Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(133,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.i (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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 9x^{8} + 6x^{7} + 59x^{6} + 2x^{5} + 47x^{4} - 26x^{3} + 38x^{2} - 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(-1.09846 + 1.90260i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.529 |
Dual form | 572.2.i.c.133.1 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.09846 | + | 1.90260i | −0.634199 | + | 1.09846i | 0.352486 | + | 0.935817i | \(0.385337\pi\) |
−0.986684 | + | 0.162647i | \(0.947997\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.151238 | 0.0676356 | 0.0338178 | − | 0.999428i | \(-0.489233\pi\) | ||||
0.0338178 | + | 0.999428i | \(0.489233\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.15500 | + | 3.73256i | 0.814512 | + | 1.41078i | 0.909678 | + | 0.415315i | \(0.136329\pi\) |
−0.0951656 | + | 0.995461i | \(0.530338\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.913248 | − | 1.58179i | −0.304416 | − | 0.527264i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.20357 | − | 1.65442i | 0.888512 | − | 0.458854i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.166129 | + | 0.287744i | −0.0428944 | + | 0.0742953i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.474268 | − | 0.821456i | −0.115027 | − | 0.199232i | 0.802764 | − | 0.596297i | \(-0.203362\pi\) |
−0.917790 | + | 0.397065i | \(0.870029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.739165 | + | 1.28027i | 0.169576 | + | 0.293714i | 0.938271 | − | 0.345901i | \(-0.112427\pi\) |
−0.768695 | + | 0.639616i | \(0.779093\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.46875 | −2.06625 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.31854 | + | 4.01583i | −0.483450 | + | 0.837359i | −0.999819 | − | 0.0190065i | \(-0.993950\pi\) |
0.516370 | + | 0.856366i | \(0.327283\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97713 | −0.995425 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.57810 | −0.496156 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.41989 | + | 4.19138i | −0.449363 | + | 0.778320i | −0.998345 | − | 0.0575149i | \(-0.981682\pi\) |
0.548982 | + | 0.835834i | \(0.315016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.94473 | 0.888099 | 0.444050 | − | 0.896002i | \(-0.353541\pi\) | ||||
0.444050 | + | 0.896002i | \(0.353541\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.09846 | − | 1.90260i | −0.191218 | − | 0.331199i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.325917 | + | 0.564504i | 0.0550900 | + | 0.0954186i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.11018 | − | 7.11904i | 0.675709 | − | 1.17036i | −0.300552 | − | 0.953765i | \(-0.597171\pi\) |
0.976261 | − | 0.216597i | \(-0.0694957\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.371316 | + | 7.91243i | −0.0594581 | + | 1.26700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.72266 | + | 2.98374i | −0.269034 | + | 0.465981i | −0.968613 | − | 0.248575i | \(-0.920038\pi\) |
0.699578 | + | 0.714556i | \(0.253371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.42438 | − | 2.46710i | −0.217216 | − | 0.376229i | 0.736740 | − | 0.676176i | \(-0.236364\pi\) |
−0.953956 | + | 0.299947i | \(0.903031\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.138118 | − | 0.239227i | −0.0205894 | − | 0.0356618i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.49363 | −1.09306 | −0.546529 | − | 0.837440i | \(-0.684051\pi\) | ||||
−0.546529 | + | 0.837440i | \(0.684051\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.78802 | + | 10.0251i | −0.826860 | + | 1.43216i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.08386 | 0.291799 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.60468 | −0.495142 | −0.247571 | − | 0.968870i | \(-0.579632\pi\) | ||||
−0.247571 | + | 0.968870i | \(0.579632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0756188 | + | 0.130976i | −0.0101964 | + | 0.0176608i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.24779 | −0.430180 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0689734 | + | 0.119465i | 0.00897958 | + | 0.0155531i | 0.870480 | − | 0.492203i | \(-0.163808\pi\) |
−0.861501 | + | 0.507756i | \(0.830475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.02285 | + | 5.23572i | 0.387036 | + | 0.670366i | 0.992049 | − | 0.125850i | \(-0.0401657\pi\) |
−0.605014 | + | 0.796215i | \(0.706832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.93609 | − | 6.81751i | 0.495901 | − | 0.858926i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.484501 | − | 0.250211i | 0.0600950 | − | 0.0310348i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.07371 | − | 5.32383i | 0.375514 | − | 0.650409i | −0.614890 | − | 0.788613i | \(-0.710800\pi\) |
0.990404 | + | 0.138204i | \(0.0441329\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.09367 | − | 8.82250i | −0.613206 | − | 1.06210i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.05292 | + | 10.4840i | 0.718349 | + | 1.24422i | 0.961654 | + | 0.274267i | \(0.0884352\pi\) |
−0.243305 | + | 0.969950i | \(0.578231\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.66197 | −0.896766 | −0.448383 | − | 0.893842i | \(-0.648000\pi\) | ||||
−0.448383 | + | 0.893842i | \(0.648000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.46720 | − | 9.46946i | 0.631298 | − | 1.09344i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.30999 | −0.491169 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1515 | 1.70468 | 0.852340 | − | 0.522988i | \(-0.175183\pi\) | ||||
0.852340 | + | 0.522988i | \(0.175183\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.57170 | − | 9.65047i | 0.619078 | − | 1.07227i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.08818 | 0.229208 | 0.114604 | − | 0.993411i | \(-0.463440\pi\) | ||||
0.114604 | + | 0.993411i | \(0.463440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0717272 | − | 0.124235i | −0.00777990 | − | 0.0134752i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.31633 | − | 9.20816i | −0.569971 | − | 0.987219i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.72324 | − | 13.3770i | 0.818662 | − | 1.41796i | −0.0880064 | − | 0.996120i | \(-0.528050\pi\) |
0.906668 | − | 0.421844i | \(-0.138617\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.0789 | + | 8.39227i | 1.37104 | + | 0.879749i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.43161 | + | 9.40782i | −0.563231 | + | 0.975545i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.111790 | + | 0.193625i | 0.0114694 | + | 0.0198655i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.202896 | + | 0.351426i | 0.0206009 | + | 0.0356819i | 0.876142 | − | 0.482053i | \(-0.160109\pi\) |
−0.855541 | + | 0.517735i | \(0.826775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.82650 | 0.183570 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.16295 | − | 5.47839i | 0.314725 | − | 0.545120i | −0.664654 | − | 0.747152i | \(-0.731421\pi\) |
0.979379 | + | 0.202031i | \(0.0647543\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.01133 | 0.296715 | 0.148357 | − | 0.988934i | \(-0.452601\pi\) | ||||
0.148357 | + | 0.988934i | \(0.452601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.43203 | −0.139752 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.37535 | − | 14.5065i | 0.809676 | − | 1.40240i | −0.103413 | − | 0.994639i | \(-0.532976\pi\) |
0.913089 | − | 0.407761i | \(-0.133690\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.98210 | 0.477198 | 0.238599 | − | 0.971118i | \(-0.423312\pi\) | ||||
