LMFDB - Embedded newform 171.2.u.a.118.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(28,171)] 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("171.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			118.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	171.118
Dual form			171.2.u.a.100.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.43969 - 0.524005i) q^{2} +(0.266044 + 0.223238i) q^{4} +(1.93969 - 1.62760i) q^{5} +(-0.266044 + 0.460802i) q^{7} +(1.26604 + 2.19285i) q^{8} +(-3.64543 + 1.32683i) q^{10} +(-2.55303 - 4.42198i) q^{11} +(0.705737 - 4.00243i) q^{13} +(0.624485 - 0.524005i) q^{14} +(-0.794263 - 4.50449i) q^{16} +(1.82635 + 0.664738i) q^{17} +(2.23396 - 3.74292i) q^{19} +0.879385 q^{20} +(1.35844 + 7.70410i) q^{22} +(-2.33022 - 1.95529i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-3.11334 + 5.39246i) q^{26} +(-0.173648 + 0.0632028i) q^{28} +(1.51367 - 0.550931i) q^{29} +(-4.93969 + 8.55580i) q^{31} +(-0.337496 + 1.91404i) q^{32} +(-2.28106 - 1.91404i) q^{34} +(0.233956 + 1.32683i) q^{35} +6.10607 q^{37} +(-5.17752 + 4.21805i) q^{38} +(6.02481 + 2.19285i) q^{40} +(1.47178 + 8.34689i) q^{41} +(-0.135630 + 0.113807i) q^{43} +(0.307934 - 1.74638i) q^{44} +(2.33022 + 4.03606i) q^{46} +(7.10354 - 2.58548i) q^{47} +(3.35844 + 5.81699i) q^{49} +(-1.08125 + 1.87278i) q^{50} +(1.08125 - 0.907278i) q^{52} +(7.58512 + 6.36467i) q^{53} +(-12.1493 - 4.42198i) q^{55} -1.34730 q^{56} -2.46791 q^{58} +(-3.58512 - 1.30488i) q^{59} +(-10.6702 - 8.95340i) q^{61} +(11.5949 - 9.72930i) q^{62} +(-3.08512 + 5.34359i) q^{64} +(-5.14543 - 8.91215i) q^{65} +(9.59627 - 3.49276i) q^{67} +(0.337496 + 0.584561i) q^{68} +(0.358441 - 2.03282i) q^{70} +(-2.92855 + 2.45734i) q^{71} +(-0.322481 - 1.82888i) q^{73} +(-8.79086 - 3.19961i) q^{74} +(1.42989 - 0.497079i) q^{76} +2.71688 q^{77} +(1.82635 + 10.3578i) q^{79} +(-8.87211 - 7.44459i) q^{80} +(2.25490 - 12.7882i) q^{82} +(-5.73783 + 9.93821i) q^{83} +(4.62449 - 1.68317i) q^{85} +(0.254900 - 0.0927760i) q^{86} +(6.46451 - 11.1969i) q^{88} +(1.02869 - 5.83396i) q^{89} +(1.65657 + 1.39003i) q^{91} +(-0.183448 - 1.04039i) q^{92} -11.5817 q^{94} +(-1.75877 - 10.8961i) q^{95} +(6.39053 + 2.32596i) q^{97} +(-1.78699 - 10.1345i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} + 3 q^{7} + 3 q^{8} - 6 q^{10} - 3 q^{11} - 6 q^{13} - 9 q^{14} - 15 q^{16} + 12 q^{17} + 18 q^{19} - 6 q^{20} + 9 q^{23} - 12 q^{26} - 12 q^{29} - 24 q^{31} + 3 q^{32}+ \cdots - 3 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 + 3 * q^7 + 3 * q^8 - 6 * q^10 - 3 * q^11 - 6 * q^13 - 9 * q^14 - 15 * q^16 + 12 * q^17 + 18 * q^19 - 6 * q^20 + 9 * q^23 - 12 * q^26 - 12 * q^29 - 24 * q^31 + 3 * q^32 + 21 * q^34 + 6 * q^35 + 12 * q^37 - 6 * q^38 + 9 * q^40 - 6 * q^41 + 18 * q^43 - 9 * q^44 - 9 * q^46 + 33 * q^47 + 12 * q^49 - 9 * q^50 + 9 * q^52 + 24 * q^53 - 33 * q^55 - 6 * q^56 - 24 * q^58 - 21 * q^61 + 51 * q^62 + 3 * q^64 - 15 * q^65 + 30 * q^67 - 3 * q^68 - 6 * q^70 - 18 * q^71 - 27 * q^73 - 21 * q^74 + 12 * q^79 - 24 * q^80 + 15 * q^82 - 15 * q^83 + 15 * q^85 + 3 * q^86 + 6 * q^88 - 45 * q^89 - 12 * q^91 - 3 * q^92 - 6 * q^94 + 12 * q^95 + 21 * q^97 - 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−1.43969	−	0.524005i	−1.01802	−	0.370528i	−0.221510	−	0.975158i	$-0.571099\pi$
$2$	−1.43969	−	0.524005i	−1.01802	−	0.370528i	−0.796506	+	0.604630i	$0.793321\pi$
$3$		0			0
$3$		0			0
$4$	0.266044	+	0.223238i	0.133022	+	0.111619i
$5$	1.93969	−	1.62760i	0.867457	−	0.727883i	−0.0961041	−	0.995371i	$-0.530638\pi$
$5$	1.93969	−	1.62760i	0.867457	−	0.727883i	0.963561	+	0.267489i	$0.0861937\pi$
$6$		0			0
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	−0.911914	−	0.410382i	$-0.865395\pi$
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	0.811358	+	0.584549i	$0.198729\pi$
$8$	1.26604	+	2.19285i	0.447614	+	0.775291i
$9$		0			0
$10$	−3.64543	+	1.32683i	−1.15279	+	0.419580i
$11$	−2.55303	−	4.42198i	−0.769769	−	1.33328i	−0.937688	−	0.347478i	$-0.887038\pi$
$11$	−2.55303	−	4.42198i	−0.769769	−	1.33328i	0.167920	−	0.985801i	$-0.446295\pi$
$12$		0			0
$13$	0.705737	−	4.00243i	0.195736	−	1.11008i	−0.715630	−	0.698479i	$-0.753860\pi$
$13$	0.705737	−	4.00243i	0.195736	−	1.11008i	0.911366	−	0.411596i	$-0.135029\pi$
$14$	0.624485	−	0.524005i	0.166901	−	0.140046i
$15$		0			0
$16$	−0.794263	−	4.50449i	−0.198566	−	1.12612i
$17$	1.82635	+	0.664738i	0.442955	+	0.161223i	0.553862	−	0.832608i	$-0.313153\pi$
$17$	1.82635	+	0.664738i	0.442955	+	0.161223i	−0.110907	+	0.993831i	$0.535376\pi$
$18$		0			0
$19$	2.23396	−	3.74292i	0.512505	−	0.858685i
$19$	2.23396	−	3.74292i	0.512505	−	0.858685i
$20$	0.879385			0.196637
$21$		0			0
$22$	1.35844	+	7.70410i	0.289621	+	1.64252i
$23$	−2.33022	−	1.95529i	−0.485885	−	0.407706i	0.366664	−	0.930353i	$-0.380500\pi$
$23$	−2.33022	−	1.95529i	−0.485885	−	0.407706i	−0.852549	+	0.522648i	$0.824944\pi$
$24$		0			0
$25$	0.245100	−	1.39003i	0.0490200	−	0.278006i
$26$	−3.11334	+	5.39246i	−0.610576	+	1.05755i
$27$		0			0
$28$	−0.173648	+	0.0632028i	−0.0328164	+	0.0119442i
$29$	1.51367	−	0.550931i	0.281082	−	0.102305i	−0.197633	−	0.980276i	$-0.563325\pi$
$29$	1.51367	−	0.550931i	0.281082	−	0.102305i	0.478714	+	0.877971i	$0.341103\pi$
$30$		0			0
$31$	−4.93969	+	8.55580i	−0.887195	+	1.53667i	−0.0440180	+	0.999031i	$0.514016\pi$
$31$	−4.93969	+	8.55580i	−0.887195	+	1.53667i	−0.843177	+	0.537636i	$0.819317\pi$
$32$	−0.337496	+	1.91404i	−0.0596615	+	0.338357i
$33$		0			0
$34$	−2.28106	−	1.91404i	−0.391198	−	0.328254i
$35$	0.233956	+	1.32683i	0.0395457	+	0.224275i
$36$		0			0
$37$	6.10607			1.00383			0.501916	−	0.864917i	$-0.332629\pi$
$37$	6.10607			1.00383			0.501916	+	0.864917i	$0.332629\pi$
$38$	−5.17752	+	4.21805i	−0.839904	+	0.684258i
$39$		0			0
$40$	6.02481	+	2.19285i	0.952607	+	0.346721i
$41$	1.47178	+	8.34689i	0.229854	+	1.30356i	0.853186	+	0.521607i	$0.174667\pi$
$41$	1.47178	+	8.34689i	0.229854	+	1.30356i	−0.623332	+	0.781957i	$0.714221\pi$
$42$		0			0
$43$	−0.135630	+	0.113807i	−0.0206833	+	0.0173554i	−0.653071	−	0.757297i	$-0.726520\pi$
$43$	−0.135630	+	0.113807i	−0.0206833	+	0.0173554i	0.632387	+	0.774652i	$0.282075\pi$
$44$	0.307934	−	1.74638i	0.0464227	−	0.263276i
$45$		0			0
$46$	2.33022	+	4.03606i	0.343573	+	0.595085i
$47$	7.10354	−	2.58548i	1.03616	−	0.377131i	0.232735	−	0.972540i	$-0.425232\pi$
$47$	7.10354	−	2.58548i	1.03616	−	0.377131i	0.803422	+	0.595409i	$0.203010\pi$
$48$		0			0
$49$	3.35844	+	5.81699i	0.479777	+	0.830999i
$50$	−1.08125	+	1.87278i	−0.152912	+	0.264852i
$51$		0			0
$52$	1.08125	−	0.907278i	0.149943	−	0.125817i
$53$	7.58512	+	6.36467i	1.04190	+	0.874255i	0.992218	−	0.124510i	$-0.0397359\pi$
$53$	7.58512	+	6.36467i	1.04190	+	0.874255i	0.0496783	+	0.998765i	$0.484180\pi$
$54$		0			0
$55$	−12.1493	−	4.42198i	−1.63821	−	0.596260i
$56$	−1.34730			−0.180040
$57$		0			0
$58$	−2.46791			−0.324053
$59$	−3.58512	−	1.30488i	−0.466743	−	0.169881i	0.0979333	−	0.995193i	$-0.468777\pi$
$59$	−3.58512	−	1.30488i	−0.466743	−	0.169881i	−0.564676	+	0.825312i	$0.690999\pi$
$60$		0			0
$61$	−10.6702	−	8.95340i	−1.36618	−	1.14637i	−0.974018	−	0.226471i	$-0.927281\pi$
$61$	−10.6702	−	8.95340i	−1.36618	−	1.14637i	−0.392167	−	0.919894i	$-0.628274\pi$
$62$	11.5949	−	9.72930i	1.47256	−	1.23562i
$63$		0			0
$64$	−3.08512	+	5.34359i	−0.385640	+	0.667949i
$65$	−5.14543	−	8.91215i	−0.638212	−	1.10542i
$66$		0			0
$67$	9.59627	−	3.49276i	1.17237	−	0.426708i	0.318869	−	0.947799i	$-0.396697\pi$
$67$	9.59627	−	3.49276i	1.17237	−	0.426708i	0.853501	+	0.521091i	$0.174475\pi$
$68$	0.337496	+	0.584561i	0.0409274	+	0.0708884i
$69$		0			0
$70$	0.358441	−	2.03282i	0.0428419	−	0.242968i
