Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1711,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1711");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.bf (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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2287.4 | ||
Character | \(\chi\) | \(=\) | 3024.2287 |
Dual form | 3024.2.bf.i.1711.13 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | − | 2.34835i | − | 1.05022i | −0.851036 | − | 0.525108i | \(-0.824025\pi\) | ||
0.851036 | − | 0.525108i | \(-0.175975\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.61922 | − | 0.373730i | −0.989973 | − | 0.141257i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.442942i | 0.133552i | 0.997768 | + | 0.0667761i | \(0.0212713\pi\) | ||||
−0.997768 | + | 0.0667761i | \(0.978729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.96099 | + | 1.13218i | −0.543881 | + | 0.314010i | −0.746650 | − | 0.665217i | \(-0.768339\pi\) |
0.202769 | + | 0.979226i | \(0.435006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.01950 | + | 2.32066i | −0.974872 | + | 0.562843i | −0.900718 | − | 0.434404i | \(-0.856959\pi\) |
−0.0741541 | + | 0.997247i | \(0.523626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.30879 | − | 5.73100i | 0.759089 | − | 1.31478i | −0.184227 | − | 0.982884i | \(-0.558978\pi\) |
0.943316 | − | 0.331897i | \(-0.107689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.13645i | − | 0.236965i | −0.992956 | − | 0.118483i | \(-0.962197\pi\) | ||
0.992956 | − | 0.118483i | \(-0.0378030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.514760 | −0.102952 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.37712 | + | 7.58140i | −0.812811 | + | 1.40783i | 0.0980775 | + | 0.995179i | \(0.468731\pi\) |
−0.910889 | + | 0.412652i | \(0.864603\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32034 | − | 4.01894i | 0.416745 | − | 0.721824i | −0.578865 | − | 0.815424i | \(-0.696504\pi\) |
0.995610 | + | 0.0935998i | \(0.0298374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.877649 | + | 6.15086i | −0.148350 | + | 1.03968i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.41316 | + | 2.44767i | −0.232323 | + | 0.402395i | −0.958491 | − | 0.285122i | \(-0.907966\pi\) |
0.726169 | + | 0.687517i | \(0.241299\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.55283 | + | 2.62858i | −0.711032 | + | 0.410515i | −0.811443 | − | 0.584431i | \(-0.801318\pi\) |
0.100411 | + | 0.994946i | \(0.467984\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.81500 | + | 2.20259i | 0.581782 | + | 0.335892i | 0.761841 | − | 0.647764i | \(-0.224296\pi\) |
−0.180059 | + | 0.983656i | \(0.557629\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.67363 | − | 4.63087i | −0.389989 | − | 0.675481i | 0.602458 | − | 0.798150i | \(-0.294188\pi\) |
−0.992448 | + | 0.122669i | \(0.960855\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.72065 | + | 1.95776i | 0.960093 | + | 0.279680i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.54428 | + | 2.67478i | 0.212124 | + | 0.367409i | 0.952379 | − | 0.304917i | \(-0.0986287\pi\) |
−0.740255 | + | 0.672326i | \(0.765295\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.04018 | 0.140259 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.689570 | + | 1.19437i | −0.0897743 | + | 0.155494i | −0.907416 | − | 0.420234i | \(-0.861948\pi\) |
0.817641 | + | 0.575728i | \(0.195281\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.88607 | + | 5.13038i | −1.13775 | + | 0.656877i | −0.945871 | − | 0.324542i | \(-0.894790\pi\) |
−0.191874 | + | 0.981420i | \(0.561456\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.65875 | + | 4.60510i | 0.329778 | + | 0.571192i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.10780 | − | 1.21694i | −0.257509 | − | 0.148673i | 0.365689 | − | 0.930737i | \(-0.380833\pi\) |
−0.623198 | + | 0.782064i | \(0.714167\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.20644i | 0.855247i | 0.903957 | + | 0.427623i | \(0.140649\pi\) | ||||
−0.903957 | + | 0.427623i | \(0.859351\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.17824 | − | 1.83496i | 0.371984 | − | 0.214765i | −0.302341 | − | 0.953200i | \(-0.597768\pi\) |
0.674325 | + | 0.738435i | \(0.264435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.165541 | − | 1.16016i | 0.0188651 | − | 0.132213i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.26542 | + | 4.19469i | −0.817423 | + | 0.471939i | −0.849527 | − | 0.527545i | \(-0.823113\pi\) |
0.0321039 | + | 0.999485i | \(0.489779\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.87941 | + | 13.6475i | −0.864878 | + | 1.49801i | 0.00229000 | + | 0.999997i | \(0.499271\pi\) |
−0.867168 | + | 0.498015i | \(0.834062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.44973 | + | 9.43920i | 0.591106 | + | 1.02383i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.32537 | − | 3.07461i | −0.564488 | − | 0.325908i | 0.190457 | − | 0.981696i | \(-0.439003\pi\) |
−0.754945 | + | 0.655788i | \(0.772336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.55940 | − | 2.23255i | 0.582783 | − | 0.234034i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.4584 | − | 7.77021i | −1.38080 | − | 0.797207i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9489 | + | 8.63074i | 1.51783 | + | 0.876319i | 0.999780 | + | 0.0209677i | \(0.00667473\pi\) |
0.518049 | + | 0.855351i | \(0.326659\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.3667i | 1.72806i | 0.503444 | + | 0.864028i | \(0.332066\pi\) | ||||
−0.503444 | + | 0.864028i | \(0.667934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.23888 | 0.910334 | 0.455167 | − | 0.890406i | \(-0.349580\pi\) | ||||
0.455167 | + | 0.890406i | \(0.349580\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.76296 | + | 4.48195i | 0.750474 | + | 0.433286i | 0.825865 | − | 0.563868i | \(-0.190687\pi\) |
