Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(177,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.q (of order \(3\), 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: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 616) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.529 |
Dual form | 1232.2.q.h.177.1 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.207107 | + | 0.358719i | −0.119573 | + | 0.207107i | −0.919599 | − | 0.392859i | \(-0.871486\pi\) |
0.800025 | + | 0.599966i | \(0.204819\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 1.22474i | −0.316228 | − | 0.547723i | 0.663470 | − | 0.748203i | \(-0.269083\pi\) |
−0.979698 | + | 0.200480i | \(0.935750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62132 | + | 0.358719i | −0.990766 | + | 0.135583i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41421 | + | 2.44949i | 0.471405 | + | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.82843 | 0.507114 | 0.253557 | − | 0.967320i | \(-0.418399\pi\) | ||||
0.253557 | + | 0.967320i | \(0.418399\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.585786 | 0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.29289 | − | 2.23936i | −0.296610 | − | 0.513744i | 0.678748 | − | 0.734371i | \(-0.262523\pi\) |
−0.975358 | + | 0.220628i | \(0.929189\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.414214 | − | 1.01461i | 0.0903888 | − | 0.221406i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.70711 | + | 4.68885i | 0.564471 | + | 0.977692i | 0.997099 | + | 0.0761195i | \(0.0242531\pi\) |
−0.432628 | + | 0.901573i | \(0.642414\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.50000 | − | 2.59808i | 0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.82843 | + | 8.36308i | −0.867211 | + | 1.50205i | −0.00237631 | + | 0.999997i | \(0.500756\pi\) |
−0.864835 | + | 0.502057i | \(0.832577\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.207107 | + | 0.358719i | 0.0360527 | + | 0.0624450i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.29289 | + | 2.95680i | 0.387570 | + | 0.499790i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.53553 | + | 7.85578i | 0.745637 | + | 1.29148i | 0.949896 | + | 0.312565i | \(0.101188\pi\) |
−0.204259 | + | 0.978917i | \(0.565479\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.378680 | + | 0.655892i | −0.0606373 | + | 0.105027i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.24264 | 0.974937 | 0.487468 | − | 0.873141i | \(-0.337920\pi\) | ||||
0.487468 | + | 0.873141i | \(0.337920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | − | 3.46410i | 0.298142 | − | 0.516398i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.41421 | + | 4.18154i | 0.352149 | + | 0.609940i | 0.986626 | − | 0.163002i | \(-0.0521176\pi\) |
−0.634477 | + | 0.772942i | \(0.718784\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.414214 | + | 0.717439i | 0.0580015 | + | 0.100462i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.29289 | + | 2.23936i | −0.177593 | + | 0.307599i | −0.941055 | − | 0.338252i | \(-0.890164\pi\) |
0.763463 | + | 0.645852i | \(0.223498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41421 | −0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.07107 | 0.141866 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.20711 | − | 3.82282i | 0.287341 | − | 0.497689i | −0.685833 | − | 0.727759i | \(-0.740562\pi\) |
0.973174 | + | 0.230070i | \(0.0738954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.08579 | + | 7.07679i | 0.523131 | + | 0.906090i | 0.999638 | + | 0.0269190i | \(0.00856962\pi\) |
−0.476506 | + | 0.879171i | \(0.658097\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.58579 | − | 5.91359i | −0.577755 | − | 0.745042i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.29289 | − | 2.23936i | −0.160364 | − | 0.277758i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.03553 | − | 6.98975i | 0.493019 | − | 0.853934i | −0.506949 | − | 0.861976i | \(-0.669227\pi\) |
0.999968 | + | 0.00804237i | \(0.00255999\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.24264 | −0.269982 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.75736 | 0.683273 | 0.341636 | − | 0.939832i | \(-0.389019\pi\) | ||||
0.341636 | + | 0.939832i | \(0.389019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.70711 | − | 2.95680i | 0.199802 | − | 0.346067i | −0.748662 | − | 0.662952i | \(-0.769304\pi\) |
0.948464 | + | 0.316885i | \(0.102637\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.621320 | + | 1.07616i | 0.0717439 | + | 0.124264i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | + | 2.44949i | −0.113961 | + | 0.279145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.03553 | + | 6.98975i | 0.454033 | + | 0.786408i | 0.998632 | − | 0.0522883i | \(-0.0166515\pi\) |
−0.544599 | + | 0.838697i | \(0.683318\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74264 | + | 6.48244i | −0.415849 | + | 0.720272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.4853 | 1.15091 | 0.575455 | − | 0.817834i | \(-0.304825\pi\) | ||||
0.575455 | + | 0.817834i | \(0.304825\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82843 | −0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.207107 | + | 0.358719i | −0.0222042 | + | 0.0384588i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.58579 | + | 7.94282i | 0.486092 | + | 0.841937i | 0.999872 | − | 0.0159854i | \(-0.00508851\pi\) |
−0.513780 | + | 0.857922i | \(0.671755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.79289 | + | 0.655892i | −0.502432 | + | 0.0687562i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | − | 3.46410i | −0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.82843 | + | 3.16693i | −0.187593 | + | 0.324920i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.8284 | −1.60713 | −0.803567 | − | 0.595215i | \(-0.797067\pi\) | ||||
−0.803567 | + | 0.595215i | \(0.797067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.82843 | 0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.74264 | − | 6.48244i | 0.372407 | − | 0.645027i | −0.617529 | − | 0.786548i | \(-0.711866\pi\) |
0.989935 | + | 0.141521i | \(0.0451993\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.94975 | − | 13.7694i | −0.783312 | − | 1.35674i | −0.930002 | − | 0.367554i | \(-0.880195\pi\) |
0.146690 | − | 0.989182i | \(-0.453138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.53553 | + | 0.210133i | −0.149853 | + | 0.0205069i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.77817 | + | 11.7401i | 0.655271 | + | 1.13496i | 0.981826 | + | 0.189784i | \(0.0607788\pi\) |
−0.326555 | + | 0.945178i | \(0.605888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.24264 | − | 7.34847i | 0.406371 | − | 0.703856i | −0.588109 | − | 0.808782i | \(-0.700127\pi\) |
0.994480 | + | 0.104926i | \(0.0334606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.75736 | −0.356633 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.48528 | −0.704156 | −0.352078 | − | 0.935971i | \(-0.614525\pi\) | ||||
−0.352078 | + | 0.935971i | \(0.614525\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.82843 | − | 6.63103i | 0.357003 | − | 0.618347i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.58579 | + | 4.47871i | 0.239056 | + | 0.414057i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | + | 4.89898i | −0.183340 | + | 0.449089i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.29289 | + | 2.23936i | −0.116576 | + | 0.201916i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3137 | −1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.41421 | −0.569169 | −0.284585 | − | 0.958651i | \(-0.591856\pi\) | ||||
