Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.a (trivial) |
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: | yes |
Analytic conductor: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26x^{14} + 268x^{12} - 1395x^{10} + 3876x^{8} - 5635x^{6} + 4042x^{4} - 1272x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 693) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.899827\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.899827 | −0.636274 | −0.318137 | − | 0.948045i | \(-0.603057\pi\) | ||||
−0.318137 | + | 0.948045i | \(0.603057\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.19031 | −0.595156 | ||||||||
\(5\) | 0.803961 | 0.359542 | 0.179771 | − | 0.983708i | \(-0.442464\pi\) | ||||
0.179771 | + | 0.983708i | \(0.442464\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.87073 | 1.01496 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.723426 | −0.228767 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.94705 | 0.817365 | 0.408682 | − | 0.912677i | \(-0.365988\pi\) | ||||
0.408682 | + | 0.912677i | \(0.365988\pi\) | |||||||
\(14\) | −0.899827 | −0.240489 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.202537 | −0.0506344 | ||||||||
\(17\) | −3.30399 | −0.801336 | −0.400668 | − | 0.916223i | \(-0.631222\pi\) | ||||
−0.400668 | + | 0.916223i | \(0.631222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.93896 | 1.82132 | 0.910661 | − | 0.413155i | \(-0.135573\pi\) | ||||
0.910661 | + | 0.413155i | \(0.135573\pi\) | |||||||
\(20\) | −0.956964 | −0.213984 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.53481 | 1.57112 | 0.785558 | − | 0.618788i | \(-0.212376\pi\) | ||||
0.785558 | + | 0.618788i | \(0.212376\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.35365 | −0.870729 | ||||||||
\(26\) | −2.65184 | −0.520068 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.19031 | −0.224948 | ||||||||
\(29\) | 0.234450 | 0.0435364 | 0.0217682 | − | 0.999763i | \(-0.493070\pi\) | ||||
0.0217682 | + | 0.999763i | \(0.493070\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.98395 | 0.715538 | 0.357769 | − | 0.933810i | \(-0.383538\pi\) | ||||
0.357769 | + | 0.933810i | \(0.383538\pi\) | |||||||
\(32\) | −5.55921 | −0.982738 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.97302 | 0.509869 | ||||||||
\(35\) | 0.803961 | 0.135894 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.536441 | −0.0881904 | −0.0440952 | − | 0.999027i | \(-0.514040\pi\) | ||||
−0.0440952 | + | 0.999027i | \(0.514040\pi\) | |||||||
\(38\) | −7.14369 | −1.15886 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.30795 | 0.364920 | ||||||||
\(41\) | 4.78449 | 0.747212 | 0.373606 | − | 0.927587i | \(-0.378121\pi\) | ||||
0.373606 | + | 0.927587i | \(0.378121\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.16645 | 0.482878 | 0.241439 | − | 0.970416i | \(-0.422381\pi\) | ||||
0.241439 | + | 0.970416i | \(0.422381\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.78003 | −0.999660 | ||||||||
\(47\) | 11.0114 | 1.60617 | 0.803085 | − | 0.595864i | \(-0.203190\pi\) | ||||
0.803085 | + | 0.595864i | \(0.203190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.91753 | 0.554022 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.50791 | −0.486459 | ||||||||
\(53\) | −11.7317 | −1.61148 | −0.805738 | − | 0.592273i | \(-0.798231\pi\) | ||||
−0.805738 | + | 0.592273i | \(0.798231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.87073 | 0.383617 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.210965 | −0.0277011 | ||||||||
\(59\) | 5.25351 | 0.683949 | 0.341974 | − | 0.939709i | \(-0.388904\pi\) | ||||
0.341974 | + | 0.939709i | \(0.388904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.65442 | 0.467901 | 0.233950 | − | 0.972249i | \(-0.424835\pi\) | ||||
0.233950 | + | 0.972249i | \(0.424835\pi\) | |||||||
\(62\) | −3.58486 | −0.455278 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.40740 | 0.675925 | ||||||||
\(65\) | 2.36931 | 0.293877 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6736 | −1.67050 | −0.835250 | − | 0.549871i | \(-0.814677\pi\) | ||||
−0.835250 | + | 0.549871i | \(0.814677\pi\) | |||||||
\(68\) | 3.93278 | 0.476920 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.723426 | −0.0864660 | ||||||||
\(71\) | 10.3371 | 1.22678 | 0.613392 | − | 0.789779i | \(-0.289805\pi\) | ||||
0.613392 | + | 0.789779i | \(0.289805\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.90937 | 1.04276 | 0.521382 | − | 0.853324i | \(-0.325417\pi\) | ||||
0.521382 | + | 0.853324i | \(0.325417\pi\) | |||||||
\(74\) | 0.482705 | 0.0561133 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.44983 | −1.08397 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.37651 | −0.942431 | −0.471215 | − | 0.882018i | \(-0.656185\pi\) | ||||
−0.471215 | + | 0.882018i | \(0.656185\pi\) | |||||||
\(80\) | −0.162832 | −0.0182052 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.30522 | −0.475432 | ||||||||
\(83\) | 7.26234 | 0.797145 | 0.398573 | − | 0.917137i | \(-0.369506\pi\) | ||||
0.398573 | + | 0.917137i | \(0.369506\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.65628 | −0.288114 | ||||||||
\(86\) | −2.84925 | −0.307243 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.03460 | −0.851666 | −0.425833 | − | 0.904802i | \(-0.640019\pi\) | ||||
−0.425833 | + | 0.904802i | \(0.640019\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.94705 | 0.308935 | ||||||||
\(92\) | −8.96877 | −0.935058 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.90831 | −1.02196 | ||||||||
\(95\) | 6.38261 | 0.654842 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.2711 | 1.95669 | 0.978343 | − | 0.206992i | \(-0.0663675\pi\) | ||||
0.978343 | + | 0.206992i | \(0.0663675\pi\) | |||||||
\(98\) | −0.899827 | −0.0908963 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.18219 | 0.518219 | ||||||||
\(101\) | −17.2794 | −1.71936 | −0.859682 | − | 0.510830i | \(-0.829338\pi\) | ||||
−0.859682 | + | 0.510830i | \(0.829338\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.3573 | 1.41467 | 0.707334 | − | 0.706880i | \(-0.249898\pi\) | ||||
0.707334 | + | 0.706880i | \(0.249898\pi\) | |||||||
\(104\) | 8.46018 | 0.829589 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.5565 | 1.02534 | ||||||||
\(107\) | −15.3202 | −1.48106 | −0.740529 | − | 0.672024i | \(-0.765425\pi\) | ||||
