LMFDB - Embedded newform 567.2.bd.a.467.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(17,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([11, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			467.17
Character	$\chi$	$=$	567.467
Dual form			567.2.bd.a.17.17

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.57155 + 0.277106i) q^{2} +(0.513586 + 0.186930i) q^{4} +(-1.78318 - 0.649025i) q^{5} +(-1.28547 - 2.31248i) q^{7} +(-2.00866 - 1.15970i) q^{8} +(-2.62250 - 1.51410i) q^{10} +(-0.432011 - 1.18694i) q^{11} +(0.326917 - 0.898197i) q^{13} +(-1.37938 - 3.99038i) q^{14} +(-3.67271 - 3.08177i) q^{16} +(2.00687 - 3.47600i) q^{17} +(6.64640 - 3.83730i) q^{19} +(-0.794495 - 0.666660i) q^{20} +(-0.350017 - 1.98504i) q^{22} +(-5.63807 + 0.994145i) q^{23} +(-1.07172 - 0.899282i) q^{25} +(0.762661 - 1.32097i) q^{26} +(-0.227929 - 1.42795i) q^{28} +(1.22870 + 3.37583i) q^{29} +(-3.04428 + 8.36408i) q^{31} +(-1.93608 - 2.30734i) q^{32} +(4.11711 - 4.90658i) q^{34} +(0.791374 + 4.95787i) q^{35} -7.99870 q^{37} +(11.5085 - 4.18874i) q^{38} +(2.82914 + 3.37163i) q^{40} +(3.01647 + 1.09790i) q^{41} +(0.111496 - 0.632326i) q^{43} -0.690352i q^{44} -9.13598 q^{46} +(8.03521 - 2.92458i) q^{47} +(-3.69512 + 5.94526i) q^{49} +(-1.43506 - 1.71024i) q^{50} +(0.335800 - 0.400191i) q^{52} +(11.3329 - 6.54305i) q^{53} +2.39691i q^{55} +(-0.0997058 + 6.13576i) q^{56} +(0.995499 + 5.64576i) q^{58} +(1.65418 - 1.38802i) q^{59} +(-1.05430 - 2.89668i) q^{61} +(-7.10196 + 12.3010i) q^{62} +(2.39111 + 4.14152i) q^{64} +(-1.16590 + 1.38947i) q^{65} +(0.371427 + 2.10647i) q^{67} +(1.68047 - 1.41008i) q^{68} +(-0.130175 + 8.01082i) q^{70} +(0.154696 - 0.0893139i) q^{71} -11.5040i q^{73} +(-12.5703 - 2.21649i) q^{74} +(4.13081 - 0.728373i) q^{76} +(-2.18944 + 2.52480i) q^{77} +(-0.211994 + 1.20228i) q^{79} +(4.54896 + 7.87903i) q^{80} +(4.43628 + 2.56129i) q^{82} +(5.11532 - 1.86183i) q^{83} +(-5.83462 + 4.89582i) q^{85} +(0.350443 - 0.962834i) q^{86} +(-0.508733 + 2.88517i) q^{88} +(-2.81958 - 4.88366i) q^{89} +(-2.49730 + 0.398619i) q^{91} +(-3.08147 - 0.543347i) q^{92} +(13.4381 - 2.36950i) q^{94} +(-14.3422 + 2.52892i) q^{95} +(5.97585 + 1.05370i) q^{97} +(-7.45452 + 8.31931i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31}+ \cdots + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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 $

$2$	1.57155	+	0.277106i	1.11125	+	0.195944i	0.698997	−	0.715125i	$-0.253630\pi$
$2$	1.57155	+	0.277106i	1.11125	+	0.195944i	0.412255	+	0.911069i	$0.364741\pi$
$3$		0			0
$3$		0			0
$4$	0.513586	+	0.186930i	0.256793	+	0.0934650i
$5$	−1.78318	−	0.649025i	−0.797463	−	0.290253i	−0.0890280	−	0.996029i	$-0.528376\pi$
$5$	−1.78318	−	0.649025i	−0.797463	−	0.290253i	−0.708435	+	0.705776i	$0.750598\pi$
$6$		0			0
$7$	−1.28547	−	2.31248i	−0.485863	−	0.874035i
$7$	−1.28547	−	2.31248i	−0.485863	−	0.874035i
$8$	−2.00866	−	1.15970i	−0.710170	−	0.410017i
$9$		0			0
$10$	−2.62250	−	1.51410i	−0.829308	−	0.478801i
$11$	−0.432011	−	1.18694i	−0.130256	−	0.357876i	0.857370	−	0.514700i	$-0.172097\pi$
$11$	−0.432011	−	1.18694i	−0.130256	−	0.357876i	−0.987627	+	0.156824i	$0.949874\pi$
$12$		0			0
$13$	0.326917	−	0.898197i	0.0906704	−	0.249115i	−0.886066	−	0.463560i	$-0.846572\pi$
$13$	0.326917	−	0.898197i	0.0906704	−	0.249115i	0.976736	+	0.214445i	$0.0687942\pi$
$14$	−1.37938	−	3.99038i	−0.368654	−	1.06647i
$15$		0			0
$16$	−3.67271	−	3.08177i	−0.918177	−	0.770442i
$17$	2.00687	−	3.47600i	0.486737	−	0.843053i	−0.513147	−	0.858301i	$-0.671520\pi$
$17$	2.00687	−	3.47600i	0.486737	−	0.843053i	0.999884	+	0.0152477i	$0.00485368\pi$
$18$		0			0
$19$	6.64640	−	3.83730i	1.52479	−	0.880338i	0.525221	−	0.850966i	$-0.323983\pi$
$19$	6.64640	−	3.83730i	1.52479	−	0.880338i	0.999569	−	0.0293716i	$-0.00935062\pi$
$20$	−0.794495	−	0.666660i	−0.177654	−	0.149070i
$21$		0			0
$22$	−0.350017	−	1.98504i	−0.0746239	−	0.423213i
$23$	−5.63807	+	0.994145i	−1.17562	+	0.207293i	−0.727133	−	0.686496i	$-0.759148\pi$
$23$	−5.63807	+	0.994145i	−1.17562	+	0.207293i	−0.448486	+	0.893790i	$0.648037\pi$
$24$		0			0
$25$	−1.07172	−	0.899282i	−0.214344	−	0.179856i
$26$	0.762661	−	1.32097i	0.149570	−	0.259063i
$27$		0			0
$28$	−0.227929	−	1.42795i	−0.0430745	−	0.269857i
$29$	1.22870	+	3.37583i	0.228164	+	0.626876i	0.999960	−	0.00899503i	$-0.00286324\pi$
$29$	1.22870	+	3.37583i	0.228164	+	0.626876i	−0.771795	+	0.635871i	$0.780641\pi$
$30$		0			0
$31$	−3.04428	+	8.36408i	−0.546768	+	1.50223i	0.291280	+	0.956638i	$0.405919\pi$
$31$	−3.04428	+	8.36408i	−0.546768	+	1.50223i	−0.838048	+	0.545596i	$0.816303\pi$
$32$	−1.93608	−	2.30734i	−0.342255	−	0.407883i
$33$		0			0
$34$	4.11711	−	4.90658i	0.706078	−	0.841471i
$35$	0.791374	+	4.95787i	0.133767	+	0.838033i
$36$		0			0
$37$	−7.99870			−1.31498			−0.657489	−	0.753464i	$-0.728381\pi$
$37$	−7.99870			−1.31498			−0.657489	+	0.753464i	$0.728381\pi$
$38$	11.5085	−	4.18874i	1.86692	−	0.679504i
$39$		0			0
$40$	2.82914	+	3.37163i	0.447326	+	0.533102i
$41$	3.01647	+	1.09790i	0.471093	+	0.171464i	0.566647	−	0.823960i	$-0.308240\pi$
$41$	3.01647	+	1.09790i	0.471093	+	0.171464i	−0.0955544	+	0.995424i	$0.530462\pi$
$42$		0			0
$43$	0.111496	−	0.632326i	0.0170030	−	0.0964289i	−0.975125	−	0.221654i	$-0.928854\pi$
$43$	0.111496	−	0.632326i	0.0170030	−	0.0964289i	0.992128	+	0.125226i	$0.0399654\pi$
$44$		−	0.690352i		−	0.104074i
$45$		0			0
$46$	−9.13598			−1.34703
$47$	8.03521	−	2.92458i	1.17206	−	0.426593i	0.318666	−	0.947867i	$-0.396765\pi$
$47$	8.03521	−	2.92458i	1.17206	−	0.426593i	0.853389	+	0.521274i	$0.174543\pi$
$48$		0			0
$49$	−3.69512	+	5.94526i	−0.527874	+	0.849323i
$50$	−1.43506	−	1.71024i	−0.202949	−	0.241865i
$51$		0			0
$52$	0.335800	−	0.400191i	0.0465671	−	0.0554965i
$53$	11.3329	−	6.54305i	1.55669	−	0.898757i	0.559123	−	0.829085i	$-0.311138\pi$
$53$	11.3329	−	6.54305i	1.55669	−	0.898757i	0.997570	−	0.0696726i	$-0.0221955\pi$
$54$		0			0
$55$			2.39691i			0.323200i
$56$	−0.0997058	+	6.13576i	−0.0133237	+	0.819926i
$57$		0			0
$58$	0.995499	+	5.64576i	0.130715	+	0.741324i
$59$	1.65418	−	1.38802i	0.215356	−	0.180705i	−0.528728	−	0.848791i	$-0.677331\pi$
$59$	1.65418	−	1.38802i	0.215356	−	0.180705i	0.744084	+	0.668086i	$0.232886\pi$
$60$		0			0
$61$	−1.05430	−	2.89668i	−0.134990	−	0.370882i	0.853718	−	0.520735i	$-0.174342\pi$
$61$	−1.05430	−	2.89668i	−0.134990	−	0.370882i	−0.988708	+	0.149853i	$0.952120\pi$
$62$	−7.10196	+	12.3010i	−0.901950	+	1.56222i
$63$		0			0
$64$	2.39111	+	4.14152i	0.298889	+	0.517690i
$65$	−1.16590	+	1.38947i	−0.144613	+	0.172343i
$66$		0			0
$67$	0.371427	+	2.10647i	0.0453770	+	0.257346i	0.999054	−	0.0434866i	$-0.0138466\pi$
$67$	0.371427	+	2.10647i	0.0453770	+	0.257346i	−0.953677	+	0.300833i	$0.902735\pi$
$68$	1.68047	−	1.41008i	0.203787	−	0.170997i
$69$		0			0
$70$	−0.130175	+	8.01082i	−0.0155589	+	0.957476i
$71$	0.154696	−	0.0893139i	0.0183591	−	0.0105996i	−0.490792	−	0.871277i	$-0.663293\pi$
$71$	0.154696	−	0.0893139i	0.0183591	−	0.0105996i	0.509151	+	0.860677i	$0.329959\pi$
$72$		0			0
$73$		−	11.5040i		−	1.34644i	−0.739443	−	0.673220i	$-0.764911\pi$
$73$		−	11.5040i		−	1.34644i	0.739443	−	0.673220i	$-0.235089\pi$
$74$	−12.5703	−	2.21649i	−1.46127	−	0.257662i
$75$		0			0
$76$	4.13081	−	0.728373i	0.473836	−	0.0835501i
$77$	−2.18944	+	2.52480i	−0.249509	+	0.287727i
$78$		0			0
$79$	−0.211994	+	1.20228i	−0.0238512	+	0.135267i	−0.994408	−	0.105605i	$-0.966322\pi$
$79$	−0.211994	+	1.20228i	−0.0238512	+	0.135267i	0.970557	+	0.240872i	$0.0774333\pi$
