LMFDB - Embedded newform 900.2.r.g.551.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(551,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.551"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,2,0,0,0,0,12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.13
Character	$\chi$	$=$	900.551
Dual form			900.2.r.g.851.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0449209 - 1.41350i) q^{2} +(-0.589100 - 1.62879i) q^{3} +(-1.99596 - 0.126991i) q^{4} +(-2.32876 + 0.759526i) q^{6} +(2.50234 + 1.44473i) q^{7} +(-0.269163 + 2.81559i) q^{8} +(-2.30592 + 1.91904i) q^{9} +(0.395318 - 0.684712i) q^{11} +(0.968981 + 3.32582i) q^{12} +(2.33373 + 4.04214i) q^{13} +(2.15453 - 3.47216i) q^{14} +(3.96775 + 0.506941i) q^{16} +5.89560i q^{17} +(2.60898 + 3.34563i) q^{18} +4.55505i q^{19} +(0.879030 - 4.92689i) q^{21} +(-0.950082 - 0.589540i) q^{22} +(0.666656 + 1.15468i) q^{23} +(4.74457 - 1.22026i) q^{24} +(5.81840 - 3.11715i) q^{26} +(4.48414 + 2.62536i) q^{27} +(-4.81112 - 3.20140i) q^{28} +(-2.29484 - 1.32492i) q^{29} +(2.26893 - 1.30997i) q^{31} +(0.894795 - 5.58564i) q^{32} +(-1.34813 - 0.240527i) q^{33} +(8.33343 + 0.264836i) q^{34} +(4.84624 - 3.53751i) q^{36} -7.44000 q^{37} +(6.43857 + 0.204617i) q^{38} +(5.20900 - 6.18239i) q^{39} +(-5.91566 + 3.41541i) q^{41} +(-6.92467 - 1.46383i) q^{42} +(10.3100 + 5.95249i) q^{43} +(-0.875994 + 1.31646i) q^{44} +(1.66209 - 0.890449i) q^{46} +(-1.50658 + 2.60947i) q^{47} +(-1.51170 - 6.76127i) q^{48} +(0.674484 + 1.16824i) q^{49} +(9.60270 - 3.47310i) q^{51} +(-4.14473 - 8.36434i) q^{52} -1.70763i q^{53} +(3.91237 - 6.22040i) q^{54} +(-4.74130 + 6.65671i) q^{56} +(7.41923 - 2.68338i) q^{57} +(-1.97587 + 3.18423i) q^{58} +(-5.29436 - 9.17010i) q^{59} +(-0.869749 + 1.50645i) q^{61} +(-1.74972 - 3.26598i) q^{62} +(-8.54271 + 1.47067i) q^{63} +(-7.85510 - 1.51570i) q^{64} +(-0.400545 + 1.89478i) q^{66} +(6.52500 - 3.76721i) q^{67} +(0.748690 - 11.7674i) q^{68} +(1.48801 - 1.76607i) q^{69} -2.88566 q^{71} +(-4.78257 - 7.00907i) q^{72} -6.50847 q^{73} +(-0.334212 + 10.5164i) q^{74} +(0.578452 - 9.09172i) q^{76} +(1.97845 - 1.14226i) q^{77} +(-8.50481 - 7.64065i) q^{78} +(3.30854 + 1.91019i) q^{79} +(1.63455 - 8.85032i) q^{81} +(4.56194 + 8.51521i) q^{82} +(4.81325 - 8.33679i) q^{83} +(-2.38019 + 9.72226i) q^{84} +(8.87697 - 14.3058i) q^{86} +(-0.806137 + 4.51832i) q^{87} +(1.82146 + 1.29735i) q^{88} +0.00741921i q^{89} +13.4864i q^{91} +(-1.18399 - 2.38937i) q^{92} +(-3.47029 - 2.92391i) q^{93} +(3.62081 + 2.24677i) q^{94} +(-9.62496 + 1.83307i) q^{96} +(-3.31933 + 5.74925i) q^{97} +(1.68161 - 0.900905i) q^{98} +(0.402417 + 2.33752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	0.0449209	−	1.41350i	0.0317639	−	0.999495i
$2$	0.0449209	−	1.41350i	0.0317639	−	0.999495i
$3$	−0.589100	−	1.62879i	−0.340117	−	0.940383i
$3$	−0.589100	−	1.62879i	−0.340117	−	0.940383i
$4$	−1.99596	−	0.126991i	−0.997982	−	0.0634957i
$5$		0			0
$5$		0			0
$6$	−2.32876	+	0.759526i	−0.950712	+	0.310075i
$7$	2.50234	+	1.44473i	0.945797	+	0.546056i	0.891773	−	0.452483i	$-0.149462\pi$
$7$	2.50234	+	1.44473i	0.945797	+	0.546056i	0.0540243	+	0.998540i	$0.482795\pi$
$8$	−0.269163	+	2.81559i	−0.0951634	+	0.995462i
$9$	−2.30592	+	1.91904i	−0.768641	+	0.639681i
$10$		0			0
$11$	0.395318	−	0.684712i	0.119193	−	0.206448i	−0.800255	−	0.599660i	$-0.795303\pi$
$11$	0.395318	−	0.684712i	0.119193	−	0.206448i	0.919448	+	0.393211i	$0.128636\pi$
$12$	0.968981	+	3.32582i	0.279721	+	0.960081i
$13$	2.33373	+	4.04214i	0.647261	+	1.12109i	0.983774	+	0.179410i	$0.0574189\pi$
$13$	2.33373	+	4.04214i	0.647261	+	1.12109i	−0.336514	+	0.941679i	$0.609248\pi$
$14$	2.15453	−	3.47216i	0.575823	−	0.927975i
$15$		0			0
$16$	3.96775	+	0.506941i	0.991937	+	0.126735i
$17$			5.89560i			1.42989i	0.699179	+	0.714946i	$0.253549\pi$
$17$			5.89560i			1.42989i	−0.699179	+	0.714946i	$0.746451\pi$
$18$	2.60898	+	3.34563i	0.614943	+	0.788571i
$19$			4.55505i			1.04500i	0.852639	+	0.522500i	$0.175001\pi$
$19$			4.55505i			1.04500i	−0.852639	+	0.522500i	$0.824999\pi$
$20$		0			0
$21$	0.879030	−	4.92689i	0.191820	−	1.07513i
$22$	−0.950082	−	0.589540i	−0.202558	−	0.125690i
$23$	0.666656	+	1.15468i	0.139007	+	0.240768i	0.927121	−	0.374762i	$-0.122275\pi$
$23$	0.666656	+	1.15468i	0.139007	+	0.240768i	−0.788114	+	0.615530i	$0.788942\pi$
$24$	4.74457	−	1.22026i	0.968482	−	0.249084i
$25$		0			0
$26$	5.81840	−	3.11715i	1.14108	−	0.611324i
$27$	4.48414	+	2.62536i	0.862973	+	0.505250i
$28$	−4.81112	−	3.20140i	−0.909216	−	0.605008i
$29$	−2.29484	−	1.32492i	−0.426140	−	0.246032i	0.271561	−	0.962421i	$-0.412460\pi$
$29$	−2.29484	−	1.32492i	−0.426140	−	0.246032i	−0.697701	+	0.716389i	$0.745794\pi$
$30$		0			0
$31$	2.26893	−	1.30997i	0.407512	−	0.235277i	−0.282208	−	0.959353i	$-0.591067\pi$
$31$	2.26893	−	1.30997i	0.407512	−	0.235277i	0.689720	+	0.724076i	$0.257734\pi$
$32$	0.894795	−	5.58564i	0.158179	−	0.987410i
$33$	−1.34813	−	0.240527i	−0.234680	−	0.0418704i
$34$	8.33343	+	0.264836i	1.42917	+	0.0454189i
$35$		0			0
$36$	4.84624	−	3.53751i	0.807707	−	0.589585i
$37$	−7.44000			−1.22313			−0.611564	−	0.791195i	$-0.709459\pi$
$37$	−7.44000			−1.22313			−0.611564	+	0.791195i	$0.709459\pi$
$38$	6.43857	+	0.204617i	1.04447	+	0.0331933i
$39$	5.20900	−	6.18239i	0.834108	−	0.989975i
$40$		0			0
$41$	−5.91566	+	3.41541i	−0.923871	+	0.533397i	−0.884868	−	0.465842i	$-0.845751\pi$
$41$	−5.91566	+	3.41541i	−0.923871	+	0.533397i	−0.0390029	+	0.999239i	$0.512418\pi$
$42$	−6.92467	−	1.46383i	−1.06850	−	0.225874i
$43$	10.3100	+	5.95249i	1.57226	+	0.907746i	0.995891	+	0.0905567i	$0.0288646\pi$
$43$	10.3100	+	5.95249i	1.57226	+	0.907746i	0.576370	+	0.817189i	$0.304469\pi$
$44$	−0.875994	+	1.31646i	−0.132061	+	0.198463i
$45$		0			0
$46$	1.66209	−	0.890449i	0.245062	−	0.131290i
$47$	−1.50658	+	2.60947i	−0.219757	+	0.380631i	−0.954734	−	0.297462i	$-0.903860\pi$
$47$	−1.50658	+	2.60947i	−0.219757	+	0.380631i	0.734976	+	0.678093i	$0.237193\pi$
$48$	−1.51170	−	6.76127i	−0.218195	−	0.975905i
$49$	0.674484	+	1.16824i	0.0963548	+	0.166891i
$50$		0			0
$51$	9.60270	−	3.47310i	1.34465	−	0.486331i
$52$	−4.14473	−	8.36434i	−0.574770	−	1.15992i
$53$		−	1.70763i		−	0.234561i	−0.993099	−	0.117281i	$-0.962582\pi$
$53$		−	1.70763i		−	0.234561i	0.993099	−	0.117281i	$-0.0374177\pi$
$54$	3.91237	−	6.22040i	0.532406	−	0.846489i
$55$		0			0
$56$	−4.74130	+	6.65671i	−0.633583	+	0.889540i
$57$	7.41923	−	2.68338i	0.982701	−	0.355423i
$58$	−1.97587	+	3.18423i	−0.259444	+	0.418111i
$59$	−5.29436	−	9.17010i	−0.689267	−	1.19385i	−0.972075	−	0.234669i	$-0.924599\pi$
$59$	−5.29436	−	9.17010i	−0.689267	−	1.19385i	0.282808	−	0.959176i	$-0.408734\pi$
$60$		0			0
$61$	−0.869749	+	1.50645i	−0.111360	+	0.192881i	−0.916319	−	0.400450i	$-0.868854\pi$
$61$	−0.869749	+	1.50645i	−0.111360	+	0.192881i	0.804959	+	0.593331i	$0.202187\pi$
$62$	−1.74972	−	3.26598i	−0.222214	−	0.414779i
$63$	−8.54271	+	1.47067i	−1.07628	+	0.185287i
$64$	−7.85510	−	1.51570i	−0.981888	−	0.189463i
$65$		0			0
$66$	−0.400545	+	1.89478i	−0.0493037	+	0.233232i
$67$	6.52500	−	3.76721i	0.797155	−	0.460238i	−0.0453201	−	0.998973i	$-0.514431\pi$
$67$	6.52500	−	3.76721i	0.797155	−	0.460238i	0.842476	+	0.538735i	$0.181097\pi$
$68$	0.748690	−	11.7674i	0.0907920	−	1.42701i
$69$	1.48801	−	1.76607i	0.179135	−	0.212610i
$70$		0			0
$71$	−2.88566			−0.342465			−0.171233	−	0.985231i	$-0.554775\pi$
$71$	−2.88566			−0.342465			−0.171233	+	0.985231i	$0.554775\pi$
$72$	−4.78257	−	7.00907i	−0.563631	−	0.826026i
$73$	−6.50847			−0.761759			−0.380880	−	0.924625i	$-0.624379\pi$
$73$	−6.50847			−0.761759			−0.380880	+	0.924625i	$0.624379\pi$
$74$	−0.334212	+	10.5164i	−0.0388513	+	1.22251i
$75$		0			0
$76$	0.578452	−	9.09172i	0.0663530	−	1.04289i
$77$	1.97845	−	1.14226i	0.225465	−	0.130172i
$78$	−8.50481	−	7.64065i	−0.962981	−	0.865133i
$79$	3.30854	+	1.91019i	0.372240	+	0.214913i	0.674436	−	0.738333i	$-0.264387\pi$
$79$	3.30854	+	1.91019i	0.372240	+	0.214913i	−0.302197	+	0.953246i	$0.597720\pi$
$80$		0			0
$81$	1.63455	−	8.85032i	0.181617	−	0.983369i
$82$	4.56194	+	8.51521i	0.503782	+	0.940347i
$83$	4.81325	−	8.33679i	0.528322	−	0.915081i	−0.471132	−	0.882063i	$-0.656155\pi$
