LMFDB - Embedded newform 380.2.bh.a.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	380.13
Dual form			380.2.bh.a.117.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84872 - 0.862074i) q^{3} +(2.22179 + 0.252247i) q^{5} +(-1.05366 - 3.93231i) q^{7} +(0.746246 - 0.889341i) q^{9} +O(q^{10})$	\(q+(1.84872 - 0.862074i) q^{3} +(2.22179 + 0.252247i) q^{5} +(-1.05366 - 3.93231i) q^{7} +(0.746246 - 0.889341i) q^{9} +(-2.62986 - 4.55506i) q^{11} +(-0.168100 + 0.360492i) q^{13} +(4.32494 - 1.44902i) q^{15} +(-0.612760 + 7.00388i) q^{17} +(3.17822 + 2.98311i) q^{19} +(-5.33787 - 6.36142i) q^{21} +(-2.31544 + 1.62129i) q^{23} +(4.87274 + 1.12088i) q^{25} +(-0.970925 + 3.62354i) q^{27} +(2.22257 + 1.86496i) q^{29} +(3.19971 + 1.84735i) q^{31} +(-8.78869 - 6.15390i) q^{33} +(-1.34910 - 9.00257i) q^{35} +(0.837316 + 0.837316i) q^{37} +0.811364i q^{39} +(2.89465 - 7.95299i) q^{41} +(-1.46246 + 2.08860i) q^{43} +(1.88234 - 1.78769i) q^{45} +(3.24199 - 0.283638i) q^{47} +(-8.29069 + 4.78663i) q^{49} +(4.90504 + 13.4765i) q^{51} +(3.42197 + 4.88708i) q^{53} +(-4.69402 - 10.7838i) q^{55} +(8.44731 + 2.77509i) q^{57} +(-9.57764 + 8.03660i) q^{59} +(0.260608 - 1.47798i) q^{61} +(-4.28345 - 1.99741i) q^{63} +(-0.464416 + 0.758536i) q^{65} +(-0.959802 - 10.9706i) q^{67} +(-2.88294 + 4.99339i) q^{69} +(9.90257 - 1.74609i) q^{71} +(-4.60382 - 9.87292i) q^{73} +(9.97464 - 2.12847i) q^{75} +(-15.1409 + 15.1409i) q^{77} +(11.6936 + 4.25614i) q^{79} +(1.93358 + 10.9659i) q^{81} +(-9.88658 + 2.64910i) q^{83} +(-3.12813 + 15.4066i) q^{85} +(5.71664 + 1.53177i) q^{87} +(-5.85780 + 2.13206i) q^{89} +(1.59468 + 0.281186i) q^{91} +(7.50794 + 0.656859i) q^{93} +(6.30887 + 7.42955i) q^{95} +(-6.89617 - 0.603337i) q^{97} +(-6.01352 - 1.06035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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			0
$2$		0			0
$3$	1.84872	−	0.862074i	1.06736	−	0.497719i	0.192103	−	0.981375i	$-0.438469\pi$
$3$	1.84872	−	0.862074i	1.06736	−	0.497719i	0.875258	+	0.483656i	$0.160691\pi$
$4$		0			0
$5$	2.22179	+	0.252247i	0.993617	+	0.112808i
$5$	2.22179	+	0.252247i	0.993617	+	0.112808i
$6$		0			0
$7$	−1.05366	−	3.93231i	−0.398246	−	1.48627i	−0.816181	−	0.577797i	$-0.803913\pi$
$7$	−1.05366	−	3.93231i	−0.398246	−	1.48627i	0.417935	−	0.908477i	$-0.362754\pi$
$8$		0			0
$9$	0.746246	−	0.889341i	0.248749	−	0.296447i
$10$		0			0
$11$	−2.62986	−	4.55506i	−0.792934	−	1.37340i	−0.924143	−	0.382047i	$-0.875219\pi$
$11$	−2.62986	−	4.55506i	−0.792934	−	1.37340i	0.131210	−	0.991355i	$-0.458114\pi$
$12$		0			0
$13$	−0.168100	+	0.360492i	−0.0466225	+	0.0999824i	−0.928239	−	0.371984i	$-0.878678\pi$
$13$	−0.168100	+	0.360492i	−0.0466225	+	0.0999824i	0.881617	+	0.471966i	$0.156456\pi$
$14$		0			0
$15$	4.32494	−	1.44902i	1.11669	−	0.374135i
$16$		0			0
$17$	−0.612760	+	7.00388i	−0.148616	+	1.69869i	0.446285	+	0.894891i	$0.352747\pi$
$17$	−0.612760	+	7.00388i	−0.148616	+	1.69869i	−0.594901	+	0.803799i	$0.702809\pi$
$18$		0			0
$19$	3.17822	+	2.98311i	0.729133	+	0.684372i
$19$	3.17822	+	2.98311i	0.729133	+	0.684372i
$20$		0			0
$21$	−5.33787	−	6.36142i	−1.16482	−	1.38818i
$22$		0			0
$23$	−2.31544	+	1.62129i	−0.482802	+	0.338062i	−0.789506	−	0.613743i	$-0.789663\pi$
$23$	−2.31544	+	1.62129i	−0.482802	+	0.338062i	0.306703	+	0.951805i	$0.400774\pi$
$24$		0			0
$25$	4.87274	+	1.12088i	0.974549	+	0.224176i
$26$		0			0
$27$	−0.970925	+	3.62354i	−0.186855	+	0.697351i
$28$		0			0
$29$	2.22257	+	1.86496i	0.412720	+	0.346313i	0.825386	−	0.564569i	$-0.190958\pi$
$29$	2.22257	+	1.86496i	0.412720	+	0.346313i	−0.412665	+	0.910883i	$0.635402\pi$
$30$		0			0
$31$	3.19971	+	1.84735i	0.574685	+	0.331794i	0.759018	−	0.651069i	$-0.225679\pi$
$31$	3.19971	+	1.84735i	0.574685	+	0.331794i	−0.184333	+	0.982864i	$0.559013\pi$
$32$		0			0
$33$	−8.78869	−	6.15390i	−1.52991	−	1.07126i
$34$		0			0
$35$	−1.34910	−	9.00257i	−0.228040	−	1.52171i
$36$		0			0
$37$	0.837316	+	0.837316i	0.137654	+	0.137654i	0.772576	−	0.634922i	$-0.218968\pi$
$37$	0.837316	+	0.837316i	0.137654	+	0.137654i	−0.634922	+	0.772576i	$0.718968\pi$
$38$		0			0
$39$			0.811364i			0.129922i
$40$		0			0
$41$	2.89465	−	7.95299i	0.452069	−	1.24205i	−0.479197	−	0.877707i	$-0.659072\pi$
$41$	2.89465	−	7.95299i	0.452069	−	1.24205i	0.931266	−	0.364341i	$-0.118706\pi$
$42$		0			0
$43$	−1.46246	+	2.08860i	−0.223023	+	0.318509i	−0.915034	−	0.403378i	$-0.867836\pi$
$43$	−1.46246	+	2.08860i	−0.223023	+	0.318509i	0.692011	+	0.721887i	$0.256725\pi$
$44$		0			0
$45$	1.88234	−	1.78769i	0.280602	−	0.266494i
$46$		0			0
$47$	3.24199	−	0.283638i	0.472894	−	0.0413728i	0.151782	−	0.988414i	$-0.451499\pi$
$47$	3.24199	−	0.283638i	0.472894	−	0.0413728i	0.321112	+	0.947041i	$0.395943\pi$
$48$		0			0
$49$	−8.29069	+	4.78663i	−1.18438	+	0.683805i
$50$		0			0
$51$	4.90504	+	13.4765i	0.686843	+	1.88709i
$52$		0			0
$53$	3.42197	+	4.88708i	0.470044	+	0.671292i	0.982251	−	0.187570i	$-0.0600611\pi$
$53$	3.42197	+	4.88708i	0.470044	+	0.671292i	−0.512208	+	0.858862i	$0.671172\pi$
$54$		0			0
$55$	−4.69402	−	10.7838i	−0.632941	−	1.45408i
$56$		0			0
$57$	8.44731	+	2.77509i	1.11887	+	0.367569i
$58$		0			0
$59$	−9.57764	+	8.03660i	−1.24690	+	1.04628i	−0.249951	+	0.968259i	$0.580414\pi$
$59$	−9.57764	+	8.03660i	−1.24690	+	1.04628i	−0.996952	+	0.0780171i	$0.975141\pi$
$60$		0			0
$61$	0.260608	−	1.47798i	0.0333674	−	0.189236i	−0.963568	−	0.267463i	$-0.913815\pi$
