Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1064,2,Mod(305,1064)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1064, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1064.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1064 = 2^{3} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1064.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.49608277506\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 305.5 | ||
Root | \(0.218288 - 0.378086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1064.305 |
Dual form | 1064.2.q.n.457.5 |
$q$-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 \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(799\) | \(913\) | \(1009\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.218288 | − | 0.378086i | 0.126029 | − | 0.218288i | −0.796106 | − | 0.605157i | \(-0.793110\pi\) |
0.922135 | + | 0.386869i | \(0.126444\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.149820 | + | 0.259496i | 0.0670015 | + | 0.116050i | 0.897580 | − | 0.440851i | \(-0.145323\pi\) |
−0.830579 | + | 0.556901i | \(0.811990\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.68999 | − | 2.03567i | 0.638756 | − | 0.769409i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.40470 | + | 2.43301i | 0.468234 | + | 0.811004i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59469 | − | 4.49414i | 0.782329 | − | 1.35503i | −0.148253 | − | 0.988949i | \(-0.547365\pi\) |
0.930582 | − | 0.366084i | \(-0.119302\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.26174 | −0.349944 | −0.174972 | − | 0.984573i | \(-0.555984\pi\) | ||||
−0.174972 | + | 0.984573i | \(0.555984\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.130816 | 0.0337764 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.979458 | + | 1.69647i | −0.237553 | + | 0.411454i | −0.960012 | − | 0.279960i | \(-0.909679\pi\) |
0.722458 | + | 0.691414i | \(0.243012\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.400752 | − | 1.08332i | −0.0874513 | − | 0.236401i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.745532 | + | 1.29130i | 0.155454 | + | 0.269254i | 0.933224 | − | 0.359294i | \(-0.116983\pi\) |
−0.777770 | + | 0.628549i | \(0.783649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.45511 | − | 4.25237i | 0.491022 | − | 0.850474i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.53625 | 0.488101 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.530372 | −0.0984876 | −0.0492438 | − | 0.998787i | \(-0.515681\pi\) | ||||
−0.0492438 | + | 0.998787i | \(0.515681\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.974190 | + | 1.68735i | −0.174970 | + | 0.303056i | −0.940151 | − | 0.340759i | \(-0.889316\pi\) |
0.765181 | + | 0.643815i | \(0.222649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.13278 | − | 1.96203i | −0.197192 | − | 0.341546i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.781440 | + | 0.133562i | 0.132088 | + | 0.0225761i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.09673 | − | 3.63165i | −0.344701 | − | 0.597039i | 0.640599 | − | 0.767876i | \(-0.278686\pi\) |
−0.985299 | + | 0.170837i | \(0.945353\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.275423 | + | 0.477047i | −0.0441030 | + | 0.0763887i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.51755 | 0.841418 | 0.420709 | − | 0.907196i | \(-0.361781\pi\) | ||||
0.420709 | + | 0.907196i | \(0.361781\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.420904 | + | 0.729027i | −0.0627447 | + | 0.108677i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.27048 | + | 7.39669i | 0.622913 | + | 1.07892i | 0.988940 | + | 0.148313i | \(0.0473844\pi\) |
−0.366027 | + | 0.930604i | \(0.619282\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.28787 | − | 6.88051i | −0.183981 | − | 0.982930i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.427608 | + | 0.740639i | 0.0598771 | + | 0.103710i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.87784 | − | 10.1807i | 0.807383 | − | 1.39843i | −0.107288 | − | 0.994228i | \(-0.534217\pi\) |
0.914671 | − | 0.404200i | \(-0.132450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.55494 | 0.209669 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.436576 | −0.0578259 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.40759 | − | 11.0983i | 0.834198 | − | 1.44487i | −0.0604842 | − | 0.998169i | \(-0.519264\pi\) |
0.894682 | − | 0.446704i | \(-0.147402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.96790 | + | 5.14056i | 0.380001 | + | 0.658181i | 0.991062 | − | 0.133403i | \(-0.0425904\pi\) |
−0.611061 | + | 0.791583i | \(0.709257\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.32673 | + | 1.25227i | 0.923081 | + | 0.157771i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.189034 | − | 0.327416i | −0.0234468 | − | 0.0406110i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.75386 | + | 4.76982i | −0.336438 | + | 0.582727i | −0.983760 | − | 0.179489i | \(-0.942555\pi\) |
0.647322 | + | 0.762216i | \(0.275889\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.650963 | 0.0783667 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.28016 | 0.270605 | 0.135303 | − | 0.990804i | \(-0.456799\pi\) | ||||
0.135303 | + | 0.990804i | \(0.456799\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.34620 | − | 4.06373i | 0.274602 | − | 0.475624i | −0.695433 | − | 0.718591i | \(-0.744787\pi\) |
0.970035 | + | 0.242967i | \(0.0781207\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.07184 | − | 1.85648i | −0.123766 | − | 0.214368i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.76356 | − | 12.8770i | −0.542858 | − | 1.46747i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.84734 | − | 4.93174i | −0.320351 | − | 0.554864i | 0.660209 | − | 0.751082i | \(-0.270468\pi\) |
−0.980560 | + | 0.196217i | \(0.937134\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.66047 | + | 6.34012i | −0.406719 | + | 0.704458i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.46325 | 0.160613 | 0.0803065 | − | 0.996770i | \(-0.474410\pi\) | ||||
0.0803065 | + | 0.996770i | \(0.474410\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.586969 | −0.0636657 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.115774 | + | 0.200526i | −0.0124123 | + | 0.0214987i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.92525 | + | 3.33463i | 0.204076 | + | 0.353470i | 0.949838 | − | 0.312742i | \(-0.101248\pi\) |
−0.745762 | + | 0.666213i | \(0.767914\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.13233 | + | 2.56848i | −0.223529 | + | 0.269250i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.425308 | + | 0.736655i | 0.0441024 | + | 0.0763876i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.149820 | − | 0.259496i | 0.0153712 | − | 0.0266237i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.69800 | −0.984683 | −0.492341 | − | 0.870402i | \(-0.663859\pi\) | ||||
−0.492341 | + | 0.870402i | \(0.663859\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.5791 | 1.46525 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.19033 | + | 14.1861i | −0.814969 | + | 1.41157i | 0.0943816 | + | 0.995536i | \(0.469913\pi\) |
−0.909350 | + | 0.416031i | \(0.863421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.43891 | − | 4.22431i | −0.240313 | − | 0.416234i | 0.720491 | − | 0.693465i | \(-0.243917\pi\) |
−0.960803 | + | 0.277231i | \(0.910583\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.221077 | − | 0.266297i | 0.0215749 | − | 0.0259879i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.67777 | − | 6.37008i | −0.355543 | − | 0.615819i | 0.631667 | − | 0.775239i | \(-0.282371\pi\) |
−0.987211 | + | 0.159420i | \(0.949037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.19435 | + | 3.80073i | −0.210181 | + | 0.364044i | −0.951771 | − | 0.306809i | \(-0.900739\pi\) |