$80$	4.54896	+	7.87903i	0.508589	+	0.880902i
$81$		0			0
$82$	4.43628	+	2.56129i	0.489906	+	0.282847i
$83$	5.11532	−	1.86183i	0.561480	−	0.204362i	−0.0456599	−	0.998957i	$-0.514539\pi$
$83$	5.11532	−	1.86183i	0.561480	−	0.204362i	0.607140	+	0.794595i	$0.292317\pi$
$84$		0			0
$85$	−5.83462	+	4.89582i	−0.632853	+	0.531027i
$86$	0.350443	−	0.962834i	0.0377892	−	0.103825i
$87$		0			0
$88$	−0.508733	+	2.88517i	−0.0542311	+	0.307560i
$89$	−2.81958	−	4.88366i	−0.298875	−	0.517667i	0.677004	−	0.735980i	$-0.263278\pi$
$89$	−2.81958	−	4.88366i	−0.298875	−	0.517667i	−0.975879	+	0.218313i	$0.929945\pi$
$90$		0			0
$91$	−2.49730	+	0.398619i	−0.261789	+	0.0417866i
$92$	−3.08147	−	0.543347i	−0.321266	−	0.0566478i
$93$		0			0
$94$	13.4381	−	2.36950i	1.38604	−	0.244396i
$95$	−14.3422	+	2.52892i	−1.47148	+	0.259462i
$96$		0			0
$97$	5.97585	+	1.05370i	0.606755	+	0.106987i	0.468581	−	0.883421i	$-0.344765\pi$
$97$	5.97585	+	1.05370i	0.606755	+	0.106987i	0.138174	+	0.990408i	$0.455877\pi$
$98$	−7.45452	+	8.31931i	−0.753020	+	0.840377i
$99$		0			0
$100$	−0.382319	−	0.662196i	−0.0382319	−	0.0662196i
$101$	−1.20524	+	6.83528i	−0.119926	+	0.680136i	0.864266	+	0.503034i	$0.167783\pi$
$101$	−1.20524	+	6.83528i	−0.119926	+	0.680136i	−0.984193	+	0.177101i	$0.943328\pi$
$102$		0			0
$103$	4.40696	−	12.1080i	0.434231	−	1.19304i	−0.508961	−	0.860790i	$-0.669970\pi$
$103$	4.40696	−	12.1080i	0.434231	−	1.19304i	0.943192	−	0.332249i	$-0.107808\pi$
$104$	−1.69831	+	1.42505i	−0.166533	+	0.139738i
$105$		0			0
$106$	19.6233	−	7.14230i	1.90598	−	0.693721i
$107$	1.24002	+	0.715923i	0.119877	+	0.0692109i	0.558739	−	0.829343i	$-0.311285\pi$
$107$	1.24002	+	0.715923i	0.119877	+	0.0692109i	−0.438863	+	0.898554i	$0.644619\pi$
$108$		0			0
$109$	−0.946256	−	1.63896i	−0.0906349	−	0.156984i	0.817144	−	0.576434i	$-0.195556\pi$
$109$	−0.946256	−	1.63896i	−0.0906349	−	0.156984i	−0.907778	+	0.419450i	$0.862223\pi$
$110$	−0.664200	+	3.76686i	−0.0633289	+	0.359156i
$111$		0			0
$112$	−2.40536	+	12.4546i	−0.227285	+	1.17685i
$113$	−0.855475	+	0.150843i	−0.0804763	+	0.0141901i	−0.213741	−	0.976890i	$-0.568565\pi$
$113$	−0.855475	+	0.150843i	−0.0804763	+	0.0141901i	0.133265	+	0.991080i	$0.457454\pi$
$114$		0			0
$115$	10.6989	+	1.88651i	0.997680	+	0.175918i
$116$			1.96346i			0.182303i
$117$		0			0
$118$	2.98425	−	1.72296i	0.274723	−	0.158611i
$119$	−10.6179	−	0.172541i	−0.973345	−	0.0158168i
$120$		0			0
$121$	7.20430	−	6.04512i	0.654936	−	0.549557i
$122$	−0.854202	−	4.84442i	−0.0773358	−	0.438593i
$123$		0			0
$124$	−3.12700	+	3.72661i	−0.280813	+	0.334659i
$125$	6.07147	+	10.5161i	0.543049	+	0.940588i
$126$		0			0
$127$	−6.79273	+	11.7654i	−0.602757	+	1.04401i	0.389644	+	0.920965i	$0.372598\pi$
$127$	−6.79273	+	11.7654i	−0.602757	+	1.04401i	−0.992402	+	0.123041i	$0.960735\pi$
$128$	4.67044	+	12.8319i	0.412812	+	1.13419i
$129$		0			0
$130$	−2.21730	+	1.86054i	−0.194470	+	0.163180i
$131$	−1.57513	−	8.93299i	−0.137620	−	0.780479i	−0.973000	−	0.230807i	$-0.925864\pi$
$131$	−1.57513	−	8.93299i	−0.137620	−	0.780479i	0.835380	−	0.549673i	$-0.185248\pi$
$132$		0			0
$133$	−17.4175	−	10.4369i	−1.51028	−	0.904996i
$134$			3.41334i			0.294867i
$135$		0			0
$136$	−8.06225	+	4.65474i	−0.691332	+	0.399141i
$137$	12.9124	−	15.3884i	1.10318	−	1.31472i	0.158263	−	0.987397i	$-0.449410\pi$
$137$	12.9124	−	15.3884i	1.10318	−	1.31472i	0.944914	−	0.327319i	$-0.106145\pi$
$138$		0			0
$139$	4.91571	+	5.85831i	0.416945	+	0.496895i	0.933109	−	0.359594i	$-0.117085\pi$
$139$	4.91571	+	5.85831i	0.416945	+	0.496895i	−0.516164	+	0.856490i	$0.672640\pi$
$140$	−0.520337	+	2.69423i	−0.0439765	+	0.227704i
$141$		0			0
$142$	0.267862	−	0.0974937i	0.0224785	−	0.00818149i
$143$	−1.20734			−0.100963
$144$		0			0
$145$		−	6.81717i		−	0.566135i
$146$	3.18782	−	18.0790i	0.263826	−	1.49623i
$147$		0			0
$148$	−4.10802	−	1.49520i	−0.337677	−	0.122904i
$149$	−4.75604	−	5.66803i	−0.389630	−	0.464343i	0.535199	−	0.844726i	$-0.320237\pi$
$149$	−4.75604	−	5.66803i	−0.389630	−	0.464343i	−0.924829	+	0.380383i	$0.875792\pi$
$150$		0			0
$151$	5.79884	−	2.11061i	0.471903	−	0.171759i	−0.0951111	−	0.995467i	$-0.530321\pi$
$151$	5.79884	−	2.11061i	0.471903	−	0.171759i	0.567014	+	0.823708i	$0.308098\pi$
$152$	−17.8005			−1.44381
$153$		0			0
$154$	−4.14044	+	3.36113i	−0.333646	+	0.270847i
$155$	10.8570	−	12.9389i	0.872055	−	1.03927i
$156$		0			0
$157$	−12.2082	−	14.5492i	−0.974322	−	1.16115i	−0.986917	−	0.161232i	$-0.948453\pi$
$157$	−12.2082	−	14.5492i	−0.974322	−	1.16115i	0.0125942	−	0.999921i	$-0.495991\pi$
$158$	−0.666317	+	1.83069i	−0.0530093	+	0.145642i
$159$		0			0
$160$	1.95487	+	5.37096i	0.154546	+	0.424612i
$161$	9.54653	+	11.7600i	0.752372	+	0.926817i
$162$		0			0
$163$	−0.709039	+	1.22809i	−0.0555362	+	0.0961915i	−0.892457	−	0.451133i	$-0.851020\pi$
$163$	−0.709039	+	1.22809i	−0.0555362	+	0.0961915i	0.836921	+	0.547324i	$0.184353\pi$
$164$	1.34398	+	1.12774i	0.104948	+	0.0880615i
$165$		0			0
$166$	8.55489	−	1.50846i	0.663989	−	0.117079i
$167$	2.73878	+	15.5324i	0.211933	+	1.20193i	0.886150	+	0.463398i	$0.153370\pi$
$167$	2.73878	+	15.5324i	0.211933	+	1.20193i	−0.674217	+	0.738533i	$0.735519\pi$
$168$		0			0
$169$	9.25869	+	7.76897i	0.712207	+	0.597613i
$170$	−10.5260	+	6.07721i	−0.807310	+	0.466101i
$171$		0			0
$172$	0.175464	−	0.303912i	0.0133790	−	0.0231731i
$173$	8.35696	+	7.01232i	0.635368	+	0.533137i	0.902592	−	0.430497i	$-0.141662\pi$
$173$	8.35696	+	7.01232i	0.635368	+	0.533137i	−0.267224	+	0.963634i	$0.586106\pi$
$174$		0			0
$175$	−0.701901	+	3.63434i	−0.0530587	+	0.274730i
$176$	−2.07122	+	5.69064i	−0.156124	+	0.428948i
$177$		0			0
$178$	−3.07781	−	8.45622i	−0.230692	−	0.633821i
$179$	−20.4739	−	11.8206i	−1.53029	−	0.883515i	−0.999348	−	0.0361087i	$-0.988504\pi$
$179$	−20.4739	−	11.8206i	−1.53029	−	0.883515i	−0.530945	−	0.847406i	$-0.678163\pi$
$180$		0			0
$181$	18.7421	+	10.8208i	1.39309	+	0.804301i	0.993656	−	0.112461i	$-0.0358733\pi$
$181$	18.7421	+	10.8208i	1.39309	+	0.804301i	0.399434	+	0.916762i	$0.369207\pi$
$182$	−4.03509	−	0.0655700i	−0.299101	−	0.00486037i
$183$		0			0
$184$	12.4779	+	4.54159i	0.919884	+	0.334810i
$185$	14.2631	+	5.19135i	1.04865	+	0.381676i
$186$		0			0
$187$	−4.99279	−	0.880363i	−0.365109	−	0.0643786i
$188$	4.67346			0.340847
$189$		0			0
$190$	−23.2403			−1.68603
$191$	−21.5750	−	3.80425i	−1.56111	−	0.275266i	−0.674675	−	0.738115i	$-0.735716\pi$
$191$	−21.5750	−	3.80425i	−1.56111	−	0.275266i	−0.886437	+	0.462849i	$0.846827\pi$
$192$		0			0
$193$	−13.6881	−	4.98206i	−0.985290	−	0.358616i	−0.201396	−	0.979510i	$-0.564548\pi$
$193$	−13.6881	−	4.98206i	−0.985290	−	0.358616i	−0.783895	+	0.620894i	$0.786770\pi$
$194$	9.09934	+	3.31189i	0.653294	+	0.237780i
$195$		0			0
$196$	−3.00911	+	2.36267i	−0.214936	+	0.168762i
$197$	2.06396	+	1.19163i	0.147051	+	0.0849001i	0.571720	−	0.820449i	$-0.306276\pi$
$197$	2.06396	+	1.19163i	0.147051	+	0.0849001i	−0.424669	+	0.905349i	$0.639610\pi$
$198$		0			0
$199$	8.88525	+	5.12990i	0.629859	+	0.363649i	0.780697	−	0.624909i	$-0.214864\pi$
$199$	8.88525	+	5.12990i	0.629859	+	0.363649i	−0.150839	+	0.988558i	$0.548197\pi$
$200$	1.10983	+	3.04923i	0.0784769	+	0.215613i
$201$		0			0
$202$	−3.78819	+	10.4080i	−0.266536	+	0.732303i
$203$	6.22708	−	7.18089i	0.437055	−	0.503999i
$204$		0			0
$205$	−4.66634	−	3.91552i	−0.325911	−	0.273472i
$206$	10.2810	−	17.8071i	0.716308	−	1.24068i
$207$		0			0
$208$	−3.96870	+	2.29133i	−0.275180	+	0.158875i
$209$	−7.42597	−	6.23113i	−0.513665	−	0.431016i
