LMFDB - Embedded newform 380.2.bh.a.357.5

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			357.5
Character	$\chi$	$=$	380.357
Dual form			380.2.bh.a.33.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0411373 - 0.0587502i) q^{3} +(-2.20598 - 0.365568i) q^{5} +(0.553309 - 0.148259i) q^{7} +(1.02430 + 2.81424i) q^{9} +O(q^{10})$	\(q+(0.0411373 - 0.0587502i) q^{3} +(-2.20598 - 0.365568i) q^{5} +(0.553309 - 0.148259i) q^{7} +(1.02430 + 2.81424i) q^{9} +(2.49421 + 4.32010i) q^{11} +(4.89698 - 3.42890i) q^{13} +(-0.112225 + 0.114563i) q^{15} +(1.10088 + 2.36084i) q^{17} +(3.41080 - 2.71412i) q^{19} +(0.0140514 - 0.0386060i) q^{21} +(4.15825 - 0.363800i) q^{23} +(4.73272 + 1.61287i) q^{25} +(0.415305 + 0.111281i) q^{27} +(-5.28906 + 1.92506i) q^{29} +(-5.80028 - 3.34880i) q^{31} +(0.356412 + 0.0311820i) q^{33} +(-1.27479 + 0.124784i) q^{35} +(-5.89970 + 5.89970i) q^{37} -0.428755i q^{39} +(-1.05503 + 0.186031i) q^{41} +(0.00412207 - 0.0471155i) q^{43} +(-1.23079 - 6.58263i) q^{45} +(10.8196 + 5.04526i) q^{47} +(-5.77801 + 3.33593i) q^{49} +(0.183987 + 0.0324418i) q^{51} +(-0.268926 - 3.07384i) q^{53} +(-3.92290 - 10.4419i) q^{55} +(-0.0191439 - 0.312037i) q^{57} +(6.31979 + 2.30021i) q^{59} +(-6.37870 - 5.35237i) q^{61} +(0.983991 + 1.40528i) q^{63} +(-12.0562 + 5.77392i) q^{65} +(5.22905 - 11.2137i) q^{67} +(0.149686 - 0.259264i) q^{69} +(-0.975910 - 1.16304i) q^{71} +(-2.22190 - 1.55579i) q^{73} +(0.289448 - 0.211699i) q^{75} +(2.02056 + 2.02056i) q^{77} +(1.81235 + 10.2784i) q^{79} +(-6.85896 + 5.75535i) q^{81} +(-1.33629 - 4.98709i) q^{83} +(-1.56547 - 5.61041i) q^{85} +(-0.104480 + 0.389925i) q^{87} +(-1.70407 + 9.66428i) q^{89} +(2.20118 - 2.62326i) q^{91} +(-0.435351 + 0.203007i) q^{93} +(-8.51636 + 4.74042i) q^{95} +(-10.0585 + 4.69035i) q^{97} +(-9.60300 + 11.4444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	0.0411373	−	0.0587502i	0.0237507	−	0.0339194i	−0.807101	−	0.590413i	$-0.798965\pi$
$3$	0.0411373	−	0.0587502i	0.0237507	−	0.0339194i	0.830852	+	0.556494i	$0.187854\pi$
$4$		0			0
$5$	−2.20598	−	0.365568i	−0.986546	−	0.163487i
$5$	−2.20598	−	0.365568i	−0.986546	−	0.163487i
$6$		0			0
$7$	0.553309	−	0.148259i	0.209131	−	0.0560365i	−0.152733	−	0.988268i	$-0.548807\pi$
$7$	0.553309	−	0.148259i	0.209131	−	0.0560365i	0.361864	+	0.932231i	$0.382141\pi$
$8$		0			0
$9$	1.02430	+	2.81424i	0.341434	+	0.938081i
$10$		0			0
$11$	2.49421	+	4.32010i	0.752034	+	1.30256i	0.946836	+	0.321718i	$0.104260\pi$
$11$	2.49421	+	4.32010i	0.752034	+	1.30256i	−0.194802	+	0.980843i	$0.562406\pi$
$12$		0			0
$13$	4.89698	−	3.42890i	1.35818	−	0.951007i	0.358330	−	0.933595i	$-0.383346\pi$
$13$	4.89698	−	3.42890i	1.35818	−	0.951007i	0.999848	−	0.0174117i	$-0.00554259\pi$
$14$		0			0
$15$	−0.112225	+	0.114563i	−0.0289765	+	0.0295802i
$16$		0			0
$17$	1.10088	+	2.36084i	0.267002	+	0.572587i	0.993402	−	0.114685i	$-0.0365858\pi$
$17$	1.10088	+	2.36084i	0.267002	+	0.572587i	−0.726400	+	0.687272i	$0.758808\pi$
$18$		0			0
$19$	3.41080	−	2.71412i	0.782491	−	0.622662i
$19$	3.41080	−	2.71412i	0.782491	−	0.622662i
$20$		0			0
$21$	0.0140514	−	0.0386060i	0.00306627	−	0.00842451i
$22$		0			0
$23$	4.15825	−	0.363800i	0.867055	−	0.0758575i	0.355057	−	0.934844i	$-0.384461\pi$
$23$	4.15825	−	0.363800i	0.867055	−	0.0758575i	0.511997	+	0.858987i	$0.328906\pi$
$24$		0			0
$25$	4.73272	+	1.61287i	0.946544	+	0.322574i
$26$		0			0
$27$	0.415305	+	0.111281i	0.0799255	+	0.0214160i
$28$		0			0
$29$	−5.28906	+	1.92506i	−0.982153	+	0.357474i	−0.782677	−	0.622428i	$-0.786146\pi$
$29$	−5.28906	+	1.92506i	−0.982153	+	0.357474i	−0.199476	+	0.979903i	$0.563924\pi$
$30$		0			0
$31$	−5.80028	−	3.34880i	−1.04176	−	0.601461i	−0.121430	−	0.992600i	$-0.538748\pi$
$31$	−5.80028	−	3.34880i	−1.04176	−	0.601461i	−0.920332	+	0.391139i	$0.872081\pi$
$32$		0			0
$33$	0.356412	+	0.0311820i	0.0620434	+	0.00542810i
$34$		0			0
$35$	−1.27479	+	0.124784i	−0.215478	+	0.0210924i
$36$		0			0
$37$	−5.89970	+	5.89970i	−0.969905	+	0.969905i	−0.999560	−	0.0296550i	$-0.990559\pi$
$37$	−5.89970	+	5.89970i	−0.969905	+	0.969905i	0.0296550	+	0.999560i	$0.490559\pi$
$38$		0			0
$39$		−	0.428755i		−	0.0686557i
$40$		0			0
$41$	−1.05503	+	0.186031i	−0.164768	+	0.0290531i	−0.255424	−	0.966829i	$-0.582215\pi$
$41$	−1.05503	+	0.186031i	−0.164768	+	0.0290531i	0.0906553	+	0.995882i	$0.471104\pi$
$42$		0			0
$43$	0.00412207	−	0.0471155i	0.000628610	−	0.00718504i	−0.995874	−	0.0907477i	$-0.971074\pi$
$43$	0.00412207	−	0.0471155i	0.000628610	−	0.00718504i	0.996503	+	0.0835627i	$0.0266299\pi$
$44$		0			0
$45$	−1.23079	−	6.58263i	−0.183476	−	0.981280i
$46$		0			0
$47$	10.8196	+	5.04526i	1.57820	+	0.735927i	0.996968	−	0.0778110i	$-0.0247931\pi$
$47$	10.8196	+	5.04526i	1.57820	+	0.735927i	0.581232	+	0.813738i	$0.302571\pi$
$48$		0			0
$49$	−5.77801	+	3.33593i	−0.825430	+	0.476562i
$50$		0			0
$51$	0.183987	+	0.0324418i	0.0257633	+	0.00454277i
$52$		0			0
$53$	−0.268926	−	3.07384i	−0.0369398	−	0.422224i	−0.992038	−	0.125936i	$-0.959807\pi$
$53$	−0.268926	−	3.07384i	−0.0369398	−	0.422224i	0.955099	−	0.296288i	$-0.0957489\pi$
$54$		0			0
$55$	−3.92290	−	10.4419i	−0.528964	−	1.40798i
$56$		0			0
$57$	−0.0191439	−	0.312037i	−0.00253567	−	0.0413303i
$58$		0			0
$59$	6.31979	+	2.30021i	0.822766	+	0.299462i	0.718886	−	0.695128i	$-0.244652\pi$
$59$	6.31979	+	2.30021i	0.822766	+	0.299462i	0.103880	+	0.994590i	$0.466874\pi$
$60$		0			0
$61$	−6.37870	−	5.35237i	−0.816709	−	0.685300i	0.135490	−	0.990779i	$-0.456739\pi$