0.741590 | + | 0.670853i | \(0.234072\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.83077 | −0.173769 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.60321 | 0.621178 | 0.310589 | − | 0.950544i | \(-0.399474\pi\) | ||||
0.310589 | + | 0.950544i | \(0.399474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.223391 | + | 0.386924i | −0.0208313 | + | 0.0360809i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.77237 | − | 3.06983i | −0.163856 | − | 0.283806i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.79817 | + | 4.86087i | 0.164838 | + | 0.445595i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.96484 | − | 13.7955i | −0.724076 | − | 1.25414i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.436576 | + | 0.756172i | −0.0393647 | + | 0.0681817i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.96949 | 0.265600 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.94961 | −0.261736 | −0.130868 | − | 0.991400i | \(-0.541776\pi\) | ||||
−0.130868 | + | 0.991400i | \(0.541776\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.20442 | − | 2.08611i | 0.106043 | − | 0.183672i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.49451 | + | 11.2488i | 0.567428 | + | 0.982815i | 0.996819 | + | 0.0796960i | \(0.0253949\pi\) |
−0.429391 | + | 0.903119i | \(0.641272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.60793 | − | 0.445742i | −0.226136 | − | 0.0386507i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.379980 | + | 0.658145i | 0.0327035 | + | 0.0566441i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.81620 | + | 11.8060i | −0.582347 | + | 1.00866i | 0.412853 | + | 0.910798i | \(0.364532\pi\) |
−0.995200 | + | 0.0978576i | \(0.968801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.6698 | 1.75319 | 0.876596 | − | 0.481226i | \(-0.159809\pi\) | ||||
0.876596 | + | 0.481226i | \(0.159809\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.72878 | 0.314020 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.27383 | + | 5.67044i | −0.273771 | + | 0.474186i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0794602 | − | 0.137629i | −0.00659881 | − | 0.0114295i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.88255 | − | 1.01501i | −0.237749 | − | 0.0837165i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.33713 | + | 5.78008i | 0.273388 | + | 0.473523i | 0.969727 | − | 0.244191i | \(-0.0785223\pi\) |
−0.696339 | + | 0.717713i | \(0.745189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.83236 | + | 13.5660i | −0.637388 | + | 1.10399i | 0.348616 | + | 0.937266i | \(0.386652\pi\) |
−0.986004 | + | 0.166723i | \(0.946681\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.50338 | −0.444922 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.583812 | −0.0468929 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.97962 | + | 5.16085i | −0.237799 | + | 0.411880i | −0.960082 | − | 0.279717i | \(-0.909759\pi\) |
0.722283 | + | 0.691597i | \(0.243093\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.56612 | − | 4.44466i | −0.203507 | − | 0.352484i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.88859 | + | 0.664629i | 0.306464 | + | 0.0523801i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.73136 | − | 15.1232i | −0.683893 | − | 1.18454i | −0.973783 | − | 0.227478i | \(-0.926952\pi\) |
0.289890 | − | 0.957060i | \(-0.406381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.339426 | − | 0.587903i | 0.0264243 | − | 0.0457682i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.72621 | 0.133578 | 0.0667892 | − | 0.997767i | \(-0.478724\pi\) | ||||
0.0667892 | + | 0.997767i | \(0.478724\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4080 | −0.877539 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.40470 | − | 2.43301i | 0.107420 | − | 0.186057i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.439572 | + | 0.761360i | 0.0334200 | + | 0.0578852i | 0.882252 | − | 0.470778i | \(-0.156027\pi\) |
−0.848832 | + | 0.528663i | \(0.822693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.50730 | − | 12.1842i | −0.340720 | − | 0.921042i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.79740 | − | 4.84524i | −0.210266 | − | 0.364191i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.67088 | + | 6.35815i | −0.274374 | + | 0.475231i | −0.969977 | − | 0.243196i | \(-0.921804\pi\) |
0.695603 | + | 0.718427i | \(0.255137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.2504 | −1.35654 | −0.678270 | − | 0.734813i | \(-0.737270\pi\) | ||||
−0.678270 | + | 0.734813i | \(0.737270\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.59143 | 0.191564 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.628264 | − | 1.08819i | 0.0461909 | − | 0.0800050i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.08278 | + | 8.80363i | 0.371690 | + | 0.643785i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.28623 | − | 5.16295i | 0.311777 | − | 0.375549i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.68604 | + | 6.38440i | 0.266712 | + | 0.461959i | 0.968011 | − | 0.250909i | \(-0.0807293\pi\) |
−0.701299 | + | 0.712868i | \(0.747396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.731428 | + | 1.26687i | −0.0526493 | + | 0.0911913i | −0.891149 | − | 0.453711i | \(-0.850100\pi\) |
0.838500 | + | 0.544902i | \(0.183433\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.165055 | −0.0118199 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.41230 | 0.171870 | 0.0859348 | − | 0.996301i | \(-0.472612\pi\) | ||||
0.0859348 | + | 0.996301i | \(0.472612\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.97857 | + | 13.8193i | −0.565586 | + | 0.979623i | 0.431409 | + | 0.902156i | \(0.358017\pi\) |
−0.996995 | + | 0.0774670i | \(0.975317\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.20227 | + | 2.08239i | 0.0848016 | + | 0.146881i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.896323 | + | 1.07966i | −0.0629096 | + | 0.0757773i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.299640 | − | 0.518991i | −0.0209277 | − | 0.0362479i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.09450 | + | 3.62778i | −0.145578 | + | 0.252148i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.18938 | −0.358957 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2835 | 0.914474 | 0.457237 | − | 0.889345i | \(-0.348839\pi\) | ||||
0.457237 | + | 0.889345i | \(0.348839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.497732 | − | 0.862097i | 0.0341040 | − | 0.0590699i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.826638 | + | 1.43178i | 0.0563763 | + | 0.0976465i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.78850 | + | 4.83472i | 0.121411 | + | 0.328202i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.02429 | − | 1.77413i | −0.0692154 | − | 0.119885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.23582 | − | 2.14051i | 0.0831304 | − | 0.143986i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.1602 | −1.88574 | −0.942872 | − | 0.333154i | \(-0.891887\pi\) | ||||
−0.942872 | + | 0.333154i | \(0.891887\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.7948 | 0.919651 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.03880 | + | 15.6557i | −0.599926 | + | 1.03910i | 0.392905 | + | 0.919579i | \(0.371470\pi\) |
−0.992831 | + | 0.119523i | \(0.961863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.60996 | − | 6.25264i | −0.238553 | − | 0.413186i | 0.721746 | − | 0.692158i | \(-0.243340\pi\) |
−0.960299 | + | 0.278972i | \(0.910006\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.90843 | − | 1.00985i | −0.388746 | − | 0.0664435i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.38604 | + | 4.13274i | 0.156314 | + | 0.270744i | 0.933537 | − | 0.358481i | \(-0.116705\pi\) |
