LMFDB - Embedded newform 380.2.bh.a.33.6

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			33.6
Character	$\chi$	$=$	380.33
Dual form			380.2.bh.a.357.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.230238 + 0.328814i) q^{3} +(-0.244120 - 2.22270i) q^{5} +(1.71755 + 0.460216i) q^{7} +(0.970951 - 2.66767i) q^{9} +O(q^{10})$	\(q+(0.230238 + 0.328814i) q^{3} +(-0.244120 - 2.22270i) q^{5} +(1.71755 + 0.460216i) q^{7} +(0.970951 - 2.66767i) q^{9} +(-0.811761 + 1.40601i) q^{11} +(-1.34171 - 0.939476i) q^{13} +(0.674649 - 0.592020i) q^{15} +(1.80828 - 3.87786i) q^{17} +(3.68688 - 2.32528i) q^{19} +(0.244119 + 0.670713i) q^{21} +(-2.59687 - 0.227196i) q^{23} +(-4.88081 + 1.08521i) q^{25} +(2.26390 - 0.606611i) q^{27} +(5.22957 + 1.90341i) q^{29} +(7.83030 - 4.52083i) q^{31} +(-0.649214 + 0.0567989i) q^{33} +(0.603635 - 3.92995i) q^{35} +(7.41769 + 7.41769i) q^{37} -0.657476i q^{39} +(-11.8810 - 2.09494i) q^{41} +(0.964681 + 11.0263i) q^{43} +(-6.16646 - 1.50691i) q^{45} +(-6.43188 + 2.99924i) q^{47} +(-3.32400 - 1.91911i) q^{49} +(1.69143 - 0.298244i) q^{51} +(-0.111246 + 1.27154i) q^{53} +(3.32331 + 1.46107i) q^{55} +(1.61344 + 0.676931i) q^{57} +(2.72183 - 0.990665i) q^{59} +(-3.26714 + 2.74146i) q^{61} +(2.89536 - 4.13500i) q^{63} +(-1.76064 + 3.21157i) q^{65} +(-1.53379 - 3.28923i) q^{67} +(-0.523192 - 0.906195i) q^{69} +(2.47896 - 2.95431i) q^{71} +(-9.16796 + 6.41948i) q^{73} +(-1.48058 - 1.35502i) q^{75} +(-2.04131 + 2.04131i) q^{77} +(-0.420678 + 2.38578i) q^{79} +(-5.80341 - 4.86964i) q^{81} +(-2.41572 + 9.01558i) q^{83} +(-9.06076 - 3.07260i) q^{85} +(0.578178 + 2.15779i) q^{87} +(0.807422 + 4.57912i) q^{89} +(-1.87209 - 2.23107i) q^{91} +(3.28934 + 1.53385i) q^{93} +(-6.06844 - 7.62719i) q^{95} +(1.40699 + 0.656091i) q^{97} +(2.96259 + 3.53068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	0.230238	+	0.328814i	0.132928	+	0.189841i	0.880098	−	0.474792i	$-0.157477\pi$
$3$	0.230238	+	0.328814i	0.132928	+	0.189841i	−0.747170	+	0.664633i	$0.768588\pi$
$4$		0			0
$5$	−0.244120	−	2.22270i	−0.109174	−	0.994023i
$5$	−0.244120	−	2.22270i	−0.109174	−	0.994023i
$6$		0			0
$7$	1.71755	+	0.460216i	0.649172	+	0.173945i	0.568355	−	0.822784i	$-0.307580\pi$
$7$	1.71755	+	0.460216i	0.649172	+	0.173945i	0.0808177	+	0.996729i	$0.474247\pi$
$8$		0			0
$9$	0.970951	−	2.66767i	0.323650	−	0.889222i
$10$		0			0
$11$	−0.811761	+	1.40601i	−0.244755	+	0.423929i	−0.962063	−	0.272828i	$-0.912041\pi$
$11$	−0.811761	+	1.40601i	−0.244755	+	0.423929i	0.717307	+	0.696757i	$0.245374\pi$
$12$		0			0
$13$	−1.34171	−	0.939476i	−0.372124	−	0.260564i	0.372523	−	0.928023i	$-0.378493\pi$
$13$	−1.34171	−	0.939476i	−0.372124	−	0.260564i	−0.744646	+	0.667459i	$0.767382\pi$
$14$		0			0
$15$	0.674649	−	0.592020i	0.174194	−	0.152859i
$16$		0			0
$17$	1.80828	−	3.87786i	0.438571	−	0.940519i	−0.555472	−	0.831535i	$-0.687463\pi$
$17$	1.80828	−	3.87786i	0.438571	−	0.940519i	0.994044	−	0.108984i	$-0.0347597\pi$
$18$		0			0
$19$	3.68688	−	2.32528i	0.845829	−	0.533455i
$19$	3.68688	−	2.32528i	0.845829	−	0.533455i
$20$		0			0
$21$	0.244119	+	0.670713i	0.0532712	+	0.146361i
$22$		0			0
$23$	−2.59687	−	0.227196i	−0.541484	−	0.0473737i	−0.186867	−	0.982385i	$-0.559833\pi$
$23$	−2.59687	−	0.227196i	−0.541484	−	0.0473737i	−0.354617	+	0.935012i	$0.615389\pi$
$24$		0			0
$25$	−4.88081	+	1.08521i	−0.976162	+	0.217042i
$26$		0			0
$27$	2.26390	−	0.606611i	0.435689	−	0.116742i
$28$		0			0
$29$	5.22957	+	1.90341i	0.971107	+	0.353454i	0.778376	−	0.627798i	$-0.216044\pi$
$29$	5.22957	+	1.90341i	0.971107	+	0.353454i	0.192730	+	0.981252i	$0.438266\pi$
$30$		0			0
$31$	7.83030	−	4.52083i	1.40636	−	0.811965i	0.411329	−	0.911487i	$-0.365065\pi$
$31$	7.83030	−	4.52083i	1.40636	−	0.811965i	0.995035	+	0.0995225i	$0.0317315\pi$
$32$		0			0
$33$	−0.649214	+	0.0567989i	−0.113014	+	0.00988742i
$34$		0			0
$35$	0.603635	−	3.92995i	0.102033	−	0.664282i
$36$		0			0
$37$	7.41769	+	7.41769i	1.21946	+	1.21946i	0.967821	+	0.251639i	$0.0809695\pi$
$37$	7.41769	+	7.41769i	1.21946	+	1.21946i	0.251639	+	0.967821i	$0.419031\pi$
$38$		0			0
$39$		−	0.657476i		−	0.105280i
$40$		0			0
$41$	−11.8810	−	2.09494i	−1.85550	−	0.327174i	−0.869500	−	0.493934i	$-0.835559\pi$
$41$	−11.8810	−	2.09494i	−1.85550	−	0.327174i	−0.985998	+	0.166759i	$0.946670\pi$
$42$		0			0
$43$	0.964681	+	11.0263i	0.147112	+	1.68150i	0.607917	+	0.794001i	$0.292005\pi$
$43$	0.964681	+	11.0263i	0.147112	+	1.68150i	−0.460804	+	0.887502i	$0.652439\pi$
$44$		0			0
$45$	−6.16646	−	1.50691i	−0.919241	−	0.224636i
$46$		0			0
$47$	−6.43188	+	2.99924i	−0.938187	+	0.437484i	−0.830698	−	0.556723i	$-0.812059\pi$
$47$	−6.43188	+	2.99924i	−0.938187	+	0.437484i	−0.107488	+	0.994206i	$0.534281\pi$
$48$		0			0
$49$	−3.32400	−	1.91911i	−0.474858	−	0.274159i
$50$		0			0
$51$	1.69143	−	0.298244i	0.236847	−	0.0417625i
$52$		0			0
$53$	−0.111246	+	1.27154i	−0.0152808	+	0.174660i	0.984719	+	0.174150i	$0.0557178\pi$
$53$	−0.111246	+	1.27154i	−0.0152808	+	0.174660i	−1.00000		0.000509831i	$0.999838\pi$
$54$		0			0
$55$	3.32331	+	1.46107i	0.448115	+	0.197010i
$56$		0			0
$57$	1.61344	+	0.676931i	0.213706	+	0.0896617i
$58$		0			0
$59$	2.72183	−	0.990665i	0.354352	−	0.128974i	−0.158710	−	0.987325i	$-0.550733\pi$
$59$	2.72183	−	0.990665i	0.354352	−	0.128974i	0.513062	+	0.858352i	$0.328511\pi$
$60$		0			0
$61$	−3.26714	+	2.74146i	−0.418315	+	0.351008i	−0.827522	−	0.561434i	$-0.810250\pi$
$61$	−3.26714	+	2.74146i	−0.418315	+	0.351008i	0.409207	+	0.912442i	$0.365805\pi$