$61$	−6.37870	−	5.35237i	−0.816709	−	0.685300i	−0.952199	+	0.305478i	$0.901184\pi$
$62$		0			0
$63$	0.983991	+	1.40528i	0.123971	+	0.177049i
$64$		0			0
$65$	−12.0562	+	5.77392i	−1.49538	+	0.716167i
$66$		0			0
$67$	5.22905	−	11.2137i	0.638830	−	1.36997i	−0.274038	−	0.961719i	$-0.588359\pi$
$67$	5.22905	−	11.2137i	0.638830	−	1.36997i	0.912868	−	0.408256i	$-0.133863\pi$
$68$		0			0
$69$	0.149686	−	0.259264i	0.0180201	−	0.0312117i
$70$		0			0
$71$	−0.975910	−	1.16304i	−0.115819	−	0.138028i	0.705020	−	0.709188i	$-0.250938\pi$
$71$	−0.975910	−	1.16304i	−0.115819	−	0.138028i	−0.820839	+	0.571160i	$0.806494\pi$
$72$		0			0
$73$	−2.22190	−	1.55579i	−0.260053	−	0.182091i	0.436278	−	0.899812i	$-0.356297\pi$
$73$	−2.22190	−	1.55579i	−0.260053	−	0.182091i	−0.696331	+	0.717721i	$0.745185\pi$
$74$		0			0
$75$	0.289448	−	0.211699i	0.0334226	−	0.0244449i
$76$		0			0
$77$	2.02056	+	2.02056i	0.230264	+	0.230264i
$78$		0			0
$79$	1.81235	+	10.2784i	0.203905	+	1.15641i	0.899153	+	0.437635i	$0.144184\pi$
$79$	1.81235	+	10.2784i	0.203905	+	1.15641i	−0.695247	+	0.718771i	$0.744705\pi$
$80$		0			0
$81$	−6.85896	+	5.75535i	−0.762106	+	0.639483i
$82$		0			0
$83$	−1.33629	−	4.98709i	−0.146676	−	0.547404i	−0.999675	−	0.0254909i	$-0.991885\pi$
$83$	−1.33629	−	4.98709i	−0.146676	−	0.547404i	0.852999	−	0.521913i	$-0.174782\pi$
$84$		0			0
$85$	−1.56547	−	5.61041i	−0.169799	−	0.608535i
$86$		0			0
$87$	−0.104480	+	0.389925i	−0.0112014	+	0.0418043i
$88$		0			0
$89$	−1.70407	+	9.66428i	−0.180631	+	1.02441i	0.750810	+	0.660519i	$0.229664\pi$
$89$	−1.70407	+	9.66428i	−0.180631	+	1.02441i	−0.931441	+	0.363892i	$0.881448\pi$
$90$		0			0
$91$	2.20118	−	2.62326i	0.230746	−	0.274993i
$92$		0			0
$93$	−0.435351	+	0.203007i	−0.0451438	+	0.0210509i
$94$		0			0
$95$	−8.51636	+	4.74042i	−0.873760	+	0.486357i
$96$		0			0
$97$	−10.0585	+	4.69035i	−1.02128	+	0.476232i	−0.859794	−	0.510642i	$-0.829408\pi$
$97$	−10.0585	+	4.69035i	−1.02128	+	0.476232i	−0.161490	+	0.986874i	$0.551630\pi$
$98$		0			0
$99$	−9.60300	+	11.4444i	−0.965138	+	1.15021i
$100$		0			0
$101$	2.26132	−	12.8246i	0.225009	−	1.27609i	−0.637658	−	0.770320i	$-0.720097\pi$
$101$	2.26132	−	12.8246i	0.225009	−	1.27609i	0.862667	−	0.505772i	$-0.168792\pi$
$102$		0			0
$103$	4.92910	−	18.3957i	0.485679	−	1.81258i	−0.0913050	−	0.995823i	$-0.529104\pi$
$103$	4.92910	−	18.3957i	0.485679	−	1.81258i	0.576984	−	0.816755i	$-0.304230\pi$
$104$		0			0
$105$	−0.0451103	+	0.0800273i	−0.00440231	+	0.00780987i
$106$		0			0
$107$	−3.44767	−	12.8669i	−0.333299	−	1.24389i	−0.905701	−	0.423916i	$-0.860655\pi$
$107$	−3.44767	−	12.8669i	−0.333299	−	1.24389i	0.572402	−	0.819973i	$-0.306012\pi$
$108$		0			0
$109$	12.6741	−	10.6348i	1.21396	−	1.01863i	0.214840	−	0.976649i	$-0.431077\pi$
$109$	12.6741	−	10.6348i	1.21396	−	1.01863i	0.999118	−	0.0419829i	$-0.0133675\pi$
$110$		0			0
$111$	0.103911	+	0.589307i	0.00986277	+	0.0559345i
$112$		0			0
$113$	−5.12344	−	5.12344i	−0.481973	−	0.481973i	0.423788	−	0.905761i	$-0.360700\pi$
$113$	−5.12344	−	5.12344i	−0.481973	−	0.481973i	−0.905761	+	0.423788i	$0.860700\pi$
$114$		0			0
$115$	−9.30602	−	0.717586i	−0.867791	−	0.0669152i
$116$		0			0
$117$	14.6658	+	10.2691i	1.35585	+	0.949376i
$118$		0			0
$119$	0.959139	+	1.14306i	0.0879241	+	0.104784i
$120$		0			0
$121$	−6.94220	+	12.0242i	−0.631109	+	1.09311i
$122$		0			0
$123$	−0.0324719	+	0.0696362i	−0.00292789	+	0.00627888i
$124$		0			0
$125$	−9.85069	−	5.28810i	−0.881072	−	0.472982i
$126$		0			0
$127$	−4.93452	−	7.04722i	−0.437868	−	0.625340i	0.538197	−	0.842819i	$-0.319106\pi$
$127$	−4.93452	−	7.04722i	−0.437868	−	0.625340i	−0.976065	+	0.217479i	$0.930217\pi$
$128$		0			0
$129$	−0.00259847	−	0.00218038i	−0.000228783	−	0.000191972i
$130$		0			0
$131$	−10.0153	−	3.64526i	−0.875038	−	0.318488i	−0.134833	−	0.990868i	$-0.543050\pi$
$131$	−10.0153	−	3.64526i	−0.875038	−	0.318488i	−0.740206	+	0.672380i	$0.765272\pi$
$132$		0			0
$133$	1.48483	−	2.00743i	0.128751	−	0.174066i
$134$		0			0
$135$	−0.875476	−	0.397306i	−0.0753489	−	0.0341946i
$136$		0			0
$137$	1.15066	+	13.1521i	0.0983074	+	1.12366i	0.871803	+	0.489857i	$0.162951\pi$
$137$	1.15066	+	13.1521i	0.0983074	+	1.12366i	−0.773496	+	0.633802i	$0.781493\pi$
$138$		0			0
$139$	−2.27203	−	0.400621i	−0.192711	−	0.0339802i	0.0764594	−	0.997073i	$-0.475638\pi$
$139$	−2.27203	−	0.400621i	−0.192711	−	0.0339802i	−0.269171	+	0.963093i	$0.586750\pi$
$140$		0			0
$141$	0.741499	−	0.428105i	0.0624455	−	0.0360529i
$142$		0			0
$143$	27.0273	+	12.6031i	2.26014	+	1.05392i
$144$		0			0
$145$	12.3713	−	2.31314i	1.02738	−	0.192096i
$146$		0			0
$147$	−0.0417050	+	0.476691i	−0.00343977	+	0.0393168i
$148$		0			0
$149$	−13.0687	+	2.30436i	−1.07063	+	0.188780i	−0.681067	−	0.732221i	$-0.738484\pi$
$149$	−13.0687	+	2.30436i	−1.07063	+	0.188780i	−0.389559	+	0.921001i	$0.627373\pi$
$150$		0			0
$151$			8.34991i			0.679506i	0.940515	+	0.339753i	$0.110343\pi$
$151$			8.34991i			0.679506i	−0.940515	+	0.339753i	$0.889657\pi$
$152$		0			0
$153$	−5.51635	+	5.51635i	−0.445970	+	0.445970i
$154$		0			0
$155$	11.5711	+	9.50778i	0.929414	+	0.763683i
$156$		0			0
$157$	23.9747	+	2.09751i	1.91339	+	0.167400i	0.980994	−	0.194040i	$-0.0621592\pi$
$157$	23.9747	+	2.09751i	1.91339	+	0.167400i	0.932395	+	0.361440i	$0.117715\pi$
$158$		0			0
$159$	−0.191652	−	0.110650i	−0.0151990	−	0.00877512i
$160$		0			0
$161$	2.24686	−	0.817790i	0.177077	−	0.0644509i
$162$		0			0
$163$	14.7321	+	3.94745i	1.15391	+	0.309188i	0.784530	−	0.620091i	$-0.212905\pi$
$163$	14.7321	+	3.94745i	1.15391	+	0.309188i	0.369377	+	0.929280i	$0.379571\pi$