−0.284585 | + | 0.958651i | \(0.591856\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.65685 | + | 2.86976i | −0.145878 | + | 0.252668i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.46447 | − | 4.26858i | −0.215321 | − | 0.372948i | 0.738051 | − | 0.674745i | \(-0.235747\pi\) |
−0.953372 | + | 0.301798i | \(0.902413\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.19239 | + | 5.40629i | 0.363526 | + | 0.468784i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.70711 | + | 2.95680i | 0.146924 | + | 0.254480i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.50000 | + | 14.7224i | −0.726204 | + | 1.25782i | 0.232273 | + | 0.972651i | \(0.425384\pi\) |
−0.958477 | + | 0.285171i | \(0.907949\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31371 | 0.281065 | 0.140533 | − | 0.990076i | \(-0.455119\pi\) | ||||
0.140533 | + | 0.990076i | \(0.455119\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.914214 | − | 1.58346i | 0.0764504 | − | 0.132416i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.707107 | − | 1.22474i | −0.0587220 | − | 0.101710i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.721825 | + | 2.80821i | −0.0595352 | + | 0.231617i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.00000 | + | 13.8564i | 0.655386 | + | 1.13516i | 0.981797 | + | 0.189933i | \(0.0608272\pi\) |
−0.326411 | + | 0.945228i | \(0.605840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.79289 | − | 4.83743i | 0.227282 | − | 0.393665i | −0.729719 | − | 0.683747i | \(-0.760349\pi\) |
0.957002 | + | 0.290082i | \(0.0936826\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.65685 | 0.457330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.6569 | 1.09694 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.65685 | − | 6.33386i | 0.291849 | − | 0.505497i | −0.682398 | − | 0.730981i | \(-0.739063\pi\) |
0.974247 | + | 0.225484i | \(0.0723963\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.535534 | − | 0.927572i | −0.0424706 | − | 0.0735612i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.77817 | − | 11.3199i | −0.691817 | − | 0.892131i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.55025 | + | 4.41717i | 0.199751 | + | 0.345979i | 0.948448 | − | 0.316934i | \(-0.102653\pi\) |
−0.748696 | + | 0.662913i | \(0.769320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.292893 | − | 0.507306i | 0.0228017 | − | 0.0394937i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.272078 | 0.0210540 | 0.0105270 | − | 0.999945i | \(-0.496649\pi\) | ||||
0.0105270 | + | 0.999945i | \(0.496649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.65685 | − | 6.33386i | 0.279647 | − | 0.484362i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.08579 | − | 1.88064i | −0.0825508 | − | 0.142982i | 0.821794 | − | 0.569785i | \(-0.192973\pi\) |
−0.904345 | + | 0.426802i | \(0.859640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.00000 | + | 7.34847i | −0.226779 | + | 0.555492i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.914214 | + | 1.58346i | 0.0687165 | + | 0.119020i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.44975 | − | 16.3674i | 0.706307 | − | 1.22336i | −0.259910 | − | 0.965633i | \(-0.583693\pi\) |
0.966218 | − | 0.257727i | \(-0.0829736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.3137 | −0.989600 | −0.494800 | − | 0.869007i | \(-0.664759\pi\) | ||||
−0.494800 | + | 0.869007i | \(0.664759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.38478 | −0.250210 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.41421 | − | 11.1097i | 0.471582 | − | 0.816805i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00000 | − | 1.73205i | −0.0731272 | − | 0.126660i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.32843 | − | 0.866025i | 0.460325 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.24264 | − | 5.61642i | −0.234629 | − | 0.406390i | 0.724536 | − | 0.689237i | \(-0.242054\pi\) |
−0.959165 | + | 0.282848i | \(0.908721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.6066 | + | 20.1032i | −0.835461 | + | 1.44706i | 0.0581927 | + | 0.998305i | \(0.481466\pi\) |
−0.893654 | + | 0.448756i | \(0.851867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.07107 | 0.0767008 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.1421 | −0.793844 | −0.396922 | − | 0.917852i | \(-0.629922\pi\) | ||||
−0.396922 | + | 0.917852i | \(0.629922\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0208 | − | 20.8207i | 0.852133 | − | 1.47594i | −0.0271465 | − | 0.999631i | \(-0.508642\pi\) |
0.879279 | − | 0.476306i | \(-0.158025\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.67157 | + | 2.89525i | 0.117904 | + | 0.204215i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.62132 | + | 0.358719i | −0.183981 | + | 0.0251772i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.41421 | − | 7.64564i | −0.308302 | − | 0.533995i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.65685 | + | 13.2621i | −0.532188 | + | 0.921777i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.58579 | −0.178863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.92893 | 0.339322 | 0.169661 | − | 0.985503i | \(-0.445733\pi\) | ||||
0.169661 | + | 0.985503i | \(0.445733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.19239 | + | 2.06528i | −0.0817011 | + | 0.141510i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.65685 | − | 9.79796i | −0.385794 | − | 0.668215i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.65685 | − | 23.6544i | 0.655550 | − | 1.60576i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.707107 | + | 1.22474i | 0.0477818 | + | 0.0827606i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.82843 | − | 3.16693i | 0.122993 | − | 0.213031i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.5563 | −1.30959 | −0.654795 | − | 0.755807i | \(-0.727245\pi\) | ||||
−0.654795 | + | 0.755807i | \(0.727245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.48528 | 0.565685 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0711 | + | 24.3718i | −0.933930 | + | 1.61761i | −0.157398 | + | 0.987535i | \(0.550311\pi\) |
−0.776532 | + | 0.630078i | \(0.783023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | + | 3.46410i | 0.132164 | + | 0.228914i | 0.924510 | − | 0.381157i | \(-0.124474\pi\) |
−0.792347 | + | 0.610071i | \(0.791141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.671573 | − | 0.866025i | −0.0441863 | − | 0.0569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1924 | − | 17.6537i | −0.667726 | − | 1.15653i | −0.978539 | − | 0.206064i | \(-0.933935\pi\) |
0.310813 | − | 0.950471i | \(-0.399399\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.41421 | − | 5.91359i | 0.222719 | − | 0.385760i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.34315 | −0.217161 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.7279 | 0.758616 | 0.379308 | − | 0.925270i | \(-0.376162\pi\) | ||||
0.379308 | + | 0.925270i | \(0.376162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3640 | − | 19.6830i | 0.732017 | − | 1.26789i | −0.224003 | − | 0.974589i | \(-0.571912\pi\) |
