Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(481,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1920.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.s (of order \(4\), 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: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1441.2 | ||
Root | \(-0.0861743 + 1.41159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1920.1441 |
Dual form | 1920.2.s.f.481.4 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.76462i | − | 1.04493i | −0.852661 | − | 0.522464i | \(-0.825013\pi\) | ||
0.852661 | − | 0.522464i | \(-0.174987\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.51009 | + | 3.51009i | −1.05833 | + | 1.05833i | −0.0601437 | + | 0.998190i | \(0.519156\pi\) |
−0.998190 | + | 0.0601437i | \(0.980844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.55960 | + | 4.55960i | 1.26461 | + | 1.26461i | 0.948835 | + | 0.315771i | \(0.102263\pi\) |
0.315771 | + | 0.948835i | \(0.397737\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.00550 | −1.21401 | −0.607006 | − | 0.794697i | \(-0.707630\pi\) | ||||
−0.607006 | + | 0.794697i | \(0.707630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.812949 | − | 0.812949i | −0.186503 | − | 0.186503i | 0.607679 | − | 0.794183i | \(-0.292101\pi\) |
−0.794183 | + | 0.607679i | \(0.792101\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.95488 | + | 1.95488i | −0.426590 | + | 0.426590i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.48205i | − | 1.56011i | −0.625708 | − | 0.780057i | \(-0.715190\pi\) | ||
0.625708 | − | 0.780057i | \(-0.284810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.03354 | − | 6.03354i | −1.12040 | − | 1.12040i | −0.991681 | − | 0.128719i | \(-0.958913\pi\) |
−0.128719 | − | 0.991681i | \(-0.541087\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.58233 | −1.36183 | −0.680913 | − | 0.732364i | \(-0.738417\pi\) | ||||
−0.680913 | + | 0.732364i | \(0.738417\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.96402 | 0.864126 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.95488 | − | 1.95488i | −0.330435 | − | 0.330435i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.08674 | + | 1.08674i | −0.178659 | + | 0.178659i | −0.790771 | − | 0.612112i | \(-0.790320\pi\) |
0.612112 | + | 0.790771i | \(0.290320\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.44825i | − | 1.03255i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.15671i | − | 0.492995i | −0.969143 | − | 0.246497i | \(-0.920720\pi\) | ||
0.969143 | − | 0.246497i | \(-0.0792797\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.10932 | + | 3.10932i | −0.474166 | + | 0.474166i | −0.903260 | − | 0.429094i | \(-0.858833\pi\) |
0.429094 | + | 0.903260i | \(0.358833\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.707107 | + | 0.707107i | 0.105409 | + | 0.105409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.76008 | 0.402599 | 0.201299 | − | 0.979530i | \(-0.435484\pi\) | ||||
0.201299 | + | 0.979530i | \(0.435484\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.643123 | −0.0918747 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.53942 | + | 3.53942i | 0.495618 | + | 0.495618i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.41096 | + | 6.41096i | −0.880613 | + | 0.880613i | −0.993597 | − | 0.112983i | \(-0.963959\pi\) |
0.112983 | + | 0.993597i | \(0.463959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.96402i | 0.669349i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.14968i | 0.152279i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.13756 | + | 5.13756i | −0.668854 | + | 0.668854i | −0.957451 | − | 0.288597i | \(-0.906811\pi\) |
0.288597 | + | 0.957451i | \(0.406811\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.49234 | + | 2.49234i | 0.319111 | + | 0.319111i | 0.848426 | − | 0.529314i | \(-0.177551\pi\) |
−0.529314 | + | 0.848426i | \(0.677551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.76462 | 0.348309 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.44825 | 0.799807 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.14625 | − | 3.14625i | −0.384376 | − | 0.384376i | 0.488300 | − | 0.872676i | \(-0.337617\pi\) |
−0.872676 | + | 0.488300i | \(0.837617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.29061 | + | 5.29061i | −0.636914 | + | 0.636914i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.50237i | − | 0.415655i | −0.978166 | − | 0.207827i | \(-0.933361\pi\) | ||
0.978166 | − | 0.207827i | \(-0.0666392\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.6145i | 1.71050i | 0.518217 | + | 0.855249i | \(0.326596\pi\) | ||||
−0.518217 | + | 0.855249i | \(0.673404\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.707107 | + | 0.707107i | −0.0816497 | + | 0.0816497i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.70408 | + | 9.70408i | 1.10588 | + | 1.10588i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.95325 | −1.00732 | −0.503660 | − | 0.863902i | \(-0.668013\pi\) | ||||
−0.503660 | + | 0.863902i | \(0.668013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.86293 | − | 2.86293i | −0.314247 | − | 0.314247i | 0.532305 | − | 0.846553i | \(-0.321326\pi\) |
−0.846553 | + | 0.532305i | \(0.821326\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.53942 | + | 3.53942i | −0.383904 | + | 0.383904i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.53271i | 0.914803i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.23560i | 0.766972i | 0.923547 | + | 0.383486i | \(0.125277\pi\) | ||||
−0.923547 | + | 0.383486i | \(0.874723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6056 | − | 12.6056i | 1.32142 | − | 1.32142i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.36151 | + | 5.36151i | 0.555963 | + | 0.555963i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.14968 | −0.117955 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.24056 | −0.836702 | −0.418351 | − | 0.908285i | \(-0.637392\pi\) | ||||
−0.418351 | + | 0.908285i | \(0.637392\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.51009 | − | 3.51009i | −0.352778 | − | 0.352778i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.07326 | + | 1.07326i | −0.106794 | + | 0.106794i | −0.758485 | − | 0.651691i | \(-0.774060\pi\) |
0.651691 | + | 0.758485i | \(0.274060\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.66763i | 0.164316i | 0.996619 | + | 0.0821582i | \(0.0261813\pi\) | ||||
−0.996619 | + | 0.0821582i | \(0.973819\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.76462i | 0.269799i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.08860 | + | 6.08860i | −0.588607 | + | 0.588607i | −0.937254 | − | 0.348647i | \(-0.886641\pi\) |
0.348647 | + | 0.937254i | \(0.386641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.92136 | − | 2.92136i | −0.279816 | − | 0.279816i | 0.553220 | − | 0.833035i | \(-0.313399\pi\) |
−0.833035 | + | 0.553220i | \(0.813399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.53688 | 0.145874 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.84395 | −0.267536 | −0.133768 | − | 0.991013i | \(-0.542708\pi\) | ||||
