LMFDB - Embedded newform 756.2.bb.a.611.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.12
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.966497 + 1.03242i) q^{2} +(-0.131768 - 1.99565i) q^{4} +(1.42201 - 0.820999i) q^{5} +(2.57988 - 0.586703i) q^{7} +(2.18770 + 1.79275i) q^{8} +O(q^{10})$	\(q+(-0.966497 + 1.03242i) q^{2} +(-0.131768 - 1.99565i) q^{4} +(1.42201 - 0.820999i) q^{5} +(2.57988 - 0.586703i) q^{7} +(2.18770 + 1.79275i) q^{8} +(-0.526757 + 2.26160i) q^{10} +(3.06085 - 5.30154i) q^{11} +(0.599586 - 1.03851i) q^{13} +(-1.88772 + 3.23056i) q^{14} +(-3.96527 + 0.525926i) q^{16} +(-2.89068 + 1.66893i) q^{17} +(-3.61550 - 2.08741i) q^{19} +(-1.82581 - 2.72966i) q^{20} +(2.51510 + 8.28399i) q^{22} +(-4.21762 - 7.30513i) q^{23} +(-1.15192 + 1.99519i) q^{25} +(0.492680 + 1.62274i) q^{26} +(-1.51080 - 5.07124i) q^{28} +(0.398864 - 0.230284i) q^{29} +4.85676i q^{31} +(3.28945 - 4.60212i) q^{32} +(1.07080 - 4.59740i) q^{34} +(3.18694 - 2.95238i) q^{35} +(2.65132 - 4.59222i) q^{37} +(5.64944 - 1.71523i) q^{38} +(4.58279 + 0.753219i) q^{40} +(4.25113 + 2.45439i) q^{41} +(-0.733230 + 0.423331i) q^{43} +(-10.9834 - 5.40982i) q^{44} +(11.6183 + 2.70605i) q^{46} -8.42989 q^{47} +(6.31156 - 3.02725i) q^{49} +(-0.946535 - 3.11760i) q^{50} +(-2.15152 - 1.05972i) q^{52} +(0.122578 - 0.0707704i) q^{53} -10.0518i q^{55} +(6.69582 + 3.34156i) q^{56} +(-0.147751 + 0.634362i) q^{58} +10.8434 q^{59} +2.20845 q^{61} +(-5.01419 - 4.69404i) q^{62} +(1.57206 + 7.84402i) q^{64} -1.96904i q^{65} +4.29540i q^{67} +(3.71151 + 5.54888i) q^{68} +(-0.0320811 + 6.14371i) q^{70} +6.07333 q^{71} +(-5.37668 - 9.31269i) q^{73} +(2.17859 + 7.17563i) q^{74} +(-3.68934 + 7.49034i) q^{76} +(4.78619 - 15.4732i) q^{77} +7.70311i q^{79} +(-5.20688 + 4.00336i) q^{80} +(-6.64265 + 2.01677i) q^{82} +(2.20287 + 3.81549i) q^{83} +(-2.74039 + 4.74649i) q^{85} +(0.271611 - 1.16615i) q^{86} +(16.2006 - 6.11084i) q^{88} +(8.60870 + 4.97023i) q^{89} +(0.937560 - 3.03102i) q^{91} +(-14.0228 + 9.37949i) q^{92} +(8.14746 - 8.70315i) q^{94} -6.85504 q^{95} +(3.92227 + 6.79358i) q^{97} +(-2.97472 + 9.44198i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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 $

$2$	−0.966497	+	1.03242i	−0.683416	+	0.730029i
$2$	−0.966497	+	1.03242i	−0.683416	+	0.730029i
$3$		0			0
$3$		0			0
$4$	−0.131768	−	1.99565i	−0.0658839	−	0.997827i
$5$	1.42201	−	0.820999i	0.635943	−	0.367162i	−0.147107	−	0.989121i	$-0.546996\pi$
$5$	1.42201	−	0.820999i	0.635943	−	0.367162i	0.783050	+	0.621959i	$0.213663\pi$
$6$		0			0
$7$	2.57988	−	0.586703i	0.975103	−	0.221753i
$7$	2.57988	−	0.586703i	0.975103	−	0.221753i
$8$	2.18770	+	1.79275i	0.773469	+	0.633834i
$9$		0			0
$10$	−0.526757	+	2.26160i	−0.166575	+	0.715181i
$11$	3.06085	−	5.30154i	0.922880	−	1.59848i	0.127945	−	0.991781i	$-0.459162\pi$
$11$	3.06085	−	5.30154i	0.922880	−	1.59848i	0.794935	−	0.606694i	$-0.207505\pi$
$12$		0			0
$13$	0.599586	−	1.03851i	0.166295	−	0.288032i	−0.770819	−	0.637054i	$-0.780153\pi$
$13$	0.599586	−	1.03851i	0.166295	−	0.288032i	0.937114	+	0.349022i	$0.113486\pi$
$14$	−1.88772	+	3.23056i	−0.504515	+	0.863403i
$15$		0			0
$16$	−3.96527	+	0.525926i	−0.991319	+	0.131481i
$17$	−2.89068	+	1.66893i	−0.701092	+	0.404776i	−0.807754	−	0.589519i	$-0.799317\pi$
$17$	−2.89068	+	1.66893i	−0.701092	+	0.404776i	0.106662	+	0.994295i	$0.465984\pi$
$18$		0			0
$19$	−3.61550	−	2.08741i	−0.829452	−	0.478884i	0.0242130	−	0.999707i	$-0.492292\pi$
$19$	−3.61550	−	2.08741i	−0.829452	−	0.478884i	−0.853665	+	0.520823i	$0.825625\pi$
$20$	−1.82581	−	2.72966i	−0.408263	−	0.610371i
$21$		0			0
$22$	2.51510	+	8.28399i	0.536221	+	1.76615i
$23$	−4.21762	−	7.30513i	−0.879434	−	1.52323i	−0.851963	−	0.523603i	$-0.824588\pi$
$23$	−4.21762	−	7.30513i	−0.879434	−	1.52323i	−0.0274717	−	0.999623i	$-0.508746\pi$
$24$		0			0
$25$	−1.15192	+	1.99519i	−0.230384	+	0.399037i
$26$	0.492680	+	1.62274i	0.0966225	+	0.318246i
$27$		0			0
$28$	−1.51080	−	5.07124i	−0.285515	−	0.958374i
$29$	0.398864	−	0.230284i	0.0740671	−	0.0427627i	−0.462509	−	0.886615i	$-0.653051\pi$
$29$	0.398864	−	0.230284i	0.0740671	−	0.0427627i	0.536576	+	0.843852i	$0.319717\pi$
$30$		0			0
$31$			4.85676i			0.872299i	0.899874	+	0.436150i	$0.143658\pi$
$31$			4.85676i			0.872299i	−0.899874	+	0.436150i	$0.856342\pi$
$32$	3.28945	−	4.60212i	0.581498	−	0.813548i
$33$		0			0
$34$	1.07080	−	4.59740i	0.183640	−	0.788448i
$35$	3.18694	−	2.95238i	0.538691	−	0.499043i
$36$		0			0
$37$	2.65132	−	4.59222i	0.435874	−	0.754956i	−0.561492	−	0.827482i	$-0.689773\pi$
$37$	2.65132	−	4.59222i	0.435874	−	0.754956i	0.997367	+	0.0725258i	$0.0231060\pi$
$38$	5.64944	−	1.71523i	0.916460	−	0.278246i
$39$		0			0
$40$	4.58279	+	0.753219i	0.724602	+	0.119094i
$41$	4.25113	+	2.45439i	0.663914	+	0.383311i	0.793767	−	0.608222i	$-0.208117\pi$
$41$	4.25113	+	2.45439i	0.663914	+	0.383311i	−0.129852	+	0.991533i	$0.541450\pi$
$42$		0			0
$43$	−0.733230	+	0.423331i	−0.111817	+	0.0645573i	−0.554865	−	0.831940i	$-0.687230\pi$
$43$	−0.733230	+	0.423331i	−0.111817	+	0.0645573i	0.443049	+	0.896498i	$0.353897\pi$
$44$	−10.9834	−	5.40982i	−1.65581	−	0.815561i
$45$		0			0
$46$	11.6183	+	2.70605i	1.71302	+	0.398985i
$47$	−8.42989			−1.22963			−0.614813	−	0.788673i	$-0.710768\pi$
$47$	−8.42989			−1.22963			−0.614813	+	0.788673i	$0.710768\pi$
$48$		0			0
$49$	6.31156	−	3.02725i	0.901651	−	0.432464i
$50$	−0.946535	−	3.11760i	−0.133860	−	0.440896i
$51$		0			0
$52$	−2.15152	−	1.05972i	−0.298362	−	0.146957i
$53$	0.122578	−	0.0707704i	0.0168374	−	0.00972107i	−0.491558	−	0.870845i	$-0.663572\pi$
$53$	0.122578	−	0.0707704i	0.0168374	−	0.00972107i	0.508395	+	0.861124i	$0.330239\pi$
$54$		0			0
$55$		−	10.0518i		−	1.35539i
$56$	6.69582	+	3.34156i	0.894766	+	0.446535i
$57$		0			0
$58$	−0.147751	+	0.634362i	−0.0194007	+	0.0832958i
$59$	10.8434			1.41169			0.705844	−	0.708367i	$-0.250568\pi$
$59$	10.8434			1.41169			0.705844	+	0.708367i	$0.250568\pi$
$60$		0			0
$61$	2.20845			0.282763			0.141381	−	0.989955i	$-0.454846\pi$
$61$	2.20845			0.282763			0.141381	+	0.989955i	$0.454846\pi$
$62$	−5.01419	−	4.69404i	−0.636803	−	0.596144i
$63$		0			0
$64$	1.57206	+	7.84402i	0.196508	+	0.980502i
$65$		−	1.96904i		−	0.244229i
$66$		0			0
$67$			4.29540i			0.524767i	0.964964	+	0.262384i	$0.0845085\pi$
$67$			4.29540i			0.524767i	−0.964964	+	0.262384i	$0.915491\pi$
$68$	3.71151	+	5.54888i	0.450087	+	0.672901i
$69$		0			0
$70$	−0.0320811	+	6.14371i	−0.00383442	+	0.734314i
$71$	6.07333			0.720772			0.360386	−	0.932803i	$-0.382645\pi$
$71$	6.07333			0.720772			0.360386	+	0.932803i	$0.382645\pi$
$72$		0			0
$73$	−5.37668	−	9.31269i	−0.629293	−	1.08997i	−0.987694	−	0.156400i	$-0.950011\pi$
$73$	−5.37668	−	9.31269i	−0.629293	−	1.08997i	0.358401	−	0.933568i	$-0.383322\pi$
$74$	2.17859	+	7.17563i	0.253256	+	0.834150i
$75$		0			0
$76$	−3.68934	+	7.49034i	−0.423196	+	0.859201i
$77$	4.78619	−	15.4732i	0.545436	−	1.76333i
$78$		0			0
$79$			7.70311i			0.866668i	0.901233	+	0.433334i	$0.142663\pi$
$79$			7.70311i			0.866668i	−0.901233	+	0.433334i	$0.857337\pi$
$80$	−5.20688	+	4.00336i	−0.582147	+	0.447589i
$81$		0			0
$82$	−6.64265	+	2.01677i	−0.733558	+	0.222715i
$83$	2.20287	+	3.81549i	0.241797	+	0.418804i	0.961226	−	0.275762i	$-0.0889300\pi$
$83$	2.20287	+	3.81549i	0.241797	+	0.418804i	−0.719430	+	0.694565i	$0.755597\pi$
$84$		0			0
