Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [71,2,Mod(5,71)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(71, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("71.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 71.c (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: | \(0.566937854351\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6 x^{19} + 28 x^{18} - 91 x^{17} + 268 x^{16} - 604 x^{15} + 1278 x^{14} - 1990 x^{13} + 3162 x^{12} - 4046 x^{11} + 6406 x^{10} - 8426 x^{9} + 12709 x^{8} - 13621 x^{7} + \cdots + 961 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 57.5 | ||
Root | \(-0.758630 - 2.33482i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 71.57 |
Dual form | 71.2.c.a.5.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.758630 | − | 2.33482i | 0.536432 | − | 1.65097i | −0.204101 | − | 0.978950i | \(-0.565427\pi\) |
0.740534 | − | 0.672019i | \(-0.234573\pi\) | |||||||
\(3\) | −0.252609 | + | 0.777449i | −0.145844 | + | 0.448860i | −0.997119 | − | 0.0758595i | \(-0.975830\pi\) |
0.851275 | + | 0.524720i | \(0.175830\pi\) | |||||||
\(4\) | −3.25785 | − | 2.36696i | −1.62892 | − | 1.18348i | ||||
\(5\) | −0.0372909 | + | 0.0270934i | −0.0166770 | + | 0.0121165i | −0.596093 | − | 0.802916i | \(-0.703281\pi\) |
0.579416 | + | 0.815032i | \(0.303281\pi\) | |||||||
\(6\) | 1.62357 | + | 1.17959i | 0.662820 | + | 0.481567i | ||||
\(7\) | 0.331946 | − | 1.02163i | 0.125464 | − | 0.386138i | −0.868521 | − | 0.495652i | \(-0.834929\pi\) |
0.993985 | + | 0.109514i | \(0.0349293\pi\) | |||||||
\(8\) | −4.02570 | + | 2.92484i | −1.42330 | + | 1.03409i | ||||
\(9\) | 1.88643 | + | 1.37058i | 0.628812 | + | 0.456858i | ||||
\(10\) | 0.0349684 | + | 0.107622i | 0.0110580 | + | 0.0340329i | ||||
\(11\) | −1.43668 | + | 4.42163i | −0.433174 | + | 1.33317i | 0.461772 | + | 0.886999i | \(0.347214\pi\) |
−0.894946 | + | 0.446174i | \(0.852786\pi\) | |||||||
\(12\) | 2.66315 | − | 1.93489i | 0.768786 | − | 0.558556i | ||||
\(13\) | 1.12919 | + | 3.47530i | 0.313182 | + | 0.963875i | 0.976496 | + | 0.215534i | \(0.0691491\pi\) |
−0.663315 | + | 0.748341i | \(0.730851\pi\) | |||||||
\(14\) | −2.13349 | − | 1.55007i | −0.570199 | − | 0.414274i | ||||
\(15\) | −0.0116438 | − | 0.0358358i | −0.00300641 | − | 0.00925276i | ||||
\(16\) | 1.28620 | + | 3.95852i | 0.321550 | + | 0.989630i | ||||
\(17\) | −2.33228 | − | 7.17803i | −0.565662 | − | 1.74093i | −0.665977 | − | 0.745972i | \(-0.731985\pi\) |
0.100315 | − | 0.994956i | \(-0.468015\pi\) | |||||||
\(18\) | 4.63116 | − | 3.36473i | 1.09157 | − | 0.793075i | ||||
\(19\) | 0.693465 | − | 2.13426i | 0.159092 | − | 0.489634i | −0.839461 | − | 0.543420i | \(-0.817129\pi\) |
0.998552 | + | 0.0537864i | \(0.0171290\pi\) | |||||||
\(20\) | 0.185617 | 0.0415052 | ||||||||
\(21\) | 0.710409 | + | 0.516143i | 0.155024 | + | 0.112632i | ||||
\(22\) | 9.23383 | + | 6.70877i | 1.96866 | + | 1.43031i | ||||
\(23\) | −6.80205 | −1.41832 | −0.709162 | − | 0.705045i | \(-0.750927\pi\) | ||||
−0.709162 | + | 0.705045i | \(0.750927\pi\) | |||||||
\(24\) | −1.25699 | − | 3.86862i | −0.256582 | − | 0.789678i | ||||
\(25\) | −1.54443 | + | 4.75326i | −0.308886 | + | 0.950652i | ||||
\(26\) | 8.97085 | 1.75933 | ||||||||
\(27\) | −3.52610 | + | 2.56186i | −0.678597 | + | 0.493030i | ||||
\(28\) | −3.49958 | + | 2.54259i | −0.661358 | + | 0.480505i | ||||
\(29\) | 2.01737 | − | 1.46571i | 0.374617 | − | 0.272175i | −0.384506 | − | 0.923122i | \(-0.625628\pi\) |
0.759123 | + | 0.650948i | \(0.225628\pi\) | |||||||
\(30\) | −0.0925036 | −0.0168888 | ||||||||
\(31\) | 1.02027 | − | 3.14007i | 0.183246 | − | 0.563974i | −0.816667 | − | 0.577109i | \(-0.804181\pi\) |
0.999914 | + | 0.0131345i | \(0.00418095\pi\) | |||||||
\(32\) | 0.266113 | 0.0470425 | ||||||||
\(33\) | −3.07468 | − | 2.23389i | −0.535233 | − | 0.388869i | ||||
\(34\) | −18.5288 | −3.17766 | ||||||||
\(35\) | 0.0153008 | + | 0.0470909i | 0.00258630 | + | 0.00795981i | ||||
\(36\) | −2.90161 | − | 8.93024i | −0.483602 | − | 1.48837i | ||||
\(37\) | 6.40886 | 1.05361 | 0.526805 | − | 0.849986i | \(-0.323390\pi\) | ||||
0.526805 | + | 0.849986i | \(0.323390\pi\) | |||||||
\(38\) | −4.45705 | − | 3.23823i | −0.723029 | − | 0.525311i | ||||
\(39\) | −2.98711 | −0.478321 | ||||||||
\(40\) | 0.0708780 | − | 0.218140i | 0.0112068 | − | 0.0344910i | ||||
\(41\) | −3.18619 | −0.497600 | −0.248800 | − | 0.968555i | \(-0.580036\pi\) | ||||
−0.248800 | + | 0.968555i | \(0.580036\pi\) | |||||||
\(42\) | 1.74404 | − | 1.26712i | 0.269111 | − | 0.195521i | ||||
\(43\) | −2.31298 | + | 1.68048i | −0.352727 | + | 0.256271i | −0.750012 | − | 0.661424i | \(-0.769952\pi\) |
0.397285 | + | 0.917695i | \(0.369952\pi\) | |||||||
\(44\) | 15.1463 | − | 11.0044i | 2.28339 | − | 1.65898i | ||||
\(45\) | −0.107480 | −0.0160222 | ||||||||
\(46\) | −5.16024 | + | 15.8816i | −0.760835 | + | 2.34161i | ||||
\(47\) | −1.09406 | − | 3.36718i | −0.159585 | − | 0.491153i | 0.839011 | − | 0.544114i | \(-0.183134\pi\) |
−0.998597 | + | 0.0529608i | \(0.983134\pi\) | |||||||
\(48\) | −3.40245 | −0.491102 | ||||||||
\(49\) | 4.72959 | + | 3.43625i | 0.675656 | + | 0.490893i | ||||
\(50\) | 9.92638 | + | 7.21193i | 1.40380 | + | 1.01992i | ||||
\(51\) | 6.16971 | 0.863932 | ||||||||
\(52\) | 4.54717 | − | 13.9947i | 0.630579 | − | 1.94072i | ||||
\(53\) | 11.2897 | − | 8.20242i | 1.55075 | − | 1.12669i | 0.607644 | − | 0.794210i | \(-0.292115\pi\) |
0.943110 | − | 0.332480i | \(-0.107885\pi\) | |||||||
\(54\) | 3.30648 | + | 10.1763i | 0.449955 | + | 1.38482i | ||||
\(55\) | −0.0662223 | − | 0.203811i | −0.00892941 | − | 0.0274819i | ||||
\(56\) | 1.65178 | + | 5.08365i | 0.220728 | + | 0.679331i | ||||
\(57\) | 1.48411 | + | 1.07827i | 0.196575 | + | 0.142820i | ||||
\(58\) | −1.89173 | − | 5.82213i | −0.248396 | − | 0.764484i | ||||
\(59\) | −6.15211 | + | 4.46977i | −0.800936 | + | 0.581914i | −0.911189 | − | 0.411990i | \(-0.864834\pi\) |
0.110253 | + | 0.993904i | \(0.464834\pi\) | |||||||
\(60\) | −0.0468885 | + | 0.144308i | −0.00605327 | + | 0.0186301i | ||||
\(61\) | −1.77784 | − | 5.47162i | −0.227629 | − | 0.700569i | −0.998014 | − | 0.0629908i | \(-0.979936\pi\) |
0.770385 | − | 0.637579i | \(-0.220064\pi\) | |||||||
\(62\) | −6.55751 | − | 4.76431i | −0.832805 | − | 0.605068i | ||||
\(63\) | 2.02641 | − | 1.47227i | 0.255304 | − | 0.185489i | ||||
\(64\) | −2.37052 | + | 7.29571i | −0.296315 | + | 0.911964i | ||||
\(65\) | −0.136266 | − | 0.0990033i | −0.0169018 | − | 0.0122798i | ||||
\(66\) | −7.54827 | + | 5.48414i | −0.929128 | + | 0.675051i | ||||
\(67\) | 2.96996 | + | 2.15780i | 0.362839 | + | 0.263618i | 0.754235 | − | 0.656604i | \(-0.228008\pi\) |
−0.391396 | + | 0.920222i | \(0.628008\pi\) | |||||||
\(68\) | −9.39191 | + | 28.9053i | −1.13894 | + | 3.50529i | ||||
\(69\) | 1.71826 | − | 5.28825i | 0.206854 | − | 0.636630i | ||||
\(70\) | 0.121556 | 0.0145288 | ||||||||
\(71\) | −0.618801 | + | 8.40340i | −0.0734382 | + | 0.997300i | ||||
\(72\) | −11.6029 | −1.36742 | ||||||||
\(73\) | 4.05110 | − | 12.4680i | 0.474146 | − | 1.45927i | −0.372961 | − | 0.927847i | \(-0.621657\pi\) |
0.847106 | − | 0.531423i | \(-0.178343\pi\) | |||||||
\(74\) | 4.86195 | − | 14.9635i | 0.565190 | − | 1.73948i | ||||
\(75\) | −3.30528 | − | 2.40143i | −0.381661 | − | 0.277293i | ||||
\(76\) | −7.31093 | + | 5.31170i | −0.838621 | + | 0.609294i | ||||
\(77\) | 4.04035 | + | 2.93549i | 0.460441 | + | 0.334530i | ||||
\(78\) | −2.26611 | + | 6.97438i | −0.256587 | + | 0.789693i | ||||
\(79\) | −0.376033 | + | 0.273204i | −0.0423070 | + | 0.0307379i | −0.608738 | − | 0.793371i | \(-0.708324\pi\) |
0.566431 | + | 0.824109i | \(0.308324\pi\) | |||||||
\(80\) | −0.155213 | − | 0.112769i | −0.0173534 | − | 0.0126080i | ||||
\(81\) | 1.06067 | + | 3.26440i | 0.117852 | + | 0.362712i | ||||
\(82\) | −2.41714 | + | 7.43920i | −0.266929 | + | 0.821522i | ||||
\(83\) | 7.07391 | − | 5.13949i | 0.776462 | − | 0.564133i | −0.127453 | − | 0.991845i | \(-0.540680\pi\) |
0.903915 | + | 0.427712i | \(0.140680\pi\) | |||||||
\(84\) | −1.09271 | − | 3.36302i | −0.119225 | − | 0.366936i | ||||
\(85\) | 0.281450 | + | 0.204486i | 0.0305276 | + | 0.0221796i | ||||
\(86\) | 2.16893 | + | 6.67527i | 0.233881 | + | 0.719813i | ||||
\(87\) | 0.629907 | + | 1.93865i | 0.0675331 | + | 0.207846i | ||||
\(88\) | −7.14896 | − | 22.0022i | −0.762081 | − | 2.34545i | ||||
\(89\) | −6.76269 | + | 4.91338i | −0.716844 | + | 0.520818i | −0.885374 | − | 0.464879i | \(-0.846098\pi\) |
0.168530 | + | 0.985696i | \(0.446098\pi\) | |||||||
\(90\) | −0.0815379 | + | 0.250948i | −0.00859485 | + | 0.0264522i | ||||
\(91\) | 3.92528 | 0.411482 | ||||||||
\(92\) | 22.1600 | + | 16.1002i | 2.31034 | + | 1.67856i | ||||
\(93\) | 2.18352 | + | 1.58642i | 0.226420 | + | 0.164504i | ||||
\(94\) | −8.69175 | −0.896486 | ||||||||
\(95\) | 0.0319646 | + | 0.0983770i | 0.00327950 | + | 0.0100933i | ||||
\(96\) | −0.0672223 | + | 0.206889i | −0.00686085 | + | 0.0211155i | ||||
\(97\) | −7.30123 | −0.741328 | −0.370664 | − | 0.928767i | \(-0.620870\pi\) | ||||
−0.370664 | + | 0.928767i | \(0.620870\pi\) | |||||||
\(98\) | 11.6110 | − | 8.43591i | 1.17289 | − | 0.852156i | ||||
\(99\) | −8.77038 | + | 6.37205i | −0.881456 | + | 0.640415i | ||||
\(100\) | 16.2823 | − | 11.8298i | 1.62823 | − | 1.18298i | ||||
\(101\) | −1.71025 | −0.170177 | −0.0850883 | − | 0.996373i | \(-0.527117\pi\) | ||||
−0.0850883 | + | 0.996373i | \(0.527117\pi\) | |||||||
\(102\) | 4.68053 | − | 14.4052i | 0.463441 | − | 1.42632i | ||||
\(103\) | 14.0771 | 1.38706 | 0.693528 | − | 0.720430i | \(-0.256056\pi\) | ||||
0.693528 | + | 0.720430i | \(0.256056\pi\) | |||||||
\(104\) | −14.7105 | − | 10.6878i | −1.44248 | − | 1.04803i | ||||
\(105\) | −0.0404759 | −0.00395004 | ||||||||
\(106\) | −10.5865 | − | 32.5820i | −1.02825 | − | 3.16464i | ||||
\(107\) | −3.48065 | − | 10.7123i | −0.336487 | − | 1.03560i | −0.965985 | − | 0.258598i | \(-0.916740\pi\) |
0.629498 | − | 0.777002i | \(-0.283260\pi\) | |||||||
\(108\) | 17.5513 | 1.68887 | ||||||||