−0.740529 | + | 0.672024i | \(0.765425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.50237 | −0.527032 | −0.263516 | − | 0.964655i | \(-0.584882\pi\) | ||||
−0.263516 | + | 0.964655i | \(0.584882\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.202537 | −0.0191380 | ||||||||
\(113\) | 6.69477 | 0.629791 | 0.314895 | − | 0.949126i | \(-0.398031\pi\) | ||||
0.314895 | + | 0.949126i | \(0.398031\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.05769 | 0.564883 | ||||||||
\(116\) | −0.279069 | −0.0259109 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.72725 | −0.435179 | ||||||||
\(119\) | −3.30399 | −0.302877 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.28835 | −0.297713 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.74214 | −0.425856 | ||||||||
\(125\) | −7.51997 | −0.672607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5436 | −1.02433 | −0.512165 | − | 0.858887i | \(-0.671156\pi\) | ||||
−0.512165 | + | 0.858887i | \(0.671156\pi\) | |||||||
\(128\) | 6.25269 | 0.552665 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.13197 | −0.186986 | ||||||||
\(131\) | −21.2008 | −1.85232 | −0.926161 | − | 0.377128i | \(-0.876912\pi\) | ||||
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.93896 | 0.688395 | ||||||||
\(134\) | 12.3039 | 1.06290 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.48487 | −0.813321 | ||||||||
\(137\) | −0.815166 | −0.0696443 | −0.0348222 | − | 0.999394i | \(-0.511086\pi\) | ||||
−0.0348222 | + | 0.999394i | \(0.511086\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.27263 | 0.786495 | 0.393247 | − | 0.919433i | \(-0.371352\pi\) | ||||
0.393247 | + | 0.919433i | \(0.371352\pi\) | |||||||
\(140\) | −0.956964 | −0.0808782 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.30157 | −0.780570 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.188489 | 0.0156532 | ||||||||
\(146\) | −8.01690 | −0.663483 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.638532 | 0.0524870 | ||||||||
\(149\) | −6.94847 | −0.569241 | −0.284621 | − | 0.958640i | \(-0.591868\pi\) | ||||
−0.284621 | + | 0.958640i | \(0.591868\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0283 | 1.14161 | 0.570803 | − | 0.821087i | \(-0.306632\pi\) | ||||
0.570803 | + | 0.821087i | \(0.306632\pi\) | |||||||
\(152\) | 22.7906 | 1.84856 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.20294 | 0.257266 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.733382 | 0.0585302 | 0.0292651 | − | 0.999572i | \(-0.490683\pi\) | ||||
0.0292651 | + | 0.999572i | \(0.490683\pi\) | |||||||
\(158\) | 7.53741 | 0.599644 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.46939 | −0.353336 | ||||||||
\(161\) | 7.53481 | 0.593826 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.96358 | 0.232125 | 0.116063 | − | 0.993242i | \(-0.462973\pi\) | ||||
0.116063 | + | 0.993242i | \(0.462973\pi\) | |||||||
\(164\) | −5.69504 | −0.444708 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.53485 | −0.507203 | ||||||||
\(167\) | −8.04008 | −0.622160 | −0.311080 | − | 0.950384i | \(-0.600691\pi\) | ||||
−0.311080 | + | 0.950384i | \(0.600691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.31490 | −0.331915 | ||||||||
\(170\) | 2.39020 | 0.183320 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.76906 | −0.287388 | ||||||||
\(173\) | −5.15560 | −0.391973 | −0.195986 | − | 0.980607i | \(-0.562791\pi\) | ||||
−0.195986 | + | 0.980607i | \(0.562791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.35365 | −0.329105 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.22975 | 0.541893 | ||||||||
\(179\) | −6.01273 | −0.449412 | −0.224706 | − | 0.974427i | \(-0.572142\pi\) | ||||
−0.224706 | + | 0.974427i | \(0.572142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.45046 | 0.182141 | 0.0910707 | − | 0.995844i | \(-0.470971\pi\) | ||||
0.0910707 | + | 0.995844i | \(0.470971\pi\) | |||||||
\(182\) | −2.65184 | −0.196567 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 21.6304 | 1.59461 | ||||||||
\(185\) | −0.431278 | −0.0317082 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −13.1069 | −0.955922 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.74325 | −0.416659 | ||||||||
\(191\) | 21.2746 | 1.53938 | 0.769689 | − | 0.638419i | \(-0.220411\pi\) | ||||
0.769689 | + | 0.638419i | \(0.220411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.39924 | −0.604590 | −0.302295 | − | 0.953214i | \(-0.597753\pi\) | ||||
−0.302295 | + | 0.953214i | \(0.597753\pi\) | |||||||
\(194\) | −17.3407 | −1.24499 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.19031 | −0.0850222 | ||||||||
\(197\) | −10.9646 | −0.781194 | −0.390597 | − | 0.920562i | \(-0.627731\pi\) | ||||
−0.390597 | + | 0.920562i | \(0.627731\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.26130 | 0.443852 | 0.221926 | − | 0.975064i | \(-0.428766\pi\) | ||||
0.221926 | + | 0.975064i | \(0.428766\pi\) | |||||||
\(200\) | −12.4981 | −0.883752 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.5485 | 1.09399 | ||||||||
\(203\) | 0.234450 | 0.0164552 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.84655 | 0.268655 | ||||||||
\(206\) | −12.9191 | −0.900116 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.596888 | −0.0413867 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.7203 | 1.15107 | 0.575537 | − | 0.817776i | \(-0.304793\pi\) | ||||
0.575537 | + | 0.817776i | \(0.304793\pi\) | |||||||
\(212\) | 13.9644 | 0.959078 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.7855 | 0.942359 | ||||||||
\(215\) | 2.54570 | 0.173615 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.98395 | 0.270448 | ||||||||
\(218\) | 4.95118 | 0.335337 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.73704 | −0.654984 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.0968 | 0.877026 | 0.438513 | − | 0.898725i | \(-0.355505\pi\) | ||||
0.438513 | + | 0.898725i | \(0.355505\pi\) | |||||||
\(224\) | −5.55921 | −0.371440 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.02413 | −0.400719 | ||||||||
\(227\) | 15.9025 | 1.05548 | 0.527742 | − | 0.849405i | \(-0.323039\pi\) | ||||
0.527742 | + | 0.849405i | \(0.323039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.01594 | 0.595790 | 0.297895 | − | 0.954599i | \(-0.403715\pi\) | ||||
0.297895 | + | 0.954599i | \(0.403715\pi\) | |||||||
\(230\) | −5.45088 | −0.359420 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.673044 | 0.0441875 | ||||||||
\(233\) | −2.54200 | −0.166532 | −0.0832659 | − | 0.996527i | \(-0.526535\pi\) | ||||
