LMFDB - Embedded newform 312.2.bt.c.115.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$312 = 2^{3} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [48,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.3
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.c.19.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.839367 + 1.13818i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.590927 - 1.91071i) q^{4} +(2.14006 - 2.14006i) q^{5} +(1.40538 + 0.157821i) q^{6} +(-1.94933 + 0.522322i) q^{7} +(2.67074 + 0.931201i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.639489 + 4.23209i) q^{10} +(-5.45997 - 1.46299i) q^{11} +(-1.35926 + 1.46711i) q^{12} +(2.42353 - 2.66955i) q^{13} +(1.04171 - 2.65712i) q^{14} +(-2.92338 - 0.783318i) q^{15} +(-3.30161 + 2.25818i) q^{16} +(-5.67618 - 3.27715i) q^{17} +(-0.566013 - 1.29601i) q^{18} +(1.56034 - 0.418091i) q^{19} +(-5.35366 - 2.82442i) q^{20} +(1.42701 + 1.42701i) q^{21} +(6.24807 - 4.98646i) q^{22} +(-0.192056 - 0.332651i) q^{23} +(-0.528927 - 2.77853i) q^{24} -4.15975i q^{25} +(1.00420 + 4.99916i) q^{26} +1.00000 q^{27} +(2.14992 + 3.41595i) q^{28} +(0.554113 - 0.319917i) q^{29} +(3.34535 - 2.66986i) q^{30} +(4.55111 - 4.55111i) q^{31} +(0.201040 - 5.65328i) q^{32} +(1.46299 + 5.45997i) q^{33} +(8.49440 - 3.70982i) q^{34} +(-3.05389 + 5.28950i) q^{35} +(1.95019 + 0.443596i) q^{36} +(0.777993 - 2.90351i) q^{37} +(-0.833830 + 2.12688i) q^{38} +(-3.52366 - 0.764069i) q^{39} +(7.70839 - 3.72273i) q^{40} +(0.451762 - 1.68600i) q^{41} +(-2.82199 + 0.426416i) q^{42} +(5.38062 + 3.10650i) q^{43} +(0.431087 + 11.2969i) q^{44} +(0.783318 + 2.92338i) q^{45} +(0.539824 + 0.0606210i) q^{46} +(-4.53305 - 4.53305i) q^{47} +(3.60644 + 1.73019i) q^{48} +(-2.53510 + 1.46364i) q^{49} +(4.73456 + 3.49156i) q^{50} +6.55429i q^{51} +(-6.53286 - 3.05316i) q^{52} -3.23972i q^{53} +(-0.839367 + 1.13818i) q^{54} +(-14.8156 + 8.55378i) q^{55} +(-5.69255 - 0.420233i) q^{56} +(-1.14225 - 1.14225i) q^{57} +(-0.100979 + 0.899211i) q^{58} +(1.99499 + 7.44540i) q^{59} +(0.230813 + 6.04861i) q^{60} +(6.35202 + 3.66734i) q^{61} +(1.35995 + 9.00005i) q^{62} +(0.522322 - 1.94933i) q^{63} +(6.26573 + 4.97400i) q^{64} +(-0.526483 - 10.8995i) q^{65} +(-7.44244 - 2.91776i) q^{66} +(2.23399 - 8.33737i) q^{67} +(-2.90746 + 12.7821i) q^{68} +(-0.192056 + 0.332651i) q^{69} +(-3.45709 - 7.91572i) q^{70} +(-3.68585 - 13.7558i) q^{71} +(-2.14182 + 1.84733i) q^{72} +(-3.28631 + 3.28631i) q^{73} +(2.65171 + 3.32261i) q^{74} +(-3.60245 + 2.07987i) q^{75} +(-1.72089 - 2.73429i) q^{76} +11.4074 q^{77} +(3.82730 - 3.36924i) q^{78} +15.2352i q^{79} +(-2.23301 + 11.8983i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.53978 + 1.92936i) q^{82} +(2.70458 + 2.70458i) q^{83} +(1.88334 - 3.56986i) q^{84} +(-19.1607 + 5.13409i) q^{85} +(-8.05209 + 3.51664i) q^{86} +(-0.554113 - 0.319917i) q^{87} +(-13.2198 - 8.99161i) q^{88} +(16.3179 + 4.37236i) q^{89} +(-3.98484 - 1.56223i) q^{90} +(-3.32991 + 6.46970i) q^{91} +(-0.522108 + 0.563536i) q^{92} +(-6.21693 - 1.66582i) q^{93} +(8.96433 - 1.35455i) q^{94} +(2.44448 - 4.23396i) q^{95} +(-4.99640 + 2.65253i) q^{96} +(-5.55609 + 1.48875i) q^{97} +(0.461986 - 4.11395i) q^{98} +(3.99697 - 3.99697i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$48 q + 2 q^{2} - 24 q^{3} + 2 q^{6} - 4 q^{8} - 24 q^{9} - 6 q^{10} + 20 q^{11} - 28 q^{14} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 20 q^{19} + 4 q^{20} + 14 q^{22} + 2 q^{24} - 12 q^{26} + 48 q^{27} - 2 q^{28}+ \cdots + 8 q^{99}+O(q^{100})$ 48 * q + 2 * q^2 - 24 * q^3 + 2 * q^6 - 4 * q^8 - 24 * q^9 - 6 * q^10 + 20 * q^11 - 28 * q^14 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 20 * q^19 + 4 * q^20 + 14 * q^22 + 2 * q^24 - 12 * q^26 + 48 * q^27 - 2 * q^28 + 6 * q^30 - 18 * q^32 - 28 * q^33 + 12 * q^35 + 52 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 + 12 * q^44 - 14 * q^46 + 4 * q^48 + 24 * q^49 - 32 * q^50 + 24 * q^52 + 2 * q^54 - 54 * q^56 - 40 * q^57 - 22 * q^58 + 96 * q^59 - 56 * q^60 - 108 * q^62 - 52 * q^65 - 28 * q^66 - 12 * q^67 - 6 * q^68 - 52 * q^70 + 2 * q^72 - 48 * q^73 + 114 * q^76 + 36 * q^78 - 16 * q^80 - 24 * q^81 - 60 * q^82 + 48 * q^83 + 10 * q^84 + 24 * q^86 + 102 * q^88 + 80 * q^89 - 152 * q^91 - 100 * q^92 - 10 * q^94 - 24 * q^96 - 64 * q^97 - 6 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$ .

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.839367	+	1.13818i	−0.593522	+	0.804818i
$2$	−0.839367	+	1.13818i	−0.593522	+	0.804818i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.590927	−	1.91071i	−0.295463	−	0.955354i
$5$	2.14006	−	2.14006i	0.957066	−	0.957066i	−0.0420497	−	0.999116i	$-0.513389\pi$
$5$	2.14006	−	2.14006i	0.957066	−	0.957066i	0.999116	+	0.0420497i	$0.0133888\pi$
$6$	1.40538	+	0.157821i	0.573744	+	0.0644301i
$7$	−1.94933	+	0.522322i	−0.736778	+	0.197419i	−0.607646	−	0.794208i	$-0.707886\pi$
$7$	−1.94933	+	0.522322i	−0.736778	+	0.197419i	−0.129133	+	0.991627i	$0.541219\pi$
$8$	2.67074	+	0.931201i	0.944250	+	0.329229i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.639489	+	4.23209i	0.202224	+	1.33830i
$11$	−5.45997	−	1.46299i	−1.64624	−	0.441109i	−0.687685	−	0.726010i	$-0.741373\pi$
$11$	−5.45997	−	1.46299i	−1.64624	−	0.441109i	−0.958557	+	0.284900i	$0.908039\pi$
$12$	−1.35926	+	1.46711i	−0.392384	+	0.423519i
$13$	2.42353	−	2.66955i	0.672168	−	0.740399i
$13$	2.42353	−	2.66955i	0.672168	−	0.740399i
$14$	1.04171	−	2.65712i	0.278408	−	0.710145i
$15$	−2.92338	−	0.783318i	−0.754814	−	0.202252i
$16$	−3.30161	+	2.25818i	−0.825403	+	0.564544i
$17$	−5.67618	−	3.27715i	−1.37668	−	0.794825i	−0.384919	−	0.922950i	$-0.625771\pi$
$17$	−5.67618	−	3.27715i	−1.37668	−	0.794825i	−0.991758	+	0.128126i	$0.959104\pi$
$18$	−0.566013	−	1.29601i	−0.133411	−	0.305471i
$19$	1.56034	−	0.418091i	0.357966	−	0.0959166i	−0.0753542	−	0.997157i	$-0.524009\pi$
$19$	1.56034	−	0.418091i	0.357966	−	0.0959166i	0.433320	+	0.901240i	$0.357342\pi$
$20$	−5.35366	−	2.82442i	−1.19711	−	0.631559i
$21$	1.42701	+	1.42701i	0.311399	+	0.311399i
$22$	6.24807	−	4.98646i	1.33209	−	1.06312i
$23$	−0.192056	−	0.332651i	−0.0400465	−	0.0693626i	0.845307	−	0.534280i	$-0.179417\pi$
$23$	−0.192056	−	0.332651i	−0.0400465	−	0.0693626i	−0.885354	+	0.464918i	$0.846084\pi$
$24$	−0.528927	−	2.77853i	−0.107967	−	0.567165i
$25$		−	4.15975i		−	0.831950i
$26$	1.00420	+	4.99916i	0.196940	+	0.980415i
$27$	1.00000			0.192450
$28$	2.14992	+	3.41595i	0.406296	+	0.645554i
$29$	0.554113	−	0.319917i	0.102896	−	0.0594072i	−0.447669	−	0.894199i	$-0.647746\pi$
$29$	0.554113	−	0.319917i	0.102896	−	0.0594072i	0.550565	+	0.834792i	$0.314412\pi$
$30$	3.34535	−	2.66986i	0.610775	−	0.487447i
$31$	4.55111	−	4.55111i	0.817403	−	0.817403i	−0.168328	−	0.985731i	$-0.553837\pi$
$31$	4.55111	−	4.55111i	0.817403	−	0.817403i	0.985731	+	0.168328i	$0.0538368\pi$
$32$	0.201040	−	5.65328i	0.0355393	−	0.999368i
$33$	1.46299	+	5.45997i	0.254674	+	0.950458i
$34$	8.49440	−	3.70982i	1.45678	−	0.636228i
$35$	−3.05389	+	5.28950i	−0.516202	+	0.894088i
$36$	1.95019	+	0.443596i	0.325031	+	0.0739327i
$37$	0.777993	−	2.90351i	0.127901	−	0.477334i	−0.872025	−	0.489461i	$-0.837194\pi$
$37$	0.777993	−	2.90351i	0.127901	−	0.477334i	0.999926	+	0.0121269i	$0.00386022\pi$
$38$	−0.833830	+	2.12688i	−0.135265	+	0.345026i
$39$	−3.52366	−	0.764069i	−0.564238	−	0.122349i
$40$	7.70839	−	3.72273i	1.21880	−	0.588615i
$41$	0.451762	−	1.68600i	0.0705534	−	0.263309i	−0.921635	−	0.388058i	$-0.873146\pi$
$41$	0.451762	−	1.68600i	0.0705534	−	0.263309i	0.992188	+	0.124749i	$0.0398126\pi$
$42$	−2.82199	+	0.426416i	−0.435442	+	0.0657974i
$43$	5.38062	+	3.10650i	0.820537	+	0.473737i	0.850602	−	0.525811i	$-0.176238\pi$
$43$	5.38062	+	3.10650i	0.820537	+	0.473737i	−0.0300644	+	0.999548i	$0.509571\pi$
$44$	0.431087	+	11.2969i	0.0649888	+	1.70308i
$45$	0.783318	+	2.92338i	0.116770	+	0.435792i
$46$	0.539824	+	0.0606210i	0.0795928	+	0.00893808i
$47$	−4.53305	−	4.53305i	−0.661213	−	0.661213i	0.294453	−	0.955666i	$-0.404862\pi$
$47$	−4.53305	−	4.53305i	−0.661213	−	0.661213i	−0.955666	+	0.294453i	$0.904862\pi$
$48$	3.60644	+	1.73019i	0.520545	+	0.249731i
$49$	−2.53510	+	1.46364i	−0.362158	+	0.209092i
$50$	4.73456	+	3.49156i	0.669568	+	0.493781i
$51$			6.55429i			0.917785i
$52$	−6.53286	−	3.05316i	−0.905944	−	0.423397i
$53$		−	3.23972i		−	0.445009i	−0.974932	−	0.222505i	$-0.928577\pi$
$53$		−	3.23972i		−	0.445009i	0.974932	−	0.222505i	$-0.0714233\pi$
$54$	−0.839367	+	1.13818i	−0.114223	+	0.154887i
$55$	−14.8156	+	8.55378i	−1.99773	+	1.15339i
$56$	−5.69255	−	0.420233i	−0.760699	−	0.0561560i
$57$	−1.14225	−	1.14225i	−0.151294	−	0.151294i
$58$	−0.100979	+	0.899211i	−0.0132592	+	0.118072i
$59$	1.99499	+	7.44540i	0.259726	+	0.969309i	0.965400	+	0.260773i	$0.0839774\pi$
$59$	1.99499	+	7.44540i	0.259726	+	0.969309i	−0.705675	+	0.708536i	$0.749356\pi$
$60$	0.230813	+	6.04861i	0.0297979	+	0.780873i