$164$		0			0
$165$	−0.774840	−	0.199080i	−0.0603212	−	0.0154983i
$166$		0			0
$167$	−11.7964	+	1.03205i	−0.912833	+	0.0798626i	−0.533887	−	0.845556i	$-0.679269\pi$
$167$	−11.7964	+	1.03205i	−0.912833	+	0.0798626i	−0.378946	+	0.925419i	$0.623714\pi$
$168$		0			0
$169$	7.77679	−	21.3665i	0.598214	−	1.64358i
$170$		0			0
$171$	11.1319	+	6.81875i	0.851276	+	0.521443i
$172$		0			0
$173$	−2.32111	−	4.97764i	−0.176471	−	0.378443i	0.798099	−	0.602526i	$-0.205839\pi$
$173$	−2.32111	−	4.97764i	−0.176471	−	0.378443i	−0.974570	+	0.224083i	$0.928061\pi$
$174$		0			0
$175$	2.85778	+	0.190749i	0.216028	+	0.0144193i
$176$		0			0
$177$	0.395117	−	0.276664i	0.0296988	−	0.0207953i
$178$		0			0
$179$	−3.20681	−	5.55435i	−0.239688	−	0.415152i	0.720937	−	0.693001i	$-0.243712\pi$
$179$	−3.20681	−	5.55435i	−0.239688	−	0.415152i	−0.960625	+	0.277849i	$0.910378\pi$
$180$		0			0
$181$	−1.00642	−	2.76511i	−0.0748064	−	0.205529i	0.896653	−	0.442733i	$-0.145991\pi$
$181$	−1.00642	−	2.76511i	−0.0748064	−	0.205529i	−0.971460	+	0.237204i	$0.923769\pi$
$182$		0			0
$183$	−0.576855	+	0.154568i	−0.0426424	+	0.0114260i
$184$		0			0
$185$	15.1714	−	10.8579i	1.11542	−	0.798289i
$186$		0			0
$187$	−7.45324	+	10.6443i	−0.545035	+	0.778391i
$188$		0			0
$189$	0.246290			0.0179150
$190$		0			0
$191$	11.6243			0.841107			0.420553	−	0.907268i	$-0.361836\pi$
$191$	11.6243			0.841107			0.420553	+	0.907268i	$0.361836\pi$
$192$		0			0
$193$	−3.29958	+	4.71228i	−0.237509	+	0.339197i	−0.920157	−	0.391549i	$-0.871939\pi$
$193$	−3.29958	+	4.71228i	−0.237509	+	0.339197i	0.682648	+	0.730747i	$0.260828\pi$
$194$		0			0
$195$	−0.156739	+	0.945825i	−0.0112243	+	0.0677320i
$196$		0			0
$197$	−14.0269	+	3.75850i	−0.999376	+	0.267782i	−0.721184	−	0.692744i	$-0.756402\pi$
$197$	−14.0269	+	3.75850i	−0.999376	+	0.267782i	−0.278192	+	0.960526i	$0.589735\pi$
$198$		0			0
$199$	2.83863	+	7.79908i	0.201225	+	0.552862i	0.998726	−	0.0504555i	$-0.0160673\pi$
$199$	2.83863	+	7.79908i	0.201225	+	0.552862i	−0.797501	+	0.603318i	$0.793845\pi$
$200$		0			0
$201$	−0.443700	−	0.768510i	−0.0312962	−	0.0542065i
$202$		0			0
$203$	−2.64107	+	1.84930i	−0.185367	+	0.129795i
$204$		0			0
$205$	2.39539	−	0.0246947i	0.167301	−	0.00172476i
$206$		0			0
$207$	5.28312	+	11.3297i	0.367202	+	0.787468i
$208$		0			0
$209$	20.2325	+	7.96542i	1.39951	+	0.550979i
$210$		0			0
$211$	1.29589	−	3.56043i	0.0892129	−	0.245110i	−0.887060	−	0.461654i	$-0.847256\pi$
$211$	1.29589	−	3.56043i	0.0892129	−	0.245110i	0.976273	+	0.216544i	$0.0694784\pi$
$212$		0			0
$213$	−0.108475	+	0.00949037i	−0.00743262	+	0.000650270i
$214$		0			0
$215$	−0.0263171	+	0.102429i	−0.00179481	+	0.00698560i
$216$		0			0
$217$	−3.70583	−	0.992975i	−0.251568	−	0.0674076i
$218$		0			0
$219$	−0.182806	+	0.0665359i	−0.0123529	+	0.00449608i
$220$		0			0
$221$	13.4861	+	7.78618i	0.907170	+	0.523755i
$222$		0			0
$223$	−7.35623	−	0.643587i	−0.492610	−	0.0430978i	−0.161855	−	0.986815i	$-0.551748\pi$
$223$	−7.35623	−	0.643587i	−0.492610	−	0.0430978i	−0.330755	+	0.943717i	$0.607303\pi$
$224$		0			0
$225$	0.308715	+	14.9711i	0.0205810	+	0.998073i
$226$		0			0
$227$	−1.30611	+	1.30611i	−0.0866897	+	0.0866897i	−0.749122	−	0.662432i	$-0.769524\pi$
$227$	−1.30611	+	1.30611i	−0.0866897	+	0.0866897i	0.662432	+	0.749122i	$0.269524\pi$
$228$		0			0
$229$		−	7.38156i		−	0.487787i	−0.969802	−	0.243893i	$-0.921575\pi$
$229$		−	7.38156i		−	0.487787i	0.969802	−	0.243893i	$-0.0784247\pi$
$230$		0			0
$231$	0.201829	−	0.0355879i	0.0132794	−	0.00234151i
$232$		0			0
$233$	1.26675	−	14.4790i	0.0829876	−	0.948553i	−0.834557	−	0.550921i	$-0.814277\pi$
$233$	1.26675	−	14.4790i	0.0829876	−	0.948553i	0.917545	−	0.397632i	$-0.130168\pi$
$234$		0			0
$235$	−22.0235	−	15.0851i	−1.43665	−	0.984040i
$236$		0			0
$237$	0.678411	+	0.316348i	0.0440675	+	0.0205490i
$238$		0			0
$239$	−18.2542	+	10.5391i	−1.18077	+	0.681717i	−0.956192	−	0.292740i	$-0.905433\pi$
$239$	−18.2542	+	10.5391i	−1.18077	+	0.681717i	−0.224576	+	0.974457i	$0.572100\pi$
$240$		0			0
$241$	−2.48055	−	0.437388i	−0.159786	−	0.0281747i	0.0931826	−	0.995649i	$-0.470296\pi$
$241$	−2.48055	−	0.437388i	−0.159786	−	0.0281747i	−0.252969	+	0.967474i	$0.581407\pi$
$242$		0			0
$243$	0.168388	+	1.92468i	0.0108021	+	0.123469i
$244$		0			0
$245$	13.9657	−	5.24676i	0.892236	−	0.335203i
$246$		0			0
$247$	7.39617	−	24.9863i	0.470607	−	1.58984i
$248$		0			0
$249$	−0.347964	−	0.126648i	−0.0220513	−	0.00802602i
$250$		0			0
$251$	10.6991	+	8.97765i	0.675324	+	0.566664i	0.914636	−	0.404279i	$-0.132477\pi$
$251$	10.6991	+	8.97765i	0.675324	+	0.566664i	−0.239312	+	0.970943i	$0.576922\pi$
$252$		0			0
$253$	11.9432	+	17.0567i	0.750863	+	1.07234i
$254$		0			0
$255$	−0.394012	−	0.138826i	−0.0246740	−	0.00869361i
$256$		0			0
$257$	5.86433	−	12.5761i	0.365807	−	0.784475i	−0.634130	−	0.773226i	$-0.718642\pi$
$257$	5.86433	−	12.5761i	0.365807	−	0.784475i	0.999937	−	0.0112485i	$-0.00358059\pi$
$258$		0			0
$259$	−2.38967	+	4.13904i	−0.148487	+	0.257187i
$260$		0			0
$261$	−10.8352	−	12.9129i	−0.670680	−	0.799286i
$262$		0			0
$263$	−19.0238	−	13.3206i	−1.17306	−	0.821386i	−0.186128	−	0.982525i	$-0.559594\pi$
$263$	−19.0238	−	13.3206i	−1.17306	−	0.821386i	−0.986932	+	0.161140i	$0.948483\pi$
$264$		0			0
$265$	−0.530450	+	6.87915i	−0.0325853	+	0.422583i
$266$		0			0
$267$	0.497677	+	0.497677i	0.0304573	+	0.0304573i
$268$		0			0
$269$	3.10231	+	17.5941i	0.189151	+	1.07273i	0.920505	+	0.390731i	$0.127778\pi$