−0.0832659 | + | 0.996527i | \(0.526535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.85270 | 0.577487 | ||||||||
\(236\) | −6.25331 | −0.407056 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.97302 | 0.192713 | ||||||||
\(239\) | −19.1749 | −1.24032 | −0.620161 | − | 0.784475i | \(-0.712933\pi\) | ||||
−0.620161 | + | 0.784475i | \(0.712933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50063 | −0.483158 | −0.241579 | − | 0.970381i | \(-0.577665\pi\) | ||||
−0.241579 | + | 0.970381i | \(0.577665\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.34990 | −0.278474 | ||||||||
\(245\) | 0.803961 | 0.0513632 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.3965 | 1.48868 | ||||||||
\(248\) | 11.4368 | 0.726239 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.76667 | 0.427962 | ||||||||
\(251\) | −14.6903 | −0.927245 | −0.463622 | − | 0.886033i | \(-0.653451\pi\) | ||||
−0.463622 | + | 0.886033i | \(0.653451\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.3872 | 0.651754 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.4411 | −1.02757 | ||||||||
\(257\) | −20.7501 | −1.29436 | −0.647178 | − | 0.762339i | \(-0.724051\pi\) | ||||
−0.647178 | + | 0.762339i | \(0.724051\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.536441 | −0.0333328 | ||||||||
\(260\) | −2.82022 | −0.174903 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.0771 | 1.17858 | ||||||||
\(263\) | 27.3462 | 1.68624 | 0.843118 | − | 0.537729i | \(-0.180717\pi\) | ||||
0.843118 | + | 0.537729i | \(0.180717\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.43185 | −0.579394 | ||||||||
\(266\) | −7.14369 | −0.438008 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.2759 | 0.994207 | ||||||||
\(269\) | 1.57905 | 0.0962763 | 0.0481381 | − | 0.998841i | \(-0.484671\pi\) | ||||
0.0481381 | + | 0.998841i | \(0.484671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1014 | 0.917342 | 0.458671 | − | 0.888606i | \(-0.348326\pi\) | ||||
0.458671 | + | 0.888606i | \(0.348326\pi\) | |||||||
\(272\) | 0.669183 | 0.0405752 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.733509 | 0.0443129 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2348 | −0.975453 | −0.487727 | − | 0.872996i | \(-0.662174\pi\) | ||||
−0.487727 | + | 0.872996i | \(0.662174\pi\) | |||||||
\(278\) | −8.34377 | −0.500426 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.30795 | 0.137927 | ||||||||
\(281\) | −17.0866 | −1.01930 | −0.509651 | − | 0.860381i | \(-0.670226\pi\) | ||||
−0.509651 | + | 0.860381i | \(0.670226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.115027 | −0.00683762 | −0.00341881 | − | 0.999994i | \(-0.501088\pi\) | ||||
−0.00341881 | + | 0.999994i | \(0.501088\pi\) | |||||||
\(284\) | −12.3043 | −0.730127 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.78449 | 0.282420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.08362 | −0.357860 | ||||||||
\(290\) | −0.169608 | −0.00995970 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.6049 | −0.620606 | ||||||||
\(293\) | −18.6601 | −1.09013 | −0.545067 | − | 0.838392i | \(-0.683496\pi\) | ||||
−0.545067 | + | 0.838392i | \(0.683496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.22362 | 0.245909 | ||||||||
\(296\) | −1.53998 | −0.0895094 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.25243 | 0.362193 | ||||||||
\(299\) | 22.2055 | 1.28417 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.16645 | 0.182511 | ||||||||
\(302\) | −12.6230 | −0.726374 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.60794 | −0.0922215 | ||||||||
\(305\) | 2.93802 | 0.168230 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.9263 | 0.794817 | 0.397408 | − | 0.917642i | \(-0.369910\pi\) | ||||
0.397408 | + | 0.917642i | \(0.369910\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.88209 | −0.163692 | ||||||||
\(311\) | 10.1568 | 0.575939 | 0.287970 | − | 0.957640i | \(-0.407020\pi\) | ||||
0.287970 | + | 0.957640i | \(0.407020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.81885 | 0.272377 | 0.136189 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136189 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(314\) | −0.659917 | −0.0372413 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.97065 | 0.560893 | ||||||||
\(317\) | −8.07318 | −0.453435 | −0.226718 | − | 0.973961i | \(-0.572799\pi\) | ||||
−0.226718 | + | 0.973961i | \(0.572799\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.34734 | 0.243024 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.78003 | −0.377836 | ||||||||
\(323\) | −26.2303 | −1.45949 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.8304 | −0.711703 | ||||||||
\(326\) | −2.66671 | −0.147695 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.7350 | 0.758387 | ||||||||
\(329\) | 11.0114 | 0.607076 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.776780 | 0.0426957 | 0.0213479 | − | 0.999772i | \(-0.493204\pi\) | ||||
0.0213479 | + | 0.999772i | \(0.493204\pi\) | |||||||
\(332\) | −8.64444 | −0.474425 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.23468 | 0.395864 | ||||||||
\(335\) | −10.9931 | −0.600615 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.209600 | 0.0114176 | 0.00570882 | − | 0.999984i | \(-0.498183\pi\) | ||||
0.00570882 | + | 0.999984i | \(0.498183\pi\) | |||||||
\(338\) | 3.88266 | 0.211189 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.16180 | 0.171473 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.09001 | 0.490100 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.63915 | 0.249402 | ||||||||
\(347\) | −22.7970 | −1.22380 | −0.611902 | − | 0.790933i | \(-0.709595\pi\) | ||||
−0.611902 | + | 0.790933i | \(0.709595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0294 | −0.750976 | −0.375488 | − | 0.926827i | \(-0.622525\pi\) | ||||
−0.375488 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(350\) | 3.91753 | 0.209401 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.3703 | 1.19065 | 0.595327 | − | 0.803484i | \(-0.297023\pi\) | ||||
0.595327 | + | 0.803484i | \(0.297023\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.31060 | 0.441081 | ||||||||
\(356\) | 9.56367 | 0.506874 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.41042 | 0.285949 | ||||||||
\(359\) | 2.70211 | 0.142612 | 0.0713060 | − | 0.997454i | \(-0.477283\pi\) | ||||