$85$	−2.74039	+	4.74649i	−0.297237	+	0.514829i
$86$	0.271611	−	1.16615i	0.0292886	−	0.125749i
$87$		0			0
$88$	16.2006	−	6.11084i	1.72699	−	0.651417i
$89$	8.60870	+	4.97023i	0.912520	+	0.526844i	0.881241	−	0.472667i	$-0.156709\pi$
$89$	8.60870	+	4.97023i	0.912520	+	0.526844i	0.0312790	+	0.999511i	$0.490042\pi$
$90$		0			0
$91$	0.937560	−	3.03102i	0.0982830	−	0.317737i
$92$	−14.0228	+	9.37949i	−1.46198	+	0.977880i
$93$		0			0
$94$	8.14746	−	8.70315i	0.840346	−	0.897662i
$95$	−6.85504			−0.703312
$96$		0			0
$97$	3.92227	+	6.79358i	0.398246	+	0.689783i	0.993510	−	0.113748i	$-0.0362855\pi$
$97$	3.92227	+	6.79358i	0.398246	+	0.689783i	−0.595263	+	0.803531i	$0.702952\pi$
$98$	−2.97472	+	9.44198i	−0.300492	+	0.953784i
$99$		0			0
$100$	4.13349	+	2.03594i	0.413349	+	0.203594i
$101$	11.7687	+	6.79468i	1.17103	+	0.676096i	0.953923	−	0.300051i	$-0.0970036\pi$
$101$	11.7687	+	6.79468i	1.17103	+	0.676096i	0.217110	+	0.976147i	$0.430337\pi$
$102$		0			0
$103$	8.93793	−	5.16032i	0.880681	−	0.508461i	0.00979785	−	0.999952i	$-0.496881\pi$
$103$	8.93793	−	5.16032i	0.880681	−	0.508461i	0.870883	+	0.491491i	$0.163548\pi$
$104$	3.17351	−	1.19704i	0.311188	−	0.117380i
$105$		0			0
$106$	−0.0454067	+	0.194951i	−0.00441029	+	0.0189353i
$107$	−4.01812	+	6.95959i	−0.388446	+	0.672809i	−0.992241	−	0.124331i	$-0.960321\pi$
$107$	−4.01812	+	6.95959i	−0.388446	+	0.672809i	0.603794	+	0.797140i	$0.293655\pi$
$108$		0			0
$109$	2.15701	+	3.73606i	0.206604	+	0.357849i	0.950643	−	0.310288i	$-0.100425\pi$
$109$	2.15701	+	3.73606i	0.206604	+	0.357849i	−0.744038	+	0.668137i	$0.767092\pi$
$110$	10.3777	+	9.71504i	0.989471	+	0.926293i
$111$		0			0
$112$	−9.92137	+	3.68326i	−0.937481	+	0.348036i
$113$	1.72901	+	0.998246i	0.162652	+	0.0939071i	0.579116	−	0.815245i	$-0.303398\pi$
$113$	1.72901	+	0.998246i	0.162652	+	0.0939071i	−0.416465	+	0.909152i	$0.636731\pi$
$114$		0			0
$115$	−11.9950	−	6.92532i	−1.11854	−	0.645790i
$116$	−0.512125	−	0.765650i	−0.0475496	−	0.0710888i
$117$		0			0
$118$	−10.4801	+	11.1949i	−0.964771	+	1.03057i
$119$	−6.47843	+	6.00162i	−0.593877	+	0.550167i
$120$		0			0
$121$	−13.2376	−	22.9281i	−1.20342	−	2.08438i
$122$	−2.13446	+	2.28004i	−0.193245	+	0.206425i
$123$		0			0
$124$	9.69241	−	0.639964i	0.870404	−	0.0574704i
$125$			11.9929i			1.07268i
$126$		0			0
$127$		−	0.873599i		−	0.0775193i	−0.999249	−	0.0387597i	$-0.987659\pi$
$127$		−	0.873599i		−	0.0775193i	0.999249	−	0.0387597i	$-0.0123407\pi$
$128$	−9.61769	−	5.95820i	−0.850091	−	0.526635i
$129$		0			0
$130$	2.03287	+	1.90307i	0.178294	+	0.166910i
$131$	−1.05918	−	1.83456i	−0.0925413	−	0.160286i	0.816039	−	0.577998i	$-0.196166\pi$
$131$	−1.05918	−	1.83456i	−0.0925413	−	0.160286i	−0.908580	+	0.417711i	$0.862832\pi$
$132$		0			0
$133$	−10.5522	−	3.26404i	−0.914995	−	0.283028i
$134$	−4.43465	−	4.15149i	−0.383095	−	0.358634i
$135$		0			0
$136$	−9.31593	−	1.53115i	−0.798834	−	0.131295i
$137$	4.98558	+	2.87843i	0.425947	+	0.245921i	0.697619	−	0.716469i	$-0.254243\pi$
$137$	4.98558	+	2.87843i	0.425947	+	0.245921i	−0.271671	+	0.962390i	$0.587576\pi$
$138$		0			0
$139$	−10.1061	−	5.83478i	−0.857191	−	0.494899i	0.00587973	−	0.999983i	$-0.498128\pi$
$139$	−10.1061	−	5.83478i	−0.857191	−	0.494899i	−0.863071	+	0.505083i	$0.831462\pi$
$140$	−6.31186	−	5.97100i	−0.533450	−	0.504641i
$141$		0			0
$142$	−5.86986	+	6.27021i	−0.492588	+	0.526184i
$143$	−3.67048	−	6.35746i	−0.306941	−	0.531637i
$144$		0			0
$145$	0.378126	−	0.654933i	0.0314017	−	0.0543893i
$146$	14.8111	+	3.44971i	1.22578	+	0.285500i
$147$		0			0
$148$	−9.51384	−	4.68601i	−0.782033	−	0.385188i
$149$	−2.00223	+	1.15599i	−0.164029	+	0.0947021i	−0.579767	−	0.814782i	$-0.696857\pi$
$149$	−2.00223	+	1.15599i	−0.164029	+	0.0947021i	0.415738	+	0.909484i	$0.363523\pi$
$150$		0			0
$151$	−17.5486	−	10.1317i	−1.42809	−	0.824507i	−0.431118	−	0.902296i	$-0.641881\pi$
$151$	−17.5486	−	10.1317i	−1.42809	−	0.824507i	−0.996970	+	0.0777891i	$0.975214\pi$
$152$	−4.16741	−	11.0483i	−0.338022	−	0.896137i
$153$		0			0
$154$	11.3489	+	19.8961i	0.914521	+	1.60327i
$155$	3.98739	+	6.90636i	0.320275	+	0.554733i
$156$		0			0
$157$	10.4640			0.835121			0.417560	−	0.908649i	$-0.362885\pi$
$157$	10.4640			0.835121			0.417560	+	0.908649i	$0.362885\pi$
$158$	−7.95282	−	7.44503i	−0.632692	−	0.592295i
$159$		0			0
$160$	0.899302	−	9.24491i	0.0710961	−	0.730874i
$161$	−15.1669	−	16.3719i	−1.19532	−	1.29028i
$162$		0			0
$163$	−6.20415	−	3.58197i	−0.485946	−	0.280561i	0.236945	−	0.971523i	$-0.423854\pi$
$163$	−6.20415	−	3.58197i	−0.485946	−	0.280561i	−0.722891	+	0.690962i	$0.757187\pi$
$164$	4.33795	−	8.80719i	0.338737	−	0.687726i
$165$		0			0
$166$	−6.06824	−	1.41337i	−0.470987	−	0.109699i
$167$	−3.96753	+	6.87197i	−0.307017	+	0.531769i	−0.977708	−	0.209968i	$-0.932664\pi$
$167$	−3.96753	+	6.87197i	−0.307017	+	0.531769i	0.670691	+	0.741736i	$0.265997\pi$
$168$		0			0
$169$	5.78099	+	10.0130i	0.444692	+	0.770229i
$170$	−2.25178	−	7.41669i	−0.172704	−	0.568834i
$171$		0			0
$172$	0.941438	+	1.40749i	0.0717840	+	0.107320i
$173$		−	0.643166i		−	0.0488990i	−0.999701	−	0.0244495i	$-0.992217\pi$
$173$		−	0.643166i		−	0.0488990i	0.999701	−	0.0244495i	$-0.00778329\pi$
$174$		0			0
$175$	−1.80124	+	5.82318i	−0.136161	+	0.440191i
$176$	−9.34888	+	22.6319i	−0.704698	+	1.70594i
$177$		0			0
$178$	−13.4516	+	4.08405i	−1.00824	+	0.306112i
$179$	−4.43088	−	7.67450i	−0.331179	−	0.573619i	0.651564	−	0.758594i	$-0.274113\pi$
$179$	−4.43088	−	7.67450i	−0.331179	−	0.573619i	−0.982743	+	0.184974i	$0.940780\pi$
$180$		0			0
$181$	2.01970			0.150123			0.0750617	−	0.997179i	$-0.476085\pi$
$181$	2.01970			0.150123			0.0750617	+	0.997179i	$0.476085\pi$
$182$	2.22312	+	3.89742i	0.164789	+	0.288896i
$183$		0			0
$184$	3.86942	−	23.5426i	0.285258	−	1.73558i
$185$		−	8.70692i		−	0.640146i
$186$		0			0
$187$			20.4334i			1.49424i
$188$	1.11079	+	16.8231i	0.0810125	+	1.22695i
$189$		0			0
$190$	6.62538	−	7.07726i	0.480655	−	0.513438i
$191$	10.2190			0.739419			0.369710	−	0.929147i	$-0.379457\pi$
$191$	10.2190			0.739419			0.369710	+	0.929147i	$0.379457\pi$
$192$		0			0
$193$	6.78717			0.488551			0.244276	−	0.969706i	$-0.421450\pi$
$193$	6.78717			0.488551			0.244276	+	0.969706i	$0.421450\pi$
$194$	−10.8047	−	2.51655i	−0.775730	−	0.180678i
$195$		0			0
$196$	−6.87300	−	12.1968i	−0.490929	−	0.871200i
$197$			3.36103i			0.239464i	0.992806	+	0.119732i	$0.0382035\pi$
$197$			3.36103i			0.239464i	−0.992806	+	0.119732i	$0.961797\pi$
$198$		0			0
$199$	15.4294	−	8.90816i	1.09376	−	0.631482i	0.159185	−	0.987249i	$-0.449113\pi$
$199$	15.4294	−	8.90816i	1.09376	−	0.631482i	0.934575	+	0.355766i	$0.115780\pi$
$200$	−6.09694	+	2.29976i	−0.431119	+	0.162617i
$201$		0			0
$202$	−18.3894	+	5.58320i	−1.29387	+	0.392833i
$203$	0.893912	−	0.828120i	0.0627403	−	0.0581226i
$204$		0			0
$205$	8.06020			0.562949
$206$	−3.31089	+	14.2151i	−0.230680	+	0.990413i
$207$		0			0
$208$	−1.83134	+	4.43333i	−0.126981	+	0.307396i
$209$	−22.1330	+	12.7785i	−1.53097	+	0.883906i
$210$		0			0
$211$	16.0838	+	9.28596i	1.10725	+	0.639272i	0.938116	−	0.346321i	$-0.112569\pi$
$211$	16.0838	+	9.28596i	1.10725	+	0.639272i	0.169136	+	0.985593i	$0.445902\pi$
$212$	−0.157385	−	0.235298i	−0.0108093	−	0.0161603i
$213$		0			0
$214$	−3.30169	−	10.8748i	−0.225699	−	0.743386i
$215$	−0.695108	+	1.20396i	−0.0474060	+	0.0821096i
$216$		0			0
$217$	2.84947	+	12.5298i	0.193435	+	0.850581i