0.238599 | + | 0.971118i | \(0.423312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.02977 | + | 15.6400i | 0.857068 | + | 1.48448i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.06694 | + | 12.2403i | 0.664801 | + | 1.15147i | 0.979339 | + | 0.202225i | \(0.0648172\pi\) |
−0.314538 | + | 0.949245i | \(0.601849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.350651 | + | 0.607345i | −0.0326984 | + | 0.0566353i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.54261 | − | 3.55649i | −0.512415 | − | 0.328798i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.04409 | − | 3.54047i | 0.187381 | − | 0.324554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.78456 | − | 6.55506i | −0.341243 | − | 0.591050i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.50892 | −0.134962 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.07241 | − | 7.05361i | 0.361368 | − | 0.625907i | −0.626819 | − | 0.779165i | \(-0.715643\pi\) |
0.988186 | + | 0.153258i | \(0.0489766\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.25853 | 0.551033 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.78100 | −0.155607 | −0.0778035 | − | 0.996969i | \(-0.524791\pi\) | ||||
−0.0778035 | + | 0.996969i | \(0.524791\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.18580 | + | 5.51796i | −0.276244 | + | 0.478468i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.389906 | −0.0335578 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.18765 | + | 15.9135i | 0.784954 | + | 1.35958i | 0.929027 | + | 0.370013i | \(0.120647\pi\) |
−0.144073 | + | 0.989567i | \(0.546020\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.69056 | + | 13.3204i | 0.652305 | + | 1.12983i | 0.982562 | + | 0.185934i | \(0.0595311\pi\) |
−0.330257 | + | 0.943891i | \(0.607136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.23149 | − | 14.2574i | 0.693216 | − | 1.20069i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.169016 | + | 3.60159i | −0.0141338 | + | 0.301180i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.365979 | + | 0.633894i | −0.0303929 | + | 0.0526421i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.7159 | − | 22.0245i | −1.04879 | − | 1.81655i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.30683 | − | 5.72760i | −0.270906 | − | 0.469223i | 0.698188 | − | 0.715914i | \(-0.253990\pi\) |
−0.969094 | + | 0.246691i | \(0.920657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.0578 | −1.55090 | −0.775451 | − | 0.631408i | \(-0.782477\pi\) | ||||
−0.775451 | + | 0.631408i | \(0.782477\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.866248 | + | 1.50039i | −0.0700320 | + | 0.121299i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.747829 | 0.0600671 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.0716 | 1.84132 | 0.920658 | − | 0.390369i | \(-0.127653\pi\) | ||||
0.920658 | + | 0.390369i | \(0.127653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.95962 | − | 6.85826i | 0.314018 | − | 0.543895i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.9858 | −1.57510 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.89069 | + | 3.27478i | 0.148091 | + | 0.256501i | 0.930522 | − | 0.366237i | \(-0.119354\pi\) |
−0.782431 | + | 0.622737i | \(0.786021\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.166129 | − | 0.287744i | −0.0129331 | − | 0.0224009i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.29783 | + | 16.1043i | −0.719488 | + | 1.24619i | 0.241716 | + | 0.970347i | \(0.422290\pi\) |
−0.961203 | + | 0.275842i | \(0.911043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.52578 | − | 10.6001i | 0.578906 | − | 0.815394i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.35008 | − | 2.33841i | 0.103243 | − | 0.178823i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.4086 | − | 21.4923i | −0.943408 | − | 1.63403i | −0.758907 | − | 0.651199i | \(-0.774266\pi\) |
−0.184502 | − | 0.982832i | \(-0.559067\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.7257 | − | 18.5774i | −0.810786 | − | 1.40432i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.303059 | −0.0227793 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.87956 | − | 10.1837i | 0.439459 | − | 0.761165i | −0.558189 | − | 0.829714i | \(-0.688503\pi\) |
0.997648 | + | 0.0685486i | \(0.0218368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.18359 | 0.236635 | 0.118317 | − | 0.992976i | \(-0.462250\pi\) | ||||
0.118317 | + | 0.992976i | \(0.462250\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.2820 | −0.981830 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.621614 | − | 1.07667i | 0.0457020 | − | 0.0791581i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.948535 | 0.0693638 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.55580 | − | 9.62293i | −0.404125 | − | 0.699965i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.11195 | − | 1.92595i | −0.0804578 | − | 0.139357i | 0.822989 | − | 0.568057i | \(-0.192305\pi\) |
−0.903447 | + | 0.428701i | \(0.858972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0387 | + | 20.8517i | −0.866568 | + | 1.50094i | −0.00108640 | + | 0.999999i | \(0.500346\pi\) |
−0.865482 | + | 0.500941i | \(0.832988\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0561570 | + | 1.19666i | −0.00402148 | + | 0.0856945i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.55281 | − | 16.5459i | 0.680609 | − | 1.17885i | −0.294186 | − | 0.955748i | \(-0.595048\pi\) |
0.974795 | − | 0.223102i | \(-0.0716182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.29135 | + | 12.6290i | 0.516870 | + | 0.895246i | 0.999808 | + | 0.0195910i | \(0.00623640\pi\) |
−0.482938 | + | 0.875655i | \(0.660430\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.75273 | + | 11.6961i | 0.476301 | + | 0.824978i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.8595 | −1.46405 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.260531 | + | 0.451253i | −0.0181963 | + | 0.0315169i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.46962 | 0.588679 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.47833 | −0.102258 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.95717 | − | 3.38991i | 0.134737 | − | 0.233371i | −0.790760 | − | 0.612126i | \(-0.790314\pi\) |
0.925497 | + | 0.378755i | \(0.123648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −26.5957 | −1.82230 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.215420 | − | 0.373119i | −0.0146915 | − | 0.0254465i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.6559 | + | 18.4565i | 0.723367 | + | 1.25291i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.41640 | − | 14.5776i | 0.568728 | − | 0.985065i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.87839 | − | 1.84696i | −0.193621 | − | 0.124240i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.10207 | + | 15.7653i | −0.609520 | + | 1.05572i | 0.381800 | + | 0.924245i | \(0.375304\pi\) |
−0.991320 | + | 0.131474i | \(0.958029\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.54535 | + | 7.87278i | 0.303024 | + | 0.524852i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.10451 | − | 3.64513i | −0.139682 | − | 0.241935i | 0.787695 | − | 0.616066i | \(-0.211275\pi\) |
−0.927376 | + | 0.374131i | \(0.877941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.04540 | −0.201246 | −0.100623 | − | 0.994925i | \(-0.532084\pi\) | ||||
−0.100623 | + | 0.994925i | \(0.532084\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.73437 | − | 8.20018i | 0.311499 | − | 0.539532i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.72464 | 0.112985 | 0.0564924 | − | 0.998403i | \(-0.482008\pi\) | ||||