$83$	4.81325	−	8.33679i	0.528322	−	0.915081i	0.999455	−	0.0330187i	$-0.0105121\pi$
$84$	−2.38019	+	9.72226i	−0.259699	+	1.06079i
$85$		0			0
$86$	8.87697	−	14.3058i	0.957229	−	1.54263i
$87$	−0.806137	+	4.51832i	−0.0864269	+	0.484415i
$88$	1.82146	+	1.29735i	0.194169	+	0.138298i
$89$			0.00741921i			0.000786434i	1.00000		0.000393217i	$0.000125165\pi$
$89$			0.00741921i			0.000786434i	−1.00000		0.000393217i	$0.999875\pi$
$90$		0			0
$91$			13.4864i			1.41376i
$92$	−1.18399	−	2.38937i	−0.123439	−	0.249109i
$93$	−3.47029	−	2.92391i	−0.359852	−	0.303195i
$94$	3.62081	+	2.24677i	0.373459	+	0.231737i
$95$		0			0
$96$	−9.62496	+	1.83307i	−0.982343	+	0.187087i
$97$	−3.31933	+	5.74925i	−0.337027	+	0.583748i	−0.983872	−	0.178874i	$-0.942755\pi$
$97$	−3.31933	+	5.74925i	−0.337027	+	0.583748i	0.646845	+	0.762621i	$0.276088\pi$
$98$	1.68161	−	0.900905i	0.169868	−	0.0910051i
$99$	0.402417	+	2.33752i	0.0404445	+	0.234930i
$100$		0			0
$101$	−2.20027	−	1.27033i	−0.218935	−	0.126402i	0.386522	−	0.922280i	$-0.373676\pi$
$101$	−2.20027	−	1.27033i	−0.218935	−	0.126402i	−0.605457	+	0.795878i	$0.707010\pi$
$102$	−4.47786	−	13.7294i	−0.443374	−	1.35942i
$103$	−6.63071	+	3.82824i	−0.653343	+	0.377208i	−0.789736	−	0.613447i	$-0.789782\pi$
$103$	−6.63071	+	3.82824i	−0.653343	+	0.377208i	0.136393	+	0.990655i	$0.456449\pi$
$104$	−12.0092	+	5.48284i	−1.17760	+	0.537637i
$105$		0			0
$106$	−2.41374	−	0.0767084i	−0.234443	−	0.00745058i
$107$	13.7118			1.32557			0.662787	−	0.748808i	$-0.269374\pi$
$107$	13.7118			1.32557			0.662787	+	0.748808i	$0.269374\pi$
$108$	−8.61678	−	5.80956i	−0.829150	−	0.559026i
$109$	13.2664			1.27069			0.635347	−	0.772227i	$-0.280857\pi$
$109$	13.2664			1.27069			0.635347	+	0.772227i	$0.280857\pi$
$110$		0			0
$111$	4.38291	+	12.1182i	0.416007	+	1.15021i
$112$	9.19627	+	7.00086i	0.868966	+	0.661519i
$113$	8.01051	−	4.62487i	0.753565	−	0.435071i	−0.0734153	−	0.997301i	$-0.523390\pi$
$113$	8.01051	−	4.62487i	0.753565	−	0.435071i	0.826981	+	0.562230i	$0.190057\pi$
$114$	−3.45968	−	10.6076i	−0.324029	−	0.993495i
$115$		0			0
$116$	4.41216	+	2.93593i	0.409659	+	0.272594i
$117$	−13.1384	−	4.84233i	−1.21465	−	0.447674i
$118$	−13.1998	+	7.07165i	−1.21514	+	0.650998i
$119$	−8.51754	+	14.7528i	−0.780802	+	1.35239i
$120$		0			0
$121$	5.18745	+	8.98492i	0.471586	+	0.816811i
$122$	2.09030	+	1.29706i	0.189247	+	0.117430i
$123$	9.04790	+	7.62336i	0.815822	+	0.687375i
$124$	−4.69506	+	2.32651i	−0.421628	+	0.208927i
$125$		0			0
$126$	1.69505	+	12.1412i	0.151007	+	1.08162i
$127$			9.77239i			0.867159i	0.901115	+	0.433580i	$0.142750\pi$
$127$			9.77239i			0.867159i	−0.901115	+	0.433580i	$0.857250\pi$
$128$	−2.49531	+	11.0351i	−0.220556	+	0.975374i
$129$	3.62173	−	20.2995i	0.318875	−	1.78727i
$130$		0			0
$131$	−6.61827	−	11.4632i	−0.578241	−	1.00154i	−0.995681	−	0.0928382i	$-0.970406\pi$
$131$	−6.61827	−	11.4632i	−0.578241	−	1.00154i	0.417440	−	0.908704i	$-0.362927\pi$
$132$	2.66028	+	0.651285i	0.231548	+	0.0566871i
$133$	−6.58082	+	11.3983i	−0.570629	+	0.988359i
$134$	−5.03184	−	9.39231i	−0.434685	−	0.811372i
$135$		0			0
$136$	−16.5996	−	1.58688i	−1.42340	−	0.136073i
$137$	2.73010	+	1.57622i	0.233248	+	0.134666i	0.612069	−	0.790804i	$-0.290337\pi$
$137$	2.73010	+	1.57622i	0.233248	+	0.134666i	−0.378822	+	0.925470i	$0.623671\pi$
$138$	−2.42949	−	2.18264i	−0.206812	−	0.185798i
$139$	−2.22556	+	1.28493i	−0.188770	+	0.108986i	−0.591407	−	0.806374i	$-0.701427\pi$
$139$	−2.22556	+	1.28493i	−0.188770	+	0.108986i	0.402637	+	0.915360i	$0.368094\pi$
$140$		0			0
$141$	5.13782	+	0.916663i	0.432682	+	0.0771970i
$142$	−0.129627	+	4.07889i	−0.0108780	+	0.342293i
$143$	3.69027			0.308596
$144$	−10.1222	+	6.44531i	−0.843513	+	0.537109i
$145$		0			0
$146$	−0.292366	+	9.19973i	−0.0241964	+	0.761375i
$147$	1.50548	−	1.78680i	0.124170	−	0.147373i
$148$	14.8500	+	0.944816i	1.22066	+	0.0776634i
$149$	−8.52719	+	4.92318i	−0.698575	+	0.403322i	−0.806816	−	0.590802i	$-0.798811\pi$
$149$	−8.52719	+	4.92318i	−0.698575	+	0.403322i	0.108242	+	0.994125i	$0.465478\pi$
$150$		0			0
$151$	−9.24153	−	5.33560i	−0.752065	−	0.434205i	0.0743744	−	0.997230i	$-0.476304\pi$
$151$	−9.24153	−	5.33560i	−0.752065	−	0.434205i	−0.826440	+	0.563025i	$0.809637\pi$
$152$	−12.8252	−	1.22605i	−1.04026	−	0.0994458i
$153$	−11.3139	−	13.5948i	−0.914675	−	1.09907i
$154$	−1.52571	−	2.84784i	−0.122945	−	0.229486i
$155$		0			0
$156$	−11.1821	+	11.6783i	−0.895284	+	0.935015i
$157$	7.50509	+	12.9992i	0.598972	+	1.03745i	0.992973	+	0.118340i	$0.0377572\pi$
$157$	7.50509	+	12.9992i	0.598972	+	1.03745i	−0.394001	+	0.919110i	$0.628909\pi$
$158$	2.84867	−	4.59081i	0.226628	−	0.365225i
$159$	−2.78138	+	1.00597i	−0.220577	+	0.0797783i
$160$		0			0
$161$			3.85255i			0.303624i
$162$	−12.4365	−	2.70800i	−0.977104	−	0.212761i
$163$		−	4.15873i		−	0.325737i	−0.986648	−	0.162869i	$-0.947925\pi$
$163$		−	4.15873i		−	0.325737i	0.986648	−	0.162869i	$-0.0520746\pi$
$164$	12.2412	−	6.06579i	0.955875	−	0.473659i
$165$		0			0
$166$	−11.5678	−	7.17802i	−0.897838	−	0.557122i
$167$	−0.0166770	−	0.0288855i	−0.00129051	−	0.00223522i	0.865379	−	0.501117i	$-0.167077\pi$
$167$	−0.0166770	−	0.0288855i	−0.00129051	−	0.00223522i	−0.866670	+	0.498882i	$0.833744\pi$
$168$	13.6355	+	3.80112i	1.05200	+	0.293263i
$169$	−4.39261	+	7.60822i	−0.337893	+	0.585248i
$170$		0			0
$171$	−8.74134	−	10.5036i	−0.668467	−	0.803230i
$172$	−19.8225	−	13.1902i	−1.51145	−	1.00575i
$173$	20.6392	+	11.9161i	1.56917	+	0.905962i	0.996266	+	0.0863411i	$0.0275175\pi$
$173$	20.6392	+	11.9161i	1.56917	+	0.905962i	0.572906	+	0.819621i	$0.305816\pi$
$174$	6.35044	+	1.34244i	0.481425	+	0.101770i
$175$		0			0
$176$	1.91563	−	2.51636i	0.144396	−	0.189678i
$177$	−11.8173	+	14.0255i	−0.888241	+	1.05422i
$178$	0.0104870		0.000333277i	0.000786037		2.49802e-5i
$179$	25.5288			1.90811			0.954055	−	0.299631i	$-0.0968635\pi$
$179$	25.5288			1.90811			0.954055	+	0.299631i	$0.0968635\pi$
$180$		0			0
$181$	25.6109			1.90364			0.951821	−	0.306653i	$-0.0992092\pi$
$181$	25.6109			1.90364			0.951821	+	0.306653i	$0.0992092\pi$
$182$	19.0631	+	0.605823i	1.41305	+	0.0449066i
$183$	2.96606	+	0.529190i	0.219258	+	0.0391188i
$184$	−3.43055	+	1.56623i	−0.252904	+	0.115464i
$185$		0			0
$186$	−4.28883	+	4.77391i	−0.314473	+	0.350040i
$187$	4.03678	+	2.33064i	0.295199	+	0.170433i
$188$	3.33846	−	5.01709i	0.243482	−	0.365909i
$189$	7.42793	+	13.0479i	0.540302	+	0.949096i
$190$		0			0
$191$	3.85863	−	6.68334i	0.279200	−	0.483589i	−0.691986	−	0.721911i	$-0.743264\pi$
$191$	3.85863	−	6.68334i	0.279200	−	0.483589i	0.971186	+	0.238322i	$0.0765973\pi$
$192$	2.15868	+	13.6872i	0.155789	+	0.987790i
$193$	−2.58291	−	4.47373i	−0.185922	−	0.322026i	0.757965	−	0.652295i	$-0.226194\pi$
$193$	−2.58291	−	4.47373i	−0.185922	−	0.322026i	−0.943887	+	0.330269i	$0.892861\pi$
$194$	7.97745	+	4.95013i	0.572748	+	0.355399i
$195$		0			0
$196$	−1.19789	−	2.41742i	−0.0855635	−	0.172673i
$197$		−	8.47116i		−	0.603545i	−0.953380	−	0.301773i	$-0.902422\pi$
$197$		−	8.47116i		−	0.603545i	0.953380	−	0.301773i	$-0.0975784\pi$
$198$	3.32217	−	0.463813i	0.236096	−	0.0329618i
$199$			0.555967i			0.0394115i	0.999806	+	0.0197057i	$0.00627293\pi$
$199$			0.555967i			0.0394115i	−0.999806	+	0.0197057i	$0.993727\pi$
$200$		0			0
$201$	−9.97988	−	8.40860i	−0.703926	−	0.593097i
$202$	−1.89444	+	3.05302i	−0.133293	+	0.214809i
$203$	−3.82831	−	6.63083i	−0.268695	−	0.465393i
$204$	−19.6077	+	5.71272i	−1.37281	+	0.399970i
$205$		0			0
$206$	5.11336	+	9.54447i	0.356265	+	0.664995i
$207$	−3.75314	−	1.38327i	−0.260861	−	0.0961436i
$208$	7.21053	+	17.2213i	0.499960	+	1.19408i
$209$	3.11890	+	1.80070i	0.215739	+	0.124557i
$210$		0			0
$211$	−21.0649	+	12.1618i	−1.45016	+	0.837253i	−0.998490	−	0.0549298i	$-0.982507\pi$
$211$	−21.0649	+	12.1618i	−1.45016	+	0.837253i	−0.451675	+	0.892183i	$0.649173\pi$
$212$	−0.216855	+	3.40837i	−0.0148936	+	0.234088i
$213$	1.69995	+	4.70015i	0.116478	+	0.322049i
$214$	0.615948	−	19.3817i	0.0421054	−	1.32490i
$215$		0			0
$216$	−8.59889	+	11.9189i	−0.585081	+	0.810975i
$217$	7.57019			0.513898
$218$	0.595940	−	18.7521i	0.0403622	−	1.27005i