−0.0753911 | + | 0.997154i | \(0.524021\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.46206 | − | 11.1926i | −0.618953 | − | 1.07206i | −0.989677 | − | 0.143315i | \(-0.954224\pi\) |
0.370724 | − | 0.928743i | \(-0.379110\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.12502 | + | 3.68064i | 0.199905 | + | 0.346246i | 0.948497 | − | 0.316785i | \(-0.102603\pi\) |
−0.748592 | + | 0.663031i | \(0.769270\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.66877 | −0.248864 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.3953 | − | 4.57612i | 1.04460 | − | 0.419492i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8038 | 0.982164 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.5329i | − | 0.942094i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.6660i | 1.74507i | 0.488549 | + | 0.872536i | \(0.337526\pi\) | ||||
−0.488549 | + | 0.872536i | \(0.662474\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0737 | 1.49173 | 0.745867 | − | 0.666095i | \(-0.232035\pi\) | ||||
0.745867 | + | 0.666095i | \(0.232035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.8083 | + | 13.7742i | −0.937199 | + | 1.19437i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.51361 | 0.300188 | 0.150094 | − | 0.988672i | \(-0.452042\pi\) | ||||
0.150094 | + | 0.988672i | \(0.452042\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.66086 | − | 15.0011i | −0.734605 | − | 1.27237i | −0.954896 | − | 0.296939i | \(-0.904034\pi\) |
0.220292 | − | 0.975434i | \(-0.429299\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.501490 | − | 0.868606i | −0.0419367 | − | 0.0726365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.8038 | + | 10.2790i | 1.47853 | + | 0.853627i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.08533 | 0.498529 | 0.249265 | − | 0.968435i | \(-0.419811\pi\) | ||||
0.249265 | + | 0.968435i | \(0.419811\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.61258i | 0.212609i | 0.994334 | + | 0.106304i | \(0.0339018\pi\) | ||||
−0.994334 | + | 0.106304i | \(0.966098\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.43790 | − | 5.44897i | −0.758070 | − | 0.437672i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.2746 | + | 9.39612i | 1.29885 | + | 0.749892i | 0.980206 | − | 0.197982i | \(-0.0634386\pi\) |
0.318646 | + | 0.947874i | \(0.396772\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.424723 | + | 2.97660i | −0.0334729 | + | 0.234589i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.90466 | + | 1.67700i | 0.227510 | + | 0.131353i | 0.609423 | − | 0.792845i | \(-0.291401\pi\) |
−0.381913 | + | 0.924198i | \(0.624734\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.58344 | − | 7.93876i | −0.354678 | − | 0.614320i | 0.632385 | − | 0.774654i | \(-0.282076\pi\) |
−0.987063 | + | 0.160335i | \(0.948743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.93635 | + | 6.81795i | −0.302796 | + | 0.524458i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.6171 | + | 11.3260i | −1.49146 | + | 0.861097i | −0.999952 | − | 0.00977454i | \(-0.996889\pi\) |
−0.491511 | + | 0.870871i | \(0.663555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.34827 | + | 0.192381i | 0.101920 | + | 0.0145426i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.2752 | − | 11.1285i | 1.44069 | − | 0.831785i | 0.442799 | − | 0.896621i | \(-0.353986\pi\) |
0.997896 | + | 0.0648357i | \(0.0206523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.33319i | − | 0.322084i | −0.986948 | − | 0.161042i | \(-0.948515\pi\) | ||
0.986948 | − | 0.161042i | \(-0.0514854\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.74799 | + | 3.31861i | 0.422601 | + | 0.243989i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.02792 | − | 1.78041i | −0.0751689 | − | 0.130196i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.5649 | + | 12.4505i | −1.56038 | + | 0.900885i | −0.563160 | + | 0.826348i | \(0.690415\pi\) |
−0.997218 | + | 0.0745371i | \(0.976252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.6627 | + | 18.4683i | −0.767517 | + | 1.32938i | 0.171389 | + | 0.985204i | \(0.445175\pi\) |
−0.938906 | + | 0.344175i | \(0.888159\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.5315 | −1.32032 | −0.660158 | − | 0.751127i | \(-0.729511\pi\) | ||||
−0.660158 | + | 0.751127i | \(0.729511\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.918721 | − | 1.59127i | −0.0651264 | − | 0.112802i | 0.831624 | − | 0.555340i | \(-0.187412\pi\) |
−0.896750 | + | 0.442537i | \(0.854078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.2981 | − | 18.2215i | 1.00353 | − | 1.27890i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.17283 | + | 10.6916i | 0.431129 | + | 0.746737i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.53850 | + | 1.46560i | 0.175592 | + | 0.101378i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.5295 | + | 10.1207i | −1.20678 | + | 0.696735i | −0.962054 | − | 0.272858i | \(-0.912031\pi\) |
−0.244725 | + | 0.969592i | \(0.578698\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.17246 | − | 8.95897i | 0.352759 | − | 0.610997i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.57948 | + | 9.65933i | −0.514529 | + | 0.655718i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.25480 | − | 9.10158i | 0.353476 | − | 0.612239i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.492098 | + | 0.852339i | −0.0329533 | + | 0.0570768i | −0.882032 | − | 0.471190i | \(-0.843825\pi\) |
0.849078 | + | 0.528267i | \(0.177158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.1928 | −0.875639 | −0.437820 | − | 0.899063i | \(-0.644249\pi\) | ||||
−0.437820 | + | 0.899063i | \(0.644249\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.67964i | − | 0.375321i | −0.982234 | − | 0.187660i | \(-0.939910\pi\) | ||
0.982234 | − | 0.187660i | \(-0.0600905\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.42995 | + | 12.8691i | −0.486752 | + | 0.843080i | −0.999884 | − | 0.0152301i | \(-0.995152\pi\) |
