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 | 101.9 | ||
Character | \(\chi\) | \(=\) | 2100.101 |
Dual form | 2100.2.bi.n.1601.9 |
$q$-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 | ||||||||
\(3\) | 0.0597684 | + | 1.73102i | 0.0345073 | + | 0.999404i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.567546 | − | 2.58416i | 0.214512 | − | 0.976721i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99286 | + | 0.206921i | −0.997618 | + | 0.0689735i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.793196 | − | 0.457952i | −0.239158 | − | 0.138078i | 0.375632 | − | 0.926769i | \(-0.377426\pi\) |
−0.614790 | + | 0.788691i | \(0.710759\pi\) | |||||||
\(12\) | 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 | −0.831623 | − | 0.555341i | \(-0.812588\pi\) |
0.896751 | + | 0.442536i | \(0.145921\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | 4.50715 | + | 0.827982i | 0.983542 | + | 0.180681i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.91920 | + | 3.99480i | −1.44275 | + | 0.832974i | −0.998033 | − | 0.0626950i | \(-0.980030\pi\) |
−0.444721 | + | 0.895669i | \(0.646697\pi\) | |||||||
\(24\) | 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 | \(0.104152\pi\) | ||||
−0.946945 | + | 0.321396i | \(0.895848\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 0.745316 | − | 1.40041i | 0.129743 | − | 0.243780i | ||||
\(34\) | 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 | ||||||||
\(39\) | −7.46334 | + | 0.257693i | −1.19509 | + | 0.0412640i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.89809 | −1.54582 | −0.772911 | − | 0.634515i | \(-0.781200\pi\) | ||||
−0.772911 | + | 0.634515i | \(0.781200\pi\) | |||||||
\(42\) | 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 | 0.979781 | − | 0.200072i | \(-0.0641176\pi\) |
−0.663158 | + | 0.748479i | \(0.730784\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.35578 | − | 2.93326i | −0.907969 | − | 0.419038i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.821162 | + | 0.437033i | 0.114986 | + | 0.0611969i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.70594 | + | 0.984927i | 0.234329 | + | 0.135290i | 0.612568 | − | 0.790418i | \(-0.290137\pi\) |
−0.378238 | + | 0.925708i | \(0.623470\pi\) | |||||||
\(54\) | 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 | \(0.548011\pi\) |
−0.781063 | + | 0.624452i | \(0.785322\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −1.16387 | + | 7.85146i | −0.146634 | + | 0.989191i | ||||
\(64\) | 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 | \(-0.982162\pi\) | ||
0.998430 | − | 0.0560102i | \(-0.0178379\pi\) | |||||||
\(72\) | 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 | ||||||||
\(81\) | 8.91437 | − | 1.23857i | 0.990485 | − | 0.137618i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.35240 | 1.02656 | 0.513279 | − | 0.858222i | \(-0.328430\pi\) | ||||
0.513279 | + | 0.858222i | \(0.328430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.99199 | + | 0.206891i | −0.642408 | + | 0.0221810i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.874507 | + | 1.51469i | 0.0926976 | + | 0.160557i | 0.908645 | − | 0.417569i | \(-0.137118\pi\) |
−0.815948 | + | 0.578126i | \(0.803784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.1417 | + | 2.44699i | 1.16797 | + | 0.256515i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.22544 | − | 9.81833i | 0.541853 | − | 1.01811i | ||||
\(94\) | 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 | −0.999934 | − | 0.0114677i | \(-0.996350\pi\) |
0.509898 | + | 0.860235i | \(0.329683\pi\) | |||||||
\(102\) | 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 | −0.435909 | − | 0.899991i | \(-0.643573\pi\) |
0.561461 | + | 0.827504i | \(0.310240\pi\) | |||||||
\(108\) | 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 | \(-0.841078\pi\) | ||
