Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(148,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.f (of order \(5\), degree \(4\), 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: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 295.2 | ||
Root | \(0.435488 - 1.34029i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.295 |
Dual form | 539.2.f.e.148.2 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.435488 | + | 1.34029i | −0.307936 | + | 0.947730i | 0.670629 | + | 0.741793i | \(0.266024\pi\) |
−0.978565 | + | 0.205937i | \(0.933976\pi\) | |||||||
\(3\) | −1.75021 | + | 1.27160i | −1.01049 | + | 0.734161i | −0.964311 | − | 0.264773i | \(-0.914703\pi\) |
−0.0461746 | + | 0.998933i | \(0.514703\pi\) | |||||||
\(4\) | 0.0112975 | + | 0.00820814i | 0.00564876 | + | 0.00410407i | ||||
\(5\) | 0.565930 | + | 1.74175i | 0.253091 | + | 0.778935i | 0.994200 | + | 0.107550i | \(0.0343005\pi\) |
−0.741108 | + | 0.671385i | \(0.765700\pi\) | |||||||
\(6\) | −0.942126 | − | 2.89957i | −0.384621 | − | 1.18374i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.29616 | + | 1.66826i | −0.811817 | + | 0.589819i | ||||
\(9\) | 0.519216 | − | 1.59798i | 0.173072 | − | 0.532661i | ||||
\(10\) | −2.58091 | −0.816157 | ||||||||
\(11\) | −2.26009 | + | 2.42734i | −0.681444 | + | 0.731871i | ||||
\(12\) | −0.0302106 | −0.00872104 | ||||||||
\(13\) | 1.43602 | − | 4.41961i | 0.398280 | − | 1.22578i | −0.528097 | − | 0.849184i | \(-0.677094\pi\) |
0.926377 | − | 0.376596i | \(-0.122906\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.20531 | − | 2.32880i | −0.827609 | − | 0.601293i | ||||
\(16\) | −1.22738 | − | 3.77748i | −0.306844 | − | 0.944370i | ||||
\(17\) | 1.69039 | + | 5.20248i | 0.409980 | + | 1.26179i | 0.916665 | + | 0.399656i | \(0.130871\pi\) |
−0.506685 | + | 0.862131i | \(0.669129\pi\) | |||||||
\(18\) | 1.91565 | + | 1.39180i | 0.451524 | + | 0.328051i | ||||
\(19\) | −4.69325 | + | 3.40985i | −1.07671 | + | 0.782272i | −0.977106 | − | 0.212755i | \(-0.931756\pi\) |
−0.0995999 | + | 0.995028i | \(0.531756\pi\) | |||||||
\(20\) | −0.00790293 | + | 0.0243227i | −0.00176715 | + | 0.00543873i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.26911 | − | 4.08626i | −0.483775 | − | 0.871194i | ||||
\(23\) | −0.719682 | −0.150064 | −0.0750321 | − | 0.997181i | \(-0.523906\pi\) | ||||
−0.0750321 | + | 0.997181i | \(0.523906\pi\) | |||||||
\(24\) | 1.89741 | − | 5.83962i | 0.387307 | − | 1.19201i | ||||
\(25\) | 1.33166 | − | 0.967509i | 0.266332 | − | 0.193502i | ||||
\(26\) | 5.29821 | + | 3.84937i | 1.03906 | + | 0.754924i | ||||
\(27\) | −0.882303 | − | 2.71545i | −0.169799 | − | 0.522588i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.948551 | + | 0.689163i | 0.176142 | + | 0.127974i | 0.672363 | − | 0.740222i | \(-0.265280\pi\) |
−0.496221 | + | 0.868196i | \(0.665280\pi\) | |||||||
\(30\) | 4.51715 | − | 3.28190i | 0.824714 | − | 0.599190i | ||||
\(31\) | 0.404153 | − | 1.24385i | 0.0725879 | − | 0.223403i | −0.908180 | − | 0.418580i | \(-0.862528\pi\) |
0.980768 | + | 0.195177i | \(0.0625281\pi\) | |||||||
\(32\) | −0.0789938 | −0.0139643 | ||||||||
\(33\) | 0.869026 | − | 7.12230i | 0.151278 | − | 1.23983i | ||||
\(34\) | −7.70900 | −1.32208 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0189823 | − | 0.0137915i | 0.00316372 | − | 0.00229858i | ||||
\(37\) | −1.69468 | − | 1.23126i | −0.278604 | − | 0.202417i | 0.439705 | − | 0.898142i | \(-0.355083\pi\) |
−0.718308 | + | 0.695725i | \(0.755083\pi\) | |||||||
\(38\) | −2.52634 | − | 7.77528i | −0.409827 | − | 1.26132i | ||||
\(39\) | 3.10666 | + | 9.56131i | 0.497463 | + | 1.53103i | ||||
\(40\) | −4.20516 | − | 3.05523i | −0.664895 | − | 0.483074i | ||||
\(41\) | −0.741582 | + | 0.538791i | −0.115816 | + | 0.0841449i | −0.644185 | − | 0.764869i | \(-0.722803\pi\) |
0.528370 | + | 0.849014i | \(0.322803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.02379 | 1.22362 | 0.611808 | − | 0.791006i | \(-0.290442\pi\) | ||||
0.611808 | + | 0.791006i | \(0.290442\pi\) | |||||||
\(44\) | −0.0454574 | + | 0.00887181i | −0.00685296 | + | 0.00133748i | ||||
\(45\) | 3.07713 | 0.458711 | ||||||||
\(46\) | 0.313413 | − | 0.964586i | 0.0462102 | − | 0.142220i | ||||
\(47\) | 4.83455 | − | 3.51251i | 0.705192 | − | 0.512352i | −0.176427 | − | 0.984314i | \(-0.556454\pi\) |
0.881619 | + | 0.471962i | \(0.156454\pi\) | |||||||
\(48\) | 6.95163 | + | 5.05065i | 1.00338 | + | 0.728999i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.716823 | + | 2.20615i | 0.101374 | + | 0.311997i | ||||
\(51\) | −9.57403 | − | 6.95594i | −1.34063 | − | 0.974027i | ||||
\(52\) | 0.0525003 | − | 0.0381437i | 0.00728048 | − | 0.00528958i | ||||
\(53\) | 3.13496 | − | 9.64840i | 0.430619 | − | 1.32531i | −0.466890 | − | 0.884315i | \(-0.654626\pi\) |
0.897510 | − | 0.440995i | \(-0.145374\pi\) | |||||||
\(54\) | 4.02373 | 0.547560 | ||||||||
\(55\) | −5.50688 | − | 2.56282i | −0.742547 | − | 0.345570i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.87821 | − | 11.9359i | 0.513682 | − | 1.58095i | ||||
\(58\) | −1.33676 | + | 0.971215i | −0.175526 | + | 0.127527i | ||||
\(59\) | −6.21390 | − | 4.51466i | −0.808981 | − | 0.587759i | 0.104554 | − | 0.994519i | \(-0.466659\pi\) |
−0.913535 | + | 0.406760i | \(0.866659\pi\) | |||||||
\(60\) | −0.0170971 | − | 0.0526193i | −0.00220722 | − | 0.00679312i | ||||
\(61\) | 1.93943 | + | 5.96895i | 0.248318 | + | 0.764246i | 0.995073 | + | 0.0991458i | \(0.0316110\pi\) |
−0.746754 | + | 0.665100i | \(0.768389\pi\) | |||||||
\(62\) | 1.49113 | + | 1.08337i | 0.189373 | + | 0.137588i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.48916 | − | 7.66083i | 0.311144 | − | 0.957604i | ||||
\(65\) | 8.51056 | 1.05560 | ||||||||
\(66\) | 9.16752 | + | 4.26643i | 1.12844 | + | 0.525161i | ||||
\(67\) | −15.4673 | −1.88963 | −0.944814 | − | 0.327608i | \(-0.893758\pi\) | ||||
−0.944814 | + | 0.327608i | \(0.893758\pi\) | |||||||
\(68\) | −0.0236055 | + | 0.0726501i | −0.00286258 | + | 0.00881012i | ||||
\(69\) | 1.25960 | − | 0.915151i | 0.151638 | − | 0.110171i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.29593 | + | 13.2215i | 0.509833 | + | 1.56910i | 0.792491 | + | 0.609883i | \(0.208784\pi\) |
−0.282659 | + | 0.959221i | \(0.591216\pi\) | |||||||
\(72\) | 1.47365 | + | 4.53542i | 0.173671 | + | 0.534504i | ||||
\(73\) | 4.86593 | + | 3.53531i | 0.569514 | + | 0.413776i | 0.834929 | − | 0.550358i | \(-0.185509\pi\) |
−0.265414 | + | 0.964134i | \(0.585509\pi\) | |||||||
\(74\) | 2.38826 | − | 1.73517i | 0.277629 | − | 0.201709i | ||||
\(75\) | −1.10040 | + | 3.38669i | −0.127064 | + | 0.391061i | ||||
\(76\) | −0.0810106 | −0.00929255 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −14.1679 | −1.60420 | ||||||||
\(79\) | −4.83332 | + | 14.8754i | −0.543791 | + | 1.67362i | 0.180058 | + | 0.983656i | \(0.442372\pi\) |
−0.723848 | + | 0.689959i | \(0.757628\pi\) | |||||||
\(80\) | 5.88482 | − | 4.27557i | 0.657943 | − | 0.478024i | ||||
\(81\) | 9.07517 | + | 6.59349i | 1.00835 | + | 0.732610i | ||||
\(82\) | −0.399188 | − | 1.22857i | −0.0440829 | − | 0.135673i | ||||
\(83\) | 1.35217 | + | 4.16157i | 0.148420 | + | 0.456791i | 0.997435 | − | 0.0715783i | \(-0.0228036\pi\) |
−0.849015 | + | 0.528370i | \(0.822804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.10479 | + | 5.88848i | −0.879088 | + | 0.638695i | ||||
\(86\) | −3.49426 | + | 10.7542i | −0.376796 | + | 1.15966i | ||||
\(87\) | −2.53651 | −0.271942 | ||||||||
\(88\) | 1.14011 | − | 9.34400i | 0.121536 | − | 0.996073i | ||||
\(89\) | −15.3437 | −1.62643 | −0.813215 | − | 0.581963i | \(-0.802285\pi\) | ||||
−0.813215 | + | 0.581963i | \(0.802285\pi\) | |||||||
\(90\) | −1.34005 | + | 4.12425i | −0.141254 | + | 0.434735i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.00813063 | − | 0.00590725i | −0.000847677 | − | 0.000615873i | ||||
\(93\) | 0.874336 | + | 2.69093i | 0.0906644 | + | 0.279036i | ||||
\(94\) | 2.60240 | + | 8.00937i | 0.268417 | + | 0.826104i | ||||
\(95\) | −8.59515 | − | 6.24474i | −0.881844 | − | 0.640697i | ||||
\(96\) | 0.138256 | − | 0.100449i | 0.0141107 | − | 0.0102520i | ||||
\(97\) | −0.745114 | + | 2.29323i | −0.0756549 | + | 0.232842i | −0.981731 | − | 0.190272i | \(-0.939063\pi\) |
0.906077 | + | 0.423114i | \(0.139063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.70537 | + | 4.87190i | 0.271900 | + | 0.489645i | ||||
\(100\) | 0.0229859 | 0.00229859 | ||||||||
\(101\) | −3.67603 | + | 11.3136i | −0.365778 | + | 1.12575i | 0.583714 | + | 0.811959i | \(0.301599\pi\) |
−0.949492 | + | 0.313790i | \(0.898401\pi\) | |||||||
\(102\) | 13.4924 | − | 9.80279i | 1.33594 | − | 0.970620i | ||||
\(103\) | 0.320625 | + | 0.232947i | 0.0315921 | + | 0.0229530i | 0.603469 | − | 0.797386i | \(-0.293785\pi\) |
−0.571877 | + | 0.820339i | \(0.693785\pi\) | |||||||
\(104\) | 4.07573 | + | 12.5438i | 0.399658 | + | 1.23002i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.5665 | + | 8.40352i | 1.12343 | + | 0.816222i | ||||
\(107\) | 2.64496 | − | 1.92168i | 0.255698 | − | 0.185776i | −0.452550 | − | 0.891739i | \(-0.649486\pi\) |
0.708248 | + | 0.705963i | \(0.249486\pi\) | |||||||
\(108\) | 0.0123209 | − | 0.0379199i | 0.00118558 | − | 0.00364885i | ||||
\(109\) | −2.84638 | −0.272634 | −0.136317 | − | 0.990665i | \(-0.543527\pi\) | ||||
−0.136317 | + | 0.990665i | \(0.543527\pi\) | |||||||
\(110\) | 5.83310 | − | 6.26476i | 0.556165 | − | 0.597321i | ||||
\(111\) | 4.53172 | 0.430132 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.7668 | + | 8.54906i | −1.10692 | + | 0.804228i | −0.982177 | − | 0.187961i | \(-0.939812\pi\) |
−0.124748 | + | 0.992188i | \(0.539812\pi\) | |||||||
\(114\) | 14.3087 | + | 10.3959i | 1.34013 | + | 0.973663i | ||||