0.0564924 | + | 0.998403i | \(0.482008\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.13332 | −0.0739296 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.6434 | + | 28.8272i | −1.08111 | + | 1.87253i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.8666 | −1.47912 | −0.739558 | − | 0.673093i | \(-0.764965\pi\) | ||||
−0.739558 | + | 0.673093i | \(0.764965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.75722 | + | 15.1679i | 0.564102 | + | 0.977054i | 0.997133 | + | 0.0756742i | \(0.0241109\pi\) |
−0.433030 | + | 0.901379i | \(0.642556\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.37347 | + | 14.5033i | 0.537159 | + | 0.930386i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.875367 | + | 1.51618i | −0.0559251 | + | 0.0968652i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.48608 | + | 2.87855i | 0.285442 | + | 0.183158i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.29379 | + | 3.97297i | −0.145363 | + | 0.251776i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4402 | + | 18.0830i | 0.658982 | + | 1.14139i | 0.980880 | + | 0.194616i | \(0.0623460\pi\) |
−0.321897 | + | 0.946775i | \(0.604321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.31854 | − | 4.01583i | −0.145766 | − | 0.252473i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.315159 | 0.0197360 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.635231 | − | 1.10025i | 0.0396246 | − | 0.0686318i | −0.845533 | − | 0.533923i | \(-0.820717\pi\) |
0.885158 | + | 0.465291i | \(0.154050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.4297 | 2.20149 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.83986 | 0.547173 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.44174 | − | 5.96127i | 0.212227 | − | 0.367588i | −0.740184 | − | 0.672404i | \(-0.765262\pi\) |
0.952411 | + | 0.304816i | \(0.0985951\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.545164 | −0.0334892 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9674 | + | 29.3884i | 1.03839 | + | 1.79854i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3236 | + | 23.0772i | 0.812355 | + | 1.40704i | 0.911212 | + | 0.411938i | \(0.135148\pi\) |
−0.0988569 | + | 0.995102i | \(0.531519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.33432 | − | 14.4355i | 0.506274 | − | 0.876892i | −0.493700 | − | 0.869632i | \(-0.664356\pi\) |
0.999974 | − | 0.00725952i | \(-0.00231080\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −30.3338 | + | 15.6653i | −1.83589 | + | 0.948107i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.48856 | − | 4.31032i | 0.150066 | − | 0.259922i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0117 | − | 17.3408i | −0.601546 | − | 1.04191i | −0.992587 | − | 0.121534i | \(-0.961219\pi\) |
0.391042 | − | 0.920373i | \(-0.372115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.51576 | − | 7.82153i | −0.270352 | − | 0.468263i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0649 | 0.600423 | 0.300211 | − | 0.953873i | \(-0.402943\pi\) | ||||
0.300211 | + | 0.953873i | \(0.402943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.913093 | − | 1.58152i | 0.0542778 | − | 0.0940118i | −0.837610 | − | 0.546269i | \(-0.816048\pi\) |
0.891888 | + | 0.452257i | \(0.149381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.491188 | −0.0290954 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.8493 | −0.876527 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.05014 | − | 13.9433i | 0.473538 | − | 0.820191i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.891495 | −0.0522604 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.1415 | − | 27.9579i | −0.942998 | − | 1.63332i | −0.759710 | − | 0.650262i | \(-0.774659\pi\) |
−0.183288 | − | 0.983059i | \(-0.558674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0104314 | + | 0.0180677i | 0.000607339 | + | 0.00105194i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.28905 | − | 2.23270i | 0.0747984 | − | 0.129555i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.783741 | + | 16.7009i | −0.0453249 | + | 0.965836i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.13907 | − | 10.6332i | 0.353850 | − | 0.612887i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.94878 | + | 12.0356i | 0.399197 | + | 0.691429i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.457168 | + | 0.791839i | 0.0261774 | + | 0.0453405i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.46700 | −0.483237 | −0.241619 | − | 0.970371i | \(-0.577678\pi\) | ||||
−0.241619 | + | 0.970371i | \(0.577678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.30783 | + | 5.72934i | −0.188176 | + | 0.325931i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.6715 | −1.68252 | −0.841258 | − | 0.540634i | \(-0.818184\pi\) | ||||
−0.841258 | + | 0.540634i | \(0.818184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.85388 | 0.330881 | 0.165441 | − | 0.986220i | \(-0.447095\pi\) | ||||
0.165441 | + | 0.986220i | \(0.447095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.595286 | − | 1.03107i | 0.0335406 | − | 0.0580939i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0582 | 0.789586 | 0.394793 | − | 0.918770i | \(-0.370816\pi\) | ||||
0.394793 | + | 0.918770i | \(0.370816\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.41989 | − | 4.19138i | −0.135488 | − | 0.234672i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.4001 | + | 31.8698i | 1.02699 | + | 1.77880i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.701124 | − | 1.21438i | 0.0390116 | − | 0.0675701i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.9446 | + | 8.23427i | −0.884447 | + | 0.456755i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.47266 | + | 9.47892i | −0.302639 | + | 0.524185i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.1487 | − | 27.9705i | −0.890309 | − | 1.54206i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.05583 | − | 5.29285i | −0.167963 | − | 0.290921i | 0.769740 | − | 0.638357i | \(-0.220386\pi\) |
−0.937704 | + | 0.347436i | \(0.887052\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.0145 | −0.822787 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.464861 | − | 0.805164i | 0.0253981 | − | 0.0439908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0759 | 0.984657 | 0.492329 | − | 0.870409i | \(-0.336146\pi\) | ||||
0.492329 | + | 0.870409i | \(0.336146\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.0511 | −1.68646 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.47236 | + | 4.28226i | −0.133886 | + | 0.231897i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7227 | −1.06493 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.770355 | − | 1.33429i | −0.0414745 | − | 0.0718360i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.49574 | + | 2.59070i | 0.0802958 | + | 0.139076i | 0.903377 | − | 0.428847i | \(-0.141080\pi\) |
−0.823081 | + | 0.567924i | \(0.807747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.20041 | − | 5.54327i | 0.171314 | − | 0.296725i | −0.767565 | − | 0.640971i | \(-0.778532\pi\) |
0.938880 | + | 0.344246i | \(0.111865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.25915 | + | 4.26527i | −0.440841 | + | 0.227663i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.98104 | + | 13.8236i | −0.424788 | + | 0.735754i | −0.996401 | − | 0.0847693i | \(-0.972985\pi\) |
0.571613 | + | 0.820524i | \(0.306318\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.915429 | + | 1.58557i | 0.0485859 | + | 0.0841533i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.49072 | + | 7.77816i | 0.237674 | + | 0.411664i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.9887 | 1.37163 | 0.685816 | − | 0.727775i | \(-0.259446\pi\) | ||||
