LMFDB - Embedded newform 380.2.bh.a.33.5

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			33.5
Character	$\chi$	$=$	380.33
Dual form			380.2.bh.a.357.5

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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
$3$	0.0411373	+	0.0587502i	0.0237507	+	0.0339194i	0.830852	−	0.556494i	$-0.187854\pi$
$3$	0.0411373	+	0.0587502i	0.0237507	+	0.0339194i	−0.807101	+	0.590413i	$0.798965\pi$
$4$		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	0.361864	−	0.932231i	$-0.382141\pi$
$7$	0.553309	+	0.148259i	0.209131	+	0.0560365i	−0.152733	+	0.988268i	$0.548807\pi$
$8$		0			0
$9$	1.02430	−	2.81424i	0.341434	−	0.938081i
$10$		0			0
$11$	2.49421	−	4.32010i	0.752034	−	1.30256i	−0.194802	−	0.980843i	$-0.562406\pi$
$11$	2.49421	−	4.32010i	0.752034	−	1.30256i	0.946836	−	0.321718i	$-0.104260\pi$
$12$		0			0
$13$	4.89698	+	3.42890i	1.35818	+	0.951007i	0.999848	+	0.0174117i	$0.00554259\pi$
$13$	4.89698	+	3.42890i	1.35818	+	0.951007i	0.358330	+	0.933595i	$0.383346\pi$
$14$		0			0
$15$	−0.112225	−	0.114563i	−0.0289765	−	0.0295802i
$16$		0			0
$17$	1.10088	−	2.36084i	0.267002	−	0.572587i	−0.726400	−	0.687272i	$-0.758808\pi$
$17$	1.10088	−	2.36084i	0.267002	−	0.572587i	0.993402	+	0.114685i	$0.0365858\pi$
$18$		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	0.511997	−	0.858987i	$-0.328906\pi$
$23$	4.15825	+	0.363800i	0.867055	+	0.0758575i	0.355057	+	0.934844i	$0.384461\pi$
$24$		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	−0.199476	−	0.979903i	$-0.563924\pi$
$29$	−5.28906	−	1.92506i	−0.982153	−	0.357474i	−0.782677	+	0.622428i	$0.786146\pi$
$30$		0			0
$31$	−5.80028	+	3.34880i	−1.04176	+	0.601461i	−0.920332	−	0.391139i	$-0.872081\pi$
$31$	−5.80028	+	3.34880i	−1.04176	+	0.601461i	−0.121430	+	0.992600i	$0.538748\pi$
$32$		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	0.0296550	−	0.999560i	$-0.490559\pi$
$37$	−5.89970	−	5.89970i	−0.969905	−	0.969905i	−0.999560	+	0.0296550i	$0.990559\pi$
$38$		0			0
$39$			0.428755i			0.0686557i
$40$		0			0
$41$	−1.05503	−	0.186031i	−0.164768	−	0.0290531i	0.0906553	−	0.995882i	$-0.471104\pi$
$41$	−1.05503	−	0.186031i	−0.164768	−	0.0290531i	−0.255424	+	0.966829i	$0.582215\pi$
$42$		0			0
$43$	0.00412207	+	0.0471155i	0.000628610	+	0.00718504i	0.996503	−	0.0835627i	$-0.0266299\pi$
$43$	0.00412207	+	0.0471155i	0.000628610	+	0.00718504i	−0.995874	+	0.0907477i	$0.971074\pi$
$44$		0			0
$45$	−1.23079	+	6.58263i	−0.183476	+	0.981280i
$46$		0			0
$47$	10.8196	−	5.04526i	1.57820	−	0.735927i	0.581232	−	0.813738i	$-0.302571\pi$
$47$	10.8196	−	5.04526i	1.57820	−	0.735927i	0.996968	+	0.0778110i	$0.0247931\pi$
$48$		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	0.955099	+	0.296288i	$0.0957489\pi$
$53$	−0.268926	+	3.07384i	−0.0369398	+	0.422224i	−0.992038	+	0.125936i	$0.959807\pi$
$54$		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	0.103880	−	0.994590i	$-0.466874\pi$
$59$	6.31979	−	2.30021i	0.822766	−	0.299462i	0.718886	+	0.695128i	$0.244652\pi$
$60$		0			0
$61$	−6.37870	+	5.35237i	−0.816709	+	0.685300i	−0.952199	−	0.305478i	$-0.901184\pi$
$61$	−6.37870	+	5.35237i	−0.816709	+	0.685300i	0.135490	+	0.990779i	$0.456739\pi$
$62$		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	0.912868	+	0.408256i	$0.133863\pi$
$67$	5.22905	+	11.2137i	0.638830	+	1.36997i	−0.274038	+	0.961719i	$0.588359\pi$
$68$		0			0
$69$	0.149686	+	0.259264i	0.0180201	+	0.0312117i
$70$		0			0
$71$	−0.975910	+	1.16304i	−0.115819	+	0.138028i	−0.820839	−	0.571160i	$-0.806494\pi$
$71$	−0.975910	+	1.16304i	−0.115819	+	0.138028i	0.705020	+	0.709188i	$0.250938\pi$
$72$		0			0
$73$	−2.22190	+	1.55579i	−0.260053	+	0.182091i	−0.696331	−	0.717721i	$-0.745185\pi$
$73$	−2.22190	+	1.55579i	−0.260053	+	0.182091i	0.436278	+	0.899812i	$0.356297\pi$
$74$		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	−0.695247	−	0.718771i	$-0.744705\pi$
$79$	1.81235	−	10.2784i	0.203905	−	1.15641i	0.899153	−	0.437635i	$-0.144184\pi$
$80$		0			0
$81$	−6.85896	−	5.75535i	−0.762106	−	0.639483i
$82$		0			0
$83$	−1.33629	+	4.98709i	−0.146676	+	0.547404i	0.852999	+	0.521913i	$0.174782\pi$
$83$	−1.33629	+	4.98709i	−0.146676	+	0.547404i	−0.999675	+	0.0254909i	$0.991885\pi$
$84$		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	−0.931441	−	0.363892i	$-0.881448\pi$
$89$	−1.70407	−	9.66428i	−0.180631	−	1.02441i	0.750810	−	0.660519i	$-0.229664\pi$
$90$		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	−0.161490	−	0.986874i	$-0.551630\pi$
$97$	−10.0585	−	4.69035i	−1.02128	−	0.476232i	−0.859794	+	0.510642i	$0.829408\pi$