$218$	−5.94191	−	1.38395i	−0.402437	−	0.0937330i
$219$		0			0
$220$	−20.0599	+	1.32450i	−1.35244	+	0.0892981i
$221$			4.00267i			0.269249i
$222$		0			0
$223$	−11.4485	+	6.60982i	−0.766651	+	0.442626i	−0.831679	−	0.555257i	$-0.812620\pi$
$223$	−11.4485	+	6.60982i	−0.766651	+	0.442626i	0.0650278	+	0.997883i	$0.479286\pi$
$224$	5.78631	−	13.8028i	0.386614	−	0.922242i
$225$		0			0
$226$	−2.70169	+	0.820259i	−0.179714	+	0.0545629i
$227$	−1.64669	+	2.85215i	−0.109295	+	0.189304i	−0.915485	−	0.402353i	$-0.868193\pi$
$227$	−1.64669	+	2.85215i	−0.109295	+	0.189304i	0.806190	+	0.591657i	$0.201526\pi$
$228$		0			0
$229$	13.0038	+	22.5233i	0.859318	+	1.48838i	0.872580	+	0.488471i	$0.162445\pi$
$229$	13.0038	+	22.5233i	0.859318	+	1.48838i	−0.0132620	+	0.999912i	$0.504222\pi$
$230$	18.7430	−	5.69055i	1.23587	−	0.375223i
$231$		0			0
$232$	1.28544	+	0.211272i	0.0843931	+	0.0138707i
$233$	−23.4417	−	13.5341i	−1.53571	−	0.886645i	−0.999082	−	0.0428292i	$-0.986363\pi$
$233$	−23.4417	−	13.5341i	−1.53571	−	0.886645i	−0.536632	−	0.843816i	$-0.680304\pi$
$234$		0			0
$235$	−11.9874	+	6.92093i	−0.781972	+	0.451472i
$236$	−1.42881	−	21.6396i	−0.0930075	−	1.40862i
$237$		0			0
$238$	0.0652147	−	12.4890i	0.00422724	−	0.809541i
$239$	−3.36578	+	5.82971i	−0.217714	+	0.377092i	−0.954109	−	0.299460i	$-0.903193\pi$
$239$	−3.36578	+	5.82971i	−0.217714	+	0.377092i	0.736394	+	0.676552i	$0.236527\pi$
$240$		0			0
$241$	−0.144624	+	0.250495i	−0.00931603	+	0.0161358i	−0.870646	−	0.491910i	$-0.836299\pi$
$241$	−0.144624	+	0.250495i	−0.00931603	+	0.0161358i	0.861330	+	0.508046i	$0.169632\pi$
$242$	36.4655	+	8.49329i	2.34409	+	0.545970i
$243$		0			0
$244$	−0.291002	−	4.40730i	−0.0186295	−	0.282148i
$245$	6.48975	−	9.48657i	0.414615	−	0.606074i
$246$		0			0
$247$	−4.33560	+	2.50316i	−0.275868	+	0.159272i
$248$	−8.70697	+	10.6251i	−0.552893	+	0.674696i
$249$		0			0
$250$	−12.3817	−	11.5911i	−0.783085	−	0.733085i
$251$	−17.9504			−1.13302			−0.566509	−	0.824056i	$-0.691706\pi$
$251$	−17.9504			−1.13302			−0.566509	+	0.824056i	$0.691706\pi$
$252$		0			0
$253$	−51.6380			−3.24645
$254$	0.901918	+	0.844330i	0.0565913	+	0.0529780i
$255$		0			0
$256$	15.4468	−	4.17088i	0.965425	−	0.260680i
$257$	−7.42673	+	4.28782i	−0.463267	+	0.267467i	−0.713417	−	0.700740i	$-0.752853\pi$
$257$	−7.42673	+	4.28782i	−0.463267	+	0.267467i	0.250150	+	0.968207i	$0.419520\pi$
$258$		0			0
$259$	4.14581	−	13.4029i	0.257608	−	0.832816i
$260$	−3.92952	+	0.259456i	−0.243698	+	0.0160907i
$261$		0			0
$262$	2.91773	+	0.679577i	0.180258	+	0.0419844i
$263$	9.11697	−	15.7911i	0.562177	−	0.973719i	−0.435129	−	0.900368i	$-0.643297\pi$
$263$	9.11697	−	15.7911i	0.562177	−	0.973719i	0.997306	−	0.0733507i	$-0.0233693\pi$
$264$		0			0
$265$	0.116205	−	0.201273i	0.00713841	−	0.0123641i
$266$	13.5686	−	7.73962i	0.831941	−	0.474547i
$267$		0			0
$268$	8.57214	−	0.565996i	0.523627	−	0.0345737i
$269$	−5.53056	+	3.19307i	−0.337204	+	0.194685i	−0.659035	−	0.752112i	$-0.729035\pi$
$269$	−5.53056	+	3.19307i	−0.337204	+	0.194685i	0.321831	+	0.946797i	$0.395702\pi$
$270$		0			0
$271$	20.7483	+	11.9790i	1.26037	+	0.727674i	0.973146	−	0.230190i	$-0.0739347\pi$
$271$	20.7483	+	11.9790i	1.26037	+	0.727674i	0.287223	+	0.957864i	$0.407268\pi$
$272$	10.5846	−	8.13806i	0.641785	−	0.493443i
$273$		0			0
$274$	−7.79029	+	2.36521i	−0.470629	+	0.142887i
$275$	7.05171	+	12.2139i	0.425234	+	0.736527i
$276$		0			0
$277$	−4.55267	+	7.88545i	−0.273543	+	0.473791i	−0.969767	−	0.244034i	$-0.921529\pi$
$277$	−4.55267	+	7.88545i	−0.273543	+	0.473791i	0.696223	+	0.717825i	$0.254862\pi$
$278$	15.7915	−	4.79444i	0.947109	−	0.287552i
$279$		0			0
$280$	12.2650	−	0.745520i	0.732971	−	0.0445534i
$281$	9.40762	−	5.43149i	0.561212	−	0.324016i	−0.192420	−	0.981313i	$-0.561634\pi$
$281$	9.40762	−	5.43149i	0.561212	−	0.324016i	0.753632	+	0.657297i	$0.228300\pi$
$282$		0			0
$283$			10.9747i			0.652380i	0.945304	+	0.326190i	$0.105765\pi$
$283$			10.9747i			0.652380i	−0.945304	+	0.326190i	$0.894235\pi$
$284$	−0.800270	−	12.1203i	−0.0474873	−	0.719206i
$285$		0			0
$286$	10.1111	+	2.35500i	0.597879	+	0.139254i
$287$	12.4074	+	3.83788i	0.732385	+	0.226543i
$288$		0			0
$289$	−2.92932	+	5.07373i	−0.172313	+	0.298455i
$290$	0.310706	+	1.02337i	0.0182453	+	0.0600946i
$291$		0			0
$292$	−17.8764	+	11.9571i	−1.04614	+	0.699737i
$293$	9.10000	+	5.25389i	0.531627	+	0.306935i	0.741679	−	0.670755i	$-0.234030\pi$
$293$	9.10000	+	5.25389i	0.531627	+	0.306935i	−0.210051	+	0.977690i	$0.567363\pi$
$294$		0			0
$295$	15.4194	−	8.90241i	0.897753	−	0.518318i
$296$	14.0330	−	5.29323i	0.815652	−	0.307663i
$297$		0			0
$298$	0.741687	−	3.18439i	0.0429648	−	0.184467i
$299$	−10.1153			−0.584983
$300$		0			0
$301$	−1.64328	+	1.52233i	−0.0947169	+	0.0877457i
$302$	27.4208	−	8.32523i	1.57789	−	0.479063i
$303$		0			0
$304$	15.4343	+	6.37566i	0.885216	+	0.365669i
$305$	3.14044	−	1.81313i	0.179821	−	0.103820i
$306$		0			0
$307$			26.0739i			1.48812i	0.668114	+	0.744059i	$0.267102\pi$
$307$			26.0739i			1.48812i	−0.668114	+	0.744059i	$0.732898\pi$
$308$	−31.5097	−	7.51271i	−1.79543	−	0.428076i
$309$		0			0
$310$	−10.9840	−	2.55833i	−0.623852	−	0.145303i
$311$	−4.49745			−0.255027			−0.127513	−	0.991837i	$-0.540700\pi$
$311$	−4.49745			−0.255027			−0.127513	+	0.991837i	$0.540700\pi$
$312$		0			0
$313$	8.23595			0.465523			0.232762	−	0.972534i	$-0.425224\pi$
$313$	8.23595			0.465523			0.232762	+	0.972534i	$0.425224\pi$
$314$	−10.1135	+	10.8032i	−0.570735	+	0.609662i
$315$		0			0
$316$	15.3727	−	1.01502i	0.864785	−	0.0570994i
$317$			11.0936i			0.623081i	0.950233	+	0.311540i	$0.100845\pi$
$317$			11.0936i			0.623081i	−0.950233	+	0.311540i	$0.899155\pi$
$318$		0			0
$319$		−	2.81946i		−	0.157859i
$320$	8.67542	+	9.86363i	0.484971	+	0.551394i
$321$		0			0
$322$	31.5613	+	0.164806i	1.75884	+	0.00918429i
$323$	13.9350			0.775363
$324$		0			0
$325$	1.38135	+	2.39257i	0.0766235	+	0.132716i
$326$	9.69437	−	2.94331i	0.536922	−	0.163015i
$327$		0			0
$328$	4.90007	+	12.9907i	0.270561	+	0.717291i
$329$	−21.7481	+	4.94584i	−1.19901	+	0.272673i
$330$		0			0
$331$		−	2.77969i		−	0.152785i	−0.997078	−	0.0763927i	$-0.975660\pi$
$331$		−	2.77969i		−	0.152785i	0.997078	−	0.0763927i	$-0.0243403\pi$
$332$	7.32412	−	4.89893i	0.401964	−	0.268864i
$333$		0			0
$334$	−3.26013	−	10.7379i	−0.178386	−	0.587551i
$335$	3.52652	+	6.10812i	0.192674	+	0.333722i
$336$		0			0
$337$	16.8337	−	29.1569i	0.916992	−	1.58828i	0.113033	−	0.993591i	$-0.463943\pi$
$337$	16.8337	−	29.1569i	0.916992	−	1.58828i	0.803959	−	0.594685i	$-0.202723\pi$
$338$	−15.9249	−	3.70912i	−0.866199	−	0.201749i
$339$		0			0
$340$	9.83345	+	4.84343i	0.533293	+	0.262672i
$341$	25.7483	+	14.8658i	1.39435	+	0.805027i
$342$		0			0
$343$	14.5070	−	11.5129i	0.783303	−	0.621641i
$344$	−2.36302	−	0.388381i	−0.127405	−	0.0209401i
$345$		0			0
$346$	0.664015	+	0.621618i	0.0356977	+	0.0334184i
$347$	−0.530187			−0.0284619			−0.0142310	−	0.999899i	$-0.504530\pi$
$347$	−0.530187			−0.0284619			−0.0142310	+	0.999899i	$0.504530\pi$
$348$		0			0
$349$	10.4789	+	18.1500i	0.560924	+	0.971548i	0.997416	+	0.0718403i	$0.0228872\pi$
$349$	10.4789	+	18.1500i	0.560924	+	0.971548i	−0.436493	+	0.899708i	$0.643779\pi$
$350$	−4.27105	−	7.48771i	−0.228297	−	0.400235i
$351$		0			0
$352$	−14.3298	−	31.5256i	−0.763783	−	1.68032i
$353$	−6.47302	−	3.73720i	−0.344524	−	0.198911i	0.317747	−	0.948176i	$-0.397074\pi$