−0.777222 | + | 0.629226i | \(0.783372\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.27960 | + | 2.21634i | −0.0834722 | + | 0.144578i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.48616 | −0.161494 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.62602 | 0.234548 | 0.117274 | − | 0.993100i | \(-0.462584\pi\) | ||||
0.117274 | + | 0.993100i | \(0.462584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.66741 | + | 15.0124i | −0.558317 | + | 0.967033i | 0.439320 | + | 0.898331i | \(0.355219\pi\) |
−0.997637 | + | 0.0687027i | \(0.978114\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.40244 | + | 9.35731i | 0.346567 | + | 0.600271i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.59251 | − | 1.36503i | 0.101742 | − | 0.0872087i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.630871 | + | 1.09270i | 0.0401414 | + | 0.0695269i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.319411 | − | 0.553236i | 0.0202418 | − | 0.0350599i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.71280 | 0.613067 | 0.306533 | − | 0.951860i | \(-0.400831\pi\) | ||||
0.306533 | + | 0.951860i | \(0.400831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.73770 | 0.486465 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.128128 | + | 0.221925i | −0.00802370 | + | 0.0138975i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.59148 | + | 6.22062i | 0.224030 | + | 0.388032i | 0.956028 | − | 0.293275i | \(-0.0947452\pi\) |
−0.731998 | + | 0.681307i | \(0.761412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.9363 | − | 1.86920i | −0.679547 | − | 0.116147i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.745014 | − | 1.29040i | −0.0461152 | − | 0.0798739i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.37024 | + | 2.37333i | −0.0844928 | + | 0.146346i | −0.905175 | − | 0.425039i | \(-0.860260\pi\) |
0.820682 | + | 0.571385i | \(0.193594\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.52247 | 0.216383 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.68104 | 0.102878 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2040 | + | 17.6738i | −0.622148 | + | 1.07759i | 0.366937 | + | 0.930246i | \(0.380406\pi\) |
−0.989085 | + | 0.147346i | \(0.952927\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.35452 | + | 12.7384i | 0.446755 | + | 0.773803i | 0.998173 | − | 0.0604265i | \(-0.0192461\pi\) |
−0.551417 | + | 0.834230i | \(0.685913\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.505646 | + | 1.36687i | 0.0306031 | + | 0.0827270i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.7405 | − | 22.0672i | −0.768281 | − | 1.33070i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0509 | + | 17.4087i | −0.603901 | + | 1.04599i | 0.388324 | + | 0.921523i | \(0.373054\pi\) |
−0.992224 | + | 0.124463i | \(0.960279\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.47378 | −0.327707 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1058 | 0.901136 | 0.450568 | − | 0.892742i | \(-0.351222\pi\) | ||||
0.450568 | + | 0.892742i | \(0.351222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.52706 | − | 4.37700i | 0.150218 | − | 0.260186i | −0.781089 | − | 0.624419i | \(-0.785336\pi\) |
0.931308 | + | 0.364234i | \(0.118669\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0654078 | − | 0.113290i | −0.00387442 | − | 0.00671070i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.37998 | + | 4.07133i | −0.199514 | + | 0.240323i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.58133 | + | 11.3992i | 0.387137 | + | 0.670541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.11696 | + | 3.66668i | −0.124098 | + | 0.214944i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.5367 | −0.790823 | −0.395411 | − | 0.918504i | \(-0.629398\pi\) | ||||
−0.395411 | + | 0.918504i | \(0.629398\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.83994 | 0.223570 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.58077 | − | 11.3982i | 0.381855 | − | 0.661393i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.940668 | − | 1.62929i | −0.0544003 | − | 0.0942240i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.32460 | − | 11.2319i | 0.537461 | − | 0.647395i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.57571 | + | 6.19330i | 0.205419 | + | 0.355796i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.889301 | + | 1.54031i | −0.0509212 | + | 0.0881982i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.853123 | 0.0486903 | 0.0243452 | − | 0.999704i | \(-0.492250\pi\) | ||||
0.0243452 | + | 0.999704i | \(0.492250\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.12954 | −0.121145 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.69648 | + | 15.0627i | −0.493132 | + | 0.854130i | −0.999969 | − | 0.00791223i | \(-0.997481\pi\) |
0.506837 | + | 0.862042i | \(0.330815\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0278 | − | 20.8328i | −0.679853 | − | 1.17754i | −0.975025 | − | 0.222096i | \(-0.928710\pi\) |
0.295172 | − | 0.955444i | \(-0.404623\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.772732 | + | 2.08887i | 0.0435385 | + | 0.117694i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.72778 | − | 6.45671i | −0.209373 | − | 0.362645i | 0.742144 | − | 0.670240i | \(-0.233809\pi\) |
−0.951517 | + | 0.307596i | \(0.900476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.37615 | + | 2.38356i | −0.0770497 | + | 0.133454i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.21125 | −0.179235 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.95892 | 0.108997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.09771 | + | 5.36540i | −0.171830 | + | 0.297619i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.958002 | + | 1.65931i | 0.0529776 | + | 0.0917600i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.2742 | + | 3.80706i | 1.22802 | + | 0.209890i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9634 | − | 29.3815i | −0.932393 | − | 1.61495i | −0.779217 | − | 0.626754i | \(-0.784383\pi\) |
−0.153176 | − | 0.988199i | \(-0.548950\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.89056 | − | 10.2028i | 0.322801 | − | 0.559108i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.65033 | −0.0901672 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.1792 | −0.881336 | −0.440668 | − | 0.897670i | \(-0.645258\pi\) | ||||
−0.440668 | + | 0.897670i | \(0.645258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.44140 | − | 2.49658i | 0.0782862 | − | 0.135596i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.05544 | + | 8.75628i | 0.273768 | + | 0.474179i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1829 | − | 9.00632i | −0.873794 | − | 0.486296i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0975271 | + | 0.168922i | 0.00525068 | + | 0.00909445i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2507 | − | 24.6829i | 0.765016 | − | 1.32505i | −0.175222 | − | 0.984529i | \(-0.556064\pi\) |
0.940238 | − | 0.340518i | \(-0.110602\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.1291 | −1.29160 | −0.645801 | − | 0.763506i | \(-0.723476\pi\) | ||||
−0.645801 | + | 0.763506i | \(0.723476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.20009 | −0.170808 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2268 | + | 21.1775i | −0.650768 | + | 1.12716i | 0.332169 | + | 0.943220i | \(0.392220\pi\) |
−0.982937 | + | 0.183943i | \(0.941114\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.341613 | + | 0.591692i | 0.0181310 | + | 0.0314037i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.23035 | + | 0.381205i | 0.118042 | + | 0.0201755i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.8696 | − | 25.7549i | −0.784789 | − | 1.35929i | −0.929125 | − | 0.369765i | \(-0.879438\pi\) |