\(115\) | −0.407290 | − | 1.25351i | −0.0379799 | − | 0.116890i | ||||
\(116\) | 0.00505954 | + | 0.0155717i | 0.000469767 | + | 0.00144579i | ||||
\(117\) | −6.31686 | − | 4.58947i | −0.583994 | − | 0.424296i | ||||
\(118\) | 8.75705 | − | 6.36237i | 0.806152 | − | 0.585704i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 11.2450 | 1.02652 | ||||||||
\(121\) | −0.783964 | − | 10.9720i | −0.0712695 | − | 0.997457i | ||||
\(122\) | −8.84474 | −0.800765 | ||||||||
\(123\) | 0.612797 | − | 1.88600i | 0.0552541 | − | 0.170054i | ||||
\(124\) | 0.0147756 | − | 0.0107351i | 0.00132689 | − | 0.000964044i | ||||
\(125\) | 9.84690 | + | 7.15419i | 0.880734 | + | 0.639890i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.55524 | + | 4.78655i | 0.138006 | + | 0.424737i | 0.996045 | − | 0.0888458i | \(-0.0283178\pi\) |
−0.858040 | + | 0.513583i | \(0.828318\pi\) | |||||||
\(128\) | 9.05595 | + | 6.57953i | 0.800440 | + | 0.581554i | ||||
\(129\) | −14.0433 | + | 10.2031i | −1.23645 | + | 0.898331i | ||||
\(130\) | −3.70624 | + | 11.4066i | −0.325059 | + | 1.00043i | ||||
\(131\) | 0.180053 | 0.0157313 | 0.00786565 | − | 0.999969i | \(-0.497496\pi\) | ||||
0.00786565 | + | 0.999969i | \(0.497496\pi\) | |||||||
\(132\) | 0.0682787 | − | 0.0733313i | 0.00594290 | − | 0.00638267i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.73581 | − | 20.7307i | 0.581885 | − | 1.79086i | ||||
\(135\) | 4.23032 | − | 3.07350i | 0.364088 | − | 0.264525i | ||||
\(136\) | −12.5605 | − | 9.12574i | −1.07705 | − | 0.782526i | ||||
\(137\) | 2.57224 | + | 7.91655i | 0.219762 | + | 0.676357i | 0.998781 | + | 0.0493570i | \(0.0157172\pi\) |
−0.779020 | + | 0.627000i | \(0.784283\pi\) | |||||||
\(138\) | 0.678031 | + | 2.08677i | 0.0577179 | + | 0.177637i | ||||
\(139\) | −5.63172 | − | 4.09169i | −0.477677 | − | 0.347052i | 0.322749 | − | 0.946485i | \(-0.395393\pi\) |
−0.800425 | + | 0.599432i | \(0.795393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.99497 | + | 12.2953i | −0.336438 | + | 1.03545i | ||||
\(142\) | −19.5915 | −1.64408 | ||||||||
\(143\) | 7.48237 | + | 13.4744i | 0.625707 | + | 1.12679i | ||||
\(144\) | −6.67362 | −0.556135 | ||||||||
\(145\) | −0.663538 | + | 2.04216i | −0.0551038 | + | 0.169592i | ||||
\(146\) | −6.85740 | + | 4.98219i | −0.567523 | + | 0.412329i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.00903937 | − | 0.0278203i | −0.000743031 | − | 0.00228682i | ||||
\(149\) | −0.993277 | − | 3.05699i | −0.0813724 | − | 0.250439i | 0.902091 | − | 0.431546i | \(-0.142032\pi\) |
−0.983463 | + | 0.181108i | \(0.942032\pi\) | |||||||
\(150\) | −4.05995 | − | 2.94972i | −0.331493 | − | 0.240844i | ||||
\(151\) | −18.0144 | + | 13.0882i | −1.46599 | + | 1.06510i | −0.484239 | + | 0.874936i | \(0.660903\pi\) |
−0.981752 | + | 0.190168i | \(0.939097\pi\) | |||||||
\(152\) | 5.08796 | − | 15.6591i | 0.412688 | − | 1.27012i | ||||
\(153\) | 9.19115 | 0.743061 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.39521 | 0.192388 | ||||||||
\(156\) | −0.0433830 | + | 0.133519i | −0.00347342 | + | 0.0106901i | ||||
\(157\) | 10.7233 | − | 7.79096i | 0.855816 | − | 0.621786i | −0.0709277 | − | 0.997481i | \(-0.522596\pi\) |
0.926743 | + | 0.375695i | \(0.122596\pi\) | |||||||
\(158\) | −17.8326 | − | 12.9561i | −1.41868 | − | 1.03073i | ||||
\(159\) | 6.78211 | + | 20.8732i | 0.537856 | + | 1.65535i | ||||
\(160\) | −0.0447049 | − | 0.137588i | −0.00353423 | − | 0.0108773i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.7893 | + | 9.29200i | −1.00483 | + | 0.730048i | ||||
\(163\) | 4.23920 | − | 13.0469i | 0.332040 | − | 1.02191i | −0.636122 | − | 0.771589i | \(-0.719462\pi\) |
0.968162 | − | 0.250325i | \(-0.0805375\pi\) | |||||||
\(164\) | −0.0128005 | −0.000999552 | ||||||||
\(165\) | 12.8971 | − | 2.51709i | 1.00404 | − | 0.195955i | ||||
\(166\) | −6.16657 | −0.478619 | ||||||||
\(167\) | −2.87651 | + | 8.85300i | −0.222591 | + | 0.685066i | 0.775936 | + | 0.630812i | \(0.217278\pi\) |
−0.998527 | + | 0.0542539i | \(0.982722\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.95361 | − | 5.05209i | −0.534893 | − | 0.388623i | ||||
\(170\) | −4.36275 | − | 13.4272i | −0.334608 | − | 1.02982i | ||||
\(171\) | 3.01206 | + | 9.27018i | 0.230338 | + | 0.708908i | ||||
\(172\) | 0.0906490 | + | 0.0658604i | 0.00691192 | + | 0.00502181i | ||||
\(173\) | 8.49927 | − | 6.17508i | 0.646188 | − | 0.469483i | −0.215783 | − | 0.976441i | \(-0.569230\pi\) |
0.861970 | + | 0.506959i | \(0.169230\pi\) | |||||||
\(174\) | 1.10462 | − | 3.39966i | 0.0837409 | − | 0.257728i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.9432 | + | 5.55819i | 0.900254 | + | 0.418964i | ||||
\(177\) | 16.6165 | 1.24897 | ||||||||
\(178\) | 6.68200 | − | 20.5651i | 0.500837 | − | 1.54142i | ||||
\(179\) | 6.73370 | − | 4.89232i | 0.503300 | − | 0.365669i | −0.306976 | − | 0.951717i | \(-0.599317\pi\) |
0.810276 | + | 0.586048i | \(0.199317\pi\) | |||||||
\(180\) | 0.0347639 | + | 0.0252575i | 0.00259115 | + | 0.00188258i | ||||
\(181\) | 4.57437 | + | 14.0785i | 0.340010 | + | 1.04644i | 0.964201 | + | 0.265172i | \(0.0854286\pi\) |
−0.624191 | + | 0.781272i | \(0.714571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.9845 | − | 7.98074i | −0.812001 | − | 0.589953i | ||||
\(184\) | 1.65251 | − | 1.20062i | 0.121825 | − | 0.0885107i | ||||
\(185\) | 1.18547 | − | 3.64852i | 0.0871578 | − | 0.268244i | ||||
\(186\) | −3.98740 | −0.292370 | ||||||||
\(187\) | −16.4486 | − | 7.65494i | −1.20284 | − | 0.559785i | ||||
\(188\) | 0.0834496 | 0.00608619 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.1129 | − | 8.80052i | 0.878760 | − | 0.638457i | ||||
\(191\) | 7.77203 | + | 5.64671i | 0.562364 | + | 0.408582i | 0.832324 | − | 0.554290i | \(-0.187010\pi\) |
−0.269959 | + | 0.962872i | \(0.587010\pi\) | |||||||
\(192\) | 5.38499 | + | 16.5733i | 0.388628 | + | 1.19607i | ||||
\(193\) | −0.459758 | − | 1.41499i | −0.0330941 | − | 0.101853i | 0.933145 | − | 0.359500i | \(-0.117053\pi\) |
−0.966239 | + | 0.257647i | \(0.917053\pi\) | |||||||
\(194\) | −2.74911 | − | 1.99734i | −0.197374 | − | 0.143401i | ||||
\(195\) | −14.8953 | + | 10.8221i | −1.06667 | + | 0.774983i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0434 | −1.00055 | −0.500274 | − | 0.865867i | \(-0.666767\pi\) | ||||
−0.500274 | + | 0.865867i | \(0.666767\pi\) | |||||||
\(198\) | −7.70793 | + | 1.50434i | −0.547779 | + | 0.106909i | ||||
\(199\) | 4.28729 | 0.303918 | 0.151959 | − | 0.988387i | \(-0.451442\pi\) | ||||
0.151959 | + | 0.988387i | \(0.451442\pi\) | |||||||
\(200\) | −1.44366 | + | 4.44312i | −0.102082 | + | 0.314176i | ||||
\(201\) | 27.0710 | − | 19.6682i | 1.90944 | − | 1.38729i | ||||
\(202\) | −13.5627 | − | 9.85391i | −0.954271 | − | 0.693318i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0510676 | − | 0.157170i | −0.00357545 | − | 0.0110041i | ||||
\(205\) | −1.35812 | − | 0.986734i | −0.0948554 | − | 0.0689165i | ||||
\(206\) | −0.451846 | + | 0.328285i | −0.0314816 | + | 0.0228727i | ||||
\(207\) | −0.373671 | + | 1.15004i | −0.0259719 | + | 0.0799333i | ||||
\(208\) | −18.4575 | −1.27980 | ||||||||
\(209\) | 2.33032 | − | 19.0987i | 0.161192 | − | 1.32108i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.449704 | + | 1.38405i | −0.0309589 | + | 0.0952816i | −0.965342 | − | 0.260988i | \(-0.915952\pi\) |
0.934383 | + | 0.356270i | \(0.115952\pi\) | |||||||
\(212\) | 0.114613 | − | 0.0832710i | 0.00787163 | − | 0.00571907i | ||||
\(213\) | −24.3313 | − | 17.6777i | −1.66715 | − | 1.21126i | ||||
\(214\) | 1.42376 | + | 4.38189i | 0.0973264 | + | 0.299540i | ||||
\(215\) | 4.54090 | + | 13.9755i | 0.309687 | + | 0.953118i | ||||
\(216\) | 6.55599 | + | 4.76320i | 0.446079 | + | 0.324095i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.23957 | − | 3.81499i | 0.0839540 | − | 0.258384i | ||||
\(219\) | −13.0119 | −0.879264 | ||||||||
\(220\) | −0.0411782 | − | 0.0741547i | −0.00277623 | − | 0.00499951i | ||||
\(221\) | 25.4204 | 1.70996 | ||||||||
\(222\) | −1.97351 | + | 6.07383i | −0.132453 | + | 0.407649i | ||||
\(223\) | −3.92893 | + | 2.85453i | −0.263101 | + | 0.191154i | −0.711513 | − | 0.702673i | \(-0.751990\pi\) |
0.448412 | + | 0.893827i | \(0.351990\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.854642 | − | 2.63032i | −0.0569761 | − | 0.175354i | ||||
\(226\) | −6.33396 | − | 19.4939i | −0.421329 | − | 1.29672i | ||||
\(227\) | 0.321296 | + | 0.233435i | 0.0213252 | + | 0.0154936i | 0.598397 | − | 0.801200i | \(-0.295805\pi\) |
−0.577072 | + | 0.816694i | \(0.695805\pi\) | |||||||
\(228\) | 0.141786 | − | 0.103013i | 0.00938999 | − | 0.00682223i | ||||
\(229\) | −0.676634 | + | 2.08246i | −0.0447132 | + | 0.137613i | −0.970921 | − | 0.239401i | \(-0.923049\pi\) |
0.926208 | + | 0.377014i | \(0.123049\pi\) | |||||||
\(230\) | 1.85744 | 0.122476 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.32773 | −0.218476 | ||||||||
\(233\) | −0.389410 | + | 1.19848i | −0.0255111 | + | 0.0785150i | −0.963001 | − | 0.269496i | \(-0.913143\pi\) |
0.937490 | + | 0.348011i | \(0.113143\pi\) | |||||||
\(234\) | 8.90215 | − | 6.46779i | 0.581952 | − | 0.422813i | ||||
\(235\) | 8.85393 | + | 6.43276i | 0.577567 | + | 0.419627i | ||||
\(236\) | −0.0331448 | − | 0.102009i | −0.00215754 | − | 0.00664023i | ||||
\(237\) | −10.4563 | − | 32.1812i | −0.679210 | − | 2.09039i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.02997 | − | 6.56066i | 0.584100 | − | 0.424374i | −0.256100 | − | 0.966650i | \(-0.582438\pi\) |
0.840200 | + | 0.542277i | \(0.182438\pi\) | |||||||
\(240\) | −4.86285 | + | 14.9663i | −0.313896 | + | 0.966072i | ||||
\(241\) | 21.4843 | 1.38392 | 0.691962 | − | 0.721934i | \(-0.256746\pi\) | ||||
0.691962 | + | 0.721934i | \(0.256746\pi\) | |||||||