$62$		0			0
$63$	2.89536	−	4.13500i	0.364781	−	0.520961i
$64$		0			0
$65$	−1.76064	+	3.21157i	−0.218380	+	0.398346i
$66$		0			0
$67$	−1.53379	−	3.28923i	−0.187383	−	0.401843i	0.790064	−	0.613024i	$-0.210047\pi$
$67$	−1.53379	−	3.28923i	−0.187383	−	0.401843i	−0.977447	+	0.211180i	$0.932269\pi$
$68$		0			0
$69$	−0.523192	−	0.906195i	−0.0629849	−	0.109093i
$70$		0			0
$71$	2.47896	−	2.95431i	0.294198	−	0.350612i	−0.598617	−	0.801036i	$-0.704283\pi$
$71$	2.47896	−	2.95431i	0.294198	−	0.350612i	0.892815	+	0.450424i	$0.148727\pi$
$72$		0			0
$73$	−9.16796	+	6.41948i	−1.07303	+	0.751343i	−0.969944	−	0.243330i	$-0.921760\pi$
$73$	−9.16796	+	6.41948i	−1.07303	+	0.751343i	−0.103085	+	0.994673i	$0.532871\pi$
$74$		0			0
$75$	−1.48058	−	1.35502i	−0.170963	−	0.156464i
$76$		0			0
$77$	−2.04131	+	2.04131i	−0.232629	+	0.232629i
$78$		0			0
$79$	−0.420678	+	2.38578i	−0.0473300	+	0.268422i	−0.999285	−	0.0378172i	$-0.987960\pi$
$79$	−0.420678	+	2.38578i	−0.0473300	+	0.268422i	0.951955	+	0.306239i	$0.0990707\pi$
$80$		0			0
$81$	−5.80341	−	4.86964i	−0.644823	−	0.541071i
$82$		0			0
$83$	−2.41572	+	9.01558i	−0.265159	+	0.989588i	0.696993	+	0.717078i	$0.254521\pi$
$83$	−2.41572	+	9.01558i	−0.265159	+	0.989588i	−0.962153	+	0.272511i	$0.912146\pi$
$84$		0			0
$85$	−9.06076	−	3.07260i	−0.982778	−	0.333270i
$86$		0			0
$87$	0.578178	+	2.15779i	0.0619872	+	0.231339i
$88$		0			0
$89$	0.807422	+	4.57912i	0.0855865	+	0.485385i	0.997228	+	0.0744000i	$0.0237042\pi$
$89$	0.807422	+	4.57912i	0.0855865	+	0.485385i	−0.911642	+	0.410985i	$0.865185\pi$
$90$		0			0
$91$	−1.87209	−	2.23107i	−0.196249	−	0.233880i
$92$		0			0
$93$	3.28934	+	1.53385i	0.341089	+	0.159052i
$94$		0			0
$95$	−6.06844	−	7.62719i	−0.622608	−	0.782534i
$96$		0			0
$97$	1.40699	+	0.656091i	0.142858	+	0.0666160i	0.492733	−	0.870181i	$-0.335998\pi$
$97$	1.40699	+	0.656091i	0.142858	+	0.0666160i	−0.349874	+	0.936797i	$0.613776\pi$
$98$		0			0
$99$	2.96259	+	3.53068i	0.297752	+	0.354847i
$100$		0			0
$101$	−1.68580	−	9.56064i	−0.167743	−	0.951320i	−0.946191	−	0.323610i	$-0.895104\pi$
$101$	−1.68580	−	9.56064i	−0.167743	−	0.951320i	0.778447	−	0.627710i	$-0.216008\pi$
$102$		0			0
$103$	4.44353	+	16.5835i	0.437834	+	1.63402i	0.734191	+	0.678942i	$0.237561\pi$
$103$	4.44353	+	16.5835i	0.437834	+	1.63402i	−0.296357	+	0.955077i	$0.595772\pi$
$104$		0			0
$105$	1.43120	−	0.706339i	0.139671	−	0.0689316i
$106$		0			0
$107$	−0.425125	+	1.58659i	−0.0410984	+	0.153381i	−0.983426	−	0.181311i	$-0.941966\pi$
$107$	−0.425125	+	1.58659i	−0.0410984	+	0.153381i	0.942327	+	0.334693i	$0.108633\pi$
$108$		0			0
$109$	4.47131	+	3.75187i	0.428274	+	0.359364i	0.831300	−	0.555824i	$-0.187597\pi$
$109$	4.47131	+	3.75187i	0.428274	+	0.359364i	−0.403026	+	0.915188i	$0.632042\pi$
$110$		0			0
$111$	−0.731205	+	4.14687i	−0.0694029	+	0.393603i
$112$		0			0
$113$	−7.42948	+	7.42948i	−0.698907	+	0.698907i	−0.964175	−	0.265268i	$-0.914540\pi$
$113$	−7.42948	+	7.42948i	−0.698907	+	0.698907i	0.265268	+	0.964175i	$0.414540\pi$
$114$		0			0
$115$	0.128956	+	5.82752i	0.0120252	+	0.543419i
$116$		0			0
$117$	−3.80895	+	2.66705i	−0.352137	+	0.246569i
$118$		0			0
$119$	4.89045	−	5.82821i	0.448307	−	0.534272i
$120$		0			0
$121$	4.18209	+	7.24359i	0.380190	+	0.658508i
$122$		0			0
$123$	−2.04661	−	4.38896i	−0.184536	−	0.395739i
$124$		0			0
$125$	3.60360	+	10.5837i	0.322316	+	0.946632i
$126$		0			0
$127$	−2.40243	+	3.43103i	−0.213181	+	0.304455i	−0.911474	−	0.411358i	$-0.865055\pi$
$127$	−2.40243	+	3.43103i	−0.213181	+	0.304455i	0.698292	+	0.715813i	$0.253944\pi$
$128$		0			0
$129$	−3.40351	+	2.85588i	−0.299662	+	0.251447i
$130$		0			0
$131$	12.7933	−	4.65637i	1.11775	−	0.406829i	0.283921	−	0.958848i	$-0.408365\pi$
$131$	12.7933	−	4.65637i	1.11775	−	0.406829i	0.833832	+	0.552019i	$0.186142\pi$
$132$		0			0
$133$	7.40253	−	2.29701i	0.641880	−	0.199176i
$134$		0			0
$135$	−1.90098	−	4.88390i	−0.163610	−	0.420339i
$136$		0			0
$137$	0.894323	−	10.2222i	0.0764072	−	0.873338i	−0.857187	−	0.515006i	$-0.827790\pi$
$137$	0.894323	−	10.2222i	0.0764072	−	0.873338i	0.933594	−	0.358332i	$-0.116655\pi$
$138$		0			0
$139$	−0.690358	+	0.121729i	−0.0585554	+	0.0103249i	−0.202849	−	0.979210i	$-0.565020\pi$
$139$	−0.690358	+	0.121729i	−0.0585554	+	0.0103249i	0.144294	+	0.989535i	$0.453909\pi$
$140$		0			0
$141$	−2.46705	−	1.42435i	−0.207763	−	0.119952i
$142$		0			0
$143$	2.41006	−	1.12383i	0.201540	−	0.0939795i
$144$		0			0
$145$	2.95407	−	12.0884i	0.245322	−	1.00389i
$146$		0			0
$147$	−0.134280	−	1.53483i	−0.0110753	−	0.126591i
$148$		0			0
$149$	4.00991	+	0.707054i	0.328504	+	0.0579242i	0.335468	−	0.942052i	$-0.391106\pi$
$149$	4.00991	+	0.707054i	0.328504	+	0.0579242i	−0.00696379	+	0.999976i	$0.502217\pi$
$150$		0			0
$151$			12.4523i			1.01335i	0.862137	+	0.506676i	$0.169126\pi$
$151$			12.4523i			1.01335i	−0.862137	+	0.506676i	$0.830874\pi$
$152$		0			0
$153$	−8.58909	−	8.58909i	−0.694387	−	0.694387i
$154$		0			0
$155$	−11.9600	−	16.3008i	−0.960649	−	1.30931i
$156$		0			0
$157$	14.3387	−	1.25448i	1.14436	−	0.100118i	0.500832	−	0.865544i	$-0.333027\pi$
$157$	14.3387	−	1.25448i	1.14436	−	0.100118i	0.643524	+	0.765426i	$0.277472\pi$
$158$		0			0
$159$	−0.443714	+	0.256179i	−0.0351888	+	0.0203163i
$160$		0			0
$161$	−4.35569	−	1.58534i	−0.343276	−	0.124942i
$162$		0			0
$163$	−10.5220	+	2.81936i	−0.824146	+	0.220829i	−0.646158	−	0.763204i	$-0.723625\pi$
$163$	−10.5220	+	2.81936i	−0.824146	+	0.220829i	−0.177988	+	0.984033i	$0.556959\pi$