$61$	6.35202	+	3.66734i	0.813292	+	0.469555i	0.848098	−	0.529840i	$-0.177748\pi$
$61$	6.35202	+	3.66734i	0.813292	+	0.469555i	−0.0348055	+	0.999394i	$0.511081\pi$
$62$	1.35995	+	9.00005i	0.172714	+	1.14301i
$63$	0.522322	−	1.94933i	0.0658064	−	0.245593i
$64$	6.26573	+	4.97400i	0.783216	+	0.621750i
$65$	−0.526483	−	10.8995i	−0.0653021	−	1.35192i
$66$	−7.44244	−	2.91776i	−0.916100	−	0.359151i
$67$	2.23399	−	8.33737i	0.272925	−	1.01857i	−0.684293	−	0.729207i	$-0.739889\pi$
$67$	2.23399	−	8.33737i	0.272925	−	1.01857i	0.957219	−	0.289365i	$-0.0934441\pi$
$68$	−2.90746	+	12.7821i	−0.352581	+	1.55006i
$69$	−0.192056	+	0.332651i	−0.0231209	+	0.0400465i
$70$	−3.45709	−	7.91572i	−0.413201	−	0.946110i
$71$	−3.68585	−	13.7558i	−0.437431	−	1.63251i	−0.735182	−	0.677870i	$-0.762903\pi$
$71$	−3.68585	−	13.7558i	−0.437431	−	1.63251i	0.297752	−	0.954643i	$-0.403763\pi$
$72$	−2.14182	+	1.84733i	−0.252415	+	0.217710i
$73$	−3.28631	+	3.28631i	−0.384633	+	0.384633i	−0.872768	−	0.488135i	$-0.837677\pi$
$73$	−3.28631	+	3.28631i	−0.384633	+	0.384633i	0.488135	+	0.872768i	$0.337677\pi$
$74$	2.65171	+	3.32261i	0.308255	+	0.386245i
$75$	−3.60245	+	2.07987i	−0.415975	+	0.240163i
$76$	−1.72089	−	2.73429i	−0.197400	−	0.313644i
$77$	11.4074			1.30000
$78$	3.82730	−	3.36924i	0.433356	−	0.381492i
$79$			15.2352i			1.71409i	0.515243	+	0.857044i	$0.327702\pi$
$79$			15.2352i			1.71409i	−0.515243	+	0.857044i	$0.672298\pi$
$80$	−2.23301	+	11.8983i	−0.249659	+	1.33027i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.53978	+	1.92936i	0.170041	+	0.213062i
$83$	2.70458	+	2.70458i	0.296866	+	0.296866i	0.839785	−	0.542919i	$-0.182681\pi$
$83$	2.70458	+	2.70458i	0.296866	+	0.296866i	−0.542919	+	0.839785i	$0.682681\pi$
$84$	1.88334	−	3.56986i	0.205489	−	0.389503i
$85$	−19.1607	+	5.13409i	−2.07827	+	0.556871i
$86$	−8.05209	+	3.51664i	−0.868279	+	0.379209i
$87$	−0.554113	−	0.319917i	−0.0594072	−	0.0342987i
$88$	−13.2198	−	8.99161i	−1.40924	−	0.958508i
$89$	16.3179	+	4.37236i	1.72969	+	0.463469i	0.980112	−	0.198445i	$-0.0635892\pi$
$89$	16.3179	+	4.37236i	1.72969	+	0.463469i	0.749579	+	0.661915i	$0.230256\pi$
$90$	−3.98484	−	1.56223i	−0.420039	−	0.164673i
$91$	−3.32991	+	6.46970i	−0.349069	+	0.678209i
$92$	−0.522108	+	0.563536i	−0.0544336	+	0.0587527i
$93$	−6.21693	−	1.66582i	−0.644665	−	0.172738i
$94$	8.96433	−	1.35455i	0.924600	−	0.139712i
$95$	2.44448	−	4.23396i	0.250798	−	0.434395i
$96$	−4.99640	+	2.65253i	−0.509943	+	0.270723i
$97$	−5.55609	+	1.48875i	−0.564135	+	0.151160i	−0.529606	−	0.848244i	$-0.677660\pi$
$97$	−5.55609	+	1.48875i	−0.564135	+	0.151160i	−0.0345298	+	0.999404i	$0.510993\pi$
$98$	0.461986	−	4.11395i	0.0466677	−	0.415571i
$99$	3.99697	−	3.99697i	0.401711	−	0.401711i
$100$	−7.94807	+	2.45811i	−0.794807	+	0.245811i
$101$	8.39225	+	14.5358i	0.835060	+	1.44637i	0.893981	+	0.448104i	$0.147901\pi$
$101$	8.39225	+	14.5358i	0.835060	+	1.44637i	−0.0589207	+	0.998263i	$0.518766\pi$
$102$	−7.45999	−	5.50146i	−0.738649	−	0.544725i
$103$	12.5606			1.23764			0.618818	−	0.785534i	$-0.287612\pi$
$103$	12.5606			1.23764			0.618818	+	0.785534i	$0.287612\pi$
$104$	8.95852	−	4.87287i	0.878455	−	0.477825i
$105$	6.10779			0.596059
$106$	3.68740	+	2.71931i	0.358152	+	0.264123i
$107$	−7.99878	−	13.8543i	−0.773271	−	1.33934i	−0.935761	−	0.352634i	$-0.885286\pi$
$107$	−7.99878	−	13.8543i	−0.773271	−	1.33934i	0.162490	−	0.986710i	$-0.448047\pi$
$108$	−0.590927	−	1.91071i	−0.0568620	−	0.183858i
$109$	10.1481	−	10.1481i	0.972008	−	0.972008i	−0.0276109	−	0.999619i	$-0.508790\pi$
$109$	10.1481	−	10.1481i	0.972008	−	0.972008i	0.999619	+	0.0276109i	$0.00878993\pi$
$110$	2.69993	−	24.0426i	0.257428	−	2.29237i
$111$	−2.90351	+	0.777993i	−0.275589	+	0.0738438i
$112$	5.25644	−	6.12644i	0.496687	−	0.578894i
$113$	−5.09342	+	8.82207i	−0.479149	+	0.829910i	−0.999714	−	0.0239117i	$-0.992388\pi$
$113$	−5.09342	+	8.82207i	−0.479149	+	0.829910i	0.520565	+	0.853822i	$0.325721\pi$
$114$	2.25885	−	0.341323i	0.211561	−	0.0319678i
$115$	−1.12291	−	0.300882i	−0.104712	−	0.0280574i
$116$	−0.938709	−	0.869701i	−0.0871569	−	0.0807497i
$117$	1.10013	+	3.43362i	0.101707	+	0.317438i
$118$	−10.1488	−	3.97876i	−0.934270	−	0.366274i
$119$	12.7765	+	3.42345i	1.17122	+	0.313827i
$120$	−7.07817	−	4.81430i	−0.646146	−	0.439483i
$121$	18.1446	+	10.4758i	1.64951	+	0.952344i
$122$	−9.50578	+	4.15152i	−0.860613	+	0.375861i
$123$	−1.68600	+	0.451762i	−0.152022	+	0.0407340i
$124$	−11.3852	−	6.00646i	−1.02242	−	0.539396i
$125$	1.79819	+	1.79819i	0.160835	+	0.160835i
$126$	1.78028	+	2.23070i	0.158600	+	0.198727i
$127$	4.84623	+	8.39392i	0.430034	+	0.744840i	0.996876	−	0.0789864i	$-0.0251684\pi$
$127$	4.84623	+	8.39392i	0.430034	+	0.744840i	−0.566842	+	0.823826i	$0.691835\pi$
$128$	−10.9206	+	2.95655i	−0.965251	+	0.261324i
$129$		−	6.21301i		−	0.547025i
$130$	12.8476	+	8.54946i	1.12681	+	0.749837i
$131$	4.01978			0.351210			0.175605	−	0.984461i	$-0.443812\pi$
$131$	4.01978			0.351210			0.175605	+	0.984461i	$0.443812\pi$
$132$	9.56788	−	6.02179i	0.832777	−	0.524130i
$133$	−2.82324	+	1.63000i	−0.244806	+	0.141339i
$134$	7.61432	+	9.54080i	0.657777	+	0.824200i
$135$	2.14006	−	2.14006i	0.184187	−	0.184187i
$136$	−12.1079	−	14.0381i	−1.03825	−	1.20376i
$137$	−1.31484	−	4.90704i	−0.112334	−	0.419237i	0.886739	−	0.462270i	$-0.152965\pi$
$137$	−1.31484	−	4.90704i	−0.112334	−	0.419237i	−0.999074	+	0.0430325i	$0.986298\pi$
$138$	−0.217413	−	0.497812i	−0.0185074	−	0.0423766i
$139$	0.331332	−	0.573884i	0.0281032	−	0.0486762i	−0.851632	−	0.524141i	$-0.824387\pi$
$139$	0.331332	−	0.573884i	0.0281032	−	0.0486762i	0.879735	+	0.475464i	$0.157720\pi$
$140$	11.9113	+	2.70939i	1.00669	+	0.228985i
$141$	−1.65921	+	6.19226i	−0.139731	+	0.521482i
$142$	18.7504	+	7.35098i	1.57350	+	0.616880i
$143$	−17.1379	+	11.0300i	−1.43315	+	0.922377i
$144$	−0.304834	−	3.98837i	−0.0254028	−	0.332364i
$145$	0.501194	−	1.87048i	0.0416219	−	0.155335i
$146$	−0.982006	−	6.49884i	−0.0812714	−	0.537848i
$147$	2.53510	+	1.46364i	0.209092	+	0.120719i
$148$	−6.00750	+	0.229244i	−0.493813	+	0.0188438i
$149$	3.58167	+	13.3670i	0.293421	+	1.09506i	0.942463	+	0.334311i	$0.108504\pi$
$149$	3.58167	+	13.3670i	0.293421	+	1.09506i	−0.649041	+	0.760753i	$0.724830\pi$
$150$	0.656495	−	5.84603i	0.0536026	−	0.477326i
$151$	−4.87170	−	4.87170i	−0.396453	−	0.396453i	0.480527	−	0.876980i	$-0.340445\pi$
$151$	−4.87170	−	4.87170i	−0.396453	−	0.396453i	−0.876980	+	0.480527i	$0.840445\pi$
$152$	4.55658	+	0.336374i	0.369588	+	0.0272835i
$153$	5.67618	−	3.27715i	0.458892	−	0.264942i
$154$	−9.57503	+	12.9838i	−0.771578	+	1.04626i
$155$		−	19.4793i		−	1.56462i
$156$	0.622314	+	7.18420i	0.0498250	+	0.575196i
$157$		−	14.3369i		−	1.14421i	−0.820182	−	0.572103i	$-0.806128\pi$
$157$		−	14.3369i		−	1.14421i	0.820182	−	0.572103i	$-0.193872\pi$
$158$	−17.3404	−	12.7879i	−1.37953	−	1.01735i
$159$	−2.80568	+	1.61986i	−0.222505	+	0.128463i
$160$	−11.6681	−	12.5286i	−0.922448	−	0.990475i
$161$	0.548133	+	0.548133i	0.0431989	+	0.0431989i
$162$	1.40538	+	0.157821i	0.110417	+	0.0123996i
$163$	−4.18581	−	15.6217i	−0.327858	−	1.22358i	−0.911408	−	0.411505i	$-0.865003\pi$
$163$	−4.18581	−	15.6217i	−0.327858	−	1.22358i	0.583550	−	0.812077i	$-0.301663\pi$
$164$	−3.48841	+	0.133117i	−0.272399	+	0.0103947i
$165$	14.8156	+	8.55378i	1.15339	+	0.665911i
$166$	−5.34844	+	0.808175i	−0.415120	+	0.0627266i
$167$	−0.0673496	+	0.251352i	−0.00521167	+	0.0194502i	−0.968483	−	0.249081i	$-0.919872\pi$
$167$	−0.0673496	+	0.251352i	−0.00521167	+	0.0194502i	0.963271	+	0.268531i	$0.0865382\pi$
$168$	2.48234	+	5.14001i	0.191517	+	0.396560i
$169$	−1.25296	−	12.9395i	−0.0963817	−	0.995344i
$170$	10.2393	−	26.1178i	0.785319	−	2.00314i
$171$	−0.418091	+	1.56034i	−0.0319722	+	0.119322i
$172$	2.75607	−	12.1165i	0.210148	−	0.923876i
$173$	10.4951	−	18.1780i	0.797927	−	1.38205i	−0.123038	−	0.992402i	$-0.539264\pi$
$173$	10.4951	−	18.1780i	0.797927	−	1.38205i	0.920964	−	0.389647i	$-0.127403\pi$
$174$	0.829229	−	0.362155i	0.0628637	−	0.0274549i
$175$	2.17273	+	8.10873i	0.164243	+	0.612963i
$176$	21.3304	−	7.49934i	1.60784	−	0.565284i
$177$	5.45041	−	5.45041i	0.409678	−	0.409678i
$178$	−18.6732	+	14.9027i	−1.39962	+	1.11701i
$179$	17.9236	−	10.3482i	1.33967	−	0.773459i	0.352912	−	0.935656i	$-0.385191\pi$
$179$	17.9236	−	10.3482i	1.33967	−	0.773459i	0.986758	+	0.162197i	$0.0518580\pi$
$180$	5.12285	−	3.22420i	0.381834	−	0.240317i
$181$	−9.07419			−0.674479			−0.337240	−	0.941419i	$-0.609493\pi$
$181$	−9.07419			−0.674479			−0.337240	+	0.941419i	$0.609493\pi$
$182$	−4.56869	−	9.22050i	−0.338654	−	0.683469i
$183$		−	7.33468i		−	0.542195i
$184$	−0.203168	−	1.06727i	−0.0149777	−	0.0786801i
$185$	−4.54874	−	7.87865i	−0.334430	−	0.579250i
$186$	7.11429	−	5.67777i	0.521645	−	0.416315i
$187$	26.1973	+	26.1973i	1.91574	+	1.91574i
$188$	−5.98263	+	11.3400i	−0.436328	+	0.827056i
$189$	−1.94933	+	0.522322i	−0.141793	+	0.0379933i