$98$		0			0
$99$	−9.60300	−	11.4444i	−0.965138	−	1.15021i
$100$		0			0
$101$	2.26132	+	12.8246i	0.225009	+	1.27609i	0.862667	+	0.505772i	$0.168792\pi$
$101$	2.26132	+	12.8246i	0.225009	+	1.27609i	−0.637658	+	0.770320i	$0.720097\pi$
$102$		0			0
$103$	4.92910	+	18.3957i	0.485679	+	1.81258i	0.576984	+	0.816755i	$0.304230\pi$
$103$	4.92910	+	18.3957i	0.485679	+	1.81258i	−0.0913050	+	0.995823i	$0.529104\pi$
$104$		0			0
$105$	−0.0451103	−	0.0800273i	−0.00440231	−	0.00780987i
$106$		0			0
$107$	−3.44767	+	12.8669i	−0.333299	+	1.24389i	0.572402	+	0.819973i	$0.306012\pi$
$107$	−3.44767	+	12.8669i	−0.333299	+	1.24389i	−0.905701	+	0.423916i	$0.860655\pi$
$108$		0			0
$109$	12.6741	+	10.6348i	1.21396	+	1.01863i	0.999118	+	0.0419829i	$0.0133675\pi$
$109$	12.6741	+	10.6348i	1.21396	+	1.01863i	0.214840	+	0.976649i	$0.431077\pi$
$110$		0			0
$111$	0.103911	−	0.589307i	0.00986277	−	0.0559345i
$112$		0			0
$113$	−5.12344	+	5.12344i	−0.481973	+	0.481973i	−0.905761	−	0.423788i	$-0.860700\pi$
$113$	−5.12344	+	5.12344i	−0.481973	+	0.481973i	0.423788	+	0.905761i	$0.360700\pi$
$114$		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	−0.976065	−	0.217479i	$-0.930217\pi$
$127$	−4.93452	+	7.04722i	−0.437868	+	0.625340i	0.538197	+	0.842819i	$0.319106\pi$
$128$		0			0
$129$	−0.00259847	+	0.00218038i	−0.000228783	+	0.000191972i
$130$		0			0
$131$	−10.0153	+	3.64526i	−0.875038	+	0.318488i	−0.740206	−	0.672380i	$-0.765272\pi$
$131$	−10.0153	+	3.64526i	−0.875038	+	0.318488i	−0.134833	+	0.990868i	$0.543050\pi$
$132$		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	−0.773496	−	0.633802i	$-0.781493\pi$
$137$	1.15066	−	13.1521i	0.0983074	−	1.12366i	0.871803	−	0.489857i	$-0.162951\pi$
$138$		0			0
$139$	−2.27203	+	0.400621i	−0.192711	+	0.0339802i	−0.269171	−	0.963093i	$-0.586750\pi$
$139$	−2.27203	+	0.400621i	−0.192711	+	0.0339802i	0.0764594	+	0.997073i	$0.475638\pi$
$140$		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	−0.389559	−	0.921001i	$-0.627373\pi$
$149$	−13.0687	−	2.30436i	−1.07063	−	0.188780i	−0.681067	+	0.732221i	$0.738484\pi$
$150$		0			0
$151$		−	8.34991i		−	0.679506i	−0.940515	−	0.339753i	$-0.889657\pi$
$151$		−	8.34991i		−	0.679506i	0.940515	−	0.339753i	$-0.110343\pi$
$152$		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	0.932395	−	0.361440i	$-0.117715\pi$
$157$	23.9747	−	2.09751i	1.91339	−	0.167400i	0.980994	+	0.194040i	$0.0621592\pi$
$158$		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	0.369377	−	0.929280i	$-0.379571\pi$
$163$	14.7321	−	3.94745i	1.15391	−	0.309188i	0.784530	+	0.620091i	$0.212905\pi$
$164$		0			0
$165$	−0.774840	+	0.199080i	−0.0603212	+	0.0154983i
$166$		0			0
$167$	−11.7964	−	1.03205i	−0.912833	−	0.0798626i	−0.378946	−	0.925419i	$-0.623714\pi$
$167$	−11.7964	−	1.03205i	−0.912833	−	0.0798626i	−0.533887	+	0.845556i	$0.679269\pi$
$168$		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	−0.974570	−	0.224083i	$-0.928061\pi$
$173$	−2.32111	+	4.97764i	−0.176471	+	0.378443i	0.798099	+	0.602526i	$0.205839\pi$
$174$		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	−0.960625	−	0.277849i	$-0.910378\pi$
$179$	−3.20681	+	5.55435i	−0.239688	+	0.415152i	0.720937	+	0.693001i	$0.243712\pi$
$180$		0			0
$181$	−1.00642	+	2.76511i	−0.0748064	+	0.205529i	−0.971460	−	0.237204i	$-0.923769\pi$
$181$	−1.00642	+	2.76511i	−0.0748064	+	0.205529i	0.896653	+	0.442733i	$0.145991\pi$
$182$		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	0.682648	−	0.730747i	$-0.260828\pi$
$193$	−3.29958	−	4.71228i	−0.237509	−	0.339197i	−0.920157	+	0.391549i	$0.871939\pi$
$194$		0			0
$195$	−0.156739	−	0.945825i	−0.0112243	−	0.0677320i
$196$		0			0
$197$	−14.0269	−	3.75850i	−0.999376	−	0.267782i	−0.278192	−	0.960526i	$-0.589735\pi$
$197$	−14.0269	−	3.75850i	−0.999376	−	0.267782i	−0.721184	+	0.692744i	$0.756402\pi$
$198$		0			0
$199$	2.83863	−	7.79908i	0.201225	−	0.552862i	−0.797501	−	0.603318i	$-0.793845\pi$
$199$	2.83863	−	7.79908i	0.201225	−	0.552862i	0.998726	+	0.0504555i	$0.0160673\pi$
$200$		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	0.976273	−	0.216544i	$-0.0694784\pi$
$211$	1.29589	+	3.56043i	0.0892129	+	0.245110i	−0.887060	+	0.461654i	$0.847256\pi$
$212$		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	−0.330755	−	0.943717i	$-0.607303\pi$
$223$	−7.35623	+	0.643587i	−0.492610	+	0.0430978i	−0.161855	+	0.986815i	$0.551748\pi$
$224$		0			0
$225$	0.308715	−	14.9711i	0.0205810	−	0.998073i
$226$		0			0
$227$	−1.30611	−	1.30611i	−0.0866897	−	0.0866897i	0.662432	−	0.749122i	$-0.269524\pi$