0.877933 | − | 0.478783i | \(-0.158922\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.892144 | − | 12.9038i | −0.0824788 | − | 1.19296i | ||||
\(118\) | 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 | ||||||||
\(123\) | −0.591593 | − | 17.1338i | −0.0533421 | − | 1.54490i | ||||
\(124\) | 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 | ||||||||
\(129\) | 0.491354 | + | 14.2306i | 0.0432613 | + | 1.25294i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.80008 | − | 15.2422i | −0.768867 | − | 1.33172i | −0.938178 | − | 0.346154i | \(-0.887488\pi\) |
0.169311 | − | 0.985563i | \(-0.445846\pi\) | |||||||
\(132\) | 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 | 0.0622758 | − | 0.998059i | \(-0.480164\pi\) |
−0.833207 | + | 0.552962i | \(0.813497\pi\) | |||||||
\(138\) | 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 | ||||||||
\(147\) | 4.69766 | − | 11.1773i | 0.387456 | − | 0.921888i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.42586 | + | 3.13262i | −0.444504 | + | 0.256634i | −0.705506 | − | 0.708704i | \(-0.749280\pi\) |
0.261003 | + | 0.965338i | \(0.415947\pi\) | |||||||
\(150\) | 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 | ||||||||
\(159\) | −1.60297 | + | 3.01189i | −0.127123 | + | 0.238858i | ||||
\(160\) | 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 | \(-0.380230\pi\) | ||||
0.367453 | + | 0.930042i | \(0.380230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.58930 | −0.429946 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.24369 | + | 2.18419i | −0.248051 | + | 0.167029i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.97492 | − | 10.3489i | −0.454264 | − | 0.786809i | 0.544381 | − | 0.838838i | \(-0.316765\pi\) |
−0.998646 | + | 0.0520289i | \(0.983431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.8757 | − | 11.6425i | −1.64428 | − | 0.875105i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.2343 | − | 9.37286i | −1.21341 | − | 0.700561i | −0.249907 | − | 0.968270i | \(-0.580400\pi\) |
−0.963500 | + | 0.267709i | \(0.913733\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | −13.6606 | − | 1.54541i | −0.993662 | − | 0.112412i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9979 | − | 8.65904i | 1.08521 | − | 0.626546i | 0.152912 | − | 0.988240i | \(-0.451135\pi\) |
0.932297 | + | 0.361694i | \(0.117801\pi\) | |||||||
\(192\) | 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 | \(-0.769020\pi\) | ||
0.748071 | − | 0.663619i | \(-0.230980\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | −18.5115 | − | 9.85204i | −1.30570 | − | 0.694909i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.94517 | + | 1.96458i | 0.627828 | + | 0.137887i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.8816 | − | 13.3876i | 1.38186 | − | 0.930502i | ||||
\(208\) | 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 | ||||||||
\(213\) | 1.63391 | − | 0.0564154i | 0.111954 | − | 0.00386552i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4532 | + | 12.5486i | −0.777495 | + | 0.851857i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.31993 | − | 15.6327i | 0.562209 | − | 1.05636i | ||||
\(220\) | 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 | −0.877116 | − | 0.480278i | \(-0.840536\pi\) |
0.854491 | + | 0.519466i | \(0.173869\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | −3.19588 | − | 2.72081i | −0.210274 | − | 0.179016i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.3282 | + | 13.4685i | −1.52828 | + | 0.882353i | −0.528847 | + | 0.848717i | \(0.677375\pi\) |
−0.999434 | + | 0.0336360i | \(0.989291\pi\) | |||||||
\(234\) | 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 | \(0.189588\pi\) | ||||