$219$	3.83414	+	10.6009i	0.259087	+	0.716345i
$220$		0			0
$221$	−23.8308	+	13.7587i	−1.60304	+	0.925513i
$222$	17.3260	−	5.65088i	1.16284	−	0.379262i
$223$	−0.293817	−	0.169636i	−0.0196755	−	0.0113596i	0.490130	−	0.871649i	$-0.336949\pi$
$223$	−0.293817	−	0.169636i	−0.0196755	−	0.0113596i	−0.509805	+	0.860290i	$0.670283\pi$
$224$	10.3088	−	12.6844i	0.688787	−	0.847515i
$225$		0			0
$226$	−6.17741	−	11.5306i	−0.410915	−	0.767005i
$227$	4.30205	−	7.45137i	0.285537	−	0.494565i	−0.687202	−	0.726466i	$-0.741161\pi$
$227$	4.30205	−	7.45137i	0.285537	−	0.494565i	0.972739	+	0.231902i	$0.0744947\pi$
$228$	−15.1493	+	4.41376i	−1.00329	+	0.292308i
$229$	−0.358866	−	0.621574i	−0.0237145	−	0.0410748i	0.853925	−	0.520397i	$-0.174216\pi$
$229$	−0.358866	−	0.621574i	−0.0237145	−	0.0410748i	−0.877639	+	0.479322i	$0.840883\pi$
$230$		0			0
$231$	−3.02600	−	2.54957i	−0.199096	−	0.167749i
$232$	4.34813	−	6.10470i	0.285469	−	0.400793i
$233$			13.8379i			0.906553i	0.891370	+	0.453276i	$0.149745\pi$
$233$			13.8379i			0.906553i	−0.891370	+	0.453276i	$0.850255\pi$
$234$	−7.43483	+	18.3537i	−0.486030	+	1.19982i
$235$		0			0
$236$	9.40283	+	18.9755i	0.612072	+	1.23520i
$237$	1.16223	−	6.51421i	0.0754951	−	0.423143i
$238$	20.4705	+	12.7023i	1.32690	+	0.823365i
$239$	−13.8553	−	23.9980i	−0.896223	−	1.55230i	−0.832284	−	0.554350i	$-0.812967\pi$
$239$	−13.8553	−	23.9980i	−0.896223	−	1.55230i	−0.0639388	−	0.997954i	$-0.520366\pi$
$240$		0			0
$241$	−5.71303	+	9.89526i	−0.368009	+	0.637410i	−0.989254	−	0.146206i	$-0.953294\pi$
$241$	−5.71303	+	9.89526i	−0.368009	+	0.637410i	0.621245	+	0.783616i	$0.286627\pi$
$242$	12.9332	−	6.92884i	0.831378	−	0.445403i
$243$	−15.3782	+	2.55139i	−0.986515	+	0.163672i
$244$	1.92729	−	2.89637i	0.123382	−	0.185421i
$245$		0			0
$246$	11.1821	−	12.4468i	0.712942	−	0.793576i
$247$	−18.4122	+	10.6303i	−1.17154	+	0.676388i
$248$	3.07762	+	6.74097i	0.195429	+	0.428052i
$249$	−16.4144	−	2.92857i	−1.04022	−	0.185591i
$250$		0			0
$251$	−5.05161			−0.318855			−0.159427	−	0.987210i	$-0.550965\pi$
$251$	−5.05161			−0.318855			−0.159427	+	0.987210i	$0.550965\pi$
$252$	17.2377	−	1.85056i	1.08587	−	0.116574i
$253$	1.05417			0.0662749
$254$	13.8133	+	0.438985i	0.866722	+	0.0275443i
$255$		0			0
$256$	15.4860	+	4.02282i	0.967876	+	0.251426i
$257$	2.29265	−	1.32366i	0.143012	−	0.0825679i	−0.426787	−	0.904352i	$-0.640355\pi$
$257$	2.29265	−	1.32366i	0.143012	−	0.0825679i	0.569799	+	0.821784i	$0.307021\pi$
$258$	−28.5306	−	6.03118i	−1.77624	−	0.375485i
$259$	−18.6174	−	10.7488i	−1.15683	−	0.667897i
$260$		0			0
$261$	7.83430	−	1.34872i	0.484931	−	0.0834835i
$262$	−16.5005	+	8.83999i	−1.01940	+	0.546136i
$263$	1.26561	−	2.19210i	0.0780408	−	0.135171i	−0.824364	−	0.566060i	$-0.808467\pi$
$263$	1.26561	−	2.19210i	0.0780408	−	0.135171i	0.902405	+	0.430890i	$0.141800\pi$
$264$	1.04009	−	3.73105i	0.0640134	−	0.229630i
$265$		0			0
$266$	15.8159	+	9.81401i	0.969734	+	0.601735i
$267$	0.0120843	−	0.00437066i	0.000739549	−	0.000267480i
$268$	−13.5021	+	6.69060i	−0.824770	+	0.408693i
$269$			5.26469i			0.320994i	0.987036	+	0.160497i	$0.0513097\pi$
$269$			5.26469i			0.320994i	−0.987036	+	0.160497i	$0.948690\pi$
$270$		0			0
$271$		−	16.6468i		−	1.01122i	−0.862761	−	0.505612i	$-0.831267\pi$
$271$		−	16.6468i		−	1.01122i	0.862761	−	0.505612i	$-0.168733\pi$
$272$	−2.98872	+	23.3922i	−0.181218	+	1.41836i
$273$	21.9666	−	7.94487i	1.32948	−	0.480845i
$274$	2.35063	−	3.78819i	0.142007	−	0.228853i
$275$		0			0
$276$	−3.19429	+	3.33604i	−0.192274	+	0.200806i
$277$	13.1963	−	22.8566i	0.792888	−	1.37332i	−0.131283	−	0.991345i	$-0.541910\pi$
$277$	13.1963	−	22.8566i	0.792888	−	1.37332i	0.924171	−	0.381978i	$-0.124757\pi$
$278$	1.71627	+	3.20355i	0.102935	+	0.192136i
$279$	−2.71809	+	7.37485i	−0.162728	+	0.441521i
$280$		0			0
$281$	−19.8511	−	11.4611i	−1.18422	−	0.683710i	−0.227233	−	0.973840i	$-0.572968\pi$
$281$	−19.8511	−	11.4611i	−1.18422	−	0.683710i	−0.956987	+	0.290131i	$0.906301\pi$
$282$	1.52650	−	7.22113i	0.0909017	−	0.430012i
$283$	5.64186	−	3.25733i	0.335374	−	0.193628i	−0.322851	−	0.946450i	$-0.604641\pi$
$283$	5.64186	−	3.25733i	0.335374	−	0.193628i	0.658224	+	0.752822i	$0.271308\pi$
$284$	5.75968	+	0.366455i	0.341774	+	0.0217451i
$285$		0			0
$286$	0.165770	−	5.21619i	0.00980220	−	0.308440i
$287$	−19.7374			−1.16506
$288$	8.65575	+	14.5972i	0.510045	+	0.860148i
$289$	−17.7581			−1.04459
$290$		0			0
$291$	11.3197	+	2.01961i	0.663575	+	0.118392i
$292$	12.9907	+	0.826520i	0.760222	+	0.0483684i
$293$	−14.5020	+	8.37272i	−0.847215	+	0.489140i	−0.859710	−	0.510782i	$-0.829356\pi$
$293$	−14.5020	+	8.37272i	−0.847215	+	0.489140i	0.0124952	+	0.999922i	$0.496023\pi$
$294$	−2.45802	−	2.20826i	−0.143355	−	0.128788i
$295$		0			0
$296$	2.00257	−	20.9480i	0.116397	−	1.21758i
$297$	3.57027	−	2.03249i	0.207168	−	0.117937i
$298$	6.57586	+	12.2743i	0.380929	+	0.711033i
$299$	−3.11159	+	5.38944i	−0.179948	+	0.311679i
$300$		0			0
$301$	17.1995	+	29.7903i	0.991360	+	1.71709i
$302$	−7.95701	+	12.8232i	−0.457874	+	0.737894i
$303$	−0.772916	+	4.33213i	−0.0444029	+	0.248874i
$304$	−2.30914	+	18.0733i	−0.132438	+	1.03657i
$305$		0			0
$306$	−19.7245	+	15.3815i	−1.12757	+	0.879303i
$307$		−	24.2759i		−	1.38550i	−0.721179	−	0.692749i	$-0.756400\pi$
$307$		−	24.2759i		−	1.38550i	0.721179	−	0.692749i	$-0.243600\pi$
$308$	−4.09396	+	2.02866i	−0.233275	+	0.115593i
$309$	10.1416	+	8.54482i	0.576933	+	0.486098i
$310$		0			0
$311$	3.81664	+	6.61061i	0.216422	+	0.374853i	0.953711	−	0.300723i	$-0.0972281\pi$
$311$	3.81664	+	6.61061i	0.216422	+	0.374853i	−0.737290	+	0.675577i	$0.763895\pi$
$312$	16.0050	+	16.3305i	0.906105	+	0.924532i
$313$	−2.22762	+	3.85836i	−0.125913	+	0.218087i	−0.922089	−	0.386977i	$-0.873519\pi$
$313$	−2.22762	+	3.85836i	−0.125913	+	0.218087i	0.796177	+	0.605064i	$0.206853\pi$
$314$	18.7115	−	10.0245i	1.05595	−	0.565716i
$315$		0			0
$316$	−6.36115	−	4.23282i	−0.357842	−	0.238115i
$317$	−4.29194	−	2.47795i	−0.241059	−	0.139176i	0.374604	−	0.927185i	$-0.377779\pi$
$317$	−4.29194	−	2.47795i	−0.241059	−	0.139176i	−0.615663	+	0.788009i	$0.711112\pi$
$318$	1.29699	+	3.97666i	0.0727317	+	0.223000i
$319$	−1.81438	+	1.04753i	−0.101586	+	0.0586506i
$320$		0			0
$321$	−8.07765	−	22.3337i	−0.450850	−	1.24655i
$322$	5.44558	+	0.173060i	0.303470	+	0.00964426i
$323$	−26.8548			−1.49424
$324$	−4.38642	+	17.4574i	−0.243690	+	0.969853i
$325$		0			0
$326$	−5.87837	−	0.186814i	−0.325573	−	0.0103467i
$327$	−7.81526	−	21.6082i	−0.432185	−	1.19494i
$328$	−8.02411	−	17.5754i	−0.443058	−	0.970438i
$329$	−7.53997	+	4.35320i	−0.415692	+	0.240000i
$330$		0			0
$331$	23.0250	+	13.2935i	1.26557	+	0.730676i	0.974146	−	0.225918i	$-0.0725382\pi$
$331$	23.0250	+	13.2935i	1.26557	+	0.730676i	0.291422	+	0.956594i	$0.405871\pi$
$332$	−10.6658	+	16.0287i	−0.585360	+	0.879689i
$333$	17.1561	−	14.2777i	0.940146	−	0.782412i
$334$	−0.0415787	+	0.0222754i	−0.00227509	+	0.00121886i
$335$		0			0
$336$	5.98541	−	19.1030i	0.326531	−	1.04216i
$337$	−6.22205	−	10.7769i	−0.338937	−	0.587056i	0.645296	−	0.763933i	$-0.276734\pi$
$337$	−6.22205	−	10.7769i	−0.338937	−	0.587056i	−0.984233	+	0.176877i	$0.943401\pi$
$338$	10.5569	+	6.55072i	0.574220	+	0.356312i
$339$	−12.2519	−	10.3229i	−0.665434	−	0.560665i
$340$		0			0
$341$		−	2.07142i		−	0.112173i
$342$	−15.2395	+	11.8841i	−0.824058	+	0.642616i
$343$		−	16.3284i		−	0.881652i
$344$	−19.5348	+	27.4266i	−1.05325	+	1.47874i
$345$		0			0
$346$	17.7705	−	28.6383i	0.955348	−	1.53960i
$347$	−8.46084	−	14.6546i	−0.454202	−	0.786701i	0.544440	−	0.838800i	$-0.316742\pi$
$347$	−8.46084	−	14.6546i	−0.454202	−	0.786701i	−0.998642	+	0.0520991i	$0.983409\pi$
$348$	2.18281	−	8.91604i	0.117011	−	0.477950i
$349$	0.955553	−	1.65507i	0.0511496	−	0.0885937i	−0.839317	−	0.543642i	$-0.817045\pi$
$349$	0.955553	−	1.65507i	0.0511496	−	0.0885937i	0.890467	+	0.455049i	$0.150378\pi$
$350$		0			0
$351$	−0.147285	+	24.2524i	−0.00786147	+	1.29450i
$352$	−3.47082	−	2.82078i	−0.184995	−	0.150348i
$353$	−19.1497	−	11.0561i	−1.01924	−	0.588457i	−0.105355	−	0.994435i	$-0.533598\pi$
$353$	−19.1497	−	11.0561i	−1.01924	−	0.588457i	−0.913883	+	0.405978i	$0.866931\pi$