$164$		0			0
$165$	0.284733	+	1.42914i	0.0221664	+	0.111259i
$166$		0			0
$167$	17.6634	+	1.54535i	1.36684	+	0.119583i	0.746830	−	0.665015i	$-0.231575\pi$
$167$	17.6634	+	1.54535i	1.36684	+	0.119583i	0.620006	+	0.784597i	$0.287130\pi$
$168$		0			0
$169$	−3.52869	−	9.69499i	−0.271438	−	0.745769i
$170$		0			0
$171$	−2.62328	−	12.0931i	−0.200607	−	0.924783i
$172$		0			0
$173$	0.143103	−	0.306886i	0.0108799	−	0.0233321i	−0.900793	−	0.434249i	$-0.857014\pi$
$173$	0.143103	−	0.306886i	0.0108799	−	0.0233321i	0.911673	+	0.410917i	$0.134791\pi$
$174$		0			0
$175$	−8.88246	−	0.382324i	−0.671451	−	0.0289010i
$176$		0			0
$177$	0.952412	+	0.666886i	0.0715877	+	0.0501262i
$178$		0			0
$179$	7.84205	−	13.5828i	0.586143	−	1.01523i	−0.408589	−	0.912718i	$-0.633979\pi$
$179$	7.84205	−	13.5828i	0.586143	−	1.01523i	0.994732	−	0.102510i	$-0.0326875\pi$
$180$		0			0
$181$	1.86778	−	5.13168i	0.138831	−	0.381435i	−0.850720	−	0.525619i	$-0.823834\pi$
$181$	1.86778	−	5.13168i	0.138831	−	0.381435i	0.989551	+	0.144185i	$0.0460559\pi$
$182$		0			0
$183$	−1.65365	−	0.443094i	−0.122241	−	0.0327545i
$184$		0			0
$185$	14.6765	−	18.2981i	1.07904	−	1.34530i
$186$		0			0
$187$	3.98443	+	5.69035i	0.291370	+	0.416120i
$188$		0			0
$189$	4.16754			0.303144
$190$		0			0
$191$	−4.08203			−0.295366			−0.147683	−	0.989035i	$-0.547181\pi$
$191$	−4.08203			−0.295366			−0.147683	+	0.989035i	$0.547181\pi$
$192$		0			0
$193$	−10.0063	−	14.2905i	−0.720269	−	1.02865i	−0.997692	−	0.0679032i	$-0.978369\pi$
$193$	−10.0063	−	14.2905i	−0.720269	−	1.02865i	0.277423	−	0.960748i	$-0.410520\pi$
$194$		0			0
$195$	−1.46137	+	0.160503i	−0.104651	+	0.0114938i
$196$		0			0
$197$	10.6794	+	2.86153i	0.760874	+	0.203876i	0.618336	−	0.785914i	$-0.287807\pi$
$197$	10.6794	+	2.86153i	0.760874	+	0.203876i	0.142538	+	0.989789i	$0.454474\pi$
$198$		0			0
$199$	2.15054	−	5.90855i	0.152448	−	0.418846i	−0.839835	−	0.542841i	$-0.817348\pi$
$199$	2.15054	−	5.90855i	0.152448	−	0.418846i	0.992283	+	0.123995i	$0.0395707\pi$
$200$		0			0
$201$	0.728407	−	1.26164i	0.0513779	−	0.0889890i
$202$		0			0
$203$	8.10606	+	5.67593i	0.568934	+	0.398372i
$204$		0			0
$205$	−1.75604	+	26.9193i	−0.122647	+	1.88013i
$206$		0			0
$207$	−3.12752	+	6.70698i	−0.217377	+	0.466167i
$208$		0			0
$209$	0.276497	+	7.07137i	0.0191257	+	0.489137i
$210$		0			0
$211$	2.01223	+	5.52855i	0.138527	+	0.380601i	0.989485	−	0.144633i	$-0.0462001\pi$
$211$	2.01223	+	5.52855i	0.138527	+	0.380601i	−0.850958	+	0.525234i	$0.823978\pi$
$212$		0			0
$213$	1.54217	+	0.134922i	0.105668	+	0.00924471i
$214$		0			0
$215$	24.2728	−	4.83595i	1.65539	−	0.329809i
$216$		0			0
$217$	15.5295	−	4.16111i	1.05421	−	0.282475i
$218$		0			0
$219$	−4.22162	−	1.53655i	−0.285271	−	0.103830i
$220$		0			0
$221$	−6.06934	+	3.50414i	−0.408268	+	0.235714i
$222$		0			0
$223$	21.4736	−	1.87870i	1.43798	−	0.125807i	0.658662	−	0.752439i	$-0.271123\pi$
$223$	21.4736	−	1.87870i	1.43798	−	0.125807i	0.779315	+	0.626632i	$0.215567\pi$
$224$		0			0
$225$	−1.84405	+	14.0741i	−0.122937	+	0.938271i
$226$		0			0
$227$	−15.0579	−	15.0579i	−0.999425	−	0.999425i	0.000574688	−	1.00000i	$-0.499817\pi$
$227$	−15.0579	−	15.0579i	−0.999425	−	0.999425i	−1.00000		0.000574688i	$0.999817\pi$
$228$		0			0
$229$			0.953108i			0.0629831i	0.999504	+	0.0314916i	$0.0100257\pi$
$229$			0.953108i			0.0629831i	−0.999504	+	0.0314916i	$0.989974\pi$
$230$		0			0
$231$	−1.14120	−	0.201224i	−0.0750852	−	0.0132396i
$232$		0			0
$233$	−1.46969	−	16.7986i	−0.0962827	−	1.10052i	−0.878575	−	0.477604i	$-0.841505\pi$
$233$	−1.46969	−	16.7986i	−0.0962827	−	1.10052i	0.782292	−	0.622911i	$-0.214050\pi$
$234$		0			0
$235$	8.23656	+	13.5640i	0.537294	+	0.884817i
$236$		0			0
$237$	−0.881335	+	0.410973i	−0.0572488	+	0.0266956i
$238$		0			0
$239$	−10.2823	−	5.93650i	−0.665108	−	0.384000i	0.129113	−	0.991630i	$-0.458787\pi$
$239$	−10.2823	−	5.93650i	−0.665108	−	0.384000i	−0.794220	+	0.607630i	$0.792120\pi$
$240$		0			0
$241$	22.8845	−	4.03516i	1.47412	−	0.259927i	0.621895	−	0.783101i	$-0.286363\pi$
$241$	22.8845	−	4.03516i	1.47412	−	0.259927i	0.852226	+	0.523173i	$0.175252\pi$
$242$		0			0
$243$	0.877858	−	10.0340i	0.0563146	−	0.643679i
$244$		0			0
$245$	−3.45417	+	7.85676i	−0.220679	+	0.501950i
$246$		0			0
$247$	−7.13127	−	0.343890i	−0.453752	−	0.0218812i
$248$		0			0
$249$	−3.52064	+	1.28141i	−0.223111	+	0.0812058i
$250$		0			0
$251$	−19.7231	+	16.5496i	−1.24491	+	1.04460i	−0.247785	+	0.968815i	$0.579703\pi$
$251$	−19.7231	+	16.5496i	−1.24491	+	1.04460i	−0.997124	+	0.0757875i	$0.975853\pi$
$252$		0			0
$253$	2.42748	−	3.46680i	0.152614	−	0.217956i
$254$		0			0
$255$	−1.07582	−	3.68673i	−0.0673704	−	0.230872i
$256$		0			0
$257$	−7.90898	−	16.9609i	−0.493349	−	1.05799i	−0.982581	−	0.185836i	$-0.940501\pi$
$257$	−7.90898	−	16.9609i	−0.493349	−	1.05799i	0.489232	−	0.872154i	$-0.337277\pi$
$258$		0			0
$259$	9.32650	+	16.1540i	0.579520	+	1.00376i
$260$		0			0
$261$	10.1553	−	12.1026i	0.628598	−	0.749134i
$262$		0			0
$263$	−19.4077	+	13.5894i	−1.19673	+	0.837959i	−0.990087	−	0.140457i	$-0.955143\pi$
$263$	−19.4077	+	13.5894i	−1.19673	+	0.837959i	−0.206643	+	0.978416i	$0.566254\pi$
$264$		0			0
$265$	2.85342	−	0.0631429i	0.175284	−	0.00387884i
$266$		0			0
$267$	−1.31978	+	1.31978i	−0.0807691	+	0.0807691i
$268$		0			0
$269$	0.598005	−	3.39146i	0.0364610	−	0.206781i	−0.961135	−	0.276079i	$-0.910965\pi$
$269$	0.598005	−	3.39146i	0.0364610	−	0.206781i	0.997596	+	0.0692982i	$0.0220760\pi$
$270$		0			0