\(109\) | 2.03044 | + | 1.47520i | 0.194481 | + | 0.141299i | 0.680764 | − | 0.732502i | \(-0.261648\pi\) |
−0.486283 | + | 0.873801i | \(0.661648\pi\) | |||||||
\(110\) | −0.526101 | −0.0501618 | ||||||||
\(111\) | −1.61893 | + | 4.98256i | −0.153662 | + | 0.472924i | ||||
\(112\) | 4.47107 | 0.422477 | ||||||||
\(113\) | −1.65362 | + | 1.20143i | −0.155560 | + | 0.113021i | −0.662842 | − | 0.748759i | \(-0.730650\pi\) |
0.507283 | + | 0.861780i | \(0.330650\pi\) | |||||||
\(114\) | 3.64345 | − | 2.64712i | 0.341240 | − | 0.247926i | ||||
\(115\) | 0.253654 | − | 0.184291i | 0.0236534 | − | 0.0171852i | ||||
\(116\) | −10.0416 | −0.932335 | ||||||||
\(117\) | −2.63301 | + | 8.10357i | −0.243422 | + | 0.749175i | ||||
\(118\) | 5.76894 | + | 17.7550i | 0.531074 | + | 1.63448i | ||||
\(119\) | −8.10745 | −0.743209 | ||||||||
\(120\) | 0.151688 | + | 0.110208i | 0.0138472 | + | 0.0100606i | ||||
\(121\) | −8.58762 | − | 6.23927i | −0.780693 | − | 0.567207i | ||||
\(122\) | −14.1240 | −1.27873 | ||||||||
\(123\) | 0.804860 | − | 2.47710i | 0.0725718 | − | 0.223353i | ||||
\(124\) | −10.7563 | + | 7.81493i | −0.965947 | + | 0.701802i | ||||
\(125\) | −0.142408 | − | 0.438288i | −0.0127374 | − | 0.0392016i | ||||
\(126\) | −1.90020 | − | 5.84822i | −0.169283 | − | 0.521000i | ||||
\(127\) | 0.769988 | + | 2.36978i | 0.0683254 | + | 0.210284i | 0.979389 | − | 0.201981i | \(-0.0647379\pi\) |
−0.911064 | + | 0.412265i | \(0.864738\pi\) | |||||||
\(128\) | 15.6664 | + | 11.3823i | 1.38473 | + | 1.00607i | ||||
\(129\) | −0.722209 | − | 2.22273i | −0.0635870 | − | 0.195701i | ||||
\(130\) | −0.334531 | + | 0.243051i | −0.0293403 | + | 0.0213170i | ||||
\(131\) | 1.52870 | − | 4.70485i | 0.133563 | − | 0.411065i | −0.861801 | − | 0.507247i | \(-0.830663\pi\) |
0.995364 | + | 0.0961824i | \(0.0306632\pi\) | |||||||
\(132\) | 4.72930 | + | 14.5553i | 0.411633 | + | 1.26688i | ||||
\(133\) | −1.95023 | − | 1.41692i | −0.169106 | − | 0.122863i | ||||
\(134\) | 7.29120 | − | 5.29736i | 0.629863 | − | 0.457623i | ||||
\(135\) | 0.0620817 | − | 0.191068i | 0.00534315 | − | 0.0164445i | ||||
\(136\) | 30.3837 | + | 22.0750i | 2.60538 | + | 1.89292i | ||||
\(137\) | −6.29737 | + | 4.57531i | −0.538021 | + | 0.390895i | −0.823349 | − | 0.567535i | \(-0.807897\pi\) |
0.285329 | + | 0.958430i | \(0.407897\pi\) | |||||||
\(138\) | −11.0436 | − | 8.02364i | −0.940094 | − | 0.683018i | ||||
\(139\) | −4.21743 | + | 12.9799i | −0.357718 | + | 1.10094i | 0.596699 | + | 0.802465i | \(0.296479\pi\) |
−0.954417 | + | 0.298477i | \(0.903521\pi\) | |||||||
\(140\) | 0.0616149 | − | 0.189631i | 0.00520741 | − | 0.0160268i | ||||
\(141\) | 2.89418 | 0.243734 | ||||||||
\(142\) | 19.1510 | + | 7.81986i | 1.60712 | + | 0.656228i | ||||
\(143\) | −16.9888 | −1.42067 | ||||||||
\(144\) | −2.99911 | + | 9.23032i | −0.249926 | + | 0.769194i | ||||
\(145\) | −0.0355186 | + | 0.109315i | −0.00294966 | + | 0.00907812i | ||||
\(146\) | −26.0373 | − | 18.9172i | −2.15486 | − | 1.56560i | ||||
\(147\) | −3.86624 | + | 2.80899i | −0.318882 | + | 0.231682i | ||||
\(148\) | −20.8791 | − | 15.1695i | −1.71625 | − | 1.24693i | ||||
\(149\) | −2.25571 | + | 6.94237i | −0.184795 | + | 0.568741i | −0.999945 | − | 0.0105093i | \(-0.996655\pi\) |
0.815150 | + | 0.579251i | \(0.196655\pi\) | |||||||
\(150\) | −8.11440 | + | 5.89546i | −0.662538 | + | 0.481362i | ||||
\(151\) | 4.84062 | + | 3.51692i | 0.393924 | + | 0.286203i | 0.767062 | − | 0.641573i | \(-0.221718\pi\) |
−0.373138 | + | 0.927776i | \(0.621718\pi\) | |||||||
\(152\) | 3.45071 | + | 10.6202i | 0.279889 | + | 0.861411i | ||||
\(153\) | 5.43833 | − | 16.7375i | 0.439663 | − | 1.35314i | ||||
\(154\) | 9.91898 | − | 7.20656i | 0.799294 | − | 0.580721i | ||||
\(155\) | 0.0470285 | + | 0.144739i | 0.00377742 | + | 0.0116257i | ||||
\(156\) | 9.73155 | + | 7.07038i | 0.779147 | + | 0.566084i | ||||
\(157\) | 4.92371 | + | 15.1536i | 0.392955 | + | 1.20939i | 0.930543 | + | 0.366183i | \(0.119335\pi\) |
−0.537588 | + | 0.843207i | \(0.680665\pi\) | |||||||
\(158\) | 0.352613 | + | 1.08523i | 0.0280524 | + | 0.0863364i | ||||
\(159\) | 3.52510 | + | 10.8491i | 0.279559 | + | 0.860393i | ||||
\(160\) | −0.00992358 | + | 0.00720990i | −0.000784528 | + | 0.000569993i | ||||
\(161\) | −2.25791 | + | 6.94914i | −0.177948 | + | 0.547669i | ||||
\(162\) | 8.42646 | 0.662045 | ||||||||
\(163\) | −15.1771 | − | 11.0268i | −1.18876 | − | 0.863687i | −0.195631 | − | 0.980678i | \(-0.562675\pi\) |
−0.993133 | + | 0.116990i | \(0.962675\pi\) | |||||||
\(164\) | 10.3801 | + | 7.54160i | 0.810552 | + | 0.588900i | ||||
\(165\) | 0.175181 | 0.0136378 | ||||||||
\(166\) | −6.63333 | − | 20.4153i | −0.514846 | − | 1.58453i | ||||
\(167\) | 6.67072 | − | 20.5304i | 0.516196 | − | 1.58869i | −0.264900 | − | 0.964276i | \(-0.585339\pi\) |
0.781096 | − | 0.624411i | \(-0.214661\pi\) | |||||||
\(168\) | −4.36953 | −0.337117 | ||||||||
\(169\) | −0.285405 | + | 0.207359i | −0.0219542 | + | 0.0159507i | ||||
\(170\) | 0.690954 | − | 0.502008i | 0.0529938 | − | 0.0385022i | ||||
\(171\) | 4.23335 | − | 3.07571i | 0.323732 | − | 0.235205i | ||||
\(172\) | 11.5130 | 0.877857 | ||||||||
\(173\) | −4.16355 | + | 12.8141i | −0.316549 | + | 0.974238i | 0.658563 | + | 0.752526i | \(0.271165\pi\) |
−0.975112 | + | 0.221713i | \(0.928835\pi\) | |||||||
\(174\) | 5.00428 | 0.379373 | ||||||||
\(175\) | 4.34338 | + | 3.15565i | 0.328329 | + | 0.238545i | ||||
\(176\) | −19.3510 | −1.45863 | ||||||||
\(177\) | −1.92094 | − | 5.91205i | −0.144387 | − | 0.444377i | ||||
\(178\) | 6.34150 | + | 19.5171i | 0.475316 | + | 1.46287i | ||||
\(179\) | −2.78978 | −0.208518 | −0.104259 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104259 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(180\) | 0.350155 | + | 0.254402i | 0.0260990 | + | 0.0189620i | ||||
\(181\) | 5.97431 | 0.444067 | 0.222033 | − | 0.975039i | \(-0.428731\pi\) | ||||
0.222033 | + | 0.975039i | \(0.428731\pi\) | |||||||
\(182\) | 2.97784 | − | 9.16484i | 0.220732 | − | 0.679343i | ||||
\(183\) | 4.70300 | 0.347656 | ||||||||
\(184\) | 27.3830 | − | 19.8949i | 2.01870 | − | 1.46667i | ||||
\(185\) | −0.238992 | + | 0.173638i | −0.0175710 | + | 0.0127661i | ||||
\(186\) | 5.36049 | − | 3.89463i | 0.393050 | − | 0.285568i | ||||
\(187\) | 35.0894 | 2.56599 | ||||||||
\(188\) | −4.40570 | + | 13.5594i | −0.321319 | + | 0.988917i | ||||
\(189\) | 1.44679 | + | 4.45275i | 0.105238 | + | 0.323890i | ||||
\(190\) | 0.253942 | 0.0184229 | ||||||||
\(191\) | −2.87909 | − | 2.09178i | −0.208324 | − | 0.151356i | 0.478731 | − | 0.877962i | \(-0.341097\pi\) |
−0.687055 | + | 0.726605i | \(0.741097\pi\) | |||||||
\(192\) | −5.07323 | − | 3.68592i | −0.366129 | − | 0.266008i | ||||
\(193\) | −14.1397 | −1.01780 | −0.508900 | − | 0.860826i | \(-0.669948\pi\) | ||||
−0.508900 | + | 0.860826i | \(0.669948\pi\) | |||||||
\(194\) | −5.53893 | + | 17.0471i | −0.397672 | + | 1.22391i | ||||
\(195\) | 0.111392 | − | 0.0809311i | 0.00797695 | − | 0.00579560i | ||||
\(196\) | −7.27480 | − | 22.3895i | −0.519628 | − | 1.59925i | ||||
\(197\) | 5.49417 | + | 16.9093i | 0.391443 | + | 1.20474i | 0.931697 | + | 0.363237i | \(0.118328\pi\) |
−0.540253 | + | 0.841502i | \(0.681672\pi\) | |||||||
\(198\) | 8.22414 | + | 25.3113i | 0.584464 | + | 1.79880i | ||||
\(199\) | −0.658239 | − | 0.478239i | −0.0466613 | − | 0.0339014i | 0.564210 | − | 0.825631i | \(-0.309181\pi\) |
−0.610871 | + | 0.791730i | \(0.709181\pi\) | |||||||
\(200\) | −7.68514 | − | 23.6524i | −0.543421 | − | 1.67248i | ||||
\(201\) | −2.42782 | + | 1.76392i | −0.171245 | + | 0.124417i | ||||
\(202\) | −1.29745 | + | 3.99314i | −0.0912883 | + | 0.280956i | ||||
\(203\) | −0.827744 | − | 2.54753i | −0.0580962 | − | 0.178802i | ||||
\(204\) | −20.1000 | − | 14.6035i | −1.40728 | − | 1.02245i | ||||
\(205\) | 0.118816 | − | 0.0863249i | 0.00829847 | − | 0.00602919i | ||||
\(206\) | 10.6793 | − | 32.8675i | 0.744061 | − | 2.28999i | ||||
\(207\) | −12.8316 | − | 9.32272i | −0.891859 | − | 0.647974i | ||||
\(208\) | −12.3047 | + | 8.93987i | −0.853175 | + | 0.619868i | ||||
\(209\) | 8.44065 | + | 6.13249i | 0.583852 | + | 0.424193i | ||||
\(210\) | −0.0307062 | + | 0.0945040i | −0.00211893 | + | 0.00652139i | ||||
\(211\) | −0.899500 | + | 2.76838i | −0.0619241 | + | 0.190583i | −0.977233 | − | 0.212171i | \(-0.931947\pi\) |
0.915309 | + | 0.402753i | \(0.131947\pi\) | |||||||
\(212\) | −56.1948 | −3.85947 | ||||||||
\(213\) | −6.37690 | − | 2.60386i | −0.436938 | − | 0.178413i | ||||
\(214\) | −27.6519 | −1.89025 | ||||||||
\(215\) | 0.0407233 | − | 0.125333i | 0.00277730 | − | 0.00854766i | ||||
\(216\) | 6.70197 | − | 20.6266i | 0.456011 | − | 1.40346i | ||||
\(217\) | −2.86930 | − | 2.08467i | −0.194781 | − | 0.141517i | ||||
\(218\) | 4.98469 | − | 3.62159i | 0.337606 | − | 0.245285i | ||||
\(219\) | 8.66990 | + | 6.29905i | 0.585858 | + | 0.425651i | ||||
\(220\) | −0.266672 | + | 0.820731i | −0.0179790 | + | 0.0553337i | ||||
\(221\) | 22.3122 | − | 16.2108i | 1.50088 | − | 1.09045i | ||||
\(222\) | 10.4052 | + | 7.55984i | 0.698353 | + | 0.507383i | ||||
\(223\) | −7.04003 | − | 21.6670i | −0.471436 | − | 1.45093i | −0.850705 | − | 0.525643i | \(-0.823825\pi\) |
0.379269 | − | 0.925286i | \(-0.376175\pi\) | |||||||
\(224\) | 0.0883351 | − | 0.271867i | 0.00590214 | − | 0.0181649i | ||||
\(225\) | −9.42817 | + | 6.84996i | −0.628544 | + | 0.456664i | ||||
\(226\) | 1.55063 | + | 4.77235i | 0.103146 | + | 0.317452i | ||||
\(227\) | 14.6971 | + | 10.6781i | 0.975481 | + | 0.708728i | 0.956694 | − | 0.291095i | \(-0.0940196\pi\) |
0.0187868 | + | 0.999824i | \(0.494020\pi\) | |||||||
\(228\) | −2.28277 | − | 7.02565i | −0.151180 | − | 0.465285i | ||||
\(229\) | −4.81678 | − | 14.8245i | −0.318302 | − | 0.979632i | −0.974374 | − | 0.224934i | \(-0.927783\pi\) |
0.656072 | − | 0.754698i | \(-0.272217\pi\) | |||||||
\(230\) | −0.237856 | − | 0.732047i | −0.0156838 | − | 0.0482697i | ||||
\(231\) | −3.30282 | + | 2.39964i | −0.217310 | + | 0.157885i | ||||
\(232\) | −3.83437 | + | 11.8010i | −0.251739 | + | 0.774773i | ||||
\(233\) | −17.6339 | −1.15524 | −0.577618 | − | 0.816307i | \(-0.696018\pi\) | ||||