$210$		0			0
$211$	−1.98228	−	11.2421i	−0.136466	−	0.773938i	−0.973828	−	0.227288i	$-0.927014\pi$
$211$	−1.98228	−	11.2421i	−0.136466	−	0.773938i	0.837361	−	0.546650i	$-0.184097\pi$
$212$	7.04351	−	1.24196i	0.483750	−	0.0852982i
$213$		0			0
$214$	1.75036	+	1.46872i	0.119652	+	0.100400i
$215$	−0.609213	+	1.05519i	−0.0415480	+	0.0719632i
$216$		0			0
$217$	23.2551	−	3.71197i	1.57866	−	0.251985i
$218$	−1.03292	−	2.83792i	−0.0699581	−	0.192208i
$219$		0			0
$220$	−0.448055	+	1.23102i	−0.0302079	+	0.0829955i
$221$	−2.46605	−	2.93892i	−0.165885	−	0.197693i
$222$		0			0
$223$	7.05545	−	8.40836i	0.472468	−	0.563065i	−0.476201	−	0.879336i	$-0.657987\pi$
$223$	7.05545	−	8.40836i	0.472468	−	0.563065i	0.948669	+	0.316271i	$0.102431\pi$
$224$	−2.84688	+	7.44317i	−0.190215	+	0.497318i
$225$		0			0
$226$	−1.38622			−0.0922098
$227$	−14.1429	+	5.14758i	−0.938695	+	0.341657i	−0.765650	−	0.643257i	$-0.777583\pi$
$227$	−14.1429	+	5.14758i	−0.938695	+	0.341657i	−0.173045	+	0.984914i	$0.555361\pi$
$228$		0			0
$229$	−14.4445	−	17.2142i	−0.954517	−	1.13755i	−0.990405	−	0.138193i	$-0.955871\pi$
$229$	−14.4445	−	17.2142i	−0.954517	−	1.13755i	0.0358884	−	0.999356i	$-0.488574\pi$
$230$	16.2911	+	5.92948i	1.07420	+	0.390978i
$231$		0			0
$232$	1.44691	−	8.20584i	0.0949944	−	0.538740i
$233$		−	29.3420i		−	1.92226i	−0.276103	−	0.961128i	$-0.589043\pi$
$233$		−	29.3420i		−	1.92226i	0.276103	−	0.961128i	$-0.410957\pi$
$234$		0			0
$235$	−16.2263			−1.05849
$236$	1.10903	−	0.403653i	0.0721915	−	0.0262756i
$237$		0			0
$238$	−16.6388	−	3.21345i	−1.07853	−	0.208297i
$239$	17.8608	+	21.2856i	1.15532	+	1.37685i	0.913655	+	0.406491i	$0.133248\pi$
$239$	17.8608	+	21.2856i	1.15532	+	1.37685i	0.241661	+	0.970361i	$0.422308\pi$
$240$		0			0
$241$	0.0482410	−	0.0574914i	0.00310747	−	0.00370334i	−0.764488	−	0.644637i	$-0.777008\pi$
$241$	0.0482410	−	0.0574914i	0.00310747	−	0.00370334i	0.767596	+	0.640934i	$0.221453\pi$
$242$	12.9970	−	7.50384i	0.835481	−	0.482365i
$243$		0			0
$244$		−	1.68477i		−	0.107857i
$245$	10.4477	−	8.20324i	0.667478	−	0.524086i
$246$		0			0
$247$	−1.27383	−	7.22426i	−0.0810519	−	0.459668i
$248$	15.8148	−	13.2702i	1.00424	−	0.842657i
$249$		0			0
$250$	6.62753	+	18.2090i	0.419162	+	1.15164i
$251$	−9.64254	+	16.7014i	−0.608632	+	1.05418i	0.382834	+	0.923817i	$0.374948\pi$
$251$	−9.64254	+	16.7014i	−0.608632	+	1.05418i	−0.991466	+	0.130364i	$0.958385\pi$
$252$		0			0
$253$	3.61570	+	6.26258i	0.227317	+	0.393725i
$254$	−13.9353	+	16.6075i	−0.874381	+	1.04205i
$255$		0			0
$256$	2.12316	+	12.0410i	0.132697	+	0.752565i
$257$	−2.39043	+	2.00581i	−0.149111	+	0.125119i	−0.714292	−	0.699848i	$-0.753251\pi$
$257$	−2.39043	+	2.00581i	−0.149111	+	0.125119i	0.565180	+	0.824967i	$0.308807\pi$
$258$		0			0
$259$	10.2821	+	18.4968i	0.638899	+	1.14934i
$260$	−0.858526	+	0.495670i	−0.0532435	+	0.0307402i
$261$		0			0
$262$		−	14.4751i		−	0.894274i
$263$	4.30219	+	0.758592i	0.265284	+	0.0467768i	0.304708	−	0.952446i	$-0.401441\pi$
$263$	4.30219	+	0.758592i	0.265284	+	0.0467768i	−0.0394238	+	0.999223i	$0.512552\pi$
$264$		0			0
$265$	−24.4552	+	4.31211i	−1.50227	+	0.264891i
$266$	−24.4802	−	21.2286i	−1.50098	−	1.30161i
$267$		0			0
$268$	−0.203002	+	1.15128i	−0.0124003	+	0.0703258i
$269$	0.429514	+	0.743940i	0.0261879	+	0.0453588i	0.878822	−	0.477149i	$-0.158330\pi$
$269$	0.429514	+	0.743940i	0.0261879	+	0.0453588i	−0.852634	+	0.522508i	$0.824997\pi$
$270$		0			0
$271$	4.73193	+	2.73198i	0.287444	+	0.165956i	0.636789	−	0.771038i	$-0.280262\pi$
$271$	4.73193	+	2.73198i	0.287444	+	0.165956i	−0.349344	+	0.936994i	$0.613596\pi$
$272$	−18.0829	+	6.58162i	−1.09643	+	0.399069i
$273$		0			0
$274$	24.5566	−	20.6054i	1.48352	−	1.24482i
$275$	−0.604398	+	1.66057i	−0.0364466	+	0.100136i
$276$		0			0
$277$	−3.39626	+	19.2611i	−0.204061	+	1.15729i	0.694848	+	0.719156i	$0.255471\pi$
$277$	−3.39626	+	19.2611i	−0.204061	+	1.15729i	−0.898910	+	0.438134i	$0.855640\pi$
$278$	6.10189	+	10.5688i	0.365967	+	0.633873i
$279$		0			0
$280$	4.16005	−	10.8765i	0.248611	−	0.649993i
$281$	13.1907	+	2.32587i	0.786890	+	0.138750i	0.552633	−	0.833425i	$-0.313623\pi$
$281$	13.1907	+	2.32587i	0.786890	+	0.138750i	0.234257	+	0.972175i	$0.424734\pi$
$282$		0			0
$283$	10.5946	−	1.86812i	0.629786	−	0.111048i	0.150361	−	0.988631i	$-0.451956\pi$
$283$	10.5946	−	1.86812i	0.629786	−	0.111048i	0.479425	+	0.877583i	$0.340845\pi$
$284$	0.0961453	−	0.0169530i	0.00570517	−	0.00100598i
$285$		0			0
$286$	−1.89739	−	0.334561i	−0.112195	−	0.0197830i
$287$	−1.33871	−	8.38684i	−0.0790213	−	0.495060i
$288$		0			0
$289$	0.444961	+	0.770696i	0.0261742	+	0.0453350i
$290$	1.88908	−	10.7135i	0.110931	−	0.629119i
$291$		0			0
$292$	2.15044	−	5.90829i	0.125845	−	0.345756i
$293$	6.87623	−	5.76984i	0.401714	−	0.337078i	−0.419442	−	0.907782i	$-0.637774\pi$
$293$	6.87623	−	5.76984i	0.401714	−	0.337078i	0.821156	+	0.570704i	$0.193330\pi$
$294$		0			0
$295$	−3.85056	+	1.40149i	−0.224188	+	0.0815979i
$296$	16.0667	+	9.27612i	0.933858	+	0.539163i
$297$		0			0
$298$	−5.90370	−	10.2255i	−0.341992	−	0.592348i
$299$	−0.950244	+	5.38910i	−0.0549540	+	0.311660i
$300$		0			0
$301$	−1.60557	+	0.555006i	−0.0925433	+	0.0319900i
$302$	9.69802	−	1.71002i	0.558058	−	0.0984007i
$303$		0			0
$304$	−36.2360	−	6.38938i	−2.07828	−	0.366456i
$305$			5.84957i			0.334945i
$306$		0			0
$307$	−17.4494	+	10.0744i	−0.995890	+	0.574977i	−0.907030	−	0.421067i	$-0.861656\pi$
$307$	−17.4494	+	10.0744i	−0.995890	+	0.574977i	−0.0888603	+	0.996044i	$0.528322\pi$
$308$	−1.59642	+	0.887428i	−0.0909647	+	0.0505659i
$309$		0			0
$310$	20.6477	−	17.3255i	1.17271	−	0.984021i
$311$	−0.493149	−	2.79678i	−0.0279639	−	0.158591i	0.967628	−	0.252380i	$-0.0812133\pi$
$311$	−0.493149	−	2.79678i	−0.0279639	−	0.158591i	−0.995592	+	0.0937888i	$0.970102\pi$
$312$		0			0
$313$	5.99493	−	7.14448i	0.338853	−	0.403830i	−0.569528	−	0.821972i	$-0.692874\pi$
$313$	5.99493	−	7.14448i	0.338853	−	0.403830i	0.908382	+	0.418142i	$0.137319\pi$
$314$	−15.1541	−	26.2477i	−0.855197	−	1.48124i
$315$		0			0
$316$	−0.333619	+	0.577845i	−0.0187675	+	0.0325063i
$317$	6.03103	+	16.5701i	0.338736	+	0.930670i	0.985754	+	0.168195i	$0.0537938\pi$
$317$	6.03103	+	16.5701i	0.338736	+	0.930670i	−0.647018	+	0.762475i	$0.723984\pi$
$318$		0			0
$319$	3.47610	−	2.91679i	0.194624	−	0.163309i
$320$	−1.57583	−	8.93697i	−0.0880915	−	0.499592i
$321$		0			0
$322$	11.7441	+	21.1268i	0.654471	+	1.17735i
$323$		−	30.8038i		−	1.71397i
$324$		0			0
$325$	−1.15810	+	0.668627i	−0.0642396	+	0.0370887i
$326$	−1.45460	+	1.73352i	−0.0805628	+	0.0960110i
$327$		0			0
$328$	−4.78583	−	5.70353i	−0.264253	−	0.314925i
$329$	−17.0921	−	14.8218i	−0.942316	−	0.817151i
$330$		0			0
$331$	−25.7166	+	9.36008i	−1.41351	+	0.514476i	−0.932159	−	0.362050i	$-0.882077\pi$
$331$	−25.7166	+	9.36008i	−1.41351	+	0.514476i	−0.481353	+	0.876527i	$0.659855\pi$
$332$	2.97519			0.163285
$333$		0			0
$334$			25.1688i			1.37718i
$335$	0.704828	−	3.99728i	0.0385089	−	0.218395i
$336$		0			0
$337$	−14.1672	−	5.15645i	−0.771738	−	0.280889i	−0.0740145	−	0.997257i	$-0.523581\pi$
$337$	−14.1672	−	5.15645i	−0.771738	−	0.280889i	−0.697723	+	0.716368i	$0.745803\pi$
$338$	12.3976	+	14.7749i	0.674343	+	0.803651i
$339$		0			0
$340$	−3.91175	+	1.42376i	−0.212145	+	0.0772144i
$341$	11.2428			0.608833
$342$		0			0
$343$	18.4983	+	0.902423i	0.998812	+	0.0487262i
$344$	−0.957269	+	1.14083i	−0.0516125	+	0.0615094i
$345$		0			0
$346$	11.1902	+	13.3360i	0.601589	+	0.716946i
$347$	−8.28375	+	22.7594i	−0.444695	+	1.22179i	0.491677	+	0.870778i	$0.336384\pi$