$227$	−1.30611	−	1.30611i	−0.0866897	−	0.0866897i	−0.749122	+	0.662432i	$0.769524\pi$
$228$		0			0
$229$			7.38156i			0.487787i	0.969802	+	0.243893i	$0.0784247\pi$
$229$			7.38156i			0.487787i	−0.969802	+	0.243893i	$0.921575\pi$
$230$		0			0
$231$	0.201829	+	0.0355879i	0.0132794	+	0.00234151i
$232$		0			0
$233$	1.26675	+	14.4790i	0.0829876	+	0.948553i	0.917545	+	0.397632i	$0.130168\pi$
$233$	1.26675	+	14.4790i	0.0829876	+	0.948553i	−0.834557	+	0.550921i	$0.814277\pi$
$234$		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	−0.224576	−	0.974457i	$-0.572100\pi$
$239$	−18.2542	−	10.5391i	−1.18077	−	0.681717i	−0.956192	+	0.292740i	$0.905433\pi$
$240$		0			0
$241$	−2.48055	+	0.437388i	−0.159786	+	0.0281747i	−0.252969	−	0.967474i	$-0.581407\pi$
$241$	−2.48055	+	0.437388i	−0.159786	+	0.0281747i	0.0931826	+	0.995649i	$0.470296\pi$
$242$		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	−0.239312	−	0.970943i	$-0.576922\pi$
$251$	10.6991	−	8.97765i	0.675324	−	0.566664i	0.914636	+	0.404279i	$0.132477\pi$
$252$		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	0.999937	+	0.0112485i	$0.00358059\pi$
$257$	5.86433	+	12.5761i	0.365807	+	0.784475i	−0.634130	+	0.773226i	$0.718642\pi$
$258$		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	−0.986932	−	0.161140i	$-0.948483\pi$
$263$	−19.0238	+	13.3206i	−1.17306	+	0.821386i	−0.186128	+	0.982525i	$0.559594\pi$
$264$		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	−0.731354	−	0.681998i	$-0.761111\pi$
$269$	3.10231	−	17.5941i	0.189151	−	1.07273i	0.920505	−	0.390731i	$-0.127778\pi$
$270$		0			0
$271$	5.40769	+	4.53759i	0.328494	+	0.275639i	0.792086	−	0.610410i	$-0.208995\pi$
$271$	5.40769	+	4.53759i	0.328494	+	0.275639i	−0.463592	+	0.886049i	$0.653440\pi$
$272$		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	0.923359	−	0.383937i	$-0.125432\pi$
$277$	−1.13610	−	4.23998i	−0.0682616	−	0.254756i	−0.991621	+	0.129181i	$0.958765\pi$
$278$		0			0
$279$	3.48309	+	19.7536i	0.208527	+	1.18262i
$280$		0			0
$281$	−10.8248	−	12.9005i	−0.645753	−	0.769578i	0.339514	−	0.940601i	$-0.389737\pi$
$281$	−10.8248	−	12.9005i	−0.645753	−	0.769578i	−0.985267	+	0.171023i	$0.945293\pi$
$282$		0			0
$283$	−0.0560064	−	0.0261162i	−0.00332923	−	0.00155245i	0.420953	−	0.907082i	$-0.361696\pi$
$283$	−0.0560064	−	0.0261162i	−0.00332923	−	0.00155245i	−0.424282	+	0.905530i	$0.639474\pi$
$284$		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	0.916537	−	0.399951i	$-0.130973\pi$
$293$	−1.32116	−	4.93062i	−0.0771827	−	0.288050i	−0.993719	+	0.111901i	$0.964306\pi$
$294$		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	−0.472067	−	0.881563i	$-0.656492\pi$
$307$	3.41448	−	2.39085i	0.194875	−	0.136453i	0.666942	+	0.745110i	$0.267603\pi$
$308$		0			0
$309$	−0.877979	+	1.04633i	−0.0499465	+	0.0595239i
$310$		0			0
$311$	−5.84352	−	10.1213i	−0.331356	−	0.573925i	0.651422	−	0.758715i	$-0.274173\pi$
$311$	−5.84352	−	10.1213i	−0.331356	−	0.573925i	−0.982778	+	0.184791i	$0.940839\pi$
$312$		0			0
$313$	−11.8028	−	25.3112i	−0.667134	−	1.43067i	−0.890063	−	0.455838i	$-0.849340\pi$
$313$	−11.8028	−	25.3112i	−0.667134	−	1.43067i	0.222929	−	0.974835i	$-0.428438\pi$
$314$		0			0
$315$	−1.65694	+	3.45975i	−0.0933580	+	0.194935i
$316$		0			0
$317$	−18.3715	+	26.2372i	−1.03185	+	1.47363i	−0.157993	+	0.987440i	$0.550502\pi$
$317$	−18.3715	+	26.2372i	−1.03185	+	1.47363i	−0.873853	+	0.486190i	$0.838386\pi$
$318$		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	0.273359	−	0.961912i	$-0.411865\pi$
$331$	−7.69584	−	4.44320i	−0.423002	−	0.244220i	−0.696361	+	0.717692i	$0.745199\pi$
$332$		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	0.918808	+	0.394704i	$0.129153\pi$
$337$	1.51447	+	17.3105i	0.0824985	+	0.942962i	−0.836310	+	0.548257i	$0.815291\pi$
$338$		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	−0.484919	−	0.874559i	$-0.661151\pi$
$347$	−15.0999	+	1.32107i	−0.810606	+	0.0709188i	−0.325687	+	0.945478i	$0.605595\pi$
$348$		0			0
$349$	−26.0156	+	15.0201i	−1.39259	+	0.804010i	−0.993601	−	0.112948i	$-0.963971\pi$
$349$	−26.0156	+	15.0201i	−1.39259	+	0.804010i	−0.398985	+	0.916958i	$0.630637\pi$
$350$		0			0
$351$	2.41531	+	0.879102i	0.128920	+	0.0469230i
$352$		0			0
$353$	−16.5143	+	4.42500i	−0.878970	+	0.235519i	−0.669963	−	0.742395i	$-0.733690\pi$
$353$	−16.5143	+	4.42500i	−0.878970	+	0.235519i	−0.209007	+	0.977914i	$0.567023\pi$
$354$		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	0.770026	−	0.638012i	$-0.220243\pi$