$190$	2.76721	+	6.33611i	0.200755	+	0.459670i
$191$	5.46209	+	3.15354i	0.395223	+	0.228182i	0.684421	−	0.729087i	$-0.260055\pi$
$191$	5.46209	+	3.15354i	0.395223	+	0.228182i	−0.289198	+	0.957269i	$0.593389\pi$
$192$	1.17474	−	7.91328i	0.0847798	−	0.571092i
$193$	−13.7202	−	3.67630i	−0.987598	−	0.264626i	−0.271357	−	0.962479i	$-0.587472\pi$
$193$	−13.7202	−	3.67630i	−0.987598	−	0.264626i	−0.716241	+	0.697853i	$0.754139\pi$
$194$	2.96913	−	7.57346i	0.213171	−	0.543743i
$195$	−9.17602	+	5.90571i	−0.657109	+	0.422917i
$196$	4.29465	+	3.97894i	0.306761	+	0.284210i
$197$	−24.3259	−	6.51810i	−1.73315	−	0.464395i	−0.752242	−	0.658887i	$-0.771028\pi$
$197$	−24.3259	−	6.51810i	−1.73315	−	0.464395i	−0.980904	+	0.194491i	$0.937694\pi$
$198$	1.19437	+	7.90422i	0.0848798	+	0.561728i
$199$	0.773978	−	1.34057i	0.0548659	−	0.0950305i	−0.837288	−	0.546762i	$-0.815860\pi$
$199$	0.773978	−	1.34057i	0.0548659	−	0.0950305i	0.892154	+	0.451732i	$0.149194\pi$
$200$	3.87356	−	11.1096i	0.273902	−	0.785569i
$201$	−8.33737	+	2.23399i	−0.588073	+	0.157574i
$202$	−23.5886	−	2.64894i	−1.65969	−	0.186379i
$203$	−0.913051	+	0.913051i	−0.0640836	+	0.0640836i
$204$	12.5233	−	3.87311i	0.876809	−	0.271172i
$205$	−2.64135	−	4.57495i	−0.184480	−	0.319528i
$206$	−10.5430	+	14.2963i	−0.734565	+	0.996072i
$207$	0.384113			0.0266977
$208$	−1.97326	+	14.2866i	−0.136821	+	0.990596i
$209$	−9.13105			−0.631608
$210$	−5.12667	+	6.95179i	−0.353774	+	0.479719i
$211$	0.803291	+	1.39134i	0.0553009	+	0.0957839i	0.892351	−	0.451343i	$-0.149055\pi$
$211$	0.803291	+	1.39134i	0.0553009	+	0.0957839i	−0.837050	+	0.547127i	$0.815722\pi$
$212$	−6.19015	+	1.91444i	−0.425142	+	0.131484i
$213$	−10.0699	+	10.0699i	−0.689981	+	0.689981i
$214$	22.4826	+	2.52475i	1.53688	+	0.172588i
$215$	18.1630	−	4.86676i	1.23871	−	0.331910i
$216$	2.67074	+	0.931201i	0.181721	+	0.0633602i
$217$	−6.49447	+	11.2488i	−0.440874	+	0.763616i
$218$	3.03242	+	20.0683i	0.205381	+	1.35920i
$219$	4.48918	+	1.20287i	0.303351	+	0.0812825i
$220$	25.0987	+	23.2536i	1.69215	+	1.56776i
$221$	−22.5049	+	7.21056i	−1.51384	+	0.485035i
$222$	1.55161	−	3.95775i	0.104137	−	0.265627i
$223$	10.5079	+	2.81559i	0.703663	+	0.188546i	0.592871	−	0.805298i	$-0.297994\pi$
$223$	10.5079	+	2.81559i	0.703663	+	0.188546i	0.110792	+	0.993844i	$0.464661\pi$
$224$	2.56094	+	11.1251i	0.171110	+	0.743329i
$225$	3.60245	+	2.07987i	0.240163	+	0.138658i
$226$	−5.76589	−	13.2022i	−0.383541	−	0.878198i
$227$	−15.9677	+	4.27853i	−1.05981	+	0.283976i	−0.746301	−	0.665609i	$-0.768172\pi$
$227$	−15.9677	+	4.27853i	−1.05981	+	0.283976i	−0.313511	+	0.949585i	$0.601505\pi$
$228$	−1.50751	+	2.85748i	−0.0998376	+	0.189241i
$229$	−19.9869	−	19.9869i	−1.32077	−	1.32077i	−0.913150	−	0.407624i	$-0.866357\pi$
$229$	−19.9869	−	19.9869i	−1.32077	−	1.32077i	−0.407624	−	0.913150i	$-0.633643\pi$
$230$	1.28499	−	1.02553i	0.0847298	−	0.0676212i
$231$	−5.70372	−	9.87913i	−0.375277	−	0.649999i
$232$	1.77780	−	0.338426i	0.116718	−	0.0222188i
$233$			20.8253i			1.36431i	0.731209	+	0.682154i	$0.238957\pi$
$233$			20.8253i			1.36431i	−0.731209	+	0.682154i	$0.761043\pi$
$234$	−4.83150	−	1.62991i	−0.315845	−	0.106551i
$235$	−19.4020			−1.26565
$236$	13.0471	−	8.21153i	0.849294	−	0.534525i
$237$	13.1940	−	7.61758i	0.857044	−	0.494815i
$238$	−14.6207	+	11.6685i	−0.947718	+	0.756355i
$239$	3.93608	−	3.93608i	0.254604	−	0.254604i	−0.568251	−	0.822855i	$-0.692380\pi$
$239$	3.93608	−	3.93608i	0.254604	−	0.254604i	0.822855	+	0.568251i	$0.192380\pi$
$240$	11.4207	−	4.01530i	0.737206	−	0.259187i
$241$	2.05467	+	7.66812i	0.132353	+	0.493947i	0.999995	−	0.00324247i	$-0.00103211\pi$
$241$	2.05467	+	7.66812i	0.132353	+	0.493947i	−0.867642	+	0.497189i	$0.834365\pi$
$242$	−27.1534	+	11.8589i	−1.74548	+	0.762317i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.25364	−	14.3040i	0.208293	−	0.915718i
$245$	−2.29299	+	8.55757i	−0.146494	+	0.546723i
$246$	0.900984	−	2.29817i	0.0574446	−	0.146526i
$247$	2.66542	−	5.17865i	0.169596	−	0.329509i
$248$	16.3928	−	7.91684i	1.04095	−	0.502720i
$249$	0.989944	−	3.69452i	0.0627352	−	0.234131i
$250$	−3.55601	+	0.537330i	−0.224902	+	0.0339838i
$251$	1.68623	+	0.973546i	0.106434	+	0.0614497i	0.552272	−	0.833664i	$-0.313761\pi$
$251$	1.68623	+	0.973546i	0.106434	+	0.0614497i	−0.445838	+	0.895114i	$0.647094\pi$
$252$	−4.03326	+	0.153908i	−0.254071	+	0.00969528i
$253$	0.561954	+	2.09724i	0.0353298	+	0.131853i
$254$	−13.6216	−	1.52967i	−0.854695	−	0.0959802i
$255$	14.0266	+	14.0266i	0.878380	+	0.878380i
$256$	5.80127	−	14.9112i	0.362579	−	0.931953i
$257$	−12.0543	+	6.95958i	−0.751930	+	0.434127i	−0.826391	−	0.563097i	$-0.809610\pi$
$257$	−12.0543	+	6.95958i	−0.751930	+	0.434127i	0.0744612	+	0.997224i	$0.476276\pi$
$258$	7.07155	+	5.21499i	0.440255	+	0.324671i
$259$			6.06627i			0.376939i
$260$	−20.5147	+	7.44677i	−1.27227	+	0.461829i
$261$			0.639835i			0.0396048i
$262$	−3.37407	+	4.57525i	−0.208451	+	0.282660i
$263$	4.34520	−	2.50870i	0.267936	−	0.154693i	−0.360013	−	0.932947i	$-0.617228\pi$
$263$	4.34520	−	2.50870i	0.267936	−	0.154693i	0.627949	+	0.778254i	$0.283894\pi$
$264$	−1.17705	+	15.9445i	−0.0724423	+	0.981316i
$265$	−6.93320	−	6.93320i	−0.425903	−	0.425903i
$266$	0.514494	−	4.58153i	0.0315457	−	0.280911i
$267$	−4.37236	−	16.3179i	−0.267584	−	0.998638i
$268$	−17.2504	+	0.658270i	−1.05374	+	0.0402102i
$269$	4.67208	+	2.69743i	0.284862	+	0.164465i	0.635622	−	0.772000i	$-0.280744\pi$
$269$	4.67208	+	2.69743i	0.284862	+	0.164465i	−0.350760	+	0.936465i	$0.614077\pi$
$270$	0.639489	+	4.23209i	0.0389180	+	0.257557i
$271$	−1.53068	+	5.71257i	−0.0929822	+	0.347014i	−0.996706	−	0.0811022i	$-0.974156\pi$
$271$	−1.53068	+	5.71257i	−0.0929822	+	0.347014i	0.903724	+	0.428116i	$0.140823\pi$
$272$	26.1409	−	1.99797i	1.58503	−	0.121145i
$273$	7.26788	−	0.351062i	0.439872	−	0.0212473i
$274$	6.68875	+	2.62228i	0.404082	+	0.158418i
$275$	−6.08569	+	22.7121i	−0.366981	+	1.36959i
$276$	0.749091	+	0.170391i	0.0450900	+	0.0102563i
$277$	−2.57456	+	4.45926i	−0.154690	+	0.267931i	−0.932946	−	0.360016i	$-0.882771\pi$
$277$	−2.57456	+	4.45926i	−0.154690	+	0.267931i	0.778256	+	0.627947i	$0.216105\pi$
$278$	0.375076	+	0.858816i	0.0224956	+	0.0515083i
$279$	1.66582	+	6.21693i	0.0997301	+	0.372198i
$280$	−13.0817	+	11.2831i	−0.781784	+	0.674294i
$281$	5.33135	−	5.33135i	0.318042	−	0.318042i	−0.529973	−	0.848015i	$-0.677798\pi$
$281$	5.33135	−	5.33135i	0.318042	−	0.318042i	0.848015	+	0.529973i	$0.177798\pi$
$282$	−5.65524	−	7.08606i	−0.336765	−	0.421969i
$283$	9.16044	−	5.28878i	0.544532	−	0.314385i	−0.202382	−	0.979307i	$-0.564868\pi$
$283$	9.16044	−	5.28878i	0.544532	−	0.314385i	0.746913	+	0.664921i	$0.231535\pi$
$284$	−24.1052	+	15.1713i	−1.43038	+	0.900249i
$285$	−4.88896			−0.289597
$286$	1.83083	−	28.7644i	0.108259	−	1.70087i
$287$			3.52254i			0.207929i
$288$	4.79536	+	3.00075i	0.282570	+	0.176821i
$289$	12.9794	+	22.4809i	0.763493	+	1.32241i
$290$	1.70827	+	2.14047i	0.100313	+	0.125693i
$291$	4.06734	+	4.06734i	0.238432	+	0.238432i
$292$	8.22114	+	4.33721i	0.481106	+	0.253816i
$293$	25.2375	−	6.76237i	1.47439	−	0.395062i	0.569957	−	0.821675i	$-0.306960\pi$
$293$	25.2375	−	6.76237i	1.47439	−	0.395062i	0.904434	+	0.426613i	$0.140293\pi$
$294$	−3.79378	+	1.65688i	−0.221258	+	0.0966313i
$295$	20.2031	+	11.6642i	1.17627	+	0.679118i
$296$	4.78157	−	7.03006i	0.277923	−	0.408614i
$297$	−5.45997	−	1.46299i	−0.316819	−	0.0848915i
$298$	−18.2204	−	7.14318i	−1.05548	−	0.413794i
$299$	−1.35348	−	0.293489i	−0.0782740	−	0.0169729i
$300$	6.10282	+	5.65417i	0.352346	+	0.326444i
$301$	−12.1112	−	3.24519i	−0.698079	−	0.187050i
$302$	9.63403	−	1.45575i	0.554376	−	0.0837689i
$303$	8.39225	−	14.5358i	0.482122	−	0.835060i
$304$	−4.20750	+	4.90389i	−0.241317	+	0.281257i
$305$	21.4421	−	5.74538i	1.22777	−	0.328980i
$306$	−1.03440	+	9.21127i	−0.0591329	+	0.526573i
$307$	−0.147072	+	0.147072i	−0.00839384	+	0.00839384i	−0.711291	−	0.702897i	$-0.751889\pi$
$307$	−0.147072	+	0.147072i	−0.00839384	+	0.00839384i	0.702897	+	0.711291i	$0.251889\pi$
$308$	−6.74096	−	21.7963i	−0.384102	−	1.24196i
$309$	−6.28032	−	10.8778i	−0.357275	−	0.618818i
$310$	22.1711	+	16.3503i	1.25923	+	0.928634i
$311$	−22.9534			−1.30157			−0.650785	−	0.759262i	$-0.725560\pi$
$311$	−22.9534			−1.30157			−0.650785	+	0.759262i	$0.725560\pi$
$312$	−8.69929	−	5.32187i	−0.492500	−	0.301292i
$313$	−24.8668			−1.40556			−0.702778	−	0.711410i	$-0.748057\pi$
$313$	−24.8668			−1.40556			−0.702778	+	0.711410i	$0.748057\pi$
$314$	16.3180	+	12.0339i	0.920877	+	0.679111i
$315$	−3.05389	−	5.28950i	−0.172067	−	0.298029i
$316$	29.1099	−	9.00286i	1.63756	−	0.506450i
$317$	6.82966	−	6.82966i	0.383592	−	0.383592i	−0.488802	−	0.872395i	$-0.662566\pi$
$317$	6.82966	−	6.82966i	0.383592	−	0.383592i	0.872395	+	0.488802i	$0.162566\pi$
$318$	0.511295	−	4.55303i	0.0286720	−	0.255321i
$319$	−3.49348	+	0.936074i	−0.195597	+	0.0524101i
$320$	24.0537	−	2.76439i	1.34464	−	0.154534i
