LMFDB - Embedded newform 666.2.bs.b.35.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			35.6
Character	$\chi$	$=$	666.35
Dual form			666.2.bs.b.647.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.898297 + 1.92640i) q^{5} +(-4.07456 + 1.48302i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.898297 + 1.92640i) q^{5} +(-4.07456 + 1.48302i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-1.06278 + 1.84078i) q^{10} +(-0.126338 - 0.218824i) q^{11} +(-2.15938 + 1.51201i) q^{13} +(-4.18831 + 1.12225i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-4.35501 - 3.04941i) q^{17} +(0.671402 + 7.67416i) q^{19} +(-1.21917 + 1.74115i) q^{20} +(-0.106786 - 0.229003i) q^{22} +(-1.07840 - 4.02463i) q^{23} +(0.309843 + 0.369257i) q^{25} +(-2.28294 + 1.31806i) q^{26} +(-4.27018 + 0.752948i) q^{28} +(-1.31898 + 4.92252i) q^{29} +(4.27380 - 4.27380i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-4.07266 - 3.41737i) q^{34} +(0.803272 - 9.18144i) q^{35} +(-5.94126 + 1.30438i) q^{37} +7.70347i q^{38} +(-1.36628 + 1.62827i) q^{40} +(-0.573486 + 3.25240i) q^{41} +(8.64105 + 8.64105i) q^{43} +(-0.0864205 - 0.237438i) q^{44} +(-0.723523 - 4.10330i) q^{46} +(-1.02563 - 0.592147i) q^{47} +(9.04037 - 7.58577i) q^{49} +(0.276481 + 0.394856i) q^{50} +(-2.38913 + 1.11407i) q^{52} +(-0.0572756 + 0.157363i) q^{53} +(0.535034 - 0.0468094i) q^{55} +(-4.31955 + 0.377912i) q^{56} +(-1.74299 + 4.78883i) q^{58} +(8.65832 - 4.03744i) q^{59} +(2.38449 + 3.40541i) q^{61} +(4.63002 - 3.88505i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.972985 - 5.51807i) q^{65} +(0.294563 + 0.809306i) q^{67} +(-3.75932 - 3.75932i) q^{68} +(1.60043 - 9.07649i) q^{70} +(10.2034 - 12.1599i) q^{71} +15.7191i q^{73} +(-6.03234 + 0.781604i) q^{74} +(-0.671402 + 7.67416i) q^{76} +(0.839294 + 0.704251i) q^{77} +(-4.40823 - 2.05559i) q^{79} +(-1.50299 + 1.50299i) q^{80} +(-0.854770 + 3.19004i) q^{82} +(1.24395 - 0.219342i) q^{83} +(9.78649 - 5.65023i) q^{85} +(7.85505 + 9.36128i) q^{86} +(-0.0653976 - 0.244067i) q^{88} +(0.207661 + 0.445331i) q^{89} +(6.55617 - 9.36319i) q^{91} +(-0.363143 - 4.15075i) q^{92} +(-0.970116 - 0.679283i) q^{94} +(-15.3866 - 5.60028i) q^{95} +(-9.38829 + 2.51559i) q^{97} +(9.66712 - 6.76899i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{19}{36}\right)$

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 $

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−0.898297	+	1.92640i	−0.401731	+	0.861514i	0.596532	+	0.802589i	$0.296545\pi$
$5$	−0.898297	+	1.92640i	−0.401731	+	0.861514i	−0.998262	+	0.0589246i	$0.981233\pi$
$6$		0			0
$7$	−4.07456	+	1.48302i	−1.54004	+	0.560528i	−0.966054	−	0.258338i	$-0.916825\pi$