$354$	19.2942	+	17.3338i	1.02548	+	0.921279i
$355$		0			0
$356$	0.000942175	−	0.0148085i	4.99352e−5	−	0.000784847i
$357$	29.0469	+	5.18241i	1.53733	+	0.274282i
$358$	1.14678	−	36.0849i	0.0606090	−	1.90715i
$359$	1.48034			0.0781296			0.0390648	−	0.999237i	$-0.487562\pi$
$359$	1.48034			0.0781296			0.0390648	+	0.999237i	$0.487562\pi$
$360$		0			0
$361$	−1.74850			−0.0920262
$362$	1.15046	−	36.2010i	0.0604671	−	1.90268i
$363$	11.5786	−	13.7423i	0.607721	−	0.721283i
$364$	1.71266	−	26.9185i	0.0897679	−	1.41091i
$365$		0			0
$366$	0.881248	−	4.16876i	0.0460636	−	0.217904i
$367$	0.109318	+	0.0631149i	0.00570636	+	0.00329457i	0.502850	−	0.864373i	$-0.332285\pi$
$367$	0.109318	+	0.0631149i	0.00570636	+	0.00329457i	−0.497144	+	0.867668i	$0.665618\pi$
$368$	2.05977	+	4.91944i	0.107373	+	0.256444i
$369$	7.08673	−	19.2281i	0.368921	−	1.00097i
$370$		0			0
$371$	2.46707	−	4.27308i	0.128084	−	0.221847i
$372$	6.55526	+	6.27672i	0.339874	+	0.325433i
$373$	−11.4620	−	19.8527i	−0.593479	−	1.02794i	−0.993760	−	0.111543i	$-0.964421\pi$
$373$	−11.4620	−	19.8527i	−0.593479	−	1.02794i	0.400280	−	0.916393i	$-0.368913\pi$
$374$	3.47569	−	5.60130i	0.179724	−	0.289636i
$375$		0			0
$376$	−6.94170	−	4.94429i	−0.357991	−	0.254982i
$377$		−	12.3681i		−	0.636988i
$378$	18.7769	−	9.91326i	0.965779	−	0.509883i
$379$		−	27.5123i		−	1.41321i	−0.707608	−	0.706605i	$-0.750226\pi$
$379$		−	27.5123i		−	1.41321i	0.707608	−	0.706605i	$-0.249774\pi$
$380$		0			0
$381$	15.9172	−	5.75692i	0.815462	−	0.294936i
$382$	−9.27357	−	5.75439i	−0.474477	−	0.294420i
$383$	11.8649	+	20.5507i	0.606270	+	1.05009i	0.991849	+	0.127416i	$0.0406684\pi$
$383$	11.8649	+	20.5507i	0.606270	+	1.05009i	−0.385579	+	0.922675i	$0.625998\pi$
$384$	19.4439	−	2.43645i	0.992240	−	0.124334i
$385$		0			0
$386$	−6.43965	+	3.44998i	−0.327770	+	0.175599i
$387$	−35.1971	+	6.05938i	−1.78917	+	0.308016i
$388$	7.35537	−	11.0538i	0.373412	−	0.561170i
$389$	1.58128	+	0.912954i	0.0801742	+	0.0462886i	0.539551	−	0.841953i	$-0.318594\pi$
$389$	1.58128	+	0.912954i	0.0801742	+	0.0462886i	−0.459377	+	0.888241i	$0.651927\pi$
$390$		0			0
$391$	−6.80755	+	3.93034i	−0.344272	+	0.198766i
$392$	−3.47083	+	1.58462i	−0.175304	+	0.0800356i
$393$	−14.7723	+	17.5327i	−0.745164	+	0.884410i
$394$	−11.9740	−	0.380532i	−0.603241	−	0.0191709i
$395$		0			0
$396$	−0.506366	−	4.71672i	−0.0254458	−	0.237024i
$397$	−19.0828			−0.957737			−0.478868	−	0.877887i	$-0.658953\pi$
$397$	−19.0828			−0.957737			−0.478868	+	0.877887i	$0.658953\pi$
$398$	0.785859	+	0.0249745i	0.0393916	+	0.00125186i
$399$	22.4422	+	4.00403i	1.12352	+	0.200452i
$400$		0			0
$401$	−15.1375	+	8.73963i	−0.755930	+	0.436436i	−0.827833	−	0.560975i	$-0.810426\pi$
$401$	−15.1375	+	8.73963i	−0.755930	+	0.436436i	0.0719025	+	0.997412i	$0.477093\pi$
$402$	−12.3339	+	13.7288i	−0.615157	+	0.684732i
$403$	10.5901	+	6.11422i	0.527533	+	0.304571i
$404$	4.23034	+	2.81494i	0.210467	+	0.140048i
$405$		0			0
$406$	−9.54466	+	5.11346i	−0.473693	+	0.253777i
$407$	−2.94117	+	5.09425i	−0.145788	+	0.252513i
$408$	7.19413	+	27.9721i	0.356163	+	1.38483i
$409$	8.17716	+	14.1633i	0.404335	+	0.700328i	0.994244	−	0.107142i	$-0.0341698\pi$
$409$	8.17716	+	14.1633i	0.404335	+	0.700328i	−0.589909	+	0.807470i	$0.700836\pi$
$410$		0			0
$411$	0.959036	−	5.37531i	0.0473057	−	0.265144i
$412$	13.7208	−	6.79899i	0.675976	−	0.334962i
$413$		−	30.5957i		−	1.50551i
$414$	−2.12384	+	5.24293i	−0.104381	+	0.257676i
$415$		0			0
$416$	24.6662	−	9.41849i	1.20936	−	0.461779i
$417$	3.40396	+	2.86803i	0.166693	+	0.140448i
$418$	2.68539	−	4.32767i	0.131347	−	0.211673i
$419$	12.3846	+	21.4508i	0.605029	+	1.04794i	0.992047	+	0.125869i	$0.0401720\pi$
$419$	12.3846	+	21.4508i	0.605029	+	1.04794i	−0.387018	+	0.922072i	$0.626495\pi$
$420$		0			0
$421$	8.38623	−	14.5254i	0.408720	−	0.707923i	−0.586027	−	0.810292i	$-0.699309\pi$
$421$	8.38623	−	14.5254i	0.408720	−	0.707923i	0.994747	+	0.102368i	$0.0326420\pi$
$422$	16.2445	+	30.3215i	0.790768	+	1.47603i
$423$	−1.53364	−	8.90844i	−0.0745679	−	0.433143i
$424$	4.80799	+	0.459631i	0.233497	+	0.0223217i
$425$		0			0
$426$	6.72002	−	2.19174i	0.325586	−	0.106190i
$427$	−4.35282	+	2.51310i	−0.210648	+	0.121618i
$428$	−27.3683	−	1.74129i	−1.32290	−	0.0841682i
$429$	−2.17394	−	6.01068i	−0.104959	−	0.290198i
$430$		0			0
$431$	15.2488			0.734510			0.367255	−	0.930120i	$-0.380298\pi$
$431$	15.2488			0.734510			0.367255	+	0.930120i	$0.380298\pi$
$432$	16.4610	+	12.6899i	0.791982	+	0.610545i
$433$	23.5695			1.13268			0.566340	−	0.824172i	$-0.308359\pi$
$433$	23.5695			1.13268			0.566340	+	0.824172i	$0.308359\pi$
$434$	0.340060	−	10.7005i	0.0163234	−	0.513639i
$435$		0			0
$436$	−26.4793	−	1.68472i	−1.26813	−	0.0806836i
$437$	−5.25964	+	3.03665i	−0.251603	+	0.145263i
$438$	15.1567	−	4.94336i	0.724214	−	0.236203i
$439$	12.8688	+	7.42979i	0.614193	+	0.354605i	0.774605	−	0.632446i	$-0.217949\pi$
$439$	12.8688	+	7.42979i	0.614193	+	0.354605i	−0.160412	+	0.987050i	$0.551282\pi$
$440$		0			0
$441$	−3.79721	−	1.39951i	−0.180820	−	0.0666432i
$442$	18.3775	+	34.3030i	0.874128	+	1.63163i
$443$	−13.5713	+	23.5062i	−0.644791	+	1.11681i	0.339558	+	0.940585i	$0.389722\pi$
$443$	−13.5713	+	23.5062i	−0.644791	+	1.11681i	−0.984350	+	0.176226i	$0.943611\pi$
$444$	−7.20922	−	24.7441i	−0.342134	−	1.17430i
$445$		0			0
$446$	−0.252978	+	0.407691i	−0.0119789	+	0.0193047i
$447$	13.0422	+	10.9888i	0.616875	+	0.519751i
$448$	−17.4664	−	15.1413i	−0.825209	−	0.715360i
$449$		−	17.4879i		−	0.825304i	−0.910889	−	0.412652i	$-0.864602\pi$
$449$		−	17.4879i		−	0.825304i	0.910889	−	0.412652i	$-0.135398\pi$
$450$		0			0
$451$			5.40069i			0.254309i
$452$	−16.5760	+	8.21381i	−0.779670	+	0.386345i
$453$	−3.24639	+	18.1957i	−0.152529	+	0.854910i
$454$	−10.3393	−	6.41567i	−0.485245	−	0.301102i
$455$		0			0
$456$	5.55833	+	21.6118i	0.260292	+	1.01206i
$457$	−2.94811	+	5.10627i	−0.137907	+	0.238861i	−0.926704	−	0.375792i	$-0.877371\pi$
$457$	−2.94811	+	5.10627i	−0.137907	+	0.238861i	0.788797	+	0.614653i	$0.210704\pi$
$458$	−0.894715	+	0.479335i	−0.0418073	+	0.0223979i
$459$	−15.4780	+	26.4367i	−0.722453	+	1.23396i
$460$		0			0
$461$	30.5948	+	17.6639i	1.42494	+	0.822691i	0.996716	−	0.0809799i	$-0.0258050\pi$
$461$	30.5948	+	17.6639i	1.42494	+	0.822691i	0.428227	+	0.903671i	$0.359138\pi$
$462$	−3.73975	+	4.16272i	−0.173989	+	0.193667i
$463$	−32.2464	+	18.6175i	−1.49862	+	0.865227i	−0.999999	−	0.00159457i	$-0.999492\pi$
$463$	−32.2464	+	18.6175i	−1.49862	+	0.865227i	−0.498618	+	0.866822i	$0.666159\pi$
$464$	−8.43367	−	6.42031i	−0.391523	−	0.298055i
$465$		0			0
$466$	19.5599	+	0.621612i	0.906095	+	0.0287956i
$467$	−6.98334			−0.323151			−0.161575	−	0.986860i	$-0.551657\pi$
$467$	−6.98334			−0.323151			−0.161575	+	0.986860i	$0.551657\pi$
$468$	25.6089	+	11.3336i	1.18377	+	0.523895i
$469$	21.7704			1.00526
$470$		0			0
$471$	16.7517	−	19.8821i	0.771879	−	0.916117i
$472$	27.2443	−	12.4385i	1.25402	−	0.572529i
$473$	8.15147	−	4.70625i	0.374805	−	0.216394i
$474$	−9.15562	−	1.93544i	−0.420532	−	0.0888977i
$475$		0			0
$476$	18.8742	−	28.3644i	0.865097	−	1.30008i
$477$	3.27702	+	3.93767i	0.150044	+	0.180293i
$478$	−34.5436	+	18.5064i	−1.57999	+	0.846463i
$479$	10.2090	−	17.6825i	0.466460	−	0.807932i	−0.532806	−	0.846237i	$-0.678863\pi$
$479$	10.2090	−	17.6825i	0.466460	−	0.807932i	0.999266	+	0.0383050i	$0.0121958\pi$
$480$		0			0
$481$	−17.3630	−	30.0735i	−0.791683	−	1.37124i
$482$	13.7303	+	8.51987i	0.625399	+	0.388070i
$483$	6.27500	−	2.26954i	0.285522	−	0.103268i
$484$	−9.21295	−	18.5923i	−0.418770	−	0.845106i
$485$		0			0
$486$	2.91558	+	21.8518i	0.132254	+	0.991216i
$487$		−	20.8264i		−	0.943735i	−0.881669	−	0.471868i	$-0.843580\pi$
$487$		−	20.8264i		−	0.943735i	0.881669	−	0.471868i	$-0.156420\pi$
$488$	−4.00744	−	2.85434i	−0.181408	−	0.129210i
$489$	−6.77371	+	2.44991i	−0.306318	+	0.110789i
$490$		0			0
$491$	−9.31608	−	16.1359i	−0.420429	−	0.728204i	0.575552	−	0.817765i	$-0.304787\pi$
$491$	−9.31608	−	16.1359i	−0.420429	−	0.728204i	−0.995981	+	0.0895606i	$0.971454\pi$
$492$	−17.0912	−	16.3650i	−0.770530	−	0.737789i
$493$	7.81122	−	13.5294i	0.351800	−	0.609335i