0.956020 | − | 0.293302i | \(-0.0947542\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.17157 | − | 8.95743i | −0.331757 | − | 0.574619i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.07107 | − | 6.92820i | −0.451754 | − | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.36396 | − | 4.09450i | −0.150415 | − | 0.260527i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.17157 | + | 3.76127i | −0.137618 | + | 0.238361i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.485281 | −0.0306307 | −0.0153153 | − | 0.999883i | \(-0.504875\pi\) | ||||
−0.0153153 | + | 0.999883i | \(0.504875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.41421 | 0.340389 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.585786 | − | 1.01461i | 0.0366834 | − | 0.0635375i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.74264 | + | 16.8747i | 0.607729 | + | 1.05262i | 0.991614 | + | 0.129237i | \(0.0412527\pi\) |
−0.383885 | + | 0.923381i | \(0.625414\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7071 | − | 18.9655i | −0.913855 | − | 1.17846i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.41421 | + | 2.44949i | 0.0875376 | + | 0.151620i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.5208 | + | 19.9546i | −0.710404 | + | 1.23046i | 0.254302 | + | 0.967125i | \(0.418154\pi\) |
−0.964706 | + | 0.263331i | \(0.915179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.65685 | 0.224639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.79899 | −0.232494 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.82843 | − | 11.8272i | 0.416337 | − | 0.721116i | −0.579231 | − | 0.815163i | \(-0.696647\pi\) |
0.995568 | + | 0.0940473i | \(0.0299805\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0355339 | − | 0.0615465i | −0.00215853 | − | 0.00373869i | 0.864944 | − | 0.501868i | \(-0.167354\pi\) |
−0.867103 | + | 0.498129i | \(0.834020\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.757359 | − | 1.85514i | 0.0458375 | − | 0.112278i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.3995 | − | 21.4766i | 0.745013 | − | 1.29040i | −0.205175 | − | 0.978725i | \(-0.565776\pi\) |
0.950188 | − | 0.311676i | \(-0.100890\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.3137 | −1.63523 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.8995 | −0.709864 | −0.354932 | − | 0.934892i | \(-0.615496\pi\) | ||||
−0.354932 | + | 0.934892i | \(0.615496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7782 | − | 23.8645i | 0.819027 | − | 1.41860i | −0.0873721 | − | 0.996176i | \(-0.527847\pi\) |
0.906400 | − | 0.422421i | \(-0.138820\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.757359 | − | 1.31178i | −0.0448621 | − | 0.0777034i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.3640 | + | 2.23936i | −0.965934 | + | 0.132185i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.27817 | − | 5.67796i | 0.192170 | − | 0.332848i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.1716 | −0.769492 | −0.384746 | − | 0.923023i | \(-0.625711\pi\) | ||||
−0.384746 | + | 0.923023i | \(0.625711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.24264 | −0.363461 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.20711 | + | 2.09077i | −0.0700434 | + | 0.121319i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.94975 | + | 8.57321i | 0.286251 | + | 0.495802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.9706 | + | 2.86976i | −1.20872 | + | 0.165410i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.55025 | + | 2.68512i | 0.0890597 | + | 0.154256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.77817 | − | 10.0081i | 0.330857 | − | 0.573062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.58579 | −0.490017 | −0.245008 | − | 0.969521i | \(-0.578791\pi\) | ||||
−0.245008 | + | 0.969521i | \(0.578791\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.58579 | 0.374652 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6066 | + | 23.5673i | −0.771560 | + | 1.33638i | 0.165148 | + | 0.986269i | \(0.447190\pi\) |
−0.936708 | + | 0.350112i | \(0.886144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.67157 | + | 8.09140i | 0.264053 | + | 0.457353i | 0.967315 | − | 0.253578i | \(-0.0816073\pi\) |
−0.703262 | + | 0.710931i | \(0.748274\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00000 | + | 9.79796i | −0.225374 | + | 0.552052i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.4853 | − | 18.1610i | −0.588912 | − | 1.02003i | −0.994375 | − | 0.105914i | \(-0.966223\pi\) |
0.405463 | − | 0.914111i | \(-0.367110\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.500000 | − | 0.866025i | 0.0279946 | − | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.61522 | −0.313411 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.17157 | −0.287754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.74264 | − | 4.75039i | 0.152134 | − | 0.263504i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.75736 | + | 3.04384i | 0.0971822 | + | 0.168324i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.82843 | − | 10.0951i | −0.431595 | − | 0.556563i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.69239 | − | 4.66335i | −0.147987 | − | 0.256321i | 0.782496 | − | 0.622655i | \(-0.213946\pi\) |
−0.930483 | + | 0.366334i | \(0.880613\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.8284 | + | 22.2195i | −0.702993 | + | 1.21762i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.4142 | −0.623625 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.24264 | −0.122164 | −0.0610822 | − | 0.998133i | \(-0.519455\pi\) | ||||
−0.0610822 | + | 0.998133i | \(0.519455\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.55025 | − | 2.68512i | 0.0841982 | − | 0.145835i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.82843 | + | 8.36308i | 0.261474 | + | 0.452886i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.58579 | + | 2.74666i | 0.0853759 | + | 0.147875i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.29289 | + | 7.43551i | −0.230455 | + | 0.399159i | −0.957942 | − | 0.286962i | \(-0.907355\pi\) |
0.727487 | + | 0.686121i | \(0.240688\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.2843 | 1.29991 | 0.649954 | − | 0.759974i | \(-0.274788\pi\) | ||||
0.649954 | + | 0.759974i | \(0.274788\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.41421 | −0.235613 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.34315 | − | 2.32640i | 0.0714884 | − | 0.123822i | −0.828065 | − | 0.560632i | \(-0.810558\pi\) |
0.899554 | + | 0.436810i | \(0.143892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.07107 | − | 7.05130i | −0.216070 | − | 0.374244i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.34315 | − | 1.73205i | −0.0710868 | − | 0.0916698i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.96447 | + | 12.0628i | 0.367570 | + | 0.636651i | 0.989185 | − | 0.146672i | \(-0.0468563\pi\) |
−0.621615 | + | 0.783323i | \(0.713523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.15685 | − | 10.6640i | 0.324045 | − | 0.561262i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.414214 | 0.0217406 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.82843 | −0.252731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.12132 | − | 7.13834i | 0.215131 | − | 0.372618i | −0.738182 | − | 0.674602i | \(-0.764315\pi\) |
0.953313 | + | 0.301984i | \(0.0976488\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.82843 | + | 15.2913i | 0.459590 | + | 0.796032i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.58579 | − | 6.33386i | 0.134247 | − | 0.328837i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.81371 | + | 11.8017i | 0.352800 | + | 0.611068i | 0.986739 | − | 0.162315i | \(-0.0518961\pi\) |