0.0713060 | + | 0.997454i | \(0.477283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.0270 | 2.31721 | ||||||||
\(362\) | −2.20499 | −0.115892 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.50791 | −0.183864 | ||||||||
\(365\) | 7.16279 | 0.374918 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.2820 | 1.47631 | 0.738155 | − | 0.674631i | \(-0.235697\pi\) | ||||
0.738155 | + | 0.674631i | \(0.235697\pi\) | |||||||
\(368\) | −1.52608 | −0.0795525 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.388076 | 0.0201751 | ||||||||
\(371\) | −11.7317 | −0.609080 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.53857 | 0.442110 | 0.221055 | − | 0.975261i | \(-0.429050\pi\) | ||||
0.221055 | + | 0.975261i | \(0.429050\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.6106 | 1.63019 | ||||||||
\(377\) | 0.690937 | 0.0355851 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.6825 | 1.78152 | 0.890759 | − | 0.454475i | \(-0.150173\pi\) | ||||
0.890759 | + | 0.454475i | \(0.150173\pi\) | |||||||
\(380\) | −7.59729 | −0.389733 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.1435 | −0.979466 | ||||||||
\(383\) | −12.7173 | −0.649826 | −0.324913 | − | 0.945744i | \(-0.605335\pi\) | ||||
−0.324913 | + | 0.945744i | \(0.605335\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.55786 | 0.384685 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.9386 | −1.16453 | ||||||||
\(389\) | −2.48749 | −0.126121 | −0.0630605 | − | 0.998010i | \(-0.520086\pi\) | ||||
−0.0630605 | + | 0.998010i | \(0.520086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.8950 | −1.25899 | ||||||||
\(392\) | 2.87073 | 0.144994 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.86622 | 0.497053 | ||||||||
\(395\) | −6.73439 | −0.338844 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.1634 | 0.961781 | 0.480891 | − | 0.876781i | \(-0.340313\pi\) | ||||
0.480891 | + | 0.876781i | \(0.340313\pi\) | |||||||
\(398\) | −5.63409 | −0.282411 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.881777 | 0.0440888 | ||||||||
\(401\) | 9.17005 | 0.457930 | 0.228965 | − | 0.973435i | \(-0.426466\pi\) | ||||
0.228965 | + | 0.973435i | \(0.426466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.7409 | 0.584855 | ||||||||
\(404\) | 20.5679 | 1.02329 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.210965 | −0.0104700 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.6366 | −1.46544 | −0.732718 | − | 0.680533i | \(-0.761748\pi\) | ||||
−0.732718 | + | 0.680533i | \(0.761748\pi\) | |||||||
\(410\) | −3.46123 | −0.170938 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.0897 | −0.841947 | ||||||||
\(413\) | 5.25351 | 0.258508 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.83864 | 0.286607 | ||||||||
\(416\) | −16.3833 | −0.803256 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.7616 | −1.55166 | −0.775828 | − | 0.630944i | \(-0.782668\pi\) | ||||
−0.775828 | + | 0.630944i | \(0.782668\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.94862 | 0.289918 | 0.144959 | − | 0.989438i | \(-0.453695\pi\) | ||||
0.144959 | + | 0.989438i | \(0.453695\pi\) | |||||||
\(422\) | −15.0454 | −0.732399 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −33.6786 | −1.63558 | ||||||||
\(425\) | 14.3844 | 0.697747 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.65442 | 0.176850 | ||||||||
\(428\) | 18.2358 | 0.881460 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.29069 | −0.110467 | ||||||||
\(431\) | −11.2906 | −0.543847 | −0.271923 | − | 0.962319i | \(-0.587660\pi\) | ||||
−0.271923 | + | 0.962319i | \(0.587660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.1930 | 0.826243 | 0.413122 | − | 0.910676i | \(-0.364438\pi\) | ||||
0.413122 | + | 0.910676i | \(0.364438\pi\) | |||||||
\(434\) | −3.58486 | −0.172079 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.54953 | 0.313666 | ||||||||
\(437\) | 59.8185 | 2.86151 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.6983 | −1.60833 | −0.804167 | − | 0.594404i | \(-0.797388\pi\) | ||||
−0.804167 | + | 0.594404i | \(0.797388\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.76165 | 0.416749 | ||||||||
\(443\) | 1.38268 | 0.0656930 | 0.0328465 | − | 0.999460i | \(-0.489543\pi\) | ||||
0.0328465 | + | 0.999460i | \(0.489543\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.45951 | −0.306210 | ||||||||
\(446\) | −11.7848 | −0.558029 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.40740 | 0.255476 | ||||||||
\(449\) | 21.4531 | 1.01243 | 0.506217 | − | 0.862406i | \(-0.331044\pi\) | ||||
0.506217 | + | 0.862406i | \(0.331044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.96886 | −0.374823 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.3095 | −0.671577 | ||||||||
\(455\) | 2.36931 | 0.111075 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.54337 | −0.165752 | −0.0828760 | − | 0.996560i | \(-0.526411\pi\) | ||||
−0.0828760 | + | 0.996560i | \(0.526411\pi\) | |||||||
\(458\) | −8.11279 | −0.379086 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.21054 | −0.336193 | ||||||||
\(461\) | 20.0540 | 0.934006 | 0.467003 | − | 0.884256i | \(-0.345334\pi\) | ||||
0.467003 | + | 0.884256i | \(0.345334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.80547 | −0.455699 | −0.227849 | − | 0.973696i | \(-0.573169\pi\) | ||||
−0.227849 | + | 0.973696i | \(0.573169\pi\) | |||||||
\(464\) | −0.0474850 | −0.00220444 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.28736 | 0.105960 | ||||||||
\(467\) | 18.1244 | 0.838697 | 0.419349 | − | 0.907825i | \(-0.362258\pi\) | ||||
0.419349 | + | 0.907825i | \(0.362258\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.6736 | −0.631389 | ||||||||
\(470\) | −7.96590 | −0.367440 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.0814 | 0.694178 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.5634 | −1.58588 | ||||||||
\(476\) | 3.93278 | 0.180259 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.2541 | 0.789185 | ||||||||
\(479\) | 38.6169 | 1.76445 | 0.882227 | − | 0.470825i | \(-0.156044\pi\) | ||||
0.882227 | + | 0.470825i | \(0.156044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.58092 | −0.0720837 | ||||||||
\(482\) | 6.74927 | 0.307421 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.4932 | 0.703511 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4315 | 0.744581 | 0.372290 | − | 0.928116i | \(-0.378573\pi\) | ||||
0.372290 | + | 0.928116i | \(0.378573\pi\) | |||||||