$359$	−4.35701	−	11.9708i	−0.229954	−	0.631794i	−0.999981	+	0.00621797i	$0.998021\pi$
$360$		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	0.933407	−	0.358820i	$-0.116821\pi$
$367$	17.5379	+	12.2802i	0.915471	+	0.641019i	−0.0179363	+	0.999839i	$0.505710\pi$
$368$		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	0.266680	−	0.963785i	$-0.414073\pi$
$373$	0.303963	+	0.0814466i	0.0157386	+	0.00421714i	−0.250941	+	0.968002i	$0.580740\pi$
$374$		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	−0.998244	−	0.0592385i	$-0.981133\pi$
$383$	−13.9437	−	19.9137i	−0.712490	−	1.01754i	0.285754	−	0.958303i	$-0.407756\pi$
$384$		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	−0.807367	−	0.590049i	$-0.799108\pi$
$389$	3.75504	−	10.3169i	0.190388	−	0.523087i	0.997756	+	0.0669621i	$0.0213307\pi$
$390$		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	−0.965930	−	0.258805i	$-0.916671\pi$
$397$	−2.92469	+	6.27201i	−0.146786	+	0.314783i	0.819144	+	0.573588i	$0.194449\pi$
$398$		0			0
$399$	−0.0568546	+	0.169814i	−0.00284629	+	0.00850136i
$400$		0			0
$401$	3.96508	+	10.8940i	0.198006	+	0.544018i	0.998466	−	0.0553686i	$-0.0176334\pi$
$401$	3.96508	+	10.8940i	0.198006	+	0.544018i	−0.800460	+	0.599387i	$0.795411\pi$
$402$		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	0.902611	−	0.430457i	$-0.141647\pi$
$409$	26.6419	+	9.69687i	1.31736	+	0.479480i	0.414748	+	0.909936i	$0.363870\pi$
$410$		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	$-0.990353\pi$
$419$		−	1.24051i		−	0.0606030i	0.999541	−	0.0303015i	$-0.00964674\pi$
$420$		0			0
$421$	4.78115	+	0.843045i	0.233019	+	0.0410875i	0.288938	−	0.957348i	$-0.406698\pi$
$421$	4.78115	+	0.843045i	0.233019	+	0.0410875i	−0.0559192	+	0.998435i	$0.517809\pi$
$422$		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	0.815078	−	0.579351i	$-0.196694\pi$
$431$	36.9361	−	6.51284i	1.77915	−	0.313712i	0.964073	+	0.265639i	$0.0855828\pi$
$432$		0			0
$433$	2.86329	−	32.7275i	0.137601	−	1.57278i	−0.542748	−	0.839896i	$-0.682616\pi$
$433$	2.86329	−	32.7275i	0.137601	−	1.57278i	0.680349	−	0.732888i	$-0.261828\pi$
$434$		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	−0.256354	−	0.966583i	$-0.582521\pi$
$439$	3.53203	−	1.28556i	0.168575	−	0.0613562i	0.424929	+	0.905227i	$0.360299\pi$
$440$		0			0
$441$	−15.3066	+	12.8437i	−0.728884	+	0.611606i
$442$		0			0
$443$	−9.12007	+	13.0248i	−0.433308	+	0.618827i	−0.975121	−	0.221671i	$-0.928849\pi$
$443$	−9.12007	+	13.0248i	−0.433308	+	0.618827i	0.541814	+	0.840498i	$0.317738\pi$
$444$		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	0.976731	+	0.214468i	$0.0688018\pi$
$449$	14.2839	+	24.7405i	0.674100	+	1.16758i	−0.302631	+	0.953108i	$0.597865\pi$
$450$		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	−0.483902	−	0.875122i	$-0.660781\pi$
$457$	8.36334	−	8.36334i	0.391221	−	0.391221i	0.875122	+	0.483902i	$0.160781\pi$
$458$		0			0
$459$	0.194484	−	1.10297i	0.00907775	−	0.0514825i
$460$		0			0
$461$	1.22094	+	1.02449i	0.0568650	+	0.0477154i	0.670777	−	0.741659i	$-0.265961\pi$
$461$	1.22094	+	1.02449i	0.0568650	+	0.0477154i	−0.613912	+	0.789374i	$0.710405\pi$
$462$		0			0
$463$	0.532428	−	1.98705i	0.0247440	−	0.0923460i	−0.952450	−	0.304696i	$-0.901445\pi$
$463$	0.532428	−	1.98705i	0.0247440	−	0.0923460i	0.977194	+	0.212350i	$0.0681117\pi$
$464$		0			0
$465$	1.03459	+	0.288681i	0.0479779	+	0.0133872i
$466$		0			0
$467$	0.645474	+	2.40894i	0.0298690	+	0.111472i	0.979251	−	0.202652i	$-0.0649559\pi$
$467$	0.645474	+	2.40894i	0.0298690	+	0.111472i	−0.949382	+	0.314124i	$0.898289\pi$
$468$		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	0.857245	−	0.514909i	$-0.172174\pi$
$479$	4.40564	+	5.25044i	0.201299	+	0.239899i	−0.655946	+	0.754808i	$0.727730\pi$
$480$		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	−0.997777	−	0.0666348i	$-0.978774\pi$
$487$	−2.21474	+	8.26552i	−0.100359	+	0.374547i	0.897418	+	0.441181i	$0.145440\pi$
$488$		0			0
$489$	0.837953	+	0.703126i	0.0378935	+	0.0317964i
$490$		0			0
$491$	−0.217133	+	1.23142i	−0.00979907	+	0.0555733i	−0.989315	−	0.145792i	$-0.953427\pi$
$491$	−0.217133	+	1.23142i	−0.00979907	+	0.0555733i	0.979516	+	0.201366i	$0.0645380\pi$
$492$		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	−0.399402	−	0.916776i	$-0.630782\pi$
$499$	12.7954	−	15.2490i	0.572802	−	0.682639i	0.972204	+	0.234137i	$0.0752265\pi$
$500$		0			0
$501$	−0.424639	−	0.735497i	−0.0189715	−	0.0328596i
$502$		0			0
$503$	16.8891	+	36.2188i	0.753047	+	1.61492i	0.788113	+	0.615531i	$0.211058\pi$
