Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(101,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bi (of order \(6\), degree \(2\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.14 | ||
Character | \(\chi\) | \(=\) | 2100.101 |
Dual form | 2100.2.bi.n.1601.14 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.52899 | − | 0.813749i | 0.882763 | − | 0.469818i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.567546 | − | 2.58416i | 0.214512 | − | 0.976721i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.67563 | − | 2.48843i | 0.558542 | − | 0.829476i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.793196 | + | 0.457952i | 0.239158 | + | 0.138078i | 0.614790 | − | 0.788691i | \(-0.289241\pi\) |
−0.375632 | + | 0.926769i | \(0.622574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.31153i | 1.19580i | 0.801569 | + | 0.597902i | \(0.203999\pi\) | ||||
−0.801569 | + | 0.597902i | \(0.796001\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.268531 | + | 0.465109i | −0.0651283 | + | 0.112805i | −0.896751 | − | 0.442536i | \(-0.854079\pi\) |
0.831623 | + | 0.555341i | \(0.187412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12887 | − | 0.651755i | 0.258981 | − | 0.149523i | −0.364889 | − | 0.931051i | \(-0.618893\pi\) |
0.623870 | + | 0.781528i | \(0.285560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.23509 | − | 4.41300i | −0.269518 | − | 0.962995i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.91920 | − | 3.99480i | 1.44275 | − | 0.832974i | 0.444721 | − | 0.895669i | \(-0.353303\pi\) |
0.998033 | + | 0.0626950i | \(0.0199695\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.537062 | − | 5.16832i | 0.103358 | − | 0.994644i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.46154i | − | 0.642791i | −0.946945 | − | 0.321396i | \(-0.895848\pi\) | ||
0.946945 | − | 0.321396i | \(-0.104152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.56113 | − | 3.21072i | −0.998809 | − | 0.576663i | −0.0909133 | − | 0.995859i | \(-0.528979\pi\) |
−0.907896 | + | 0.419196i | \(0.862312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.58545 | + | 0.0547421i | 0.275991 | + | 0.00952938i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.52172 | + | 4.36775i | 0.414569 | + | 0.718054i | 0.995383 | − | 0.0959820i | \(-0.0305991\pi\) |
−0.580814 | + | 0.814036i | \(0.697266\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.50850 | + | 6.59229i | 0.561810 | + | 1.05561i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.89809 | 1.54582 | 0.772911 | − | 0.634515i | \(-0.218800\pi\) | ||||
0.772911 | + | 0.634515i | \(0.218800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.22096 | 1.25369 | 0.626843 | − | 0.779146i | \(-0.284347\pi\) | ||||
0.626843 | + | 0.779146i | \(0.284347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.17066 | − | 3.75969i | −0.316623 | − | 0.548407i | 0.663158 | − | 0.748479i | \(-0.269216\pi\) |
−0.979781 | + | 0.200072i | \(0.935882\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.35578 | − | 2.93326i | −0.907969 | − | 0.419038i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0320993 | + | 0.929664i | −0.00449480 | + | 0.130179i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.70594 | − | 0.984927i | −0.234329 | − | 0.135290i | 0.378238 | − | 0.925708i | \(-0.376530\pi\) |
−0.612568 | + | 0.790418i | \(0.709863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.19567 | − | 1.91514i | 0.158370 | − | 0.253667i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.15363 | − | 12.3904i | 0.931323 | − | 1.61310i | 0.150260 | − | 0.988647i | \(-0.451989\pi\) |
0.781063 | − | 0.624452i | \(-0.214678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.38395 | + | 4.84048i | −1.07345 | + | 0.619759i | −0.929123 | − | 0.369770i | \(-0.879436\pi\) |
−0.144331 | + | 0.989529i | \(0.546103\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.47951 | − | 5.74239i | −0.690353 | − | 0.723473i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.05349 | + | 10.4850i | −0.739551 | + | 1.28094i | 0.213146 | + | 0.977020i | \(0.431629\pi\) |
−0.952697 | + | 0.303920i | \(0.901704\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.32863 | − | 11.7385i | 0.882264 | − | 1.41315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.943900i | 0.112020i | 0.998430 | + | 0.0560102i | \(0.0178379\pi\) | ||||
−0.998430 | + | 0.0560102i | \(0.982162\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.85442 | − | 5.11210i | −1.03633 | − | 0.598326i | −0.117540 | − | 0.993068i | \(-0.537501\pi\) |
−0.918792 | + | 0.394742i | \(0.870834\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.63360 | − | 1.78984i | 0.186166 | − | 0.203971i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.71817 | − | 9.90416i | −0.643345 | − | 1.11431i | −0.984681 | − | 0.174364i | \(-0.944213\pi\) |
0.341337 | − | 0.939941i | \(-0.389120\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.38455 | − | 8.33935i | −0.376062 | − | 0.926595i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.35240 | −1.02656 | −0.513279 | − | 0.858222i | \(-0.671570\pi\) | ||||
−0.513279 | + | 0.858222i | \(0.671570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.81682 | − | 5.29266i | −0.301995 | − | 0.567433i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.874507 | − | 1.51469i | −0.0926976 | − | 0.160557i | 0.815948 | − | 0.578126i | \(-0.196216\pi\) |
−0.908645 | + | 0.417569i | \(0.862882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.1417 | + | 2.44699i | 1.16797 | + | 0.256515i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.1156 | − | 0.383799i | −1.15264 | − | 0.0397981i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7844i | 1.09499i | 0.836809 | + | 0.547494i | \(0.184418\pi\) | ||||
−0.836809 | + | 0.547494i | \(0.815582\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.46868 | − | 1.20646i | 0.248112 | − | 0.121253i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.92480 | − | 8.53000i | 0.490036 | − | 0.848767i | −0.509898 | − | 0.860235i | \(-0.670317\pi\) |
0.999934 | + | 0.0114677i | \(0.00365037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.12863 | + | 1.22897i | −0.209741 | + | 0.121094i | −0.601191 | − | 0.799106i | \(-0.705307\pi\) |
0.391450 | + | 0.920199i | \(0.371974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.29872 | + | 0.749815i | −0.125552 | + | 0.0724873i | −0.561461 | − | 0.827504i | \(-0.689760\pi\) |
0.435909 | + | 0.899991i | \(0.356427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.93226 | + | 3.34677i | −0.185077 | + | 0.320563i | −0.943602 | − | 0.331081i | \(-0.892587\pi\) |
0.758525 | + | 0.651643i | \(0.225920\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.40994 | + | 4.62620i | 0.703321 | + | 0.439100i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1791i | 0.957567i | 0.877933 | + | 0.478783i | \(0.158922\pi\) | ||||
