Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(521,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.u (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.39040727770\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1097.6 | ||
Root | \(-0.441628 - 1.67480i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1097 |
Dual form | 1176.2.u.b.521.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.21986 | − | 1.22961i | 0.704288 | − | 0.709915i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.40397 | − | 2.43175i | 0.627876 | − | 1.08751i | −0.360101 | − | 0.932913i | \(-0.617258\pi\) |
0.987977 | − | 0.154600i | \(-0.0494089\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0238727 | − | 2.99991i | −0.00795756 | − | 0.999968i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.74645 | + | 2.74036i | −1.43111 | + | 0.826250i | −0.997205 | − | 0.0747101i | \(-0.976197\pi\) |
−0.433902 | + | 0.900960i | \(0.642864\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.35669i | − | 0.376279i | −0.982142 | − | 0.188139i | \(-0.939754\pi\) | ||
0.982142 | − | 0.188139i | \(-0.0602457\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.27745 | − | 4.69274i | −0.329836 | − | 1.21166i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.88753 | − | 5.00135i | −0.700329 | − | 1.21301i | −0.968351 | − | 0.249593i | \(-0.919703\pi\) |
0.268022 | − | 0.963413i | \(-0.413630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.71973 | − | 0.992889i | −0.394534 | − | 0.227784i | 0.289589 | − | 0.957151i | \(-0.406481\pi\) |
−0.684123 | + | 0.729367i | \(0.739815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.09928 | + | 1.21202i | 0.437730 | + | 0.252723i | 0.702634 | − | 0.711551i | \(-0.252007\pi\) |
−0.264904 | + | 0.964275i | \(0.585340\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.44228 | − | 2.49811i | −0.288457 | − | 0.499622i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.71783 | − | 3.63012i | −0.715497 | − | 0.698616i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.05668i | − | 1.31039i | −0.755458 | − | 0.655197i | \(-0.772586\pi\) | ||
0.755458 | − | 0.655197i | \(-0.227414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.07596 | − | 1.77591i | 0.552459 | − | 0.318962i | −0.197654 | − | 0.980272i | \(-0.563332\pi\) |
0.750113 | + | 0.661309i | \(0.229999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.42044 | + | 9.17913i | −0.421344 | + | 1.59788i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.14377 | + | 3.71312i | −0.352434 | + | 0.610434i | −0.986675 | − | 0.162701i | \(-0.947979\pi\) |
0.634241 | + | 0.773135i | \(0.281313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.66820 | − | 1.65498i | −0.267126 | − | 0.265009i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.81976 | 0.284199 | 0.142100 | − | 0.989852i | \(-0.454615\pi\) | ||||
0.142100 | + | 0.989852i | \(0.454615\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2288 | 1.71238 | 0.856188 | − | 0.516665i | \(-0.172827\pi\) | ||||
0.856188 | + | 0.516665i | \(0.172827\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.32855 | − | 4.15374i | −1.09248 | − | 0.619202i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.201213 | − | 0.348512i | 0.0293500 | − | 0.0508356i | −0.850977 | − | 0.525202i | \(-0.823990\pi\) |
0.880327 | + | 0.474367i | \(0.157323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.67209 | − | 2.55043i | −1.35436 | − | 0.357131i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.28097 | + | 3.04897i | −0.725397 | + | 0.418808i | −0.816736 | − | 0.577012i | \(-0.804219\pi\) |
0.0913389 | + | 0.995820i | \(0.470885\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.3896i | 2.07513i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.31870 | + | 0.903412i | −0.439573 | + | 0.119660i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.28234 | − | 2.22108i | −0.166947 | − | 0.289161i | 0.770398 | − | 0.637563i | \(-0.220058\pi\) |
−0.937345 | + | 0.348403i | \(0.886724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.75817 | + | 2.74713i | 0.609222 | + | 0.351734i | 0.772661 | − | 0.634819i | \(-0.218925\pi\) |
−0.163439 | + | 0.986553i | \(0.552259\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.29914 | − | 1.90476i | −0.409208 | − | 0.236257i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.45238 | + | 5.97970i | 0.421775 | + | 0.730536i | 0.996113 | − | 0.0880819i | \(-0.0280737\pi\) |
−0.574338 | + | 0.818618i | \(0.694740\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.05114 | − | 1.10279i | 0.487700 | − | 0.132761i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.08251i | − | 0.247148i | −0.992335 | − | 0.123574i | \(-0.960564\pi\) | ||
0.992335 | − | 0.123574i | \(-0.0394357\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.295696 | − | 0.170720i | 0.0346086 | − | 0.0199813i | −0.482596 | − | 0.875843i | \(-0.660306\pi\) |
0.517204 | + | 0.855862i | \(0.326973\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.83108 | − | 1.27390i | −0.557846 | − | 0.147098i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.19139 | − | 2.06355i | 0.134042 | − | 0.232168i | −0.791189 | − | 0.611572i | \(-0.790538\pi\) |
0.925231 | + | 0.379404i | \(0.123871\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.99886 | + | 0.143232i | −0.999873 | + | 0.0159146i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8717 | 1.30309 | 0.651543 | − | 0.758611i | \(-0.274122\pi\) | ||||
0.651543 | + | 0.758611i | \(0.274122\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.2161 | −1.75888 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.67696 | − | 8.60818i | −0.930267 | − | 0.922894i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.576571 | − | 0.998650i | 0.0611164 | − | 0.105857i | −0.833848 | − | 0.551994i | \(-0.813867\pi\) |
0.894965 | + | 0.446137i | \(0.147201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.56858 | − | 5.94859i | 0.162654 | − | 0.616840i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.82892 | + | 2.78798i | −0.495437 | + | 0.286041i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 16.0187i | − | 1.62645i | −0.581950 | − | 0.813225i | \(-0.697710\pi\) | ||
0.581950 | − | 0.813225i | \(-0.302290\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.33413 | + | 14.1735i | 0.837612 | + | 1.42449i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.33982 | + | 12.7129i | 0.730339 | + | 1.26498i | 0.956738 | + | 0.290950i | \(0.0939712\pi\) |
−0.226399 | + | 0.974035i | \(0.572695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.06960 | − | 2.34958i | −0.400989 | − | 0.231511i | 0.285922 | − | 0.958253i | \(-0.407700\pi\) |
−0.686911 | + | 0.726742i | \(0.741034\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.14150 | + | 4.12315i | 0.690395 | + | 0.398600i | 0.803760 | − | 0.594954i | \(-0.202830\pi\) |
−0.113365 | + | 0.993553i | \(0.536163\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.41113 | − | 7.64030i | −0.422509 | − | 0.731808i | 0.573675 | − | 0.819083i | \(-0.305517\pi\) |
−0.996184 | + | 0.0872755i | \(0.972184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.95058 | + | 7.16550i | 0.185141 | + | 0.680119i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.00000i | − | 0.376288i | −0.982141 | − | 0.188144i | \(-0.939753\pi\) | ||