\(488\) | 10.4909 | 0.474899 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.723426 | −0.0326811 | ||||||||
\(491\) | 26.0846 | 1.17718 | 0.588590 | − | 0.808431i | \(-0.299683\pi\) | ||||
0.588590 | + | 0.808431i | \(0.299683\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.774623 | −0.0348873 | ||||||||
\(494\) | −21.0528 | −0.947210 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.806899 | −0.0362308 | ||||||||
\(497\) | 10.3371 | 0.463680 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.7320 | −1.46528 | −0.732642 | − | 0.680615i | \(-0.761713\pi\) | ||||
−0.732642 | + | 0.680615i | \(0.761713\pi\) | |||||||
\(500\) | 8.95110 | 0.400306 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.2187 | 0.589982 | ||||||||
\(503\) | 18.6428 | 0.831241 | 0.415621 | − | 0.909538i | \(-0.363564\pi\) | ||||
0.415621 | + | 0.909538i | \(0.363564\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.8920 | −0.618184 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.7405 | 0.609635 | ||||||||
\(509\) | 23.8913 | 1.05896 | 0.529482 | − | 0.848321i | \(-0.322386\pi\) | ||||
0.529482 | + | 0.848321i | \(0.322386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.90937 | 0.394127 | ||||||||
\(512\) | 2.28881 | 0.101152 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.6715 | 0.823565 | ||||||||
\(515\) | 11.5427 | 0.508633 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.482705 | 0.0212088 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.80166 | 0.298272 | ||||||||
\(521\) | 36.0222 | 1.57816 | 0.789080 | − | 0.614290i | \(-0.210557\pi\) | ||||
0.789080 | + | 0.614290i | \(0.210557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3402 | 1.23923 | 0.619615 | − | 0.784906i | \(-0.287289\pi\) | ||||
0.619615 | + | 0.784906i | \(0.287289\pi\) | |||||||
\(524\) | 25.2355 | 1.10242 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.6068 | −1.07291 | ||||||||
\(527\) | −13.1629 | −0.573387 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.7733 | 1.46841 | ||||||||
\(530\) | 8.48703 | 0.368653 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.44983 | −0.409702 | ||||||||
\(533\) | 14.1001 | 0.610745 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3168 | −0.532503 | ||||||||
\(536\) | −39.2533 | −1.69548 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.42087 | −0.0612581 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.7194 | 1.10576 | 0.552882 | − | 0.833259i | \(-0.313528\pi\) | ||||
0.552882 | + | 0.833259i | \(0.313528\pi\) | |||||||
\(542\) | −13.5886 | −0.583681 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.3676 | 0.787504 | ||||||||
\(545\) | −4.42369 | −0.189490 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.1803 | 1.41869 | 0.709343 | − | 0.704864i | \(-0.248992\pi\) | ||||
0.709343 | + | 0.704864i | \(0.248992\pi\) | |||||||
\(548\) | 0.970301 | 0.0414492 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.86129 | 0.0792937 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.37651 | −0.356205 | ||||||||
\(554\) | 14.6085 | 0.620656 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.0373 | −0.468087 | ||||||||
\(557\) | −32.3919 | −1.37249 | −0.686245 | − | 0.727370i | \(-0.740742\pi\) | ||||
−0.686245 | + | 0.727370i | \(0.740742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.33167 | 0.394688 | ||||||||
\(560\) | −0.162832 | −0.00688092 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.3750 | 0.648555 | ||||||||
\(563\) | 34.6650 | 1.46096 | 0.730478 | − | 0.682937i | \(-0.239298\pi\) | ||||
0.730478 | + | 0.682937i | \(0.239298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.38233 | 0.226437 | ||||||||
\(566\) | 0.103504 | 0.00435060 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.6749 | 1.24513 | ||||||||
\(569\) | 18.4658 | 0.774127 | 0.387064 | − | 0.922053i | \(-0.373489\pi\) | ||||
0.387064 | + | 0.922053i | \(0.373489\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2034 | 0.594394 | 0.297197 | − | 0.954816i | \(-0.403948\pi\) | ||||
0.297197 | + | 0.954816i | \(0.403948\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.30522 | −0.179696 | ||||||||
\(575\) | −32.8039 | −1.36802 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.9012 | 0.703606 | 0.351803 | − | 0.936074i | \(-0.385569\pi\) | ||||
0.351803 | + | 0.936074i | \(0.385569\pi\) | |||||||
\(578\) | 5.47421 | 0.227697 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.224361 | −0.00931607 | ||||||||
\(581\) | 7.26234 | 0.301292 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 25.5764 | 1.05836 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.7909 | 0.693624 | ||||||||
\(587\) | −34.7412 | −1.43392 | −0.716962 | − | 0.697113i | \(-0.754468\pi\) | ||||
−0.716962 | + | 0.697113i | \(0.754468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.6284 | 1.30322 | ||||||||
\(590\) | −3.80053 | −0.156465 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.108649 | 0.00446547 | ||||||||
\(593\) | −2.43045 | −0.0998068 | −0.0499034 | − | 0.998754i | \(-0.515891\pi\) | ||||
−0.0499034 | + | 0.998754i | \(0.515891\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.65628 | −0.108897 | ||||||||
\(596\) | 8.27085 | 0.338787 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19.9811 | −0.817087 | ||||||||
\(599\) | 16.7195 | 0.683142 | 0.341571 | − | 0.939856i | \(-0.389041\pi\) | ||||
0.341571 | + | 0.939856i | \(0.389041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.429964 | 0.0175386 | 0.00876929 | − | 0.999962i | \(-0.497209\pi\) | ||||
0.00876929 | + | 0.999962i | \(0.497209\pi\) | |||||||
\(602\) | −2.84925 | −0.116127 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.6980 | −0.679433 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5440 | 0.468557 | 0.234279 | − | 0.972169i | \(-0.424727\pi\) | ||||
0.234279 | + | 0.972169i | \(0.424727\pi\) | |||||||
\(608\) | −44.1343 | −1.78988 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.64371 | −0.107041 | ||||||||
\(611\) | 32.4510 | 1.31283 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.0048 | −0.727209 | −0.363604 | − | 0.931554i | \(-0.618454\pi\) | ||||
−0.363604 | + | 0.931554i | \(0.618454\pi\) | |||||||
\(614\) | −12.5313 | −0.505721 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.1061 | −1.29254 | −0.646272 | − | 0.763107i | \(-0.723673\pi\) | ||||
−0.646272 | + | 0.763107i | \(0.723673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.280294 | −0.0112660 | −0.00563298 | − | 0.999984i | \(-0.501793\pi\) | ||||