$61$	0.260608	−	1.47798i	0.0333674	−	0.189236i	0.996936	+	0.0782267i	$0.0249258\pi$
$62$		0			0
$63$	−4.28345	−	1.99741i	−0.539664	−	0.251650i
$64$		0			0
$65$	−0.464416	+	0.758536i	−0.0576038	+	0.0940848i
$66$		0			0
$67$	−0.959802	−	10.9706i	−0.117258	−	1.34027i	−0.795733	−	0.605647i	$-0.792914\pi$
$67$	−0.959802	−	10.9706i	−0.117258	−	1.34027i	0.678475	−	0.734624i	$-0.262641\pi$
$68$		0			0
$69$	−2.88294	+	4.99339i	−0.347065	+	0.601134i
$70$		0			0
$71$	9.90257	−	1.74609i	1.17522	−	0.207223i	0.448260	−	0.893903i	$-0.352044\pi$
$71$	9.90257	−	1.74609i	1.17522	−	0.207223i	0.726959	+	0.686681i	$0.240933\pi$
$72$		0			0
$73$	−4.60382	−	9.87292i	−0.538836	−	1.15554i	−0.967685	−	0.252162i	$-0.918859\pi$
$73$	−4.60382	−	9.87292i	−0.538836	−	1.15554i	0.428849	−	0.903376i	$-0.358919\pi$
$74$		0			0
$75$	9.97464	−	2.12847i	1.15177	−	0.245774i
$76$		0			0
$77$	−15.1409	+	15.1409i	−1.72547	+	1.72547i
$78$		0			0
$79$	11.6936	+	4.25614i	1.31564	+	0.478853i	0.902058	−	0.431615i	$-0.142056\pi$
$79$	11.6936	+	4.25614i	1.31564	+	0.478853i	0.413580	+	0.910468i	$0.364278\pi$
$80$		0			0
$81$	1.93358	+	10.9659i	0.214842	+	1.21843i
$82$		0			0
$83$	−9.88658	+	2.64910i	−1.08519	+	0.290777i	−0.756722	−	0.653737i	$-0.773200\pi$
$83$	−9.88658	+	2.64910i	−1.08519	+	0.290777i	−0.328472	+	0.944514i	$0.606534\pi$
$84$		0			0
$85$	−3.12813	+	15.4066i	−0.339294	+	1.67108i
$86$		0			0
$87$	5.71664	+	1.53177i	0.612888	+	0.164223i
$88$		0			0
$89$	−5.85780	+	2.13206i	−0.620925	+	0.225998i	−0.633277	−	0.773925i	$-0.718291\pi$
$89$	−5.85780	+	2.13206i	−0.620925	+	0.225998i	0.0123514	+	0.999924i	$0.496068\pi$
$90$		0			0
$91$	1.59468	+	0.281186i	0.167168	+	0.0294763i
$92$		0			0
$93$	7.50794	+	0.656859i	0.778537	+	0.0681131i
$94$		0			0
$95$	6.30887	+	7.42955i	0.647276	+	0.762256i
$96$		0			0
$97$	−6.89617	−	0.603337i	−0.700200	−	0.0612596i	−0.268504	−	0.963279i	$-0.586529\pi$
$97$	−6.89617	−	0.603337i	−0.700200	−	0.0612596i	−0.431696	+	0.902019i	$0.642085\pi$
$98$		0			0
$99$	−6.01352	−	1.06035i	−0.604382	−	0.106569i
$100$		0			0
$101$	−5.62463	+	2.04720i	−0.559672	+	0.203704i	−0.606338	−	0.795207i	$-0.707362\pi$
$101$	−5.62463	+	2.04720i	−0.559672	+	0.203704i	0.0466668	+	0.998911i	$0.485140\pi$
$102$		0			0
$103$	−10.9932	−	2.94562i	−1.08319	−	0.290240i	−0.327289	−	0.944924i	$-0.606135\pi$
$103$	−10.9932	−	2.94562i	−1.08319	−	0.290240i	−0.755903	+	0.654684i	$0.772802\pi$
$104$		0			0
$105$	−10.2550	−	15.4802i	−1.00079	−	1.51072i
$106$		0			0
$107$	2.58131	−	0.691659i	0.249544	−	0.0668652i	−0.131879	−	0.991266i	$-0.542101\pi$
$107$	2.58131	−	0.691659i	0.249544	−	0.0668652i	0.381423	+	0.924401i	$0.375434\pi$
$108$		0			0
$109$	−2.65819	−	15.0753i	−0.254608	−	1.44395i	−0.797076	−	0.603879i	$-0.793621\pi$
$109$	−2.65819	−	15.0753i	−0.254608	−	1.44395i	0.542468	−	0.840076i	$-0.317490\pi$
$110$		0			0
$111$	2.26979	+	0.826137i	0.215439	+	0.0784135i
$112$		0			0
$113$	−12.2464	+	12.2464i	−1.15204	+	1.15204i	−0.165901	+	0.986142i	$0.553053\pi$
$113$	−12.2464	+	12.2464i	−1.15204	+	1.15204i	−0.986142	+	0.165901i	$0.946947\pi$
$114$		0			0
$115$	−5.55339	+	3.01811i	−0.517856	+	0.281440i
$116$		0			0
$117$	0.195156	+	0.418513i	0.0180422	+	0.0386916i
$118$		0			0
$119$	28.1871	−	4.97014i	2.58390	−	0.455612i
$120$		0			0
$121$	−8.33236	+	14.4321i	−0.757487	+	1.31201i
$122$		0			0
$123$	−1.50466	−	17.1983i	−0.135670	−	1.55072i
$124$		0			0
$125$	10.5435	+	3.71950i	0.943039	+	0.332682i
$126$		0			0
$127$	−19.3007	−	9.00008i	−1.71266	−	0.798628i	−0.994731	−	0.102515i	$-0.967311\pi$
$127$	−19.3007	−	9.00008i	−1.71266	−	0.798628i	−0.717932	−	0.696113i	$-0.754911\pi$
$128$		0			0
$129$	−0.903147	+	5.12200i	−0.0795176	+	0.450967i
$130$		0			0
$131$	−2.93763	+	2.46496i	−0.256662	+	0.215365i	−0.762035	−	0.647536i	$-0.775799\pi$
$131$	−2.93763	+	2.46496i	−0.256662	+	0.215365i	0.505373	+	0.862901i	$0.331355\pi$
$132$		0			0
$133$	8.38175	−	15.6409i	0.726790	−	1.35624i
$134$		0			0
$135$	−3.07122	+	7.80585i	−0.264329	+	0.671821i
$136$		0			0
$137$	0.829699	+	1.18493i	0.0708859	+	0.101236i	0.853030	−	0.521863i	$-0.174763\pi$
$137$	0.829699	+	1.18493i	0.0708859	+	0.101236i	−0.782144	+	0.623098i	$0.785874\pi$
$138$		0			0
$139$	−1.85801	−	5.10484i	−0.157594	−	0.432987i	0.835617	−	0.549313i	$-0.185110\pi$
$139$	−1.85801	−	5.10484i	−0.157594	−	0.432987i	−0.993211	+	0.116326i	$0.962888\pi$
$140$		0			0
$141$	5.74904	−	3.31921i	0.484156	−	0.279528i
$142$		0			0
$143$	2.08414	−	0.182339i	0.174284	−	0.0152479i
$144$		0			0
$145$	4.46766	+	4.70418i	0.371019	+	0.390661i
$146$		0			0
$147$	−11.2008	+	15.9964i	−0.923824	+	1.31936i
$148$		0			0
$149$	1.23147	−	3.38343i	0.100886	−	0.277181i	−0.878973	−	0.476871i	$-0.841771\pi$
$149$	1.23147	−	3.38343i	0.100886	−	0.277181i	0.979859	+	0.199689i	$0.0639932\pi$
$150$		0			0
$151$		−	15.6972i		−	1.27742i	−0.769448	−	0.638709i	$-0.779469\pi$
$151$		−	15.6972i		−	1.27742i	0.769448	−	0.638709i	$-0.220531\pi$
$152$		0			0
$153$	5.77157	+	5.77157i	0.466603	+	0.466603i
$154$		0			0
$155$	6.64311	+	4.91156i	0.533587	+	0.394506i
$156$		0			0
$157$	−3.65663	−	2.56040i	−0.291831	−	0.204342i	0.418488	−	0.908222i	$-0.362560\pi$
$157$	−3.65663	−	2.56040i	−0.291831	−	0.204342i	−0.710319	+	0.703880i	$0.751449\pi$
$158$		0			0
$159$	10.5393	+	6.08487i	0.835821	+	0.482561i
$160$		0			0
$161$	8.81509	+	7.39674i	0.694726	+	0.582944i
$162$		0			0
$163$	−1.59204	+	5.94158i	−0.124698	+	0.465381i	−0.999829	−	0.0185066i	$-0.994109\pi$
