LMFDB - Embedded newform 378.2.bf.a.101.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$378 = 2 \cdot 3^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$ , degree $6$ , 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.20
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.20

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(0.520556 - 1.65197i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.37026 - 1.14979i) q^{5} +(-0.930879 - 1.46064i) q^{6} +(-1.38267 + 2.25571i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.45804 - 1.71989i) q^{9} -1.78875i q^{10} +(3.15337 - 3.75804i) q^{11} +(-1.71727 - 0.225785i) q^{12} +(0.0313706 - 0.0861899i) q^{13} +(0.839205 + 2.50913i) q^{14} +(-1.18612 - 2.86216i) q^{15} +(-0.939693 + 0.342020i) q^{16} -0.123596 q^{17} +(-2.89751 + 0.777445i) q^{18} -2.33825i q^{19} +(-1.37026 - 1.14979i) q^{20} +(3.00661 + 3.45837i) q^{21} +(-0.851879 - 4.83124i) q^{22} +(-1.95762 + 5.37851i) q^{23} +(-1.27680 + 1.17037i) q^{24} +(-0.312632 + 1.77303i) q^{25} +(-0.0458607 - 0.0794331i) q^{26} +(-4.12077 + 3.16533i) q^{27} +(2.46154 + 0.969969i) q^{28} +(1.25242 + 3.44100i) q^{29} +(-2.95497 - 0.931144i) q^{30} +(4.32390 - 0.762419i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-4.56668 - 7.16556i) q^{33} +(-0.0794458 + 0.0946798i) q^{34} +(0.698953 + 4.68069i) q^{35} +(-1.26693 + 2.71936i) q^{36} +(-2.72254 + 4.71557i) q^{37} +(-1.79121 - 1.50300i) q^{38} +(-0.126053 - 0.0966901i) q^{39} +(-1.76157 + 0.310613i) q^{40} +(5.84036 + 2.12572i) q^{41} +(4.58187 - 0.0802028i) q^{42} +(1.72827 - 9.80152i) q^{43} +(-4.24852 - 2.45289i) q^{44} +(-5.34567 + 0.469522i) q^{45} +(2.86184 + 4.95686i) q^{46} +(1.03169 - 5.85102i) q^{47} +(0.0758460 + 1.73039i) q^{48} +(-3.17642 - 6.23782i) q^{49} +(1.15726 + 1.37917i) q^{50} +(-0.0643385 + 0.204177i) q^{51} +(-0.0903280 - 0.0159273i) q^{52} +(11.1984 + 6.46537i) q^{53} +(-0.223998 + 5.19132i) q^{54} -8.77520i q^{55} +(2.32528 - 1.26216i) q^{56} +(-3.86273 - 1.21719i) q^{57} +(3.44100 + 1.25242i) q^{58} +(7.47193 + 2.71956i) q^{59} +(-2.61271 + 1.66511i) q^{60} +(8.83921 + 1.55859i) q^{61} +(2.19530 - 3.80237i) q^{62} +(7.27824 - 3.16657i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.0561141 - 0.154172i) q^{65} +(-8.42454 - 1.10765i) q^{66} +(-1.05687 + 0.886817i) q^{67} +(0.0214622 + 0.121718i) q^{68} +(7.86611 + 6.03375i) q^{69} +(4.03489 + 2.47326i) q^{70} +(-13.4588 + 7.77044i) q^{71} +(1.26878 + 2.71849i) q^{72} +(-9.74286 + 5.62505i) q^{73} +(1.86233 + 5.11670i) q^{74} +(2.76625 + 1.43942i) q^{75} +(-2.30273 + 0.406033i) q^{76} +(4.11695 + 12.3092i) q^{77} +(-0.155095 + 0.0344114i) q^{78} +(-7.96208 - 6.68098i) q^{79} +(-0.894374 + 1.54910i) q^{80} +(3.08395 + 8.45513i) q^{81} +(5.38251 - 3.10759i) q^{82} +(3.01564 - 1.09760i) q^{83} +(2.88373 - 3.56147i) q^{84} +(-0.169358 + 0.142109i) q^{85} +(-6.39749 - 7.62423i) q^{86} +(6.33640 - 0.277736i) q^{87} +(-4.60992 + 1.67787i) q^{88} +2.60829 q^{89} +(-3.07645 + 4.39682i) q^{90} +(0.151044 + 0.189935i) q^{91} +(5.63673 + 0.993908i) q^{92} +(0.991332 - 7.53985i) q^{93} +(-3.81898 - 4.55128i) q^{94} +(-2.68849 - 3.20402i) q^{95} +(1.37431 + 1.05417i) q^{96} +(9.86169 + 1.73888i) q^{97} +(-6.82021 - 1.57631i) q^{98} +(-14.2145 + 3.81397i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100})$ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$ .

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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

)

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

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	0.520556	−	1.65197i	0.300543	−	0.953768i
$3$	0.520556	−	1.65197i	0.300543	−	0.953768i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	1.37026	−	1.14979i	0.612799	−	0.514200i	−0.282732	−	0.959199i	$-0.591241\pi$
$5$	1.37026	−	1.14979i	0.612799	−	0.514200i	0.895531	+	0.444999i	$0.146796\pi$
$6$	−0.930879	−	1.46064i	−0.380030	−	0.596303i
$7$	−1.38267	+	2.25571i	−0.522602	+	0.852577i
$7$	−1.38267	+	2.25571i	−0.522602	+	0.852577i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−2.45804	−	1.71989i	−0.819348	−	0.573297i
$10$		−	1.78875i		−	0.565652i
$11$	3.15337	−	3.75804i	0.950777	−	1.13309i	−0.0402177	−	0.999191i	$-0.512805\pi$
$11$	3.15337	−	3.75804i	0.950777	−	1.13309i	0.990995	−	0.133901i	$-0.0427504\pi$
$12$	−1.71727	−	0.225785i	−0.495734	−	0.0651786i
$13$	0.0313706	−	0.0861899i	0.00870063	−	0.0239048i	−0.935266	−	0.353945i	$-0.884840\pi$
$13$	0.0313706	−	0.0861899i	0.00870063	−	0.0239048i	0.943967	+	0.330040i	$0.107062\pi$
$14$	0.839205	+	2.50913i	0.224287	+	0.670593i
$15$	−1.18612	−	2.86216i	−0.306255	−	0.739008i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.123596			−0.0299764			−0.0149882	−	0.999888i	$-0.504771\pi$
$17$	−0.123596			−0.0299764			−0.0149882	+	0.999888i	$0.504771\pi$
$18$	−2.89751	+	0.777445i	−0.682950	+	0.183246i
$19$		−	2.33825i		−	0.536432i	−0.963359	−	0.268216i	$-0.913566\pi$
$19$		−	2.33825i		−	0.536432i	0.963359	−	0.268216i	$-0.0864341\pi$
$20$	−1.37026	−	1.14979i	−0.306400	−	0.257100i
$21$	3.00661	+	3.45837i	0.656096	+	0.754677i
$22$	−0.851879	−	4.83124i	−0.181621	−	1.03002i
$23$	−1.95762	+	5.37851i	−0.408191	+	1.12150i	0.549949	+	0.835198i	$0.314647\pi$
$23$	−1.95762	+	5.37851i	−0.408191	+	1.12150i	−0.958141	+	0.286298i	$0.907575\pi$
$24$	−1.27680	+	1.17037i	−0.260626	+	0.238902i
$25$	−0.312632	+	1.77303i	−0.0625265	+	0.354605i
$26$	−0.0458607	−	0.0794331i	−0.00899403	−	0.0155781i
$27$	−4.12077	+	3.16533i	−0.793042	+	0.609167i
$28$	2.46154	+	0.969969i	0.465187	+	0.183307i
$29$	1.25242	+	3.44100i	0.232569	+	0.638978i	0.999998	−	0.00215645i	$-0.000686419\pi$
$29$	1.25242	+	3.44100i	0.232569	+	0.638978i	−0.767429	+	0.641134i	$0.778464\pi$
$30$	−2.95497	−	0.931144i	−0.539501	−	0.170003i
$31$	4.32390	−	0.762419i	0.776594	−	0.136935i	0.228717	−	0.973493i	$-0.426547\pi$
$31$	4.32390	−	0.762419i	0.776594	−	0.136935i	0.547878	+	0.836558i	$0.315436\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−4.56668	−	7.16556i	−0.794957	−	1.24736i
$34$	−0.0794458	+	0.0946798i	−0.0136248	+	0.0162375i
$35$	0.698953	+	4.68069i	0.118145	+	0.791180i
$36$	−1.26693	+	2.71936i	−0.211155	+	0.453226i
$37$	−2.72254	+	4.71557i	−0.447582	+	0.775236i	−0.998228	−	0.0595036i	$-0.981048\pi$
$37$	−2.72254	+	4.71557i	−0.447582	+	0.775236i	0.550646	+	0.834739i	$0.314382\pi$
$38$	−1.79121	−	1.50300i	−0.290572	−	0.243819i
$39$	−0.126053	−	0.0966901i	−0.0201847	−	0.0154828i
$40$	−1.76157	+	0.310613i	−0.278529	+	0.0491122i
$41$	5.84036	+	2.12572i	0.912111	+	0.331981i	0.755096	−	0.655615i	$-0.227590\pi$
$41$	5.84036	+	2.12572i	0.912111	+	0.331981i	0.157016	+	0.987596i	$0.449813\pi$
$42$	4.58187	−	0.0802028i	0.706998	−	0.0123756i
$43$	1.72827	−	9.80152i	0.263559	−	1.49472i	−0.509548	−	0.860442i	$-0.670188\pi$
$43$	1.72827	−	9.80152i	0.263559	−	1.49472i	0.773107	−	0.634275i	$-0.218701\pi$
$44$	−4.24852	−	2.45289i	−0.640489	−	0.369787i
$45$	−5.34567	+	0.469522i	−0.796885	+	0.0699922i
$46$	2.86184	+	4.95686i	0.421956	+	0.730849i
$47$	1.03169	−	5.85102i	0.150488	−	0.853459i	−0.812308	−	0.583229i	$-0.801789\pi$
$47$	1.03169	−	5.85102i	0.150488	−	0.853459i	0.962796	−	0.270230i	$-0.0870997\pi$
$48$	0.0758460	+	1.73039i	0.0109474	+	0.249760i
$49$	−3.17642	−	6.23782i	−0.453775	−	0.891117i
$50$	1.15726	+	1.37917i	0.163661	+	0.195044i
$51$	−0.0643385	+	0.204177i	−0.00900919	+	0.0285905i
$52$	−0.0903280	−	0.0159273i	−0.0125262	−	0.00220871i
$53$	11.1984	+	6.46537i	1.53821	+	0.888087i	0.998944	+	0.0459534i	$0.0146326\pi$
$53$	11.1984	+	6.46537i	1.53821	+	0.888087i	0.539269	+	0.842134i	$0.318701\pi$
$54$	−0.223998	+	5.19132i	−0.0304823	+	0.706449i
$55$		−	8.77520i		−	1.18325i
$56$	2.32528	−	1.26216i	0.310729	−	0.168663i
$57$	−3.86273	−	1.21719i	−0.511632	−	0.161221i
$58$	3.44100	+	1.25242i	0.451825	+	0.164451i
$59$	7.47193	+	2.71956i	0.972762	+	0.354056i	0.779022	−	0.626997i	$-0.215716\pi$
$59$	7.47193	+	2.71956i	0.972762	+	0.354056i	0.193740	+	0.981053i	$0.437938\pi$
$60$	−2.61271	+	1.66511i	−0.337300	+	0.214965i
$61$	8.83921	+	1.55859i	1.13174	+	0.199557i	0.707992	−	0.706221i	$-0.249601\pi$
$61$	8.83921	+	1.55859i	1.13174	+	0.199557i	0.423753	+	0.905778i	$0.360712\pi$
$62$	2.19530	−	3.80237i	0.278803	−	0.482901i
$63$	7.27824	−	3.16657i	0.916972	−	0.398951i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.0561141	−	0.154172i	−0.00696009	−	0.0191227i
$66$	−8.42454	−	1.10765i	−1.03699	−	0.136342i
$67$	−1.05687	+	0.886817i	−0.129117	+	0.108342i	−0.705059	−	0.709148i	$-0.749080\pi$
$67$	−1.05687	+	0.886817i	−0.129117	+	0.108342i	0.575942	+	0.817490i	$0.304635\pi$
$68$	0.0214622	+	0.121718i	0.00260267	+	0.0147605i
$69$	7.86611	+	6.03375i	0.946968	+	0.726378i
$70$	4.03489	+	2.47326i	0.482262	+	0.295611i
$71$	−13.4588	+	7.77044i	−1.59727	+	0.922182i	−0.605255	+	0.796032i	$0.706929\pi$
