LMFDB - Embedded newform 756.2.bb.a.611.33

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			611.33
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.966497 + 1.03242i) q^{2} +(-0.131768 + 1.99565i) q^{4} +(1.42201 - 0.820999i) q^{5} +(-2.57988 + 0.586703i) q^{7} +(-2.18770 + 1.79275i) q^{8} +O(q^{10})$	\(q+(0.966497 + 1.03242i) q^{2} +(-0.131768 + 1.99565i) q^{4} +(1.42201 - 0.820999i) q^{5} +(-2.57988 + 0.586703i) q^{7} +(-2.18770 + 1.79275i) q^{8} +(2.22198 + 0.674616i) q^{10} +(-3.06085 + 5.30154i) q^{11} +(0.599586 - 1.03851i) q^{13} +(-3.09917 - 2.09646i) q^{14} +(-3.96527 - 0.525926i) q^{16} +(-2.89068 + 1.66893i) q^{17} +(3.61550 + 2.08741i) q^{19} +(1.45106 + 2.94603i) q^{20} +(-8.43170 + 1.96386i) q^{22} +(4.21762 + 7.30513i) q^{23} +(-1.15192 + 1.99519i) q^{25} +(1.65168 - 0.384697i) q^{26} +(-0.830912 - 5.22586i) q^{28} +(0.398864 - 0.230284i) q^{29} -4.85676i q^{31} +(-3.28945 - 4.60212i) q^{32} +(-4.51687 - 1.37136i) q^{34} +(-3.18694 + 2.95238i) q^{35} +(2.65132 - 4.59222i) q^{37} +(1.33929 + 5.75017i) q^{38} +(-1.63909 + 4.34542i) q^{40} +(4.25113 + 2.45439i) q^{41} +(0.733230 - 0.423331i) q^{43} +(-10.1767 - 6.80697i) q^{44} +(-3.46562 + 11.4147i) q^{46} +8.42989 q^{47} +(6.31156 - 3.02725i) q^{49} +(-3.17319 + 0.739078i) q^{50} +(1.99351 + 1.33341i) q^{52} +(0.122578 - 0.0707704i) q^{53} +10.0518i q^{55} +(4.59219 - 5.90862i) q^{56} +(0.623249 + 0.189225i) q^{58} -10.8434 q^{59} +2.20845 q^{61} +(5.01419 - 4.69404i) q^{62} +(1.57206 - 7.84402i) q^{64} -1.96904i q^{65} -4.29540i q^{67} +(-2.94972 - 5.98871i) q^{68} +(-6.12825 - 0.436783i) q^{70} -6.07333 q^{71} +(-5.37668 - 9.31269i) q^{73} +(7.30357 - 1.70110i) q^{74} +(-4.64215 + 6.94023i) q^{76} +(4.78619 - 15.4732i) q^{77} -7.70311i q^{79} +(-6.07045 + 2.50761i) q^{80} +(1.57475 + 6.76109i) q^{82} +(-2.20287 - 3.81549i) q^{83} +(-2.74039 + 4.74649i) q^{85} +(1.14572 + 0.347851i) q^{86} +(-2.80815 - 17.0855i) q^{88} +(8.60870 + 4.97023i) q^{89} +(-0.937560 + 3.03102i) q^{91} +(-15.1343 + 7.45433i) q^{92} +(8.14746 + 8.70315i) q^{94} +6.85504 q^{95} +(3.92227 + 6.79358i) q^{97} +(9.22548 + 3.59033i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$10$	2.22198	+	0.674616i	0.702653	+	0.213332i
$11$	−3.06085	+	5.30154i	−0.922880	+	1.59848i	−0.127945	+	0.991781i	$0.540838\pi$
$11$	−3.06085	+	5.30154i	−0.922880	+	1.59848i	−0.794935	+	0.606694i	$0.792495\pi$
$12$		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	$0.113486\pi$
$14$	−3.09917	−	2.09646i	−0.828287	−	0.560303i
$15$		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	0.853665	−	0.520823i	$-0.174375\pi$
$19$	3.61550	+	2.08741i	0.829452	+	0.478884i	−0.0242130	+	0.999707i	$0.507708\pi$
$20$	1.45106	+	2.94603i	0.324466	+	0.658751i
$21$		0			0
$22$	−8.43170	+	1.96386i	−1.79764	+	0.418695i
$23$	4.21762	+	7.30513i	0.879434	+	1.52323i	0.851963	+	0.523603i	$0.175412\pi$
$23$	4.21762	+	7.30513i	0.879434	+	1.52323i	0.0274717	+	0.999623i	$0.491254\pi$
$24$		0			0
$25$	−1.15192	+	1.99519i	−0.230384	+	0.399037i
$26$	1.65168	−	0.384697i	0.323920	−	0.0754453i
$27$		0			0
$28$	−0.830912	−	5.22586i	−0.157028	−	0.987594i
$29$	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	$-0.856342\pi$
$31$		−	4.85676i		−	0.872299i	0.899874	−	0.436150i	$-0.143658\pi$
$32$	−3.28945	−	4.60212i	−0.581498	−	0.813548i
$33$		0			0
$34$	−4.51687	−	1.37136i	−0.774636	−	0.235187i
$35$	−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	$0.0231060\pi$
$38$	1.33929	+	5.75017i	0.217262	+	0.932801i
$39$		0			0
$40$	−1.63909	+	4.34542i	−0.259162	+	0.687071i
$41$	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	−0.443049	−	0.896498i	$-0.646103\pi$
$43$	0.733230	−	0.423331i	0.111817	−	0.0645573i	0.554865	+	0.831940i	$0.312770\pi$
$44$	−10.1767	−	6.80697i	−1.53420	−	1.02619i
$45$		0			0
$46$	−3.46562	+	11.4147i	−0.510978	+	1.68301i
$47$	8.42989			1.22963			0.614813	−	0.788673i	$-0.289232\pi$
$47$	8.42989			1.22963			0.614813	+	0.788673i	$0.289232\pi$
$48$		0			0
$49$	6.31156	−	3.02725i	0.901651	−	0.432464i
$50$	−3.17319	+	0.739078i	−0.448757	+	0.104521i
$51$		0			0
$52$	1.99351	+	1.33341i	0.276450	+	0.184910i
$53$	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
$56$	4.59219	−	5.90862i	0.613657	−	0.789573i
$57$		0			0
$58$	0.623249	+	0.189225i	0.0818367	+	0.0248464i
$59$	−10.8434			−1.41169			−0.705844	−	0.708367i	$-0.749432\pi$
$59$	−10.8434			−1.41169			−0.705844	+	0.708367i	$0.749432\pi$
$60$		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	$-0.915491\pi$
$67$		−	4.29540i		−	0.524767i	0.964964	−	0.262384i	$-0.0845085\pi$
$68$	−2.94972	−	5.98871i	−0.357706	−	0.726237i
$69$		0			0
$70$	−6.12825	−	0.436783i	−0.732466	−	0.0522055i
$71$	−6.07333			−0.720772			−0.360386	−	0.932803i	$-0.617355\pi$
$71$	−6.07333			−0.720772			−0.360386	+	0.932803i	$0.617355\pi$
$72$		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	$-0.383322\pi$
$74$	7.30357	−	1.70110i	0.849023	−	0.197749i
$75$		0			0
$76$	−4.64215	+	6.94023i	−0.532491	+	0.796099i
$77$	4.78619	−	15.4732i	0.545436	−	1.76333i
$78$		0			0