−0.633939 | + | 0.773383i | \(0.718563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.34315 | − | 4.05845i | 0.121000 | − | 0.209577i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.82843 | 0.0941688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.38478 | 0.379330 | 0.189665 | − | 0.981849i | \(-0.439260\pi\) | ||||
0.189665 | + | 0.981849i | \(0.439260\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.32843 | − | 2.30090i | 0.0680574 | − | 0.117879i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.05025 | − | 7.01524i | −0.206958 | − | 0.358462i | 0.743797 | − | 0.668406i | \(-0.233023\pi\) |
−0.950755 | + | 0.309944i | \(0.899690\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.70711 | − | 0.507306i | 0.188932 | − | 0.0258547i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.3137 | + | 19.5959i | 0.575108 | + | 0.996116i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.6066 | + | 28.7635i | −0.841988 | + | 1.45837i | 0.0462232 | + | 0.998931i | \(0.485281\pi\) |
−0.888211 | + | 0.459435i | \(0.848052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8284 | 0.547617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.04163 | 0.102987 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.70711 | − | 9.88500i | 0.287156 | − | 0.497368i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.8284 | − | 30.8797i | −0.894783 | − | 1.54981i | −0.834073 | − | 0.551654i | \(-0.813997\pi\) |
−0.0607103 | − | 0.998155i | \(-0.519337\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.80761 | + | 0.384213i | −0.140556 | + | 0.0192347i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.5000 | + | 21.6506i | 0.624220 | + | 1.08118i | 0.988691 | + | 0.149966i | \(0.0479165\pi\) |
−0.364471 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.82843 | + | 15.2913i | −0.439775 | + | 0.761713i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.5858 | 0.526012 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.07107 | 0.449636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9497 | − | 29.3578i | 0.838111 | − | 1.45165i | −0.0533610 | − | 0.998575i | \(-0.516993\pi\) |
0.891472 | − | 0.453076i | \(-0.149673\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.52082 | − | 6.09823i | −0.173669 | − | 0.300804i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.41421 | + | 10.8126i | −0.217209 | + | 0.532052i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.41421 | − | 12.8418i | −0.363949 | − | 0.630379i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.686292 | + | 1.18869i | −0.0336078 | + | 0.0582105i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4558 | 1.24360 | 0.621800 | − | 0.783176i | \(-0.286402\pi\) | ||||
0.621800 | + | 0.783176i | \(0.286402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.65685 | 0.470646 | 0.235323 | − | 0.971917i | \(-0.424385\pi\) | ||||
0.235323 | + | 0.971917i | \(0.424385\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.82843 | + | 11.8272i | −0.332009 | + | 0.575057i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | − | 5.19615i | −0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.2487 | − | 17.0849i | −0.641151 | − | 0.826795i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.378680 | + | 0.655892i | 0.0182828 | + | 0.0316668i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.86396 | − | 6.69258i | 0.186120 | − | 0.322370i | −0.757833 | − | 0.652449i | \(-0.773742\pi\) |
0.943954 | + | 0.330078i | \(0.107075\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.4558 | −0.646647 | −0.323323 | − | 0.946289i | \(-0.604800\pi\) | ||||
−0.323323 | + | 0.946289i | \(0.604800\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.585786 | 0.0280863 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.00000 | − | 12.1244i | 0.334855 | − | 0.579987i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.964466 | + | 1.67050i | 0.0460315 | + | 0.0797288i | 0.888123 | − | 0.459606i | \(-0.152009\pi\) |
−0.842092 | + | 0.539334i | \(0.818676\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.1421 | + | 13.8564i | 0.673435 | + | 0.659829i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.65685 | + | 4.60181i | 0.126231 | + | 0.218638i | 0.922213 | − | 0.386681i | \(-0.126379\pi\) |
−0.795982 | + | 0.605320i | \(0.793045\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.48528 | − | 11.2328i | 0.307432 | − | 0.532488i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.62742 | −0.313466 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.12132 | − | 5.40629i | 0.146977 | − | 0.254572i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.15685 | + | 2.00373i | 0.0543538 | + | 0.0941435i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.19239 | + | 5.40629i | 0.196542 | + | 0.253451i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6569 | − | 25.3864i | −0.685619 | − | 1.18753i | −0.973242 | − | 0.229783i | \(-0.926198\pi\) |
0.287623 | − | 0.957744i | \(-0.407135\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.41421 | + | 4.18154i | −0.112686 | + | 0.195178i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.0000 | −0.605470 | −0.302735 | − | 0.953075i | \(-0.597900\pi\) | ||||
−0.302735 | + | 0.953075i | \(0.597900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.7990 | 0.641293 | 0.320647 | − | 0.947199i | \(-0.396100\pi\) | ||||
0.320647 | + | 0.947199i | \(0.396100\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.82843 | + | 4.89898i | −0.131165 | + | 0.227185i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.9706 | + | 31.1259i | 0.831578 | + | 1.44034i | 0.896786 | + | 0.442464i | \(0.145896\pi\) |
−0.0652076 | + | 0.997872i | \(0.520771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.07107 | + | 19.7700i | −0.372687 | + | 0.912894i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.51472 | + | 2.62357i | 0.0697946 | + | 0.120888i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.75736 | −0.355932 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.31371 | −0.334872 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.03553 | − | 12.1859i | 0.321462 | − | 0.556788i | −0.659328 | − | 0.751855i | \(-0.729159\pi\) |
0.980790 | + | 0.195067i | \(0.0624925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.29289 | + | 14.3637i | 0.378123 | + | 0.654929i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.87868 | − | 0.804479i | 0.267489 | − | 0.0366051i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.1924 | + | 19.3858i | 0.508220 | + | 0.880263i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.6569 | + | 20.1903i | −0.528222 | + | 0.914908i | 0.471236 | + | 0.882007i | \(0.343808\pi\) |
−0.999459 | + | 0.0329011i | \(0.989525\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.11270 | −0.0955395 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.828427 | 0.0373864 | 0.0186932 | − | 0.999825i | \(-0.494049\pi\) | ||||
0.0186932 | + | 0.999825i | \(0.494049\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.00000 | − | 1.73205i | 0.0450377 | − | 0.0780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | − | 3.46410i | −0.0898933 | − | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.0919 | + | 2.06528i | −0.676963 | + | 0.0926403i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.8995 | − | 20.6105i | −0.532695 | − | 0.922654i | −0.999271 | − | 0.0381732i | \(-0.987846\pi\) |