$71$	−13.4588	+	7.77044i	−1.59727	+	0.922182i	−0.992011	+	0.126151i	$0.959738\pi$
$72$	1.26878	+	2.71849i	0.149527	+	0.320377i
$73$	−9.74286	+	5.62505i	−1.14032	+	0.658362i	−0.946509	−	0.322678i	$-0.895417\pi$
$73$	−9.74286	+	5.62505i	−1.14032	+	0.658362i	−0.193807	+	0.981040i	$0.562084\pi$
$74$	1.86233	+	5.11670i	0.216491	+	0.594804i
$75$	2.76625	+	1.43942i	0.319419	+	0.166210i
$76$	−2.30273	+	0.406033i	−0.264141	+	0.0465752i
$77$	4.11695	+	12.3092i	0.469170	+	1.40277i
$78$	−0.155095	+	0.0344114i	−0.0175610	+	0.00389632i
$79$	−7.96208	−	6.68098i	−0.895804	−	0.751668i	0.0735621	−	0.997291i	$-0.476563\pi$
$79$	−7.96208	−	6.68098i	−0.895804	−	0.751668i	−0.969366	+	0.245622i	$0.921008\pi$
$80$	−0.894374	+	1.54910i	−0.0999941	+	0.173195i
$81$	3.08395	+	8.45513i	0.342661	+	0.939459i
$82$	5.38251	−	3.10759i	0.594398	−	0.343176i
$83$	3.01564	−	1.09760i	0.331010	−	0.120478i	−0.171169	−	0.985242i	$-0.554754\pi$
$83$	3.01564	−	1.09760i	0.331010	−	0.120478i	0.502178	+	0.864764i	$0.332532\pi$
$84$	2.88373	−	3.56147i	0.314641	−	0.388588i
$85$	−0.169358	+	0.142109i	−0.0183695	+	0.0154138i
$86$	−6.39749	−	7.62423i	−0.689859	−	0.822141i
$87$	6.33640	−	0.277736i	0.679334	−	0.0297764i
$88$	−4.60992	+	1.67787i	−0.491419	+	0.178862i
$89$	2.60829			0.276478			0.138239	−	0.990399i	$-0.455856\pi$
$89$	2.60829			0.276478			0.138239	+	0.990399i	$0.455856\pi$
$90$	−3.07645	+	4.39682i	−0.324287	+	0.463466i
$91$	0.151044	+	0.189935i	0.0158337	+	0.0199106i
$92$	5.63673	+	0.993908i	0.587670	+	0.103622i
$93$	0.991332	−	7.53985i	0.102796	−	0.781846i
$94$	−3.81898	−	4.55128i	−0.393898	−	0.469429i
$95$	−2.68849	−	3.20402i	−0.275833	−	0.328725i
$96$	1.37431	+	1.05417i	0.140265	+	0.107591i
$97$	9.86169	+	1.73888i	1.00130	+	0.176557i	0.650186	−	0.759775i	$-0.274691\pi$
$97$	9.86169	+	1.73888i	1.00130	+	0.176557i	0.351117	+	0.936332i	$0.385802\pi$
$98$	−6.82021	−	1.57631i	−0.688945	−	0.159231i
$99$	−14.2145	+	3.81397i	−1.42862	+	0.383318i
$100$	1.80038			0.180038
$101$	13.0482	−	4.74915i	1.29834	−	0.472558i	0.401885	−	0.915690i	$-0.368355\pi$
$101$	13.0482	−	4.74915i	1.29834	−	0.472558i	0.896456	+	0.443132i	$0.146133\pi$
$102$	0.115053	+	0.180529i	0.0113919	+	0.0178750i
$103$	−7.60612	−	9.06462i	−0.749453	−	0.893163i	0.247679	−	0.968842i	$-0.420332\pi$
$103$	−7.60612	−	9.06462i	−0.749453	−	0.893163i	−0.997132	+	0.0756789i	$0.975888\pi$
$104$	−0.0702627	+	0.0589574i	−0.00688982	+	0.00578125i
$105$	8.09622	+	1.28191i	0.790110	+	0.125101i
$106$	12.1509	−	4.42258i	1.18020	−	0.429558i
$107$	−5.53361	+	3.19483i	−0.534954	+	0.308856i	−0.743032	−	0.669256i	$-0.766613\pi$
$107$	−5.53361	+	3.19483i	−0.534954	+	0.308856i	0.208077	+	0.978112i	$0.433279\pi$
$108$	3.83280	+	3.50851i	0.368811	+	0.337607i
$109$	−3.16597	+	5.48362i	−0.303245	+	0.525235i	−0.976869	−	0.213839i	$-0.931403\pi$
$109$	−3.16597	+	5.48362i	−0.303245	+	0.525235i	0.673624	+	0.739074i	$0.264737\pi$
$110$	−6.72219	−	5.64059i	−0.640936	−	0.537809i
$111$	6.37278	+	6.95228i	0.604877	+	0.659882i
$112$	0.527792	−	2.59257i	0.0498717	−	0.244975i
$113$	−5.12722	+	0.904067i	−0.482328	+	0.0850475i	−0.409525	−	0.912299i	$-0.634306\pi$
$113$	−5.12722	+	0.904067i	−0.482328	+	0.0850475i	−0.0728031	+	0.997346i	$0.523194\pi$
$114$	−3.41534	+	2.17663i	−0.319876	+	0.203860i
$115$	3.50168	+	9.62080i	0.326534	+	0.897144i
$116$	3.17124	−	1.83092i	0.294443	−	0.169996i
$117$	−0.225348	+	0.157905i	−0.0208334	+	0.0145983i
$118$	6.88616	−	3.97573i	0.633923	−	0.365996i
$119$	0.170893	−	0.278796i	0.0156657	−	0.0255572i
$120$	−0.403873	+	3.07177i	−0.0368684	+	0.280413i
$121$	−2.26899	−	12.8681i	−0.206272	−	1.16983i
$122$	6.87568	−	5.76938i	0.622495	−	0.522335i
$123$	6.55187	−	8.54158i	0.590762	−	0.770168i
$124$	−1.50167	−	4.12581i	−0.134854	−	0.370509i
$125$	6.08208	+	10.5345i	0.543998	+	0.942232i
$126$	2.25263	−	7.61089i	0.200680	−	0.678032i
$127$	−7.30569	+	12.6538i	−0.648276	+	1.12285i	0.335259	+	0.942126i	$0.391176\pi$
$127$	−7.30569	+	12.6538i	−0.648276	+	1.12285i	−0.983535	+	0.180720i	$0.942157\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−15.2922	−	7.95730i	−1.34640	−	0.700601i
$130$	−0.154172	−	0.0561141i	−0.0135218	−	0.00492153i
$131$	−5.06735	−	1.84437i	−0.442737	−	0.161143i	0.111026	−	0.993817i	$-0.464586\pi$
$131$	−5.06735	−	1.84437i	−0.442737	−	0.161143i	−0.553763	+	0.832675i	$0.686809\pi$
$132$	−6.26370	+	5.74159i	−0.545185	+	0.499741i
$133$	5.27441	+	3.23304i	0.457349	+	0.280340i
$134$			1.37964i			0.119183i
$135$	−2.00708	+	9.07532i	−0.172742	+	0.781079i
$136$	0.107037	+	0.0617979i	0.00917835	+	0.00529912i
$137$	−12.1500	−	2.14237i	−1.03804	−	0.183035i	−0.371447	−	0.928454i	$-0.621138\pi$
$137$	−12.1500	−	2.14237i	−1.03804	−	0.183035i	−0.666596	+	0.745419i	$0.732249\pi$
$138$	9.67836	−	2.14737i	0.823876	−	0.182796i
$139$	−5.54547	−	6.60884i	−0.470361	−	0.560554i	0.477749	−	0.878496i	$-0.341453\pi$
$139$	−5.54547	−	6.60884i	−0.470361	−	0.560554i	−0.948110	+	0.317942i	$0.897008\pi$
$140$	4.48820	−	1.50113i	0.379322	−	0.126868i
$141$	−9.12868	−	4.75011i	−0.768774	−	0.400032i
$142$	−2.69865	+	15.3048i	−0.226465	+	1.28435i
$143$	−0.224982	−	0.389681i	−0.0188140	−	0.0325867i
$144$	2.89804	+	0.775469i	0.241504	+	0.0646224i
$145$	5.67256	+	3.27505i	0.471080	+	0.271978i
$146$	−1.95356	+	11.0792i	−0.161678	+	0.916919i
$147$	−11.9582	+	2.00024i	−0.986297	+	0.164977i
$148$	5.11670	+	1.86233i	0.420590	+	0.153082i
$149$	−18.9608	+	3.34331i	−1.55333	+	0.273894i	−0.883433	−	0.468558i	$-0.844774\pi$
$149$	−18.9608	+	3.34331i	−1.55333	+	0.273894i	−0.669899	+	0.742452i	$0.733663\pi$
$150$	2.88077	−	1.19383i	0.235214	−	0.0974759i
$151$	3.88001	+	3.25571i	0.315750	+	0.264946i	0.786864	−	0.617127i	$-0.211703\pi$
$151$	3.88001	+	3.25571i	0.315750	+	0.264946i	−0.471114	+	0.882073i	$0.656148\pi$
$152$	−1.16913	+	2.02499i	−0.0948287	+	0.164248i
$153$	0.303804	+	0.212571i	0.0245611	+	0.0171854i
$154$	12.0757	+	4.75845i	0.973091	+	0.383447i
$155$	5.04825	−	6.01627i	0.405485	−	0.483238i
$156$	−0.0733322	+	0.140929i	−0.00587128	+	0.0112833i
$157$	−3.46321	+	9.51510i	−0.276394	+	0.759387i	0.721369	+	0.692550i	$0.243513\pi$
$157$	−3.46321	+	9.51510i	−0.276394	+	0.759387i	−0.997764	+	0.0668371i	$0.978709\pi$
$158$	−10.2358	+	1.80486i	−0.814320	+	0.143587i
$159$	16.5100	−	15.1338i	1.30933	−	1.20019i
$160$	0.611788	+	1.68087i	0.0483661	+	0.132885i
$161$	−9.42558	−	11.8525i	−0.742840	−	0.934110i
$162$	8.45933	+	3.07241i	0.664628	+	0.241392i
$163$	−6.93173	−	12.0061i	−0.542935	−	0.940391i	−0.998734	−	0.0503079i	$-0.983980\pi$
$163$	−6.93173	−	12.0061i	−0.542935	−	0.940391i	0.455799	−	0.890083i	$-0.349354\pi$
$164$	1.07926	−	6.12076i	0.0842757	−	0.477951i
$165$	−14.4964	−	4.56798i	−1.12854	−	0.355617i
$166$	1.09760	−	3.01564i	0.0851906	−	0.234059i
$167$	0.926021	+	5.25173i	0.0716577	+	0.406391i	0.999446	+	0.0332837i	$0.0105965\pi$
$167$	0.926021	+	5.25173i	0.0716577	+	0.406391i	−0.927788	+	0.373107i	$0.878292\pi$
$168$	−0.874618	−	4.49834i	−0.0674783	−	0.347054i
$169$	9.95213	+	8.35083i	0.765549	+	0.642372i
$170$			0.221082i			0.0169562i
$171$	−4.02154	+	5.74752i	−0.307535	+	0.439524i
$172$	−9.95272			−0.758888
$173$	2.42262	−	0.881763i	0.184189	−	0.0670392i	−0.248279	−	0.968688i	$-0.579865\pi$
$173$	2.42262	−	0.881763i	0.184189	−	0.0670392i	0.432468	+	0.901649i	$0.357643\pi$
$174$	3.86020	−	5.03249i	0.292641	−	0.381512i
$175$	−3.56716	−	3.15673i	−0.269652	−	0.238626i
$176$	−1.67787	+	4.60992i	−0.126474	+	0.347486i
$177$	8.38220	−	10.9278i	0.630045	−	0.821380i
$178$	1.67658	−	1.99807i	0.125665	−	0.149762i
$179$			14.3820i			1.07496i	0.843275	+	0.537482i	$0.180625\pi$
$179$			14.3820i			1.07496i	−0.843275	+	0.537482i	$0.819375\pi$
$180$	1.39065	+	5.18292i	0.103653	+	0.386312i
$181$	−14.9263	−	8.61768i	−1.10946	−	0.640547i	−0.170770	−	0.985311i	$-0.554626\pi$
$181$	−14.9263	−	8.61768i	−1.10946	−	0.640547i	−0.938689	+	0.344764i	$0.887959\pi$
$182$	0.242588	+	0.00638181i	0.0179818	+	0.000473052i
$183$	7.17606	−	13.7908i	0.530469	−	1.01945i
$184$	4.38460	−	3.67911i	0.323237	−	0.271228i
$185$	1.69131	+	9.59190i	0.124348	+	0.705211i
$186$	−5.13864	−	5.60593i	−0.376784	−	0.411046i
$187$	−0.389743	+	0.464478i	−0.0285008	+	0.0339660i
$188$	−5.94128			−0.433312
$189$	−1.44236	−	13.6719i	−0.104917	−	0.994481i
$190$	−4.18255			−0.303434
$191$	15.2245	−	18.1439i	1.10161	−	1.31284i	0.155918	−	0.987770i	$-0.450166\pi$
$191$	15.2245	−	18.1439i	1.10161	−	1.31284i	0.945689	−	0.325074i	$-0.105389\pi$
$192$	1.69093	−	0.375173i	0.122032	−	0.0270758i
$193$	2.43394	+	13.8036i	0.175199	+	0.993603i	0.937914	+	0.346868i	$0.112755\pi$
$193$	2.43394	+	13.8036i	0.175199	+	0.993603i	−0.762715	+	0.646735i	$0.776134\pi$
$194$	7.67103	−	6.43676i	0.550748	−	0.462132i
$195$	−0.283899	+	0.0124438i	−0.0203304	+	0.000891118i
$196$	−5.59147	+	4.21135i	−0.399391	+	0.300811i
$197$	−3.41389	−	1.97101i	−0.243229	−	0.140429i	0.373431	−	0.927658i	$-0.378181\pi$
$197$	−3.41389	−	1.97101i	−0.243229	−	0.140429i	−0.616660	+	0.787230i	$0.711515\pi$