$79$		−	7.70311i		−	0.866668i	−0.901233	−	0.433334i	$-0.857337\pi$
$79$		−	7.70311i		−	0.866668i	0.901233	−	0.433334i	$-0.142663\pi$
$80$	−6.07045	+	2.50761i	−0.678697	+	0.280360i
$81$		0			0
$82$	1.57475	+	6.76109i	0.173902	+	0.746638i
$83$	−2.20287	−	3.81549i	−0.241797	−	0.418804i	0.719430	−	0.694565i	$-0.244403\pi$
$83$	−2.20287	−	3.81549i	−0.241797	−	0.418804i	−0.961226	+	0.275762i	$0.911070\pi$
$84$		0			0
$85$	−2.74039	+	4.74649i	−0.297237	+	0.514829i
$86$	1.14572	+	0.347851i	0.123546	+	0.0375098i
$87$		0			0
$88$	−2.80815	−	17.0855i	−0.299350	−	1.82132i
$89$	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
$92$	−15.1343	+	7.45433i	−1.57786	+	0.777168i
$93$		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	$0.702952\pi$
$98$	9.22548	+	3.59033i	0.931914	+	0.362678i
$99$		0			0
$100$	−3.82992	−	2.56174i	−0.382992	−	0.256174i
$101$	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	−0.870883	−	0.491491i	$-0.836452\pi$
$103$	−8.93793	+	5.16032i	−0.880681	+	0.508461i	−0.00979785	+	0.999952i	$0.503119\pi$
$104$	0.550085	+	3.34686i	0.0539403	+	0.328187i
$105$		0			0
$106$	0.191536	+	0.0581521i	0.0186036	+	0.00564823i
$107$	4.01812	−	6.95959i	0.388446	−	0.672809i	−0.603794	−	0.797140i	$-0.706345\pi$
$107$	4.01812	−	6.95959i	0.388446	−	0.672809i	0.992241	+	0.124331i	$0.0396785\pi$
$108$		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
$112$	10.5385	−	0.969614i	0.995794	−	0.0916199i
$113$	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
$116$	0.407010	+	0.826338i	0.0377899	+	0.0767236i
$117$		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	$0.0123407\pi$
$127$			0.873599i			0.0775193i	−0.999249	+	0.0387597i	$0.987659\pi$
$128$	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	0.908580	−	0.417711i	$-0.137168\pi$
$131$	1.05918	+	1.83456i	0.0925413	+	0.160286i	−0.816039	+	0.577998i	$0.803834\pi$
$132$		0			0
$133$	−10.5522	−	3.26404i	−0.914995	−	0.283028i
$134$	4.43465	−	4.15149i	0.383095	−	0.358634i
$135$		0			0
$136$	3.33195	−	8.83340i	0.285712	−	0.757458i
$137$	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	0.863071	−	0.505083i	$-0.168538\pi$
$139$	10.1061	+	5.83478i	0.857191	+	0.494899i	−0.00587973	+	0.999983i	$0.501872\pi$
$140$	−5.47199	−	6.74905i	−0.462468	−	0.570399i
$141$		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
$146$	4.41803	−	14.5517i	0.365638	−	1.20430i
$147$		0			0
$148$	8.81512	+	5.89622i	0.724599	+	0.484667i
$149$	−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	0.996970	−	0.0777891i	$-0.0247861\pi$
$151$	17.5486	+	10.1317i	1.42809	+	0.824507i	0.431118	+	0.902296i	$0.358119\pi$
$152$	−11.6518	+	1.91508i	−0.945089	+	0.155333i
$153$		0			0
$154$	20.6006	−	10.0134i	1.66004	−	0.806904i
$155$	−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
$160$	−8.45598	−	3.84364i	−0.668504	−	0.303866i
$161$	−15.1669	−	16.3719i	−1.19532	−	1.29028i
$162$		0			0
$163$	6.20415	+	3.58197i	0.485946	+	0.280561i	0.722891	−	0.690962i	$-0.242813\pi$
$163$	6.20415	+	3.58197i	0.485946	+	0.280561i	−0.236945	+	0.971523i	$0.576146\pi$
$164$	−5.45827	+	8.16037i	−0.426220	+	0.637218i
$165$		0			0
$166$	1.81010	−	5.96194i	0.140491	−	0.462736i
$167$	3.96753	−	6.87197i	0.307017	−	0.531769i	−0.670691	−	0.741736i	$-0.734003\pi$
$167$	3.96753	−	6.87197i	0.307017	−	0.531769i	0.977708	+	0.209968i	$0.0673358\pi$
$168$		0			0
$169$	5.78099	+	10.0130i	0.444692	+	0.770229i
$170$	−7.54893	+	1.75825i	−0.578976	+	0.134851i
$171$		0			0
$172$	0.748206	+	1.51906i	0.0570502	+	0.115827i
$173$		−	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
$176$	14.9253	−	19.4123i	1.12504	−	1.46326i
$177$		0			0
$178$	3.18893	+	13.6915i	0.239020	+	1.02622i
$179$	4.43088	+	7.67450i	0.331179	+	0.573619i	0.982743	−	0.184974i	$-0.0592202\pi$
$179$	4.43088	+	7.67450i	0.331179	+	0.573619i	−0.651564	+	0.758594i	$0.725887\pi$
$180$		0			0
$181$	2.01970			0.150123			0.0750617	−	0.997179i	$-0.476085\pi$
$181$	2.01970			0.150123			0.0750617	+	0.997179i	$0.476085\pi$
$182$	−4.03542	+	1.96152i	−0.299125	+	0.145397i
$183$		0			0
$184$	−22.3232	−	8.42028i	−1.64569	−	0.620751i
$185$		−	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	$-0.620543\pi$
$191$	−10.2190			−0.739419			−0.369710	+	0.929147i	$0.620543\pi$
$192$		0			0
$193$	6.78717			0.488551			0.244276	−	0.969706i	$-0.421450\pi$
$193$	6.78717			0.488551			0.244276	+	0.969706i	$0.421450\pi$
$194$	−3.22294	+	10.6154i	−0.231393	+	0.762141i
$195$		0			0
$196$	5.20968	+	12.9946i	0.372120	+	0.928185i
$197$			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	−0.934575	−	0.355766i	$-0.884220\pi$
$199$	−15.4294	+	8.90816i	−1.09376	+	0.631482i	−0.159185	+	0.987249i	$0.550887\pi$
$200$	−1.05682	−	6.42998i	−0.0747285	−	0.454668i
$201$		0			0
$202$	4.35950	+	18.7173i	0.306734	+	1.31694i
$203$	−0.893912	+	0.828120i	−0.0627403	+	0.0581226i
$204$		0			0
$205$	8.06020			0.562949
$206$	−13.9661	−	4.24024i	−0.973063	−	0.295431i
$207$		0			0
$208$	−2.92370	+	3.80265i	−0.202722	+	0.263666i
$209$	−22.1330	+	12.7785i	−1.53097	+	0.883906i
$210$		0			0
$211$	−16.0838	−	9.28596i	−1.10725	−	0.639272i	−0.169136	−	0.985593i	$-0.554098\pi$