−0.877933 | + | 0.478783i | \(0.841078\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.7289 | + | 7.22451i | 0.991891 | + | 0.667907i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.04951 | + | 0.957898i | 0.0962087 | + | 0.0878104i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.08056 | − | 8.79979i | −0.461869 | − | 0.799981i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.1341 | − | 8.05456i | 1.36459 | − | 0.726255i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.73798 | 0.864106 | 0.432053 | − | 0.901848i | \(-0.357789\pi\) | ||||
0.432053 | + | 0.901848i | \(0.357789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5698 | − | 6.68980i | 1.10671 | − | 0.589004i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.80008 | + | 15.2422i | 0.768867 | + | 1.33172i | 0.938178 | + | 0.346154i | \(0.112512\pi\) |
−0.169311 | + | 0.985563i | \(0.554154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.04355 | − | 3.28709i | −0.0904874 | − | 0.285027i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.02351 | + | 5.20973i | 0.770931 | + | 0.445097i | 0.833207 | − | 0.552962i | \(-0.186503\pi\) |
−0.0622758 | + | 0.998059i | \(0.519836\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.09182i | − | 0.601520i | −0.953700 | − | 0.300760i | \(-0.902760\pi\) | ||
0.953700 | − | 0.300760i | \(-0.0972403\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.37836 | − | 3.98216i | −0.537155 | − | 0.335359i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.97447 | + | 3.41989i | −0.165114 | + | 0.285986i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.1049 | + | 0.687078i | −0.998393 | + | 0.0566692i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.42586 | − | 3.13262i | 0.444504 | − | 0.256634i | −0.261003 | − | 0.965338i | \(-0.584053\pi\) |
0.705506 | + | 0.708704i | \(0.250720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.85578 | − | 15.3387i | 0.720673 | − | 1.24824i | −0.240057 | − | 0.970759i | \(-0.577166\pi\) |
0.960730 | − | 0.277484i | \(-0.0895006\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.707433 | + | 1.44757i | 0.0571926 | + | 0.117029i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.670256 | + | 0.386973i | 0.0534923 | + | 0.0308838i | 0.526508 | − | 0.850170i | \(-0.323501\pi\) |
−0.473015 | + | 0.881054i | \(0.656834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.40985 | − | 0.117735i | −0.270419 | − | 0.00933699i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.39625 | − | 20.1476i | −0.504095 | − | 1.58785i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.44352 | + | 5.96435i | 0.269717 | + | 0.467164i | 0.968789 | − | 0.247888i | \(-0.0797365\pi\) |
−0.699072 | + | 0.715052i | \(0.746403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.49709 | −0.734907 | −0.367453 | − | 0.930042i | \(-0.619770\pi\) | ||||
−0.367453 | + | 0.930042i | \(0.619770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.58930 | −0.429946 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.269723 | − | 3.90121i | 0.0206262 | − | 0.298333i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.97492 | + | 10.3489i | 0.454264 | + | 0.786809i | 0.998646 | − | 0.0520289i | \(-0.0165688\pi\) |
−0.544381 | + | 0.838838i | \(0.683235\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.855122 | − | 24.7661i | 0.0642749 | − | 1.86154i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.2343 | + | 9.37286i | 1.21341 | + | 0.700561i | 0.963500 | − | 0.267709i | \(-0.0862667\pi\) |
0.249907 | + | 0.968270i | \(0.419600\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1024i | 1.19688i | 0.801167 | + | 0.598441i | \(0.204213\pi\) | ||||
−0.801167 | + | 0.598441i | \(0.795787\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.88005 | + | 14.2235i | −0.656432 | + | 1.05143i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.425995 | + | 0.245948i | −0.0311519 | + | 0.0179855i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.0510 | − | 4.32112i | −0.949319 | − | 0.314315i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9979 | + | 8.65904i | −1.08521 | + | 0.626546i | −0.932297 | − | 0.361694i | \(-0.882199\pi\) |
−0.152912 | + | 0.988240i | \(0.548865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.56517 | + | 13.1033i | −0.544553 | + | 0.943193i | 0.454082 | + | 0.890960i | \(0.349967\pi\) |
−0.998635 | + | 0.0522332i | \(0.983366\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.6287i | 1.32724i | 0.748071 | + | 0.663619i | \(0.230980\pi\) | ||||
−0.748071 | + | 0.663619i | \(0.769020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.70283 | + | 5.02458i | 0.616927 | + | 0.356183i | 0.775672 | − | 0.631137i | \(-0.217411\pi\) |
−0.158745 | + | 0.987320i | \(0.550745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.723615 | + | 20.9574i | −0.0510398 | + | 1.47822i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.94517 | − | 1.96458i | −0.627828 | − | 0.137887i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.65321 | − | 23.9117i | 0.114906 | − | 1.66198i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.19389 | 0.0825830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.68592 | −0.116064 | −0.0580319 | − | 0.998315i | \(-0.518483\pi\) | ||||
−0.0580319 | + | 0.998315i | \(0.518483\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.768097 | + | 1.44321i | 0.0526292 | + | 0.0988874i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4532 | + | 12.5486i | −0.777495 | + | 0.851857i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.6983 | − | 0.611084i | −1.19594 | − | 0.0412933i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00533 | − | 1.15778i | −0.134893 | − | 0.0778806i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.2095i | 0.951541i | 0.879570 | + | 0.475770i | \(0.157831\pi\) | ||||
−0.879570 | + | 0.475770i | \(0.842169\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.340877 | − | 0.590416i | 0.0226248 | − | 0.0391873i | −0.854491 | − | 0.519466i | \(-0.826131\pi\) |
0.877116 | + | 0.480278i | \(0.159464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.56113 | − | 1.47867i | 0.169244 | − | 0.0977133i | −0.412985 | − | 0.910738i | \(-0.635514\pi\) |
0.582230 | + | 0.813024i | \(0.302181\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.04128 | − | 4.06598i | 0.0685110 | − | 0.267522i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.3282 | − | 13.4685i | 1.52828 | − | 0.882353i | 0.528847 | − | 0.848717i | \(-0.322625\pi\) |
0.999434 | − | 0.0336360i | \(-0.0107087\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.8025 | − | 10.4902i | −1.09144 | − | 0.681413i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 17.3461i | − | 1.12202i | −0.827808 | − | 0.561012i | \(-0.810412\pi\) | ||
0.827808 | − | 0.561012i | \(-0.189588\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.32282 | + | 0.763728i | 0.0852101 | + | 0.0491961i | 0.542000 | − | 0.840379i | \(-0.317667\pi\) |