−0.577618 | + | 0.816307i | \(0.696018\pi\) | |||||||
\(234\) | 16.9229 | + | 12.2952i | 1.10629 | + | 0.803764i | ||||
\(235\) | 0.132027 | + | 0.0959232i | 0.00861249 | + | 0.00625734i | ||||
\(236\) | 30.6224 | 1.99335 | ||||||||
\(237\) | −0.117413 | − | 0.361360i | −0.00762680 | − | 0.0234729i | ||||
\(238\) | −6.15055 | + | 18.9295i | −0.398681 | + | 1.22701i | ||||
\(239\) | 27.5931 | 1.78485 | 0.892426 | − | 0.451193i | \(-0.149002\pi\) | ||||
0.892426 | + | 0.451193i | \(0.149002\pi\) | |||||||
\(240\) | 0.126881 | − | 0.0921841i | 0.00819010 | − | 0.00595046i | ||||
\(241\) | −2.92979 | + | 2.12862i | −0.188725 | + | 0.137116i | −0.678136 | − | 0.734937i | \(-0.737212\pi\) |
0.489411 | + | 0.872053i | \(0.337212\pi\) | |||||||
\(242\) | −21.0824 | + | 15.3173i | −1.35523 | + | 0.984632i | ||||
\(243\) | −15.8813 | −1.01879 | ||||||||
\(244\) | −7.15921 | + | 22.0338i | −0.458321 | + | 1.41057i | ||||
\(245\) | −0.269470 | −0.0172158 | ||||||||
\(246\) | −5.17301 | − | 3.75841i | −0.329819 | − | 0.239627i | ||||
\(247\) | 8.20026 | 0.521770 | ||||||||
\(248\) | 5.07691 | + | 15.6251i | 0.322384 | + | 0.992197i | ||||
\(249\) | 2.20877 | + | 6.79788i | 0.139975 | + | 0.430798i | ||||
\(250\) | −1.13136 | −0.0715534 | ||||||||
\(251\) | 23.8825 | + | 17.3516i | 1.50745 | + | 1.09523i | 0.967293 | + | 0.253661i | \(0.0816349\pi\) |
0.540156 | + | 0.841565i | \(0.318365\pi\) | |||||||
\(252\) | −10.0865 | −0.635392 | ||||||||
\(253\) | 9.77234 | − | 30.0762i | 0.614382 | − | 1.89087i | ||||
\(254\) | 6.11715 | 0.383824 | ||||||||
\(255\) | −0.230074 | + | 0.167158i | −0.0144078 | + | 0.0104679i | ||||
\(256\) | 26.0485 | − | 18.9254i | 1.62803 | − | 1.18284i | ||||
\(257\) | −13.8636 | + | 10.0725i | −0.864790 | + | 0.628307i | −0.929184 | − | 0.369618i | \(-0.879489\pi\) |
0.0643938 | + | 0.997925i | \(0.479489\pi\) | |||||||
\(258\) | −5.73757 | −0.357206 | ||||||||
\(259\) | 2.12740 | − | 6.54745i | 0.132190 | − | 0.406839i | ||||
\(260\) | 0.209598 | + | 0.645075i | 0.0129987 | + | 0.0400058i | ||||
\(261\) | 5.81450 | 0.359909 | ||||||||
\(262\) | −9.82527 | − | 7.13848i | −0.607007 | − | 0.441017i | ||||
\(263\) | 19.8893 | + | 14.4504i | 1.22643 | + | 0.891052i | 0.996617 | − | 0.0821828i | \(-0.0261891\pi\) |
0.229811 | + | 0.973235i | \(0.426189\pi\) | |||||||
\(264\) | 18.9115 | 1.16392 | ||||||||
\(265\) | −0.198770 | + | 0.611751i | −0.0122103 | + | 0.0375796i | ||||
\(266\) | −4.78776 | + | 3.47851i | −0.293556 | + | 0.213281i | ||||
\(267\) | −2.11159 | − | 6.49881i | −0.129227 | − | 0.397721i | ||||
\(268\) | −4.56824 | − | 14.0596i | −0.279050 | − | 0.858826i | ||||
\(269\) | −3.76723 | − | 11.5944i | −0.229692 | − | 0.706920i | −0.997781 | − | 0.0665771i | \(-0.978792\pi\) |
0.768089 | − | 0.640343i | \(-0.221208\pi\) | |||||||
\(270\) | −0.399013 | − | 0.289900i | −0.0242831 | − | 0.0176427i | ||||
\(271\) | −5.84872 | − | 18.0005i | −0.355284 | − | 1.09345i | −0.955845 | − | 0.293873i | \(-0.905056\pi\) |
0.600560 | − | 0.799579i | \(-0.294944\pi\) | |||||||
\(272\) | 25.4146 | − | 18.4648i | 1.54099 | − | 1.11959i | ||||
\(273\) | −0.991560 | + | 3.05171i | −0.0600120 | + | 0.184698i | ||||
\(274\) | 5.90516 | + | 18.1742i | 0.356744 | + | 1.09794i | ||||
\(275\) | −18.7983 | − | 13.6578i | −1.13358 | − | 0.823596i | ||||
\(276\) | −18.1149 | + | 13.1612i | −1.09039 | + | 0.792214i | ||||
\(277\) | −0.320186 | + | 0.985432i | −0.0192381 | + | 0.0592089i | −0.960215 | − | 0.279263i | \(-0.909910\pi\) |
0.940977 | + | 0.338472i | \(0.109910\pi\) | |||||||
\(278\) | 27.1063 | + | 19.6939i | 1.62573 | + | 1.18116i | ||||
\(279\) | 6.22839 | − | 4.52519i | 0.372884 | − | 0.270916i | ||||
\(280\) | −0.199330 | − | 0.144821i | −0.0119122 | − | 0.00865474i | ||||
\(281\) | 3.40318 | − | 10.4739i | 0.203017 | − | 0.624821i | −0.796772 | − | 0.604279i | \(-0.793461\pi\) |
0.999789 | − | 0.0205412i | \(-0.00653893\pi\) | |||||||
\(282\) | 2.19561 | − | 6.75740i | 0.130747 | − | 0.402397i | ||||
\(283\) | 0.0206694 | 0.00122867 | 0.000614335 | − | 1.00000i | \(-0.499804\pi\) | ||||
0.000614335 | 1.00000i | \(0.499804\pi\) | ||||||||
\(284\) | 21.9065 | − | 25.9123i | 1.29991 | − | 1.53761i | ||||
\(285\) | −0.0845576 | −0.00500876 | ||||||||
\(286\) | −12.8882 | + | 39.6658i | −0.762095 | + | 2.34549i | ||||
\(287\) | −1.05764 | + | 3.25510i | −0.0624308 | + | 0.192142i | ||||
\(288\) | 0.502004 | + | 0.364727i | 0.0295809 | + | 0.0214918i | ||||
\(289\) | −32.3313 | + | 23.4900i | −1.90184 | + | 1.38177i | ||||
\(290\) | 0.228286 | + | 0.165859i | 0.0134054 | + | 0.00973959i | ||||
\(291\) | 1.84435 | − | 5.67634i | 0.108118 | − | 0.332753i | ||||
\(292\) | −42.7092 | + | 31.0300i | −2.49937 | + | 1.81590i | ||||
\(293\) | 19.8023 | + | 14.3872i | 1.15686 | + | 0.840511i | 0.989378 | − | 0.145364i | \(-0.0464352\pi\) |
0.167486 | + | 0.985875i | \(0.446435\pi\) | |||||||
\(294\) | 3.62545 | + | 11.1580i | 0.211440 | + | 0.650746i | ||||
\(295\) | 0.108316 | − | 0.333363i | 0.00630642 | − | 0.0194092i | ||||
\(296\) | −25.8001 | + | 18.7449i | −1.49960 | + | 1.08953i | ||||
\(297\) | −6.26174 | − | 19.2717i | −0.363343 | − | 1.11826i | ||||
\(298\) | 14.4980 | + | 10.5334i | 0.839844 | + | 0.610183i | ||||
\(299\) | −7.68082 | − | 23.6391i | −0.444194 | − | 1.36709i | ||||
\(300\) | 5.08401 | + | 15.6470i | 0.293525 | + | 0.903378i | ||||
\(301\) | 0.949036 | + | 2.92083i | 0.0547015 | + | 0.168354i | ||||
\(302\) | 11.8836 | − | 8.63395i | 0.683825 | − | 0.496828i | ||||
\(303\) | 0.432025 | − | 1.32964i | 0.0248192 | − | 0.0763856i | ||||
\(304\) | 9.34046 | 0.535712 | ||||||||
\(305\) | 0.214542 | + | 0.155874i | 0.0122846 | + | 0.00892532i | ||||
\(306\) | −34.9533 | − | 25.3951i | −1.99815 | − | 1.45174i | ||||
\(307\) | 8.69769 | 0.496403 | 0.248202 | − | 0.968708i | \(-0.420160\pi\) | ||||
0.248202 | + | 0.968708i | \(0.420160\pi\) | |||||||
\(308\) | −6.21465 | − | 19.1267i | −0.354113 | − | 1.08985i | ||||
\(309\) | −3.55599 | + | 10.9442i | −0.202293 | + | 0.622594i | ||||
\(310\) | 0.373617 | 0.0212200 | ||||||||
\(311\) | −15.8249 | + | 11.4975i | −0.897349 | + | 0.651963i | −0.937784 | − | 0.347220i | \(-0.887126\pi\) |
0.0404344 | + | 0.999182i | \(0.487126\pi\) | |||||||
\(312\) | 12.0252 | − | 8.73683i | 0.680794 | − | 0.494626i | ||||
\(313\) | −18.1030 | + | 13.1526i | −1.02324 | + | 0.743427i | −0.966944 | − | 0.254987i | \(-0.917929\pi\) |
−0.0562953 | + | 0.998414i | \(0.517929\pi\) | |||||||
\(314\) | 39.1163 | 2.20746 | ||||||||
\(315\) | −0.0356777 | + | 0.109805i | −0.00201021 | + | 0.00618679i | ||||
\(316\) | 1.87172 | 0.105293 | ||||||||
\(317\) | −0.0186102 | − | 0.0135211i | −0.00104525 | − | 0.000759420i | 0.587263 | − | 0.809397i | \(-0.300206\pi\) |
−0.588308 | + | 0.808637i | \(0.700206\pi\) | |||||||
\(318\) | 28.0051 | 1.57045 | ||||||||
\(319\) | 3.58251 | + | 11.0258i | 0.200582 | + | 0.617328i | ||||
\(320\) | −0.109267 | − | 0.336289i | −0.00610821 | − | 0.0187991i | ||||
\(321\) | 9.20753 | 0.513914 | ||||||||
\(322\) | 14.5121 | + | 10.5437i | 0.808728 | + | 0.587575i | ||||
\(323\) | −16.9372 | −0.942409 | ||||||||
\(324\) | 4.27123 | − | 13.1455i | 0.237290 | − | 0.730305i | ||||
\(325\) | −18.2630 | −1.01305 | ||||||||
\(326\) | −37.2595 | + | 27.0706i | −2.06361 | + | 1.49930i | ||||
\(327\) | −1.65980 | + | 1.20592i | −0.0917872 | + | 0.0666873i | ||||
\(328\) | 12.8267 | − | 9.31912i | 0.708234 | − | 0.514562i | ||||
\(329\) | −3.80316 | −0.209675 | ||||||||
\(330\) | 0.132898 | − | 0.409017i | 0.00731577 | − | 0.0225156i | ||||
\(331\) | −3.25188 | − | 10.0083i | −0.178739 | − | 0.550103i | 0.821045 | − | 0.570863i | \(-0.193391\pi\) |
−0.999784 | + | 0.0207601i | \(0.993391\pi\) | |||||||
\(332\) | −35.2107 | −1.93244 | ||||||||
\(333\) | 12.0899 | + | 8.78382i | 0.662522 | + | 0.481350i | ||||
\(334\) | −42.8741 | − | 31.1499i | −2.34597 | − | 1.70445i | ||||
\(335\) | −0.169215 | −0.00924520 | ||||||||
\(336\) | −1.12943 | + | 3.47603i | −0.0616155 | + | 0.189633i | ||||
\(337\) | −1.60117 | + | 1.16332i | −0.0872212 | + | 0.0633699i | −0.630541 | − | 0.776156i | \(-0.717167\pi\) |
0.543320 | + | 0.839526i | \(0.317167\pi\) | |||||||
\(338\) | 0.267629 | + | 0.823678i | 0.0145571 | + | 0.0448022i | ||||
\(339\) | −0.516329 | − | 1.58910i | −0.0280431 | − | 0.0863079i | ||||
\(340\) | −0.432912 | − | 1.33236i | −0.0234779 | − | 0.0722576i | ||||
\(341\) | 12.4185 | + | 9.02254i | 0.672497 | + | 0.488598i | ||||
\(342\) | −3.96969 | − | 12.2174i | −0.214656 | − | 0.660643i | ||||
\(343\) | 11.1638 | − | 8.11101i | 0.602791 | − | 0.437953i | ||||
\(344\) | 4.39624 | − | 13.5302i | 0.237029 | − | 0.729501i | ||||
\(345\) | 0.0792014 | + | 0.243757i | 0.00426406 | + | 0.0131234i | ||||
\(346\) | 26.7601 | + | 19.4423i | 1.43863 | + | 1.04523i | ||||
\(347\) | 5.02508 | − | 3.65094i | 0.269761 | − | 0.195993i | −0.444678 | − | 0.895690i | \(-0.646682\pi\) |
0.714439 | + | 0.699698i | \(0.246682\pi\) | |||||||
\(348\) | 2.53658 | − | 7.80680i | 0.135975 | − | 0.418488i | ||||
\(349\) | −17.0779 | − | 12.4078i | −0.914159 | − | 0.664175i | 0.0279044 | − | 0.999611i | \(-0.491117\pi\) |
−0.942063 | + | 0.335435i | \(0.891117\pi\) | |||||||
\(350\) | 10.6629 | − | 7.74706i | 0.569957 | − | 0.414098i | ||||
\(351\) | −12.8849 | − | 9.36140i | −0.687743 | − | 0.499675i | ||||
\(352\) | −0.382318 | + | 1.17665i | −0.0203776 | + | 0.0627158i | ||||
\(353\) | 6.60892 | − | 20.3402i | 0.351757 | − | 1.08260i | −0.606109 | − | 0.795382i | \(-0.707270\pi\) |
0.957866 | − | 0.287216i | \(-0.0927296\pi\) | |||||||
\(354\) | −15.2609 | −0.811106 | ||||||||
\(355\) | −0.204601 | − | 0.330136i | −0.0108591 | − | 0.0175218i | ||||
\(356\) | 33.6616 | 1.78406 | ||||||||
\(357\) | 2.04801 | − | 6.30313i | 0.108392 | − | 0.333597i | ||||
\(358\) | −2.11641 | + | 6.51363i | −0.111856 | + | 0.344256i | ||||
\(359\) | 7.96414 | + | 5.78629i | 0.420331 | + | 0.305389i | 0.777771 | − | 0.628548i | \(-0.216350\pi\) |
−0.357440 | + | 0.933936i | \(0.616350\pi\) | |||||||
\(360\) | 0.432684 | − | 0.314363i | 0.0228044 | − | 0.0165684i | ||||