$347$	−8.28375	+	22.7594i	−0.444695	+	1.22179i	−0.936371	+	0.351011i	$0.885838\pi$
$348$		0			0
$349$	−1.92048	−	5.27647i	−0.102801	−	0.282443i	0.877620	−	0.479357i	$-0.159130\pi$
$349$	−1.92048	−	5.27647i	−0.102801	−	0.282443i	−0.980421	+	0.196914i	$0.936908\pi$
$350$	−2.11017	+	5.51703i	−0.112793	+	0.294898i
$351$		0			0
$352$	−1.90226	+	3.29481i	−0.101391	+	0.175614i
$353$	−16.6130	−	13.9399i	−0.884218	−	0.741947i	0.0828238	−	0.996564i	$-0.473606\pi$
$353$	−16.6130	−	13.9399i	−0.884218	−	0.741947i	−0.967042	+	0.254617i	$0.918051\pi$
$354$		0			0
$355$	−0.333818	+	0.0588611i	−0.0177172	+	0.00312403i
$356$	−0.535195	−	3.03524i	−0.0283653	−	0.160868i
$357$		0			0
$358$	−28.9002	−	24.2501i	−1.52742	−	1.28166i
$359$	19.0007	−	10.9700i	1.00282	−	0.578976i	0.0937359	−	0.995597i	$-0.470119\pi$
$359$	19.0007	−	10.9700i	1.00282	−	0.578976i	0.909080	+	0.416621i	$0.136786\pi$
$360$		0			0
$361$	19.9498	−	34.5540i	1.04999	−	1.81863i
$362$	26.4556	+	22.1989i	1.39048	+	1.16675i
$363$		0			0
$364$	−1.35709	−	0.262096i	−0.0711311	−	0.0137376i
$365$	−7.46637	+	20.5137i	−0.390808	+	1.07374i
$366$		0			0
$367$	−3.89839	−	10.7107i	−0.203494	−	0.559096i	0.795401	−	0.606083i	$-0.207260\pi$
$367$	−3.89839	−	10.7107i	−0.203494	−	0.559096i	−0.998895	+	0.0469871i	$0.985038\pi$
$368$	23.7707	+	13.7240i	1.23913	+	0.715415i
$369$		0			0
$370$	20.9766	+	12.1109i	1.09052	+	0.629613i
$371$	−29.6988	−	17.7962i	−1.54188	−	0.923931i
$372$		0			0
$373$	35.2170	+	12.8179i	1.82346	+	0.663687i	0.994544	+	0.104322i	$0.0332672\pi$
$373$	35.2170	+	12.8179i	1.82346	+	0.663687i	0.828921	+	0.559365i	$0.188955\pi$
$374$	−7.60245	−	2.76706i	−0.393113	−	0.143082i
$375$		0			0
$376$	−19.5317	−	3.44396i	−1.00727	−	0.177609i
$377$	3.43384			0.176852
$378$		0			0
$379$	4.71335			0.242108			0.121054	−	0.992646i	$-0.461373\pi$
$379$	4.71335			0.242108			0.121054	+	0.992646i	$0.461373\pi$
$380$	−7.83871	−	1.38218i	−0.402117	−	0.0709041i
$381$		0			0
$382$	−32.8519	−	11.9571i	−1.68085	−	0.611780i
$383$	−7.04901	−	2.56563i	−0.360188	−	0.131098i	0.155586	−	0.987822i	$-0.450273\pi$
$383$	−7.04901	−	2.56563i	−0.360188	−	0.131098i	−0.515774	+	0.856725i	$0.672496\pi$
$384$		0			0
$385$	5.54281	−	3.08117i	0.282488	−	0.157031i
$386$	−20.1309	−	11.6226i	−1.02464	−	0.591574i
$387$		0			0
$388$	2.87214	+	1.65823i	0.145811	+	0.0841840i
$389$	−7.89174	−	21.6824i	−0.400127	−	1.09934i	−0.962222	−	0.272267i	$-0.912226\pi$
$389$	−7.89174	−	21.6824i	−0.400127	−	1.09934i	0.562094	−	0.827073i	$-0.309996\pi$
$390$		0			0
$391$	−7.85923	+	21.5931i	−0.397458	+	1.09201i
$392$	14.3170	−	7.65679i	0.723117	−	0.386726i
$393$		0			0
$394$	2.91341	+	2.44464i	0.146775	+	0.123159i
$395$	1.15833	−	2.00629i	0.0582820	−	0.100947i
$396$		0			0
$397$	15.0855	−	8.70960i	0.757118	−	0.437122i	−0.0711419	−	0.997466i	$-0.522664\pi$
$397$	15.0855	−	8.70960i	0.757118	−	0.437122i	0.828260	+	0.560344i	$0.189331\pi$
$398$	12.5421	+	10.5240i	0.628677	+	0.527522i
$399$		0			0
$400$	1.16475	+	6.60560i	0.0582373	+	0.330280i
$401$	21.1914	−	3.73662i	1.05825	−	0.186598i	0.382670	−	0.923885i	$-0.375005\pi$
$401$	21.1914	−	3.73662i	1.05825	−	0.186598i	0.675579	+	0.737287i	$0.263894\pi$
$402$		0			0
$403$	6.51737	+	5.46872i	0.324653	+	0.272416i
$404$	−1.89672	+	3.28521i	−0.0943651	+	0.163445i
$405$		0			0
$406$	11.7760	−	9.55954i	0.584433	−	0.474432i
$407$	3.45553	+	9.49398i	0.171284	+	0.470599i
$408$		0			0
$409$	9.10354	−	25.0118i	0.450141	−	1.23675i	−0.482484	−	0.875905i	$-0.660265\pi$
$409$	9.10354	−	25.0118i	0.450141	−	1.23675i	0.932625	−	0.360847i	$-0.117512\pi$
$410$	−6.24836	−	7.44650i	−0.308584	−	0.367756i
$411$		0			0
$412$	4.52671	−	5.39472i	0.223015	−	0.265779i
$413$	−5.33618	−	2.04099i	−0.262576	−	0.100431i
$414$		0			0
$415$	−10.3299			−0.507076
$416$	−2.70538	+	0.984678i	−0.132642	+	0.0482778i
$417$		0			0
$418$	−9.94357	−	11.8503i	−0.486356	−	0.579616i
$419$	−5.47160	−	1.99150i	−0.267305	−	0.0972911i	0.204890	−	0.978785i	$-0.434316\pi$
$419$	−5.47160	−	1.99150i	−0.267305	−	0.0972911i	−0.472196	+	0.881494i	$0.656538\pi$
$420$		0			0
$421$	−0.858573	+	4.86921i	−0.0418443	+	0.237311i	−0.998556	−	0.0537277i	$-0.982890\pi$
$421$	−0.858573	+	4.86921i	−0.0418443	+	0.237311i	0.956711	+	0.291039i	$0.0940008\pi$
$422$		−	18.2168i		−	0.886779i
$423$		0			0
$424$	−30.3520			−1.47402
$425$	−5.27670	+	1.92056i	−0.255958	+	0.0931610i
$426$		0			0
$427$	−5.34323	+	6.16166i	−0.258577	+	0.298183i
$428$	0.503027	+	0.599485i	0.0243147	+	0.0289772i
$429$		0			0
$430$	−1.24981	+	1.48946i	−0.0602710	+	0.0718282i
$431$	−10.1898	+	5.88309i	−0.490826	+	0.283378i	−0.724917	−	0.688836i	$-0.758122\pi$
$431$	−10.1898	+	5.88309i	−0.490826	+	0.283378i	0.234091	+	0.972215i	$0.424789\pi$
$432$		0			0
$433$		−	28.6389i		−	1.37630i	−0.725569	−	0.688150i	$-0.758423\pi$
$433$		−	28.6389i		−	1.37630i	0.725569	−	0.688150i	$-0.241577\pi$
$434$	37.5751	+	0.610593i	1.80366	+	0.0293094i
$435$		0			0
$436$	−0.179612	−	1.01863i	−0.00860187	−	0.0487836i
$437$	−33.6581	+	28.2425i	−1.61008	+	1.35102i
$438$		0			0
$439$	3.67117	+	10.0865i	0.175216	+	0.481401i	0.995950	−	0.0899091i	$-0.0286577\pi$
$439$	3.67117	+	10.0865i	0.175216	+	0.481401i	−0.820734	+	0.571310i	$0.806435\pi$
$440$	2.77971	−	4.81460i	0.132517	−	0.229527i
$441$		0			0
$442$	−3.06112	−	5.30202i	−0.145603	−	0.252191i
$443$	−10.3006	+	12.2757i	−0.489394	+	0.583237i	−0.953063	−	0.302771i	$-0.902088\pi$
$443$	−10.3006	+	12.2757i	−0.489394	+	0.583237i	0.463669	+	0.886008i	$0.346533\pi$
$444$		0			0
$445$	1.85821	+	10.5384i	0.0880875	+	0.499569i
$446$	13.4180	−	11.2590i	0.635360	−	0.533130i
$447$		0			0
$448$	6.50348	−	10.8532i	0.307261	−	0.512766i
$449$	15.5368	−	8.97017i	0.733226	−	0.423328i	−0.0863750	−	0.996263i	$-0.527528\pi$
$449$	15.5368	−	8.97017i	0.733226	−	0.423328i	0.819601	+	0.572934i	$0.194195\pi$
$450$		0			0
$451$		−	4.05467i		−	0.190927i
$452$	−0.467557	−	0.0824429i	−0.0219920	−	0.00387779i
$453$		0			0
$454$	−23.6526	+	4.17059i	−1.11007	+	0.195736i
$455$	4.71186	+	0.910003i	0.220895	+	0.0426616i
$456$		0			0
$457$	−3.98062	+	22.5752i	−0.186205	+	1.05602i	0.738191	+	0.674591i	$0.235680\pi$
$457$	−3.98062	+	22.5752i	−0.186205	+	1.05602i	−0.924397	+	0.381432i	$0.875431\pi$
$458$	−17.9300	−	31.0556i	−0.837813	−	1.45113i
$459$		0			0
$460$	5.14218	+	2.96884i	0.239755	+	0.138423i
$461$	−11.2905	+	4.10942i	−0.525852	+	0.191395i	−0.591285	−	0.806462i	$-0.701379\pi$
$461$	−11.2905	+	4.10942i	−0.525852	+	0.191395i	0.0654330	+	0.997857i	$0.479157\pi$
$462$		0			0
$463$	−0.859491	+	0.721198i	−0.0399439	+	0.0335169i	−0.662541	−	0.749026i	$-0.730522\pi$
$463$	−0.859491	+	0.721198i	−0.0399439	+	0.0335169i	0.622597	+	0.782543i	$0.286078\pi$
$464$	5.89086	−	16.1850i	0.273476	−	0.751370i
$465$		0			0
$466$	8.13084	−	46.1123i	0.376654	−	2.13611i
$467$	6.58419	+	11.4042i	0.304680	+	0.527721i	0.977190	−	0.212367i	$-0.0681171\pi$
$467$	6.58419	+	11.4042i	0.304680	+	0.527721i	−0.672510	+	0.740088i	$0.734784\pi$
$468$		0			0
$469$	4.39370	−	3.56672i	0.202882	−	0.164696i
$470$	−25.5005	−	4.49642i	−1.17625	−	0.207404i
$471$		0			0
$472$	−4.93239	+	0.869713i	−0.227032	+	0.0400318i
$473$	−0.798701	+	0.140833i	−0.0367243	+	0.00647549i
$474$		0			0
$475$	−10.5739	−	1.86447i	−0.485164	−	0.0855476i
$476$	−5.42098	−	2.07343i	−0.248470	−	0.0950354i
$477$		0			0
$478$	22.1706	+	38.4007i	1.01406	+	1.75641i
$479$	−3.88749	+	22.0470i	−0.177624	+	1.00736i	0.757448	+	0.652896i	$0.226446\pi$
$479$	−3.88749	+	22.0470i	−0.177624	+	1.00736i	−0.935071	+	0.354459i	$0.884665\pi$