$163$	−1.59204	+	5.94158i	−0.124698	+	0.465381i	0.875130	+	0.483887i	$0.160775\pi$
$164$		0			0
$165$	−17.9744	−	15.8896i	−1.39930	−	1.23701i
$166$		0			0
$167$	3.72654	−	2.60935i	0.288368	−	0.201917i	−0.420437	−	0.907322i	$-0.638123\pi$
$167$	3.72654	−	2.60935i	0.288368	−	0.201917i	0.708805	+	0.705404i	$0.249234\pi$
$168$		0			0
$169$	8.25454	+	9.83738i	0.634965	+	0.756722i
$170$		0			0
$171$	5.02473	−	0.600386i	0.384251	−	0.0459127i
$172$		0			0
$173$	0.318280	−	3.63796i	0.0241984	−	0.276589i	−0.974450	−	0.224606i	$-0.927890\pi$
$173$	0.318280	−	3.63796i	0.0241984	−	0.276589i	0.998648	−	0.0519827i	$-0.0165541\pi$
$174$		0			0
$175$	−0.726561	−	20.3422i	−0.0549228	−	1.53772i
$176$		0			0
$177$	−10.7783	+	23.1141i	−0.810145	+	1.73736i
$178$		0			0
$179$	5.59134	+	9.68449i	0.417916	+	0.723852i	0.995730	−	0.0923165i	$-0.0294272\pi$
$179$	5.59134	+	9.68449i	0.417916	+	0.723852i	−0.577813	+	0.816169i	$0.696094\pi$
$180$		0			0
$181$	12.4728	−	14.8645i	0.927098	−	1.10487i	−0.0671470	−	0.997743i	$-0.521390\pi$
$181$	12.4728	−	14.8645i	0.927098	−	1.10487i	0.994245	−	0.107129i	$-0.0341659\pi$
$182$		0			0
$183$	−0.792338	−	2.95704i	−0.0585713	−	0.218591i
$184$		0			0
$185$	1.64913	+	2.07155i	0.121247	+	0.152304i
$186$		0			0
$187$	33.5145	−	15.6281i	2.45083	−	1.14284i
$188$		0			0
$189$	15.2719			1.11087
$190$		0			0
$191$	19.5898			1.41747			0.708734	−	0.705476i	$-0.249267\pi$
$191$	19.5898			1.41747			0.708734	+	0.705476i	$0.249267\pi$
$192$		0			0
$193$	−11.0040	+	5.13126i	−0.792088	+	0.369357i	−0.776176	−	0.630517i	$-0.782843\pi$
$193$	−11.0040	+	5.13126i	−0.792088	+	0.369357i	−0.0159121	+	0.999873i	$0.505065\pi$
$194$		0			0
$195$	−0.204664	+	1.80268i	−0.0146563	+	0.129093i
$196$		0			0
$197$	−0.0253016	−	0.0944268i	−0.00180266	−	0.00672763i	0.965019	−	0.262181i	$-0.0844418\pi$
$197$	−0.0253016	−	0.0944268i	−0.00180266	−	0.00672763i	−0.966821	+	0.255454i	$0.917775\pi$
$198$		0			0
$199$	−4.28819	+	5.11047i	−0.303982	+	0.362271i	−0.896312	−	0.443424i	$-0.853764\pi$
$199$	−4.28819	+	5.11047i	−0.303982	+	0.362271i	0.592330	+	0.805695i	$0.298208\pi$
$200$		0			0
$201$	−11.2319	−	19.4542i	−0.792235	−	1.37219i
$202$		0			0
$203$	4.99175	−	10.7049i	0.350352	−	0.751333i
$204$		0			0
$205$	8.43744	−	16.9397i	0.589296	−	1.18312i
$206$		0			0
$207$	−0.286008	+	3.26909i	−0.0198790	+	0.227218i
$208$		0			0
$209$	5.22995	−	22.3221i	0.361763	−	1.54405i
$210$		0			0
$211$	−10.1097	−	12.0482i	−0.695978	−	0.829434i	0.296087	−	0.955161i	$-0.404318\pi$
$211$	−10.1097	−	12.0482i	−0.695978	−	0.829434i	−0.992065	+	0.125727i	$0.959874\pi$
$212$		0			0
$213$	16.8019	−	11.7648i	1.15124	−	0.806110i
$214$		0			0
$215$	−3.77612	+	4.27155i	−0.257529	+	0.291317i
$216$		0			0
$217$	3.89296	−	14.5287i	0.264272	−	0.986275i
$218$		0			0
$219$	−17.0224	−	14.2835i	−1.15027	−	0.965187i
$220$		0			0
$221$	−2.42183	−	1.39825i	−0.162910	−	0.0940562i
$222$		0			0
$223$	−2.36749	−	1.65774i	−0.158539	−	0.111010i	0.491615	−	0.870813i	$-0.336407\pi$
$223$	−2.36749	−	1.65774i	−0.158539	−	0.111010i	−0.650154	+	0.759802i	$0.725296\pi$
$224$		0			0
$225$	4.63311	−	3.49708i	0.308874	−	0.233138i
$226$		0			0
$227$	−16.8631	−	16.8631i	−1.11924	−	1.11924i	−0.991853	−	0.127388i	$-0.959341\pi$
$227$	−16.8631	−	16.8631i	−1.11924	−	1.11924i	−0.127388	−	0.991853i	$-0.540659\pi$
$228$		0			0
$229$		−	4.66862i		−	0.308511i	−0.988031	−	0.154255i	$-0.950702\pi$
$229$		−	4.66862i		−	0.308511i	0.988031	−	0.154255i	$-0.0492979\pi$
$230$		0			0
$231$	−14.9388	+	41.0440i	−0.982900	+	2.70049i
$232$		0			0
$233$	15.2434	−	21.7698i	0.998628	−	1.42619i	0.0961929	−	0.995363i	$-0.469333\pi$
$233$	15.2434	−	21.7698i	0.998628	−	1.42619i	0.902435	−	0.430826i	$-0.141778\pi$
$234$		0			0
$235$	7.27459	+	0.187597i	0.474542	+	0.0122375i
$236$		0			0
$237$	25.2874	−	2.21236i	1.64259	−	0.143708i
$238$		0			0
$239$	−19.0167	+	10.9793i	−1.23009	+	0.710192i	−0.967048	−	0.254593i	$-0.918058\pi$
$239$	−19.0167	+	10.9793i	−1.23009	+	0.710192i	−0.263040	+	0.964785i	$0.584725\pi$
$240$		0			0
$241$	−0.217853	−	0.598547i	−0.0140332	−	0.0385558i	0.932478	−	0.361226i	$-0.117642\pi$
$241$	−0.217853	−	0.598547i	−0.0140332	−	0.0385558i	−0.946511	+	0.322670i	$0.895420\pi$
$242$		0			0
$243$	6.57297	+	9.38718i	0.421656	+	0.602188i
$244$		0			0
$245$	−19.6276	+	8.54362i	−1.25396	+	0.545832i
$246$		0			0
$247$	−1.60964	+	0.644260i	−0.102419	+	0.0409933i
$248$		0			0
$249$	−15.9938	+	13.4204i	−1.01357	+	0.850485i
$250$		0			0
$251$	−0.494465	+	2.80425i	−0.0312104	+	0.177003i	−0.996428	−	0.0844442i	$-0.973089\pi$
$251$	−0.494465	+	2.80425i	−0.0312104	+	0.177003i	0.965218	+	0.261447i	$0.0841997\pi$
$252$		0			0
$253$	13.4743	+	6.28319i	0.847124	+	0.395021i
$254$		0			0
$255$	7.49859	+	31.1793i	0.469580	+	1.95252i
$256$		0			0
$257$	0.600604	+	6.86493i	0.0374646	+	0.428223i	0.991646	+	0.128992i	$0.0411743\pi$
$257$	0.600604	+	6.86493i	0.0374646	+	0.428223i	−0.954181	+	0.299230i	$0.903270\pi$
$258$		0			0
$259$	2.41034	−	4.17483i	0.149771	−	0.259411i
$260$		0			0
$261$	3.31716	−	0.584905i	0.205327	−	0.0362047i
$262$		0			0
$263$	9.58685	+	20.5591i	0.591151	+	1.26773i	0.943349	+	0.331801i	$0.107656\pi$
$263$	9.58685	+	20.5591i	0.591151	+	1.26773i	−0.352199	+	0.935925i	$0.614566\pi$
$264$		0			0
$265$	6.37016	+	11.7213i	0.391316	+	0.720031i
$266$		0			0
$267$	−8.99146	+	8.99146i	−0.550268	+	0.550268i
$268$		0			0
$269$	15.1901	+	5.52876i	0.926159	+	0.337094i	0.760686	−	0.649120i	$-0.224863\pi$