$71$	−2.92855	+	2.45734i	−0.347555	+	0.291633i	−0.799807	−	0.600257i	$-0.795065\pi$
$71$	−2.92855	+	2.45734i	−0.347555	+	0.291633i	0.452253	+	0.891890i	$0.350621\pi$
$72$		0			0
$73$	−0.322481	−	1.82888i	−0.0377436	−	0.214055i	0.960103	−	0.279647i	$-0.0902174\pi$
$73$	−0.322481	−	1.82888i	−0.0377436	−	0.214055i	−0.997847	+	0.0655924i	$0.979106\pi$
$74$	−8.79086	−	3.19961i	−1.02192	−	0.371947i
$75$		0			0
$76$	1.42989	−	0.497079i	0.164020	−	0.0570189i
$77$	2.71688			0.309617
$78$		0			0
$79$	1.82635	+	10.3578i	0.205481	+	1.16534i	0.896682	+	0.442676i	$0.145971\pi$
$79$	1.82635	+	10.3578i	0.205481	+	1.16534i	−0.691201	+	0.722663i	$0.742918\pi$
$80$	−8.87211	−	7.44459i	−0.991932	−	0.832330i
$81$		0			0
$82$	2.25490	−	12.7882i	0.249012	−	1.41222i
$83$	−5.73783	+	9.93821i	−0.629808	+	1.09086i	0.357782	+	0.933805i	$0.383533\pi$
$83$	−5.73783	+	9.93821i	−0.629808	+	1.09086i	−0.987590	+	0.157055i	$0.949800\pi$
$84$		0			0
$85$	4.62449	−	1.68317i	0.501596	−	0.182566i
$86$	0.254900	−	0.0927760i	0.0274866	−	0.0100043i
$87$		0			0
$88$	6.46451	−	11.1969i	0.689119	−	1.19359i
$89$	1.02869	−	5.83396i	0.109040	−	0.618399i	−0.880489	−	0.474067i	$-0.842786\pi$
$89$	1.02869	−	5.83396i	0.109040	−	0.618399i	0.989529	−	0.144332i	$-0.0461034\pi$
$90$		0			0
$91$	1.65657	+	1.39003i	0.173656	+	0.145715i
$92$	−0.183448	−	1.04039i	−0.0191258	−	0.108468i
$93$		0			0
$94$	−11.5817			−1.19456
$95$	−1.75877	−	10.8961i	−0.180446	−	1.11792i
$96$		0			0
$97$	6.39053	+	2.32596i	0.648860	+	0.236166i	0.645419	−	0.763828i	$-0.276683\pi$
$97$	6.39053	+	2.32596i	0.648860	+	0.236166i	0.00344055	+	0.999994i	$0.498905\pi$
$98$	−1.78699	−	10.1345i	−0.180513	−	1.02374i
$99$		0			0
$100$	0.375515	−	0.315094i	0.0375515	−	0.0315094i
$101$	1.52094	−	8.62571i	0.151340	−	0.858290i	−0.810717	−	0.585439i	$-0.800922\pi$
$101$	1.52094	−	8.62571i	0.151340	−	0.858290i	0.962056	−	0.272851i	$-0.0879666\pi$
$102$		0			0
$103$	1.92262	+	3.33007i	0.189441	+	0.328122i	0.945064	−	0.326885i	$-0.105999\pi$
$103$	1.92262	+	3.33007i	0.189441	+	0.328122i	−0.755623	+	0.655007i	$0.772666\pi$
$104$	9.67024	−	3.51968i	0.948245	−	0.345133i
$105$		0			0
$106$	−7.58512	−	13.1378i	−0.736732	−	1.27606i
$107$	−2.83750	+	4.91469i	−0.274311	+	0.475121i	−0.969961	−	0.243260i	$-0.921783\pi$
$107$	−2.83750	+	4.91469i	−0.274311	+	0.475121i	0.695650	+	0.718381i	$0.255116\pi$
$108$		0			0
$109$	−1.59833	+	1.34115i	−0.153092	+	0.128459i	−0.716116	−	0.697981i	$-0.754082\pi$
$109$	−1.59833	+	1.34115i	−0.153092	+	0.128459i	0.563025	+	0.826440i	$0.309638\pi$
$110$	15.1741	+	12.7326i	1.44680	+	1.21401i
$111$		0			0
$112$	2.28699	+	0.832396i	0.216100	+	0.0786540i
$113$	−7.27631			−0.684498			−0.342249	−	0.939609i	$-0.611189\pi$
$113$	−7.27631			−0.684498			−0.342249	+	0.939609i	$0.611189\pi$
$114$		0			0
$115$	−7.70233			−0.718246
$116$	0.525692	+	0.191336i	0.0488093	+	0.0177651i
$117$		0			0
$118$	4.47771	+	3.75725i	0.412207	+	0.345883i
$119$	−0.792204	+	0.664738i	−0.0726212	+	0.0609364i
$120$		0			0
$121$	−7.53596	+	13.0527i	−0.685087	+	1.18661i
$122$	10.6702	+	18.4814i	0.966039	+	1.67323i
$123$		0			0
$124$	−3.22416	+	1.17350i	−0.289538	+	0.105383i
$125$	4.54323	+	7.86911i	0.406359	+	0.703835i
$126$		0			0
$127$	0.317734	−	1.80196i	0.0281943	−	0.159898i	−0.967460	−	0.253024i	$-0.918575\pi$
$127$	0.317734	−	1.80196i	0.0281943	−	0.159898i	0.995654	+	0.0931261i	$0.0296860\pi$
$128$	10.2194	−	8.57510i	0.903277	−	0.757939i
$129$		0			0
$130$	2.73783	+	15.5270i	0.240123	+	1.36181i
$131$	−8.25624	−	3.00503i	−0.721351	−	0.262550i	−0.0448520	−	0.998994i	$-0.514282\pi$
$131$	−8.25624	−	3.00503i	−0.721351	−	0.262550i	−0.676499	+	0.736443i	$0.736504\pi$
$132$		0			0
$133$	1.13041	+	2.02520i	0.0980194	+	0.175607i
$134$	−15.6459			−1.35160
$135$		0			0
$136$	0.854570	+	4.84651i	0.0732788	+	0.415585i
$137$	9.67546	+	8.11867i	0.826630	+	0.693625i	0.954515	−	0.298164i	$-0.0963742\pi$
$137$	9.67546	+	8.11867i	0.826630	+	0.693625i	−0.127884	+	0.991789i	$0.540819\pi$
$138$		0			0
$139$	−0.703211	+	3.98811i	−0.0596456	+	0.338267i	−0.999998	−	0.00193468i	$-0.999384\pi$
$139$	−0.703211	+	3.98811i	−0.0596456	+	0.338267i	0.940353	+	0.340201i	$0.110495\pi$
$140$	−0.233956	+	0.405223i	−0.0197729	+	0.0342476i
$141$		0			0
$142$	5.50387	−	2.00324i	0.461875	−	0.168109i
$143$	−19.5005	+	7.09759i	−1.63071	+	0.593530i
$144$		0			0
$145$	2.03936	−	3.53228i	0.169360	−	0.293340i
$146$	−0.494070	+	2.80201i	−0.0408895	+	0.231896i
$147$		0			0
$148$	1.62449	+	1.36310i	0.133532	+	0.112047i
$149$	−1.05391	−	5.97702i	−0.0863397	−	0.489657i	−0.997059	−	0.0766320i	$-0.975583\pi$
$149$	−1.05391	−	5.97702i	−0.0863397	−	0.489657i	0.910720	−	0.413025i	$-0.135528\pi$
$150$		0			0
$151$	−0.162504			−0.0132244			−0.00661219	−	0.999978i	$-0.502105\pi$
$151$	−0.162504			−0.0132244			−0.00661219	+	0.999978i	$0.502105\pi$
$152$	11.0360	+	0.160035i	0.895134	+	0.0129806i
$153$		0			0
$154$	−3.91147	−	1.42366i	−0.315196	−	0.114722i
$155$	4.34389	+	24.6354i	0.348910	+	1.97877i
$156$		0			0
$157$	5.10220	−	4.28125i	0.407200	−	0.341681i	−0.416069	−	0.909333i	$-0.636593\pi$
$157$	5.10220	−	4.28125i	0.407200	−	0.341681i	0.823269	+	0.567652i	$0.192148\pi$
$158$	2.79813	−	15.8690i	0.222608	−	1.26247i
$159$		0			0
$160$	2.46064	+	4.26195i	0.194530	+	0.336937i
$161$	1.52094	−	0.553579i	0.119867	−	0.0436281i
$162$		0			0
$163$	0.224155	+	0.388249i	0.0175572	+	0.0304100i	0.874671	−	0.484718i	$-0.161078\pi$
$163$	0.224155	+	0.388249i	0.0175572	+	0.0304100i	−0.857113	+	0.515128i	$0.827744\pi$
$164$	−1.47178	+	2.54920i	−0.114927	+	0.199059i
$165$		0			0
$166$	13.4684	−	11.3013i	1.04535	−	0.877152i
$167$	−2.59627	−	2.17853i	−0.200905	−	0.168579i	0.536785	−	0.843719i	$-0.319639\pi$
$167$	−2.59627	−	2.17853i	−0.200905	−	0.168579i	−0.737690	+	0.675140i	$0.764083\pi$
$168$		0			0
$169$	−3.30541	−	1.20307i	−0.254262	−	0.0925438i
$170$	−7.53983			−0.578279
$171$		0			0
$172$	−0.0614894			−0.00468852
$173$	−1.51842	−	0.552659i	−0.115443	−	0.0420179i	0.283653	−	0.958927i	$-0.408454\pi$
$173$	−1.51842	−	0.552659i	−0.115443	−	0.0420179i	−0.399096	+	0.916909i	$0.630676\pi$
$174$		0			0
$175$	0.575322	+	0.482753i	0.0434903	+	0.0364927i
$176$	−17.8910	+	15.0123i	−1.34858	+	1.13160i
$177$		0			0
$178$	−4.53802	+	7.86008i	−0.340139	+	0.589138i
$179$	1.05690	+	1.83061i	0.0789967	+	0.136826i	0.902817	−	0.430024i	$-0.141495\pi$
$179$	1.05690	+	1.83061i	0.0789967	+	0.136826i	−0.823821	+	0.566851i	$0.808162\pi$
$180$		0			0
$181$	−8.22416	+	2.99335i	−0.611297	+	0.222494i	−0.629071	−	0.777348i	$-0.716564\pi$
$181$	−8.22416	+	2.99335i	−0.611297	+	0.222494i	0.0177739	+	0.999842i	$0.494342\pi$
$182$	−1.65657	−	2.86927i	−0.122793	−	0.212684i
$183$		0			0
$184$	1.33750	−	7.58532i	0.0986015	−	0.559197i
$185$	11.8439	−	9.93821i	0.870780	−	0.730671i
$186$		0			0
$187$	−1.72328	−	9.77320i	−0.126019	−	0.714687i
$188$	2.46703	+	0.897927i	0.179927	+	0.0654880i
$189$		0			0
$190$	−3.17752	+	16.6086i	−0.230521	+	1.20492i
$191$	19.0719			1.38000			0.689998	−	0.723811i	$-0.257611\pi$
$191$	19.0719			1.38000			0.689998	+	0.723811i	$0.257611\pi$
$192$		0			0
$193$	−4.13903	−	23.4736i	−0.297934	−	1.68967i	−0.655032	−	0.755601i	$-0.727345\pi$
$193$	−4.13903	−	23.4736i	−0.297934	−	1.68967i	0.357098	−	0.934067i	$-0.383766\pi$
$194$	−7.98158	−	6.69734i	−0.573044	−	0.480841i
$195$		0			0
$196$	−0.405078	+	2.29731i	−0.0289341	+	0.164093i
$197$	−2.19459	+	3.80115i	−0.156358	+	0.270820i	−0.933553	−	0.358440i	$-0.883309\pi$
$197$	−2.19459	+	3.80115i	−0.156358	+	0.270820i	0.777195	+	0.629260i	$0.216642\pi$
$198$		0			0
$199$	18.8293	−	6.85332i	1.33478	−	0.485819i	0.426613	−	0.904434i	$-0.359707\pi$
$199$	18.8293	−	6.85332i	1.33478	−	0.485819i	0.908164	+	0.418615i	$0.137484\pi$