$198$	−6.21526	+	13.3405i	−0.441699	+	0.948071i
$199$		−	4.91064i		−	0.348106i	−0.984736	−	0.174053i	$-0.944314\pi$
$199$		−	4.91064i		−	0.348106i	0.984736	−	0.174053i	$-0.0556864\pi$
$200$	1.15726	−	1.37917i	0.0818307	−	0.0975220i
$201$	0.914841	+	2.20756i	0.0645279	+	0.155709i
$202$	4.74915	−	13.0482i	0.334149	−	0.918066i
$203$	−9.49358	−	1.93269i	−0.666319	−	0.135648i
$204$	0.212247	+	0.0279061i	0.0148603	+	0.00195382i
$205$	10.4469	−	3.80237i	0.729646	−	0.265569i
$206$	−11.8330			−0.824445
$207$	14.0624	−	9.85371i	0.977401	−	0.684880i
$208$			0.0917214i			0.00635974i
$209$	−8.78725	−	7.37338i	−0.607827	−	0.510027i
$210$	6.18615	−	5.37807i	0.426885	−	0.371122i
$211$	−2.29132	−	12.9947i	−0.157741	−	0.894593i	−0.956237	−	0.292593i	$-0.905482\pi$
$211$	−2.29132	−	12.9947i	−0.157741	−	0.894593i	0.798496	−	0.602000i	$-0.205629\pi$
$212$	4.42258	−	12.1509i	0.303744	−	0.834529i
$213$	5.83052	+	26.2786i	0.399500	+	1.80058i
$214$	−1.10955	+	6.29259i	−0.0758475	+	0.430153i
$215$	−8.90146	−	15.4178i	−0.607074	−	1.05148i
$216$	5.15135	−	0.680869i	0.350505	−	0.0463272i
$217$	−4.25875	+	10.8076i	−0.289103	+	0.733669i
$218$	2.16565	+	5.95008i	0.146676	+	0.402990i
$219$	4.22073	+	19.0231i	0.285210	+	1.28546i
$220$	−8.64188	+	1.52380i	−0.582636	+	0.102734i
$221$	−0.00387727	+	0.0106527i	−0.000260813	+	0.000716579i
$222$	9.42210	−	0.412987i	0.632370	−	0.0277179i
$223$	−2.23540	+	2.66405i	−0.149694	+	0.178398i	−0.835680	−	0.549216i	$-0.814926\pi$
$223$	−2.23540	+	2.66405i	−0.149694	+	0.178398i	0.685987	+	0.727614i	$0.259371\pi$
$224$	−1.64677	−	2.07079i	−0.110029	−	0.138360i
$225$	3.81788	−	3.82048i	0.254525	−	0.254699i
$226$	−2.60316	+	4.50880i	−0.173159	+	0.299921i
$227$	−15.1114	−	12.6800i	−1.00298	−	0.841602i	−0.0155872	−	0.999879i	$-0.504962\pi$
$227$	−15.1114	−	12.6800i	−1.00298	−	0.841602i	−0.987395	+	0.158277i	$0.949406\pi$
$228$	−0.527943	+	4.01541i	−0.0349639	+	0.265927i
$229$	−25.1654	+	4.43735i	−1.66298	+	0.293228i	−0.924538	−	0.381090i	$-0.875549\pi$
$229$	−25.1654	+	4.43735i	−1.66298	+	0.293228i	−0.738441	+	0.674318i	$0.764438\pi$
$230$	9.62080	+	3.50168i	0.634376	+	0.230894i
$231$	22.4776	−	0.393457i	1.47892	−	0.0258875i
$232$	0.635871	−	3.60620i	0.0417470	−	0.236759i
$233$	−5.84982	−	3.37740i	−0.383235	−	0.221261i	0.295990	−	0.955191i	$-0.404350\pi$
$233$	−5.84982	−	3.37740i	−0.383235	−	0.221261i	−0.679225	+	0.733930i	$0.737684\pi$
$234$	−0.0238887	+	0.274125i	−0.00156165	+	0.0179201i
$235$	−5.31373	−	9.20365i	−0.346629	−	0.600380i
$236$	1.38076	−	7.83066i	0.0898796	−	0.509732i
$237$	−15.1815	+	9.67533i	−0.986145	+	0.628480i
$238$	−0.103722	−	0.310118i	−0.00672331	−	0.0201019i
$239$	4.36790	+	5.20546i	0.282536	+	0.336713i	0.888583	−	0.458716i	$-0.151690\pi$
$239$	4.36790	+	5.20546i	0.282536	+	0.336713i	−0.606047	+	0.795428i	$0.707246\pi$
$240$	2.09351	+	2.28388i	0.135135	+	0.147424i
$241$	−22.0860	−	3.89435i	−1.42268	−	0.250857i	−0.591252	−	0.806487i	$-0.701366\pi$
$241$	−22.0860	−	3.89435i	−1.42268	−	0.250857i	−0.831430	+	0.555630i	$0.812477\pi$
$242$	−11.3160	−	6.53331i	−0.727421	−	0.419977i
$243$	15.5730	−	0.693233i	0.999011	−	0.0444709i
$244$		−	8.97557i		−	0.574602i
$245$	−11.5247	−	4.89523i	−0.736285	−	0.312745i
$246$	−2.33177	−	10.5094i	−0.148668	−	0.670057i
$247$	−0.201534	−	0.0733523i	−0.0128233	−	0.00466730i
$248$	−4.12581	−	1.50167i	−0.261989	−	0.0953563i
$249$	−0.243403	−	5.55313i	−0.0154251	−	0.351915i
$250$	11.9794	+	2.11229i	0.757642	+	0.133593i
$251$	9.56297	−	16.5636i	0.603610	−	1.04548i	−0.388660	−	0.921381i	$-0.627062\pi$
$251$	9.56297	−	16.5636i	0.603610	−	1.04548i	0.992270	−	0.124101i	$-0.0396047\pi$
$252$	−4.38232	−	6.61780i	−0.276060	−	0.416882i
$253$	14.0396	+	24.3172i	0.882659	+	1.52881i
$254$	4.99739	+	13.7302i	0.313564	+	0.861510i
$255$	0.146599	+	0.353751i	0.00918040	+	0.0221528i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−1.07488	−	6.09597i	−0.0670494	−	0.380256i	−0.999805	−	0.0197468i	$-0.993714\pi$
$257$	−1.07488	−	6.09597i	−0.0670494	−	0.380256i	0.932756	−	0.360509i	$-0.117397\pi$
$258$	−15.9253	+	6.59965i	−0.991465	+	0.410876i
$259$	−6.87257	−	12.6613i	−0.427040	−	0.786738i
$260$	−0.142086	+	0.0820333i	−0.00881179	+	0.00508749i
$261$	2.83964	−	10.6122i	0.175769	−	0.656876i
$262$	−4.67010	+	2.69628i	−0.288520	+	0.166577i
$263$	2.94920	+	8.10287i	0.181856	+	0.499644i	0.996804	−	0.0798898i	$-0.0254568\pi$
$263$	2.94920	+	8.10287i	0.181856	+	0.499644i	−0.814948	+	0.579534i	$0.803235\pi$
$264$	0.372083	+	8.48890i	0.0229001	+	0.522456i
$265$	22.7785	−	4.01646i	1.39927	−	0.246729i
$266$	5.86698	−	1.96227i	0.359728	−	0.120315i
$267$	1.35776	−	4.30883i	0.0830937	−	0.263696i
$268$	1.05687	+	0.886817i	0.0645585	+	0.0541710i
$269$	9.70614	−	16.8115i	0.591794	−	1.02502i	−0.402197	−	0.915553i	$-0.631753\pi$
$269$	9.70614	−	16.8115i	0.591794	−	1.02502i	0.993991	−	0.109463i	$-0.0349133\pi$
$270$	5.66197	+	7.37102i	0.344577	+	0.448586i
$271$	−17.5323	+	10.1223i	−1.06501	+	0.614884i	−0.926814	−	0.375521i	$-0.877464\pi$
$271$	−17.5323	+	10.1223i	−1.06501	+	0.614884i	−0.138196	+	0.990405i	$0.544130\pi$
$272$	0.116142	−	0.0422722i	0.00704214	−	0.00256313i
$273$	0.392395	−	0.150649i	0.0237489	−	0.00911767i
$274$	−9.45101	+	7.93034i	−0.570957	+	0.479089i
$275$	5.67726	+	6.76589i	0.342352	+	0.407999i
$276$	4.57615	−	8.79435i	0.275452	−	0.529358i
$277$	−15.1602	+	5.51786i	−0.910888	+	0.331536i	−0.754607	−	0.656177i	$-0.772173\pi$
$277$	−15.1602	+	5.51786i	−0.910888	+	0.331536i	−0.156281	+	0.987713i	$0.549950\pi$
$278$	−8.62722			−0.517427
$279$	−11.9396	−	5.56257i	−0.714805	−	0.333022i
$280$	1.73503	−	4.40307i	0.103688	−	0.263134i
$281$	−11.4515	−	2.01920i	−0.683138	−	0.120456i	−0.178700	−	0.983904i	$-0.557189\pi$
$281$	−11.4515	−	2.01920i	−0.683138	−	0.120456i	−0.504438	+	0.863448i	$0.668300\pi$
$282$	−9.50660	+	3.93966i	−0.566110	+	0.234603i
$283$	21.5596	+	25.6937i	1.28159	+	1.52733i	0.701100	+	0.713063i	$0.252692\pi$
$283$	21.5596	+	25.6937i	1.28159	+	1.52733i	0.580485	+	0.814271i	$0.302863\pi$
$284$	9.98949	+	11.9050i	0.592767	+	0.706432i
$285$	−6.69246	+	2.77345i	−0.396427	+	0.164285i
$286$	−0.443129	−	0.0781355i	−0.0262027	−	0.00462025i
$287$	−12.8703	+	10.2350i	−0.759711	+	0.604151i
$288$	2.45687	−	1.72157i	0.144772	−	0.101444i
$289$	−16.9847			−0.999101
$290$	6.15508	−	2.24027i	0.361439	−	0.131553i
$291$	8.00615	−	15.3861i	0.469329	−	0.901948i
$292$	7.23142	+	8.61807i	0.423187	+	0.504334i
$293$	6.60266	−	5.54029i	0.385731	−	0.323667i	−0.429216	−	0.903202i	$-0.641210\pi$
$293$	6.60266	−	5.54029i	0.385731	−	0.323667i	0.814948	+	0.579535i	$0.196766\pi$
$294$	−6.15433	+	10.4463i	−0.358928	+	0.609238i
$295$	13.3654	−	4.86461i	0.778164	−	0.283228i
$296$	4.71557	−	2.72254i	0.274087	−	0.158244i
$297$	−1.09888	+	25.4675i	−0.0637637	+	1.47777i
$298$	−9.62667	+	16.6739i	−0.557658	+	0.965892i
$299$	0.402162	+	0.337454i	0.0232576	+	0.0195154i
$300$	0.937198	−	2.97418i	0.0541091	−	0.171714i
$301$	19.7197	+	17.4508i	1.13662	+	1.00585i
$302$	4.98804	−	0.879526i	0.287029	−	0.0506110i
$303$	−1.05316	−	24.0274i	−0.0605027	−	1.38034i
$304$	0.799729	+	2.19724i	0.0458676	+	0.126020i
$305$	13.9041	−	8.02752i	0.796145	−	0.459654i
$306$	0.358120	−	0.0960889i	0.0204724	−	0.00549304i
$307$	−16.6093	+	9.58941i	−0.947945	+	0.547296i	−0.892442	−	0.451162i	$-0.851010\pi$
$307$	−16.6093	+	9.58941i	−0.947945	+	0.547296i	−0.0555031	+	0.998459i	$0.517676\pi$
$308$	11.4073	−	6.19188i	0.649992	−	0.352815i
$309$	−18.9339	+	7.84647i	−1.07711	+	0.446370i
$310$	−1.36378	−	7.73436i	−0.0774573	−	0.439282i
$311$	12.1273	−	10.1760i	0.687676	−	0.577028i	−0.230562	−	0.973058i	$-0.574057\pi$
$311$	12.1273	−	10.1760i	0.687676	−	0.577028i	0.918238	+	0.396029i	$0.129612\pi$
$312$	0.0608205	+	0.146763i	0.00344328	+	0.00830881i
$313$	11.9084	+	32.7179i	0.673100	+	1.84933i	0.503939	+	0.863739i	$0.331883\pi$
$313$	11.9084	+	32.7179i	0.673100	+	1.84933i	0.169161	+	0.985588i	$0.445894\pi$
$314$	5.06288	+	8.76916i	0.285715	+	0.494872i
$315$	6.33221	−	12.7074i	0.356780	−	0.715984i
$316$	−5.19688	+	9.00125i	−0.292347	+	0.506360i
$317$	14.4470	+	2.54739i	0.811424	+	0.143076i	0.563940	−	0.825816i	$-0.309285\pi$
$317$	14.4470	+	2.54739i	0.811424	+	0.143076i	0.247484	+	0.968892i	$0.420396\pi$
$318$	−0.980745	−	22.3752i	−0.0549974	−	1.25474i
$319$	16.8808	+	6.14410i	0.945142	+	0.344003i
$320$	1.68087	+	0.611788i	0.0939637	+	0.0342000i
$321$	2.39723	+	10.8045i	0.133800	+	0.603047i
$322$	−15.1382	−	0.398244i	−0.843620	−	0.0221933i
$323$			0.288998i			0.0160803i
$324$	7.79116	−	4.50531i	0.432842	−	0.250295i
$325$	0.143010	+	0.0825666i	0.00793275	+	0.00457997i
$326$	−13.6528	−	2.40736i	−0.756161	−	0.133332i
$327$	7.41074	+	8.08463i	0.409815	+	0.447081i
$328$	−3.99504	−	4.76111i	−0.220589	−	0.262888i
$329$	11.7717	+	10.4172i	0.648994	+	0.574322i
$330$	−12.8174	+	8.16865i	−0.705574	+	0.449669i