$480$		0			0
$481$	−2.61491	+	7.18441i	−0.119230	+	0.327581i
$482$	0.0917442	−	0.0769825i	0.00417883	−	0.00350646i
$483$		0			0
$484$	4.83004	−	1.75799i	0.219547	−	0.0799087i
$485$	−9.97214	−	5.75742i	−0.452811	−	0.261431i
$486$		0			0
$487$	14.1370	+	24.4860i	0.640609	+	1.10957i	0.985297	+	0.170850i	$0.0546514\pi$
$487$	14.1370	+	24.4860i	0.640609	+	1.10957i	−0.344688	+	0.938717i	$0.612015\pi$
$488$	−1.24154	+	7.04114i	−0.0562020	+	0.318737i
$489$		0			0
$490$	18.6922	−	9.99666i	0.844427	−	0.451603i
$491$	−36.4384	+	6.42508i	−1.64444	+	0.289960i	−0.917796	−	0.397052i	$-0.870033\pi$
$491$	−36.4384	+	6.42508i	−1.64444	+	0.289960i	−0.726647	+	0.687012i	$0.758922\pi$
$492$		0			0
$493$	14.2002	+	2.50388i	0.639546	+	0.112769i
$494$		−	11.7062i		−	0.526689i
$495$		0			0
$496$	36.9569	−	21.3371i	1.65941	−	0.958063i
$497$	−0.405394	−	0.242921i	−0.0181844	−	0.0108965i
$498$		0			0
$499$	−12.5678	+	10.5456i	−0.562611	+	0.472087i	−0.879185	−	0.476481i	$-0.841912\pi$
$499$	−12.5678	+	10.5456i	−0.562611	+	0.472087i	0.316573	+	0.948568i	$0.397468\pi$
$500$	1.15245	+	6.53586i	0.0515391	+	0.292293i
$501$		0			0
$502$	−19.7818	+	23.5750i	−0.882903	+	1.05220i
$503$	4.98173	+	8.62860i	0.222124	+	0.384730i	0.955453	−	0.295144i	$-0.0953676\pi$
$503$	4.98173	+	8.62860i	0.222124	+	0.384730i	−0.733329	+	0.679874i	$0.762034\pi$
$504$		0			0
$505$	6.58543	−	11.4063i	0.293048	−	0.507574i
$506$	3.94684	+	10.8439i	0.175459	+	0.482068i
$507$		0			0
$508$	−5.68795	+	4.77276i	−0.252362	+	0.211757i
$509$	−1.19429	−	6.77313i	−0.0529358	−	0.300214i	0.946833	−	0.321726i	$-0.104263\pi$
$509$	−1.19429	−	6.77313i	−0.0529358	−	0.300214i	−0.999769	+	0.0215123i	$0.993152\pi$
$510$		0			0
$511$	−26.6027	+	14.7881i	−1.17684	+	0.654185i
$512$		−	7.79950i		−	0.344692i
$513$		0			0
$514$	−4.31250	+	2.48982i	−0.190216	+	0.109821i
$515$	−15.7168	+	18.7306i	−0.692566	+	0.825367i
$516$		0			0
$517$	−6.94259	−	8.27386i	−0.305335	−	0.363884i
$518$	11.0332	+	31.9179i	0.484772	+	1.40239i
$519$		0			0
$520$	3.95328	−	1.43888i	0.173363	−	0.0630989i
$521$	13.4866			0.590858			0.295429	−	0.955365i	$-0.404537\pi$
$521$	13.4866			0.590858			0.295429	+	0.955365i	$0.404537\pi$
$522$		0			0
$523$			34.9984i			1.53038i	0.643807	+	0.765188i	$0.277354\pi$
$523$			34.9984i			1.53038i	−0.643807	+	0.765188i	$0.722646\pi$
$524$	0.860881	−	4.88230i	0.0376078	−	0.213284i
$525$		0			0
$526$	6.55088	+	2.38432i	0.285632	+	0.103961i
$527$	22.9641	+	27.3675i	1.00033	+	1.19215i
$528$		0			0
$529$	9.18663	−	3.34366i	0.399419	−	0.145377i
$530$	−39.6274			−1.72130
$531$		0			0
$532$	−6.99439	−	8.61610i	−0.303245	−	0.373555i
$533$	1.97227	−	2.35046i	0.0854284	−	0.101810i
$534$		0			0
$535$	−1.74652	−	2.08142i	−0.0755087	−	0.0899877i
$536$	1.69680	−	4.66193i	0.0732908	−	0.201365i
$537$		0			0
$538$	0.468851	+	1.28816i	0.0202136	+	0.0555364i
$539$	8.65300	+	1.81747i	0.372711	+	0.0782840i
$540$		0			0
$541$	0.619421	−	1.07287i	0.0266310	−	0.0461262i	−0.852403	−	0.522886i	$-0.824855\pi$
$541$	0.619421	−	1.07287i	0.0266310	−	0.0461262i	0.879034	+	0.476760i	$0.158189\pi$
$542$	6.67940	+	5.60469i	0.286905	+	0.240742i
$543$		0			0
$544$	−11.9058	+	2.09931i	−0.510455	+	0.0900070i
$545$	0.623617	+	3.53671i	0.0267128	+	0.151496i
$546$		0			0
$547$	21.3784	+	17.9386i	0.914076	+	0.767000i	0.972890	−	0.231269i	$-0.0742876\pi$
$547$	21.3784	+	17.9386i	0.914076	+	0.767000i	−0.0588145	+	0.998269i	$0.518732\pi$
$548$	9.50816	−	5.48954i	0.406168	−	0.234501i
$549$		0			0
$550$	−1.40999	+	2.44218i	−0.0601223	+	0.104135i
$551$	21.1205	+	17.7222i	0.899765	+	0.754992i
$552$		0			0
$553$	3.05275	−	1.05526i	0.129816	−	0.0448744i
$554$	−10.6748	+	29.3287i	−0.453527	+	1.24606i
$555$		0			0
$556$	1.42954	+	3.92764i	0.0606262	+	0.166569i
$557$	−2.66791	−	1.54032i	−0.113043	−	0.0652654i	0.442412	−	0.896812i	$-0.354123\pi$
$557$	−2.66791	−	1.54032i	−0.113043	−	0.0652654i	−0.555455	+	0.831546i	$0.687456\pi$
$558$		0			0
$559$	−0.531504	−	0.306864i	−0.0224802	−	0.0129790i
$560$	12.3725	−	20.6476i	0.522835	−	0.872522i
$561$		0			0
$562$	20.0853	+	7.31043i	0.847245	+	0.308372i
$563$	4.55950	+	1.65952i	0.192160	+	0.0699406i	0.436308	−	0.899798i	$-0.356286\pi$
$563$	4.55950	+	1.65952i	0.192160	+	0.0699406i	−0.244148	+	0.969738i	$0.578508\pi$
$564$		0			0
$565$	1.62337	+	0.286243i	0.0682956	+	0.0120423i
$566$	17.1676			0.721610
$567$		0			0
$568$	−0.414310			−0.0173841
$569$	9.00123	+	1.58716i	0.377351	+	0.0665372i	0.359107	−	0.933296i	$-0.383081\pi$
$569$	9.00123	+	1.58716i	0.377351	+	0.0665372i	0.0182441	+	0.999834i	$0.494192\pi$
$570$		0			0
$571$	39.9573	+	14.5433i	1.67216	+	0.608617i	0.992203	−	0.124632i	$-0.0397750\pi$
$571$	39.9573	+	14.5433i	1.67216	+	0.608617i	0.679960	+	0.733250i	$0.261997\pi$
$572$	−0.620072	−	0.225688i	−0.0259265	−	0.00943648i
$573$		0			0
$574$	0.220208	−	13.5513i	0.00919129	−	0.565620i
$575$	6.93646	+	4.00477i	0.289271	+	0.167010i
$576$		0			0
$577$	31.9551	+	18.4493i	1.33031	+	0.768053i	0.985347	−	0.170564i	$-0.0545589\pi$
$577$	31.9551	+	18.4493i	1.33031	+	0.768053i	0.344961	+	0.938617i	$0.387892\pi$
$578$	0.485713	+	1.33449i	0.0202030	+	0.0555073i
$579$		0			0
$580$	1.27433	−	3.50121i	0.0529139	−	0.145380i
$581$	−10.8810	−	9.43576i	−0.451422	−	0.391461i
$582$		0			0
$583$	−12.6621	−	10.6248i	−0.524412	−	0.440034i
$584$	−13.3412	+	23.1076i	−0.552063	+	0.956201i
$585$		0			0
$586$	12.4052	−	7.16213i	0.512453	−	0.295865i
$587$	21.4793	+	18.0233i	0.886545	+	0.743900i	0.967514	−	0.252817i	$-0.0813570\pi$
$587$	21.4793	+	18.0233i	0.886545	+	0.743900i	−0.0809690	+	0.996717i	$0.525801\pi$
$588$		0			0
$589$	11.8620	+	67.2729i	0.488766	+	2.77193i
$590$	−6.43970	+	1.13549i	−0.265118	+	0.0467475i
$591$		0			0
$592$	29.3769	+	24.6501i	1.20738	+	1.01311i
$593$	−12.0746	+	20.9138i	−0.495845	+	0.858828i	−0.999989	−	0.00479135i	$-0.998475\pi$
$593$	−12.0746	+	20.9138i	−0.495845	+	0.858828i	0.504144	+	0.863620i	$0.331808\pi$
$594$		0			0
$595$	18.8217	+	7.19898i	0.771616	+	0.295129i
$596$	−1.38311	−	3.80007i	−0.0566545	−	0.155657i
$597$		0			0
$598$	−2.98671	+	8.20591i	−0.122136	+	0.335565i
$599$	23.4872	+	27.9909i	0.959660	+	1.14368i	0.989559	+	0.144126i	$0.0460370\pi$
$599$	23.4872	+	27.9909i	0.959660	+	1.14368i	−0.0298990	+	0.999553i	$0.509519\pi$
$600$		0			0
$601$	−7.41347	+	8.83503i	−0.302402	+	0.360388i	−0.895750	−	0.444557i	$-0.853361\pi$
$601$	−7.41347	+	8.83503i	−0.302402	+	0.360388i	0.593349	+	0.804945i	$0.297805\pi$
$602$	−2.67702	+	0.427305i	−0.109107	+	0.0174156i
$603$		0			0
$604$	3.37274			0.137235
$605$	−16.7700	+	6.10378i	−0.681797	+	0.248154i
$606$		0			0
$607$	−15.4572	−	18.4212i	−0.627389	−	0.747693i	0.354933	−	0.934892i	$-0.384504\pi$
$607$	−15.4572	−	18.4212i	−0.627389	−	0.747693i	−0.982322	+	0.187199i	$0.940059\pi$
$608$	−21.7219	−	7.90614i	−0.880941	−	0.320636i
$609$		0			0
$610$	−1.62095	+	9.19287i	−0.0656304	+	0.372208i
$611$		−	8.17329i		−	0.330656i
$612$		0			0
$613$	−33.6863			−1.36058			−0.680289	−	0.732944i	$-0.738146\pi$
$613$	−33.6863			−1.36058			−0.680289	+	0.732944i	$0.738146\pi$
$614$	−30.2142	+	10.9971i	−1.21935	+	0.443806i
$615$		0			0
$616$	7.32586	−	2.53237i	0.295167	−	0.102032i
$617$	−5.69508	−	6.78713i	−0.229275	−	0.273240i	0.639126	−	0.769102i	$-0.279296\pi$
$617$	−5.69508	−	6.78713i	−0.229275	−	0.273240i	−0.868401	+	0.495863i	$0.834852\pi$
$618$		0			0
$619$	−2.57718	+	3.07137i	−0.103586	+	0.123449i	−0.815347	−	0.578973i	$-0.803454\pi$
$619$	−2.57718	+	3.07137i	−0.103586	+	0.123449i	0.711761	+	0.702422i	$0.247898\pi$