\(361\) | 11.2971 | + | 8.20785i | 0.594586 | + | 0.431992i | ||||
\(362\) | 4.53229 | − | 13.9490i | 0.238212 | − | 0.733141i | ||||
\(363\) | 7.02002 | − | 5.10035i | 0.368456 | − | 0.267699i | ||||
\(364\) | −12.7880 | − | 9.29100i | −0.670272 | − | 0.486981i | ||||
\(365\) | 0.186732 | + | 0.574701i | 0.00977399 | + | 0.0300812i | ||||
\(366\) | 3.56784 | − | 10.9807i | 0.186494 | − | 0.573970i | ||||
\(367\) | 1.51466 | − | 1.10046i | 0.0790645 | − | 0.0574437i | −0.547551 | − | 0.836772i | \(-0.684440\pi\) |
0.626615 | + | 0.779329i | \(0.284440\pi\) | |||||||
\(368\) | −8.74880 | − | 26.9260i | −0.456063 | − | 1.40362i | ||||
\(369\) | −6.01055 | − | 4.36692i | −0.312897 | − | 0.227333i | ||||
\(370\) | 0.224107 | + | 0.689731i | 0.0116508 | + | 0.0358574i | ||||
\(371\) | −4.63224 | − | 14.2566i | −0.240494 | − | 0.740164i | ||||
\(372\) | −3.35857 | − | 10.3366i | −0.174134 | − | 0.535929i | ||||
\(373\) | −8.95874 | + | 6.50891i | −0.463866 | + | 0.337018i | −0.795046 | − | 0.606549i | \(-0.792553\pi\) |
0.331180 | + | 0.943568i | \(0.392553\pi\) | |||||||
\(374\) | 26.6198 | − | 81.9274i | 1.37648 | − | 4.23637i | ||||
\(375\) | 0.376720 | 0.0194537 | ||||||||
\(376\) | 14.2528 | + | 10.3553i | 0.735034 | + | 0.534033i | ||||
\(377\) | 7.37177 | + | 5.35590i | 0.379665 | + | 0.275843i | ||||
\(378\) | 11.4940 | 0.591185 | ||||||||
\(379\) | 9.51931 | + | 29.2974i | 0.488974 | + | 1.50491i | 0.826141 | + | 0.563463i | \(0.190531\pi\) |
−0.337167 | + | 0.941445i | \(0.609469\pi\) | |||||||
\(380\) | 0.128719 | − | 0.396156i | 0.00660314 | − | 0.0203224i | ||||
\(381\) | −2.03689 | −0.104353 | ||||||||
\(382\) | −7.06811 | + | 5.13528i | −0.361636 | + | 0.262744i | ||||
\(383\) | −6.47388 | + | 4.70355i | −0.330800 | + | 0.240340i | −0.740770 | − | 0.671759i | \(-0.765539\pi\) |
0.409970 | + | 0.912099i | \(0.365539\pi\) | |||||||
\(384\) | −12.8067 | + | 9.30458i | −0.653537 | + | 0.474822i | ||||
\(385\) | −0.230201 | −0.0117321 | ||||||||
\(386\) | −10.7268 | + | 33.0137i | −0.545980 | + | 1.68035i | ||||
\(387\) | −6.66652 | −0.338878 | ||||||||
\(388\) | 23.7863 | + | 17.2817i | 1.20757 | + | 0.877348i | ||||
\(389\) | 5.76622 | 0.292359 | 0.146179 | − | 0.989258i | \(-0.453302\pi\) | ||||
0.146179 | + | 0.989258i | \(0.453302\pi\) | |||||||
\(390\) | −0.104454 | − | 0.321478i | −0.00528925 | − | 0.0162786i | ||||
\(391\) | 15.8643 | + | 48.8253i | 0.802292 | + | 2.46920i | ||||
\(392\) | −29.0904 | −1.46929 | ||||||||
\(393\) | 3.27162 | + | 2.37697i | 0.165031 | + | 0.119902i | ||||
\(394\) | 43.6483 | 2.19897 | ||||||||
\(395\) | 0.00662058 | − | 0.0203760i | 0.000333117 | − | 0.00102523i | ||||
\(396\) | 43.6549 | 2.19374 | ||||||||
\(397\) | −1.21396 | + | 0.881991i | −0.0609267 | + | 0.0442659i | −0.617832 | − | 0.786310i | \(-0.711989\pi\) |
0.556905 | + | 0.830576i | \(0.311989\pi\) | |||||||
\(398\) | −1.61596 | + | 1.17407i | −0.0810009 | + | 0.0588506i | ||||
\(399\) | 1.59423 | − | 1.15827i | 0.0798112 | − | 0.0579863i | ||||
\(400\) | −20.8023 | −1.04012 | ||||||||
\(401\) | 5.94498 | − | 18.2968i | 0.296878 | − | 0.913697i | −0.685706 | − | 0.727879i | \(-0.740506\pi\) |
0.982584 | − | 0.185818i | \(-0.0594935\pi\) | |||||||
\(402\) | 2.27661 | + | 7.00669i | 0.113547 | + | 0.349462i | ||||
\(403\) | 12.0648 | 0.600990 | ||||||||
\(404\) | 5.57174 | + | 4.04811i | 0.277205 | + | 0.201401i | ||||
\(405\) | −0.127997 | − | 0.0929954i | −0.00636023 | − | 0.00462098i | ||||
\(406\) | −6.57599 | −0.326361 | ||||||||
\(407\) | −9.20745 | + | 28.3376i | −0.456396 | + | 1.40464i | ||||
\(408\) | −24.8374 | + | 18.0454i | −1.22963 | + | 0.893382i | ||||
\(409\) | −7.78862 | − | 23.9709i | −0.385123 | − | 1.18529i | −0.936391 | − | 0.350958i | \(-0.885856\pi\) |
0.551269 | − | 0.834328i | \(-0.314144\pi\) | |||||||
\(410\) | −0.111416 | − | 0.342903i | −0.00550244 | − | 0.0169348i | ||||
\(411\) | −1.96630 | − | 6.05165i | −0.0969904 | − | 0.298506i | ||||
\(412\) | −45.8609 | − | 33.3199i | −2.25941 | − | 1.64155i | ||||
\(413\) | 2.52426 | + | 7.76887i | 0.124211 | + | 0.382281i | ||||
\(414\) | −31.5013 | + | 22.8871i | −1.54821 | + | 1.12484i | ||||
\(415\) | −0.124546 | + | 0.383313i | −0.00611371 | + | 0.0188161i | ||||
\(416\) | 0.300493 | + | 0.924821i | 0.0147329 | + | 0.0453431i | ||||
\(417\) | −9.02587 | − | 6.55768i | −0.441999 | − | 0.321131i | ||||
\(418\) | 20.7216 | − | 15.0551i | 1.01353 | − | 0.736371i | ||||
\(419\) | −5.78535 | + | 17.8055i | −0.282633 | + | 0.869854i | 0.704466 | + | 0.709738i | \(0.251187\pi\) |
−0.987098 | + | 0.160116i | \(0.948813\pi\) | |||||||
\(420\) | 0.131864 | + | 0.0958049i | 0.00643431 | + | 0.00467480i | ||||
\(421\) | −18.5039 | + | 13.4439i | −0.901825 | + | 0.655214i | −0.938934 | − | 0.344097i | \(-0.888185\pi\) |
0.0371089 | + | 0.999311i | \(0.488185\pi\) | |||||||
\(422\) | 5.78128 | + | 4.20034i | 0.281428 | + | 0.204470i | ||||
\(423\) | 2.55109 | − | 7.85146i | 0.124038 | − | 0.381751i | ||||
\(424\) | −21.4580 | + | 66.0410i | −1.04209 | + | 3.20723i | ||||
\(425\) | 37.7211 | 1.82974 | ||||||||
\(426\) | −10.9173 | + | 12.9136i | −0.528943 | + | 0.625664i | ||||
\(427\) | −6.18009 | −0.299076 | ||||||||
\(428\) | −14.0163 | + | 43.1377i | −0.677502 | + | 2.08514i | ||||
\(429\) | 4.29151 | − | 13.2079i | 0.207196 | − | 0.637684i | ||||
\(430\) | −0.261737 | − | 0.190163i | −0.0126221 | − | 0.00917048i | ||||
\(431\) | −4.99972 | + | 3.63251i | −0.240828 | + | 0.174972i | −0.701652 | − | 0.712520i | \(-0.747554\pi\) |
0.460824 | + | 0.887491i | \(0.347554\pi\) | |||||||
\(432\) | −14.6764 | − | 10.6631i | −0.706120 | − | 0.513026i | ||||
\(433\) | 4.91298 | − | 15.1206i | 0.236103 | − | 0.726650i | −0.760870 | − | 0.648904i | \(-0.775228\pi\) |
0.996973 | − | 0.0777457i | \(-0.0247722\pi\) | |||||||
\(434\) | −7.04408 | + | 5.11782i | −0.338127 | + | 0.245663i | ||||
\(435\) | −0.0760145 | − | 0.0552278i | −0.00364462 | − | 0.00264797i | ||||
\(436\) | −3.12311 | − | 9.61196i | −0.149570 | − | 0.460329i | ||||
\(437\) | −4.71698 | + | 14.5174i | −0.225644 | + | 0.694460i | ||||
\(438\) | 21.2844 | − | 15.4640i | 1.01701 | − | 0.738900i | ||||
\(439\) | 3.36789 | + | 10.3653i | 0.160741 | + | 0.494708i | 0.998697 | − | 0.0510283i | \(-0.0162499\pi\) |
−0.837957 | + | 0.545737i | \(0.816250\pi\) | |||||||
\(440\) | 0.862707 | + | 0.626793i | 0.0411279 | + | 0.0298812i | ||||
\(441\) | 4.21243 | + | 12.9645i | 0.200592 | + | 0.617358i | ||||
\(442\) | −20.9226 | − | 64.3930i | −0.995185 | − | 3.06286i | ||||
\(443\) | 2.31867 | + | 7.13613i | 0.110163 | + | 0.339048i | 0.990908 | − | 0.134544i | \(-0.0429571\pi\) |
−0.880744 | + | 0.473592i | \(0.842957\pi\) | |||||||
\(444\) | 17.0678 | − | 12.4005i | 0.810000 | − | 0.588500i | ||||
\(445\) | 0.119067 | − | 0.366449i | 0.00564429 | − | 0.0173713i | ||||
\(446\) | −55.9294 | −2.64833 | ||||||||
\(447\) | −4.82753 | − | 3.50741i | −0.228334 | − | 0.165895i | ||||
\(448\) | 6.66660 | + | 4.84357i | 0.314967 | + | 0.228837i | ||||
\(449\) | −13.1622 | −0.621162 | −0.310581 | − | 0.950547i | \(-0.600524\pi\) | ||||
−0.310581 | + | 0.950547i | \(0.600524\pi\) | |||||||
\(450\) | 8.84096 | + | 27.2097i | 0.416767 | + | 1.28268i | ||||
\(451\) | 4.57753 | − | 14.0882i | 0.215547 | − | 0.663387i | ||||
\(452\) | 8.23097 | 0.387152 | ||||||||
\(453\) | −3.95701 | + | 2.87493i | −0.185916 | + | 0.135076i | ||||
\(454\) | 36.0811 | − | 26.2144i | 1.69337 | − | 1.23030i | ||||
\(455\) | −0.146377 | + | 0.106349i | −0.00686228 | + | 0.00498574i | ||||
\(456\) | −9.12833 | −0.427473 | ||||||||
\(457\) | −4.99366 | + | 15.3689i | −0.233594 | + | 0.718927i | 0.763711 | + | 0.645558i | \(0.223375\pi\) |
−0.997305 | + | 0.0733691i | \(0.976625\pi\) | |||||||
\(458\) | −38.2668 | −1.78809 | ||||||||
\(459\) | 26.6129 | + | 19.3354i | 1.24219 | + | 0.902501i | ||||
\(460\) | −1.26258 | −0.0588679 | ||||||||
\(461\) | 2.19559 | + | 6.75732i | 0.102259 | + | 0.314720i | 0.989077 | − | 0.147398i | \(-0.0470898\pi\) |
−0.886819 | + | 0.462118i | \(0.847090\pi\) | |||||||
\(462\) | 3.09712 | + | 9.53194i | 0.144091 | + | 0.443466i | ||||
\(463\) | −7.46619 | −0.346983 | −0.173492 | − | 0.984835i | \(-0.555505\pi\) | ||||
−0.173492 | + | 0.984835i | \(0.555505\pi\) | |||||||
\(464\) | 8.39677 | + | 6.10061i | 0.389810 | + | 0.283214i | ||||
\(465\) | −0.124407 | −0.00576923 | ||||||||
\(466\) | −13.3776 | + | 41.1721i | −0.619706 | + | 1.90726i | ||||
\(467\) | −17.5885 | −0.813898 | −0.406949 | − | 0.913451i | \(-0.633407\pi\) | ||||
−0.406949 | + | 0.913451i | \(0.633407\pi\) | |||||||
\(468\) | 27.7588 | − | 20.1679i | 1.28315 | − | 0.932263i | ||||
\(469\) | 3.19034 | − | 2.31791i | 0.147316 | − | 0.107031i | ||||
\(470\) | 0.324123 | − | 0.235489i | 0.0149507 | − | 0.0108623i | ||||
\(471\) | −13.0249 | −0.600157 | ||||||||
\(472\) | 11.6932 | − | 35.9879i | 0.538222 | − | 1.65648i | ||||
\(473\) | −4.10746 | − | 12.6415i | −0.188861 | − | 0.581256i | ||||
\(474\) | −0.932785 | −0.0428442 | ||||||||
\(475\) | 9.07371 | + | 6.59244i | 0.416330 | + | 0.302482i | ||||
\(476\) | 26.4128 | + | 19.1900i | 1.21063 | + | 0.879574i | ||||
\(477\) | 32.5392 | 1.48987 | ||||||||
\(478\) | 20.9330 | − | 64.4251i | 0.957453 | − | 2.94674i | ||||
\(479\) | 20.9233 | − | 15.2016i | 0.956008 | − | 0.694581i | 0.00378806 | − | 0.999993i | \(-0.498794\pi\) |
0.952220 | + | 0.305412i | \(0.0987942\pi\) | |||||||
\(480\) | −0.00309855 | − | 0.00953636i | −0.000141429 | − | 0.000435273i | ||||
\(481\) | 7.23684 | + | 22.2727i | 0.329971 | + | 1.01555i | ||||
\(482\) | 2.74732 | + | 8.45538i | 0.125137 | + | 0.385132i | ||||
\(483\) | −4.83224 | − | 3.51083i | −0.219874 | − | 0.159748i | ||||
\(484\) | 13.2090 | + | 40.6532i | 0.600410 | + | 1.84787i | ||||
\(485\) | 0.272269 | − | 0.197815i | 0.0123631 | − | 0.00898233i | ||||
\(486\) | −12.0480 | + | 37.0801i | −0.546511 | + | 1.68199i | ||||
\(487\) | −7.47523 | − | 23.0064i | −0.338735 | − | 1.04252i | −0.964853 | − | 0.262790i | \(-0.915357\pi\) |
0.626118 | − | 0.779728i | \(-0.284643\pi\) | |||||||