−0.133768 | + | 0.991013i | \(0.542708\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.29061 | − | 5.29061i | −0.493352 | − | 0.493352i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.55960 | + | 4.55960i | −0.421535 | + | 0.421535i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.8383i | 1.26856i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 13.6415i | − | 1.24014i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.23213 | + | 2.23213i | −0.201264 | + | 0.201264i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.61073 | 0.586607 | 0.293304 | − | 0.956019i | \(-0.405245\pi\) | ||||
0.293304 | + | 0.956019i | \(0.405245\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.39724 | 0.387155 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.70125 | − | 6.70125i | −0.585491 | − | 0.585491i | 0.350916 | − | 0.936407i | \(-0.385870\pi\) |
−0.936407 | + | 0.350916i | \(0.885870\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.24749 | + | 2.24749i | −0.194883 | + | 0.194883i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 14.3908i | − | 1.22949i | −0.788725 | − | 0.614746i | \(-0.789258\pi\) | ||
0.788725 | − | 0.614746i | \(-0.210742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.292743 | − | 0.292743i | 0.0248302 | − | 0.0248302i | −0.694583 | − | 0.719413i | \(-0.744411\pi\) |
0.719413 | + | 0.694583i | \(0.244411\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.95167 | − | 1.95167i | −0.164360 | − | 0.164360i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −32.0093 | −2.67675 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.53271 | −0.708603 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.454757 | + | 0.454757i | 0.0375077 | + | 0.0375077i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9363 | − | 10.9363i | 0.895934 | − | 0.895934i | −0.0991393 | − | 0.995074i | \(-0.531609\pi\) |
0.995074 | + | 0.0991393i | \(0.0316089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.5225i | − | 1.10045i | −0.835017 | − | 0.550223i | \(-0.814543\pi\) | ||
0.835017 | − | 0.550223i | \(-0.185457\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.00550i | − | 0.404671i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.36151 | + | 5.36151i | −0.430647 | + | 0.430647i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.76487 | − | 2.76487i | −0.220661 | − | 0.220661i | 0.588116 | − | 0.808777i | \(-0.299870\pi\) |
−0.808777 | + | 0.588116i | \(0.799870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.06647 | 0.719018 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.6850 | −1.63021 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.4942 | + | 15.4942i | 1.21360 | + | 1.21360i | 0.969834 | + | 0.243767i | \(0.0783834\pi\) |
0.243767 | + | 0.969834i | \(0.421617\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.51009 | − | 3.51009i | 0.273261 | − | 0.273261i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.76898i | 0.136888i | 0.997655 | + | 0.0684439i | \(0.0218034\pi\) | ||||
−0.997655 | + | 0.0684439i | \(0.978197\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.5800i | 2.19846i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.812949 | − | 0.812949i | 0.0621678 | − | 0.0621678i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.01351 | − | 4.01351i | −0.305142 | − | 0.305142i | 0.537880 | − | 0.843022i | \(-0.319225\pi\) |
−0.843022 | + | 0.537880i | \(0.819225\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.76462 | −0.208986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.26561 | 0.546117 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.31340 | − | 5.31340i | −0.397142 | − | 0.397142i | 0.480082 | − | 0.877224i | \(-0.340607\pi\) |
−0.877224 | + | 0.480082i | \(0.840607\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.74918 | − | 8.74918i | 0.650321 | − | 0.650321i | −0.302749 | − | 0.953070i | \(-0.597904\pi\) |
0.953070 | + | 0.302749i | \(0.0979044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.52470i | − | 0.260553i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.53688i | 0.112994i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.5698 | − | 17.5698i | 1.28483 | − | 1.28483i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.95488 | − | 1.95488i | −0.142197 | − | 0.142197i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.03787 | 0.292170 | 0.146085 | − | 0.989272i | \(-0.453333\pi\) | ||||
0.146085 | + | 0.989272i | \(0.453333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.437111 | 0.0314639 | 0.0157320 | − | 0.999876i | \(-0.494992\pi\) | ||||
0.0157320 | + | 0.999876i | \(0.494992\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.55960 | − | 4.55960i | −0.326520 | − | 0.326520i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6836 | + | 11.6836i | −0.832424 | + | 0.832424i | −0.987848 | − | 0.155424i | \(-0.950326\pi\) |
0.155424 | + | 0.987848i | \(0.450326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7412i | 1.11587i | 0.829886 | + | 0.557933i | \(0.188405\pi\) | ||||
−0.829886 | + | 0.557933i | \(0.811595\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.44947i | 0.313842i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.6804 | + | 16.6804i | −1.17074 | + | 1.17074i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.23213 | − | 2.23213i | −0.155899 | − | 0.155899i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.48205 | 0.520038 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.70706 | 0.394765 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.13765 | − | 2.13765i | −0.147162 | − | 0.147162i | 0.629687 | − | 0.776849i | \(-0.283183\pi\) |
−0.776849 | + | 0.629687i | \(0.783183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.47655 | + | 2.47655i | −0.169690 | + | 0.169690i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.39724i | 0.299889i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.9622i | 1.42301i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3340 | − | 10.3340i | 0.698308 | − | 0.698308i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.8231 | − | 22.8231i | −1.53525 | − | 1.53525i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4768 | −0.902476 | −0.451238 | − | 0.892404i | \(-0.649017\pi\) | ||||
−0.451238 | + | 0.892404i | \(0.649017\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.70567 | − | 2.70567i | −0.179582 | − | 0.179582i | 0.611592 | − | 0.791174i | \(-0.290530\pi\) |
−0.791174 | + | 0.611592i | \(0.790530\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.507051 | + | 0.507051i | −0.0335069 | + | 0.0335069i | −0.723662 | − | 0.690155i | \(-0.757542\pi\) |
0.690155 | + | 0.723662i | \(0.257542\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 13.7236i | − | 0.902949i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.16109i | 0.534651i | 0.963606 | + | 0.267325i | \(0.0861399\pi\) | ||||
−0.963606 | + | 0.267325i | \(0.913860\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.95167 | − | 1.95167i | 0.127313 | − | 0.127313i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.33090 | + | 6.33090i | 0.411236 | + | 0.411236i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.46397 | 0.159381 | 0.0796905 | − | 0.996820i | \(-0.474607\pi\) | ||||
0.0796905 | + | 0.996820i | \(0.474607\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.38073 | 0.475434 | 0.237717 | − | 0.971334i | \(-0.423601\pi\) | ||||