−0.827808 | + | 0.561012i | \(0.810412\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 2.67678 | + | 15.3569i | 0.171716 | + | 0.985147i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.81006 | + | 4.86717i | 0.178800 | + | 0.309690i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.558978 | + | 16.1892i | 0.0354238 | + | 1.02595i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.56268 | 0.414233 | 0.207116 | − | 0.978316i | \(-0.433592\pi\) | ||||
0.207116 | + | 0.978316i | \(0.433592\pi\) | |||||||
\(252\) | 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 | \(0.0109051\pi\) |
−0.470043 | + | 0.882644i | \(0.655762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.7182 | − | 4.03764i | 0.790269 | − | 0.250887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.716263 | − | 10.3599i | −0.0443356 | − | 0.641260i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.60699 | + | 2.65984i | 0.284079 | + | 0.164013i | 0.635269 | − | 0.772291i | \(-0.280889\pi\) |
−0.351190 | + | 0.936304i | \(0.614223\pi\) | |||||||
\(264\) | 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 | −0.748607 | − | 0.663014i | \(-0.769277\pi\) |
0.948491 | + | 0.316805i | \(0.102610\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −3.56987 | + | 19.4327i | −0.216058 | + | 1.17612i | ||||
\(274\) | 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 | \(0.233384\pi\) | ||||
−0.743038 | + | 0.669250i | \(0.766616\pi\) | |||||||
\(282\) | 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 | ||||||||
\(291\) | −18.6680 | + | 0.644566i | −1.09434 | + | 0.0377851i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.1686 | 1.52879 | 0.764393 | − | 0.644750i | \(-0.223039\pi\) | ||||
0.764393 | + | 0.644750i | \(0.223039\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.94085 | + | 4.34544i | −0.112619 | + | 0.252148i | ||||
\(298\) | 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 | ||||||||
\(303\) | −15.0599 | − | 8.01510i | −0.865171 | − | 0.460455i | ||||
\(304\) | 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 | \(-0.645482\pi\) |
0.997786 | − | 0.0665052i | \(-0.0211849\pi\) | |||||||
\(312\) | 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 | −0.0585306 | − | 0.998286i | \(-0.518642\pi\) |
0.835275 | + | 0.549832i | \(0.185308\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −5.90882 | − | 3.14475i | −0.326758 | − | 0.173905i | ||||
\(328\) | 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 | ||||||||
\(333\) | −8.45093 | − | 12.5503i | −0.463108 | − | 0.687750i | ||||
\(334\) | 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 | ||||||||
\(339\) | 17.6202 | − | 0.608387i | 0.956996 | − | 0.0330430i | ||||
\(340\) | 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 | −0.338388 | − | 0.941007i | \(-0.609882\pi\) |
−0.984130 | + | 0.177451i | \(0.943215\pi\) | |||||||
\(348\) | 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 | \(0.539196\pi\) |
−0.798055 | + | 0.602585i | \(0.794138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.59541 | − | 1.87398i | 0.0844382 | − | 0.0991815i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.8260 | − | 11.4465i | 1.04638 | − | 0.604126i | 0.124743 | − | 0.992189i | \(-0.460189\pi\) |
0.921633 | + | 0.388064i | \(0.126856\pi\) | |||||||
\(360\) | 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 | ||||||||
\(369\) | 29.6235 | − | 2.04812i | 1.54214 | − | 0.106621i | ||||
\(370\) | 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 | ||||||||
\(381\) | 0.582023 | + | 16.8566i | 0.0298180 | + | 0.863591i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.7015 | − | 25.4637i | −0.751211 | − | 1.30114i | −0.947236 | − | 0.320537i | \(-0.896137\pi\) |
0.196025 | − | 0.980599i | \(-0.437197\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.6042 | + | 1.70109i | −1.25070 | + | 0.0864711i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.2730 | + | 11.7046i | 1.02788 | + | 0.593448i | 0.916377 | − | 0.400316i | \(-0.131100\pi\) |