0.685816 | + | 0.727775i | \(0.259446\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.40727 | − | 14.5618i | 0.442488 | − | 0.766412i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.19693 | 0.115309 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.15878 | −0.0606532 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.86696 | + | 6.69777i | −0.201854 | + | 0.349621i | −0.949126 | − | 0.314897i | \(-0.898030\pi\) |
0.747272 | + | 0.664518i | \(0.231363\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.29287 | 0.327594 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.76808 | − | 13.4547i | −0.403299 | − | 0.698534i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.16398 | − | 12.4084i | −0.370937 | − | 0.642481i | 0.618773 | − | 0.785570i | \(-0.287630\pi\) |
−0.989710 | + | 0.143088i | \(0.954297\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.65749 | − | 2.87086i | 0.0855925 | − | 0.148251i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.818001 | + | 17.4309i | −0.0421292 | + | 0.897738i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.69939 | − | 6.40753i | 0.190025 | − | 0.329133i | −0.755233 | − | 0.655456i | \(-0.772476\pi\) |
0.945258 | + | 0.326323i | \(0.105810\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.94679 | + | 15.4963i | 0.458358 | + | 0.793899i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.09974 | + | 7.10096i | 0.209487 | + | 0.362842i | 0.951553 | − | 0.307485i | \(-0.0994873\pi\) |
−0.742066 | + | 0.670327i | \(0.766154\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.651833 | −0.0332205 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.60163 | + | 4.50615i | −0.132248 | + | 0.229061i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.29767 | 0.116497 | 0.0582483 | − | 0.998302i | \(-0.481448\pi\) | ||||
0.0582483 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.39844 | 0.222439 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.95637 | − | 3.38853i | 0.0986857 | − | 0.170929i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.29148 | 0.115297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.28037 | + | 10.8779i | 0.315203 | + | 0.545947i | 0.979481 | − | 0.201539i | \(-0.0645942\pi\) |
−0.664278 | + | 0.747486i | \(0.731261\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.99897 | − | 12.1226i | −0.350387 | − | 0.606887i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.77773 | − | 11.7394i | 0.338463 | − | 0.586236i | −0.645680 | − | 0.763608i | \(-0.723426\pi\) |
0.984144 | + | 0.177372i | \(0.0567595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.8408 | − | 8.18066i | 0.789086 | − | 0.407508i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.842651 | − | 1.45951i | 0.0418717 | − | 0.0725239i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.11018 | + | 7.11904i | 0.203734 | + | 0.352878i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.13507 | + | 5.43010i | 0.155019 | + | 0.268501i | 0.933066 | − | 0.359705i | \(-0.117123\pi\) |
−0.778047 | + | 0.628206i | \(0.783789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −40.3692 | −1.99127 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.297275 | + | 0.514895i | −0.0146279 | + | 0.0253363i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.315812 | 0.0155026 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.7912 | −1.65476 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0739 | + | 20.9126i | −0.589848 | + | 1.02165i | 0.404404 | + | 0.914581i | \(0.367479\pi\) |
−0.994252 | + | 0.107066i | \(0.965854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.7932 | 0.623504 | 0.311752 | − | 0.950164i | \(-0.399084\pi\) | ||||
0.311752 | + | 0.950164i | \(0.399084\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.84355 | + | 11.8534i | 0.332745 | + | 0.576331i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.36049 | + | 4.08849i | 0.114501 | + | 0.198321i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.0284 | + | 22.5659i | −0.630491 | + | 1.09204i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.66671 | − | 4.27779i | −0.321872 | − | 0.206533i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0307 | + | 22.5699i | −0.627668 | + | 1.08715i | 0.360350 | + | 0.932817i | \(0.382657\pi\) |
−0.988018 | + | 0.154336i | \(0.950676\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.17254 | + | 3.76296i | 0.104406 | + | 0.180836i | 0.913495 | − | 0.406849i | \(-0.133373\pi\) |
−0.809090 | + | 0.587685i | \(0.800039\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.804030 | − | 1.39262i | −0.0385503 | − | 0.0667711i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.85514 | −0.327926 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.5022 | − | 19.9224i | 0.548970 | − | 0.950843i | −0.449376 | − | 0.893343i | \(-0.648354\pi\) |
0.998345 | − | 0.0575005i | \(-0.0183131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.1436 | 1.00684 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.9959 | −1.66270 | −0.831352 | − | 0.555746i | \(-0.812433\pi\) | ||||
−0.831352 | + | 0.555746i | \(0.812433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.16805 | − | 2.02311i | 0.0553707 | − | 0.0959048i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.5297 | 0.687233 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5030 | − | 33.7802i | −0.920403 | − | 1.59418i | −0.798793 | − | 0.601606i | \(-0.794528\pi\) |
−0.121610 | − | 0.992578i | \(-0.538806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.72266 | − | 2.98374i | −0.0811169 | − | 0.140499i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.9343 | − | 36.2593i | 0.983579 | − | 1.70361i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.97803 | + | 1.26923i | 0.0927313 | + | 0.0595023i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.0031 | − | 31.1823i | 0.842149 | − | 1.45865i | −0.0459246 | − | 0.998945i | \(-0.514623\pi\) |
0.888074 | − | 0.459701i | \(-0.152043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.22271 | + | 2.11780i | 0.0570713 | + | 0.0988503i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.61490 | − | 11.4573i | −0.308086 | − | 0.533621i | 0.669857 | − | 0.742490i | \(-0.266355\pi\) |
−0.977944 | + | 0.208869i | \(0.933022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2667 | −0.616554 | −0.308277 | − | 0.951297i | \(-0.599752\pi\) | ||||
−0.308277 | + | 0.951297i | \(0.599752\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.821464 | + | 1.42282i | −0.0380945 | + | 0.0659815i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.3401 | 1.35770 | 0.678849 | − | 0.734278i | \(-0.262479\pi\) | ||||
0.678849 | + | 0.734278i | \(0.262479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.4954 | 1.22344 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.3434 | + | 43.8960i | −1.16776 | + | 2.02262i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.84876 | 0.130986 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.67892 | − | 6.37207i | −0.168800 | − | 0.292371i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.29197 | + | 5.70186i | 0.150729 | + | 0.261070i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.72784 | − | 6.45681i | 0.170329 | − | 0.295019i | −0.768206 | − | 0.640203i | \(-0.778850\pi\) |
0.938535 | + | 0.345184i | \(0.112184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.38937 | − | 29.6063i | 0.0633498 | − | 1.34993i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.9537 | − | 38.0249i | 0.998928 | − | 1.73019i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0306855 | + | 0.0531488i | 0.00139336 | + | 0.00241336i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6278 | − | 28.8002i | −0.753477 | − | 1.30506i | −0.946128 | − | 0.323793i | \(-0.895042\pi\) |