0.982141 | − | 0.188144i | \(-0.0602472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.89467 | − | 3.40329i | 0.549680 | − | 0.317358i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.06995 | + | 0.0323879i | −0.376267 | + | 0.00299426i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.51916 | − | 16.4877i | 0.865378 | − | 1.49888i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.21986 | − | 2.23760i | 0.200158 | − | 0.201757i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.94002 | 0.531291 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.93769 | −0.615620 | −0.307810 | − | 0.951448i | \(-0.599596\pi\) | ||||
−0.307810 | + | 0.951448i | \(0.599596\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.6976 | − | 13.8070i | 1.20601 | − | 1.21564i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.118734 | + | 0.205654i | −0.0103739 | + | 0.0179680i | −0.871166 | − | 0.490989i | \(-0.836635\pi\) |
0.860792 | + | 0.508957i | \(0.169969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.0473 | + | 3.94426i | −1.20900 | + | 0.339468i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.58873 | − | 5.53606i | 0.819221 | − | 0.472977i | −0.0309270 | − | 0.999522i | \(-0.509846\pi\) |
0.850148 | + | 0.526544i | \(0.176513\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.02466i | 0.0869108i | 0.999055 | + | 0.0434554i | \(0.0138366\pi\) | ||||
−0.999055 | + | 0.0434554i | \(0.986163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.183080 | − | 0.672550i | −0.0154181 | − | 0.0566389i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.71783 | + | 6.43947i | 0.310900 | + | 0.538495i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.1601 | − | 9.90740i | −1.42507 | − | 0.822765i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.0549 | + | 11.0013i | 1.56104 | + | 0.901266i | 0.997152 | + | 0.0754127i | \(0.0240274\pi\) |
0.563886 | + | 0.825853i | \(0.309306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.63368 | + | 6.29371i | 0.295704 | + | 0.512175i | 0.975149 | − | 0.221552i | \(-0.0711123\pi\) |
−0.679444 | + | 0.733727i | \(0.737779\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.9346 | + | 8.78171i | −1.20739 | + | 0.709959i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 9.97331i | − | 0.801075i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.6994 | + | 11.3735i | −1.57219 | + | 0.907702i | −0.576285 | + | 0.817249i | \(0.695498\pi\) |
−0.995901 | + | 0.0904525i | \(0.971169\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.69302 | + | 10.2128i | −0.213570 | + | 0.809931i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.06678 | + | 15.7041i | −0.710165 | + | 1.23004i | 0.254630 | + | 0.967039i | \(0.418046\pi\) |
−0.964795 | + | 0.263003i | \(0.915287\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.9232 | + | 18.7732i | 1.47317 | + | 1.46149i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.0942 | −1.86447 | −0.932233 | − | 0.361858i | \(-0.882143\pi\) | ||||
−0.932233 | + | 0.361858i | \(0.882143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1594 | 0.858414 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.93752 | + | 5.18274i | −0.224638 | + | 0.396334i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.18802 | − | 8.98592i | 0.394438 | − | 0.683187i | −0.598591 | − | 0.801055i | \(-0.704273\pi\) |
0.993029 | + | 0.117868i | \(0.0376059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.29535 | − | 1.13264i | −0.322858 | − | 0.0851342i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.5922 | − | 6.69274i | 0.866439 | − | 0.500239i | 0.000276030 | − | 1.00000i | \(-0.499912\pi\) |
0.866163 | + | 0.499761i | \(0.166579\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.4339i | − | 1.37018i | −0.728457 | − | 0.685092i | \(-0.759762\pi\) | ||
0.728457 | − | 0.685092i | \(-0.240238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.18221 | − | 2.49957i | 0.678769 | − | 0.184773i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.01960 | + | 10.4263i | 0.442570 | + | 0.766554i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.4110 | + | 15.8258i | 2.00449 | + | 1.15729i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.59492 | − | 2.07553i | −0.260119 | − | 0.150180i | 0.364270 | − | 0.931293i | \(-0.381319\pi\) |
−0.624389 | + | 0.781114i | \(0.714652\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.75462 | − | 16.8955i | −0.702153 | − | 1.21616i | −0.967709 | − | 0.252069i | \(-0.918889\pi\) |
0.265556 | − | 0.964095i | \(-0.414444\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.36661 | + | 1.73311i | −0.455922 | + | 0.124110i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.80952i | 0.271417i | 0.990749 | + | 0.135709i | \(0.0433311\pi\) | ||||
−0.990749 | + | 0.135709i | \(0.956669\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.30327 | − | 3.06185i | 0.375939 | − | 0.217049i | −0.300111 | − | 0.953904i | \(-0.597024\pi\) |
0.676050 | + | 0.736856i | \(0.263690\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.5641 | + | 3.04933i | 0.815670 | + | 0.215083i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.55490 | − | 4.42522i | 0.178442 | − | 0.309071i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.58583 | − | 6.32657i | 0.249232 | − | 0.439727i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.8835 | 0.752827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.93058 | 0.201750 | 0.100875 | − | 0.994899i | \(-0.467836\pi\) | ||||
0.100875 | + | 0.994899i | \(0.467836\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.56067 | − | 2.54037i | −0.175454 | − | 0.174063i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.7649 | − | 27.3057i | 1.07516 | − | 1.86223i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.150789 | − | 0.571845i | 0.0101894 | − | 0.0386417i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.78530 | + | 3.91749i | −0.456428 | + | 0.263519i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.61145i | − | 0.308806i | −0.988008 | − | 0.154403i | \(-0.950655\pi\) | ||
0.988008 | − | 0.154403i | \(-0.0493454\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.45966 | + | 4.38635i | −0.497311 | + | 0.292424i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.62344 | + | 14.9362i | 0.572358 | + | 0.991353i | 0.996323 | + | 0.0856745i | \(0.0273045\pi\) |
−0.423965 | + | 0.905678i | \(0.639362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5705 | + | 6.68024i | 0.764601 | + | 0.441443i | 0.830945 | − | 0.556354i | \(-0.187800\pi\) |
−0.0663443 | + | 0.997797i | \(0.521134\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.5908 | + | 9.00135i | 1.02139 | + | 0.589698i | 0.914505 | − | 0.404574i | \(-0.132580\pi\) |
0.106882 | + | 0.994272i | \(0.465913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.564996 | − | 0.978602i | −0.0368563 | − | 0.0638370i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.08403 | − | 3.98220i | −0.0704151 | − | 0.258671i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.6499i | 1.52979i | 0.644158 | + | 0.764893i | \(0.277208\pi\) | ||||