$331$	1.36812	−	7.75899i	0.0751986	−	0.426473i	−0.923846	−	0.382765i	$-0.874972\pi$
$331$	1.36812	−	7.75899i	0.0751986	−	0.426473i	0.999044	−	0.0437076i	$-0.0139170\pi$
$332$	−1.60459	−	2.77923i	−0.0880633	−	0.152530i
$333$	14.8024	−	6.90861i	0.811166	−	0.378590i
$334$	4.61829	+	2.66637i	0.252702	+	0.145897i
$335$	−0.428535	+	2.43034i	−0.0234134	+	0.132784i
$336$	−4.00812	−	2.22148i	−0.218661	−	0.121192i
$337$	−2.90980	−	1.05908i	−0.158507	−	0.0576917i	0.261548	−	0.965190i	$-0.415767\pi$
$337$	−2.90980	−	1.05908i	−0.158507	−	0.0576917i	−0.420055	+	0.907499i	$0.637989\pi$
$338$	12.7942	−	2.25597i	0.695914	−	0.122708i
$339$	−1.17551	+	8.94065i	−0.0638449	+	0.485590i
$340$	0.169358	+	0.142109i	0.00918475	+	0.00770692i
$341$	10.7696	−	18.6536i	0.583209	−	1.01015i
$342$	1.81786	+	6.77512i	0.0982988	+	0.366356i
$343$	18.4626	+	1.45980i	0.996889	+	0.0788215i
$344$	−6.39749	+	7.62423i	−0.344929	+	0.411071i
$345$	17.7161	−	0.776529i	0.953805	−	0.0418069i
$346$	0.881763	−	2.42262i	0.0474039	−	0.130241i
$347$	3.80742	−	0.671350i	0.204393	−	0.0360400i	−0.0705143	−	0.997511i	$-0.522464\pi$
$347$	3.80742	−	0.671350i	0.204393	−	0.0360400i	0.274907	+	0.961471i	$0.411353\pi$
$348$	−1.37382	−	6.19191i	−0.0736445	−	0.331921i
$349$	−11.0905	−	30.4709i	−0.593661	−	1.63107i	−0.763655	−	0.645625i	$-0.776597\pi$
$349$	−11.0905	−	30.4709i	−0.593661	−	1.63107i	0.169994	−	0.985445i	$-0.445625\pi$
$350$	−4.71112	+	0.703497i	−0.251820	+	0.0376035i
$351$	0.143548	+	0.454467i	0.00766205	+	0.0242576i
$352$	2.45289	+	4.24852i	0.130739	+	0.226447i
$353$	2.53267	−	14.3635i	0.134800	−	0.764490i	−0.840198	−	0.542279i	$-0.817561\pi$
$353$	2.53267	−	14.3635i	0.134800	−	0.764490i	0.974999	−	0.222211i	$-0.0713274\pi$
$354$	−2.98317	−	13.4454i	−0.158554	−	0.714613i
$355$	−9.50773	+	26.1223i	−0.504618	+	1.38643i
$356$	−0.452925	−	2.56867i	−0.0240050	−	0.136139i
$357$	−0.371604	−	0.427439i	−0.0196674	−	0.0226225i
$358$	11.0173	+	9.24460i	0.582282	+	0.488592i
$359$			13.9229i			0.734820i	0.930059	+	0.367410i	$0.119755\pi$
$359$			13.9229i			0.734820i	−0.930059	+	0.367410i	$0.880245\pi$
$360$	4.86424	+	2.26622i	0.256368	+	0.119440i
$361$	13.5326			0.712241
$362$	−16.1959	+	5.89484i	−0.851240	+	0.309826i
$363$	−22.4389	−	2.95025i	−1.17774	−	0.154848i
$364$	0.160821	−	0.181731i	0.00842933	−	0.00952530i
$365$	−6.88267	+	18.9100i	−0.360256	+	0.989794i
$366$	−5.95170	−	14.3617i	−0.311100	−	0.750701i
$367$	20.4196	−	24.3351i	1.06589	−	1.27028i	0.104670	−	0.994507i	$-0.466621\pi$
$367$	20.4196	−	24.3351i	1.06589	−	1.27028i	0.961222	−	0.275775i	$-0.0889343\pi$
$368$		−	5.72369i		−	0.298368i
$369$	−10.6999	−	15.2699i	−0.557012	−	0.794919i
$370$	8.43498	+	4.86994i	0.438514	+	0.253176i
$371$	−30.0677	+	16.3207i	−1.56104	+	0.847328i
$372$	−7.59744	+	0.333009i	−0.393909	+	0.0172657i
$373$	−3.77754	+	3.16973i	−0.195593	+	0.164122i	−0.735325	−	0.677715i	$-0.762970\pi$
$373$	−3.77754	+	3.16973i	−0.195593	+	0.164122i	0.539731	+	0.841837i	$0.318526\pi$
$374$	0.105289	+	0.597121i	0.00544434	+	0.0308764i
$375$	20.5688	−	4.56366i	1.06217	−	0.235667i
$376$	−3.81898	+	4.55128i	−0.196949	+	0.234715i
$377$	0.335869			0.0172981
$378$	−11.4004	−	7.68318i	−0.586372	−	0.395180i
$379$	8.10939			0.416551			0.208276	−	0.978070i	$-0.433215\pi$
$379$	8.10939			0.416551			0.208276	+	0.978070i	$0.433215\pi$
$380$	−2.68849	+	3.20402i	−0.137917	+	0.164363i
$381$	17.1008	+	18.6559i	0.876100	+	0.955768i
$382$	−4.11288	−	23.3253i	−0.210433	−	1.19343i
$383$	−6.51296	+	5.46502i	−0.332797	+	0.279250i	−0.793838	−	0.608129i	$-0.791920\pi$
$383$	−6.51296	+	5.46502i	−0.332797	+	0.279250i	0.461041	+	0.887379i	$0.347476\pi$
$384$	0.799510	−	1.53648i	0.0407998	−	0.0784084i
$385$	19.7943	+	12.1332i	1.00881	+	0.618367i
$386$	12.1387	+	7.00826i	0.617842	+	0.356711i
$387$	−21.1057	+	21.1201i	−1.07286	+	1.07360i
$388$		−	10.0138i		−	0.508375i
$389$	2.27371	−	2.70970i	0.115282	−	0.137387i	−0.705317	−	0.708892i	$-0.749196\pi$
$389$	2.27371	−	2.70970i	0.115282	−	0.137387i	0.820599	+	0.571504i	$0.193640\pi$
$390$	−0.172954	+	0.225478i	−0.00875788	+	0.0114175i
$391$	0.241953	−	0.664760i	0.0122361	−	0.0336184i
$392$	−0.368046	+	6.99032i	−0.0185891	+	0.353064i
$393$	−5.68469	+	7.41104i	−0.286754	+	0.373838i
$394$	−3.70429	+	1.34825i	−0.186619	+	0.0679238i
$395$	−18.5918			−0.935456
$396$	6.22436	+	13.3363i	0.312786	+	0.670174i
$397$			9.87407i			0.495565i	0.968816	+	0.247783i	$0.0797019\pi$
$397$			9.87407i			0.495565i	−0.968816	+	0.247783i	$0.920298\pi$
$398$	−3.76176	−	3.15650i	−0.188560	−	0.158221i
$399$	8.08653	−	7.03021i	0.404833	−	0.351951i
$400$	−0.312632	−	1.77303i	−0.0156316	−	0.0886513i
$401$	3.32384	−	9.13217i	0.165985	−	0.456039i	−0.828616	−	0.559818i	$-0.810871\pi$
$401$	3.32384	−	9.13217i	0.165985	−	0.456039i	0.994600	+	0.103779i	$0.0330934\pi$
$402$	2.27914	+	0.718182i	0.113673	+	0.0358196i
$403$	0.0699302	−	0.396594i	0.00348347	−	0.0197557i
$404$	−6.94279	−	12.0253i	−0.345417	−	0.598279i
$405$	13.9474	+	8.03986i	0.693052	+	0.399504i
$406$	−7.58288	+	6.03019i	−0.376332	+	0.299274i
$407$	9.13615	+	25.1014i	0.452862	+	1.24423i
$408$	0.157807	−	0.144653i	0.00781263	−	0.00716140i
$409$	10.7521	−	1.89588i	0.531655	−	0.0937451i	0.0986250	−	0.995125i	$-0.468556\pi$
$409$	10.7521	−	1.89588i	0.531655	−	0.0937451i	0.433030	+	0.901380i	$0.357444\pi$
$410$	3.80237	−	10.4469i	0.187786	−	0.515938i
$411$	−9.86389	+	18.9563i	−0.486550	+	0.935043i
$412$	−7.60612	+	9.06462i	−0.374726	+	0.446582i
$413$	−16.4658	+	13.0942i	−0.810228	+	0.644324i
$414$	1.49072	−	17.1062i	0.0732651	−	0.840725i
$415$	2.87021	−	4.97135i	0.140893	−	0.244034i
$416$	0.0702627	+	0.0589574i	0.00344491	+	0.00289062i
$417$	−13.8044	+	5.72071i	−0.676003	+	0.280144i
$418$	−11.2967	+	1.99191i	−0.552538	+	0.0974274i
$419$	−17.3011	−	6.29707i	−0.845212	−	0.307632i	−0.117125	−	0.993117i	$-0.537368\pi$
$419$	−17.3011	−	6.29707i	−0.845212	−	0.307632i	−0.728087	+	0.685485i	$0.759590\pi$
$420$	−0.143463	−	8.19582i	−0.00700026	−	0.399915i
$421$	5.03832	−	28.5737i	0.245553	−	1.39260i	−0.573653	−	0.819099i	$-0.694474\pi$
$421$	5.03832	−	28.5737i	0.245553	−	1.39260i	0.819206	−	0.573500i	$-0.194415\pi$
$422$	−11.4274	−	6.59759i	−0.556275	−	0.321166i
$423$	−12.5991	+	12.6077i	−0.612587	+	0.613005i
$424$	−6.46537	−	11.1984i	−0.313986	−	0.543840i
$425$	0.0386400	−	0.219138i	0.00187432	−	0.0106298i
$426$	23.8783	+	12.4251i	1.15691	+	0.601998i
$427$	−15.7375	+	17.7836i	−0.761590	+	0.860610i
$428$	4.10720	+	4.89477i	0.198529	+	0.236597i
$429$	−0.760859	+	0.168814i	−0.0367346	+	0.00815044i
$430$	−17.5324	−	3.09144i	−0.845490	−	0.149083i
$431$	34.3324	+	19.8218i	1.65373	+	0.954782i	0.975519	+	0.219917i	$0.0705787\pi$
$431$	34.3324	+	19.8218i	1.65373	+	0.954782i	0.678213	+	0.734865i	$0.262755\pi$
$432$	2.78965	−	4.38382i	0.134217	−	0.210917i
$433$			16.6647i			0.800855i	0.916328	+	0.400428i	$0.131138\pi$
$433$			16.6647i			0.800855i	−0.916328	+	0.400428i	$0.868862\pi$
$434$	5.54164	+	10.2094i	0.266007	+	0.490066i
$435$	8.36319	−	7.66607i	0.400984	−	0.367560i
$436$	5.95008	+	2.16565i	0.284957	+	0.103716i
$437$	12.5763	+	4.57740i	0.601606	+	0.218967i
$438$	17.2856	+	8.99456i	0.825937	+	0.429777i
$439$	−9.55013	−	1.68395i	−0.455803	−	0.0803704i	−0.0589671	−	0.998260i	$-0.518781\pi$
$439$	−9.55013	−	1.68395i	−0.455803	−	0.0803704i	−0.396836	+	0.917890i	$0.629892\pi$
$440$	−4.38760	+	7.59954i	−0.209171	+	0.362294i
$441$	−2.92059	+	20.7959i	−0.139075	+	0.990282i
$442$	0.00566819	+	0.00981759i	0.000269608	+	0.000466975i
$443$	11.0476	+	30.3530i	0.524887	+	1.44211i	0.865020	+	0.501737i	$0.167306\pi$
$443$	11.0476	+	30.3530i	0.524887	+	1.44211i	−0.340133	+	0.940377i	$0.610472\pi$
$444$	5.74004	−	7.48321i	0.272410	−	0.355137i
$445$	3.57404	−	2.99898i	0.169426	−	0.142165i
$446$	0.603891	+	3.42484i	0.0285951	+	0.162171i
$447$	−4.34712	+	33.0632i	−0.205612	+	1.56384i
$448$	−2.64484	−	0.0695782i	−0.124957	−	0.00328726i
$449$	26.9462	−	15.5574i	1.27167	−	0.734198i	0.296366	−	0.955074i	$-0.404225\pi$
$449$	26.9462	−	15.5574i	1.27167	−	0.734198i	0.975302	+	0.220877i	$0.0708918\pi$
$450$	−0.472574	−	5.38042i	−0.0222774	−	0.253635i
$451$	26.4054	−	15.2451i	1.24338	−	0.717866i
$452$	1.78066	+	4.89233i	0.0837554	+	0.230116i
$453$	7.39811	−	4.71489i	0.347594	−	0.221525i
$454$	−19.4269	+	3.42549i	−0.911750	+	0.160766i
$455$	0.425355	+	0.0865931i	0.0199409	+	0.00405954i
$456$	2.73663	+	2.98549i	0.128154	+	0.139808i
$457$	−10.9750	−	9.20912i	−0.513389	−	0.430784i	0.348931	−	0.937148i	$-0.386545\pi$
$457$	−10.9750	−	9.20912i	−0.513389	−	0.430784i	−0.862320	+	0.506364i	$0.830989\pi$
$458$	−12.7768	+	22.1301i	−0.597022	+	1.03407i
$459$	0.509309	−	0.391221i	0.0237725	−	0.0182606i
$460$	8.86657	−	5.11912i	0.413406	−	0.238680i
$461$	37.4784	−	13.6410i	1.74554	−	0.635326i	0.746012	−	0.665933i	$-0.231966\pi$
$461$	37.4784	−	13.6410i	1.74554	−	0.635326i	0.999531	+	0.0306073i	$0.00974414\pi$
$462$	14.1469	−	17.4718i	0.658175	−	0.812861i