$503$	16.8891	+	36.2188i	0.753047	+	1.61492i	−0.0350656	+	0.999385i	$0.511164\pi$
$504$		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	−0.726885	−	0.686760i	$-0.759033\pi$
$509$	−3.98835	+	3.34663i	−0.176781	+	0.148337i	0.550104	+	0.835096i	$0.314588\pi$
$510$		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	0.796671	−	0.604413i	$-0.206592\pi$
$521$	15.3289	+	8.85013i	0.671570	+	0.387731i	−0.125101	+	0.992144i	$0.539926\pi$
$522$		0			0
$523$	5.22571	−	2.43679i	0.228504	−	0.106553i	−0.304994	−	0.952354i	$-0.598655\pi$
$523$	5.22571	−	2.43679i	0.228504	−	0.106553i	0.533499	+	0.845801i	$0.320877\pi$
$524$		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	0.843594	−	0.536982i	$-0.180436\pi$
$541$	26.6241	+	9.69037i	1.14466	+	0.416622i	0.301065	+	0.953604i	$0.402658\pi$
$542$		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	0.942409	−	0.334464i	$-0.108555\pi$
$547$	42.3890	+	3.70855i	1.81242	+	0.158566i	0.870012	+	0.493030i	$0.164111\pi$
$548$		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	0.282927	−	0.959141i	$-0.408695\pi$
$557$	−12.3103	−	8.61976i	−0.521604	−	0.365231i	−0.804531	+	0.593910i	$0.797583\pi$
$558$		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	0.607762	−	0.794119i	$-0.292067\pi$
$563$	17.4882	+	4.68595i	0.737040	+	0.197489i	0.129278	+	0.991608i	$0.458734\pi$
$564$		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	0.529251	−	0.848466i	$-0.322473\pi$
$577$	13.5324	+	3.62600i	0.563362	+	0.150952i	0.0341116	+	0.999418i	$0.489140\pi$
$578$		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	0.0164193	+	0.999865i	$0.494773\pi$
$587$	−18.4152	+	39.4915i	−0.760076	+	1.62999i	−0.776495	+	0.630123i	$0.783004\pi$
$588$		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	0.0961510	−	0.995367i	$-0.469347\pi$
$593$	0.438269	+	0.0383436i	0.0179976	+	0.00157458i	−0.0781534	+	0.996941i	$0.524902\pi$
$594$		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	0.909105	−	0.416568i	$-0.136767\pi$
$599$	32.7408	+	11.9167i	1.33775	+	0.486903i	0.428650	+	0.903471i	$0.358989\pi$
$600$		0			0
$601$	6.31556	−	3.64629i	0.257617	−	0.148735i	−0.365630	−	0.930760i	$-0.619146\pi$
$601$	6.31556	−	3.64629i	0.257617	−	0.148735i	0.623247	+	0.782025i	$0.285813\pi$
$602$		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	0.465380	−	0.885111i	$-0.345918\pi$
$607$	−10.3411	−	10.3411i	−0.419731	−	0.419731i	−0.885111	+	0.465380i	$0.845918\pi$
$608$		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	0.996459	+	0.0840744i	$0.0267933\pi$
$613$	0.736274	+	8.41565i	0.0297378	+	0.339905i	−0.966722	+	0.255830i	$0.917651\pi$
$614$		0			0
$615$	0.0970891	+	0.141745i	0.00391501	+	0.00571573i
$616$		0			0
$617$	−20.6417	+	9.62538i	−0.831003	+	0.387503i	−0.791090	−	0.611700i	$-0.790486\pi$
$617$	−20.6417	+	9.62538i	−0.831003	+	0.387503i	−0.0399132	+	0.999203i	$0.512708\pi$
$618$		0			0
$619$	8.52728	+	4.92323i	0.342740	+	0.197881i	0.661483	−	0.749960i	$-0.269927\pi$
$619$	8.52728	+	4.92323i	0.342740	+	0.197881i	−0.318743	+	0.947841i	$0.603261\pi$
$620$		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	−0.534781	−	0.844991i	$-0.679606\pi$
$631$	5.13721	−	4.31063i	0.204509	−	0.171604i	0.739290	+	0.673387i	$0.235161\pi$
$632$		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	−0.561545	−	0.827446i	$-0.689793\pi$
$641$	8.88258	−	10.5859i	0.350841	−	0.418116i	0.912386	+	0.409330i	$0.134237\pi$
$642$		0			0
$643$	−13.2318	+	9.26501i	−0.521811	+	0.365376i	−0.804610	−	0.593803i	$-0.797626\pi$
$643$	−13.2318	+	9.26501i	−0.521811	+	0.365376i	0.282799	+	0.959179i	$0.408737\pi$
$644$		0			0
$645$	0.00493511	−	0.00575979i	0.000194320	−	0.000226792i
$646$		0			0
$647$	3.83578	−	3.83578i	0.150800	−	0.150800i	−0.627675	−	0.778475i	$-0.715993\pi$
$647$	3.83578	−	3.83578i	0.150800	−	0.150800i	0.778475	+	0.627675i	$0.215993\pi$
$648$		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	−0.631931	−	0.775024i	$-0.717738\pi$
$653$	7.73897	−	28.8822i	0.302849	−	1.13025i	0.934781	−	0.355225i	$-0.115596\pi$
$654$		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	−0.786769	−	0.617247i	$-0.788248\pi$
$659$	−6.63747	−	37.6429i	−0.258559	−	1.46636i	0.528210	−	0.849114i	$-0.322863\pi$
$660$		0			0
$661$	−26.4831	−	31.5613i	−1.03007	−	1.22759i	−0.973379	−	0.229201i	$-0.926389\pi$
$661$	−26.4831	−	31.5613i	−1.03007	−	1.22759i	−0.0566935	−	0.998392i	$-0.518056\pi$
$662$		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	0.994427	+	0.105427i	$0.0336210\pi$
$673$	4.82374	+	18.0025i	0.185942	+	0.693944i	−0.808485	+	0.588516i	$0.799712\pi$