0.111504 | + | 0.993764i | \(0.464433\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | 5.62764 | − | 2.00287i | 0.281734 | − | 0.100269i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.6844 | − | 12.5195i | 1.08287 | − | 0.625193i | 0.151198 | − | 0.988504i | \(-0.451687\pi\) |
0.931668 | + | 0.363311i | \(0.118354\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 8.47882 | − | 15.9313i | 0.418229 | − | 0.785831i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.9589 | + | 25.5183i | 1.37577 | + | 1.25567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.2761 | − | 0.423867i | 0.601162 | − | 0.0207568i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.85560 | 0.481477 | 0.240739 | − | 0.970590i | \(-0.422610\pi\) | ||||
0.240739 | + | 0.970590i | \(0.422610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.16112 | −0.397749 | −0.198874 | − | 0.980025i | \(-0.563729\pi\) | ||||
−0.198874 | + | 0.980025i | \(0.563729\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.27443 | − | 10.8031i | −0.353695 | − | 0.525263i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.75029 | + | 24.4127i | 0.375063 | + | 1.18141i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.03791 | + | 3.21345i | 0.291513 | + | 0.155147i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.84702 | − | 1.64373i | −0.137136 | − | 0.0791755i | 0.429862 | − | 0.902894i | \(-0.358562\pi\) |
−0.566998 | + | 0.823719i | \(0.691895\pi\) | |||||||
\(432\) | 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 | ||||||||
\(441\) | 19.6289 | + | 7.46369i | 0.934709 | + | 0.355414i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.4179 | + | 9.47885i | −0.780036 | + | 0.450354i | −0.836443 | − | 0.548054i | \(-0.815369\pi\) |
0.0564073 | + | 0.998408i | \(0.482035\pi\) | |||||||
\(444\) | 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 | \(-0.606960\pi\) | ||
0.329737 | − | 0.944073i | \(-0.393040\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.85112 | + | 4.53285i | 0.369695 | + | 0.213444i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.0808 | + | 14.4128i | 1.27237 | + | 0.677171i | ||||
\(454\) | 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 | ||||||||
\(459\) | −2.54805 | − | 1.13806i | −0.118933 | − | 0.0531202i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.71020 | −0.405674 | −0.202837 | − | 0.979212i | \(-0.565016\pi\) | ||||
−0.202837 | + | 0.979212i | \(0.565016\pi\) | |||||||
\(462\) | 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 | 0.741263 | − | 0.671215i | \(-0.234227\pi\) |
−0.951921 | + | 0.306345i | \(0.900894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.6592 | + | 21.5939i | 1.09248 | + | 0.997113i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.629797 | + | 1.18336i | −0.0290195 | + | 0.0545261i | ||||
\(472\) | 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 | \(-0.627087\pi\) |
0.992279 | − | 0.124022i | \(-0.0395794\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.8317 | + | 10.8725i | −0.858652 | + | 0.495743i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −34.4935 | + | 12.2762i | −1.56951 | + | 0.558587i | ||||
\(484\) | 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 | \(-0.731761\pi\) | ||
0.665453 | − | 0.746440i | \(-0.268239\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | 0.567626 | + | 16.4396i | 0.0253597 | + | 0.734469i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.1753 | 0.944158 | 0.472079 | − | 0.881556i | \(-0.343504\pi\) | ||||
0.472079 | + | 0.881556i | \(0.343504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.334063 | − | 9.67518i | −0.0148363 | − | 0.429690i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.5918 | + | 27.0059i | 0.691096 | + | 1.19701i | 0.971479 | + | 0.237125i | \(0.0762052\pi\) |