0.513132 | + | 0.858310i | \(0.328485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.8749 | + | 6.27863i | −0.709401 | + | 0.409573i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6484 | − | 9.03459i | 1.01221 | − | 0.584399i | 0.100371 | − | 0.994950i | \(-0.467997\pi\) |
0.911837 | + | 0.410551i | \(0.134664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.7503i | − | 1.33664i | −0.743872 | − | 0.668322i | \(-0.767013\pi\) | ||
0.743872 | − | 0.668322i | \(-0.232987\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.59752 | − | 15.7825i | 0.293725 | − | 1.00830i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.9846i | 0.953445i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.53037 | −0.601552 | −0.300776 | − | 0.953695i | \(-0.597246\pi\) | ||||
−0.300776 | + | 0.953695i | \(0.597246\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.503380 | 0.0316472 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.3949i | 0.710796i | 0.934715 | + | 0.355398i | \(0.115655\pi\) | ||||
−0.934715 | + | 0.355398i | \(0.884345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.61616 | − | 5.88285i | 0.286834 | − | 0.365543i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6.23768i | − | 0.384632i | −0.981333 | − | 0.192316i | \(-0.938400\pi\) | ||
0.981333 | − | 0.192316i | \(-0.0615998\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.28132 | − | 3.62652i | 0.385859 | − | 0.222776i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.5563 | + | 13.0229i | −1.37528 | + | 0.794018i | −0.991587 | − | 0.129443i | \(-0.958681\pi\) |
−0.383693 | + | 0.923461i | \(0.625348\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3180 | − | 17.8713i | 0.626775 | − | 1.08561i | −0.361420 | − | 0.932403i | \(-0.617708\pi\) |
0.988195 | − | 0.153203i | \(-0.0489589\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.228009i | − | 0.0137494i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0722 | −0.725350 | −0.362675 | − | 0.931916i | \(-0.618136\pi\) | ||||
−0.362675 | + | 0.931916i | \(0.618136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.67299 | − | 6.36180i | 0.219112 | − | 0.379513i | −0.735425 | − | 0.677606i | \(-0.763017\pi\) |
0.954537 | + | 0.298093i | \(0.0963507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.65315 | + | 14.9877i | −0.514376 | + | 0.890926i | 0.485484 | + | 0.874245i | \(0.338643\pi\) |
−0.999861 | + | 0.0166808i | \(0.994690\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9072 | − | 5.18330i | 0.761891 | − | 0.305961i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.27092 | − | 3.93336i | 0.133584 | − | 0.231374i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.965862 | + | 0.557641i | −0.0564263 | + | 0.0325777i | −0.527948 | − | 0.849277i | \(-0.677038\pi\) |
0.471521 | + | 0.881855i | \(0.343705\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.80480 | + | 1.61935i | 0.163302 | + | 0.0942823i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.28666 | + | 2.22856i | 0.0744094 | + | 0.128881i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.16916 | − | 7.19486i | −0.528502 | − | 0.414705i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0479 | + | 20.8676i | 0.689863 | + | 1.19488i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.5465 | −1.74338 | −0.871690 | − | 0.490058i | \(-0.836975\pi\) | ||||
−0.871690 | + | 0.490058i | \(0.836975\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.44800 | − | 5.97210i | 0.195518 | − | 0.338647i | −0.751552 | − | 0.659674i | \(-0.770695\pi\) |
0.947070 | + | 0.321027i | \(0.104028\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.1393 | − | 7.00865i | 0.686156 | − | 0.396153i | −0.116014 | − | 0.993248i | \(-0.537012\pi\) |
0.802171 | + | 0.597095i | \(0.203678\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.0887 | − | 17.4742i | −0.566638 | − | 0.981446i | −0.996895 | − | 0.0787397i | \(-0.974910\pi\) |
0.430257 | − | 0.902706i | \(-0.358423\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.35812 | − | 1.93881i | −0.188019 | − | 0.108553i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.7143i | 1.70899i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00944 | − | 0.582800i | 0.0559936 | − | 0.0323279i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.27214 | + | 13.1285i | 0.290663 | + | 0.723797i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.9703 | − | 16.1486i | 1.53738 | − | 0.887609i | 0.538394 | − | 0.842693i | \(-0.319031\pi\) |
0.998991 | − | 0.0449159i | \(-0.0143020\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.85780 | + | 4.94986i | −0.156138 | + | 0.270440i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1378 | − | 17.5591i | −0.552239 | − | 0.956506i | −0.998113 | − | 0.0614102i | \(-0.980440\pi\) |
0.445873 | − | 0.895096i | \(-0.352893\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.78016 | + | 1.02778i | 0.0964011 | + | 0.0556572i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.8712 | − | 7.63953i | −0.910960 | − | 0.412496i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.63139 | − | 2.09658i | −0.194943 | − | 0.112550i | 0.399352 | − | 0.916798i | \(-0.369235\pi\) |
−0.594295 | + | 0.804247i | \(0.702569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.54079 | − | 3.77632i | −0.350120 | − | 0.202142i | 0.314618 | − | 0.949218i | \(-0.398124\pi\) |
−0.664738 | + | 0.747076i | \(0.731457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5410i | 0.933613i | 0.884359 | + | 0.466807i | \(0.154596\pi\) | ||||
−0.884359 | + | 0.466807i | \(0.845404\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9233 | 0.898193 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.3430 | + | 10.5904i | 0.968108 | + | 0.558937i | 0.898659 | − | 0.438648i | \(-0.144543\pi\) |
0.0694490 | + | 0.997586i | \(0.477876\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3962 | − | 21.4709i | −0.652432 | − | 1.13005i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.30912 | − | 7.46362i | −0.225550 | − | 0.390664i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.22135 | 0.115954 | 0.0579768 | − | 0.998318i | \(-0.481535\pi\) | ||||