$353$	−6.47302	−	3.73720i	−0.344524	−	0.198911i	−0.662271	+	0.749265i	$0.730407\pi$
$354$		0			0
$355$	8.63635	−	4.98620i	0.458370	−	0.264640i
$356$	8.78452	−	17.8349i	0.465579	−	0.945248i
$357$		0			0
$358$	12.2057	+	2.84287i	0.645092	+	0.150250i
$359$	−2.61803	+	4.53456i	−0.138174	+	0.239325i	−0.926806	−	0.375541i	$-0.877457\pi$
$359$	−2.61803	+	4.53456i	−0.138174	+	0.239325i	0.788631	+	0.614866i	$0.210790\pi$
$360$		0			0
$361$	−0.785453	−	1.36044i	−0.0413396	−	0.0716023i
$362$	−1.95204	+	2.08518i	−0.102597	+	0.109594i
$363$		0			0
$364$	−6.17240	−	1.47166i	−0.323522	−	0.0771357i
$365$	−15.2914	−	8.82850i	−0.800389	−	0.462105i
$366$		0			0
$367$	13.3026	+	7.68026i	0.694390	+	0.400906i	0.805255	−	0.592929i	$-0.202029\pi$
$367$	13.3026	+	7.68026i	0.694390	+	0.400906i	−0.110864	+	0.993836i	$0.535362\pi$
$368$	20.5660	+	26.7487i	1.07208	+	1.39437i
$369$		0			0
$370$	8.98917	+	8.41521i	0.467325	+	0.437486i
$371$	0.274715	−	0.254496i	0.0142625	−	0.0132128i
$372$		0			0
$373$	1.57329	+	2.72503i	0.0814621	+	0.141097i	0.903878	−	0.427790i	$-0.140708\pi$
$373$	1.57329	+	2.72503i	0.0814621	+	0.141097i	−0.822416	+	0.568886i	$0.807374\pi$
$374$	−21.0958	−	19.7488i	−1.09084	−	1.02119i
$375$		0			0
$376$	−18.4421	−	15.1127i	−0.951077	−	0.779379i
$377$		−	0.552300i		−	0.0284449i
$378$		0			0
$379$		−	21.8027i		−	1.11993i	−0.828516	−	0.559965i	$-0.810815\pi$
$379$		−	21.8027i		−	1.11993i	0.828516	−	0.559965i	$-0.189185\pi$
$380$	0.903273	+	13.6803i	0.0463369	+	0.701784i
$381$		0			0
$382$	−9.87661	+	10.5502i	−0.505331	+	0.539797i
$383$	18.5862	+	32.1922i	0.949708	+	1.64494i	0.746038	+	0.665903i	$0.231954\pi$
$383$	18.5862	+	32.1922i	0.949708	+	1.64494i	0.203670	+	0.979040i	$0.434713\pi$
$384$		0			0
$385$	−5.89743	−	25.9325i	−0.300561	−	1.32164i
$386$	−6.55978	+	7.00719i	−0.333884	+	0.356656i
$387$		0			0
$388$	13.0408	−	8.72268i	0.662046	−	0.442827i
$389$	−21.2347	−	12.2599i	−1.07664	−	0.621599i	−0.146653	−	0.989188i	$-0.546850\pi$
$389$	−21.2347	−	12.2599i	−1.07664	−	0.621599i	−0.929988	+	0.367589i	$0.880183\pi$
$390$		0			0
$391$	24.3836	+	14.0779i	1.23313	+	0.711948i
$392$	19.2349	+	4.69237i	0.971510	+	0.237000i
$393$		0			0
$394$	−3.46999	−	3.24843i	−0.174815	−	0.163653i
$395$	6.32425	+	10.9539i	0.318207	+	0.551151i
$396$		0			0
$397$	1.52209	−	2.63634i	0.0763916	−	0.132314i	−0.825299	−	0.564696i	$-0.808993\pi$
$397$	1.52209	−	2.63634i	0.0763916	−	0.132314i	0.901691	+	0.432382i	$0.142327\pi$
$398$	−5.71552	+	24.5393i	−0.286493	+	1.23004i
$399$		0			0
$400$	3.51836	−	8.51728i	0.175918	−	0.425864i
$401$	−22.2303	+	12.8347i	−1.11013	+	0.640934i	−0.938863	−	0.344290i	$-0.888120\pi$
$401$	−22.2303	+	12.8347i	−1.11013	+	0.640934i	−0.171267	+	0.985225i	$0.554786\pi$
$402$		0			0
$403$	5.04380	+	2.91204i	0.251250	+	0.145059i
$404$	12.0091	−	24.3817i	0.597475	−	1.21303i
$405$		0			0
$406$	−0.00899850	+	1.72326i	−0.000446588	+	0.0855242i
$407$	−16.2306	−	28.1122i	−0.804519	−	1.39347i
$408$		0			0
$409$	−28.9239			−1.43020			−0.715098	−	0.699024i	$-0.753618\pi$
$409$	−28.9239			−1.43020			−0.715098	+	0.699024i	$0.753618\pi$
$410$	−7.79016	+	8.32149i	−0.384729	+	0.410969i
$411$		0			0
$412$	−11.4759	−	17.1571i	−0.565379	−	0.845268i
$413$	27.9746	−	6.36185i	1.37654	−	0.313046i
$414$		0			0
$415$	6.26502	+	3.61711i	0.307538	+	0.177557i
$416$	−2.80705	−	6.17550i	−0.137627	−	0.302779i
$417$		0			0
$418$	8.19874	−	35.2008i	0.401013	−	1.72173i
$419$	18.5974	−	32.2117i	0.908545	−	1.57365i	0.0924578	−	0.995717i	$-0.470528\pi$
$419$	18.5974	−	32.2117i	0.908545	−	1.57365i	0.816087	−	0.577929i	$-0.196139\pi$
$420$		0			0
$421$	1.74288	+	3.01876i	0.0849428	+	0.147125i	0.905367	−	0.424630i	$-0.139596\pi$
$421$	1.74288	+	3.01876i	0.0849428	+	0.147125i	−0.820424	+	0.571756i	$0.806263\pi$
$422$	−25.1319	+	7.63029i	−1.22340	+	0.371437i
$423$		0			0
$424$	0.395038	+	0.0649278i	0.0191847	+	0.00315317i
$425$		−	7.68992i		−	0.373016i
$426$		0			0
$427$	5.69753	−	1.29570i	0.275723	−	0.0627035i
$428$	14.4184	+	7.10173i	0.696940	+	0.343275i
$429$		0			0
$430$	−0.571171	−	1.88127i	−0.0275443	−	0.0907228i
$431$	4.90250	+	8.49137i	0.236145	+	0.409015i	0.959605	−	0.281351i	$-0.0907826\pi$
$431$	4.90250	+	8.49137i	0.236145	+	0.409015i	−0.723460	+	0.690366i	$0.757449\pi$
$432$		0			0
$433$	−9.57915			−0.460345			−0.230172	−	0.973150i	$-0.573929\pi$
$433$	−9.57915			−0.460345			−0.230172	+	0.973150i	$0.573929\pi$
$434$	−15.6900	−	9.16821i	−0.753145	−	0.440088i
$435$		0			0
$436$	7.17165	−	4.79695i	0.343460	−	0.229732i
$437$			35.2156i			1.68459i
$438$		0			0
$439$			20.3416i			0.970853i	0.874277	+	0.485427i	$0.161336\pi$
$439$			20.3416i			0.970853i	−0.874277	+	0.485427i	$0.838664\pi$
$440$	18.0204	−	21.9903i	0.859090	−	1.04835i
$441$		0			0
$442$	−4.13243	−	3.86857i	−0.196560	−	0.184009i
$443$	8.85905			0.420906			0.210453	−	0.977604i	$-0.432506\pi$
$443$	8.85905			0.420906			0.210453	+	0.977604i	$0.432506\pi$
$444$		0			0
$445$	16.3222			0.773748
$446$	4.24089	−	18.2080i	0.200812	−	0.862175i
$447$		0			0
$448$	8.65784	+	19.3143i	0.409045	+	0.912514i
$449$		−	29.6361i		−	1.39861i	−0.714822	−	0.699306i	$-0.753492\pi$
$449$		−	29.6361i		−	1.39861i	0.714822	−	0.699306i	$-0.246508\pi$
$450$		0			0
$451$	26.0241	−	15.0250i	1.22543	−	0.707500i
$452$	1.76433	−	3.58205i	0.0829869	−	0.168485i
$453$		0			0
$454$	−1.35309	−	4.45667i	−0.0635036	−	0.209162i
$455$	−1.15524	−	5.07988i	−0.0541585	−	0.238148i
$456$		0			0
$457$	−1.33459			−0.0624293			−0.0312147	−	0.999513i	$-0.509938\pi$
$457$	−1.33459			−0.0624293			−0.0312147	+	0.999513i	$0.509938\pi$
$458$	−35.8216	−	8.34333i	−1.67383	−	0.389858i
$459$		0			0
$460$	−12.2400	+	24.8504i	−0.570693	+	1.15866i
$461$	1.88551	−	1.08860i	0.0878168	−	0.0507011i	−0.455449	−	0.890262i	$-0.650521\pi$
$461$	1.88551	−	1.08860i	0.0878168	−	0.0507011i	0.543265	+	0.839561i	$0.317188\pi$
$462$		0			0
$463$	−20.7873	−	12.0015i	−0.966066	−	0.557758i	−0.0680311	−	0.997683i	$-0.521672\pi$
$463$	−20.7873	−	12.0015i	−0.966066	−	0.557758i	−0.898035	+	0.439925i	$0.855005\pi$
$464$	−1.46049	+	1.12291i	−0.0678016	+	0.0521299i
$465$		0			0
$466$	36.6291	−	11.1209i	1.69681	−	0.515168i
$467$	−16.1452	+	27.9642i	−0.747109	+	1.29403i	0.202094	+	0.979366i	$0.435225\pi$
$467$	−16.1452	+	27.9642i	−0.747109	+	1.29403i	−0.949203	+	0.314664i	$0.898108\pi$
$468$		0			0
$469$	2.52013	+	11.0816i	0.116369	+	0.511702i
$470$	4.44050	−	19.0650i	0.204825	−	0.879405i
$471$		0			0
$472$	23.7221	+	19.4395i	1.09190	+	0.894777i
$473$			5.18300i			0.238315i
$474$		0			0
$475$	8.32954	−	4.80906i	0.382185	−	0.220655i
$476$	12.8308	+	12.1379i	0.588099	+	0.556340i
$477$		0			0
$478$	−2.76567	−	9.10928i	−0.126499	−	0.416649i
$479$	−8.48860	+	14.7027i	−0.387854	+	0.671783i	−0.992161	−	0.124969i	$-0.960117\pi$
$479$	−8.48860	+	14.7027i	−0.387854	+	0.671783i	0.604306	+	0.796752i	$0.293450\pi$
$480$		0			0
$481$	−3.17938	−	5.50686i	−0.144967	−	0.251091i
$482$	−0.118837	−	0.391415i	−0.00541290	−	0.0178285i
$483$		0			0
$484$	−44.0124	+	29.4388i	−2.00056	+	1.33813i
$485$	11.1550	+	6.44036i	0.506524	+	0.292442i
$486$		0			0
$487$	−32.6884	+	18.8727i	−1.48125	+	0.855202i	−0.999774	−	0.0212564i	$-0.993233\pi$
$487$	−32.6884	+	18.8727i	−1.48125	+	0.855202i	−0.481478	+	0.876458i	$0.659900\pi$
$488$	4.83142	+	3.95920i	0.218708	+	0.179225i
$489$		0			0
$490$	3.52177	+	15.8689i	0.159097	+	0.716882i