0.192651 | − | 0.981267i | \(-0.438291\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.30744 | −0.375676 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1155 | − | 24.4488i | 0.637024 | − | 1.10336i | −0.349059 | − | 0.937101i | \(-0.613499\pi\) |
0.986083 | − | 0.166256i | \(-0.0531679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.59071 | 0.206755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.276235 | 0.0124158 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.0880 | + | 45.1858i | −1.17021 | + | 2.02686i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.31861 | −0.0590292 | −0.0295146 | − | 0.999564i | \(-0.509396\pi\) | ||||
−0.0295146 | + | 0.999564i | \(0.509396\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.4267 | − | 35.3800i | −0.912596 | − | 1.58066i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.9365 | − | 24.1388i | −0.621398 | − | 1.07629i | −0.989226 | − | 0.146399i | \(-0.953232\pi\) |
0.367827 | − | 0.929894i | \(-0.380102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.478357 | − | 0.828539i | 0.0212866 | − | 0.0368695i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.9010 | + | 25.9624i | 0.528540 | + | 1.15303i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.1375 | − | 31.4151i | 0.803931 | − | 1.39245i | −0.113080 | − | 0.993586i | \(-0.536072\pi\) |
0.917011 | − | 0.398863i | \(-0.130595\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.5115 | − | 28.5988i | −0.730426 | − | 1.26514i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.90564 | − | 3.30067i | −0.0841362 | − | 0.145728i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.455426 | 0.0200685 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.74682 | − | 6.48967i | 0.164785 | − | 0.285416i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 54.5216 | 2.39323 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.6407 | 1.82431 | 0.912156 | − | 0.409843i | \(-0.134416\pi\) | ||||
0.912156 | + | 0.409843i | \(0.134416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.3056 | + | 33.4382i | −0.844173 | + | 1.46215i | 0.0421640 | + | 0.999111i | \(0.486575\pi\) |
−0.886337 | + | 0.463040i | \(0.846759\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 47.1272 | 2.05680 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.34512 | − | 4.06187i | −0.102155 | − | 0.176938i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.748720 | + | 1.29682i | 0.0325530 | + | 0.0563835i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.125980 | − | 0.218203i | 0.00546706 | − | 0.00946922i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.582314 | + | 12.4086i | −0.0252228 | + | 0.537477i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.26667 | − | 2.19393i | 0.0547629 | − | 0.0948521i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.9170 | + | 22.3729i | 0.557409 | + | 0.965460i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.78802 | − | 10.0251i | −0.249308 | − | 0.431814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.2454 | 0.612456 | 0.306228 | − | 0.951958i | \(-0.400933\pi\) | ||||
0.306228 | + | 0.951958i | \(0.400933\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.49706 | + | 6.05709i | −0.150073 | + | 0.259935i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.753481 | 0.0322756 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.6344 | 0.668479 | 0.334240 | − | 0.942488i | \(-0.391521\pi\) | ||||
0.334240 | + | 0.942488i | \(0.391521\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.52122 | − | 9.56303i | 0.235640 | − | 0.408140i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.15480 | −0.304805 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.6515 | + | 56.5540i | 1.38848 | + | 2.40492i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.36564 | + | 2.36536i | 0.0579682 | + | 0.100404i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.7441 | − | 23.8054i | 0.582354 | − | 1.00867i | −0.412845 | − | 0.910801i | \(-0.635465\pi\) |
0.995200 | − | 0.0978662i | \(-0.0312017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.64474 | − | 5.54701i | −0.365633 | − | 0.234614i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.04193 | + | 1.80468i | −0.0439904 | + | 0.0761936i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.64552 | + | 8.04628i | 0.195786 | + | 0.339110i | 0.947158 | − | 0.320768i | \(-0.103941\pi\) |
−0.751372 | + | 0.659879i | \(0.770608\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.06879 | + | 1.85119i | 0.0449642 | + | 0.0778803i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 48.0280 | 2.01699 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.23410 | + | 3.86958i | −0.0936585 | + | 0.162221i | −0.909048 | − | 0.416692i | \(-0.863190\pi\) |
0.815389 | + | 0.578913i | \(0.196523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7999 | −0.828600 | −0.414300 | − | 0.910140i | \(-0.635974\pi\) | ||||
−0.414300 | + | 0.910140i | \(0.635974\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.88574 | 0.204105 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.5397 | − | 19.9873i | 0.481238 | − | 0.833529i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.0858 | 0.628031 | 0.314016 | − | 0.949418i | \(-0.398326\pi\) | ||||
0.314016 | + | 0.949418i | \(0.398326\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.4483 | − | 45.8098i | −1.09915 | − | 1.90379i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.50002 | + | 7.79427i | 0.186692 | + | 0.323361i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.80234 | − | 3.12175i | 0.0746454 | − | 0.129290i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.838252 | − | 0.537876i | −0.0346574 | − | 0.0222384i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.5739 | + | 33.9030i | −0.807901 | + | 1.39933i | 0.106414 | + | 0.994322i | \(0.466063\pi\) |
−0.914315 | + | 0.405004i | \(0.867270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.65497 | + | 6.33059i | 0.150600 | + | 0.260848i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.9868 | + | 36.3503i | 0.863283 | + | 1.49525i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.3769 | 0.631452 | 0.315726 | − | 0.948850i | \(-0.397752\pi\) | ||||
0.315726 | + | 0.948850i | \(0.397752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.309144 | − | 0.535452i | 0.0126736 | − | 0.0219514i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.0372 | −1.31119 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.1546 | 1.39552 | 0.697760 | − | 0.716331i | \(-0.254180\pi\) | ||||
0.697760 | + | 0.716331i | \(0.254180\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.5133 | + | 35.5300i | −0.836754 | + | 1.44930i | 0.0558400 | + | 0.998440i | \(0.482216\pi\) |
−0.892594 | + | 0.450861i | \(0.851117\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.2283 | −0.457250 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0756188 | − | 0.130976i | −0.00307434 | − | 0.00532492i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.4466 | − | 31.9504i | −0.748723 | − | 1.29683i | −0.948435 | − | 0.316972i | \(-0.897334\pi\) |
0.199712 | − | 0.979855i | \(-0.435999\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.9134 | − | 39.6871i | 0.928496 | − | 1.60820i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.0064 | + | 12.3976i | −0.971195 | + | 0.501554i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.38792 | + | 12.7962i | −0.298395 | + | 0.516836i | −0.975769 | − | 0.218803i | \(-0.929785\pi\) |
0.677374 | + | 0.735639i | \(0.263118\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.572369 | − | 0.991372i | −0.0230801 | − | 0.0399760i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.1197 | − | 29.6521i | −0.689212 | − | 1.19375i | −0.972093 | − | 0.234595i | \(-0.924624\pi\) |