$269$	15.1901	+	5.52876i	0.926159	+	0.337094i	0.165473	+	0.986214i	$0.447085\pi$
$270$		0			0
$271$	−2.69830	−	15.3028i	−0.163910	−	0.929580i	−0.950181	−	0.311698i	$-0.899102\pi$
$271$	−2.69830	−	15.3028i	−0.163910	−	0.929580i	0.786271	−	0.617882i	$-0.212009\pi$
$272$		0			0
$273$	3.19054	−	0.854901i	0.193100	−	0.0517410i
$274$		0			0
$275$	−7.70897	−	25.1434i	−0.464869	−	1.51620i
$276$		0			0
$277$	16.3234	+	4.37384i	0.980778	+	0.262799i	0.713372	−	0.700785i	$-0.247167\pi$
$277$	16.3234	+	4.37384i	0.980778	+	0.262799i	0.267406	+	0.963584i	$0.413834\pi$
$278$		0			0
$279$	4.03070	−	1.46705i	0.241311	−	0.0878302i
$280$		0			0
$281$	−22.7557	−	4.01245i	−1.35749	−	0.239363i	−0.552929	−	0.833228i	$-0.686490\pi$
$281$	−22.7557	−	4.01245i	−1.35749	−	0.239363i	−0.804564	+	0.593866i	$0.797601\pi$
$282$		0			0
$283$	−2.17185	−	0.190012i	−0.129103	−	0.0112951i	0.0224210	−	0.999749i	$-0.492863\pi$
$283$	−2.17185	−	0.190012i	−0.129103	−	0.0112951i	−0.151524	+	0.988454i	$0.548418\pi$
$284$		0			0
$285$	18.0682	+	8.29648i	1.07027	+	0.491441i
$286$		0			0
$287$	−34.3236	−	3.00293i	−2.02606	−	0.177257i
$288$		0			0
$289$	−31.9371	−	5.63137i	−1.87865	−	0.331257i
$290$		0			0
$291$	−13.2692	+	4.82961i	−0.777856	+	0.283117i
$292$		0			0
$293$	−11.0113	−	2.95046i	−0.643285	−	0.172368i	−0.0775942	−	0.996985i	$-0.524724\pi$
$293$	−11.0113	−	2.95046i	−0.643285	−	0.172368i	−0.565691	+	0.824617i	$0.691391\pi$
$294$		0			0
$295$	−23.3068	+	15.4397i	−1.35697	+	0.898936i
$296$		0			0
$297$	19.0588	−	5.10680i	1.10591	−	0.296327i
$298$		0			0
$299$	−0.195235	−	1.10723i	−0.0112907	−	0.0640330i
$300$		0			0
$301$	9.75398	+	3.55016i	0.562210	+	0.204628i
$302$		0			0
$303$	−8.63355	+	8.63355i	−0.495985	+	0.495985i
$304$		0			0
$305$	0.951834	−	3.21804i	0.0545018	−	0.184264i
$306$		0			0
$307$	5.88095	+	12.6117i	0.335644	+	0.719790i	0.999609	−	0.0279735i	$-0.00890542\pi$
$307$	5.88095	+	12.6117i	0.335644	+	0.719790i	−0.663965	+	0.747764i	$0.731128\pi$
$308$		0			0
$309$	−22.8627	+	4.03131i	−1.30061	+	0.229333i
$310$		0			0
$311$	−16.2585	+	28.1606i	−0.921936	+	1.59684i	−0.125520	+	0.992091i	$0.540060\pi$
$311$	−16.2585	+	28.1606i	−0.921936	+	1.59684i	−0.796416	+	0.604749i	$0.793273\pi$
$312$		0			0
$313$	1.67825	+	19.1825i	0.0948603	+	1.08426i	0.883193	+	0.469009i	$0.155389\pi$
$313$	1.67825	+	19.1825i	0.0948603	+	1.08426i	−0.788333	+	0.615249i	$0.789056\pi$
$314$		0			0
$315$	−9.01311	−	5.51831i	−0.507831	−	0.310922i
$316$		0			0
$317$	15.1734	+	7.07545i	0.852221	+	0.397397i	0.799105	−	0.601191i	$-0.205307\pi$
$317$	15.1734	+	7.07545i	0.852221	+	0.397397i	0.0531156	+	0.998588i	$0.483085\pi$
$318$		0			0
$319$	2.64993	−	15.0285i	0.148368	−	0.841434i
$320$		0			0
$321$	4.17586	−	3.50396i	0.233074	−	0.195572i
$322$		0			0
$323$	−22.8408	+	20.4319i	−1.27090	+	1.13686i
$324$		0			0
$325$	−1.22318	+	1.56816i	−0.0678496	+	0.0869860i
$326$		0			0
$327$	−17.9103	−	25.5786i	−0.990442	−	1.41450i
$328$		0			0
$329$	−4.53131	−	12.4497i	−0.249819	−	0.686373i
$330$		0			0
$331$	16.6870	−	9.63424i	0.917200	−	0.529545i	0.0344590	−	0.999406i	$-0.489029\pi$
$331$	16.6870	−	9.63424i	0.917200	−	0.529545i	0.882741	+	0.469861i	$0.155696\pi$
$332$		0			0
$333$	1.36950	−	0.119816i	0.0750482	−	0.00656587i
$334$		0			0
$335$	0.634811	−	24.6165i	0.0346834	−	1.34494i
$336$		0			0
$337$	13.0318	−	18.6113i	0.709886	−	1.01382i	−0.288526	−	0.957472i	$-0.593165\pi$
$337$	13.0318	−	18.6113i	0.709886	−	1.01382i	0.998411	−	0.0563494i	$-0.0179461\pi$
$338$		0			0
$339$	−12.0829	+	33.1975i	−0.656253	+	1.80304i
$340$		0			0
$341$		−	19.4331i		−	1.05236i
$342$		0			0
$343$	7.40753	+	7.40753i	0.399969	+	0.399969i
$344$		0			0
$345$	−7.66486	+	10.3671i	−0.412662	+	0.558145i
$346$		0			0
$347$	6.08353	+	4.25973i	0.326581	+	0.228674i	0.725355	−	0.688375i	$-0.241676\pi$
$347$	6.08353	+	4.25973i	0.326581	+	0.228674i	−0.398775	+	0.917049i	$0.630564\pi$
$348$		0			0
$349$	10.7167	+	6.18731i	0.573653	+	0.331199i	0.758607	−	0.651548i	$-0.225880\pi$
$349$	10.7167	+	6.18731i	0.573653	+	0.331199i	−0.184954	+	0.982747i	$0.559214\pi$
$350$		0			0
$351$	−1.14304	−	0.959127i	−0.0610111	−	0.0511944i
$352$		0			0
$353$	−0.735596	+	2.74528i	−0.0391518	+	0.146117i	−0.982735	−	0.185019i	$-0.940765\pi$
$353$	−0.735596	+	2.74528i	−0.0391518	+	0.146117i	0.943583	+	0.331136i	$0.107432\pi$
$354$		0			0
$355$	22.4419	−	1.38156i	1.19109	−	0.0733258i
$356$		0			0
$357$	47.8255	−	33.4878i	2.53119	−	1.77236i
$358$		0			0
$359$	4.44916	+	5.30230i	0.234817	+	0.279845i	0.870566	−	0.492052i	$-0.163753\pi$
$359$	4.44916	+	5.30230i	0.234817	+	0.279845i	−0.635749	+	0.771896i	$0.719308\pi$
$360$		0			0
$361$	1.20212	+	18.9619i	0.0632697	+	0.997996i
$362$		0			0
$363$	−2.96272	+	33.8640i	−0.155502	+	1.77740i
$364$		0			0
$365$	−7.73833	−	23.0969i	−0.405043	−	1.20895i
$366$		0			0
$367$	−10.4094	+	22.3231i	−0.543367	+	1.16525i	0.422535	+	0.906347i	$0.361140\pi$
$367$	−10.4094	+	22.3231i	−0.543367	+	1.16525i	−0.965902	+	0.258908i	$0.916637\pi$
$368$		0			0
$369$	−4.91280	−	8.50921i	−0.255750	−	0.442972i
$370$		0			0
$371$	15.6119	−	18.6056i	0.810530	−	0.965952i
$372$		0			0
$373$	4.38742	+	16.3741i	0.227172	+	0.847817i	0.981523	+	0.191346i	$0.0612852\pi$
$373$	4.38742	+	16.3741i	0.227172	+	0.847817i	−0.754351	+	0.656472i	$0.772048\pi$
$374$		0			0
$375$	22.6985	−	2.21295i	1.17215	−	0.114276i
$376$		0			0
$377$	−1.04591	+	0.487718i	−0.0538673	+	0.0251187i
$378$		0			0