$271$	−12.0550	−	10.1154i	−0.732291	−	0.614465i	0.198464	−	0.980108i	$-0.436405\pi$
$271$	−12.0550	−	10.1154i	−0.732291	−	0.614465i	−0.930755	+	0.365643i	$0.880849\pi$
$272$		0			0
$273$	0.302581	−	1.12925i	0.0183130	−	0.0683451i
$274$		0			0
$275$	2.43623	−	7.74341i	0.146910	−	0.466945i
$276$		0			0
$277$	2.12399	+	7.92685i	0.127618	+	0.476278i	0.999919	−	0.0126908i	$-0.00403971\pi$
$277$	2.12399	+	7.92685i	0.127618	+	0.476278i	−0.872301	+	0.488969i	$0.837373\pi$
$278$		0			0
$279$	−4.45722	−	25.2781i	−0.266847	−	1.51336i
$280$		0			0
$281$	1.73446	+	2.06705i	0.103469	+	0.123310i	0.815294	−	0.579047i	$-0.196575\pi$
$281$	1.73446	+	2.06705i	0.103469	+	0.123310i	−0.711825	+	0.702357i	$0.752131\pi$
$282$		0			0
$283$	15.4404	+	7.19999i	0.917838	+	0.427995i	0.823352	−	0.567531i	$-0.192101\pi$
$283$	15.4404	+	7.19999i	0.917838	+	0.427995i	0.0944861	+	0.995526i	$0.469879\pi$
$284$		0			0
$285$	1.11074	−	3.75145i	0.0657947	−	0.222217i
$286$		0			0
$287$	−19.4420	−	9.06597i	−1.14763	−	0.535147i
$288$		0			0
$289$	−0.840542	−	1.00172i	−0.0494436	−	0.0589246i
$290$		0			0
$291$	0.108211	+	0.613695i	0.00634344	+	0.0359755i
$292$		0			0
$293$	3.91641	+	14.6162i	0.228799	+	0.853889i	0.980847	+	0.194781i	$0.0623995\pi$
$293$	3.91641	+	14.6162i	0.228799	+	0.853889i	−0.752048	+	0.659108i	$0.770934\pi$
$294$		0			0
$295$	−2.86641	−	5.80798i	−0.166889	−	0.338153i
$296$		0			0
$297$	−0.984848	+	3.67550i	−0.0571467	+	0.213274i
$298$		0			0
$299$	3.27080	+	2.74453i	0.189155	+	0.158720i
$300$		0			0
$301$	−3.41761	+	19.3823i	−0.196988	+	1.11717i
$302$		0			0
$303$	2.75554	−	2.75554i	0.158301	−	0.158301i
$304$		0			0
$305$	6.89102	+	6.59264i	0.394579	+	0.377494i
$306$		0			0
$307$	−20.2148	+	14.1546i	−1.15372	+	0.807844i	−0.984091	−	0.177664i	$-0.943146\pi$
$307$	−20.2148	+	14.1546i	−1.15372	+	0.807844i	−0.169629	+	0.985508i	$0.554257\pi$
$308$		0			0
$309$	−4.42981	+	5.27924i	−0.252003	+	0.300326i
$310$		0			0
$311$	11.7457	+	20.3442i	0.666038	+	1.15361i	0.979003	+	0.203847i	$0.0653446\pi$
$311$	11.7457	+	20.3442i	0.666038	+	1.15361i	−0.312965	+	0.949765i	$0.601322\pi$
$312$		0			0
$313$	−0.361610	−	0.775475i	−0.0204394	−	0.0438324i	0.895823	−	0.444411i	$-0.146587\pi$
$313$	−0.361610	−	0.775475i	−0.0204394	−	0.0438324i	−0.916262	+	0.400578i	$0.868809\pi$
$314$		0			0
$315$	−9.89769	−	5.42609i	−0.557672	−	0.305725i
$316$		0			0
$317$	−10.1717	+	14.5267i	−0.571298	+	0.815898i	−0.995992	−	0.0894387i	$-0.971493\pi$
$317$	−10.1717	+	14.5267i	−0.571298	+	0.815898i	0.424694	+	0.905337i	$0.360382\pi$
$318$		0			0
$319$	−6.92138	+	5.80773i	−0.387523	+	0.325170i
$320$		0			0
$321$	−0.619572	+	0.225506i	−0.0345812	+	0.0125865i
$322$		0			0
$323$	−2.35019	−	18.5019i	−0.130768	−	1.02948i
$324$		0			0
$325$	7.56817	+	3.12937i	0.419807	+	0.173586i
$326$		0			0
$327$	−0.204203	+	2.33405i	−0.0112924	+	0.129073i
$328$		0			0
$329$	−12.4274	+	2.19128i	−0.685143	+	0.120809i
$330$		0			0
$331$	13.7804	+	7.95612i	0.757439	+	0.437308i	0.828376	−	0.560173i	$-0.189265\pi$
$331$	13.7804	+	7.95612i	0.757439	+	0.437308i	−0.0709364	+	0.997481i	$0.522599\pi$
$332$		0			0
$333$	26.9901	−	12.5857i	1.47905	−	0.689692i
$334$		0			0
$335$	−6.93655	+	4.21213i	−0.378984	+	0.230133i
$336$		0			0
$337$	−0.640167	−	7.31714i	−0.0348721	−	0.398590i	−0.993492	−	0.113901i	$-0.963665\pi$
$337$	−0.640167	−	7.31714i	−0.0348721	−	0.398590i	0.958620	−	0.284689i	$-0.0918903\pi$
$338$		0			0
$339$	−4.15347	−	0.732368i	−0.225585	−	0.0397768i
$340$		0			0
$341$			14.6793i			0.794931i
$342$		0			0
$343$	−13.6273	−	13.6273i	−0.735803	−	0.735803i
$344$		0			0
$345$	−1.88648	+	1.38412i	−0.101565	+	0.0745185i
$346$		0			0
$347$	−35.1086	+	3.07160i	−1.88473	+	0.164892i	−0.970626	−	0.240595i	$-0.922657\pi$
$347$	−35.1086	+	3.07160i	−1.88473	+	0.164892i	−0.914101	+	0.405487i	$0.867102\pi$
$348$		0			0
$349$	−20.8646	+	12.0462i	−1.11686	+	0.644818i	−0.940597	−	0.339525i	$-0.889734\pi$
$349$	−20.8646	+	12.0462i	−1.11686	+	0.644818i	−0.176261	+	0.984343i	$0.556400\pi$
$350$		0			0
$351$	−3.60740	−	1.31299i	−0.192549	−	0.0700821i
$352$		0			0
$353$	13.8653	−	3.71520i	0.737977	−	0.197740i	0.129798	−	0.991540i	$-0.458567\pi$
$353$	13.8653	−	3.71520i	0.737977	−	0.197740i	0.608179	+	0.793800i	$0.291900\pi$
$354$		0			0
$355$	−7.17171	−	4.78878i	−0.380635	−	0.254162i
$356$		0			0
$357$	3.04236	+	0.266172i	0.161019	+	0.0140873i
$358$		0			0
$359$	10.9858	+	30.1831i	0.579806	+	1.59301i	0.788507	+	0.615026i	$0.210854\pi$
$359$	10.9858	+	30.1831i	0.579806	+	1.59301i	−0.208701	+	0.977980i	$0.566923\pi$
$360$		0			0
$361$	8.18619	−	17.1460i	0.430852	−	0.902423i
$362$		0			0
$363$	−1.41892	+	3.04288i	−0.0744738	+	0.159710i
$364$		0			0
$365$	16.5067	+	18.8105i	0.863998	+	0.984588i
$366$		0			0
$367$	−15.2082	−	10.6489i	−0.793859	−	0.555866i	0.104810	−	0.994492i	$-0.466576\pi$
$367$	−15.2082	−	10.6489i	−0.793859	−	0.555866i	−0.898670	+	0.438626i	$0.855465\pi$
$368$		0			0
$369$	−17.1244	+	29.6604i	−0.891463	+	1.54406i
$370$		0			0
$371$	−0.776255	+	2.13274i	−0.0403011	+	0.110726i
$372$		0			0
$373$	5.43066	+	1.45514i	0.281189	+	0.0753444i	0.396657	−	0.917967i	$-0.370170\pi$
$373$	5.43066	+	1.45514i	0.281189	+	0.0753444i	−0.115468	+	0.993311i	$0.536837\pi$
$374$		0			0
$375$	−2.65037	+	3.62168i	−0.136865	+	0.187023i
$376$		0			0
$377$	−5.22837	−	7.46688i	−0.269275	−	0.384564i
$378$		0			0
$379$	−18.4277			−0.946568			−0.473284	−	0.880910i	$-0.656932\pi$
$379$	−18.4277			−0.946568			−0.473284	+	0.880910i	$0.656932\pi$