\(488\) | 23.1607 | + | 16.8272i | 1.04843 | + | 0.761732i | ||||
\(489\) | 12.4067 | − | 9.01397i | 0.561049 | − | 0.407626i | ||||
\(490\) | −0.204428 | + | 0.629165i | −0.00923513 | + | 0.0284228i | ||||
\(491\) | 8.75437 | + | 6.36042i | 0.395079 | + | 0.287042i | 0.767534 | − | 0.641009i | \(-0.221484\pi\) |
−0.372455 | + | 0.928050i | \(0.621484\pi\) | |||||||
\(492\) | −8.48532 | + | 6.16495i | −0.382548 | + | 0.277937i | ||||
\(493\) | −15.2260 | − | 11.0623i | −0.685743 | − | 0.498221i | ||||
\(494\) | 6.22097 | − | 19.1462i | 0.279894 | − | 0.861427i | ||||
\(495\) | 0.154415 | − | 0.475239i | 0.00694042 | − | 0.0213604i | ||||
\(496\) | 13.7423 | 0.617048 | ||||||||
\(497\) | 8.37971 | + | 3.42166i | 0.375882 | + | 0.153482i | ||||
\(498\) | 17.5475 | 0.786322 | ||||||||
\(499\) | 10.3666 | − | 31.9050i | 0.464071 | − | 1.42826i | −0.396077 | − | 0.918217i | \(-0.629629\pi\) |
0.860148 | − | 0.510045i | \(-0.170371\pi\) | |||||||
\(500\) | −0.573466 | + | 1.76495i | −0.0256462 | + | 0.0789309i | ||||
\(501\) | 14.2762 | + | 10.3723i | 0.637815 | + | 0.463400i | ||||
\(502\) | 58.6310 | − | 42.5979i | 2.61683 | − | 1.90124i | ||||
\(503\) | −7.73870 | − | 5.62250i | −0.345052 | − | 0.250695i | 0.401739 | − | 0.915754i | \(-0.368406\pi\) |
−0.746790 | + | 0.665060i | \(0.768406\pi\) | |||||||
\(504\) | −3.85155 | + | 11.8539i | −0.171562 | + | 0.528013i | ||||
\(505\) | 0.0637769 | − | 0.0463366i | 0.00283804 | − | 0.00206195i | ||||
\(506\) | −62.8089 | − | 45.6334i | −2.79220 | − | 2.02865i | ||||
\(507\) | −0.0891152 | − | 0.274268i | −0.00395774 | − | 0.0121807i | ||||
\(508\) | 3.10068 | − | 9.54291i | 0.137570 | − | 0.423398i | ||||
\(509\) | −25.2645 | + | 18.3558i | −1.11983 | + | 0.813605i | −0.984183 | − | 0.177152i | \(-0.943312\pi\) |
−0.135648 | + | 0.990757i | \(0.543312\pi\) | |||||||
\(510\) | 0.215744 | + | 0.663993i | 0.00955333 | + | 0.0294021i | ||||
\(511\) | −11.3929 | − | 8.27742i | −0.503992 | − | 0.366171i | ||||
\(512\) | −12.4581 | − | 38.3421i | −0.550575 | − | 1.69450i | ||||
\(513\) | 3.02246 | + | 9.30218i | 0.133445 | + | 0.410701i | ||||
\(514\) | 13.0002 | + | 40.0105i | 0.573414 | + | 1.76479i | ||||
\(515\) | −0.524947 | + | 0.381396i | −0.0231319 | + | 0.0168063i | ||||
\(516\) | −2.90828 | + | 8.95076i | −0.128030 | + | 0.394035i | ||||
\(517\) | 16.4602 | 0.723921 | ||||||||
\(518\) | −13.6732 | − | 9.93418i | −0.600767 | − | 0.436483i | ||||
\(519\) | −8.91056 | − | 6.47390i | −0.391130 | − | 0.284173i | ||||
\(520\) | 0.838137 | 0.0367547 | ||||||||
\(521\) | −4.32774 | − | 13.3194i | −0.189602 | − | 0.583534i | 0.810395 | − | 0.585883i | \(-0.199252\pi\) |
−0.999997 | + | 0.00234900i | \(0.999252\pi\) | |||||||
\(522\) | 4.41105 | − | 13.5758i | 0.193067 | − | 0.594198i | ||||
\(523\) | −40.9589 | −1.79101 | −0.895504 | − | 0.445054i | \(-0.853185\pi\) | ||||
−0.895504 | + | 0.445054i | \(0.853185\pi\) | |||||||
\(524\) | −16.1165 | + | 11.7093i | −0.704051 | + | 0.511523i | ||||
\(525\) | −3.55054 | + | 2.57962i | −0.154958 | + | 0.112584i | ||||
\(526\) | 48.8279 | − | 35.4755i | 2.12900 | − | 1.54681i | ||||
\(527\) | −24.9191 | −1.08549 | ||||||||
\(528\) | 4.88822 | − | 15.0444i | 0.212733 | − | 0.654724i | ||||
\(529\) | 23.2678 | 1.01165 | ||||||||
\(530\) | 1.27754 | + | 0.928186i | 0.0554927 | + | 0.0403178i | ||||
\(531\) | −17.7317 | −0.769490 | ||||||||
\(532\) | 2.99973 | + | 9.23222i | 0.130055 | + | 0.400268i | ||||
\(533\) | −3.59783 | − | 11.0730i | −0.155839 | − | 0.479624i | ||||
\(534\) | −16.7755 | −0.725947 | ||||||||
\(535\) | 0.420030 | + | 0.305170i | 0.0181595 | + | 0.0131936i | ||||
\(536\) | −18.2674 | −0.789033 | ||||||||
\(537\) | 0.704721 | − | 2.16891i | 0.0304110 | − | 0.0935954i | ||||
\(538\) | −29.9287 | −1.29032 | ||||||||
\(539\) | −21.9887 | + | 15.9757i | −0.947121 | + | 0.688124i | ||||
\(540\) | −0.654504 | + | 0.475525i | −0.0281653 | + | 0.0204633i | ||||
\(541\) | −1.80270 | + | 1.30974i | −0.0775041 | + | 0.0563100i | −0.625863 | − | 0.779933i | \(-0.715253\pi\) |
0.548359 | + | 0.836243i | \(0.315253\pi\) | |||||||
\(542\) | −46.4650 | −1.99584 | ||||||||
\(543\) | −1.50916 | + | 4.64472i | −0.0647643 | + | 0.199324i | ||||
\(544\) | −0.620650 | − | 1.91016i | −0.0266102 | − | 0.0818976i | ||||
\(545\) | −0.115685 | −0.00495541 | ||||||||
\(546\) | 6.37297 | + | 4.63024i | 0.272738 | + | 0.198156i | ||||
\(547\) | −15.5044 | − | 11.2646i | −0.662920 | − | 0.481640i | 0.204728 | − | 0.978819i | \(-0.434369\pi\) |
−0.867648 | + | 0.497179i | \(0.834369\pi\) | |||||||
\(548\) | 31.3455 | 1.33901 | ||||||||
\(549\) | 4.14549 | − | 12.7585i | 0.176925 | − | 0.544520i | ||||
\(550\) | −46.1495 | + | 33.5296i | −1.96782 | + | 1.42971i | ||||
\(551\) | −1.72923 | − | 5.32202i | −0.0736676 | − | 0.226726i | ||||
\(552\) | 8.55011 | + | 26.3145i | 0.363917 | + | 1.12002i | ||||
\(553\) | 0.154289 | + | 0.474854i | 0.00656105 | + | 0.0201928i | ||||
\(554\) | 2.05791 | + | 1.49516i | 0.0874321 | + | 0.0635231i | ||||
\(555\) | −0.0746232 | − | 0.229667i | −0.00316758 | − | 0.00974880i | ||||
\(556\) | 44.4627 | − | 32.3041i | 1.88564 | − | 1.37000i | ||||
\(557\) | 8.43538 | − | 25.9614i | 0.357419 | − | 1.10002i | −0.597175 | − | 0.802111i | \(-0.703710\pi\) |
0.954594 | − | 0.297911i | \(-0.0962897\pi\) | |||||||
\(558\) | −5.84047 | − | 17.9751i | −0.247247 | − | 0.760947i | ||||
\(559\) | −8.45198 | − | 6.14072i | −0.357481 | − | 0.259725i | ||||
\(560\) | −0.166730 | + | 0.121137i | −0.00704564 | + | 0.00511896i | ||||
\(561\) | −8.86387 | + | 27.2802i | −0.374233 | + | 1.15177i | ||||
\(562\) | −21.8730 | − | 15.8916i | −0.922655 | − | 0.670348i | ||||
\(563\) | −7.78656 | + | 5.65727i | −0.328165 | + | 0.238425i | −0.739651 | − | 0.672990i | \(-0.765010\pi\) |
0.411487 | + | 0.911416i | \(0.365010\pi\) | |||||||
\(564\) | −9.42879 | − | 6.85042i | −0.397024 | − | 0.288455i | ||||
\(565\) | 0.0291143 | − | 0.0896045i | 0.00122485 | − | 0.00376969i | ||||
\(566\) | 0.0156804 | − | 0.0482594i | 0.000659098 | − | 0.00202850i | ||||
\(567\) | 3.68708 | 0.154843 | ||||||||
\(568\) | −22.0875 | − | 35.6395i | −0.926771 | − | 1.49540i | ||||
\(569\) | −2.48976 | −0.104376 | −0.0521881 | − | 0.998637i | \(-0.516620\pi\) | ||||
−0.0521881 | + | 0.998637i | \(0.516620\pi\) | |||||||
\(570\) | −0.0641480 | + | 0.197427i | −0.00268686 | + | 0.00826931i | ||||
\(571\) | −12.2982 | + | 37.8501i | −0.514666 | + | 1.58398i | 0.269224 | + | 0.963078i | \(0.413233\pi\) |
−0.783889 | + | 0.620900i | \(0.786767\pi\) | |||||||
\(572\) | 55.3468 | + | 40.2118i | 2.31417 | + | 1.68134i | ||||
\(573\) | 2.35354 | − | 1.70995i | 0.0983205 | − | 0.0714340i | ||||
\(574\) | 6.79771 | + | 4.93883i | 0.283731 | + | 0.206143i | ||||
\(575\) | 10.5053 | − | 32.3319i | 0.438100 | − | 1.34833i | ||||
\(576\) | −14.4712 | + | 10.5139i | −0.602965 | + | 0.438080i | ||||
\(577\) | 9.96039 | + | 7.23664i | 0.414656 | + | 0.301265i | 0.775484 | − | 0.631367i | \(-0.217506\pi\) |
−0.360828 | + | 0.932632i | \(0.617506\pi\) | |||||||
\(578\) | 30.3176 | + | 93.3080i | 1.26105 | + | 3.88110i | ||||
\(579\) | 3.57181 | − | 10.9929i | 0.148440 | − | 0.456850i | ||||
\(580\) | 0.374459 | − | 0.272060i | 0.0155485 | − | 0.0112967i | ||||
\(581\) | −2.90248 | − | 8.93292i | −0.120415 | − | 0.370600i | ||||
\(582\) | −11.8541 | − | 8.61248i | −0.491367 | − | 0.356999i | ||||
\(583\) | 20.0485 | + | 61.7030i | 0.830325 | + | 2.55548i | ||||
\(584\) | 20.1584 | + | 62.0413i | 0.834162 | + | 2.56729i | ||||
\(585\) | −0.121366 | − | 0.373527i | −0.00501787 | − | 0.0154434i | ||||
\(586\) | 48.6143 | − | 35.3203i | 2.00824 | − | 1.45907i | ||||
\(587\) | 2.51331 | − | 7.73517i | 0.103735 | − | 0.319265i | −0.885696 | − | 0.464265i | \(-0.846318\pi\) |
0.989432 | + | 0.145001i | \(0.0463184\pi\) | |||||||
\(588\) | 19.2444 | 0.793625 | ||||||||
\(589\) | −5.99423 | − | 4.35506i | −0.246988 | − | 0.179447i | ||||
\(590\) | −0.696172 | − | 0.505799i | −0.0286609 | − | 0.0208234i | ||||
\(591\) | −14.5340 | −0.597849 | ||||||||
\(592\) | 8.24308 | + | 25.3696i | 0.338788 | + | 1.04268i | ||||
\(593\) | 8.78999 | − | 27.0528i | 0.360962 | − | 1.11093i | −0.591510 | − | 0.806298i | \(-0.701468\pi\) |
0.952471 | − | 0.304628i | \(-0.0985322\pi\) | |||||||
\(594\) | −49.7463 | −2.04111 | ||||||||
\(595\) | 0.302334 | − | 0.219658i | 0.0123945 | − | 0.00900512i | ||||
\(596\) | 23.7811 | − | 17.2780i | 0.974112 | − | 0.707734i | ||||
\(597\) | 0.538083 | − | 0.390940i | 0.0220223 | − | 0.0160001i | ||||
\(598\) | −61.0201 | −2.49530 | ||||||||
\(599\) | 8.15920 | − | 25.1114i | 0.333376 | − | 1.02603i | −0.634140 | − | 0.773218i | \(-0.718646\pi\) |
0.967516 | − | 0.252808i | \(-0.0813541\pi\) | |||||||
\(600\) | 20.3299 | 0.829964 | ||||||||
\(601\) | 23.1430 | + | 16.8143i | 0.944021 | + | 0.685871i | 0.949385 | − | 0.314114i | \(-0.101708\pi\) |
−0.00536437 | + | 0.999986i | \(0.501708\pi\) | |||||||
\(602\) | 7.53959 | 0.307291 | ||||||||
\(603\) | 2.64521 | + | 8.14112i | 0.107721 | + | 0.331532i | ||||
\(604\) | −7.44558 | − | 22.9151i | −0.302956 | − | 0.932404i | ||||
\(605\) | 0.489283 | 0.0198922 | ||||||||
\(606\) | −2.77672 | − | 2.01740i | −0.112796 | − | 0.0819514i | ||||
\(607\) | −36.4871 | −1.48097 | −0.740483 | − | 0.672075i | \(-0.765403\pi\) | ||||
−0.740483 | + | 0.672075i | \(0.765403\pi\) | |||||||
\(608\) | 0.184540 | − | 0.567955i | 0.00748408 | − | 0.0230336i | ||||
\(609\) | 2.18967 | 0.0887300 | ||||||||
\(610\) | 0.526696 | − | 0.382667i | 0.0213253 | − | 0.0154937i | ||||
\(611\) | 10.4665 | − | 7.60439i | 0.423431 | − | 0.307641i | ||||
\(612\) | −57.3342 | + | 41.6557i | −2.31760 | + | 1.68383i | ||||
\(613\) | −16.7551 | −0.676733 | −0.338367 | − | 0.941014i | \(-0.609874\pi\) | ||||
−0.338367 | + | 0.941014i | \(0.609874\pi\) | |||||||
\(614\) | 6.59833 | − | 20.3076i | 0.266287 | − | 0.819547i | ||||
\(615\) | 0.0370993 | + | 0.114180i | 0.00149599 | + | 0.00460417i | ||||
\(616\) | −24.8511 | −1.00128 | ||||||||
\(617\) | 9.16332 | + | 6.65754i | 0.368901 | + | 0.268022i | 0.756755 | − | 0.653698i | \(-0.226784\pi\) |
−0.387854 | + | 0.921721i | \(0.626784\pi\) | |||||||