$491$	0.0780327	−	0.135157i	0.00352157	−	0.00609953i	−0.864259	−	0.503047i	$-0.832212\pi$
$491$	0.0780327	−	0.135157i	0.00352157	−	0.00609953i	0.867781	+	0.496947i	$0.165546\pi$
$492$		0			0
$493$	−0.768658	+	1.33135i	−0.0346186	+	0.0599612i
$494$	1.60604	−	6.89544i	0.0722592	−	0.310241i
$495$		0			0
$496$	−2.55429	−	19.2584i	−0.114691	−	0.864726i
$497$	15.6685	−	3.56324i	0.702827	−	0.159833i
$498$		0			0
$499$	30.6234	−	17.6804i	1.37089	−	0.791485i	0.379851	−	0.925048i	$-0.375975\pi$
$499$	30.6234	−	17.6804i	1.37089	−	0.791485i	0.991040	+	0.133563i	$0.0426419\pi$
$500$	23.9337	−	1.58028i	1.07035	−	0.0706721i
$501$		0			0
$502$	17.3490	−	18.5323i	0.774323	−	0.827136i
$503$	−25.3456			−1.13011			−0.565053	−	0.825055i	$-0.691144\pi$
$503$	−25.3456			−1.13011			−0.565053	+	0.825055i	$0.691144\pi$
$504$		0			0
$505$	22.3137			0.992947
$506$	49.9079	−	53.3119i	2.21868	−	2.37000i
$507$		0			0
$508$	−1.74340	+	0.115112i	−0.0773509	+	0.00510727i
$509$	17.5962	−	10.1592i	0.779938	−	0.450297i	−0.0564704	−	0.998404i	$-0.517985\pi$
$509$	17.5962	−	10.1592i	0.779938	−	0.450297i	0.836408	+	0.548107i	$0.184651\pi$
$510$		0			0
$511$	−19.3350	−	20.8711i	−0.855329	−	0.923283i
$512$	−10.6232	+	19.9787i	−0.469484	+	0.882941i
$513$		0			0
$514$	2.75109	−	11.8116i	0.121345	−	0.520989i
$515$	8.47323	−	14.6761i	0.373375	−	0.646705i
$516$		0			0
$517$	−25.8026	+	44.6914i	−1.13480	+	1.96553i
$518$	9.83047	+	17.2341i	0.431926	+	0.757222i
$519$		0			0
$520$	3.53000	−	4.30766i	0.154801	−	0.188903i
$521$	24.6315	−	14.2210i	1.07912	−	0.623033i	0.148464	−	0.988918i	$-0.452567\pi$
$521$	24.6315	−	14.2210i	1.07912	−	0.623033i	0.930660	+	0.365885i	$0.119234\pi$
$522$		0			0
$523$	−28.3635	−	16.3756i	−1.24025	−	0.716057i	−0.271103	−	0.962550i	$-0.587388\pi$
$523$	−28.3635	−	16.3756i	−1.24025	−	0.716057i	−0.969144	+	0.246493i	$0.920722\pi$
$524$	−3.52158	+	2.35550i	−0.153841	+	0.102900i
$525$		0			0
$526$	7.49143	+	24.6745i	0.326642	+	1.07586i
$527$	−8.10560	−	14.0393i	−0.353086	−	0.611562i
$528$		0			0
$529$	−24.0766	+	41.7019i	−1.04681	+	1.81313i
$530$	0.0954857	+	0.314501i	0.00414763	+	0.0136611i
$531$		0			0
$532$	−5.12345	+	21.4887i	−0.222130	+	0.931654i
$533$	5.09783	−	2.94323i	0.220811	−	0.127486i
$534$		0			0
$535$			13.1955i			0.570491i
$536$	−7.70060	+	9.39705i	−0.332615	+	0.405891i
$537$		0			0
$538$	2.04869	−	8.79593i	0.0883253	−	0.379220i
$539$	3.26963	−	42.7269i	0.140833	−	1.84038i
$540$		0			0
$541$	0.0796412	−	0.137943i	0.00342404	−	0.00593061i	−0.864308	−	0.502962i	$-0.832243\pi$
$541$	0.0796412	−	0.137943i	0.00342404	−	0.00593061i	0.867732	+	0.497032i	$0.165577\pi$
$542$	−32.4205	+	9.84318i	−1.39258	+	0.422801i
$543$		0			0
$544$	−1.82811	+	18.7931i	−0.0783795	+	0.805749i
$545$	6.13460	+	3.54181i	0.262777	+	0.151715i
$546$		0			0
$547$	−4.52878	+	2.61469i	−0.193636	+	0.111796i	−0.593684	−	0.804698i	$-0.702327\pi$
$547$	−4.52878	+	2.61469i	−0.193636	+	0.111796i	0.400047	+	0.916494i	$0.368994\pi$
$548$	5.08741	−	10.3288i	0.217323	−	0.441224i
$549$		0			0
$550$	−19.4253	−	4.52441i	−0.828298	−	0.192922i
$551$	−1.92279			−0.0819135
$552$		0			0
$553$	4.51944	+	19.8731i	0.192186	+	0.845090i
$554$	−3.74093	−	12.3215i	−0.158937	−	0.523491i
$555$		0			0
$556$	−10.3125	+	20.9372i	−0.437349	+	0.887934i
$557$	−21.2934	+	12.2938i	−0.902232	+	0.520904i	−0.877924	−	0.478801i	$-0.841072\pi$
$557$	−21.2934	+	12.2938i	−0.902232	+	0.520904i	−0.0243082	+	0.999705i	$0.507738\pi$
$558$		0			0
$559$			1.01529i			0.0429423i
$560$	−11.0843	+	13.3831i	−0.468399	+	0.565538i
$561$		0			0
$562$	−3.48487	+	14.9621i	−0.147001	+	0.631138i
$563$	−28.6466			−1.20731			−0.603655	−	0.797246i	$-0.706289\pi$
$563$	−28.6466			−1.20731			−0.603655	+	0.797246i	$0.706289\pi$
$564$		0			0
$565$	3.27823			0.137916
$566$	−11.3305	−	10.6070i	−0.476256	−	0.445847i
$567$		0			0
$568$	13.2866	+	10.8880i	0.557495	+	0.456850i
$569$			12.1322i			0.508608i	0.967124	+	0.254304i	$0.0818464\pi$
$569$			12.1322i			0.508608i	−0.967124	+	0.254304i	$0.918154\pi$
$570$		0			0
$571$		−	19.8947i		−	0.832568i	−0.909235	−	0.416284i	$-0.863332\pi$
$571$		−	19.8947i		−	0.832568i	0.909235	−	0.416284i	$-0.136668\pi$
$572$	−12.2036	+	8.16272i	−0.510260	+	0.341300i
$573$		0			0
$574$	−15.9540	+	9.10030i	−0.665907	+	0.379839i
$575$	19.4335			0.810431
$576$		0			0
$577$	−10.2405	−	17.7370i	−0.426317	−	0.738403i	0.570225	−	0.821488i	$-0.306856\pi$
$577$	−10.2405	−	17.7370i	−0.426317	−	0.738403i	−0.996542	+	0.0830856i	$0.973523\pi$
$578$	−2.40703	−	7.92802i	−0.100119	−	0.329762i
$579$		0			0
$580$	−1.35685	−	0.668310i	−0.0563399	−	0.0277500i
$581$	7.92170	+	8.55106i	0.328648	+	0.354758i
$582$		0			0
$583$		−	0.866470i		−	0.0358855i
$584$	4.93280	−	30.0124i	0.204121	−	1.24192i
$585$		0			0
$586$	−14.2193	+	4.31712i	−0.587395	+	0.178339i
$587$	8.87326	+	15.3689i	0.366239	+	0.634344i	0.988974	−	0.148089i	$-0.0473121\pi$
$587$	8.87326	+	15.3689i	0.366239	+	0.634344i	−0.622736	+	0.782432i	$0.713979\pi$
$588$		0			0
$589$	10.1380	−	17.5596i	0.417730	−	0.723530i
$590$	−5.71183	+	24.5234i	−0.235152	+	1.00961i
$591$		0			0
$592$	−8.09804	+	19.6038i	−0.332827	+	0.805711i
$593$	−12.5710	−	7.25785i	−0.516227	−	0.298044i	0.219162	−	0.975688i	$-0.429668\pi$
$593$	−12.5710	−	7.25785i	−0.516227	−	0.298044i	−0.735390	+	0.677644i	$0.763001\pi$
$594$		0			0
$595$	−4.28509	+	13.8532i	−0.175671	+	0.567924i
$596$	2.57078	+	3.84343i	0.105303	+	0.157433i
$597$		0			0
$598$	9.77640	−	10.4432i	0.399787	−	0.427054i
$599$	−20.9835			−0.857363			−0.428681	−	0.903456i	$-0.641022\pi$
$599$	−20.9835			−0.857363			−0.428681	+	0.903456i	$0.641022\pi$
$600$		0			0
$601$	−23.3640	−	40.4676i	−0.953036	−	1.65071i	−0.738801	−	0.673924i	$-0.764608\pi$
$601$	−23.3640	−	40.4676i	−0.953036	−	1.65071i	−0.214235	−	0.976782i	$-0.568726\pi$
$602$	0.0165419	−	3.16787i	0.000674199	−	0.129113i
$603$		0			0
$604$	−17.9070	+	36.3560i	−0.728627	+	1.47931i
$605$	−37.6480	−	21.7361i	−1.53061	−	0.883697i
$606$		0			0
$607$	−22.2120	+	12.8241i	−0.901559	+	0.520515i	−0.877706	−	0.479200i	$-0.840927\pi$
$607$	−22.2120	+	12.8241i	−0.901559	+	0.520515i	−0.0238532	+	0.999715i	$0.507593\pi$
$608$	−21.4995	+	9.77253i	−0.871920	+	0.396328i
$609$		0			0
$610$	−1.16332	+	4.99463i	−0.0471013	+	0.202227i
$611$	−5.05444	+	8.75454i	−0.204481	+	0.354171i
$612$		0			0
$613$	20.5463	+	35.5872i	0.829857	+	1.43735i	0.898150	+	0.439689i	$0.144911\pi$
$613$	20.5463	+	35.5872i	0.829857	+	1.43735i	−0.0682937	+	0.997665i	$0.521755\pi$
$614$	−26.9192	−	25.2004i	−1.08637	−	1.01700i
$615$		0			0
$616$	38.2103	−	25.2702i	1.53954	−	1.01816i
$617$	−0.995182	−	0.574568i	−0.0400645	−	0.0231313i	0.479834	−	0.877359i	$-0.340697\pi$
$617$	−0.995182	−	0.574568i	−0.0400645	−	0.0231313i	−0.519898	+	0.854228i	$0.674030\pi$
$618$		0			0
$619$	−20.3462	−	11.7469i	−0.817781	−	0.472146i	0.0318698	−	0.999492i	$-0.489854\pi$
$619$	−20.3462	−	11.7469i	−0.817781	−	0.472146i	−0.849651	+	0.527346i	$0.823187\pi$
$620$	13.2573	−	8.86749i	0.532426	−	0.356127i
$621$		0			0
$622$	4.34677	−	4.64324i	0.174290	−	0.186177i
$623$	25.1255	+	7.77185i	1.00663	+	0.311373i
$624$		0			0
$625$	4.08655	+	7.07811i	0.163462	+	0.283124i
$626$	−7.96002	+	8.50293i	−0.318146	+	0.339845i
$627$		0			0
$628$	−1.37882	−	20.8826i	−0.0550210	−	0.833306i
$629$			17.6995i			0.705725i
$630$		0			0
$631$		−	2.66350i		−	0.106032i	−0.998594	−	0.0530162i	$-0.983117\pi$