0.237717 | + | 0.971334i | \(0.423601\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.454757 | + | 0.454757i | −0.0290533 | + | 0.0290533i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7.41345i | − | 0.471707i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.04880i | 0.256582i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.15322 | + | 5.15322i | −0.325268 | + | 0.325268i | −0.850784 | − | 0.525516i | \(-0.823872\pi\) |
0.525516 | + | 0.850784i | \(0.323872\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.2627 | + | 26.2627i | 1.65112 | + | 1.65112i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.00550 | 0.313457 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.84129 | 0.613883 | 0.306942 | − | 0.951728i | \(-0.400694\pi\) | ||||
0.306942 | + | 0.951728i | \(0.400694\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00442 | + | 3.00442i | 0.186686 | + | 0.186686i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.03354 | − | 6.03354i | 0.373467 | − | 0.373467i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.5027i | 1.69589i | 0.530086 | + | 0.847944i | \(0.322160\pi\) | ||||
−0.530086 | + | 0.847944i | \(0.677840\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.06647i | 0.556949i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.11634 | − | 5.11634i | 0.313115 | − | 0.313115i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.35280 | − | 7.35280i | −0.448308 | − | 0.448308i | 0.446484 | − | 0.894792i | \(-0.352676\pi\) |
−0.894792 | + | 0.446484i | \(0.852676\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.1826 | 0.983023 | 0.491511 | − | 0.870871i | \(-0.336445\pi\) | ||||
0.491511 | + | 0.870871i | \(0.336445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.8270 | −1.07894 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.51009 | + | 3.51009i | 0.211667 | + | 0.211667i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3725 | − | 19.3725i | 1.16398 | − | 1.16398i | 0.180381 | − | 0.983597i | \(-0.442267\pi\) |
0.983597 | − | 0.180381i | \(-0.0577331\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 7.58233i | − | 0.453942i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.1786i | − | 1.08445i | −0.840235 | − | 0.542223i | \(-0.817583\pi\) | ||
0.840235 | − | 0.542223i | \(-0.182417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.74925 | + | 7.74925i | −0.460645 | + | 0.460645i | −0.898867 | − | 0.438222i | \(-0.855609\pi\) |
0.438222 | + | 0.898867i | \(0.355609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.812949 | + | 0.812949i | 0.0481549 | + | 0.0481549i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.72709 | −0.515144 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.05503 | 0.473825 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.82695 | + | 5.82695i | 0.341582 | + | 0.341582i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.24572 | − | 1.24572i | 0.0727760 | − | 0.0727760i | −0.669782 | − | 0.742558i | \(-0.733612\pi\) |
0.742558 | + | 0.669782i | \(0.233612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.26561i | 0.423020i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.96402i | 0.288042i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 34.1152 | − | 34.1152i | 1.97293 | − | 1.97293i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.59608 | + | 8.59608i | 0.495470 | + | 0.495470i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.51782 | 0.0871966 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.52470 | 0.201824 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5042 | + | 13.5042i | 0.770727 | + | 0.770727i | 0.978234 | − | 0.207506i | \(-0.0665348\pi\) |
−0.207506 | + | 0.978234i | \(0.566535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.17919 | − | 1.17919i | 0.0670819 | − | 0.0670819i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.9549i | − | 0.677901i | −0.940804 | − | 0.338951i | \(-0.889928\pi\) | ||
0.940804 | − | 0.338951i | \(-0.110072\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 15.2385i | − | 0.861333i | −0.902511 | − | 0.430667i | \(-0.858279\pi\) | ||
0.902511 | − | 0.430667i | \(-0.141721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.95488 | − | 1.95488i | 0.110145 | − | 0.110145i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.4062 | − | 22.4062i | −1.25846 | − | 1.25846i | −0.951830 | − | 0.306625i | \(-0.900800\pi\) |
−0.306625 | − | 0.951830i | \(-0.599200\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.3566 | 2.37151 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.61058 | 0.480595 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.06922 | + | 4.06922i | 0.226417 | + | 0.226417i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.55960 | − | 4.55960i | 0.252921 | − | 0.252921i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.13143i | 0.228469i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7.63057i | − | 0.420687i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.11650 | − | 8.11650i | 0.446123 | − | 0.446123i | −0.447940 | − | 0.894063i | \(-0.647842\pi\) |
0.894063 | + | 0.447940i | \(0.147842\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.08674 | − | 1.08674i | −0.0595529 | − | 0.0595529i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.44947 | −0.243101 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.1995 | −1.04587 | −0.522933 | − | 0.852374i | \(-0.675162\pi\) | ||||
−0.522933 | + | 0.852374i | \(0.675162\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.01097 | + | 2.01097i | 0.109221 | + | 0.109221i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.6147 | − | 26.6147i | 1.44127 | − | 1.44127i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.5743i | − | 0.948926i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.48205i | 0.402820i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.64968 | + | 3.64968i | −0.195925 | + | 0.195925i | −0.798251 | − | 0.602325i | \(-0.794241\pi\) |
0.602325 | + | 0.798251i | \(0.294241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.7180 | − | 16.7180i | −0.894896 | − | 0.894896i | 0.100083 | − | 0.994979i | \(-0.468089\pi\) |
−0.994979 | + | 0.100083i | \(0.968089\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.44825 | 0.344182 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.42887 | 0.501848 | 0.250924 | − | 0.968007i | \(-0.419266\pi\) | ||||
0.250924 | + | 0.968007i | \(0.419266\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.47655 | − | 2.47655i | −0.131442 | − | 0.131442i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.78516 | − | 9.78516i | 0.517886 | − | 0.517886i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.12135i | 0.0591826i | 0.999562 | + | 0.0295913i | \(0.00942059\pi\) | ||||
−0.999562 | + | 0.0295913i | \(0.990579\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 17.6782i | − | 0.930433i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.64602 | + | 9.64602i | −0.506285 | + | 0.506285i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.3340 | + | 10.3340i | 0.540907 | + | 0.540907i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.22666 | 0.377228 | 0.188614 | − | 0.982051i | \(-0.439600\pi\) | ||||
0.188614 | + | 0.982051i | \(0.439600\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.15671 | 0.164332 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.7239 | + | 17.7239i | 0.920178 | + | 0.920178i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.83590 | − | 8.83590i | 0.457506 | − | 0.457506i | −0.440330 | − | 0.897836i | \(-0.645139\pi\) |