$463$	28.0855	−	23.5666i	1.30525	−	1.09523i	0.316032	−	0.948748i	$-0.397649\pi$
$463$	28.0855	−	23.5666i	1.30525	−	1.09523i	0.989213	−	0.146483i	$-0.0467952\pi$
$464$	−2.35378	−	2.80513i	−0.109272	−	0.130225i
$465$	−7.31082	−	11.4714i	−0.339031	−	0.531973i
$466$	−6.34743	+	2.31028i	−0.294039	+	0.107021i
$467$	−6.76549			−0.313070			−0.156535	−	0.987672i	$-0.550032\pi$
$467$	−6.76549			−0.313070			−0.156535	+	0.987672i	$0.550032\pi$
$468$	0.194637	+	0.194504i	0.00899709	+	0.00899096i
$469$	−0.539095	−	3.61016i	−0.0248931	−	0.166702i
$470$	−10.4660	−	1.84544i	−0.482761	−	0.0851237i
$471$	13.9159	+	10.6743i	0.641211	+	0.491845i
$472$	−5.11110	−	6.09117i	−0.235257	−	0.280369i
$473$	−31.3846	−	37.4027i	−1.44307	−	1.71978i
$474$	−2.34676	+	17.8489i	−0.107790	+	0.819827i
$475$	4.14578	+	0.731013i	0.190222	+	0.0335412i
$476$	−0.304235	−	0.119884i	−0.0139446	−	0.00549488i
$477$	−16.4063	−	35.1521i	−0.751193	−	1.60950i
$478$	6.79524			0.310807
$479$	−19.3648	+	7.04821i	−0.884800	+	0.322041i	−0.744145	−	0.668018i	$-0.767143\pi$
$479$	−19.3648	+	7.04821i	−0.884800	+	0.322041i	−0.140655	+	0.990059i	$0.544921\pi$
$480$	3.09523	−	0.135669i	0.141277	−	0.00619243i
$481$	0.321027	+	0.382586i	0.0146376	+	0.0174444i
$482$	−17.1798	+	14.4156i	−0.782519	+	0.656612i
$483$	−24.4866	+	9.40092i	−1.11418	+	0.427757i
$484$	−12.2786	+	4.46905i	−0.558118	+	0.203138i
$485$	15.5124	−	8.95610i	0.704383	−	0.406676i
$486$	9.47911	−	12.3752i	0.429981	−	0.561352i
$487$	2.75969	−	4.77993i	0.125054	−	0.216599i	−0.796700	−	0.604375i	$-0.793423\pi$
$487$	2.75969	−	4.77993i	0.125054	−	0.216599i	0.921754	+	0.387775i	$0.126756\pi$
$488$	−6.87568	−	5.76938i	−0.311248	−	0.261168i
$489$	−23.4421	+	5.20119i	−1.06009	+	0.235206i
$490$	−11.1579	+	5.68182i	−0.504062	+	0.256678i
$491$	−32.6357	+	5.75455i	−1.47283	+	0.259699i	−0.851708	−	0.524017i	$-0.824433\pi$
$491$	−32.6357	+	5.75455i	−1.47283	+	0.259699i	−0.621119	+	0.783716i	$0.713322\pi$
$492$	−9.54953	−	4.96910i	−0.430526	−	0.224024i
$493$	−0.154794	−	0.425293i	−0.00697157	−	0.0191542i
$494$	−0.185735	+	0.107234i	−0.00835659	+	0.00482468i
$495$	−15.0924	+	21.5698i	−0.678352	+	0.969491i
$496$	−3.80237	+	2.19530i	−0.170731	+	0.0985718i
$497$	1.08131	−	41.1031i	0.0485033	−	1.84373i
$498$	−4.41040	−	3.38303i	−0.197635	−	0.151597i
$499$	4.88923	+	27.7282i	0.218872	+	1.24128i	0.874060	+	0.485818i	$0.161478\pi$
$499$	4.88923	+	27.7282i	0.218872	+	1.24128i	−0.655188	+	0.755466i	$0.727411\pi$
$500$	9.31829	−	7.81898i	0.416727	−	0.349675i
$501$	9.15777	+	1.20405i	0.409139	+	0.0537932i
$502$	−6.54146	−	17.9725i	−0.291960	−	0.802152i
$503$	9.78177	+	16.9425i	0.436147	+	0.755430i	0.997389	−	0.0722228i	$-0.0230093\pi$
$503$	9.78177	+	16.9425i	0.436147	+	0.755430i	−0.561241	+	0.827652i	$0.689676\pi$
$504$	−7.88643	−	0.896790i	−0.351289	−	0.0399462i
$505$	12.4189	−	21.5102i	0.552634	−	0.957190i
$506$	27.6525	+	4.87589i	1.22930	+	0.216760i
$507$	18.9760	−	12.0936i	0.842754	−	0.537096i
$508$	13.7302	+	4.99739i	0.609180	+	0.221723i
$509$	28.4987	+	10.3727i	1.26318	+	0.459761i	0.884836	−	0.465903i	$-0.154271\pi$
$509$	28.4987	+	10.3727i	1.26318	+	0.459761i	0.378346	+	0.925664i	$0.376493\pi$
$510$	0.365221	+	0.115085i	0.0161723	+	0.00509607i
$511$	0.782761	−	29.7546i	0.0346273	−	1.31627i
$512$		−	1.00000i		−	0.0441942i
$513$	7.40133	+	9.63539i	0.326777	+	0.425413i
$514$	−5.36071	−	3.09501i	−0.236451	−	0.136515i
$515$	−20.8447	−	3.67549i	−0.918528	−	0.161961i
$516$	−5.18095	+	16.4416i	−0.228079	+	0.723803i
$517$	−18.7351	−	22.3276i	−0.823967	−	0.981965i
$518$	−14.1168	−	2.87387i	−0.620255	−	0.126271i
$519$	−0.195539	−	4.46112i	−0.00858320	−	0.195821i
$520$	−0.0284899	+	0.161574i	−0.00124936	+	0.00708549i
$521$	11.7195	+	20.2988i	0.513441	+	0.889306i	0.999878	+	0.0155903i	$0.00496276\pi$
$521$	11.7195	+	20.2988i	0.513441	+	0.889306i	−0.486438	+	0.873715i	$0.661704\pi$
$522$	−6.30410	−	8.99665i	−0.275923	−	0.393773i
$523$	−30.8053	−	17.7855i	−1.34702	−	0.777705i	−0.359197	−	0.933262i	$-0.616949\pi$
$523$	−30.8053	−	17.7855i	−1.34702	−	0.777705i	−0.987827	+	0.155557i	$0.950283\pi$
$524$	−0.936409	+	5.31064i	−0.0409072	+	0.231996i
$525$	−7.07174	+	4.24960i	−0.308636	+	0.185468i
$526$	8.10287	+	2.94920i	0.353302	+	0.128591i
$527$	−0.534415	+	0.0942318i	−0.0232795	+	0.00410480i
$528$	6.74204	+	5.17153i	0.293410	+	0.225062i
$529$	−7.47705	−	6.27399i	−0.325089	−	0.272782i
$530$	11.5649	−	20.0310i	0.502348	−	0.870093i
$531$	−13.6890	−	19.5357i	−0.594051	−	0.847777i
$532$	2.26803	−	5.75569i	0.0983317	−	0.249541i
$533$	0.366431	−	0.436695i	0.0158719	−	0.0189154i
$534$	−2.42801	−	3.80977i	−0.105070	−	0.164865i
$535$	−3.90912	+	10.7402i	−0.169006	+	0.464340i
$536$	1.35868	−	0.239572i	0.0586862	−	0.0103480i
$537$	23.7588	+	7.48666i	1.02527	+	0.323073i
$538$	−6.63939	−	18.2416i	−0.286244	−	0.786450i
$539$	−33.4584	−	7.73302i	−1.44116	−	0.333085i
$540$	9.28597	+	0.400676i	0.399605	+	0.0172424i
$541$	−6.25290	−	10.8303i	−0.268833	−	0.465633i	0.699728	−	0.714410i	$-0.253305\pi$
$541$	−6.25290	−	10.8303i	−0.268833	−	0.465633i	−0.968561	+	0.248777i	$0.919971\pi$
$542$	−3.51543	+	19.9370i	−0.151000	+	0.856366i
$543$	−22.0061	+	20.1718i	−0.944374	+	0.865656i
$544$	0.0422722	−	0.116142i	0.00181241	−	0.00497955i
$545$	1.96678	+	11.1542i	0.0842477	+	0.477792i
$546$	0.136823	−	0.397427i	0.00585550	−	0.0170083i
$547$	10.1999	+	8.55869i	0.436114	+	0.365943i	0.834253	−	0.551382i	$-0.185899\pi$
$547$	10.1999	+	8.55869i	0.436114	+	0.365943i	−0.398139	+	0.917325i	$0.630344\pi$
$548$			12.3374i			0.527028i
$549$	−19.0465	−	19.0336i	−0.812887	−	0.812333i
$550$	8.83225			0.376608
$551$	8.04593	−	2.92848i	0.342768	−	0.124757i
$552$	−3.79538	−	9.15843i	−0.161542	−	0.389809i
$553$	26.0793	−	8.72249i	1.10900	−	0.370918i
$554$	−5.51786	+	15.1602i	−0.234431	+	0.644095i
$555$	16.7260	+	2.19912i	0.709979	+	0.0933474i
$556$	−5.54547	+	6.60884i	−0.235180	+	0.280277i
$557$		−	18.8804i		−	0.799987i	−0.916518	−	0.399993i	$-0.869012\pi$
$557$		−	18.8804i		−	0.799987i	0.916518	−	0.399993i	$-0.130988\pi$
$558$	−11.9358	+	5.57071i	−0.505283	+	0.235827i
$559$	−0.790575	−	0.456439i	−0.0334378	−	0.0193053i
$560$	−2.25769	−	4.15935i	−0.0954048	−	0.175765i
$561$	0.564422	+	0.885633i	0.0238299	+	0.0373914i
$562$	−8.90767	+	7.47442i	−0.375747	+	0.315289i
$563$	−6.34007	−	35.9563i	−0.267202	−	1.51538i	−0.762690	−	0.646764i	$-0.776122\pi$
$563$	−6.34007	−	35.9563i	−0.267202	−	1.51538i	0.495488	−	0.868615i	$-0.334989\pi$
$564$	−3.09277	+	9.81485i	−0.130229	+	0.413280i
$565$	−5.98614	+	7.13401i	−0.251839	+	0.300130i
$566$	33.5408			1.40982
$567$	−23.3364	−	4.73422i	−0.980036	−	0.198818i
$568$	15.5409			0.652081
$569$	−20.4837	+	24.4115i	−0.858720	+	1.02338i	0.140724	+	0.990049i	$0.455057\pi$
$569$	−20.4837	+	24.4115i	−0.858720	+	1.02338i	−0.999444	+	0.0333343i	$0.989387\pi$
$570$	−2.17725	+	6.90946i	−0.0911950	+	0.289405i
$571$	−6.36827	−	36.1163i	−0.266504	−	1.51142i	−0.764718	−	0.644365i	$-0.777122\pi$
$571$	−6.36827	−	36.1163i	−0.266504	−	1.51142i	0.498214	−	0.867054i	$-0.333989\pi$
$572$	−0.344693	+	0.289232i	−0.0144123	+	0.0120934i
$573$	−22.0480	−	34.5954i	−0.921068	−	1.44524i
$574$	−0.432441	+	16.4381i	−0.0180498	+	0.686115i
$575$	−8.92422	−	5.15240i	−0.372166	−	0.214870i
$576$	0.260448	−	2.98867i	0.0108520	−	0.124528i
$577$		−	22.5847i		−	0.940212i	−0.882610	−	0.470106i	$-0.844216\pi$
$577$		−	22.5847i		−	0.940212i	0.882610	−	0.470106i	$-0.155784\pi$
$578$	−10.9176	+	13.0111i	−0.454111	+	0.541188i
$579$	24.0702	+	3.16472i	1.00032	+	0.131521i
$580$	2.24027	−	6.15508i	0.0930221	−	0.255576i
$581$	−1.69378	+	8.32003i	−0.0702698	+	0.345173i
$582$	−6.64016	−	16.0230i	−0.275244	−	0.664177i
$583$	59.6097	−	21.6962i	2.46878	−	0.898563i
$584$	11.2501			0.465532
$585$	−0.127229	+	0.475472i	−0.00526025	+	0.0196583i
$586$		−	8.61916i		−	0.356054i
$587$	−5.09594	−	4.27600i	−0.210332	−	0.176490i	0.531535	−	0.847036i	$-0.321615\pi$
$587$	−5.09594	−	4.27600i	−0.210332	−	0.176490i	−0.741868	+	0.670546i	$0.766060\pi$
$588$	4.04637	+	11.4292i	0.166870	+	0.471333i
$589$	−1.78273	−	10.1104i	−0.0734561	−	0.416590i
$590$	4.86461	−	13.3654i	0.200273	−	0.550245i
$591$	−5.03318	+	4.61364i	−0.207037	+	0.189780i
$592$	0.945527	−	5.36235i	0.0388609	−	0.220391i
$593$	−5.97092	−	10.3419i	−0.245196	−	0.424692i	0.716990	−	0.697083i	$-0.245519\pi$
$593$	−5.97092	−	10.3419i	−0.245196	−	0.424692i	−0.962187	+	0.272391i	$0.912186\pi$
$594$	18.8029	+	17.2120i	0.771490	+	0.706215i
$595$	−0.0863876	−	0.578513i	−0.00354155	−	0.0237167i
$596$	6.58503	+	18.0922i	0.269733	+	0.741086i
$597$	−8.11225	−	2.55626i	−0.332012	−	0.104621i
$598$	0.517009	−	0.0911626i	0.0211421	−	0.00372792i
$599$	3.53812	−	9.72091i	0.144564	−	0.397186i	−0.846186	−	0.532888i	$-0.821107\pi$
$599$	3.53812	−	9.72091i	0.144564	−	0.397186i	0.990750	+	0.135702i	$0.0433290\pi$
$600$	−1.67593	−	2.62970i	−0.0684197	−	0.107357i