$379$	−4.98516			−0.256071			−0.128035	−	0.991770i	$-0.540867\pi$
$379$	−4.98516			−0.256071			−0.128035	+	0.991770i	$0.540867\pi$
$380$		0			0
$381$	−43.4405			−2.22552
$382$		0			0
$383$	−10.8911	+	5.07862i	−0.556511	+	0.259505i	−0.680462	−	0.732783i	$-0.738221\pi$
$383$	−10.8911	+	5.07862i	−0.556511	+	0.259505i	0.123952	+	0.992288i	$0.460443\pi$
$384$		0			0
$385$	−37.4593	+	29.8208i	−1.90910	+	1.51981i
$386$		0			0
$387$	0.766130	+	2.85923i	0.0389446	+	0.145343i
$388$		0			0
$389$	17.1250	−	20.4087i	0.868271	−	1.03476i	−0.130789	−	0.991410i	$-0.541751\pi$
$389$	17.1250	−	20.4087i	0.868271	−	1.03476i	0.999060	−	0.0433544i	$-0.0138045\pi$
$390$		0			0
$391$	−9.93649	−	17.2105i	−0.502510	−	0.870373i
$392$		0			0
$393$	−3.30588	+	7.08949i	−0.166760	+	0.357617i
$394$		0			0
$395$	24.9073	+	12.4059i	1.25322	+	0.624211i
$396$		0			0
$397$	−0.813936	+	9.30333i	−0.0408503	+	0.466921i	0.948027	+	0.318189i	$0.103075\pi$
$397$	−0.813936	+	9.30333i	−0.0408503	+	0.466921i	−0.988878	+	0.148732i	$0.952481\pi$
$398$		0			0
$399$	2.01192	−	36.1414i	0.100722	−	1.80933i
$400$		0			0
$401$	2.44981	+	2.91957i	0.122338	+	0.145796i	0.823737	−	0.566972i	$-0.191885\pi$
$401$	2.44981	+	2.91957i	0.122338	+	0.145796i	−0.701399	+	0.712769i	$0.747441\pi$
$402$		0			0
$403$	−1.20383	+	0.842928i	−0.0599669	+	0.0419893i
$404$		0			0
$405$	1.52991	+	24.8517i	0.0760219	+	1.23489i
$406$		0			0
$407$	1.61199	−	6.01604i	0.0799036	−	0.298204i
$408$		0			0
$409$	6.42996	+	5.39538i	0.317941	+	0.266784i	0.787765	−	0.615976i	$-0.211238\pi$
$409$	6.42996	+	5.39538i	0.317941	+	0.266784i	−0.469824	+	0.882760i	$0.655683\pi$
$410$		0			0
$411$	2.55538	+	1.47535i	0.126048	+	0.0727737i
$412$		0			0
$413$	41.6940	+	29.1944i	2.05163	+	1.43656i
$414$		0			0
$415$	−22.6342	+	3.39190i	−1.11107	+	0.166502i
$416$		0			0
$417$	−7.83570	−	7.83570i	−0.383716	−	0.383716i
$418$		0			0
$419$		−	16.3902i		−	0.800715i	−0.916359	−	0.400358i	$-0.868886\pi$
$419$		−	16.3902i		−	0.800715i	0.916359	−	0.400358i	$-0.131114\pi$
$420$		0			0
$421$	10.8336	−	29.7649i	0.527995	−	1.45065i	−0.333432	−	0.942774i	$-0.608207\pi$
$421$	10.8336	−	29.7649i	0.527995	−	1.45065i	0.861428	−	0.507881i	$-0.169571\pi$
$422$		0			0
$423$	2.16707	−	3.09490i	0.105367	−	0.150479i
$424$		0			0
$425$	−10.8363	+	33.4413i	−0.525639	+	1.62214i
$426$		0			0
$427$	−6.08648	+	0.532498i	−0.294545	+	0.0257694i
$428$		0			0
$429$	3.69581	−	2.13378i	0.178435	−	0.103020i
$430$		0			0
$431$	5.21178	+	14.3193i	0.251043	+	0.689734i	0.999643	+	0.0267129i	$0.00850399\pi$
$431$	5.21178	+	14.3193i	0.251043	+	0.689734i	−0.748600	+	0.663021i	$0.769274\pi$
$432$		0			0
$433$	−11.4790	−	16.3937i	−0.551644	−	0.787830i	0.442399	−	0.896819i	$-0.354128\pi$
$433$	−11.4790	−	16.3937i	−0.551644	−	0.787830i	−0.994043	+	0.108989i	$0.965239\pi$
$434$		0			0
$435$	12.3148	+	4.84528i	0.590451	+	0.232313i
$436$		0			0
$437$	−12.1954	−	1.75440i	−0.583387	−	0.0839244i
$438$		0			0
$439$	27.5013	−	23.0763i	1.31256	−	1.10137i	0.324738	−	0.945804i	$-0.394724\pi$
$439$	27.5013	−	23.0763i	1.31256	−	1.10137i	0.987825	−	0.155568i	$-0.0497206\pi$
$440$		0			0
$441$	−1.92994	+	10.9453i	−0.0919021	+	0.521203i
$442$		0			0
$443$	20.1578	+	9.39973i	0.957725	+	0.446595i	0.837673	−	0.546173i	$-0.183916\pi$
$443$	20.1578	+	9.39973i	0.957725	+	0.446595i	0.120053	+	0.992767i	$0.461694\pi$
$444$		0			0
$445$	−13.5526	+	3.25940i	−0.642456	+	0.154510i
$446$		0			0
$447$	−0.640124	−	7.31665i	−0.0302768	−	0.346066i
$448$		0			0
$449$	5.53111	−	9.58017i	0.261029	−	0.452116i	−0.705486	−	0.708724i	$-0.749271\pi$
$449$	5.53111	−	9.58017i	0.261029	−	0.452116i	0.966516	+	0.256607i	$0.0826047\pi$
$450$		0			0
$451$	−43.8389	+	7.72997i	−2.06429	+	0.363990i
$452$		0			0
$453$	−13.5321	−	29.0198i	−0.635795	−	1.36347i
$454$		0			0
$455$	3.47213	+	1.02699i	0.162776	+	0.0481461i
$456$		0			0
$457$	−19.3619	+	19.3619i	−0.905711	+	0.905711i	−0.995923	−	0.0902119i	$-0.971246\pi$
$457$	−19.3619	+	19.3619i	−0.905711	+	0.905711i	0.0902119	+	0.995923i	$0.471246\pi$
$458$		0			0
$459$	−24.7839	−	9.02060i	−1.15681	−	0.421046i
$460$		0			0
$461$	3.18798	+	18.0799i	0.148479	+	0.842065i	0.964508	+	0.264054i	$0.0850598\pi$
$461$	3.18798	+	18.0799i	0.148479	+	0.842065i	−0.816029	+	0.578011i	$0.803829\pi$
$462$		0			0
$463$	32.4922	−	8.70627i	1.51004	−	0.404614i	0.593593	−	0.804766i	$-0.297709\pi$
$463$	32.4922	−	8.70627i	1.51004	−	0.404614i	0.916449	+	0.400151i	$0.131042\pi$
$464$		0			0
$465$	16.5154	+	3.35326i	0.765883	+	0.155504i
$466$		0			0
$467$	−17.2230	−	4.61489i	−0.796986	−	0.213552i	−0.162726	−	0.986671i	$-0.552029\pi$
$467$	−17.2230	−	4.61489i	−0.796986	−	0.213552i	−0.634260	+	0.773119i	$0.718695\pi$
$468$		0			0
$469$	−42.1285	+	15.3335i	−1.94531	+	0.708035i
$470$		0			0
$471$	−8.96735	−	1.58119i	−0.413194	−	0.0728572i
$472$		0			0
$473$	13.3598	+	1.16883i	0.614283	+	0.0537428i
$474$		0			0
$475$	12.1429	+	18.0983i	0.557156	+	0.830408i
$476$		0			0
$477$	6.89991	+	0.603664i	0.315925	+	0.0276399i
$478$		0			0
$479$	−2.38679	−	0.420856i	−0.109055	−	0.0192294i	0.118854	−	0.992912i	$-0.462078\pi$
$479$	−2.38679	−	0.420856i	−0.109055	−	0.0192294i	−0.227909	+	0.973682i	$0.573189\pi$
$480$		0			0
$481$	−0.442598	+	0.161092i	−0.0201807	+	0.00734518i
$482$		0			0
$483$	22.6732	+	6.07526i	1.03167	+	0.276434i
$484$		0			0
$485$	−15.1697	−	3.08003i	−0.688820	−	0.139857i
$486$		0			0
$487$	−3.55271	+	0.951946i	−0.160989	+	0.0431368i	−0.338413	−	0.940998i	$-0.609890\pi$