0.144336 | − | 0.989529i | \(-0.453895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.500000 | + | 0.866025i | −0.0263158 | + | 0.0455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.95452 | −0.365018 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.40603 | 0.0735949 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.1623 | + | 21.0657i | −0.634865 | + | 1.09962i | 0.351679 | + | 0.936121i | \(0.385611\pi\) |
−0.986544 | + | 0.163498i | \(0.947722\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.80940 | − | 4.86603i | −0.146252 | − | 0.253315i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.7910 | − | 29.1706i | −0.560243 | − | 1.51446i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5850 | + | 21.7979i | 0.651628 | + | 1.12865i | 0.982728 | + | 0.185057i | \(0.0592471\pi\) |
−0.331100 | + | 0.943596i | \(0.607420\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.648205 | − | 1.12272i | 0.0334732 | − | 0.0579772i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.669192 | 0.0344652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.07880 | 0.260880 | 0.130440 | − | 0.991456i | \(-0.458361\pi\) | ||||
0.130440 | + | 0.991456i | \(0.458361\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.643865 | + | 1.11521i | −0.0329862 | + | 0.0571338i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.07557 | − | 3.59500i | −0.106057 | − | 0.183696i | 0.808113 | − | 0.589028i | \(-0.200489\pi\) |
−0.914169 | + | 0.405332i | \(0.867156\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.62784 | − | 3.16535i | 0.133927 | − | 0.161321i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.75050 | + | 13.4243i | 0.393980 | + | 0.682394i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.91951 | − | 6.78879i | 0.198727 | − | 0.344205i | −0.749389 | − | 0.662130i | \(-0.769653\pi\) |
0.948116 | + | 0.317925i | \(0.102986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.92087 | −0.147715 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.67070 | 0.286049 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.853177 | − | 1.47775i | 0.0429280 | − | 0.0743534i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.53879 | − | 2.66526i | −0.0772295 | − | 0.133765i | 0.824824 | − | 0.565389i | \(-0.191274\pi\) |
−0.902054 | + | 0.431624i | \(0.857941\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.737809 | + | 0.888723i | −0.0369367 | + | 0.0444918i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.7483 | + | 32.4730i | 0.936246 | + | 1.62163i | 0.772396 | + | 0.635141i | \(0.219058\pi\) |
0.163850 | + | 0.986485i | \(0.447609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.22918 | − | 2.12900i | 0.0612296 | − | 0.106053i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.19364 | −0.109003 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.7615 | −1.07868 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3776 | − | 30.0988i | 0.859265 | − | 1.48829i | −0.0133656 | − | 0.999911i | \(-0.504255\pi\) |
0.872631 | − | 0.488380i | \(-0.162412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.97579 | + | 5.15422i | 0.146785 | + | 0.254239i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.7636 | − | 31.7997i | −0.578850 | − | 1.56476i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.219225 | + | 0.379708i | 0.0107613 | + | 0.0186391i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.51198 | − | 7.81498i | 0.220953 | − | 0.382701i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.5451 | 1.05255 | 0.526274 | − | 0.850315i | \(-0.323589\pi\) | ||||
0.526274 | + | 0.850315i | \(0.323589\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.66307 | 0.129790 | 0.0648951 | − | 0.997892i | \(-0.479329\pi\) | ||||
0.0648951 | + | 0.997892i | \(0.479329\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.9975 | + | 20.7803i | −0.583338 | + | 1.01037i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.80935 | + | 8.33004i | 0.233288 | + | 0.404066i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.4802 | + | 2.64583i | 0.749138 | + | 0.128041i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.42928 | + | 2.47558i | 0.0690061 | + | 0.119522i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.3588 | − | 21.4060i | 0.595302 | − | 1.03109i | −0.398202 | − | 0.917298i | \(-0.630366\pi\) |
0.993504 | − | 0.113795i | \(-0.0363008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.26963 | −0.349356 | −0.174678 | − | 0.984626i | \(-0.555888\pi\) | ||||
−0.174678 | + | 0.984626i | \(0.555888\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0693809 | −0.00332656 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.745532 | − | 1.29130i | 0.0356636 | − | 0.0617712i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5101 | + | 30.3283i | 0.835710 | + | 1.44749i | 0.893451 | + | 0.449160i | \(0.148277\pi\) |
−0.0577412 | + | 0.998332i | \(0.518390\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.9313 | − | 12.7985i | 0.711014 | − | 0.609450i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.05984 | + | 5.29981i | 0.145378 | + | 0.251801i | 0.929514 | − | 0.368787i | \(-0.120227\pi\) |
−0.784136 | + | 0.620589i | \(0.786894\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.576881 | + | 0.999188i | −0.0273468 | + | 0.0473660i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.91382 | 0.137819 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.7695 | 1.64087 | 0.820436 | − | 0.571738i | \(-0.193731\pi\) | ||||
0.820436 | + | 0.571738i | \(0.193731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.18938 | + | 8.98827i | −0.244358 | + | 0.423241i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.41942 | + | 5.92261i | 0.160658 | + | 0.278268i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.985976 | − | 0.168521i | −0.0462233 | − | 0.00790037i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2863 | + | 19.5485i | 0.527953 | + | 0.914442i | 0.999469 | + | 0.0325841i | \(0.0103737\pi\) |
−0.471516 | + | 0.881858i | \(0.656293\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.48415 | + | 4.30267i | −0.115950 | + | 0.200831i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.1756 | 1.17254 | 0.586272 | − | 0.810115i | \(-0.300595\pi\) | ||||
0.586272 | + | 0.810115i | \(0.300595\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.74829 | −0.360093 | −0.180047 | − | 0.983658i | \(-0.557625\pi\) | ||||
−0.180047 | + | 0.983658i | \(0.557625\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.127439 | + | 0.220731i | −0.00590985 | + | 0.0102362i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.5390 | − | 26.9144i | −0.719060 | − | 1.24545i | −0.961372 | − | 0.275251i | \(-0.911239\pi\) |
0.242312 | − | 0.970198i | \(-0.422094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.05577 | + | 13.6669i | 0.233454 | + | 0.631078i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.30083 | + | 2.25310i | 0.0599390 | + | 0.103817i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.3163 | − | 24.7966i | 0.658266 | − | 1.14015i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.91022 | −0.225296 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.0264 | 1.51217 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6603 | − | 23.6603i | 0.624154 | − | 1.08107i | −0.364550 | − | 0.931184i | \(-0.618777\pi\) |
0.988704 | − | 0.149882i | \(-0.0478895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.64554 | + | 4.58220i | 0.120626 | + | 0.208930i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.10012 | − | 1.32514i | 0.0500572 | − | 0.0602961i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.45295 | − | 2.51659i | −0.0659752 | − | 0.114272i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5451 | + | 21.7288i | −0.568475 | + | 0.984627i | 0.428242 | + | 0.903664i | \(0.359133\pi\) |