0.282882 | − | 0.959155i | \(-0.408710\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.6164 | −0.949225 | −0.474612 | − | 0.880195i | \(-0.657412\pi\) | ||||
−0.474612 | + | 0.880195i | \(0.657412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.97744 | − | 10.3532i | 0.239867 | − | 0.415461i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 66.5742 | 2.66724 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.6574 | 0.986297 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.62389 | − | 2.81267i | 0.0648520 | − | 0.112327i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.79730 | −0.310899 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.55599 | − | 14.8194i | −0.340609 | − | 0.589952i | 0.643937 | − | 0.765078i | \(-0.277300\pi\) |
−0.984546 | + | 0.175127i | \(0.943966\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.29976 | + | 7.44740i | 0.170900 | + | 0.296008i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.615901 | − | 1.06677i | 0.0244413 | − | 0.0423336i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.95653 | + | 41.6921i | −0.0775207 | + | 1.65190i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.0556 | − | 19.1489i | 0.437354 | − | 0.757519i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.2197 | + | 22.8972i | 0.522148 | + | 0.904386i | 0.999668 | + | 0.0257657i | \(0.00820237\pi\) |
−0.477520 | + | 0.878621i | \(0.658464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.8136 | + | 18.7297i | 0.426446 | + | 0.738626i | 0.996554 | − | 0.0829434i | \(-0.0264321\pi\) |
−0.570108 | + | 0.821570i | \(0.693099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.946525 | 0.0372694 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.9635 | − | 34.5778i | 0.784847 | − | 1.35939i | −0.144244 | − | 0.989542i | \(-0.546075\pi\) |
0.929091 | − | 0.369852i | \(-0.120592\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.137947 | −0.00541489 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −46.8204 | −1.83504 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.66357 | − | 9.80959i | 0.221633 | − | 0.383879i | −0.733671 | − | 0.679505i | \(-0.762195\pi\) |
0.955304 | + | 0.295626i | \(0.0955281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.269355 | −0.0105246 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.99728 | + | 12.1196i | 0.272990 | + | 0.472832i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.42568 | + | 16.3258i | 0.367173 | + | 0.635962i | 0.989122 | − | 0.147096i | \(-0.0469925\pi\) |
−0.621950 | + | 0.783057i | \(0.713659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2650 | + | 28.1719i | −0.632636 | + | 1.09576i | 0.354375 | + | 0.935104i | \(0.384694\pi\) |
−0.987011 | + | 0.160654i | \(0.948640\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.67582 | − | 3.44759i | 0.259267 | − | 0.133893i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.481812 | + | 0.834524i | −0.0186839 | + | 0.0323614i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.2213 | − | 19.4358i | −0.434489 | − | 0.752556i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.9966 | − | 34.6351i | −0.773114 | − | 1.33907i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.04569 | −0.233391 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3195 | + | 28.2663i | −0.629072 | + | 1.08959i | 0.358666 | + | 0.933466i | \(0.383232\pi\) |
−0.987738 | + | 0.156119i | \(0.950102\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.8315 | 0.493887 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.3235 | −1.31916 | −0.659580 | − | 0.751634i | \(-0.729266\pi\) | ||||
−0.659580 | + | 0.751634i | \(0.729266\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.874479 | + | 1.51464i | −0.0335594 | + | 0.0581266i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.24694 | 0.354343 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.3779 | − | 31.8315i | −0.703213 | − | 1.21800i | −0.967333 | − | 0.253510i | \(-0.918415\pi\) |
0.264120 | − | 0.964490i | \(-0.414918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.38952 | + | 2.40672i | 0.0530908 | + | 0.0919560i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.34527 | − | 5.79417i | 0.127630 | − | 0.221062i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.5479 | + | 5.96367i | −0.439939 | + | 0.227198i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.09435 | + | 14.0198i | −0.307923 | + | 0.533339i | −0.977908 | − | 0.209036i | \(-0.932967\pi\) |
0.669985 | + | 0.742375i | \(0.266301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.93609 | + | 6.81751i | 0.149520 | + | 0.258976i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.16310 | + | 2.01455i | 0.0441190 | + | 0.0764163i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.26801 | 0.123785 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.89445 | + | 3.28129i | −0.0716548 | + | 0.124110i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.6393 | −0.855074 | −0.427537 | − | 0.903998i | \(-0.640619\pi\) | ||||
−0.427537 | + | 0.903998i | \(0.640619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.1524 | 0.458336 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.24491 | − | 2.15625i | 0.0468861 | − | 0.0812090i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.2646 | 1.02539 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.44263 | − | 12.8910i | −0.279514 | − | 0.484132i | 0.691750 | − | 0.722137i | \(-0.256840\pi\) |
−0.971264 | + | 0.238005i | \(0.923507\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8371 | − | 23.9666i | −0.518932 | − | 0.898817i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.4646 | + | 19.8572i | −0.429351 | + | 0.743658i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0255616 | + | 0.544696i | −0.000955949 | + | 0.0203705i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.1181 | − | 43.5059i | 0.938054 | − | 1.62476i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.6862 | − | 21.9731i | −0.473115 | − | 0.819460i | 0.526411 | − | 0.850230i | \(-0.323537\pi\) |
−0.999526 | + | 0.0307705i | \(0.990204\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.48940 | + | 11.2400i | 0.241678 | + | 0.418598i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −38.4780 | −1.43101 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0441 | − | 20.8610i | 0.447307 | − | 0.774759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.7515 | −1.95645 | −0.978223 | − | 0.207558i | \(-0.933448\pi\) | ||||
−0.978223 | + | 0.207558i | \(0.933448\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.36165 | −0.124506 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.35108 | + | 2.34013i | −0.0499714 | + | 0.0865529i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.4824 | −1.56912 | −0.784561 | − | 0.620051i | \(-0.787112\pi\) | ||||
−0.784561 | + | 0.620051i | \(0.787112\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.92312 | − | 3.33094i | −0.0709353 | − | 0.122864i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.07371 | + | 5.32383i | 0.113222 | + | 0.196106i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.32128 | − | 7.48468i | 0.158961 | − | 0.275329i | −0.775533 | − | 0.631307i | \(-0.782519\pi\) |
0.934494 | + | 0.355978i | \(0.115852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.4045 | + | 5.37321i | −0.382220 | + | 0.197390i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.12153 | + | 15.7989i | −0.334636 | + | 0.579607i | −0.983415 | − | 0.181370i | \(-0.941947\pi\) |