$321$	−7.99878	+	13.8543i	−0.446448	+	0.773271i
$322$	−1.08396	+	0.163792i	−0.0604068	+	0.00912775i
$323$	−10.2269	−	2.74029i	−0.569040	−	0.152474i
$324$	−1.35926	+	1.46711i	−0.0755144	+	0.0815062i
$325$	−11.1046	−	10.0813i	−0.615975	−	0.559210i
$326$	21.2937	+	8.34807i	1.17935	+	0.462357i
$327$	−13.8625	−	3.71445i	−0.766598	−	0.205409i
$328$	2.77655	−	4.08219i	0.153309	−	0.225401i
$329$	11.2041	+	6.46870i	0.617703	+	0.356631i
$330$	−22.1715	+	9.68310i	−1.22050	+	0.533037i
$331$	15.6172	−	4.18461i	0.858398	−	0.230007i	0.197334	−	0.980336i	$-0.436772\pi$
$331$	15.6172	−	4.18461i	0.858398	−	0.230007i	0.661064	+	0.750329i	$0.270105\pi$
$332$	3.56945	−	6.76587i	0.195899	−	0.371325i
$333$	2.12552	+	2.12552i	0.116478	+	0.116478i
$334$	−0.229554	−	0.287633i	−0.0125606	−	0.0157386i
$335$	−13.0616	−	22.6234i	−0.713632	−	1.23605i
$336$	−7.93387	−	1.48899i	−0.432828	−	0.0812311i
$337$			3.86354i			0.210460i	0.994448	+	0.105230i	$0.0335579\pi$
$337$			3.86354i			0.210460i	−0.994448	+	0.105230i	$0.966442\pi$
$338$	15.7792	+	9.43487i	0.858276	+	0.513189i
$339$	10.1868			0.553274
$340$	21.1323	+	33.5766i	1.14606	+	1.82095i
$341$	−31.5071	+	18.1906i	−1.70621	+	0.985079i
$342$	−1.42502	−	1.78556i	−0.0770562	−	0.0965520i
$343$	14.1663	−	14.1663i	0.764910	−	0.764910i
$344$	11.4775	+	13.3071i	0.618824	+	0.717472i
$345$	0.300882	+	1.12291i	0.0161990	+	0.0604554i
$346$	11.8807	+	27.2034i	0.638711	+	1.46246i
$347$	2.98579	−	5.17154i	0.160286	−	0.277623i	−0.774685	−	0.632347i	$-0.782092\pi$
$347$	2.98579	−	5.17154i	0.160286	−	0.277623i	0.934971	+	0.354724i	$0.115425\pi$
$348$	−0.283828	+	1.24780i	−0.0152148	+	0.0668889i
$349$	2.28028	−	8.51010i	0.122060	−	0.455535i	−0.877658	−	0.479288i	$-0.840895\pi$
$349$	2.28028	−	8.51010i	0.122060	−	0.455535i	0.999718	+	0.0237529i	$0.00756149\pi$
$350$	−11.0529	−	4.33324i	−0.590805	−	0.231621i
$351$	2.42353	−	2.66955i	0.129359	−	0.142490i
$352$	−9.36839	+	30.5726i	−0.499337	+	1.62952i
$353$	5.18074	−	19.3348i	0.275743	−	1.02909i	−0.679599	−	0.733584i	$-0.737846\pi$
$353$	5.18074	−	19.3348i	0.275743	−	1.02909i	0.955342	−	0.295503i	$-0.0954873\pi$
$354$	1.62868	+	10.7785i	0.0865633	+	0.572869i
$355$	−37.3263	−	21.5503i	−1.98107	−	1.14377i
$356$	−1.28836	−	33.7624i	−0.0682832	−	1.78941i
$357$	−3.42345	−	12.7765i	−0.181188	−	0.676204i
$358$	−3.26632	+	29.0863i	−0.172630	+	1.53726i
$359$	4.68016	+	4.68016i	0.247009	+	0.247009i	0.819742	−	0.572733i	$-0.194117\pi$
$359$	4.68016	+	4.68016i	0.247009	+	0.247009i	−0.572733	+	0.819742i	$0.694117\pi$
$360$	−0.630217	+	8.53703i	−0.0332153	+	0.449941i
$361$	−14.1946	+	8.19528i	−0.747086	+	0.431330i
$362$	7.61658	−	10.3281i	0.400318	−	0.542833i
$363$		−	20.9516i		−	1.09967i
$364$	14.3294	+	2.53937i	0.751067	+	0.133099i
$365$			14.0658i			0.736238i
$366$	8.34821	+	6.15648i	0.436368	+	0.321805i
$367$	2.27876	−	1.31564i	0.118950	−	0.0686760i	−0.439344	−	0.898319i	$-0.644789\pi$
$367$	2.27876	−	1.31564i	0.118950	−	0.0686760i	0.558295	+	0.829643i	$0.311456\pi$
$368$	1.38528	+	0.664588i	0.0722128	+	0.0346440i
$369$	1.23424	+	1.23424i	0.0642519	+	0.0642519i
$370$	12.7854	+	1.43577i	0.664682	+	0.0746422i
$371$	1.69218	+	6.31528i	0.0878534	+	0.327873i
$372$	0.490852	+	12.8631i	0.0254495	+	0.666921i
$373$	19.0380	+	10.9916i	0.985750	+	0.569123i	0.904001	−	0.427530i	$-0.140616\pi$
$373$	19.0380	+	10.9916i	0.985750	+	0.569123i	0.0817490	+	0.996653i	$0.473949\pi$
$374$	−51.8066	+	7.82822i	−2.67885	+	0.404788i
$375$	0.658183	−	2.45637i	0.0339884	−	0.126847i
$376$	−7.88542	−	16.3278i	−0.406659	−	0.842041i
$377$	0.488878	−	2.25456i	0.0251785	−	0.116116i
$378$	1.04171	−	2.65712i	0.0535796	−	0.136667i
$379$	2.00036	−	7.46544i	0.102752	−	0.383474i	−0.895329	−	0.445406i	$-0.853059\pi$
$379$	2.00036	−	7.46544i	0.102752	−	0.383474i	0.998080	+	0.0619317i	$0.0197261\pi$
$380$	−9.53437	−	2.16872i	−0.489103	−	0.111253i
$381$	4.84623	−	8.39392i	0.248280	−	0.430034i
$382$	−8.17400	+	3.56989i	−0.418218	+	0.182651i
$383$	−4.12761	−	15.4044i	−0.210911	−	0.787130i	−0.987566	−	0.157204i	$-0.949752\pi$
$383$	−4.12761	−	15.4044i	−0.210911	−	0.787130i	0.776655	−	0.629926i	$-0.216915\pi$
$384$	8.02073	+	7.97922i	0.409306	+	0.407188i
$385$	24.4127	−	24.4127i	1.24418	−	1.24418i
$386$	15.7006	−	12.5303i	0.799137	−	0.637775i
$387$	−5.38062	+	3.10650i	−0.273512	+	0.157912i
$388$	6.12781	+	9.73632i	0.311092	+	0.494287i
$389$	−31.6884			−1.60667			−0.803333	−	0.595531i	$-0.796942\pi$
$389$	−31.6884			−1.60667			−0.803333	+	0.595531i	$0.796942\pi$
$390$	0.980263	−	15.4011i	0.0496376	−	0.779863i
$391$			2.51759i			0.127320i
$392$	−8.13355	+	1.54832i	−0.410806	+	0.0782020i
$393$	−2.00989	−	3.48123i	−0.101386	−	0.175605i
$394$	27.8371	−	22.2162i	1.40241	−	1.11924i
$395$	32.6042	+	32.6042i	1.64050	+	1.64050i
$396$	−9.99897	−	5.27513i	−0.502467	−	0.265085i
$397$	−2.55011	+	0.683299i	−0.127986	+	0.0342938i	−0.322244	−	0.946657i	$-0.604437\pi$
$397$	−2.55011	+	0.683299i	−0.127986	+	0.0342938i	0.194257	+	0.980951i	$0.437770\pi$
$398$	0.876164	+	2.00616i	0.0439181	+	0.100560i
$399$	2.82324	+	1.63000i	0.141339	+	0.0816018i
$400$	9.39345	+	13.7339i	0.469673	+	0.686694i
$401$	20.1455	+	5.39796i	1.00602	+	0.269561i	0.723964	−	0.689838i	$-0.242318\pi$
$401$	20.1455	+	5.39796i	1.00602	+	0.269561i	0.282052	+	0.959399i	$0.408985\pi$
$402$	4.45542	−	11.3646i	0.222216	−	0.566815i
$403$	−1.11963	−	23.1792i	−0.0557727	−	1.15464i
$404$	22.8145	−	24.6247i	1.13506	−	1.22513i
$405$	−2.92338	−	0.783318i	−0.145264	−	0.0389234i
$406$	−0.272835	−	1.80560i	−0.0135406	−	0.0896106i
$407$	−8.49563	+	14.7149i	−0.421113	+	0.729389i
$408$	−6.10337	+	17.5048i	−0.302162	+	0.866618i
$409$	−30.9777	+	8.30045i	−1.53175	+	0.410431i	−0.923589	−	0.383384i	$-0.874759\pi$
$409$	−30.9777	+	8.30045i	−1.53175	+	0.410431i	−0.608160	+	0.793815i	$0.708092\pi$
$410$	7.42420	+	0.833720i	0.366655	+	0.0411745i
$411$	−3.59221	+	3.59221i	−0.177190	+	0.177190i
$412$	−7.42242	−	23.9997i	−0.365676	−	1.18238i
$413$	−7.77780	−	13.4715i	−0.382720	−	0.662891i
$414$	−0.322411	+	0.437191i	−0.0158457	+	0.0214868i
$415$	11.5759			0.568241
$416$	−14.6045	−	14.2376i	−0.716043	−	0.698056i
$417$	−0.662664			−0.0324508
$418$	7.66430	−	10.3928i	0.374873	−	0.508329i
$419$	−4.29484	−	7.43889i	−0.209817	−	0.363413i	0.741840	−	0.670577i	$-0.233953\pi$
$419$	−4.29484	−	7.43889i	−0.209817	−	0.363413i	−0.951657	+	0.307164i	$0.900620\pi$
$420$	−3.60925	−	11.6702i	−0.176114	−	0.569447i
$421$	−9.64411	+	9.64411i	−0.470025	+	0.470025i	−0.901923	−	0.431898i	$-0.857844\pi$
$421$	−9.64411	+	9.64411i	−0.470025	+	0.470025i	0.431898	+	0.901923i	$0.357844\pi$
$422$	−2.25786	−	0.253552i	−0.109911	−	0.0123427i
$423$	6.19226	−	1.65921i	0.301078	−	0.0806735i
$424$	3.01683	−	8.65245i	0.146510	−	0.420200i
$425$	−13.6321	+	23.6115i	−0.661254	+	1.14533i
$426$	−3.00908	−	19.9138i	−0.145790	−	0.964828i
$427$	−14.2977	−	3.83106i	−0.691915	−	0.185398i
$428$	−21.7448	+	23.4702i	−1.05107	+	1.13447i
$429$	18.1213	+	9.32689i	0.874902	+	0.450306i
$430$	−9.70615	+	24.7578i	−0.468072	+	1.19393i
$431$	21.6924	+	5.81246i	1.04489	+	0.279976i	0.740137	−	0.672456i	$-0.234761\pi$
$431$	21.6924	+	5.81246i	1.04489	+	0.279976i	0.304749	+	0.952433i	$0.401427\pi$
$432$	−3.30161	+	2.25818i	−0.158849	+	0.108647i
$433$	−0.162501	−	0.0938199i	−0.00780929	−	0.00450870i	0.496090	−	0.868271i	$-0.334769\pi$
$433$	−0.162501	−	0.0938199i	−0.00780929	−	0.00450870i	−0.503900	+	0.863762i	$0.668102\pi$
$434$	−7.35192	−	16.8337i	−0.352903	−	0.808046i
$435$	−1.87048	+	0.501194i	−0.0896827	+	0.0240304i
$436$	−25.3867	−	13.3932i	−1.21580	−	0.641419i
$437$	−0.438751	−	0.438751i	−0.0209883	−	0.0209883i
$438$	−5.13716	+	4.09986i	−0.245463	+	0.195899i
$439$	−8.34993	−	14.4625i	−0.398520	−	0.690257i	0.595023	−	0.803708i	$-0.297143\pi$
$439$	−8.34993	−	14.4625i	−0.398520	−	0.690257i	−0.993544	+	0.113451i	$0.963809\pi$
$440$	−47.5339	+	9.04865i	−2.26609	+	0.431378i
$441$		−	2.92728i		−	0.139395i
$442$	10.6829	−	31.6671i	0.508135	−	1.50625i
$443$	−30.9433			−1.47016			−0.735081	−	0.677979i	$-0.762856\pi$
$443$	−30.9433			−1.47016			−0.735081	+	0.677979i	$0.762856\pi$
$444$	3.20228	+	5.08802i	0.151973	+	0.241467i
$445$	44.2784	−	25.5642i	2.09900	−	1.21186i
$446$	−12.0247	+	9.59665i	−0.569385	+	0.454414i
$447$	9.78529	−	9.78529i	0.462828	−	0.462828i
$448$	−14.8120	−	6.42324i	−0.699802	−	0.303470i
$449$	6.57967	+	24.5557i	0.310514	+	1.15885i	0.928094	+	0.372346i	$0.121446\pi$
$449$	6.57967	+	24.5557i	0.310514	+	1.15885i	−0.617580	+	0.786508i	$0.711887\pi$
$450$	−5.39106	+	2.35447i	−0.254137	+	0.110991i
$451$	−4.93321	+	8.54458i	−0.232296	+	0.402349i
$452$	19.8662	+	4.51885i	0.934429	+	0.212549i
$453$	−1.78316	+	6.65486i	−0.0837804	+	0.312673i
$454$	8.53299	−	21.7654i	0.400473	−	1.02150i
$455$	6.71935	+	20.9718i	0.315008	+	0.983173i
$456$	−1.98698	−	4.11430i	−0.0930490	−	0.192670i
$457$	7.33011	−	27.3564i	0.342888	−	1.27968i	−0.552172	−	0.833730i	$-0.686201\pi$