$601$	−2.73888	+	3.26407i	−0.111721	+	0.133144i	−0.819007	−	0.573784i	$-0.805475\pi$
$601$	−2.73888	+	3.26407i	−0.111721	+	0.133144i	0.707286	+	0.706928i	$0.249919\pi$
$602$	26.0437	−	3.88902i	1.06146	−	0.158505i
$603$	4.12306	−	0.362137i	0.167904	−	0.0147474i
$604$	2.53249	−	4.38641i	0.103046	−	0.178480i
$605$	−17.9047	−	15.0238i	−0.727928	−	0.610805i
$606$	−19.0831	−	14.6378i	−0.775196	−	0.594619i
$607$	−31.2660	+	5.51304i	−1.26905	+	0.223767i	−0.767323	−	0.641260i	$-0.778412\pi$
$607$	−31.2660	+	5.51304i	−1.26905	+	0.223767i	−0.501724	+	0.865028i	$0.667301\pi$
$608$	2.19724	+	0.799729i	0.0891098	+	0.0324333i
$609$	−8.13469	+	14.6771i	−0.329634	+	0.594745i
$610$	2.78793	−	15.8111i	0.112880	−	0.640174i
$611$	−0.471934	−	0.272471i	−0.0190924	−	0.0110230i
$612$	0.156587	−	0.336101i	0.00632965	−	0.0135861i
$613$	−5.67779	−	9.83422i	−0.229324	−	0.397201i	0.728284	−	0.685275i	$-0.240318\pi$
$613$	−5.67779	−	9.83422i	−0.229324	−	0.397201i	−0.957608	+	0.288075i	$0.906985\pi$
$614$	−3.33037	+	18.8874i	−0.134403	+	0.762235i
$615$	−0.843210	−	19.2374i	−0.0340015	−	0.775728i
$616$	2.58923	−	12.7186i	0.104323	−	0.512446i
$617$	−18.3278	−	21.8422i	−0.737848	−	0.879333i	0.258386	−	0.966042i	$-0.416809\pi$
$617$	−18.3278	−	21.8422i	−0.737848	−	0.879333i	−0.996234	+	0.0867092i	$0.972365\pi$
$618$	−6.15975	+	19.5478i	−0.247781	+	0.786330i
$619$	−30.2790	−	5.33900i	−1.21701	−	0.214593i	−0.471975	−	0.881612i	$-0.656459\pi$
$619$	−30.2790	−	5.33900i	−1.21701	−	0.214593i	−0.745040	+	0.667020i	$0.767570\pi$
$620$	−6.80148	−	3.92684i	−0.273154	−	0.157706i
$621$	−8.95784	−	28.3601i	−0.359466	−	1.13805i
$622$		−	15.8311i		−	0.634768i
$623$	−3.60642	+	5.88354i	−0.144488	+	0.235719i
$624$	0.151521	+	0.0477461i	0.00606571	+	0.00191138i
$625$	11.9874	+	4.36306i	0.479497	+	0.174523i
$626$	32.7179	+	11.9084i	1.30767	+	0.475954i
$627$	−16.7549	+	10.6781i	−0.669126	+	0.426441i
$628$	9.97192	+	1.75832i	0.397923	+	0.0701646i
$629$	0.336494	−	0.582825i	0.0134169	−	0.0232387i
$630$	−5.66420	−	13.0189i	−0.225667	−	0.518687i
$631$	−11.9369	−	20.6753i	−0.475200	−	0.823071i	0.524396	−	0.851474i	$-0.324291\pi$
$631$	−11.9369	−	20.6753i	−0.475200	−	0.823071i	−0.999597	+	0.0284036i	$0.990958\pi$
$632$	3.55487	+	9.76693i	0.141405	+	0.388508i
$633$	−22.6597	−	2.97928i	−0.900642	−	0.118416i
$634$	11.2378	−	9.42960i	0.446309	−	0.374497i
$635$	4.53849	+	25.7390i	0.180104	+	1.02142i
$636$	−17.7708	−	13.6312i	−0.704659	−	0.540513i
$637$	−0.637283	+	0.0780917i	−0.0252501	+	0.00309411i
$638$	15.5574	−	8.98207i	0.615923	−	0.355604i
$639$	46.4466	+	4.04760i	1.83740	+	0.160120i
$640$	1.54910	−	0.894374i	0.0612336	−	0.0353532i
$641$	−2.04961	−	5.63125i	−0.0809547	−	0.222421i	0.892611	−	0.450827i	$-0.148871\pi$
$641$	−2.04961	−	5.63125i	−0.0809547	−	0.222421i	−0.973566	+	0.228406i	$0.926649\pi$
$642$	9.81762	+	5.10860i	0.387470	+	0.201620i
$643$	39.7221	−	7.00408i	1.56649	−	0.276214i	0.677981	−	0.735079i	$-0.262855\pi$
$643$	39.7221	−	7.00408i	1.56649	−	0.276214i	0.888506	+	0.458865i	$0.151744\pi$
$644$	−10.0357	+	11.3406i	−0.395463	+	0.446881i
$645$	−30.1035	+	6.67917i	−1.18532	+	0.262992i
$646$	0.221385	+	0.185764i	0.00871029	+	0.00730880i
$647$	−6.87094	+	11.9008i	−0.270124	+	0.467869i	−0.968894	−	0.247478i	$-0.920398\pi$
$647$	−6.87094	+	11.9008i	−0.270124	+	0.467869i	0.698769	+	0.715347i	$0.253732\pi$
$648$	1.55679	−	8.86433i	0.0611565	−	0.348224i
$649$	33.7820	−	19.5040i	1.32606	−	0.765600i
$650$	0.155175	−	0.0564789i	0.00608644	−	0.00221528i
$651$	15.6370	+	12.6613i	0.612862	+	0.496236i
$652$	−10.6200	+	8.91126i	−0.415912	+	0.348992i
$653$	−5.50558	−	6.56129i	−0.215450	−	0.256763i	0.647485	−	0.762078i	$-0.275821\pi$
$653$	−5.50558	−	6.56129i	−0.215450	−	0.256763i	−0.862935	+	0.505315i	$0.831376\pi$
$654$	10.9567	−	0.480252i	0.428442	−	0.0187793i
$655$	−9.06422	+	3.29911i	−0.354168	+	0.128907i
$656$	−6.21518			−0.242662
$657$	33.6228	+	2.93007i	1.31175	+	0.114313i
$658$	15.5468	−	2.32155i	0.606076	−	0.0905036i
$659$	43.5501	+	7.67907i	1.69647	+	0.299134i	0.936460	−	0.350774i	$-0.114082\pi$
$659$	43.5501	+	7.67907i	1.69647	+	0.299134i	0.760013	+	0.649908i	$0.225193\pi$
$660$	−1.98131	+	15.0694i	−0.0771224	+	0.586575i
$661$	25.6444	+	30.5618i	0.997452	+	1.18872i	0.982009	+	0.188837i	$0.0604717\pi$
$661$	25.6444	+	30.5618i	0.997452	+	1.18872i	0.0154438	+	0.999881i	$0.495084\pi$
$662$	−5.06432	−	6.03542i	−0.196830	−	0.234573i
$663$	0.0155797	+	0.0119505i	0.000605064	+	0.000464118i
$664$	−3.16043	−	0.557268i	−0.122648	−	0.0216262i
$665$	10.9446	−	1.63433i	0.424414	−	0.0633766i
$666$	4.22249	−	15.7801i	0.163618	−	0.611465i
$667$	−20.9592			−0.811544
$668$	5.01114	−	1.82391i	0.193887	−	0.0705690i
$669$	3.23729	+	5.07962i	0.125161	+	0.196389i
$670$	1.58629	+	1.89047i	0.0612839	+	0.0730353i
$671$	33.7306	−	28.3033i	1.30215	−	1.09264i
$672$	−4.27812	+	1.64246i	−0.165032	+	0.0633592i
$673$	−17.5753	+	6.39687i	−0.677477	+	0.246581i	−0.657764	−	0.753224i	$-0.728497\pi$
$673$	−17.5753	+	6.39687i	−0.677477	+	0.246581i	−0.0197130	+	0.999806i	$0.506275\pi$
$674$	−2.68168	+	1.54827i	−0.103295	+	0.0596372i
$675$	−4.32392	−	8.29581i	−0.166428	−	0.319306i
$676$	6.49579	−	11.2510i	0.249838	−	0.432732i
$677$	13.0184	+	10.9237i	0.500337	+	0.419833i	0.857714	−	0.514128i	$-0.171884\pi$
$677$	13.0184	+	10.9237i	0.500337	+	0.419833i	−0.357376	+	0.933960i	$0.616329\pi$
$678$	6.09334	+	6.64743i	0.234013	+	0.255293i
$679$	−17.5579	+	19.8408i	−0.673811	+	0.761419i
$680$	0.217723	−	0.0383904i	0.00834929	−	0.00147221i
$681$	−28.8134	+	18.3631i	−1.10413	+	0.703675i
$682$	−7.36687	−	20.2403i	−0.282092	−	0.775041i
$683$	9.00061	−	5.19650i	0.344399	−	0.198839i	−0.317817	−	0.948152i	$-0.602950\pi$
$683$	9.00061	−	5.19650i	0.344399	−	0.198839i	0.662216	+	0.749313i	$0.269616\pi$
$684$	6.35854	+	2.96240i	0.243125	+	0.113270i
$685$	−19.1119	+	11.0343i	−0.730229	+	0.421598i
$686$	12.9858	−	13.2049i	0.495801	−	0.504164i
$687$	−5.76964	+	43.8826i	−0.220125	+	1.67422i
$688$	1.72827	+	9.80152i	0.0658897	+	0.373679i
$689$	0.908549	−	0.762363i	0.0346130	−	0.0290437i
$690$	10.7929	−	14.0705i	0.410877	−	0.535654i
$691$	−4.64621	−	12.7654i	−0.176750	−	0.485617i	0.819406	−	0.573214i	$-0.194304\pi$
$691$	−4.64621	−	12.7654i	−0.176750	−	0.485617i	−0.996156	+	0.0875966i	$0.972081\pi$
$692$	−1.28905	−	2.23270i	−0.0490024	−	0.0848746i
$693$	11.0509	−	37.3373i	0.419789	−	1.41833i
$694$	1.93308	−	3.34818i	0.0733785	−	0.127095i
$695$	−15.1975	−	2.67973i	−0.576474	−	0.101648i
$696$	−5.62635	−	2.92768i	−0.213266	−	0.110973i
$697$	−0.721844	−	0.262730i	−0.0273418	−	0.00995159i
$698$	−30.4709	−	11.0905i	−1.15334	−	0.419782i
$699$	−8.62454	+	7.90564i	−0.326210	+	0.299019i
$700$	−2.48934	+	4.06112i	−0.0940881	+	0.153496i
$701$			35.0801i			1.32496i	0.749081	+	0.662479i	$0.230496\pi$
$701$			35.0801i			1.32496i	−0.749081	+	0.662479i	$0.769504\pi$
$702$	0.440413	+	0.182161i	0.0166223	+	0.00687523i
$703$	11.0262	+	6.36598i	0.415861	+	0.240097i
$704$	4.83124	+	0.851879i	0.182084	+	0.0321064i
$705$	−17.9703	+	3.98713i	−0.676800	+	0.150164i
$706$	−9.37509	−	11.1728i	−0.352836	−	0.420494i
$707$	−7.32870	+	35.9994i	−0.275624	+	1.35390i
$708$	−12.2173	−	6.35727i	−0.459154	−	0.238921i
$709$	−3.89535	+	22.0917i	−0.146293	+	0.829669i	0.820027	+	0.572325i	$0.193959\pi$
$709$	−3.89535	+	22.0917i	−0.146293	+	0.829669i	−0.966320	+	0.257344i	$0.917153\pi$
$710$	13.8994	+	24.0744i	0.521634	+	0.903497i
$711$	8.08057	+	30.1160i	0.303045	+	1.12944i
$712$	−2.25885	−	1.30415i	−0.0846539	−	0.0488749i
$713$	−4.36385	+	24.7486i	−0.163427	+	0.926843i
$714$	−0.566300	+	0.00991272i	−0.0211932	+	0.000370974i
$715$	−0.756334	−	0.275283i	−0.0282853	−	0.0102950i
$716$	14.1636	−	2.49742i	0.529317	−	0.0933328i
$717$	10.8730	−	4.50592i	0.406060	−	0.168277i
$718$	10.6655	+	8.94944i	0.398034	+	0.333990i
$719$	−19.8787	+	34.4310i	−0.741351	+	1.28406i	0.210529	+	0.977588i	$0.432481\pi$
$719$	−19.8787	+	34.4310i	−0.741351	+	1.28406i	−0.951880	+	0.306470i	$0.900852\pi$
$720$	4.86270	−	2.26953i	0.181222	−	0.0845804i
$721$	30.9639	−	4.62375i	1.15316	−	0.172197i
$722$	8.69857	−	10.3666i	0.323727	−	0.385803i
$723$	−17.9303	+	34.4582i	−0.666837	+	1.28151i
$724$	−5.89484	+	16.1959i	−0.219080	+	0.601917i
$725$	−6.49253	+	1.14481i	−0.241127	+	0.0425171i
$726$	−16.6835	+	15.2928i	−0.619182	+	0.567570i
$727$	4.79149	+	13.1645i	0.177707	+	0.488245i	0.996282	−	0.0861544i	$-0.0274578\pi$
$727$	4.79149	+	13.1645i	0.177707	+	0.488245i	−0.818575	+	0.574399i	$0.805236\pi$
$728$	−0.0358401	−	0.240011i	−0.00132832	−	0.00889540i
$729$	6.96144	−	26.0871i	0.257831	−	0.966190i
$730$	10.0618	+	17.4275i	0.372404	+	0.645022i
$731$	−0.213607	+	1.21143i	−0.00790054	+	0.0448062i
$732$	−14.8274	−	4.67229i	−0.548037	−	0.172693i
$733$	−2.34325	+	6.43802i	−0.0865498	+	0.237794i	−0.975415	−	0.220375i	$-0.929272\pi$
$733$	−2.34325	+	6.43802i	−0.0865498	+	0.237794i	0.888866	+	0.458168i	$0.151494\pi$
$734$	−5.51632	−	31.2846i	−0.203611	−	1.15474i