$674$		0			0
$675$	1.78604	−	1.19649i	0.0687448	−	0.0460531i
$676$		0			0
$677$	−6.35350	+	23.7116i	−0.244185	+	0.911310i	0.729607	+	0.683867i	$0.239703\pi$
$677$	−6.35350	+	23.7116i	−0.244185	+	0.911310i	−0.973791	+	0.227443i	$0.926963\pi$
$678$		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	0.0788208	−	0.996889i	$-0.474885\pi$
$683$	28.1129	−	28.1129i	1.07571	−	1.07571i	0.996889	−	0.0788208i	$-0.0251155\pi$
$684$		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	0.999805	+	0.0197651i	$0.00629184\pi$
$691$	13.5908	+	23.5400i	0.517019	+	0.895504i	−0.482785	+	0.875739i	$0.660375\pi$
$692$		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	−0.378289	−	0.925687i	$-0.623488\pi$
$701$	−1.93424	+	0.704004i	−0.0730551	+	0.0265899i	0.305234	+	0.952277i	$0.401265\pi$
$702$		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	0.114206	−	0.993457i	$-0.463568\pi$
$709$	14.9459	−	2.63537i	0.561307	−	0.0989735i	0.447101	+	0.894484i	$0.352457\pi$
$710$		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	0.338670	−	0.940905i	$-0.390023\pi$
$719$	8.98563	+	1.58441i	0.335107	+	0.0590885i	−0.00356275	+	0.999994i	$0.501134\pi$
$720$		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	−0.478700	−	0.877978i	$-0.658892\pi$
$727$	−21.5075	+	1.88166i	−0.797668	+	0.0697869i	−0.318968	+	0.947765i	$0.603336\pi$
$728$		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	−0.275458	−	0.961313i	$-0.588830\pi$
$733$	−0.903059	+	0.241974i	−0.0333552	+	0.00893751i	0.242103	+	0.970251i	$0.422163\pi$
$734$		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	0.889587	−	0.456766i	$-0.150992\pi$
$739$	−2.32373	−	6.38438i	−0.0854796	−	0.234853i	−0.975067	+	0.221913i	$0.928770\pi$
$740$		0			0
$741$	−1.16369	+	1.46240i	−0.0427493	+	0.0537225i
$742$		0			0
$743$	−16.9052	+	36.2534i	−0.620193	+	1.33001i	0.305665	+	0.952139i	$0.401121\pi$
$743$	−16.9052	+	36.2534i	−0.620193	+	1.33001i	−0.925859	+	0.377870i	$0.876657\pi$
$744$		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	−0.934353	−	0.356349i	$-0.884021\pi$
$751$	0.286639	−	0.787535i	0.0104596	−	0.0287375i	0.944813	+	0.327611i	$0.106244\pi$
$752$		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	0.407325	−	0.913283i	$-0.366462\pi$
$757$	−16.2384	−	23.1908i	−0.590194	−	0.842885i	−0.997519	+	0.0703986i	$0.977573\pi$
$758$		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	−0.397549	−	0.917581i	$-0.630139\pi$
$769$	13.7767	−	37.8512i	0.496801	−	1.36495i	0.894350	−	0.447369i	$-0.147639\pi$
$770$		0			0
$771$	−0.497605	+	0.861877i	−0.0179208	+	0.0310398i
$772$		0			0
$773$	16.3872	+	11.4745i	0.589408	+	0.412708i	0.829875	−	0.557949i	$-0.188412\pi$
$773$	16.3872	+	11.4745i	0.589408	+	0.412708i	−0.240467	+	0.970657i	$0.577301\pi$
$774$		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	0.393268	−	0.919424i	$-0.371344\pi$
$787$	33.4836	−	8.97190i	1.19356	−	0.319814i	0.800292	+	0.599610i	$0.204678\pi$
$788$		0			0
$789$	−1.56518	−	0.569679i	−0.0557219	−	0.0202811i
$790$		0			0
$791$	−3.59444	+	2.07525i	−0.127804	+	0.0737874i
$792$		0			0
$793$	−49.5891	+	4.33849i	−1.76096	+	0.154064i
$794$		0			0
$795$	0.382330	−	0.314154i	0.0135598	−	0.0111419i
$796$		0			0
$797$	−21.9252	−	21.9252i	−0.776631	−	0.776631i	0.202625	−	0.979256i	$-0.435053\pi$
$797$	−21.9252	−	21.9252i	−0.776631	−	0.776631i	−0.979256	+	0.202625i	$0.935053\pi$
$798$		0			0
$799$		−	31.0975i		−	1.10015i
$800$		0			0
$801$	−28.9431	−	5.10345i	−1.02265	−	0.180322i
$802$		0			0
$803$	1.17929	+	13.4793i	0.0416161	+	0.475674i
$804$		0			0
$805$	−5.25549	−	0.982651i	−0.185232	−	0.0346339i
$806$		0			0
$807$	1.16128	−	0.541512i	0.0408788	−	0.0190621i
$808$		0			0
$809$	4.68374	+	2.70416i	0.164672	+	0.0950732i	0.580071	−	0.814566i	$-0.303025\pi$
$809$	4.68374	+	2.70416i	0.164672	+	0.0950732i	−0.415399	+	0.909639i	$0.636358\pi$
$810$		0			0
$811$	−1.35083	+	0.238188i	−0.0474342	+	0.00836393i	−0.197315	−	0.980340i	$-0.563222\pi$
$811$	−1.35083	+	0.238188i	−0.0474342	+	0.00836393i	0.149881	+	0.988704i	$0.452111\pi$
$812$		0			0
$813$	−0.0441265	+	0.504368i	−0.00154758	+	0.0176890i
$814$		0			0
$815$	−31.0557	+	14.0936i	−1.08783	+	0.493677i
$816$		0			0
$817$	−0.113817	+	0.171889i	−0.00398197	+	0.00601364i
$818$		0			0
$819$	9.63717	−	3.50764i	0.336750	−	0.122567i
$820$		0			0
$821$	−25.6930	+	21.5590i	−0.896692	+	0.752414i	−0.969541	−	0.244929i	$-0.921235\pi$
$821$	−25.6930	+	21.5590i	−0.896692	+	0.752414i	0.0728490	+	0.997343i	$0.476791\pi$
$822$		0			0
$823$	−9.80408	+	14.0017i	−0.341749	+	0.488068i	−0.952832	−	0.303499i	$-0.901845\pi$