$494$	14.1988	+	26.5031i	0.638834	+	1.19243i
$495$		0			0
$496$	9.66661	−	4.04740i	0.434044	−	0.181734i
$497$	−7.22093	−	4.16900i	−0.323903	−	0.187005i
$498$	−4.87688	+	23.0702i	−0.218538	+	1.03380i
$499$	4.48667	−	2.59038i	0.200851	−	0.115961i	−0.396201	−	0.918164i	$-0.629672\pi$
$499$	4.48667	−	2.59038i	0.200851	−	0.115961i	0.597052	+	0.802202i	$0.296338\pi$
$500$		0			0
$501$	−0.0372239	+	0.0441798i	−0.00166304	+	0.00197381i
$502$	−0.226923	+	7.14045i	−0.0101281	+	0.318694i
$503$	27.8846			1.24331			0.621657	−	0.783290i	$-0.286460\pi$
$503$	27.8846			1.24331			0.621657	+	0.783290i	$0.286460\pi$
$504$	−1.84144	−	24.4486i	−0.0820241	−	1.08903i
$505$		0			0
$506$	0.0473541	−	1.49006i	0.00210515	−	0.0662414i
$507$	14.9799	+	2.67264i	0.665281	+	0.118696i
$508$	1.24101	−	19.5053i	0.0550609	−	0.865410i
$509$	−18.6724	+	10.7805i	−0.827640	+	0.477838i	−0.853044	−	0.521839i	$-0.825246\pi$
$509$	−18.6724	+	10.7805i	−0.827640	+	0.477838i	0.0254039	+	0.999677i	$0.491913\pi$
$510$		0			0
$511$	−16.2864	−	9.40298i	−0.720470	−	0.415963i
$512$	6.38191	−	21.7088i	0.282043	−	0.959402i
$513$	−11.9586	+	20.4255i	−0.527987	+	0.901807i
$514$	−1.76801	−	3.30013i	−0.0779837	−	0.145562i
$515$		0			0
$516$	−9.80670	+	40.0571i	−0.431716	+	1.76341i
$517$	1.19116	+	2.06315i	0.0523871	+	0.0907371i
$518$	−16.0297	+	25.8329i	−0.704306	+	1.13503i
$519$	7.25021	−	40.6368i	0.318249	−	1.78376i
$520$		0			0
$521$		−	19.9411i		−	0.873633i	−0.899551	−	0.436817i	$-0.856106\pi$
$521$		−	19.9411i		−	0.873633i	0.899551	−	0.436817i	$-0.143894\pi$
$522$	−1.55449	−	11.1344i	−0.0680381	−	0.487338i
$523$		−	18.9360i		−	0.828013i	−0.910274	−	0.414006i	$-0.864129\pi$
$523$		−	18.9360i		−	0.828013i	0.910274	−	0.414006i	$-0.135871\pi$
$524$	11.7541	+	23.7206i	0.513480	+	1.03624i
$525$		0			0
$526$	−3.04168	−	1.88741i	−0.132624	−	0.0822950i
$527$	7.72304	+	13.3767i	0.336421	+	0.582698i
$528$	−5.22712	−	1.63778i	−0.227481	−	0.0712750i
$529$	10.6111	−	18.3790i	0.461354	−	0.799088i
$530$		0			0
$531$	29.8062	+	10.9854i	1.29348	+	0.476727i
$532$	14.5826	−	21.9149i	0.632234	−	0.950132i
$533$	−27.6111	−	15.9413i	−1.19597	−	0.690494i
$534$	−0.00563508	−	0.0172775i	−0.000243854	−	0.000747672i
$535$		0			0
$536$	8.85063	+	19.3857i	0.382289	+	0.837335i
$537$	−15.0390	−	41.5810i	−0.648981	−	1.79435i
$538$	7.44164	+	0.236495i	0.320832	+	0.0101960i
$539$	1.06654			0.0459393
$540$		0			0
$541$	−13.2697			−0.570511			−0.285255	−	0.958452i	$-0.592078\pi$
$541$	−13.2697			−0.570511			−0.285255	+	0.958452i	$0.592078\pi$
$542$	−23.5303	−	0.747791i	−1.01071	−	0.0321204i
$543$	−15.0874	−	41.7148i	−0.647462	−	1.79015i
$544$	32.9307	+	5.27535i	1.41189	+	0.226179i
$545$		0			0
$546$	−10.2433	−	31.4067i	−0.438373	−	1.34408i
$547$	−7.81809	−	4.51377i	−0.334277	−	0.192995i	0.323461	−	0.946241i	$-0.395153\pi$
$547$	−7.81809	−	4.51377i	−0.334277	−	0.192995i	−0.657738	+	0.753246i	$0.728487\pi$
$548$	−5.24901	−	3.49278i	−0.224227	−	0.149204i
$549$	−0.885368	−	5.14284i	−0.0377866	−	0.219491i
$550$		0			0
$551$	6.03510	−	10.4531i	0.257104	−	0.445317i
$552$	4.57201	+	4.66499i	0.194598	+	0.198555i
$553$	5.51940	+	9.55988i	0.234709	+	0.406527i
$554$	−31.7151	−	19.6797i	−1.34744	−	0.836110i
$555$		0			0
$556$	4.60532	−	2.28205i	0.195309	−	0.0967803i
$557$			30.4174i			1.28883i	0.764677	+	0.644414i	$0.222899\pi$
$557$			30.4174i			1.28883i	−0.764677	+	0.644414i	$0.777101\pi$
$558$	10.3023	+	4.17331i	0.436129	+	0.176670i
$559$			55.5660i			2.35019i
$560$		0			0
$561$	1.41805	−	7.94806i	0.0598702	−	0.335567i
$562$	−17.0919	+	27.5448i	−0.720980	+	1.16191i
$563$	−22.6283	−	39.1934i	−0.953669	−	1.65180i	−0.737385	−	0.675473i	$-0.763940\pi$
$563$	−22.6283	−	39.1934i	−0.953669	−	1.65180i	−0.216284	−	0.976330i	$-0.569394\pi$
$564$	−10.1385	−	2.48209i	−0.426907	−	0.104515i
$565$		0			0
$566$	−4.35080	−	8.12109i	−0.182878	−	0.341355i
$567$	16.8765	−	19.7851i	0.708747	−	0.830895i
$568$	0.776714	−	8.12485i	0.0325902	−	0.340911i
$569$	4.42750	+	2.55622i	0.185610	+	0.107162i	0.589926	−	0.807457i	$-0.299157\pi$
$569$	4.42750	+	2.55622i	0.185610	+	0.107162i	−0.404316	+	0.914620i	$0.632490\pi$
$570$		0			0
$571$	30.6553	−	17.6989i	1.28289	−	0.740675i	0.305511	−	0.952189i	$-0.401173\pi$
$571$	30.6553	−	17.6989i	1.28289	−	0.740675i	0.977375	+	0.211514i	$0.0678394\pi$
$572$	−7.36564	−	0.468632i	−0.307973	−	0.0195945i
$573$	−13.1589	−	2.34774i	−0.549720	−	0.0980783i
$574$	−0.886620	+	27.8987i	−0.0370068	+	1.16447i
$575$		0			0
$576$	21.0220	−	11.5792i	0.875915	−	0.482466i
$577$	30.4257			1.26664			0.633320	−	0.773890i	$-0.281692\pi$
$577$	30.4257			1.26664			0.633320	+	0.773890i	$0.281692\pi$
$578$	−0.797709	+	25.1010i	−0.0331803	+	1.04407i
$579$	−5.76519	+	6.84250i	−0.239593	+	0.284365i
$580$		0			0
$581$	24.0888	−	13.9077i	0.999372	−	0.576987i
$582$	3.36321	−	15.9097i	0.139410	−	0.659480i
$583$	−1.16924	−	0.675058i	−0.0484248	−	0.0279581i
$584$	1.75184	−	18.3252i	0.0724916	−	0.758302i
$585$		0			0
$586$	11.1834	+	20.8747i	0.461982	+	0.862324i
$587$	−14.6186	+	25.3201i	−0.603372	+	1.04507i	0.388934	+	0.921265i	$0.372843\pi$
$587$	−14.6186	+	25.3201i	−0.603372	+	1.04507i	−0.992306	+	0.123806i	$0.960490\pi$
$588$	−3.23179	+	3.37521i	−0.133277	+	0.139191i
$589$	5.96697	+	10.3351i	0.245865	+	0.425850i
$590$		0			0
$591$	−13.7978	+	4.99036i	−0.567564	+	0.205276i
$592$	−29.5200	−	3.77164i	−1.21327	−	0.155013i
$593$			1.73460i			0.0712314i	0.999366	+	0.0356157i	$0.0113392\pi$
$593$			1.73460i			0.0712314i	−0.999366	+	0.0356157i	$0.988661\pi$
$594$	−2.71254	−	5.13788i	−0.111297	−	0.210810i
$595$		0			0
$596$	17.6452	−	8.74360i	0.722774	−	0.358152i
$597$	0.905554	−	0.327520i	0.0370619	−	0.0134045i
$598$	7.47820	+	4.64034i	0.305806	+	0.189758i
$599$	1.94974	+	3.37704i	0.0796641	+	0.137982i	0.903105	−	0.429420i	$-0.141282\pi$
$599$	1.94974	+	3.37704i	0.0796641	+	0.137982i	−0.823441	+	0.567402i	$0.807949\pi$
$600$		0			0
$601$	2.16133	−	3.74354i	0.0881625	−	0.152702i	−0.818572	−	0.574404i	$-0.805234\pi$
$601$	2.16133	−	3.74354i	0.0881625	−	0.152702i	0.906734	+	0.421702i	$0.138567\pi$
$602$	42.8812	−	22.9732i	1.74771	−	0.936319i
$603$	−7.81670	+	21.2086i	−0.318321	+	0.863683i
$604$	17.7682	+	11.8233i	0.722978	+	0.481082i
$605$		0			0
$606$	6.08874	+	1.28712i	0.247338	+	0.0522857i
$607$	−10.9725	+	6.33497i	−0.445360	+	0.257128i	−0.705868	−	0.708343i	$-0.749443\pi$
$607$	−10.9725	+	6.33497i	−0.445360	+	0.257128i	0.260509	+	0.965471i	$0.416110\pi$
$608$	25.4429	+	4.07584i	1.03184	+	0.165297i
$609$	−8.54498	+	10.1418i	−0.346260	+	0.410964i
$610$		0			0
$611$	−14.0638			−0.568961
$612$	20.8557	+	28.5715i	0.843043	+	1.15493i
$613$	47.3059			1.91067			0.955334	−	0.295527i	$-0.0954952\pi$
$613$	47.3059			1.91067			0.955334	+	0.295527i	$0.0954952\pi$
$614$	−34.3139	−	1.09049i	−1.38480	−	0.0440088i
$615$		0			0
$616$	2.68360	+	5.87794i	0.108125	+	0.236829i
$617$	6.04277	−	3.48880i	0.243273	−	0.140454i	−0.373407	−	0.927668i	$-0.621811\pi$
$617$	6.04277	−	3.48880i	0.243273	−	0.140454i	0.616680	+	0.787214i	$0.288477\pi$
$618$	12.5337	−	13.9512i	0.504178	−	0.561202i
$619$	24.9827	+	14.4238i	1.00414	+	0.579741i	0.909471	−	0.415768i	$-0.136487\pi$
$619$	24.9827	+	14.4238i	1.00414	+	0.579741i	0.0946695	+	0.995509i	$0.469821\pi$
$620$		0			0
$621$	−0.0420735	+	6.92797i	−0.00168835	+	0.278010i
$622$	9.51554	−	5.09786i	0.381538	−	0.204406i
$623$	−0.0107187	+	0.0185654i	−0.000429437	+	0.000743807i
$624$	23.8021	−	21.8895i	0.952847	−	0.876281i
$625$		0			0
$626$	5.35372	+	3.32207i	0.213978	+	0.132777i
$627$	1.09561	−	6.14082i	0.0437546	−	0.245241i
$628$	−13.3291	−	26.8990i	−0.531890	−	1.07339i
$629$		−	43.8633i		−	1.74894i
$630$		0			0
$631$			31.3427i			1.24774i	0.781530	+	0.623868i	$0.214440\pi$
$631$			31.3427i			1.24774i	−0.781530	+	0.623868i	$0.785560\pi$
$632$	−6.26884	+	8.80134i	−0.249361	+	0.350098i
$633$	32.2184	+	27.1457i	1.28056	+	1.07895i
$634$	−3.69538	+	5.95534i	−0.146762	+	0.236517i
$635$		0			0
$636$	5.67928	−	1.65466i	0.225198	−	0.0656116i
$637$	−3.14813	+	5.45272i	−0.124733	+	0.216045i
$638$	1.39919	+	2.61169i	0.0553943	+	0.103398i
$639$	6.65412	−	5.53771i	0.263233	−	0.219069i
$640$		0			0
$641$	−17.6686	−	10.2010i	−0.697869	−	0.402915i	0.108684	−	0.994076i	$-0.465336\pi$