$200$	3.35844	−	1.22237i	0.237478	−	0.0864348i
$201$		0			0
$202$	−6.70961	+	11.6214i	−0.472086	+	0.817678i
$203$	−0.148833	+	0.844075i	−0.0104460	+	0.0592425i
$204$		0			0
$205$	16.4402	+	13.7949i	1.14823	+	0.963480i
$206$	−1.02300	−	5.80174i	−0.0712761	−	0.404227i
$207$		0			0
$208$	−18.5895			−1.28895
$209$	−22.2545	−	0.322718i	−1.53938	−	0.0223228i
$210$		0			0
$211$	−25.5526	−	9.30039i	−1.75912	−	0.640266i	−0.759172	−	0.650891i	$-0.774396\pi$
$211$	−25.5526	−	9.30039i	−1.75912	−	0.640266i	−0.999944	+	0.0106250i	$0.996618\pi$
$212$	0.597144	+	3.38657i	0.0410120	+	0.232591i
$213$		0			0
$214$	6.66044	−	5.58878i	0.455299	−	0.382041i
$215$	−0.0778483	+	0.441500i	−0.00530921	+	0.0301100i
$216$		0			0
$217$	−2.62836	−	4.55245i	−0.178424	−	0.309040i
$218$	3.00387	−	1.09332i	0.203448	−	0.0740489i
$219$		0			0
$220$	−2.24510	−	3.88863i	−0.151365	−	0.262171i
$221$	3.94949	−	6.84072i	0.265672	−	0.460157i
$222$		0			0
$223$	−9.20233	+	7.72167i	−0.616234	+	0.517082i	−0.896617	−	0.442807i	$-0.853983\pi$
$223$	−9.20233	+	7.72167i	−0.616234	+	0.517082i	0.280383	+	0.959888i	$0.409538\pi$
$224$	−0.792204	−	0.664738i	−0.0529313	−	0.0444147i
$225$		0			0
$226$	10.4757	+	3.81283i	0.696830	+	0.253625i
$227$	−4.34049			−0.288088			−0.144044	−	0.989571i	$-0.546011\pi$
$227$	−4.34049			−0.288088			−0.144044	+	0.989571i	$0.546011\pi$
$228$		0			0
$229$	3.29591			0.217800			0.108900	−	0.994053i	$-0.465267\pi$
$229$	3.29591			0.217800			0.108900	+	0.994053i	$0.465267\pi$
$230$	11.0890	+	4.03606i	0.731187	+	0.266130i
$231$		0			0
$232$	3.12449	+	2.62175i	0.205132	+	0.172127i
$233$	11.8209	−	9.91890i	0.774412	−	0.649809i	−0.167423	−	0.985885i	$-0.553544\pi$
$233$	11.8209	−	9.91890i	0.774412	−	0.649809i	0.941835	+	0.336076i	$0.109100\pi$
$234$		0			0
$235$	9.57057	−	16.5767i	0.624315	−	1.08135i
$236$	−0.662504	−	1.14749i	−0.0431253	−	0.0746953i
$237$		0			0
$238$	1.48886	−	0.541899i	0.0965082	−	0.0351261i
$239$	7.91147	+	13.7031i	0.511751	+	0.886378i	0.999907	+	0.0136221i	$0.00433619\pi$
$239$	7.91147	+	13.7031i	0.511751	+	0.886378i	−0.488156	+	0.872756i	$0.662330\pi$
$240$		0			0
$241$	−4.10607	+	23.2867i	−0.264495	+	1.50003i	0.505974	+	0.862549i	$0.331133\pi$
$241$	−4.10607	+	23.2867i	−0.264495	+	1.50003i	−0.770469	+	0.637477i	$0.779978\pi$
$242$	17.6891	−	14.8429i	1.13710	−	0.954140i
$243$		0			0
$244$	−0.840022	−	4.76400i	−0.0537769	−	0.304984i
$245$	15.9820	+	5.81699i	1.02106	+	0.371634i
$246$		0			0
$247$	−13.4042	−	11.5828i	−0.852889	−	0.736994i
$248$	−25.0155			−1.58848
$249$		0			0
$250$	−2.41740	−	13.7098i	−0.152890	−	0.867083i
$251$	−14.8701	−	12.4775i	−0.938589	−	0.787570i	0.0387499	−	0.999249i	$-0.487662\pi$
$251$	−14.8701	−	12.4775i	−0.938589	−	0.787570i	−0.977339	+	0.211679i	$0.932107\pi$
$252$		0			0
$253$	−2.69712	+	15.2961i	−0.169566	+	0.961659i
$254$	−1.40167	+	2.42777i	−0.0879488	+	0.152332i
$255$		0			0
$256$	−7.60994	+	2.76979i	−0.475621	+	0.173112i
$257$	11.5544	−	4.20545i	0.720742	−	0.262329i	0.0445014	−	0.999009i	$-0.485830\pi$
$257$	11.5544	−	4.20545i	0.720742	−	0.262329i	0.676241	+	0.736681i	$0.263608\pi$
$258$		0			0
$259$	−1.62449	+	2.81369i	−0.100941	+	0.174834i
$260$	0.620615	−	3.51968i	0.0384889	−	0.218281i
$261$		0			0
$262$	10.3118	+	8.65263i	0.637065	+	0.534561i
$263$	−1.10101	−	6.24416i	−0.0678915	−	0.385032i	−0.999753	−	0.0222179i	$-0.992927\pi$
$263$	−1.10101	−	6.24416i	−0.0678915	−	0.385032i	0.931862	−	0.362814i	$-0.118184\pi$
$264$		0			0
$265$	25.0719			1.54016
$266$	−0.566237	−	3.50800i	−0.0347182	−	0.215089i
$267$		0			0
$268$	3.33275	+	1.21302i	0.203580	+	0.0740971i
$269$	0.403733	+	2.28969i	0.0246161	+	0.139605i	0.994639	−	0.103409i	$-0.0329751\pi$
$269$	0.403733	+	2.28969i	0.0246161	+	0.139605i	−0.970023	+	0.243014i	$0.921864\pi$
$270$		0			0
$271$	11.4474	−	9.60554i	0.695382	−	0.583495i	−0.225074	−	0.974342i	$-0.572262\pi$
$271$	11.4474	−	9.60554i	0.695382	−	0.583495i	0.920456	+	0.390847i	$0.127818\pi$
$272$	1.54370	−	8.75476i	0.0936006	−	0.530835i
$273$		0			0
$274$	−9.67546	−	16.7584i	−0.584516	−	1.01241i
$275$	−6.77244	+	2.46497i	−0.408394	+	0.148643i
$276$		0			0
$277$	11.9829	+	20.7550i	0.719984	+	1.24705i	0.961005	+	0.276529i	$0.0891843\pi$
$277$	11.9829	+	20.7550i	0.719984	+	1.24705i	−0.241021	+	0.970520i	$0.577482\pi$
$278$	3.10220	−	5.37316i	0.186057	−	0.322261i
$279$		0			0
$280$	−2.61334	+	2.19285i	−0.156177	+	0.131048i
$281$	−19.5804	−	16.4299i	−1.16807	−	0.980125i	−0.168083	−	0.985773i	$-0.553758\pi$
$281$	−19.5804	−	16.4299i	−1.16807	−	0.980125i	−0.999984	+	0.00564805i	$0.998202\pi$
$282$		0			0
$283$	7.05778	+	2.56882i	0.419542	+	0.152701i	0.543160	−	0.839629i	$-0.317228\pi$
$283$	7.05778	+	2.56882i	0.419542	+	0.152701i	−0.123619	+	0.992330i	$0.539450\pi$
$284$	−1.32770			−0.0787843
$285$		0			0
$286$	31.7939			1.88001
$287$	−4.23783	−	1.54244i	−0.250151	−	0.0910475i
$288$		0			0
$289$	−10.1291	−	8.49930i	−0.595828	−	0.499959i
$290$	−4.78699	+	4.01676i	−0.281102	+	0.235872i
$291$		0			0
$292$	0.322481	−	0.558554i	0.0188718	−	0.0326869i
$293$	7.38326	+	12.7882i	0.431334	+	0.747093i	0.996989	−	0.0775495i	$-0.0247096\pi$
$293$	7.38326	+	12.7882i	0.431334	+	0.747093i	−0.565654	+	0.824643i	$0.691376\pi$
$294$		0			0
$295$	−9.07785	+	3.30407i	−0.528533	+	0.192370i
$296$	7.73055	+	13.3897i	0.449329	+	0.778261i
$297$		0			0
$298$	−1.61468	+	9.15733i	−0.0935362	+	0.530470i
$299$	−9.47044	+	7.94664i	−0.547690	+	0.459566i
$300$		0			0
$301$	−0.0163589	−	0.0927760i	−0.000942912	−	0.00534752i
$302$	0.233956	+	0.0851529i	0.0134626	+	0.00490000i
$303$		0			0
$304$	−18.6343	−	7.08997i	−1.06875	−	0.406637i
$305$	−35.2695			−2.01953
$306$		0			0
$307$	0.957234	+	5.42874i	0.0546322	+	0.309835i	0.999863	−	0.0165689i	$-0.00527428\pi$
$307$	0.957234	+	5.42874i	0.0546322	+	0.309835i	−0.945231	+	0.326404i	$0.894163\pi$
$308$	0.722811	+	0.606511i	0.0411860	+	0.0345591i
$309$		0			0
$310$	6.65523	−	37.7437i	0.377992	−	2.14370i
$311$	8.69981	−	15.0685i	0.493321	−	0.854457i	−0.506650	−	0.862152i	$-0.669116\pi$
$311$	8.69981	−	15.0685i	0.493321	−	0.854457i	0.999970	+	0.00769537i	$0.00244954\pi$
$312$		0			0
$313$	−14.9820	+	5.45302i	−0.846835	+	0.308223i	−0.728749	−	0.684780i	$-0.759898\pi$
$313$	−14.9820	+	5.45302i	−0.846835	+	0.308223i	−0.118086	+	0.993003i	$0.537676\pi$
$314$	−9.58899	+	3.49011i	−0.541138	+	0.196958i
$315$		0			0
$316$	−1.82635	+	3.16333i	−0.102740	+	0.177951i
$317$	−0.342711	+	1.94361i	−0.0192486	+	0.109164i	−0.992918	−	0.118799i	$-0.962095\pi$
$317$	−0.342711	+	1.94361i	−0.0192486	+	0.109164i	0.973670	+	0.227963i	$0.0732066\pi$
$318$		0			0
$319$	−6.30066	−	5.28688i	−0.352769	−	0.296009i
$320$	2.71301	+	15.3863i	0.151662	+	0.860118i
$321$		0			0
$322$	−2.47977			−0.138192
$323$	6.56805	−	5.35089i	0.365456	−	0.297732i
$324$		0			0
$325$	−5.39053	−	1.96199i	−0.299013	−	0.108832i
$326$	−0.119271	−	0.676417i	−0.00660579	−	0.0374633i
$327$		0			0
$328$	−16.4402	+	13.7949i	−0.907756	+	0.761698i
$329$	−0.698463	+	3.96118i	−0.0385075	+	0.218387i
$330$		0			0
$331$	0.418748	+	0.725293i	0.0230165	+	0.0398657i	0.877304	−	0.479935i	$-0.159340\pi$
$331$	0.418748	+	0.725293i	0.0230165	+	0.0398657i	−0.854288	+	0.519800i	$0.826006\pi$
$332$	−3.74510	+	1.36310i	−0.205539	+	0.0748101i
$333$		0			0
$334$	2.59627	+	4.49687i	0.142061	+	0.246058i
$335$	12.9290	−	22.3937i	0.706388	−	1.22350i
$336$		0			0
$337$	−2.54916	+	2.13900i	−0.138862	+	0.116519i	−0.709573	−	0.704632i	$-0.751112\pi$
$337$	−2.54916	+	2.13900i	−0.138862	+	0.116519i	0.570711	+	0.821151i	$0.306668\pi$
$338$	4.12836	+	3.46410i	0.224553	+	0.188422i
$339$		0			0
$340$	1.60607	+	0.584561i	0.0871012	+	0.0317022i
$341$	50.4448			2.73174
$342$		0			0
$343$	−7.29860			−0.394087
$344$	−0.421274	−	0.153331i	−0.0227136	−	0.00826707i