−0.456790 | + | 0.889575i | \(0.651001\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.9611 | − | 9.99662i | −0.767304 | − | 0.641283i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.81006 | + | 4.86717i | 0.178800 | + | 0.309690i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.2997 | + | 7.61050i | −0.906208 | + | 0.482296i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.56268 | −0.414233 | −0.207116 | − | 0.978316i | \(-0.566408\pi\) | ||||
−0.207116 | + | 0.978316i | \(0.566408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.31771 | 0.460061 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.48645 | − | 14.6990i | −0.529370 | − | 0.916896i | −0.999413 | − | 0.0342527i | \(-0.989095\pi\) |
0.470043 | − | 0.882644i | \(-0.344238\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.7182 | − | 4.03764i | 0.790269 | − | 0.250887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.61379 | − | 5.80024i | −0.533180 | − | 0.359026i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.60699 | − | 2.65984i | −0.284079 | − | 0.164013i | 0.351190 | − | 0.936304i | \(-0.385777\pi\) |
−0.635269 | + | 0.772291i | \(0.719111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.56969 | − | 1.60432i | −0.157263 | − | 0.0981828i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.27834 | + | 5.67825i | −0.199884 | + | 0.346209i | −0.948491 | − | 0.316805i | \(-0.897390\pi\) |
0.748607 | + | 0.663014i | \(0.230723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.54171 | − | 2.62216i | 0.275889 | − | 0.159285i | −0.355672 | − | 0.934611i | \(-0.615748\pi\) |
0.631561 | + | 0.775326i | \(0.282415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.0268 | − | 5.32511i | 1.15155 | − | 0.322290i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.38663 | + | 2.40171i | −0.0833145 | + | 0.144305i | −0.904672 | − | 0.426109i | \(-0.859884\pi\) |
0.821357 | + | 0.570414i | \(0.193217\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.3080 | + | 8.45851i | −1.03620 | + | 0.506398i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.4373i | − | 1.33850i | −0.743038 | − | 0.669250i | \(-0.766616\pi\) | ||
0.743038 | − | 0.669250i | \(-0.233384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.27592 | + | 3.62340i | 0.373064 | + | 0.215389i | 0.674796 | − | 0.738004i | \(-0.264231\pi\) |
−0.301732 | + | 0.953393i | \(0.597565\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.61762 | − | 25.5783i | 0.331598 | − | 1.50984i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.35578 | + | 14.4726i | 0.491517 | + | 0.851332i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.77578 | + | 16.4892i | 0.514445 | + | 0.966616i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.1686 | −1.52879 | −0.764393 | − | 0.644750i | \(-0.776961\pi\) | ||||
−0.764393 | + | 0.644750i | \(0.776961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.79284 | − | 3.85355i | 0.162057 | − | 0.223605i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.2237 | + | 29.8324i | 0.996073 | + | 1.72525i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.66578 | − | 21.2443i | 0.268931 | − | 1.22450i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.588695 | − | 17.0498i | 0.0338196 | − | 0.979488i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.4144i | 1.27926i | 0.768683 | + | 0.639630i | \(0.220912\pi\) | ||||
−0.768683 | + | 0.639630i | \(0.779088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.25459 | + | 3.61125i | −0.128259 | + | 0.205437i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.81378 | + | 16.9980i | −0.556488 | + | 0.963866i | 0.441298 | + | 0.897361i | \(0.354518\pi\) |
−0.997786 | + | 0.0665052i | \(0.978815\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.1139 | − | 6.41664i | 0.628197 | − | 0.362690i | −0.151856 | − | 0.988403i | \(-0.548525\pi\) |
0.780054 | + | 0.625713i | \(0.215192\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.8295 | + | 7.98449i | −0.776745 | + | 0.448454i | −0.835275 | − | 0.549832i | \(-0.814692\pi\) |
0.0585306 | + | 0.998286i | \(0.481358\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.58522 | − | 2.74568i | 0.0887552 | − | 0.153728i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.37557 | + | 2.20329i | −0.0767766 | + | 0.122976i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.700065i | 0.0389526i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.230976 | + | 6.68956i | −0.0127730 | + | 0.369934i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.9476 | + | 3.47553i | −0.603561 | + | 0.191612i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.81888 | + | 17.0068i | 0.539694 | + | 0.934778i | 0.998920 | + | 0.0464584i | \(0.0147935\pi\) |
−0.459226 | + | 0.888319i | \(0.651873\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.0943 | + | 1.04359i | 0.827163 | + | 0.0571885i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.304237 | −0.0165729 | −0.00828643 | − | 0.999966i | \(-0.502638\pi\) | ||||
−0.00828643 | + | 0.999966i | \(0.502638\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.28321 | + | 15.5637i | 0.449882 | + | 0.845305i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.94071 | − | 5.09346i | −0.159249 | − | 0.275827i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.1872 | + | 14.7596i | −0.604053 | + | 0.796944i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.6358 | + | 14.2235i | 1.32252 | + | 0.763556i | 0.984130 | − | 0.177451i | \(-0.0567851\pi\) |
0.338388 | + | 0.941007i | \(0.390118\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.9719i | 0.747897i | 0.927450 | + | 0.373948i | \(0.121996\pi\) | ||||
−0.927450 | + | 0.373948i | \(0.878004\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.2834 | + | 2.31556i | 1.18940 | + | 0.123595i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.3018 | − | 29.9676i | 0.920881 | − | 1.59501i | 0.122826 | − | 0.992428i | \(-0.460804\pi\) |
0.798055 | − | 0.602585i | \(-0.205862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.38418 | + | 0.610577i | 0.126184 | + | 0.0323152i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.8260 | + | 11.4465i | −1.04638 | + | 0.604126i | −0.921633 | − | 0.388064i | \(-0.873144\pi\) |
−0.124743 | + | 0.992189i | \(0.539811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.65043 | + | 14.9830i | −0.455286 | + | 0.788578i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.9289 | − | 9.32050i | −0.783566 | − | 0.489199i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.1145 | + | 14.4999i | 1.31097 | + | 0.756887i | 0.982256 | − | 0.187543i | \(-0.0600525\pi\) |
0.328711 | + | 0.944431i | \(0.393386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.5855 | − | 24.6307i | 0.863406 | − | 1.28222i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.51341 | + | 3.84944i | −0.182407 | + | 0.199853i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0154 | − | 20.8113i | −0.622136 | − | 1.07757i | −0.989087 | − | 0.147331i | \(-0.952932\pi\) |