−0.644158 | + | 0.764893i | \(0.722792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.53574 | + | 2.04136i | −0.227757 | + | 0.131496i | −0.609537 | − | 0.792758i | \(-0.708645\pi\) |
0.381780 | + | 0.924253i | \(0.375311\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.8013 | + | 11.2398i | −0.692901 | + | 0.721033i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.34705 | + | 2.33315i | −0.0857105 | + | 0.148455i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.4818 | − | 14.5975i | 0.917748 | − | 0.925080i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.78085 | 0.364884 | 0.182442 | − | 0.983217i | \(-0.441600\pi\) | ||||
0.182442 | + | 0.983217i | \(0.441600\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.2855 | −0.835251 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.7814 | + | 19.9394i | −1.23876 | + | 1.24865i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.4824 | − | 18.1560i | 0.653871 | − | 1.13254i | −0.328304 | − | 0.944572i | \(-0.606477\pi\) |
0.982175 | − | 0.187966i | \(-0.0601896\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.1694 | + | 0.168462i | −1.31035 | + | 0.0104275i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.32937 | + | 2.49957i | −0.266961 | + | 0.154130i | −0.627506 | − | 0.778612i | \(-0.715924\pi\) |
0.360545 | + | 0.932742i | \(0.382591\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.1227i | 1.05184i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.524611 | − | 1.92717i | −0.0321057 | − | 0.117941i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.67602 | − | 13.2953i | −0.468015 | − | 0.810626i | 0.531317 | − | 0.847173i | \(-0.321697\pi\) |
−0.999332 | + | 0.0365470i | \(0.988364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.4761 | − | 8.35779i | −0.879362 | − | 0.507700i | −0.00891391 | − | 0.999960i | \(-0.502837\pi\) |
−0.870448 | + | 0.492260i | \(0.836171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.6914 | + | 7.90476i | 0.825625 | + | 0.476675i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2571 | + | 19.4979i | 0.676376 | + | 1.17152i | 0.976065 | + | 0.217481i | \(0.0697839\pi\) |
−0.299689 | + | 0.954037i | \(0.596883\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.40098 | − | 9.18520i | −0.323348 | − | 0.549903i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.1134i | 1.08055i | 0.841488 | + | 0.540276i | \(0.181680\pi\) | ||||
−0.841488 | + | 0.540276i | \(0.818320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00728 | − | 2.89095i | 0.297652 | − | 0.171849i | −0.343736 | − | 0.939066i | \(-0.611692\pi\) |
0.641388 | + | 0.767217i | \(0.278359\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.46250 | + | 9.33864i | −0.145866 | + | 0.553173i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.17567 | + | 14.1607i | −0.480921 | + | 0.832980i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.6967 | − | 19.5406i | −1.15464 | − | 1.14549i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.38786 | −0.548445 | −0.274222 | − | 0.961666i | \(-0.588420\pi\) | ||||
−0.274222 | + | 0.961666i | \(0.588420\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.20151 | −0.419288 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.5943 | + | 7.04195i | 1.60118 | + | 0.408616i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.64434 | − | 2.84808i | 0.0950945 | − | 0.164709i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.5855 | + | 6.48293i | 1.41240 | + | 0.372435i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.3607 | − | 7.71380i | 0.765031 | − | 0.441691i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.7599i | 1.12776i | 0.825857 | + | 0.563880i | \(0.190692\pi\) | ||||
−0.825857 | + | 0.563880i | \(0.809308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.85341 | + | 2.13784i | −0.446765 | + | 0.121618i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1911 | + | 17.6515i | 0.577884 | + | 1.00092i | 0.995722 | + | 0.0924025i | \(0.0294546\pi\) |
−0.417838 | + | 0.908522i | \(0.637212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.19972 | − | 3.57941i | −0.350429 | − | 0.202320i | 0.314445 | − | 0.949276i | \(-0.398182\pi\) |
−0.664874 | + | 0.746955i | \(0.731515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.81412 | − | 5.66618i | −0.551216 | − | 0.318245i | 0.198396 | − | 0.980122i | \(-0.436427\pi\) |
−0.749612 | + | 0.661877i | \(0.769760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.3379 | + | 33.4942i | 1.08271 | + | 1.87531i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.7815 | − | 3.75158i | 0.769208 | − | 0.209393i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.4680i | 0.638096i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.38917 | + | 1.95674i | −0.187997 | + | 0.108540i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.7755 | − | 3.89615i | −0.817089 | − | 0.215458i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.41383 | − | 16.3052i | 0.517431 | − | 0.896216i | −0.482364 | − | 0.875971i | \(-0.660222\pi\) |
0.999795 | − | 0.0202456i | \(-0.00644480\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.1902 | + | 6.34247i | 0.613219 | + | 0.347565i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.3882 | 1.05929 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.9739 | 1.57831 | 0.789156 | − | 0.614193i | \(-0.210518\pi\) | ||||
0.789156 | + | 0.614193i | \(0.210518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.91843 | − | 4.87945i | −0.267133 | − | 0.265015i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.73325 | + | 16.8585i | −0.527085 | + | 0.912939i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.00597 | − | 11.3997i | 0.161836 | − | 0.613738i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.6525 | − | 9.03697i | 0.840270 | − | 0.485130i | −0.0170860 | − | 0.999854i | \(-0.505439\pi\) |
0.857356 | + | 0.514724i | \(0.172106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8624i | 0.688510i | 0.938876 | + | 0.344255i | \(0.111868\pi\) | ||||
−0.938876 | + | 0.344255i | \(0.888132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.92495 | + | 5.04395i | −0.262875 | + | 0.269226i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.6386 | + | 23.6227i | 0.725909 | + | 1.25731i | 0.958599 | + | 0.284760i | \(0.0919140\pi\) |
−0.232690 | + | 0.972551i | \(0.574753\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.06415 | − | 2.92379i | −0.268777 | − | 0.155178i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.773273 | + | 0.446450i | 0.0408118 | + | 0.0235627i | 0.520267 | − | 0.854004i | \(-0.325832\pi\) |
−0.479455 | + | 0.877566i | \(0.659166\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.52834 | − | 13.0395i | −0.396229 | − | 0.686288i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.66131 | − | 31.8175i | −0.454601 | − | 1.66999i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.958746i | − | 0.0501831i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.57418 | − | 5.52765i | 0.499768 | − | 0.288541i | −0.228850 | − | 0.973462i | \(-0.573496\pi\) |