$211$	−16.0838	−	9.28596i	−1.10725	−	0.639272i	−0.938116	+	0.346321i	$0.887431\pi$
$212$	0.125082	+	0.253949i	0.00859063	+	0.0174413i
$213$		0			0
$214$	11.0687	−	2.57805i	0.756641	−	0.176232i
$215$	0.695108	−	1.20396i	0.0474060	−	0.0821096i
$216$		0			0
$217$	2.84947	+	12.5298i	0.193435	+	0.850581i
$218$	−1.77242	+	5.83782i	−0.120043	+	0.395387i
$219$		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	−0.0650278	−	0.997883i	$-0.520714\pi$
$223$	11.4485	−	6.60982i	0.766651	−	0.442626i	0.831679	+	0.555257i	$0.187380\pi$
$224$	11.1865	+	9.94299i	0.747427	+	0.664344i
$225$		0			0
$226$	0.640480	+	2.74986i	0.0426041	+	0.182918i
$227$	1.64669	−	2.85215i	0.109295	−	0.189304i	−0.806190	−	0.591657i	$-0.798474\pi$
$227$	1.64669	−	2.85215i	0.109295	−	0.189304i	0.915485	+	0.402353i	$0.131807\pi$
$228$		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	$0.504222\pi$
$230$	4.44332	+	19.0772i	0.292984	+	1.25791i
$231$		0			0
$232$	−0.459751	+	1.21886i	−0.0301841	+	0.0800219i
$233$	−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
$238$	12.4576	+	0.887896i	0.807503	+	0.0575537i
$239$	3.36578	−	5.82971i	0.217714	−	0.377092i	−0.736394	−	0.676552i	$-0.763473\pi$
$239$	3.36578	−	5.82971i	0.217714	−	0.377092i	0.954109	+	0.299460i	$0.0968065\pi$
$240$		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	$0.169632\pi$
$242$	10.8773	−	35.8267i	0.699221	−	2.30303i
$243$		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	$-0.308294\pi$
$251$	17.9504			1.13302			0.566509	+	0.824056i	$0.308294\pi$
$252$		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
$262$	−0.870332	+	2.86661i	−0.0537693	+	0.177100i
$263$	−9.11697	+	15.7911i	−0.562177	+	0.973719i	0.435129	+	0.900368i	$0.356703\pi$
$263$	−9.11697	+	15.7911i	−0.562177	+	0.973719i	−0.997306	+	0.0733507i	$0.976631\pi$
$264$		0			0
$265$	0.116205	−	0.201273i	0.00713841	−	0.0123641i
$266$	−6.82886	−	14.0490i	−0.418704	−	0.861399i
$267$		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	−0.287223	−	0.957864i	$-0.592732\pi$
$271$	−20.7483	−	11.9790i	−1.26037	−	0.727674i	−0.973146	+	0.230190i	$0.926065\pi$
$272$	12.3401	−	5.09750i	0.748227	−	0.309081i
$273$		0			0
$274$	1.84681	+	7.92919i	0.111570	+	0.479020i
$275$	−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	$0.254862\pi$
$278$	3.74362	+	16.0730i	0.224528	+	0.963996i
$279$		0			0
$280$	1.67917	−	12.1723i	0.100350	−	0.727435i
$281$	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	$-0.894235\pi$
$283$		−	10.9747i		−	0.652380i	0.945304	−	0.326190i	$-0.105765\pi$
$284$	0.800270	−	12.1203i	0.0474873	−	0.719206i
$285$		0			0
$286$	−3.01604	+	9.93393i	−0.178342	+	0.587405i
$287$	−12.4074	−	3.83788i	−0.732385	−	0.226543i
$288$		0			0
$289$	−2.92932	+	5.07373i	−0.172313	+	0.298455i
$290$	1.04162	−	0.242608i	0.0611661	−	0.0142464i
$291$		0			0
$292$	19.2934	−	9.50289i	1.12906	−	0.556115i
$293$	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
$296$	2.43243	+	14.7996i	0.141382	+	0.860207i
$297$		0			0
$298$	−3.12861	−	0.949876i	−0.181235	−	0.0550248i
$299$	10.1153			0.584983
$300$		0			0
$301$	−1.64328	+	1.52233i	−0.0947169	+	0.0877457i
$302$	6.50056	+	27.9098i	0.374065	+	1.60603i
$303$		0			0
$304$	−13.2386	−	10.1786i	−0.759287	−	0.583784i
$305$	3.14044	−	1.81313i	0.179821	−	0.103820i
$306$		0			0
$307$		−	26.0739i		−	1.48812i	−0.668114	−	0.744059i	$-0.732898\pi$
$307$		−	26.0739i		−	1.48812i	0.668114	−	0.744059i	$-0.267102\pi$
$308$	30.2484	+	11.5904i	1.72356	+	0.660426i
$309$		0			0
$310$	3.27644	−	10.7916i	0.186089	−	0.612923i
$311$	4.49745			0.255027			0.127513	−	0.991837i	$-0.459300\pi$
$311$	4.49745			0.255027			0.127513	+	0.991837i	$0.459300\pi$
$312$		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
$320$	−4.20444	−	12.4449i	−0.235035	−	0.695694i
$321$		0			0
$322$	2.24383	−	31.4819i	0.125044	−	1.75442i
$323$	−13.9350			−0.775363
$324$		0			0
$325$	1.38135	+	2.39257i	0.0766235	+	0.132716i
$326$	2.29821	+	9.86723i	0.127286	+	0.546495i
$327$		0			0
$328$	−13.7003	+	2.25176i	−0.756473	+	0.124333i
$329$	−21.7481	+	4.94584i	−1.19901	+	0.272673i
$330$		0			0
$331$			2.77969i			0.152785i	0.997078	+	0.0763927i	$0.0243403\pi$
$331$			2.77969i			0.152785i	−0.997078	+	0.0763927i	$0.975660\pi$
$332$	7.90466	−	3.89341i	0.433824	−	0.213679i
$333$		0			0
$334$	10.9293	−	2.54559i	0.598027	−	0.139288i
$335$	−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	$-0.202723\pi$
$338$	−4.75025	+	15.6459i	−0.258379	+	0.851025i
$339$		0			0
$340$	−9.11126	−	6.09430i	−0.494127	−	0.330510i
$341$	25.7483	+	14.8658i	1.39435	+	0.805027i
$342$		0			0
$343$	−14.5070	+	11.5129i	−0.783303	+	0.621641i
$344$	−0.845160	+	2.24062i	−0.0455680	+	0.120806i
$345$		0			0
$346$	0.664015	−	0.621618i	0.0356977	−	0.0334184i
$347$	0.530187			0.0284619			0.0142310	−	0.999899i	$-0.495470\pi$
$347$	0.530187			0.0284619			0.0142310	+	0.999899i	$0.495470\pi$
$348$		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	$0.643779\pi$
$350$	7.75283	−	3.76845i	0.414406	−	0.201432i
$351$		0			0
$352$	34.4668	−	3.35278i	1.83709	−	0.178704i