$457$	7.33011	−	27.3564i	0.342888	−	1.27968i	0.895060	−	0.445946i	$-0.147133\pi$
$458$	39.5252	−	5.97245i	1.84689	−	0.279074i
$459$	−5.67618	−	3.27715i	−0.264942	−	0.152964i
$460$	0.0886583	+	2.32335i	0.00413371	+	0.108327i
$461$	−5.14616	−	19.2057i	−0.239681	−	0.894500i	−0.975983	−	0.217847i	$-0.930097\pi$
$461$	−5.14616	−	19.2057i	−0.239681	−	0.894500i	0.736302	−	0.676653i	$-0.236570\pi$
$462$	16.0318	+	1.80033i	0.745866	+	0.0837590i
$463$	−17.2055	−	17.2055i	−0.799606	−	0.799606i	0.183427	−	0.983033i	$-0.441281\pi$
$463$	−17.2055	−	17.2055i	−0.799606	−	0.799606i	−0.983033	+	0.183427i	$0.941281\pi$
$464$	−1.10704	+	2.30753i	−0.0513928	+	0.107124i
$465$	−16.8696	+	9.73966i	−0.782308	+	0.451666i
$466$	−23.7030	−	17.4800i	−1.09802	−	0.809747i
$467$			27.3110i			1.26380i	0.775049	+	0.631901i	$0.217725\pi$
$467$			27.3110i			1.26380i	−0.775049	+	0.631901i	$0.782275\pi$
$468$	5.91054	−	4.13104i	0.273215	−	0.190957i
$469$			17.4192i			0.804342i
$470$	16.2854	−	22.0831i	0.751190	−	1.01862i
$471$	−12.4161	+	7.16843i	−0.572103	+	0.330304i
$472$	−1.60507	+	21.7425i	−0.0738791	+	1.00078i
$473$	−24.8332	−	24.8332i	−1.14183	−	1.14183i
$474$	−2.40442	+	21.4112i	−0.110439	+	0.983448i
$475$	−1.73915	−	6.49061i	−0.0797978	−	0.297810i
$476$	−1.00876	−	26.4352i	−0.0462363	−	1.21165i
$477$	2.80568	+	1.61986i	0.128463	+	0.0741682i
$478$	1.17617	+	7.78379i	0.0537967	+	0.356022i
$479$	−0.729765	+	2.72352i	−0.0333438	+	0.124441i	−0.980592	−	0.196061i	$-0.937185\pi$
$479$	−0.729765	+	2.72352i	−0.0333438	+	0.124441i	0.947248	+	0.320502i	$0.103852\pi$
$480$	−5.01603	+	16.3692i	−0.228950	+	0.747149i
$481$	−5.86556	−	9.11364i	−0.267447	−	0.415546i
$482$	−10.4523	−	4.09777i	−0.476091	−	0.186649i
$483$	0.200631	−	0.748763i	0.00912900	−	0.0340699i
$484$	9.29404	−	40.8595i	0.422457	−	1.85725i
$485$	−8.70437	+	15.0764i	−0.395245	+	0.684584i
$486$	−0.566013	−	1.29601i	−0.0256749	−	0.0587880i
$487$	4.75278	+	17.7376i	0.215369	+	0.803767i	0.986036	+	0.166530i	$0.0532562\pi$
$487$	4.75278	+	17.7376i	0.215369	+	0.803767i	−0.770668	+	0.637237i	$0.780077\pi$
$488$	13.5496	+	15.7095i	0.613360	+	0.711137i
$489$	−11.4358	+	11.4358i	−0.517147	+	0.517147i
$490$	−7.81543	−	9.79279i	−0.353065	−	0.442393i
$491$	−2.95448	+	1.70577i	−0.133334	+	0.0769803i	−0.565183	−	0.824965i	$-0.691195\pi$
$491$	−2.95448	+	1.70577i	−0.133334	+	0.0769803i	0.431849	+	0.901946i	$0.357861\pi$
$492$	1.85949	+	2.95450i	0.0838322	+	0.133199i
$493$	−4.19366			−0.188873
$494$	3.65699	+	7.38052i	0.164536	+	0.332065i
$495$		−	17.1076i		−	0.768927i
$496$	−4.74878	+	25.3032i	−0.213226	+	1.13615i
$497$	14.3699	+	24.8894i	0.644579	+	1.11644i
$498$	3.37412	+	4.22780i	0.151198	+	0.189452i
$499$	15.4529	+	15.4529i	0.691767	+	0.691767i	0.962621	−	0.270853i	$-0.0873059\pi$
$499$	15.4529	+	15.4529i	0.691767	+	0.691767i	−0.270853	+	0.962621i	$0.587306\pi$
$500$	2.37322	−	4.49841i	0.106133	−	0.201175i
$501$	0.251352	−	0.0673496i	0.0112296	−	0.00300896i
$502$	−2.52344	+	1.10208i	−0.112627	+	0.0491882i
$503$	32.5066	+	18.7677i	1.44940	+	0.836809i	0.998445	−	0.0557399i	$-0.0177518\pi$
$503$	32.5066	+	18.7677i	1.44940	+	0.836809i	0.450950	+	0.892549i	$0.351085\pi$
$504$	3.21021	−	4.71978i	0.142994	−	0.210236i
$505$	49.0675	+	13.1476i	2.18348	+	0.585061i
$506$	−2.85873	−	1.12075i	−0.127086	−	0.0498233i
$507$	−10.5794	+	7.55484i	−0.469849	+	0.335522i
$508$	13.1746	−	14.2199i	0.584527	−	0.630907i
$509$	20.9745	+	5.62011i	0.929680	+	0.249107i	0.691718	−	0.722168i	$-0.256854\pi$
$509$	20.9745	+	5.62011i	0.929680	+	0.249107i	0.237962	+	0.971275i	$0.423521\pi$
$510$	−27.7383	+	4.19140i	−1.22827	+	0.185598i
$511$	4.68959	−	8.12261i	0.207455	−	0.359323i
$512$	12.1024	+	19.1189i	0.534854	+	0.844945i
$513$	1.56034	−	0.418091i	0.0688905	−	0.0184592i
$514$	2.19673	−	19.5617i	0.0968938	−	0.862830i
$515$	26.8806	−	26.8806i	1.18450	−	1.18450i
$516$	−11.8712	+	3.67143i	−0.522602	+	0.161626i
$517$	18.1185	+	31.3821i	0.796849	+	1.38018i
$518$	−6.90453	−	5.09182i	−0.303368	−	0.223722i
$519$	−20.9902			−0.921366
$520$	8.74355	−	29.6001i	0.383430	−	1.29805i
$521$	−25.5951			−1.12134			−0.560671	−	0.828039i	$-0.689457\pi$
$521$	−25.5951			−1.12134			−0.560671	+	0.828039i	$0.689457\pi$
$522$	−0.728250	−	0.537056i	−0.0318746	−	0.0235063i
$523$	−4.87205	−	8.43864i	−0.213040	−	0.368996i	0.739624	−	0.673020i	$-0.235003\pi$
$523$	−4.87205	−	8.43864i	−0.213040	−	0.368996i	−0.952664	+	0.304024i	$0.901670\pi$
$524$	−2.37540	−	7.68063i	−0.103770	−	0.335530i
$525$	5.93600	−	5.93600i	0.259068	−	0.259068i
$526$	−0.791851	+	7.05136i	−0.0345263	+	0.307454i
$527$	−40.7476	+	10.9183i	−1.77499	+	0.475608i
$528$	−17.1598	−	14.7230i	−0.746785	−	0.640736i
$529$	11.4262	−	19.7908i	0.496793	−	0.860470i
$530$	13.7108	−	2.07176i	0.595558	−	0.0899916i
$531$	−7.44540	−	1.99499i	−0.323103	−	0.0865752i
$532$	4.78277	+	4.43117i	0.207359	+	0.192116i
$533$	−3.40600	−	5.29208i	−0.147530	−	0.229225i
$534$	22.2428	+	8.72013i	0.962539	+	0.377357i
$535$	−46.7670	−	12.5312i	−2.02191	−	0.541770i
$536$	13.7302	−	20.1867i	0.593054	−	0.871931i
$537$	−17.9236	−	10.3482i	−0.773459	−	0.446557i
$538$	−6.99176	+	3.05356i	−0.301436	+	0.131648i
$539$	15.9829	−	4.28260i	0.688431	−	0.184465i
$540$	−5.35366	−	2.82442i	−0.230385	−	0.121544i
$541$	6.38555	+	6.38555i	0.274536	+	0.274536i	0.830923	−	0.556387i	$-0.187813\pi$
$541$	6.38555	+	6.38555i	0.274536	+	0.274536i	−0.556387	+	0.830923i	$0.687813\pi$
$542$	−5.21716	−	6.53714i	−0.224096	−	0.280794i
$543$	4.53710	+	7.85848i	0.194705	+	0.337240i
$544$	−19.6678	+	31.4302i	−0.843249	+	1.34756i
$545$		−	43.4350i		−	1.86055i
$546$	−5.70084	+	8.56685i	−0.243974	+	0.366628i
$547$	27.2746			1.16618			0.583090	−	0.812408i	$-0.301844\pi$
$547$	27.2746			1.16618			0.583090	+	0.812408i	$0.301844\pi$
$548$	−8.59895	+	5.41198i	−0.367329	+	0.231188i
$549$	−6.35202	+	3.66734i	−0.271097	+	0.156518i
$550$	−20.7424	−	25.9904i	−0.884460	−	1.10823i
$551$	0.730848	−	0.730848i	0.0311352	−	0.0311352i
$552$	−0.822698	+	0.709583i	−0.0350164	+	0.0302019i
$553$	−7.95765	−	29.6984i	−0.338394	−	1.26290i
$554$	−2.91446	−	6.67327i	−0.123824	−	0.283520i
$555$	−4.54874	+	7.87865i	−0.193083	+	0.334430i
$556$	−1.29232	−	0.293955i	−0.0548065	−	0.0124665i
$557$	0.477883	−	1.78348i	0.0202486	−	0.0755686i	−0.955062	−	0.296405i	$-0.904212\pi$
$557$	0.477883	−	1.78348i	0.0202486	−	0.0755686i	0.975311	+	0.220837i	$0.0708788\pi$
$558$	−8.47424	−	3.32227i	−0.358743	−	0.140643i
$559$	21.3331	−	6.83511i	0.902293	−	0.289094i
$560$	−1.86186	−	24.3601i	−0.0786779	−	1.02940i
$561$	9.58889	−	35.7862i	0.404843	−	1.51090i
$562$	1.59310	+	10.5430i	0.0672009	+	0.444730i
$563$	25.0364	+	14.4548i	1.05516	+	0.609196i	0.924089	−	0.382177i	$-0.124826\pi$
$563$	25.0364	+	14.4548i	1.05516	+	0.609196i	0.131069	+	0.991373i	$0.458159\pi$
$564$	12.8121	−	0.488904i	0.539485	−	0.0205866i
$565$	7.97954	+	29.7800i	0.335702	+	1.25286i
$566$	−1.66936	+	14.8655i	−0.0701684	+	0.624843i
$567$	1.42701	+	1.42701i	0.0599288	+	0.0599288i
$568$	2.96545	−	40.1705i	0.124427	−	1.68552i
$569$	16.6849	−	9.63300i	0.699465	−	0.403837i	−0.107683	−	0.994185i	$-0.534343\pi$
$569$	16.6849	−	9.63300i	0.699465	−	0.403837i	0.807148	+	0.590349i	$0.201010\pi$
$570$	4.10363	−	5.56453i	0.171882	−	0.233073i
$571$			12.8987i			0.539793i	0.962889	+	0.269897i	$0.0869895\pi$
$571$			12.8987i			0.539793i	−0.962889	+	0.269897i	$0.913011\pi$
$572$	31.2024	+	26.2277i	1.30464	+	1.09663i
$573$		−	6.30707i		−	0.263482i
$574$	−4.00930	−	2.95670i	−0.167345	−	0.123410i
$575$	−1.38375	+	0.798906i	−0.0577062	+	0.0333167i
$576$	−7.44047	+	2.93928i	−0.310020	+	0.122470i
$577$	6.51540	+	6.51540i	0.271240	+	0.271240i	0.829599	−	0.558360i	$-0.188569\pi$
$577$	6.51540	+	6.51540i	0.271240	+	0.271240i	−0.558360	+	0.829599i	$0.688569\pi$
$578$	−36.4819	−	4.09683i	−1.51745	−	0.170406i
$579$	3.67630	+	13.7202i	0.152782	+	0.570190i
$580$	−3.87011	+	0.147682i	−0.160698	+	0.00613217i
$581$	−6.68478	−	3.85946i	−0.277331	−	0.160117i
$582$	−8.04337	+	1.21539i	−0.333408	+	0.0503796i
$583$	−4.73969	+	17.6887i	−0.196298	+	0.732593i
$584$	−11.8371	+	5.71667i	−0.489822	+	0.236557i
$585$	9.70250	+	4.99381i	0.401149	+	0.206469i
$586$	−13.4867	+	34.4010i	−0.557131	+	1.42109i
$587$	−8.38093	+	31.2780i	−0.345918	+	1.29098i	0.545618	+	0.838034i	$0.316295\pi$
$587$	−8.38093	+	31.2780i	−0.345918	+	1.29098i	−0.891536	+	0.452949i	$0.850372\pi$
$588$	1.29853	−	5.70875i	0.0535506	−	0.235425i
$589$	5.19848	−	9.00403i	0.214200	−	0.371005i
$590$	−30.2338	+	13.2042i	−1.24471	+	0.543609i
$591$	6.51810	+	24.3259i	0.268119	+	1.00063i
$592$	3.98801	+	11.3431i	0.163906	+	0.466199i
$593$	−5.55065	+	5.55065i	−0.227938	+	0.227938i	−0.811831	−	0.583893i	$-0.801529\pi$
$593$	−5.55065	+	5.55065i	−0.227938	+	0.227938i	0.583893	+	0.811831i	$0.301529\pi$
$594$	6.24807	−	4.98646i	0.256361	−	0.204597i
$595$	34.6689	−	20.0161i	1.42129	−	0.820580i
$596$	23.4239	−	14.7424i	0.959478	−	0.603873i