−0.996717 | + | 0.0809632i | \(0.974200\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.62381 | −0.344761 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4362 | 1.32844 | 0.664219 | − | 0.747538i | \(-0.268764\pi\) | ||||
0.664219 | + | 0.747538i | \(0.268764\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.519477 | − | 0.899760i | 0.0233961 | − | 0.0405232i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.18423 | + | 3.78320i | 0.0981739 | + | 0.170042i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.85345 | − | 4.64164i | 0.172851 | − | 0.208206i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1239 | − | 36.5877i | −0.945637 | − | 1.63789i | −0.754471 | − | 0.656333i | \(-0.772107\pi\) |
−0.191166 | − | 0.981558i | \(-0.561227\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.376812 | − | 0.652657i | 0.0168347 | − | 0.0291586i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.25390 | −0.412611 | −0.206305 | − | 0.978488i | \(-0.566144\pi\) | ||||
−0.206305 | + | 0.978488i | \(0.566144\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.90830 | −0.218416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.49023 | + | 4.31321i | −0.110595 | + | 0.191556i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.9025 | + | 20.6157i | 0.527568 | + | 0.913774i | 0.999484 | + | 0.0321303i | \(0.0102292\pi\) |
−0.471916 | + | 0.881643i | \(0.656438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.30735 | − | 11.6437i | −0.190546 | − | 0.515089i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.26812 | − | 2.19645i | −0.0559890 | − | 0.0969758i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.730793 | − | 1.26577i | 0.0322026 | − | 0.0557766i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.3223 | 1.94929 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.383813 | 0.0168475 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.0422 | + | 27.7860i | −0.702823 | + | 1.21733i | 0.264648 | + | 0.964345i | \(0.414744\pi\) |
−0.967471 | + | 0.252981i | \(0.918589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.77620 | − | 15.2008i | −0.383756 | − | 0.664685i | 0.607839 | − | 0.794060i | \(-0.292036\pi\) |
−0.991596 | + | 0.129374i | \(0.958703\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.59058 | − | 0.955529i | −0.243993 | − | 0.0417027i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.90836 | − | 3.30537i | −0.0831293 | − | 0.143984i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.3884 | − | 17.9932i | 0.451668 | − | 0.782312i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.0030 | 1.56240 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.52348 | 0.109304 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.10201 | − | 1.90873i | 0.0476439 | − | 0.0825216i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.60262 | + | 2.77582i | 0.0691581 | + | 0.119785i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.2636 | − | 12.0649i | −1.47584 | − | 0.519674i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.6885 | − | 28.9053i | −0.717495 | − | 1.24274i | −0.961989 | − | 0.273087i | \(-0.911955\pi\) |
0.244495 | − | 0.969651i | \(-0.421378\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.98384 | + | 6.90021i | −0.170963 | + | 0.296116i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.31503 | −0.0563297 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.4470 | 1.68663 | 0.843316 | − | 0.537418i | \(-0.180600\pi\) | ||||
0.843316 | + | 0.537418i | \(0.180600\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.33803 | + | 14.4419i | −0.355858 | + | 0.616365i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.265186 | + | 0.459316i | 0.0112973 | + | 0.0195675i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.8514 | − | 2.53836i | −0.631544 | − | 0.107942i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.274285 | − | 0.475076i | −0.0116428 | − | 0.0201659i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.7422 | − | 30.7304i | 0.751760 | − | 1.30209i | −0.195209 | − | 0.980762i | \(-0.562538\pi\) |
0.946969 | − | 0.321325i | \(-0.104128\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.96172 | −0.294449 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.43804 | 0.187374 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.3555 | − | 38.7208i | 0.942170 | − | 1.63189i | 0.180850 | − | 0.983511i | \(-0.442115\pi\) |
0.761320 | − | 0.648376i | \(-0.224551\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.989292 | + | 1.71350i | 0.0416198 | + | 0.0720876i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.72020 | + | 18.1662i | 0.282222 | + | 0.762910i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.51888 | + | 7.82692i | 0.189441 | + | 0.328122i | 0.945064 | − | 0.326885i | \(-0.105999\pi\) |
−0.755623 | + | 0.655007i | \(0.772666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.48214 | + | 14.6915i | −0.354966 | + | 0.614820i | −0.987112 | − | 0.160030i | \(-0.948841\pi\) |
0.632146 | + | 0.774849i | \(0.282174\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.21847 | 0.134454 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.32144 | 0.305325 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.83382 | − | 15.3006i | 0.367757 | − | 0.636973i | −0.621458 | − | 0.783448i | \(-0.713459\pi\) |
0.989214 | + | 0.146474i | \(0.0467926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.319324 | + | 0.553086i | 0.0132707 | + | 0.0229855i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.47289 | − | 2.97870i | 0.102593 | − | 0.123577i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.5023 | − | 52.8316i | −1.26328 | − | 2.18806i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.531072 | − | 0.919844i | 0.0219571 | − | 0.0380309i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.6759 | −0.647014 | −0.323507 | − | 0.946226i | \(-0.604862\pi\) | ||||
−0.323507 | + | 0.946226i | \(0.604862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.94838 | 0.0802816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.526577 | − | 0.912059i | 0.0216605 | − | 0.0375171i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.29460 | + | 14.3667i | 0.340619 | + | 0.589969i | 0.984548 | − | 0.175116i | \(-0.0560302\pi\) |
−0.643929 | + | 0.765085i | \(0.722697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.991971 | + | 1.19487i | −0.0406669 | + | 0.0489850i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.48325 | + | 6.03317i | 0.142560 | + | 0.246921i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.3146 | + | 42.1142i | −0.993469 | + | 1.72074i | −0.397916 | + | 0.917422i | \(0.630267\pi\) |
−0.595552 | + | 0.803317i | \(0.703067\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.2984 | −0.950362 | −0.475181 | − | 0.879888i | \(-0.657617\pi\) | ||||
−0.475181 | + | 0.879888i | \(0.657617\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.4734 | −0.630125 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.38658 | − | 4.13368i | 0.0970283 | − | 0.168058i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.5411 | − | 25.1860i | −0.590206 | − | 1.02227i | −0.994204 | − | 0.107507i | \(-0.965713\pi\) |
0.403998 | − | 0.914760i | \(-0.367620\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.212548 | + | 0.574564i | 0.00861287 | + | 0.0232825i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.38824 | − | 9.33271i | −0.217985 | − | 0.377561i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.52670 | − | 9.57253i | 0.223221 | − | 0.386631i | −0.732563 | − | 0.680699i | \(-0.761676\pi\) |
0.955784 | + | 0.294068i | \(0.0950094\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.261631 | −0.0105500 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.7605 | −1.52018 | −0.760090 | − | 0.649817i | \(-0.774845\pi\) | ||||