$735$	−14.0860	+	16.4902i	−0.519571	+	0.608251i
$736$	−4.38460	−	3.67911i	−0.161618	−	0.135614i
$737$			6.76822i			0.249310i
$738$	−18.5751	−	1.61873i	−0.683761	−	0.0595864i
$739$	−20.0040			−0.735858			−0.367929	−	0.929854i	$-0.619933\pi$
$739$	−20.0040			−0.735858			−0.367929	+	0.929854i	$0.619933\pi$
$740$	9.15249	−	3.33123i	0.336452	−	0.122459i
$741$	−0.226086	+	0.294745i	−0.00830547	+	0.0108277i
$742$	−6.82475	+	33.5239i	−0.250544	+	1.23070i
$743$	3.16394	−	8.69287i	0.116074	−	0.318910i	−0.868028	−	0.496515i	$-0.834613\pi$
$743$	3.16394	−	8.69287i	0.116074	−	0.318910i	0.984102	+	0.177605i	$0.0568349\pi$
$744$	−4.62844	+	6.03403i	−0.169687	+	0.221218i
$745$	−22.1372	+	26.3821i	−0.811044	+	0.966565i
$746$			4.93123i			0.180545i
$747$	−9.30034	−	2.48862i	−0.340282	−	0.0910538i
$748$	0.525099	+	0.303166i	0.0191995	+	0.0110849i
$749$	0.444581	−	16.8996i	0.0162447	−	0.617499i
$750$	9.72538	−	18.6901i	0.355120	−	0.682464i
$751$	−21.6506	+	18.1670i	−0.790043	+	0.662925i	−0.945756	−	0.324877i	$-0.894677\pi$
$751$	−21.6506	+	18.1670i	−0.790043	+	0.662925i	0.155713	+	0.987802i	$0.450233\pi$
$752$	1.03169	+	5.85102i	0.0376220	+	0.213365i
$753$	−22.3845	−	24.4201i	−0.815737	−	0.889916i
$754$	0.215892	−	0.257290i	0.00786233	−	0.00936997i
$755$	9.05999			0.329727
$756$	−13.2137	+	3.79454i	−0.480577	+	0.138006i
$757$	34.1282			1.24041			0.620204	−	0.784440i	$-0.287050\pi$
$757$	34.1282			1.24041			0.620204	+	0.784440i	$0.287050\pi$
$758$	5.21262	−	6.21215i	0.189331	−	0.225636i
$759$	47.4798	−	10.5345i	1.72341	−	0.382379i
$760$	0.726291	+	4.11900i	0.0263454	+	0.149412i
$761$	6.51383	−	5.46576i	0.236126	−	0.198134i	−0.517044	−	0.855959i	$-0.672968\pi$
$761$	6.51383	−	5.46576i	0.236126	−	0.198134i	0.753171	+	0.657825i	$0.228523\pi$
$762$	25.2834	−	1.10822i	0.915921	−	0.0401464i
$763$	−7.99193	−	14.7236i	−0.289327	−	0.533029i
$764$	−20.5119	−	11.8426i	−0.742095	−	0.428449i
$765$	0.660701	−	0.0580309i	0.0238877	−	0.00209811i
$766$			8.50207i			0.307192i
$767$	0.468797	−	0.558691i	0.0169273	−	0.0201732i
$768$	−0.663100	−	1.60009i	−0.0239276	−	0.0577384i
$769$	0.623380	−	1.71272i	0.0224797	−	0.0617623i	−0.927945	−	0.372717i	$-0.878426\pi$
$769$	0.623380	−	1.71272i	0.0224797	−	0.0617623i	0.950425	+	0.310954i	$0.100649\pi$
$770$	22.0181	−	7.36419i	0.793478	−	0.265387i
$771$	−10.6299	−	1.39761i	−0.382828	−	0.0503338i
$772$	13.1712	−	4.79393i	0.474043	−	0.172537i
$773$	27.5336			0.990315			0.495157	−	0.868803i	$-0.335110\pi$
$773$	27.5336			0.990315			0.495157	+	0.868803i	$0.335110\pi$
$774$	2.61245	+	29.7437i	0.0939026	+	1.06911i
$775$			7.90474i			0.283947i
$776$	−7.67103	−	6.43676i	−0.275374	−	0.231066i
$777$	−24.4938	+	4.76236i	−0.878710	+	0.170849i
$778$	−0.614239	−	3.48352i	−0.0220215	−	0.124890i
$779$	4.97046	−	13.6562i	0.178085	−	0.489286i
$780$	0.0615533	+	0.277425i	0.00220396	+	0.00993341i
$781$	−13.2390	+	75.0818i	−0.473727	+	2.68664i
$782$	−0.353712	−	0.612646i	−0.0126487	−	0.0219082i
$783$	−16.0528	−	10.2152i	−0.573681	−	0.365063i
$784$	5.11832	+	4.77523i	0.182797	+	0.170544i
$785$	6.19482	+	17.0201i	0.221102	+	0.607474i
$786$	2.02314	+	9.11845i	0.0721631	+	0.325244i
$787$	−33.8385	+	5.96664i	−1.20621	+	0.212688i	−0.740382	−	0.672186i	$-0.765355\pi$
$787$	−33.8385	+	5.96664i	−1.20621	+	0.212688i	−0.465830	+	0.884874i	$0.654244\pi$
$788$	−1.34825	+	3.70429i	−0.0480294	+	0.131960i
$789$	14.9210	−	0.654012i	0.531200	−	0.0232834i
$790$	−11.9506	+	14.2422i	−0.425183	+	0.506713i
$791$	5.04997	−	12.8155i	0.179556	−	0.455668i
$792$	14.2171	+	3.80428i	0.505184	+	0.135179i
$793$	0.411626	−	0.712957i	0.0146173	−	0.0253178i
$794$	7.56398	+	6.34693i	0.268435	+	0.225244i
$795$	5.22238	−	39.7202i	0.185219	−	1.40873i
$796$	−4.83603	+	0.852723i	−0.171409	+	0.0302240i
$797$	14.1555	+	5.15219i	0.501414	+	0.182500i	0.580330	−	0.814381i	$-0.302924\pi$
$797$	14.1555	+	5.15219i	0.501414	+	0.182500i	−0.0789156	+	0.996881i	$0.525146\pi$
$798$	−0.187534	−	10.7136i	−0.00663864	−	0.379257i
$799$	−0.127513	+	0.723161i	−0.00451108	+	0.0255836i
$800$	−1.55917	−	0.900189i	−0.0551251	−	0.0318265i
$801$	−6.41129	−	4.48598i	−0.226532	−	0.158504i
$802$	−4.85913	−	8.41625i	−0.171582	−	0.297188i
$803$	−9.58371	+	54.3519i	−0.338202	+	1.91804i
$804$	2.01516	−	1.28428i	0.0710692	−	0.0452931i
$805$	−26.5434	−	5.40366i	−0.935531	−	0.190454i
$806$	−0.258858	−	0.308495i	−0.00911789	−	0.0108663i
$807$	−22.7196	−	24.7856i	−0.799769	−	0.872496i
$808$	−13.6746	−	2.41120i	−0.481071	−	0.0848259i
$809$	6.61330	+	3.81819i	0.232511	+	0.134240i	0.611730	−	0.791067i	$-0.290474\pi$
$809$	6.61330	+	3.81819i	0.232511	+	0.134240i	−0.379219	+	0.925307i	$0.623807\pi$
$810$	15.1241	−	5.51641i	0.531407	−	0.193827i
$811$		−	12.7120i		−	0.446377i	−0.974775	−	0.223189i	$-0.928353\pi$
$811$		−	12.7120i		−	0.446377i	0.974775	−	0.223189i	$-0.0716466\pi$
$812$	−0.254784	+	9.68496i	−0.00894117	+	0.339875i
$813$	7.59519	+	34.2321i	0.266375	+	1.20057i
$814$	25.1014	+	9.13615i	0.879802	+	0.320222i
$815$	−23.3027	−	8.48150i	−0.816259	−	0.297094i
$816$	−0.00937424	−	0.213869i	−0.000328164	−	0.00748690i
$817$	−22.9184	−	4.04114i	−0.801814	−	0.141381i
$818$	5.45896	−	9.45520i	0.190868	−	0.330593i
$819$	−0.0446040	−	0.726649i	−0.00155859	−	0.0253912i
$820$	−5.55870	−	9.62795i	−0.194118	−	0.336223i
$821$	−8.17262	−	22.4541i	−0.285226	−	0.783653i	−0.996718	−	0.0809578i	$-0.974202\pi$
$821$	−8.17262	−	22.4541i	−0.285226	−	0.783653i	0.711491	−	0.702695i	$-0.248020\pi$
$822$	8.18094	+	19.7410i	0.285343	+	0.688547i
$823$	21.7075	−	18.2147i	0.756675	−	0.634926i	−0.180584	−	0.983560i	$-0.557799\pi$
$823$	21.7075	−	18.2147i	0.756675	−	0.634926i	0.937259	+	0.348634i	$0.113354\pi$
$824$	2.05478	+	11.6532i	0.0715817	+	0.405960i
$825$	14.1324	−	5.85666i	0.492028	−	0.203903i
$826$	−0.553248	+	21.0303i	−0.0192500	+	0.731738i
$827$	24.1858	−	13.9637i	0.841022	−	0.485564i	−0.0165893	−	0.999862i	$-0.505281\pi$
$827$	24.1858	−	13.9637i	0.841022	−	0.485564i	0.857612	+	0.514298i	$0.171947\pi$
$828$	−12.1459	−	12.1376i	−0.422100	−	0.421812i
$829$	15.5437	−	8.97417i	0.539856	−	0.311686i	−0.205165	−	0.978727i	$-0.565773\pi$
$829$	15.5437	−	8.97417i	0.539856	−	0.311686i	0.745020	+	0.667042i	$0.232440\pi$
$830$	−1.96334	−	5.39423i	−0.0681485	−	0.187236i
$831$	1.22363	+	27.9166i	0.0424474	+	0.968417i
$832$	0.0903280	−	0.0159273i	0.00313156	−	0.000552178i
$833$	0.392592	+	0.770967i	0.0136025	+	0.0267124i
$834$	−4.49095	+	14.2520i	−0.155509	+	0.493505i
$835$	7.30725	+	6.13151i	0.252878	+	0.212190i
$836$	−5.73547	+	9.93412i	−0.198365	+	0.343579i
$837$	−15.4045	+	16.8283i	−0.532456	+	0.581671i
$838$	−15.9447	+	9.20570i	−0.550802	+	0.318006i
$839$	16.6399	−	6.05644i	0.574474	−	0.209092i	−0.0384128	−	0.999262i	$-0.512230\pi$
$839$	16.6399	−	6.05644i	0.574474	−	0.209092i	0.612887	+	0.790170i	$0.290008\pi$
$840$	−6.37058	−	5.15827i	−0.219806	−	0.177977i
$841$	11.9434	−	10.0217i	0.411840	−	0.345575i
$842$	−18.6502	−	22.2264i	−0.642728	−	0.765973i
$843$	−9.29681	+	17.8664i	−0.320199	+	0.615353i
$844$	−12.3994	+	4.51302i	−0.426805	+	0.155344i
$845$	23.2387			0.799435
$846$	1.55950	+	17.7555i	0.0536168	+	0.610446i
$847$	32.1639	+	12.6742i	1.10517	+	0.435491i
$848$	−12.7343	−	2.24540i	−0.437298	−	0.0771074i
$849$	53.6684	−	22.2409i	1.84189	−	0.763305i
$850$	−0.143032	−	0.170459i	−0.00490597	−	0.00584671i
$851$	−20.0331	−	23.8745i	−0.686724	−	0.818406i
$852$	24.8669	−	10.3052i	0.851925	−	0.353049i
$853$	7.80707	+	1.37660i	0.267309	+	0.0471338i	0.305696	−	0.952129i	$-0.401111\pi$
$853$	7.80707	+	1.37660i	0.267309	+	0.0471338i	−0.0383871	+	0.999263i	$0.512222\pi$
$854$	3.50720	+	23.4867i	0.120014	+	0.803699i
$855$	1.09786	+	12.4995i	0.0375460	+	0.427474i
$856$	6.38966			0.218394
$857$	−30.3594	+	11.0499i	−1.03706	+	0.377458i	−0.803764	−	0.594948i	$-0.797173\pi$
$857$	−30.3594	+	11.0499i	−1.03706	+	0.377458i	−0.233294	+	0.972406i	$0.574950\pi$
$858$	−0.359751	+	0.691363i	−0.0122817	+	0.0236028i
$859$	26.1088	+	31.1152i	0.890820	+	1.06164i	0.997728	+	0.0673690i	$0.0214605\pi$
$859$	26.1088	+	31.1152i	0.890820	+	1.06164i	−0.106908	+	0.994269i	$0.534095\pi$
$860$	−13.6378	+	11.4435i	−0.465046	+	0.390220i
$861$	10.2082	+	26.5893i	0.347894	+	0.906161i
$862$	37.2528	−	13.5589i	1.26884	−	0.461818i
$863$	18.6261	−	10.7538i	0.634040	−	0.366063i	−0.148275	−	0.988946i	$-0.547372\pi$
$863$	18.6261	−	10.7538i	0.634040	−	0.366063i	0.782315	+	0.622883i	$0.214039\pi$
$864$	−1.56505	−	4.95486i	−0.0532440	−	0.168568i
$865$	2.30579	−	3.99374i	0.0783992	−	0.135791i
$866$	12.7659	+	10.7119i	0.433804	+	0.364004i
$867$	−8.84150	+	28.0583i	−0.300273	+	0.952911i
$868$	11.3829	+	2.31732i	0.386362	+	0.0786551i
$869$	−50.2148	+	8.85422i	−1.70342	+	0.300359i
$870$	−0.496799	−	11.3342i	−0.0168431	−	0.384266i
$871$	0.0432802	+	0.118911i	0.00146649	+	0.00402916i
$872$	5.48362	−	3.16597i	0.185699	−	0.107213i
$873$	−21.2498	−	21.2353i	−0.719195	−	0.718705i