$597$	−1.54796			−0.0633537
$598$	1.47011	−	1.29417i	0.0601174	−	0.0529225i
$599$			26.2642i			1.07313i	0.843860	+	0.536564i	$0.180278\pi$
$599$			26.2642i			1.07313i	−0.843860	+	0.536564i	$0.819722\pi$
$600$	−11.5580	+	2.20020i	−0.471853	+	0.0898230i
$601$	13.1909	+	22.8473i	0.538067	+	0.931959i	0.999008	+	0.0445287i	$0.0141786\pi$
$601$	13.1909	+	22.8473i	0.538067	+	0.931959i	−0.460941	+	0.887431i	$0.652488\pi$
$602$	13.8594	−	11.0609i	0.564866	−	0.450808i
$603$	6.10338	+	6.10338i	0.248549	+	0.248549i
$604$	−6.42957	+	12.1872i	−0.261616	+	0.495890i
$605$	61.2495	−	16.4117i	2.49014	−	0.667232i
$606$	9.50025	+	21.7528i	0.385921	+	0.883647i
$607$	−25.3345	−	14.6269i	−1.02830	−	0.593688i	−0.111801	−	0.993731i	$-0.535662\pi$
$607$	−25.3345	−	14.6269i	−1.02830	−	0.593688i	−0.916496	+	0.400043i	$0.868995\pi$
$608$	−2.04989	−	8.90507i	−0.0831342	−	0.361148i
$609$	1.24725	+	0.334200i	0.0505411	+	0.0135425i
$610$	−11.4585	+	29.2275i	−0.463939	+	1.18339i
$611$	−23.0872	+	1.11519i	−0.934007	+	0.0451156i
$612$	−9.61588	−	8.90898i	−0.388699	−	0.360124i
$613$	42.9715	+	11.5142i	1.73560	+	0.465053i	0.981461	−	0.191661i	$-0.0613873\pi$
$613$	42.9715	+	11.5142i	1.73560	+	0.465053i	0.754140	+	0.656714i	$0.228054\pi$
$614$	−0.0439477	−	0.290842i	−0.00177358	−	0.0117374i
$615$	−2.64135	+	4.57495i	−0.106509	+	0.184480i
$616$	30.4663	+	10.6226i	1.22752	+	0.427998i
$617$	12.9985	−	3.48295i	0.523301	−	0.140218i	0.0125082	−	0.999922i	$-0.496018\pi$
$617$	12.9985	−	3.48295i	0.523301	−	0.140218i	0.510793	+	0.859704i	$0.329352\pi$
$618$	17.6525	+	1.98233i	0.710087	+	0.0797410i
$619$	14.3690	−	14.3690i	0.577539	−	0.577539i	−0.356686	−	0.934224i	$-0.616093\pi$
$619$	14.3690	−	14.3690i	0.577539	−	0.577539i	0.934224	+	0.356686i	$0.116093\pi$
$620$	−37.2193	+	11.5109i	−1.49476	+	0.462287i
$621$	−0.192056	−	0.332651i	−0.00770696	−	0.0133488i
$622$	19.2664	−	26.1252i	0.772510	−	1.04753i
$623$	−34.0927			−1.36590
$624$	13.3592	−	5.43440i	0.534795	−	0.217550i
$625$	28.4952			1.13981
$626$	20.8724	−	28.3030i	0.834228	−	1.13122i
$627$	4.56552	+	7.90772i	0.182329	+	0.315804i
$628$	−27.3936	+	8.47204i	−1.09312	+	0.338071i
$629$	−13.9313	+	13.9313i	−0.555476	+	0.555476i
$630$	8.58376	+	0.963936i	0.341985	+	0.0384041i
$631$	−18.6313	+	4.99223i	−0.741699	+	0.198738i	−0.609833	−	0.792530i	$-0.708763\pi$
$631$	−18.6313	+	4.99223i	−0.741699	+	0.198738i	−0.131866	+	0.991268i	$0.542097\pi$
$632$	−14.1870	+	40.6892i	−0.564328	+	1.61853i
$633$	0.803291	−	1.39134i	0.0319280	−	0.0553009i
$634$	2.04082	+	13.5060i	0.0810514	+	0.536392i
$635$	28.3348	+	7.59228i	1.12443	+	0.301290i
$636$	4.75303	+	4.40361i	0.188470	+	0.174615i
$637$	−2.23665	+	10.3148i	−0.0886192	+	0.408686i
$638$	1.86688	−	4.76193i	0.0739106	−	0.188527i
$639$	13.7558	+	3.68585i	0.544171	+	0.145810i
$640$	−17.0435	+	29.6979i	−0.673704	+	1.17391i
$641$	9.68124	+	5.58947i	0.382386	+	0.220771i	0.678856	−	0.734271i	$-0.262476\pi$
$641$	9.68124	+	5.58947i	0.382386	+	0.220771i	−0.296470	+	0.955042i	$0.595809\pi$
$642$	−9.05482	−	20.7329i	−0.357365	−	0.818263i
$643$	−29.4413	+	7.88878i	−1.16105	+	0.311103i	−0.787386	−	0.616460i	$-0.788566\pi$
$643$	−29.4413	+	7.88878i	−1.16105	+	0.311103i	−0.373666	+	0.927563i	$0.621899\pi$
$644$	0.723415	−	1.37123i	0.0285066	−	0.0540340i
$645$	−13.2962	−	13.2962i	−0.523539	−	0.523539i
$646$	11.7031	−	9.33999i	0.460451	−	0.367477i
$647$	−4.73251	−	8.19695i	−0.186054	−	0.322255i	0.757877	−	0.652397i	$-0.226237\pi$
$647$	−4.73251	−	8.19695i	−0.186054	−	0.322255i	−0.943931	+	0.330142i	$0.892903\pi$
$648$	−0.528927	−	2.77853i	−0.0207782	−	0.109151i
$649$		−	43.5703i		−	1.71028i
$650$	20.7952	−	4.17723i	0.815657	−	0.163844i
$651$	12.9889			0.509077
$652$	−27.3749	+	17.2291i	−1.07208	+	0.674744i
$653$	2.68322	−	1.54916i	0.105003	−	0.0606233i	−0.446579	−	0.894744i	$-0.647358\pi$
$653$	2.68322	−	1.54916i	0.105003	−	0.0606233i	0.551582	+	0.834121i	$0.314024\pi$
$654$	15.8635	−	12.6603i	0.620310	−	0.495057i
$655$	8.60259	−	8.60259i	0.336131	−	0.336131i
$656$	2.31574	+	6.58668i	0.0904146	+	0.257167i
$657$	−1.20287	−	4.48918i	−0.0469285	−	0.175140i
$658$	−16.7669	+	7.32274i	−0.653643	+	0.285470i
$659$	16.9703	−	29.3934i	0.661068	−	1.14500i	−0.319267	−	0.947665i	$-0.603437\pi$
$659$	16.9703	−	29.3934i	0.661068	−	1.14500i	0.980335	−	0.197339i	$-0.0632299\pi$
$660$	7.58885	−	33.3629i	0.295396	−	1.29865i
$661$	7.79236	−	29.0815i	0.303088	−	1.13114i	−0.631491	−	0.775383i	$-0.717557\pi$
$661$	7.79236	−	29.0815i	0.303088	−	1.13114i	0.934579	−	0.355756i	$-0.115777\pi$
$662$	−8.34569	+	21.2877i	−0.324364	+	0.827368i
$663$	17.4970	+	15.8846i	0.679527	+	0.616905i
$664$	4.70472	+	9.74174i	0.182579	+	0.378053i
$665$	−2.55361	+	9.53020i	−0.0990247	+	0.369565i
$666$	−4.20332	+	0.635142i	−0.162875	+	0.0246112i
$667$	−0.212842	−	0.122884i	−0.00824127	−	0.00475810i
$668$	0.520059	−	0.0198453i	0.0201217	−	0.000767837i
$669$	−2.81559	−	10.5079i	−0.108857	−	0.406260i
$670$	36.7131	+	4.12279i	1.41835	+	0.159277i
$671$	−29.3165	−	29.3165i	−1.13175	−	1.13175i
$672$	8.35418	−	7.78040i	0.322269	−	0.300136i
$673$	−26.6178	+	15.3678i	−1.02604	+	0.592386i	−0.915848	−	0.401524i	$-0.868481\pi$
$673$	−26.6178	+	15.3678i	−1.02604	+	0.592386i	−0.110194	+	0.993910i	$0.535147\pi$
$674$	−4.39742	−	3.24293i	−0.169382	−	0.124913i
$675$		−	4.15975i		−	0.160109i
$676$	−23.9832	+	10.0403i	−0.922429	+	0.386167i
$677$			21.4417i			0.824072i	0.911168	+	0.412036i	$0.135182\pi$
$677$			21.4417i			0.824072i	−0.911168	+	0.412036i	$0.864818\pi$
$678$	−8.55050	+	11.5945i	−0.328380	+	0.445284i
$679$	10.0531	−	5.80413i	0.385801	−	0.222742i
$680$	−55.9542	−	4.13063i	−2.14574	−	0.158402i
$681$	11.6892	+	11.6892i	0.447929	+	0.447929i
$682$	5.74173	−	51.1295i	0.219862	−	1.95785i
$683$	−1.79418	−	6.69597i	−0.0686524	−	0.256214i	0.923067	−	0.384640i	$-0.125674\pi$
$683$	−1.79418	−	6.69597i	−0.0686524	−	0.256214i	−0.991719	+	0.128426i	$0.959008\pi$
$684$	3.22841	−	0.123195i	0.123441	−	0.00471048i
$685$	−13.3152	−	7.68755i	−0.508749	−	0.293726i
$686$	4.23315	+	28.0147i	0.161622	+	1.06960i
$687$	−7.31573	+	27.3027i	−0.279112	+	1.04166i
$688$	−24.7798	+	1.89393i	−0.944720	+	0.0722055i
$689$	−8.64858	−	7.85157i	−0.329485	−	0.299121i
$690$	−1.53063	−	0.600072i	−0.0582700	−	0.0228444i
$691$	−6.26415	+	23.3781i	−0.238300	+	0.889346i	0.738334	+	0.674435i	$0.235613\pi$
$691$	−6.26415	+	23.3781i	−0.238300	+	0.889346i	−0.976634	+	0.214911i	$0.931054\pi$
$692$	−40.9347	−	9.31116i	−1.55610	−	0.353957i
$693$	−5.70372	+	9.87913i	−0.216666	+	0.375277i
$694$	3.38000	+	7.73920i	0.128303	+	0.293776i
$695$	−0.519076	−	1.93722i	−0.0196897	−	0.0734829i
$696$	−1.18199	−	1.37041i	−0.0448031	−	0.0519452i
$697$	−8.08956	+	8.08956i	−0.306414	+	0.306414i
$698$	7.77208	+	9.73847i	0.294178	+	0.368607i
$699$	18.0352	−	10.4126i	0.682154	−	0.393842i
$700$	14.2095	−	8.94312i	0.537069	−	0.338018i
$701$	19.1039			0.721544			0.360772	−	0.932654i	$-0.382513\pi$
$701$	19.1039			0.721544			0.360772	+	0.932654i	$0.382513\pi$
$702$	1.00420	+	4.99916i	0.0379012	+	0.188681i
$703$		−	4.85572i		−	0.183137i
$704$	−26.9337	−	36.3246i	−1.01510	−	1.36903i
$705$	9.70101	+	16.8026i	0.365361	+	0.632824i
$706$	17.6580	+	22.1256i	0.664568	+	0.832709i
$707$	−23.9517	−	23.9517i	−0.900795	−	0.900795i
$708$	−13.6349	−	7.19335i	−0.512433	−	0.270343i
$709$	−14.7947	+	3.96424i	−0.555628	+	0.148880i	−0.525697	−	0.850672i	$-0.676195\pi$
$709$	−14.7947	+	3.96424i	−0.555628	+	0.148880i	−0.0299311	+	0.999552i	$0.509529\pi$
$710$	55.8587	−	24.3955i	2.09634	−	0.915548i
$711$	−13.1940	−	7.61758i	−0.494815	−	0.285681i
$712$	39.5093	+	26.8727i	1.48067	+	1.00710i
$713$	−2.38800	−	0.639863i	−0.0894313	−	0.0239631i
$714$	17.4155	+	6.82765i	0.651760	+	0.255518i
$715$	−13.0714	+	60.2813i	−0.488841	+	2.25439i
$716$	−30.3639	−	28.1317i	−1.13475	−	1.05133i
$717$	−5.37678	−	1.44070i	−0.200800	−	0.0538041i
$718$	−9.25526	+	1.39851i	−0.345403	+	0.0521921i
$719$	−13.6019	+	23.5592i	−0.507266	+	0.878610i	0.492699	+	0.870200i	$0.336010\pi$
$719$	−13.6019	+	23.5592i	−0.507266	+	0.878610i	−0.999965	+	0.00840997i	$0.997323\pi$
$720$	−9.18773	−	7.88300i	−0.342406	−	0.293782i
$721$	−24.4849	+	6.56070i	−0.911864	+	0.244333i
$722$	2.58677	−	23.0350i	0.0962696	−	0.857272i
$723$	5.61345	−	5.61345i	0.208766	−	0.208766i
$724$	5.36218	+	17.3381i	0.199284	+	0.644367i
$725$	−1.33078	−	2.30497i	−0.0494238	−	0.0856045i
$726$	23.8468	+	17.5861i	0.885036	+	0.652680i
$727$	−13.8943			−0.515313			−0.257656	−	0.966237i	$-0.582950\pi$
$727$	−13.8943			−0.515313			−0.257656	+	0.966237i	$0.582950\pi$
$728$	−14.9179	+	14.1781i	−0.552895	+	0.525475i
$729$	1.00000			0.0370370
$730$	−16.0095	−	11.8064i	−0.592538	−	0.436974i
$731$	−20.3609	−	35.2662i	−0.753076	−	1.30437i
$732$	−14.0144	+	4.33426i	−0.517988	+	0.160199i
$733$	4.98282	−	4.98282i	0.184045	−	0.184045i	−0.609071	−	0.793116i	$-0.708458\pi$
$733$	4.98282	−	4.98282i	0.184045	−	0.184045i	0.793116	+	0.609071i	$0.208458\pi$