0.366952 | − | 0.930240i | \(-0.380401\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.9245 | 0.768652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0820 | 0.723342 | 0.361671 | − | 0.932306i | \(-0.382206\pi\) | ||||
0.361671 | + | 0.932306i | \(0.382206\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.8893 | − | 7.92427i | 0.762801 | − | 0.405972i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.7015 | + | 25.4637i | 0.751211 | + | 1.30114i | 0.947236 | + | 0.320537i | \(0.103863\pi\) |
−0.196025 | + | 0.980599i | \(0.562803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.7753 | − | 20.4573i | 0.700236 | − | 1.03990i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.2730 | − | 11.7046i | −1.02788 | − | 0.593448i | −0.111504 | − | 0.993764i | \(-0.535567\pi\) |
−0.916377 | + | 0.400316i | \(0.868900\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.29091i | 0.217001i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.8586 | + | 16.1441i | 1.30439 | + | 0.814363i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3384 | + | 5.96889i | −0.518871 | + | 0.299570i | −0.736473 | − | 0.676467i | \(-0.763510\pi\) |
0.217602 | + | 0.976038i | \(0.430177\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.27045 | − | 4.17674i | −0.213790 | − | 0.209099i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.6844 | + | 12.5195i | −1.08287 | + | 0.625193i | −0.931668 | − | 0.363311i | \(-0.881646\pi\) |
−0.151198 | + | 0.988504i | \(0.548313\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.8431 | − | 23.9770i | 0.689575 | − | 1.19438i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.61931i | 0.228971i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.1378 | − | 15.0906i | −1.29243 | − | 0.746184i | −0.313345 | − | 0.949640i | \(-0.601449\pi\) |
−0.979084 | + | 0.203455i | \(0.934783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0363 | + | 0.622754i | 0.889664 | + | 0.0307182i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.9589 | − | 25.5183i | −1.37577 | − | 1.25567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.77096 | − | 10.8433i | −0.282605 | − | 0.531000i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.85560 | −0.481477 | −0.240739 | − | 0.970590i | \(-0.577390\pi\) | ||||
−0.240739 | + | 0.970590i | \(0.577390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.16112 | −0.397749 | −0.198874 | − | 0.980025i | \(-0.563729\pi\) | ||||
−0.198874 | + | 0.980025i | \(0.563729\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.9929 | − | 0.898308i | −0.631738 | − | 0.0436772i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.75029 | + | 24.4127i | 0.375063 | + | 1.18141i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.236022 | + | 6.83571i | −0.0113953 | + | 0.330031i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.84702 | + | 1.64373i | 0.137136 | + | 0.0791755i | 0.566998 | − | 0.823719i | \(-0.308105\pi\) |
−0.429862 | + | 0.902894i | \(0.641438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.9717i | 1.53646i | 0.640173 | + | 0.768231i | \(0.278863\pi\) | ||||
−0.640173 | + | 0.768231i | \(0.721137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.20726 | − | 9.01924i | 0.249097 | − | 0.431449i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.1217 | + | 20.8549i | −1.72399 | + | 0.995349i | −0.813827 | + | 0.581107i | \(0.802620\pi\) |
−0.910167 | + | 0.414242i | \(0.864047\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.9491 | + | 10.9009i | −0.854720 | + | 0.519089i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.4179 | − | 9.47885i | 0.780036 | − | 0.450354i | −0.0564073 | − | 0.998408i | \(-0.517965\pi\) |
0.836443 | + | 0.548054i | \(0.184631\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.74692 | − | 9.20503i | 0.271820 | − | 0.435383i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.0091i | 1.88815i | 0.329737 | + | 0.944073i | \(0.393040\pi\) | ||||
−0.329737 | + | 0.944073i | \(0.606960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.85112 | + | 4.53285i | 0.369695 | + | 0.213444i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.05859 | − | 30.6591i | 0.0497370 | − | 1.44049i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.69340 | + | 9.86127i | 0.266326 | + | 0.461291i | 0.967910 | − | 0.251296i | \(-0.0808568\pi\) |
−0.701584 | + | 0.712587i | \(0.747523\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.25962 | + | 1.63765i | 0.105470 | + | 0.0764388i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.71020 | 0.405674 | 0.202837 | − | 0.979212i | \(-0.434984\pi\) | ||||
0.202837 | + | 0.979212i | \(0.434984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.1154 | 0.748944 | 0.374472 | − | 0.927238i | \(-0.377824\pi\) | ||||
0.374472 | + | 0.927238i | \(0.377824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.55236 | + | 7.88492i | 0.210658 | + | 0.364870i | 0.951921 | − | 0.306345i | \(-0.0991060\pi\) |
−0.741263 | + | 0.671215i | \(0.765773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.6592 | + | 21.5939i | 1.09248 | + | 0.997113i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.33971 | + | 0.0462575i | 0.0617308 | + | 0.00213143i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.52084 | + | 3.76481i | 0.299828 | + | 0.173106i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.30944 | + | 2.59475i | −0.243103 | + | 0.118805i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.2092 | + | 22.8791i | −0.603546 | + | 1.04537i | 0.388733 | + | 0.921350i | \(0.372913\pi\) |
−0.992279 | + | 0.124022i | \(0.960421\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.8317 | + | 10.8725i | −0.858652 | + | 0.495743i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.1749 | − | 25.6005i | −1.19100 | − | 1.16486i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.58065 | − | 7.93392i | 0.207569 | − | 0.359520i | −0.743379 | − | 0.668870i | \(-0.766778\pi\) |
0.950948 | + | 0.309350i | \(0.100111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.1186 | + | 6.31727i | 0.457578 | + | 0.285677i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0800i | 1.49288i | 0.665453 | + | 0.746440i | \(0.268239\pi\) | ||||
−0.665453 | + | 0.746440i | \(0.731761\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.60999 | + | 0.929529i | 0.0725104 | + | 0.0418639i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.43919 | + | 0.535707i | 0.109413 | + | 0.0240297i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.54365 | + | 14.7980i | 0.382466 | + | 0.662451i | 0.991414 | − | 0.130759i | \(-0.0417414\pi\) |
−0.608948 | + | 0.793210i | \(0.708408\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.5210 | + | 7.72824i | −0.648749 | + | 0.345272i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.1753 | −0.944158 | −0.472079 | − | 0.881556i | \(-0.656496\pi\) | ||||
−0.472079 | + | 0.881556i | \(0.656496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.54599 | + | 4.54828i | −0.379541 | + | 0.201996i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.5918 | − | 27.0059i | −0.691096 | − | 1.19701i | −0.971479 | − | 0.237125i | \(-0.923795\pi\) |