−0.760090 | + | 0.649817i | \(0.774845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.314476 | + | 0.544689i | −0.0126399 | + | 0.0218929i | −0.872276 | − | 0.489014i | \(-0.837357\pi\) |
0.859636 | + | 0.510907i | \(0.170690\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.89085 | + | 3.27505i | 0.0758773 | + | 0.131423i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.0418 | + | 1.71633i | 0.402318 | + | 0.0687632i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.8307 | − | 20.4913i | −0.473226 | − | 0.819652i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.13278 | + | 1.96203i | −0.0452389 | + | 0.0783560i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.21464 | 0.327539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1786 | 0.683870 | 0.341935 | − | 0.939724i | \(-0.388918\pi\) | ||||
0.341935 | + | 0.939724i | \(0.388918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.89963 | − | 5.02231i | 0.115250 | − | 0.199619i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.441911 | − | 0.765412i | −0.0175367 | − | 0.0303744i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.62496 | + | 8.68143i | 0.0643831 | + | 0.343971i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.20294 | + | 5.54766i | 0.126706 | + | 0.219462i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.06894 | + | 7.04762i | −0.160714 | + | 0.278364i | −0.935125 | − | 0.354318i | \(-0.884713\pi\) |
0.774411 | + | 0.632683i | \(0.218046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.21363 | 0.363350 | 0.181675 | − | 0.983359i | \(-0.441848\pi\) | ||||
0.181675 | + | 0.983359i | \(0.441848\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.721781 | 0.0284201 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.65112 | − | 16.7162i | 0.379425 | − | 0.657183i | −0.611554 | − | 0.791203i | \(-0.709455\pi\) |
0.990979 | + | 0.134020i | \(0.0427885\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.2515 | − | 57.5932i | −1.30523 | − | 2.26073i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.21835 | + | 0.379155i | 0.0869440 | + | 0.0148603i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.37203 | − | 4.10848i | −0.0928248 | − | 0.160777i | 0.815874 | − | 0.578230i | \(-0.196256\pi\) |
−0.908699 | + | 0.417453i | \(0.862923\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.94601 | + | 3.37060i | −0.0760371 | + | 0.131700i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.1828 | 0.514311 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.2932 | 0.595738 | 0.297869 | − | 0.954607i | \(-0.403724\pi\) | ||||
0.297869 | + | 0.954607i | \(0.403724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.95467 | + | 3.38560i | −0.0760280 | + | 0.131684i | −0.901533 | − | 0.432711i | \(-0.857557\pi\) |
0.825505 | + | 0.564395i | \(0.190891\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.539531 | − | 0.934495i | −0.0209536 | − | 0.0362928i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.275052 | − | 0.743528i | −0.0106661 | − | 0.0288328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.395409 | − | 0.684869i | −0.0153103 | − | 0.0265182i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.14703 | + | 10.6470i | −0.237658 | + | 0.411636i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.8031 | 1.18914 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.12569 | −0.0433923 | −0.0216962 | − | 0.999765i | \(-0.506907\pi\) | ||||
−0.0216962 | + | 0.999765i | \(0.506907\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.22676 | − | 10.7851i | 0.239668 | − | 0.415117i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.5143 | + | 35.5319i | 0.788430 | + | 1.36560i | 0.926929 | + | 0.375238i | \(0.122439\pi\) |
−0.138499 | + | 0.990363i | \(0.544228\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.3895 | + | 19.7419i | −0.628972 | + | 0.757624i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.94612 | + | 6.83489i | 0.151216 | + | 0.261913i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.86946 | − | 4.97006i | 0.109797 | − | 0.190174i | −0.805891 | − | 0.592064i | \(-0.798313\pi\) |
0.915688 | + | 0.401890i | \(0.131647\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.08481 | −0.156073 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.15205 | −0.120258 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.41631 | + | 12.8454i | −0.282539 | + | 0.489372i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.18435 | − | 3.78341i | −0.0830968 | − | 0.143928i | 0.821482 | − | 0.570235i | \(-0.193148\pi\) |
−0.904579 | + | 0.426307i | \(0.859814\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.6385 | − | 29.6781i | 0.935938 | − | 1.12738i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.09675 | + | 5.36373i | 0.117466 | + | 0.203458i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.95892 | − | 3.39294i | 0.0741992 | − | 0.128517i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.08337 | 0.0788004 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.2974 | 1.37093 | 0.685466 | − | 0.728105i | \(-0.259598\pi\) | ||||
0.685466 | + | 0.728105i | \(0.259598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.09673 | + | 3.63165i | −0.0790798 | + | 0.136970i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.558645 | + | 0.967601i | 0.0210398 | + | 0.0364420i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.0365 | + | 40.6471i | 0.565507 | + | 1.52869i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.94144 | − | 8.55882i | −0.185580 | − | 0.321433i | 0.758192 | − | 0.652031i | \(-0.226083\pi\) |
−0.943772 | + | 0.330598i | \(0.892750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.99933 | − | 13.8552i | 0.299998 | − | 0.519612i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.90516 | −0.108799 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.96194 | −0.0733723 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.791518 | − | 1.37095i | 0.0295598 | − | 0.0511990i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.9771 | + | 24.2090i | 0.521257 | + | 0.902844i | 0.999694 | + | 0.0247225i | \(0.00787022\pi\) |
−0.478437 | + | 0.878122i | \(0.658796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7210 | − | 2.17424i | −0.473755 | − | 0.0809731i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.78398 | + | 6.55405i | 0.140728 | + | 0.243748i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.30212 | + | 2.25534i | −0.0483595 | + | 0.0837612i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.8007 | 1.21651 | 0.608255 | − | 0.793742i | \(-0.291870\pi\) | ||||
0.608255 | + | 0.793742i | \(0.291870\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.2457 | −0.638728 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.40420 | + | 9.36036i | −0.199882 | + | 0.346205i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0931 | − | 20.9458i | −0.446668 | − | 0.773651i | 0.551499 | − | 0.834175i | \(-0.314056\pi\) |
−0.998167 | + | 0.0605246i | \(0.980723\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.168473 | − | 0.900078i | −0.00621422 | − | 0.0331999i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.2908 | + | 24.7524i | 0.526409 | + | 0.911768i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.2300 | + | 22.9150i | −0.486673 | + | 0.842943i | −0.999883 | − | 0.0153208i | \(-0.995123\pi\) |
0.513210 | + | 0.858263i | \(0.328456\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.550846 | 0.0202358 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.3257 | 1.22260 | 0.611301 | − | 0.791398i | \(-0.290646\pi\) | ||||