$353$	−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
$356$	−11.0532	+	16.5251i	−0.585819	+	0.875827i
$357$		0			0
$358$	−3.64086	+	11.9919i	−0.192425	+	0.633791i
$359$	2.61803	−	4.53456i	0.138174	−	0.239325i	−0.788631	−	0.614866i	$-0.789210\pi$
$359$	2.61803	−	4.53456i	0.138174	−	0.239325i	0.926806	+	0.375541i	$0.122543\pi$
$360$		0			0
$361$	−0.785453	−	1.36044i	−0.0413396	−	0.0716023i
$362$	1.95204	+	2.08518i	0.102597	+	0.109594i
$363$		0			0
$364$	−5.92532	−	2.27044i	−0.310571	−	0.119003i
$365$	−15.2914	−	8.82850i	−0.800389	−	0.462105i
$366$		0			0
$367$	−13.3026	−	7.68026i	−0.694390	−	0.400906i	0.110864	−	0.993836i	$-0.464638\pi$
$367$	−13.3026	−	7.68026i	−0.694390	−	0.400906i	−0.805255	+	0.592929i	$0.797971\pi$
$368$	−12.8821	−	31.1850i	−0.671524	−	1.62563i
$369$		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	$0.189185\pi$
$379$			21.8027i			1.11993i	−0.828516	+	0.559965i	$0.810815\pi$
$380$	−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	$-0.768046\pi$
$383$	−18.5862	−	32.1922i	−0.949708	−	1.64494i	−0.203670	−	0.979040i	$-0.565287\pi$
$384$		0			0
$385$	−5.89743	−	25.9325i	−0.300561	−	1.32164i
$386$	6.55978	+	7.00719i	0.333884	+	0.356656i
$387$		0			0
$388$	−14.0745	+	6.93233i	−0.714522	+	0.351936i
$389$	−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
$392$	−8.38068	+	17.9378i	−0.423288	+	0.905995i
$393$		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	$0.142327\pi$
$398$	−24.1094	−	7.31984i	−1.20849	−	0.366910i
$399$		0			0
$400$	5.61700	−	7.30563i	0.280850	−	0.365282i
$401$	−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
$404$	−15.1106	+	22.5910i	−0.751780	+	1.12395i
$405$		0			0
$406$	−1.71893	−	0.122514i	−0.0853089	−	0.00608028i
$407$	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
$412$	−9.12048	−	18.5170i	−0.449334	−	0.912267i
$413$	27.9746	−	6.36185i	1.37654	−	0.313046i
$414$		0			0
$415$	−6.26502	−	3.61711i	−0.307538	−	0.177557i
$416$	−6.75167	+	0.656771i	−0.331028	+	0.0322009i
$417$		0			0
$418$	−34.5842	−	10.5001i	−1.69157	−	0.513576i
$419$	−18.5974	+	32.2117i	−0.908545	+	1.57365i	−0.0924578	+	0.995717i	$0.529472\pi$
$419$	−18.5974	+	32.2117i	−0.908545	+	1.57365i	−0.816087	+	0.577929i	$0.803861\pi$
$420$		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	$0.806263\pi$
$422$	−5.95792	−	25.5800i	−0.290027	−	1.24521i
$423$		0			0
$424$	−0.141290	+	0.374577i	−0.00686164	+	0.0181911i
$425$		−	7.68992i		−	0.373016i
$426$		0			0
$427$	−5.69753	+	1.29570i	−0.275723	+	0.0627035i
$428$	13.3595	+	8.93583i	0.645755	+	0.431930i
$429$		0			0
$430$	1.91481	−	0.445985i	0.0923404	−	0.0215073i
$431$	−4.90250	−	8.49137i	−0.236145	−	0.409015i	0.723460	−	0.690366i	$-0.242551\pi$
$431$	−4.90250	−	8.49137i	−0.236145	−	0.409015i	−0.959605	+	0.281351i	$0.909217\pi$
$432$		0			0
$433$	−9.57915			−0.460345			−0.230172	−	0.973150i	$-0.573929\pi$
$433$	−9.57915			−0.460345			−0.230172	+	0.973150i	$0.573929\pi$
$434$	−10.1820	+	15.0519i	−0.488752	+	0.722514i
$435$		0			0
$436$	−7.74010	+	3.81236i	−0.370684	+	0.182579i
$437$			35.2156i			1.68459i
$438$		0			0
$439$		−	20.3416i		−	0.970853i	−0.874277	−	0.485427i	$-0.838664\pi$
$439$		−	20.3416i		−	0.970853i	0.874277	−	0.485427i	$-0.161336\pi$
$440$	−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	$-0.567494\pi$
$443$	−8.85905			−0.420906			−0.210453	+	0.977604i	$0.567494\pi$
$444$		0			0
$445$	16.3222			0.773748
$446$	17.8891	+	5.43129i	0.847071	+	0.257179i
$447$		0			0
$448$	0.546381	+	21.1590i	0.0258141	+	0.999667i
$449$		−	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
$452$	−2.21998	+	3.31897i	−0.104419	+	0.156111i
$453$		0			0
$454$	4.53613	−	1.05653i	0.212891	−	0.0495852i
$455$	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	$0.509938\pi$
$458$	−10.6853	+	35.1941i	−0.499290	+	1.64451i
$459$		0			0
$460$	−15.4011	+	23.0254i	−0.718080	+	1.07356i
$461$	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	0.898035	−	0.439925i	$-0.144995\pi$
$463$	20.7873	+	12.0015i	0.966066	+	0.557758i	0.0680311	+	0.997683i	$0.478328\pi$
$464$	−1.70272	+	0.703367i	−0.0790466	+	0.0326530i
$465$		0			0
$466$	−8.68352	−	37.2822i	−0.402256	−	1.72706i
$467$	16.1452	−	27.9642i	0.747109	−	1.29403i	−0.202094	−	0.979366i	$-0.564775\pi$
$467$	16.1452	−	27.9642i	0.747109	−	1.29403i	0.949203	−	0.314664i	$-0.101892\pi$
$468$		0			0
$469$	2.52013	+	11.0816i	0.116369	+	0.511702i
$470$	18.7311	+	5.68693i	0.864000	+	0.262319i
$471$		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
$476$	11.1235	+	13.7195i	0.509845	+	0.628834i
$477$		0			0
$478$	9.27170	−	2.15950i	0.424078	−	0.0987734i
$479$	8.48860	−	14.7027i	0.387854	−	0.671783i	−0.604306	−	0.796752i	$-0.706550\pi$
$479$	8.48860	−	14.7027i	0.387854	−	0.671783i	0.992161	+	0.124969i	$0.0398831\pi$
$480$		0			0
$481$	−3.17938	−	5.50686i	−0.144967	−	0.251091i
$482$	−0.398394	+	0.0927913i	−0.0181463	+	0.00422653i
$483$		0			0
$484$	47.5009	−	23.3964i	2.15913	−	1.06347i
$485$	11.1550	+	6.44036i	0.506524	+	0.292442i
$486$		0			0
$487$	32.6884	−	18.8727i	1.48125	−	0.855202i	0.481478	−	0.876458i	$-0.340100\pi$