0.0579768 | + | 0.998318i | \(0.481535\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.04518 | − | 7.58298i | −0.158098 | − | 0.393689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.61418 | −0.394248 | −0.197124 | − | 0.980379i | \(-0.563160\pi\) | ||||
−0.197124 | + | 0.980379i | \(0.563160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 19.8227i | − | 1.02092i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.06894i | 0.209007i | 0.994525 | + | 0.104504i | \(0.0333254\pi\) | ||||
−0.994525 | + | 0.104504i | \(0.966675\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.04253 | 0.104368 | 0.0521842 | − | 0.998637i | \(-0.483382\pi\) | ||||
0.0521842 | + | 0.998637i | \(0.483382\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.72448 | − | 0.388748i | −0.138852 | − | 0.0198124i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.3587 | 1.23503 | 0.617517 | − | 0.786558i | \(-0.288139\pi\) | ||||
0.617517 | + | 0.786558i | \(0.288139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.63730 | + | 4.56794i | 0.133374 | + | 0.231011i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.85061 | + | 17.0618i | 0.495638 | + | 0.858470i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.6996 | − | 7.33213i | −0.637375 | − | 0.367989i | 0.146227 | − | 0.989251i | \(-0.453287\pi\) |
−0.783603 | + | 0.621262i | \(0.786620\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5778 | −0.678045 | −0.339022 | − | 0.940778i | \(-0.610096\pi\) | ||||
−0.339022 | + | 0.940778i | \(0.610096\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5081i | 0.523448i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.08418 | − | 0.625950i | −0.0537407 | − | 0.0310272i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.70365 | − | 3.29300i | −0.282027 | − | 0.162828i | 0.352314 | − | 0.935882i | \(-0.385395\pi\) |
−0.634341 | + | 0.773054i | \(0.718728\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.25251 | − | 2.87061i | 0.110839 | − | 0.141253i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.0493 | + | 18.5036i | 1.57324 | + | 0.908308i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.4919 | − | 19.9046i | −0.561416 | − | 0.972401i | −0.997373 | − | 0.0724336i | \(-0.976923\pi\) |
0.435957 | − | 0.899967i | \(-0.356410\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00338 | + | 1.73790i | −0.0489017 | + | 0.0847003i | −0.889440 | − | 0.457052i | \(-0.848905\pi\) |
0.840538 | + | 0.541752i | \(0.182239\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.06908 | − | 1.19458i | 0.100365 | − | 0.0579457i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.1920 | − | 10.1166i | 1.21913 | − | 0.489577i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.7684 | + | 16.6095i | −1.38573 | + | 0.800049i | −0.992830 | − | 0.119534i | \(-0.961860\pi\) |
−0.392896 | + | 0.919583i | \(0.628527\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.6573i | 1.71358i | 0.515663 | + | 0.856791i | \(0.327546\pi\) | ||||
−0.515663 | + | 0.856791i | \(0.672454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.51296 | − | 3.76026i | −0.311557 | − | 0.179878i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.29613 | − | 7.44111i | −0.205043 | − | 0.355145i | 0.745103 | − | 0.666949i | \(-0.232400\pi\) |
−0.950146 | + | 0.311804i | \(0.899067\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.5462 | + | 18.2132i | −1.49880 | + | 0.865335i | −0.999999 | − | 0.00137907i | \(-0.999561\pi\) |
−0.498805 | + | 0.866714i | \(0.666228\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.22026 | + | 12.5059i | −0.342273 | + | 0.592834i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.2858 | 0.579801 | 0.289900 | − | 0.957057i | \(-0.406378\pi\) | ||||
0.289900 | + | 0.957057i | \(0.406378\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.16431 | − | 2.01664i | −0.0548251 | − | 0.0949599i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.24280 | − | 13.0554i | −0.245786 | − | 0.612048i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.64674 | + | 6.31634i | 0.170587 | + | 0.295466i | 0.938625 | − | 0.344938i | \(-0.112100\pi\) |
−0.768038 | + | 0.640404i | \(0.778767\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.33329 | − | 4.23388i | −0.341545 | − | 0.197191i | 0.319410 | − | 0.947617i | \(-0.396515\pi\) |
−0.660955 | + | 0.750425i | \(0.729849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.53400 | − | 2.61771i | 0.210713 | − | 0.121655i | −0.390930 | − | 0.920421i | \(-0.627846\pi\) |
0.601643 | + | 0.798765i | \(0.294513\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.96542 | + | 17.2606i | −0.461145 | + | 0.798726i | −0.999018 | − | 0.0442995i | \(-0.985894\pi\) |
0.537874 | + | 0.843025i | \(0.319228\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.06599 | + | 3.97518i | 0.233926 | + | 0.183557i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.975621 | + | 1.68983i | −0.0448591 | + | 0.0776983i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.70323 | + | 2.95008i | −0.0781497 | + | 0.135359i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.0246 | −1.32617 | −0.663083 | − | 0.748545i | \(-0.730753\pi\) | ||||
−0.663083 | + | 0.748545i | \(0.730753\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 6.39981i | − | 0.291806i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.2680 | − | 35.1052i | 0.920323 | − | 1.59405i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9472 | + | 6.89770i | −0.541378 | + | 0.312565i | −0.745637 | − | 0.666352i | \(-0.767855\pi\) |
0.204259 | + | 0.978917i | \(0.434521\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.6069 | + | 8.43329i | −0.659200 | + | 0.380589i | −0.791972 | − | 0.610557i | \(-0.790945\pi\) |
0.132772 | + | 0.991147i | \(0.457612\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 40.6313i | − | 1.82994i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.69326 | − | 18.8753i | 0.120809 | − | 0.846671i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.7654i | 0.750523i | 0.926919 | + | 0.375262i | \(0.122447\pi\) | ||||