\(242\) | 15.0471 | + | 3.72744i | 0.967267 | + | 0.239609i | ||||
\(243\) | −15.7022 | −1.00730 | ||||||||
\(244\) | −0.0270832 | + | 0.0833535i | −0.00173382 | + | 0.00533616i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.26092 | + | 1.64266i | 0.144151 | + | 0.104732i | ||||
\(247\) | 8.33060 | + | 25.6390i | 0.530063 | + | 1.63137i | ||||
\(248\) | 1.14707 | + | 3.53032i | 0.0728391 | + | 0.224176i | ||||
\(249\) | −7.65846 | − | 5.56419i | −0.485335 | − | 0.352616i | ||||
\(250\) | −13.8769 | + | 10.0822i | −0.877653 | + | 0.637652i | ||||
\(251\) | 0.130968 | − | 0.403077i | 0.00826660 | − | 0.0254420i | −0.946838 | − | 0.321710i | \(-0.895742\pi\) |
0.955105 | + | 0.296268i | \(0.0957423\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.62655 | − | 1.74691i | 0.102260 | − | 0.109828i | ||||
\(254\) | −7.09267 | −0.445033 | ||||||||
\(255\) | 6.69730 | − | 20.6122i | 0.419401 | − | 1.29078i | ||||
\(256\) | 0.271127 | − | 0.196986i | 0.0169455 | − | 0.0123116i | ||||
\(257\) | 14.1093 | + | 10.2510i | 0.880115 | + | 0.639441i | 0.933282 | − | 0.359145i | \(-0.116932\pi\) |
−0.0531672 | + | 0.998586i | \(0.516932\pi\) | |||||||
\(258\) | −7.55942 | − | 23.2655i | −0.470629 | − | 1.44845i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.0961483 | + | 0.0698558i | 0.00596286 | + | 0.00433227i | ||||
\(261\) | 1.59377 | − | 1.15794i | 0.0986521 | − | 0.0716749i | ||||
\(262\) | −0.0784109 | + | 0.241324i | −0.00484424 | + | 0.0149090i | ||||
\(263\) | 1.51519 | 0.0934307 | 0.0467153 | − | 0.998908i | \(-0.485125\pi\) | ||||
0.0467153 | + | 0.998908i | \(0.485125\pi\) | |||||||
\(264\) | 9.88643 | + | 17.8037i | 0.608468 | + | 1.09574i | ||||
\(265\) | 18.5793 | 1.14132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.8548 | − | 19.5111i | 1.64348 | − | 1.19406i | ||||
\(268\) | −0.174742 | − | 0.126957i | −0.0106741 | − | 0.00775516i | ||||
\(269\) | 0.627622 | + | 1.93162i | 0.0382668 | + | 0.117773i | 0.968365 | − | 0.249538i | \(-0.0802786\pi\) |
−0.930098 | + | 0.367311i | \(0.880279\pi\) | |||||||
\(270\) | 2.27715 | + | 7.00834i | 0.138583 | + | 0.426514i | ||||
\(271\) | 6.15212 | + | 4.46978i | 0.373715 | + | 0.271520i | 0.758750 | − | 0.651382i | \(-0.225811\pi\) |
−0.385035 | + | 0.922902i | \(0.625811\pi\) | |||||||
\(272\) | 17.5775 | − | 12.7708i | 1.06579 | − | 0.774344i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.7307 | −0.708676 | ||||||||
\(275\) | −0.661205 | + | 5.41905i | −0.0398722 | + | 0.326781i | ||||
\(276\) | 0.0217420 | 0.00130872 | ||||||||
\(277\) | 4.45813 | − | 13.7207i | 0.267863 | − | 0.824398i | −0.723157 | − | 0.690684i | \(-0.757310\pi\) |
0.991020 | − | 0.133714i | \(-0.0426903\pi\) | |||||||
\(278\) | 7.93661 | − | 5.76628i | 0.476006 | − | 0.345839i | ||||
\(279\) | −1.77781 | − | 1.29166i | −0.106435 | − | 0.0773295i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.48494 | + | 16.8809i | 0.327204 | + | 1.00703i | 0.970436 | + | 0.241359i | \(0.0775933\pi\) |
−0.643232 | + | 0.765672i | \(0.722407\pi\) | |||||||
\(282\) | −14.7395 | − | 10.7089i | −0.877725 | − | 0.637704i | ||||
\(283\) | −25.1897 | + | 18.3014i | −1.49737 | + | 1.08790i | −0.525956 | + | 0.850512i | \(0.676292\pi\) |
−0.971414 | + | 0.237392i | \(0.923708\pi\) | |||||||
\(284\) | −0.0599905 | + | 0.184632i | −0.00355978 | + | 0.0109559i | ||||
\(285\) | 22.9842 | 1.36147 | ||||||||
\(286\) | −21.3182 | + | 4.16062i | −1.26057 | + | 0.246022i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.0410148 | + | 0.126231i | −0.00241682 | + | 0.00743821i | ||||
\(289\) | −10.4551 | + | 7.59609i | −0.615007 | + | 0.446829i | ||||
\(290\) | −2.44813 | − | 1.77867i | −0.143759 | − | 0.104447i | ||||
\(291\) | −1.61197 | − | 4.96112i | −0.0944951 | − | 0.290826i | ||||
\(292\) | 0.0259547 | + | 0.0798805i | 0.00151889 | + | 0.00467465i | ||||
\(293\) | −19.4409 | − | 14.1247i | −1.13575 | − | 0.825171i | −0.149229 | − | 0.988803i | \(-0.547679\pi\) |
−0.986522 | + | 0.163632i | \(0.947679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.34679 | − | 13.3781i | 0.253080 | − | 0.778901i | ||||
\(296\) | 5.94532 | 0.345565 | ||||||||
\(297\) | 8.58540 | + | 3.99552i | 0.498176 | + | 0.231843i | ||||
\(298\) | 4.52983 | 0.262406 | ||||||||
\(299\) | −1.03348 | + | 3.18072i | −0.0597676 | + | 0.183946i | ||||
\(300\) | −0.0402302 | + | 0.0292290i | −0.00232269 | + | 0.00168754i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.69701 | − | 29.8443i | −0.558000 | − | 1.71735i | ||||
\(303\) | −7.95265 | − | 24.4757i | −0.456868 | − | 1.40609i | ||||
\(304\) | 18.6410 | + | 13.5435i | 1.06914 | + | 0.776772i | ||||
\(305\) | −9.29885 | + | 6.75601i | −0.532450 | + | 0.386848i | ||||
\(306\) | −4.00263 | + | 12.3188i | −0.228815 | + | 0.704221i | ||||
\(307\) | 5.46298 | 0.311789 | 0.155894 | − | 0.987774i | \(-0.450174\pi\) | ||||
0.155894 | + | 0.987774i | \(0.450174\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.857378 | −0.0487745 | ||||||||
\(310\) | −1.04308 | + | 3.21028i | −0.0592431 | + | 0.182332i | ||||
\(311\) | 11.2360 | − | 8.16342i | 0.637134 | − | 0.462905i | −0.221730 | − | 0.975108i | \(-0.571170\pi\) |
0.858864 | + | 0.512203i | \(0.171170\pi\) | |||||||
\(312\) | −23.0842 | − | 16.7716i | −1.30688 | − | 0.949506i | ||||
\(313\) | −8.48207 | − | 26.1051i | −0.479435 | − | 1.47555i | −0.839882 | − | 0.542770i | \(-0.817376\pi\) |
0.360447 | − | 0.932780i | \(-0.382624\pi\) | |||||||
\(314\) | 5.77229 | + | 17.7653i | 0.325749 | + | 1.00255i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.176704 | + | 0.128383i | −0.00994038 | + | 0.00722211i | ||||
\(317\) | 2.41828 | − | 7.44269i | 0.135824 | − | 0.418023i | −0.859893 | − | 0.510474i | \(-0.829470\pi\) |
0.995717 | + | 0.0924507i | \(0.0294701\pi\) | |||||||
\(318\) | −30.9297 | −1.73445 | ||||||||
\(319\) | −3.81665 | + | 0.744885i | −0.213691 | + | 0.0417056i | ||||
\(320\) | 14.7520 | 0.824659 | ||||||||
\(321\) | −2.18563 | + | 6.72669i | −0.121990 | + | 0.375447i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.6731 | − | 18.6526i | −1.42849 | − | 1.03786i | ||||
\(324\) | 0.0484067 | + | 0.148980i | 0.00268926 | + | 0.00827669i | ||||
\(325\) | −2.36372 | − | 7.27479i | −0.131116 | − | 0.403533i | ||||
\(326\) | 15.6406 | + | 11.3635i | 0.866252 | + | 0.629369i | ||||
\(327\) | 4.98178 | − | 3.61947i | 0.275493 | − | 0.200157i | ||||
\(328\) | 0.803950 | − | 2.47430i | 0.0443907 | − | 0.136621i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.24288 | + | 18.3820i | −0.123467 | + | 1.01190i | ||||
\(331\) | −28.1462 | −1.54705 | −0.773527 | − | 0.633764i | \(-0.781509\pi\) | ||||
−0.773527 | + | 0.633764i | \(0.781509\pi\) | |||||||
\(332\) | −0.0188825 | + | 0.0581143i | −0.00103631 | + | 0.00318943i | ||||
\(333\) | −2.84743 | + | 2.06878i | −0.156038 | + | 0.113368i | ||||
\(334\) | −10.6129 | − | 7.71075i | −0.580714 | − | 0.421913i | ||||
\(335\) | −8.75338 | − | 26.9401i | −0.478248 | − | 1.47190i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.2084 | + | 14.6823i | 1.10082 | + | 0.799793i | 0.981194 | − | 0.193025i | \(-0.0618300\pi\) |
0.119628 | + | 0.992819i | \(0.461830\pi\) | |||||||
\(338\) | 9.79950 | − | 7.11975i | 0.533022 | − | 0.387263i | ||||
\(339\) | 9.72333 | − | 29.9253i | 0.528099 | − | 1.62532i | ||||
\(340\) | −0.139898 | −0.00758701 | ||||||||
\(341\) | 2.10583 | + | 3.79224i | 0.114037 | + | 0.205361i | ||||
\(342\) | −13.7365 | −0.742783 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.4239 | + | 13.3858i | −0.993352 | + | 0.721713i | ||||
\(345\) | 2.30681 | + | 1.67599i | 0.124194 | + | 0.0902325i | ||||
\(346\) | 4.57509 | + | 14.0807i | 0.245959 | + | 0.756983i | ||||
\(347\) | 6.38096 | + | 19.6386i | 0.342548 | + | 1.05425i | 0.962883 | + | 0.269918i | \(0.0869965\pi\) |
−0.620335 | + | 0.784337i | \(0.713003\pi\) | |||||||
\(348\) | −0.0286563 | − | 0.0208200i | −0.00153614 | − | 0.00111607i | ||||
\(349\) | −4.85185 | + | 3.52507i | −0.259713 | + | 0.188693i | −0.710021 | − | 0.704181i | \(-0.751314\pi\) |
0.450307 | + | 0.892874i | \(0.351314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.2682 | −0.708206 | ||||||||
\(352\) | 0.178533 | − | 0.191745i | 0.00951585 | − | 0.0102200i | ||||
\(353\) | −24.0382 | −1.27942 | −0.639712 | − | 0.768615i | \(-0.720946\pi\) | ||||
−0.639712 | + | 0.768615i | \(0.720946\pi\) | |||||||
\(354\) | −7.23629 | + | 22.2710i | −0.384604 | + | 1.18369i | ||||
\(355\) | −20.5974 | + | 14.9649i | −1.09320 | + | 0.794253i | ||||
\(356\) | −0.173346 | − | 0.125943i | −0.00918732 | − | 0.00667498i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.62470 | + | 11.1557i | 0.191571 | + | 0.589596i | ||||
\(359\) | 8.85883 | + | 6.43632i | 0.467551 | + | 0.339696i | 0.796486 | − | 0.604657i | \(-0.206690\pi\) |
−0.328935 | + | 0.944353i | \(0.606690\pi\) | |||||||
\(360\) | −7.06559 | + | 5.13345i | −0.372389 | + | 0.270557i | ||||
\(361\) | 4.52822 | − | 13.9364i | 0.238328 | − | 0.733497i | ||||
\(362\) | −20.8613 | −1.09645 | ||||||||
\(363\) | 15.3242 | + | 18.2065i | 0.804311 | + | 0.955593i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.40385 | + | 10.4760i | −0.178166 | + | 0.548338i | ||||
\(366\) | 15.4802 | − | 11.2470i | 0.809161 | − | 0.587890i | ||||
\(367\) | 8.58995 | + | 6.24096i | 0.448392 | + | 0.325776i | 0.788960 | − | 0.614444i | \(-0.210620\pi\) |
−0.340569 | + | 0.940220i | \(0.610620\pi\) | |||||||
\(368\) | 0.883322 | + | 2.71859i | 0.0460463 | + | 0.141716i | ||||
\(369\) | 0.475937 | + | 1.46478i | 0.0247763 | + | 0.0762535i | ||||
\(370\) | 4.37382 | + | 3.17777i | 0.227384 | + | 0.165204i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.0122097 | + | 0.0375775i | −0.000633042 | + | 0.00194830i | ||||
\(373\) | 36.6036 | 1.89526 | 0.947631 | − | 0.319367i | \(-0.103470\pi\) | ||||