$487$	32.6884	−	18.8727i	1.48125	−	0.855202i	0.999774	+	0.0212564i	$0.00676662\pi$
$488$	−4.83142	+	3.95920i	−0.218708	+	0.179225i
$489$		0			0
$490$	16.0664	−	2.46862i	0.725806	−	0.111521i
$491$	−0.0780327	+	0.135157i	−0.00352157	+	0.00609953i	−0.867781	−	0.496947i	$-0.834454\pi$
$491$	−0.0780327	+	0.135157i	−0.00352157	+	0.00609953i	0.864259	+	0.503047i	$0.167788\pi$
$492$		0			0
$493$	−0.768658	+	1.33135i	−0.0346186	+	0.0599612i
$494$	6.77465	+	2.05685i	0.304806	+	0.0925420i
$495$		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	−0.991040	−	0.133563i	$-0.957358\pi$
$499$	−30.6234	+	17.6804i	−1.37089	+	0.791485i	−0.379851	+	0.925048i	$0.624025\pi$
$500$	−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	$-0.308856\pi$
$503$	25.3456			1.13011			0.565053	+	0.825055i	$0.308856\pi$
$504$		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
$514$	−11.6047	−	3.52331i	−0.511863	−	0.155407i
$515$	−8.47323	+	14.6761i	−0.373375	+	0.646705i
$516$		0			0
$517$	−25.8026	+	44.6914i	−1.13480	+	1.96553i
$518$	−17.8443	+	8.67366i	−0.784034	+	0.381099i
$519$		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	0.969144	−	0.246493i	$-0.0792784\pi$
$523$	28.3635	+	16.3756i	1.24025	+	0.716057i	0.271103	+	0.962550i	$0.412612\pi$
$524$	−3.80071	+	1.87203i	−0.166035	+	0.0817799i
$525$		0			0
$526$	−25.1145	+	5.84950i	−1.09504	+	0.255050i
$527$	8.10560	+	14.0393i	0.353086	+	0.611562i
$528$		0			0
$529$	−24.0766	+	41.7019i	−1.04681	+	1.81313i
$530$	0.320109	−	0.0745577i	0.0139046	−	0.00323858i
$531$		0			0
$532$	7.90434	−	20.6285i	0.342697	−	0.894360i
$533$	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
$538$	−8.64185	−	2.62375i	−0.372577	−	0.113118i
$539$	−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	$0.165577\pi$
$542$	−7.68580	−	32.9986i	−0.330134	−	1.41741i
$543$		0			0
$544$	17.1894	+	7.81337i	0.736989	+	0.334996i
$545$	6.13460	+	3.54181i	0.262777	+	0.151715i
$546$		0			0
$547$	4.52878	−	2.61469i	0.193636	−	0.111796i	−0.400047	−	0.916494i	$-0.631006\pi$
$547$	4.52878	−	2.61469i	0.193636	−	0.111796i	0.593684	+	0.804698i	$0.297673\pi$
$548$	−6.40129	+	9.57022i	−0.273449	+	0.408820i
$549$		0			0
$550$	5.79440	−	19.0850i	0.247074	−	0.813788i
$551$	1.92279			0.0819135
$552$		0			0
$553$	4.51944	+	19.8731i	0.192186	+	0.845090i
$554$	−12.5412	+	2.92101i	−0.532825	+	0.124102i
$555$		0			0
$556$	−12.9759	+	19.3995i	−0.550299	+	0.822723i
$557$	−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
$560$	14.1898	−	10.0309i	0.599629	−	0.423883i
$561$		0			0
$562$	14.7000	+	4.46306i	0.620082	+	0.188263i
$563$	28.6466			1.20731			0.603655	−	0.797246i	$-0.293711\pi$
$563$	28.6466			1.20731			0.603655	+	0.797246i	$0.293711\pi$
$564$		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	$0.136668\pi$
$571$			19.8947i			0.832568i	−0.909235	+	0.416284i	$0.863332\pi$
$572$	−13.1709	+	6.48730i	−0.550705	+	0.271248i
$573$		0			0
$574$	−8.02942	−	16.5189i	−0.335141	−	0.689485i
$575$	−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	$0.973523\pi$
$578$	−8.06938	+	1.87947i	−0.335642	+	0.0781755i
$579$		0			0
$580$	1.25720	+	0.840908i	0.0522022	+	0.0349168i
$581$	7.92170	+	8.55106i	0.328648	+	0.354758i
$582$		0			0
$583$			0.866470i			0.0358855i
$584$	28.4579	+	10.7343i	1.17760	+	0.444188i
$585$		0			0
$586$	3.37092	+	14.4729i	0.139251	+	0.597868i
$587$	−8.87326	−	15.3689i	−0.366239	−	0.634344i	0.622736	−	0.782432i	$-0.286021\pi$
$587$	−8.87326	−	15.3689i	−0.366239	−	0.634344i	−0.988974	+	0.148089i	$0.952688\pi$
$588$		0			0
$589$	10.1380	−	17.5596i	0.417730	−	0.723530i
$590$	−24.0938	−	7.31512i	−0.991927	−	0.301159i
$591$		0			0
$592$	−12.9284	+	16.8150i	−0.531353	+	0.691093i
$593$	−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
$596$	−2.04312	−	4.14808i	−0.0836895	−	0.169912i
$597$		0			0
$598$	9.77640	+	10.4432i	0.399787	+	0.427054i
$599$	20.9835			0.857363			0.428681	−	0.903456i	$-0.358978\pi$
$599$	20.9835			0.857363			0.428681	+	0.903456i	$0.358978\pi$
$600$		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	$-0.568726\pi$
$602$	−3.15990	−	0.225218i	−0.128788	−	0.00917919i
$603$		0			0
$604$	−22.5317	+	33.6860i	−0.916803	+	1.37066i
$605$	−37.6480	−	21.7361i	−1.53061	−	0.883697i
$606$		0			0
$607$	22.2120	−	12.8241i	0.901559	−	0.520515i	0.0238532	−	0.999715i	$-0.492407\pi$
$607$	22.2120	−	12.8241i	0.901559	−	0.520515i	0.877706	+	0.479200i	$0.159073\pi$
$608$	−2.28650	−	23.5054i	−0.0927296	−	0.953269i
$609$		0			0
$610$	4.90713	+	1.48985i	0.198684	+	0.0603224i
$611$	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
$616$	17.2688	+	42.4311i	0.695781	+	1.70960i
$617$	−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	0.849651	−	0.527346i	$-0.176813\pi$
$619$	20.3462	+	11.7469i	0.817781	+	0.472146i	−0.0318698	+	0.999492i	$0.510146\pi$
$620$	14.3081	−	7.04742i	0.574628	−	0.283031i
$621$		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	$0.0168835\pi$
$631$			2.66350i			0.106032i	−0.998594	+	0.0530162i	$0.983117\pi$
$632$	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
$640$	8.78479	−	16.3687i	0.347249	−	0.647031i