$380$		0			0
$381$	−1.68130			−0.0861356
$382$		0			0
$383$	−11.8973	−	16.9912i	−0.607926	−	0.868208i	0.390705	−	0.920516i	$-0.372231\pi$
$383$	−11.8973	−	16.9912i	−0.607926	−	0.868208i	−0.998631	+	0.0523080i	$0.983342\pi$
$384$		0			0
$385$	5.03554	+	4.03890i	0.256635	+	0.205841i
$386$		0			0
$387$	30.3513	+	8.13260i	1.54284	+	0.413403i
$388$		0			0
$389$	0.376845	−	1.03537i	0.0191068	−	0.0524955i	−0.929773	−	0.368134i	$-0.879997\pi$
$389$	0.376845	−	1.03537i	0.0191068	−	0.0524955i	0.948879	+	0.315639i	$0.102219\pi$
$390$		0			0
$391$	−5.57689	+	9.65945i	−0.282035	+	0.488499i
$392$		0			0
$393$	4.47657	+	3.13453i	0.225813	+	0.158116i
$394$		0			0
$395$	5.40559	+	0.352625i	0.271985	+	0.0177425i
$396$		0			0
$397$	15.8441	−	33.9777i	0.795190	−	1.70529i	0.0903667	−	0.995909i	$-0.471196\pi$
$397$	15.8441	−	33.9777i	0.795190	−	1.70529i	0.704824	−	0.709383i	$-0.251026\pi$
$398$		0			0
$399$	2.45963	+	1.90519i	0.123136	+	0.0953789i
$400$		0			0
$401$	−4.22889	−	11.6188i	−0.211181	−	0.580214i	0.788199	−	0.615420i	$-0.211014\pi$
$401$	−4.22889	−	11.6188i	−0.211181	−	0.580214i	−0.999380	+	0.0352056i	$0.988791\pi$
$402$		0			0
$403$	−14.7532	−	1.29074i	−0.734910	−	0.0642963i
$404$		0			0
$405$	−9.40703	+	14.0880i	−0.467439	+	0.700039i
$406$		0			0
$407$	−16.4507	+	4.40796i	−0.815433	+	0.218495i
$408$		0			0
$409$	20.0360	+	7.29251i	0.990716	+	0.360591i	0.785998	−	0.618230i	$-0.212150\pi$
$409$	20.0360	+	7.29251i	0.990716	+	0.360591i	0.204719	+	0.978821i	$0.434372\pi$
$410$		0			0
$411$	3.56709	−	2.05946i	0.175952	−	0.101586i
$412$		0			0
$413$	5.13079	−	0.448886i	0.252470	−	0.0220882i
$414$		0			0
$415$	20.6287	+	3.16854i	1.01262	+	0.155537i
$416$		0			0
$417$	−0.198973	−	0.198973i	−0.00974374	−	0.00974374i
$418$		0			0
$419$			4.51709i			0.220675i	0.993894	+	0.110337i	$0.0351931\pi$
$419$			4.51709i			0.220675i	−0.993894	+	0.110337i	$0.964807\pi$
$420$		0			0
$421$	−30.2872	−	5.34045i	−1.47611	−	0.260278i	−0.623086	−	0.782153i	$-0.714121\pi$
$421$	−30.2872	−	5.34045i	−1.47611	−	0.260278i	−0.853022	+	0.521876i	$0.825232\pi$
$422$		0			0
$423$	1.75592	+	20.0702i	0.0853757	+	0.975848i
$424$		0			0
$425$	−4.61756	+	20.8895i	−0.223984	+	1.01329i
$426$		0			0
$427$	−6.87314	+	3.20500i	−0.332615	+	0.155101i
$428$		0			0
$429$	0.924419	+	0.533714i	0.0446314	+	0.0257679i
$430$		0			0
$431$	29.7998	−	5.25451i	1.43541	−	0.253101i	0.598797	−	0.800901i	$-0.295645\pi$
$431$	29.7998	−	5.25451i	1.43541	−	0.253101i	0.836610	+	0.547800i	$0.184534\pi$
$432$		0			0
$433$	1.12033	−	12.8054i	0.0538394	−	0.615387i	−0.920566	−	0.390588i	$-0.872272\pi$
$433$	1.12033	−	12.8054i	0.0538394	−	0.615387i	0.974405	−	0.224800i	$-0.0721727\pi$
$434$		0			0
$435$	4.65498	−	1.81188i	0.223189	−	0.0868729i
$436$		0			0
$437$	−10.1026	+	5.20078i	−0.483275	+	0.248787i
$438$		0			0
$439$	−17.0871	+	6.21918i	−0.815521	+	0.296825i	−0.715902	−	0.698200i	$-0.753984\pi$
$439$	−17.0871	+	6.21918i	−0.815521	+	0.296825i	−0.0996184	+	0.995026i	$0.531762\pi$
$440$		0			0
$441$	−8.34700	+	7.00397i	−0.397476	+	0.333522i
$442$		0			0
$443$	11.8993	−	16.9939i	0.565351	−	0.807405i	−0.430090	−	0.902786i	$-0.641518\pi$
$443$	11.8993	−	16.9939i	0.565351	−	0.807405i	0.995441	+	0.0953810i	$0.0304069\pi$
$444$		0			0
$445$	9.98090	−	2.91251i	0.473140	−	0.138066i
$446$		0			0
$447$	0.690743	+	1.48130i	0.0326710	+	0.0700632i
$448$		0			0
$449$	−11.9599	−	20.7151i	−0.564422	−	0.977607i	−0.997103	−	0.0760604i	$-0.975766\pi$
$449$	−11.9599	−	20.7151i	−0.564422	−	0.977607i	0.432681	−	0.901547i	$-0.357568\pi$
$450$		0			0
$451$	12.5900	−	15.0042i	0.592841	−	0.706521i
$452$		0			0
$453$	−4.09448	+	2.86699i	−0.192375	+	0.134703i
$454$		0			0
$455$	−4.50200	+	4.70575i	−0.211057	+	0.220609i
$456$		0			0
$457$	12.7595	−	12.7595i	0.596864	−	0.596864i	−0.342613	−	0.939477i	$-0.611312\pi$
$457$	12.7595	−	12.7595i	0.596864	−	0.596864i	0.939477	+	0.342613i	$0.111312\pi$
$458$		0			0
$459$	1.74141	−	9.87602i	0.0812820	−	0.460973i
$460$		0			0
$461$	3.68477	+	3.09189i	0.171617	+	0.144004i	0.724551	−	0.689222i	$-0.242047\pi$
$461$	3.68477	+	3.09189i	0.171617	+	0.144004i	−0.552934	+	0.833225i	$0.686492\pi$
$462$		0			0
$463$	3.57621	−	13.3466i	0.166201	−	0.620269i	−0.831683	−	0.555250i	$-0.812623\pi$
$463$	3.57621	−	13.3466i	0.166201	−	0.620269i	0.997884	−	0.0650189i	$-0.0207108\pi$
$464$		0			0
$465$	2.60629	−	7.68567i	0.120864	−	0.356414i
$466$		0			0
$467$	0.155885	+	0.581772i	0.00721351	+	0.0269212i	0.969439	−	0.245333i	$-0.0788974\pi$
$467$	0.155885	+	0.581772i	0.00721351	+	0.0269212i	−0.962225	+	0.272255i	$0.912231\pi$
$468$		0			0
$469$	−1.12061	−	6.35529i	−0.0517449	−	0.293460i
$470$		0			0
$471$	3.71381	+	4.42594i	0.171123	+	0.203937i
$472$		0			0
$473$	−16.2863	−	7.59441i	−0.748844	−	0.349191i
$474$		0			0
$475$	−15.4716	+	15.3503i	−0.709884	+	0.704319i
$476$		0			0
$477$	3.28404	+	1.53137i	0.150366	+	0.0701168i
$478$		0			0
$479$	−2.58927	−	3.08577i	−0.118307	−	0.140992i	0.703641	−	0.710556i	$-0.251557\pi$
$479$	−2.58927	−	3.08577i	−0.118307	−	0.140992i	−0.821947	+	0.569564i	$0.807112\pi$
$480$		0			0
$481$	−2.98365	−	16.9211i	−0.136043	−	0.771537i
$482$		0			0
$483$	−0.481562	−	1.79721i	−0.0219118	−	0.0817761i
$484$		0			0
$485$	1.11482	−	3.28749i	0.0506214	−	0.149277i
$486$		0			0
$487$	−11.2391	+	41.9448i	−0.509292	+	1.90070i	−0.0818884	+	0.996642i	$0.526095\pi$
$487$	−11.2391	+	41.9448i	−0.509292	+	1.90070i	−0.427403	+	0.904061i	$0.640572\pi$
$488$		0			0