0.648779 | + | 0.760977i | \(0.275280\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.500117 | − | 0.866229i | −0.0183229 | − | 0.0317362i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.90703 | − | 3.30307i | −0.0697745 | − | 0.120853i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 72.1954 | 2.63796 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.3297 | − | 26.5517i | 0.559387 | − | 0.968887i | −0.438161 | − | 0.898897i | \(-0.644370\pi\) |
0.997548 | − | 0.0699901i | \(-0.0222968\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −45.8729 | −1.67170 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.88226 | −0.104896 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.863776 | − | 1.49610i | 0.0313945 | − | 0.0543768i | −0.849901 | − | 0.526942i | \(-0.823339\pi\) |
0.881296 | + | 0.472565i | \(0.156672\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.1873 | 0.369777 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.119357 | − | 0.206733i | −0.00432669 | − | 0.00749405i | 0.863854 | − | 0.503742i | \(-0.168044\pi\) |
−0.868181 | + | 0.496248i | \(0.834711\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.7364 | + | 18.5960i | 0.388684 | + | 0.673220i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.131009 | + | 0.226915i | −0.00473666 | + | 0.00820413i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.418608 | + | 0.268605i | 0.0151151 | + | 0.00969878i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.19637 | + | 2.07218i | −0.0431422 | + | 0.0747246i | −0.886790 | − | 0.462172i | \(-0.847070\pi\) |
0.843648 | + | 0.536897i | \(0.180404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.39556 | + | 2.41718i | 0.0502598 | + | 0.0870525i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.91610 | + | 5.05083i | 0.104885 | + | 0.181666i | 0.913691 | − | 0.406409i | \(-0.133219\pi\) |
−0.808806 | + | 0.588075i | \(0.799886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.6105 | −0.884036 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −38.9182 | + | 67.4084i | −1.39618 | + | 2.41826i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.09332 | −0.182487 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1058 | −0.433181 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.23874 | − | 10.8058i | 0.222954 | − | 0.386168i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.48930 | 0.124538 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.5596 | − | 23.4858i | −0.483346 | − | 0.837180i | 0.516471 | − | 0.856305i | \(-0.327245\pi\) |
−0.999817 | + | 0.0191248i | \(0.993912\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.56126 | + | 13.0965i | 0.269188 | + | 0.466247i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.4584 | + | 52.7556i | −1.08298 | + | 1.87577i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.3460 | + | 11.7720i | 0.651486 | + | 0.418035i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.598844 | − | 1.03723i | 0.0212388 | − | 0.0367867i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.23685 | − | 7.33843i | −0.150077 | − | 0.259941i | 0.781179 | − | 0.624308i | \(-0.214619\pi\) |
−0.931256 | + | 0.364367i | \(0.881285\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.55399 | + | 6.15569i | 0.125731 | + | 0.217773i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.2130 | −0.996856 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.83098 | − | 6.63546i | 0.135192 | − | 0.234160i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.02261 | −0.106533 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −58.5420 | −2.06078 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.81414 | − | 10.0704i | 0.204414 | − | 0.354056i | −0.745532 | − | 0.666470i | \(-0.767804\pi\) |
0.949946 | + | 0.312414i | \(0.101138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.7551 | −1.53645 | −0.768224 | − | 0.640181i | \(-0.778859\pi\) | ||||
−0.768224 | + | 0.640181i | \(0.778859\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.3099 | + | 31.7137i | 0.642156 | + | 1.11225i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.285944 | + | 0.495270i | 0.0100162 | + | 0.0173486i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.10571 | − | 3.64719i | 0.0736693 | − | 0.127599i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.33052 | − | 28.3524i | 0.0464923 | − | 0.990712i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.5277 | + | 45.9473i | −0.925823 | + | 1.60357i | −0.135592 | + | 0.990765i | \(0.543294\pi\) |
−0.790231 | + | 0.612809i | \(0.790040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.94924 | + | 13.7685i | 0.277093 | + | 0.479939i | 0.970661 | − | 0.240452i | \(-0.0772956\pi\) |
−0.693568 | + | 0.720391i | \(0.743962\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.46720 | + | 9.46946i | 0.190343 | + | 0.329684i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.77095 | −0.270222 | −0.135111 | − | 0.990830i | \(-0.543139\pi\) | ||||
−0.135111 | + | 0.990830i | \(0.543139\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.6929 | + | 37.5732i | −0.753426 | + | 1.30497i | 0.192728 | + | 0.981252i | \(0.438267\pi\) |
−0.946153 | + | 0.323719i | \(0.895067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.9900 | 1.52600 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.9803 | 0.380444 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.40618 | + | 2.43558i | −0.0486629 | + | 0.0842867i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.7480 | −0.440636 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.7824 | + | 48.1206i | 0.959156 | + | 1.66131i | 0.724557 | + | 0.689215i | \(0.242044\pi\) |
0.234599 | + | 0.972092i | \(0.424622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.78823 | + | 4.82935i | 0.0961458 | + | 0.166529i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.0560 | + | 19.1495i | −0.380787 | + | 0.659543i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.13818 | − | 1.60314i | 0.0391546 | − | 0.0551496i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.15500 | − | 3.73256i | 0.0740466 | − | 0.128252i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.00600 | + | 3.47450i | 0.0688458 | + | 0.119244i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.0592 | + | 33.0116i | 0.653342 | + | 1.13162i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.13239 | 0.175730 | 0.0878649 | − | 0.996132i | \(-0.471996\pi\) | ||||
0.0878649 | + | 0.996132i | \(0.471996\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.204183 | − | 0.353656i | 0.00698292 | − | 0.0120948i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.9653 | −0.921118 | −0.460559 | − | 0.887629i | \(-0.652351\pi\) | ||||
−0.460559 | + | 0.887629i | \(0.652351\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.93622 | 0.134302 | 0.0671510 | − | 0.997743i | \(-0.478609\pi\) | ||||
0.0671510 | + | 0.997743i | \(0.478609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.3114 | − | 28.2523i | 0.555893 | − | 0.962834i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.1075 | −0.480225 | −0.240113 | − | 0.970745i | \(-0.577184\pi\) | ||||
−0.240113 | + | 0.970745i | \(0.577184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.87665 | − | 3.25045i | −0.0638080 | − | 0.110519i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.6856 | + | 30.6323i | 0.600634 | + | 1.04033i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.57576 | + | 13.1216i | −0.256990 | + | 0.445120i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.03901 | − | 22.1405i | 0.0352056 | − | 0.750202i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.370588 | − | 0.641878i | 0.0125425 | − | 0.0217243i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.25171 | − | 5.63213i | −0.109928 | − | 0.190401i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.92118 | − | 11.9878i | −0.233711 | − | 0.404800i | 0.725186 | − | 0.688553i | \(-0.241754\pi\) |