$641$	−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	0.996898	−	0.0787077i	$-0.0250794\pi$
$643$	36.1897	+	20.8942i	1.42718	+	0.823985i	0.430286	+	0.902693i	$0.358413\pi$
$644$	34.6711	−	28.1106i	1.36623	−	1.10771i
$645$		0			0
$646$	−13.4681	−	14.3867i	−0.529896	−	0.566038i
$647$	−16.9405	−	29.3418i	−0.665999	−	1.15354i	−0.979014	−	0.203795i	$-0.934672\pi$
$647$	−16.9405	−	29.3418i	−0.665999	−	1.15354i	0.313015	−	0.949748i	$-0.398661\pi$
$648$		0			0
$649$	33.1899	−	57.4867i	1.30282	−	2.25655i
$650$	−1.13506	+	3.73854i	−0.0445206	+	0.146638i
$651$		0			0
$652$	−7.96588	+	11.9094i	−0.311968	+	0.466406i
$653$	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
$656$	−15.5661	−	11.9681i	−0.607752	−	0.467276i
$657$		0			0
$658$	−26.1256	−	17.6730i	−1.01848	−	0.688963i
$659$	−17.1903	−	29.7745i	−0.669640	−	1.15985i	−0.978005	−	0.208583i	$-0.933115\pi$
$659$	−17.1903	−	29.7745i	−0.669640	−	1.15985i	0.308364	−	0.951268i	$-0.400218\pi$
$660$		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
$664$	11.6595	+	4.39793i	0.452474	+	0.170673i
$665$	−17.6852	+	4.02187i	−0.685802	+	0.155962i
$666$		0			0
$667$	3.36451	+	1.94250i	0.130274	+	0.0752139i
$668$	13.1913	+	8.82333i	0.510386	+	0.341385i
$669$		0			0
$670$	2.89775	−	9.54431i	0.111950	−	0.368729i
$671$	−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	$-0.513216\pi$
$674$	46.3718	−	10.8006i	1.78617	−	0.416024i
$675$		0			0
$676$	−20.7442	+	10.2175i	−0.797853	+	0.392980i
$677$			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
$680$	−2.51415	−	15.2967i	−0.0964131	−	0.586603i
$681$		0			0
$682$	9.53796	+	40.9507i	0.365228	+	1.56808i
$683$	18.1138	+	31.3741i	0.693106	+	1.20049i	0.970815	+	0.239830i	$0.0770916\pi$
$683$	18.1138	+	31.3741i	0.693106	+	1.20049i	−0.277709	+	0.960665i	$0.589575\pi$
$684$		0			0
$685$	9.45275			0.361171
$686$	−25.9071	−	3.85001i	−0.989137	−	0.146994i
$687$		0			0
$688$	−3.13010	+	1.29300i	−0.119334	+	0.0492951i
$689$		−	0.169732i		−	0.00646626i
$690$		0			0
$691$		−	35.1152i		−	1.33584i	−0.744231	−	0.667922i	$-0.767184\pi$
$691$		−	35.1152i		−	1.33584i	0.744231	−	0.667922i	$-0.232816\pi$
$692$	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
$698$	−8.61054	+	28.3605i	−0.325914	+	1.07346i
$699$		0			0
$700$	11.3837	+	4.36195i	0.430263	+	0.164866i
$701$			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
$704$	36.7736	+	32.3437i	1.38596	+	1.21900i
$705$		0			0
$706$	−2.39781	−	10.2948i	−0.0902426	−	0.387451i
$707$	−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	$0.364361\pi$
$710$	−13.4948	−	4.09717i	−0.506453	−	0.153764i
$711$		0			0
$712$	−27.7437	+	4.55990i	−1.03974	+	0.170890i
$713$	35.4792	−	20.4839i	1.32871	−	0.767130i
$714$		0			0
$715$	10.4389	+	6.02692i	0.390394	+	0.225394i
$716$	−15.8995	+	7.83125i	−0.594192	+	0.292667i
$717$		0			0
$718$	7.21187	−	1.67974i	0.269145	−	0.0626874i
$719$	−23.6193	+	40.9097i	−0.880850	+	1.52568i	−0.0304516	+	0.999536i	$0.509695\pi$
$719$	−23.6193	+	40.9097i	−0.880850	+	1.52568i	−0.850398	+	0.526140i	$0.823639\pi$
$720$		0			0
$721$	20.0312	−	18.5569i	0.746001	−	0.691096i
$722$	0.645407	−	2.12578i	0.0240196	−	0.0791133i
$723$		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	−0.380850	−	0.924637i	$-0.624369\pi$
$727$	6.18756	−	3.57239i	0.229484	−	0.132493i	0.610334	+	0.792144i	$0.291035\pi$
$728$	−3.38277	−	8.31177i	−0.125374	−	0.308055i
$729$		0			0
$730$	−5.66441	−	24.3198i	−0.209649	−	0.900117i
$731$	−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	$0.858767\pi$
$734$	−4.92770	−	21.1568i	−0.181885	−	0.780911i
$735$		0			0
$736$	19.7454	−	43.4399i	0.727827	−	1.60121i
$737$	22.7723	+	13.1476i	0.838827	+	0.484297i
$738$		0			0
$739$	−21.4614	+	12.3907i	−0.789469	+	0.455800i	−0.839776	−	0.542934i	$-0.817314\pi$
$739$	−21.4614	+	12.3907i	−0.789469	+	0.455800i	0.0503065	+	0.998734i	$0.483980\pi$
$740$	17.3760	+	1.14729i	0.638755	+	0.0421753i
$741$		0			0
$742$	−0.528257	−	0.0376508i	−0.0193929	−	0.00138221i
$743$	6.52841	−	11.3075i	0.239504	−	0.414833i	−0.721068	−	0.692864i	$-0.756348\pi$
$743$	6.52841	−	11.3075i	0.239504	−	0.414833i	0.960572	+	0.278031i	$0.0896818\pi$
$744$		0			0
$745$	−1.89813	+	3.28765i	−0.0695420	+	0.120450i
$746$	−1.29278	+	4.25802i	−0.0473320	+	0.155897i
$747$		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	−0.132303	−	0.991209i	$-0.542237\pi$
$751$	18.0857	−	10.4418i	0.659958	−	0.381027i	0.792261	+	0.610182i	$0.208904\pi$
$752$	−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
$766$	15.2723	−	50.3023i	0.551809	−	1.81750i
$767$	−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	$-0.154630\pi$
$770$	21.0733	−	31.1522i	0.759427	−	1.12265i
$771$		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
$776$	−20.7600	−	7.83063i	−0.745240	−	0.281103i
$777$		0			0
$778$	−7.86598	−	33.7721i	−0.282009	−	1.21079i
$779$	10.2466	+	17.7477i	0.367123	+	0.635876i
$780$		0			0
$781$	18.5895	−	32.1980i	0.665186	−	1.15214i
$782$	−9.03242	−	38.7802i	−0.322999	−	1.38678i
$783$		0			0
$784$	−26.6192	+	8.68446i	−0.950685	+	0.310159i
$785$	14.8800	−	8.59096i	0.531089	−	0.306625i