$489$	−3.34960	−	2.81065i	−0.151474	−	0.127102i
$490$		0			0
$491$	−6.61275	+	37.5028i	−0.298429	+	1.69248i	0.354500	+	0.935056i	$0.384651\pi$
$491$	−6.61275	+	37.5028i	−0.298429	+	1.69248i	−0.652929	+	0.757419i	$0.726460\pi$
$492$		0			0
$493$	16.8376	−	16.8376i	0.758330	−	0.758330i
$494$		0			0
$495$	7.12442	−	7.44687i	0.320219	−	0.334712i
$496$		0			0
$497$	5.61735	−	3.93331i	0.251973	−	0.176433i
$498$		0			0
$499$	1.01589	−	1.21069i	0.0454774	−	0.0541978i	−0.742826	−	0.669484i	$-0.766515\pi$
$499$	1.01589	−	1.21069i	0.0454774	−	0.0541978i	0.788304	+	0.615286i	$0.210960\pi$
$500$		0			0
$501$	3.55865	+	6.16377i	0.158989	+	0.275377i
$502$		0			0
$503$	−7.98292	−	17.1194i	−0.355941	−	0.763317i	0.644058	−	0.764977i	$-0.277250\pi$
$503$	−7.98292	−	17.1194i	−0.355941	−	0.763317i	−0.999999	+	0.00165954i	$0.999472\pi$
$504$		0			0
$505$	−20.8389	+	6.08097i	−0.927320	+	0.270600i
$506$		0			0
$507$	2.37541	−	3.39244i	0.105496	−	0.150663i
$508$		0			0
$509$	−6.95872	+	5.83906i	−0.308440	+	0.258812i	−0.783847	−	0.620954i	$-0.786745\pi$
$509$	−6.95872	+	5.83906i	−0.308440	+	0.258812i	0.475407	+	0.879766i	$0.342301\pi$
$510$		0			0
$511$	−18.7008	+	6.80652i	−0.827273	+	0.301103i
$512$		0			0
$513$	6.93621	−	7.50071i	0.306241	−	0.331164i
$514$		0			0
$515$	35.7754	−	13.9250i	1.57645	−	0.613609i
$516$		0			0
$517$	1.00419	−	11.4780i	0.0441643	−	0.504801i
$518$		0			0
$519$	0.133856	−	0.0236024i	0.00587563	−	0.00103603i
$520$		0			0
$521$	23.4292	+	13.5268i	1.02645	+	0.592621i	0.915966	−	0.401257i	$-0.131426\pi$
$521$	23.4292	+	13.5268i	1.02645	+	0.592621i	0.110485	+	0.993878i	$0.464760\pi$
$522$		0			0
$523$	10.8279	−	5.04911i	0.473469	−	0.220782i	−0.171211	−	0.985234i	$-0.554768\pi$
$523$	10.8279	−	5.04911i	0.473469	−	0.220782i	0.644681	+	0.764452i	$0.276990\pi$
$524$		0			0
$525$	−1.91937	−	3.00870i	−0.0837680	−	0.131310i
$526$		0			0
$527$	−3.37179	−	38.5397i	−0.146877	−	1.67882i
$528$		0			0
$529$	−15.9585	−	2.81391i	−0.693847	−	0.122344i
$530$		0			0
$531$		−	8.22282i		−	0.356840i
$532$		0			0
$533$	13.9727	+	13.9727i	0.605225	+	0.605225i
$534$		0			0
$535$	3.63030	+	0.557610i	0.156951	+	0.0241076i
$536$		0			0
$537$	6.27176	−	0.548708i	0.270646	−	0.0236785i
$538$		0			0
$539$	5.39660	−	3.11573i	0.232448	−	0.134204i
$540$		0			0
$541$	−21.2367	−	7.72953i	−0.913037	−	0.332318i	−0.157572	−	0.987507i	$-0.550367\pi$
$541$	−21.2367	−	7.72953i	−0.913037	−	0.332318i	−0.755465	+	0.655189i	$0.772589\pi$
$542$		0			0
$543$	2.11740	−	0.567355i	0.0908663	−	0.0243475i
$544$		0			0
$545$	7.24776	−	10.8543i	0.310460	−	0.464947i
$546$		0			0
$547$	11.0261	+	0.964659i	0.471442	+	0.0412458i	0.320402	−	0.947282i	$-0.396182\pi$
$547$	11.0261	+	0.964659i	0.471442	+	0.0412458i	0.151040	+	0.988528i	$0.451738\pi$
$548$		0			0
$549$	4.14106	+	11.3775i	0.176736	+	0.485579i
$550$		0			0
$551$	23.7068	−	5.14255i	1.00994	−	0.219080i
$552$		0			0
$553$	−1.82051	+	3.90410i	−0.0774160	+	0.166019i
$554$		0			0
$555$	9.39576	+	0.612918i	0.398828	+	0.0260169i
$556$		0			0
$557$	17.4404	+	12.2119i	0.738972	+	0.517433i	0.881399	−	0.472372i	$-0.156602\pi$
$557$	17.4404	+	12.2119i	0.738972	+	0.517433i	−0.142428	+	0.989805i	$0.545491\pi$
$558$		0			0
$559$	9.06467	−	15.7005i	0.383395	−	0.664059i
$560$		0			0
$561$	−0.953700	+	2.62027i	−0.0402653	+	0.110628i
$562$		0			0
$563$	38.8368	+	10.4063i	1.63678	+	0.438573i	0.955868	−	0.293796i	$-0.0949188\pi$
$563$	38.8368	+	10.4063i	1.63678	+	0.438573i	0.680908	+	0.732369i	$0.261585\pi$
$564$		0			0
$565$	18.3272	+	14.6998i	0.771032	+	0.618427i
$566$		0			0
$567$	−7.72655	−	11.0347i	−0.324485	−	0.463412i
$568$		0			0
$569$	11.1892			0.469076			0.234538	−	0.972107i	$-0.424642\pi$
$569$	11.1892			0.469076			0.234538	+	0.972107i	$0.424642\pi$
$570$		0			0
$571$	−5.54906			−0.232221			−0.116110	−	0.993236i	$-0.537043\pi$
$571$	−5.54906			−0.232221			−0.116110	+	0.993236i	$0.537043\pi$
$572$		0			0
$573$	−0.939838	−	1.34223i	−0.0392623	−	0.0560724i
$574$		0			0
$575$	12.9214	−	1.70924i	0.538858	−	0.0712804i
$576$		0			0
$577$	−0.243158	−	0.0651540i	−0.0101228	−	0.00271240i	0.253754	−	0.967269i	$-0.418335\pi$
$577$	−0.243158	−	0.0651540i	−0.0101228	−	0.00271240i	−0.263877	+	0.964556i	$0.585001\pi$
$578$		0			0
$579$	2.39508	−	6.58042i	0.0995360	−	0.273473i
$580$		0			0
$581$	−8.29822	+	14.3729i	−0.344268	+	0.596290i
$582$		0			0
$583$	−1.69750	−	1.18860i	−0.0703033	−	0.0492269i
$584$		0			0
$585$	6.85790	+	7.81507i	0.283539	+	0.323114i
$586$		0			0
$587$	9.11075	−	19.5381i	0.376041	−	0.806422i	−0.623654	−	0.781701i	$-0.714352\pi$
$587$	9.11075	−	19.5381i	0.376041	−	0.806422i	0.999694	−	0.0247211i	$-0.00786978\pi$
$588$		0			0
$589$	18.3572	−	34.8754i	0.756396	−	1.43701i
$590$		0			0
$591$	1.51789	+	4.17036i	0.0624375	+	0.171546i
$592$		0			0
$593$	−44.5928	−	3.90137i	−1.83121	−	0.160210i	−0.881262	−	0.472628i	$-0.843306\pi$
$593$	−44.5928	−	3.90137i	−1.83121	−	0.160210i	−0.949945	+	0.312418i	$0.898861\pi$
$594$		0			0
$595$	−14.1482	−	9.44724i	−0.580021	−	0.387299i
$596$		0			0
$597$	2.43795	−	0.653246i	0.0997786	−	0.0267356i
$598$		0			0
$599$	−20.5392	−	7.47564i	−0.839207	−	0.305446i	−0.113575	−	0.993529i	$-0.536230\pi$
$599$	−20.5392	−	7.47564i	−0.839207	−	0.305446i	−0.725632	+	0.688083i	$0.758452\pi$
$600$		0			0
$601$	23.9752	−	13.8421i	0.977967	−	0.564630i	0.0763113	−	0.997084i	$-0.475686\pi$
$601$	23.9752	−	13.8421i	0.977967	−	0.564630i	0.901656	+	0.432455i	$0.142352\pi$
$602$		0			0
$603$	−10.2638	+	0.897967i	−0.417975	+	0.0365680i