0.947631 | + | 0.319367i | \(0.103470\pi\) | |||||||
\(374\) | 17.4230 | − | 18.7124i | 0.900924 | − | 0.967593i | ||||
\(375\) | −26.3315 | −1.35975 | ||||||||
\(376\) | −5.24115 | + | 16.1306i | −0.270292 | + | 0.831872i | ||||
\(377\) | 4.40797 | − | 3.20258i | 0.227022 | − | 0.164941i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.91147 | − | 12.0383i | −0.200919 | − | 0.618364i | −0.999856 | − | 0.0169501i | \(-0.994604\pi\) |
0.798938 | − | 0.601414i | \(-0.205396\pi\) | |||||||
\(380\) | −0.0458463 | − | 0.141100i | −0.00235187 | − | 0.00723830i | ||||
\(381\) | −8.80860 | − | 6.39982i | −0.451278 | − | 0.327873i | ||||
\(382\) | −10.9529 | + | 7.95773i | −0.560398 | + | 0.407153i | ||||
\(383\) | 4.77984 | − | 14.7108i | 0.244238 | − | 0.751688i | −0.751522 | − | 0.659708i | \(-0.770680\pi\) |
0.995761 | − | 0.0919809i | \(-0.0293199\pi\) | |||||||
\(384\) | −24.2164 | −1.23579 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.09672 | 0.106720 | ||||||||
\(387\) | 4.16608 | − | 12.8219i | 0.211774 | − | 0.651773i | ||||
\(388\) | −0.0272411 | + | 0.0197918i | −0.00138296 | + | 0.00100478i | ||||
\(389\) | 10.2850 | + | 7.47249i | 0.521470 | + | 0.378870i | 0.817157 | − | 0.576415i | \(-0.195549\pi\) |
−0.295687 | + | 0.955285i | \(0.595549\pi\) | |||||||
\(390\) | −8.01801 | − | 24.6769i | −0.406008 | − | 1.24956i | ||||
\(391\) | −1.21654 | − | 3.74414i | −0.0615232 | − | 0.189349i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.315131 | + | 0.228956i | −0.0158963 | + | 0.0115493i | ||||
\(394\) | 6.11571 | − | 18.8222i | 0.308105 | − | 0.948250i | ||||
\(395\) | −28.6446 | −1.44127 | ||||||||
\(396\) | −0.00942522 | + | 0.0772465i | −0.000473635 | + | 0.00388178i | ||||
\(397\) | 18.9574 | 0.951445 | 0.475722 | − | 0.879596i | \(-0.342187\pi\) | ||||
0.475722 | + | 0.879596i | \(0.342187\pi\) | |||||||
\(398\) | −1.86706 | + | 5.74622i | −0.0935873 | + | 0.288032i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.28919 | − | 3.84282i | −0.264460 | − | 0.192141i | ||||
\(401\) | −2.68291 | − | 8.25715i | −0.133978 | − | 0.412343i | 0.861451 | − | 0.507840i | \(-0.169556\pi\) |
−0.995430 | + | 0.0954974i | \(0.969556\pi\) | |||||||
\(402\) | 14.5721 | + | 44.8484i | 0.726791 | + | 2.23683i | ||||
\(403\) | −4.91698 | − | 3.57240i | −0.244932 | − | 0.177954i | ||||
\(404\) | −0.134394 | + | 0.0976429i | −0.00668635 | + | 0.00485792i | ||||
\(405\) | −6.34833 | + | 19.5381i | −0.315451 | + | 0.970858i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.81881 | − | 1.33081i | 0.337996 | − | 0.0659658i | ||||
\(408\) | 33.5879 | 1.66285 | ||||||||
\(409\) | −1.76574 | + | 5.43440i | −0.0873104 | + | 0.268714i | −0.985173 | − | 0.171561i | \(-0.945119\pi\) |
0.897863 | + | 0.440275i | \(0.145119\pi\) | |||||||
\(410\) | 1.91396 | − | 1.39057i | 0.0945237 | − | 0.0686755i | ||||
\(411\) | −14.5687 | − | 10.5848i | −0.718620 | − | 0.522108i | ||||
\(412\) | 0.00171020 | + | 0.00526346i | 8.42556e−5 | + | 0.000259312i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.37866 | − | 1.00166i | −0.0677575 | − | 0.0492287i | ||||
\(415\) | −6.48318 | + | 4.71031i | −0.318247 | + | 0.231220i | ||||
\(416\) | −0.113437 | + | 0.349122i | −0.00556169 | + | 0.0171171i | ||||
\(417\) | 15.0597 | 0.737477 | ||||||||
\(418\) | 24.5830 | + | 11.4406i | 1.20239 | + | 0.559576i | ||||
\(419\) | 27.1909 | 1.32836 | 0.664181 | − | 0.747571i | \(-0.268780\pi\) | ||||
0.664181 | + | 0.747571i | \(0.268780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3881 | − | 14.0863i | 0.944921 | − | 0.686525i | −0.00467947 | − | 0.999989i | \(-0.501490\pi\) |
0.949600 | + | 0.313464i | \(0.101490\pi\) | |||||||
\(422\) | −1.65919 | − | 1.20547i | −0.0807679 | − | 0.0586813i | ||||
\(423\) | −3.10275 | − | 9.54928i | −0.150861 | − | 0.464302i | ||||
\(424\) | 8.89768 | + | 27.3842i | 0.432110 | + | 1.32990i | ||||
\(425\) | 7.28447 | + | 5.29248i | 0.353349 | + | 0.256723i | ||||
\(426\) | 34.2893 | − | 24.9126i | 1.66132 | − | 1.20702i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.0456549 | 0.00220681 | ||||||||
\(429\) | −30.2299 | − | 14.0685i | −1.45951 | − | 0.679235i | ||||
\(430\) | −20.7087 | −0.998663 | ||||||||
\(431\) | 5.09049 | − | 15.6669i | 0.245200 | − | 0.754649i | −0.750403 | − | 0.660980i | \(-0.770141\pi\) |
0.995603 | − | 0.0936683i | \(-0.0298593\pi\) | |||||||
\(432\) | −9.17463 | + | 6.66576i | −0.441415 | + | 0.320706i | ||||
\(433\) | 16.2539 | + | 11.8092i | 0.781113 | + | 0.567512i | 0.905313 | − | 0.424745i | \(-0.139636\pi\) |
−0.124200 | + | 0.992257i | \(0.539636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.43548 | − | 4.41797i | −0.0688262 | − | 0.211825i | ||||
\(436\) | −0.0321571 | − | 0.0233635i | −0.00154005 | − | 0.00111891i | ||||
\(437\) | 3.37765 | − | 2.45401i | 0.161575 | − | 0.117391i | ||||
\(438\) | 5.66653 | − | 17.4398i | 0.270757 | − | 0.833306i | ||||
\(439\) | −26.7682 | −1.27758 | −0.638788 | − | 0.769383i | \(-0.720564\pi\) | ||||
−0.638788 | + | 0.769383i | \(0.720564\pi\) | |||||||
\(440\) | 16.9201 | − | 3.30226i | 0.806636 | − | 0.157429i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.0703 | + | 34.0708i | −0.526559 | + | 1.62058i | ||||
\(443\) | −21.2086 | + | 15.4090i | −1.00765 | + | 0.732103i | −0.963716 | − | 0.266931i | \(-0.913990\pi\) |
−0.0439378 | + | 0.999034i | \(0.513990\pi\) | |||||||
\(444\) | 0.0511972 | + | 0.0371970i | 0.00242971 | + | 0.00176529i | ||||
\(445\) | −8.68346 | − | 26.7249i | −0.411635 | − | 1.26688i | ||||
\(446\) | −2.11491 | − | 6.50903i | −0.100144 | − | 0.308212i | ||||
\(447\) | 5.62573 | + | 4.08733i | 0.266088 | + | 0.193324i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.01211 | − | 9.27033i | 0.142150 | − | 0.437494i | −0.854483 | − | 0.519479i | \(-0.826126\pi\) |
0.996634 | + | 0.0819851i | \(0.0261260\pi\) | |||||||
\(450\) | 3.89758 | 0.183734 | ||||||||
\(451\) | 0.368215 | − | 3.01779i | 0.0173386 | − | 0.142102i | ||||
\(452\) | −0.203107 | −0.00955336 | ||||||||
\(453\) | 14.8860 | − | 45.8143i | 0.699404 | − | 2.15254i | ||||
\(454\) | −0.452792 | + | 0.328973i | −0.0212506 | + | 0.0154395i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.0072 | + | 33.8767i | 0.515459 | + | 1.58642i | ||||
\(457\) | 3.67276 | + | 11.3036i | 0.171805 | + | 0.528760i | 0.999473 | − | 0.0324572i | \(-0.0103333\pi\) |
−0.827669 | + | 0.561217i | \(0.810333\pi\) | |||||||
\(458\) | −2.49645 | − | 1.81378i | −0.116651 | − | 0.0847522i | ||||
\(459\) | 12.6356 | − | 9.18033i | 0.589781 | − | 0.428501i | ||||
\(460\) | 0.00568760 | − | 0.0175046i | 0.000265186 | − | 0.000816158i | ||||
\(461\) | −9.14737 | −0.426035 | −0.213018 | − | 0.977048i | \(-0.568329\pi\) | ||||
−0.213018 | + | 0.977048i | \(0.568329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.9342 | 1.80943 | 0.904713 | − | 0.426021i | \(-0.140085\pi\) | ||||
0.904713 | + | 0.426021i | \(0.140085\pi\) | |||||||
\(464\) | 1.43907 | − | 4.42899i | 0.0668070 | − | 0.205611i | ||||
\(465\) | −4.19212 | + | 3.04575i | −0.194405 | + | 0.141243i | ||||
\(466\) | −1.43673 | − | 1.04385i | −0.0665553 | − | 0.0483552i | ||||
\(467\) | 6.42243 | + | 19.7662i | 0.297195 | + | 0.914671i | 0.982475 | + | 0.186392i | \(0.0596795\pi\) |
−0.685281 | + | 0.728279i | \(0.740320\pi\) | |||||||
\(468\) | −0.0336939 | − | 0.103699i | −0.00155750 | − | 0.00479350i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −12.4776 | + | 9.06548i | −0.575547 | + | 0.418159i | ||||
\(471\) | −8.86110 | + | 27.2717i | −0.408298 | + | 1.25661i | ||||
\(472\) | 21.7998 | 1.00342 | ||||||||
\(473\) | −18.1345 | + | 19.4765i | −0.833826 | + | 0.895529i | ||||
\(474\) | 47.6858 | 2.19028 | ||||||||
\(475\) | −2.95076 | + | 9.08152i | −0.135390 | + | 0.416689i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.7903 | − | 10.0192i | −0.631413 | − | 0.458748i | ||||
\(478\) | 4.86076 | + | 14.9599i | 0.222326 | + | 0.684249i | ||||
\(479\) | 7.58214 | + | 23.3354i | 0.346437 | + | 1.06622i | 0.960810 | + | 0.277207i | \(0.0894088\pi\) |
−0.614374 | + | 0.789015i | \(0.710591\pi\) | |||||||
\(480\) | 0.253200 | + | 0.183960i | 0.0115569 | + | 0.00839661i | ||||
\(481\) | −7.87527 | + | 5.72172i | −0.359081 | + | 0.260888i | ||||
\(482\) | −9.35614 | + | 28.7952i | −0.426161 | + | 1.31159i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0812030 | − | 0.130392i | 0.00369105 | − | 0.00592690i | ||||
\(485\) | −4.41591 | −0.200516 | ||||||||
\(486\) | 6.83811 | − | 21.0456i | 0.310183 | − | 0.954646i | ||||
\(487\) | 10.0086 | − | 7.27168i | 0.453533 | − | 0.329511i | −0.337456 | − | 0.941341i | \(-0.609566\pi\) |
0.790989 | + | 0.611830i | \(0.209566\pi\) | |||||||
\(488\) | −14.4110 | − | 10.4702i | −0.652356 | − | 0.473964i | ||||
\(489\) | 9.17101 | + | 28.2255i | 0.414727 | + | 1.27640i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3691 | − | 9.71320i | −0.603338 | − | 0.438350i | 0.243724 | − | 0.969845i | \(-0.421631\pi\) |
−0.847062 | + | 0.531494i | \(0.821631\pi\) | |||||||
\(492\) | 0.0224036 | − | 0.0162772i | 0.00101003 | − | 0.000733831i | ||||
\(493\) | −1.98194 | + | 6.09977i | −0.0892620 | + | 0.274720i | ||||
\(494\) | −37.9916 | −1.70932 | ||||||||
\(495\) | −6.95459 | + | 7.46924i | −0.312586 | + | 0.335717i | ||||
\(496\) | −5.19468 | −0.233248 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.7928 | − | 7.84144i | 0.483638 | − | 0.351383i | ||||
\(499\) | 11.1167 | + | 8.07673i | 0.497650 | + | 0.361564i | 0.808119 | − | 0.589020i | \(-0.200486\pi\) |
−0.310469 | + | 0.950584i | \(0.600486\pi\) | |||||||
\(500\) | 0.0525231 | + | 0.161649i | 0.00234890 | + | 0.00722918i | ||||
\(501\) | −6.22300 | − | 19.1524i | −0.278023 | − | 0.855667i | ||||
\(502\) | 0.483206 | + | 0.351070i | 0.0215665 | + | 0.0156690i | ||||