−0.958897 | + | 0.283753i | \(0.908420\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 70.9236 | 2.39219 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.1005 | − | 36.5471i | 0.710894 | − | 1.23130i | −0.253628 | − | 0.967302i | \(-0.581624\pi\) |
0.964522 | − | 0.264002i | \(-0.0850426\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.14690 | −0.206860 | −0.103430 | − | 0.994637i | \(-0.532982\pi\) | ||||
−0.103430 | + | 0.994637i | \(0.532982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0458340 | −0.00154069 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.58834 | + | 9.67928i | −0.187638 | + | 0.324999i | −0.944462 | − | 0.328620i | \(-0.893417\pi\) |
0.756824 | + | 0.653618i | \(0.226750\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.1041 | 1.17735 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.57170 | + | 9.65047i | 0.186659 | + | 0.323303i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.53903 | − | 9.59388i | −0.185357 | − | 0.321047i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.889211 | − | 1.54016i | 0.0297231 | − | 0.0514818i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.9141 | − | 19.8365i | −1.03219 | − | 0.662320i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.9657 | + | 20.7252i | −0.399079 | + | 0.691225i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.70959 | + | 2.96109i | 0.0569546 | + | 0.0986482i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.4871 | + | 23.3604i | 0.448823 | + | 0.777384i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.481479 | 0.0160049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.1027 | − | 24.4265i | 0.468271 | − | 0.811069i | −0.531071 | − | 0.847327i | \(-0.678210\pi\) |
0.999342 | + | 0.0362578i | \(0.0115437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.5542 | −0.383230 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.5478 | 1.44280 | 0.721402 | − | 0.692517i | \(-0.243498\pi\) | ||||
0.721402 | + | 0.692517i | \(0.243498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.04409 | + | 1.80842i | −0.0345544 | + | 0.0598499i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.00873 | −0.0664066 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.83805 | − | 6.64771i | −0.126744 | − | 0.219527i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.88587 | − | 15.3908i | −0.293118 | − | 0.507695i | 0.681428 | − | 0.731886i | \(-0.261359\pi\) |
−0.974545 | + | 0.224191i | \(0.928026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.30070 | − | 16.1093i | 0.306469 | − | 0.530819i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.7359 | + | 23.5721i | 1.20918 | + | 0.775884i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.4569 | + | 35.4323i | −0.672618 | + | 1.16501i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.75009 | − | 4.76329i | −0.0903248 | − | 0.156447i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.8757 | − | 22.3014i | −0.422439 | − | 0.731686i | 0.573739 | − | 0.819039i | \(-0.305493\pi\) |
−0.996177 | + | 0.0873529i | \(0.972159\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.1132 | −0.560863 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.5931 | − | 56.4529i | 1.06705 | − | 1.84818i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.143454 | 0.00469146 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.98935 | 0.261001 | 0.130500 | − | 0.991448i | \(-0.458342\pi\) | ||||
0.130500 | + | 0.991448i | \(0.458342\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.43028 | + | 11.1376i | −0.209844 | + | 0.363461i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.60320 | −0.150060 | −0.0750301 | − | 0.997181i | \(-0.523905\pi\) | ||||
−0.0750301 | + | 0.997181i | \(0.523905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.98813 | − | 13.8358i | −0.260129 | − | 0.450557i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.840247 | − | 1.45535i | −0.0273332 | − | 0.0473425i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.12626 | − | 1.95073i | 0.0365984 | − | 0.0633903i | −0.847146 | − | 0.531360i | \(-0.821681\pi\) |
0.883744 | + | 0.467970i | \(0.155014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.5457 | + | 12.6761i | −0.796787 | + | 0.411484i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.4424 | + | 26.7470i | −0.500754 | + | 0.867332i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.58355 | + | 13.1351i | 0.245655 | + | 0.425487i | 0.962316 | − | 0.271935i | \(-0.0876635\pi\) |
−0.716660 | + | 0.697422i | \(0.754330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.168169 | − | 0.291276i | −0.00544181 | − | 0.00942549i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.6327 | 0.343705 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.5987 | + | 68.5870i | −1.27871 | + | 2.21479i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.54968 | −0.211280 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.5951 | −0.985913 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.82071 | + | 3.15357i | −0.0586108 | + | 0.101517i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.3320 | −1.07188 | −0.535942 | − | 0.844255i | \(-0.680043\pi\) | ||||
−0.535942 | + | 0.844255i | \(0.680043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.54032 | + | 2.66791i | 0.0494822 | + | 0.0857057i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.03438 | − | 1.79160i | −0.0331949 | − | 0.0574952i | 0.848951 | − | 0.528472i | \(-0.177235\pi\) |
−0.882146 | + | 0.470977i | \(0.843902\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.1463 | + | 57.4110i | −1.06262 | + | 1.84051i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.84809 | − | 39.3812i | 0.0591861 | − | 1.26121i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.0195 | − | 26.0145i | 0.480516 | − | 0.832279i | −0.519234 | − | 0.854632i | \(-0.673783\pi\) |
0.999750 | + | 0.0223534i | \(0.00711591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.72324 | + | 13.3770i | 0.246836 | + | 0.427532i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.54989 | − | 7.88064i | −0.145267 | − | 0.251610i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.6884 | 1.39344 | 0.696722 | − | 0.717341i | \(-0.254641\pi\) | ||||
0.696722 | + | 0.717341i | \(0.254641\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.44474 | − | 2.50237i | 0.0460334 | − | 0.0797322i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 70.9553 | 2.25853 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.2100 | 0.420052 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.3072 | − | 33.4410i | 0.613313 | − | 1.06229i | −0.377365 | − | 0.926064i | \(-0.623170\pi\) |
0.990678 | − | 0.136224i | \(-0.0434967\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.4269 | 0.426089 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.10273 | + | 1.90998i | 0.0349588 | + | 0.0605504i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.6879 | + | 30.6363i | 0.560180 | + | 0.970261i | 0.997480 | + | 0.0709452i | \(0.0226015\pi\) |
−0.437300 | + | 0.899316i | \(0.644065\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.5965 | + | 18.3536i | −0.335257 | + | 0.580683i |
(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 | 572.2.i.c.529.1 | yes | 10 | |
13.3 | even | 3 | inner | 572.2.i.c.133.1 | ✓ | 10 | |
13.4 | even | 6 | 7436.2.a.q.1.5 | 5 | |||
13.9 | even | 3 | 7436.2.a.r.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.i.c.133.1 | ✓ | 10 | 13.3 | even | 3 | inner | |
572.2.i.c.529.1 | yes | 10 | 1.1 | even | 1 | trivial | |
7436.2.a.q.1.5 | 5 | 13.4 | even | 6 | |||
7436.2.a.r.1.5 | 5 | 13.9 | even | 3 |