0.466577 | − | 0.884481i | \(-0.345487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0563492 | + | 0.0975997i | −0.00251750 | + | 0.00436043i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.7279 | 0.879625 | 0.439812 | − | 0.898090i | \(-0.355045\pi\) | ||||
0.439812 | + | 0.898090i | \(0.355045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5858 | −0.471061 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.00000 | − | 3.46410i | 0.0888231 | − | 0.153846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.8284 | − | 30.8797i | −0.790231 | − | 1.36872i | −0.925824 | − | 0.377956i | \(-0.876627\pi\) |
0.135593 | − | 0.990765i | \(-0.456706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.41421 | + | 8.36308i | −0.151036 | + | 0.369961i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.12132 | + | 5.40629i | 0.137810 | + | 0.238693i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.2426 | + | 19.4728i | −0.495410 | + | 0.858075i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.82843 | 0.212354 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.899495 | 0.0394834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | + | 10.3923i | −0.262865 | + | 0.455295i | −0.967002 | − | 0.254769i | \(-0.918001\pi\) |
0.704137 | + | 0.710064i | \(0.251334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.53553 | − | 11.3199i | −0.285779 | − | 0.494984i | 0.687019 | − | 0.726640i | \(-0.258919\pi\) |
−0.972798 | + | 0.231656i | \(0.925586\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.01472 | − | 2.59808i | −0.0879295 | − | 0.113389i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.65685 | + | 16.7262i | 0.420659 | + | 0.728603i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.15685 | + | 5.46783i | −0.137255 | + | 0.237732i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.4853 | 0.541815 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.4142 | 0.494404 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.58579 | − | 16.6031i | 0.414430 | − | 0.717813i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.91421 | + | 6.77962i | 0.168911 | + | 0.292562i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.74264 | − | 6.77962i | 0.0750608 | − | 0.292019i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.42893 | + | 7.67114i | 0.190415 | + | 0.329808i | 0.945388 | − | 0.325948i | \(-0.105683\pi\) |
−0.754973 | + | 0.655756i | \(0.772350\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.75736 | − | 4.77589i | 0.118330 | − | 0.204953i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.6985 | 1.86841 | 0.934206 | − | 0.356734i | \(-0.116110\pi\) | ||||
0.934206 | + | 0.356734i | \(0.116110\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.5563 | + | 20.0162i | −0.493213 | + | 0.854270i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.29289 | − | 2.23936i | −0.0550791 | − | 0.0953998i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.0858 | − | 16.8747i | −0.556464 | − | 0.717587i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.65685 | + | 4.60181i | 0.112777 | + | 0.195336i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.41421 | − | 16.3059i | 0.398893 | − | 0.690903i | −0.594697 | − | 0.803950i | \(-0.702728\pi\) |
0.993590 | + | 0.113047i | \(0.0360611\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6274 | 0.618674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.828427 | 0.0349762 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.39340 | − | 2.41344i | 0.0587247 | − | 0.101714i | −0.835168 | − | 0.549994i | \(-0.814630\pi\) |
0.893893 | + | 0.448280i | \(0.147963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.29289 | + | 9.16756i | 0.222674 | + | 0.385682i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.48528 | − | 18.3351i | 0.314352 | − | 0.770003i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.48528 | + | 11.2328i | 0.271877 | + | 0.470905i | 0.969343 | − | 0.245713i | \(-0.0790222\pi\) |
−0.697465 | + | 0.716618i | \(0.745689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.70711 | − | 6.42090i | 0.155138 | − | 0.268706i | −0.777972 | − | 0.628300i | \(-0.783751\pi\) |
0.933109 | + | 0.359593i | \(0.117085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.68629 | 0.112221 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.2426 | 0.677365 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.98528 | + | 13.8309i | −0.332432 | + | 0.575788i | −0.982988 | − | 0.183669i | \(-0.941202\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.80761 | − | 8.32703i | −0.199798 | − | 0.346059i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.4853 | + | 3.76127i | −1.14028 | + | 0.156044i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.29289 | + | 2.23936i | 0.0535462 | + | 0.0927447i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.65685 | − | 6.33386i | 0.151192 | − | 0.261873i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.2132 | −0.669191 | −0.334595 | − | 0.942362i | \(-0.608600\pi\) | ||||
−0.334595 | + | 0.942362i | \(0.608600\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.9706 | 1.02889 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.30761 | − | 3.99690i | 0.0949225 | − | 0.164411i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.29289 | + | 9.16756i | 0.217353 | + | 0.376467i | 0.953998 | − | 0.299813i | \(-0.0969244\pi\) |
−0.736645 | + | 0.676280i | \(0.763591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.41421 | − | 1.01461i | 0.303953 | − | 0.0415950i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.97918 | + | 8.62420i | 0.203784 | + | 0.352965i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.4853 | − | 38.9456i | 0.918724 | − | 1.59128i | 0.117368 | − | 0.993089i | \(-0.462554\pi\) |
0.801356 | − | 0.598188i | \(-0.204112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.6569 | −0.964983 | −0.482492 | − | 0.875901i | \(-0.660268\pi\) | ||||
−0.482492 | + | 0.875901i | \(0.660268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.8284 | 0.929645 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.707107 | + | 1.22474i | −0.0287480 | + | 0.0497930i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.1421 | + | 19.2987i | 0.452245 | + | 0.783312i | 0.998525 | − | 0.0542908i | \(-0.0172898\pi\) |
−0.546280 | + | 0.837603i | \(0.683956\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.414214 | − | 1.01461i | 0.0167848 | − | 0.0411141i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.41421 | + | 7.64564i | 0.178580 | + | 0.309310i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.3137 | + | 24.7921i | −0.578125 | + | 1.00134i | 0.417569 | + | 0.908645i | \(0.362882\pi\) |
−0.995694 | + | 0.0926971i | \(0.970451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.65685 | 0.147459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.6274 | 1.35379 | 0.676894 | − | 0.736080i | \(-0.263325\pi\) | ||||
0.676894 | + | 0.736080i | \(0.263325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.343146 | − | 0.594346i | 0.0137922 | − | 0.0238888i | −0.859047 | − | 0.511897i | \(-0.828943\pi\) |
0.872839 | + | 0.488008i | \(0.162276\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.53553 | − | 11.3199i | −0.262262 | − | 0.454251i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.8701 | − | 19.1757i | −0.595756 | − | 0.768256i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.535534 | − | 0.927572i | 0.0213872 | − | 0.0370437i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.1421 | 0.723374 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.38478 | 0.174555 | 0.0872776 | − | 0.996184i | \(-0.472183\pi\) | ||||