$786$		0			0
$787$		−	24.8009i		−	0.884057i	−0.897001	−	0.442028i	$-0.854259\pi$
$787$		−	24.8009i		−	0.884057i	0.897001	−	0.442028i	$-0.145741\pi$
$788$	−6.70746	−	0.442876i	−0.238943	−	0.0157768i
$789$		0			0
$790$	5.19664	−	17.1162i	0.184888	−	0.608966i
$791$	−5.04632	−	1.56094i	−0.179426	−	0.0555005i
$792$		0			0
$793$	1.32415	−	2.29350i	0.0470221	−	0.0814446i
$794$	4.19290	−	0.976582i	0.148800	−	0.0346576i
$795$		0			0
$796$	−15.7445	−	31.9655i	−0.558049	−	1.13299i
$797$	−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
$800$	12.9713	−	1.26179i	0.458604	−	0.0446109i
$801$		0			0
$802$	−34.7363	−	10.5463i	−1.22658	−	0.372402i
$803$	65.8288			2.32305
$804$		0			0
$805$	−35.0088	−	10.8290i	−1.23390	−	0.381672i
$806$	−1.86838	−	8.02178i	−0.0658109	−	0.282555i
$807$		0			0
$808$	−37.9277	+	6.23373i	−1.33429	+	0.219302i
$809$	−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	$-0.895708\pi$
$811$		−	18.3292i		−	0.643626i	0.946803	−	0.321813i	$-0.104292\pi$
$812$	−1.53485	−	1.89306i	−0.0538628	−	0.0664333i
$813$		0			0
$814$	−13.3367	+	43.9270i	−0.467450	+	1.53964i
$815$	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	$0.258669\pi$
$823$			41.6607i			1.45220i	−0.687590	+	0.726100i	$0.741331\pi$
$824$	10.3023	−	27.3127i	0.358899	−	0.951485i
$825$		0			0
$826$	33.6055	+	22.7328i	1.16928	+	0.790974i
$827$	−25.0154			−0.869870			−0.434935	−	0.900462i	$-0.643229\pi$
$827$	−25.0154			−0.869870			−0.434935	+	0.900462i	$0.643229\pi$
$828$		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	$0.691894\pi$
$830$	−2.32076	−	9.96404i	−0.0805546	−	0.345857i
$831$		0			0
$832$	−7.20353	−	6.33577i	−0.249737	−	0.219653i
$833$	−13.1924	+	19.2844i	−0.457090	+	0.668164i
$834$		0			0
$835$		−	13.0294i		−	0.450900i
$836$	−22.5850	−	45.8536i	−0.781119	−	1.58588i
$837$		0			0
$838$	−51.2303	+	11.9322i	−1.76972	+	0.412192i
$839$	2.67610	+	4.63515i	0.0923894	+	0.160023i	0.908516	−	0.417850i	$-0.137216\pi$
$839$	2.67610	+	4.63515i	0.0923894	+	0.160023i	−0.816127	+	0.577873i	$0.803883\pi$
$840$		0			0
$841$	−14.3939	+	24.9310i	−0.496343	+	0.859691i
$842$	−1.43213	+	4.71700i	−0.0493544	+	0.162559i
$843$		0			0
$844$	20.6509	−	30.8740i	0.710833	−	1.06273i
$845$	16.4413	+	9.49238i	0.565597	+	0.326548i
$846$		0			0
$847$	47.6034	+	51.3853i	1.63567	+	1.76562i
$848$	−0.523275	+	0.216157i	−0.0179693	+	0.00742287i
$849$		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	$0.508375\pi$
$854$	−6.84435	−	4.62993i	−0.234209	−	0.158433i
$855$		0			0
$856$	3.68639	+	22.4290i	0.125998	+	0.766607i
$857$	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	−0.316243	−	0.948678i	$-0.602421\pi$
$859$	10.1764	−	5.87537i	0.347215	−	0.200465i	0.663458	+	0.748213i	$0.269088\pi$
$860$	2.31110	+	1.54584i	0.0788079	+	0.0527127i
$861$		0			0
$862$	4.02839	−	13.2683i	0.137207	−	0.451920i
$863$	−6.55720	+	11.3574i	−0.223210	+	0.386610i	−0.955781	−	0.294080i	$-0.904987\pi$
$863$	−6.55720	+	11.3574i	−0.223210	+	0.386610i	0.732571	+	0.680690i	$0.238320\pi$
$864$		0			0
$865$	−0.528039	−	0.914590i	−0.0179538	−	0.0310970i
$866$	−9.25822	−	9.88968i	−0.314607	−	0.336065i
$867$		0			0
$868$	−25.3807	+	4.03554i	−0.861477	+	0.136975i
$869$	40.8384	+	23.5780i	1.38535	+	0.799830i
$870$		0			0
$871$	−4.46083	−	2.57546i	−0.151149	−	0.0872662i
$872$	−11.4167	−	4.30638i	−0.386619	−	0.145832i
$873$		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	$-0.705195\pi$
$883$		−	47.5039i		−	1.59863i	0.600911	−	0.799316i	$-0.294805\pi$
$884$	−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	0.747999	−	0.663700i	$-0.231015\pi$
$887$	−5.97980	−	10.3573i	−0.200782	−	0.347764i	−0.948781	+	0.315936i	$0.897682\pi$
$888$		0			0
$889$	−0.512543	−	2.25378i	−0.0171901	−	0.0755893i
$890$	15.7754	+	16.8513i	0.528792	+	0.564858i
$891$		0			0
$892$	11.6824	+	23.7183i	0.391154	+	0.794147i
$893$	30.4782	+	17.5966i	1.01992	+	0.588848i
$894$		0			0
$895$	12.6015	+	7.27549i	0.421222	+	0.243193i
$896$	−21.3168	+	21.0142i	−0.712144	+	0.702034i
$897$		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
$902$	−40.6643	−	12.3461i	−1.35397	−	0.411079i
$903$		0			0
$904$	−5.57217	+	0.915833i	−0.185328	+	0.0304601i
$905$	2.87204	−	1.65818i	0.0954700	−	0.0551196i
$906$		0			0
$907$	−29.0510	−	16.7726i	−0.964623	−	0.556925i	−0.0670301	−	0.997751i	$-0.521352\pi$
$907$	−29.0510	−	16.7726i	−0.964623	−	0.556925i	−0.897593	+	0.440826i	$0.854686\pi$
$908$	5.47493	+	3.66205i	0.181692	+	0.121529i
$909$		0			0
$910$	−4.12801	+	6.10238i	−0.136842	+	0.202292i
$911$	19.6281	+	33.9969i	0.650309	+	1.12637i	0.983048	+	0.183349i	$0.0586937\pi$
$911$	19.6281	+	33.9969i	0.650309	+	1.12637i	−0.332739	+	0.943019i	$0.607973\pi$
$912$		0			0
$913$	26.9706			0.892597
$914$	−1.28987	−	1.37785i	−0.0426652	−	0.0455752i
$915$		0			0
$916$	−46.6623	+	22.9833i	−1.54176	+	0.759391i
$917$	−3.80891	−	4.11152i	−0.125781	−	0.135774i
$918$		0			0
$919$	−25.8613	−	14.9310i	−0.853087	−	0.492530i	0.00860439	−	0.999963i	$-0.497261\pi$
$919$	−25.8613	−	14.9310i	−0.853087	−	0.492530i	−0.861691	+	0.507433i	$0.830594\pi$
$920$	−38.6569	+	6.35358i	−1.27448	+	0.209471i