−0.280383 | + | 0.959888i | \(0.590461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.2358 | + | 19.9799i | −0.806704 | + | 0.883859i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.97475 | − | 5.48434i | −0.175490 | − | 0.242140i | ||||
\(514\) | 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 | \(0.491498\pi\) |
−0.879070 | + | 0.476693i | \(0.841835\pi\) | |||||||
\(522\) | 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 | ||||||||
\(537\) | 15.2543 | − | 28.6620i | 0.658272 | − | 1.23686i | ||||
\(538\) | 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 | ||||||||
\(543\) | −27.8736 | + | 0.962414i | −1.19617 | + | 0.0413012i | ||||
\(544\) | 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 | ||||||||
\(549\) | 24.0904 | − | 16.2217i | 1.02815 | − | 0.692323i | ||||
\(550\) | 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 | 0.992202 | − | 0.124644i | \(-0.0397789\pi\) |
0.388156 | + | 0.921594i | \(0.373112\pi\) | |||||||
\(558\) | 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 | −0.953116 | − | 0.302606i | \(-0.902143\pi\) |
0.738622 | + | 0.674120i | \(0.235477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.85866 | − | 23.7391i | 0.0780564 | − | 0.996949i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.744706 | − | 0.429956i | 0.0312197 | − | 0.0180247i | −0.484309 | − | 0.874897i | \(-0.660929\pi\) |
0.515529 | + | 0.856872i | \(0.327596\pi\) | |||||||
\(570\) | 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 | ||||||||
\(579\) | −23.1341 | − | 12.3123i | −0.961422 | − | 0.511681i | ||||
\(580\) | 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 | \(-0.346225\pi\) | ||||
0.464524 | + | 0.885561i | \(0.346225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.37041 | −0.344897 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.2466 | − | 1.11341i | 1.32645 | − | 0.0457994i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.8863 | − | 20.5878i | −0.488114 | − | 0.845438i | 0.511793 | − | 0.859109i | \(-0.328982\pi\) |
−0.999907 | + | 0.0136712i | \(0.995648\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.17749 | + | 15.3651i | −0.334682 | + | 0.628850i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.6990 | + | 21.7655i | 1.54034 | + | 0.889314i | 0.998817 | + | 0.0486270i | \(0.0154846\pi\) |
0.541521 | + | 0.840687i | \(0.317849\pi\) | |||||||
\(600\) | 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 | ||||||||
\(609\) | −2.86609 | + | 15.6017i | −0.116140 | + | 0.632212i | ||||
\(610\) | 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 | \(-0.952417\pi\) | ||
0.988848 | − | 0.148929i | \(-0.0475826\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | 24.3625 | + | 33.6152i | 0.977632 | + | 1.34893i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.41053 | − | 1.40021i | 0.176704 | − | 0.0560983i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0713568 | − | 2.06665i | −0.00284972 | − | 0.0825339i | ||||
\(628\) | 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 | ||||||||
\(633\) | −0.100765 | − | 2.91837i | −0.00400505 | − | 0.115995i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6469 | − | 27.4032i | 0.501087 | − | 1.08575i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.195312 | + | 2.82496i | 0.00772643 | + | 0.111754i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.2389 | − | 7.06611i | −0.483406 | − | 0.279094i | 0.238429 | − | 0.971160i | \(-0.423368\pi\) |
−0.721835 | + | 0.692065i | \(0.756701\pi\) | |||||||
\(642\) | 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 | −0.527610 | − | 0.849487i | \(-0.676912\pi\) |
0.999482 | + | 0.0321804i | \(0.0102451\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3485 | − | 6.55204i | 0.445466 | − | 0.257190i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.4065 | − | 19.0757i | −0.878179 | − | 0.747637i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.0705 | + | 14.4745i | −0.981085 | + | 0.566430i | −0.902598 | − | 0.430485i | \(-0.858342\pi\) |