0.0872776 | + | 0.996184i | \(0.472183\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.02082 | + | 1.76810i | −0.0405738 | + | 0.0702758i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.53553 | + | 7.85578i | 0.179987 | + | 0.311747i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.3284 | − | 3.43861i | 0.488470 | − | 0.136243i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.14214 | + | 14.1026i | 0.322098 | + | 0.557890i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.1274 | + | 38.3258i | −0.873980 | + | 1.51378i | −0.0161355 | + | 0.999870i | \(0.505136\pi\) |
−0.857845 | + | 0.513909i | \(0.828197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.5858 | −1.40337 | −0.701683 | − | 0.712489i | \(-0.747568\pi\) | ||||
−0.701683 | + | 0.712489i | \(0.747568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.68629 | 0.184523 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.53553 | + | 11.3199i | −0.256938 | + | 0.445030i | −0.965420 | − | 0.260699i | \(-0.916047\pi\) |
0.708482 | + | 0.705729i | \(0.249380\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.20711 | − | 3.82282i | −0.0866365 | − | 0.150059i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.48528 | + | 8.36308i | 0.254178 | + | 0.327775i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.5355 | + | 42.4968i | 0.960150 | + | 1.66303i | 0.722117 | + | 0.691771i | \(0.243169\pi\) |
0.238032 | + | 0.971257i | \(0.423498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.48528 | + | 6.03668i | −0.136181 | + | 0.235873i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.65685 | 0.376750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.3137 | −1.21981 | −0.609904 | − | 0.792475i | \(-0.708792\pi\) | ||||
−0.609904 | + | 0.792475i | \(0.708792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.31371 | − | 4.00746i | 0.0899928 | − | 0.155872i | −0.817515 | − | 0.575907i | \(-0.804649\pi\) |
0.907508 | + | 0.420035i | \(0.137982\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.757359 | + | 1.31178i | 0.0294134 | + | 0.0509455i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.65685 | − | 8.95743i | 0.141807 | − | 0.347354i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.70711 | + | 4.68885i | 0.104820 | + | 0.181553i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.05025 | − | 7.01524i | 0.156592 | − | 0.271225i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.17157 | 0.315460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.2426 | 0.626108 | 0.313054 | − | 0.949735i | \(-0.398648\pi\) | ||||
0.313054 | + | 0.949735i | \(0.398648\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.62132 | + | 6.27231i | −0.139385 | + | 0.241421i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.14214 | − | 7.17439i | −0.159195 | − | 0.275734i | 0.775383 | − | 0.631491i | \(-0.217557\pi\) |
−0.934579 | + | 0.355756i | \(0.884223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.4914 | − | 5.67796i | 1.59229 | − | 0.217900i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.82843 | − | 10.0951i | −0.223346 | − | 0.386846i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.44975 | − | 12.9033i | 0.285057 | − | 0.493733i | −0.687566 | − | 0.726122i | \(-0.741321\pi\) |
0.972623 | + | 0.232389i | \(0.0746542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0416 | 0.918583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.65685 | −0.0632129 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.36396 | + | 4.09450i | −0.0900597 | + | 0.155988i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.6924 | + | 25.4480i | 0.558925 | + | 0.968086i | 0.997587 | + | 0.0694339i | \(0.0221193\pi\) |
−0.438662 | + | 0.898652i | \(0.644547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.41421 | + | 1.01461i | −0.281643 | + | 0.0385419i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.34315 | − | 4.05845i | −0.0888806 | − | 0.153946i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.24264 | − | 10.8126i | 0.236457 | − | 0.409555i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.44365 | 0.319368 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.4558 | 1.60354 | 0.801768 | − | 0.597636i | \(-0.203893\pi\) | ||||
0.801768 | + | 0.597636i | \(0.203893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.7279 | − | 20.3134i | 0.442327 | − | 0.766133i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.41421 | + | 2.44949i | 0.0532624 | + | 0.0922531i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.48528 | + | 18.3351i | −0.281513 | + | 0.689563i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.46447 | − | 16.3929i | −0.355445 | − | 0.615650i | 0.631749 | − | 0.775173i | \(-0.282337\pi\) |
−0.987194 | + | 0.159524i | \(0.949004\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.4142 | + | 19.7700i | −0.428066 | + | 0.741433i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −52.2843 | −1.95806 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.58579 | −0.0967029 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.42893 | + | 4.20703i | −0.0907101 | + | 0.157115i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.4142 | + | 24.9662i | 0.537559 | + | 0.931080i | 0.999035 | + | 0.0439272i | \(0.0139870\pi\) |
−0.461475 | + | 0.887153i | \(0.652680\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.7782 | + | 33.2422i | 0.960029 | + | 1.23800i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.70711 | + | 8.15295i | 0.175059 | + | 0.303211i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50000 | − | 2.59808i | 0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.7990 | 0.511776 | 0.255888 | − | 0.966706i | \(-0.417632\pi\) | ||||
0.255888 | + | 0.966706i | \(0.417632\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | − | 13.8564i | 0.295891 | − | 0.512498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3284 | − | 24.8176i | −0.529233 | − | 0.916658i | −0.999419 | − | 0.0340904i | \(-0.989147\pi\) |
0.470186 | − | 0.882567i | \(-0.344187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.94975 | − | 1.10165i | 0.145689 | − | 0.0406350i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.03553 | − | 6.98975i | −0.148651 | − | 0.257471i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.2132 | − | 31.5462i | 0.669984 | − | 1.16045i | −0.307925 | − | 0.951411i | \(-0.599634\pi\) |
0.977908 | − | 0.209035i | \(-0.0670322\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.95837 | 0.0719425 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.0000 | −1.24734 | −0.623670 | − | 0.781688i | \(-0.714359\pi\) | ||||
−0.623670 | + | 0.781688i | \(0.714359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.3137 | − | 19.5959i | 0.414502 | − | 0.717939i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.8284 | + | 25.6836i | 0.542544 | + | 0.939713i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.9792 | − | 28.3432i | −0.803102 | − | 1.03564i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.65685 | + | 9.79796i | 0.206422 | + | 0.357533i | 0.950585 | − | 0.310465i | \(-0.100485\pi\) |
−0.744163 | + | 0.667998i | \(0.767152\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.100505 | − | 0.174080i | 0.00366261 | − | 0.00634382i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.89949 | −0.287492 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.3137 | 0.629277 | 0.314639 | − | 0.949212i | \(-0.398117\pi\) | ||||