$345$		0			0
$346$	1.89646	+	1.59132i	0.101954	+	0.0855498i
$347$	−3.07011	+	2.57613i	−0.164812	+	0.138294i	−0.721464	−	0.692452i	$-0.756530\pi$
$347$	−3.07011	+	2.57613i	−0.164812	+	0.138294i	0.556652	+	0.830746i	$0.312086\pi$
$348$		0			0
$349$	13.9513	−	24.1644i	0.746796	−	1.29349i	−0.202555	−	0.979271i	$-0.564924\pi$
$349$	13.9513	−	24.1644i	0.746796	−	1.29349i	0.949351	−	0.314218i	$-0.101742\pi$
$350$	−0.575322	−	0.996487i	−0.0307523	−	0.0532645i
$351$		0			0
$352$	9.32547	−	3.39420i	0.497049	−	0.180911i
$353$	6.47178	+	11.2095i	0.344458	+	0.596619i	0.985255	−	0.171091i	$-0.0547293\pi$
$353$	6.47178	+	11.2095i	0.344458	+	0.596619i	−0.640797	+	0.767710i	$0.721396\pi$
$354$		0			0
$355$	−1.68092	+	9.53298i	−0.0892141	+	0.505958i
$356$	1.57604	−	1.32245i	0.0835298	−	0.0700898i
$357$		0			0
$358$	−0.562367	−	3.18934i	−0.0297220	−	0.168562i
$359$	10.7562	+	3.91495i	0.567693	+	0.206623i	0.609890	−	0.792486i	$-0.291214\pi$
$359$	10.7562	+	3.91495i	0.567693	+	0.206623i	−0.0421972	+	0.999109i	$0.513436\pi$
$360$		0			0
$361$	−9.01889	−	16.7230i	−0.474678	−	0.880159i
$362$	13.4088			0.704750
$363$		0			0
$364$	0.130415	+	0.739620i	0.00683560	+	0.0387666i
$365$	−3.60220	−	3.02260i	−0.188548	−	0.158210i
$366$		0			0
$367$	−4.96657	+	28.1668i	−0.259253	+	1.47030i	0.525663	+	0.850693i	$0.323817\pi$
$367$	−4.96657	+	28.1668i	−0.259253	+	1.47030i	−0.784916	+	0.619602i	$0.787294\pi$
$368$	−6.95677	+	12.0495i	−0.362647	+	0.628122i
$369$		0			0
$370$	−22.2592	+	8.10170i	−1.15720	+	0.421187i
$371$	−4.95084	+	1.80196i	−0.257035	+	0.0935530i
$372$		0			0
$373$	6.28312	−	10.8827i	0.325328	−	0.563484i	−0.656251	−	0.754543i	$-0.727859\pi$
$373$	6.28312	−	10.8827i	0.325328	−	0.563484i	0.981579	+	0.191059i	$0.0611921\pi$
$374$	−2.64022	+	14.9734i	−0.136522	+	0.774256i
$375$		0			0
$376$	14.6630	+	12.3037i	0.756185	+	0.634515i
$377$	−1.13681	−	6.44718i	−0.0585488	−	0.332047i
$378$		0			0
$379$	−2.19934			−0.112973			−0.0564863	−	0.998403i	$-0.517990\pi$
$379$	−2.19934			−0.112973			−0.0564863	+	0.998403i	$0.517990\pi$
$380$	1.96451	−	3.29147i	0.100777	−	0.168849i
$381$		0			0
$382$	−27.4577	−	9.99379i	−1.40486	−	0.511327i
$383$	1.02940	+	5.83802i	0.0525999	+	0.298309i	0.999747	−	0.0224905i	$-0.00715956\pi$
$383$	1.02940	+	5.83802i	0.0525999	+	0.298309i	−0.947147	+	0.320799i	$0.896048\pi$
$384$		0			0
$385$	5.26991	−	4.42198i	0.268580	−	0.225365i
$386$	−6.34137	+	35.9637i	−0.322767	+	1.83050i
$387$		0			0
$388$	1.18092	+	2.04542i	0.0599522	+	0.103840i
$389$	−31.1215	+	11.3273i	−1.57793	+	0.574318i	−0.974752	−	0.223292i	$-0.928320\pi$
$389$	−31.1215	+	11.3273i	−1.57793	+	0.574318i	−0.603174	+	0.797610i	$0.706097\pi$
$390$		0			0
$391$	−2.95605	−	5.12003i	−0.149494	−	0.258931i
$392$	−8.50387	+	14.7291i	−0.429510	+	0.743934i
$393$		0			0
$394$	5.15136	−	4.32250i	0.259522	−	0.217765i
$395$	20.4008	+	17.1183i	1.02648	+	0.861315i
$396$		0			0
$397$	24.4786	+	8.90950i	1.22855	+	0.447155i	0.873100	−	0.487541i	$-0.162106\pi$
$397$	24.4786	+	8.90950i	1.22855	+	0.447155i	0.355448	+	0.934696i	$0.384328\pi$
$398$	−30.6996			−1.53883
$399$		0			0
$400$	−6.45605			−0.322803
$401$	−15.0052	−	5.46145i	−0.749325	−	0.272732i	−0.0610031	−	0.998138i	$-0.519430\pi$
$401$	−15.0052	−	5.46145i	−0.749325	−	0.272732i	−0.688322	+	0.725406i	$0.741652\pi$
$402$		0			0
$403$	30.7579	+	25.8089i	1.53216	+	1.28563i
$404$	2.33022	−	1.95529i	0.115933	−	0.0972792i
$405$		0			0
$406$	0.656574	−	1.13722i	0.0325852	−	0.0564393i
$407$	−15.5890	−	27.0009i	−0.772718	−	1.33839i
$408$		0			0
$409$	2.77079	−	1.00849i	0.137007	−	0.0498664i	−0.272607	−	0.962126i	$-0.587886\pi$
$409$	2.77079	−	1.00849i	0.137007	−	0.0498664i	0.409614	+	0.912259i	$0.365664\pi$
$410$	−16.4402	−	28.4752i	−0.811922	−	1.40629i
$411$		0			0
$412$	−0.231896	+	1.31515i	−0.0114247	+	0.0647927i
$413$	1.55509	−	1.30488i	0.0765211	−	0.0642088i
$414$		0			0
$415$	5.04576	+	28.6159i	0.247687	+	1.40470i
$416$	7.42262	+	2.70161i	0.363924	+	0.132457i
$417$		0			0
$418$	31.8705	+	12.1261i	1.55884	+	0.593106i
$419$	33.4962			1.63640			0.818198	−	0.574937i	$-0.194973\pi$
$419$	33.4962			1.63640			0.818198	+	0.574937i	$0.194973\pi$
$420$		0			0
$421$	3.12877	+	17.7441i	0.152487	+	0.864795i	0.961048	+	0.276383i	$0.0891357\pi$
$421$	3.12877	+	17.7441i	0.152487	+	0.864795i	−0.808561	+	0.588412i	$0.799753\pi$
$422$	31.9145	+	26.7794i	1.55357	+	1.30360i
$423$		0			0
$424$	−4.35369	+	24.6910i	−0.211434	+	1.19910i
$425$	1.37164	−	2.37576i	0.0665345	−	0.115241i
$426$		0			0
$427$	6.96451	−	2.53487i	0.337036	−	0.122671i
$428$	−1.85204	+	0.674089i	−0.0895219	+	0.0325833i
$429$		0			0
$430$	0.343426	−	0.594831i	0.0165615	−	0.0286853i
$431$	−3.70233	+	20.9970i	−0.178335	+	1.01139i	0.755888	+	0.654701i	$0.227205\pi$
$431$	−3.70233	+	20.9970i	−0.178335	+	1.01139i	−0.934223	+	0.356688i	$0.883906\pi$
$432$		0			0
$433$	−16.8931	−	14.1750i	−0.811828	−	0.681205i	0.139215	−	0.990262i	$-0.455542\pi$
$433$	−16.8931	−	14.1750i	−0.811828	−	0.681205i	−0.951043	+	0.309057i	$0.899987\pi$
$434$	1.39852	+	7.93139i	0.0671310	+	0.380719i
$435$		0			0
$436$	−0.724622			−0.0347031
$437$	−12.5241	+	4.35381i	−0.599109	+	0.208271i
$438$		0			0
$439$	3.18257	+	1.15836i	0.151896	+	0.0552856i	0.416849	−	0.908976i	$-0.363134\pi$
$439$	3.18257	+	1.15836i	0.151896	+	0.0552856i	−0.264953	+	0.964261i	$0.585357\pi$
$440$	−5.68479	−	32.2401i	−0.271012	−	1.53698i
$441$		0			0
$442$	−9.27063	+	7.77898i	−0.440959	+	0.370008i
$443$	5.23799	−	29.7061i	0.248864	−	1.41138i	−0.562480	−	0.826811i	$-0.690153\pi$
$443$	5.23799	−	29.7061i	0.248864	−	1.41138i	0.811344	−	0.584569i	$-0.198736\pi$
$444$		0			0
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$	17.2947	−	6.29477i	0.818929	−	0.298066i
$447$		0			0
$448$	−1.64156	−	2.84326i	−0.0775564	−	0.134332i
$449$	−15.4559	+	26.7704i	−0.729409	+	1.26337i	0.227725	+	0.973725i	$0.426871\pi$
$449$	−15.4559	+	26.7704i	−0.729409	+	1.26337i	−0.957134	+	0.289647i	$0.906462\pi$
$450$		0			0
$451$	33.1523	−	27.8181i	1.56108	−	1.30990i
$452$	−1.93582	−	1.62435i	−0.0910534	−	0.0764029i
$453$		0			0
$454$	6.24897	+	2.27444i	0.293279	+	0.106745i
$455$	5.47565			0.256703
$456$		0			0
$457$	−39.0479			−1.82658			−0.913291	−	0.407307i	$-0.866468\pi$
$457$	−39.0479			−1.82658			−0.913291	+	0.407307i	$0.866468\pi$
$458$	−4.74510	−	1.72708i	−0.221724	−	0.0807009i
$459$		0			0
$460$	−2.04916	−	1.71945i	−0.0955427	−	0.0801699i
$461$	1.15476	−	0.968961i	0.0537827	−	0.0451290i	−0.615500	−	0.788137i	$-0.711046\pi$
$461$	1.15476	−	0.968961i	0.0537827	−	0.0451290i	0.669283	+	0.743008i	$0.266601\pi$
$462$		0			0
$463$	1.64156	−	2.84326i	0.0762897	−	0.132138i	−0.825357	−	0.564612i	$-0.809026\pi$
$463$	1.64156	−	2.84326i	0.0762897	−	0.132138i	0.901646	+	0.432474i	$0.142359\pi$
$464$	−3.68392	−	6.38073i	−0.171021	−	0.296218i
$465$		0			0
$466$	−22.2160	+	8.08596i	−1.02914	+	0.374575i
$467$	−11.4436	−	19.8208i	−0.529545	−	0.917199i	−0.999406	−	0.0344584i	$-0.989029\pi$
$467$	−11.4436	−	19.8208i	−0.529545	−	0.917199i	0.469861	−	0.882740i	$-0.344304\pi$
$468$		0			0
$469$	−0.943563	+	5.35121i	−0.0435697	+	0.247096i
$470$	−22.4650	+	18.8504i	−1.03623	+	0.869502i
$471$		0			0
$472$	−1.67752	−	9.51368i	−0.0772141	−	0.437903i
$473$	0.849518	+	0.309199i	0.0390609	+	0.0142170i
$474$		0			0
$475$	−4.65523	−	4.02266i	−0.213597	−	0.184572i
$476$	−0.359156			−0.0164619
$477$		0			0
$478$	−4.20961	−	23.8739i	−0.192543	−	1.09197i
$479$	7.39827	+	6.20789i	0.338036	+	0.283646i	0.795965	−	0.605343i	$-0.206964\pi$
$479$	7.39827	+	6.20789i	0.338036	+	0.283646i	−0.457929	+	0.888989i	$0.651409\pi$
$480$		0			0
$481$	4.30928	−	24.4391i	0.196486	−	1.11433i
$482$	18.1138	−	31.3740i	0.825061	−	1.42905i