$269$	3.10231	+	17.5941i	0.189151	+	1.07273i	−0.731354	+	0.681998i	$0.761111\pi$
$270$		0			0
$271$	5.40769	−	4.53759i	0.328494	−	0.275639i	−0.463592	−	0.886049i	$-0.653440\pi$
$271$	5.40769	−	4.53759i	0.328494	−	0.275639i	0.792086	+	0.610410i	$0.208995\pi$
$272$		0			0
$273$	−0.0635666	−	0.237234i	−0.00384722	−	0.0143580i
$274$		0			0
$275$	4.83664	+	24.4687i	0.291660	+	1.47552i
$276$		0			0
$277$	−1.13610	+	4.23998i	−0.0682616	+	0.254756i	−0.991621	−	0.129181i	$-0.958765\pi$
$277$	−1.13610	+	4.23998i	−0.0682616	+	0.254756i	0.923359	+	0.383937i	$0.125432\pi$
$278$		0			0
$279$	3.48309	−	19.7536i	0.208527	−	1.18262i
$280$		0			0
$281$	−10.8248	+	12.9005i	−0.645753	+	0.769578i	−0.985267	−	0.171023i	$-0.945293\pi$
$281$	−10.8248	+	12.9005i	−0.645753	+	0.769578i	0.339514	+	0.940601i	$0.389737\pi$
$282$		0			0
$283$	−0.0560064	+	0.0261162i	−0.00332923	+	0.00155245i	−0.424282	−	0.905530i	$-0.639474\pi$
$283$	−0.0560064	+	0.0261162i	−0.00332923	+	0.00155245i	0.420953	+	0.907082i	$0.361696\pi$
$284$		0			0
$285$	−0.0718395	+	0.695346i	−0.00425541	+	0.0411888i
$286$		0			0
$287$	−0.556178	+	0.259350i	−0.0328301	+	0.0153089i
$288$		0			0
$289$	6.56576	−	7.82477i	0.386221	−	0.460281i
$290$		0			0
$291$	−0.138220	+	0.783886i	−0.00810262	+	0.0459522i
$292$		0			0
$293$	−1.32116	+	4.93062i	−0.0771827	+	0.288050i	−0.993719	−	0.111901i	$-0.964306\pi$
$293$	−1.32116	+	4.93062i	−0.0771827	+	0.288050i	0.916537	+	0.399951i	$0.130973\pi$
$294$		0			0
$295$	−13.1005	−	7.38454i	−0.762738	−	0.429945i
$296$		0			0
$297$	0.555116	+	2.07172i	0.0322111	+	0.120213i
$298$		0			0
$299$	19.1154	−	16.0398i	1.10547	−	0.927603i
$300$		0			0
$301$	−0.00470450	−	0.0266805i	−0.000271163	−	0.00153784i
$302$		0			0
$303$	−0.660421	−	0.660421i	−0.0379402	−	0.0379402i
$304$		0			0
$305$	12.1147	+	14.1391i	0.693683	+	0.809601i
$306$		0			0
$307$	3.41448	+	2.39085i	0.194875	+	0.136453i	0.666942	−	0.745110i	$-0.267603\pi$
$307$	3.41448	+	2.39085i	0.194875	+	0.136453i	−0.472067	+	0.881563i	$0.656492\pi$
$308$		0			0
$309$	−0.877979	−	1.04633i	−0.0499465	−	0.0595239i
$310$		0			0
$311$	−5.84352	+	10.1213i	−0.331356	+	0.573925i	−0.982778	−	0.184791i	$-0.940839\pi$
$311$	−5.84352	+	10.1213i	−0.331356	+	0.573925i	0.651422	+	0.758715i	$0.274173\pi$
$312$		0			0
$313$	−11.8028	+	25.3112i	−0.667134	+	1.43067i	0.222929	+	0.974835i	$0.428438\pi$
$313$	−11.8028	+	25.3112i	−0.667134	+	1.43067i	−0.890063	+	0.455838i	$0.849340\pi$
$314$		0			0
$315$	−1.65694	−	3.45975i	−0.0933580	−	0.194935i
$316$		0			0
$317$	−18.3715	−	26.2372i	−1.03185	−	1.47363i	−0.873853	−	0.486190i	$-0.838386\pi$
$317$	−18.3715	−	26.2372i	−1.03185	−	1.47363i	−0.157993	−	0.987440i	$-0.550502\pi$
$318$		0			0
$319$	−21.5085	−	18.0478i	−1.20424	−	1.01048i
$320$		0			0
$321$	−0.897761	−	0.326758i	−0.0501081	−	0.0182379i
$322$		0			0
$323$	10.1625	+	5.06443i	0.565455	+	0.281793i
$324$		0			0
$325$	28.7064	−	8.32984i	1.59235	−	0.462056i
$326$		0			0
$327$	−0.103420	−	1.18209i	−0.00571913	−	0.0653700i
$328$		0			0
$329$	6.73458	+	1.18749i	0.371289	+	0.0654683i
$330$		0			0
$331$	−7.69584	+	4.44320i	−0.423002	+	0.244220i	−0.696361	−	0.717692i	$-0.745199\pi$
$331$	−7.69584	+	4.44320i	−0.423002	+	0.244220i	0.273359	+	0.961912i	$0.411865\pi$
$332$		0			0
$333$	−22.6463	−	10.5601i	−1.24101	−	0.578692i
$334$		0			0
$335$	−15.6346	+	22.8257i	−0.854207	+	1.24710i
$336$		0			0
$337$	1.51447	−	17.3105i	0.0824985	−	0.942962i	−0.836310	−	0.548257i	$-0.815291\pi$
$337$	1.51447	−	17.3105i	0.0824985	−	0.942962i	0.918808	−	0.394704i	$-0.129153\pi$
$338$		0			0
$339$	−0.511768	+	0.0902385i	−0.0277954	+	0.00490108i
$340$		0			0
$341$		−	33.4104i		−	1.80928i
$342$		0			0
$343$	−5.53779	+	5.53779i	−0.299013	+	0.299013i
$344$		0			0
$345$	−0.424983	+	0.517211i	−0.0228803	+	0.0278457i
$346$		0			0
$347$	−15.0999	−	1.32107i	−0.810606	−	0.0709188i	−0.325687	−	0.945478i	$-0.605595\pi$
$347$	−15.0999	−	1.32107i	−0.810606	−	0.0709188i	−0.484919	+	0.874559i	$0.661151\pi$
$348$		0			0
$349$	−26.0156	−	15.0201i	−1.39259	−	0.804010i	−0.398985	−	0.916958i	$-0.630637\pi$
$349$	−26.0156	−	15.0201i	−1.39259	−	0.804010i	−0.993601	+	0.112948i	$0.963971\pi$
$350$		0			0
$351$	2.41531	−	0.879102i	0.128920	−	0.0469230i
$352$		0			0
$353$	−16.5143	−	4.42500i	−0.878970	−	0.235519i	−0.209007	−	0.977914i	$-0.567023\pi$
$353$	−16.5143	−	4.42500i	−0.878970	−	0.235519i	−0.669963	+	0.742395i	$0.733690\pi$
$354$		0			0
$355$	1.72767	+	2.92242i	0.0916952	+	0.155106i
$356$		0			0
$357$	0.106611	−	0.00932728i	0.00564247	−	0.000493652i
$358$		0			0
$359$	−4.35701	+	11.9708i	−0.229954	+	0.631794i	−0.999981	−	0.00621797i	$-0.998021\pi$
$359$	−4.35701	+	11.9708i	−0.229954	+	0.631794i	0.770026	+	0.638012i	$0.220243\pi$
$360$		0			0
$361$	4.26711	−	18.5146i	0.224585	−	0.974455i
$362$		0			0
$363$	0.420843	+	0.902501i	0.0220885	+	0.0473690i
$364$		0			0
$365$	4.33272	+	4.24430i	0.226785	+	0.222157i
$366$		0			0
$367$	17.5379	−	12.2802i	0.915471	−	0.641019i	−0.0179363	−	0.999839i	$-0.505710\pi$
$367$	17.5379	−	12.2802i	0.915471	−	0.641019i	0.933407	+	0.358820i	$0.116821\pi$
$368$		0			0
$369$	−1.60421	−	2.77857i	−0.0835116	−	0.144646i
$370$		0			0
$371$	−0.604522	−	1.66091i	−0.0313852	−	0.0862302i
$372$		0			0
$373$	0.303963	−	0.0814466i	0.0157386	−	0.00421714i	−0.250941	−	0.968002i	$-0.580740\pi$
$373$	0.303963	−	0.0814466i	0.0157386	−	0.00421714i	0.266680	+	0.963785i	$0.414073\pi$
$374$		0			0
$375$	−0.715908	+	0.361192i	−0.0369693	+	0.0186519i
$376$		0			0
$377$	−19.2996	+	27.5626i	−0.993978	+	1.41955i
$378$		0			0