−0.926919 | + | 0.375262i | \(0.877553\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.2366 | 1.61571 | 0.807856 | − | 0.589380i | \(-0.200628\pi\) | ||||
0.807856 | + | 0.589380i | \(0.200628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.7832 | 1.81483 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 29.0797i | − | 1.28894i | −0.764631 | − | 0.644468i | \(-0.777079\pi\) | ||
0.764631 | − | 0.644468i | \(-0.222921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.01028 | + | 3.61835i | −0.398591 | + | 0.160067i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 21.6962i | − | 0.956047i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.05121 | − | 1.18427i | 0.0902120 | − | 0.0520839i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.1742 | − | 17.9984i | 1.36576 | − | 0.788524i | 0.375381 | − | 0.926871i | \(-0.377512\pi\) |
0.990384 | + | 0.138346i | \(0.0441787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0333 | − | 29.5026i | 0.744816 | − | 1.29006i | −0.205465 | − | 0.978664i | \(-0.565871\pi\) |
0.950281 | − | 0.311394i | \(-0.100796\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.5389i | 0.938248i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7085 | 0.943848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.95203 | − | 10.3092i | 0.257811 | − | 0.446542i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.5252 | − | 18.2302i | 0.455044 | − | 0.788159i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.867176 | + | 2.97686i | −0.0373519 | + | 0.128223i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.04194 | + | 7.00084i | −0.173777 | + | 0.300990i | −0.939737 | − | 0.341898i | \(-0.888930\pi\) |
0.765961 | + | 0.642887i | \(0.222264\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.2842 | + | 15.1752i | −1.12589 | + | 0.650034i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.5917 | − | 13.0433i | −0.965950 | − | 0.557691i | −0.0679508 | − | 0.997689i | \(-0.521646\pi\) |
−0.897999 | + | 0.439997i | \(0.854979\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.9660 | + | 50.1705i | 1.23399 | + | 2.13734i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.5974 | − | 8.27152i | 0.875891 | − | 0.351741i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.12408 | − | 10.6072i | −0.259486 | − | 0.449442i | 0.706619 | − | 0.707595i | \(-0.250220\pi\) |
−0.966104 | + | 0.258152i | \(0.916886\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.97491 | −0.421894 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.4252 | − | 19.7890i | 0.481515 | − | 0.834008i | −0.518260 | − | 0.855223i | \(-0.673420\pi\) |
0.999775 | + | 0.0212152i | \(0.00675352\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.64345 | − | 4.99030i | 0.363633 | − | 0.209943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.86898 | − | 4.96922i | −0.120274 | − | 0.208321i | 0.799602 | − | 0.600531i | \(-0.205044\pi\) |
−0.919876 | + | 0.392210i | \(0.871711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.6157 | − | 12.4798i | −0.904588 | − | 0.522264i | −0.0259018 | − | 0.999664i | \(-0.508246\pi\) |
−0.878686 | + | 0.477401i | \(0.841579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.584996i | 0.0243960i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7652 | + | 10.8341i | −0.781206 | + | 0.451030i | −0.836858 | − | 0.547421i | \(-0.815610\pi\) |
0.0556514 | + | 0.998450i | \(0.482276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.7384 | − | 32.8012i | 1.06781 | − | 1.36082i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.18477 | + | 0.684029i | −0.0490683 | + | 0.0283296i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.7121 | − | 25.4821i | 0.607233 | − | 1.05176i | −0.384461 | − | 0.923141i | \(-0.625613\pi\) |
0.991694 | − | 0.128617i | \(-0.0410539\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.3550 | − | 26.5957i | −0.632693 | − | 1.09586i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.5917 | + | 14.7754i | 1.05092 | + | 0.606752i | 0.922908 | − | 0.385020i | \(-0.125806\pi\) |
0.128017 | + | 0.991772i | \(0.459139\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.7463 | − | 26.7601i | −0.440557 | − | 1.09706i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.4099 | − | 19.8666i | −1.40595 | − | 0.811727i | −0.410957 | − | 0.911655i | \(-0.634805\pi\) |
−0.994995 | + | 0.0999281i | \(0.968139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.64604 | + | 5.56915i | 0.393470 | + | 0.227170i | 0.683663 | − | 0.729798i | \(-0.260386\pi\) |
−0.290192 | + | 0.956968i | \(0.593719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 25.3711i | − | 1.03148i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.6629 | 1.40692 | 0.703461 | − | 0.710734i | \(-0.251637\pi\) | ||||
0.703461 | + | 0.710734i | \(0.251637\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4859 | + | 6.05406i | 0.424215 | + | 0.244921i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.1482 | − | 27.9695i | −0.652219 | − | 1.12968i | −0.982583 | − | 0.185823i | \(-0.940505\pi\) |
0.330365 | − | 0.943853i | \(-0.392828\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0343 | + | 38.1645i | 0.887067 | + | 1.53644i | 0.843327 | + | 0.537401i | \(0.180594\pi\) |
0.0437400 | + | 0.999043i | \(0.486073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.30313 | 0.373924 | 0.186962 | − | 0.982367i | \(-0.440136\pi\) | ||||
0.186962 | + | 0.982367i | \(0.440136\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.7993 | + | 10.0433i | 0.512792 | + | 0.402377i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.3088 | −1.09235 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 13.1179i | − | 0.523044i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 28.6463i | − | 1.14039i | −0.821509 | − | 0.570196i | \(-0.806867\pi\) | ||