0.728618 | + | 0.684921i | \(0.240163\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0434426 | − | 5.45912i | −0.00226153 | − | 0.284190i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5503 | + | 20.0057i | −0.598053 | + | 1.03586i | 0.395055 | + | 0.918657i | \(0.370725\pi\) |
−0.993108 | + | 0.117201i | \(0.962608\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.24600 | − | 7.30390i | 0.374182 | − | 0.377172i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.57375 | −0.493073 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.3938 | −1.20166 | −0.600830 | − | 0.799377i | \(-0.705163\pi\) | ||||
−0.600830 | + | 0.799377i | \(0.705163\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.46302 | + | 8.53063i | −0.433574 | + | 0.437038i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.5139 | + | 19.9426i | −0.588331 | + | 1.01902i | 0.406120 | + | 0.913820i | \(0.366881\pi\) |
−0.994451 | + | 0.105200i | \(0.966452\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.268062 | − | 33.6853i | −0.0136263 | − | 1.71232i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.45545 | − | 3.14970i | 0.276602 | − | 0.159696i | −0.355282 | − | 0.934759i | \(-0.615615\pi\) |
0.631884 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13.9990i | − | 0.707958i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.108034 | + | 0.396866i | 0.00544960 | + | 0.0200192i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.34537 | − | 5.79435i | −0.168324 | − | 0.291545i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.27940 | − | 3.62541i | −0.315154 | − | 0.181954i | 0.334077 | − | 0.942546i | \(-0.391576\pi\) |
−0.649230 | + | 0.760592i | \(0.724909\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8188 | + | 6.82360i | 0.590204 | + | 0.340755i | 0.765178 | − | 0.643819i | \(-0.222651\pi\) |
−0.174974 | + | 0.984573i | \(0.555984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.40936 | − | 4.17314i | −0.120019 | − | 0.207879i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.2859 | + | 22.0841i | −0.610489 | + | 1.09737i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 23.4989i | − | 1.16479i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.9303 | − | 6.88797i | 0.589916 | − | 0.340588i | −0.175148 | − | 0.984542i | \(-0.556041\pi\) |
0.765064 | + | 0.643954i | \(0.222707\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.88975 | − | 18.5436i | 0.241194 | − | 0.914689i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.6675 | − | 28.8690i | 0.818177 | − | 1.41712i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.25993 | + | 1.24995i | 0.0616992 | + | 0.0612102i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.94914 | 0.339488 | 0.169744 | − | 0.985488i | \(-0.445706\pi\) | ||||
0.169744 | + | 0.985488i | \(0.445706\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.349861 | −0.0170512 | −0.00852560 | − | 0.999964i | \(-0.502714\pi\) | ||||
−0.00852560 | + | 0.999964i | \(0.502714\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.05031 | − | 0.595301i | −0.0510676 | − | 0.0289445i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.32928 | + | 14.4267i | −0.404029 | + | 0.699800i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.4533 | + | 3.28379i | 0.601249 | + | 0.158543i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.4513 | − | 10.0755i | 0.840601 | − | 0.485321i | −0.0168676 | − | 0.999858i | \(-0.505369\pi\) |
0.857468 | + | 0.514537i | \(0.172036\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.42453i | − | 0.0684585i | −0.999414 | − | 0.0342292i | \(-0.989102\pi\) | ||
0.999414 | − | 0.0342292i | \(-0.0108976\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −33.1152 | + | 9.01456i | −1.58775 | + | 0.432215i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.40680 | − | 4.16870i | −0.115133 | − | 0.199416i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.76541 | − | 1.01926i | −0.0842583 | − | 0.0486465i | 0.457279 | − | 0.889323i | \(-0.348824\pi\) |
−0.541537 | + | 0.840677i | \(0.682157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1751 | − | 6.45195i | −0.530945 | − | 0.306541i | 0.210456 | − | 0.977603i | \(-0.432505\pi\) |
−0.741401 | + | 0.671062i | \(0.765838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.61898 | − | 2.80416i | −0.0767471 | − | 0.132930i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.7717 | − | 10.0099i | 1.73924 | − | 0.473453i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.49432i | 0.117714i | 0.998266 | + | 0.0588572i | \(0.0187457\pi\) | ||||
−0.998266 | + | 0.0588572i | \(0.981254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.63741 | + | 4.98681i | −0.406720 | + | 0.234820i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.1714 | + | 3.20946i | 0.571862 | + | 0.150794i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.30952 | + | 12.6605i | −0.341925 | + | 0.592232i | −0.984790 | − | 0.173748i | \(-0.944412\pi\) |
0.642865 | + | 0.765979i | \(0.277746\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.42014 | + | 29.0762i | −0.346342 | + | 1.35716i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.83467 | −0.132024 | −0.0660120 | − | 0.997819i | \(-0.521028\pi\) | ||||
−0.0660120 | + | 0.997819i | \(0.521028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.1594 | 0.658042 | 0.329021 | − | 0.944323i | \(-0.393281\pi\) | ||||
0.329021 | + | 0.944323i | \(0.393281\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.2633 | − | 12.1661i | −0.568695 | − | 0.564188i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.98809 | − | 8.63963i | 0.230821 | − | 0.399794i | −0.727229 | − | 0.686395i | \(-0.759192\pi\) |
0.958050 | + | 0.286601i | \(0.0925254\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0457 | + | 38.0966i | −0.462880 | + | 1.75540i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −53.2969 | + | 30.7710i | −2.45059 | + | 1.41485i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.72811i | 0.262824i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.27269 | + | 15.7696i | 0.424567 | + | 0.722041i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.7575 | − | 37.6850i | −0.994124 | − | 1.72187i | −0.590805 | − | 0.806815i | \(-0.701190\pi\) |
−0.403320 | − | 0.915059i | \(-0.632144\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.03757 | + | 2.90844i | 0.229693 | + | 0.132614i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −38.9535 | − | 22.4898i | −1.76879 | − | 1.02121i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5796 | − | 32.1808i | −0.841921 | − | 1.45825i | −0.888269 | − | 0.459324i | \(-0.848092\pi\) |
0.0463476 | − | 0.998925i | \(-0.485242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.24970 | + | 30.3055i | 0.373064 | + | 1.37046i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.1831i | − | 1.00111i | −0.865704 | − | 0.500556i | \(-0.833129\pi\) | ||
0.865704 | − | 0.500556i | \(-0.166871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.2929 | + | 20.3764i | −1.58951 | + | 0.917707i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 46.1673 | − | 0.367391i | 2.07507 | − | 0.0165130i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.33695 | + | 14.4400i | −0.373213 | + | 0.646424i | −0.990058 | − | 0.140661i | \(-0.955077\pi\) |