0.897836 | + | 0.440330i | \(0.145139\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 55.0211i | − | 2.83373i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.2339 | + | 26.2339i | −1.34754 | + | 1.34754i | −0.459223 | + | 0.888321i | \(0.651872\pi\) |
−0.888321 | + | 0.459223i | \(0.848128\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.67449 | − | 4.67449i | −0.239481 | − | 0.239481i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.3557 | −0.733544 | −0.366772 | − | 0.930311i | \(-0.619537\pi\) | ||||
−0.366772 | + | 0.930311i | \(0.619537\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.7236 | 0.699421 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.10932 | − | 3.10932i | −0.158055 | − | 0.158055i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.07721 | − | 1.07721i | 0.0546168 | − | 0.0546168i | −0.679271 | − | 0.733888i | \(-0.737704\pi\) |
0.733888 | + | 0.679271i | \(0.237704\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.4514i | 1.89400i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.47700i | 0.478052i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.33090 | + | 6.33090i | −0.318542 | + | 0.318542i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.8838 | − | 16.8838i | −0.847376 | − | 0.847376i | 0.142429 | − | 0.989805i | \(-0.454509\pi\) |
−0.989805 | + | 0.142429i | \(0.954509\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.17844 | 0.159121 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.406306 | −0.0202900 | −0.0101450 | − | 0.999949i | \(-0.503229\pi\) | ||||
−0.0101450 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.5724 | − | 34.5724i | −1.72217 | − | 1.72217i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.707107 | + | 0.707107i | −0.0351364 | + | 0.0351364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.62911i | − | 0.378161i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 38.0171i | − | 1.87983i | −0.341413 | − | 0.939913i | \(-0.610906\pi\) | ||
0.341413 | − | 0.939913i | \(-0.389094\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1759 | + | 10.1759i | −0.501938 | + | 0.501938i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.2034 | + | 14.2034i | 0.698904 | + | 0.698904i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.04880 | −0.198748 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.414002 | −0.0202737 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.2302 | − | 23.2302i | −1.13487 | − | 1.13487i | −0.989357 | − | 0.145512i | \(-0.953517\pi\) |
−0.145512 | − | 0.989357i | \(-0.546483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.7883 | + | 26.7883i | −1.30558 | + | 1.30558i | −0.381009 | + | 0.924572i | \(0.624423\pi\) |
−0.924572 | + | 0.381009i | \(0.875577\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.76008i | 0.134200i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.00550i | 0.242802i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.89037 | − | 6.89037i | 0.333448 | − | 0.333448i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.6340 | + | 22.6340i | 1.09278 | + | 1.09278i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.17509 | 0.441949 | 0.220974 | − | 0.975280i | \(-0.429076\pi\) | ||||
0.220974 | + | 0.975280i | \(0.429076\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.5762 | 1.75774 | 0.878869 | − | 0.477063i | \(-0.158299\pi\) | ||||
0.878869 | + | 0.477063i | \(0.158299\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.03354 | + | 6.03354i | 0.289286 | + | 0.289286i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.08252 | + | 6.08252i | −0.290967 | + | 0.290967i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.96346i | − | 0.332348i | −0.986096 | − | 0.166174i | \(-0.946859\pi\) | ||
0.986096 | − | 0.166174i | \(-0.0531413\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 0.643123i | − | 0.0306249i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.15777 | − | 2.15777i | 0.102519 | − | 0.102519i | −0.653987 | − | 0.756506i | \(-0.726905\pi\) |
0.756506 | + | 0.653987i | \(0.226905\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.11634 | + | 5.11634i | 0.242538 | + | 0.242538i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.4662 | −0.731527 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.1720 | 0.621627 | 0.310814 | − | 0.950471i | \(-0.399398\pi\) | ||||
0.310814 | + | 0.950471i | \(0.399398\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.0803 | + | 11.0803i | 0.521753 | + | 0.521753i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.56186 | + | 9.56186i | −0.449256 | + | 0.449256i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 17.8270i | − | 0.835741i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.0012i | − | 0.467834i | −0.972257 | − | 0.233917i | \(-0.924846\pi\) | ||
0.972257 | − | 0.233917i | \(-0.0751545\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.53942 | + | 3.53942i | −0.165206 | + | 0.165206i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.79443 | + | 1.79443i | 0.0835750 | + | 0.0835750i | 0.747658 | − | 0.664083i | \(-0.231178\pi\) |
−0.664083 | + | 0.747658i | \(0.731178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.58325 | 0.120054 | 0.0600269 | − | 0.998197i | \(-0.480881\pi\) | ||||
0.0600269 | + | 0.998197i | \(0.480881\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.58233 | 0.351622 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.6809 | + | 24.6809i | 1.14210 | + | 1.14210i | 0.988066 | + | 0.154029i | \(0.0492250\pi\) |
0.154029 | + | 0.988066i | \(0.450775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.69819 | + | 8.69819i | −0.401645 | + | 0.401645i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.91012i | 0.180169i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 21.8280i | − | 1.00365i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.812949 | + | 0.812949i | −0.0373007 | + | 0.0373007i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.41096 | − | 6.41096i | −0.293538 | − | 0.293538i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.39344 | −0.0636679 | −0.0318339 | − | 0.999493i | \(-0.510135\pi\) | ||||
−0.0318339 | + | 0.999493i | \(0.510135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.91020 | −0.451866 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.6265 | + | 14.6265i | 0.665530 | + | 0.665530i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.82695 | + | 5.82695i | −0.264588 | + | 0.264588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 26.7044i | − | 1.21009i | −0.796191 | − | 0.605045i | \(-0.793155\pi\) | ||
0.796191 | − | 0.605045i | \(-0.206845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 21.9121i | − | 0.990901i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.3259 | − | 16.3259i | 0.736775 | − | 0.736775i | −0.235177 | − | 0.971953i | \(-0.575567\pi\) |
0.971953 | + | 0.235177i | \(0.0755670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.2009 | + | 30.2009i | 1.36018 | + | 1.36018i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.96402 | −0.223116 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.68272 | −0.434329 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.4923 | + | 26.4923i | 1.18596 | + | 1.18596i | 0.978175 | + | 0.207783i | \(0.0666247\pi\) |