0.611301 | + | 0.791398i | \(0.290646\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.999937 | + | 1.73194i | −0.0366348 | + | 0.0634534i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.05543 | + | 3.56012i | 0.0752044 | + | 0.130258i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.1827 | − | 3.27867i | −0.700922 | − | 0.119800i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.32153 | + | 4.02100i | 0.0847138 | + | 0.146729i | 0.905269 | − | 0.424838i | \(-0.139669\pi\) |
−0.820555 | + | 0.571567i | \(0.806336\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.12019 | − | 3.67228i | 0.0772640 | − | 0.133825i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.69377 | −0.170824 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.0481 | 1.63730 | 0.818651 | − | 0.574291i | \(-0.194722\pi\) | ||||
0.818651 | + | 0.574291i | \(0.194722\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.68905 | − | 2.92551i | 0.0613085 | − | 0.106189i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.50637 | − | 13.0014i | −0.272106 | − | 0.471301i | 0.697295 | − | 0.716784i | \(-0.254387\pi\) |
−0.969401 | + | 0.245483i | \(0.921053\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.02858 | + | 10.8902i | 0.145844 | + | 0.394250i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.824515 | − | 1.42810i | −0.0298104 | − | 0.0516332i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.08473 | + | 14.0032i | −0.291923 | + | 0.505625i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.05311 | 0.146159 | 0.0730794 | − | 0.997326i | \(-0.476717\pi\) | ||||
0.0730794 | + | 0.997326i | \(0.476717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.13591 | 0.112937 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.19701 | + | 10.7335i | −0.222891 | + | 0.386058i | −0.955685 | − | 0.294392i | \(-0.904883\pi\) |
0.732794 | + | 0.680451i | \(0.238216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.78348 | + | 8.28524i | 0.171828 | + | 0.297614i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.09398 | + | 3.72683i | −0.110996 | + | 0.133699i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00000 | + | 1.73205i | 0.0358287 | + | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.91631 | − | 10.2474i | 0.211702 | − | 0.366679i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.34515 | −0.0480719 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.78562 | −0.0637316 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.7116 | − | 18.5530i | 0.381826 | − | 0.661343i | −0.609497 | − | 0.792788i | \(-0.708629\pi\) |
0.991323 | + | 0.131446i | \(0.0419619\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.598215 | + | 1.03614i | 0.0212970 | + | 0.0368875i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1594 | − | 13.4419i | 0.396781 | − | 0.477940i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.74473 | − | 6.48605i | −0.132979 | − | 0.230327i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.768912 | − | 1.33180i | 0.0272705 | − | 0.0472339i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.1622 | −1.31635 | −0.658175 | − | 0.752865i | \(-0.728672\pi\) | ||||
−0.658175 | + | 0.752865i | \(0.728672\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.7310 | −0.591901 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.40880 | + | 9.36832i | −0.191111 | + | 0.331013i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.1753 | − | 21.0883i | −0.429658 | − | 0.744189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.410120 | + | 1.10865i | 0.0144548 | + | 0.0390747i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.45482 | + | 7.71597i | 0.156817 | + | 0.271615i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.04208 | + | 1.80494i | −0.0366376 | + | 0.0634582i | −0.883763 | − | 0.467935i | \(-0.844998\pi\) |
0.847125 | + | 0.531393i | \(0.178331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.2776 | −0.396009 | −0.198005 | − | 0.980201i | \(-0.563446\pi\) | ||||
−0.198005 | + | 0.980201i | \(0.563446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.42162 | 0.225216 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.61626 | − | 4.53150i | 0.0916437 | − | 0.158731i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.75877 | − | 4.77834i | −0.0965173 | − | 0.167173i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.24444 | − | 1.58004i | −0.323027 | − | 0.0552110i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2873 | + | 36.8707i | 0.742931 | + | 1.28679i | 0.951155 | + | 0.308714i | \(0.0998985\pi\) |
−0.208224 | + | 0.978081i | \(0.566768\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.8342 | + | 18.7654i | −0.377657 | + | 0.654121i | −0.990721 | − | 0.135913i | \(-0.956603\pi\) |
0.613064 | + | 0.790033i | \(0.289937\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.1244 | −0.387302 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.7162 | −1.10288 | −0.551440 | − | 0.834215i | \(-0.685921\pi\) | ||||
−0.551440 | + | 0.834215i | \(0.685921\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.14498 | + | 15.8396i | −0.317618 | + | 0.550131i | −0.979991 | − | 0.199044i | \(-0.936216\pi\) |
0.662372 | + | 0.749175i | \(0.269550\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.38799 | + | 7.60022i | 0.152218 | + | 0.263649i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.9340 | + | 4.55434i | 0.448136 | + | 0.157798i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.258621 | + | 0.447945i | 0.00894995 | + | 0.0155018i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.47079 | + | 4.27953i | −0.0854028 | + | 0.147922i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.8422 | −1.03027 | −0.515134 | − | 0.857109i | \(-0.672258\pi\) | ||||
−0.515134 | + | 0.857109i | \(0.672258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7187 | −0.990300 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.29741 | − | 5.71129i | 0.113569 | − | 0.196707i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.70915 | − | 2.96033i | −0.0587964 | − | 0.101838i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −41.5435 | − | 7.10052i | −1.42745 | − | 0.243977i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.10326 | − | 1.91089i | −0.0378636 | − | 0.0655817i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.12636 | − | 5.41502i | 0.107170 | − | 0.185624i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.2641 | −0.591111 | −0.295555 | − | 0.955326i | \(-0.595505\pi\) | ||||
−0.295555 | + | 0.955326i | \(0.595505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.841808 | 0.0287892 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.35965 | − | 9.28319i | 0.183082 | − | 0.317108i | −0.759846 | − | 0.650103i | \(-0.774726\pi\) |
0.942929 | + | 0.332995i | \(0.108059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0515 | + | 26.0700i | 0.513551 | + | 0.889496i | 0.999876 | + | 0.0157186i | \(0.00500360\pi\) |
−0.486326 | + | 0.873778i | \(0.661663\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.801504 | + | 2.16665i | 0.0273152 | + | 0.0738391i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.7628 | − | 32.4981i | −0.638693 | − | 1.10625i | −0.985720 | − | 0.168393i | \(-0.946142\pi\) |
0.347027 | − | 0.937855i | \(-0.387191\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.131713 | + | 0.228134i | −0.00447838 | + | 0.00775678i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.74650 | 0.195161 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.5519 | −1.00248 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.47466 | − | 6.01829i | 0.117734 | − | 0.203922i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.6228 | − | 23.5954i | −0.461061 | − | 0.798582i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.01842 | − | 6.04490i | 0.169653 | − | 0.204355i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.0926 | − | 29.6052i | −0.577175 | − | 0.999696i | −0.995802 | − | 0.0915375i | \(-0.970822\pi\) |