$483$		0			0
$484$	−4.91875	+	1.79028i	−0.223579	+	0.0813763i
$485$	16.1814	−	5.88954i	0.734759	−	0.267430i
$486$		0			0
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	−0.489903	−	0.871777i	$-0.662968\pi$
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	0.999932	−	0.0116199i	$-0.00369881\pi$
$488$	6.12449	−	34.7337i	0.277242	−	1.57232i
$489$		0			0
$490$	−19.9611	−	16.7494i	−0.901751	−	0.756659i
$491$	−1.26264	−	7.16079i	−0.0569822	−	0.323162i	0.942971	−	0.332876i	$-0.108019\pi$
$491$	−1.26264	−	7.16079i	−0.0569822	−	0.323162i	−0.999953	+	0.00971390i	$0.996908\pi$
$492$		0			0
$493$	3.13072			0.141001
$494$	13.2285	+	23.6995i	0.595178	+	1.06629i
$495$		0			0
$496$	42.4629	+	15.4552i	1.90664	+	0.693961i
$497$	−0.353226	−	2.00324i	−0.0158444	−	0.0898578i
$498$		0			0
$499$	−9.81386	+	8.23481i	−0.439329	+	0.368641i	−0.835458	−	0.549554i	$-0.814798\pi$
$499$	−9.81386	+	8.23481i	−0.439329	+	0.368641i	0.396129	+	0.918195i	$0.370353\pi$
$500$	−0.547981	+	3.10775i	−0.0245065	+	0.138983i
$501$		0			0
$502$	14.8701	+	25.7557i	0.663683	+	1.14953i
$503$	7.86571	−	2.86289i	0.350715	−	0.127650i	−0.160655	−	0.987011i	$-0.551361\pi$
$503$	7.86571	−	2.86289i	0.350715	−	0.127650i	0.511370	+	0.859361i	$0.329138\pi$
$504$		0			0
$505$	−11.0890	−	19.2067i	−0.493454	−	0.854687i
$506$	11.8983	−	20.6084i	0.528943	−	0.916156i
$507$		0			0
$508$	0.486796	−	0.408471i	0.0215981	−	0.0181230i
$509$	−10.4816	−	8.79509i	−0.464588	−	0.389836i	0.380228	−	0.924893i	$-0.375846\pi$
$509$	−10.4816	−	8.79509i	−0.464588	−	0.389836i	−0.844816	+	0.535057i	$0.820290\pi$
$510$		0			0
$511$	0.928548	+	0.337964i	0.0410766	+	0.0149506i
$512$	−14.2736			−0.630811
$513$		0			0
$514$	−18.8384			−0.830928
$515$	9.14930	+	3.33007i	0.403166	+	0.146741i
$516$		0			0
$517$	−29.5685	−	24.8109i	−1.30042	−	1.09118i
$518$	3.81315	−	3.19961i	0.167540	−	0.140583i
$519$		0			0
$520$	13.0287	−	22.5663i	0.571346	−	0.989600i
$521$	−8.48205	−	14.6913i	−0.371605	−	0.643639i	0.618207	−	0.786015i	$-0.287859\pi$
$521$	−8.48205	−	14.6913i	−0.371605	−	0.643639i	−0.989813	+	0.142376i	$0.954526\pi$
$522$		0			0
$523$	3.67112	−	1.33618i	0.160527	−	0.0584270i	−0.260507	−	0.965472i	$-0.583890\pi$
$523$	3.67112	−	1.33618i	0.160527	−	0.0584270i	0.421034	+	0.907045i	$0.361667\pi$
$524$	−1.52569	−	2.64258i	−0.0666502	−	0.115441i
$525$		0			0
$526$	−1.68685	+	9.56661i	−0.0735502	+	0.417124i
$527$	−14.7090	+	12.3423i	−0.640733	+	0.537639i
$528$		0			0
$529$	−2.38713	−	13.5381i	−0.103788	−	0.588611i
$530$	−36.0959	−	13.1378i	−1.56790	−	0.570670i
$531$		0			0
$532$	−0.151359	+	0.791143i	−0.00656227	+	0.0343004i
$533$	34.4466			1.49205
$534$		0			0
$535$	2.49525	+	14.1513i	0.107879	+	0.611813i
$536$	19.8084	+	16.6212i	0.855593	+	0.717927i
$537$		0			0
$538$	0.618555	−	3.50800i	0.0266678	−	0.151241i
$539$	17.1484	−	29.7019i	0.738635	−	1.27935i
$540$		0			0
$541$	−12.4017	+	4.51384i	−0.533190	+	0.194065i	−0.594562	−	0.804050i	$-0.702675\pi$
$541$	−12.4017	+	4.51384i	−0.533190	+	0.194065i	0.0613724	+	0.998115i	$0.480452\pi$
$542$	−21.5141	+	7.83051i	−0.924111	+	0.336349i
$543$		0			0
$544$	−1.88872	+	3.27136i	−0.0809781	+	0.140258i
$545$	−0.917404	+	5.20286i	−0.0392973	+	0.222866i
$546$		0			0
$547$	−24.1878	−	20.2960i	−1.03420	−	0.867793i	−0.0428509	−	0.999081i	$-0.513644\pi$
$547$	−24.1878	−	20.2960i	−1.03420	−	0.867793i	−0.991344	+	0.131289i	$0.958088\pi$
$548$	0.761707	+	4.31986i	0.0325385	+	0.184535i
$549$		0			0
$550$	11.0419			0.470828
$551$	1.31938	−	6.89630i	0.0562076	−	0.293792i
$552$		0			0
$553$	−5.25877	−	1.91404i	−0.223626	−	0.0813931i
$554$	−6.37598	−	36.1600i	−0.270890	−	1.53629i
$555$		0			0
$556$	−1.07738	+	0.904030i	−0.0456912	+	0.0383394i
$557$	−6.18748	+	35.0909i	−0.262172	+	1.48685i	0.514797	+	0.857312i	$0.327867\pi$
$557$	−6.18748	+	35.0909i	−0.262172	+	1.48685i	−0.776969	+	0.629539i	$0.783244\pi$
$558$		0			0
$559$	0.359785	+	0.623166i	0.0152173	+	0.0263571i
$560$	5.79086	−	2.10770i	0.244708	−	0.0890666i
$561$		0			0
$562$	19.5804	+	33.9142i	0.825948	+	1.43058i
$563$	−10.9957	+	19.0451i	−0.463414	+	0.802657i	−0.999128	−	0.0417423i	$-0.986709\pi$
$563$	−10.9957	+	19.0451i	−0.463414	+	0.802657i	0.535714	+	0.844399i	$0.320042\pi$
$564$		0			0
$565$	−14.1138	+	11.8429i	−0.593772	+	0.498234i
$566$	−8.81496	−	7.39663i	−0.370520	−	0.310904i
$567$		0			0
$568$	−9.09627	−	3.31077i	−0.381671	−	0.138917i
$569$	−28.7588			−1.20563			−0.602815	−	0.797881i	$-0.705954\pi$
$569$	−28.7588			−1.20563			−0.602815	+	0.797881i	$0.705954\pi$
$570$		0			0
$571$	7.30365			0.305648			0.152824	−	0.988253i	$-0.451163\pi$
$571$	7.30365			0.305648			0.152824	+	0.988253i	$0.451163\pi$
$572$	−6.77244	−	2.46497i	−0.283170	−	0.103065i
$573$		0			0
$574$	5.29292	+	4.44129i	0.220922	+	0.185376i
$575$	−3.28905	+	2.75984i	−0.137163	+	0.115093i
$576$		0			0
$577$	−15.7545	+	27.2876i	−0.655868	+	1.13600i	0.325807	+	0.945436i	$0.394364\pi$
$577$	−15.7545	+	27.2876i	−0.655868	+	1.13600i	−0.981675	+	0.190561i	$0.938969\pi$
$578$	10.1291	+	17.5441i	0.421314	+	0.729737i
$579$		0			0
$580$	1.33110	−	0.484481i	0.0552709	−	0.0201170i
$581$	−3.05303	−	5.28801i	−0.126661	−	0.219384i
$582$		0			0
$583$	8.77941	−	49.7905i	0.363606	−	2.06211i
$584$	3.60220	−	3.02260i	0.149060	−	0.125076i
$585$		0			0
$586$	−3.92855	−	22.2799i	−0.162287	−	0.920374i
$587$	25.6434	+	9.33342i	1.05842	+	0.385232i	0.811833	−	0.583890i	$-0.198470\pi$
$587$	25.6434	+	9.33342i	1.05842	+	0.385232i	0.246583	+	0.969122i	$0.420692\pi$
$588$		0			0
$589$	20.9886	+	37.6021i	0.864820	+	1.54937i
$590$	14.8007			0.609334
$591$		0			0
$592$	−4.84982	−	27.5047i	−0.199326	−	1.13044i
$593$	−26.6366	−	22.3507i	−1.09383	−	0.917834i	−0.0968375	−	0.995300i	$-0.530873\pi$
$593$	−26.6366	−	22.3507i	−1.09383	−	0.917834i	−0.996995	+	0.0774657i	$0.975317\pi$
$594$		0			0
$595$	−0.454707	+	2.57877i	−0.0186412	+	0.105719i
$596$	1.05391	−	1.82543i	0.0431699	−	0.0747724i
$597$		0			0
$598$	17.7986	−	6.47816i	0.727839	−	0.264912i
$599$	14.9402	−	5.43777i	0.610438	−	0.222181i	−0.0182567	−	0.999833i	$-0.505812\pi$
$599$	14.9402	−	5.43777i	0.610438	−	0.222181i	0.628695	+	0.777652i	$0.283589\pi$
$600$		0			0
$601$	12.3464	−	21.3846i	0.503621	−	0.872297i	−0.496370	−	0.868111i	$-0.665334\pi$
$601$	12.3464	−	21.3846i	0.503621	−	0.872297i	0.999991	−	0.00418616i	$-0.00133250\pi$
$602$	−0.0250633	+	0.142141i	−0.00102150	+	0.00579324i
$603$		0			0
$604$	−0.0432332	−	0.0362770i	−0.00175914	−	0.00147609i
$605$	6.62701	+	37.5836i	0.269426	+	1.52799i
$606$		0			0
$607$	4.01455			0.162945			0.0814727	−	0.996676i	$-0.474038\pi$
$607$	4.01455			0.162945			0.0814727	+	0.996676i	$0.474038\pi$
$608$	6.41013	+	5.53909i	0.259965	+	0.224640i
$609$		0			0
$610$	50.7772	+	18.4814i	2.05591	+	0.748290i
$611$	−5.33497	−	30.2561i	−0.215830	−	1.22403i
$612$		0			0
$613$	−30.8082	+	25.8511i	−1.24433	+	1.04412i	−0.247157	+	0.968976i	$0.579496\pi$
$613$	−30.8082	+	25.8511i	−1.24433	+	1.04412i	−0.997173	+	0.0751409i	$0.976059\pi$
$614$	1.46657	−	8.31731i	0.0591858	−	0.335659i
$615$		0			0
$616$	3.43969	+	5.95772i	0.138589	+	0.240043i
$617$	−20.8427	+	7.58613i	−0.839096	+	0.305406i	−0.725586	−	0.688131i	$-0.758431\pi$
$617$	−20.8427	+	7.58613i	−0.839096	+	0.305406i	−0.113509	+	0.993537i	$0.536209\pi$
$618$		0			0
$619$	11.6177	+	20.1224i	0.466954	+	0.808788i	0.999287	−	0.0377469i	$-0.0120181\pi$
$619$	11.6177	+	20.1224i	0.466954	+	0.808788i	−0.532333	+	0.846535i	$0.678685\pi$
$620$	−4.34389	+	7.52384i	−0.174455	+	0.302165i
$621$		0			0
$622$	−20.4210	+	17.1353i	−0.818809	+	0.687062i
$623$	2.41463	+	2.02611i	0.0967401	+	0.0811746i
$624$		0			0
$625$	28.2520	+	10.2829i	1.13008	+	0.411315i
$626$	24.4270			0.976298
$627$		0			0
$628$	2.31315			0.0923047