0.616845 | + | 0.787085i | \(0.288411\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.3916 | + | 29.6265i | −1.31312 | + | 1.32361i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.55884 | 0.381620 | 0.190810 | − | 0.981627i | \(-0.438889\pi\) | ||||
0.190810 | + | 0.981627i | \(0.438889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.2196 | 1.83425 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.6129 | − | 13.7217i | 0.604571 | − | 0.609401i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.1072 | + | 24.4345i | −0.625292 | + | 1.08304i | 0.363192 | + | 0.931714i | \(0.381687\pi\) |
−0.988484 | + | 0.151324i | \(0.951646\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.78938 | + | 9.93423i | 0.123154 | + | 0.438607i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.4272 | + | 6.59750i | −0.503543 | + | 0.290721i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.20559i | 0.0970017i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.72049 | − | 17.3408i | −0.207206 | − | 0.761177i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00041 | − | 15.5892i | −0.394315 | − | 0.682974i | 0.598698 | − | 0.800975i | \(-0.295685\pi\) |
−0.993014 | + | 0.118001i | \(0.962352\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9049 | + | 6.87332i | 0.520567 | + | 0.300549i | 0.737167 | − | 0.675711i | \(-0.236163\pi\) |
−0.216600 | + | 0.976260i | \(0.569497\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.7639 | − | 10.2560i | −0.773806 | − | 0.446757i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.56202 | − | 14.8299i | −0.372262 | − | 0.644776i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.63243 | + | 3.89993i | −0.287823 | + | 0.169243i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.46886i | − | 0.106938i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.0530 | − | 11.5776i | 0.866965 | − | 0.500542i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.91140 | − | 22.4180i | 0.255096 | − | 0.967410i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.6272 | + | 33.9953i | −0.843839 | + | 1.46157i | 0.0427866 | + | 0.999084i | \(0.486376\pi\) |
−0.886626 | + | 0.462488i | \(0.846957\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.6665 | − | 22.4869i | −0.972714 | − | 0.965004i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.7724 | −1.06113 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.4980 | −0.534375 | −0.267188 | − | 0.963645i | \(-0.586094\pi\) | ||||
−0.267188 | + | 0.963645i | \(0.586094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.12755 | − | 14.3396i | 0.346875 | − | 0.612001i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.00651 | + | 12.1356i | −0.298487 | + | 0.516995i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20.1633 | + | 5.31684i | 0.855884 | + | 0.225687i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.4816 | − | 8.93830i | 0.655976 | − | 0.378728i | −0.134766 | − | 0.990877i | \(-0.543028\pi\) |
0.790742 | + | 0.612150i | \(0.209695\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.2340i | − | 0.644331i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.8971 | − | 14.3996i | 2.23332 | − | 0.607950i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.36644 | + | 2.36674i | 0.0575885 | + | 0.0997462i | 0.893382 | − | 0.449297i | \(-0.148326\pi\) |
−0.835794 | + | 0.549043i | \(0.814992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.72702 | − | 5.61589i | −0.409219 | − | 0.236262i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.72971 | − | 0.998650i | −0.0725133 | − | 0.0418656i | 0.463305 | − | 0.886199i | \(-0.346663\pi\) |
−0.535818 | + | 0.844333i | \(0.679997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.00728 | + | 1.74466i | 0.0421534 | + | 0.0730118i | 0.886332 | − | 0.463050i | \(-0.153245\pi\) |
−0.844179 | + | 0.536061i | \(0.819912\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.93739 | + | 1.88848i | −0.289814 | + | 0.0788926i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.99231i | − | 0.291599i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0199 | − | 12.7132i | 0.916701 | − | 0.529258i | 0.0341199 | − | 0.999418i | \(-0.489137\pi\) |
0.882581 | + | 0.470160i | \(0.155804\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32.6741 | − | 8.61582i | −1.35789 | − | 0.358061i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.7106 | − | 28.9435i | 0.692080 | − | 1.19872i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.63534 | + | 9.94259i | −0.232993 | + | 0.411075i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.4645 | −1.42250 | −0.711251 | − | 0.702939i | \(-0.751871\pi\) | ||||
−0.711251 | + | 0.702939i | \(0.751871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.05312 | −0.290619 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.68422 | + | 4.64709i | 0.192683 | + | 0.191156i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.62199 | − | 6.27347i | 0.148737 | − | 0.257620i | −0.782024 | − | 0.623249i | \(-0.785812\pi\) |
0.930761 | + | 0.365628i | \(0.119146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.70439 | − | 10.2560i | 0.110683 | − | 0.419749i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.5464 | + | 18.7907i | −1.32981 | + | 0.767766i | −0.985270 | − | 0.171005i | \(-0.945299\pi\) |
−0.344540 | + | 0.938772i | \(0.611965\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.78103i | 0.154232i | 0.997022 | + | 0.0771158i | \(0.0245711\pi\) | ||||
−0.997022 | + | 0.0771158i | \(0.975429\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.8561 | − | 10.4996i | 0.727157 | − | 0.427575i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.7293 | − | 46.2965i | −1.08670 | − | 1.88222i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0353 | + | 13.8768i | 0.975565 | + | 0.563242i | 0.900928 | − | 0.433968i | \(-0.142887\pi\) |
0.0746364 | + | 0.997211i | \(0.476220\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.472823 | − | 0.272985i | −0.0191284 | − | 0.0110438i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.3570 | + | 26.5991i | 0.620264 | + | 1.07433i | 0.989436 | + | 0.144968i | \(0.0463080\pi\) |
−0.369172 | + | 0.929361i | \(0.620359\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.32466 | − | 8.53968i | −0.0937392 | − | 0.344353i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 44.3075i | − | 1.78375i | −0.452279 | − | 0.891877i | \(-0.649389\pi\) | ||
0.452279 | − | 0.891877i | \(-0.350611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.4026 | + | 15.8209i | −1.10140 | + | 0.635895i | −0.936589 | − | 0.350430i | \(-0.886035\pi\) |
−0.164813 | + | 0.986325i | \(0.552702\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.40499 | − | 12.1267i | −0.136638 | − | 0.486628i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5511 | − | 26.9352i | 0.622042 | − | 1.07741i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.2764 | − | 13.3824i | 0.530207 | − | 0.534443i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.7608 | 0.987279 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.7528 | −0.826157 | −0.413079 | − | 0.910695i | \(-0.635547\pi\) | ||||