$631$		−	2.66350i		−	0.106032i	0.998594	−	0.0530162i	$-0.0168835\pi$
$632$	−13.8098	+	16.8521i	−0.549324	+	0.670340i
$633$		0			0
$634$	−11.4533	−	10.7220i	−0.454867	−	0.425824i
$635$	−0.717224	−	1.24227i	−0.0284622	−	0.0492979i
$636$		0			0
$637$	0.640485	−	8.36973i	0.0253769	−	0.331621i
$638$	2.91085	+	2.72500i	0.115242	+	0.107884i
$639$		0			0
$640$	−18.5681	−	0.576516i	−0.733970	−	0.0227888i
$641$	−35.2181	−	20.3332i	−1.39103	−	0.803113i	−0.397602	−	0.917558i	$-0.630158\pi$
$641$	−35.2181	−	20.3332i	−1.39103	−	0.803113i	−0.993430	+	0.114445i	$0.963491\pi$
$642$		0			0
$643$	−36.1897	−	20.8942i	−1.42718	−	0.823985i	−0.430286	−	0.902693i	$-0.641587\pi$
$643$	−36.1897	−	20.8942i	−1.42718	−	0.823985i	−0.996898	+	0.0787077i	$0.974921\pi$
$644$	−30.6741	+	32.4252i	−1.20873	+	1.27773i
$645$		0			0
$646$	−13.4681	+	14.3867i	−0.529896	+	0.566038i
$647$	16.9405	+	29.3418i	0.665999	+	1.15354i	0.979014	+	0.203795i	$0.0653277\pi$
$647$	16.9405	+	29.3418i	0.665999	+	1.15354i	−0.313015	+	0.949748i	$0.601339\pi$
$648$		0			0
$649$	33.1899	−	57.4867i	1.30282	−	2.25655i
$650$	−3.80520	−	0.886282i	−0.149252	−	0.0347628i
$651$		0			0
$652$	−6.33086	+	12.8533i	−0.247936	+	0.503375i
$653$	35.9486	−	20.7549i	1.40678	−	0.812204i	0.411702	−	0.911319i	$-0.364935\pi$
$653$	35.9486	−	20.7549i	1.40678	−	0.812204i	0.995076	+	0.0991150i	$0.0316012\pi$
$654$		0			0
$655$	−3.01234	−	1.73918i	−0.117702	−	0.0679553i
$656$	−18.1477	−	7.49655i	−0.708549	−	0.292691i
$657$		0			0
$658$	15.9133	−	27.2332i	0.620365	−	1.06166i
$659$	17.1903	+	29.7745i	0.669640	+	1.15985i	0.978005	+	0.208583i	$0.0668851\pi$
$659$	17.1903	+	29.7745i	0.669640	+	1.15985i	−0.308364	+	0.951268i	$0.599782\pi$
$660$		0			0
$661$	1.96882			0.0765780			0.0382890	−	0.999267i	$-0.487809\pi$
$661$	1.96882			0.0765780			0.0382890	+	0.999267i	$0.487809\pi$
$662$	2.86980	+	2.68656i	0.111538	+	0.104416i
$663$		0			0
$664$	−2.02101	+	12.2963i	−0.0784303	+	0.477191i
$665$	−17.6852	+	4.02187i	−0.685802	+	0.155962i
$666$		0			0
$667$	−3.36451	−	1.94250i	−0.130274	−	0.0752139i
$668$	14.2369	+	7.01232i	0.550841	+	0.271315i
$669$		0			0
$670$	−9.71449	−	2.26263i	−0.375304	−	0.0874132i
$671$	6.75972	−	11.7082i	0.260956	−	0.451989i
$672$		0			0
$673$	−22.9857	−	39.8123i	−0.886032	−	1.53465i	−0.844526	−	0.535515i	$-0.820118\pi$
$673$	−22.9857	−	39.8123i	−0.886032	−	1.53465i	−0.0415062	−	0.999138i	$-0.513216\pi$
$674$	13.8323	+	45.5595i	0.532800	+	1.75488i
$675$		0			0
$676$	19.2207	−	12.8563i	0.739257	−	0.494471i
$677$			34.7721i			1.33640i	0.743981	+	0.668201i	$0.232935\pi$
$677$			34.7721i			1.33640i	−0.743981	+	0.668201i	$0.767065\pi$
$678$		0			0
$679$	14.1048	+	15.2254i	0.541293	+	0.584297i
$680$	−14.5044	+	5.47105i	−0.556220	+	0.209805i
$681$		0			0
$682$	−40.2333	+	12.2152i	−1.54061	+	0.467745i
$683$	−18.1138	−	31.3741i	−0.693106	−	1.20049i	−0.970815	−	0.239830i	$-0.922908\pi$
$683$	−18.1138	−	31.3741i	−0.693106	−	1.20049i	0.277709	−	0.960665i	$-0.410425\pi$
$684$		0			0
$685$	9.45275			0.361171
$686$	−2.13478	+	26.1045i	−0.0815063	+	0.996673i
$687$		0			0
$688$	2.68482	−	2.06425i	0.102358	−	0.0786987i
$689$		−	0.169732i		−	0.00646626i
$690$		0			0
$691$			35.1152i			1.33584i	0.744231	+	0.667922i	$0.232816\pi$
$691$			35.1152i			1.33584i	−0.744231	+	0.667922i	$0.767184\pi$
$692$	−1.28354	+	0.0847485i	−0.0487928	+	0.00322166i
$693$		0			0
$694$	0.512424	−	0.547374i	0.0194514	−	0.0207780i
$695$	−19.1614			−0.726833
$696$		0			0
$697$	−16.3848			−0.620620
$698$	−28.8662	−	6.72333i	−1.09260	−	0.254482i
$699$		0			0
$700$	11.8584	+	2.82734i	0.448205	+	0.106863i
$701$			8.07988i			0.305173i	0.988290	+	0.152586i	$0.0487602\pi$
$701$			8.07988i			0.305173i	−0.988290	+	0.152586i	$0.951240\pi$
$702$		0			0
$703$	−19.1717	+	11.0688i	−0.723073	+	0.417467i
$704$	46.3972	+	15.6750i	1.74866	+	0.590773i
$705$		0			0
$706$	10.1145	−	3.07086i	0.380664	−	0.115573i
$707$	34.3484	+	10.6247i	1.29180	+	0.399583i
$708$		0			0
$709$	22.0122			0.826685			0.413343	−	0.910576i	$-0.364361\pi$
$709$	22.0122			0.826685			0.413343	+	0.910576i	$0.364361\pi$
$710$	−3.19917	+	13.7355i	−0.120063	+	0.515483i
$711$		0			0
$712$	9.92284	+	26.3067i	0.371874	+	0.985884i
$713$	35.4792	−	20.4839i	1.32871	−	0.767130i
$714$		0			0
$715$	−10.4389	−	6.02692i	−0.390394	−	0.225394i
$716$	−14.7318	+	9.85375i	−0.550554	+	0.368252i
$717$		0			0
$718$	−2.15124	−	7.08554i	−0.0802835	−	0.264430i
$719$	23.6193	−	40.9097i	0.880850	−	1.52568i	0.0304516	−	0.999536i	$-0.490305\pi$
$719$	23.6193	−	40.9097i	0.880850	−	1.52568i	0.850398	−	0.526140i	$-0.176361\pi$
$720$		0			0
$721$	20.0312	−	18.5569i	0.746001	−	0.691096i
$722$	2.16368	+	0.503951i	0.0805239	+	0.0187551i
$723$		0			0
$724$	−0.266132	−	4.03063i	−0.00989071	−	0.149797i
$725$			1.06108i			0.0394074i
$726$		0			0
$727$	−6.18756	+	3.57239i	−0.229484	+	0.132493i	−0.610334	−	0.792144i	$-0.708965\pi$
$727$	−6.18756	+	3.57239i	−0.229484	+	0.132493i	0.380850	+	0.924637i	$0.375631\pi$
$728$	7.48497	−	4.95014i	0.277411	−	0.183464i
$729$		0			0
$730$	23.8938	−	7.25439i	0.884349	−	0.268497i
$731$	1.41302	−	2.44743i	0.0522625	−	0.0905213i
$732$		0			0
$733$	−2.16099	−	3.74295i	−0.0798182	−	0.138249i	0.823353	−	0.567529i	$-0.192101\pi$
$733$	−2.16099	−	3.74295i	−0.0798182	−	0.138249i	−0.903171	+	0.429280i	$0.858767\pi$
$734$	−20.7862	+	6.31088i	−0.767231	+	0.232939i
$735$		0			0
$736$	−47.4927	−	4.61988i	−1.75061	−	0.170291i
$737$	22.7723	+	13.1476i	0.838827	+	0.484297i
$738$		0			0
$739$	21.4614	−	12.3907i	0.789469	−	0.455800i	−0.0503065	−	0.998734i	$-0.516020\pi$
$739$	21.4614	−	12.3907i	0.789469	−	0.455800i	0.839776	+	0.542934i	$0.182686\pi$
$740$	−17.3760	+	1.14729i	−0.638755	+	0.0421753i
$741$		0			0
$742$	−0.00276540	+	0.529590i	−0.000101521	+	0.0194419i
$743$	−6.52841	+	11.3075i	−0.239504	+	0.414833i	−0.960572	−	0.278031i	$-0.910318\pi$
$743$	−6.52841	+	11.3075i	−0.239504	+	0.414833i	0.721068	+	0.692864i	$0.243652\pi$
$744$		0			0
$745$	−1.89813	+	3.28765i	−0.0695420	+	0.120450i
$746$	−4.33395	−	1.00943i	−0.158677	−	0.0369580i
$747$		0			0
$748$	40.7780	−	2.69246i	1.49099	−	0.0984462i
$749$	−6.28306	+	20.3124i	−0.229578	+	0.742197i
$750$		0			0
$751$	−18.0857	+	10.4418i	−0.659958	+	0.381027i	−0.792261	−	0.610182i	$-0.791096\pi$
$751$	−18.0857	+	10.4418i	−0.659958	+	0.381027i	0.132303	+	0.991209i	$0.457763\pi$
$752$	33.4268	−	4.43350i	1.21895	−	0.161673i
$753$		0			0
$754$	0.570204	+	0.533796i	0.0207656	+	0.0194397i
$755$	−33.2725			−1.21091
$756$		0			0
$757$	3.35349			0.121885			0.0609423	−	0.998141i	$-0.480589\pi$
$757$	3.35349			0.121885			0.0609423	+	0.998141i	$0.480589\pi$
$758$	22.5095	+	21.0722i	0.817581	+	0.765379i
$759$		0			0
$760$	−14.9968	−	12.2894i	−0.543990	−	0.445784i
$761$	5.25256	−	3.03257i	0.190405	−	0.109931i	−0.401767	−	0.915742i	$-0.631604\pi$
$761$	5.25256	−	3.03257i	0.190405	−	0.109931i	0.592172	+	0.805811i	$0.298270\pi$
$762$		0			0
$763$	7.75679	+	8.37305i	0.280815	+	0.303125i
$764$	−1.34653	−	20.3936i	−0.0487158	−	0.737813i
$765$		0			0
$766$	−51.1992	−	11.9250i	−1.84990	−	0.430867i
$767$	6.50154	−	11.2610i	0.234757	−	0.406611i
$768$		0			0
$769$	23.4743	−	40.6586i	0.846504	−	1.46619i	−0.0378053	−	0.999285i	$-0.512037\pi$
$769$	23.4743	−	40.6586i	0.846504	−	1.46619i	0.884309	−	0.466902i	$-0.154630\pi$
$770$	32.4730	+	18.9750i	1.17024	+	0.683813i
$771$		0			0
$772$	−0.894330	−	13.5448i	−0.0321877	−	0.487490i