0.418627 | − | 0.908158i | \(-0.362511\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.95490 | + | 5.11804i | −0.0996664 | + | 0.172627i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.6527 | −1.67284 | −0.836420 | − | 0.548089i | \(-0.815356\pi\) | ||||
−0.836420 | + | 0.548089i | \(0.815356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.4134 | −0.653314 | −0.326657 | − | 0.945143i | \(-0.605922\pi\) | ||||
−0.326657 | + | 0.945143i | \(0.605922\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.838213 | − | 1.45183i | 0.0281762 | − | 0.0488026i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.1285 | − | 34.8636i | −0.675849 | − | 1.17060i | −0.976220 | − | 0.216782i | \(-0.930444\pi\) |
0.300371 | − | 0.953822i | \(-0.402889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.98482 | + | 6.00442i | −0.167185 | + | 0.201382i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.9956 | + | 32.9013i | 0.636376 | + | 1.10223i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.27048 | − | 7.39669i | 0.142906 | − | 0.247521i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.19988 | −0.0735340 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.821347 | −0.0274240 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.516683 | − | 0.894921i | 0.0172323 | − | 0.0298473i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.5142 | + | 19.9431i | 0.383593 | + | 0.664403i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.21117 | − | 5.97729i | −0.0735831 | − | 0.198912i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.73427 | − | 4.73589i | −0.0908902 | − | 0.157426i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.3124 | + | 28.2539i | −0.541645 | + | 0.938156i | 0.457165 | + | 0.889382i | \(0.348865\pi\) |
−0.998810 | + | 0.0487743i | \(0.984468\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −46.0199 | −1.52638 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.6499 | 0.717292 | 0.358646 | − | 0.933474i | \(-0.383238\pi\) | ||||
0.358646 | + | 0.933474i | \(0.383238\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.79669 | − | 6.57606i | 0.125652 | − | 0.217636i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.388248 | + | 0.672465i | 0.0128351 | + | 0.0222310i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.8745 | + | 5.78975i | 1.11864 | + | 0.191194i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.82521 | − | 13.5537i | −0.258130 | − | 0.447094i | 0.707611 | − | 0.706602i | \(-0.249773\pi\) |
−0.965741 | + | 0.259508i | \(0.916440\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.186227 | − | 0.322554i | 0.00613638 | − | 0.0106285i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.87697 | −0.0946967 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.5908 | −0.677022 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.85187 | − | 11.8678i | 0.225045 | − | 0.389789i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.7667 | + | 32.5049i | 0.615717 | + | 1.06645i | 0.990258 | + | 0.139243i | \(0.0444668\pi\) |
−0.374542 | + | 0.927210i | \(0.622200\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.31476 | + | 4.55558i | −0.174184 | + | 0.149303i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.79668 | + | 6.57604i | 0.124298 | + | 0.215290i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.52300 | + | 2.63792i | −0.0498075 | + | 0.0862691i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.1876 | 1.54155 | 0.770776 | − | 0.637106i | \(-0.219869\pi\) | ||||
0.770776 | + | 0.637106i | \(0.219869\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.5021 | −0.342724 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.6250 | + | 47.8479i | −0.900550 | + | 1.55980i | −0.0737682 | + | 0.997275i | \(0.523502\pi\) |
−0.826782 | + | 0.562523i | \(0.809831\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.49106 | − | 2.58260i | −0.0485557 | − | 0.0841009i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.98192 | + | 0.338746i | 0.0644720 | + | 0.0110194i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.0575 | + | 38.2047i | 0.716772 | + | 1.24149i | 0.962272 | + | 0.272089i | \(0.0877145\pi\) |
−0.245500 | + | 0.969397i | \(0.578952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.96030 | + | 5.12738i | −0.0960953 | + | 0.166442i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.25492 | −0.105548 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.9855 | −0.906540 | −0.453270 | − | 0.891373i | \(-0.649743\pi\) | ||||
−0.453270 | + | 0.891373i | \(0.649743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.10448 | + | 1.91302i | −0.0357402 | + | 0.0619039i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.600795 | + | 1.04061i | 0.0194209 | + | 0.0336381i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.5138 | + | 33.8275i | 0.404091 | + | 1.09235i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6019 | + | 23.5592i | 0.438771 | + | 0.759974i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.3323 | − | 17.8961i | 0.332955 | − | 0.576694i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.438330 | −0.0141103 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.3705 | −1.61981 | −0.809904 | − | 0.586563i | \(-0.800481\pi\) | ||||
−0.809904 | + | 0.586563i | \(0.800481\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.427608 | − | 0.740639i | 0.0137367 | − | 0.0237927i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.36711 | + | 9.29611i | 0.172239 | + | 0.298327i | 0.939202 | − | 0.343364i | \(-0.111567\pi\) |
−0.766963 | + | 0.641691i | \(0.778233\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.9318 | − | 42.0769i | 1.11986 | − | 1.34892i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.35239 | + | 2.34240i | 0.0433111 | + | 0.0750170i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.8592 | + | 39.5932i | −0.731329 | + | 1.26670i | 0.224986 | + | 0.974362i | \(0.427766\pi\) |
−0.956315 | + | 0.292337i | \(0.905567\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.9817 | 0.638618 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.3296 | −0.393655 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.2010 | − | 28.0609i | 0.516731 | − | 0.895005i | −0.483080 | − | 0.875576i | \(-0.660482\pi\) |
0.999811 | − | 0.0194288i | \(-0.00618476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.361411 | + | 0.625982i | 0.0115155 | + | 0.0199455i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.30160 | − | 7.59054i | 0.200582 | − | 0.241610i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.11351 | + | 7.12480i | 0.130802 | + | 0.226556i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.21739 | − | 14.2329i | 0.261034 | − | 0.452124i | −0.705483 | − | 0.708727i | \(-0.749270\pi\) |
0.966517 | + | 0.256603i | \(0.0826032\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.8116 | −0.470033 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.78139 | −0.151580 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.42064 | + | 9.38882i | −0.171673 | + | 0.297347i | −0.939005 | − | 0.343903i | \(-0.888251\pi\) |
0.767332 | + | 0.641250i | \(0.221584\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.31783 | − | 9.21075i | −0.168249 | − | 0.291415i |
(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 | 1064.2.q.n.305.5 | ✓ | 16 | |
7.2 | even | 3 | inner | 1064.2.q.n.457.5 | yes | 16 | |
7.3 | odd | 6 | 7448.2.a.br.1.5 | 8 | |||
7.4 | even | 3 | 7448.2.a.bq.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.q.n.305.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1064.2.q.n.457.5 | yes | 16 | 7.2 | even | 3 | inner | |
7448.2.a.bq.1.4 | 8 | 7.4 | even | 3 | |||
7448.2.a.br.1.5 | 8 | 7.3 | odd | 6 |