−0.413079 | + | 0.910695i | \(0.635547\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.57491 | − | 3.60347i | 0.142090 | − | 0.143225i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.74033 | + | 16.8707i | −0.386533 | + | 0.669495i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.24732 | + | 0.0497150i | −0.247140 | + | 0.00196670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.0033 | − | 19.0545i | 1.30355 | − | 0.752606i | 0.322541 | − | 0.946556i | \(-0.395463\pi\) |
0.981012 | + | 0.193949i | \(0.0621298\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.5791i | − | 1.16648i | −0.812298 | − | 0.583242i | \(-0.801784\pi\) | ||
0.812298 | − | 0.583242i | \(-0.198216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.3442 | − | 52.6939i | −0.564804 | − | 2.07482i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.5935 | − | 18.3485i | −0.416474 | − | 0.721354i | 0.579108 | − | 0.815251i | \(-0.303401\pi\) |
−0.995582 | + | 0.0938966i | \(0.970068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.1731 | + | 7.02817i | 0.477838 | + | 0.275880i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.0548 | − | 13.3107i | −0.902204 | − | 0.520888i | −0.0242893 | − | 0.999705i | \(-0.507732\pi\) |
−0.877915 | + | 0.478817i | \(0.841066\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.333399 | + | 0.577465i | 0.0130270 | + | 0.0225634i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.519203 | − | 0.882984i | −0.0202560 | − | 0.0344485i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 16.3864i | − | 0.638322i | −0.947701 | − | 0.319161i | \(-0.896599\pi\) | ||
0.947701 | − | 0.319161i | \(-0.103401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0227 | − | 9.25072i | 0.623211 | − | 0.359811i | −0.154907 | − | 0.987929i | \(-0.549508\pi\) |
0.778118 | + | 0.628118i | \(0.216174\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.46014 | + | 13.1221i | −0.134381 | + | 0.509618i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.55284 | − | 14.8139i | 0.331167 | − | 0.573598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.67028 | − | 5.62534i | −0.219226 | − | 0.217488i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.1125 | −1.16248 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.4357 | −1.75142 | −0.875708 | − | 0.482841i | \(-0.839605\pi\) | ||||
−0.875708 | + | 0.482841i | \(0.839605\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.70626 | + | 14.5232i | −0.142654 | + | 0.558998i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8566 | − | 27.4644i | 0.609419 | − | 1.05554i | −0.381917 | − | 0.924196i | \(-0.624736\pi\) |
0.991336 | − | 0.131348i | \(-0.0419305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.8851 | + | 7.61670i | 1.10688 | + | 0.291872i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.0917 | + | 17.9508i | −1.18969 | + | 0.686868i | −0.958236 | − | 0.285978i | \(-0.907682\pi\) |
−0.231454 | + | 0.972846i | \(0.574348\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 31.0899i | − | 1.18788i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.3285 | − | 6.07823i | 0.851886 | − | 0.231899i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.13651 | + | 7.16465i | 0.157589 | + | 0.272952i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.2415 | − | 12.8411i | −0.846106 | − | 0.488499i | 0.0132293 | − | 0.999912i | \(-0.495789\pi\) |
−0.859335 | + | 0.511413i | \(0.829122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.49173 | + | 1.43860i | 0.0945167 | + | 0.0545692i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.25462 | − | 9.10127i | −0.199033 | − | 0.344735i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.0868 | − | 8.19016i | 1.13799 | − | 0.309780i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.29881i | 0.0490553i | 0.999699 | + | 0.0245276i | \(0.00780818\pi\) | ||||
−0.999699 | + | 0.0245276i | \(0.992192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.37344 | − | 4.25706i | 0.278095 | − | 0.160558i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.89252 | − | 0.499036i | −0.0712762 | − | 0.0187948i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.8609 | − | 24.0077i | 0.520556 | − | 0.901629i | −0.479158 | − | 0.877728i | \(-0.659058\pi\) |
0.999714 | − | 0.0239010i | \(-0.00760863\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.21890 | − | 3.52480i | −0.233227 | − | 0.132190i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.60973 | 0.322437 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.8789 | 0.780828 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.0801 | + | 28.8496i | 1.08602 | + | 1.07741i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.9122 | + | 36.2210i | −0.779893 | + | 1.35081i | 0.152109 | + | 0.988364i | \(0.451393\pi\) |
−0.932003 | + | 0.362451i | \(0.881940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.80304 | + | 6.83775i | −0.0670558 | + | 0.254299i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.6284 | + | 10.1777i | −0.654701 | + | 0.377992i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.19295i | 0.0813319i | 0.999173 | + | 0.0406660i | \(0.0129479\pi\) | ||||
−0.999173 | + | 0.0406660i | \(0.987052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.644508 | + | 26.9923i | 0.0238707 | + | 0.999715i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.4235 | − | 56.1592i | −1.19923 | − | 2.07712i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0850 | − | 10.4414i | −0.667986 | − | 0.385662i | 0.127327 | − | 0.991861i | \(-0.459360\pi\) |
−0.795313 | + | 0.606199i | \(0.792693\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.7731 | − | 18.9215i | −1.20721 | − | 0.696984i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.65032 | + | 11.5187i | 0.244636 | + | 0.423722i | 0.962029 | − | 0.272947i | \(-0.0879982\pi\) |
−0.717393 | + | 0.696668i | \(0.754665\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.22565 | + | 4.50246i | 0.0450255 | + | 0.165402i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.8226i | 0.910653i | 0.890324 | + | 0.455327i | \(0.150478\pi\) | ||||
−0.890324 | + | 0.455327i | \(0.849522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.5051 | − | 30.8912i | 1.96028 | − | 1.13177i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.283409 | − | 35.6139i | −0.0103694 | − | 1.30305i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.98635 | − | 10.3687i | 0.218445 | − | 0.378358i | −0.735888 | − | 0.677104i | \(-0.763235\pi\) |
0.954333 | + | 0.298746i | \(0.0965682\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.05184 | − | 7.10818i | 0.256983 | − | 0.259037i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.4063 | 0.742663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.8095 | 1.08345 | 0.541723 | − | 0.840557i | \(-0.317772\pi\) | ||||
0.541723 | + | 0.840557i | \(0.317772\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.2065 | + | 16.3359i | −0.588257 | + | 0.592957i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.7439 | + | 29.0013i | −0.606967 | + | 1.05130i | 0.384770 | + | 0.923012i | \(0.374281\pi\) |
−0.991737 | + | 0.128286i | \(0.959053\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.387121 | + | 48.6467i | 0.0139964 | + | 1.75882i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.01333 | + | 1.73975i | −0.108805 | + | 0.0628186i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.6491i | 0.708566i | 0.935138 | + | 0.354283i | \(0.115275\pi\) | ||||