$641$	−17.6686	−	10.2010i	−0.697869	−	0.402915i	−0.806553	+	0.591162i	$0.798670\pi$
$642$	−31.9316	+	10.4145i	−1.26024	+	0.411028i
$643$	−25.7560	+	14.8702i	−1.01572	+	0.586424i	−0.912860	−	0.408272i	$-0.866131\pi$
$643$	−25.7560	+	14.8702i	−1.01572	+	0.586424i	−0.102856	+	0.994696i	$0.532798\pi$
$644$	0.489241	−	7.68956i	0.0192788	−	0.303011i
$645$		0			0
$646$	−1.20634	+	37.9592i	−0.0474628	+	1.49348i
$647$	−7.37854			−0.290081			−0.145040	−	0.989426i	$-0.546331\pi$
$647$	−7.37854			−0.290081			−0.145040	+	0.989426i	$0.546331\pi$
$648$	24.4789	+	6.98440i	0.961623	+	0.274373i
$649$	−8.37183			−0.328623
$650$		0			0
$651$	−4.45960	−	12.3303i	−0.174786	−	0.483261i
$652$	−0.528123	+	8.30068i	−0.0206829	+	0.325080i
$653$	−12.6906	+	7.32692i	−0.496621	+	0.286724i	−0.727317	−	0.686301i	$-0.759233\pi$
$653$	−12.6906	+	7.32692i	−0.496621	+	0.286724i	0.230696	+	0.973026i	$0.425900\pi$
$654$	−30.8943	+	10.0762i	−1.20806	+	0.394011i
$655$		0			0
$656$	−25.2032	+	10.5526i	−0.984021	+	0.412009i
$657$	15.0080	−	12.4900i	0.585519	−	0.487283i
$658$	5.81455	+	10.8533i	0.226675	+	0.423105i
$659$	−3.26655	+	5.65782i	−0.127247	+	0.220398i	−0.922609	−	0.385737i	$-0.873947\pi$
$659$	−3.26655	+	5.65782i	−0.127247	+	0.220398i	0.795362	+	0.606134i	$0.207281\pi$
$660$		0			0
$661$	13.4007	+	23.2106i	0.521225	+	0.902788i	0.999695	+	0.0246846i	$0.00785816\pi$
$661$	13.4007	+	23.2106i	0.521225	+	0.902788i	−0.478470	+	0.878104i	$0.658809\pi$
$662$	19.8247	−	31.9487i	0.770507	−	1.24172i
$663$	36.4489	+	30.7102i	1.41556	+	1.19269i
$664$	22.1774	+	15.7961i	0.860651	+	0.613007i
$665$		0			0
$666$	−19.4108	−	24.8915i	−0.752155	−	0.964524i
$667$		−	3.53308i		−	0.136801i
$668$	0.0296185	+	0.0597722i	0.00114598	+	0.00231266i
$669$	−0.103213	+	0.578500i	−0.00399044	+	0.0223661i
$670$		0			0
$671$	0.687656	+	1.19105i	0.0265466	+	0.0459801i
$672$	−26.7332	−	9.31850i	−1.03126	−	0.359469i
$673$	9.43992	−	16.3504i	0.363882	−	0.630262i	−0.624714	−	0.780854i	$-0.714784\pi$
$673$	9.43992	−	16.3504i	0.363882	−	0.630262i	0.988596	+	0.150591i	$0.0481177\pi$
$674$	−15.5127	+	8.31076i	−0.597526	+	0.320119i
$675$		0			0
$676$	9.73367	−	14.6279i	0.374372	−	0.562612i
$677$	17.5219	+	10.1163i	0.673421	+	0.388800i	0.797372	−	0.603488i	$-0.206223\pi$
$677$	17.5219	+	10.1163i	0.673421	+	0.388800i	−0.123950	+	0.992288i	$0.539556\pi$
$678$	−15.1418	+	16.8544i	−0.581519	+	0.647289i
$679$	−16.6122	+	9.59106i	−0.637518	+	0.368071i
$680$		0			0
$681$	−14.6711	−	2.61754i	−0.562196	−	0.100304i
$682$	−2.92795	−	0.0930499i	−0.112117	−	0.00356306i
$683$	15.3795			0.588481			0.294241	−	0.955731i	$-0.404933\pi$
$683$	15.3795			0.588481			0.294241	+	0.955731i	$0.404933\pi$
$684$	16.1135	+	22.0749i	0.616116	+	0.844054i
$685$		0			0
$686$	−23.0802	−	0.733487i	−0.881207	−	0.0280047i
$687$	−0.801006	+	0.950687i	−0.0305603	+	0.0362710i
$688$	37.8899	+	28.8445i	1.44454	+	1.09969i
$689$	6.90249	−	3.98516i	0.262964	−	0.151822i
$690$		0			0
$691$	−13.7773	−	7.95434i	−0.524114	−	0.302598i	0.214502	−	0.976724i	$-0.431187\pi$
$691$	−13.7773	−	7.95434i	−0.524114	−	0.302598i	−0.738616	+	0.674126i	$0.764520\pi$
$692$	−39.6819	−	26.4051i	−1.50848	−	1.00377i
$693$	−2.37010	+	6.43067i	−0.0900327	+	0.244281i
$694$	−21.0944	+	11.3011i	−0.800731	+	0.428984i
$695$		0			0
$696$	−12.5048	−	3.48592i	−0.473992	−	0.132133i
$697$	−20.1359	−	34.8763i	−0.762700	−	1.32104i
$698$	−2.29651	−	1.42502i	−0.0869242	−	0.0539378i
$699$	22.5391	−	8.15193i	0.852507	−	0.308334i
$700$		0			0
$701$			38.9767i			1.47213i	0.676912	+	0.736064i	$0.263318\pi$
$701$			38.9767i			1.47213i	−0.676912	+	0.736064i	$0.736682\pi$
$702$	34.2742	+	1.29763i	1.29359	+	0.0489758i
$703$		−	33.8896i		−	1.27817i
$704$	−4.14309	+	4.77929i	−0.156148	+	0.180126i
$705$		0			0
$706$	−16.4880	+	26.5715i	−0.620535	+	1.00003i
$707$	−3.67055	−	6.35758i	−0.138045	−	0.239102i
$708$	25.3680	−	26.4937i	0.953387	−	0.995696i
$709$	6.59388	−	11.4209i	0.247638	−	0.428922i	−0.715232	−	0.698887i	$-0.753679\pi$
$709$	6.59388	−	11.4209i	0.247638	−	0.428922i	0.962870	+	0.269965i	$0.0870121\pi$
$710$		0			0
$711$	−11.2950	+	1.94449i	−0.423594	+	0.0729240i
$712$	−0.0208894	−	0.00199697i	−0.000782865	−	7.48398e-5i
$713$	3.02519	+	1.74660i	0.113294	+	0.0654105i
$714$	8.63015	−	40.8251i	0.322975	−	1.52784i
$715$		0			0
$716$	−50.9545	−	3.24193i	−1.90426	−	0.121157i
$717$	−30.9256	+	36.7046i	−1.15494	+	1.37076i
$718$	0.0664984	−	2.09247i	0.00248170	−	0.0780902i
$719$	−43.7650			−1.63216			−0.816079	−	0.577940i	$-0.803857\pi$
$719$	−43.7650			−1.63216			−0.816079	+	0.577940i	$0.803857\pi$
$720$		0			0
$721$	−22.1231			−0.823907
$722$	−0.0785441	+	2.47150i	−0.00292311	+	0.0919798i
$723$	19.4829	+	3.47603i	0.724575	+	0.129275i
$724$	−51.1184	−	3.25236i	−1.89980	−	0.120873i
$725$		0			0
$726$	−18.9046	−	16.9837i	−0.701616	−	0.630325i
$727$	8.58770	+	4.95811i	0.318500	+	0.183886i	0.650724	−	0.759314i	$-0.274466\pi$
$727$	8.58770	+	4.95811i	0.318500	+	0.183886i	−0.332224	+	0.943201i	$0.607799\pi$
$728$	−37.9723	−	3.63005i	−1.40735	−	0.134539i
$729$	13.2150	+	23.5449i	0.489445	+	0.872034i
$730$		0			0
$731$	−35.0935	+	60.7837i	−1.29798	+	2.24816i
$732$	−5.85295	−	1.43291i	−0.216331	−	0.0529618i
$733$	−13.9862	−	24.2247i	−0.516591	−	0.894761i	−0.999814	−	0.0192642i	$-0.993868\pi$
$733$	−13.9862	−	24.2247i	−0.516591	−	0.894761i	0.483224	−	0.875497i	$-0.339466\pi$
$734$	0.0941235	−	0.151686i	0.00347416	−	0.00559883i
$735$		0			0
$736$	7.04616	−	2.69050i	0.259725	−	0.0991730i
$737$		−	5.95699i		−	0.219428i
$738$	−26.8605	−	10.8808i	−0.988750	−	0.400529i
$739$		−	24.2237i		−	0.891082i	−0.895262	−	0.445541i	$-0.853011\pi$
$739$		−	24.2237i		−	0.891082i	0.895262	−	0.445541i	$-0.146989\pi$
$740$		0			0
$741$	28.1611	+	23.7273i	1.03452	+	0.871644i
$742$	−5.92918	−	3.67915i	−0.217667	−	0.135066i
$743$	25.3632	+	43.9304i	0.930486	+	1.61165i	0.782492	+	0.622660i	$0.213948\pi$
$743$	25.3632	+	43.9304i	0.930486	+	1.61165i	0.147993	+	0.988988i	$0.452719\pi$
$744$	9.16661	−	8.98391i	0.336064	−	0.329366i
$745$		0			0
$746$	−28.5767	+	15.3097i	−1.04627	+	0.560528i
$747$	4.89968	+	28.4608i	0.179270	+	1.04133i
$748$	−7.76131	−	5.16451i	−0.283781	−	0.188833i
$749$	34.3117	+	19.8099i	1.25372	+	0.723838i
$750$		0			0
$751$	−0.581286	+	0.335605i	−0.0212114	+	0.0122464i	−0.510568	−	0.859837i	$-0.670565\pi$
$751$	−0.581286	+	0.335605i	−0.0212114	+	0.0122464i	0.489357	+	0.872084i	$0.337232\pi$
$752$	−7.30058	+	9.58999i	−0.266225	+	0.349711i
$753$	2.97591	+	8.22802i	0.108448	+	0.299846i
$754$	−17.4823	−	0.555585i	−0.636667	−	0.0202332i
$755$		0			0
$756$	−13.1689	−	26.9864i	−0.478949	−	0.981488i
$757$	17.0611			0.620095			0.310048	−	0.950721i	$-0.399655\pi$
$757$	17.0611			0.620095			0.310048	+	0.950721i	$0.399655\pi$
$758$	−38.8886	−	1.23588i	−1.41250	−	0.0448890i
$759$	−0.621010	−	1.71702i	−0.0225412	−	0.0623238i
$760$		0			0
$761$	6.74677	−	3.89525i	0.244570	−	0.141203i	−0.372705	−	0.927950i	$-0.621570\pi$
$761$	6.74677	−	3.89525i	0.244570	−	0.141203i	0.617275	+	0.786747i	$0.288236\pi$
$762$	−7.42239	−	22.7575i	−0.268885	−	0.824419i
$763$	33.1972	+	19.1664i	1.20182	+	0.693870i
$764$	−8.55041	+	12.8497i	−0.309343	+	0.464886i
$765$		0			0
$766$	29.5814	−	15.8479i	1.06882	−	0.572609i
$767$	24.7112	−	42.8011i	0.892271	−	1.54546i
$768$	−2.57048	−	27.5933i	−0.0927543	−	0.995689i
$769$	−4.58773	−	7.94618i	−0.165438	−	0.286546i	0.771373	−	0.636383i	$-0.219570\pi$
$769$	−4.58773	−	7.94618i	−0.165438	−	0.286546i	−0.936811	+	0.349837i	$0.886237\pi$
$770$		0			0
$771$	−3.50658	−	2.95448i	−0.126286	−	0.106403i
$772$	4.58727	+	9.25742i	0.165100	+	0.333182i
$773$			32.0512i			1.15280i	0.817167	+	0.576401i	$0.195543\pi$
$773$			32.0512i			1.15280i	−0.817167	+	0.576401i	$0.804457\pi$
$774$	6.98385	+	50.0234i	0.251029	+	1.79805i
$775$		0			0
$776$	−15.2941	−	10.8934i	−0.549026	−	0.391049i
$777$	−6.53999	+	36.6560i	−0.234621	+	1.31503i
$778$	1.36149	−	2.19413i	0.0488119	−	0.0786634i
$779$	−15.5574	−	26.9461i	−0.557400	−	0.965445i
$780$		0			0
$781$	−1.14076	+	1.97585i	−0.0408195	+	0.0707014i
$782$	5.24973	+	9.79902i	0.187730	+	0.350412i