$620$	7.99466	−	4.61572i	0.321073	−	0.185372i
$621$		0			0
$622$		−	4.53193i		−	0.181714i
$623$	−7.66886	+	12.7980i	−0.307247	+	0.512742i
$624$		0			0
$625$	−2.78663	−	15.8037i	−0.111465	−	0.632150i
$626$	11.4011	−	9.56665i	0.455679	−	0.382360i
$627$		0			0
$628$	−3.55029	−	9.75435i	−0.141672	−	0.389241i
$629$	−16.0523	+	27.8035i	−0.640049	+	1.10860i
$630$		0			0
$631$	−6.55511	−	11.3538i	−0.260955	−	0.451987i	0.705541	−	0.708669i	$-0.250704\pi$
$631$	−6.55511	−	11.3538i	−0.260955	−	0.451987i	−0.966496	+	0.256682i	$0.917371\pi$
$632$	1.82011	−	2.16912i	0.0724001	−	0.0862831i
$633$		0			0
$634$	4.88636	+	27.7119i	0.194062	+	1.10058i
$635$	19.7487	−	16.5711i	0.783702	−	0.657604i
$636$		0			0
$637$	4.13201	+	5.26255i	0.163716	+	0.208510i
$638$	6.27111	−	3.62063i	0.248276	−	0.143342i
$639$		0			0
$640$		−	25.9129i		−	1.02430i
$641$	7.86581	+	1.38695i	0.310681	+	0.0547814i	0.326815	−	0.945088i	$-0.394025\pi$
$641$	7.86581	+	1.38695i	0.310681	+	0.0547814i	−0.0161339	+	0.999870i	$0.505136\pi$
$642$		0			0
$643$	38.0449	−	6.70834i	1.50034	−	0.264551i	0.637669	−	0.770310i	$-0.279899\pi$
$643$	38.0449	−	6.70834i	1.50034	−	0.264551i	0.862675	+	0.505759i	$0.168787\pi$
$644$	2.70467	+	7.82430i	0.106579	+	0.308321i
$645$		0			0
$646$	8.53593	−	48.4097i	0.335842	−	1.90465i
$647$	19.9091	+	34.4836i	0.782707	+	1.35569i	0.930359	+	0.366650i	$0.119495\pi$
$647$	19.9091	+	34.4836i	0.782707	+	1.35569i	−0.147652	+	0.989039i	$0.547171\pi$
$648$		0			0
$649$	−2.36212	−	1.36377i	−0.0927214	−	0.0535327i
$650$	−2.00528	+	0.729863i	−0.0786536	+	0.0286276i
$651$		0			0
$652$	−0.593720	+	0.498190i	−0.0232519	+	0.0195106i
$653$	9.97502	−	27.4061i	0.390353	−	1.07249i	−0.576488	−	0.817106i	$-0.695577\pi$
$653$	9.97502	−	27.4061i	0.390353	−	1.07249i	0.966841	−	0.255380i	$-0.0822005\pi$
$654$		0			0
$655$	−2.98900	+	16.9514i	−0.116790	+	0.662347i
$656$	−7.69512	−	13.3283i	−0.300444	−	0.520384i
$657$		0			0
$658$	−22.7538	−	28.0294i	−0.887034	−	1.09270i
$659$	−20.9180	−	3.68841i	−0.814851	−	0.143680i	−0.249335	−	0.968417i	$-0.580212\pi$
$659$	−20.9180	−	3.68841i	−0.814851	−	0.143680i	−0.565516	+	0.824737i	$0.691323\pi$
$660$		0			0
$661$	−21.8151	+	3.84658i	−0.848507	+	0.149615i	−0.580962	−	0.813931i	$-0.697324\pi$
$661$	−21.8151	+	3.84658i	−0.848507	+	0.149615i	−0.267545	+	0.963545i	$0.586212\pi$
$662$	−43.0086	+	7.58357i	−1.67158	+	0.294744i
$663$		0			0
$664$	−12.4341	−	2.19247i	−0.482538	−	0.0850845i
$665$	24.2846	+	29.9153i	0.941718	+	1.16006i
$666$		0			0
$667$	−10.2836	−	17.8117i	−0.398182	−	0.689671i
$668$	−1.49687	+	8.48918i	−0.0579157	+	0.328456i
$669$		0			0
$670$	2.21534	−	6.08660i	0.0855861	−	0.235146i
$671$	−2.98271	+	2.50279i	−0.115146	+	0.0966192i
$672$		0			0
$673$	15.9545	−	5.80696i	0.615000	−	0.223842i	−0.0156895	−	0.999877i	$-0.504994\pi$
$673$	15.9545	−	5.80696i	0.615000	−	0.223842i	0.630690	+	0.776035i	$0.282772\pi$
$674$	−20.8356	−	12.0294i	−0.802556	−	0.463356i
$675$		0			0
$676$	3.30288	+	5.72076i	0.127034	+	0.220029i
$677$	7.28066	−	41.2907i	0.279818	−	1.58693i	−0.443410	−	0.896319i	$-0.646231\pi$
$677$	7.28066	−	41.2907i	0.279818	−	1.58693i	0.723228	−	0.690610i	$-0.242658\pi$
$678$		0			0
$679$	−5.24512	−	15.1735i	−0.201289	−	0.582307i
$680$	17.3975	−	3.06765i	0.667163	−	0.117639i
$681$		0			0
$682$	17.6686	+	3.11546i	0.676567	+	0.119297i
$683$		−	1.56964i		−	0.0600606i	−0.999549	−	0.0300303i	$-0.990440\pi$
$683$		−	1.56964i		−	0.0600606i	0.999549	−	0.0300303i	$-0.00956038\pi$
$684$		0			0
$685$	−33.0125	+	19.0598i	−1.26134	+	0.728236i
$686$	28.8208	+	6.54418i	1.10038	+	0.249858i
$687$		0			0
$688$	−2.35818	+	1.97874i	−0.0899046	+	0.0754389i
$689$	−2.17203	−	12.3182i	−0.0827478	−	0.469286i
$690$		0			0
$691$	−23.8441	+	28.4163i	−0.907071	+	1.08101i	0.0893094	+	0.996004i	$0.471534\pi$
$691$	−23.8441	+	28.4163i	−0.907071	+	1.08101i	−0.996381	+	0.0850017i	$0.972910\pi$
$692$	2.98121	+	5.16360i	0.113328	+	0.196291i
$693$		0			0
$694$	−19.3251	+	33.4720i	−0.733569	+	1.27058i
$695$	−4.96340	−	13.6368i	−0.188273	−	0.517275i
$696$		0			0
$697$	9.86997	−	8.28188i	0.373852	−	0.313699i
$698$	−1.55598	−	8.82439i	−0.0588946	−	0.334008i
$699$		0			0
$700$	−1.03985	+	1.73534i	−0.0393028	+	0.0655896i
$701$			8.24161i			0.311281i	0.987814	+	0.155641i	$0.0497442\pi$
$701$			8.24161i			0.311281i	−0.987814	+	0.155641i	$0.950256\pi$
$702$		0			0
$703$	−53.1626	+	30.6934i	−2.00506	+	1.15762i
$704$	3.88275	−	4.62729i	0.146337	−	0.174397i
$705$		0			0
$706$	−22.2452	−	26.5108i	−0.837209	−	0.997747i
$707$	17.3557	−	5.99946i	0.652730	−	0.225633i
$708$		0			0
$709$	−12.4403	+	4.52790i	−0.467206	+	0.170049i	−0.564886	−	0.825169i	$-0.691080\pi$
$709$	−12.4403	+	4.52790i	−0.467206	+	0.170049i	0.0976805	+	0.995218i	$0.468858\pi$
$710$	−0.540922			−0.0203004
$711$		0			0
$712$			13.0795i			0.490175i
$713$	8.84875	−	50.1838i	0.331388	−	1.87940i
$714$		0			0
$715$	2.15290	+	0.783592i	0.0805139	+	0.0293047i
$716$	−8.30549	−	9.89810i	−0.310391	−	0.369909i
$717$		0			0
$718$	32.9003	−	11.9747i	1.22783	−	0.446893i
$719$	−11.3474			−0.423187			−0.211594	−	0.977358i	$-0.567865\pi$
$719$	−11.3474			−0.423187			−0.211594	+	0.977358i	$0.567865\pi$
$720$		0			0
$721$	−33.6646	+	5.37353i	−1.25373	+	0.200121i
$722$	40.9271	−	48.7751i	1.52315	−	1.81522i
$723$		0			0
$724$	7.60296	+	9.06086i	0.282562	+	0.336744i
$725$	1.71900	−	4.72290i	0.0638419	−	0.175404i
$726$		0			0
$727$	−7.94102	−	21.8178i	−0.294516	−	0.809176i	−0.995392	−	0.0958928i	$-0.969429\pi$
$727$	−7.94102	−	21.8178i	−0.294516	−	0.809176i	0.700876	−	0.713284i	$-0.252793\pi$
$728$	5.47853	+	2.09544i	0.203048	+	0.0776622i
$729$		0			0
$730$	−17.4182	+	30.1692i	−0.644677	+	1.11661i
$731$	−1.97421	−	1.65656i	−0.0730187	−	0.0612699i
$732$		0			0
$733$	16.0347	−	2.82735i	0.592255	−	0.104431i	0.130516	−	0.991446i	$-0.458337\pi$
$733$	16.0347	−	2.82735i	0.592255	−	0.104431i	0.461739	+	0.887016i	$0.347226\pi$
$734$	−3.15849	−	17.9127i	−0.116582	−	0.661170i
$735$		0			0
$736$	13.2096	+	11.0842i	0.486913	+	0.408568i
$737$	2.33979	−	1.35088i	0.0861873	−	0.0497603i
$738$		0			0
$739$	5.44795	−	9.43613i	0.200406	−	0.347114i	−0.748253	−	0.663413i	$-0.769107\pi$
$739$	5.44795	−	9.43613i	0.200406	−	0.347114i	0.948659	+	0.316300i	$0.102440\pi$
$740$	6.35492	+	5.33241i	0.233612	+	0.196023i
$741$		0			0
$742$	−41.7416	−	36.1972i	−1.53238	−	1.32884i
$743$	16.4197	−	45.1128i	0.602381	−	1.65503i	−0.144054	−	0.989570i	$-0.546014\pi$
$743$	16.4197	−	45.1128i	0.602381	−	1.65503i	0.746435	−	0.665458i	$-0.231764\pi$
$744$		0			0
$745$	4.80219	+	13.1939i	0.175939	+	0.483388i
$746$	51.7932	+	29.9028i	1.89628	+	1.09482i
$747$		0			0
$748$	−2.39966	−	1.38544i	−0.0877403	−	0.0506569i
$749$	0.0615517	−	3.78781i	0.00224905	−	0.138404i
$750$		0			0
$751$	−19.7103	−	7.17395i	−0.719237	−	0.261781i	−0.0436354	−	0.999048i	$-0.513894\pi$
$751$	−19.7103	−	7.17395i	−0.719237	−	0.261781i	−0.675602	+	0.737266i	$0.736116\pi$
$752$	−38.5238	−	14.0215i	−1.40482	−	0.511313i
$753$		0			0
$754$	5.39645	+	0.951539i	0.196527	+	0.0346530i
$755$	−11.7102			−0.426179
$756$		0			0
$757$	−24.6333			−0.895314			−0.447657	−	0.894205i	$-0.647741\pi$
$757$	−24.6333			−0.895314			−0.447657	+	0.894205i	$0.647741\pi$
$758$	7.40724	+	1.30610i	0.269043	+	0.0474396i
$759$		0			0
$760$	31.7416	+	11.5530i	1.15139	+	0.419071i
$761$	8.78216	+	3.19644i	0.318353	+	0.115871i	0.496254	−	0.868177i	$-0.334708\pi$
$761$	8.78216	+	3.19644i	0.318353	+	0.115871i	−0.177901	+	0.984048i	$0.556931\pi$
$762$		0			0