0.207783 | + | 0.978175i | \(0.433375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.25086 | − | 1.25086i | 0.0558842 | − | 0.0558842i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.2132i | 0.633737i | 0.948470 | + | 0.316868i | \(0.102631\pi\) | ||||
−0.948470 | + | 0.316868i | \(0.897369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.51782i | 0.0675422i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.2091 | − | 20.2091i | 0.897517 | − | 0.897517i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.26128 | − | 4.26128i | −0.188878 | − | 0.188878i | 0.606333 | − | 0.795211i | \(-0.292640\pi\) |
−0.795211 | + | 0.606333i | \(0.792640\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.4036 | 1.78735 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.14968 | −0.0507598 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.17919 | + | 1.17919i | 0.0519614 | + | 0.0519614i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.68814 | + | 9.68814i | −0.426084 | + | 0.426084i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.67597i | 0.249147i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 31.9522i | − | 1.39985i | −0.714215 | − | 0.699926i | \(-0.753216\pi\) | ||
0.714215 | − | 0.699926i | \(-0.246784\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.3608 | − | 12.3608i | 0.540498 | − | 0.540498i | −0.383177 | − | 0.923675i | \(-0.625170\pi\) |
0.923675 | + | 0.383177i | \(0.125170\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.95488 | + | 1.95488i | 0.0853180 | + | 0.0853180i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.9533 | 1.65327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −32.9810 | −1.43396 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.13756 | − | 5.13756i | −0.222951 | − | 0.222951i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.3933 | − | 14.3933i | 0.623444 | − | 0.623444i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.61058i | 0.372268i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.51428i | 0.324265i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.25742 | − | 2.25742i | 0.0972341 | − | 0.0972341i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.6126 | − | 25.6126i | −1.10117 | − | 1.10117i | −0.994270 | − | 0.106902i | \(-0.965907\pi\) |
−0.106902 | − | 0.994270i | \(-0.534093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.3732 | −0.530985 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.13143 | −0.176971 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.56643 | + | 1.56643i | 0.0669759 | + | 0.0669759i | 0.739801 | − | 0.672825i | \(-0.234919\pi\) |
−0.672825 | + | 0.739801i | \(0.734919\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.49234 | + | 2.49234i | −0.106370 | + | 0.106370i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.80992i | 0.417917i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.7523i | 1.05258i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.08674 | − | 1.08674i | 0.0461295 | − | 0.0461295i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.96707 | − | 3.96707i | −0.168090 | − | 0.168090i | 0.618049 | − | 0.786139i | \(-0.287923\pi\) |
−0.786139 | + | 0.618049i | \(0.787923\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.3545 | −1.19927 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.8474 | −1.04906 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.0565 | + | 23.0565i | 0.971715 | + | 0.971715i | 0.999611 | − | 0.0278956i | \(-0.00888059\pi\) |
−0.0278956 | + | 0.999611i | \(0.508881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.01097 | + | 2.01097i | −0.0846023 | + | 0.0846023i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.76462i | 0.116103i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.6228i | 1.36762i | 0.729660 | + | 0.683810i | \(0.239678\pi\) | ||||
−0.729660 | + | 0.683810i | \(0.760322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.3559 | − | 13.3559i | 0.558926 | − | 0.558926i | −0.370076 | − | 0.929002i | \(-0.620668\pi\) |
0.929002 | + | 0.370076i | \(0.120668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.85521 | − | 2.85521i | −0.119278 | − | 0.119278i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.48205 | −0.312023 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.5999 | 1.93998 | 0.969989 | − | 0.243147i | \(-0.0781798\pi\) | ||||
0.969989 | + | 0.243147i | \(0.0781798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.309084 | − | 0.309084i | −0.0128451 | − | 0.0128451i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.91492 | + | 7.91492i | −0.328366 | + | 0.328366i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 45.0062i | − | 1.86397i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.44825i | 0.266602i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.5590 | + | 29.5590i | −1.22003 | + | 1.22003i | −0.252408 | + | 0.967621i | \(0.581222\pi\) |
−0.967621 | + | 0.252408i | \(0.918778\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.16404 | + | 6.16404i | 0.253985 | + | 0.253985i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.5231 | 0.679671 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.4555 | −1.45598 | −0.727991 | − | 0.685587i | \(-0.759546\pi\) | ||||
−0.727991 | + | 0.685587i | \(0.759546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.78516 | + | 9.78516i | 0.401152 | + | 0.401152i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.1307 | − | 11.1307i | 0.455551 | − | 0.455551i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.8571i | 0.933915i | 0.884280 | + | 0.466958i | \(0.154650\pi\) | ||||
−0.884280 | + | 0.466958i | \(0.845350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.4253i | − | 0.792374i | −0.918170 | − | 0.396187i | \(-0.870333\pi\) | ||
0.918170 | − | 0.396187i | \(-0.129667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.14625 | − | 3.14625i | 0.128125 | − | 0.128125i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.64602 | − | 9.64602i | −0.392166 | − | 0.392166i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.2455 | 0.781149 | 0.390574 | − | 0.920571i | \(-0.372276\pi\) | ||||
0.390574 | + | 0.920571i | \(0.372276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.5897 | 0.955903 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.5849 | + | 12.5849i | 0.509129 | + | 0.509129i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3922 | + | 17.3922i | −0.702465 | + | 0.702465i | −0.964939 | − | 0.262474i | \(-0.915462\pi\) |
0.262474 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.15671i | 0.127291i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.7863i | 1.19915i | 0.800318 | + | 0.599576i | \(0.204664\pi\) | ||||
−0.800318 | + | 0.599576i | \(0.795336\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6404 | + | 10.6404i | −0.427673 | + | 0.427673i | −0.887835 | − | 0.460162i | \(-0.847791\pi\) |
0.460162 | + | 0.887835i | \(0.347791\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.29061 | − | 5.29061i | −0.212305 | − | 0.212305i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.0037 | 0.801430 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.03550 | − | 4.03550i | −0.161162 | − | 0.161162i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.43967 | − | 5.43967i | 0.216894 | − | 0.216894i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.7660i | − | 1.54325i | −0.636078 | − | 0.771625i | \(-0.719444\pi\) | ||