0.280383 | − | 0.959888i | \(-0.409539\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.2358 | + | 19.9799i | −0.806704 | + | 0.883859i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.76220 | − | 6.18441i | −0.121954 | − | 0.273048i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.97623i | − | 0.174874i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.5570 | + | 10.9612i | 0.770665 | + | 0.481145i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.4555 | − | 33.6980i | 0.852363 | − | 1.47634i | −0.0267070 | − | 0.999643i | \(-0.508502\pi\) |
0.879070 | − | 0.476693i | \(-0.158165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.25839 | + | 1.88123i | −0.142480 | + | 0.0822606i | −0.569545 | − | 0.821960i | \(-0.692881\pi\) |
0.427066 | + | 0.904221i | \(0.359547\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.98667 | − | 1.72436i | 0.130101 | − | 0.0751141i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.4169 | − | 35.3631i | 0.887692 | − | 1.53753i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.8459 | − | 38.5630i | −0.817844 | − | 1.67349i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.6759i | 1.84850i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.4492 | + | 1.12040i | 1.40029 | + | 0.0483489i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.69809 | − | 5.23730i | −0.159288 | − | 0.225586i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.6223 | − | 23.5945i | −0.585667 | − | 1.01440i | −0.994792 | − | 0.101927i | \(-0.967499\pi\) |
0.409125 | − | 0.912478i | \(-0.365834\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.1033 | + | 24.6204i | 0.562316 | + | 1.05656i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4516 | −0.575148 | −0.287574 | − | 0.957758i | \(-0.592849\pi\) | ||||
−0.287574 | + | 0.957758i | \(0.592849\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00319 | + | 28.9737i | −0.0854939 | + | 1.23657i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.25607 | − | 3.90763i | −0.0961119 | − | 0.166471i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.8393 | + | 9.15561i | −1.22637 | + | 0.389336i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.5776 | − | 18.8087i | −1.38036 | − | 0.796950i | −0.388156 | − | 0.921594i | \(-0.626888\pi\) |
−0.992202 | + | 0.124644i | \(0.960221\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.4449i | 1.49916i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.451203 | + | 0.722706i | −0.0190498 | + | 0.0305127i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.08942 | − | 8.81514i | 0.214494 | − | 0.371514i | −0.738622 | − | 0.674120i | \(-0.764523\pi\) |
0.953116 | + | 0.302606i | \(0.0978566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.4711 | + | 4.01327i | −0.985695 | + | 0.168541i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.744706 | + | 0.429956i | −0.0312197 | + | 0.0180247i | −0.515529 | − | 0.856872i | \(-0.672404\pi\) |
0.484309 | + | 0.874897i | \(0.339071\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.71817 | + | 2.97596i | −0.0719032 | + | 0.124540i | −0.899735 | − | 0.436436i | \(-0.856241\pi\) |
0.827832 | + | 0.560976i | \(0.189574\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.8854 | + | 25.4441i | −0.663620 | + | 1.06294i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.2565 | − | 12.8498i | −0.926550 | − | 0.534944i | −0.0408310 | − | 0.999166i | \(-0.513001\pi\) |
−0.885719 | + | 0.464222i | \(0.846334\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.904316 | + | 26.1909i | −0.0375821 | + | 1.08846i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.30792 | + | 24.1681i | −0.220210 | + | 1.00266i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.902098 | − | 1.56248i | −0.0373611 | − | 0.0647113i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.5090 | −0.929048 | −0.464524 | − | 0.885561i | \(-0.653775\pi\) | ||||
−0.464524 | + | 0.885561i | \(0.653775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.37041 | −0.344897 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.1591 | + | 28.4831i | 0.623560 | + | 1.17164i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8863 | + | 20.5878i | 0.488114 | + | 0.845438i | 0.999907 | − | 0.0136712i | \(-0.00435181\pi\) |
−0.511793 | + | 0.859109i | \(0.671018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.3953 | + | 0.600622i | 0.711942 | + | 0.0245818i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.6990 | − | 21.7655i | −1.54034 | − | 0.889314i | −0.998817 | − | 0.0486270i | \(-0.984515\pi\) |
−0.541521 | − | 0.840687i | \(-0.682151\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.9347i | − | 0.813153i | −0.913617 | − | 0.406577i | \(-0.866722\pi\) | ||
0.913617 | − | 0.406577i | \(-0.133278\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.9477 | + | 32.6325i | 0.649439 | + | 1.32890i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.20867 | + | 5.31663i | −0.373768 | + | 0.215795i | −0.675103 | − | 0.737723i | \(-0.735901\pi\) |
0.301335 | + | 0.953518i | \(0.402568\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.2758 | + | 4.27529i | −0.619005 | + | 0.173244i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.2100 | − | 9.35886i | 0.655788 | − | 0.378619i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.56721 | − | 13.1068i | 0.305637 | − | 0.529378i | −0.671766 | − | 0.740763i | \(-0.734464\pi\) |
0.977403 | + | 0.211385i | \(0.0677974\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.39865i | 0.297858i | 0.988848 | + | 0.148929i | \(0.0475826\pi\) | ||||
−0.988848 | + | 0.148929i | \(0.952417\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0456 | − | 9.26396i | −0.644929 | − | 0.372350i | 0.141582 | − | 0.989927i | \(-0.454781\pi\) |
−0.786511 | + | 0.617577i | \(0.788115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.9304 | − | 37.9061i | −0.679394 | − | 1.52112i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.41053 | + | 1.40021i | −0.176704 | + | 0.0560983i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.82545 | − | 0.971526i | 0.0729013 | − | 0.0387990i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.70864 | −0.108001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1786 | 0.524632 | 0.262316 | − | 0.964982i | \(-0.415514\pi\) | ||||
0.262316 | + | 0.964982i | \(0.415514\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.57776 | + | 1.37192i | −0.102457 | + | 0.0545288i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6469 | − | 27.4032i | 0.501087 | − | 1.08575i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.34883 | + | 1.58162i | 0.0929182 | + | 0.0625681i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2389 | + | 7.06611i | 0.483406 | + | 0.279094i | 0.721835 | − | 0.692065i | \(-0.243299\pi\) |