−0.00563298 | + | 0.999984i | \(0.501793\pi\) | |||||||
\(620\) | −3.81249 | −0.153113 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.13936 | −0.366455 | ||||||||
\(623\) | −8.03460 | −0.321899 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.7225 | 0.628899 | ||||||||
\(626\) | −4.33613 | −0.173307 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.872952 | −0.0348346 | ||||||||
\(629\) | 1.77240 | 0.0706702 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.3354 | 1.20763 | 0.603816 | − | 0.797124i | \(-0.293646\pi\) | ||||
0.603816 | + | 0.797124i | \(0.293646\pi\) | |||||||
\(632\) | −24.0467 | −0.956525 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.26447 | 0.288509 | ||||||||
\(635\) | −9.28061 | −0.368290 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.94705 | 0.116766 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.02692 | 0.198706 | ||||||||
\(641\) | −3.93047 | −0.155244 | −0.0776222 | − | 0.996983i | \(-0.524733\pi\) | ||||
−0.0776222 | + | 0.996983i | \(0.524733\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.7243 | −0.541234 | −0.270617 | − | 0.962687i | \(-0.587228\pi\) | ||||
−0.270617 | + | 0.962687i | \(0.587228\pi\) | |||||||
\(644\) | −8.96877 | −0.353419 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.6027 | 0.928636 | ||||||||
\(647\) | 2.01034 | 0.0790345 | 0.0395173 | − | 0.999219i | \(-0.487418\pi\) | ||||
0.0395173 | + | 0.999219i | \(0.487418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 11.5452 | 0.452838 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.52758 | −0.138151 | ||||||||
\(653\) | 0.795349 | 0.0311244 | 0.0155622 | − | 0.999879i | \(-0.495046\pi\) | ||||
0.0155622 | + | 0.999879i | \(0.495046\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.0446 | −0.665988 | ||||||||
\(656\) | −0.969039 | −0.0378346 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.90831 | −0.386266 | ||||||||
\(659\) | 21.9135 | 0.853628 | 0.426814 | − | 0.904340i | \(-0.359636\pi\) | ||||
0.426814 | + | 0.904340i | \(0.359636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4952 | −0.758276 | −0.379138 | − | 0.925340i | \(-0.623779\pi\) | ||||
−0.379138 | + | 0.925340i | \(0.623779\pi\) | |||||||
\(662\) | −0.698968 | −0.0271662 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.8482 | 0.809067 | ||||||||
\(665\) | 6.38261 | 0.247507 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.76654 | 0.0684007 | ||||||||
\(668\) | 9.57020 | 0.370282 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.89186 | 0.382156 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00748 | −0.270118 | −0.135059 | − | 0.990838i | \(-0.543122\pi\) | ||||
−0.135059 | + | 0.990838i | \(0.543122\pi\) | |||||||
\(674\) | −0.188604 | −0.00726474 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.13607 | 0.197541 | ||||||||
\(677\) | 5.85627 | 0.225075 | 0.112537 | − | 0.993647i | \(-0.464102\pi\) | ||||
0.112537 | + | 0.993647i | \(0.464102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.2711 | 0.739557 | ||||||||
\(680\) | −7.62547 | −0.292423 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.2255 | −1.30960 | −0.654802 | − | 0.755801i | \(-0.727248\pi\) | ||||
−0.654802 | + | 0.755801i | \(0.727248\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.655362 | −0.0250401 | ||||||||
\(686\) | −0.899827 | −0.0343556 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.641324 | −0.0244502 | ||||||||
\(689\) | −34.5740 | −1.31716 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0086 | 0.570954 | 0.285477 | − | 0.958386i | \(-0.407848\pi\) | ||||
0.285477 | + | 0.958386i | \(0.407848\pi\) | |||||||
\(692\) | 6.13676 | 0.233285 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.5133 | 0.778675 | ||||||||
\(695\) | 7.45484 | 0.282778 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.8079 | −0.598768 | ||||||||
\(698\) | 12.6240 | 0.477826 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.18219 | 0.195868 | ||||||||
\(701\) | −11.9907 | −0.452884 | −0.226442 | − | 0.974025i | \(-0.572709\pi\) | ||||
−0.226442 | + | 0.974025i | \(0.572709\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.25878 | −0.160623 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.1294 | −0.757582 | ||||||||
\(707\) | −17.2794 | −0.649858 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.5551 | 1.48552 | 0.742762 | − | 0.669556i | \(-0.233515\pi\) | ||||
0.742762 | + | 0.669556i | \(0.233515\pi\) | |||||||
\(710\) | −7.47810 | −0.280648 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.0651 | −0.864403 | ||||||||
\(713\) | 30.0183 | 1.12419 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.15702 | 0.267470 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.43143 | −0.0907403 | ||||||||
\(719\) | 44.3811 | 1.65514 | 0.827568 | − | 0.561366i | \(-0.189724\pi\) | ||||
0.827568 | + | 0.561366i | \(0.189724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3573 | 0.534694 | ||||||||
\(722\) | −39.6167 | −1.47438 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.91681 | −0.108402 | ||||||||
\(725\) | −1.02071 | −0.0379084 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.1325 | −1.67387 | −0.836935 | − | 0.547302i | \(-0.815655\pi\) | ||||
−0.836935 | + | 0.547302i | \(0.815655\pi\) | |||||||
\(728\) | 8.46018 | 0.313555 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.44527 | −0.238550 | ||||||||
\(731\) | −10.4619 | −0.386948 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.7971 | 0.509608 | 0.254804 | − | 0.966993i | \(-0.417989\pi\) | ||||
0.254804 | + | 0.966993i | \(0.417989\pi\) | |||||||
\(734\) | −25.4490 | −0.939338 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41.8876 | −1.54400 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.7453 | −0.615985 | −0.307993 | − | 0.951389i | \(-0.599657\pi\) | ||||
−0.307993 | + | 0.951389i | \(0.599657\pi\) | |||||||
\(740\) | 0.513355 | 0.0188713 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.5565 | 0.387542 | ||||||||
\(743\) | 10.8932 | 0.399631 | 0.199815 | − | 0.979834i | \(-0.435966\pi\) | ||||
0.199815 | + | 0.979834i | \(0.435966\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.58631 | −0.204666 | ||||||||
\(746\) | −7.68323 | −0.281303 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.3202 | −0.559788 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.0918 | −0.988596 | −0.494298 | − | 0.869293i | \(-0.664575\pi\) | ||||