−0.0784876 | + | 0.996915i | \(0.525009\pi\) | |||||||
\(654\) | 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 | \(0.0316168\pi\) | ||||
−0.995071 | + | 0.0991638i | \(0.968383\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −1.88428 | + | 3.54047i | −0.0731794 | + | 0.137500i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8282 | − | 23.9511i | −0.535429 | − | 0.927389i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.5970 | + | 0.849281i | −0.950974 | + | 0.0328351i | ||||
\(670\) | 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 | 0.988722 | − | 0.149763i | \(-0.0478511\pi\) |
−0.624060 | + | 0.781377i | \(0.714518\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.8686 | + | 6.12064i | 1.06950 | + | 0.234889i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.04239 | − | 0.554776i | −0.0399447 | − | 0.0212591i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.1149 | − | 10.4587i | −0.693149 | − | 0.400190i | 0.111642 | − | 0.993749i | \(-0.464389\pi\) |
−0.804791 | + | 0.593559i | \(0.797722\pi\) | |||||||
\(684\) | 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 | ||||||||
\(693\) | 4.51877 | − | 5.69475i | 0.171654 | − | 0.216326i | ||||
\(694\) | 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 | \(-0.883338\pi\) | ||
0.933586 | − | 0.358353i | \(-0.116662\pi\) | |||||||
\(702\) | 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 | ||||||||
\(711\) | 19.1630 | + | 28.4585i | 0.718670 | + | 1.06728i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 51.3048 | 1.92138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.0264 | + | 1.03675i | −1.12136 | + | 0.0387180i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.70106 | − | 11.6066i | −0.249907 | − | 0.432852i | 0.713593 | − | 0.700561i | \(-0.247067\pi\) |
−0.963500 | + | 0.267709i | \(0.913733\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.96775 | + | 6.19823i | 0.0732829 | + | 0.230834i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.24297 | + | 2.33547i | −0.0462264 | + | 0.0868569i | ||||
\(724\) | 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 | \(-0.916800\pi\) | ||
0.966034 | − | 0.258415i | \(-0.0832003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.9904 | + | 1.93520i | −1.02411 | + | 0.0708054i | ||||
\(748\) | 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 | ||||||||
\(753\) | 0.392241 | + | 11.3601i | 0.0142941 | + | 0.413986i | ||||
\(754\) | 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 | ||||||||
\(759\) | 0.437368 | + | 12.6671i | 0.0158755 | + | 0.459787i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.76529 | + | 16.9140i | 0.353991 | + | 0.613131i | 0.986945 | − | 0.161059i | \(-0.0514909\pi\) |
−0.632953 | + | 0.774190i | \(0.718158\pi\) | |||||||
\(762\) | 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 | −0.611146 | − | 0.791518i | \(-0.709291\pi\) |
0.991048 | + | 0.133509i | \(0.0426246\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.74937 | + | 21.7741i | 0.278007 | + | 0.781141i | ||||
\(778\) | 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 | ||||||||
\(789\) | −4.32889 | + | 8.13376i | −0.154113 | + | 0.289569i | ||||
\(790\) | 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 | \(-0.463233\pi\) | ||||
0.115250 | + | 0.993337i | \(0.463233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.33156 | 0.0824845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.93069 | − | 4.35230i | −0.103551 | − | 0.153781i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.68219 | + | 8.10980i | 0.165231 | + | 0.286189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0251 | + | 5.33549i | 0.352900 | + | 0.187818i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.41519 | − | 0.817063i | −0.0497556 | − | 0.0287264i | 0.474916 | − | 0.880031i | \(-0.342478\pi\) |