−0.238429 | + | 0.971160i | \(0.576632\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.9278i | 0.707005i | 0.935434 | + | 0.353503i | \(0.115009\pi\) | ||||
−0.935434 | + | 0.353503i | \(0.884991\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0026 | + | 20.7892i | −0.471872 | + | 0.817306i | −0.999482 | − | 0.0321804i | \(-0.989755\pi\) |
0.527610 | + | 0.849487i | \(0.323088\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3485 | − | 6.55204i | 0.445466 | − | 0.257190i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.30044 | + | 28.5068i | −0.286127 | + | 1.11727i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.0705 | − | 14.4745i | 0.981085 | − | 0.566430i | 0.0784876 | − | 0.996915i | \(-0.474991\pi\) |
0.902598 | + | 0.430485i | \(0.141658\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.5578 | + | 13.4676i | −1.07513 | + | 0.525422i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.09127i | − | 0.198328i | −0.995071 | − | 0.0991638i | \(-0.968383\pi\) | ||
0.995071 | − | 0.0991638i | \(-0.0316168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.1768 | + | 14.5358i | 0.979264 | + | 0.565378i | 0.902048 | − | 0.431636i | \(-0.142064\pi\) |
0.0772160 | + | 0.997014i | \(0.475397\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.00827 | − | 0.138397i | −0.155669 | − | 0.00537490i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8282 | − | 23.9511i | −0.535429 | − | 0.927389i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.5630 | + | 21.7262i | 0.447051 | + | 0.839985i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.86682 | −0.342300 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.51862 | 0.328369 | 0.164184 | − | 0.986430i | \(-0.447501\pi\) | ||||
0.164184 | + | 0.986430i | \(0.447501\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.48823 | − | 16.4341i | −0.364662 | − | 0.631614i | 0.624060 | − | 0.781377i | \(-0.285482\pi\) |
−0.988722 | + | 0.149763i | \(0.952149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.8686 | + | 6.12064i | 1.06950 | + | 0.234889i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0407473 | − | 1.18013i | 0.00156144 | − | 0.0452226i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.1149 | + | 10.4587i | 0.693149 | + | 0.400190i | 0.804791 | − | 0.593559i | \(-0.202278\pi\) |
−0.111642 | + | 0.993749i | \(0.535611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.71268 | − | 4.34499i | 0.103495 | − | 0.165772i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.24654 | − | 7.35523i | 0.161780 | − | 0.280212i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.4902 | − | 17.0261i | 1.12186 | − | 0.647705i | 0.179984 | − | 0.983670i | \(-0.442396\pi\) |
0.941875 | + | 0.335964i | \(0.109062\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.71659 | − | 7.06419i | −0.0652077 | − | 0.268346i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.65794 | + | 4.60369i | −0.100677 | + | 0.174377i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.7086 | − | 39.5766i | 0.934565 | − | 1.49692i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.9758i | 0.716706i | 0.933586 | + | 0.358353i | \(0.116662\pi\) | ||||
−0.933586 | + | 0.358353i | \(0.883338\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.69340 | + | 3.28709i | 0.214731 | + | 0.123975i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.2479 | − | 17.5676i | −0.723890 | − | 0.660699i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.53691 | + | 2.66200i | 0.0577197 | + | 0.0999735i | 0.893441 | − | 0.449180i | \(-0.148284\pi\) |
−0.835722 | + | 0.549153i | \(0.814950\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.2273 | − | 2.36641i | −1.28362 | − | 0.0887475i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −51.3048 | −1.92138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.1153 | − | 26.5220i | −0.527147 | − | 0.990482i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.70106 | + | 11.6066i | 0.249907 | + | 0.432852i | 0.963500 | − | 0.267709i | \(-0.0862665\pi\) |
−0.713593 | + | 0.700561i | \(0.752933\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.96775 | + | 6.19823i | 0.0732829 | + | 0.230834i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.64406 | + | 0.0912936i | 0.0983335 | + | 0.00339525i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.88627i | 0.181222i | 0.995886 | + | 0.0906109i | \(0.0288820\pi\) | ||||
−0.995886 | + | 0.0906109i | \(0.971118\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.4231 | − | 5.55142i | −0.978634 | − | 0.205608i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.20758 | + | 3.82364i | −0.0816504 | + | 0.141423i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.0351 | + | 18.4955i | −1.18324 | + | 0.683145i | −0.956762 | − | 0.290871i | \(-0.906055\pi\) |
−0.226480 | + | 0.974016i | \(0.572722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.60321 | + | 5.54441i | −0.353739 | + | 0.204231i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.9759 | − | 32.8672i | 0.698040 | − | 1.20904i | −0.271105 | − | 0.962550i | \(-0.587389\pi\) |
0.969145 | − | 0.246491i | \(-0.0792777\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.25721 | + | 5.15517i | 0.303336 | + | 0.189380i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.0878i | 0.516830i | 0.966034 | + | 0.258415i | \(0.0832003\pi\) | ||||
−0.966034 | + | 0.258415i | \(0.916800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.6711 | + | 23.2728i | −0.573376 | + | 0.851506i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.20056 | + | 3.78165i | 0.0438675 | + | 0.138178i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8752 | + | 22.3005i | 0.469823 | + | 0.813757i | 0.999405 | − | 0.0345016i | \(-0.0109844\pi\) |
−0.529582 | + | 0.848259i | \(0.677651\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.0343 | + | 5.34037i | −0.365669 | + | 0.194614i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.3111 | 1.46513 | 0.732565 | − | 0.680697i | \(-0.238323\pi\) | ||||
0.732565 | + | 0.680697i | \(0.238323\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.1887 | − | 5.95478i | 0.406125 | − | 0.216145i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.76529 | − | 16.9140i | −0.353991 | − | 0.613131i | 0.632953 | − | 0.774190i | \(-0.281842\pi\) |
−0.986945 | + | 0.161059i | \(0.948509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.55196 | + | 6.89272i | 0.273399 | + | 0.249533i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.4218 | + | 30.8431i | 1.92895 | + | 1.11368i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.6475i | 1.71821i | 0.511797 | + | 0.859107i | \(0.328980\pi\) | ||||
−0.511797 | + | 0.859107i | \(0.671020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9370 | − | 15.5687i | −0.898083 | − | 0.560695i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.5624 | + | 18.2945i | −0.379901 | + | 0.658009i | −0.991048 | − | 0.133509i | \(-0.957375\pi\) |