$763$	−2.57368	+	4.29504i	−0.0931735	+	0.155491i
$764$	−10.3695	−	5.98683i	−0.375155	−	0.216596i
$765$		0			0
$766$	−10.3669	−	5.98533i	−0.374571	−	0.216259i
$767$	−0.705937	−	1.93955i	−0.0254899	−	0.0700330i
$768$		0			0
$769$	3.02496	−	8.31100i	0.109083	−	0.299702i	−0.873126	−	0.487494i	$-0.837911\pi$
$769$	3.02496	−	8.31100i	0.109083	−	0.299702i	0.982209	+	0.187792i	$0.0601332\pi$
$770$	9.56460	−	3.30625i	0.344684	−	0.119149i
$771$		0			0
$772$	−6.09872	−	5.11743i	−0.219498	−	0.184180i
$773$	−7.06558	+	12.2379i	−0.254131	+	0.440168i	−0.964659	−	0.263501i	$-0.915123\pi$
$773$	−7.06558	+	12.2379i	−0.254131	+	0.440168i	0.710528	+	0.703669i	$0.248456\pi$
$774$		0			0
$775$	10.7843	−	6.22631i	0.387383	−	0.223656i
$776$	−10.7815	−	9.04675i	−0.387033	−	0.324759i
$777$		0			0
$778$	−6.39392	−	36.2617i	−0.229233	−	1.30005i
$779$	24.2617	−	4.27798i	0.869264	−	0.153275i
$780$		0			0
$781$	−0.172841	−	0.145031i	−0.00618472	−	0.00518960i
$782$	−18.3347	+	31.7566i	−0.655648	+	1.13562i
$783$		0			0
$784$	31.8930	−	10.4477i	1.13904	−	0.373132i
$785$	12.3267	+	33.8673i	0.439958	+	1.20878i
$786$		0			0
$787$	−9.44389	+	25.9469i	−0.336638	+	0.924907i	0.649702	+	0.760189i	$0.274894\pi$
$787$	−9.44389	+	25.9469i	−0.336638	+	0.924907i	−0.986341	+	0.164718i	$0.947329\pi$
$788$	0.837271	+	0.997821i	0.0298265	+	0.0355459i
$789$		0			0
$790$	2.37633	−	2.83200i	0.0845459	−	0.100758i
$791$	1.44851	+	1.78436i	0.0515031	+	0.0634446i
$792$		0			0
$793$	−2.94646			−0.104632
$794$	26.1210	−	9.50727i	0.927000	−	0.337400i
$795$		0			0
$796$	3.60441	+	4.29557i	0.127755	+	0.152252i
$797$	−32.0647	−	11.6706i	−1.13579	−	0.413394i	−0.295399	−	0.955374i	$-0.595453\pi$
$797$	−32.0647	−	11.6706i	−1.13579	−	0.413394i	−0.840391	+	0.541980i	$0.817675\pi$
$798$		0			0
$799$	5.95978	−	33.7996i	0.210842	−	1.19574i
$800$			4.21391i			0.148984i
$801$		0			0
$802$	34.3388			1.21254
$803$	−13.6545	+	4.96985i	−0.481858	+	0.175382i
$804$		0			0
$805$	−9.39067	−	27.1661i	−0.330978	−	0.957480i
$806$	8.72693	+	10.4004i	0.307393	+	0.366337i
$807$		0			0
$808$	10.3478	−	12.3321i	0.364035	−	0.433840i
$809$	8.13629	−	4.69749i	0.286057	−	0.165155i	−0.350105	−	0.936710i	$-0.613854\pi$
$809$	8.13629	−	4.69749i	0.286057	−	0.165155i	0.636162	+	0.771555i	$0.280521\pi$
$810$		0			0
$811$		−	31.3300i		−	1.10014i	−0.835117	−	0.550072i	$-0.814600\pi$
$811$		−	31.3300i		−	1.10014i	0.835117	−	0.550072i	$-0.185400\pi$
$812$	4.54046	−	2.52398i	0.159339	−	0.0885742i
$813$		0			0
$814$	2.79968	+	15.8778i	0.0981287	+	0.556516i
$815$	2.06141	−	1.72972i	0.0722079	−	0.0605896i
$816$		0			0
$817$	−1.68538	−	4.63054i	−0.0589639	−	0.162002i
$818$	21.2375	−	36.7845i	0.742554	−	1.28614i
$819$		0			0
$820$	−1.66464	−	2.88324i	−0.0581317	−	0.100687i
$821$	−4.21759	+	5.02633i	−0.147195	+	0.175420i	−0.834604	−	0.550850i	$-0.814304\pi$
$821$	−4.21759	+	5.02633i	−0.147195	+	0.175420i	0.687409	+	0.726270i	$0.258748\pi$
$822$		0			0
$823$	−4.04297	−	22.9288i	−0.140929	−	0.799248i	−0.970546	−	0.240915i	$-0.922552\pi$
$823$	−4.04297	−	22.9288i	−0.140929	−	0.799248i	0.829617	−	0.558333i	$-0.188559\pi$
$824$	−22.8938	+	19.2102i	−0.797544	+	0.669219i
$825$		0			0
$826$	−7.82048	−	4.68620i	−0.272109	−	0.163054i
$827$	−33.9354	+	19.5926i	−1.18005	+	0.681302i	−0.956026	−	0.293282i	$-0.905252\pi$
$827$	−33.9354	+	19.5926i	−1.18005	+	0.681302i	−0.224023	+	0.974584i	$0.571919\pi$
$828$		0			0
$829$			36.1621i			1.25596i	0.778229	+	0.627981i	$0.216118\pi$
$829$			36.1621i			1.25596i	−0.778229	+	0.627981i	$0.783882\pi$
$830$	−16.2339	−	2.86248i	−0.563489	−	0.0993582i
$831$		0			0
$832$	4.50160	−	0.793753i	0.156065	−	0.0275184i
$833$	13.2501	+	24.7756i	0.459088	+	0.858423i
$834$		0			0
$835$	5.19716	−	29.4746i	0.179855	−	1.02001i
$836$	−2.64909	−	4.58836i	−0.0916206	−	0.158692i
$837$		0			0
$838$	−8.04702	−	4.64595i	−0.277980	−	0.160492i
$839$	−35.7513	+	13.0124i	−1.23427	+	0.449238i	−0.875058	−	0.484018i	$-0.839177\pi$
$839$	−35.7513	+	13.0124i	−1.23427	+	0.449238i	−0.359212	+	0.933256i	$0.616955\pi$
$840$		0			0
$841$	12.3288	−	10.3451i	0.425130	−	0.356726i
$842$	−2.69858	+	7.41428i	−0.0929991	+	0.255513i
$843$		0			0
$844$	1.08341	−	6.14433i	0.0372926	−	0.211497i
$845$	−11.4677	−	19.8626i	−0.394500	−	0.683294i
$846$		0			0
$847$	−23.2401	−	8.88895i	−0.798541	−	0.305428i
$848$	−61.7866	−	10.8946i	−2.12176	−	0.374124i
$849$		0			0
$850$	−8.82479	+	1.55605i	−0.302688	+	0.0533720i
$851$	45.0973	−	7.95187i	1.54591	−	0.272586i
$852$		0			0
$853$	30.3259	+	5.34727i	1.03834	+	0.183087i	0.666728	−	0.745301i	$-0.267694\pi$
$853$	30.3259	+	5.34727i	1.03834	+	0.183087i	0.371611	+	0.928389i	$0.378806\pi$
$854$	−10.1046	+	8.20269i	−0.345771	+	0.280690i
$855$		0			0
$856$	−1.66052	−	2.87610i	−0.0567553	−	0.0983031i
$857$	3.52209	−	19.9748i	0.120312	−	0.682325i	−0.863670	−	0.504058i	$-0.831840\pi$
$857$	3.52209	−	19.9748i	0.120312	−	0.682325i	0.983982	−	0.178267i	$-0.0570490\pi$
$858$		0			0
$859$	11.8516	−	32.5620i	0.404371	−	1.11100i	−0.555734	−	0.831360i	$-0.687563\pi$
$859$	11.8516	−	32.5620i	0.404371	−	1.11100i	0.960105	−	0.279640i	$-0.0902153\pi$
$860$	−0.510130	+	0.428050i	−0.0173953	+	0.0145964i
$861$		0			0
$862$	−17.6440	+	6.42189i	−0.600957	+	0.218731i
$863$	−32.8141	−	18.9452i	−1.11700	−	0.644902i	−0.176369	−	0.984324i	$-0.556435\pi$
$863$	−32.8141	−	18.9452i	−1.11700	−	0.644902i	−0.940634	+	0.339422i	$0.889769\pi$
$864$		0			0
$865$	−10.3508	−	17.9281i	−0.351938	−	0.609574i
$866$	7.93603	−	45.0074i	0.269677	−	1.52941i
$867$		0			0
$868$	12.6374	+	2.44066i	0.428941	+	0.0828414i
$869$	1.51862	−	0.267773i	0.0515155	−	0.00908357i
$870$		0			0
$871$	2.01345	+	0.355025i	0.0682231	+	0.0120296i
$872$			4.38950i			0.148647i
$873$		0			0
$874$	−60.7214	+	35.0575i	−2.05393	+	1.18584i
$875$	16.5135	−	27.5583i	0.558260	−	0.931641i
$876$		0			0
$877$	−9.10894	+	7.64331i	−0.307587	+	0.258096i	−0.783494	−	0.621399i	$-0.786564\pi$
$877$	−9.10894	+	7.64331i	−0.307587	+	0.258096i	0.475907	+	0.879496i	$0.342120\pi$
$878$	2.97440	+	16.8687i	0.100381	+	0.569290i
$879$		0			0
$880$	7.38673	−	8.80317i	0.249007	−	0.296755i
$881$	19.8758	+	34.4258i	0.669631	+	1.15984i	0.978007	+	0.208571i	$0.0668813\pi$
$881$	19.8758	+	34.4258i	0.669631	+	1.15984i	−0.308376	+	0.951265i	$0.599785\pi$
$882$		0			0
$883$	25.4955	−	44.1595i	0.857992	−	1.48609i	−0.0158499	−	0.999874i	$-0.505045\pi$
$883$	25.4955	−	44.1595i	0.857992	−	1.48609i	0.873842	−	0.486211i	$-0.161621\pi$
$884$	−0.717156	−	1.97037i	−0.0241206	−	0.0662707i
$885$		0			0
$886$	−19.5895	+	16.4375i	−0.658122	+	0.552230i
$887$	−4.66549	−	26.4593i	−0.156652	−	0.888416i	−0.957260	−	0.289228i	$-0.906601\pi$
$887$	−4.66549	−	26.4593i	−0.156652	−	0.888416i	0.800608	−	0.599188i	$-0.204510\pi$
$888$		0			0
$889$	35.9390	+	0.584007i	1.20536	+	0.0195870i
$890$			17.0765i			0.572407i
$891$		0			0
$892$	5.19536	−	2.99954i	0.173953	−	0.100432i
$893$	42.1827	−	50.2714i	1.41159	−	1.68227i
$894$		0			0
$895$	28.8368	+	34.3664i	0.963909	+	1.14874i
$896$	23.6698	−	27.2954i	0.790754	−	0.911874i
$897$		0			0
$898$	26.9025	−	9.79170i	0.897747	−	0.326753i
$899$	−31.9762			−1.06647
$900$		0			0
$901$		−	52.5242i		−	1.74983i
$902$	1.12357	−	6.37211i	0.0374109	−	0.212168i
$903$		0			0
$904$	1.89330	+	0.689103i	0.0629701	+	0.0229192i
$905$	−26.3976	−	31.4595i	−0.877487	−	1.04575i
$906$		0			0
$907$	38.0140	−	13.8359i	1.26223	−	0.459415i	0.377715	−	0.925922i	$-0.376710\pi$
$907$	38.0140	−	13.8359i	1.26223	−	0.459415i	0.884518	+	0.466507i	$0.154488\pi$
$908$	−8.22582			−0.272983
$909$		0			0