0.636078 | − | 0.771625i | \(-0.280556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.02309i | 0.120157i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.67449 | − | 4.67449i | 0.185502 | − | 0.185502i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.93239 | − | 2.93239i | −0.116185 | − | 0.116185i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.50237 | 0.138552 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.84117 | 0.151717 | 0.0758585 | − | 0.997119i | \(-0.475830\pi\) | ||||
0.0758585 | + | 0.997119i | \(0.475830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.00729 | − | 4.00729i | −0.158032 | − | 0.158032i | 0.623662 | − | 0.781694i | \(-0.285644\pi\) |
−0.781694 | + | 0.623662i | \(0.785644\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.10932 | − | 3.10932i | 0.122429 | − | 0.122429i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 25.3385i | − | 0.996158i | −0.867132 | − | 0.498079i | \(-0.834039\pi\) | ||
0.867132 | − | 0.498079i | \(-0.165961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.0667i | − | 1.41574i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.8225 | − | 14.8225i | 0.580941 | − | 0.580941i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.690132 | − | 0.690132i | −0.0270069 | − | 0.0270069i | 0.693474 | − | 0.720481i | \(-0.256079\pi\) |
−0.720481 | + | 0.693474i | \(0.756079\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.47700 | −0.370297 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.6145 | −0.570166 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.4031 | − | 27.4031i | −1.06747 | − | 1.06747i | −0.997552 | − | 0.0699222i | \(-0.977725\pi\) |
−0.0699222 | − | 0.997552i | \(-0.522275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.4586 | + | 14.4586i | −0.562373 | + | 0.562373i | −0.929981 | − | 0.367608i | \(-0.880177\pi\) |
0.367608 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 32.2767i | 1.25352i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.17844i | 0.123255i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.1432 | + | 45.1432i | −1.74795 | + | 1.74795i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.52957 | + | 9.52957i | 0.368434 | + | 0.368434i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.4967 | −0.675452 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.4496 | 1.48212 | 0.741061 | − | 0.671438i | \(-0.234323\pi\) | ||||
0.741061 | + | 0.671438i | \(0.234323\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.707107 | − | 0.707107i | −0.0272166 | − | 0.0272166i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.2625 | − | 15.2625i | 0.586586 | − | 0.586586i | −0.350119 | − | 0.936705i | \(-0.613859\pi\) |
0.936705 | + | 0.350119i | \(0.113859\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.7820i | 0.874293i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.82640i | 0.146628i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.6516 | + | 31.6516i | −1.21111 | + | 1.21111i | −0.240453 | + | 0.970661i | \(0.577296\pi\) |
−0.970661 | + | 0.240453i | \(0.922704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.1759 | − | 10.1759i | −0.388800 | − | 0.388800i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.717078 | 0.0273582 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −58.4629 | −2.22726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0010 | − | 12.0010i | −0.456539 | − | 0.456539i | 0.440979 | − | 0.897518i | \(-0.354631\pi\) |
−0.897518 | + | 0.440979i | \(0.854631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.70408 | + | 9.70408i | −0.368627 | + | 0.368627i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.414002i | − | 0.0157040i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.8009i | 0.598502i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.77076 | − | 5.77076i | 0.218270 | − | 0.218270i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.298277 | + | 0.298277i | 0.0112658 | + | 0.0112658i | 0.712717 | − | 0.701451i | \(-0.247464\pi\) |
−0.701451 | + | 0.712717i | \(0.747464\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.76693 | 0.0666409 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.76008 | −0.103951 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.96716 | + | 2.96716i | 0.111592 | + | 0.111592i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.6489 | − | 11.6489i | 0.437485 | − | 0.437485i | −0.453680 | − | 0.891165i | \(-0.649889\pi\) |
0.891165 | + | 0.453680i | \(0.149889\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.95325i | − | 0.335773i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 56.7313i | 2.12460i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.6340 | + | 22.6340i | −0.846463 | + | 0.846463i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.74229 | − | 1.74229i | −0.0650670 | − | 0.0650670i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.69024 | −0.0630353 | −0.0315177 | − | 0.999503i | \(-0.510034\pi\) | ||||
−0.0315177 | + | 0.999503i | \(0.510034\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.61036 | 0.171699 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.21896 | − | 5.21896i | −0.194095 | − | 0.194095i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.03354 | + | 6.03354i | −0.224080 | + | 0.224080i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.2221i | 1.00961i | 0.863233 | + | 0.504805i | \(0.168436\pi\) | ||||
−0.863233 | + | 0.504805i | \(0.831564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.5637 | − | 15.5637i | 0.575644 | − | 0.575644i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.9172 | − | 20.9172i | −0.772596 | − | 0.772596i | 0.205963 | − | 0.978560i | \(-0.433967\pi\) |
−0.978560 | + | 0.205963i | \(0.933967\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.643123 | 0.0237219 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.0873 | 0.813596 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.53634 | − | 3.53634i | −0.130086 | − | 0.130086i | 0.639066 | − | 0.769152i | \(-0.279321\pi\) |
−0.769152 | + | 0.639066i | \(0.779321\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.24210 | + | 5.24210i | −0.192573 | + | 0.192573i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.5438i | 1.41403i | 0.707196 | + | 0.707017i | \(0.249960\pi\) | ||||
−0.707196 | + | 0.707017i | \(0.750040\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 15.4662i | − | 0.566639i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.86293 | − | 2.86293i | 0.104749 | − | 0.104749i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.8327 | + | 16.8327i | 0.615052 | + | 0.615052i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.07646 | 0.258224 | 0.129112 | − | 0.991630i | \(-0.458787\pi\) | ||||
0.129112 | + | 0.991630i | \(0.458787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.28775 | 0.265580 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.56186 | − | 9.56186i | −0.347992 | − | 0.347992i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.5233 | − | 32.5233i | 1.18208 | − | 1.18208i | 0.202873 | − | 0.979205i | \(-0.434972\pi\) |
0.979205 | − | 0.202873i | \(-0.0650280\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 37.1411i | − | 1.34814i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.1903i | 1.56565i | 0.622243 | + | 0.782824i | \(0.286222\pi\) | ||||