$783$	−6.81197	−	11.9659i	−0.243440	−	0.427627i
$784$	2.08395	+	4.97720i	0.0744269	+	0.177757i
$785$		0			0
$786$	24.1189	+	21.6682i	0.860294	+	0.772880i
$787$	3.42695	−	1.97855i	0.122157	−	0.0705276i	−0.437676	−	0.899133i	$-0.644198\pi$
$787$	3.42695	−	1.97855i	0.122157	−	0.0705276i	0.559834	+	0.828605i	$0.310865\pi$
$788$	−1.07576	+	16.9081i	−0.0383225	+	0.602327i
$789$	−4.31604	−	0.770047i	−0.153655	−	0.0274144i
$790$		0			0
$791$	26.7267			0.950293
$792$	−6.68983	+	0.503868i	−0.237713	+	0.0179042i
$793$	−8.11904			−0.288316
$794$	−0.857215	+	26.9735i	−0.0304214	+	0.957253i
$795$		0			0
$796$	0.0706030	−	1.10969i	0.00250246	−	0.0393319i
$797$	−8.64602	+	4.99178i	−0.306258	+	0.176818i	−0.645251	−	0.763971i	$-0.723247\pi$
$797$	−8.64602	+	4.99178i	−0.306258	+	0.176818i	0.338993	+	0.940789i	$0.389914\pi$
$798$	6.66782	−	31.5422i	0.236038	−	1.11658i
$799$	−15.3844	−	8.88219i	−0.544261	−	0.314229i
$800$		0			0
$801$	−0.0142378	−	0.0171081i	−0.000503067	−	0.000604485i
$802$	11.6735	+	21.7894i	0.412205	+	0.769412i
$803$	−2.57292	+	4.45643i	−0.0907963	+	0.157264i
$804$	18.8517	+	18.0506i	0.664847	+	0.636596i
$805$		0			0
$806$	9.11817	−	14.6945i	0.321174	−	0.517592i
$807$	8.57508	−	3.10143i	0.301857	−	0.109176i
$808$	4.16895	−	5.85313i	0.146663	−	0.205912i
$809$			37.9989i			1.33597i	0.744174	+	0.667986i	$0.232843\pi$
$809$			37.9989i			1.33597i	−0.744174	+	0.667986i	$0.767157\pi$
$810$		0			0
$811$		−	21.3193i		−	0.748622i	−0.927303	−	0.374311i	$-0.877879\pi$
$811$		−	21.3193i		−	0.748622i	0.927303	−	0.374311i	$-0.122121\pi$
$812$	6.79912	+	13.7211i	0.238602	+	0.481515i
$813$	−27.1142	+	9.80666i	−0.950937	+	0.343934i
$814$	7.06861	+	4.38618i	0.247755	+	0.153736i
$815$		0			0
$816$	39.8617	−	8.91238i	1.39544	−	0.311996i
$817$	−27.1139	+	46.9626i	−0.948595	+	1.64301i
$818$	20.3871	−	10.9222i	0.712818	−	0.381885i
$819$	−25.8811	−	31.0987i	−0.904357	−	1.08668i
$820$		0			0
$821$	−4.11744	−	2.37721i	−0.143700	−	0.0829651i	0.426426	−	0.904522i	$-0.359772\pi$
$821$	−4.11744	−	2.37721i	−0.143700	−	0.0829651i	−0.570126	+	0.821557i	$0.693106\pi$
$822$	−7.55492	−	1.59706i	−0.263508	−	0.0557039i
$823$	−35.4554	+	20.4702i	−1.23590	+	0.713546i	−0.968253	−	0.249972i	$-0.919578\pi$
$823$	−35.4554	+	20.4702i	−1.23590	+	0.713546i	−0.267644	+	0.963518i	$0.586245\pi$
$824$	−8.99402	−	19.6998i	−0.313322	−	0.686274i
$825$		0			0
$826$	−43.2470	−	1.37438i	−1.50475	−	0.0478210i
$827$	26.4974			0.921406			0.460703	−	0.887554i	$-0.347597\pi$
$827$	26.4974			0.921406			0.460703	+	0.887554i	$0.347597\pi$
$828$	7.31548	+	3.23757i	0.254230	+	0.112513i
$829$	−38.1524			−1.32509			−0.662544	−	0.749023i	$-0.730523\pi$
$829$	−38.1524			−1.32509			−0.662544	+	0.749023i	$0.730523\pi$
$830$		0			0
$831$	−45.0026	−	8.02915i	−1.56112	−	0.278528i
$832$	−12.2050	−	35.2887i	−0.423133	−	1.22342i
$833$	−6.88748	+	3.97649i	−0.238637	+	0.137777i
$834$	4.20686	−	4.68267i	0.145672	−	0.162147i
$835$		0			0
$836$	−5.99653	−	3.99020i	−0.207394	−	0.138004i
$837$	13.6133	+	0.0826736i	0.470545	+	0.00285762i
$838$	30.8771	−	16.5421i	1.06663	−	0.571437i
$839$	−8.60385	+	14.9023i	−0.297038	+	0.514485i	−0.975457	−	0.220190i	$-0.929332\pi$
$839$	−8.60385	+	14.9023i	−0.297038	+	0.514485i	0.678419	+	0.734675i	$0.262665\pi$
$840$		0			0
$841$	−10.9891	−	19.0338i	−0.378936	−	0.656337i
$842$	−20.1549	−	12.5064i	−0.694584	−	0.431000i
$843$	−6.97337	+	39.0851i	−0.240175	+	1.34616i
$844$	43.5892	−	21.5995i	1.50040	−	0.743484i
$845$		0			0
$846$	−12.6610	+	1.76762i	−0.435293	+	0.0607720i
$847$			29.9778i			1.03005i
$848$	0.865668	−	6.77545i	0.0297272	−	0.232670i
$849$	−8.62913	−	7.27052i	−0.296151	−	0.249524i
$850$		0			0
$851$	−4.95992	−	8.59084i	−0.170024	−	0.294490i
$852$	−2.79615	−	9.59720i	−0.0957946	−	0.328795i
$853$	−21.7324	+	37.6416i	−0.744102	+	1.28882i	0.206511	+	0.978444i	$0.433789\pi$
$853$	−21.7324	+	37.6416i	−0.744102	+	1.28882i	−0.950613	+	0.310378i	$0.899544\pi$
$854$	3.35674	+	6.26561i	0.114865	+	0.214405i
$855$		0			0
$856$	−3.69072	+	38.6069i	−0.126146	+	1.31956i
$857$	−11.6506	−	6.72648i	−0.397977	−	0.229772i	0.287634	−	0.957741i	$-0.407131\pi$
$857$	−11.6506	−	6.72648i	−0.397977	−	0.229772i	−0.685611	+	0.727968i	$0.740465\pi$
$858$	−8.59375	+	2.80286i	−0.293386	+	0.0956879i
$859$	−1.00899	+	0.582541i	−0.0344263	+	0.0198760i	−0.517114	−	0.855916i	$-0.672994\pi$
$859$	−1.00899	+	0.582541i	−0.0344263	+	0.0198760i	0.482688	+	0.875792i	$0.339660\pi$
$860$		0			0
$861$	11.6273	+	32.1480i	0.396257	+	1.09560i
$862$	0.684991	−	21.5542i	0.0233309	−	0.734139i
$863$	−0.0600669			−0.00204470			−0.00102235	−	0.999999i	$-0.500325\pi$
$863$	−0.0600669			−0.00204470			−0.00102235	+	0.999999i	$0.500325\pi$
$864$	18.6767	−	22.6976i	0.635393	−	0.772189i
$865$		0			0
$866$	1.05877	−	33.3156i	0.0359783	−	1.13211i
$867$	10.4613	+	28.9242i	0.355284	+	0.982317i
$868$	−15.1098	−	0.961349i	−0.512861	−	0.0326303i
$869$	2.61585	−	1.51026i	0.0887367	−	0.0512321i
$870$		0			0
$871$	30.4552	+	17.5833i	1.03193	+	0.595788i
$872$	−3.57083	+	37.3528i	−0.120924	+	1.26493i
$873$	−3.37894	−	19.6273i	−0.114360	−	0.664282i
$874$	4.05604	+	7.57091i	0.137198	+	0.256090i
$875$		0			0
$876$	−6.30658	−	21.6460i	−0.213080	−	0.731351i
$877$	−3.25771	−	5.64252i	−0.110005	−	0.190534i	0.805767	−	0.592233i	$-0.201753\pi$
$877$	−3.25771	−	5.64252i	−0.110005	−	0.190534i	−0.915772	+	0.401698i	$0.868420\pi$
$878$	11.0801	−	17.8563i	0.373935	−	0.602620i
$879$	22.1805	+	18.6883i	0.748131	+	0.630342i
$880$		0			0
$881$			12.1468i			0.409237i	0.978842	+	0.204619i	$0.0655954\pi$
$881$			12.1468i			0.409237i	−0.978842	+	0.204619i	$0.934405\pi$
$882$	−2.14878	+	5.30449i	−0.0723531	+	0.178611i
$883$		−	30.7337i		−	1.03427i	−0.855904	−	0.517135i	$-0.826998\pi$
$883$		−	30.7337i		−	1.03427i	0.855904	−	0.517135i	$-0.173002\pi$
$884$	49.3128	−	24.4357i	1.65857	−	0.821860i
$885$		0			0
$886$	32.6163	+	20.2389i	1.09577	+	0.679940i
$887$	27.8345	+	48.2108i	0.934592	+	1.61876i	0.775361	+	0.631519i	$0.217568\pi$
$887$	27.8345	+	48.2108i	0.934592	+	1.61876i	0.159231	+	0.987241i	$0.449099\pi$
$888$	−35.2996	+	9.07870i	−1.18458	+	0.304661i
$889$	−14.1185	+	24.4539i	−0.473518	+	0.820157i
$890$		0			0
$891$	−5.41375	−	4.61789i	−0.181368	−	0.154705i
$892$	0.564907	+	0.375899i	0.0189145	+	0.0125860i
$893$	−11.8863	−	6.86255i	−0.397760	−	0.229647i
$894$	16.1185	−	17.9415i	0.539083	−	0.600054i
$895$		0			0
$896$	−22.1868	+	24.0086i	−0.741211	+	0.802070i
$897$	10.6113	+	1.89322i	0.354301	+	0.0632127i
$898$	−24.7191	−	0.785572i	−0.824888	−	0.0262149i
$899$	−6.94243			−0.231543
$900$		0			0
$901$	10.0675			0.335397
$902$	7.63388	+	0.242604i	0.254180	+	0.00807783i
$903$	38.3900	−	45.5638i	1.27754	−	1.51627i
$904$	10.8656	+	23.7992i	0.361385	+	0.791548i
$905$		0			0
$906$	25.5738	+	5.40614i	0.849634	+	0.179607i
$907$	14.3978	+	8.31258i	0.478072	+	0.276015i	0.719612	−	0.694376i	$-0.244319\pi$
$907$	14.3978	+	8.31258i	0.478072	+	0.276015i	−0.241541	+	0.970391i	$0.577653\pi$
$908$	−9.53299	+	14.3263i	−0.316363	+	0.475436i
$909$	7.51146	−	1.29314i	0.249139	−	0.0428907i
$910$		0			0
$911$	−9.29200	+	16.0942i	−0.307858	+	0.533225i	−0.977893	−	0.209104i	$-0.932945\pi$
$911$	−9.29200	+	16.0942i	−0.307858	+	0.533225i	0.670036	+	0.742329i	$0.266279\pi$
$912$	30.7979	−	6.88587i	1.01982	−	0.228014i
$913$	−3.80553	−	6.59137i	−0.125945	−	0.218143i
$914$	7.08529	+	4.39653i	0.234360	+	0.145424i
$915$		0			0
$916$	0.637349	+	1.28621i	0.0210586	+	0.0424977i
$917$		−	38.2464i		−	1.26301i
$918$	36.6730	+	23.0658i	1.21039	+	0.761284i
$919$		−	31.1617i		−	1.02793i	−0.857811	−	0.513965i	$-0.828176\pi$
$919$		−	31.1617i		−	1.02793i	0.857811	−	0.513965i	$-0.171824\pi$
$920$		0			0
$921$	−39.5403	+	14.3009i	−1.30290	+	0.471231i
$922$	26.3423	−	42.4523i	0.867538	−	1.39809i
$923$	−6.73437	−	11.6643i	−0.221664	−	0.383934i
$924$	5.71601	+	5.47313i	0.188043	+	0.180053i
$925$		0			0
$926$	24.8672	+	46.4166i	0.817189	+	1.52534i
$927$	7.94333	−	21.5522i	0.260893	−	0.707868i
$928$	−9.45396	+	11.6326i	−0.310341	+	0.381858i
$929$	−24.5849	−	14.1941i	−0.806604	−	0.465693i	0.0391715	−	0.999233i	$-0.487528\pi$
$929$	−24.5849	−	14.1941i	−0.806604	−	0.465693i	−0.845775	+	0.533540i	$0.820861\pi$