\(618\) | 22.8551 | + | 16.6052i | 0.919368 | + | 0.667960i | ||||
\(619\) | 35.4878 | 1.42638 | 0.713188 | − | 0.700973i | \(-0.247251\pi\) | ||||
0.713188 | + | 0.700973i | \(0.247251\pi\) | |||||||
\(620\) | 0.189380 | − | 0.582851i | 0.00760568 | − | 0.0234079i | ||||
\(621\) | 23.9847 | − | 17.4259i | 0.962472 | − | 0.699276i | ||||
\(622\) | 14.8393 | + | 45.6707i | 0.595003 | + | 1.83123i | ||||
\(623\) | 2.77479 | + | 8.53992i | 0.111170 | + | 0.342145i | ||||
\(624\) | −3.84203 | − | 11.8245i | −0.153804 | − | 0.473360i | ||||
\(625\) | −20.1996 | − | 14.6759i | −0.807986 | − | 0.587036i | ||||
\(626\) | 16.9755 | + | 52.2451i | 0.678476 | + | 2.08814i | ||||
\(627\) | −6.89988 | + | 5.01306i | −0.275555 | + | 0.200202i | ||||
\(628\) | 19.8274 | − | 61.0224i | 0.791198 | − | 2.43506i | ||||
\(629\) | −14.9473 | − | 46.0030i | −0.595987 | − | 1.83426i | ||||
\(630\) | 0.229308 | + | 0.166602i | 0.00913586 | + | 0.00663759i | ||||
\(631\) | 23.0308 | − | 16.7329i | 0.916843 | − | 0.666125i | −0.0258931 | − | 0.999665i | \(-0.508243\pi\) |
0.942736 | + | 0.333539i | \(0.108243\pi\) | |||||||
\(632\) | 0.714718 | − | 2.19968i | 0.0284299 | − | 0.0874984i | ||||
\(633\) | −1.92505 | − | 1.39863i | −0.0765139 | − | 0.0555906i | ||||
\(634\) | −0.0456876 | + | 0.0331940i | −0.00181449 | + | 0.00131830i | ||||
\(635\) | −0.0929190 | − | 0.0675096i | −0.00368738 | − | 0.00267904i | ||||
\(636\) | 14.1953 | − | 43.6886i | 0.562880 | − | 1.73237i | ||||
\(637\) | −6.60137 | + | 20.3169i | −0.261556 | + | 0.804986i | ||||
\(638\) | 28.4611 | 1.12679 | ||||||||
\(639\) | −12.6848 | + | 15.0043i | −0.501804 | + | 0.593563i | ||||
\(640\) | −0.892601 | −0.0352832 | ||||||||
\(641\) | 7.79176 | − | 23.9806i | 0.307756 | − | 0.947175i | −0.670878 | − | 0.741567i | \(-0.734083\pi\) |
0.978634 | − | 0.205608i | \(-0.0659172\pi\) | |||||||
\(642\) | 6.98511 | − | 21.4980i | 0.275680 | − | 0.848457i | ||||
\(643\) | 5.09407 | + | 3.70106i | 0.200891 | + | 0.145956i | 0.683683 | − | 0.729779i | \(-0.260377\pi\) |
−0.482792 | + | 0.875735i | \(0.660377\pi\) | |||||||
\(644\) | 23.8043 | − | 17.2948i | 0.938021 | − | 0.681512i | ||||
\(645\) | 0.0871532 | + | 0.0633205i | 0.00343165 | + | 0.00249324i | ||||
\(646\) | −12.8490 | + | 39.5453i | −0.505539 | + | 1.55589i | ||||
\(647\) | 10.6643 | − | 7.74806i | 0.419256 | − | 0.304607i | −0.358082 | − | 0.933690i | \(-0.616569\pi\) |
0.777338 | + | 0.629083i | \(0.216569\pi\) | |||||||
\(648\) | −13.8178 | − | 10.0392i | −0.542815 | − | 0.394378i | ||||
\(649\) | −10.9251 | − | 33.6240i | −0.428847 | − | 1.31986i | ||||
\(650\) | −13.8548 | + | 42.6408i | −0.543431 | + | 1.67251i | ||||
\(651\) | 2.34554 | − | 1.70413i | 0.0919288 | − | 0.0667902i | ||||
\(652\) | 23.3446 | + | 71.8474i | 0.914246 | + | 2.81376i | ||||
\(653\) | −10.7278 | − | 7.79418i | −0.419810 | − | 0.305010i | 0.357751 | − | 0.933817i | \(-0.383544\pi\) |
−0.777561 | + | 0.628807i | \(0.783544\pi\) | |||||||
\(654\) | 1.55643 | + | 4.79019i | 0.0608611 | + | 0.187311i | ||||
\(655\) | 0.0704639 | + | 0.216866i | 0.00275325 | + | 0.00847364i | ||||
\(656\) | −4.09808 | − | 12.6126i | −0.160003 | − | 0.492440i | ||||
\(657\) | 24.7305 | − | 17.9677i | 0.964828 | − | 0.700989i | ||||
\(658\) | −2.88519 | + | 8.87972i | −0.112477 | + | 0.346167i | ||||
\(659\) | −17.7262 | −0.690514 | −0.345257 | − | 0.938508i | \(-0.612208\pi\) | ||||
−0.345257 | + | 0.938508i | \(0.612208\pi\) | |||||||
\(660\) | −0.570713 | − | 0.414647i | −0.0222150 | − | 0.0161401i | ||||
\(661\) | −19.8499 | − | 14.4218i | −0.772072 | − | 0.560943i | 0.130517 | − | 0.991446i | \(-0.458336\pi\) |
−0.902589 | + | 0.430503i | \(0.858336\pi\) | |||||||
\(662\) | −25.8345 | −1.00409 | ||||||||
\(663\) | 6.96679 | + | 21.4416i | 0.270568 | + | 0.832722i | ||||
\(664\) | −13.4452 | + | 41.3801i | −0.521776 | + | 1.60586i | ||||
\(665\) | 0.111115 | 0.00430885 | ||||||||
\(666\) | 29.6804 | − | 21.5641i | 1.15009 | − | 0.835591i | ||||
\(667\) | −13.7223 | + | 9.96980i | −0.531328 | + | 0.386032i | ||||
\(668\) | −70.3268 | + | 51.0954i | −2.72102 | + | 1.97694i | ||||
\(669\) | 18.6234 | 0.720021 | ||||||||
\(670\) | −0.128372 | + | 0.395087i | −0.00495942 | + | 0.0152635i | ||||
\(671\) | 26.7477 | 1.03258 | ||||||||
\(672\) | 0.189049 | + | 0.137352i | 0.00729272 | + | 0.00529847i | ||||
\(673\) | 32.8103 | 1.26475 | 0.632373 | − | 0.774664i | \(-0.282081\pi\) | ||||
0.632373 | + | 0.774664i | \(0.282081\pi\) | |||||||
\(674\) | 1.50145 | + | 4.62097i | 0.0578335 | + | 0.177993i | ||||
\(675\) | −6.73138 | − | 20.7171i | −0.259091 | − | 0.797400i | ||||
\(676\) | 1.42062 | 0.0546390 | ||||||||
\(677\) | 25.6589 | + | 18.6423i | 0.986150 | + | 0.716480i | 0.959075 | − | 0.283153i | \(-0.0913806\pi\) |
0.0270755 | + | 0.999633i | \(0.491381\pi\) | |||||||
\(678\) | −4.10196 | −0.157535 | ||||||||
\(679\) | −2.42362 | + | 7.45912i | −0.0930098 | + | 0.286255i | ||||
\(680\) | −1.73112 | −0.0663855 | ||||||||
\(681\) | −12.0143 | + | 8.72888i | −0.460388 | + | 0.334491i | ||||
\(682\) | 30.4871 | − | 22.1501i | 1.16741 | − | 0.848173i | ||||
\(683\) | −17.5821 | + | 12.7741i | −0.672761 | + | 0.488789i | −0.870948 | − | 0.491375i | \(-0.836495\pi\) |
0.198188 | + | 0.980164i | \(0.436495\pi\) | |||||||
\(684\) | −21.0717 | −0.805695 | ||||||||
\(685\) | 0.110874 | − | 0.341235i | 0.00423627 | − | 0.0130379i | ||||
\(686\) | −10.4685 | − | 32.2189i | −0.399691 | − | 1.23012i | ||||
\(687\) | 12.7421 | 0.486140 | ||||||||
\(688\) | −9.62718 | − | 6.99455i | −0.367033 | − | 0.266665i | ||||
\(689\) | 41.2541 | + | 29.9728i | 1.57165 | + | 1.14187i | ||||
\(690\) | 0.629214 | 0.0239538 | ||||||||
\(691\) | −8.76590 | + | 26.9787i | −0.333471 | + | 1.02632i | 0.634000 | + | 0.773333i | \(0.281412\pi\) |
−0.967471 | + | 0.252984i | \(0.918588\pi\) | |||||||
\(692\) | 43.8947 | − | 31.8914i | 1.66863 | − | 1.21233i | ||||
\(693\) | 3.59856 | + | 11.0752i | 0.136698 | + | 0.420713i | ||||
\(694\) | −4.71211 | − | 14.5024i | −0.178869 | − | 0.550503i | ||||
\(695\) | −0.194399 | − | 0.598298i | −0.00737396 | − | 0.0226947i | ||||
\(696\) | −8.20607 | − | 5.96206i | −0.311050 | − | 0.225991i | ||||
\(697\) | 7.43111 | + | 22.8706i | 0.281473 | + | 0.866285i | ||||
\(698\) | −41.9259 | + | 30.4609i | −1.58692 | + | 1.15296i | ||||
\(699\) | 4.45448 | − | 13.7095i | 0.168484 | − | 0.518540i | ||||
\(700\) | −6.68076 | − | 20.5613i | −0.252509 | − | 0.777143i | ||||
\(701\) | 0.861950 | + | 0.626244i | 0.0325554 | + | 0.0236529i | 0.603944 | − | 0.797027i | \(-0.293595\pi\) |
−0.571389 | + | 0.820680i | \(0.693595\pi\) | |||||||
\(702\) | −31.6321 | + | 22.9820i | −1.19388 | + | 0.867401i | ||||
\(703\) | 4.44432 | − | 13.6782i | 0.167621 | − | 0.515883i | ||||
\(704\) | −28.8533 | − | 20.9631i | −1.08745 | − | 0.790078i | ||||
\(705\) | −0.107927 | + | 0.0784132i | −0.00406475 | + | 0.00295321i | ||||
\(706\) | −42.4769 | − | 30.8613i | −1.59864 | − | 1.16148i | ||||
\(707\) | −0.567712 | + | 1.74724i | −0.0213510 | + | 0.0657117i | ||||
\(708\) | −7.73547 | + | 23.8073i | −0.290717 | + | 0.894735i | ||||
\(709\) | 38.2390 | 1.43610 | 0.718049 | − | 0.695993i | \(-0.245036\pi\) | ||||
0.718049 | + | 0.695993i | \(0.245036\pi\) | |||||||
\(710\) | −0.926025 | + | 0.227257i | −0.0347531 | + | 0.00852879i | ||||
\(711\) | −1.08381 | −0.0406460 | ||||||||
\(712\) | 12.8537 | − | 39.5596i | 0.481713 | − | 1.48256i | ||||
\(713\) | −6.93994 | + | 21.3589i | −0.259903 | + | 0.799898i | ||||
\(714\) | −13.1630 | − | 9.56348i | −0.492613 | − | 0.357904i | ||||
\(715\) | 0.633527 | − | 0.460284i | 0.0236926 | − | 0.0172137i | ||||
\(716\) | 9.08866 | + | 6.60330i | 0.339659 | + | 0.246777i | ||||
\(717\) | −6.97027 | + | 21.4523i | −0.260309 | + | 0.801150i | ||||
\(718\) | 19.5518 | − | 14.2052i | 0.729667 | − | 0.530134i | ||||
\(719\) | −22.9466 | − | 16.6717i | −0.855765 | − | 0.621750i | 0.0709643 | − | 0.997479i | \(-0.477392\pi\) |
−0.926730 | + | 0.375729i | \(0.877392\pi\) | |||||||
\(720\) | −0.138241 | − | 0.425463i | −0.00515195 | − | 0.0158561i | ||||
\(721\) | 4.67283 | − | 14.3815i | 0.174025 | − | 0.535595i | ||||
\(722\) | 27.7342 | − | 20.1501i | 1.03216 | − | 0.749908i | ||||
\(723\) | −0.914802 | − | 2.81547i | −0.0340219 | − | 0.104709i | ||||
\(724\) | −19.4634 | − | 14.1410i | −0.723351 | − | 0.525545i | ||||
\(725\) | 3.85120 | + | 11.8528i | 0.143030 | + | 0.440201i | ||||
\(726\) | −6.58281 | − | 20.2598i | −0.244311 | − | 0.751911i | ||||
\(727\) | −3.99736 | − | 12.3026i | −0.148254 | − | 0.456279i | 0.849161 | − | 0.528134i | \(-0.177108\pi\) |
−0.997415 | + | 0.0718550i | \(0.977108\pi\) | |||||||
\(728\) | −15.8020 | + | 11.4808i | −0.585662 | + | 0.425508i | ||||
\(729\) | 0.829750 | − | 2.55371i | 0.0307315 | − | 0.0945818i | ||||
\(730\) | 1.48349 | 0.0549063 | ||||||||
\(731\) | 17.4571 | + | 12.6833i | 0.645673 | + | 0.469109i | ||||
\(732\) | −15.3217 | − | 11.1318i | −0.566305 | − | 0.411445i | ||||
\(733\) | 17.0281 | 0.628945 | 0.314473 | − | 0.949267i | \(-0.398172\pi\) | ||||
0.314473 | + | 0.949267i | \(0.398172\pi\) | |||||||
\(734\) | −1.42032 | − | 4.37130i | −0.0524251 | − | 0.161348i | ||||
\(735\) | 0.0680705 | − | 0.209499i | 0.00251082 | − | 0.00772750i | ||||
\(736\) | −1.81011 | −0.0667216 | ||||||||
\(737\) | −13.8079 | + | 10.0320i | −0.508621 | + | 0.369534i | ||||
\(738\) | −14.7558 | + | 10.7207i | −0.543167 | + | 0.394634i | ||||
\(739\) | 19.0150 | − | 13.8152i | 0.699479 | − | 0.508201i | −0.180284 | − | 0.983615i | \(-0.557702\pi\) |
0.879762 | + | 0.475414i | \(0.157702\pi\) | |||||||
\(740\) | 1.18959 | 0.0437303 | ||||||||
\(741\) | −2.07146 | + | 6.37529i | −0.0760969 | + | 0.234202i | ||||
\(742\) | −36.8007 | −1.35100 | ||||||||
\(743\) | −36.9203 | − | 26.8242i | −1.35448 | − | 0.984084i | −0.998775 | − | 0.0494845i | \(-0.984242\pi\) |
−0.355701 | − | 0.934600i | \(-0.615758\pi\) | |||||||
\(744\) | −13.4302 | −0.492376 | ||||||||
\(745\) | −0.103975 | − | 0.320002i | −0.00380935 | − | 0.0117240i | ||||
\(746\) | 8.40078 | + | 25.8549i | 0.307574 | + | 0.946616i | ||||