$487$	−3.55271	+	0.951946i	−0.160989	+	0.0431368i	0.177424	+	0.984134i	$0.443223\pi$
$488$		0			0
$489$	2.17884	+	12.3568i	0.0985304	+	0.558794i
$490$		0			0
$491$	16.1030	+	5.86101i	0.726718	+	0.264504i	0.678775	−	0.734346i	$-0.262511\pi$
$491$	16.1030	+	5.86101i	0.726718	+	0.264504i	0.0479433	+	0.998850i	$0.484733\pi$
$492$		0			0
$493$	−14.4238	+	14.4238i	−0.649616	+	0.649616i
$494$		0			0
$495$	−13.0933	−	3.87276i	−0.588502	−	0.174068i
$496$		0			0
$497$	−17.3001	−	37.1002i	−0.776016	−	1.66417i
$498$		0			0
$499$	14.1455	−	2.49424i	0.633241	−	0.111657i	0.152192	−	0.988351i	$-0.451367\pi$
$499$	14.1455	−	2.49424i	0.633241	−	0.111657i	0.481049	+	0.876694i	$0.340256\pi$
$500$		0			0
$501$	4.63988	−	8.03652i	0.207295	−	0.359045i
$502$		0			0
$503$	−1.42794	−	16.3215i	−0.0636688	−	0.727738i	−0.959198	−	0.282735i	$-0.908758\pi$
$503$	−1.42794	−	16.3215i	−0.0636688	−	0.727738i	0.895529	−	0.445003i	$-0.146797\pi$
$504$		0			0
$505$	−13.0132	+	3.12966i	−0.579079	+	0.139268i
$506$		0			0
$507$	23.7409	+	11.0706i	1.05437	+	0.491661i
$508$		0			0
$509$	4.01451	−	22.7674i	0.177940	−	1.00915i	−0.756755	−	0.653698i	$-0.773217\pi$
$509$	4.01451	−	22.7674i	0.177940	−	1.00915i	0.934695	−	0.355450i	$-0.115672\pi$
$510$		0			0
$511$	−33.9725	+	28.5063i	−1.50286	+	1.26105i
$512$		0			0
$513$	−13.8952	+	8.62003i	−0.613489	+	0.380583i
$514$		0			0
$515$	−23.6816	−	9.31755i	−1.04354	−	0.410581i
$516$		0			0
$517$	−9.81799	−	14.0215i	−0.431795	−	0.616667i
$518$		0			0
$519$	−2.54778	−	6.99997i	−0.111835	−	0.307264i
$520$		0			0
$521$	15.5585	−	8.98273i	0.681632	−	0.393540i	−0.118838	−	0.992914i	$-0.537917\pi$
$521$	15.5585	−	8.98273i	0.681632	−	0.393540i	0.800470	+	0.599373i	$0.204583\pi$
$522$		0			0
$523$	17.4782	−	1.52914i	0.764266	−	0.0668646i	0.301645	−	0.953420i	$-0.402464\pi$
$523$	17.4782	−	1.52914i	0.764266	−	0.0668646i	0.462622	+	0.886556i	$0.346909\pi$
$524$		0			0
$525$	−18.8797	−	36.9807i	−0.823976	−	1.61397i
$526$		0			0
$527$	−14.8993	+	21.2784i	−0.649023	+	0.926902i
$528$		0			0
$529$	−5.13378	+	14.1050i	−0.223208	+	0.613259i
$530$		0			0
$531$			14.5151i			0.629900i
$532$		0			0
$533$	2.38039	+	2.38039i	0.103106	+	0.103106i
$534$		0			0
$535$	5.90960	−	0.885598i	0.255494	−	0.0382877i
$536$		0			0
$537$	18.6856	+	13.0838i	0.806343	+	0.564607i
$538$		0			0
$539$	43.6068	+	25.1764i	1.87828	+	1.08442i
$540$		0			0
$541$	−11.9865	−	10.0579i	−0.515339	−	0.432421i	0.347664	−	0.937619i	$-0.386975\pi$
$541$	−11.9865	−	10.0579i	−0.515339	−	0.432421i	−0.863003	+	0.505198i	$0.831419\pi$
$542$		0			0
$543$	10.2445	−	38.2329i	0.439633	−	1.64073i
$544$		0			0
$545$	−2.10324	−	34.1648i	−0.0900931	−	1.46346i
$546$		0			0
$547$	26.4714	−	18.5355i	1.13184	−	0.792520i	0.151228	−	0.988499i	$-0.451677\pi$
$547$	26.4714	−	18.5355i	1.13184	−	0.792520i	0.980608	+	0.195979i	$0.0627885\pi$
$548$		0			0
$549$	−1.11995	−	1.33471i	−0.0477984	−	0.0569639i
$550$		0			0
$551$	1.50044	+	12.5574i	0.0639207	+	0.534963i
$552$		0			0
$553$	4.41534	−	50.4675i	0.187759	−	2.14610i
$554$		0			0
$555$	4.83462	+	2.40806i	0.205218	+	0.102216i
$556$		0			0
$557$	8.31662	−	17.8351i	0.352387	−	0.755696i	−0.647594	−	0.761986i	$-0.724225\pi$
$557$	8.31662	−	17.8351i	0.352387	−	0.755696i	0.999980	+	0.00629033i	$0.00200229\pi$
$558$		0			0
$559$	−0.507085	−	0.878298i	−0.0214474	−	0.0371480i
$560$		0			0
$561$	48.4866	−	57.7840i	2.04710	−	2.43964i
$562$		0			0
$563$	0.299976	+	1.11952i	0.0126425	+	0.0471823i	0.971959	−	0.235151i	$-0.0755584\pi$
$563$	0.299976	+	1.11952i	0.0126425	+	0.0471823i	−0.959316	+	0.282333i	$0.908892\pi$
$564$		0			0
$565$	−30.2981	+	24.1199i	−1.27465	+	1.01473i
$566$		0			0
$567$	41.0839	−	19.1577i	1.72536	−	0.804550i
$568$		0			0
$569$	10.4782			0.439270			0.219635	−	0.975582i	$-0.429513\pi$
$569$	10.4782			0.439270			0.219635	+	0.975582i	$0.429513\pi$
$570$		0			0
$571$	9.27426			0.388116			0.194058	−	0.980990i	$-0.437835\pi$
$571$	9.27426			0.388116			0.194058	+	0.980990i	$0.437835\pi$
$572$		0			0
$573$	36.2161	−	16.8879i	1.51295	−	0.705501i
$574$		0			0
$575$	−13.0998	+	5.30479i	−0.546300	+	0.221225i
$576$		0			0
$577$	10.6611	+	39.7878i	0.443828	+	1.65639i	0.719013	+	0.694996i	$0.244594\pi$
$577$	10.6611	+	39.7878i	0.443828	+	1.65639i	−0.275186	+	0.961391i	$0.588739\pi$
$578$		0			0
$579$	−15.9199	+	18.9726i	−0.661608	+	0.788474i
$580$		0			0
$581$	20.8342	+	36.0859i	0.864348	+	1.49709i
$582$		0			0
$583$	13.2616	−	28.4396i	0.549240	−	1.17785i
$584$		0			0
$585$	0.328028	+	0.979078i	0.0135623	+	0.0404799i
$586$		0			0
$587$	−0.0480237	+	0.548913i	−0.00198215	+	0.0226561i	−0.997121	−	0.0758221i	$-0.975842\pi$
$587$	−0.0480237	+	0.548913i	−0.00198215	+	0.0226561i	0.995139	+	0.0984781i	$0.0313975\pi$
$588$		0			0
$589$	4.65852	+	15.4164i	0.191951	+	0.635221i
$590$		0			0
$591$	−0.128179	−	0.152757i	−0.00527256	−	0.00628359i
$592$		0			0
$593$	−8.04565	+	5.63362i	−0.330395	+	0.231345i	−0.726989	−	0.686649i	$-0.759081\pi$
$593$	−8.04565	+	5.63362i	−0.330395	+	0.231345i	0.396594	+	0.917994i	$0.370192\pi$
$594$		0			0
$595$	63.8796	−	3.93254i	2.61881	−	0.161218i
$596$		0			0
$597$	−3.52208	+	13.1446i	−0.144149	+	0.537972i
$598$		0			0
$599$	−23.5760	−	19.7826i	−0.963289	−	0.808295i	0.0181960	−	0.999834i	$-0.494208\pi$
$599$	−23.5760	−	19.7826i	−0.963289	−	0.808295i	−0.981485	+	0.191539i	$0.938652\pi$
$600$		0			0
$601$	36.2792	+	20.9458i	1.47986	+	0.854398i	0.999740	−	0.0228041i	$-0.00725940\pi$