0.821509 | − | 0.570196i | \(-0.193133\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.1826 | 1.83270 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.3957 | + | 3.76982i | −0.609999 | + | 0.149366i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.03251 | −0.0802795 | −0.0401397 | − | 0.999194i | \(-0.512780\pi\) | ||||
−0.0401397 | + | 0.999194i | \(0.512780\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.7575 | + | 25.5608i | 0.581980 | + | 1.00802i | 0.995245 | + | 0.0974077i | \(0.0310551\pi\) |
−0.413265 | + | 0.910611i | \(0.635612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.18434 | + | 14.1757i | 0.321759 | + | 0.557304i | 0.980851 | − | 0.194759i | \(-0.0623924\pi\) |
−0.659092 | + | 0.752063i | \(0.729059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.529037 | − | 0.305440i | −0.0207665 | − | 0.0119896i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.178525 | −0.00698623 | −0.00349312 | − | 0.999994i | \(-0.501112\pi\) | ||||
−0.00349312 | + | 0.999994i | \(0.501112\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 40.0950i | − | 1.56664i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.4428 | − | 10.0706i | −0.679474 | − | 0.392294i | 0.120183 | − | 0.992752i | \(-0.461652\pi\) |
−0.799657 | + | 0.600457i | \(0.794985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.59315 | − | 4.38391i | −0.295339 | − | 0.170514i | 0.345008 | − | 0.938600i | \(-0.387876\pi\) |
−0.640347 | + | 0.768086i | \(0.721210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.3466 | + | 25.3817i | 1.25435 | + | 0.984261i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.61584 | + | 4.97436i | 0.333607 | + | 0.192608i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.27246 | − | 3.93602i | −0.0877274 | − | 0.151948i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.04120 | + | 1.80341i | −0.0401353 | + | 0.0695164i | −0.885395 | − | 0.464839i | \(-0.846112\pi\) |
0.845260 | + | 0.534355i | \(0.179446\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0742 | − | 6.97106i | 0.464050 | − | 0.267919i | −0.249696 | − | 0.968324i | \(-0.580331\pi\) |
0.713746 | + | 0.700405i | \(0.246997\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.9289 | − | 28.1927i | −1.37882 | − | 1.08194i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.5049 | + | 7.79708i | −0.516752 | + | 0.298347i | −0.735605 | − | 0.677411i | \(-0.763102\pi\) |
0.218853 | + | 0.975758i | \(0.429769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.25120i | − | 0.315262i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.05665 | − | 3.49681i | −0.230740 | − | 0.133218i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.986734 | − | 1.70907i | −0.0375371 | − | 0.0650162i | 0.846646 | − | 0.532156i | \(-0.178618\pi\) |
−0.884184 | + | 0.467139i | \(0.845285\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.2278 | + | 20.3388i | −1.33627 | + | 0.771493i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.2001 | − | 21.1311i | 0.462110 | − | 0.800399i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.57171 | 0.134902 | 0.0674508 | − | 0.997723i | \(-0.478513\pi\) | ||||
0.0674508 | + | 0.997723i | \(0.478513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.35173 | + | 16.1977i | 0.352707 | + | 0.610907i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.49047 | − | 45.4874i | 0.244099 | − | 1.71073i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.6279 | − | 21.8721i | −0.474250 | − | 0.821425i | 0.525316 | − | 0.850907i | \(-0.323947\pi\) |
−0.999565 | + | 0.0294829i | \(0.990614\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.56731 | − | 2.63694i | −0.171047 | − | 0.0987541i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.03979 | + | 1.17767i | −0.0762839 | + | 0.0440425i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.0045 | − | 32.9168i | 0.708749 | − | 1.22759i | −0.256572 | − | 0.966525i | \(-0.582593\pi\) |
0.965321 | − | 0.261065i | \(-0.0840737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.1987 | − | 3.45285i | −0.901206 | − | 0.128591i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.25317 | − | 3.90260i | 0.0836805 | − | 0.144939i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.14853 | + | 14.1137i | −0.302212 | + | 0.523447i | −0.976637 | − | 0.214897i | \(-0.931059\pi\) |
0.674424 | + | 0.738344i | \(0.264392\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.4459 | −0.756218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.7119i | − | 0.469525i | −0.972053 | − | 0.234763i | \(-0.924569\pi\) | ||
0.972053 | − | 0.234763i | \(-0.0754313\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.539034 | − | 0.933634i | 0.0198556 | − | 0.0343909i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.2467 | + | 12.2668i | −0.781574 | + | 0.451242i | −0.836988 | − | 0.547222i | \(-0.815685\pi\) |
0.0554141 | + | 0.998463i | \(0.482352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.5305 | + | 14.7400i | −0.936624 | + | 0.540760i | −0.888900 | − | 0.458101i | \(-0.848530\pi\) |
−0.0477233 | + | 0.998861i | \(0.515197\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 14.2905i | − | 0.523563i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.6579 | − | 14.6405i | −0.681745 | − | 0.534951i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.7434i | 1.45026i | 0.688613 | + | 0.725129i | \(0.258220\pi\) | ||||
−0.688613 | + | 0.725129i | \(0.741780\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.13526 | 0.223285 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.23130 | −0.117444 | −0.0587218 | − | 0.998274i | \(-0.518702\pi\) | ||||
−0.0587218 | + | 0.998274i | \(0.518702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 36.8650i | − | 1.33636i | −0.744001 | − | 0.668178i | \(-0.767074\pi\) | ||
0.744001 | − | 0.668178i | \(-0.232926\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.7426 | + | 31.7310i | 0.461312 | + | 1.14874i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.12286i | − | 0.112760i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.3838 | + | 12.3460i | −0.771120 | + | 0.445206i | −0.833274 | − | 0.552860i | \(-0.813536\pi\) |