$773$	24.3693	−	14.0696i	0.876502	−	0.506049i	0.00699871	−	0.999976i	$-0.497772\pi$
$773$	24.3693	−	14.0696i	0.876502	−	0.506049i	0.869504	+	0.493927i	$0.164439\pi$
$774$		0			0
$775$	−9.69013	−	5.59460i	−0.348080	−	0.200964i
$776$	−3.59846	+	21.8940i	−0.129177	+	0.785948i
$777$		0			0
$778$	33.1805	−	10.0739i	1.18958	−	0.361168i
$779$	−10.2466	−	17.7477i	−0.367123	−	0.635876i
$780$		0			0
$781$	18.5895	−	32.1980i	0.665186	−	1.15214i
$782$	−38.1008	+	11.5678i	−1.36248	+	0.413663i
$783$		0			0
$784$	−23.4350	+	15.3233i	−0.836963	+	0.547260i
$785$	14.8800	−	8.59096i	0.531089	−	0.306625i
$786$		0			0
$787$			24.8009i			0.884057i	0.897001	+	0.442028i	$0.145741\pi$
$787$			24.8009i			0.884057i	−0.897001	+	0.442028i	$0.854259\pi$
$788$	6.70746	−	0.442876i	0.238943	−	0.0157768i
$789$		0			0
$790$	−17.4214	−	4.05767i	−0.619825	−	0.144365i
$791$	5.04632	+	1.56094i	0.179426	+	0.0555005i
$792$		0			0
$793$	1.32415	−	2.29350i	0.0470221	−	0.0814446i
$794$	1.25070	+	4.11945i	0.0443858	+	0.146194i
$795$		0			0
$796$	−19.8107	−	29.6179i	−0.702172	−	1.04978i
$797$	−28.2313	−	16.2993i	−1.00000	−	0.577352i	−0.0917534	−	0.995782i	$-0.529247\pi$
$797$	−28.2313	−	16.2993i	−1.00000	−	0.577352i	−0.908249	+	0.418430i	$0.862580\pi$
$798$		0			0
$799$	24.3681	−	14.0689i	0.862081	−	0.497723i
$800$	5.39290	+	11.8643i	0.190668	+	0.419468i
$801$		0			0
$802$	8.23481	−	35.3557i	0.290781	−	1.24845i
$803$	−65.8288			−2.32305
$804$		0			0
$805$	−35.0088	−	10.8290i	−1.23390	−	0.381672i
$806$	−7.88126	+	2.39283i	−0.277605	+	0.0842837i
$807$		0			0
$808$	13.5653	+	35.9632i	0.477224	+	1.26518i
$809$	−20.9030	+	12.0684i	−0.734910	+	0.424301i	−0.820216	−	0.572054i	$-0.806147\pi$
$809$	−20.9030	+	12.0684i	−0.734910	+	0.424301i	0.0853056	+	0.996355i	$0.472813\pi$
$810$		0			0
$811$			18.3292i			0.643626i	0.946803	+	0.321813i	$0.104292\pi$
$811$			18.3292i			0.643626i	−0.946803	+	0.321813i	$0.895708\pi$
$812$	−1.77043	−	1.67482i	−0.0621299	−	0.0587747i
$813$		0			0
$814$	44.7102	+	10.4136i	1.56709	+	0.364997i
$815$	−11.7632			−0.412046
$816$		0			0
$817$	3.53466			0.123662
$818$	27.9549	−	29.8615i	0.977420	−	1.04408i
$819$		0			0
$820$	−1.06207	−	16.0854i	−0.0370893	−	0.561726i
$821$		−	23.0043i		−	0.802856i	−0.915891	−	0.401428i	$-0.868514\pi$
$821$		−	23.0043i		−	0.802856i	0.915891	−	0.401428i	$-0.131486\pi$
$822$		0			0
$823$		−	41.6607i		−	1.45220i	−0.687590	−	0.726100i	$-0.741331\pi$
$823$		−	41.6607i		−	1.45220i	0.687590	−	0.726100i	$-0.258669\pi$
$824$	28.8047	+	4.73429i	1.00346	+	0.164927i
$825$		0			0
$826$	−20.4693	+	35.0302i	−0.712218	+	1.21886i
$827$	25.0154			0.869870			0.434935	−	0.900462i	$-0.356771\pi$
$827$	25.0154			0.869870			0.434935	+	0.900462i	$0.356771\pi$
$828$		0			0
$829$	12.3769	+	21.4374i	0.429867	+	0.744551i	0.996861	−	0.0791705i	$-0.0252272\pi$
$829$	12.3769	+	21.4374i	0.429867	+	0.744551i	−0.566994	+	0.823722i	$0.691894\pi$
$830$	−9.78949	+	2.97218i	−0.339798	+	0.103166i
$831$		0			0
$832$	9.08870	+	3.07055i	0.315094	+	0.106452i
$833$	−13.1924	+	19.2844i	−0.457090	+	0.668164i
$834$		0			0
$835$			13.0294i			0.450900i
$836$	28.4178	+	42.4860i	0.982851	+	1.46941i
$837$		0			0
$838$	15.2815	+	50.3328i	0.527892	+	1.73872i
$839$	−2.67610	−	4.63515i	−0.0923894	−	0.160023i	0.816127	−	0.577873i	$-0.196117\pi$
$839$	−2.67610	−	4.63515i	−0.0923894	−	0.160023i	−0.908516	+	0.417850i	$0.862784\pi$
$840$		0			0
$841$	−14.3939	+	24.9310i	−0.496343	+	0.859691i
$842$	−4.80111	−	1.11824i	−0.165457	−	0.0385372i
$843$		0			0
$844$	16.4123	−	33.3212i	0.564933	−	1.14696i
$845$	16.4413	+	9.49238i	0.565597	+	0.326548i
$846$		0			0
$847$	−47.6034	−	51.3853i	−1.63567	−	1.76562i
$848$	−0.448835	+	0.345091i	−0.0154131	+	0.0118505i
$849$		0			0
$850$	7.93920	+	7.43228i	0.272312	+	0.254925i
$851$	−44.7290			−1.53329
$852$		0			0
$853$	24.9004	+	43.1287i	0.852572	+	1.47670i	0.878880	+	0.477044i	$0.158292\pi$
$853$	24.9004	+	43.1287i	0.852572	+	1.47670i	−0.0263077	+	0.999654i	$0.508375\pi$
$854$	−4.16894	+	7.13452i	−0.142658	+	0.244138i
$855$		0			0
$856$	−21.2673	+	8.02199i	−0.726901	+	0.274186i
$857$	12.3858	+	7.15093i	0.423090	+	0.244271i	0.696398	−	0.717655i	$-0.254785\pi$
$857$	12.3858	+	7.15093i	0.423090	+	0.244271i	−0.273309	+	0.961926i	$0.588118\pi$
$858$		0			0
$859$	−10.1764	+	5.87537i	−0.347215	+	0.200465i	−0.663458	−	0.748213i	$-0.730912\pi$
$859$	−10.1764	+	5.87537i	−0.347215	+	0.200465i	0.316243	+	0.948678i	$0.397579\pi$
$860$	2.49429	+	1.22855i	0.0850545	+	0.0418933i
$861$		0			0
$862$	−13.5049	−	3.14547i	−0.459978	−	0.107135i
$863$	6.55720	−	11.3574i	0.223210	−	0.386610i	−0.732571	−	0.680690i	$-0.761680\pi$
$863$	6.55720	−	11.3574i	0.223210	−	0.386610i	0.955781	+	0.294080i	$0.0950132\pi$
$864$		0			0
$865$	−0.528039	−	0.914590i	−0.0179538	−	0.0310970i
$866$	9.25822	−	9.88968i	0.314607	−	0.336065i
$867$		0			0
$868$	24.6298	−	7.33760i	0.835989	−	0.249054i
$869$	40.8384	+	23.5780i	1.38535	+	0.799830i
$870$		0			0
$871$	4.46083	+	2.57546i	0.151149	+	0.0872662i
$872$	−1.97894	+	12.0404i	−0.0670152	+	0.407738i
$873$		0			0
$874$	−36.3571	−	34.0357i	−1.22980	−	1.15128i
$875$	7.03627	+	30.9402i	0.237869	+	1.04597i
$876$		0			0
$877$	4.35294	+	7.53951i	0.146988	+	0.254591i	0.930113	−	0.367273i	$-0.119709\pi$
$877$	4.35294	+	7.53951i	0.146988	+	0.254591i	−0.783125	+	0.621865i	$0.786375\pi$
$878$	−21.0010	−	19.6601i	−0.708751	−	0.663497i
$879$		0			0
$880$	5.28651	+	39.8582i	0.178208	+	1.34362i
$881$			3.18544i			0.107320i	0.998559	+	0.0536601i	$0.0170888\pi$
$881$			3.18544i			0.107320i	−0.998559	+	0.0536601i	$0.982911\pi$
$882$		0			0
$883$			47.5039i			1.59863i	0.600911	+	0.799316i	$0.294805\pi$
$883$			47.5039i			1.59863i	−0.600911	+	0.799316i	$0.705195\pi$
$884$	7.98796	−	0.527423i	0.268664	−	0.0177392i
$885$		0			0
$886$	−8.56224	+	9.14623i	−0.287654	+	0.307274i
$887$	5.97980	+	10.3573i	0.200782	+	0.347764i	0.948781	−	0.315936i	$-0.102318\pi$
$887$	5.97980	+	10.3573i	0.200782	+	0.347764i	−0.747999	+	0.663700i	$0.768985\pi$
$888$		0			0
$889$	−0.512543	−	2.25378i	−0.0171901	−	0.0755893i
$890$	−15.7754	+	16.8513i	−0.528792	+	0.564858i
$891$		0			0
$892$	14.6995	+	21.9764i	0.492174	+	0.735823i
$893$	30.4782	+	17.5966i	1.01992	+	0.588848i
$894$		0			0
$895$	−12.6015	−	7.27549i	−0.421222	−	0.243193i
$896$	−28.3082	−	9.72870i	−0.945710	−	0.325013i
$897$		0			0
$898$	30.5968	+	28.6432i	1.02103	+	0.955835i
$899$	1.11843	+	1.93718i	0.0373018	+	0.0646087i
$900$		0			0
$901$	−0.236222	+	0.409149i	−0.00786971	+	0.0136307i
$902$	−9.64013	+	41.3893i	−0.320981	+	1.37811i
$903$		0			0
$904$	1.99295	+	5.28356i	0.0662845	+	0.175728i
$905$	2.87204	−	1.65818i	0.0954700	−	0.0551196i
$906$		0			0
$907$	29.0510	+	16.7726i	0.964623	+	0.556925i	0.897593	−	0.440826i	$-0.145314\pi$
$907$	29.0510	+	16.7726i	0.964623	+	0.556925i	0.0670301	+	0.997751i	$0.478648\pi$
$908$	5.90889	+	2.91040i	0.196093	+	0.0965852i
$909$		0			0
$910$	6.36109	+	3.71700i	0.210868	+	0.123217i
$911$	−19.6281	−	33.9969i	−0.650309	−	1.12637i	−0.983048	−	0.183349i	$-0.941306\pi$
$911$	−19.6281	−	33.9969i	−0.650309	−	1.12637i	0.332739	−	0.943019i	$-0.392027\pi$
$912$		0			0
$913$	26.9706			0.892597
$914$	1.28987	−	1.37785i	0.0426652	−	0.0455752i
$915$		0			0
$916$	43.2353	−	28.9190i	1.42853	−	0.955512i
$917$	−3.80891	−	4.11152i	−0.125781	−	0.135774i
$918$		0			0
$919$	25.8613	+	14.9310i	0.853087	+	0.492530i	0.861691	−	0.507433i	$-0.169406\pi$