−0.524671 | + | 0.851305i | \(0.675812\pi\) | |||||||
\(810\) | 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 | ||||||||
\(819\) | −33.8518 | − | 5.01805i | −1.18288 | − | 0.175345i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.6357 | + | 11.3367i | −0.685292 | + | 0.395654i | −0.801846 | − | 0.597531i | \(-0.796149\pi\) |
0.116554 | + | 0.993184i | \(0.462815\pi\) | |||||||
\(822\) | 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 | \(-0.808800\pi\) | ||
0.824957 | − | 0.565196i | \(-0.191200\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | −4.24029 | − | 2.25674i | −0.147094 | − | 0.0782853i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.07101 | + | 2.16846i | −0.106404 | + | 0.0751327i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.6074 | + | 30.4661i | −0.470340 | + | 1.05306i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.88841 | 0.0997192 | 0.0498596 | − | 0.998756i | \(-0.484123\pi\) | ||||
0.0498596 | + | 0.998756i | \(0.484123\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0178 | 0.586819 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.8395 | + | 1.34104i | −1.33770 | + | 0.0461880i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.6235 | + | 8.13470i | −0.880435 | + | 0.279512i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.89708 | + | 11.0803i | −0.202387 | + | 0.380275i | ||||
\(850\) | 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 | −0.975898 | − | 0.218228i | \(-0.929972\pi\) |
0.676940 | + | 0.736038i | \(0.263306\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −44.6122 | − | 8.19544i | −1.52038 | − | 0.279300i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.4595 | + | 17.0085i | −1.00281 | + | 0.578975i | −0.909080 | − | 0.416622i | \(-0.863214\pi\) |
−0.0937342 | + | 0.995597i | \(0.529880\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | −2.23151 | − | 32.2761i | −0.0755252 | − | 1.09238i | ||||
\(874\) | 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 | ||||||||
\(879\) | 1.56406 | + | 45.2984i | 0.0527543 | + | 1.52788i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.9119 | 0.872993 | 0.436496 | − | 0.899706i | \(-0.356219\pi\) | ||||
0.436496 | + | 0.899706i | \(0.356219\pi\) | |||||||
\(882\) | 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 | 0.962951 | − | 0.269678i | \(-0.0869171\pi\) |
−0.715023 | + | 0.699101i | \(0.753584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.52675 | − | 25.1645i | 0.185361 | − | 0.843990i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.63805 | − | 3.09993i | −0.255884 | − | 0.103851i | ||||
\(892\) | 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 | ||||||||
\(903\) | 37.0532 | + | 6.80681i | 1.23305 | + | 0.226517i | ||||
\(904\) | 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 | \(0.167407\pi\) | ||||
−0.864860 | + | 0.502013i | \(0.832593\pi\) | |||||||
\(912\) | 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 | ||||||||
\(921\) | −38.7998 | + | 1.33968i | −1.27850 | + | 0.0441438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.06965 | 0.133954 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.11640 | − | 4.11858i | 0.200889 | − | 0.135272i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.62508 | + | 14.9391i | 0.282980 | + | 0.490135i | 0.972117 | − | 0.234495i | \(-0.0753438\pi\) |
−0.689138 | + | 0.724631i | \(0.742010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.08663 | + | 0.831132i | −0.297802 | + | 0.0272393i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.0104 | + | 15.9719i | 0.982495 | + | 0.522896i | ||||
\(934\) | 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 | \(-0.660915\pi\) |
0.999837 | − | 0.0180673i | \(-0.00575131\pi\) | |||||||
\(942\) | 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 | −0.947186 | − | 0.320685i | \(-0.896087\pi\) |