\(503\) | −18.2812 | + | 13.2820i | −0.815117 | + | 0.592217i | −0.915310 | − | 0.402751i | \(-0.868054\pi\) |
0.100193 | + | 0.994968i | \(0.468054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.7859 | −0.969461 | ||||||||
\(506\) | 1.63304 | + | 2.94081i | 0.0725973 | + | 0.130735i | ||||
\(507\) | 18.5946 | 0.825813 | ||||||||
\(508\) | −0.0217182 | + | 0.0668418i | −0.000963590 | + | 0.00296563i | ||||
\(509\) | −17.3644 | + | 12.6160i | −0.769664 | + | 0.559194i | −0.901859 | − | 0.432030i | \(-0.857798\pi\) |
0.132195 | + | 0.991224i | \(0.457798\pi\) | |||||||
\(510\) | 24.7098 | + | 17.9527i | 1.09417 | + | 0.794958i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7.06408 | + | 21.7410i | 0.312191 | + | 0.960825i | ||||
\(513\) | 13.4001 | + | 9.73576i | 0.591630 | + | 0.429844i | ||||
\(514\) | −19.8838 | + | 14.4464i | −0.877037 | + | 0.637204i | ||||
\(515\) | −0.224286 | + | 0.690280i | −0.00988321 | + | 0.0304174i | ||||
\(516\) | −0.242403 | −0.0106712 | ||||||||
\(517\) | −2.40048 | + | 19.6737i | −0.105573 | + | 0.865248i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.02327 | + | 21.6154i | −0.308287 | + | 0.948811i | ||||
\(520\) | −19.5416 | + | 14.1978i | −0.856957 | + | 0.622616i | ||||
\(521\) | 28.0822 | + | 20.4029i | 1.23031 | + | 0.893869i | 0.996913 | − | 0.0785132i | \(-0.0250173\pi\) |
0.233393 | + | 0.972383i | \(0.425017\pi\) | |||||||
\(522\) | 0.857916 | + | 2.64039i | 0.0375500 | + | 0.115567i | ||||
\(523\) | −6.09633 | − | 18.7626i | −0.266574 | − | 0.820430i | −0.991327 | − | 0.131421i | \(-0.958046\pi\) |
0.724753 | − | 0.689009i | \(-0.241954\pi\) | |||||||
\(524\) | 0.00203415 | + | 0.00147790i | 8.88624e−5 | + | 6.45623e-5i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.659847 | + | 2.03080i | −0.0287707 | + | 0.0885471i | ||||
\(527\) | 7.15430 | 0.311646 | ||||||||
\(528\) | −27.9710 | + | 5.45902i | −1.21728 | + | 0.237573i | ||||
\(529\) | −22.4821 | −0.977481 | ||||||||
\(530\) | −8.09105 | + | 24.9017i | −0.351453 | + | 1.08166i | ||||
\(531\) | −10.4407 | + | 7.58562i | −0.453088 | + | 0.329188i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.31632 | + | 4.05122i | 0.0570162 | + | 0.175478i | ||||
\(534\) | 14.4557 | + | 44.4901i | 0.625560 | + | 1.92527i | ||||
\(535\) | 4.84395 | + | 3.51933i | 0.209422 | + | 0.152154i | ||||
\(536\) | 35.5154 | − | 25.8034i | 1.53403 | − | 1.11454i | ||||
\(537\) | −5.56431 | + | 17.1252i | −0.240118 | + | 0.739006i | ||||
\(538\) | −2.86226 | −0.123401 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.0730199 | 0.00314227 | ||||||||
\(541\) | −1.71487 | + | 5.27782i | −0.0737279 | + | 0.226911i | −0.981129 | − | 0.193355i | \(-0.938063\pi\) |
0.907401 | + | 0.420266i | \(0.138063\pi\) | |||||||
\(542\) | −8.66998 | + | 6.29911i | −0.372408 | + | 0.270570i | ||||
\(543\) | −25.9083 | − | 18.8235i | −1.11183 | − | 0.807794i | ||||
\(544\) | −0.133530 | − | 0.410964i | −0.00572506 | − | 0.0176199i | ||||
\(545\) | −1.61085 | − | 4.95770i | −0.0690014 | − | 0.212364i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.83353 | − | 4.96485i | 0.292181 | − | 0.212282i | −0.432032 | − | 0.901858i | \(-0.642203\pi\) |
0.724213 | + | 0.689576i | \(0.242203\pi\) | |||||||
\(548\) | −0.0359201 | + | 0.110551i | −0.00153443 | + | 0.00472250i | ||||
\(549\) | 10.5453 | 0.450061 | ||||||||
\(550\) | −6.97518 | − | 3.24614i | −0.297422 | − | 0.138416i | ||||
\(551\) | −6.80173 | −0.289763 | ||||||||
\(552\) | −1.36553 | + | 4.20267i | −0.0581209 | + | 0.178878i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16.4483 | + | 11.9504i | 0.698822 | + | 0.507724i | ||||
\(555\) | 2.56463 | + | 7.89313i | 0.108863 | + | 0.335045i | ||||
\(556\) | −0.0300394 | − | 0.0924519i | −0.00127396 | − | 0.00392083i | ||||
\(557\) | 9.85665 | + | 7.16128i | 0.417640 | + | 0.303433i | 0.776687 | − | 0.629886i | \(-0.216898\pi\) |
−0.359048 | + | 0.933319i | \(0.616898\pi\) | |||||||
\(558\) | 2.50542 | − | 1.82029i | 0.106063 | − | 0.0770591i | ||||
\(559\) | 11.5223 | − | 35.4620i | 0.487342 | − | 1.49988i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.5226 | − | 7.51837i | 1.62643 | − | 0.317426i | ||||
\(562\) | −25.0140 | −1.05515 | ||||||||
\(563\) | 8.45270 | − | 26.0147i | 0.356239 | − | 1.09639i | −0.599049 | − | 0.800713i | \(-0.704454\pi\) |
0.955288 | − | 0.295678i | \(-0.0955456\pi\) | |||||||
\(564\) | −0.146055 | + | 0.106115i | −0.00615001 | + | 0.00446824i | ||||
\(565\) | −21.5495 | − | 15.6566i | −0.906594 | − | 0.658679i | ||||
\(566\) | −13.5594 | − | 41.7316i | −0.569944 | − | 1.75411i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.9211 | − | 23.1920i | −1.33938 | − | 0.973115i | ||||
\(569\) | −5.77253 | + | 4.19399i | −0.241997 | + | 0.175821i | −0.702173 | − | 0.712007i | \(-0.747786\pi\) |
0.460176 | + | 0.887828i | \(0.347786\pi\) | |||||||
\(570\) | −10.0093 | + | 30.8055i | −0.419245 | + | 1.29030i | ||||
\(571\) | 32.4839 | 1.35941 | 0.679705 | − | 0.733486i | \(-0.262108\pi\) | ||||
0.679705 | + | 0.733486i | \(0.262108\pi\) | |||||||
\(572\) | −0.0260678 | + | 0.213644i | −0.00108995 | + | 0.00893291i | ||||
\(573\) | −20.7831 | −0.868226 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.958373 | + | 0.696299i | −0.0399669 | + | 0.0290377i | ||||
\(576\) | −10.9495 | − | 7.95525i | −0.456228 | − | 0.331469i | ||||
\(577\) | −10.7482 | − | 33.0795i | −0.447453 | − | 1.37712i | −0.879771 | − | 0.475398i | \(-0.842304\pi\) |
0.432317 | − | 0.901721i | \(-0.357696\pi\) | |||||||
\(578\) | −5.62791 | − | 17.3209i | −0.234090 | − | 0.720456i | ||||
\(579\) | 2.60398 | + | 1.89190i | 0.108218 | + | 0.0786248i | ||||
\(580\) | −0.0242587 | + | 0.0176249i | −0.00100729 | + | 0.000731836i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.35135 | 0.304723 | ||||||||
\(583\) | 16.3347 | + | 29.4159i | 0.676513 | + | 1.21828i | ||||
\(584\) | −17.0708 | −0.706395 | ||||||||
\(585\) | 4.41882 | − | 13.5997i | 0.182696 | − | 0.562279i | ||||
\(586\) | 27.3975 | − | 19.9054i | 1.13178 | − | 0.822285i | ||||
\(587\) | −11.7105 | − | 8.50816i | −0.483343 | − | 0.351169i | 0.319276 | − | 0.947662i | \(-0.396560\pi\) |
−0.802618 | + | 0.596493i | \(0.796560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.34456 | + | 7.21581i | 0.0966059 | + | 0.297322i | ||||
\(590\) | 16.0375 | + | 11.6520i | 0.660255 | + | 0.479704i | ||||
\(591\) | 24.5789 | − | 17.8576i | 1.01104 | − | 0.734563i | ||||
\(592\) | −2.57103 | + | 7.91283i | −0.105669 | + | 0.325215i | ||||
\(593\) | 15.0291 | 0.617169 | 0.308585 | − | 0.951197i | \(-0.400145\pi\) | ||||
0.308585 | + | 0.951197i | \(0.400145\pi\) | |||||||
\(594\) | −9.09400 | + | 9.76696i | −0.373131 | + | 0.400743i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0138706 | − | 0.0426894i | 0.000568163 | − | 0.00174863i | ||||
\(597\) | −7.50366 | + | 5.45173i | −0.307104 | + | 0.223124i | ||||
\(598\) | −3.81303 | − | 2.77033i | −0.155926 | − | 0.113287i | ||||
\(599\) | 0.544010 | + | 1.67429i | 0.0222276 | + | 0.0684097i | 0.961555 | − | 0.274612i | \(-0.0885495\pi\) |
−0.939327 | + | 0.343022i | \(0.888549\pi\) | |||||||
\(600\) | −3.12318 | − | 9.61216i | −0.127503 | − | 0.392415i | ||||
\(601\) | 18.9605 | + | 13.7756i | 0.773415 | + | 0.561919i | 0.902995 | − | 0.429650i | \(-0.141363\pi\) |
−0.129581 | + | 0.991569i | \(0.541363\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.03085 | + | 24.7164i | −0.327042 | + | 1.00653i | ||||
\(604\) | −0.310948 | −0.0126523 | ||||||||
\(605\) | 18.6669 | − | 7.57487i | 0.758917 | − | 0.307962i | ||||
\(606\) | 36.2679 | 1.47328 | ||||||||
\(607\) | 7.81149 | − | 24.0413i | 0.317059 | − | 0.975806i | −0.657840 | − | 0.753158i | \(-0.728530\pi\) |
0.974899 | − | 0.222649i | \(-0.0714703\pi\) | |||||||
\(608\) | 0.370738 | − | 0.269357i | 0.0150354 | − | 0.0109239i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.00550 | − | 15.4053i | −0.202667 | − | 0.623744i | ||||
\(611\) | −8.58142 | − | 26.4109i | −0.347167 | − | 1.06847i | ||||
\(612\) | 0.103837 | + | 0.0754422i | 0.00419737 | + | 0.00304957i | ||||
\(613\) | −0.939222 | + | 0.682385i | −0.0379348 | + | 0.0275613i | −0.606591 | − | 0.795014i | \(-0.707463\pi\) |
0.568656 | + | 0.822575i | \(0.307463\pi\) | |||||||
\(614\) | −2.37906 | + | 7.32199i | −0.0960110 | + | 0.295492i | ||||
\(615\) | 3.63174 | 0.146446 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.9711 | 0.522197 | 0.261098 | − | 0.965312i | \(-0.415915\pi\) | ||||
0.261098 | + | 0.965312i | \(0.415915\pi\) | |||||||
\(618\) | 0.373377 | − | 1.14914i | 0.0150194 | − | 0.0462251i | ||||
\(619\) | 37.0465 | − | 26.9158i | 1.48902 | − | 1.08184i | 0.514517 | − | 0.857480i | \(-0.327971\pi\) |
0.974507 | − | 0.224358i | \(-0.0720286\pi\) | |||||||
\(620\) | 0.0270599 | + | 0.0196602i | 0.00108675 | + | 0.000789572i | ||||
\(621\) | 0.634978 | + | 1.95426i | 0.0254808 | + | 0.0784218i | ||||
\(622\) | 6.04824 | + | 18.6146i | 0.242512 | + | 0.746377i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 32.3046 | − | 23.4707i | 1.29322 | − | 0.939578i | ||||
\(625\) | −4.34493 | + | 13.3723i | −0.173797 | + | 0.534893i | ||||
\(626\) | 38.6824 | 1.54606 | ||||||||
\(627\) | 20.2074 | + | 36.3900i | 0.807006 | + | 1.45328i | ||||
\(628\) | 0.185097 | 0.00738615 | ||||||||
\(629\) | 3.54092 | − | 10.8978i | 0.141186 | − | 0.434525i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2103 | + | 7.41824i | 0.406467 | + | 0.295316i | 0.772170 | − | 0.635416i | \(-0.219171\pi\) |
−0.365703 | + | 0.930732i | \(0.619171\pi\) | |||||||
\(632\) | −13.7180 | − | 42.2196i | −0.545672 | − | 1.67941i | ||||
\(633\) | −0.972881 | − | 2.99422i | −0.0386685 | − | 0.119009i | ||||
\(634\) | 8.92225 | + | 6.48240i | 0.354348 | + | 0.257449i | ||||