0.611146 | + | 0.791518i | \(0.290709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.1603 | − | 16.5229i | 0.579749 | − | 0.592756i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.1737 | − | 6.45112i | 0.400338 | − | 0.231135i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.432261 | + | 0.748698i | −0.0154675 | + | 0.0267905i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.8903 | − | 1.85906i | −0.639349 | − | 0.0664373i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.66953 | − | 3.27330i | −0.202097 | − | 0.116681i | 0.395536 | − | 0.918450i | \(-0.370559\pi\) |
−0.597633 | + | 0.801770i | \(0.703892\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.20848 | − | 0.317949i | −0.327831 | − | 0.0113193i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.3044 | + | 5.77709i | 0.935276 | + | 0.205410i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.8699 | − | 36.1477i | −0.741110 | − | 1.28364i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.50728 | −0.230500 | −0.115250 | − | 0.993337i | \(-0.536767\pi\) | ||||
−0.115250 | + | 0.993337i | \(0.536767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.33156 | 0.0824845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.23455 | − | 0.361907i | −0.184954 | − | 0.0127874i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.68219 | − | 8.10980i | −0.165231 | − | 0.286189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.391882 | + | 11.3497i | −0.0137949 | + | 0.399530i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.41519 | + | 0.817063i | 0.0497556 | + | 0.0287264i | 0.524671 | − | 0.851305i | \(-0.324188\pi\) |
−0.474916 | + | 0.880031i | \(0.657522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29.4411i | − | 1.03382i | −0.856041 | − | 0.516909i | \(-0.827083\pi\) | ||
0.856041 | − | 0.516909i | \(-0.172917\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.81045 | − | 7.70506i | 0.168710 | − | 0.270228i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.28042 | − | 5.35805i | 0.324681 | − | 0.187454i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.7585 | − | 23.6251i | 0.865131 | − | 0.825526i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6357 | − | 11.3367i | 0.685292 | − | 0.395654i | −0.116554 | − | 0.993184i | \(-0.537185\pi\) |
0.801846 | + | 0.597531i | \(0.203851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.59438 | + | 16.6180i | −0.334439 | + | 0.579266i | −0.983377 | − | 0.181576i | \(-0.941880\pi\) |
0.648938 | + | 0.760841i | \(0.275214\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.5074i | 1.13039i | 0.824957 | + | 0.565196i | \(0.191200\pi\) | ||||
−0.824957 | + | 0.565196i | \(0.808800\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.7613 | − | 25.8429i | −1.55462 | − | 0.897563i | −0.997756 | − | 0.0669618i | \(-0.978669\pi\) |
−0.556868 | − | 0.830601i | \(-0.687997\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.165753 | + | 4.80057i | −0.00574992 | + | 0.166530i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.07101 | − | 2.16846i | 0.106404 | − | 0.0751327i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.5807 | + | 27.0174i | −0.676809 | + | 0.933857i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.88841 | −0.0997192 | −0.0498596 | − | 0.998756i | \(-0.515877\pi\) | ||||
−0.0498596 | + | 0.998756i | \(0.515877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0178 | 0.586819 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.2584 | − | 34.3065i | −0.628851 | − | 1.18158i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.6235 | + | 8.13470i | −0.880435 | + | 0.279512i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.5444 | + | 0.433130i | 0.430521 | + | 0.0148650i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.8966 | + | 20.1476i | 1.19624 | + | 0.690650i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 49.3673i | − | 1.69031i | −0.534525 | − | 0.845153i | \(-0.679509\pi\) | ||
0.534525 | − | 0.845153i | \(-0.320491\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.75185 | − | 15.1586i | 0.298957 | − | 0.517809i | −0.676940 | − | 0.736038i | \(-0.736694\pi\) |
0.975898 | + | 0.218228i | \(0.0700278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.23153 | − | 3.02042i | 0.178497 | − | 0.103056i | −0.408089 | − | 0.912942i | \(-0.633805\pi\) |
0.586586 | + | 0.809887i | \(0.300471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.2250 | − | 43.6803i | −0.416626 | − | 1.48862i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.4595 | − | 17.0085i | 1.00281 | − | 0.578975i | 0.0937342 | − | 0.995597i | \(-0.470120\pi\) |
0.909080 | + | 0.416622i | \(0.136786\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.5530 | + | 15.3290i | 0.833864 | + | 0.520601i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.4746i | − | 0.355326i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.2062 | − | 26.0998i | −1.53175 | − | 0.884358i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26.8362 | + | 18.0706i | 0.908267 | + | 0.611597i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.62002 | + | 6.27005i | 0.122239 | + | 0.211725i | 0.920650 | − | 0.390388i | \(-0.127659\pi\) |
−0.798411 | + | 0.602113i | \(0.794326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.0116 | + | 21.2947i | −1.34956 | + | 0.718252i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.9119 | −0.872993 | −0.436496 | − | 0.899706i | \(-0.643781\pi\) | ||||
−0.436496 | + | 0.899706i | \(0.643781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.5664 | 0.591155 | 0.295577 | − | 0.955319i | \(-0.404488\pi\) | ||||
0.295577 | + | 0.955319i | \(0.404488\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.38392 | − | 12.7893i | −0.247928 | − | 0.429423i | 0.715023 | − | 0.699101i | \(-0.246416\pi\) |
−0.962951 | + | 0.269678i | \(0.913083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.52675 | − | 25.1645i | 0.185361 | − | 0.843990i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.13441 | − | 8.16471i | 0.0380041 | − | 0.273528i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.90079 | − | 2.82947i | −0.163999 | − | 0.0946847i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 50.6110 | + | 31.5976i | 1.68985 | + | 1.05501i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.1140 | + | 19.2501i | −0.370674 | + | 0.642026i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.916197 | − | 0.528966i | 0.0305229 | − | 0.0176224i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.1536 | − | 36.2791i | −0.337890 | − | 1.20729i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.6622 | − | 25.3957i | 0.486851 | − | 0.843250i | −0.513035 | − | 0.858368i | \(-0.671479\pi\) |
0.999886 | + | 0.0151176i | \(0.00481225\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.9742 | − | 26.5481i | −0.430326 | − | 0.880545i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 30.3043i | − | 1.00403i | −0.864860 | − | 0.502013i | \(-0.832593\pi\) | ||