$379$	−20.8232			−1.06961			−0.534807	−	0.844974i	$-0.679616\pi$
$379$	−20.8232			−1.06961			−0.534807	+	0.844974i	$0.679616\pi$
$380$		0			0
$381$	−0.617019			−0.0316108
$382$		0			0
$383$	−13.9437	+	19.9137i	−0.712490	+	1.01754i	0.285754	+	0.958303i	$0.407756\pi$
$383$	−13.9437	+	19.9137i	−0.712490	+	1.01754i	−0.998244	+	0.0592385i	$0.981133\pi$
$384$		0			0
$385$	−3.71867	−	5.19598i	−0.189521	−	0.264812i
$386$		0			0
$387$	0.136817	−	0.0366599i	0.00695478	−	0.00186353i
$388$		0			0
$389$	3.75504	+	10.3169i	0.190388	+	0.523087i	0.997756	−	0.0669621i	$-0.0213307\pi$
$389$	3.75504	+	10.3169i	0.190388	+	0.523087i	−0.807367	+	0.590049i	$0.799108\pi$
$390$		0			0
$391$	5.43659	+	9.41645i	0.274940	+	0.476211i
$392$		0			0
$393$	−0.626162	+	0.438443i	−0.0315857	+	0.0221165i
$394$		0			0
$395$	−0.240582	−	23.3364i	−0.0121050	−	1.17418i
$396$		0			0
$397$	−2.92469	−	6.27201i	−0.146786	−	0.314783i	0.819144	−	0.573588i	$-0.194449\pi$
$397$	−2.92469	−	6.27201i	−0.146786	−	0.314783i	−0.965930	+	0.258805i	$0.916671\pi$
$398$		0			0
$399$	−0.0568546	−	0.169814i	−0.00284629	−	0.00850136i
$400$		0			0
$401$	3.96508	−	10.8940i	0.198006	−	0.544018i	−0.800460	−	0.599387i	$-0.795411\pi$
$401$	3.96508	−	10.8940i	0.198006	−	0.544018i	0.998466	+	0.0553686i	$0.0176334\pi$
$402$		0			0
$403$	−39.8866	+	3.48962i	−1.98689	+	0.173831i
$404$		0			0
$405$	17.2347	−	10.1888i	0.856400	−	0.506285i
$406$		0			0
$407$	−40.2024	−	10.7722i	−1.99276	−	0.533959i
$408$		0			0
$409$	26.6419	−	9.69687i	1.31736	−	0.479480i	0.414748	−	0.909936i	$-0.363870\pi$
$409$	26.6419	−	9.69687i	1.31736	−	0.479480i	0.902611	+	0.430457i	$0.141647\pi$
$410$		0			0
$411$	0.820023	+	0.473440i	0.0404487	+	0.0233531i
$412$		0			0
$413$	3.83782	+	0.335766i	0.188847	+	0.0165219i
$414$		0			0
$415$	1.12471	+	11.4899i	0.0552097	+	0.564019i
$416$		0			0
$417$	−0.117002	+	0.117002i	−0.00572961	+	0.00572961i
$418$		0			0
$419$			1.24051i			0.0606030i	0.999541	+	0.0303015i	$0.00964674\pi$
$419$			1.24051i			0.0606030i	−0.999541	+	0.0303015i	$0.990353\pi$
$420$		0			0
$421$	4.78115	−	0.843045i	0.233019	−	0.0410875i	−0.0559192	−	0.998435i	$-0.517809\pi$
$421$	4.78115	−	0.843045i	0.233019	−	0.0410875i	0.288938	+	0.957348i	$0.406698\pi$
$422$		0			0
$423$	−3.11607	+	35.6168i	−0.151509	+	1.73175i
$424$		0			0
$425$	1.40241	+	12.9488i	0.0680270	+	0.628107i
$426$		0			0
$427$	−4.32293	−	2.01581i	−0.209201	−	0.0975520i
$428$		0			0
$429$	1.85226	−	1.06941i	0.0894282	−	0.0516314i
$430$		0			0
$431$	36.9361	+	6.51284i	1.77915	+	0.313712i	0.964073	−	0.265639i	$-0.0855828\pi$
$431$	36.9361	+	6.51284i	1.77915	+	0.313712i	0.815078	+	0.579351i	$0.196694\pi$
$432$		0			0
$433$	2.86329	+	32.7275i	0.137601	+	1.57278i	0.680349	+	0.732888i	$0.261828\pi$
$433$	2.86329	+	32.7275i	0.137601	+	1.57278i	−0.542748	+	0.839896i	$0.682616\pi$
$434$		0			0
$435$	0.373025	−	0.821973i	0.0178852	−	0.0394106i
$436$		0			0
$437$	13.1956	−	12.5268i	0.631229	−	0.599240i
$438$		0			0
$439$	3.53203	+	1.28556i	0.168575	+	0.0613562i	0.424929	−	0.905227i	$-0.360299\pi$
$439$	3.53203	+	1.28556i	0.168575	+	0.0613562i	−0.256354	+	0.966583i	$0.582521\pi$
$440$		0			0
$441$	−15.3066	−	12.8437i	−0.728884	−	0.611606i
$442$		0			0
$443$	−9.12007	−	13.0248i	−0.433308	−	0.618827i	0.541814	−	0.840498i	$-0.317738\pi$
$443$	−9.12007	−	13.0248i	−0.433308	−	0.618827i	−0.975121	+	0.221671i	$0.928849\pi$
$444$		0			0
$445$	7.29210	−	20.6963i	0.345679	−	0.981097i
$446$		0			0
$447$	−0.402229	+	0.862582i	−0.0190248	+	0.0407987i
$448$		0			0
$449$	14.2839	−	24.7405i	0.674100	−	1.16758i	−0.302631	−	0.953108i	$-0.597865\pi$
$449$	14.2839	−	24.7405i	0.674100	−	1.16758i	0.976731	−	0.214468i	$-0.0688018\pi$
$450$		0			0
$451$	−3.43515	−	4.09385i	−0.161755	−	0.192772i
$452$		0			0
$453$	0.490559	+	0.343493i	0.0230485	+	0.0161387i
$454$		0			0
$455$	−5.81474	+	4.98219i	−0.272599	+	0.233569i
$456$		0			0
$457$	8.36334	+	8.36334i	0.391221	+	0.391221i	0.875122	−	0.483902i	$-0.160781\pi$
$457$	8.36334	+	8.36334i	0.391221	+	0.391221i	−0.483902	+	0.875122i	$0.660781\pi$
$458$		0			0
$459$	0.194484	+	1.10297i	0.00907775	+	0.0514825i
$460$		0			0
$461$	1.22094	−	1.02449i	0.0568650	−	0.0477154i	−0.613912	−	0.789374i	$-0.710405\pi$
$461$	1.22094	−	1.02449i	0.0568650	−	0.0477154i	0.670777	+	0.741659i	$0.265961\pi$
$462$		0			0
$463$	0.532428	+	1.98705i	0.0247440	+	0.0923460i	0.977194	−	0.212350i	$-0.0681117\pi$
$463$	0.532428	+	1.98705i	0.0247440	+	0.0923460i	−0.952450	+	0.304696i	$0.901445\pi$
$464$		0			0
$465$	1.03459	−	0.288681i	0.0479779	−	0.0133872i
$466$		0			0
$467$	0.645474	−	2.40894i	0.0298690	−	0.111472i	−0.949382	−	0.314124i	$-0.898289\pi$
$467$	0.645474	−	2.40894i	0.0298690	−	0.111472i	0.979251	+	0.202652i	$0.0649559\pi$
$468$		0			0
$469$	1.23074	−	6.97990i	0.0568305	−	0.322302i
$470$		0			0
$471$	1.10948	−	1.32223i	0.0511224	−	0.0609252i
$472$		0			0
$473$	0.213825	−	0.0997083i	0.00983169	−	0.00458459i
$474$		0			0
$475$	20.5199	−	7.34399i	0.941517	−	0.336965i
$476$		0			0
$477$	8.37507	−	3.90536i	0.383468	−	0.178814i
$478$		0			0
$479$	4.40564	−	5.25044i	0.201299	−	0.239899i	−0.655946	−	0.754808i	$-0.727730\pi$
$479$	4.40564	−	5.25044i	0.201299	−	0.239899i	0.857245	+	0.514909i	$0.172174\pi$
$480$		0			0
$481$	−8.66122	+	49.1202i	−0.394918	+	2.23969i
$482$		0			0
$483$	0.0443845	−	0.165645i	0.00201956	−	0.00753711i
$484$		0			0
$485$	23.9035	−	6.66977i	1.08540	−	0.302859i
$486$		0			0
$487$	−2.21474	−	8.26552i	−0.100359	−	0.374547i	0.897418	−	0.441181i	$-0.145440\pi$