\(635\) | −7.45682 | + | 5.41770i | −0.295915 | + | 0.214995i | ||||
\(636\) | −0.0947088 | + | 0.291484i | −0.00375545 | + | 0.0115581i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.663738 | − | 5.43981i | 0.0262776 | − | 0.215364i | ||||
\(639\) | 23.3582 | 0.924038 | ||||||||
\(640\) | −6.33488 | + | 19.4968i | −0.250408 | + | 0.770678i | ||||
\(641\) | −22.6175 | + | 16.4326i | −0.893336 | + | 0.649047i | −0.936746 | − | 0.350011i | \(-0.886178\pi\) |
0.0434095 | + | 0.999057i | \(0.486178\pi\) | |||||||
\(642\) | −8.06392 | − | 5.85878i | −0.318257 | − | 0.231228i | ||||
\(643\) | 15.3575 | + | 47.2657i | 0.605642 | + | 1.86398i | 0.492313 | + | 0.870418i | \(0.336152\pi\) |
0.113330 | + | 0.993557i | \(0.463848\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.7188 | − | 18.6858i | −1.01268 | − | 0.735752i | ||||
\(646\) | 36.1802 | − | 26.2865i | 1.42349 | − | 1.03423i | ||||
\(647\) | 3.40125 | − | 10.4680i | 0.133717 | − | 0.411539i | −0.861671 | − | 0.507467i | \(-0.830582\pi\) |
0.995388 | + | 0.0959281i | \(0.0305819\pi\) | |||||||
\(648\) | −31.8377 | −1.25070 | ||||||||
\(649\) | 25.0026 | − | 4.87970i | 0.981439 | − | 0.191545i | ||||
\(650\) | 10.7797 | 0.422816 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.154983 | − | 0.112602i | 0.00606962 | − | 0.00440984i | ||||
\(653\) | −23.4100 | − | 17.0084i | −0.916106 | − | 0.665590i | 0.0264458 | − | 0.999650i | \(-0.491581\pi\) |
−0.942552 | + | 0.334060i | \(0.891581\pi\) | |||||||
\(654\) | 2.68165 | + | 8.25328i | 0.104861 | + | 0.322729i | ||||
\(655\) | 0.101897 | + | 0.313608i | 0.00398146 | + | 0.0122537i | ||||
\(656\) | 2.94547 | + | 2.14001i | 0.115001 | + | 0.0835533i | ||||
\(657\) | 8.17583 | − | 5.94009i | 0.318969 | − | 0.231745i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.8405 | 0.422288 | 0.211144 | − | 0.977455i | \(-0.432281\pi\) | ||||
0.211144 | + | 0.977455i | \(0.432281\pi\) | |||||||
\(660\) | 0.166366 | + | 0.0774241i | 0.00647578 | + | 0.00301373i | ||||
\(661\) | −20.3444 | −0.791305 | −0.395652 | − | 0.918400i | \(-0.629481\pi\) | ||||
−0.395652 | + | 0.918400i | \(0.629481\pi\) | |||||||
\(662\) | 12.2573 | − | 37.7241i | 0.476394 | − | 1.46619i | ||||
\(663\) | −44.4911 | + | 32.3247i | −1.72789 | + | 1.25539i | ||||
\(664\) | −10.0474 | − | 7.29986i | −0.389915 | − | 0.283289i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.53275 | − | 4.71732i | −0.0593929 | − | 0.182792i | ||||
\(667\) | −0.682656 | − | 0.495978i | −0.0264325 | − | 0.0192044i | ||||
\(668\) | −0.105164 | + | 0.0764062i | −0.00406892 | + | 0.00295625i | ||||
\(669\) | 3.24662 | − | 9.99208i | 0.125522 | − | 0.386316i | ||||
\(670\) | 39.9197 | 1.54223 | ||||||||
\(671\) | −18.8720 | − | 8.78272i | −0.728544 | − | 0.339053i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.73255 | + | 11.4876i | −0.143879 | + | 0.442815i | −0.996865 | − | 0.0791188i | \(-0.974789\pi\) |
0.852986 | + | 0.521934i | \(0.174789\pi\) | |||||||
\(674\) | −28.4790 | + | 20.6912i | −1.09697 | + | 0.796996i | ||||
\(675\) | −3.80215 | − | 2.76242i | −0.146345 | − | 0.106326i | ||||
\(676\) | −0.0370903 | − | 0.114152i | −0.00142655 | − | 0.00439047i | ||||
\(677\) | −1.04951 | − | 3.23007i | −0.0403361 | − | 0.124142i | 0.928861 | − | 0.370429i | \(-0.120789\pi\) |
−0.969197 | + | 0.246287i | \(0.920789\pi\) | |||||||
\(678\) | 35.8743 | + | 26.0642i | 1.37775 | + | 1.00099i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.78642 | − | 27.0418i | 0.336944 | − | 1.03701i | ||||
\(681\) | −0.859173 | −0.0329236 | ||||||||
\(682\) | −5.99978 | + | 1.17096i | −0.229743 | + | 0.0448384i | ||||
\(683\) | −4.75643 | −0.182000 | −0.0909999 | − | 0.995851i | \(-0.529006\pi\) | ||||
−0.0909999 | + | 0.995851i | \(0.529006\pi\) | |||||||
\(684\) | −0.0420620 | + | 0.129454i | −0.00160828 | + | 0.00494978i | ||||
\(685\) | −12.3330 | + | 8.96042i | −0.471218 | + | 0.342360i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.46382 | − | 4.50516i | −0.0558481 | − | 0.171883i | ||||
\(688\) | −9.84822 | − | 30.3097i | −0.375460 | − | 1.15555i | ||||
\(689\) | −38.1404 | − | 27.7106i | −1.45303 | − | 1.05569i | ||||
\(690\) | −3.25091 | + | 2.36193i | −0.123760 | + | 0.0899170i | ||||
\(691\) | −2.04998 | + | 6.30920i | −0.0779850 | + | 0.240013i | −0.982447 | − | 0.186540i | \(-0.940272\pi\) |
0.904462 | + | 0.426554i | \(0.140272\pi\) | |||||||
\(692\) | 0.146707 | 0.00557695 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.1003 | −1.10463 | ||||||||
\(695\) | 3.93955 | − | 12.1247i | 0.149435 | − | 0.459915i | ||||
\(696\) | 5.82424 | − | 4.23156i | 0.220767 | − | 0.160397i | ||||
\(697\) | −4.05661 | − | 2.94730i | −0.153655 | − | 0.111637i | ||||
\(698\) | −2.61171 | − | 8.03802i | −0.0988547 | − | 0.304244i | ||||
\(699\) | −0.842441 | − | 2.59277i | −0.0318641 | − | 0.0980675i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.45134 | + | 1.78101i | −0.0925860 | + | 0.0672677i | −0.633115 | − | 0.774058i | \(-0.718224\pi\) |
0.540529 | + | 0.841325i | \(0.318224\pi\) | |||||||
\(702\) | 5.77815 | − | 17.7833i | 0.218082 | − | 0.671188i | ||||
\(703\) | 12.1519 | 0.458319 | ||||||||
\(704\) | 12.9697 | + | 23.3562i | 0.488815 | + | 0.880270i | ||||
\(705\) | −23.6762 | −0.891697 | ||||||||
\(706\) | 10.4683 | − | 32.2182i | 0.393981 | − | 1.21255i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.187726 | + | 0.136391i | 0.00705516 | + | 0.00512587i | ||||
\(709\) | −4.22026 | − | 12.9886i | −0.158495 | − | 0.487798i | 0.840003 | − | 0.542582i | \(-0.182553\pi\) |
−0.998498 | + | 0.0547836i | \(0.982553\pi\) | |||||||
\(710\) | −11.0874 | − | 34.1236i | −0.416103 | − | 1.28063i | ||||
\(711\) | 21.2611 | + | 15.4471i | 0.797354 | + | 0.579312i | ||||
\(712\) | 35.2317 | − | 25.5973i | 1.32036 | − | 0.959300i | ||||
\(713\) | −0.290862 | + | 0.895180i | −0.0108928 | + | 0.0335247i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.2346 | + | 20.6580i | −0.719335 | + | 0.772566i | ||||
\(716\) | 0.116231 | 0.00434376 | ||||||||
\(717\) | −7.46181 | + | 22.9651i | −0.278666 | + | 0.857647i | ||||
\(718\) | −12.4845 | + | 9.07050i | −0.465916 | + | 0.338508i | ||||
\(719\) | −1.53737 | − | 1.11696i | −0.0573341 | − | 0.0416557i | 0.558749 | − | 0.829337i | \(-0.311281\pi\) |
−0.616083 | + | 0.787681i | \(0.711281\pi\) | |||||||
\(720\) | −3.77680 | − | 11.6238i | −0.140753 | − | 0.433193i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.7069 | + | 12.1383i | 0.621768 | + | 0.451741i | ||||
\(723\) | −37.6021 | + | 27.3195i | −1.39844 | + | 1.01602i | ||||
\(724\) | −0.0638788 | + | 0.196599i | −0.00237404 | + | 0.00730654i | ||||
\(725\) | 1.92992 | 0.0716754 | ||||||||
\(726\) | −31.0755 | + | 12.6102i | −1.15332 | + | 0.468008i | ||||
\(727\) | 13.8211 | 0.512595 | 0.256298 | − | 0.966598i | \(-0.417497\pi\) | ||||
0.256298 | + | 0.966598i | \(0.417497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.256684 | − | 0.186492i | 0.00950682 | − | 0.00690711i | ||||
\(730\) | −12.5586 | − | 9.12432i | −0.464813 | − | 0.337706i | ||||
\(731\) | 13.5633 | + | 41.7436i | 0.501658 | + | 1.54394i | ||||
\(732\) | −0.0585912 | − | 0.180325i | −0.00216559 | − | 0.00666502i | ||||
\(733\) | 39.1357 | + | 28.4337i | 1.44551 | + | 1.05022i | 0.986855 | + | 0.161610i | \(0.0516685\pi\) |
0.458655 | + | 0.888615i | \(0.348331\pi\) | |||||||
\(734\) | −12.1055 | + | 8.79519i | −0.446824 | + | 0.324636i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0568504 | 0.00209553 | ||||||||
\(737\) | 34.9575 | − | 37.5443i | 1.28767 | − | 1.38296i | ||||
\(738\) | −2.17050 | −0.0798973 | ||||||||
\(739\) | 7.17170 | − | 22.0722i | 0.263815 | − | 0.811939i | −0.728149 | − | 0.685419i | \(-0.759619\pi\) |
0.991964 | − | 0.126520i | \(-0.0403809\pi\) | |||||||
\(740\) | 0.0433404 | − | 0.0314887i | 0.00159323 | − | 0.00115755i | ||||
\(741\) | −47.1829 | − | 34.2804i | −1.73331 | − | 1.25932i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.8536 | − | 42.6369i | −0.508238 | − | 1.56420i | −0.795257 | − | 0.606272i | \(-0.792664\pi\) |
0.287019 | − | 0.957925i | \(-0.407336\pi\) | |||||||
\(744\) | −6.49679 | − | 4.72020i | −0.238184 | − | 0.173051i | ||||
\(745\) | 4.76240 | − | 3.46009i | 0.174481 | − | 0.126768i | ||||
\(746\) | −15.9404 | + | 49.0596i | −0.583620 | + | 1.79620i | ||||
\(747\) | 7.35218 | 0.269002 | ||||||||
\(748\) | −0.122996 | − | 0.221495i | −0.00449718 | − | 0.00809864i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.4670 | − | 35.2919i | 0.418717 | − | 1.28868i | ||||
\(751\) | 33.3199 | − | 24.2083i | 1.21586 | − | 0.883373i | 0.220109 | − | 0.975475i | \(-0.429359\pi\) |
0.995750 | + | 0.0921022i | \(0.0293587\pi\) | |||||||
\(752\) | −19.2022 | − | 13.9512i | −0.700234 | − | 0.508750i | ||||
\(753\) | 0.283333 | + | 0.872008i | 0.0103252 | + | 0.0317777i | ||||
\(754\) | 2.37278 | + | 7.30266i | 0.0864115 | + | 0.265947i | ||||
\(755\) | −32.9913 | − | 23.9696i | −1.20068 | − | 0.872343i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.76401 | + | 20.8175i | −0.245842 | + | 0.756624i | 0.749655 | + | 0.661829i | \(0.230219\pi\) |
−0.995497 | + | 0.0947948i | \(0.969781\pi\) | |||||||
\(758\) | 17.8382 | 0.647912 | ||||||||
\(759\) | −0.625423 | + | 5.12580i | −0.0227014 | + | 0.186055i | ||||
\(760\) | 30.1537 | 1.09379 | ||||||||
\(761\) | 11.0367 | − | 33.9673i | 0.400078 | − | 1.23131i | −0.524857 | − | 0.851190i | \(-0.675881\pi\) |
0.924935 | − | 0.380124i | \(-0.124119\pi\) | |||||||
\(762\) | 12.4137 | − | 9.01906i | 0.449700 | − | 0.326726i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.0414558 | + | 0.127588i | 0.00149982 | + | 0.00461596i | ||||
\(765\) | 5.20154 | + | 16.0087i | 0.188062 | + | 0.578796i | ||||
\(766\) | 17.6353 | + | 12.8128i | 0.637188 | + | 0.462944i | ||||