0.864860 | − | 0.502013i | \(-0.167407\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.41828 | − | 4.28295i | −0.245509 | − | 0.141745i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.3827 | − | 14.0902i | 1.46565 | − | 0.465299i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.81888 | − | 6.61449i | −0.125973 | − | 0.218192i | 0.796140 | − | 0.605113i | \(-0.206872\pi\) |
−0.922113 | + | 0.386921i | \(0.873539\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.2397 | + | 34.2715i | 0.601019 | + | 1.12928i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.06965 | −0.133954 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.508597 | + | 7.35624i | −0.0167045 | + | 0.241611i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.62508 | − | 14.9391i | −0.282980 | − | 0.490135i | 0.689138 | − | 0.724631i | \(-0.257990\pi\) |
−0.972117 | + | 0.234495i | \(0.924656\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.08663 | + | 0.831132i | −0.297802 | + | 0.0272393i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.17311 | + | 33.9757i | −0.0384058 | + | 1.11231i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.0492i | 1.17768i | 0.808251 | + | 0.588839i | \(0.200415\pi\) | ||||
−0.808251 | + | 0.588839i | \(0.799585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.7716 | − | 18.8549i | 0.384151 | − | 0.615308i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.8153 | + | 27.3930i | −0.515565 | + | 0.892985i | 0.484272 | + | 0.874918i | \(0.339085\pi\) |
−0.999837 | + | 0.0180673i | \(0.994249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 68.4869 | − | 39.5409i | 2.23024 | − | 1.28763i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.1757 | − | 20.3087i | 1.14306 | − | 0.659944i | 0.195871 | − | 0.980630i | \(-0.437247\pi\) |
0.947186 | + | 0.320685i | \(0.103913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.0410 | − | 38.1761i | 0.715481 | − | 1.23925i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.6479 | + | 23.4620i | −0.474990 | + | 0.760807i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.31938i | 0.172312i | 0.996282 | + | 0.0861558i | \(0.0274583\pi\) | ||||
−0.996282 | + | 0.0861558i | \(0.972542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.189492 | − | 5.48808i | 0.00612540 | − | 0.177405i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.5840 | − | 20.3615i | 0.600110 | − | 0.657506i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.11747 | + | 8.86371i | 0.165080 | + | 0.285926i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.310304 | + | 4.48817i | −0.00999941 | + | 0.144629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.75930 | −0.217364 | −0.108682 | − | 0.994077i | \(-0.534663\pi\) | ||||
−0.108682 | + | 0.994077i | \(0.534663\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.569677 | + | 1.07039i | 0.0183007 | + | 0.0343860i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.9851 | − | 38.0793i | −0.705535 | − | 1.22202i | −0.966498 | − | 0.256674i | \(-0.917373\pi\) |
0.260963 | − | 0.965349i | \(-0.415960\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3264 | − | 4.02493i | −0.587517 | − | 0.129033i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.00974 | − | 4.62443i | −0.256254 | − | 0.147949i | 0.366370 | − | 0.930469i | \(-0.380600\pi\) |
−0.622625 | + | 0.782521i | \(0.713934\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.60193i | − | 0.0511979i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.09046 | + | 10.4162i | 0.162526 | + | 0.332565i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.56947 | − | 11.3787i | 0.209533 | − | 0.362923i | −0.742034 | − | 0.670362i | \(-0.766139\pi\) |
0.951568 | + | 0.307439i | \(0.0994722\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.9106 | + | 14.2227i | −0.442778 | + | 0.452712i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.8825 | − | 32.8411i | 1.80876 | − | 1.04429i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.18520 | − | 5.51694i | 0.101181 | − | 0.175251i | −0.810990 | − | 0.585060i | \(-0.801071\pi\) |
0.912172 | + | 0.409808i | \(0.134404\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.8522 | + | 18.0131i | 0.915598 | + | 0.571630i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.3595 | − | 11.7546i | −0.644792 | − | 0.372271i | 0.141666 | − | 0.989915i | \(-0.454754\pi\) |
−0.786458 | + | 0.617644i | \(0.788087\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.9283 | − | 10.6873i | 0.757057 | − | 0.338132i |
(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 | 2100.2.bi.n.101.14 | 32 | ||
3.2 | odd | 2 | inner | 2100.2.bi.n.101.9 | 32 | ||
5.2 | odd | 4 | 420.2.bn.a.269.6 | yes | 32 | ||
5.3 | odd | 4 | 420.2.bn.a.269.11 | yes | 32 | ||
5.4 | even | 2 | inner | 2100.2.bi.n.101.3 | 32 | ||
7.5 | odd | 6 | inner | 2100.2.bi.n.1601.9 | 32 | ||
15.2 | even | 4 | 420.2.bn.a.269.16 | yes | 32 | ||
15.8 | even | 4 | 420.2.bn.a.269.1 | yes | 32 | ||
15.14 | odd | 2 | inner | 2100.2.bi.n.101.8 | 32 | ||
21.5 | even | 6 | inner | 2100.2.bi.n.1601.14 | 32 | ||
35.3 | even | 12 | 2940.2.f.a.1469.12 | 32 | |||
35.12 | even | 12 | 420.2.bn.a.89.1 | ✓ | 32 | ||
35.17 | even | 12 | 2940.2.f.a.1469.22 | 32 | |||
35.18 | odd | 12 | 2940.2.f.a.1469.21 | 32 | |||
35.19 | odd | 6 | inner | 2100.2.bi.n.1601.8 | 32 | ||
35.32 | odd | 12 | 2940.2.f.a.1469.11 | 32 | |||
35.33 | even | 12 | 420.2.bn.a.89.16 | yes | 32 | ||
105.17 | odd | 12 | 2940.2.f.a.1469.23 | 32 | |||
105.32 | even | 12 | 2940.2.f.a.1469.10 | 32 | |||
105.38 | odd | 12 | 2940.2.f.a.1469.9 | 32 | |||
105.47 | odd | 12 | 420.2.bn.a.89.11 | yes | 32 | ||
105.53 | even | 12 | 2940.2.f.a.1469.24 | 32 | |||
105.68 | odd | 12 | 420.2.bn.a.89.6 | yes | 32 | ||
105.89 | even | 6 | inner | 2100.2.bi.n.1601.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bn.a.89.1 | ✓ | 32 | 35.12 | even | 12 | ||
420.2.bn.a.89.6 | yes | 32 | 105.68 | odd | 12 | ||
420.2.bn.a.89.11 | yes | 32 | 105.47 | odd | 12 | ||
420.2.bn.a.89.16 | yes | 32 | 35.33 | even | 12 | ||
420.2.bn.a.269.1 | yes | 32 | 15.8 | even | 4 | ||
420.2.bn.a.269.6 | yes | 32 | 5.2 | odd | 4 | ||
420.2.bn.a.269.11 | yes | 32 | 5.3 | odd | 4 | ||
420.2.bn.a.269.16 | yes | 32 | 15.2 | even | 4 | ||
2100.2.bi.n.101.3 | 32 | 5.4 | even | 2 | inner | ||
2100.2.bi.n.101.8 | 32 | 15.14 | odd | 2 | inner | ||
2100.2.bi.n.101.9 | 32 | 3.2 | odd | 2 | inner | ||
2100.2.bi.n.101.14 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.bi.n.1601.3 | 32 | 105.89 | even | 6 | inner | ||
2100.2.bi.n.1601.8 | 32 | 35.19 | odd | 6 | inner | ||
2100.2.bi.n.1601.9 | 32 | 7.5 | odd | 6 | inner | ||
2100.2.bi.n.1601.14 | 32 | 21.5 | even | 6 | inner | ||
2940.2.f.a.1469.9 | 32 | 105.38 | odd | 12 | |||
2940.2.f.a.1469.10 | 32 | 105.32 | even | 12 | |||
2940.2.f.a.1469.11 | 32 | 35.32 | odd | 12 | |||
2940.2.f.a.1469.12 | 32 | 35.3 | even | 12 | |||
2940.2.f.a.1469.21 | 32 | 35.18 | odd | 12 | |||
2940.2.f.a.1469.22 | 32 | 35.17 | even | 12 | |||
2940.2.f.a.1469.23 | 32 | 105.17 | odd | 12 | |||
2940.2.f.a.1469.24 | 32 | 105.53 | even | 12 |