0.314639 | + | 0.949212i | \(0.398117\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.12132 | + | 1.94218i | −0.0407013 | + | 0.0704968i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.9706 | + | 24.1977i | 0.506433 | + | 0.877167i | 0.999972 | + | 0.00744361i | \(0.00236940\pi\) |
−0.493540 | + | 0.869723i | \(0.664297\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.48528 | + | 20.7846i | −0.307188 | + | 0.752453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | − | 6.92820i | −0.144620 | − | 0.250490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.03553 | − | 6.98975i | 0.145715 | − | 0.252385i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.9706 | 1.11683 | 0.558414 | − | 0.829563i | \(-0.311410\pi\) | ||||
0.558414 | + | 0.829563i | \(0.311410\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.07107 | −0.290672 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.3137 | + | 29.9882i | −0.622731 | + | 1.07860i | 0.366244 | + | 0.930519i | \(0.380643\pi\) |
−0.988975 | + | 0.148083i | \(0.952690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.4853 | + | 25.0892i | 0.520327 | + | 0.901232i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.84924 | − | 1.34784i | 0.353340 | − | 0.0483534i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.07107 | − | 13.9795i | −0.289176 | − | 0.500868i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.87868 | − | 4.98602i | 0.103007 | − | 0.178414i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.41421 | −0.0862770 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.3431 | −0.369163 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.80761 | − | 4.86293i | 0.100081 | − | 0.173345i | −0.811637 | − | 0.584162i | \(-0.801423\pi\) |
0.911718 | + | 0.410817i | \(0.134757\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.77208 | − | 8.26548i | −0.169890 | − | 0.294259i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.6213 | − | 2.68512i | 0.697654 | − | 0.0954717i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.47056 | + | 12.9394i | 0.265287 | + | 0.459491i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.757359 | + | 1.31178i | −0.0268608 | + | 0.0465242i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.31371 | 0.329908 | 0.164954 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164954 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.65685 | 0.341635 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.9706 | + | 22.4657i | −0.458292 | + | 0.793786i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.70711 | − | 2.95680i | −0.0602425 | − | 0.104343i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.65685 | + | 18.7554i | −0.269869 | + | 0.661040i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.82843 | + | 4.89898i | 0.0995654 | + | 0.172452i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.00000 | − | 6.92820i | 0.140633 | − | 0.243583i | −0.787102 | − | 0.616822i | \(-0.788420\pi\) |
0.927735 | + | 0.373240i | \(0.121753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.6569 | −1.74369 | −0.871844 | − | 0.489784i | \(-0.837076\pi\) | ||||
−0.871844 | + | 0.489784i | \(0.837076\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0294373 | 0.00103241 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.60660 | − | 6.24682i | 0.126334 | − | 0.218816i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.3431 | − | 17.9149i | −0.361861 | − | 0.626761i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.38478 | − | 10.8126i | −0.292988 | − | 0.377822i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.0858 | + | 19.2011i | 0.386897 | + | 0.670125i | 0.992030 | − | 0.125999i | \(-0.0402137\pi\) |
−0.605134 | + | 0.796124i | \(0.706880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.5858 | + | 23.5313i | −0.473571 | + | 0.820249i | −0.999542 | − | 0.0302536i | \(-0.990369\pi\) |
0.525972 | + | 0.850502i | \(0.323702\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.24264 | 0.0432632 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.5269 | −1.13107 | −0.565536 | − | 0.824724i | \(-0.691331\pi\) | ||||
−0.565536 | + | 0.824724i | \(0.691331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.7071 | + | 32.4017i | −0.649725 | + | 1.12536i | 0.333464 | + | 0.942763i | \(0.391782\pi\) |
−0.983189 | + | 0.182593i | \(0.941551\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.13604 | + | 8.89588i | 0.178167 | + | 0.308595i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.48528 | − | 13.5592i | 0.120758 | − | 0.469800i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.192388 | − | 0.333226i | −0.00665787 | − | 0.0115318i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.6569 | − | 20.1903i | 0.402920 | − | 0.697878i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.4853 | −0.914373 | −0.457187 | − | 0.889371i | \(-0.651143\pi\) | ||||
−0.457187 | + | 0.889371i | \(0.651143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.46447 | − | 4.26858i | 0.0848807 | − | 0.147018i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.82843 | + | 11.8272i | 0.234905 | + | 0.406867i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.62132 | + | 2.09077i | 0.0557092 | + | 0.0718397i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.70711 | + | 9.88500i | 0.195867 | + | 0.339252i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.5563 | + | 42.5328i | −0.841781 | + | 1.45801i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.0000 | −1.71197 | −0.855984 | − | 0.517003i | \(-0.827048\pi\) | ||||
−0.855984 | + | 0.517003i | \(0.827048\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.3431 | −0.353728 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.1421 | − | 41.8154i | 0.824680 | − | 1.42839i | −0.0774842 | − | 0.996994i | \(-0.524689\pi\) |
0.902164 | − | 0.431393i | \(-0.141978\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.20711 | − | 10.7510i | −0.211784 | − | 0.366820i | 0.740489 | − | 0.672068i | \(-0.234594\pi\) |
−0.952273 | + | 0.305248i | \(0.901261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.58579 | − | 6.33386i | 0.0881234 | − | 0.215857i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.1924 | − | 22.8499i | −0.449074 | − | 0.777819i | 0.549252 | − | 0.835657i | \(-0.314913\pi\) |
−0.998326 | + | 0.0578377i | \(0.981579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.53553 | + | 2.65962i | −0.0522097 | + | 0.0904299i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.38478 | −0.182877 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.07107 | 0.273792 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.37868 | − | 12.7802i | 0.250017 | − | 0.433042i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.3848 | − | 38.7716i | −0.757610 | − | 1.31222i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.6569 | − | 4.05845i | 1.00258 | − | 0.137201i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.64214 | − | 11.5045i | −0.224289 | − | 0.388480i | 0.731817 | − | 0.681501i | \(-0.238673\pi\) |
−0.956106 | + | 0.293021i | \(0.905339\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.72792 | − | 4.72490i | 0.0920105 | − | 0.159367i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8284 | 0.668037 | 0.334018 | − | 0.942567i | \(-0.391595\pi\) | ||||
0.334018 | + | 0.942567i | \(0.391595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.6690 | −1.33497 | −0.667485 | − | 0.744623i | \(-0.732629\pi\) | ||||