0.0621539 | + | 0.998067i | \(0.480203\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.1598 | − | 10.4846i | 0.653164 | − | 0.377104i | −0.136503 | − | 0.990640i | \(-0.543586\pi\) |
0.789667 | + | 0.613535i | \(0.210253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.19442 | + | 2.06879i | −0.0429047 | + | 0.0743131i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.7897i | 1.24647i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.19204 | −0.114220 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.0654 | − | 38.2184i | 0.787548 | − | 1.36407i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.44418 | + | 12.8937i | −0.265356 | + | 0.459611i | −0.967657 | − | 0.252270i | \(-0.918823\pi\) |
0.702300 | + | 0.711881i | \(0.252156\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.19033 | − | 10.4346i | −0.148991 | − | 0.371012i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.6170 | − | 20.1212i | 0.412532 | − | 0.714526i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.5335 | + | 10.1230i | −0.621068 | + | 0.358574i | −0.777285 | − | 0.629149i | \(-0.783404\pi\) |
0.156216 | + | 0.987723i | \(0.450070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.4933 | + | 12.4092i | 0.760380 | + | 0.439005i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.812779 | + | 1.40778i | 0.0286824 | + | 0.0496793i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.99011 | + | 0.997400i | 0.246369 | + | 0.0351537i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.2300 | + | 29.8433i | 0.605775 | + | 1.04923i | 0.991928 | + | 0.126799i | \(0.0404703\pi\) |
−0.386153 | + | 0.922435i | \(0.626196\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.5905 | 1.74136 | 0.870679 | − | 0.491852i | \(-0.163680\pi\) | ||||
0.870679 | + | 0.491852i | \(0.163680\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.93820 | − | 6.82116i | 0.137949 | − | 0.238935i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.2461 | − | 14.5758i | 0.883249 | − | 0.509944i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.5801 | + | 33.9137i | 0.683349 | + | 1.18360i | 0.973953 | + | 0.226752i | \(0.0728106\pi\) |
−0.290604 | + | 0.956844i | \(0.593856\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.6699 | − | 19.4393i | −1.17366 | − | 0.677612i | −0.219119 | − | 0.975698i | \(-0.570318\pi\) |
−0.954539 | + | 0.298087i | \(0.903652\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 41.0227i | − | 1.42650i | −0.700909 | − | 0.713250i | \(-0.747222\pi\) | ||
0.700909 | − | 0.713250i | \(-0.252778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.4951 | + | 6.63672i | −0.399242 | + | 0.230503i | −0.686157 | − | 0.727453i | \(-0.740704\pi\) |
0.286915 | + | 0.957956i | \(0.407370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.5570 | + | 7.72712i | −1.09338 | + | 0.267729i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.6430 | + | 10.7635i | −0.645168 | + | 0.372488i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.9028 | − | 27.5445i | 0.549025 | − | 0.950940i | −0.449316 | − | 0.893373i | \(-0.648332\pi\) |
0.998342 | − | 0.0575672i | \(-0.0183344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8184 | − | 41.2547i | −0.821325 | − | 1.42258i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.0110 | + | 9.24393i | 0.550793 | + | 0.318001i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.2976 | − | 4.03770i | −0.972316 | − | 0.138737i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.78164 | + | 1.60598i | 0.0953535 | + | 0.0550524i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.551551 | − | 0.318438i | −0.0188847 | − | 0.0109031i | 0.490528 | − | 0.871425i | \(-0.336804\pi\) |
−0.509413 | + | 0.860522i | \(0.670137\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 4.54984i | − | 0.155420i | −0.996976 | − | 0.0777098i | \(-0.975239\pi\) | ||
0.996976 | − | 0.0777098i | \(-0.0247608\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.5634 | −0.462776 | −0.231388 | − | 0.972862i | \(-0.574327\pi\) | ||||
−0.231388 | + | 0.972862i | \(0.574327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.1996 | − | 8.19817i | −0.483361 | − | 0.279069i | 0.238455 | − | 0.971154i | \(-0.423359\pi\) |
−0.721816 | + | 0.692085i | \(0.756692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.5973 | + | 46.0680i | 0.904337 | + | 1.56636i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.85801 | − | 3.21816i | −0.0630285 | − | 0.109169i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.51117 | 0.186739 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.93647 | + | 27.5881i | −0.133077 | + | 0.932647i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.5189 | −1.67214 | −0.836068 | − | 0.548626i | \(-0.815151\pi\) | ||||
−0.836068 | + | 0.548626i | \(0.815151\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 16.2659i | − | 0.548012i | −0.961728 | − | 0.274006i | \(-0.911651\pi\) | ||
0.961728 | − | 0.274006i | \(-0.0883488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.6667i | 0.897404i | 0.893681 | + | 0.448702i | \(0.148114\pi\) | ||||
−0.893681 | + | 0.448702i | \(0.851886\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.9957 | 1.81300 | 0.906499 | − | 0.422208i | \(-0.138745\pi\) | ||||
0.906499 | + | 0.422208i | \(0.138745\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.34976 | − | 51.5096i | 0.246503 | − | 1.72758i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.3860 | −1.18415 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.1337 | − | 45.2649i | −0.873554 | − | 1.51304i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.3128 | + | 35.1828i | 0.677470 | + | 1.17341i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.4145 | − | 7.16752i | −0.413587 | − | 0.238785i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.1759 | −0.338257 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.5452i | 1.51230i | 0.654397 | + | 0.756151i | \(0.272923\pi\) | ||||