$487$	−2.21474	−	8.26552i	−0.100359	−	0.374547i	−0.997777	+	0.0666348i	$0.978774\pi$
$488$		0			0
$489$	0.837953	−	0.703126i	0.0378935	−	0.0317964i
$490$		0			0
$491$	−0.217133	−	1.23142i	−0.00979907	−	0.0555733i	0.979516	−	0.201366i	$-0.0645380\pi$
$491$	−0.217133	−	1.23142i	−0.00979907	−	0.0555733i	−0.989315	+	0.145792i	$0.953427\pi$
$492$		0			0
$493$	−10.3674	−	10.3674i	−0.466922	−	0.466922i
$494$		0			0
$495$	25.3678	−	21.7356i	1.14020	−	0.976944i
$496$		0			0
$497$	−0.712411	−	0.498835i	−0.0319560	−	0.0223758i
$498$		0			0
$499$	12.7954	+	15.2490i	0.572802	+	0.682639i	0.972204	−	0.234137i	$-0.0752265\pi$
$499$	12.7954	+	15.2490i	0.572802	+	0.682639i	−0.399402	+	0.916776i	$0.630782\pi$
$500$		0			0
$501$	−0.424639	+	0.735497i	−0.0189715	+	0.0328596i
$502$		0			0
$503$	16.8891	−	36.2188i	0.753047	−	1.61492i	−0.0350656	−	0.999385i	$-0.511164\pi$
$503$	16.8891	−	36.2188i	0.753047	−	1.61492i	0.788113	−	0.615531i	$-0.211058\pi$
$504$		0			0
$505$	−9.67667	+	27.4641i	−0.430606	+	1.22214i
$506$		0			0
$507$	−0.935373	−	1.33585i	−0.0415414	−	0.0593272i
$508$		0			0
$509$	−3.98835	−	3.34663i	−0.176781	−	0.148337i	0.550104	−	0.835096i	$-0.314588\pi$
$509$	−3.98835	−	3.34663i	−0.176781	−	0.148337i	−0.726885	+	0.686760i	$0.759033\pi$
$510$		0			0
$511$	−1.46005	−	0.531416i	−0.0645890	−	0.0235085i
$512$		0			0
$513$	1.71855	−	0.747632i	0.0758759	−	0.0330088i
$514$		0			0
$515$	−17.5984	+	38.7786i	−0.775477	+	1.70879i
$516$		0			0
$517$	5.19033	+	59.3257i	0.228270	+	2.60914i
$518$		0			0
$519$	−0.387922	−	0.0684011i	−0.0170279	−	0.00300248i
$520$		0			0
$521$	15.3289	−	8.85013i	0.671570	−	0.387731i	−0.125101	−	0.992144i	$-0.539926\pi$
$521$	15.3289	−	8.85013i	0.671570	−	0.387731i	0.796671	+	0.604413i	$0.206592\pi$
$522$		0			0
$523$	5.22571	+	2.43679i	0.228504	+	0.106553i	0.533499	−	0.845801i	$-0.320877\pi$
$523$	5.22571	+	2.43679i	0.228504	+	0.106553i	−0.304994	+	0.952354i	$0.598655\pi$
$524$		0			0
$525$	0.128768	−	0.160048i	0.00561989	−	0.00698507i
$526$		0			0
$527$	1.52057	−	17.3801i	0.0662369	−	0.757091i
$528$		0			0
$529$	−5.49189	+	0.968369i	−0.238778	+	0.0421030i
$530$		0			0
$531$			20.1415i			0.874068i
$532$		0			0
$533$	−4.52859	+	4.52859i	−0.196155	+	0.196155i
$534$		0			0
$535$	2.90179	+	29.6445i	0.125455	+	1.28164i
$536$		0			0
$537$	−0.458239	−	0.0400907i	−0.0197745	−	0.00173004i
$538$		0			0
$539$	−28.8232	−	16.6411i	−1.24150	−	0.716781i
$540$		0			0
$541$	26.6241	−	9.69037i	1.14466	−	0.416622i	0.301065	−	0.953604i	$-0.402658\pi$
$541$	26.6241	−	9.69037i	1.14466	−	0.416622i	0.843594	+	0.536982i	$0.180436\pi$
$542$		0			0
$543$	−0.203852	−	0.0546220i	−0.00874813	−	0.00234405i
$544$		0			0
$545$	−31.8466	+	18.8270i	−1.36416	+	0.806461i
$546$		0			0
$547$	42.3890	−	3.70855i	1.81242	−	0.158566i	0.870012	−	0.493030i	$-0.164111\pi$
$547$	42.3890	−	3.70855i	1.81242	−	0.158566i	0.942409	+	0.334464i	$0.108555\pi$
$548$		0			0
$549$	8.52915	−	23.4337i	0.364015	−	1.00012i
$550$		0			0
$551$	−12.8151	+	20.9211i	−0.545940	+	0.891270i
$552$		0			0
$553$	2.52664	+	5.41841i	0.107444	+	0.230414i
$554$		0			0
$555$	−0.0137937	−	1.33799i	−0.000585509	−	0.0567944i
$556$		0			0
$557$	−12.3103	+	8.61976i	−0.521604	+	0.365231i	−0.804531	−	0.593910i	$-0.797583\pi$
$557$	−12.3103	+	8.61976i	−0.521604	+	0.365231i	0.282927	+	0.959141i	$0.408695\pi$
$558$		0			0
$559$	−0.141369	−	0.244858i	−0.00597926	−	0.0103564i
$560$		0			0
$561$	0.318750	+	0.875759i	0.0134576	+	0.0369746i
$562$		0			0
$563$	17.4882	−	4.68595i	0.737040	−	0.197489i	0.129278	−	0.991608i	$-0.458734\pi$
$563$	17.4882	−	4.68595i	0.737040	−	0.197489i	0.607762	+	0.794119i	$0.292067\pi$
$564$		0			0
$565$	9.42926	+	13.1752i	0.396692	+	0.554284i
$566$		0			0
$567$	−2.94184	+	4.20138i	−0.123546	+	0.176441i
$568$		0			0
$569$	15.0164			0.629521			0.314761	−	0.949171i	$-0.398076\pi$
$569$	15.0164			0.629521			0.314761	+	0.949171i	$0.398076\pi$
$570$		0			0
$571$	−38.2880			−1.60230			−0.801152	−	0.598461i	$-0.795779\pi$
$571$	−38.2880			−1.60230			−0.801152	+	0.598461i	$0.795779\pi$
$572$		0			0
$573$	0.478194	−	0.682931i	0.0199768	−	0.0285299i
$574$		0			0
$575$	20.2666	+	4.98496i	0.845175	+	0.207887i
$576$		0			0
$577$	13.5324	−	3.62600i	0.563362	−	0.150952i	0.0341116	−	0.999418i	$-0.489140\pi$
$577$	13.5324	−	3.62600i	0.563362	−	0.150952i	0.529251	+	0.848466i	$0.322473\pi$
$578$		0			0
$579$	0.141112	+	0.387701i	0.00586441	+	0.0161123i
$580$		0			0
$581$	−1.47876	−	2.56128i	−0.0613492	−	0.106260i
$582$		0			0
$583$	12.6085	−	8.82860i	0.522192	−	0.365643i
$584$		0			0
$585$	−28.5984	−	28.0147i	−1.18240	−	1.15827i
$586$		0			0
$587$	−18.4152	−	39.4915i	−0.760076	−	1.62999i	−0.776495	−	0.630123i	$-0.783004\pi$
$587$	−18.4152	−	39.4915i	−0.760076	−	1.62999i	0.0164193	−	0.999865i	$-0.494773\pi$
$588$		0			0
$589$	−28.8726	+	4.32059i	−1.18968	+	0.178027i
$590$		0			0
$591$	−0.356217	+	0.978698i	−0.0146528	+	0.0402583i
$592$		0			0
$593$	0.438269	−	0.0383436i	0.0179976	−	0.00157458i	−0.0781534	−	0.996941i	$-0.524902\pi$
$593$	0.438269	−	0.0383436i	0.0179976	−	0.00157458i	0.0961510	+	0.995367i	$0.469347\pi$
$594$		0			0
$595$	−1.69798	−	2.87220i	−0.0696104	−	0.117749i
$596$		0			0
$597$	0.574971	+	0.154063i	0.0235320	+	0.00630538i
$598$		0			0
$599$	32.7408	−	11.9167i	1.33775	−	0.486903i	0.428650	−	0.903471i	$-0.358989\pi$
$599$	32.7408	−	11.9167i	1.33775	−	0.486903i	0.909105	+	0.416568i	$0.136767\pi$
$600$		0			0
$601$	6.31556	+	3.64629i	0.257617	+	0.148735i	0.623247	−	0.782025i	$-0.285813\pi$
$601$	6.31556	+	3.64629i	0.257617	+	0.148735i	−0.365630	+	0.930760i	$0.619146\pi$