$910$	7.15274	+	2.73580i	0.237111	+	0.0906908i
$911$	−12.3517	+	14.7202i	−0.409231	+	0.487702i	−0.930811	−	0.365500i	$-0.880898\pi$
$911$	−12.3517	+	14.7202i	−0.409231	+	0.487702i	0.521581	+	0.853202i	$0.325342\pi$
$912$		0			0
$913$	−4.41975	−	5.26725i	−0.146272	−	0.174321i
$914$	−12.5115	+	34.3749i	−0.413842	+	1.13702i
$915$		0			0
$916$	−4.20062	−	11.5411i	−0.138792	−	0.381329i
$917$	−18.6326	+	15.1256i	−0.615302	+	0.499490i
$918$		0			0
$919$	1.00540	−	1.74140i	0.0331650	−	0.0574435i	−0.848966	−	0.528447i	$-0.822775\pi$
$919$	1.00540	−	1.74140i	0.0331650	−	0.0574435i	0.882132	+	0.471003i	$0.156108\pi$
$920$	−19.3028	−	16.1970i	−0.636394	−	0.533998i
$921$		0			0
$922$	−18.8823	+	3.32947i	−0.621857	+	0.109650i
$923$	−0.0296486	−	0.168146i	−0.000975897	−	0.00553459i
$924$		0			0
$925$	8.57238	+	7.19308i	0.281858	+	0.236507i
$926$	−1.55058	+	0.895227i	−0.0509552	+	0.0294190i
$927$		0			0
$928$	5.41030	−	9.37092i	0.177602	−	0.307616i
$929$	2.67605	+	2.24547i	0.0877982	+	0.0736714i	0.685630	−	0.727950i	$-0.259527\pi$
$929$	2.67605	+	2.24547i	0.0877982	+	0.0736714i	−0.597832	+	0.801621i	$0.703971\pi$
$930$		0			0
$931$	−1.74551	+	53.6939i	−0.0572066	+	1.75975i
$932$	5.48490	−	15.0696i	0.179664	−	0.493622i
$933$		0			0
$934$	7.18720	+	19.7467i	0.235172	+	0.646131i
$935$	8.33167	+	4.81029i	0.272475	+	0.157313i
$936$		0			0
$937$	−29.0222	−	16.7560i	−0.948114	−	0.547394i	−0.0556194	−	0.998452i	$-0.517713\pi$
$937$	−29.0222	−	16.7560i	−0.948114	−	0.547394i	−0.892495	+	0.451058i	$0.851047\pi$
$938$	7.89327	−	4.38775i	0.257724	−	0.143265i
$939$		0			0
$940$	−8.33363	−	3.03319i	−0.271813	−	0.0989318i
$941$	31.7471	+	11.5550i	1.03493	+	0.376682i	0.802955	−	0.596040i	$-0.203260\pi$
$941$	31.7471	+	11.5550i	1.03493	+	0.376682i	0.231972	+	0.972722i	$0.425482\pi$
$942$		0			0
$943$	−18.0985	−	3.19126i	−0.589370	−	0.103922i
$944$	−10.3529			−0.336958
$945$		0			0
$946$	−1.29422			−0.0420788
$947$	1.54156	+	0.271818i	0.0500939	+	0.00883291i	0.198639	−	0.980073i	$-0.436348\pi$
$947$	1.54156	+	0.271818i	0.0500939	+	0.00883291i	−0.148545	+	0.988906i	$0.547459\pi$
$948$		0			0
$949$	−10.3328	−	3.76085i	−0.335418	−	0.122082i
$950$	−16.1007	−	5.86019i	−0.522377	−	0.190130i
$951$		0			0
$952$	21.1278	+	12.6602i	0.684756	+	0.410321i
$953$	13.8156	+	7.97645i	0.447532	+	0.258383i	0.706787	−	0.707426i	$-0.250144\pi$
$953$	13.8156	+	7.97645i	0.447532	+	0.258383i	−0.259255	+	0.965809i	$0.583477\pi$
$954$		0			0
$955$	36.0031	+	20.7864i	1.16503	+	0.672631i
$956$	5.19411	+	14.2707i	0.167990	+	0.461548i
$957$		0			0
$958$	−12.2187	+	33.5707i	−0.394770	+	1.08462i
$959$	−52.1837	−	10.0783i	−1.68510	−	0.325444i
$960$		0			0
$961$	−36.9429	−	30.9988i	−1.19171	−	0.999960i
$962$	−6.10030	+	10.5660i	−0.196681	+	0.340662i
$963$		0			0
$964$	0.0355228	−	0.0205091i	0.00114411	−	0.000660553i
$965$	21.1749	+	17.7678i	0.681643	+	0.571966i
$966$		0			0
$967$	0.704391	+	3.99480i	0.0226517	+	0.128464i	0.994037	−	0.109046i	$-0.0347797\pi$
$967$	0.704391	+	3.99480i	0.0226517	+	0.128464i	−0.971385	+	0.237510i	$0.923669\pi$
$968$	−21.4816	+	3.78778i	−0.690444	+	0.121744i
$969$		0			0
$970$	−14.0763	−	11.8114i	−0.451962	−	0.379241i
$971$	20.1944	−	34.9777i	0.648068	−	1.12249i	−0.335515	−	0.942035i	$-0.608910\pi$
$971$	20.1944	−	34.9777i	0.648068	−	1.12249i	0.983584	−	0.180453i	$-0.0577563\pi$
$972$		0			0
$973$	7.22821	−	18.8982i	0.231726	−	0.605847i
$974$	15.4317	+	42.3984i	0.494465	+	1.35853i
$975$		0			0
$976$	−5.05474	+	13.8878i	−0.161798	+	0.444537i
$977$	5.59190	+	6.66416i	0.178901	+	0.213205i	0.848041	−	0.529931i	$-0.177782\pi$
$977$	5.59190	+	6.66416i	0.178901	+	0.213205i	−0.669140	+	0.743136i	$0.733338\pi$
$978$		0			0
$979$	−4.57852	+	5.45647i	−0.146330	+	0.174389i
$980$	6.89922	−	2.26009i	0.220387	−	0.0721958i
$981$		0			0
$982$	−59.0451			−1.88420
$983$	31.7045	−	11.5395i	1.01122	−	0.368053i	0.217317	−	0.976101i	$-0.430269\pi$
$983$	31.7045	−	11.5395i	1.01122	−	0.368053i	0.793900	+	0.608048i	$0.208047\pi$
$984$		0			0
$985$	−2.90702	−	3.46445i	−0.0926254	−	0.110387i
$986$	21.6225	+	7.86994i	0.688600	+	0.250630i
$987$		0			0
$988$	0.696209	−	3.94840i	0.0221493	−	0.125615i
$989$			3.67595i			0.116888i
$990$		0			0
$991$	−25.4615			−0.808810			−0.404405	−	0.914580i	$-0.632521\pi$
$991$	−25.4615			−0.808810			−0.404405	+	0.914580i	$0.632521\pi$
$992$	25.1927	−	9.16940i	0.799870	−	0.291129i
$993$		0			0
$994$	−0.569781	−	0.494099i	−0.0180724	−	0.0156719i
$995$	−12.5146	−	14.9143i	−0.396739	−	0.472815i
$996$		0			0
$997$	5.62019	−	6.69788i	0.177993	−	0.212124i	−0.669670	−	0.742659i	$-0.733564\pi$
$997$	5.62019	−	6.69788i	0.177993	−	0.212124i	0.847663	+	0.530535i	$0.178009\pi$
$998$	−22.6731	+	13.0903i	−0.717705	+	0.414367i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.467.17		132
3.2	odd	2		189.2.bd.a.47.6	yes	132
7.3	odd	6		567.2.ba.a.143.6		132
21.17	even	6		189.2.ba.a.101.17	✓	132
27.4	even	9		189.2.ba.a.131.17	yes	132
27.23	odd	18		567.2.ba.a.341.6		132
189.31	odd	18		189.2.bd.a.185.6	yes	132
189.185	even	18	inner	567.2.bd.a.17.17		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.17	✓	132	21.17	even	6
189.2.ba.a.131.17	yes	132	27.4	even	9
189.2.bd.a.47.6	yes	132	3.2	odd	2
189.2.bd.a.185.6	yes	132	189.31	odd	18
567.2.ba.a.143.6		132	7.3	odd	6
567.2.ba.a.341.6		132	27.23	odd	18
567.2.bd.a.17.17		132	189.185	even	18	inner
567.2.bd.a.467.17		132	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.57155 + 0.277106i) q^{2} +(0.513586 + 0.186930i) q^{4} +(-1.78318 - 0.649025i) q^{5} +(-1.28547 - 2.31248i) q^{7} +(-2.00866 - 1.15970i) q^{8} +(-2.62250 - 1.51410i) q^{10} +(-0.432011 - 1.18694i) q^{11} +(0.326917 - 0.898197i) q^{13} +(-1.37938 - 3.99038i) q^{14} +(-3.67271 - 3.08177i) q^{16} +(2.00687 - 3.47600i) q^{17} +(6.64640 - 3.83730i) q^{19} +(-0.794495 - 0.666660i) q^{20} +(-0.350017 - 1.98504i) q^{22} +(-5.63807 + 0.994145i) q^{23} +(-1.07172 - 0.899282i) q^{25} +(0.762661 - 1.32097i) q^{26} +(-0.227929 - 1.42795i) q^{28} +(1.22870 + 3.37583i) q^{29} +(-3.04428 + 8.36408i) q^{31} +(-1.93608 - 2.30734i) q^{32} +(4.11711 - 4.90658i) q^{34} +(0.791374 + 4.95787i) q^{35} -7.99870 q^{37} +(11.5085 - 4.18874i) q^{38} +(2.82914 + 3.37163i) q^{40} +(3.01647 + 1.09790i) q^{41} +(0.111496 - 0.632326i) q^{43} -0.690352i q^{44} -9.13598 q^{46} +(8.03521 - 2.92458i) q^{47} +(-3.69512 + 5.94526i) q^{49} +(-1.43506 - 1.71024i) q^{50} +(0.335800 - 0.400191i) q^{52} +(11.3329 - 6.54305i) q^{53} +2.39691i q^{55} +(-0.0997058 + 6.13576i) q^{56} +(0.995499 + 5.64576i) q^{58} +(1.65418 - 1.38802i) q^{59} +(-1.05430 - 2.89668i) q^{61} +(-7.10196 + 12.3010i) q^{62} +(2.39111 + 4.14152i) q^{64} +(-1.16590 + 1.38947i) q^{65} +(0.371427 + 2.10647i) q^{67} +(1.68047 - 1.41008i) q^{68} +(-0.130175 + 8.01082i) q^{70} +(0.154696 - 0.0893139i) q^{71} -11.5040i q^{73} +(-12.5703 - 2.21649i) q^{74} +(4.13081 - 0.728373i) q^{76} +(-2.18944 + 2.52480i) q^{77} +(-0.211994 + 1.20228i) q^{79} +(4.54896 + 7.87903i) q^{80} +(4.43628 + 2.56129i) q^{82} +(5.11532 - 1.86183i) q^{83} +(-5.83462 + 4.89582i) q^{85} +(0.350443 - 0.962834i) q^{86} +(-0.508733 + 2.88517i) q^{88} +(-2.81958 - 4.88366i) q^{89} +(-2.49730 + 0.398619i) q^{91} +(-3.08147 - 0.543347i) q^{92} +(13.4381 - 2.36950i) q^{94} +(-14.3422 + 2.52892i) q^{95} +(5.97585 + 1.05370i) q^{97} +(-7.45452 + 8.31931i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31}+ \cdots + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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