$823$	−9.80408	+	14.0017i	−0.341749	+	0.488068i	0.611083	+	0.791566i	$0.290734\pi$
$824$		0			0
$825$	1.63651	−	0.722423i	0.0569759	−	0.0251515i
$826$		0			0
$827$	−7.85545	−	16.8461i	−0.273161	−	0.585795i	0.721094	−	0.692837i	$-0.243640\pi$
$827$	−7.85545	−	16.8461i	−0.273161	−	0.585795i	−0.994254	+	0.107043i	$0.965862\pi$
$828$		0			0
$829$	−18.7711	−	32.5126i	−0.651949	−	1.12921i	−0.982649	−	0.185473i	$-0.940618\pi$
$829$	−18.7711	−	32.5126i	−0.651949	−	1.12921i	0.330701	−	0.943736i	$-0.392715\pi$
$830$		0			0
$831$	0.202364	−	0.241168i	0.00701992	−	0.00836602i
$832$		0			0
$833$	−14.2365	+	9.96849i	−0.493265	+	0.345388i
$834$		0			0
$835$	26.3999	−	2.03570i	0.913608	−	0.0704482i
$836$		0			0
$837$	−2.03623	+	2.03623i	−0.0703825	+	0.0703825i
$838$		0			0
$839$	−7.47146	+	42.3728i	−0.257944	+	1.46287i	0.530459	+	0.847711i	$0.322020\pi$
$839$	−7.47146	+	42.3728i	−0.257944	+	1.46287i	−0.788402	+	0.615160i	$0.789091\pi$
$840$		0			0
$841$	2.05297	+	1.72264i	0.0707920	+	0.0594015i
$842$		0			0
$843$	0.312603	−	1.16665i	0.0107666	−	0.0401816i
$844$		0			0
$845$	−24.9664	−	44.2913i	−0.858870	−	1.52367i
$846$		0			0
$847$	−2.05848	−	7.68235i	−0.0707302	−	0.263969i
$848$		0			0
$849$	−0.000769621	−	0.00436474i	−2.64133e−5	−	0.000149797i
$850$		0			0
$851$	−22.3861	−	26.6787i	−0.767386	−	0.914536i
$852$		0			0
$853$	1.98496	+	0.925604i	0.0679639	+	0.0316921i	0.456303	−	0.889824i	$-0.349173\pi$
$853$	1.98496	+	0.925604i	0.0679639	+	0.0316921i	−0.388339	+	0.921517i	$0.626951\pi$
$854$		0			0
$855$	−22.0640	+	19.1115i	−0.754574	+	0.653599i
$856$		0			0
$857$	6.57598	+	3.06643i	0.224631	+	0.104747i	0.531676	−	0.846948i	$-0.321562\pi$
$857$	6.57598	+	3.06643i	0.224631	+	0.104747i	−0.307045	+	0.951695i	$0.599340\pi$
$858$		0			0
$859$	22.8684	+	27.2536i	0.780261	+	0.929879i	0.998945	−	0.0459164i	$-0.0146208\pi$
$859$	22.8684	+	27.2536i	0.780261	+	0.929879i	−0.218684	+	0.975796i	$0.570176\pi$
$860$		0			0
$861$	−0.00764281	−	0.0433445i	−0.000260466	−	0.00147718i
$862$		0			0
$863$	−6.02248	−	22.4762i	−0.205008	−	0.765098i	−0.989447	−	0.144893i	$-0.953716\pi$
$863$	−6.02248	−	22.4762i	−0.205008	−	0.765098i	0.784440	−	0.620205i	$-0.212951\pi$
$864$		0			0
$865$	3.30067	−	11.8291i	0.112226	−	0.402202i
$866$		0			0
$867$	−0.189609	+	0.707630i	−0.00643946	+	0.0240324i
$868$		0			0
$869$	−39.8832	−	33.4660i	−1.35294	−	1.13525i
$870$		0			0
$871$	−12.8442	+	72.8433i	−0.435210	+	2.46820i
$872$		0			0
$873$	−23.5027	+	23.5027i	−0.795446	+	0.795446i
$874$		0			0
$875$	−6.23448	+	1.46550i	−0.210764	+	0.0495430i
$876$		0			0
$877$	11.6033	−	8.12475i	0.391817	−	0.274353i	−0.361023	−	0.932557i	$-0.617572\pi$
$877$	11.6033	−	8.12475i	0.391817	−	0.274353i	0.752840	+	0.658204i	$0.228683\pi$
$878$		0			0
$879$	0.235326	−	0.280451i	0.00793735	−	0.00945937i
$880$		0			0
$881$	−2.66918	−	4.62316i	−0.0899271	−	0.155758i	0.817553	−	0.575853i	$-0.195330\pi$
$881$	−2.66918	−	4.62316i	−0.0899271	−	0.155758i	−0.907480	+	0.420095i	$0.861997\pi$
$882$		0			0
$883$	10.3573	+	22.2113i	0.348550	+	0.747468i	0.999936	−	0.0112781i	$-0.00359001\pi$
$883$	10.3573	+	22.2113i	0.348550	+	0.747468i	−0.651386	+	0.758746i	$0.725812\pi$
$884$		0			0
$885$	−0.972761	−	0.465874i	−0.0326990	−	0.0156602i
$886$		0			0
$887$	−11.8848	+	16.9732i	−0.399052	+	0.569905i	−0.967518	−	0.252802i	$-0.918648\pi$
$887$	−11.8848	+	16.9732i	−0.399052	+	0.569905i	0.568466	+	0.822706i	$0.307537\pi$
$888$		0			0
$889$	−3.77512	+	3.16770i	−0.126614	+	0.106241i
$890$		0			0
$891$	−41.9714	+	15.2763i	−1.40609	+	0.511777i
$892$		0			0
$893$	50.5969	+	12.1573i	1.69316	+	0.406829i
$894$		0			0
$895$	5.04367	−	13.4251i	0.168591	−	0.448752i
$896$		0			0
$897$	−0.155981	+	1.78287i	−0.00520805	+	0.0595283i
$898$		0			0
$899$	37.1246	−	6.54608i	1.23818	−	0.218324i
$900$		0			0
$901$	6.96078	+	4.01881i	0.231897	+	0.133886i
$902$		0			0
$903$	−0.00176102		0.000821176i	−5.86030e−5		2.73270e-5i
$904$		0			0
$905$	1.20930	−	6.46769i	0.0401986	−	0.214993i
$906$		0			0
$907$	−1.87846	−	21.4709i	−0.0623731	−	0.712928i	−0.961422	−	0.275079i	$-0.911296\pi$
$907$	−1.87846	−	21.4709i	−0.0623731	−	0.712928i	0.899049	−	0.437849i	$-0.144260\pi$
$908$		0			0
$909$	38.4077	+	6.77232i	1.27390	+	0.224624i
$910$		0			0
$911$		−	33.1465i		−	1.09819i	−0.835759	−	0.549097i	$-0.814972\pi$
$911$		−	33.1465i		−	1.09819i	0.835759	−	0.549097i	$-0.185028\pi$
$912$		0			0
$913$	18.2118	+	18.2118i	0.602721	+	0.602721i
$914$		0			0
$915$	1.32904	+	0.130095i	0.0439367	+	0.00430079i
$916$		0			0