−0.654397 | + | 0.756151i | \(0.727077\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.7265 | − | 6.19296i | −0.355385 | − | 0.205182i | 0.311669 | − | 0.950191i | \(-0.399112\pi\) |
−0.667055 | + | 0.745009i | \(0.732445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.04508 | − | 3.49013i | −0.200063 | − | 0.115506i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.7198 | − | 6.38094i | −1.47678 | − | 0.210717i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.9097 | + | 22.4645i | 1.28351 | + | 0.741037i | 0.977489 | − | 0.210987i | \(-0.0676678\pi\) |
0.306024 | + | 0.952024i | \(0.401001\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.15897 | − | 14.1318i | −0.268556 | − | 0.465152i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.727439 | − | 1.25996i | 0.0239181 | − | 0.0414273i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.1152 | + | 12.7682i | −0.725578 | + | 0.418912i | −0.816802 | − | 0.576918i | \(-0.804255\pi\) |
0.0912245 | + | 0.995830i | \(0.470922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.4572 | − | 32.0382i | 1.09651 | − | 1.05001i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.18102 | + | 2.41392i | −0.136734 | + | 0.0789435i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 29.7933i | − | 0.973304i | −0.873596 | − | 0.486652i | \(-0.838218\pi\) | ||
0.873596 | − | 0.486652i | \(-0.161782\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.9292 | − | 19.0117i | −1.07346 | − | 0.619763i | −0.144336 | − | 0.989529i | \(-0.546105\pi\) |
−0.929125 | + | 0.369766i | \(0.879438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.98723 | + | 5.17404i | 0.0972777 | + | 0.168490i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.9431 | − | 13.8235i | 0.778045 | − | 0.449205i | −0.0576920 | − | 0.998334i | \(-0.518374\pi\) |
0.835737 | + | 0.549130i | \(0.185041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.15499 | + | 7.19666i | −0.134877 | + | 0.233613i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.4588 | −1.24580 | −0.622901 | − | 0.782301i | \(-0.714046\pi\) | ||||
−0.622901 | + | 0.782301i | \(0.714046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.2381 | + | 50.6419i | 0.946123 | + | 1.63873i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.20294 | − | 1.31314i | −0.297178 | − | 0.0424036i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.73206 | + | 8.19616i | 0.152647 | + | 0.264392i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.3701 | + | 25.0397i | 1.39613 | + | 0.806058i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.40644 | + | 0.812009i | −0.0452281 | + | 0.0261125i | −0.522444 | − | 0.852674i | \(-0.674979\pi\) |
0.477215 | + | 0.878786i | \(0.341646\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2966 | + | 33.4227i | −0.619257 | + | 1.07258i | 0.370365 | + | 0.928886i | \(0.379233\pi\) |
−0.989622 | + | 0.143698i | \(0.954101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.0784 | + | 42.5279i | 0.547508 | + | 1.36338i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.20038 | − | 10.7394i | 0.198368 | − | 0.343583i | −0.749632 | − | 0.661855i | \(-0.769769\pi\) |
0.947999 | + | 0.318272i | \(0.103103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.36187 | − | 2.35883i | 0.0435257 | − | 0.0753886i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9967 | 0.542112 | 0.271056 | − | 0.962564i | \(-0.412627\pi\) | ||||
0.271056 | + | 0.962564i | \(0.412627\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.5185i | 1.38662i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.50313 | − | 4.33554i | 0.0795947 | − | 0.137862i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.0008 | + | 22.5171i | −1.23890 | + | 0.715280i | −0.968870 | − | 0.247571i | \(-0.920368\pi\) |
−0.270032 | + | 0.962851i | \(0.587034\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.73687 | + | 2.15748i | −0.118467 | + | 0.0683967i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.00101i | 0.253395i | 0.991941 | + | 0.126697i | \(0.0404377\pi\) | ||||
−0.991941 | + | 0.126697i | \(0.959562\pi\) | |||||||
\(998\) | 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 | 3024.2.bf.i.2287.4 | 32 | ||
3.2 | odd | 2 | 1008.2.bf.i.943.6 | yes | 32 | ||
4.3 | odd | 2 | inner | 3024.2.bf.i.2287.3 | 32 | ||
7.3 | odd | 6 | 3024.2.cz.i.2719.3 | 32 | |||
9.4 | even | 3 | 3024.2.cz.i.1279.4 | 32 | |||
9.5 | odd | 6 | 1008.2.cz.i.607.6 | yes | 32 | ||
12.11 | even | 2 | 1008.2.bf.i.943.11 | yes | 32 | ||
21.17 | even | 6 | 1008.2.cz.i.367.11 | yes | 32 | ||
28.3 | even | 6 | 3024.2.cz.i.2719.4 | 32 | |||
36.23 | even | 6 | 1008.2.cz.i.607.11 | yes | 32 | ||
36.31 | odd | 6 | 3024.2.cz.i.1279.3 | 32 | |||
63.31 | odd | 6 | inner | 3024.2.bf.i.1711.14 | 32 | ||
63.59 | even | 6 | 1008.2.bf.i.31.11 | yes | 32 | ||
84.59 | odd | 6 | 1008.2.cz.i.367.6 | yes | 32 | ||
252.31 | even | 6 | inner | 3024.2.bf.i.1711.13 | 32 | ||
252.59 | odd | 6 | 1008.2.bf.i.31.6 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.bf.i.31.6 | ✓ | 32 | 252.59 | odd | 6 | ||
1008.2.bf.i.31.11 | yes | 32 | 63.59 | even | 6 | ||
1008.2.bf.i.943.6 | yes | 32 | 3.2 | odd | 2 | ||
1008.2.bf.i.943.11 | yes | 32 | 12.11 | even | 2 | ||
1008.2.cz.i.367.6 | yes | 32 | 84.59 | odd | 6 | ||
1008.2.cz.i.367.11 | yes | 32 | 21.17 | even | 6 | ||
1008.2.cz.i.607.6 | yes | 32 | 9.5 | odd | 6 | ||
1008.2.cz.i.607.11 | yes | 32 | 36.23 | even | 6 | ||
3024.2.bf.i.1711.13 | 32 | 252.31 | even | 6 | inner | ||
3024.2.bf.i.1711.14 | 32 | 63.31 | odd | 6 | inner | ||
3024.2.bf.i.2287.3 | 32 | 4.3 | odd | 2 | inner | ||
3024.2.bf.i.2287.4 | 32 | 1.1 | even | 1 | trivial | ||
3024.2.cz.i.1279.3 | 32 | 36.31 | odd | 6 | |||
3024.2.cz.i.1279.4 | 32 | 9.4 | even | 3 | |||
3024.2.cz.i.2719.3 | 32 | 7.3 | odd | 6 | |||
3024.2.cz.i.2719.4 | 32 | 28.3 | even | 6 |