$874$	11.5904	−	6.69171i	0.392051	−	0.226351i
$875$	−32.1722	−	0.846361i	−1.08762	−	0.0286122i
$876$	18.0012	−	7.45993i	0.608204	−	0.252048i
$877$	−7.29848	−	41.3917i	−0.246452	−	1.39770i	−0.817096	−	0.576502i	$-0.804417\pi$
$877$	−7.29848	−	41.3917i	−0.246452	−	1.39770i	0.570643	−	0.821198i	$-0.306694\pi$
$878$	−7.42869	+	6.23341i	−0.250706	+	0.210367i
$879$	−5.71536	−	13.7915i	−0.192774	−	0.465174i
$880$	3.00129	+	8.24599i	0.101174	+	0.277972i
$881$	1.99799	+	3.46062i	0.0673140	+	0.116591i	0.897718	−	0.440570i	$-0.145224\pi$
$881$	1.99799	+	3.46062i	0.0673140	+	0.116591i	−0.830404	+	0.557162i	$0.811890\pi$
$882$	14.0533	+	15.6047i	0.473199	+	0.525436i
$883$	−20.9975	+	36.3687i	−0.706621	+	1.22390i	0.259483	+	0.965748i	$0.416448\pi$
$883$	−20.9975	+	36.3687i	−0.706621	+	1.22390i	−0.966103	+	0.258155i	$0.916885\pi$
$884$	0.0111642	+	0.00196854i	0.000375491	+	6.62092e-5i
$885$	−1.07877	−	24.6116i	−0.0362624	−	0.827310i
$886$	30.3530	+	11.0476i	1.01973	+	0.371151i
$887$	−6.49170	−	2.36279i	−0.217970	−	0.0793346i	0.230727	−	0.973019i	$-0.425890\pi$
$887$	−6.49170	−	2.36279i	−0.217970	−	0.0793346i	−0.448697	+	0.893684i	$0.648112\pi$
$888$	−2.04284	−	9.20724i	−0.0685533	−	0.308975i
$889$	−18.4419	−	33.9756i	−0.618523	−	1.13951i
$890$		−	4.66558i		−	0.156391i
$891$	41.4996	+	15.0726i	1.39029	+	0.504950i
$892$	3.01175	+	1.73884i	0.100841	+	0.0582205i
$893$	−13.6812	−	2.41236i	−0.457822	−	0.0807265i
$894$	22.5336	+	24.5827i	0.753636	+	0.822168i
$895$	16.5363	+	19.7072i	0.552747	+	0.658738i
$896$	−1.75337	+	1.98134i	−0.0585759	+	0.0661919i
$897$	0.766813	−	0.488697i	0.0256031	−	0.0163171i
$898$	5.40302	−	30.6420i	0.180301	−	1.02254i
$899$	8.03883	+	13.9237i	0.268110	+	0.464380i
$900$	−4.42541	−	3.09646i	−0.147514	−	0.103215i
$901$	−1.38407	−	0.799092i	−0.0461100	−	0.0266216i
$902$	5.29458	−	30.0271i	0.176290	−	0.999792i
$903$	39.0935	−	23.4923i	1.30095	−	0.781776i
$904$	4.89233	+	1.78066i	0.162717	+	0.0592240i
$905$	−30.3613	+	5.35352i	−1.00925	+	0.177957i
$906$	1.14360	−	8.69796i	0.0379935	−	0.288970i
$907$	17.4276	+	14.6235i	0.578674	+	0.485565i	0.884511	−	0.466519i	$-0.154492\pi$
$907$	17.4276	+	14.6235i	0.578674	+	0.485565i	−0.305837	+	0.952084i	$0.598936\pi$
$908$	−9.86330	+	17.0837i	−0.327325	+	0.566944i
$909$	−40.2410	−	10.7678i	−1.33471	−	0.357146i
$910$	0.339747	−	0.270180i	0.0112625	−	0.00895637i
$911$	21.5197	−	25.6462i	0.712979	−	0.849695i	−0.280950	−	0.959722i	$-0.590649\pi$
$911$	21.5197	−	25.6462i	0.712979	−	0.849695i	0.993929	+	0.110027i	$0.0350939\pi$
$912$	4.04609	−	0.177347i	0.133979	−	0.00587255i
$913$	5.38460	−	14.7941i	0.178204	−	0.489612i
$914$	−14.1092	+	2.48783i	−0.466690	+	0.0822901i
$915$	−6.02341	−	27.1479i	−0.199128	−	0.897483i
$916$	8.73986	+	24.0126i	0.288773	+	0.793398i
$917$	11.1668	−	8.88030i	0.368762	−	0.293253i
$918$	0.0276852	−	0.641625i	0.000913748	−	0.0211768i
$919$	−5.65900	−	9.80167i	−0.186673	−	0.323327i	0.757466	−	0.652875i	$-0.226437\pi$
$919$	−5.65900	−	9.80167i	−0.186673	−	0.323327i	−0.944139	+	0.329547i	$0.893104\pi$
$920$	1.77785	−	10.0827i	0.0586140	−	0.332417i
$921$	7.19537	+	32.4300i	0.237095	+	1.06861i
$922$	13.6410	−	37.4784i	0.449243	−	1.23429i
$923$	0.247524	+	1.40378i	0.00814734	+	0.0462059i
$924$	−4.29068	−	22.0678i	−0.141153	−	0.725978i
$925$	−7.50968	−	6.30137i	−0.246917	−	0.207188i
$926$		−	36.6631i		−	1.20482i
$927$	3.10600	+	35.3629i	0.102015	+	1.16147i
$928$	−3.66184			−0.120206
$929$	26.6602	−	9.70352i	0.874693	−	0.318362i	0.134627	−	0.990896i	$-0.457016\pi$
$929$	26.6602	−	9.70352i	0.874693	−	0.318362i	0.740066	+	0.672534i	$0.234794\pi$
$930$	−13.4869	−	1.77324i	−0.442253	−	0.0581470i
$931$	−14.5856	+	7.42728i	−0.478023	+	0.243419i
$932$	−2.31028	+	6.34743i	−0.0756756	+	0.207917i
$933$	−10.4976	−	25.3312i	−0.343675	−	0.829305i
$934$	−4.34878	+	5.18267i	−0.142296	+	0.169582i
$935$			1.08458i			0.0354695i
$936$	0.274109	−	0.0240756i	0.00895953	−	0.000786936i
$937$	47.6682	+	27.5212i	1.55725	+	0.899080i	0.997518	+	0.0704076i	$0.0224300\pi$
$937$	47.6682	+	27.5212i	1.55725	+	0.899080i	0.559734	+	0.828672i	$0.310903\pi$
$938$	−3.11207	−	1.90760i	−0.101613	−	0.0622853i
$939$	60.2482	−	2.64078i	1.96613	−	0.0861787i
$940$	−8.14110	+	6.83120i	−0.265534	+	0.222809i
$941$	3.22305	+	18.2788i	0.105068	+	0.595872i	0.991193	+	0.132425i	$0.0422764\pi$
$941$	3.22305	+	18.2788i	0.105068	+	0.595872i	−0.886125	+	0.463447i	$0.846613\pi$
$942$	17.1219	−	3.79891i	0.557863	−	0.123775i
$943$	−22.8664	+	27.2511i	−0.744632	+	0.887417i
$944$	−7.95146			−0.258798
$945$	−17.6961	−	17.0756i	−0.575655	−	0.555469i
$946$	−48.8258			−1.58746
$947$	−17.4764	+	20.8276i	−0.567908	+	0.676806i	−0.971200	−	0.238265i	$-0.923421\pi$
$947$	−17.4764	+	20.8276i	−0.567908	+	0.676806i	0.403292	+	0.915071i	$0.367866\pi$
$948$	12.1646	+	13.2708i	0.395087	+	0.431014i
$949$	0.179183	+	1.01620i	0.00581653	+	0.0329872i
$950$	3.22485	−	2.70597i	0.104628	−	0.0877932i
$951$	11.7287	−	22.5400i	0.380329	−	0.730910i
$952$	−0.287395	+	0.155998i	−0.00931453	+	0.00505592i
$953$	−25.4274	−	14.6805i	−0.823675	−	0.475549i	0.0280070	−	0.999608i	$-0.491084\pi$
$953$	−25.4274	−	14.6805i	−0.823675	−	0.475549i	−0.851682	+	0.524059i	$0.824417\pi$
$954$	−37.4738	−	10.0274i	−1.21326	−	0.324649i
$955$		−	42.3668i		−	1.37096i
$956$	4.36790	−	5.20546i	0.141268	−	0.168356i
$957$	18.9373	−	24.6883i	0.612155	−	0.798058i
$958$	−7.04821	+	19.3648i	−0.227717	+	0.625648i
$959$	21.6320	−	24.4446i	0.698535	−	0.789357i
$960$	1.88565	−	2.45829i	0.0608590	−	0.0793410i
$961$	−11.0157	+	4.00938i	−0.355345	+	0.129335i
$962$	0.499430			0.0161023
$963$	19.0966	+	1.66418i	0.615380	+	0.0536274i
$964$			22.4267i			0.722314i
$965$	19.2063	+	16.1160i	0.618272	+	0.518792i
$966$	−8.53818	+	24.8006i	−0.274711	+	0.797948i
$967$	0.308047	+	1.74702i	0.00990611	+	0.0561804i	0.989360	−	0.145487i	$-0.0464750\pi$
$967$	0.308047	+	1.74702i	0.00990611	+	0.0561804i	−0.979454	+	0.201668i	$0.935364\pi$
$968$	−4.46905	+	12.2786i	−0.143641	+	0.394649i
$969$	0.477417	+	0.150440i	0.0153369	+	0.00483282i
$970$	3.11042	−	17.6401i	0.0998696	−	0.566389i
$971$	−1.15506	−	2.00062i	−0.0370676	−	0.0642029i	0.846896	−	0.531758i	$-0.178468\pi$
$971$	−1.15506	−	2.00062i	−0.0370676	−	0.0642029i	−0.883964	+	0.467555i	$0.845135\pi$
$972$	−3.38693	−	15.2161i	−0.108636	−	0.488056i
$973$	22.5752	−	3.37109i	0.723727	−	0.108072i
$974$	−1.88774	−	5.18653i	−0.0604871	−	0.166187i
$975$	0.210843	−	0.193268i	0.00675236	−	0.00618952i
$976$	−8.83921	+	1.55859i	−0.282936	+	0.0498893i
$977$	3.96069	−	10.8819i	0.126714	−	0.348143i	−0.860072	−	0.510172i	$-0.829582\pi$
$977$	3.96069	−	10.8819i	0.126714	−	0.348143i	0.986786	+	0.162029i	$0.0518038\pi$
$978$	−11.0840	+	21.3010i	−0.354426	+	0.681130i
$979$	8.22491	−	9.80207i	0.262869	−	0.313275i
$980$	−2.81962	+	12.1996i	−0.0900696	+	0.389703i
$981$	17.2133	−	8.03385i	0.549579	−	0.256501i
$982$	−16.5696	+	28.6993i	−0.528756	+	0.915832i
$983$	23.5350	+	19.7482i	0.750649	+	0.629869i	0.935674	−	0.352864i	$-0.114792\pi$
$983$	23.5350	+	19.7482i	0.750649	+	0.629869i	−0.185025	+	0.982734i	$0.559237\pi$
$984$	−9.94487	+	4.12129i	−0.317031	+	0.131382i
$985$	−6.94415	+	1.22444i	−0.221259	+	0.0390140i
$986$	−0.425293	−	0.154794i	−0.0135441	−	0.00492964i
$987$	23.3369	−	14.0238i	0.742820	−	0.446381i
$988$	−0.0372419	+	0.211210i	−0.00118482	+	0.00671947i
$989$	49.3342	+	28.4831i	1.56874	+	0.905711i
$990$	6.82223	+	25.4262i	0.216825	+	0.808099i
$991$	−5.22638	−	9.05236i	−0.166021	−	0.287558i	0.770996	−	0.636840i	$-0.219759\pi$
$991$	−5.22638	−	9.05236i	−0.166021	−	0.287558i	−0.937018	+	0.349282i	$0.886425\pi$
$992$	−0.762419	+	4.32390i	−0.0242068	+	0.137284i
$993$	−12.1055	−	6.29909i	−0.384156	−	0.199895i
$994$	−30.7918	−	27.2489i	−0.976655	−	0.864283i
$995$	−5.64618	−	6.72885i	−0.178996	−	0.213319i
$996$	−5.42650	+	1.20400i	−0.171945	+	0.0381501i
$997$	−56.5396	−	9.96945i	−1.79063	−	0.315736i	−0.822984	−	0.568064i	$-0.807693\pi$
$997$	−56.5396	−	9.96945i	−1.79063	−	0.315736i	−0.967642	+	0.252328i	$0.918804\pi$
$998$	24.3838	+	14.0780i	0.771854	+	0.445630i
$999$	−3.70738	−	28.0495i	−0.117296	−	0.887447i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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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	378.2.bf.a.101.20	yes	144
7.5	odd	6		378.2.ba.a.47.4	✓	144
27.23	odd	18		378.2.ba.a.185.4	yes	144
189.131	even	18	inner	378.2.bf.a.131.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.4	✓	144	7.5	odd	6
378.2.ba.a.185.4	yes	144	27.23	odd	18
378.2.bf.a.101.20	yes	144	1.1	even	1	trivial
378.2.bf.a.131.20	yes	144	189.131	even	18	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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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	378.2.bf.a.101.20

Level	$378$
Weight	$2$
Character	378.101
Analytic conductor	$3.018$
Analytic rank	$0$
Dimension	$144$
Inner twists	$2$