$604$		0			0
$605$	15.0794	−	11.0638i	0.613065	−	0.449809i
$606$		0			0
$607$	17.4146	+	17.4146i	0.706839	+	0.706839i	0.965869	−	0.259030i	$-0.0834030\pi$
$607$	17.4146	+	17.4146i	0.706839	+	0.706839i	−0.259030	+	0.965869i	$0.583403\pi$
$608$		0			0
$609$			3.97220i			0.160962i
$610$		0			0
$611$	11.4474	+	2.01849i	0.463114	+	0.0816595i
$612$		0			0
$613$	−2.10515	−	24.0619i	−0.0850261	−	0.971852i	−0.912156	−	0.409842i	$-0.865584\pi$
$613$	−2.10515	−	24.0619i	−0.0850261	−	0.971852i	0.827130	−	0.562010i	$-0.189972\pi$
$614$		0			0
$615$	−9.25574	+	5.62043i	−0.373227	+	0.226638i
$616$		0			0
$617$	−39.5363	+	18.4361i	−1.59167	+	0.742208i	−0.998043	−	0.0625322i	$-0.980082\pi$
$617$	−39.5363	+	18.4361i	−1.59167	+	0.742208i	−0.593627	+	0.804740i	$0.702305\pi$
$618$		0			0
$619$	−14.8899	−	8.59667i	−0.598474	−	0.345529i	0.169967	−	0.985450i	$-0.445634\pi$
$619$	−14.8899	−	8.59667i	−0.598474	−	0.345529i	−0.768441	+	0.639921i	$0.778967\pi$
$620$		0			0
$621$	−6.01688	+	1.06094i	−0.241449	+	0.0425740i
$622$		0			0
$623$	−0.720595	+	8.23644i	−0.0288700	+	0.329986i
$624$		0			0
$625$	22.6446	−	10.5934i	0.905785	−	0.423737i
$626$		0			0
$627$	−2.26150	+	1.71901i	−0.0903157	+	0.0686508i
$628$		0			0
$629$	42.1780	−	15.3515i	1.68175	−	0.612105i
$630$		0			0
$631$	9.27401	−	7.78182i	0.369193	−	0.309789i	−0.439249	−	0.898365i	$-0.644756\pi$
$631$	9.27401	−	7.78182i	0.369193	−	0.309789i	0.808442	+	0.588576i	$0.200311\pi$
$632$		0			0
$633$	−1.35457	+	1.93453i	−0.0538394	+	0.0768906i
$634$		0			0
$635$	8.21264	+	4.50231i	0.325909	+	0.178669i
$636$		0			0
$637$	2.65689	+	5.69772i	0.105270	+	0.225752i
$638$		0			0
$639$	−5.47416	−	9.48153i	−0.216554	−	0.375083i
$640$		0			0
$641$	−30.5448	+	36.4019i	−1.20645	+	1.43779i	−0.338620	+	0.940923i	$0.609960\pi$
$641$	−30.5448	+	36.4019i	−1.20645	+	1.43779i	−0.867828	+	0.496865i	$0.834484\pi$
$642$		0			0
$643$	−1.10850	+	0.776183i	−0.0437151	+	0.0306097i	−0.595230	−	0.803556i	$-0.702939\pi$
$643$	−1.10850	+	0.776183i	−0.0437151	+	0.0306097i	0.551515	+	0.834165i	$0.314050\pi$
$644$		0			0
$645$	7.17864	+	6.86781i	0.282659	+	0.270420i
$646$		0			0
$647$	8.12755	−	8.12755i	0.319527	−	0.319527i	−0.529059	−	0.848585i	$-0.677455\pi$
$647$	8.12755	−	8.12755i	0.319527	−	0.319527i	0.848585	+	0.529059i	$0.177455\pi$
$648$		0			0
$649$	−0.816589	+	4.63111i	−0.0320539	+	0.181787i
$650$		0			0
$651$	4.94370	+	4.14826i	0.193759	+	0.162583i
$652$		0			0
$653$	−4.34918	+	16.2314i	−0.170197	+	0.635182i	0.827124	+	0.562020i	$0.189976\pi$
$653$	−4.34918	+	16.2314i	−0.170197	+	0.635182i	−0.997320	+	0.0731619i	$0.976691\pi$
$654$		0			0
$655$	−13.4728	−	27.2989i	−0.526426	−	1.06666i
$656$		0			0
$657$	8.22338	+	30.6901i	0.320825	+	1.19733i
$658$		0			0
$659$	1.98022	+	11.2304i	0.0771386	+	0.437475i	0.998778	+	0.0494267i	$0.0157394\pi$
$659$	1.98022	+	11.2304i	0.0771386	+	0.437475i	−0.921639	+	0.388048i	$0.873149\pi$
$660$		0			0
$661$	−27.8656	−	33.2090i	−1.08385	−	1.29168i	−0.953889	−	0.300159i	$-0.902960\pi$
$661$	−27.8656	−	33.2090i	−1.08385	−	1.29168i	−0.129958	−	0.991520i	$-0.541484\pi$
$662$		0			0
$663$	−2.54960	−	1.18890i	−0.0990183	−	0.0461730i
$664$		0			0
$665$	−6.91268	−	15.8929i	−0.268062	−	0.616299i
$666$		0			0
$667$	−13.1480	−	6.13104i	−0.509094	−	0.237395i
$668$		0			0
$669$	5.56177	+	6.62826i	0.215031	+	0.256263i
$670$		0			0
$671$	−1.20238	−	6.81905i	−0.0464175	−	0.263247i
$672$		0			0
$673$	−8.64329	−	32.2572i	−0.333174	−	1.24342i	−0.905835	−	0.423631i	$-0.860755\pi$
$673$	−8.64329	−	32.2572i	−0.333174	−	1.24342i	0.572661	−	0.819792i	$-0.305911\pi$
$674$		0			0
$675$	−10.3914	+	5.41757i	−0.399965	+	0.208522i
$676$		0			0
$677$	11.4706	−	42.8088i	0.440850	−	1.64528i	−0.285816	−	0.958285i	$-0.592265\pi$
$677$	11.4706	−	42.8088i	0.440850	−	1.64528i	0.726666	−	0.686991i	$-0.241069\pi$
$678$		0			0
$679$	2.11463	+	1.77439i	0.0811522	+	0.0680948i
$680$		0			0
$681$	1.48434	−	8.41812i	0.0568801	−	0.322583i
$682$		0			0
$683$	−35.6299	+	35.6299i	−1.36334	+	1.36334i	−0.493721	+	0.869621i	$0.664363\pi$
$683$	−35.6299	+	35.6299i	−1.36334	+	1.36334i	−0.869621	+	0.493721i	$0.835637\pi$
$684$		0			0
$685$	−22.9391	+	0.507616i	−0.876459	+	0.0193950i
$686$		0			0
$687$	−0.313395	+	0.219442i	−0.0119568	+	0.00837222i
$688$		0			0
$689$	1.34385	−	1.60153i	0.0511964	−	0.0610135i
$690$		0			0
$691$	−21.9173	−	37.9619i	−0.833773	−	1.44414i	−0.895026	−	0.446015i	$-0.852843\pi$
$691$	−21.9173	−	37.9619i	−0.833773	−	1.44414i	0.0612526	−	0.998122i	$-0.480490\pi$
$692$		0			0
$693$	3.46352	+	7.42754i	0.131568	+	0.282149i
$694$		0			0
$695$	0.439097	+	1.50474i	0.0166559	+	0.0570782i
$696$		0			0
$697$	−29.6080	+	42.2845i	−1.12148	+	1.60164i
$698$		0			0
$699$	5.18525	−	4.35094i	0.196124	−	0.164568i
$700$		0			0
$701$	5.22521	−	1.90182i	0.197353	−	0.0718307i	−0.241453	−	0.970413i	$-0.577624\pi$
$701$	5.22521	−	1.90182i	0.197353	−	0.0718307i	0.438806	+	0.898582i	$0.355402\pi$
$702$		0			0
$703$	44.5963	+	10.1000i	1.68198	+	0.380927i
$704$		0			0
$705$	−2.56366	+	5.83124i	−0.0965530	+	0.219617i
$706$		0			0
$707$	1.50452	−	17.1967i	0.0565832	−	0.646749i
$708$		0			0
$709$	−18.6302	+	3.28501i	−0.699672	+	0.123371i	−0.512158	−	0.858891i	$-0.671154\pi$
$709$	−18.6302	+	3.28501i	−0.699672	+	0.123371i	−0.187513	+	0.982262i	$0.560043\pi$
$710$		0			0
$711$	5.95602	+	3.43871i	0.223368	+	0.128962i
$712$		0			0
$713$	−21.3614	+	9.96097i	−0.799990	+	0.373041i
$714$		0			0
$715$	−3.08629	−	5.08251i	−0.115421	−	0.190075i
$716$		0			0