−0.494298 | + | 0.869293i | \(0.664575\pi\) | |||||||
\(752\) | −2.23021 | −0.0813275 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.621724 | −0.0226419 | ||||||||
\(755\) | 11.2782 | 0.410456 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.2302 | 1.09873 | 0.549367 | − | 0.835581i | \(-0.314869\pi\) | ||||
0.549367 | + | 0.835581i | \(0.314869\pi\) | |||||||
\(758\) | −31.2082 | −1.13353 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.3227 | 0.664636 | ||||||||
\(761\) | −38.5957 | −1.39909 | −0.699547 | − | 0.714587i | \(-0.746615\pi\) | ||||
−0.699547 | + | 0.714587i | \(0.746615\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.50237 | −0.199199 | ||||||||
\(764\) | −25.3234 | −0.916170 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.4434 | 0.413467 | ||||||||
\(767\) | 15.4824 | 0.559035 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.5122 | 1.46091 | 0.730454 | − | 0.682962i | \(-0.239309\pi\) | ||||
0.730454 | + | 0.682962i | \(0.239309\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.99770 | 0.359825 | ||||||||
\(773\) | 22.1942 | 0.798270 | 0.399135 | − | 0.916892i | \(-0.369310\pi\) | ||||
0.399135 | + | 0.916892i | \(0.369310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3447 | −0.623040 | ||||||||
\(776\) | 55.3221 | 1.98595 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.23831 | 0.0802474 | ||||||||
\(779\) | 37.9839 | 1.36091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 22.4012 | 0.801064 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.202537 | −0.00723348 | ||||||||
\(785\) | 0.589610 | 0.0210441 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0781 | 0.537478 | 0.268739 | − | 0.963213i | \(-0.413393\pi\) | ||||
0.268739 | + | 0.963213i | \(0.413393\pi\) | |||||||
\(788\) | 13.0513 | 0.464932 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.05978 | 0.215597 | ||||||||
\(791\) | 6.69477 | 0.238039 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.7698 | 0.382446 | ||||||||
\(794\) | −17.2437 | −0.611956 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.45290 | −0.264161 | ||||||||
\(797\) | −22.9577 | −0.813202 | −0.406601 | − | 0.913606i | \(-0.633286\pi\) | ||||
−0.406601 | + | 0.913606i | \(0.633286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.3815 | −1.28708 | ||||||||
\(800\) | 24.2028 | 0.855699 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.25146 | −0.291369 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.05769 | 0.213506 | ||||||||
\(806\) | −10.5648 | −0.372128 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −49.6044 | −1.74508 | ||||||||
\(809\) | −27.6048 | −0.970531 | −0.485266 | − | 0.874367i | \(-0.661277\pi\) | ||||
−0.485266 | + | 0.874367i | \(0.661277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.0296 | −1.75678 | −0.878389 | − | 0.477947i | \(-0.841381\pi\) | ||||
−0.878389 | + | 0.477947i | \(0.841381\pi\) | |||||||
\(812\) | −0.279069 | −0.00979340 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.38260 | 0.0834589 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.1383 | 0.879477 | ||||||||
\(818\) | 26.6678 | 0.932418 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.57859 | −0.159891 | ||||||||
\(821\) | 27.1692 | 0.948213 | 0.474107 | − | 0.880467i | \(-0.342771\pi\) | ||||
0.474107 | + | 0.880467i | \(0.342771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.4262 | 0.607439 | 0.303720 | − | 0.952761i | \(-0.401771\pi\) | ||||
0.303720 | + | 0.952761i | \(0.401771\pi\) | |||||||
\(824\) | 41.2159 | 1.43583 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.72725 | −0.164482 | ||||||||
\(827\) | −30.4545 | −1.05901 | −0.529503 | − | 0.848308i | \(-0.677622\pi\) | ||||
−0.529503 | + | 0.848308i | \(0.677622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.4137 | 0.952118 | 0.476059 | − | 0.879413i | \(-0.342065\pi\) | ||||
0.476059 | + | 0.879413i | \(0.342065\pi\) | |||||||
\(830\) | −5.25377 | −0.182361 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.9359 | 0.552477 | ||||||||
\(833\) | −3.30399 | −0.114477 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.46391 | −0.223693 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28.5800 | 0.987278 | ||||||||
\(839\) | 29.3429 | 1.01303 | 0.506514 | − | 0.862231i | \(-0.330934\pi\) | ||||
0.506514 | + | 0.862231i | \(0.330934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9450 | −0.998105 | ||||||||
\(842\) | −5.35273 | −0.184467 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.9024 | −0.685068 | ||||||||
\(845\) | −3.46901 | −0.119338 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.37611 | 0.0815960 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.9435 | −0.443958 | ||||||||
\(851\) | −4.04198 | −0.138557 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.5073 | −0.667916 | −0.333958 | − | 0.942588i | \(-0.608384\pi\) | ||||
−0.333958 | + | 0.942588i | \(0.608384\pi\) | |||||||
\(854\) | −3.28835 | −0.112525 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −43.9801 | −1.50321 | ||||||||
\(857\) | −10.9432 | −0.373811 | −0.186906 | − | 0.982378i | \(-0.559846\pi\) | ||||
−0.186906 | + | 0.982378i | \(0.559846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3191 | −0.522680 | −0.261340 | − | 0.965247i | \(-0.584164\pi\) | ||||
−0.261340 | + | 0.965247i | \(0.584164\pi\) | |||||||
\(860\) | −3.03017 | −0.103328 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.1595 | 0.346036 | ||||||||
\(863\) | −13.4613 | −0.458227 | −0.229114 | − | 0.973400i | \(-0.573583\pi\) | ||||
−0.229114 | + | 0.973400i | \(0.573583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.14490 | −0.140931 | ||||||||
\(866\) | −15.4707 | −0.525717 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.74214 | −0.160959 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.2969 | −1.36541 | ||||||||
\(872\) | −15.7958 | −0.534914 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −53.8263 | −1.82070 | ||||||||
\(875\) | −7.51997 | −0.254221 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.22081 | 0.108759 | 0.0543796 | − | 0.998520i | \(-0.482682\pi\) | ||||
0.0543796 | + | 0.998520i | \(0.482682\pi\) | |||||||
\(878\) | 30.3227 | 1.02334 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.3721 | 0.652661 | 0.326331 | − | 0.945256i | \(-0.394188\pi\) | ||||