$919$	25.8613	+	14.9310i	0.853087	+	0.492530i	−0.00860439	+	0.999963i	$0.502739\pi$
$920$	−13.8261	−	36.6546i	−0.455832	−	1.20847i
$921$		0			0
$922$	−0.698450	+	2.99875i	−0.0230022	+	0.0987587i
$923$	3.64148	−	6.30723i	0.119861	−	0.207605i
$924$		0			0
$925$	6.10822	+	10.5797i	0.200837	+	0.347860i
$926$	32.4814	−	9.86167i	1.06740	−	0.324074i
$927$		0			0
$928$	0.252247	−	2.59313i	0.00828043	−	0.0851235i
$929$			6.07975i			0.199470i	0.995014	+	0.0997350i	$0.0317995\pi$
$929$			6.07975i			0.199470i	−0.995014	+	0.0997350i	$0.968200\pi$
$930$		0			0
$931$	−29.1385	−	2.22979i	−0.954977	−	0.0730786i
$932$	−23.9204	+	48.5648i	−0.783540	+	1.59079i
$933$		0			0
$934$	−13.2665	−	43.6959i	−0.434093	−	1.42977i
$935$	16.7758	+	29.0566i	0.548628	+	0.950251i
$936$		0			0
$937$	20.7870			0.679083			0.339542	−	0.940591i	$-0.389728\pi$
$937$	20.7870			0.679083			0.339542	+	0.940591i	$0.389728\pi$
$938$	−13.8765	−	8.10853i	−0.453085	−	0.264753i
$939$		0			0
$940$	15.3913	+	23.0108i	0.502010	+	0.750528i
$941$		−	47.7302i		−	1.55596i	−0.628289	−	0.777980i	$-0.716244\pi$
$941$		−	47.7302i		−	1.55596i	0.628289	−	0.777980i	$-0.283756\pi$
$942$		0			0
$943$		−	41.4067i		−	1.34839i
$944$	−42.9970	+	5.70281i	−1.39943	+	0.185611i
$945$		0			0
$946$	−5.35102	−	5.00936i	−0.173977	−	0.162868i
$947$	−13.0641			−0.424526			−0.212263	−	0.977213i	$-0.568083\pi$
$947$	−13.0641			−0.424526			−0.212263	+	0.977213i	$0.568083\pi$
$948$		0			0
$949$	−12.8951			−0.418593
$950$	−3.08552	+	13.2475i	−0.100107	+	0.429805i
$951$		0			0
$952$	−24.9323	+	1.51550i	−0.808060	+	0.0491176i
$953$			12.2141i			0.395653i	0.980237	+	0.197827i	$0.0633883\pi$
$953$			12.2141i			0.395653i	−0.980237	+	0.197827i	$0.936612\pi$
$954$		0			0
$955$	14.5315	−	8.38977i	0.470229	−	0.271487i
$956$	12.0776	+	5.94877i	0.390617	+	0.192397i
$957$		0			0
$958$	−6.97509	−	22.9739i	−0.225355	−	0.742252i
$959$	14.5510	+	4.50094i	0.469876	+	0.145343i
$960$		0			0
$961$	7.41193			0.239094
$962$	8.75823	+	2.03991i	0.282377	+	0.0657693i
$963$		0			0
$964$	0.518959	+	0.255612i	0.0167146	+	0.00823270i
$965$	9.65144	−	5.57226i	0.310691	−	0.179377i
$966$		0			0
$967$	−28.7435	−	16.5951i	−0.924330	−	0.533662i	−0.0393162	−	0.999227i	$-0.512518\pi$
$967$	−28.7435	−	16.5951i	−0.924330	−	0.533662i	−0.885014	+	0.465565i	$0.845851\pi$
$968$	12.1447	−	73.8916i	0.390346	−	2.37497i
$969$		0			0
$970$	−17.4304	+	5.29205i	−0.559658	+	0.169918i
$971$	11.8551	−	20.5337i	0.380449	−	0.658957i	−0.610678	−	0.791879i	$-0.709103\pi$
$971$	11.8551	−	20.5337i	0.380449	−	0.658957i	0.991126	+	0.132923i	$0.0424362\pi$
$972$		0			0
$973$	−29.4959	−	9.12372i	−0.945595	−	0.292493i
$974$	12.1088	−	51.9884i	0.387991	−	1.66582i
$975$		0			0
$976$	−8.75710	+	1.16148i	−0.280308	+	0.0371781i
$977$		−	47.2616i		−	1.51203i	−0.654552	−	0.756017i	$-0.727143\pi$
$977$		−	47.2616i		−	1.51203i	0.654552	−	0.756017i	$-0.272857\pi$
$978$		0			0
$979$	52.6998	−	30.4263i	1.68429	−	0.972427i
$980$	−19.7870	−	11.7013i	−0.632074	−	0.373783i
$981$		0			0
$982$	0.0641196	+	0.211191i	0.00204614	+	0.00673937i
$983$	28.1689	−	48.7899i	0.898447	−	1.55616i	0.0689683	−	0.997619i	$-0.478029\pi$
$983$	28.1689	−	48.7899i	0.898447	−	1.55616i	0.829479	−	0.558538i	$-0.188637\pi$
$984$		0			0
$985$	2.75940	+	4.77943i	0.0879219	+	0.152285i
$986$	−0.631607	−	2.08032i	−0.0201145	−	0.0662510i
$987$		0			0
$988$	5.56673	+	8.32252i	0.177101	+	0.264775i
$989$	6.18497	+	3.57090i	0.196671	+	0.113548i
$990$		0			0
$991$	−25.7259	+	14.8529i	−0.817211	+	0.471817i	−0.849454	−	0.527663i	$-0.823068\pi$
$991$	−25.7259	+	14.8529i	−0.817211	+	0.471817i	0.0322431	+	0.999480i	$0.489735\pi$
$992$	22.3514	+	15.9761i	0.709657	+	0.507240i
$993$		0			0
$994$	−11.4648	+	19.6203i	−0.363641	+	0.622317i
$995$	14.6272	−	25.3350i	0.463713	−	0.803174i
$996$		0			0
$997$	29.7416	−	51.5140i	0.941927	−	1.63146i	0.180136	−	0.983642i	$-0.442346\pi$
$997$	29.7416	−	51.5140i	0.941927	−	1.63146i	0.761791	−	0.647823i	$-0.224320\pi$
$998$	−11.3439	+	48.7042i	−0.359083	+	1.54170i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.12		88
3.2	odd	2		252.2.bb.a.23.33	yes	88
4.3	odd	2	inner	756.2.bb.a.611.33		88
7.4	even	3		756.2.o.a.179.18		88
9.2	odd	6		756.2.o.a.359.4		88
9.7	even	3		252.2.o.a.191.41	yes	88
12.11	even	2		252.2.bb.a.23.12	yes	88
21.11	odd	6		252.2.o.a.95.27	✓	88
28.11	odd	6		756.2.o.a.179.4		88
36.7	odd	6		252.2.o.a.191.27	yes	88
36.11	even	6		756.2.o.a.359.18		88
63.11	odd	6	inner	756.2.bb.a.683.33		88
63.25	even	3		252.2.bb.a.11.12	yes	88
84.11	even	6		252.2.o.a.95.41	yes	88
252.11	even	6	inner	756.2.bb.a.683.12		88
252.151	odd	6		252.2.bb.a.11.33	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.27	✓	88	21.11	odd	6
252.2.o.a.95.41	yes	88	84.11	even	6
252.2.o.a.191.27	yes	88	36.7	odd	6
252.2.o.a.191.41	yes	88	9.7	even	3
252.2.bb.a.11.12	yes	88	63.25	even	3
252.2.bb.a.11.33	yes	88	252.151	odd	6
252.2.bb.a.23.12	yes	88	12.11	even	2
252.2.bb.a.23.33	yes	88	3.2	odd	2
756.2.o.a.179.4		88	28.11	odd	6
756.2.o.a.179.18		88	7.4	even	3
756.2.o.a.359.4		88	9.2	odd	6
756.2.o.a.359.18		88	36.11	even	6
756.2.bb.a.611.12		88	1.1	even	1	trivial
756.2.bb.a.611.33		88	4.3	odd	2	inner
756.2.bb.a.683.12		88	252.11	even	6	inner
756.2.bb.a.683.33		88	63.11	odd	6	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.966497 + 1.03242i) q^{2} +(-0.131768 - 1.99565i) q^{4} +(1.42201 - 0.820999i) q^{5} +(2.57988 - 0.586703i) q^{7} +(2.18770 + 1.79275i) q^{8} +O(q^{10})\)	\(q+(-0.966497 + 1.03242i) q^{2} +(-0.131768 - 1.99565i) q^{4} +(1.42201 - 0.820999i) q^{5} +(2.57988 - 0.586703i) q^{7} +(2.18770 + 1.79275i) q^{8} +(-0.526757 + 2.26160i) q^{10} +(3.06085 - 5.30154i) q^{11} +(0.599586 - 1.03851i) q^{13} +(-1.88772 + 3.23056i) q^{14} +(-3.96527 + 0.525926i) q^{16} +(-2.89068 + 1.66893i) q^{17} +(-3.61550 - 2.08741i) q^{19} +(-1.82581 - 2.72966i) q^{20} +(2.51510 + 8.28399i) q^{22} +(-4.21762 - 7.30513i) q^{23} +(-1.15192 + 1.99519i) q^{25} +(0.492680 + 1.62274i) q^{26} +(-1.51080 - 5.07124i) q^{28} +(0.398864 - 0.230284i) q^{29} +4.85676i q^{31} +(3.28945 - 4.60212i) q^{32} +(1.07080 - 4.59740i) q^{34} +(3.18694 - 2.95238i) q^{35} +(2.65132 - 4.59222i) q^{37} +(5.64944 - 1.71523i) q^{38} +(4.58279 + 0.753219i) q^{40} +(4.25113 + 2.45439i) q^{41} +(-0.733230 + 0.423331i) q^{43} +(-10.9834 - 5.40982i) q^{44} +(11.6183 + 2.70605i) q^{46} -8.42989 q^{47} +(6.31156 - 3.02725i) q^{49} +(-0.946535 - 3.11760i) q^{50} +(-2.15152 - 1.05972i) q^{52} +(0.122578 - 0.0707704i) q^{53} -10.0518i q^{55} +(6.69582 + 3.34156i) q^{56} +(-0.147751 + 0.634362i) q^{58} +10.8434 q^{59} +2.20845 q^{61} +(-5.01419 - 4.69404i) q^{62} +(1.57206 + 7.84402i) q^{64} -1.96904i q^{65} +4.29540i q^{67} +(3.71151 + 5.54888i) q^{68} +(-0.0320811 + 6.14371i) q^{70} +6.07333 q^{71} +(-5.37668 - 9.31269i) q^{73} +(2.17859 + 7.17563i) q^{74} +(-3.68934 + 7.49034i) q^{76} +(4.78619 - 15.4732i) q^{77} +7.70311i q^{79} +(-5.20688 + 4.00336i) q^{80} +(-6.64265 + 2.01677i) q^{82} +(2.20287 + 3.81549i) q^{83} +(-2.74039 + 4.74649i) q^{85} +(0.271611 - 1.16615i) q^{86} +(16.2006 - 6.11084i) q^{88} +(8.60870 + 4.97023i) q^{89} +(0.937560 - 3.03102i) q^{91} +(-14.0228 + 9.37949i) q^{92} +(8.14746 - 8.70315i) q^{94} -6.85504 q^{95} +(3.92227 + 6.79358i) q^{97} +(-2.97472 + 9.44198i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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