\(767\) | −28.8764 | + | 20.9799i | −1.04266 | + | 0.757540i | ||||
\(768\) | −0.224043 | + | 0.689533i | −0.00808445 | + | 0.0248814i | ||||
\(769\) | −5.30246 | −0.191212 | −0.0956058 | − | 0.995419i | \(-0.530479\pi\) | ||||
−0.0956058 | + | 0.995419i | \(0.530479\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.7295 | −1.35880 | ||||||||
\(772\) | 0.00642030 | − | 0.0197596i | 0.000231072 | − | 0.000711165i | ||||
\(773\) | −40.3628 | + | 29.3253i | −1.45175 | + | 1.05476i | −0.466332 | + | 0.884610i | \(0.654425\pi\) |
−0.985418 | + | 0.170149i | \(0.945575\pi\) | |||||||
\(774\) | 15.3708 | + | 11.1675i | 0.552492 | + | 0.401409i | ||||
\(775\) | −0.665245 | − | 2.04741i | −0.0238963 | − | 0.0735452i | ||||
\(776\) | −2.11479 | − | 6.50867i | −0.0759167 | − | 0.233648i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.4943 | + | 10.5307i | −0.519646 | + | 0.377545i | ||||
\(779\) | 1.64324 | − | 5.05736i | 0.0588750 | − | 0.181199i | ||||
\(780\) | −0.257109 | −0.00920597 | ||||||||
\(781\) | −41.8023 | − | 19.4541i | −1.49580 | − | 0.696124i | ||||
\(782\) | 5.54803 | 0.198397 | ||||||||
\(783\) | 1.03448 | − | 3.18379i | 0.0369692 | − | 0.113779i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.6386 | + | 14.2683i | 0.700931 | + | 0.509256i | ||||
\(786\) | −0.169633 | − | 0.522075i | −0.00605059 | − | 0.0186218i | ||||
\(787\) | −11.0804 | − | 34.1020i | −0.394974 | − | 1.21560i | −0.928982 | − | 0.370125i | \(-0.879315\pi\) |
0.534008 | − | 0.845479i | \(-0.320685\pi\) | |||||||
\(788\) | −0.158655 | − | 0.115270i | −0.00565186 | − | 0.00410632i | ||||
\(789\) | −2.65191 | + | 1.92672i | −0.0944103 | + | 0.0685931i | ||||
\(790\) | 12.4744 | − | 38.3922i | 0.443818 | − | 1.36593i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.3396 | − | 6.67342i | −0.509535 | − | 0.237130i | ||||
\(793\) | 29.1655 | 1.03570 | ||||||||
\(794\) | −8.25571 | + | 25.4085i | −0.292984 | + | 0.901713i | ||||
\(795\) | −32.5177 | + | 23.6255i | −1.15328 | + | 0.837910i | ||||
\(796\) | 0.0484357 | + | 0.0351906i | 0.00171676 | + | 0.00124730i | ||||
\(797\) | −4.55530 | − | 14.0198i | −0.161357 | − | 0.496606i | 0.837392 | − | 0.546602i | \(-0.184079\pi\) |
−0.998749 | + | 0.0499962i | \(0.984079\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.4460 | + | 19.2142i | 0.935593 | + | 0.679748i | ||||
\(800\) | −0.105193 | + | 0.0764272i | −0.00371913 | + | 0.00270211i | ||||
\(801\) | −7.96670 | + | 24.5190i | −0.281489 | + | 0.866336i | ||||
\(802\) | 12.2354 | 0.432046 | ||||||||
\(803\) | −19.5789 | + | 3.82116i | −0.690923 | + | 0.134846i | ||||
\(804\) | 0.467275 | 0.0164795 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.92934 | − | 5.03446i | 0.244076 | − | 0.177331i | ||||
\(807\) | −3.55473 | − | 2.58266i | −0.125132 | − | 0.0909140i | ||||
\(808\) | −10.4334 | − | 32.1106i | −0.367044 | − | 1.12965i | ||||
\(809\) | −8.33599 | − | 25.6556i | −0.293078 | − | 0.902001i | −0.983860 | − | 0.178938i | \(-0.942734\pi\) |
0.690782 | − | 0.723063i | \(-0.257266\pi\) | |||||||
\(810\) | −23.4222 | − | 17.0172i | −0.822973 | − | 0.597925i | ||||
\(811\) | 1.18472 | − | 0.860750i | 0.0416012 | − | 0.0302250i | −0.566790 | − | 0.823862i | \(-0.691815\pi\) |
0.608392 | + | 0.793637i | \(0.291815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.4513 | −0.576972 | ||||||||
\(814\) | −1.18583 | + | 9.71876i | −0.0415634 | + | 0.340642i | ||||
\(815\) | 25.1236 | 0.880041 | ||||||||
\(816\) | −14.5250 | + | 44.7033i | −0.508476 | + | 1.56493i | ||||
\(817\) | −37.6577 | + | 27.3599i | −1.31747 | + | 0.957201i | ||||
\(818\) | −6.51473 | − | 4.73323i | −0.227782 | − | 0.165493i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.00724418 | − | 0.0222953i | −0.000252978 | − | 0.000778586i | ||||
\(821\) | −24.7791 | − | 18.0031i | −0.864797 | − | 0.628312i | 0.0643886 | − | 0.997925i | \(-0.479490\pi\) |
−0.929186 | + | 0.369613i | \(0.879490\pi\) | |||||||
\(822\) | 20.5312 | − | 14.9168i | 0.716107 | − | 0.520282i | ||||
\(823\) | −7.58137 | + | 23.3330i | −0.264270 | + | 0.813339i | 0.727591 | + | 0.686011i | \(0.240640\pi\) |
−0.991861 | + | 0.127328i | \(0.959360\pi\) | |||||||
\(824\) | −1.12482 | −0.0391851 | ||||||||
\(825\) | −5.73364 | − | 10.3253i | −0.199620 | − | 0.359480i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.02927 | + | 6.24545i | −0.0705646 | + | 0.217176i | −0.980119 | − | 0.198408i | \(-0.936423\pi\) |
0.909555 | + | 0.415584i | \(0.136423\pi\) | |||||||
\(828\) | −0.0136612 | + | 0.00992547i | −0.000474761 | + | 0.000344934i | ||||
\(829\) | −16.0543 | − | 11.6642i | −0.557590 | − | 0.405113i | 0.272986 | − | 0.962018i | \(-0.411989\pi\) |
−0.830576 | + | 0.556905i | \(0.811989\pi\) | |||||||
\(830\) | −3.48985 | − | 10.7406i | −0.121134 | − | 0.372813i | ||||
\(831\) | 9.64463 | + | 29.6831i | 0.334569 | + | 1.02970i | ||||
\(832\) | −30.2834 | − | 22.0022i | −1.04989 | − | 0.762789i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.55832 | + | 20.1844i | −0.227096 | + | 0.698930i | ||||
\(835\) | −17.0476 | −0.589958 | ||||||||
\(836\) | 0.183091 | − | 0.196640i | 0.00633235 | − | 0.00680095i | ||||
\(837\) | −3.73421 | −0.129073 | ||||||||
\(838\) | −11.8413 | + | 36.4438i | −0.409051 | + | 1.25893i | ||||
\(839\) | −6.44019 | + | 4.67907i | −0.222340 | + | 0.161539i | −0.693379 | − | 0.720573i | \(-0.743879\pi\) |
0.471039 | + | 0.882112i | \(0.343879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.53669 | − | 26.2732i | −0.294369 | − | 0.905973i | ||||
\(842\) | 10.4365 | + | 32.1202i | 0.359665 | + | 1.10694i | ||||
\(843\) | −31.0656 | − | 22.5705i | −1.06996 | − | 0.777370i | ||||
\(844\) | −0.0164410 | + | 0.0119451i | −0.000565922 | + | 0.000411166i | ||||
\(845\) | 4.86424 | − | 14.9706i | 0.167335 | − | 0.515004i | ||||
\(846\) | 14.1500 | 0.486489 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −40.2944 | −1.38372 | ||||||||
\(849\) | 20.8152 | − | 64.0625i | 0.714375 | − | 2.19862i | ||||
\(850\) | −10.2658 | + | 7.45852i | −0.352113 | + | 0.255825i | ||||
\(851\) | 1.21963 | + | 0.886114i | 0.0418084 | + | 0.0303756i | ||||
\(852\) | −0.129782 | − | 0.399429i | −0.00444627 | − | 0.0136842i | ||||
\(853\) | −10.5292 | − | 32.4055i | −0.360513 | − | 1.10954i | −0.952744 | − | 0.303776i | \(-0.901753\pi\) |
0.592231 | − | 0.805768i | \(-0.298247\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.4417 | + | 10.4925i | −0.493897 | + | 0.358837i | ||||
\(856\) | −2.86741 | + | 8.82497i | −0.0980060 | + | 0.301631i | ||||
\(857\) | −24.8539 | −0.848992 | −0.424496 | − | 0.905430i | \(-0.639549\pi\) | ||||
−0.424496 | + | 0.905430i | \(0.639549\pi\) | |||||||
\(858\) | 32.0207 | − | 34.3902i | 1.09317 | − | 1.17406i | ||||
\(859\) | −2.05654 | −0.0701683 | −0.0350841 | − | 0.999384i | \(-0.511170\pi\) | ||||
−0.0350841 | + | 0.999384i | \(0.511170\pi\) | |||||||
\(860\) | −0.0634115 | + | 0.195160i | −0.00216231 | + | 0.00665491i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.7814 | + | 13.6455i | 0.639697 | + | 0.464767i | ||||
\(863\) | −0.0801824 | − | 0.246776i | −0.00272944 | − | 0.00840035i | 0.949683 | − | 0.313214i | \(-0.101406\pi\) |
−0.952412 | + | 0.304814i | \(0.901406\pi\) | |||||||
\(864\) | 0.0696964 | + | 0.214504i | 0.00237112 | + | 0.00729756i | ||||
\(865\) | 15.5655 | + | 11.3090i | 0.529241 | + | 0.384516i | ||||
\(866\) | −22.9061 | + | 16.6423i | −0.778381 | + | 0.565527i | ||||
\(867\) | 8.63946 | − | 26.5895i | 0.293412 | − | 0.903028i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.1840 | − | 45.3519i | −0.854307 | − | 1.53846i | ||||
\(870\) | 6.54651 | 0.221947 | ||||||||
\(871\) | −22.2113 | + | 68.3593i | −0.752601 | + | 2.31627i | ||||
\(872\) | 6.53577 | − | 4.74851i | 0.221329 | − | 0.160805i | ||||
\(873\) | 3.27766 | + | 2.38136i | 0.110932 | + | 0.0805968i | ||||
\(874\) | 1.81816 | + | 5.59573i | 0.0615003 | + | 0.189278i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.147003 | − | 0.106804i | −0.00496676 | − | 0.00360856i | ||||
\(877\) | −15.0420 | + | 10.9287i | −0.507934 | + | 0.369035i | −0.812039 | − | 0.583603i | \(-0.801642\pi\) |
0.304106 | + | 0.952638i | \(0.401642\pi\) | |||||||
\(878\) | 11.6572 | − | 35.8772i | 0.393412 | − | 1.21080i | ||||
\(879\) | 51.9867 | 1.75347 | ||||||||
\(880\) | −2.92197 | + | 23.9477i | −0.0984996 | + | 0.807275i | ||||
\(881\) | −6.45292 | −0.217404 | −0.108702 | − | 0.994074i | \(-0.534670\pi\) | ||||
−0.108702 | + | 0.994074i | \(0.534670\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.225301 | − | 0.163691i | 0.00758198 | − | 0.00550863i | −0.583988 | − | 0.811762i | \(-0.698508\pi\) |
0.591570 | + | 0.806254i | \(0.298508\pi\) | |||||||
\(884\) | 0.287188 | + | 0.208654i | 0.00965917 | + | 0.00701779i | ||||
\(885\) | 9.40377 | + | 28.9418i | 0.316104 | + | 0.972869i | ||||
\(886\) | −11.4165 | − | 35.1362i | −0.383543 | − | 1.18042i | ||||
\(887\) | 24.7211 | + | 17.9609i | 0.830054 | + | 0.603069i | 0.919575 | − | 0.392916i | \(-0.128534\pi\) |
−0.0895209 | + | 0.995985i | \(0.528534\pi\) | |||||||
\(888\) | −10.4056 | + | 7.56009i | −0.349188 | + | 0.253700i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 39.6008 | 1.32742 | ||||||||
\(891\) | −36.5154 | + | 7.12661i | −1.22331 | + | 0.238750i | ||||
\(892\) | −0.0678176 | −0.00227070 | ||||||||
\(893\) | −10.7127 | + | 32.9702i | −0.358485 | + | 1.10330i | ||||
\(894\) | −7.92816 | + | 5.76014i | −0.265157 | + | 0.192648i | ||||
\(895\) | 12.3320 | + | 8.95972i | 0.412213 | + | 0.299491i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.23581 | − | 6.88111i | −0.0746514 | − | 0.229753i | ||||
\(898\) | 11.1132 | + | 8.07423i | 0.370853 | + | 0.269441i | ||||
\(899\) | 1.24058 | − | 0.901332i | 0.0413756 | − | 0.0300611i | ||||