−0.667485 | + | 0.744623i | \(0.732629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.29289 | − | 2.23936i | 0.0434601 | − | 0.0752752i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.8640 | − | 27.4772i | −0.532660 | − | 0.922594i | −0.999273 | − | 0.0381321i | \(-0.987859\pi\) |
0.466613 | − | 0.884462i | \(-0.345474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8137 | − | 2.30090i | 0.563914 | − | 0.0771698i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.74264 | + | 6.48244i | 0.125383 | + | 0.217170i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.24264 | − | 10.8126i | 0.208902 | − | 0.361829i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.7279 | −0.893416 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.10051 | −0.136912 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.82843 | + | 8.36308i | −0.161037 | + | 0.278924i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.58579 | + | 4.47871i | 0.0861450 | + | 0.149208i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.31371 | − | 8.11689i | 0.110273 | − | 0.270113i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.41421 | + | 16.3059i | 0.312939 | + | 0.542026i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.31371 | + | 10.9357i | −0.209643 | + | 0.363113i | −0.951602 | − | 0.307333i | \(-0.900564\pi\) |
0.741959 | + | 0.670445i | \(0.233897\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.1716 | 0.702217 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.4853 | −1.27507 | −0.637537 | − | 0.770420i | \(-0.720047\pi\) | ||||
−0.637537 | + | 0.770420i | \(0.720047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.24264 | − | 9.08052i | 0.173506 | − | 0.300521i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.39340 | + | 4.14549i | 0.0791233 | + | 0.137046i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.99138 | + | 10.3053i | 0.263899 | + | 0.340310i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.72792 | + | 4.72490i | 0.0899858 | + | 0.155860i | 0.907505 | − | 0.420041i | \(-0.137984\pi\) |
−0.817519 | + | 0.575902i | \(0.804651\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.77817 | − | 3.07989i | 0.0585928 | − | 0.101486i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.5269 | 0.346498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.2132 | 0.894765 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.4853 | − | 38.9456i | 0.738514 | − | 1.27914i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.7132 | + | 35.8763i | 0.679578 | + | 1.17706i | 0.975108 | + | 0.221730i | \(0.0711705\pi\) |
−0.295530 | + | 0.955334i | \(0.595496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.9289 | − | 12.6677i | −0.423729 | − | 0.415168i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.63604 | − | 9.76191i | −0.184516 | − | 0.319590i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.41421 | + | 2.44949i | −0.0462497 | + | 0.0801069i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.4142 | −0.699572 | −0.349786 | − | 0.936830i | \(-0.613746\pi\) | ||||
−0.349786 | + | 0.936830i | \(0.613746\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.87006 | −0.126295 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.4706 | − | 44.1163i | 0.830317 | − | 1.43815i | −0.0674707 | − | 0.997721i | \(-0.521493\pi\) |
0.897787 | − | 0.440429i | \(-0.145174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.8995 | + | 29.2708i | 0.550323 | + | 0.953188i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.53553 | − | 7.13834i | −0.180071 | − | 0.232210i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.100505 | + | 0.174080i | 0.00326598 | + | 0.00565684i | 0.867654 | − | 0.497169i | \(-0.165627\pi\) |
−0.864388 | + | 0.502826i | \(0.832294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.12132 | − | 5.40629i | 0.101322 | − | 0.175495i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.68629 | 0.281672 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.6152 | 0.570613 | 0.285307 | − | 0.958436i | \(-0.407905\pi\) | ||||
0.285307 | + | 0.958436i | \(0.407905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.58579 | + | 7.94282i | −0.148393 | + | 0.257023i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.207107 | + | 0.358719i | 0.00669481 | + | 0.0115958i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.0000 | − | 41.6413i | 0.548959 | − | 1.34467i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.1274 | − | 53.9143i | −1.00411 | − | 1.73917i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.1716 | + | 33.2061i | −0.617795 | + | 1.07005i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.8284 | 1.05678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3431 | 0.589876 | 0.294938 | − | 0.955516i | \(-0.404701\pi\) | ||||
0.294938 | + | 0.955516i | \(0.404701\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.07107 | − | 1.85514i | 0.0344077 | − | 0.0595958i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.1066 | + | 26.1654i | 0.484794 | + | 0.839688i | 0.999847 | − | 0.0174704i | \(-0.00556127\pi\) |
−0.515053 | + | 0.857158i | \(0.672228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.68629 | + | 1.18869i | −0.278470 | + | 0.0381077i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.13604 | + | 1.96768i | 0.0363824 | + | 0.0630161i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.51472 | + | 2.62357i | −0.0484601 | + | 0.0839354i | −0.889238 | − | 0.457445i | \(-0.848765\pi\) |
0.840778 | + | 0.541380i | \(0.182098\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.17157 | 0.293125 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.0000 | 0.766261 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.7574 | + | 25.5605i | −0.470687 | + | 0.815253i | −0.999438 | − | 0.0335236i | \(-0.989327\pi\) |
0.528751 | + | 0.848777i | \(0.322660\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.87868 | + | 13.6463i | 0.251036 | + | 0.434806i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.24264 | − | 0.717439i | 0.166875 | − | 0.0228363i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.6569 | + | 37.5108i | 0.688648 | + | 1.19277i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.0502525 | − | 0.0870399i | 0.00159632 | − | 0.00276491i | −0.865226 | − | 0.501382i | \(-0.832825\pi\) |
0.866822 | + | 0.498617i | \(0.166159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.23045 | 0.0707811 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.0000 | −1.07787 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.7279 | + | 35.9018i | −0.656460 | + | 1.13702i | 0.325066 | + | 0.945691i | \(0.394614\pi\) |
−0.981526 | + | 0.191330i | \(0.938720\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.9497 | − | 18.9655i | −0.346435 | − | 0.600042i |
(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 | 1232.2.q.h.529.1 | 4 | ||
4.3 | odd | 2 | 616.2.q.b.529.2 | yes | 4 | ||
7.2 | even | 3 | inner | 1232.2.q.h.177.1 | 4 | ||
7.3 | odd | 6 | 8624.2.a.cd.1.1 | 2 | |||
7.4 | even | 3 | 8624.2.a.bg.1.2 | 2 | |||
28.3 | even | 6 | 4312.2.a.m.1.2 | 2 | |||
28.11 | odd | 6 | 4312.2.a.u.1.1 | 2 | |||
28.23 | odd | 6 | 616.2.q.b.177.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.2.q.b.177.2 | ✓ | 4 | 28.23 | odd | 6 | ||
616.2.q.b.529.2 | yes | 4 | 4.3 | odd | 2 | ||
1232.2.q.h.177.1 | 4 | 7.2 | even | 3 | inner | ||
1232.2.q.h.529.1 | 4 | 1.1 | even | 1 | trivial | ||
4312.2.a.m.1.2 | 2 | 28.3 | even | 6 | |||
4312.2.a.u.1.1 | 2 | 28.11 | odd | 6 | |||
8624.2.a.bg.1.2 | 2 | 7.4 | even | 3 | |||
8624.2.a.cd.1.1 | 2 | 7.3 | odd | 6 |