−0.195871 | + | 0.980630i | \(0.562753\pi\) | |||||||
\(948\) | 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 | \(-0.972542\pi\) | ||
0.996282 | − | 0.0861558i | \(-0.0274583\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.84757 | + | 2.57994i | 0.156700 | + | 0.0833975i | ||||
\(958\) | 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 | ||||||||
\(963\) | −3.73172 | + | 2.51282i | −0.120253 | + | 0.0809745i | ||||
\(964\) | 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 | ||||||||
\(969\) | 1.21183 | − | 0.0418417i | 0.0389294 | − | 0.00134415i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.9851 | + | 38.0793i | 0.705535 | + | 1.22202i | 0.966498 | + | 0.256674i | \(0.0826266\pi\) |
−0.260963 | + | 0.965349i | \(0.584040\pi\) | |||||||
\(972\) | 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 | 0.622625 | − | 0.782521i | \(-0.286066\pi\) |
−0.366370 | + | 0.930469i | \(0.619400\pi\) | |||||||
\(978\) | 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 | −0.951568 | − | 0.307439i | \(-0.900528\pi\) |
0.742034 | + | 0.670362i | \(0.233861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.67054 | + | 18.7428i | 0.212326 | + | 0.596589i | ||||
\(988\) | 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 | ||||||||
\(999\) | 21.2196 | − | 15.3788i | 0.671359 | − | 0.486565i |
(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.101.9 | 32 | ||
3.2 | odd | 2 | inner | 2100.2.bi.n.101.14 | 32 | ||
5.2 | odd | 4 | 420.2.bn.a.269.16 | yes | 32 | ||
5.3 | odd | 4 | 420.2.bn.a.269.1 | yes | 32 | ||
5.4 | even | 2 | inner | 2100.2.bi.n.101.8 | 32 | ||
7.5 | odd | 6 | inner | 2100.2.bi.n.1601.14 | 32 | ||
15.2 | even | 4 | 420.2.bn.a.269.6 | yes | 32 | ||
15.8 | even | 4 | 420.2.bn.a.269.11 | yes | 32 | ||
15.14 | odd | 2 | inner | 2100.2.bi.n.101.3 | 32 | ||
21.5 | even | 6 | inner | 2100.2.bi.n.1601.9 | 32 | ||
35.3 | even | 12 | 2940.2.f.a.1469.9 | 32 | |||
35.12 | even | 12 | 420.2.bn.a.89.11 | yes | 32 | ||
35.17 | even | 12 | 2940.2.f.a.1469.23 | 32 | |||
35.18 | odd | 12 | 2940.2.f.a.1469.24 | 32 | |||
35.19 | odd | 6 | inner | 2100.2.bi.n.1601.3 | 32 | ||
35.32 | odd | 12 | 2940.2.f.a.1469.10 | 32 | |||
35.33 | even | 12 | 420.2.bn.a.89.6 | yes | 32 | ||
105.17 | odd | 12 | 2940.2.f.a.1469.22 | 32 | |||
105.32 | even | 12 | 2940.2.f.a.1469.11 | 32 | |||
105.38 | odd | 12 | 2940.2.f.a.1469.12 | 32 | |||
105.47 | odd | 12 | 420.2.bn.a.89.1 | ✓ | 32 | ||
105.53 | even | 12 | 2940.2.f.a.1469.21 | 32 | |||
105.68 | odd | 12 | 420.2.bn.a.89.16 | yes | 32 | ||
105.89 | even | 6 | inner | 2100.2.bi.n.1601.8 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bn.a.89.1 | ✓ | 32 | 105.47 | odd | 12 | ||
420.2.bn.a.89.6 | yes | 32 | 35.33 | even | 12 | ||
420.2.bn.a.89.11 | yes | 32 | 35.12 | even | 12 | ||
420.2.bn.a.89.16 | yes | 32 | 105.68 | odd | 12 | ||
420.2.bn.a.269.1 | yes | 32 | 5.3 | odd | 4 | ||
420.2.bn.a.269.6 | yes | 32 | 15.2 | even | 4 | ||
420.2.bn.a.269.11 | yes | 32 | 15.8 | even | 4 | ||
420.2.bn.a.269.16 | yes | 32 | 5.2 | odd | 4 | ||
2100.2.bi.n.101.3 | 32 | 15.14 | odd | 2 | inner | ||
2100.2.bi.n.101.8 | 32 | 5.4 | even | 2 | inner | ||
2100.2.bi.n.101.9 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.bi.n.101.14 | 32 | 3.2 | odd | 2 | inner | ||
2100.2.bi.n.1601.3 | 32 | 35.19 | odd | 6 | inner | ||
2100.2.bi.n.1601.8 | 32 | 105.89 | even | 6 | inner | ||
2100.2.bi.n.1601.9 | 32 | 21.5 | even | 6 | inner | ||
2100.2.bi.n.1601.14 | 32 | 7.5 | odd | 6 | inner | ||
2940.2.f.a.1469.9 | 32 | 35.3 | even | 12 | |||
2940.2.f.a.1469.10 | 32 | 35.32 | odd | 12 | |||
2940.2.f.a.1469.11 | 32 | 105.32 | even | 12 | |||
2940.2.f.a.1469.12 | 32 | 105.38 | odd | 12 | |||
2940.2.f.a.1469.21 | 32 | 105.53 | even | 12 | |||
2940.2.f.a.1469.22 | 32 | 105.17 | odd | 12 | |||
2940.2.f.a.1469.23 | 32 | 35.17 | even | 12 | |||
2940.2.f.a.1469.24 | 32 | 35.18 | odd | 12 |