\(747\) | 20.3885 | 0.745977 | ||||||||
\(748\) | −114.316 | − | 83.0552i | −4.17980 | − | 3.03680i | ||||
\(749\) | −12.0994 | −0.442101 | ||||||||
\(750\) | 0.285791 | − | 0.879574i | 0.0104356 | − | 0.0321175i | ||||
\(751\) | −5.90633 | −0.215525 | −0.107762 | − | 0.994177i | \(-0.534369\pi\) | ||||
−0.107762 | + | 0.994177i | \(0.534369\pi\) | |||||||
\(752\) | 11.9219 | − | 8.66174i | 0.434745 | − | 0.315861i | ||||
\(753\) | −19.5229 | + | 14.1842i | −0.711456 | + | 0.516903i | ||||
\(754\) | 18.0975 | − | 13.1486i | 0.659073 | − | 0.478845i | ||||
\(755\) | −0.275796 | −0.0100373 | ||||||||
\(756\) | 5.82609 | − | 17.9308i | 0.211893 | − | 0.652139i | ||||
\(757\) | −8.15429 | − | 25.0963i | −0.296373 | − | 0.912142i | −0.982757 | − | 0.184902i | \(-0.940803\pi\) |
0.686384 | − | 0.727239i | \(-0.259197\pi\) | |||||||
\(758\) | 75.6259 | 2.74686 | ||||||||
\(759\) | 20.9141 | + | 15.1950i | 0.759134 | + | 0.551543i | ||||
\(760\) | −0.416417 | − | 0.302545i | −0.0151050 | − | 0.0109745i | ||||
\(761\) | −3.89929 | −0.141349 | −0.0706746 | − | 0.997499i | \(-0.522515\pi\) | ||||
−0.0706746 | + | 0.997499i | \(0.522515\pi\) | |||||||
\(762\) | −1.54525 | + | 4.75578i | −0.0559783 | + | 0.172284i | ||||
\(763\) | 2.18110 | − | 1.58466i | 0.0789611 | − | 0.0573686i | ||||
\(764\) | 4.42846 | + | 13.6294i | 0.160216 | + | 0.493095i | ||||
\(765\) | 0.250675 | + | 0.771497i | 0.00906316 | + | 0.0278936i | ||||
\(766\) | 6.07067 | + | 18.6836i | 0.219342 | + | 0.675066i | ||||
\(767\) | −22.4807 | − | 16.3332i | −0.811731 | − | 0.589757i | ||||
\(768\) | 8.13343 | + | 25.0321i | 0.293490 | + | 0.903269i | ||||
\(769\) | −6.48774 | + | 4.71362i | −0.233954 | + | 0.169977i | −0.698585 | − | 0.715527i | \(-0.746187\pi\) |
0.464632 | + | 0.885504i | \(0.346187\pi\) | |||||||
\(770\) | −0.174637 | + | 0.537478i | −0.00629349 | + | 0.0193694i | ||||
\(771\) | −4.32880 | − | 13.3227i | −0.155898 | − | 0.479805i | ||||
\(772\) | 46.0650 | + | 33.4682i | 1.65792 | + | 1.20455i | ||||
\(773\) | −12.8995 | + | 9.37207i | −0.463964 | + | 0.337090i | −0.795084 | − | 0.606499i | \(-0.792573\pi\) |
0.331120 | + | 0.943589i | \(0.392573\pi\) | |||||||
\(774\) | −5.05742 | + | 15.5651i | −0.181785 | + | 0.559477i | ||||
\(775\) | 13.3499 | + | 9.69924i | 0.479541 | + | 0.348407i | ||||
\(776\) | 29.3926 | − | 21.3550i | 1.05513 | − | 0.766598i | ||||
\(777\) | 4.55291 | + | 3.30788i | 0.163335 | + | 0.118670i | ||||
\(778\) | 4.37442 | − | 13.4631i | 0.156831 | − | 0.482675i | ||||
\(779\) | −2.20951 | + | 6.80018i | −0.0791640 | + | 0.243642i | ||||
\(780\) | −0.554459 | −0.0198528 | ||||||||
\(781\) | −36.2677 | − | 14.8091i | −1.29776 | − | 0.529910i | ||||
\(782\) | 126.034 | 4.50695 | ||||||||
\(783\) | −3.35851 | + | 10.3364i | −0.120023 | + | 0.369394i | ||||
\(784\) | −7.51925 | + | 23.1419i | −0.268545 | + | 0.826496i | ||||
\(785\) | −0.594173 | − | 0.431692i | −0.0212069 | − | 0.0154077i | ||||
\(786\) | 8.03175 | − | 5.83541i | 0.286483 | − | 0.208142i | ||||
\(787\) | 5.27755 | + | 3.83437i | 0.188124 | + | 0.136680i | 0.677861 | − | 0.735190i | \(-0.262907\pi\) |
−0.489737 | + | 0.871870i | \(0.662907\pi\) | |||||||
\(788\) | 22.1246 | − | 68.0924i | 0.788155 | − | 2.42569i | ||||
\(789\) | −16.2587 | + | 11.8126i | −0.578825 | + | 0.420541i | ||||
\(790\) | −0.0425519 | − | 0.0309158i | −0.00151393 | − | 0.00109993i | ||||
\(791\) | 0.678494 | + | 2.08819i | 0.0241245 | + | 0.0742475i | ||||
\(792\) | 16.6697 | − | 51.3040i | 0.592331 | − | 1.82301i | ||||
\(793\) | 17.0080 | − | 12.3570i | 0.603972 | − | 0.438811i | ||||
\(794\) | 1.13835 | + | 3.50348i | 0.0403985 | + | 0.124334i | ||||
\(795\) | −0.425394 | − | 0.309067i | −0.0150872 | − | 0.0109615i | ||||
\(796\) | 1.01247 | + | 3.11606i | 0.0358860 | + | 0.110446i | ||||
\(797\) | 3.30088 | + | 10.1591i | 0.116923 | + | 0.359853i | 0.992343 | − | 0.123510i | \(-0.0394152\pi\) |
−0.875420 | + | 0.483363i | \(0.839415\pi\) | |||||||
\(798\) | −1.49494 | − | 4.60094i | −0.0529202 | − | 0.162872i | ||||
\(799\) | −21.6180 | + | 15.7064i | −0.764791 | + | 0.555653i | ||||
\(800\) | −0.410992 | + | 1.26490i | −0.0145308 | + | 0.0447211i | ||||
\(801\) | −19.4915 | −0.688700 | ||||||||
\(802\) | −38.2097 | − | 27.7609i | −1.34923 | − | 0.980273i | ||||
\(803\) | 49.3089 | + | 35.8250i | 1.74007 | + | 1.26424i | ||||
\(804\) | 12.0846 | 0.426191 | ||||||||
\(805\) | −0.104076 | − | 0.320314i | −0.00366821 | − | 0.0112896i | ||||
\(806\) | 9.15271 | − | 28.1691i | 0.322390 | − | 0.992215i | ||||
\(807\) | 9.96566 | 0.350808 | ||||||||
\(808\) | 6.88497 | − | 5.00223i | 0.242212 | − | 0.175978i | ||||
\(809\) | 2.03654 | − | 1.47963i | 0.0716009 | − | 0.0520211i | −0.551409 | − | 0.834235i | \(-0.685910\pi\) |
0.623010 | + | 0.782214i | \(0.285910\pi\) | |||||||
\(810\) | −0.314230 | + | 0.228302i | −0.0110409 | + | 0.00802170i | ||||
\(811\) | 7.42334 | 0.260669 | 0.130334 | − | 0.991470i | \(-0.458395\pi\) | ||||
0.130334 | + | 0.991470i | \(0.458395\pi\) | |||||||
\(812\) | −3.33326 | + | 10.2587i | −0.116974 | + | 0.360010i | ||||
\(813\) | 15.4719 | 0.542624 | ||||||||
\(814\) | 59.1783 | + | 42.9955i | 2.07420 | + | 1.50699i | ||||
\(815\) | 0.864723 | 0.0302899 | ||||||||
\(816\) | 7.93548 | + | 24.4229i | 0.277797 | + | 0.854973i | ||||
\(817\) | 1.98262 | + | 6.10187i | 0.0693631 | + | 0.213478i | ||||
\(818\) | −61.8765 | −2.16346 | ||||||||
\(819\) | 7.40479 | + | 5.37990i | 0.258744 | + | 0.187989i | ||||
\(820\) | −0.591412 | −0.0206530 | ||||||||
\(821\) | 5.20610 | − | 16.0227i | 0.181694 | − | 0.559197i | −0.818182 | − | 0.574960i | \(-0.805018\pi\) |
0.999876 | + | 0.0157630i | \(0.00501773\pi\) | |||||||
\(822\) | −15.6212 | −0.544853 | ||||||||
\(823\) | 4.63854 | − | 3.37010i | 0.161689 | − | 0.117474i | −0.503998 | − | 0.863705i | \(-0.668138\pi\) |
0.665688 | + | 0.746230i | \(0.268138\pi\) | |||||||
\(824\) | −56.6701 | + | 41.1732i | −1.97420 | + | 1.43434i | ||||
\(825\) | 15.3669 | − | 11.1647i | 0.535005 | − | 0.388704i | ||||
\(826\) | 20.0539 | 0.697765 | ||||||||
\(827\) | −4.31284 | + | 13.2736i | −0.149972 | + | 0.461567i | −0.997617 | − | 0.0689976i | \(-0.978020\pi\) |
0.847645 | + | 0.530564i | \(0.178020\pi\) | |||||||
\(828\) | 19.7369 | + | 60.7439i | 0.685905 | + | 2.11100i | ||||
\(829\) | −52.5333 | −1.82456 | −0.912278 | − | 0.409571i | \(-0.865678\pi\) | ||||
−0.912278 | + | 0.409571i | \(0.865678\pi\) | |||||||
\(830\) | 0.800483 | + | 0.581585i | 0.0277852 | + | 0.0201871i | ||||
\(831\) | −0.685241 | − | 0.497857i | −0.0237708 | − | 0.0172705i | ||||
\(832\) | −28.0316 | −0.971819 | ||||||||
\(833\) | 13.6347 | − | 41.9634i | 0.472416 | − | 1.45395i | ||||
\(834\) | −22.1583 | + | 16.0990i | −0.767280 | + | 0.557461i | ||||
\(835\) | 0.307481 | + | 0.946328i | 0.0106408 | + | 0.0327490i | ||||
\(836\) | −12.9830 | − | 39.9574i | −0.449025 | − | 1.38196i | ||||
\(837\) | 4.44685 | + | 13.6860i | 0.153706 | + | 0.473057i | ||||
\(838\) | 37.1837 | + | 27.0155i | 1.28449 | + | 0.933236i | ||||
\(839\) | −4.48967 | − | 13.8178i | −0.155001 | − | 0.477043i | 0.843160 | − | 0.537662i | \(-0.180693\pi\) |
−0.998161 | + | 0.0606191i | \(0.980693\pi\) | |||||||
\(840\) | 0.162944 | − | 0.118386i | 0.00562209 | − | 0.00408469i | ||||
\(841\) | −7.04000 | + | 21.6669i | −0.242759 | + | 0.747134i | ||||
\(842\) | 17.3515 | + | 53.4023i | 0.597971 | + | 1.84036i | ||||
\(843\) | 7.28326 | + | 5.29159i | 0.250849 | + | 0.182252i | ||||
\(844\) | 9.48307 | − | 6.88986i | 0.326421 | − | 0.237159i | ||||
\(845\) | 0.00502494 | − | 0.0154652i | 0.000172863 | − | 0.000532018i | ||||
\(846\) | −16.3964 | − | 11.9127i | −0.563721 | − | 0.409567i | ||||
\(847\) | −9.22483 | + | 6.70223i | −0.316969 | + | 0.230291i | ||||
\(848\) | 46.9902 | + | 34.1404i | 1.61365 | + | 1.17239i | ||||
\(849\) | −0.00522127 | + | 0.0160694i | −0.000179194 | + | 0.000551501i | ||||
\(850\) | 28.6164 | − | 88.0721i | 0.981533 | − | 3.02085i | ||||
\(851\) | −43.5934 | −1.49436 | ||||||||
\(852\) | 14.6117 | + | 23.5768i | 0.500589 | + | 0.807730i | ||||
\(853\) | −45.7488 | −1.56641 | −0.783204 | − | 0.621765i | \(-0.786416\pi\) | ||||
−0.783204 | + | 0.621765i | \(0.786416\pi\) | |||||||
\(854\) | −4.68840 | + | 14.4294i | −0.160434 | + | 0.493765i | ||||
\(855\) | −0.0745339 | + | 0.229392i | −0.00254900 | + | 0.00784503i | ||||
\(856\) | 45.3439 | + | 32.9443i | 1.54982 | + | 1.12601i | ||||
\(857\) | −23.3744 | + | 16.9825i | −0.798453 | + | 0.580110i | −0.910460 | − | 0.413597i | \(-0.864272\pi\) |
0.112007 | + | 0.993707i | \(0.464272\pi\) | |||||||
\(858\) | −27.5825 | − | 20.0398i | −0.941650 | − | 0.684149i | ||||
\(859\) | 4.75705 | − | 14.6407i | 0.162309 | − | 0.499535i | −0.836519 | − | 0.547938i | \(-0.815413\pi\) |
0.998828 | + | 0.0484029i | \(0.0154132\pi\) | |||||||
\(860\) | −0.429329 | + | 0.311926i | −0.0146400 | + | 0.0106366i | ||||
\(861\) | −2.26350 | − | 1.64453i | −0.0771399 | − | 0.0560454i | ||||
\(862\) | 4.68832 | + | 14.4292i | 0.159685 | + | 0.491460i | ||||
\(863\) | −2.59354 | + | 7.98209i | −0.0882851 | + | 0.271714i | −0.985446 | − | 0.169991i | \(-0.945626\pi\) |
0.897161 | + | 0.441705i | \(0.145626\pi\) | |||||||
\(864\) | −0.938339 | + | 0.681743i | −0.0319229 | + | 0.0231934i | ||||
\(865\) | −0.191915 | − | 0.590654i | −0.00652531 | − | 0.0200828i | ||||
\(866\) | −31.5768 | − | 22.9419i | −1.07302 | − | 0.779597i | ||||
\(867\) | −10.0952 | − | 31.0697i | −0.342850 | − | 1.05518i | ||||
\(868\) | 4.41341 | + | 13.5831i | 0.149801 | + | 0.461040i | ||||
\(869\) | −0.667770 | − | 2.05519i | −0.0226526 | − | 0.0697174i | ||||
\(870\) | −0.186614 | + | 0.135583i | −0.00632681 | + | 0.00459670i | ||||
\(871\) | −4.14535 | + | 12.7581i | −0.140460 | + | 0.432291i | ||||
\(872\) | −12.4887 | −0.422920 | ||||||||
\(873\) | −13.7733 | − | 10.0069i | −0.466155 | − | 0.338682i | ||||
\(874\) | 30.3170 | + | 22.0266i | 1.02549 | + | 0.745062i | ||||
\(875\) | −0.495038 | −0.0167353 | ||||||||
\(876\) | −13.3356 | − | 41.0427i | −0.450567 | − | 1.38670i | ||||