$629$	11.1518	+	4.05893i	0.444652	+	0.161840i
$630$		0			0
$631$	21.4893	+	18.0317i	0.855476	+	0.717830i	0.960989	−	0.276588i	$-0.0892037\pi$
$631$	21.4893	+	18.0317i	0.855476	+	0.717830i	−0.105512	+	0.994418i	$0.533648\pi$
$632$	−20.4008	+	17.1183i	−0.811500	+	0.680929i
$633$		0			0
$634$	1.51186	−	2.61862i	0.0600436	−	0.103999i
$635$	−2.31655	−	4.01239i	−0.0919295	−	0.159227i
$636$		0			0
$637$	25.6523	−	9.33667i	1.01638	−	0.369932i
$638$	6.30066	+	10.9131i	0.249446	+	0.432052i
$639$		0			0
$640$	5.86571	−	33.2661i	0.231863	−	1.31496i
$641$	−33.3068	+	27.9477i	−1.31554	+	1.10387i	−0.328309	+	0.944570i	$0.606479\pi$
$641$	−33.3068	+	27.9477i	−1.31554	+	1.10387i	−0.987230	+	0.159299i	$0.949077\pi$
$642$		0			0
$643$	6.83322	+	38.7531i	0.269476	+	1.52827i	0.755980	+	0.654595i	$0.227161\pi$
$643$	6.83322	+	38.7531i	0.269476	+	1.52827i	−0.486504	+	0.873678i	$0.661728\pi$
$644$	0.528218	+	0.192256i	0.0208147	+	0.00757594i
$645$		0			0
$646$	−12.2599	+	4.26195i	−0.482358	+	0.167684i
$647$	−18.8862			−0.742493			−0.371246	−	0.928534i	$-0.621069\pi$
$647$	−18.8862			−0.742493			−0.371246	+	0.928534i	$0.621069\pi$
$648$		0			0
$649$	3.38279	+	19.1847i	0.132786	+	0.753067i
$650$	6.73261	+	5.64933i	0.264075	+	0.221585i
$651$		0			0
$652$	−0.0270364	+	0.153331i	−0.00105883	+	0.00600492i
$653$	−23.3714	+	40.4804i	−0.914593	+	1.58412i	−0.107098	+	0.994248i	$0.534156\pi$
$653$	−23.3714	+	40.4804i	−0.914593	+	1.58412i	−0.807495	+	0.589874i	$0.799177\pi$
$654$		0			0
$655$	−20.9055	+	7.60900i	−0.816847	+	0.297308i
$656$	36.4295	−	13.2592i	1.42233	−	0.517687i
$657$		0			0
$658$	3.08125	−	5.33688i	0.120120	−	0.208053i
$659$	−0.362778	+	2.05742i	−0.0141318	+	0.0801455i	−0.991058	−	0.133432i	$-0.957400\pi$
$659$	−0.362778	+	2.05742i	−0.0141318	+	0.0801455i	0.976926	+	0.213577i	$0.0685115\pi$
$660$		0			0
$661$	−9.53596	−	8.00162i	−0.370906	−	0.311227i	0.438214	−	0.898871i	$-0.355611\pi$
$661$	−9.53596	−	8.00162i	−0.370906	−	0.311227i	−0.809120	+	0.587644i	$0.800056\pi$
$662$	−0.222811	−	1.26363i	−0.00865980	−	0.0491122i
$663$		0			0
$664$	−29.0574			−1.12764
$665$	5.48886	+	2.08840i	0.212849	+	0.0809846i
$666$		0			0
$667$	−4.60442	−	1.67587i	−0.178284	−	0.0648900i
$668$	−0.204393	−	1.15917i	−0.00790820	−	0.0448496i
$669$		0			0
$670$	−30.3482	+	25.4652i	−1.17245	+	0.983806i
$671$	−12.3503	+	70.0420i	−0.476778	+	2.70394i
$672$		0			0
$673$	5.41060	+	9.37143i	0.208563	+	0.361242i	0.951262	−	0.308383i	$-0.0997880\pi$
$673$	5.41060	+	9.37143i	0.208563	+	0.361242i	−0.742699	+	0.669625i	$0.766455\pi$
$674$	4.79086	−	1.74373i	0.184537	−	0.0671660i
$675$		0			0
$676$	−0.610815	−	1.05796i	−0.0234929	−	0.0406908i
$677$	2.18092	−	3.77747i	0.0838196	−	0.145180i	−0.821068	−	0.570830i	$-0.806621\pi$
$677$	2.18092	−	3.77747i	0.0838196	−	0.145180i	0.904888	+	0.425651i	$0.139955\pi$
$678$		0			0
$679$	−2.77197	+	2.32596i	−0.106379	+	0.0892623i
$680$	9.54576	+	8.00984i	0.366063	+	0.307163i
$681$		0			0
$682$	−72.6250	−	26.4333i	−2.78096	−	1.01218i
$683$	44.6441			1.70826			0.854130	−	0.520059i	$-0.174090\pi$
$683$	44.6441			1.70826			0.854130	+	0.520059i	$0.174090\pi$
$684$		0			0
$685$	31.9813			1.22194
$686$	10.5077	+	3.82450i	0.401187	+	0.146020i
$687$		0			0
$688$	0.620366	+	0.520549i	0.0236512	+	0.0198458i
$689$	30.8273	−	25.8672i	1.17443	−	0.985460i
$690$		0			0
$691$	−12.1604	+	21.0625i	−0.462605	+	0.801256i	−0.999090	−	0.0426544i	$-0.986419\pi$
$691$	−12.1604	+	21.0625i	−0.462605	+	0.801256i	0.536485	+	0.843910i	$0.319752\pi$
$692$	−0.280592	−	0.486000i	−0.0106665	−	0.0184750i
$693$		0			0
$694$	5.76991	−	2.10008i	0.219023	−	0.0797178i
$695$	5.12701	+	8.88024i	0.194479	+	0.336847i
$696$		0			0
$697$	−2.86050	+	16.2227i	−0.108349	+	0.614479i
$698$	−32.7478	+	27.4787i	−1.23952	+	1.04008i
$699$		0			0
$700$	0.0452926	+	0.256867i	0.00171190	+	0.00970867i
$701$	−22.1386	−	8.05780i	−0.836164	−	0.304339i	−0.111778	−	0.993733i	$-0.535655\pi$
$701$	−22.1386	−	8.05780i	−0.836164	−	0.304339i	−0.724386	+	0.689394i	$0.757877\pi$
$702$		0			0
$703$	13.6407	−	22.8545i	0.514468	−	0.861974i
$704$	31.5057			1.18742
$705$		0			0
$706$	−3.44356	−	19.5294i	−0.129600	−	0.734999i
$707$	3.57011	+	2.99568i	0.134268	+	0.112664i
$708$		0			0
$709$	−1.06851	+	6.05985i	−0.0401289	+	0.227582i	−0.998276	−	0.0586939i	$-0.981306\pi$
$709$	−1.06851	+	6.05985i	−0.0401289	+	0.227582i	0.958147	+	0.286276i	$0.0924175\pi$
$710$	7.41534	−	12.8438i	0.278293	−	0.482017i
$711$		0			0
$712$	14.0954	−	5.13030i	0.528247	−	0.192266i
$713$	28.2396	−	10.2784i	1.05758	−	0.384929i
$714$		0			0
$715$	−26.2729	+	45.5060i	−0.982551	+	1.70183i
$716$	−0.127478	+	0.722965i	−0.00476408	+	0.0270185i
$717$		0			0
$718$	−13.4342	−	11.2727i	−0.501361	−	0.420692i
$719$	−5.65657	−	32.0800i	−0.210955	−	1.19638i	−0.887790	−	0.460249i	$-0.847760\pi$
$719$	−5.65657	−	32.0800i	−0.210955	−	1.19638i	0.676835	−	0.736134i	$-0.263351\pi$
$720$		0			0
$721$	−2.04601			−0.0761973
$722$	4.22147	+	28.8020i	0.157107	+	1.07190i
$723$		0			0
$724$	−2.85622	−	1.03958i	−0.106151	−	0.0386356i
$725$	−0.394811	−	2.23908i	−0.0146629	−	0.0831574i
$726$		0			0
$727$	24.6896	−	20.7170i	0.915686	−	0.768352i	−0.0575058	−	0.998345i	$-0.518315\pi$
$727$	24.6896	−	20.7170i	0.915686	−	0.768352i	0.973192	+	0.229993i	$0.0738703\pi$
$728$	−0.950837	+	5.39246i	−0.0352404	+	0.199858i
$729$		0			0
$730$	3.60220	+	6.23919i	0.133323	+	0.230923i
$731$	−0.323359	+	0.117693i	−0.0119599	+	0.00435303i
$732$		0			0
$733$	−4.89053	−	8.47065i	−0.180636	−	0.312870i	0.761461	−	0.648210i	$-0.224482\pi$
$733$	−4.89053	−	8.47065i	−0.180636	−	0.312870i	−0.942097	+	0.335340i	$0.891149\pi$
$734$	21.9099	−	37.9490i	0.808708	−	1.40072i
$735$		0			0
$736$	4.52893	−	3.80023i	0.166939	−	0.140078i
$737$	−39.9445	−	33.5174i	−1.47137	−	1.23463i
$738$		0			0
$739$	−26.0993	−	9.49935i	−0.960077	−	0.349439i	−0.186013	−	0.982547i	$-0.559557\pi$
$739$	−26.0993	−	9.49935i	−0.960077	−	0.349439i	−0.774064	+	0.633108i	$0.781779\pi$
$740$	5.36959			0.197390
$741$		0			0
$742$	8.07192			0.296329
$743$	−30.3542	−	11.0480i	−1.11359	−	0.405312i	−0.281278	−	0.959626i	$-0.590758\pi$
$743$	−30.3542	−	11.0480i	−1.11359	−	0.405312i	−0.832308	+	0.554314i	$0.812981\pi$
$744$		0			0
$745$	−11.7724	−	9.87825i	−0.431309	−	0.361911i
$746$	−14.7483	+	12.3753i	−0.539975	+	0.453093i
$747$		0			0
$748$	1.72328	−	2.98481i	0.0630093	−	0.109135i
$749$	−1.50980	−	2.61505i	−0.0551669	−	0.0955519i
$750$		0			0
$751$	−3.27497	+	1.19199i	−0.119505	+	0.0434964i	−0.401081	−	0.916043i	$-0.631365\pi$
$751$	−3.27497	+	1.19199i	−0.119505	+	0.0434964i	0.281575	+	0.959539i	$0.409143\pi$
$752$	−17.2883	−	29.9443i	−0.630441	−	1.09196i
$753$		0			0
$754$	−1.74170	+	9.87765i	−0.0634288	+	0.359723i
$755$	−0.315207	+	0.264490i	−0.0114716	+	0.00962579i
$756$		0			0
$757$	−6.41353	−	36.3730i	−0.233104	−	1.32200i	−0.846570	−	0.532277i	$-0.821337\pi$
$757$	−6.41353	−	36.3730i	−0.233104	−	1.32200i	0.613467	−	0.789721i	$-0.289775\pi$
$758$	3.16637	+	1.15247i	0.115008	+	0.0418594i
$759$		0			0
$760$	21.6668	−	17.6517i	0.785939	−	0.640293i
$761$	−31.3429			−1.13618			−0.568089	−	0.822967i	$-0.692317\pi$
$761$	−31.3429			−1.13618			−0.568089	+	0.822967i	$0.692317\pi$
$762$		0			0
$763$	−0.192782	−	1.09332i	−0.00697917	−	0.0395808i
$764$	5.07398	+	4.25757i	0.183570	+	0.154034i
$765$		0			0
$766$	1.57713	−	8.94437i	0.0569841	−	0.323173i
$767$	−7.75284	+	13.4283i	−0.279939	+	0.484868i
$768$		0			0
$769$	29.8282	−	10.8566i	1.07563	−	0.391498i	0.257351	−	0.966318i	$-0.417150\pi$
$769$	29.8282	−	10.8566i	1.07563	−	0.391498i	0.818280	+	0.574820i	$0.194928\pi$
$770$	−9.90420	+	3.60483i	−0.356923	+	0.129909i
$771$		0			0
$772$	4.13903	−	7.16902i	0.148967	−	0.258019i