0.326331 | + | 0.945256i | \(0.394188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.93248 | −0.0986858 | −0.0493429 | − | 0.998782i | \(-0.515713\pi\) | ||||
−0.0493429 | + | 0.998782i | \(0.515713\pi\) | |||||||
\(884\) | 11.5901 | 0.389817 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.24417 | −0.0417987 | ||||||||
\(887\) | −7.68647 | −0.258087 | −0.129043 | − | 0.991639i | \(-0.541191\pi\) | ||||
−0.129043 | + | 0.991639i | \(0.541191\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.5436 | −0.387160 | ||||||||
\(890\) | 5.81244 | 0.194833 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.5893 | −0.521967 | ||||||||
\(893\) | 87.4186 | 2.92535 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.83400 | −0.161583 | ||||||||
\(896\) | 6.25269 | 0.208888 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.3041 | −0.644185 | ||||||||
\(899\) | 0.934038 | 0.0311519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.7615 | 1.29133 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.2189 | 0.639210 | ||||||||
\(905\) | 1.97008 | 0.0654875 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7746 | −0.424172 | −0.212086 | − | 0.977251i | \(-0.568026\pi\) | ||||
−0.212086 | + | 0.977251i | \(0.568026\pi\) | |||||||
\(908\) | −18.9289 | −0.628177 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.13197 | −0.0706742 | ||||||||
\(911\) | −11.0831 | −0.367200 | −0.183600 | − | 0.983001i | \(-0.558775\pi\) | ||||
−0.183600 | + | 0.983001i | \(0.558775\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.18843 | 0.105464 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.7318 | −0.354588 | ||||||||
\(917\) | −21.2008 | −0.700112 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.5522 | 0.447046 | 0.223523 | − | 0.974699i | \(-0.428244\pi\) | ||||
0.223523 | + | 0.974699i | \(0.428244\pi\) | |||||||
\(920\) | 17.3900 | 0.573331 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.0451 | −0.594284 | ||||||||
\(923\) | 30.4638 | 1.00273 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.33548 | 0.0767900 | ||||||||
\(926\) | 8.82323 | 0.289949 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.30336 | −0.0427849 | ||||||||
\(929\) | −43.0169 | −1.41134 | −0.705670 | − | 0.708541i | \(-0.749354\pi\) | ||||
−0.705670 | + | 0.708541i | \(0.749354\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.93896 | 0.260189 | ||||||||
\(932\) | 3.02577 | 0.0991124 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.3088 | −0.533641 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.56484 | −0.0837896 | −0.0418948 | − | 0.999122i | \(-0.513339\pi\) | ||||
−0.0418948 | + | 0.999122i | \(0.513339\pi\) | |||||||
\(938\) | 12.3039 | 0.401737 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.5375 | −0.343694 | ||||||||
\(941\) | −16.5640 | −0.539972 | −0.269986 | − | 0.962864i | \(-0.587019\pi\) | ||||
−0.269986 | + | 0.962864i | \(0.587019\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0502 | 1.17396 | ||||||||
\(944\) | −1.06403 | −0.0346313 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.5682 | −1.51326 | −0.756632 | − | 0.653841i | \(-0.773157\pi\) | ||||
−0.756632 | + | 0.653841i | \(0.773157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.2564 | 0.852318 | ||||||||
\(950\) | 31.1011 | 1.00905 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.48487 | −0.307406 | ||||||||
\(953\) | 39.9493 | 1.29409 | 0.647043 | − | 0.762454i | \(-0.276006\pi\) | ||||
0.647043 | + | 0.762454i | \(0.276006\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.1040 | 0.553472 | ||||||||
\(956\) | 22.8241 | 0.738185 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.7486 | −1.12268 | ||||||||
\(959\) | −0.815166 | −0.0263231 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1282 | −0.488005 | ||||||||
\(962\) | 1.42255 | 0.0458650 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.92809 | 0.287554 | ||||||||
\(965\) | −6.75266 | −0.217376 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.2572 | 1.13380 | 0.566898 | − | 0.823788i | \(-0.308143\pi\) | ||||
0.566898 | + | 0.823788i | \(0.308143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.9412 | −0.447626 | ||||||||
\(971\) | −34.8319 | −1.11781 | −0.558905 | − | 0.829232i | \(-0.688778\pi\) | ||||
−0.558905 | + | 0.829232i | \(0.688778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.27263 | 0.297267 | ||||||||
\(974\) | −14.7855 | −0.473757 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.740158 | −0.0236919 | ||||||||
\(977\) | 23.2137 | 0.742672 | 0.371336 | − | 0.928499i | \(-0.378900\pi\) | ||||
0.371336 | + | 0.928499i | \(0.378900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.956964 | −0.0305691 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23.4716 | −0.749010 | ||||||||
\(983\) | 50.8764 | 1.62271 | 0.811353 | − | 0.584557i | \(-0.198732\pi\) | ||||
0.811353 | + | 0.584557i | \(0.198732\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.81509 | −0.280872 | ||||||||
\(986\) | 0.697027 | 0.0221979 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.8491 | −0.885998 | ||||||||
\(989\) | 23.8586 | 0.758658 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.0338 | −1.55761 | −0.778805 | − | 0.627266i | \(-0.784174\pi\) | ||||
−0.778805 | + | 0.627266i | \(0.784174\pi\) | |||||||
\(992\) | −22.1476 | −0.703187 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.30157 | −0.295028 | ||||||||
\(995\) | 5.03384 | 0.159584 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.64075 | −0.146974 | −0.0734870 | − | 0.997296i | \(-0.523413\pi\) | ||||
−0.0734870 | + | 0.997296i | \(0.523413\pi\) | |||||||
\(998\) | 29.4531 | 0.932322 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7623.2.a.dc.1.6 | 16 | ||
3.2 | odd | 2 | inner | 7623.2.a.dc.1.11 | 16 | ||
11.5 | even | 5 | 693.2.m.k.190.6 | yes | 32 | ||
11.9 | even | 5 | 693.2.m.k.631.6 | yes | 32 | ||
11.10 | odd | 2 | 7623.2.a.db.1.11 | 16 | |||
33.5 | odd | 10 | 693.2.m.k.190.3 | ✓ | 32 | ||
33.20 | odd | 10 | 693.2.m.k.631.3 | yes | 32 | ||
33.32 | even | 2 | 7623.2.a.db.1.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.k.190.3 | ✓ | 32 | 33.5 | odd | 10 | ||
693.2.m.k.190.6 | yes | 32 | 11.5 | even | 5 | ||
693.2.m.k.631.3 | yes | 32 | 33.20 | odd | 10 | ||
693.2.m.k.631.6 | yes | 32 | 11.9 | even | 5 | ||
7623.2.a.db.1.6 | 16 | 33.32 | even | 2 | |||
7623.2.a.db.1.11 | 16 | 11.10 | odd | 2 | |||
7623.2.a.dc.1.6 | 16 | 1.1 | even | 1 | trivial | ||
7623.2.a.dc.1.11 | 16 | 3.2 | odd | 2 | inner |