−0.622243 | + | 0.782824i | \(0.713778\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.07645 | + | 8.07645i | −0.292387 | + | 0.292387i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.53942 | − | 3.53942i | −0.127968 | − | 0.127968i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −46.8505 | −1.69167 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.1675 | −1.12393 | −0.561965 | − | 0.827161i | \(-0.689955\pi\) | ||||
−0.561965 | + | 0.827161i | \(0.689955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.95885 | − | 6.95885i | −0.250617 | − | 0.250617i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.7904 | + | 11.7904i | −0.424072 | + | 0.424072i | −0.886603 | − | 0.462531i | \(-0.846941\pi\) |
0.462531 | + | 0.886603i | \(0.346941\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.58233i | 0.272365i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.24889i | − | 0.152428i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.56624 | + | 2.56624i | −0.0919452 | + | 0.0919452i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.2936 | + | 12.2936i | 0.439901 | + | 0.439901i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.53271 | −0.304934 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.91012 | −0.139558 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.50469 | − | 3.50469i | −0.124929 | − | 0.124929i | 0.641878 | − | 0.766807i | \(-0.278156\pi\) |
−0.766807 | + | 0.641878i | \(0.778156\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.4473 | − | 19.4473i | 0.692343 | − | 0.692343i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.86243i | 0.279556i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.7282i | 0.807100i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.41096 | − | 6.41096i | 0.227373 | − | 0.227373i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.1882 | + | 34.1882i | 1.21101 | + | 1.21101i | 0.970696 | + | 0.240312i | \(0.0772497\pi\) |
0.240312 | + | 0.970696i | \(0.422750\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.8156 | −0.488760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.23560 | −0.255657 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −51.2983 | − | 51.2983i | −1.81028 | − | 1.81028i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.6265 | + | 14.6265i | −0.515517 | + | 0.515517i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.3984i | 0.366042i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 0.637755i | − | 0.0224223i | −0.999937 | − | 0.0112111i | \(-0.996431\pi\) | ||
0.999937 | − | 0.0112111i | \(-0.00356869\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.6724 | − | 30.6724i | 1.07705 | − | 1.07705i | 0.0802798 | − | 0.996772i | \(-0.474419\pi\) |
0.996772 | − | 0.0802798i | \(-0.0255814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.4428 | − | 11.4428i | −0.401317 | − | 0.401317i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.9121 | 0.767549 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.05543 | 0.176867 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.6056 | + | 12.6056i | 0.440474 | + | 0.440474i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.40778 | + | 2.40778i | −0.0840320 | + | 0.0840320i | −0.747873 | − | 0.663841i | \(-0.768925\pi\) |
0.663841 | + | 0.747873i | \(0.268925\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.4455i | 1.13098i | 0.824755 | + | 0.565490i | \(0.191313\pi\) | ||||
−0.824755 | + | 0.565490i | \(0.808687\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.96402i | − | 0.172825i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.2278 | − | 32.2278i | 1.12067 | − | 1.12067i | 0.129028 | − | 0.991641i | \(-0.458814\pi\) |
0.991641 | − | 0.129028i | \(-0.0411857\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.6767 | − | 29.6767i | −1.03072 | − | 1.03072i | −0.999513 | − | 0.0312027i | \(-0.990066\pi\) |
−0.0312027 | − | 0.999513i | \(-0.509934\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.3968 | −0.950384 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.21915 | 0.111537 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.25086 | + | 1.25086i | 0.0432877 | + | 0.0432877i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.36151 | + | 5.36151i | −0.185321 | + | 0.185321i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 42.4417i | − | 1.46525i | −0.680632 | − | 0.732625i | \(-0.738295\pi\) | ||
0.680632 | − | 0.732625i | \(-0.261705\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.8072i | 1.51059i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.8542 | + | 12.8542i | −0.442723 | + | 0.442723i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.2091 | + | 20.2091i | 0.695214 | + | 0.695214i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.7136 | −1.29586 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.9591 | 0.376115 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.13103 | + | 8.13103i | 0.278728 | + | 0.278728i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.7844 | − | 16.7844i | 0.574686 | − | 0.574686i | −0.358748 | − | 0.933434i | \(-0.616796\pi\) |
0.933434 | + | 0.358748i | \(0.116796\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.14968i | − | 0.0393183i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 31.0924i | − | 1.06210i | −0.847341 | − | 0.531049i | \(-0.821798\pi\) | ||
0.847341 | − | 0.531049i | \(-0.178202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.2508 | + | 16.2508i | −0.554469 | + | 0.554469i | −0.927727 | − | 0.373258i | \(-0.878241\pi\) |
0.373258 | + | 0.927727i | \(0.378241\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.17099 | + | 6.17099i | 0.210307 | + | 0.210307i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.4656 | 0.764739 | 0.382369 | − | 0.924010i | \(-0.375108\pi\) | ||||
0.382369 | + | 0.924010i | \(0.375108\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.67597 | −0.192989 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.69577 | − | 5.69577i | −0.193438 | − | 0.193438i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.4268 | − | 31.4268i | 1.06608 | − | 1.06608i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 28.6913i | − | 0.972169i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.24056i | − | 0.278901i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.95488 | + | 1.95488i | −0.0660871 | + | 0.0660871i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.46527 | − | 1.46527i | −0.0494785 | − | 0.0494785i | 0.681935 | − | 0.731413i | \(-0.261139\pi\) |
−0.731413 | + | 0.681935i | \(0.761139\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.76172 | −0.0594213 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.578022 | 0.0194740 | 0.00973702 | − | 0.999953i | \(-0.496901\pi\) | ||||
0.00973702 | + | 0.999953i | \(0.496901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.1372 | − | 10.1372i | −0.341144 | − | 0.341144i | 0.515653 | − | 0.856797i | \(-0.327549\pi\) |
−0.856797 | + | 0.515653i | \(0.827549\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.13756 | − | 5.13756i | 0.172697 | − | 0.172697i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 56.0202i | − | 1.88097i | −0.339831 | − | 0.940487i | \(-0.610370\pi\) | ||