$773$	−1.90269	+	10.7907i	−0.0684351	+	0.388115i	0.931281	+	0.364301i	$0.118692\pi$
$773$	−1.90269	+	10.7907i	−0.0684351	+	0.388115i	−0.999716	+	0.0238140i	$0.992419\pi$
$774$		0			0
$775$	10.6821	+	8.96335i	0.383713	+	0.321973i
$776$	2.99020	+	16.9583i	0.107342	+	0.608766i
$777$		0			0
$778$	50.7410			1.81915
$779$	34.5296	+	13.1378i	1.23715	+	0.470711i
$780$		0			0
$781$	18.3430	+	6.67631i	0.656365	+	0.238897i
$782$	1.57288	+	8.92026i	0.0562462	+	0.318988i
$783$		0			0
$784$	23.5351	−	19.7483i	0.840539	−	0.705296i
$785$	2.92855	−	16.6086i	0.104524	−	0.592787i
$786$		0			0
$787$	−23.1771	−	40.1439i	−0.826175	−	1.43098i	−0.901018	−	0.433781i	$-0.857179\pi$
$787$	−23.1771	−	40.1439i	−0.826175	−	1.43098i	0.0748436	−	0.997195i	$-0.476154\pi$
$788$	−1.43242	+	0.521358i	−0.0510278	+	0.0185726i
$789$		0			0
$790$	−20.4008	−	35.3352i	−0.725828	−	1.25717i
$791$	1.93582	−	3.35294i	0.0688299	−	0.119217i
$792$		0			0
$793$	−43.3658	+	36.3882i	−1.53996	+	1.29218i
$794$	−30.5731	−	25.6539i	−1.08500	−	0.910422i
$795$		0			0
$796$	6.53936	+	2.38013i	0.231782	+	0.0843616i
$797$	3.47296			0.123019			0.0615093	−	0.998107i	$-0.480409\pi$
$797$	3.47296			0.123019			0.0615093	+	0.998107i	$0.480409\pi$
$798$		0			0
$799$	14.6922			0.519774
$800$	2.57785	+	0.938260i	0.0911407	+	0.0331725i
$801$		0			0
$802$	18.7411	+	15.7256i	0.661770	+	0.555291i
$803$	−7.26399	+	6.09521i	−0.256340	+	0.215095i
$804$		0			0
$805$	2.04916	−	3.54925i	0.0722235	−	0.125095i
$806$	−30.7579	−	53.2742i	−1.08340	−	1.87650i
$807$		0			0
$808$	20.8405	−	7.58532i	0.733166	−	0.266851i
$809$	−25.9748	−	44.9896i	−0.913224	−	1.58175i	−0.809480	−	0.587147i	$-0.800251\pi$
$809$	−25.9748	−	44.9896i	−0.913224	−	1.58175i	−0.103744	−	0.994604i	$-0.533082\pi$
$810$		0			0
$811$	2.91329	−	16.5221i	0.102299	−	0.580168i	−0.889965	−	0.456028i	$-0.849272\pi$
$811$	2.91329	−	16.5221i	0.102299	−	0.580168i	0.992265	−	0.124140i	$-0.0396172\pi$
$812$	−0.228026	+	0.191336i	−0.00800214	+	0.00671459i
$813$		0			0
$814$	8.29473	+	47.0418i	0.290730	+	1.64881i
$815$	1.06670	+	0.388249i	0.0373650	+	0.0135998i
$816$		0			0
$817$	0.122979	+	0.761889i	0.00430249	+	0.0266551i
$818$	−4.51754			−0.157952
$819$		0			0
$820$	1.29426	+	7.34013i	0.0451976	+	0.256328i
$821$	28.5330	+	23.9420i	0.995809	+	0.835583i	0.986398	−	0.164372i	$-0.0525599\pi$
$821$	28.5330	+	23.9420i	0.995809	+	0.835583i	0.00941101	+	0.999956i	$0.497004\pi$
$822$		0			0
$823$	−0.763985	+	4.33277i	−0.0266308	+	0.151031i	−0.995224	−	0.0976214i	$-0.968877\pi$
$823$	−0.763985	+	4.33277i	−0.0266308	+	0.151031i	0.968593	+	0.248652i	$0.0799877\pi$
$824$	−4.86824	+	8.43204i	−0.169593	+	0.293744i
$825$		0			0
$826$	−2.92262	+	1.06375i	−0.101691	+	0.0370125i
$827$	−13.0265	+	4.74125i	−0.452975	+	0.164869i	−0.558424	−	0.829555i	$-0.688594\pi$
$827$	−13.0265	+	4.74125i	−0.452975	+	0.164869i	0.105450	+	0.994425i	$0.466372\pi$
$828$		0			0
$829$	−8.18850	+	14.1829i	−0.284398	+	0.492592i	−0.972463	−	0.233057i	$-0.925127\pi$
$829$	−8.18850	+	14.1829i	−0.284398	+	0.492592i	0.688065	+	0.725649i	$0.258461\pi$
$830$	7.73055	−	43.8421i	0.268331	−	1.52178i
$831$		0			0
$832$	19.2101	+	16.1192i	0.665989	+	0.558832i
$833$	2.26692	+	12.8564i	0.0785442	+	0.445446i
$834$		0			0
$835$	−8.58172			−0.296983
$836$	−5.84864	−	5.05390i	−0.202279	−	0.174793i
$837$		0			0
$838$	−48.2242	−	17.5522i	−1.66588	−	0.606330i
$839$	6.64883	+	37.7074i	0.229543	+	1.30180i	0.853807	+	0.520590i	$0.174288\pi$
$839$	6.64883	+	37.7074i	0.229543	+	1.30180i	−0.624263	+	0.781214i	$0.714601\pi$
$840$		0			0
$841$	−20.2276	+	16.9730i	−0.697504	+	0.585275i
$842$	4.79355	−	27.1856i	0.165197	−	0.936876i
$843$		0			0
$844$	−4.72193	−	8.17863i	−0.162536	−	0.281520i
$845$	−8.36959	+	3.04628i	−0.287922	+	0.104795i
$846$		0			0
$847$	−4.00980	−	6.94518i	−0.137778	−	0.238639i
$848$	22.6450	−	39.2223i	0.777633	−	1.34690i
$849$		0			0
$850$	−3.21966	+	2.70161i	−0.110433	+	0.0926645i
$851$	−14.2285	−	11.9391i	−0.487746	−	0.409268i
$852$		0			0
$853$	−20.7579	−	7.55526i	−0.710737	−	0.258687i	−0.0387487	−	0.999249i	$-0.512337\pi$
$853$	−20.7579	−	7.55526i	−0.710737	−	0.258687i	−0.671988	+	0.740562i	$0.734559\pi$
$854$	−11.3550			−0.388561
$855$		0			0
$856$	−14.3696			−0.491142
$857$	42.2934	+	15.3936i	1.44472	+	0.525834i	0.941110	−	0.338100i	$-0.109784\pi$
$857$	42.2934	+	15.3936i	1.44472	+	0.525834i	0.503606	+	0.863933i	$0.332006\pi$
$858$		0			0
$859$	−12.2358	−	10.2670i	−0.417479	−	0.350306i	0.409724	−	0.912209i	$-0.365625\pi$
$859$	−12.2358	−	10.2670i	−0.417479	−	0.350306i	−0.827203	+	0.561903i	$0.810069\pi$
$860$	−0.119271	+	0.100080i	−0.00406709	+	0.00341270i
$861$		0			0
$862$	16.3327	−	28.2892i	0.556296	−	0.963532i
$863$	20.6288	+	35.7302i	0.702213	+	1.21627i	0.967688	+	0.252151i	$0.0811380\pi$
$863$	20.6288	+	35.7302i	0.702213	+	1.21627i	−0.265475	+	0.964118i	$0.585529\pi$
$864$		0			0
$865$	−3.84477	+	1.39938i	−0.130726	+	0.0475804i
$866$	16.8931	+	29.2596i	0.574049	+	0.994283i
$867$		0			0
$868$	0.317018	−	1.79790i	0.0107603	−	0.0610247i
$869$	41.1391	−	34.5198i	1.39555	−	1.17100i
$870$		0			0
$871$	−7.20708	−	40.8734i	−0.244203	−	1.38494i
$872$	−4.96451	−	1.80693i	−0.168119	−	0.0611905i
$873$		0			0
$874$	20.3123	+	0.294553i	0.687073	+	0.00996340i
$875$	−4.83481			−0.163446
$876$		0			0
$877$	8.01650	+	45.4638i	0.270698	+	1.53520i	0.752304	+	0.658817i	$0.228943\pi$
$877$	8.01650	+	45.4638i	0.270698	+	1.53520i	−0.481606	+	0.876388i	$0.659946\pi$
$878$	−3.97494	−	3.33537i	−0.134148	−	0.112563i
$879$		0			0
$880$	−10.2690	+	58.2386i	−0.346169	+	1.96322i
$881$	9.47906	−	16.4182i	0.319357	−	0.553143i	−0.660997	−	0.750389i	$-0.729866\pi$
$881$	9.47906	−	16.4182i	0.319357	−	0.553143i	0.980354	+	0.197245i	$0.0631996\pi$
$882$		0			0
$883$	−32.9359	+	11.9877i	−1.10838	+	0.403418i	−0.830399	−	0.557169i	$-0.811888\pi$
$883$	−32.9359	+	11.9877i	−1.10838	+	0.403418i	−0.277981	+	0.960586i	$0.589665\pi$
$884$	2.57785	−	0.938260i	0.0867024	−	0.0315571i
$885$		0			0
$886$	−23.1072	+	40.0229i	−0.776303	+	1.34460i
$887$	3.09745	−	17.5665i	0.104002	−	0.589825i	−0.887612	−	0.460592i	$-0.847637\pi$
$887$	3.09745	−	17.5665i	0.104002	−	0.589825i	0.991614	−	0.129234i	$-0.0412517\pi$
$888$		0			0
$889$	0.745815	+	0.625813i	0.0250138	+	0.0209891i
$890$	3.99067	+	22.6322i	0.133767	+	0.758633i
$891$		0			0
$892$	−4.17200			−0.139689
$893$	6.19176	−	32.3638i	0.207199	−	1.08301i
$894$		0			0
$895$	5.02956	+	1.83061i	0.168120	+	0.0611906i
$896$	1.23261	+	6.99049i	0.0411787	+	0.233536i
$897$		0			0
$898$	36.2796	−	30.4422i	1.21066	−	1.01587i
$899$	−2.76341	+	15.6721i	−0.0921650	+	0.522693i
$900$		0			0
$901$	9.62226	+	16.6662i	0.320564	+	0.555233i
$902$	−62.3059	+	22.6775i	−2.07456	+	0.755078i
$903$		0			0
$904$	−9.21213	−	15.9559i	−0.306391	−	0.530685i
$905$	−11.0804	+	19.1918i	−0.368324	+	0.637956i
$906$		0			0
$907$	−10.9172	+	9.16058i	−0.362498	+	0.304172i	−0.805786	−	0.592207i	$-0.798257\pi$
$907$	−10.9172	+	9.16058i	−0.362498	+	0.304172i	0.443287	+	0.896380i	$0.353812\pi$
$908$	−1.15476	−	0.968961i	−0.0383222	−	0.0321561i
$909$		0			0
$910$	−7.88326	−	2.86927i	−0.261327	−	0.0951154i
$911$	16.4466			0.544899			0.272449	−	0.962170i	$-0.412166\pi$
$911$	16.4466			0.544899			0.272449	+	0.962170i	$0.412166\pi$
$912$		0			0
$913$	58.5954			1.93923
$914$	56.2169	+	20.4613i	1.85949	+	0.676799i
$915$		0			0
$916$	0.876859	+	0.735772i	0.0289722	+	0.0243106i
$917$	3.58125	−	3.00503i	0.118263	−	0.0992347i
$918$		0			0
$919$	16.9500	−	29.3582i	0.559128	−	0.968437i	−0.438442	−	0.898760i	$-0.644470\pi$
$919$	16.9500	−	29.3582i	0.559128	−	0.968437i	0.997570	−	0.0696779i	$-0.0221971\pi$
$920$	−9.75150	−	16.8901i	−0.321497	−	0.556850i
$921$		0			0