\(877\) | −2.86602 | + | 8.82069i | −0.0967785 | + | 0.297853i | −0.987713 | − | 0.156278i | \(-0.950050\pi\) |
0.890935 | + | 0.454132i | \(0.150050\pi\) | |||||||
\(878\) | 26.7561 | 0.902975 | ||||||||
\(879\) | −16.1876 | + | 11.7610i | −0.545993 | + | 0.396687i | ||||
\(880\) | 0.721615 | − | 0.524284i | 0.0243256 | − | 0.0176736i | ||||
\(881\) | 2.90353 | − | 2.10954i | 0.0978223 | − | 0.0710721i | −0.537799 | − | 0.843073i | \(-0.680744\pi\) |
0.635621 | + | 0.772001i | \(0.280744\pi\) | |||||||
\(882\) | 33.4655 | 1.12684 | ||||||||
\(883\) | −14.3137 | + | 44.0529i | −0.481693 | + | 1.48250i | 0.355022 | + | 0.934858i | \(0.384474\pi\) |
−0.836714 | + | 0.547640i | \(0.815526\pi\) | |||||||
\(884\) | −111.060 | −3.73535 | ||||||||
\(885\) | 0.231811 | + | 0.168421i | 0.00779225 | + | 0.00566140i | ||||
\(886\) | 18.4206 | 0.618853 | ||||||||
\(887\) | 3.07456 | + | 9.46251i | 0.103234 | + | 0.317720i | 0.989312 | − | 0.145816i | \(-0.0465806\pi\) |
−0.886078 | + | 0.463536i | \(0.846581\pi\) | |||||||
\(888\) | −8.05587 | − | 24.7934i | −0.270337 | − | 0.832013i | ||||
\(889\) | 2.67662 | 0.0897710 | ||||||||
\(890\) | −0.765266 | − | 0.555998i | −0.0256518 | − | 0.0186371i | ||||
\(891\) | −15.9578 | −0.534608 | ||||||||
\(892\) | −28.3496 | + | 87.2512i | −0.949216 | + | 2.92139i | ||||
\(893\) | −7.94514 | −0.265874 | ||||||||
\(894\) | −11.8515 | + | 8.61060i | −0.396373 | + | 0.287982i | ||||
\(895\) | 0.104033 | − | 0.0755846i | 0.00347745 | − | 0.00252651i | ||||
\(896\) | 16.8289 | − | 12.2269i | 0.562213 | − | 0.408472i | ||||
\(897\) | 20.3185 | 0.678414 | ||||||||
\(898\) | −9.98523 | + | 30.7314i | −0.333211 | + | 1.02552i | ||||
\(899\) | −2.54416 | − | 7.83012i | −0.0848525 | − | 0.261149i | ||||
\(900\) | 46.9291 | 1.56430 | ||||||||
\(901\) | −85.2079 | − | 61.9072i | −2.83869 | − | 2.06243i | ||||
\(902\) | −29.4208 | − | 21.3754i | −0.979604 | − | 0.711724i | ||||
\(903\) | −2.51053 | −0.0835453 | ||||||||
\(904\) | 3.14300 | − | 9.67316i | 0.104535 | − | 0.321725i | ||||
\(905\) | −0.222787 | + | 0.161864i | −0.00740570 | + | 0.00538056i | ||||
\(906\) | 3.71056 | + | 11.4199i | 0.123275 | + | 0.379401i | ||||
\(907\) | −5.17980 | − | 15.9418i | −0.171992 | − | 0.529338i | 0.827491 | − | 0.561479i | \(-0.189767\pi\) |
−0.999483 | + | 0.0321409i | \(0.989767\pi\) | |||||||
\(908\) | −22.6063 | − | 69.5750i | −0.750216 | − | 2.30893i | ||||
\(909\) | −3.22628 | − | 2.34403i | −0.107009 | − | 0.0777466i | ||||
\(910\) | 0.137261 | + | 0.422445i | 0.00455015 | + | 0.0140039i | ||||
\(911\) | 25.0425 | − | 18.1945i | 0.829696 | − | 0.602810i | −0.0897771 | − | 0.995962i | \(-0.528615\pi\) |
0.919473 | + | 0.393152i | \(0.128615\pi\) | |||||||
\(912\) | −2.35948 | + | 7.26174i | −0.0781302 | + | 0.240460i | ||||
\(913\) | 12.5620 | + | 38.6620i | 0.415743 | + | 1.27953i | ||||
\(914\) | 32.0953 | + | 23.3186i | 1.06162 | + | 0.771312i | ||||
\(915\) | −0.175379 | + | 0.127420i | −0.00579786 | + | 0.00421239i | ||||
\(916\) | −19.3968 | + | 59.6971i | −0.640887 | + | 1.97245i | ||||
\(917\) | −4.29915 | − | 3.12351i | −0.141970 | − | 0.103147i | ||||
\(918\) | 65.3342 | − | 47.4681i | 2.15635 | − | 1.56668i | ||||
\(919\) | 28.5867 | + | 20.7694i | 0.942987 | + | 0.685120i | 0.949138 | − | 0.314861i | \(-0.101958\pi\) |
−0.00615103 | + | 0.999981i | \(0.501958\pi\) | |||||||
\(920\) | −0.482115 | + | 1.48380i | −0.0158949 | + | 0.0489194i | ||||
\(921\) | −2.19711 | + | 6.76201i | −0.0723973 | + | 0.222816i | ||||
\(922\) | 17.4428 | 0.574448 | ||||||||
\(923\) | −29.9031 | + | 7.33854i | −0.984271 | + | 0.241551i | ||||
\(924\) | 16.4399 | 0.540834 | ||||||||
\(925\) | −9.89802 | + | 30.4630i | −0.325445 | + | 1.00162i | ||||
\(926\) | −5.66408 | + | 17.4322i | −0.186133 | + | 0.572859i | ||||
\(927\) | 26.5555 | + | 19.2937i | 0.872197 | + | 0.633688i | ||||
\(928\) | 0.536848 | − | 0.390043i | 0.0176229 | − | 0.0128038i | ||||
\(929\) | 21.9212 | + | 15.9267i | 0.719210 | + | 0.522537i | 0.886132 | − | 0.463433i | \(-0.153383\pi\) |
−0.166921 | + | 0.985970i | \(0.553383\pi\) | |||||||
\(930\) | −0.0943788 | + | 0.290468i | −0.00309480 | + | 0.00952482i | ||||
\(931\) | 10.6137 | − | 7.71128i | 0.347849 | − | 0.252727i | ||||
\(932\) | 57.4486 | + | 41.7388i | 1.88179 | + | 1.36720i | ||||
\(933\) | −4.94120 | − | 15.2074i | −0.161768 | − | 0.497869i | ||||
\(934\) | −13.3432 | + | 41.0660i | −0.436601 | + | 1.34372i | ||||
\(935\) | −1.30851 | + | 0.950691i | −0.0427930 | + | 0.0310909i | ||||
\(936\) | −13.1020 | − | 40.3237i | −0.428251 | − | 1.31802i | ||||
\(937\) | 35.7948 | + | 26.0064i | 1.16936 | + | 0.849593i | 0.990933 | − | 0.134359i | \(-0.0428975\pi\) |
0.178432 | + | 0.983952i | \(0.442897\pi\) | |||||||
\(938\) | −2.99164 | − | 9.20731i | −0.0976804 | − | 0.300629i | ||||
\(939\) | −5.65249 | − | 17.3966i | −0.184462 | − | 0.567716i | ||||
\(940\) | −0.203077 | − | 0.625006i | −0.00662363 | − | 0.0203854i | ||||
\(941\) | −9.78443 | + | 7.10880i | −0.318963 | + | 0.231740i | −0.735733 | − | 0.677272i | \(-0.763162\pi\) |
0.416770 | + | 0.909012i | \(0.363162\pi\) | |||||||
\(942\) | −9.88111 | + | 30.4109i | −0.321944 | + | 0.990841i | ||||
\(943\) | 21.6726 | 0.705758 | ||||||||
\(944\) | −25.6065 | − | 18.6042i | −0.833421 | − | 0.605515i | ||||
\(945\) | −0.174592 | − | 0.126849i | −0.00567948 | − | 0.00412638i | ||||
\(946\) | −32.6317 | −1.06095 | ||||||||
\(947\) | −0.144306 | − | 0.444127i | −0.00468931 | − | 0.0144322i | 0.948684 | − | 0.316224i | \(-0.102415\pi\) |
−0.953374 | + | 0.301792i | \(0.902415\pi\) | |||||||
\(948\) | −0.472813 | + | 1.45517i | −0.0153562 | + | 0.0472617i | ||||
\(949\) | 47.9045 | 1.55505 | ||||||||
\(950\) | 22.2758 | − | 16.1843i | 0.722721 | − | 0.525088i | ||||
\(951\) | 0.0152131 | − | 0.0110529i | 0.000493317 | − | 0.000358416i | ||||
\(952\) | 32.6382 | − | 23.7130i | 1.05781 | − | 0.768543i | ||||
\(953\) | −47.2896 | −1.53186 | −0.765931 | − | 0.642923i | \(-0.777721\pi\) | ||||
−0.765931 | + | 0.642923i | \(0.777721\pi\) | |||||||
\(954\) | 24.6852 | − | 75.9734i | 0.799214 | − | 2.45973i | ||||
\(955\) | 0.164038 | 0.00530813 | ||||||||
\(956\) | −89.8942 | − | 65.3120i | −2.90739 | − | 2.11234i | ||||
\(957\) | −9.47699 | −0.306348 | ||||||||
\(958\) | −19.6201 | − | 60.3845i | −0.633898 | − | 1.95094i | ||||
\(959\) | 2.58386 | + | 7.95231i | 0.0834373 | + | 0.256794i | ||||
\(960\) | 0.289049 | 0.00932903 | ||||||||
\(961\) | 16.2604 | + | 11.8139i | 0.524529 | + | 0.381093i | ||||
\(962\) | 57.4929 | 1.85365 | ||||||||
\(963\) | 8.11604 | − | 24.9786i | 0.261536 | − | 0.804924i | ||||
\(964\) | 14.5832 | 0.469692 | ||||||||
\(965\) | 0.527283 | − | 0.383093i | 0.0169738 | − | 0.0123322i | ||||
\(966\) | −11.8630 | + | 8.61900i | −0.381687 | + | 0.277312i | ||||
\(967\) | 8.17108 | − | 5.93664i | 0.262764 | − | 0.190909i | −0.448601 | − | 0.893732i | \(-0.648077\pi\) |
0.711365 | + | 0.702823i | \(0.248077\pi\) | |||||||
\(968\) | 52.8201 | 1.69770 | ||||||||
\(969\) | 4.27847 | − | 13.1678i | 0.137444 | − | 0.423010i | ||||
\(970\) | −0.255312 | − | 0.785770i | −0.00819757 | − | 0.0252295i | ||||
\(971\) | 37.9632 | 1.21830 | 0.609148 | − | 0.793057i | \(-0.291512\pi\) | ||||
0.609148 | + | 0.793057i | \(0.291512\pi\) | |||||||
\(972\) | 51.7389 | + | 37.5905i | 1.65953 | + | 1.20572i | ||||
\(973\) | 11.8607 | + | 8.61727i | 0.380235 | + | 0.276257i | ||||
\(974\) | −59.3868 | −1.90287 | ||||||||
\(975\) | 4.61338 | − | 14.1985i | 0.147746 | − | 0.454717i | ||||
\(976\) | 19.3729 | − | 14.0752i | 0.620110 | − | 0.450536i | ||||
\(977\) | −5.96992 | − | 18.3735i | −0.190995 | − | 0.587821i | −1.00000 | 1.98463e-5i | \(-0.999994\pi\) | |
0.809005 | − | 0.587801i | \(-0.200006\pi\) | |||||||
\(978\) | −11.6340 | − | 35.8056i | −0.372013 | − | 1.14494i | ||||
\(979\) | −12.0094 | − | 36.9611i | −0.383822 | − | 1.18128i | ||||
\(980\) | 0.877893 | + | 0.637826i | 0.0280432 | + | 0.0203746i | ||||
\(981\) | 1.80842 | + | 5.56574i | 0.0577384 | + | 0.177701i | ||||
\(982\) | 21.4918 | − | 15.6147i | 0.685830 | − | 0.498285i | ||||
\(983\) | −3.98686 | + | 12.2703i | −0.127161 | + | 0.391362i | −0.994289 | − | 0.106724i | \(-0.965964\pi\) |
0.867127 | + | 0.498086i | \(0.165964\pi\) | |||||||
\(984\) | 4.00501 | + | 12.3262i | 0.127675 | + | 0.392944i | ||||
\(985\) | −0.663014 | − | 0.481708i | −0.0211254 | − | 0.0153485i | ||||
\(986\) | −37.3794 | + | 27.1577i | −1.19040 | + | 0.864878i | ||||
\(987\) | 0.960712 | − | 2.95677i | 0.0305798 | − | 0.0941149i | ||||
\(988\) | −26.7152 | − | 19.4097i | −0.849923 | − | 0.617505i | ||||
\(989\) | 15.7330 | − | 11.4307i | 0.500281 | − | 0.363475i | ||||
\(990\) | −0.992456 | − | 0.721061i | −0.0315423 | − | 0.0229168i | ||||
\(991\) | 15.9502 | − | 49.0895i | 0.506673 | − | 1.55938i | −0.291265 | − | 0.956642i | \(-0.594076\pi\) |
0.797939 | − | 0.602738i | \(-0.205924\pi\) | |||||||
\(992\) | 0.271507 | − | 0.835614i | 0.00862037 | − | 0.0265308i | ||||
\(993\) | 8.60236 | 0.272988 | ||||||||
\(994\) | 14.3461 | − | 16.9694i | 0.455030 | − | 0.538236i | ||||
\(995\) | 0.0375035 | 0.00118894 | ||||||||
\(996\) | 8.89452 | − | 27.3745i | 0.281834 | − | 0.867395i | ||||
\(997\) | −2.93531 | + | 9.03394i | −0.0929621 | + | 0.286108i | −0.986717 | − | 0.162447i | \(-0.948061\pi\) |
0.893755 | + | 0.448555i | \(0.148061\pi\) | |||||||
\(998\) | −66.6281 | − | 48.4081i | −2.10907 | − | 1.53233i | ||||
\(999\) | −22.5982 | + | 16.4186i | −0.714977 | + | 0.519461i |
(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 | 71.2.c.a.57.5 | yes | 20 | |
3.2 | odd | 2 | 639.2.f.c.199.1 | 20 | |||
71.5 | even | 5 | inner | 71.2.c.a.5.5 | ✓ | 20 | |
71.17 | odd | 10 | 5041.2.a.j.1.9 | 10 | |||
71.54 | even | 5 | 5041.2.a.i.1.9 | 10 | |||
213.5 | odd | 10 | 639.2.f.c.289.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
71.2.c.a.5.5 | ✓ | 20 | 71.5 | even | 5 | inner | |
71.2.c.a.57.5 | yes | 20 | 1.1 | even | 1 | trivial | |
639.2.f.c.199.1 | 20 | 3.2 | odd | 2 | |||
639.2.f.c.289.1 | 20 | 213.5 | odd | 10 | |||
5041.2.a.i.1.9 | 10 | 71.54 | even | 5 | |||
5041.2.a.j.1.9 | 10 | 71.17 | odd | 10 |