\(900\) | 0.0119347 | − | 0.0367311i | 0.000397822 | − | 0.00122437i | ||||
\(901\) | 55.4949 | 1.84880 | ||||||||
\(902\) | 3.88437 | + | 1.80773i | 0.129335 | + | 0.0601907i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.7564 | − | 39.2601i | 0.424271 | − | 1.30577i | ||||
\(905\) | −21.9324 | + | 15.9348i | −0.729058 | + | 0.529692i | ||||
\(906\) | 54.9220 | + | 39.9031i | 1.82466 | + | 1.32569i | ||||
\(907\) | 9.86836 | + | 30.3717i | 0.327674 | + | 1.00848i | 0.970219 | + | 0.242228i | \(0.0778782\pi\) |
−0.642546 | + | 0.766247i | \(0.722122\pi\) | |||||||
\(908\) | 0.00171378 | + | 0.00527448i | 5.68739e−5 | + | 0.000175040i | ||||
\(909\) | 16.1704 | + | 11.7484i | 0.536337 | + | 0.389671i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.865378 | − | 2.66336i | 0.0286713 | − | 0.0882411i | −0.935697 | − | 0.352805i | \(-0.885228\pi\) |
0.964368 | + | 0.264564i | \(0.0852280\pi\) | |||||||
\(912\) | −49.8477 | −1.65062 | ||||||||
\(913\) | −13.1576 | − | 6.12334i | −0.435452 | − | 0.202653i | ||||
\(914\) | −16.7496 | −0.554027 | ||||||||
\(915\) | 7.68399 | − | 23.6489i | 0.254025 | − | 0.781808i | ||||
\(916\) | −0.0247374 | + | 0.0179728i | −0.000817348 | + | 0.000593838i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.80167 | + | 20.9334i | 0.224488 | + | 0.690904i | ||||
\(919\) | −4.89293 | − | 15.0589i | −0.161403 | − | 0.496747i | 0.837350 | − | 0.546667i | \(-0.184104\pi\) |
−0.998753 | + | 0.0499194i | \(0.984104\pi\) | |||||||
\(920\) | 3.02638 | + | 2.19880i | 0.0997769 | + | 0.0724922i | ||||
\(921\) | −9.56137 | + | 6.94674i | −0.315058 | + | 0.228903i | ||||
\(922\) | 3.98356 | − | 12.2602i | 0.131192 | − | 0.403767i | ||||
\(923\) | 64.6030 | 2.12643 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.44799 | −0.113369 | ||||||||
\(926\) | −16.9554 | + | 52.1833i | −0.557188 | + | 1.71485i | ||||
\(927\) | 0.538719 | − | 0.391402i | 0.0176939 | − | 0.0128553i | ||||
\(928\) | −0.0749296 | − | 0.0544396i | −0.00245969 | − | 0.00178707i | ||||
\(929\) | 8.49282 | + | 26.1382i | 0.278640 | + | 0.857567i | 0.988233 | + | 0.152955i | \(0.0488790\pi\) |
−0.709593 | + | 0.704612i | \(0.751121\pi\) | |||||||
\(930\) | −2.25659 | − | 6.94506i | −0.0739964 | − | 0.227737i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.0142366 | + | 0.0103435i | −0.000466337 | + | 0.000338814i | ||||
\(933\) | −9.28472 | + | 28.5754i | −0.303968 | + | 0.935517i | ||||
\(934\) | −29.2894 | −0.958379 | ||||||||
\(935\) | 4.02424 | − | 32.9816i | 0.131607 | − | 1.07861i | ||||
\(936\) | 22.1610 | 0.724354 | ||||||||
\(937\) | 3.80357 | − | 11.7062i | 0.124257 | − | 0.382425i | −0.869508 | − | 0.493919i | \(-0.835564\pi\) |
0.993765 | + | 0.111495i | \(0.0355638\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.0408 | + | 34.9037i | 1.56775 | + | 1.13904i | ||||
\(940\) | 0.0472266 | + | 0.145349i | 0.00154036 | + | 0.00474075i | ||||
\(941\) | −0.451208 | − | 1.38867i | −0.0147089 | − | 0.0452695i | 0.943433 | − | 0.331564i | \(-0.107576\pi\) |
−0.958142 | + | 0.286295i | \(0.907576\pi\) | |||||||
\(942\) | −32.6931 | − | 23.7530i | −1.06520 | − | 0.773913i | ||||
\(943\) | 0.533703 | − | 0.387758i | 0.0173798 | − | 0.0126271i | ||||
\(944\) | −9.42725 | + | 29.0141i | −0.306831 | + | 0.944328i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.2068 | − | 32.7873i | −0.591955 | − | 1.06601i | ||||
\(947\) | 11.0714 | 0.359771 | 0.179885 | − | 0.983688i | \(-0.442427\pi\) | ||||
0.179885 | + | 0.983688i | \(0.442427\pi\) | |||||||
\(948\) | 0.146017 | − | 0.449395i | 0.00474242 | − | 0.0145957i | ||||
\(949\) | 22.6123 | − | 16.4288i | 0.734025 | − | 0.533301i | ||||
\(950\) | −10.8869 | − | 7.90978i | −0.353217 | − | 0.256627i | ||||
\(951\) | 5.23165 | + | 16.1014i | 0.169648 | + | 0.522123i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.9924 | + | 8.71296i | 0.388471 | + | 0.282240i | 0.764828 | − | 0.644234i | \(-0.222824\pi\) |
−0.376358 | + | 0.926474i | \(0.622824\pi\) | |||||||
\(954\) | 19.4342 | − | 14.1197i | 0.629204 | − | 0.457144i | ||||
\(955\) | −5.43675 | + | 16.7326i | −0.175929 | + | 0.541454i | ||||
\(956\) | 0.155867 | 0.00504110 | ||||||||
\(957\) | 5.73274 | − | 6.15697i | 0.185313 | − | 0.199027i | ||||
\(958\) | −34.5782 | −1.11717 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −25.8191 | + | 18.7586i | −0.833306 | + | 0.605432i | ||||
\(961\) | 23.6957 | + | 17.2159i | 0.764377 | + | 0.555353i | ||||
\(962\) | −4.23920 | − | 13.0469i | −0.136677 | − | 0.420649i | ||||
\(963\) | −1.69750 | − | 5.22437i | −0.0547012 | − | 0.168353i | ||||
\(964\) | 0.242719 | + | 0.176346i | 0.00781746 | + | 0.00567972i | ||||
\(965\) | 2.20437 | − | 1.60157i | 0.0709612 | − | 0.0515563i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5193 | 0.531224 | 0.265612 | − | 0.964080i | \(-0.414426\pi\) | ||||
0.265612 | + | 0.964080i | \(0.414426\pi\) | |||||||
\(968\) | 20.1043 | + | 23.8857i | 0.646177 | + | 0.767716i | ||||
\(969\) | 68.6520 | 2.20542 | ||||||||
\(970\) | 1.92308 | − | 5.91862i | 0.0617462 | − | 0.190035i | ||||
\(971\) | 33.0073 | − | 23.9812i | 1.05926 | − | 0.769595i | 0.0853055 | − | 0.996355i | \(-0.472813\pi\) |
0.973951 | + | 0.226760i | \(0.0728134\pi\) | |||||||
\(972\) | −0.177396 | − | 0.128886i | −0.00568998 | − | 0.00413401i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.38755 | + | 16.5812i | 0.172628 | + | 0.531296i | ||||
\(975\) | 13.3877 | + | 9.72671i | 0.428748 | + | 0.311504i | ||||
\(976\) | 20.1672 | − | 14.6523i | 0.645535 | − | 0.469009i | ||||
\(977\) | 15.1772 | − | 46.7107i | 0.485562 | − | 1.49441i | −0.345603 | − | 0.938381i | \(-0.612326\pi\) |
0.831165 | − | 0.556025i | \(-0.187674\pi\) | |||||||
\(978\) | −41.8243 | −1.33739 | ||||||||
\(979\) | 34.6782 | − | 37.2444i | 1.10832 | − | 1.19034i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.47789 | + | 4.54847i | −0.0471853 | + | 0.145222i | ||||
\(982\) | 18.8406 | − | 13.6885i | 0.601228 | − | 0.436817i | ||||
\(983\) | 0.895411 | + | 0.650554i | 0.0285592 | + | 0.0207495i | 0.601973 | − | 0.798516i | \(-0.294381\pi\) |
−0.573414 | + | 0.819266i | \(0.694381\pi\) | |||||||
\(984\) | 1.73925 | + | 5.35286i | 0.0554453 | + | 0.170643i | ||||
\(985\) | −7.94756 | − | 24.4601i | −0.253230 | − | 0.779362i | ||||
\(986\) | −7.31238 | − | 5.31275i | −0.232874 | − | 0.169193i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.116333 | + | 0.358036i | −0.00370104 | + | 0.0113906i | ||||
\(989\) | −5.77458 | −0.183621 | ||||||||
\(990\) | −6.98233 | − | 12.5740i | −0.221913 | − | 0.399627i | ||||
\(991\) | 41.7851 | 1.32735 | 0.663674 | − | 0.748022i | \(-0.268996\pi\) | ||||
0.663674 | + | 0.748022i | \(0.268996\pi\) | |||||||
\(992\) | −0.0319255 | + | 0.0982567i | −0.00101364 | + | 0.00311965i | ||||
\(993\) | 49.2618 | − | 35.7908i | 1.56328 | − | 1.13579i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.42630 | + | 7.46739i | 0.0769189 | + | 0.236732i | ||||
\(996\) | −0.0408500 | − | 0.125723i | −0.00129438 | − | 0.00398369i | ||||
\(997\) | 35.7541 | + | 25.9769i | 1.13234 | + | 0.822695i | 0.986034 | − | 0.166543i | \(-0.0532606\pi\) |
0.146309 | + | 0.989239i | \(0.453261\pi\) | |||||||
\(998\) | −15.6664 | + | 11.3823i | −0.495910 | + | 0.360300i | ||||
\(999\) | −1.84819 | + | 5.68816i | −0.0584743 | + | 0.179965i |
(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 | 539.2.f.e.295.2 | 16 | ||
7.2 | even | 3 | 539.2.q.f.361.3 | 32 | |||
7.3 | odd | 6 | 539.2.q.g.471.2 | 32 | |||
7.4 | even | 3 | 539.2.q.f.471.2 | 32 | |||
7.5 | odd | 6 | 539.2.q.g.361.3 | 32 | |||
7.6 | odd | 2 | 77.2.f.b.64.2 | ✓ | 16 | ||
11.4 | even | 5 | 5929.2.a.bt.1.3 | 8 | |||
11.5 | even | 5 | inner | 539.2.f.e.148.2 | 16 | ||
11.7 | odd | 10 | 5929.2.a.bs.1.6 | 8 | |||
21.20 | even | 2 | 693.2.m.i.64.3 | 16 | |||
77.5 | odd | 30 | 539.2.q.g.214.2 | 32 | |||
77.6 | even | 10 | 847.2.f.x.148.3 | 16 | |||
77.13 | even | 10 | 847.2.f.v.729.2 | 16 | |||
77.16 | even | 15 | 539.2.q.f.214.2 | 32 | |||
77.20 | odd | 10 | 847.2.f.w.729.3 | 16 | |||
77.27 | odd | 10 | 77.2.f.b.71.2 | yes | 16 | ||
77.38 | odd | 30 | 539.2.q.g.324.3 | 32 | |||
77.41 | even | 10 | 847.2.f.v.323.2 | 16 | |||
77.48 | odd | 10 | 847.2.a.p.1.3 | 8 | |||
77.60 | even | 15 | 539.2.q.f.324.3 | 32 | |||
77.62 | even | 10 | 847.2.a.o.1.6 | 8 | |||
77.69 | odd | 10 | 847.2.f.w.323.3 | 16 | |||
77.76 | even | 2 | 847.2.f.x.372.3 | 16 | |||
231.62 | odd | 10 | 7623.2.a.cw.1.3 | 8 | |||
231.104 | even | 10 | 693.2.m.i.379.3 | 16 | |||
231.125 | even | 10 | 7623.2.a.ct.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.64.2 | ✓ | 16 | 7.6 | odd | 2 | ||
77.2.f.b.71.2 | yes | 16 | 77.27 | odd | 10 | ||
539.2.f.e.148.2 | 16 | 11.5 | even | 5 | inner | ||
539.2.f.e.295.2 | 16 | 1.1 | even | 1 | trivial | ||
539.2.q.f.214.2 | 32 | 77.16 | even | 15 | |||
539.2.q.f.324.3 | 32 | 77.60 | even | 15 | |||
539.2.q.f.361.3 | 32 | 7.2 | even | 3 | |||
539.2.q.f.471.2 | 32 | 7.4 | even | 3 | |||
539.2.q.g.214.2 | 32 | 77.5 | odd | 30 | |||
539.2.q.g.324.3 | 32 | 77.38 | odd | 30 | |||
539.2.q.g.361.3 | 32 | 7.5 | odd | 6 | |||
539.2.q.g.471.2 | 32 | 7.3 | odd | 6 | |||
693.2.m.i.64.3 | 16 | 21.20 | even | 2 | |||
693.2.m.i.379.3 | 16 | 231.104 | even | 10 | |||
847.2.a.o.1.6 | 8 | 77.62 | even | 10 | |||
847.2.a.p.1.3 | 8 | 77.48 | odd | 10 | |||
847.2.f.v.323.2 | 16 | 77.41 | even | 10 | |||
847.2.f.v.729.2 | 16 | 77.13 | even | 10 | |||
847.2.f.w.323.3 | 16 | 77.69 | odd | 10 | |||
847.2.f.w.729.3 | 16 | 77.20 | odd | 10 | |||
847.2.f.x.148.3 | 16 | 77.6 | even | 10 | |||
847.2.f.x.372.3 | 16 | 77.76 | even | 2 | |||
5929.2.a.bs.1.6 | 8 | 11.7 | odd | 10 | |||
5929.2.a.bt.1.3 | 8 | 11.4 | even | 5 | |||
7623.2.a.ct.1.6 | 8 | 231.125 | even | 10 | |||
7623.2.a.cw.1.3 | 8 | 231.62 | odd | 10 |