$602$		0			0
$603$	36.9143	+	3.22958i	1.50327	+	0.131519i
$604$		0			0
$605$	19.7100	−	23.9874i	0.801327	−	0.975227i
$606$		0			0
$607$	−10.3411	+	10.3411i	−0.419731	+	0.419731i	−0.885111	−	0.465380i	$-0.845918\pi$
$607$	−10.3411	+	10.3411i	−0.419731	+	0.419731i	0.465380	+	0.885111i	$0.345918\pi$
$608$		0			0
$609$			0.231239i			0.00937027i
$610$		0			0
$611$	70.2831	−	12.3928i	2.84335	−	0.501359i
$612$		0			0
$613$	0.736274	−	8.41565i	0.0297378	−	0.339905i	−0.966722	−	0.255830i	$-0.917651\pi$
$613$	0.736274	−	8.41565i	0.0297378	−	0.339905i	0.996459	−	0.0840744i	$-0.0267933\pi$
$614$		0			0
$615$	0.0970891	−	0.141745i	0.00391501	−	0.00571573i
$616$		0			0
$617$	−20.6417	−	9.62538i	−0.831003	−	0.387503i	−0.0399132	−	0.999203i	$-0.512708\pi$
$617$	−20.6417	−	9.62538i	−0.831003	−	0.387503i	−0.791090	+	0.611700i	$0.790486\pi$
$618$		0			0
$619$	8.52728	−	4.92323i	0.342740	−	0.197881i	−0.318743	−	0.947841i	$-0.603261\pi$
$619$	8.52728	−	4.92323i	0.342740	−	0.197881i	0.661483	+	0.749960i	$0.269927\pi$
$620$		0			0
$621$	1.76743	+	0.311645i	0.0709244	+	0.0125059i
$622$		0			0
$623$	0.489934	+	5.59997i	0.0196288	+	0.224358i
$624$		0			0
$625$	19.7973	+	15.2665i	0.791892	+	0.610662i
$626$		0			0
$627$	1.30028	−	0.860990i	0.0519283	−	0.0343846i
$628$		0			0
$629$	−20.4231	−	7.43340i	−0.814322	−	0.296389i
$630$		0			0
$631$	5.13721	+	4.31063i	0.204509	+	0.171604i	0.739290	−	0.673387i	$-0.235161\pi$
$631$	5.13721	+	4.31063i	0.204509	+	0.171604i	−0.534781	+	0.844991i	$0.679606\pi$
$632$		0			0
$633$	−0.155867	−	0.222601i	−0.00619514	−	0.00884758i
$634$		0			0
$635$	8.30923	+	17.3500i	0.329742	+	0.688512i
$636$		0			0
$637$	−16.8562	+	36.1482i	−0.667867	+	1.43225i
$638$		0			0
$639$	2.27347	−	3.93776i	0.0899369	−	0.155775i
$640$		0			0
$641$	8.88258	+	10.5859i	0.350841	+	0.418116i	0.912386	−	0.409330i	$-0.134237\pi$
$641$	8.88258	+	10.5859i	0.350841	+	0.418116i	−0.561545	+	0.827446i	$0.689793\pi$
$642$		0			0
$643$	−13.2318	−	9.26501i	−0.521811	−	0.365376i	0.282799	−	0.959179i	$-0.408737\pi$
$643$	−13.2318	−	9.26501i	−0.521811	−	0.365376i	−0.804610	+	0.593803i	$0.797626\pi$
$644$		0			0
$645$	0.00493511	+	0.00575979i	0.000194320	+	0.000226792i
$646$		0			0
$647$	3.83578	+	3.83578i	0.150800	+	0.150800i	0.778475	−	0.627675i	$-0.215993\pi$
$647$	3.83578	+	3.83578i	0.150800	+	0.150800i	−0.627675	+	0.778475i	$0.715993\pi$
$648$		0			0
$649$	5.82573	+	33.0394i	0.228680	+	1.29691i
$650$		0			0
$651$	−0.210786	+	0.176870i	−0.00826134	+	0.00693209i
$652$		0			0
$653$	7.73897	+	28.8822i	0.302849	+	1.13025i	0.934781	+	0.355225i	$0.115596\pi$
$653$	7.73897	+	28.8822i	0.302849	+	1.13025i	−0.631931	+	0.775024i	$0.717738\pi$
$654$		0			0
$655$	20.7609	+	11.7026i	0.811197	+	0.457260i
$656$		0			0
$657$	2.10248	−	7.84656i	0.0820255	−	0.306123i
$658$		0			0
$659$	−6.63747	+	37.6429i	−0.258559	+	1.46636i	0.528210	+	0.849114i	$0.322863\pi$
$659$	−6.63747	+	37.6429i	−0.258559	+	1.46636i	−0.786769	+	0.617247i	$0.788248\pi$
$660$		0			0
$661$	−26.4831	+	31.5613i	−1.03007	+	1.22759i	−0.0566935	+	0.998392i	$0.518056\pi$
$661$	−26.4831	+	31.5613i	−1.03007	+	1.22759i	−0.973379	+	0.229201i	$0.926389\pi$
$662$		0			0
$663$	1.01222	−	0.472006i	0.0393114	−	0.0183312i
$664$		0			0
$665$	−4.00937	+	3.88554i	−0.155477	+	0.150675i
$666$		0			0
$667$	−21.2929	+	9.92903i	−0.824463	+	0.384454i
$668$		0			0
$669$	−0.340427	+	0.405705i	−0.0131617	+	0.0156855i
$670$		0			0
$671$	7.21294	−	40.9066i	0.278452	−	1.57918i
$672$		0			0
$673$	4.82374	−	18.0025i	0.185942	−	0.693944i	−0.808485	−	0.588516i	$-0.799712\pi$
$673$	4.82374	−	18.0025i	0.185942	−	0.693944i	0.994427	−	0.105427i	$-0.0336210\pi$
$674$		0			0
$675$	1.78604	+	1.19649i	0.0687448	+	0.0460531i
$676$		0			0
$677$	−6.35350	−	23.7116i	−0.244185	−	0.911310i	−0.973791	−	0.227443i	$-0.926963\pi$
$677$	−6.35350	−	23.7116i	−0.244185	−	0.911310i	0.729607	−	0.683867i	$-0.239703\pi$
$678$		0			0
$679$	−4.87006	+	4.08646i	−0.186896	+	0.156824i
$680$		0			0
$681$	0.0230044	+	0.130464i	0.000881529	+	0.00499940i
$682$		0			0
$683$	28.1129	+	28.1129i	1.07571	+	1.07571i	0.996889	+	0.0788208i	$0.0251155\pi$
$683$	28.1129	+	28.1129i	1.07571	+	1.07571i	0.0788208	+	0.996889i	$0.474885\pi$
$684$		0			0
$685$	2.26964	−	29.4339i	0.0867187	−	1.12461i
$686$		0			0
$687$	−0.433668	−	0.303658i	−0.0165455	−	0.0115853i
$688$		0			0
$689$	−11.8568	−	14.1304i	−0.451709	−	0.538326i
$690$		0			0
$691$	13.5908	−	23.5400i	0.517019	−	0.895504i	−0.482785	−	0.875739i	$-0.660375\pi$
$691$	13.5908	−	23.5400i	0.517019	−	0.895504i	0.999805	−	0.0197651i	$-0.00629184\pi$
$692$		0			0
$693$	−3.61669	+	7.75602i	−0.137387	+	0.294627i
$694$		0			0
$695$	4.86561	+	1.71434i	0.184563	+	0.0650288i
$696$		0			0
$697$	−1.60065	−	2.28596i	−0.0606289	−	0.0865870i
$698$		0			0
$699$	−0.798535	−	0.670051i	−0.0302034	−	0.0253436i
$700$		0			0
$701$	−1.93424	−	0.704004i	−0.0730551	−	0.0265899i	0.305234	−	0.952277i	$-0.401265\pi$
$701$	−1.93424	−	0.704004i	−0.0730551	−	0.0265899i	−0.378289	+	0.925687i	$0.623488\pi$
$702$		0			0
$703$	−4.11020	+	36.1352i	−0.155019	+	1.36287i
$704$		0			0
$705$	−1.79224	+	0.673324i	−0.0674995	+	0.0253588i
$706$		0			0
$707$	−0.650146	−	7.43120i	−0.0244512	−	0.279479i
$708$		0			0
$709$	14.9459	+	2.63537i	0.561307	+	0.0989735i	0.447101	−	0.894484i	$-0.352457\pi$
$709$	14.9459	+	2.63537i	0.561307	+	0.0989735i	0.114206	+	0.993457i	$0.463568\pi$
$710$		0			0
$711$	−27.0694	+	15.6285i	−1.01518	+	0.586116i
$712$		0			0
$713$	−25.3373	−	11.8150i	−0.948890	−	0.442475i