$734$	−0.415272	+	3.69796i	−0.0153280	+	0.136494i
$735$	8.55757	−	2.29299i	0.315651	−	0.0845784i
$736$	−1.91918	+	1.01887i	−0.0707420	+	0.0375561i
$737$	−24.3950	+	42.2534i	−0.898602	+	1.55643i
$738$	−2.44077	+	0.368812i	−0.0898459	+	0.0135762i
$739$	−10.6069	−	2.84210i	−0.390180	−	0.104548i	0.0583951	−	0.998294i	$-0.481402\pi$
$739$	−10.6069	−	2.84210i	−0.390180	−	0.104548i	−0.448575	+	0.893745i	$0.648068\pi$
$740$	−12.3658	+	13.3470i	−0.454577	+	0.490646i
$741$	−5.81755	+	0.281007i	−0.213713	+	0.0103230i
$742$	−8.60831	−	3.37483i	−0.316021	−	0.123894i
$743$	6.08271	+	1.62986i	0.223153	+	0.0597937i	0.368663	−	0.929563i	$-0.379816\pi$
$743$	6.08271	+	1.62986i	0.223153	+	0.0597937i	−0.145510	+	0.989357i	$0.546482\pi$
$744$	−15.0526	−	10.2382i	−0.551855	−	0.375350i
$745$	36.2711	+	20.9412i	1.32887	+	0.767224i
$746$	−28.4903	+	12.4428i	−1.04310	+	0.455562i
$747$	−3.69452	+	0.989944i	−0.135176	+	0.0362202i
$748$	34.5747	−	65.5362i	1.26418	−	2.39624i
$749$	22.8287	+	22.8287i	0.834141	+	0.834141i
$750$	2.24335	+	2.81093i	0.0819155	+	0.102641i
$751$	1.52313	+	2.63814i	0.0555798	+	0.0962670i	0.892477	−	0.451094i	$-0.148966\pi$
$751$	1.52313	+	2.63814i	0.0555798	+	0.0962670i	−0.836897	+	0.547361i	$0.815633\pi$
$752$	25.2028	+	4.72993i	0.919051	+	0.172483i
$753$		−	1.94709i		−	0.0709560i
$754$	2.15576	+	2.44884i	0.0785081	+	0.0891814i
$755$	−20.8515			−0.758863
$756$	2.14992	+	3.41595i	0.0781917	+	0.124237i
$757$	−0.430375	+	0.248477i	−0.0156422	+	0.00903105i	−0.507801	−	0.861475i	$-0.669541\pi$
$757$	−0.430375	+	0.248477i	−0.0156422	+	0.00903105i	0.492158	+	0.870506i	$0.336208\pi$
$758$	6.81801	+	8.54302i	0.247641	+	0.310297i
$759$	1.53529	−	1.53529i	0.0557274	−	0.0557274i
$760$	10.4712	−	9.03152i	0.379832	−	0.327608i
$761$	10.3019	+	38.4472i	0.373444	+	1.39371i	0.855605	+	0.517629i	$0.173185\pi$
$761$	10.3019	+	38.4472i	0.373444	+	1.39371i	−0.482161	+	0.876082i	$0.660148\pi$
$762$	5.48606	+	12.5615i	0.198739	+	0.455055i
$763$	−14.4814	+	25.0825i	−0.524261	+	0.908047i
$764$	2.79780	−	12.3000i	0.101221	−	0.444997i
$765$	5.13409	−	19.1607i	0.185624	−	0.692757i
$766$	20.9977	+	8.23200i	0.758676	+	0.297434i
$767$	24.7108	+	12.7185i	0.892255	+	0.459237i
$768$	−15.8142	+	2.43158i	−0.570644	+	0.0877420i
$769$	−4.72877	+	17.6480i	−0.170524	+	0.636404i	0.826747	+	0.562574i	$0.190189\pi$
$769$	−4.72877	+	17.6480i	−0.170524	+	0.636404i	−0.997271	+	0.0738298i	$0.976478\pi$
$770$	7.29493	+	48.2773i	0.262891	+	1.73979i
$771$	12.0543	+	6.95958i	0.434127	+	0.250643i
$772$	1.08326	+	28.3876i	0.0389875	+	1.02169i
$773$	−2.76848	−	10.3321i	−0.0995752	−	0.371620i	0.898098	−	0.439795i	$-0.144949\pi$
$773$	−2.76848	−	10.3321i	−0.0995752	−	0.371620i	−0.997673	+	0.0681754i	$0.978282\pi$
$774$	0.980542	−	8.73164i	0.0352449	−	0.313852i
$775$	−18.9315	−	18.9315i	−0.680038	−	0.680038i
$776$	−16.2252	−	1.19777i	−0.582451	−	0.0429975i
$777$	5.25354	−	3.03313i	0.188470	−	0.108813i
$778$	26.5982	−	36.0672i	0.953591	−	1.29307i
$779$		−	2.81960i		−	0.101023i
$780$	16.7064	+	14.0429i	0.598187	+	0.502815i
$781$			80.4986i			2.88047i
$782$	−2.86548	−	2.11318i	−0.102469	−	0.0755671i
$783$	0.554113	−	0.319917i	0.0198024	−	0.0114329i
$784$	5.06476	−	10.5571i	0.180884	−	0.377039i
$785$	−30.6818	−	30.6818i	−1.09508	−	1.09508i
$786$	5.64932	+	0.634405i	0.201505	+	0.0226285i
$787$	8.91143	+	33.2579i	0.317658	+	1.18552i	0.921489	+	0.388404i	$0.126974\pi$
$787$	8.91143	+	33.2579i	0.317658	+	1.18552i	−0.603831	+	0.797113i	$0.706360\pi$
$788$	1.92063	+	50.3314i	0.0684196	+	1.79298i
$789$	−4.34520	−	2.50870i	−0.154693	−	0.0893121i
$790$	−64.4765	+	9.74271i	−2.29397	+	0.346630i
$791$	5.32081	−	19.8575i	0.189186	−	0.706053i
$792$	14.3969	−	6.95290i	0.511570	−	0.247060i
$793$	25.1845	−	8.06909i	0.894327	−	0.286542i
$794$	1.36275	−	3.47603i	0.0483624	−	0.123360i
$795$	−2.53773	+	9.47093i	−0.0900040	+	0.335899i
$796$	−3.01880	−	0.686668i	−0.106999	−	0.0243383i
$797$	11.1615	−	19.3323i	0.395362	−	0.684786i	−0.597786	−	0.801656i	$-0.703953\pi$
$797$	11.1615	−	19.3323i	0.395362	−	0.684786i	0.993147	+	0.116870i	$0.0372860\pi$
$798$	−4.22496	+	1.84520i	−0.149562	+	0.0653193i
$799$	10.8749	+	40.5859i	0.384728	+	1.43582i
$800$	−23.5162	−	0.836278i	−0.831424	−	0.0295669i
$801$	−11.9455	+	11.9455i	−0.422074	+	0.422074i
$802$	−23.0533	+	18.3984i	−0.814040	+	0.649669i
$803$	22.7510	−	13.1353i	0.802864	−	0.463534i
$804$	9.19528	+	14.6102i	0.324293	+	0.515260i
$805$	2.34608			0.0826884
$806$	27.3219	+	18.1815i	0.962374	+	0.640415i
$807$		−	5.39486i		−	0.189908i
$808$	8.87778	+	46.6363i	0.312319	+	1.64066i
$809$	−7.83338	−	13.5678i	−0.275407	−	0.477019i	0.694831	−	0.719173i	$-0.255479\pi$
$809$	−7.83338	−	13.5678i	−0.275407	−	0.477019i	−0.970238	+	0.242154i	$0.922146\pi$
$810$	3.34535	−	2.66986i	0.117544	−	0.0938092i
$811$	−18.7650	−	18.7650i	−0.658930	−	0.658930i	0.296197	−	0.955127i	$-0.404281\pi$
$811$	−18.7650	−	18.7650i	−0.658930	−	0.658930i	−0.955127	+	0.296197i	$0.904281\pi$
$812$	2.28412	+	1.20503i	0.0801569	+	0.0422882i
$813$	5.71257	−	1.53068i	0.200349	−	0.0536833i
$814$	−9.61728	−	22.0208i	−0.337085	−	0.771827i
$815$	−42.3892	−	24.4734i	−1.48483	−	0.857267i
$816$	−14.8008	−	21.6397i	−0.518130	−	0.757542i
$817$	9.69438	+	2.59760i	0.339163	+	0.0908786i
$818$	16.5542	−	42.2255i	0.578804	−	1.47638i
$819$	−3.93797	−	6.11864i	−0.137604	−	0.213802i
$820$	−7.18055	+	7.75031i	−0.250756	+	0.270652i
$821$	27.3688	+	7.33344i	0.955177	+	0.255939i	0.702558	−	0.711627i	$-0.252041\pi$
$821$	27.3688	+	7.33344i	0.955177	+	0.255939i	0.252619	+	0.967566i	$0.418708\pi$
$822$	−1.07341	−	7.10377i	−0.0374396	−	0.247772i
$823$	−4.58266	+	7.93739i	−0.159741	+	0.276680i	−0.934775	−	0.355239i	$-0.884399\pi$
$823$	−4.58266	+	7.93739i	−0.159741	+	0.276680i	0.775034	+	0.631920i	$0.217733\pi$
$824$	33.5462	+	11.6965i	1.16864	+	0.407466i
$825$	22.7121	−	6.08569i	0.790734	−	0.211876i
$826$	21.8615	+	2.45500i	0.760659	+	0.0854202i
$827$	−10.5467	+	10.5467i	−0.366745	+	0.366745i	−0.866289	−	0.499543i	$-0.833501\pi$
$827$	−10.5467	+	10.5467i	−0.366745	+	0.366745i	0.499543	+	0.866289i	$0.333501\pi$
$828$	−0.226983	−	0.733927i	−0.00788819	−	0.0255057i
$829$	5.56947	+	9.64660i	0.193436	+	0.335040i	0.946387	−	0.323036i	$-0.104704\pi$
$829$	5.56947	+	9.64660i	0.193436	+	0.335040i	−0.752951	+	0.658077i	$0.771370\pi$
$830$	−9.71646	+	13.1756i	−0.337263	+	0.457330i
$831$	5.14911			0.178621
$832$	28.4635	−	4.67200i	0.986795	−	0.161973i
$833$	19.1863			0.664765
$834$	0.556218	−	0.754234i	0.0192603	−	0.0261170i
$835$	0.393777	+	0.682042i	0.0136272	+	0.0236030i
$836$	5.39578	+	17.4468i	0.186617	+	0.603409i
$837$	4.55111	−	4.55111i	0.157309	−	0.157309i
$838$	12.0718	+	1.35563i	0.417012	+	0.0468295i
$839$	22.8055	−	6.11071i	0.787332	−	0.210965i	0.157317	−	0.987548i	$-0.449715\pi$
$839$	22.8055	−	6.11071i	0.787332	−	0.210965i	0.630015	+	0.776583i	$0.283049\pi$
$840$	16.3123	+	5.68758i	0.562829	+	0.196240i
$841$	−14.2953	+	24.7602i	−0.492942	+	0.853800i
$842$	−2.88183	−	19.0717i	−0.0993143	−	0.657255i
$843$	−7.28276	−	1.95141i	−0.250832	−	0.0672101i
$844$	2.18376	−	2.35704i	0.0751682	−	0.0811325i
$845$	−30.3727	−	25.0099i	−1.04485	−	0.860367i
$846$	−3.30909	+	8.44061i	−0.113769	+	0.290194i
$847$	−40.8416	−	10.9435i	−1.40333	−	0.376022i
$848$	7.31586	+	10.6963i	0.251228	+	0.367312i
$849$	−9.16044	−	5.28878i	−0.314385	−	0.181511i
$850$	−15.4319	−	35.3346i	−0.529310	−	1.21197i
$851$	−1.11528	+	0.298837i	−0.0382311	+	0.0102440i
$852$	25.1913	+	13.2901i	0.863040	+	0.455312i
$853$	−9.07626	−	9.07626i	−0.310765	−	0.310765i	0.534441	−	0.845206i	$-0.320522\pi$
$853$	−9.07626	−	9.07626i	−0.310765	−	0.310765i	−0.845206	+	0.534441i	$0.820522\pi$
$854$	16.3615	−	13.0578i	0.559879	−	0.446828i
$855$	2.44448	+	4.23396i	0.0835994	+	0.144798i
$856$	−8.46154	−	44.4497i	−0.289209	−	1.51926i
$857$		−	35.2366i		−	1.20366i	−0.798625	−	0.601829i	$-0.794439\pi$
$857$		−	35.2366i		−	1.20366i	0.798625	−	0.601829i	$-0.205561\pi$
$858$	−25.8261	+	12.7966i	−0.881688	+	0.436870i
$859$	−51.5506			−1.75888			−0.879441	−	0.476008i	$-0.842083\pi$
$859$	−51.5506			−1.75888			−0.879441	+	0.476008i	$0.842083\pi$
$860$	−20.0320	−	31.8283i	−0.683084	−	1.08534i
$861$	3.05061	−	1.76127i	0.103964	−	0.0600239i
$862$	−24.8235	+	19.8112i	−0.845492	+	0.674771i
$863$	−1.05809	+	1.05809i	−0.0360179	+	0.0360179i	−0.724886	−	0.688868i	$-0.758108\pi$
$863$	−1.05809	+	1.05809i	−0.0360179	+	0.0360179i	0.688868	+	0.724886i	$0.258108\pi$
$864$	0.201040	−	5.65328i	0.00683954	−	0.192329i
$865$	−16.4420	−	61.3623i	−0.559044	−	2.08638i
$866$	0.243182	−	0.106207i	0.00826367	−	0.00360905i
$867$	12.9794	−	22.4809i	0.440803	−	0.763493i
$868$	25.3309	+	5.76185i	0.859785	+	0.195570i
$869$	22.2889	−	83.1834i	0.756100	−	2.82180i
$870$	0.999569	−	2.54964i	0.0338886	−	0.0864408i
$871$	−16.8428	−	26.1696i	−0.570698	−	0.886725i
$872$	36.5527	−	17.6530i	1.23783	−	0.597805i
