.11605 | − | 14.7655i | −0.195470 | − | 0.471906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.7012 | − | 17.7012i | 0.564581 | − | 0.564581i | −0.366024 | − | 0.930605i | \(-0.619281\pi\) |
0.930605 | + | 0.366024i | \(0.119281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.69271 | + | 7.69271i | 0.245110 | + | 0.245110i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.31825 | − | 0.546036i | 0.0419178 | − | 0.0173629i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 58.1793i | − | 1.84813i | −0.382240 | − | 0.924063i | \(-0.624847\pi\) | ||
0.382240 | − | 0.924063i | \(-0.375153\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.69297 | − | 11.3298i | −0.148777 | − | 0.359180i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.72099 | − | 4.02656i | −0.307867 | − | 0.127523i | 0.223401 | − | 0.974727i | \(-0.428284\pi\) |
−0.531268 | + | 0.847204i | \(0.678284\pi\) | |||||||
\(998\) | 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 | 1152.2.w.b.143.6 | 32 | ||
3.2 | odd | 2 | 1152.2.w.a.143.3 | 32 | |||
4.3 | odd | 2 | 288.2.w.a.251.1 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.b.251.8 | yes | 32 | ||
32.13 | even | 8 | 288.2.w.b.179.8 | yes | 32 | ||
32.19 | odd | 8 | 1152.2.w.a.1007.3 | 32 | |||
96.77 | odd | 8 | 288.2.w.a.179.1 | ✓ | 32 | ||
96.83 | even | 8 | inner | 1152.2.w.b.1007.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.179.1 | ✓ | 32 | 96.77 | odd | 8 | ||
288.2.w.a.251.1 | yes | 32 | 4.3 | odd | 2 | ||
288.2.w.b.179.8 | yes | 32 | 32.13 | even | 8 | ||
288.2.w.b.251.8 | yes | 32 | 12.11 | even | 2 | ||
1152.2.w.a.143.3 | 32 | 3.2 | odd | 2 | |||
1152.2.w.a.1007.3 | 32 | 32.19 | odd | 8 | |||
1152.2.w.b.143.6 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.b.1007.6 | 32 | 96.83 | even | 8 | inner |