$917$	−6.08198	+	0.532104i	−0.200845	+	0.0175716i
$918$		0			0
$919$	27.9467	−	16.1350i	0.921876	−	0.532246i	0.0376432	−	0.999291i	$-0.488015\pi$
$919$	27.9467	−	16.1350i	0.921876	−	0.532246i	0.884233	+	0.467046i	$0.154682\pi$
$920$		0			0
$921$	0.280926	+	0.102249i	0.00925681	+	0.00336920i
$922$		0			0
$923$	−8.76698	+	2.34911i	−0.288569	+	0.0773218i
$924$		0			0
$925$	−37.4371	−	18.4062i	−1.23092	−	0.605191i
$926$		0			0
$927$	56.8188	+	4.97100i	1.86617	+	0.163269i
$928$		0			0
$929$	−6.18304	−	16.9878i	−0.202859	−	0.557350i	0.795990	−	0.605309i	$-0.206951\pi$
$929$	−6.18304	−	16.9878i	−0.202859	−	0.557350i	−0.998849	+	0.0479591i	$0.984728\pi$
$930$		0			0
$931$	−10.6535	−	27.0604i	−0.349154	−	0.886869i
$932$		0			0
$933$	0.354240	−	0.759670i	0.0115973	−	0.0248705i
$934$		0			0
$935$	20.3330	+	20.7566i	0.664959	+	0.678812i
$936$		0			0
$937$	41.5269	+	29.0775i	1.35663	+	0.949919i	0.999876	+	0.0157192i	$0.00500377\pi$
$937$	41.5269	+	29.0775i	1.35663	+	0.949919i	0.356749	+	0.934200i	$0.383885\pi$
$938$		0			0
$939$	1.00150	−	1.73465i	0.0326828	−	0.0566082i
$940$		0			0
$941$	−2.77035	+	7.61148i	−0.0903109	+	0.248127i	−0.976622	−	0.214963i	$-0.931037\pi$
$941$	−2.77035	+	7.61148i	−0.0903109	+	0.248127i	0.886311	+	0.463090i	$0.153259\pi$
$942$		0			0
$943$	−4.31941	−	1.15738i	−0.140659	−	0.0376895i
$944$		0			0
$945$	−0.543312	+	0.0900358i	−0.0176739	+	0.00292886i
$946$		0			0
$947$	−17.4314	−	24.8946i	−0.566444	−	0.808966i	0.429101	−	0.903257i	$-0.358831\pi$
$947$	−17.4314	−	24.8946i	−0.566444	−	0.808966i	−0.995545	+	0.0942907i	$0.969942\pi$
$948$		0			0
$949$	−16.2152			−0.526369
$950$		0			0
$951$	−2.29720			−0.0744917
$952$		0			0
$953$	34.1477	+	48.7680i	1.10615	+	1.57975i	0.770118	+	0.637901i	$0.220197\pi$
$953$	34.1477	+	48.7680i	1.10615	+	1.57975i	0.336035	+	0.941850i	$0.390914\pi$
$954$		0			0
$955$	−25.6431	+	4.24948i	−0.829790	+	0.137510i
$956$		0			0
$957$	−1.94511	−	0.521191i	−0.0628765	−	0.0168477i
$958$		0			0
$959$	2.58658	−	7.10657i	0.0835250	−	0.229483i
$960$		0			0
$961$	6.92886	−	12.0011i	0.223512	−	0.387133i
$962$		0			0
$963$	32.6791	+	22.8822i	1.05307	+	0.737367i
$964$		0			0
$965$	9.00146	+	9.18900i	0.289767	+	0.295804i
$966$		0			0
$967$	21.6276	−	46.3806i	0.695498	−	1.49150i	−0.167276	−	0.985910i	$-0.553497\pi$
$967$	21.6276	−	46.3806i	0.695498	−	1.49150i	0.862774	−	0.505590i	$-0.168725\pi$
$968$		0			0
$969$	0.715593	+	0.388710i	0.0229882	+	0.0124872i
$970$		0			0
$971$	7.08238	+	19.4587i	0.227284	+	0.624459i	0.999946	−	0.0103588i	$-0.00329738\pi$
$971$	7.08238	+	19.4587i	0.227284	+	0.624459i	−0.772662	+	0.634818i	$0.781075\pi$
$972$		0			0
$973$	−1.31653	−	0.115181i	−0.0422060	−	0.00369255i
$974$		0			0
$975$	0.691526	+	2.02918i	0.0221466	+	0.0649856i
$976$		0			0
$977$	−35.3308	+	9.46686i	−1.13033	+	0.302872i	−0.775058	−	0.631890i	$-0.782279\pi$
$977$	−35.3308	+	9.46686i	−1.13033	+	0.302872i	−0.355275	+	0.934762i	$0.615613\pi$
$978$		0			0
$979$	−46.0010	−	16.7430i	−1.47020	−	0.535108i
$980$		0			0
$981$	42.9111	−	24.7747i	1.37005	−	0.790997i
$982$		0			0
$983$	45.1366	−	3.94894i	1.43963	−	0.125952i	0.659566	−	0.751646i	$-0.270740\pi$
$983$	45.1366	−	3.94894i	1.43963	−	0.125952i	0.780068	+	0.625695i	$0.215184\pi$
$984$		0			0
$985$	32.3171	+	3.16340i	1.02971	+	0.100794i
$986$		0			0
$987$	0.346808	+	0.346808i	0.0110390	+	0.0110390i
$988$		0			0
$989$			0.197417i			0.00627751i
$990$		0			0
$991$	−33.6491	−	5.93324i	−1.06890	−	0.188475i	−0.388596	−	0.921408i	$-0.627040\pi$
$991$	−33.6491	−	5.93324i	−1.06890	−	0.188475i	−0.680301	+	0.732933i	$0.738151\pi$
$992$		0			0
$993$	−0.0555478	−	0.634914i	−0.00176275	−	0.0201484i
$994$		0			0
$995$	−3.41088	+	18.2424i	−0.108132	+	0.578321i
$996$		0			0
$997$	−41.6110	+	19.4035i	−1.31783	+	0.614516i	−0.949087	−	0.315014i	$-0.897991\pi$
$997$	−41.6110	+	19.4035i	−1.31783	+	0.614516i	−0.368746	+	0.929530i	$0.620213\pi$
$998$		0			0
$999$	−3.10670	−	1.79365i	−0.0982917	−	0.0567487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.33.5	✓	120
5.2	odd	4	inner	380.2.bh.a.337.5	yes	120
19.15	odd	18	inner	380.2.bh.a.53.5	yes	120
95.72	even	36	inner	380.2.bh.a.357.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.33.5	✓	120	1.1	even	1	trivial
380.2.bh.a.53.5	yes	120	19.15	odd	18	inner
380.2.bh.a.337.5	yes	120	5.2	odd	4	inner
380.2.bh.a.357.5	yes	120	95.72	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
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

Fields

Representations

Groups

Database

Properties

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