$921$		0			0
$922$	2.94622	+	0.894502i	0.0970287	+	0.0294589i
$923$	−3.64148	+	6.30723i	−0.119861	+	0.207605i
$924$		0			0
$925$	6.10822	+	10.5797i	0.200837	+	0.347860i
$926$	7.70024	+	33.0605i	0.253046	+	1.08644i
$927$		0			0
$928$	−2.37184	−	1.07811i	−0.0778594	−	0.0353907i
$929$			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
$932$	30.0982	−	44.9981i	0.985898	−	1.47396i
$933$		0			0
$934$	44.4750	−	10.3588i	1.45527	−	0.338951i
$935$	−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	$0.389728\pi$
$938$	−9.00516	+	13.3122i	−0.294029	+	0.434658i
$939$		0			0
$940$	12.2322	+	24.8347i	0.398971	+	0.810018i
$941$		−	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	$-0.431917\pi$
$947$	13.0641			0.424526			0.212263	+	0.977213i	$0.431917\pi$
$948$		0			0
$949$	−12.8951			−0.418593
$950$	−13.0154	−	3.95161i	−0.422276	−	0.128207i
$951$		0			0
$952$	−3.41344	+	24.7440i	−0.110630	+	0.801957i
$953$			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
$956$	11.1906	+	7.48511i	0.361929	+	0.242086i
$957$		0			0
$958$	23.3835	−	5.44633i	0.755487	−	0.175963i
$959$	−14.5510	−	4.50094i	−0.469876	−	0.145343i
$960$		0			0
$961$	7.41193			0.239094
$962$	2.61250	−	8.60481i	0.0842305	−	0.277430i
$963$		0			0
$964$	−0.480846	−	0.321626i	−0.0154870	−	0.0103589i
$965$	9.65144	−	5.57226i	0.310691	−	0.179377i
$966$		0			0
$967$	28.7435	+	16.5951i	0.924330	+	0.533662i	0.885014	−	0.465565i	$-0.154149\pi$
$967$	28.7435	+	16.5951i	0.924330	+	0.533662i	0.0393162	+	0.999227i	$0.487482\pi$
$968$	70.0644	+	26.4282i	2.25195	+	0.849434i
$969$		0			0
$970$	4.13217	+	17.7412i	0.132676	+	0.569637i
$971$	−11.8551	+	20.5337i	−0.380449	+	0.658957i	−0.991126	−	0.132923i	$-0.957564\pi$
$971$	−11.8551	+	20.5337i	−0.380449	+	0.658957i	0.610678	+	0.791879i	$0.290897\pi$
$972$		0			0
$973$	−29.4959	−	9.12372i	−0.945595	−	0.292493i
$974$	51.0777	+	15.5077i	1.63663	+	0.496898i
$975$		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
$980$	18.0768	+	14.2013i	0.577441	+	0.453644i
$981$		0			0
$982$	−0.214956	+	0.0500662i	−0.00685953	+	0.00159768i
$983$	−28.1689	+	48.7899i	−0.898447	+	1.55616i	−0.0689683	+	0.997619i	$0.521971\pi$
$983$	−28.1689	+	48.7899i	−0.898447	+	1.55616i	−0.829479	+	0.558538i	$0.811363\pi$
$984$		0			0
$985$	2.75940	+	4.77943i	0.0879219	+	0.152285i
$986$	−2.11742	+	0.493175i	−0.0674323	+	0.0157059i
$987$		0			0
$988$	4.42415	+	8.98220i	0.140751	+	0.285762i
$989$	6.18497	+	3.57090i	0.196671	+	0.113548i
$990$		0			0
$991$	25.7259	−	14.8529i	0.817211	−	0.471817i	−0.0322431	−	0.999480i	$-0.510265\pi$
$991$	25.7259	−	14.8529i	0.817211	−	0.471817i	0.849454	+	0.527663i	$0.176932\pi$
$992$	−22.3514	+	15.9761i	−0.709657	+	0.507240i
$993$		0			0
$994$	18.8223	+	12.7325i	0.597007	+	0.403851i
$995$	−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	$-0.224320\pi$
$998$	−47.8510	−	14.5280i	−1.51470	−	0.459877i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.966497 + 1.03242i) q^{2} +(-0.131768 + 1.99565i) q^{4} +(1.42201 - 0.820999i) q^{5} +(-2.57988 + 0.586703i) q^{7} +(-2.18770 + 1.79275i) q^{8} +O(q^{10})\)	\(q+(0.966497 + 1.03242i) q^{2} +(-0.131768 + 1.99565i) q^{4} +(1.42201 - 0.820999i) q^{5} +(-2.57988 + 0.586703i) q^{7} +(-2.18770 + 1.79275i) q^{8} +(2.22198 + 0.674616i) q^{10} +(-3.06085 + 5.30154i) q^{11} +(0.599586 - 1.03851i) q^{13} +(-3.09917 - 2.09646i) q^{14} +(-3.96527 - 0.525926i) q^{16} +(-2.89068 + 1.66893i) q^{17} +(3.61550 + 2.08741i) q^{19} +(1.45106 + 2.94603i) q^{20} +(-8.43170 + 1.96386i) q^{22} +(4.21762 + 7.30513i) q^{23} +(-1.15192 + 1.99519i) q^{25} +(1.65168 - 0.384697i) q^{26} +(-0.830912 - 5.22586i) q^{28} +(0.398864 - 0.230284i) q^{29} -4.85676i q^{31} +(-3.28945 - 4.60212i) q^{32} +(-4.51687 - 1.37136i) q^{34} +(-3.18694 + 2.95238i) q^{35} +(2.65132 - 4.59222i) q^{37} +(1.33929 + 5.75017i) q^{38} +(-1.63909 + 4.34542i) q^{40} +(4.25113 + 2.45439i) q^{41} +(0.733230 - 0.423331i) q^{43} +(-10.1767 - 6.80697i) q^{44} +(-3.46562 + 11.4147i) q^{46} +8.42989 q^{47} +(6.31156 - 3.02725i) q^{49} +(-3.17319 + 0.739078i) q^{50} +(1.99351 + 1.33341i) q^{52} +(0.122578 - 0.0707704i) q^{53} +10.0518i q^{55} +(4.59219 - 5.90862i) q^{56} +(0.623249 + 0.189225i) q^{58} -10.8434 q^{59} +2.20845 q^{61} +(5.01419 - 4.69404i) q^{62} +(1.57206 - 7.84402i) q^{64} -1.96904i q^{65} -4.29540i q^{67} +(-2.94972 - 5.98871i) q^{68} +(-6.12825 - 0.436783i) q^{70} -6.07333 q^{71} +(-5.37668 - 9.31269i) q^{73} +(7.30357 - 1.70110i) q^{74} +(-4.64215 + 6.94023i) q^{76} +(4.78619 - 15.4732i) q^{77} -7.70311i q^{79} +(-6.07045 + 2.50761i) q^{80} +(1.57475 + 6.76109i) q^{82} +(-2.20287 - 3.81549i) q^{83} +(-2.74039 + 4.74649i) q^{85} +(1.14572 + 0.347851i) q^{86} +(-2.80815 - 17.0855i) q^{88} +(8.60870 + 4.97023i) q^{89} +(-0.937560 + 3.03102i) q^{91} +(-15.1343 + 7.45433i) q^{92} +(8.14746 + 8.70315i) q^{94} +6.85504 q^{95} +(3.92227 + 6.79358i) q^{97} +(9.22548 + 3.59033i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 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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