$717$	−0.415376	−	4.74777i	−0.0155125	−	0.177309i
$718$		0			0
$719$	50.2784	+	8.86545i	1.87507	+	0.330625i	0.990689	−	0.136142i	$-0.0434704\pi$
$719$	50.2784	+	8.86545i	1.87507	+	0.330625i	0.884380	+	0.466768i	$0.154582\pi$
$720$		0			0
$721$			30.5279i			1.13692i
$722$		0			0
$723$	6.59570	+	6.59570i	0.245297	+	0.245297i
$724$		0			0
$725$	−27.5901	−	3.61499i	−1.02467	−	0.134257i
$726$		0			0
$727$	21.5255	−	1.88324i	0.798336	−	0.0698454i	0.319315	−	0.947649i	$-0.396547\pi$
$727$	21.5255	−	1.88324i	0.798336	−	0.0698454i	0.479021	+	0.877803i	$0.340992\pi$
$728$		0			0
$729$	−16.1811	+	9.34217i	−0.599301	+	0.346006i
$730$		0			0
$731$	44.5030	+	16.1978i	1.64600	+	0.599097i
$732$		0			0
$733$	−0.949951	+	0.254538i	−0.0350872	+	0.00940159i	−0.276320	−	0.961066i	$-0.589115\pi$
$733$	−0.949951	+	0.254538i	−0.0350872	+	0.00940159i	0.241233	+	0.970467i	$0.422448\pi$
$734$		0			0
$735$	−3.37869	+	0.673148i	−0.124625	+	0.0248294i
$736$		0			0
$737$	5.86977	+	0.513538i	0.216216	+	0.0189164i
$738$		0			0
$739$	1.44989	+	3.98355i	0.0533352	+	0.146537i	0.963499	−	0.267710i	$-0.0862670\pi$
$739$	1.44989	+	3.98355i	0.0533352	+	0.146537i	−0.910164	+	0.414248i	$0.864045\pi$
$740$		0			0
$741$	−1.52881	−	2.42404i	−0.0561624	−	0.0890492i
$742$		0			0
$743$	−11.4075	+	24.4634i	−0.418500	+	0.897476i	0.578169	+	0.815917i	$0.303768\pi$
$743$	−11.4075	+	24.4634i	−0.418500	+	0.897476i	−0.996669	+	0.0815587i	$0.974010\pi$
$744$		0			0
$745$	0.592675	−	9.08543i	0.0217139	−	0.332864i
$746$		0			0
$747$	21.7050	+	15.1980i	0.794145	+	0.556066i
$748$		0			0
$749$	−1.46035	+	2.52940i	−0.0533599	+	0.0924221i
$750$		0			0
$751$	16.6302	−	45.6910i	0.606844	−	1.66729i	−0.130235	−	0.991483i	$-0.541573\pi$
$751$	16.6302	−	45.6910i	0.606844	−	1.66729i	0.737079	−	0.675807i	$-0.236205\pi$
$752$		0			0
$753$	−9.98274	−	2.67487i	−0.363791	−	0.0974776i
$754$		0			0
$755$	27.6777	−	3.03985i	1.00729	−	0.110631i
$756$		0			0
$757$	−12.6341	−	18.0433i	−0.459193	−	0.655795i	0.521066	−	0.853517i	$-0.325535\pi$
$757$	−12.6341	−	18.0433i	−0.459193	−	0.655795i	−0.980258	+	0.197722i	$0.936646\pi$
$758$		0			0
$759$	1.69883			0.0616635
$760$		0			0
$761$	−5.23743			−0.189857			−0.0949284	−	0.995484i	$-0.530262\pi$
$761$	−5.23743			−0.189857			−0.0949284	+	0.995484i	$0.530262\pi$
$762$		0			0
$763$	5.95302	+	8.50179i	0.215514	+	0.307785i
$764$		0			0
$765$	−16.9942	+	21.1878i	−0.614427	+	0.766045i
$766$		0			0
$767$	−4.58262	−	1.22791i	−0.165469	−	0.0443372i
$768$		0			0
$769$	−8.83572	+	24.2760i	−0.318624	+	0.875413i	0.672214	+	0.740357i	$0.265344\pi$
$769$	−8.83572	+	24.2760i	−0.318624	+	0.875413i	−0.990838	+	0.135056i	$0.956879\pi$
$770$		0			0
$771$	3.75602	−	6.50562i	0.135270	−	0.234294i
$772$		0			0
$773$	35.7168	+	25.0092i	1.28465	+	0.899518i	0.998281	−	0.0586028i	$-0.0186645\pi$
$773$	35.7168	+	25.0092i	1.28465	+	0.899518i	0.286364	+	0.958121i	$0.407553\pi$
$774$		0			0
$775$	−33.3122	+	30.5628i	−1.19661	+	1.09785i
$776$		0			0
$777$	−3.16433	+	6.78594i	−0.113520	+	0.243444i
$778$		0			0
$779$	−48.6751	+	19.9028i	−1.74397	+	0.713090i
$780$		0			0
$781$	2.14147	+	5.88364i	0.0766278	+	0.210533i
$782$		0			0
$783$	12.9939	+	1.13682i	0.464363	+	0.0406265i
$784$		0			0
$785$	−6.28870	−	31.5645i	−0.224453	−	1.12659i
$786$		0			0
$787$	−24.9028	+	6.67268i	−0.887689	+	0.237855i	−0.673721	−	0.738985i	$-0.735305\pi$
$787$	−24.9028	+	6.67268i	−0.887689	+	0.237855i	−0.213967	+	0.976841i	$0.568639\pi$
$788$		0			0
$789$	−8.93677	−	3.25272i	−0.318157	−	0.115800i
$790$		0			0
$791$	−16.1797	+	9.34133i	−0.575283	+	0.332140i

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)

\(f(q)\)	\(=\)	\(q+(0.230238 + 0.328814i) q^{3} +(-0.244120 - 2.22270i) q^{5} +(1.71755 + 0.460216i) q^{7} +(0.970951 - 2.66767i) q^{9} +O(q^{10})\)	\(q+(0.230238 + 0.328814i) q^{3} +(-0.244120 - 2.22270i) q^{5} +(1.71755 + 0.460216i) q^{7} +(0.970951 - 2.66767i) q^{9} +(-0.811761 + 1.40601i) q^{11} +(-1.34171 - 0.939476i) q^{13} +(0.674649 - 0.592020i) q^{15} +(1.80828 - 3.87786i) q^{17} +(3.68688 - 2.32528i) q^{19} +(0.244119 + 0.670713i) q^{21} +(-2.59687 - 0.227196i) q^{23} +(-4.88081 + 1.08521i) q^{25} +(2.26390 - 0.606611i) q^{27} +(5.22957 + 1.90341i) q^{29} +(7.83030 - 4.52083i) q^{31} +(-0.649214 + 0.0567989i) q^{33} +(0.603635 - 3.92995i) q^{35} +(7.41769 + 7.41769i) q^{37} -0.657476i q^{39} +(-11.8810 - 2.09494i) q^{41} +(0.964681 + 11.0263i) q^{43} +(-6.16646 - 1.50691i) q^{45} +(-6.43188 + 2.99924i) q^{47} +(-3.32400 - 1.91911i) q^{49} +(1.69143 - 0.298244i) q^{51} +(-0.111246 + 1.27154i) q^{53} +(3.32331 + 1.46107i) q^{55} +(1.61344 + 0.676931i) q^{57} +(2.72183 - 0.990665i) q^{59} +(-3.26714 + 2.74146i) q^{61} +(2.89536 - 4.13500i) q^{63} +(-1.76064 + 3.21157i) q^{65} +(-1.53379 - 3.28923i) q^{67} +(-0.523192 - 0.906195i) q^{69} +(2.47896 - 2.95431i) q^{71} +(-9.16796 + 6.41948i) q^{73} +(-1.48058 - 1.35502i) q^{75} +(-2.04131 + 2.04131i) q^{77} +(-0.420678 + 2.38578i) q^{79} +(-5.80341 - 4.86964i) q^{81} +(-2.41572 + 9.01558i) q^{83} +(-9.06076 - 3.07260i) q^{85} +(0.578178 + 2.15779i) q^{87} +(0.807422 + 4.57912i) q^{89} +(-1.87209 - 2.23107i) q^{91} +(3.28934 + 1.53385i) q^{93} +(-6.06844 - 7.62719i) q^{95} +(1.40699 + 0.656091i) q^{97} +(2.96259 + 3.53068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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

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Groups

Database

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