$601$	36.2792	+	20.9458i	1.47986	+	0.854398i	0.480121	+	0.877202i	$0.340593\pi$
$602$		0			0
$603$	−10.4728	−	7.33316i	−0.426487	−	0.298629i
$604$		0			0
$605$	−22.1532	+	29.9633i	−0.900657	+	1.21818i
$606$		0			0
$607$	−17.1418	−	17.1418i	−0.695766	−	0.695766i	0.267728	−	0.963494i	$-0.413727\pi$
$607$	−17.1418	−	17.1418i	−0.695766	−	0.695766i	−0.963494	+	0.267728i	$0.913727\pi$
$608$		0			0
$609$		−	24.0936i		−	0.976321i
$610$		0			0
$611$	−0.442730	+	1.21639i	−0.0179109	+	0.0492099i
$612$		0			0
$613$	−9.83494	+	14.0458i	−0.397230	+	0.567303i	−0.967089	−	0.254440i	$-0.918109\pi$
$613$	−9.83494	+	14.0458i	−0.397230	+	0.567303i	0.569859	+	0.821742i	$0.306998\pi$
$614$		0			0
$615$	0.995176	−	38.5906i	0.0401294	−	1.55612i
$616$		0			0
$617$	−7.20414	+	0.630280i	−0.290028	+	0.0253741i	−0.231241	−	0.972896i	$-0.574279\pi$
$617$	−7.20414	+	0.630280i	−0.290028	+	0.0253741i	−0.0587865	+	0.998271i	$0.518723\pi$
$618$		0			0
$619$	16.5254	−	9.54095i	0.664212	−	0.383483i	−0.129668	−	0.991557i	$-0.541391\pi$
$619$	16.5254	−	9.54095i	0.664212	−	0.383483i	0.793880	+	0.608074i	$0.208058\pi$
$620$		0			0
$621$	−3.62668	−	9.96423i	−0.145534	−	0.399851i
$622$		0			0
$623$	14.5561	+	20.7882i	0.583176	+	0.832862i
$624$		0			0
$625$	22.4873	+	10.9235i	0.899490	+	0.436941i
$626$		0			0
$627$	−9.57459	−	45.7761i	−0.382372	−	1.82812i
$628$		0			0
$629$	−6.37753	+	5.35138i	−0.254289	+	0.213374i
$630$		0			0
$631$	−5.30314	+	30.0756i	−0.211115	+	1.19729i	0.676408	+	0.736527i	$0.263536\pi$
$631$	−5.30314	+	30.0756i	−0.211115	+	1.19729i	−0.887523	+	0.460764i	$0.847575\pi$
$632$		0			0
$633$	−29.0765	−	13.5586i	−1.15569	−	0.538905i
$634$		0			0
$635$	−40.6120	−	24.8649i	−1.61164	−	0.986733i
$636$		0			0
$637$	−0.331876	−	3.79336i	−0.0131494	−	0.150298i
$638$		0			0
$639$	5.83688	−	10.1098i	0.230903	−	0.399936i
$640$		0			0
$641$	−3.58740	+	0.632556i	−0.141694	+	0.0249844i	−0.244045	−	0.969764i	$-0.578475\pi$
$641$	−3.58740	+	0.632556i	−0.141694	+	0.0249844i	0.102351	+	0.994748i	$0.467363\pi$
$642$		0			0
$643$	−1.31852	−	2.82757i	−0.0519972	−	0.111508i	0.878593	−	0.477572i	$-0.158483\pi$
$643$	−1.31852	−	2.82757i	−0.0519972	−	0.111508i	−0.930590	+	0.366064i	$0.880705\pi$
$644$		0			0
$645$	−3.29861	+	11.1522i	−0.129883	+	0.439118i
$646$		0			0
$647$	0.268782	−	0.268782i	0.0105669	−	0.0105669i	−0.701804	−	0.712370i	$-0.747622\pi$
$647$	0.268782	−	0.268782i	0.0105669	−	0.0105669i	0.712370	+	0.701804i	$0.247622\pi$
$648$		0			0
$649$	61.7950	+	22.4916i	2.42567	+	0.882871i
$650$		0			0
$651$	−5.32783	−	30.2156i	−0.208814	−	1.18424i
$652$		0			0
$653$	24.9123	−	6.67522i	0.974893	−	0.261222i	0.264000	−	0.964523i	$-0.414958\pi$
$653$	24.9123	−	6.67522i	0.974893	−	0.261222i	0.710892	+	0.703301i	$0.248291\pi$
$654$		0			0
$655$	−7.14858	+	4.73563i	−0.279318	+	0.185036i
$656$		0			0
$657$	−12.2160	−	3.27326i	−0.476590	−	0.127702i
$658$		0			0
$659$	−11.4747	+	4.17644i	−0.446989	+	0.162691i	−0.555701	−	0.831383i	$-0.687550\pi$
$659$	−11.4747	+	4.17644i	−0.446989	+	0.162691i	0.108711	+	0.994073i	$0.465328\pi$
$660$		0			0
$661$	17.7226	+	3.12498i	0.689330	+	0.121547i	0.507331	−	0.861751i	$-0.330632\pi$
$661$	17.7226	+	3.12498i	0.689330	+	0.121547i	0.181999	+	0.983299i	$0.441743\pi$
$662$		0			0
$663$	−5.68269	−	0.497171i	−0.220698	−	0.0193085i
$664$		0			0
$665$	22.5679	−	32.6366i	0.875146	−	1.26559i
$666$		0			0
$667$	−8.16984	−	0.714769i	−0.316338	−	0.0276760i
$668$		0			0
$669$	−5.80593	−	1.02374i	−0.224470	−	0.0395801i
$670$		0			0
$671$	−7.41765	+	2.69981i	−0.286355	+	0.104225i
$672$		0			0
$673$	−19.6606	−	5.26805i	−0.757861	−	0.203068i	−0.140859	−	0.990030i	$-0.544986\pi$
$673$	−19.6606	−	5.26805i	−0.757861	−	0.203068i	−0.617002	+	0.786961i	$0.711653\pi$
$674$		0			0
$675$	−8.79263	+	16.5683i	−0.338428	+	0.637714i
$676$		0			0
$677$	−31.7583	+	8.50962i	−1.22057	+	0.327051i	−0.810902	−	0.585182i	$-0.801023\pi$
$677$	−31.7583	+	8.50962i	−1.22057	+	0.327051i	−0.409670	+	0.912234i	$0.634356\pi$
$678$		0			0
$679$	4.89371	+	27.7536i	0.187803	+	1.06509i
$680$		0			0
$681$	−45.7124	−	16.6379i	−1.75170	−	0.637567i
$682$		0			0
$683$	0.945060	−	0.945060i	0.0361617	−	0.0361617i	−0.688795	−	0.724956i	$-0.741860\pi$
$683$	0.945060	−	0.945060i	0.0361617	−	0.0361617i	0.724956	+	0.688795i	$0.241860\pi$
$684$		0			0
$685$	1.54452	+	2.84197i	0.0590133	+	0.108586i
$686$		0			0
$687$	−4.02469	−	8.63099i	−0.153552	−	0.329293i
$688$		0			0
$689$	−2.33698	+	0.412073i	−0.0890320	+	0.0156987i
$690$		0			0
$691$	2.61682	−	4.53247i	0.0995486	−	0.172423i	−0.811949	−	0.583728i	$-0.801593\pi$
$691$	2.61682	−	4.53247i	0.0995486	−	0.172423i	0.911498	+	0.411305i	$0.134927\pi$
$692$		0			0
$693$	2.16659	+	24.7643i	0.0823021	+	0.940717i
$694$		0			0
$695$	−2.84044	−	11.8106i	−0.107744	−	0.448001i
$696$		0			0
$697$	53.9280	+	25.1471i	2.04267	+	0.952513i
$698$		0			0
$699$	9.41363	−	53.3873i	0.356056	−	2.01929i
$700$		0			0
$701$	19.6502	−	16.4885i	0.742178	−	0.622761i	−0.191244	−	0.981543i	$-0.561252\pi$
$701$	19.6502	−	16.4885i	0.742178	−	0.622761i	0.933422	+	0.358781i	$0.116808\pi$
$702$		0			0
$703$	0.163367	+	5.15897i	0.00616151	+	0.194574i
$704$		0			0
$705$	13.6104	−	5.92442i	0.512599	−	0.223127i
$706$		0			0
$707$	13.9767	+	19.9607i	0.525647	+	0.750701i
$708$		0			0
$709$	−1.38818	−	3.81398i	−0.0521340	−	0.143237i	0.910892	−	0.412644i	$-0.135395\pi$
$709$	−1.38818	−	3.81398i	−0.0521340	−	0.143237i	−0.963026	+	0.269407i	$0.913172\pi$
$710$		0			0