−0.935138 | + | 0.354283i | \(0.884725\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.53770 | − | 35.0370i | −0.343492 | − | 1.26183i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.51659 | − | 11.2871i | −0.234385 | − | 0.405968i | 0.724708 | − | 0.689056i | \(-0.241974\pi\) |
−0.959094 | + | 0.283088i | \(0.908641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.87282 | − | 5.12273i | −0.318721 | − | 0.184014i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.12951 | − | 1.80682i | −0.112126 | − | 0.0647362i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.70682 | + | 9.88451i | 0.204206 | + | 0.353695i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.6166 | + | 26.2355i | −0.915462 | + | 0.937582i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 63.8722i | 2.27970i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.1053 | + | 12.1852i | −0.752324 | + | 0.434354i | −0.826533 | − | 0.562888i | \(-0.809690\pi\) |
0.0742091 | + | 0.997243i | \(0.476357\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.20775 | + | 8.37256i | −0.0785981 | + | 0.298071i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.72702 | − | 6.45538i | 0.132350 | − | 0.229237i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.0542 | + | 20.8873i | 0.746715 | + | 0.740797i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.14465 | 0.111389 | 0.0556947 | − | 0.998448i | \(-0.482263\pi\) | ||||
0.0556947 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.32404 | −0.0822186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00962 | − | 1.70582i | −0.106340 | − | 0.0602721i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.935670 | + | 1.62063i | −0.0330191 | + | 0.0571907i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.7117 | − | 6.77989i | −0.905093 | − | 0.238663i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.76799 | + | 3.33015i | −0.202792 | + | 0.117082i | −0.597957 | − | 0.801528i | \(-0.704021\pi\) |
0.395165 | + | 0.918610i | \(0.370687\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.8504i | 1.71537i | 0.514176 | + | 0.857685i | \(0.328098\pi\) | ||||
−0.514176 | + | 0.857685i | \(0.671902\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.9357 | + | 7.60460i | −0.979747 | + | 0.266705i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.4590 | + | 44.0964i | 0.891791 | + | 1.54463i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.3106 | − | 11.1490i | −0.675591 | − | 0.390053i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.0636 | + | 20.2440i | 1.22373 | + | 0.706520i | 0.965711 | − | 0.259621i | \(-0.0835975\pi\) |
0.258017 | + | 0.966140i | \(0.416931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.2956 | − | 29.9568i | −0.602886 | − | 1.04423i | −0.992382 | − | 0.123201i | \(-0.960684\pi\) |
0.389496 | − | 0.921028i | \(-0.372649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.4214 | − | 7.19240i | 0.919876 | − | 0.250407i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.3071i | 1.01911i | 0.860438 | + | 0.509555i | \(0.170190\pi\) | ||||
−0.860438 | + | 0.509555i | \(0.829810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.7957 | + | 7.38763i | −0.444414 | + | 0.256583i | −0.705468 | − | 0.708741i | \(-0.749263\pi\) |
0.261054 | + | 0.965324i | \(0.415930\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 37.7070 | + | 9.94293i | 1.30804 | + | 0.344916i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.8277 | + | 58.5912i | −1.17065 | + | 2.02763i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.8826 | − | 4.56358i | −0.618115 | − | 0.157740i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.0373 | 1.10605 | 0.553026 | − | 0.833164i | \(-0.313473\pi\) | ||||
0.553026 | + | 0.833164i | \(0.313473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7968 | −0.717131 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.2723 | + | 22.0958i | 0.767100 | + | 0.761020i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.6675 | − | 27.1369i | 0.538978 | − | 0.933537i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.55345 | − | 9.68356i | 0.0876342 | − | 0.332339i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.00076 | + | 5.19659i | −0.308542 | + | 0.178137i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.1110i | 1.13370i | 0.823821 | + | 0.566850i | \(0.191838\pi\) | ||||
−0.823821 | + | 0.566850i | \(0.808162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.47896 | + | 14.4198i | 0.289974 | + | 0.493145i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.00041 | − | 15.5892i | −0.307448 | − | 0.532516i | 0.670355 | − | 0.742040i | \(-0.266142\pi\) |
−0.977803 | + | 0.209524i | \(0.932808\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.1107 | + | 13.3430i | 0.788528 | + | 0.455257i | 0.839444 | − | 0.543446i | \(-0.182881\pi\) |
−0.0509160 | + | 0.998703i | \(0.516214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.69289 | − | 5.01884i | −0.295909 | − | 0.170843i | 0.344694 | − | 0.938715i | \(-0.387983\pi\) |
−0.640604 | + | 0.767872i | \(0.721316\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.5677 | − | 25.2320i | −0.495317 | − | 0.857913i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.43889 | + | 27.3269i | 0.252638 | + | 0.928071i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.0594i | 0.443009i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.11262 | − | 4.68382i | 0.274885 | − | 0.158705i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −48.0545 | + | 0.382409i | −1.62640 | + | 0.0129426i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.38102 | − | 12.7843i | 0.249239 | − | 0.431695i | −0.714076 | − | 0.700069i | \(-0.753153\pi\) |
0.963315 | + | 0.268373i | \(0.0864861\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.4519 | + | 11.5434i | −0.386263 | + | 0.389349i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.42345 | 0.149030 | 0.0745148 | − | 0.997220i | \(-0.476259\pi\) | ||||
0.0745148 | + | 0.997220i | \(0.476259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.5403 | −0.354711 | −0.177355 | − | 0.984147i | \(-0.556754\pi\) | ||||
−0.177355 | + | 0.984147i | \(0.556754\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.78485 | + | 8.85503i | −0.295299 | + | 0.297659i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.92026 | − | 8.52213i | 0.165206 | − | 0.286145i | −0.771522 | − | 0.636202i | \(-0.780504\pi\) |
0.936728 | + | 0.350057i | \(0.113838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 42.3201 | − | 25.3400i | 1.41778 | − | 0.848921i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.692067 | + | 0.399565i | −0.0231591 | + | 0.0133709i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 37.5857i | − | 1.25635i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.49615 | − | 5.49615i | −0.0499551 | − | 0.183511i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.5320 | − | 21.7061i | −0.417966 | − | 0.723939i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.4979 | + | 17.6080i | 1.01603 | + | 0.586607i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.8268 | − | 25.8808i | −1.49009 | − | 0.860306i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.10609 | + | 7.11195i | 0.136340 | + | 0.236148i | 0.926109 | − | 0.377257i | \(-0.123133\pi\) |