$930$		0			0
$931$	−5.32140	+	3.07231i	−0.174402	+	0.100691i
$932$	1.75730	−	27.6200i	0.0575622	−	0.904723i
$933$	8.51892	−	10.1108i	0.278897	−	0.331013i
$934$	−0.313698	+	9.87095i	−0.0102645	+	0.322988i
$935$		0			0
$936$	17.1704	−	35.6891i	0.561232	−	1.16654i
$937$	25.1998			0.823241			0.411620	−	0.911355i	$-0.364963\pi$
$937$	25.1998			0.823241			0.411620	+	0.911355i	$0.364963\pi$
$938$	0.977945	−	30.7724i	0.0319311	−	1.00476i
$939$	7.59676	+	1.35538i	0.247911	+	0.0442310i
$940$		0			0
$941$	35.0946	−	20.2619i	1.14405	−	0.660519i	0.196622	−	0.980479i	$-0.437003\pi$
$941$	35.0946	−	20.2619i	1.14405	−	0.660519i	0.947431	+	0.319960i	$0.103670\pi$
$942$	−27.3508	−	24.5717i	−0.891137	−	0.800589i
$943$	−7.88742	−	4.55381i	−0.256850	−	0.148292i
$944$	−16.3580	−	39.0686i	−0.532407	−	1.27157i
$945$		0			0
$946$	−6.28612	−	11.7335i	−0.204379	−	0.381489i
$947$	−0.299207	+	0.518242i	−0.00972293	+	0.0168406i	−0.870846	−	0.491556i	$-0.836428\pi$
$947$	−0.299207	+	0.518242i	−0.00972293	+	0.0168406i	0.861123	+	0.508397i	$0.169762\pi$
$948$	−3.14702	+	12.8545i	−0.102211	+	0.417496i
$949$	−15.1890	−	26.3082i	−0.493057	−	0.853999i
$950$		0			0
$951$	−1.50768	+	8.45043i	−0.0488900	+	0.274024i
$952$	−39.2453	−	27.9528i	−1.27195	−	0.905956i
$953$			2.50405i			0.0811142i	0.999177	+	0.0405571i	$0.0129133\pi$
$953$			2.50405i			0.0811142i	−0.999177	+	0.0405571i	$0.987087\pi$
$954$	5.71310	−	4.45518i	0.184968	−	0.144242i
$955$		0			0
$956$	24.6071	+	49.6587i	0.795850	+	1.60608i
$957$	2.77507	+	2.33815i	0.0897052	+	0.0755816i
$958$	−24.5356	−	15.2247i	−0.792708	−	0.491888i
$959$	4.55443	+	7.88850i	0.147070	+	0.254733i
$960$		0			0
$961$	−12.0680	+	20.9023i	−0.389289	+	0.674269i
$962$	−43.2889	+	23.1916i	−1.39569	+	0.747728i
$963$	−31.6184	+	26.3136i	−1.01889	+	0.847944i
$964$	12.6596	−	19.0251i	0.407739	−	0.612756i
$965$		0			0
$966$	−2.92612	−	8.97167i	−0.0941462	−	0.288659i
$967$	32.1736	−	18.5754i	1.03463	−	0.597346i	0.116325	−	0.993211i	$-0.462889\pi$
$967$	32.1736	−	18.5754i	1.03463	−	0.597346i	0.918308	+	0.395866i	$0.129555\pi$
$968$	−26.6941	+	12.1873i	−0.857982	+	0.391715i
$969$	15.8201	+	43.7408i	0.508216	+	1.40516i
$970$		0			0
$971$	14.7960			0.474826			0.237413	−	0.971409i	$-0.423701\pi$
$971$	14.7960			0.474826			0.237413	+	0.971409i	$0.423701\pi$
$972$	31.0184	−	3.13958i	0.994917	−	0.100702i
$973$	−7.42550			−0.238051
$974$	−29.4381	−	0.935542i	−0.943259	−	0.0299767i
$975$		0			0
$976$	−4.21462	+	5.53630i	−0.134907	+	0.177213i
$977$	−28.0175	+	16.1759i	−0.896360	+	0.517514i	−0.876018	−	0.482279i	$-0.839809\pi$
$977$	−28.0175	+	16.1759i	−0.896360	+	0.517514i	−0.0203428	+	0.999793i	$0.506476\pi$
$978$	3.15867	+	9.68469i	0.101003	+	0.309682i
$979$	0.00508002	+	0.00293295i	0.000162358	+	9.37374e-5i
$980$		0			0
$981$	−30.5913	+	25.4588i	−0.976707	+	0.812838i
$982$	−23.2266	+	12.4434i	−0.741191	+	0.397086i
$983$	1.69312	−	2.93257i	0.0540022	−	0.0935346i	−0.837761	−	0.546038i	$-0.816136\pi$
$983$	1.69312	−	2.93257i	0.0540022	−	0.0935346i	0.891763	+	0.452503i	$0.149469\pi$
$984$	−23.8996	+	23.4233i	−0.761892	+	0.746706i
$985$		0			0
$986$	−18.7730	−	11.6489i	−0.597853	−	0.370977i
$987$	11.5323	+	9.71656i	0.367076	+	0.309281i
$988$	38.1000	−	18.8795i	1.21212	−	0.600635i
$989$			15.8731i			0.504734i
$990$		0			0
$991$		−	39.7022i		−	1.26118i	−0.776116	−	0.630591i	$-0.782813\pi$
$991$		−	39.7022i		−	1.26118i	0.776116	−	0.630591i	$-0.217187\pi$
$992$	−5.28677	−	13.8456i	−0.167855	−	0.439597i
$993$	8.08829	−	45.3341i	0.256674	−	1.43864i
$994$	−6.21726	+	10.0195i	−0.197199	+	0.317799i
$995$		0			0
$996$	32.3906	+	7.92980i	1.02634	+	0.251265i
$997$	−10.2956	+	17.8325i	−0.326064	+	0.564760i	−0.981727	−	0.190294i	$-0.939056\pi$
$997$	−10.2956	+	17.8325i	−0.326064	+	0.564760i	0.655663	+	0.755054i	$0.272389\pi$
$998$	−3.45995	−	6.45827i	−0.109523	−	0.204433i
$999$	−33.3620	−	19.5327i	−1.05553	−	0.617986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.g.551.13		48
4.3	odd	2	inner	900.2.r.g.551.5		48
5.2	odd	4		180.2.n.d.119.24	yes	48
5.3	odd	4		180.2.n.d.119.1	yes	48
5.4	even	2	inner	900.2.r.g.551.12		48
9.5	odd	6	inner	900.2.r.g.851.5		48
15.2	even	4		540.2.n.d.359.1		48
15.8	even	4		540.2.n.d.359.24		48
20.3	even	4		180.2.n.d.119.17	yes	48
20.7	even	4		180.2.n.d.119.8	yes	48
20.19	odd	2	inner	900.2.r.g.551.20		48
36.23	even	6	inner	900.2.r.g.851.13		48
45.13	odd	12		540.2.n.d.179.17		48
45.14	odd	6	inner	900.2.r.g.851.20		48
45.22	odd	12		540.2.n.d.179.8		48
45.23	even	12		180.2.n.d.59.8	yes	48
45.32	even	12		180.2.n.d.59.17	yes	48
60.23	odd	4		540.2.n.d.359.8		48
60.47	odd	4		540.2.n.d.359.17		48
180.23	odd	12		180.2.n.d.59.24	yes	48
180.59	even	6	inner	900.2.r.g.851.12		48
180.67	even	12		540.2.n.d.179.24		48
180.103	even	12		540.2.n.d.179.1		48
180.167	odd	12		180.2.n.d.59.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.1	✓	48	180.167	odd	12
180.2.n.d.59.8	yes	48	45.23	even	12
180.2.n.d.59.17	yes	48	45.32	even	12
180.2.n.d.59.24	yes	48	180.23	odd	12
180.2.n.d.119.1	yes	48	5.3	odd	4
180.2.n.d.119.8	yes	48	20.7	even	4
180.2.n.d.119.17	yes	48	20.3	even	4
180.2.n.d.119.24	yes	48	5.2	odd	4
540.2.n.d.179.1		48	180.103	even	12
540.2.n.d.179.8		48	45.22	odd	12
540.2.n.d.179.17		48	45.13	odd	12
540.2.n.d.179.24		48	180.67	even	12
540.2.n.d.359.1		48	15.2	even	4
540.2.n.d.359.8		48	60.23	odd	4
540.2.n.d.359.17		48	60.47	odd	4
540.2.n.d.359.24		48	15.8	even	4
900.2.r.g.551.5		48	4.3	odd	2	inner
900.2.r.g.551.12		48	5.4	even	2	inner
900.2.r.g.551.13		48	1.1	even	1	trivial
900.2.r.g.551.20		48	20.19	odd	2	inner
900.2.r.g.851.5		48	9.5	odd	6	inner
900.2.r.g.851.12		48	180.59	even	6	inner
900.2.r.g.851.13		48	36.23	even	6	inner
900.2.r.g.851.20		48	45.14	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0449209 - 1.41350i) q^{2} +(-0.589100 - 1.62879i) q^{3} +(-1.99596 - 0.126991i) q^{4} +(-2.32876 + 0.759526i) q^{6} +(2.50234 + 1.44473i) q^{7} +(-0.269163 + 2.81559i) q^{8} +(-2.30592 + 1.91904i) q^{9} +(0.395318 - 0.684712i) q^{11} +(0.968981 + 3.32582i) q^{12} +(2.33373 + 4.04214i) q^{13} +(2.15453 - 3.47216i) q^{14} +(3.96775 + 0.506941i) q^{16} +5.89560i q^{17} +(2.60898 + 3.34563i) q^{18} +4.55505i q^{19} +(0.879030 - 4.92689i) q^{21} +(-0.950082 - 0.589540i) q^{22} +(0.666656 + 1.15468i) q^{23} +(4.74457 - 1.22026i) q^{24} +(5.81840 - 3.11715i) q^{26} +(4.48414 + 2.62536i) q^{27} +(-4.81112 - 3.20140i) q^{28} +(-2.29484 - 1.32492i) q^{29} +(2.26893 - 1.30997i) q^{31} +(0.894795 - 5.58564i) q^{32} +(-1.34813 - 0.240527i) q^{33} +(8.33343 + 0.264836i) q^{34} +(4.84624 - 3.53751i) q^{36} -7.44000 q^{37} +(6.43857 + 0.204617i) q^{38} +(5.20900 - 6.18239i) q^{39} +(-5.91566 + 3.41541i) q^{41} +(-6.92467 - 1.46383i) q^{42} +(10.3100 + 5.95249i) q^{43} +(-0.875994 + 1.31646i) q^{44} +(1.66209 - 0.890449i) q^{46} +(-1.50658 + 2.60947i) q^{47} +(-1.51170 - 6.76127i) q^{48} +(0.674484 + 1.16824i) q^{49} +(9.60270 - 3.47310i) q^{51} +(-4.14473 - 8.36434i) q^{52} -1.70763i q^{53} +(3.91237 - 6.22040i) q^{54} +(-4.74130 + 6.65671i) q^{56} +(7.41923 - 2.68338i) q^{57} +(-1.97587 + 3.18423i) q^{58} +(-5.29436 - 9.17010i) q^{59} +(-0.869749 + 1.50645i) q^{61} +(-1.74972 - 3.26598i) q^{62} +(-8.54271 + 1.47067i) q^{63} +(-7.85510 - 1.51570i) q^{64} +(-0.400545 + 1.89478i) q^{66} +(6.52500 - 3.76721i) q^{67} +(0.748690 - 11.7674i) q^{68} +(1.48801 - 1.76607i) q^{69} -2.88566 q^{71} +(-4.78257 - 7.00907i) q^{72} -6.50847 q^{73} +(-0.334212 + 10.5164i) q^{74} +(0.578452 - 9.09172i) q^{76} +(1.97845 - 1.14226i) q^{77} +(-8.50481 - 7.64065i) q^{78} +(3.30854 + 1.91019i) q^{79} +(1.63455 - 8.85032i) q^{81} +(4.56194 + 8.51521i) q^{82} +(4.81325 - 8.33679i) q^{83} +(-2.38019 + 9.72226i) q^{84} +(8.87697 - 14.3058i) q^{86} +(-0.806137 + 4.51832i) q^{87} +(1.82146 + 1.29735i) q^{88} +0.00741921i q^{89} +13.4864i q^{91} +(-1.18399 - 2.38937i) q^{92} +(-3.47029 - 2.92391i) q^{93} +(3.62081 + 2.24677i) q^{94} +(-9.62496 + 1.83307i) q^{96} +(-3.31933 + 5.74925i) q^{97} +(1.68161 - 0.900905i) q^{98} +(0.402417 + 2.33752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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