$873$	1.48875	−	5.55609i	0.0503865	−	0.188045i
$874$	0.867652	−	0.131106i	0.0293488	−	0.00443474i
$875$	−4.44450	−	2.56603i	−0.150252	−	0.0867478i
$876$	−0.354439	−	9.28832i	−0.0119754	−	0.313823i
$877$	−5.39910	−	20.1497i	−0.182315	−	0.680407i	−0.995189	−	0.0979688i	$-0.968765\pi$
$877$	−5.39910	−	20.1497i	−0.182315	−	0.680407i	0.812875	−	0.582438i	$-0.197901\pi$
$878$	23.4696	+	2.63558i	0.792062	+	0.0889467i
$879$	−18.4751	−	18.4751i	−0.623151	−	0.623151i
$880$	29.5993	−	61.6974i	0.997793	−	2.07982i
$881$	−8.27395	+	4.77697i	−0.278756	+	0.160940i	−0.632860	−	0.774266i	$-0.718119\pi$
$881$	−8.27395	+	4.77697i	−0.278756	+	0.160940i	0.354104	+	0.935206i	$0.384786\pi$
$882$	3.33179	+	2.45707i	0.112187	+	0.0827337i
$883$			35.6265i			1.19893i	0.800403	+	0.599463i	$0.204619\pi$
$883$			35.6265i			1.19893i	−0.800403	+	0.599463i	$0.795381\pi$
$884$	27.0760	+	38.7394i	0.910666	+	1.30295i
$885$		−	23.3285i		−	0.784178i
$886$	25.9728	−	35.2192i	0.872574	−	1.18321i
$887$	14.9150	−	8.61120i	0.500798	−	0.289136i	−0.228245	−	0.973604i	$-0.573299\pi$
$887$	14.9150	−	8.61120i	0.500798	−	0.289136i	0.729043	+	0.684468i	$0.239965\pi$
$888$	−8.47899	−	0.625933i	−0.284536	−	0.0210049i
$889$	−13.8312	−	13.8312i	−0.463885	−	0.463885i
$890$	−8.06912	+	71.8547i	−0.270477	+	2.40858i
$891$	1.46299	+	5.45997i	0.0490121	+	0.182916i
$892$	−0.829645	−	21.7414i	−0.0277786	−	0.727956i
$893$	−8.96830	−	5.17785i	−0.300113	−	0.173270i
$894$	2.92402	+	19.3509i	0.0977937	+	0.647191i
$895$	16.2118	−	60.5034i	0.541902	−	2.02240i
$896$	19.7435	−	11.4673i	0.659586	−	0.383097i
$897$	0.422573	+	1.31890i	0.0141093	+	0.0440366i
$898$	−33.4716	−	13.1223i	−1.11696	−	0.437898i
$899$	1.06585	−	3.97781i	0.0355481	−	0.132667i
$900$	1.84525	−	8.11228i	0.0615083	−	0.270409i
$901$	−10.6170	+	18.3892i	−0.353705	+	0.612634i
$902$	−5.58453	−	12.7869i	−0.185944	−	0.425759i
$903$	3.24519	+	12.1112i	0.107993	+	0.403036i
$904$	−21.8183	+	18.8185i	−0.725667	+	0.625893i
$905$	−19.4194	+	19.4194i	−0.645521	+	0.645521i
$906$	−6.07773	−	7.61544i	−0.201919	−	0.253006i
$907$	19.3561	−	11.1752i	0.642708	−	0.371068i	−0.142949	−	0.989730i	$-0.545658\pi$
$907$	19.3561	−	11.1752i	0.642708	−	0.371068i	0.785657	+	0.618662i	$0.212325\pi$
$908$	17.6107	+	27.9813i	0.584433	+	0.928591i
$909$	−16.7845			−0.556707
$910$	−29.5098	−	9.95517i	−0.978239	−	0.330011i
$911$		−	18.2434i		−	0.604431i	−0.953240	−	0.302215i	$-0.902274\pi$
$911$		−	18.2434i		−	0.604431i	0.953240	−	0.302215i	$-0.0977262\pi$
$912$	6.35064	+	1.19186i	0.210291	+	0.0394663i
$913$	−10.8101	−	18.7237i	−0.357763	−	0.619664i
$914$	24.9839	+	31.3050i	0.826395	+	1.03548i
$915$	−15.6967	−	15.6967i	−0.518916	−	0.518916i
$916$	−26.3784	+	50.0000i	−0.871566	+	1.65205i
$917$	−7.83589	+	2.09962i	−0.258764	+	0.0693356i
$918$	8.49440	−	3.70982i	0.280357	−	0.122442i
$919$	−35.3967	−	20.4363i	−1.16763	−	0.674131i	−0.214509	−	0.976722i	$-0.568815\pi$
$919$	−35.3967	−	20.4363i	−1.16763	−	0.674131i	−0.953121	+	0.302591i	$0.902148\pi$
$920$	−2.71882	−	1.84923i	−0.0896367	−	0.0609674i
$921$	0.200904	+	0.0538321i	0.00662001	+	0.00177383i
$922$	26.1792	+	10.2634i	0.862165	+	0.338006i
$923$	−45.6545	−	23.4981i	−1.50274	−	0.773449i
$924$	−15.5057	+	16.7360i	−0.510099	+	0.550574i
$925$	−12.0779	−	3.23626i	−0.397118	−	0.106407i
$926$	34.0247	−	5.14130i	1.11812	−	0.168954i
$927$	−6.28032	+	10.8778i	−0.206273	+	0.357275i
$928$	−1.69718	−	3.19687i	−0.0557128	−	0.104943i
$929$	−7.06937	+	1.89423i	−0.231939	+	0.0621477i	−0.372916	−	0.927865i	$-0.621642\pi$
$929$	−7.06937	+	1.89423i	−0.231939	+	0.0621477i	0.140978	+	0.990013i	$0.454975\pi$
$930$	3.07424	−	27.3758i	0.100808	−	0.897689i
$931$	−3.34368	+	3.34368i	−0.109585	+	0.109585i
$932$	39.7910	−	12.3062i	1.30340	−	0.403103i
$933$	11.4767	+	19.8783i	0.375731	+	0.650785i
$934$	−31.0849	−	22.9239i	−1.01713	−	0.750094i
$935$	112.128			3.66698
$936$	−0.259228	+	10.1947i	−0.00847314	+	0.333226i
$937$	36.3958			1.18900			0.594499	−	0.804096i	$-0.297350\pi$
$937$	36.3958			1.18900			0.594499	+	0.804096i	$0.297350\pi$
$938$	−19.8262	−	14.6211i	−0.647349	−	0.477395i
$939$	12.4334	+	21.5353i	0.405749	+	0.702778i
$940$	11.4652	+	37.0716i	0.373953	+	1.20914i
$941$	−2.60051	+	2.60051i	−0.0847743	+	0.0847743i	−0.748222	−	0.663448i	$-0.769092\pi$
$941$	−2.60051	+	2.60051i	−0.0847743	+	0.0847743i	0.663448	+	0.748222i	$0.269092\pi$
$942$	2.26265	−	20.1487i	0.0737213	−	0.656481i
$943$	−0.647614	+	0.173528i	−0.0210892	+	0.00565084i
$944$	−23.3997	−	20.0768i	−0.761596	−	0.653444i
$945$	−3.05389	+	5.28950i	−0.0993432	+	0.172067i
$946$	49.1090	−	7.42060i	1.59667	−	0.241265i
$947$	29.5599	+	7.92054i	0.960567	+	0.257383i	0.704840	−	0.709366i	$-0.251019\pi$
$947$	29.5599	+	7.92054i	0.960567	+	0.257383i	0.255726	+	0.966749i	$0.417685\pi$
$948$	−22.3517	−	20.7085i	−0.725948	−	0.672581i
$949$	0.808473	+	16.7374i	0.0262441	+	0.543320i
$950$	8.84730	+	3.46852i	0.287044	+	0.112534i
$951$	−9.32950	−	2.49983i	−0.302530	−	0.0810626i
$952$	30.9348	+	21.0406i	1.00260	+	0.681931i
$953$	−17.9259	−	10.3495i	−0.580677	−	0.335254i	0.180725	−	0.983534i	$-0.442156\pi$
$953$	−17.9259	−	10.3495i	−0.580677	−	0.335254i	−0.761402	+	0.648279i	$0.775489\pi$
$954$	−4.19869	+	1.83372i	−0.135938	+	0.0593690i
$955$	18.4380	−	4.94044i	0.596639	−	0.159869i
$956$	−9.84662	−	5.19476i	−0.318463	−	0.168011i
$957$	2.55740	+	2.55740i	0.0826691	+	0.0826691i
$958$	−2.48733	−	3.11664i	−0.0803619	−	0.100694i
$959$	5.12611	+	8.87869i	0.165531	+	0.286708i
$960$	−14.4209	−	19.4490i	−0.465432	−	0.627712i
$961$		−	10.4251i		−	0.336295i
$962$	15.2964	+	0.973600i	0.493175	+	0.0313901i
$963$	15.9976			0.515514
$964$	13.4374	−	8.45716i	0.432789	−	0.272387i
$965$	−37.2295	+	21.4945i	−1.19846	+	0.691932i
$966$	0.683828	+	0.856841i	0.0220018	+	0.0275684i
$967$	11.7809	−	11.7809i	0.378848	−	0.378848i	−0.491838	−	0.870687i	$-0.663675\pi$
$967$	11.7809	−	11.7809i	0.378848	−	0.378848i	0.870687	+	0.491838i	$0.163675\pi$
$968$	38.7045	+	44.8744i	1.24401	+	1.44232i
$969$	2.74029	+	10.2269i	0.0880308	+	0.328535i
$970$	−9.85357	−	22.5618i	−0.316379	−	0.724416i
$971$	16.7807	−	29.0650i	0.538517	−	0.932739i	−0.460467	−	0.887677i	$-0.652318\pi$
$971$	16.7807	−	29.0650i	0.538517	−	0.932739i	0.998984	−	0.0450621i	$-0.0143486\pi$
$972$	1.95019	+	0.443596i	0.0625522	+	0.0142284i
$973$	−0.346124	+	1.29175i	−0.0110962	+	0.0414117i
$974$	−24.1780	−	9.47882i	−0.774712	−	0.303721i
$975$	−3.17834	+	14.6576i	−0.101788	+	0.469417i
$976$	−29.2534	+	2.23586i	−0.936378	+	0.0715680i
$977$	1.82586	−	6.81419i	0.0584143	−	0.218005i	−0.930549	−	0.366168i	$-0.880669\pi$
$977$	1.82586	−	6.81419i	0.0584143	−	0.218005i	0.988963	+	0.148163i	$0.0473361\pi$
$978$	−3.41723	−	22.6150i	−0.109271	−	0.723147i
$979$	−82.6983	−	47.7459i	−2.64305	−	1.52597i
$980$	17.7060	−	0.675656i	0.565598	−	0.0215830i
$981$	3.71445	+	13.8625i	0.118593	+	0.442596i
$982$	0.538412	−	4.79451i	0.0171814	−	0.152999i
$983$	34.9395	+	34.9395i	1.11440	+	1.11440i	0.992549	+	0.121848i	$0.0388820\pi$
$983$	34.9395	+	34.9395i	1.11440	+	1.11440i	0.121848	+	0.992549i	$0.461118\pi$
$984$	−4.92355	−	0.363465i	−0.156957	−	0.0115868i
$985$	−66.0081	+	38.1098i	−2.10319	+	1.21428i
$986$	3.52002	−	4.77316i	0.112100	−	0.152008i
$987$		−	12.9374i		−	0.411802i
$988$	−11.4700	−	2.03263i	−0.364908	−	0.0646665i
$989$		−	2.38650i		−	0.0758861i
$990$	19.4716	+	14.3595i	0.618846	+	0.456375i
$991$	50.5421	−	29.1805i	1.60552	−	0.926950i	0.615169	−	0.788395i	$-0.289088\pi$
$991$	50.5421	−	29.1805i	1.60552	−	0.926950i	0.990355	−	0.138554i	$-0.0442455\pi$
$992$	−24.8137	−	26.6436i	−0.787837	−	0.845936i
$993$	−11.4326	−	11.4326i	−0.362802	−	0.362802i
$994$	−40.3904	−	4.53574i	−1.28110	−	0.143865i
$995$	−1.21254	−	4.52527i	−0.0384402	−	0.143461i
$996$	−7.64414	+	0.291698i	−0.242214	+	0.00924280i
$997$	−3.45063	−	1.99222i	−0.109283	−	0.0630943i	0.444363	−	0.895847i	$-0.353430\pi$
$997$	−3.45063	−	1.99222i	−0.109283	−	0.0630943i	−0.553645	+	0.832753i	$0.686764\pi$
$998$	−30.5589	+	4.61760i	−0.967326	+	0.146168i
$999$	0.777993	−	2.90351i	0.0246146	−	0.0918630i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.c.115.3	yes	48
3.2	odd	2		936.2.ed.c.739.10		48
8.3	odd	2	inner	312.2.bt.c.115.7	yes	48
13.6	odd	12	inner	312.2.bt.c.19.7	yes	48
24.11	even	2		936.2.ed.c.739.6		48
39.32	even	12		936.2.ed.c.19.6		48
104.19	even	12	inner	312.2.bt.c.19.3	✓	48
312.227	odd	12		936.2.ed.c.19.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.c.19.3	✓	48	104.19	even	12	inner
312.2.bt.c.19.7	yes	48	13.6	odd	12	inner
312.2.bt.c.115.3	yes	48	1.1	even	1	trivial
312.2.bt.c.115.7	yes	48	8.3	odd	2	inner
936.2.ed.c.19.6		48	39.32	even	12
936.2.ed.c.19.10		48	312.227	odd	12
936.2.ed.c.739.6		48	24.11	even	2
936.2.ed.c.739.10		48	3.2	odd	2

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	312.2.bt.c.115.3

Level	$312$
Weight	$2$
Character	312.115
Analytic conductor	$2.491$
Analytic rank	$0$
Dimension	$48$
Inner twists	$4$