0.339831 | − | 0.940487i | \(-0.389630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 18.2762i | − | 0.612962i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.51009 | − | 3.51009i | 0.117593 | − | 0.117593i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.24380 | − | 2.24380i | −0.0750860 | − | 0.0750860i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.51428 | −0.251175 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −48.2461 | −1.61089 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.7483 | + | 45.7483i | 1.52579 | + | 1.52579i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0901 | − | 32.0901i | 1.06908 | − | 1.06908i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 12.1567i | − | 0.404549i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 12.3732i | − | 0.411299i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.3292 | − | 31.3292i | 1.04027 | − | 1.04027i | 0.0411133 | − | 0.999154i | \(-0.486910\pi\) |
0.999154 | − | 0.0411133i | \(-0.0130905\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.07326 | − | 1.07326i | −0.0355979 | − | 0.0355979i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7701 | 0.820670 | 0.410335 | − | 0.911935i | \(-0.365412\pi\) | ||||
0.410335 | + | 0.911935i | \(0.365412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0983 | 0.665157 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.49234 | − | 2.49234i | −0.0823942 | − | 0.0823942i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.5264 | + | 18.5264i | −0.611796 | + | 0.611796i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.82495i | − | 0.258121i | −0.991637 | − | 0.129061i | \(-0.958804\pi\) | ||
0.991637 | − | 0.129061i | \(-0.0411962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 19.0979i | − | 0.629296i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.9694 | − | 15.9694i | 0.525640 | − | 0.525640i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.08674 | + | 1.08674i | 0.0357318 | + | 0.0357318i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.66763 | −0.0547721 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.8650 | 1.80006 | 0.900031 | − | 0.435826i | \(-0.143544\pi\) | ||||
0.900031 | + | 0.435826i | \(0.143544\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.522826 | + | 0.522826i | 0.0171349 | + | 0.0171349i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.45340 | + | 8.45340i | −0.276752 | + | 0.276752i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 24.8474i | − | 0.812598i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.3306i | 0.631504i | 0.948842 | + | 0.315752i | \(0.102257\pi\) | ||||
−0.948842 | + | 0.315752i | \(0.897743\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.7753 | + | 10.7753i | −0.351638 | + | 0.351638i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.4226 | − | 11.4226i | −0.372365 | − | 0.372365i | 0.495973 | − | 0.868338i | \(-0.334812\pi\) |
−0.868338 | + | 0.495973i | \(0.834812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.6186 | −0.769129 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.76462 | −0.0899331 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.8761 | − | 26.8761i | −0.873357 | − | 0.873357i | 0.119480 | − | 0.992837i | \(-0.461877\pi\) |
−0.992837 | + | 0.119480i | \(0.961877\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −66.6364 | + | 66.6364i | −2.16311 | + | 2.16311i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.6871i | 1.02752i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.6661i | 1.18773i | 0.804564 | + | 0.593866i | \(0.202399\pi\) | ||||
−0.804564 | + | 0.593866i | \(0.797601\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.85521 | − | 2.85521i | 0.0923923 | − | 0.0923923i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.9506 | − | 29.9506i | −0.968167 | − | 0.968167i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.7852 | −1.28473 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.4917 | 0.854570 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.08860 | − | 6.08860i | −0.196202 | − | 0.196202i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.309084 | − | 0.309084i | 0.00994976 | − | 0.00994976i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.0462i | 1.38427i | 0.721767 | + | 0.692136i | \(0.243330\pi\) | ||||
−0.721767 | + | 0.692136i | \(0.756670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.75474i | − | 0.184869i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.26831 | + | 3.26831i | −0.104885 | + | 0.104885i | −0.757602 | − | 0.652717i | \(-0.773629\pi\) |
0.652717 | + | 0.757602i | \(0.273629\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.809324 | − | 0.809324i | −0.0259457 | − | 0.0259457i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.44825 | −0.206509 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.62437 | 0.0519681 | 0.0259840 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259840 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.3976 | − | 25.3976i | −0.811712 | − | 0.811712i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.92136 | − | 2.92136i | 0.0932719 | − | 0.0932719i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.7756i | 1.46001i | 0.683439 | + | 0.730007i | \(0.260483\pi\) | ||||
−0.683439 | + | 0.730007i | \(0.739517\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.5231i | 0.526471i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.39563 | + | 5.39563i | −0.171745 | + | 0.171745i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.2641 | + | 23.2641i | 0.739754 | + | 0.739754i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.0608 | −0.351357 | −0.175679 | − | 0.984448i | \(-0.556212\pi\) | ||||
−0.175679 | + | 0.984448i | \(0.556212\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.4785 | −0.364258 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.1307 | + | 11.1307i | 0.352868 | + | 0.352868i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.9716 | + | 21.9716i | −0.695848 | + | 0.695848i | −0.963512 | − | 0.267664i | \(-0.913748\pi\) |
0.267664 | + | 0.963512i | \(0.413748\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.53688i | 0.0486248i |
(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 | 1920.2.s.f.1441.2 | 20 | ||
4.3 | odd | 2 | 1920.2.s.e.1441.9 | 20 | |||
8.3 | odd | 2 | 240.2.s.c.61.6 | ✓ | 20 | ||
8.5 | even | 2 | 960.2.s.c.721.7 | 20 | |||
16.3 | odd | 4 | 240.2.s.c.181.6 | yes | 20 | ||
16.5 | even | 4 | inner | 1920.2.s.f.481.4 | 20 | ||
16.11 | odd | 4 | 1920.2.s.e.481.7 | 20 | |||
16.13 | even | 4 | 960.2.s.c.241.9 | 20 | |||
24.5 | odd | 2 | 2880.2.t.d.721.7 | 20 | |||
24.11 | even | 2 | 720.2.t.d.541.5 | 20 | |||
48.29 | odd | 4 | 2880.2.t.d.2161.9 | 20 | |||
48.35 | even | 4 | 720.2.t.d.181.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.c.61.6 | ✓ | 20 | 8.3 | odd | 2 | ||
240.2.s.c.181.6 | yes | 20 | 16.3 | odd | 4 | ||
720.2.t.d.181.5 | 20 | 48.35 | even | 4 | |||
720.2.t.d.541.5 | 20 | 24.11 | even | 2 | |||
960.2.s.c.241.9 | 20 | 16.13 | even | 4 | |||
960.2.s.c.721.7 | 20 | 8.5 | even | 2 | |||
1920.2.s.e.481.7 | 20 | 16.11 | odd | 4 | |||
1920.2.s.e.1441.9 | 20 | 4.3 | odd | 2 | |||
1920.2.s.f.481.4 | 20 | 16.5 | even | 4 | inner | ||
1920.2.s.f.1441.2 | 20 | 1.1 | even | 1 | trivial | ||
2880.2.t.d.721.7 | 20 | 24.5 | odd | 2 | |||
2880.2.t.d.2161.9 | 20 | 48.29 | odd | 4 |