$922$	−2.17024	+	0.789904i	−0.0714732	+	0.0260141i
$923$	7.76857	+	13.4556i	0.255706	+	0.442895i
$924$		0			0
$925$	1.49660	−	8.48762i	0.0492078	−	0.279071i
$926$	−3.85323	+	3.23324i	−0.126625	+	0.106251i
$927$		0			0
$928$	0.543644	+	3.08316i	0.0178460	+	0.101210i
$929$	20.2358	+	7.36522i	0.663914	+	0.241645i	0.651925	−	0.758283i	$-0.273962\pi$
$929$	20.2358	+	7.36522i	0.663914	+	0.241645i	0.0119887	+	0.999928i	$0.496184\pi$
$930$		0			0
$931$	29.2751	+	0.424525i	0.959454	+	0.0139133i
$932$	5.35916			0.175545
$933$		0			0
$934$	6.08899	+	34.5324i	0.199238	+	1.12993i
$935$	−19.2494	−	16.1522i	−0.629524	−	0.528233i
$936$		0			0
$937$	1.31386	−	7.45129i	0.0429220	−	0.243423i	−0.955797	−	0.294028i	$-0.905004\pi$
$937$	1.31386	−	7.45129i	0.0429220	−	0.243423i	0.998719	+	0.0506054i	$0.0161151\pi$
$938$	4.16250	−	7.20967i	0.135911	−	0.235404i
$939$		0			0
$940$	6.24675	−	2.27363i	0.203746	−	0.0741577i
$941$	17.9740	−	6.54200i	0.585936	−	0.213263i	−0.0320052	−	0.999488i	$-0.510189\pi$
$941$	17.9740	−	6.54200i	0.585936	−	0.213263i	0.617941	+	0.786225i	$0.287967\pi$
$942$		0			0
$943$	12.8910	−	22.3279i	0.419789	−	0.727095i
$944$	−3.03028	+	17.1856i	−0.0986271	+	0.559342i
$945$		0			0
$946$	−1.06102	−	0.890304i	−0.0344968	−	0.0289463i
$947$	−10.4549	−	59.2925i	−0.339738	−	1.92675i	−0.374214	−	0.927342i	$-0.622088\pi$
$947$	−10.4549	−	59.2925i	−0.339738	−	1.92675i	0.0344768	−	0.999405i	$-0.489024\pi$
$948$		0			0
$949$	−7.54757			−0.245005
$950$	4.59421	+	8.23075i	0.149056	+	0.267041i
$951$		0			0
$952$	−2.46064	−	0.895599i	−0.0797497	−	0.0290265i
$953$	3.42918	+	19.4478i	0.111082	+	0.629977i	0.988616	+	0.150462i	$0.0480762\pi$
$953$	3.42918	+	19.4478i	0.111082	+	0.629977i	−0.877534	+	0.479515i	$0.840813\pi$
$954$		0			0
$955$	36.9937	−	31.0414i	1.19709	−	1.00448i
$956$	−0.954241	+	5.41177i	−0.0308623	+	0.175029i
$957$		0			0
$958$	−7.39827	−	12.8142i	−0.239027	−	0.414007i
$959$	−6.31521	+	2.29855i	−0.203929	+	0.0742240i
$960$		0			0
$961$	−33.3011	−	57.6792i	−1.07423	−	1.86062i
$962$	−19.0103	+	32.9267i	−0.612916	+	1.06160i
$963$		0			0
$964$	−6.29086	+	5.27866i	−0.202615	+	0.170014i
$965$	−46.2340	−	38.7949i	−1.48833	−	1.24885i
$966$		0			0
$967$	4.85679	+	1.76773i	0.156184	+	0.0568463i	0.418929	−	0.908019i	$-0.362406\pi$
$967$	4.85679	+	1.76773i	0.156184	+	0.0568463i	−0.262745	+	0.964865i	$0.584628\pi$
$968$	−38.1634			−1.22662
$969$		0			0
$970$	−26.3824			−0.847087
$971$	−8.22967	−	2.99536i	−0.264103	−	0.0961256i	0.206575	−	0.978431i	$-0.433768\pi$
$971$	−8.22967	−	2.99536i	−0.264103	−	0.0961256i	−0.470678	+	0.882305i	$0.655991\pi$
$972$		0			0
$973$	−1.65064	−	1.38505i	−0.0529172	−	0.0444028i
$974$	−26.4197	+	22.1687i	−0.846541	+	0.710332i
$975$		0			0
$976$	−31.8555	+	55.1754i	−1.01967	+	1.76612i
$977$	20.3640	+	35.2714i	0.651501	+	1.12843i	0.982759	+	0.184892i	$0.0591936\pi$
$977$	20.3640	+	35.2714i	0.651501	+	1.12843i	−0.331258	+	0.943540i	$0.607473\pi$
$978$		0			0
$979$	−28.4240	+	10.3455i	−0.908434	+	0.330643i
$980$	2.95336	+	5.11538i	0.0943417	+	0.163405i
$981$		0			0
$982$	−1.93448	+	10.9710i	−0.0617317	+	0.350098i
$983$	−3.02616	+	2.53925i	−0.0965195	+	0.0809895i	−0.689771	−	0.724028i	$-0.742289\pi$
$983$	−3.02616	+	2.53925i	−0.0965195	+	0.0809895i	0.593251	+	0.805018i	$0.297844\pi$
$984$		0			0
$985$	1.92989	+	10.9450i	0.0614915	+	0.348736i
$986$	−4.50727	−	1.64051i	−0.143541	−	0.0522446i
$987$		0			0
$988$	−0.980400	−	6.07386i	−0.0311907	−	0.193235i
$989$	0.538572			0.0171256
$990$		0			0
$991$	−3.22328	−	18.2801i	−0.102391	−	0.580687i	−0.992230	−	0.124414i	$-0.960295\pi$
$991$	−3.22328	−	18.2801i	−0.102391	−	0.580687i	0.889840	−	0.456273i	$-0.150816\pi$
$992$	−14.7090	−	12.3423i	−0.467011	−	0.391868i
$993$		0			0
$994$	−0.541174	+	3.06915i	−0.0171650	+	0.0973475i
$995$	25.3687	−	43.9399i	0.804242	−	1.39299i
$996$		0			0
$997$	−2.57398	+	0.936851i	−0.0815187	+	0.0296704i	−0.382458	−	0.923973i	$-0.624922\pi$
$997$	−2.57398	+	0.936851i	−0.0815187	+	0.0296704i	0.300939	+	0.953643i	$0.402700\pi$
$998$	18.4440	−	6.71308i	0.583836	−	0.212499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.u.a.118.1		6
3.2	odd	2		57.2.i.a.4.1	✓	6
12.11	even	2		912.2.bo.b.289.1		6
19.5	even	9	inner	171.2.u.a.100.1		6
19.9	even	9		3249.2.a.w.1.3		3
19.10	odd	18		3249.2.a.x.1.1		3
57.5	odd	18		57.2.i.a.43.1	yes	6
57.29	even	18		1083.2.a.n.1.3		3
57.47	odd	18		1083.2.a.m.1.1		3
228.119	even	18		912.2.bo.b.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.4.1	✓	6	3.2	odd	2
57.2.i.a.43.1	yes	6	57.5	odd	18
171.2.u.a.100.1		6	19.5	even	9	inner
171.2.u.a.118.1		6	1.1	even	1	trivial
912.2.bo.b.289.1		6	12.11	even	2
912.2.bo.b.385.1		6	228.119	even	18
1083.2.a.m.1.1		3	57.47	odd	18
1083.2.a.n.1.3		3	57.29	even	18
3249.2.a.w.1.3		3	19.9	even	9
3249.2.a.x.1.1		3	19.10	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43969 - 0.524005i) q^{2} +(0.266044 + 0.223238i) q^{4} +(1.93969 - 1.62760i) q^{5} +(-0.266044 + 0.460802i) q^{7} +(1.26604 + 2.19285i) q^{8} +(-3.64543 + 1.32683i) q^{10} +(-2.55303 - 4.42198i) q^{11} +(0.705737 - 4.00243i) q^{13} +(0.624485 - 0.524005i) q^{14} +(-0.794263 - 4.50449i) q^{16} +(1.82635 + 0.664738i) q^{17} +(2.23396 - 3.74292i) q^{19} +0.879385 q^{20} +(1.35844 + 7.70410i) q^{22} +(-2.33022 - 1.95529i) q^{23} +(0.245100 - 1.39003i) q^{25} +(-3.11334 + 5.39246i) q^{26} +(-0.173648 + 0.0632028i) q^{28} +(1.51367 - 0.550931i) q^{29} +(-4.93969 + 8.55580i) q^{31} +(-0.337496 + 1.91404i) q^{32} +(-2.28106 - 1.91404i) q^{34} +(0.233956 + 1.32683i) q^{35} +6.10607 q^{37} +(-5.17752 + 4.21805i) q^{38} +(6.02481 + 2.19285i) q^{40} +(1.47178 + 8.34689i) q^{41} +(-0.135630 + 0.113807i) q^{43} +(0.307934 - 1.74638i) q^{44} +(2.33022 + 4.03606i) q^{46} +(7.10354 - 2.58548i) q^{47} +(3.35844 + 5.81699i) q^{49} +(-1.08125 + 1.87278i) q^{50} +(1.08125 - 0.907278i) q^{52} +(7.58512 + 6.36467i) q^{53} +(-12.1493 - 4.42198i) q^{55} -1.34730 q^{56} -2.46791 q^{58} +(-3.58512 - 1.30488i) q^{59} +(-10.6702 - 8.95340i) q^{61} +(11.5949 - 9.72930i) q^{62} +(-3.08512 + 5.34359i) q^{64} +(-5.14543 - 8.91215i) q^{65} +(9.59627 - 3.49276i) q^{67} +(0.337496 + 0.584561i) q^{68} +(0.358441 - 2.03282i) q^{70} +(-2.92855 + 2.45734i) q^{71} +(-0.322481 - 1.82888i) q^{73} +(-8.79086 - 3.19961i) q^{74} +(1.42989 - 0.497079i) q^{76} +2.71688 q^{77} +(1.82635 + 10.3578i) q^{79} +(-8.87211 - 7.44459i) q^{80} +(2.25490 - 12.7882i) q^{82} +(-5.73783 + 9.93821i) q^{83} +(4.62449 - 1.68317i) q^{85} +(0.254900 - 0.0927760i) q^{86} +(6.46451 - 11.1969i) q^{88} +(1.02869 - 5.83396i) q^{89} +(1.65657 + 1.39003i) q^{91} +(-0.183448 - 1.04039i) q^{92} -11.5817 q^{94} +(-1.75877 - 10.8961i) q^{95} +(6.39053 + 2.32596i) q^{97} +(-1.78699 - 10.1345i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} + 3 q^{7} + 3 q^{8} - 6 q^{10} - 3 q^{11} - 6 q^{13} - 9 q^{14} - 15 q^{16} + 12 q^{17} + 18 q^{19} - 6 q^{20} + 9 q^{23} - 12 q^{26} - 12 q^{29} - 24 q^{31} + 3 q^{32}+ \cdots - 3 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 + 3 * q^7 + 3 * q^8 - 6 * q^10 - 3 * q^11 - 6 * q^13 - 9 * q^14 - 15 * q^16 + 12 * q^17 + 18 * q^19 - 6 * q^20 + 9 * q^23 - 12 * q^26 - 12 * q^29 - 24 * q^31 + 3 * q^32 + 21 * q^34 + 6 * q^35 + 12 * q^37 - 6 * q^38 + 9 * q^40 - 6 * q^41 + 18 * q^43 - 9 * q^44 - 9 * q^46 + 33 * q^47 + 12 * q^49 - 9 * q^50 + 9 * q^52 + 24 * q^53 - 33 * q^55 - 6 * q^56 - 24 * q^58 - 21 * q^61 + 51 * q^62 + 3 * q^64 - 15 * q^65 + 30 * q^67 - 3 * q^68 - 6 * q^70 - 18 * q^71 - 27 * q^73 - 21 * q^74 + 12 * q^79 - 24 * q^80 + 15 * q^82 - 15 * q^83 + 15 * q^85 + 3 * q^86 + 6 * q^88 - 45 * q^89 - 12 * q^91 - 3 * q^92 - 6 * q^94 + 12 * q^95 + 21 * q^97 - 3 * q^98

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