$711$	12.5115	−	7.22351i	0.469217	−	0.270903i
$712$		0			0
$713$	−10.4038	+	0.910216i	−0.389626	+	0.0340879i
$714$		0			0
$715$	4.67652	+	0.120598i	0.174892	+	0.00451012i
$716$		0			0
$717$	−25.6917	+	36.6915i	−0.959473	+	1.37027i
$718$		0			0
$719$	−15.8467	+	43.5384i	−0.590981	+	1.62371i	0.177707	+	0.984083i	$0.443132\pi$
$719$	−15.8467	+	43.5384i	−0.590981	+	1.62371i	−0.768688	+	0.639624i	$0.779090\pi$
$720$		0			0
$721$			46.3323i			1.72551i
$722$		0			0
$723$	−0.918742	−	0.918742i	−0.0341684	−	0.0341684i
$724$		0			0
$725$	8.73961	+	11.5787i	0.324581	+	0.430021i
$726$		0			0
$727$	−18.8800	−	13.2199i	−0.700220	−	0.490299i	0.168438	−	0.985712i	$-0.446128\pi$
$727$	−18.8800	−	13.2199i	−0.700220	−	0.490299i	−0.868657	+	0.495413i	$0.835017\pi$
$728$		0			0
$729$	−8.68564	−	5.01466i	−0.321691	−	0.185728i
$730$		0			0
$731$	−13.7322	−	11.5227i	−0.507904	−	0.426182i
$732$		0			0
$733$	−2.56734	+	9.58146i	−0.0948270	+	0.353899i	−0.996993	−	0.0774895i	$-0.975310\pi$
$733$	−2.56734	+	9.58146i	−0.0948270	+	0.353899i	0.902166	+	0.431389i	$0.141976\pi$
$734$		0			0
$735$	−28.9208	+	32.7153i	−1.06676	+	1.20672i
$736$		0			0
$737$	−47.4475	+	33.2231i	−1.74775	+	1.22379i
$738$		0			0
$739$	−21.0344	−	25.0678i	−0.773762	−	0.922133i	0.224872	−	0.974388i	$-0.427804\pi$
$739$	−21.0344	−	25.0678i	−0.773762	−	0.922133i	−0.998634	+	0.0522552i	$0.983359\pi$
$740$		0			0
$741$	−2.42039	+	2.57869i	−0.0889151	+	0.0947306i
$742$		0			0
$743$	0.239017	−	2.73197i	0.00876867	−	0.100226i	−0.990549	−	0.137159i	$-0.956203\pi$
$743$	0.239017	−	2.73197i	0.00876867	−	0.100226i	0.999318	+	0.0369322i	$0.0117586\pi$
$744$		0			0
$745$	3.58953	−	7.20666i	0.131510	−	0.264031i
$746$		0			0
$747$	−5.02186	+	10.7694i	−0.183740	+	0.394033i
$748$		0			0
$749$	−5.43964	−	9.42173i	−0.198760	−	0.344262i
$750$		0			0
$751$	−28.4315	+	33.8833i	−1.03748	+	1.23642i	−0.0663661	+	0.997795i	$0.521141\pi$
$751$	−28.4315	+	33.8833i	−1.03748	+	1.23642i	−0.971112	+	0.238623i	$0.923304\pi$
$752$		0			0
$753$	1.50334	+	5.61055i	0.0547849	+	0.204460i
$754$		0			0
$755$	3.95956	−	34.8759i	0.144103	−	1.26926i
$756$		0			0
$757$	38.3336	−	17.8752i	1.39326	−	0.649687i	0.426291	−	0.904586i	$-0.359820\pi$
$757$	38.3336	−	17.8752i	1.39326	−	0.649687i	0.966968	+	0.254899i	$0.0820424\pi$
$758$		0			0
$759$	30.3269			1.10080
$760$		0			0
$761$	11.9286			0.432412			0.216206	−	0.976348i	$-0.430632\pi$
$761$	11.9286			0.432412			0.216206	+	0.976348i	$0.430632\pi$
$762$		0			0
$763$	−56.4801	+	26.3371i	−2.04472	+	0.953467i
$764$		0			0
$765$	11.3674	+	14.2791i	0.410988	+	0.516262i
$766$		0			0
$767$	−1.28712	−	4.80361i	−0.0464753	−	0.173448i
$768$		0			0
$769$	−19.7272	+	23.5099i	−0.711380	+	0.847789i	−0.993763	−	0.111512i	$-0.964431\pi$
$769$	−19.7272	+	23.5099i	−0.711380	+	0.847789i	0.282383	+	0.959302i	$0.408875\pi$
$770$		0			0
$771$	7.02843	+	12.1736i	0.253123	+	0.438421i
$772$		0			0
$773$	1.08502	−	2.32684i	0.0390255	−	0.0836906i	−0.885828	−	0.464013i	$-0.846409\pi$
$773$	1.08502	−	2.32684i	0.0390255	−	0.0836906i	0.924854	+	0.380322i	$0.124187\pi$
$774$		0			0
$775$	13.5207	+	12.5882i	0.485678	+	0.452181i
$776$		0			0
$777$	0.857039	−	9.79600i	0.0307461	−	0.351430i
$778$		0			0
$779$	32.9245	−	16.6413i	1.17964	−	0.596235i
$780$		0			0
$781$	−33.9959	−	40.5148i	−1.21647	−	1.44973i
$782$		0			0
$783$	−8.91569	+	6.24283i	−0.318621	+	0.223101i
$784$		0			0
$785$	−7.47842	−	6.61105i	−0.266916	−	0.235959i
$786$		0			0
$787$	−11.7654	+	43.9090i	−0.419390	+	1.56519i	0.356486	+	0.934301i	$0.383975\pi$
$787$	−11.7654	+	43.9090i	−0.419390	+	1.56519i	−0.775876	+	0.630885i	$0.782692\pi$
$788$		0			0
$789$	35.4469	+	29.7435i	1.26194	+	1.05890i
$790$		0			0
$791$	61.0601	+	35.2531i	2.17105	+	1.25346i

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84872 - 0.862074i) q^{3} +(2.22179 + 0.252247i) q^{5} +(-1.05366 - 3.93231i) q^{7} +(0.746246 - 0.889341i) q^{9} +O(q^{10})\)	\(q+(1.84872 - 0.862074i) q^{3} +(2.22179 + 0.252247i) q^{5} +(-1.05366 - 3.93231i) q^{7} +(0.746246 - 0.889341i) q^{9} +(-2.62986 - 4.55506i) q^{11} +(-0.168100 + 0.360492i) q^{13} +(4.32494 - 1.44902i) q^{15} +(-0.612760 + 7.00388i) q^{17} +(3.17822 + 2.98311i) q^{19} +(-5.33787 - 6.36142i) q^{21} +(-2.31544 + 1.62129i) q^{23} +(4.87274 + 1.12088i) q^{25} +(-0.970925 + 3.62354i) q^{27} +(2.22257 + 1.86496i) q^{29} +(3.19971 + 1.84735i) q^{31} +(-8.78869 - 6.15390i) q^{33} +(-1.34910 - 9.00257i) q^{35} +(0.837316 + 0.837316i) q^{37} +0.811364i q^{39} +(2.89465 - 7.95299i) q^{41} +(-1.46246 + 2.08860i) q^{43} +(1.88234 - 1.78769i) q^{45} +(3.24199 - 0.283638i) q^{47} +(-8.29069 + 4.78663i) q^{49} +(4.90504 + 13.4765i) q^{51} +(3.42197 + 4.88708i) q^{53} +(-4.69402 - 10.7838i) q^{55} +(8.44731 + 2.77509i) q^{57} +(-9.57764 + 8.03660i) q^{59} +(0.260608 - 1.47798i) q^{61} +(-4.28345 - 1.99741i) q^{63} +(-0.464416 + 0.758536i) q^{65} +(-0.959802 - 10.9706i) q^{67} +(-2.88294 + 4.99339i) q^{69} +(9.90257 - 1.74609i) q^{71} +(-4.60382 - 9.87292i) q^{73} +(9.97464 - 2.12847i) q^{75} +(-15.1409 + 15.1409i) q^{77} +(11.6936 + 4.25614i) q^{79} +(1.93358 + 10.9659i) q^{81} +(-9.88658 + 2.64910i) q^{83} +(-3.12813 + 15.4066i) q^{85} +(5.71664 + 1.53177i) q^{87} +(-5.85780 + 2.13206i) q^{89} +(1.59468 + 0.281186i) q^{91} +(7.50794 + 0.656859i) q^{93} +(6.30887 + 7.42955i) q^{95} +(-6.89617 - 0.603337i) q^{97} +(-6.01352 - 1.06035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more