$714$		0			0
$715$	−55.0146	−	37.6824i	−2.05743	−	1.40924i
$716$		0			0
$717$	−0.131757	+	1.50599i	−0.00492056	+	0.0562422i
$718$		0			0
$719$	8.98563	−	1.58441i	0.335107	−	0.0590885i	−0.00356275	−	0.999994i	$-0.501134\pi$
$719$	8.98563	−	1.58441i	0.335107	−	0.0590885i	0.338670	+	0.940905i	$0.390023\pi$
$720$		0			0
$721$		−	10.9093i		−	0.406282i
$722$		0			0
$723$	−0.127740	+	0.127740i	−0.00475070	+	0.00475070i
$724$		0			0
$725$	−28.1365	+	0.580196i	−1.04496	+	0.0215479i
$726$		0			0
$727$	−21.5075	−	1.88166i	−0.797668	−	0.0697869i	−0.318968	−	0.947765i	$-0.603336\pi$
$727$	−21.5075	−	1.88166i	−0.797668	−	0.0697869i	−0.478700	+	0.877978i	$0.658892\pi$
$728$		0			0
$729$	−23.1425	−	13.3613i	−0.857129	−	0.494863i
$730$		0			0
$731$	0.115770	−	0.0421368i	0.00428190	−	0.00155849i
$732$		0			0
$733$	−0.903059	−	0.241974i	−0.0333552	−	0.00893751i	0.242103	−	0.970251i	$-0.422163\pi$
$733$	−0.903059	−	0.241974i	−0.0333552	−	0.00893751i	−0.275458	+	0.961313i	$0.588830\pi$
$734$		0			0
$735$	0.266263	−	1.03633i	0.00982127	−	0.0382254i
$736$		0			0
$737$	61.4868	−	5.37940i	2.26490	−	0.198153i
$738$		0			0
$739$	−2.32373	+	6.38438i	−0.0854796	+	0.234853i	−0.975067	−	0.221913i	$-0.928770\pi$
$739$	−2.32373	+	6.38438i	−0.0854796	+	0.234853i	0.889587	+	0.456766i	$0.150992\pi$
$740$		0			0
$741$	−1.16369	−	1.46240i	−0.0427493	−	0.0537225i
$742$		0			0
$743$	−16.9052	−	36.2534i	−0.620193	−	1.33001i	−0.925859	−	0.377870i	$-0.876657\pi$
$743$	−16.9052	−	36.2534i	−0.620193	−	1.33001i	0.305665	−	0.952139i	$-0.401121\pi$
$744$		0			0
$745$	29.6716	−	0.305893i	1.08708	−	0.0112071i
$746$		0			0
$747$	12.6661	−	8.86892i	0.463429	−	0.324497i
$748$		0			0
$749$	−3.81525	−	6.60821i	−0.139406	−	0.241459i
$750$		0			0
$751$	0.286639	+	0.787535i	0.0104596	+	0.0287375i	0.944813	−	0.327611i	$-0.106244\pi$
$751$	0.286639	+	0.787535i	0.0104596	+	0.0287375i	−0.934353	+	0.356349i	$0.884021\pi$
$752$		0			0
$753$	0.967573	−	0.259260i	0.0352603	−	0.00944797i
$754$		0			0
$755$	3.05246	−	18.4197i	0.111090	−	0.670363i
$756$		0			0
$757$	−16.2384	+	23.1908i	−0.590194	+	0.842885i	−0.997519	−	0.0703986i	$-0.977573\pi$
$757$	−16.2384	+	23.1908i	−0.590194	+	0.842885i	0.407325	+	0.913283i	$0.366462\pi$
$758$		0			0
$759$	1.49340			0.0542068
$760$		0			0
$761$	−30.2473			−1.09646			−0.548232	−	0.836326i	$-0.684699\pi$
$761$	−30.2473			−1.09646			−0.548232	+	0.836326i	$0.684699\pi$
$762$		0			0
$763$	5.43598	−	7.76339i	0.196796	−	0.281054i
$764$		0			0
$765$	14.1856	−	10.1524i	0.512880	−	0.367060i
$766$		0			0
$767$	38.8351	−	10.4058i	1.40225	−	0.375733i
$768$		0			0
$769$	13.7767	+	37.8512i	0.496801	+	1.36495i	0.894350	+	0.447369i	$0.147639\pi$
$769$	13.7767	+	37.8512i	0.496801	+	1.36495i	−0.397549	+	0.917581i	$0.630139\pi$
$770$		0			0
$771$	−0.497605	−	0.861877i	−0.0179208	−	0.0310398i
$772$		0			0
$773$	16.3872	−	11.4745i	0.589408	−	0.412708i	−0.240467	−	0.970657i	$-0.577301\pi$
$773$	16.3872	−	11.4745i	0.589408	−	0.412708i	0.829875	+	0.557949i	$0.188412\pi$
$774$		0			0
$775$	−22.0499	−	25.2040i	−0.792057	−	0.905355i
$776$		0			0
$777$	0.144864	+	0.310663i	0.00519698	+	0.0111450i
$778$		0			0
$779$	−3.09359	+	3.49800i	−0.110839	+	0.125329i
$780$		0			0
$781$	2.59034	−	7.11691i	0.0926898	−	0.254663i
$782$		0			0
$783$	−2.41079	+	0.210917i	−0.0861548	+	0.00753757i
$784$		0			0
$785$	−52.1210	−	13.3915i	−1.86028	−	0.477961i
$786$		0			0
$787$	33.4836	+	8.97190i	1.19356	+	0.319814i	0.800292	−	0.599610i	$-0.204678\pi$
$787$	33.4836	+	8.97190i	1.19356	+	0.319814i	0.393268	+	0.919424i	$0.371344\pi$
$788$		0			0
$789$	−1.56518	+	0.569679i	−0.0557219	+	0.0202811i
$790$		0			0
$791$	−3

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)

\(f(q)\)	\(=\)	\(q+(0.0411373 - 0.0587502i) q^{3} +(-2.20598 - 0.365568i) q^{5} +(0.553309 - 0.148259i) q^{7} +(1.02430 + 2.81424i) q^{9} +O(q^{10})\)	\(q+(0.0411373 - 0.0587502i) q^{3} +(-2.20598 - 0.365568i) q^{5} +(0.553309 - 0.148259i) q^{7} +(1.02430 + 2.81424i) q^{9} +(2.49421 + 4.32010i) q^{11} +(4.89698 - 3.42890i) q^{13} +(-0.112225 + 0.114563i) q^{15} +(1.10088 + 2.36084i) q^{17} +(3.41080 - 2.71412i) q^{19} +(0.0140514 - 0.0386060i) q^{21} +(4.15825 - 0.363800i) q^{23} +(4.73272 + 1.61287i) q^{25} +(0.415305 + 0.111281i) q^{27} +(-5.28906 + 1.92506i) q^{29} +(-5.80028 - 3.34880i) q^{31} +(0.356412 + 0.0311820i) q^{33} +(-1.27479 + 0.124784i) q^{35} +(-5.89970 + 5.89970i) q^{37} -0.428755i q^{39} +(-1.05503 + 0.186031i) q^{41} +(0.00412207 - 0.0471155i) q^{43} +(-1.23079 - 6.58263i) q^{45} +(10.8196 + 5.04526i) q^{47} +(-5.77801 + 3.33593i) q^{49} +(0.183987 + 0.0324418i) q^{51} +(-0.268926 - 3.07384i) q^{53} +(-3.92290 - 10.4419i) q^{55} +(-0.0191439 - 0.312037i) q^{57} +(6.31979 + 2.30021i) q^{59} +(-6.37870 - 5.35237i) q^{61} +(0.983991 + 1.40528i) q^{63} +(-12.0562 + 5.77392i) q^{65} +(5.22905 - 11.2137i) q^{67} +(0.149686 - 0.259264i) q^{69} +(-0.975910 - 1.16304i) q^{71} +(-2.22190 - 1.55579i) q^{73} +(0.289448 - 0.211699i) q^{75} +(2.02056 + 2.02056i) q^{77} +(1.81235 + 10.2784i) q^{79} +(-6.85896 + 5.75535i) q^{81} +(-1.33629 - 4.98709i) q^{83} +(-1.56547 - 5.61041i) q^{85} +(-0.104480 + 0.389925i) q^{87} +(-1.70407 + 9.66428i) q^{89} +(2.20118 - 2.62326i) q^{91} +(-0.435351 + 0.203007i) q^{93} +(-8.51636 + 4.74042i) q^{95} +(-10.0585 + 4.69035i) q^{97} +(-9.60300 + 11.4444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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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