−0.789768 | + | 0.613405i | \(0.789799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.9624 | − | 22.3222i | 1.25913 | − | 0.740382i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.6131i | 1.47810i | 0.673652 | + | 0.739049i | \(0.264725\pi\) | ||||
−0.673652 | + | 0.739049i | \(0.735275\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.3483 | + | 32.5327i | −1.86486 | + | 1.07668i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.81326 | − | 25.8382i | 0.225239 | − | 0.854185i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.3222 | + | 26.5388i | −0.505431 | + | 0.875433i | 0.494549 | + | 0.869150i | \(0.335333\pi\) |
−0.999980 | + | 0.00628290i | \(0.998000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.2970 | + | 24.1044i | 0.800613 | + | 0.794267i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.82532 | −0.0929966 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.3677 | 0.406648 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.95137 | + | 12.2645i | −0.228313 | + | 0.402819i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.7198 | + | 18.5673i | −0.351706 | + | 0.609173i | −0.986548 | − | 0.163469i | \(-0.947732\pi\) |
0.634842 | + | 0.772642i | \(0.281065\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.1361 | + | 9.00133i | 1.11757 | + | 0.294690i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 76.9687 | − | 44.4379i | 2.51714 | − | 1.45327i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 25.1409i | − | 0.821319i | −0.911789 | − | 0.410659i | \(-0.865299\pi\) | ||
0.911789 | − | 0.410659i | \(-0.134701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9641 | + | 3.25684i | −0.390433 | + | 0.106283i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0598 | + | 45.1369i | 0.849525 | + | 1.47142i | 0.881633 | + | 0.471936i | \(0.156445\pi\) |
−0.0321082 | + | 0.999484i | \(0.510222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.82019 | + | 2.20559i | 0.124403 | + | 0.0718238i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.8943 | − | 20.7236i | −1.16641 | − | 0.673427i | −0.213578 | − | 0.976926i | \(-0.568512\pi\) |
−0.952832 | + | 0.303500i | \(0.901845\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.231615 | − | 0.401169i | −0.00751853 | − | 0.0130225i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.9391 | + | 5.15556i | −0.614141 | + | 0.167180i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 29.7579i | − | 0.963952i | −0.876184 | − | 0.481976i | \(-0.839919\pi\) | ||
0.876184 | − | 0.481976i | \(-0.160081\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.0943 | + | 5.82797i | −0.326645 | + | 0.188589i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 64.7742 | + | 17.0803i | 2.09385 | + | 0.552127i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.19231 | + | 15.9215i | −0.296526 | + | 0.513598i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.1986 | − | 21.5222i | 0.393093 | − | 0.693545i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54.7809 | −1.76346 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.6814 | −0.536436 | −0.268218 | − | 0.963358i | \(-0.586435\pi\) | ||||
−0.268218 | + | 0.963358i | \(0.586435\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.1011 | + | 13.9894i | 0.452994 | + | 0.449403i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.6466 | + | 44.4211i | −0.823037 | + | 1.42554i | 0.0803734 | + | 0.996765i | \(0.474389\pi\) |
−0.903410 | + | 0.428777i | \(0.858945\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.72830 | + | 6.55430i | −0.0553498 | + | 0.209906i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.6912 | − | 9.63669i | 0.534000 | − | 0.308305i | −0.208644 | − | 0.977992i | \(-0.566905\pi\) |
0.742644 | + | 0.669687i | \(0.233572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.32005i | 0.201990i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.8149 | + | 13.4154i | −0.728422 | + | 0.428319i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.85925 | − | 3.22031i | −0.0593008 | − | 0.102712i | 0.834851 | − | 0.550476i | \(-0.185554\pi\) |
−0.894152 | + | 0.447764i | \(0.852220\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.26382 | + | 5.34847i | 0.295170 | + | 0.170416i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.5724 | + | 13.6095i | 0.749558 | + | 0.432758i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.4914 | + | 44.1525i | 0.809762 | + | 1.40255i | 0.913029 | + | 0.407896i | \(0.133737\pi\) |
−0.103266 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.56547 | − | 31.4654i | −0.271817 | − | 0.998526i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 17.1950i | − | 0.545118i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.6801 | + | 26.3734i | −1.44670 | + | 0.835254i | −0.998283 | − | 0.0585692i | \(-0.981346\pi\) |
−0.448419 | + | 0.893823i | \(0.648013\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.4493 | − | 6.02261i | 0.678624 | − | 0.190547i |
(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 | 1176.2.u.b.1097.6 | 16 | ||
3.2 | odd | 2 | inner | 1176.2.u.b.1097.8 | 16 | ||
7.2 | even | 3 | 1176.2.k.a.881.10 | 16 | |||
7.3 | odd | 6 | inner | 1176.2.u.b.521.8 | 16 | ||
7.4 | even | 3 | 168.2.u.a.17.1 | ✓ | 16 | ||
7.5 | odd | 6 | 1176.2.k.a.881.7 | 16 | |||
7.6 | odd | 2 | 168.2.u.a.89.3 | yes | 16 | ||
21.2 | odd | 6 | 1176.2.k.a.881.8 | 16 | |||
21.5 | even | 6 | 1176.2.k.a.881.9 | 16 | |||
21.11 | odd | 6 | 168.2.u.a.17.3 | yes | 16 | ||
21.17 | even | 6 | inner | 1176.2.u.b.521.6 | 16 | ||
21.20 | even | 2 | 168.2.u.a.89.1 | yes | 16 | ||
28.11 | odd | 6 | 336.2.bc.f.17.8 | 16 | |||
28.19 | even | 6 | 2352.2.k.i.881.10 | 16 | |||
28.23 | odd | 6 | 2352.2.k.i.881.7 | 16 | |||
28.27 | even | 2 | 336.2.bc.f.257.6 | 16 | |||
84.11 | even | 6 | 336.2.bc.f.17.6 | 16 | |||
84.23 | even | 6 | 2352.2.k.i.881.9 | 16 | |||
84.47 | odd | 6 | 2352.2.k.i.881.8 | 16 | |||
84.83 | odd | 2 | 336.2.bc.f.257.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.u.a.17.1 | ✓ | 16 | 7.4 | even | 3 | ||
168.2.u.a.17.3 | yes | 16 | 21.11 | odd | 6 | ||
168.2.u.a.89.1 | yes | 16 | 21.20 | even | 2 | ||
168.2.u.a.89.3 | yes | 16 | 7.6 | odd | 2 | ||
336.2.bc.f.17.6 | 16 | 84.11 | even | 6 | |||
336.2.bc.f.17.8 | 16 | 28.11 | odd | 6 | |||
336.2.bc.f.257.6 | 16 | 28.27 | even | 2 | |||
336.2.bc.f.257.8 | 16 | 84.83 | odd | 2 | |||
1176.2.k.a.881.7 | 16 | 7.5 | odd | 6 | |||
1176.2.k.a.881.8 | 16 | 21.2 | odd | 6 | |||
1176.2.k.a.881.9 | 16 | 21.5 | even | 6 | |||
1176.2.k.a.881.10 | 16 | 7.2 | even | 3 | |||
1176.2.u.b.521.6 | 16 | 21.17 | even | 6 | inner | ||
1176.2.u.b.521.8 | 16 | 7.3 | odd | 6 | inner | ||
1176.2.u.b.1097.6 | 16 | 1.1 | even | 1 | trivial | ||
1176.2.u.b.1097.8 | 16 | 3.2 | odd | 2 | inner | ||
2352.2.k.i.881.7 | 16 | 28.23 | odd | 6 | |||
2352.2.k.i.881.8 | 16 | 84.47 | odd | 6 | |||
2352.2.k.i.881.9 | 16 | 84.23 | even | 6 | |||
2352.2.k.i.881.10 | 16 | 28.19 | even | 6 |