$7$	−4.07456	+	1.48302i	−1.54004	+	0.560528i	−0.573984	+	0.818867i	$0.694603\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	−1.06278	+	1.84078i	−0.336079	+	0.582106i
$11$	−0.126338	−	0.218824i	−0.0380925	−	0.0659781i	0.846351	−	0.532626i	$-0.178795\pi$
$11$	−0.126338	−	0.218824i	−0.0380925	−	0.0659781i	−0.884443	+	0.466648i	$0.845461\pi$
$12$		0			0
$13$	−2.15938	+	1.51201i	−0.598904	+	0.419357i	−0.833329	−	0.552777i	$-0.813568\pi$
$13$	−2.15938	+	1.51201i	−0.598904	+	0.419357i	0.234425	+	0.972134i	$0.424679\pi$
$14$	−4.18831	+	1.12225i	−1.11937	+	0.299935i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−4.35501	−	3.04941i	−1.05624	−	0.739591i	−0.0896691	−	0.995972i	$-0.528581\pi$
$17$	−4.35501	−	3.04941i	−1.05624	−	0.739591i	−0.966576	+	0.256381i	$0.917470\pi$
$18$		0			0
$19$	0.671402	+	7.67416i	0.154030	+	1.76057i	0.543384	+	0.839484i	$0.317143\pi$
$19$	0.671402	+	7.67416i	0.154030	+	1.76057i	−0.389354	+	0.921088i	$0.627302\pi$
$20$	−1.21917	+	1.74115i	−0.272614	+	0.389333i
$21$		0			0
$22$	−0.106786	−	0.229003i	−0.0227668	−	0.0488236i
$23$	−1.07840	−	4.02463i	−0.224861	−	0.839193i	−0.982460	−	0.186473i	$-0.940294\pi$
$23$	−1.07840	−	4.02463i	−0.224861	−	0.839193i	0.757599	−	0.652720i	$-0.226372\pi$
$24$		0			0
$25$	0.309843	+	0.369257i	0.0619686	+	0.0738514i
$26$	−2.28294	+	1.31806i	−0.447722	+	0.258492i
$27$		0			0
$28$	−4.27018	+	0.752948i	−0.806988	+	0.142294i
$29$	−1.31898	+	4.92252i	−0.244929	+	0.914088i	0.728490	+	0.685057i	$0.240223\pi$
$29$	−1.31898	+	4.92252i	−0.244929	+	0.914088i	−0.973419	+	0.229032i	$0.926444\pi$
$30$		0			0
$31$	4.27380	−	4.27380i	0.767597	−	0.767597i	−0.210086	−	0.977683i	$-0.567374\pi$
$31$	4.27380	−	4.27380i	0.767597	−	0.767597i	0.977683	+	0.210086i	$0.0673743\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$		0			0
$34$	−4.07266	−	3.41737i	−0.698456	−	0.586074i
$35$	0.803272	−	9.18144i	0.135778	−	1.55195i
$36$		0			0
$37$	−5.94126	+	1.30438i	−0.976737	+	0.214439i
$37$	−5.94126	+	1.30438i	−0.976737	+	0.214439i
$38$			7.70347i			1.24967i
$39$		0			0
$40$	−1.36628	+	1.62827i	−0.216028	+	0.257452i
$41$	−0.573486	+	3.25240i	−0.0895635	+	0.507940i	0.906715	+	0.421744i	$0.138582\pi$
$41$	−0.573486	+	3.25240i	−0.0895635	+	0.507940i	−0.996278	+	0.0861955i	$0.972529\pi$
$42$		0			0
$43$	8.64105	+	8.64105i	1.31775	+	1.31775i	0.915555	+	0.402192i	$0.131752\pi$
$43$	8.64105	+	8.64105i	1.31775	+	1.31775i	0.402192	+	0.915555i	$0.368248\pi$
$44$	−0.0864205	−	0.237438i	−0.0130284	−	0.0357952i
$45$		0			0
$46$	−0.723523	−	4.10330i	−0.106678	−	0.604999i
$47$	−1.02563	−	0.592147i	−0.149603	−	0.0863735i	0.423330	−	0.905976i	$-0.360861\pi$
$47$	−1.02563	−	0.592147i	−0.149603	−	0.0863735i	−0.572933	+	0.819602i	$0.694194\pi$
$48$		0			0
$49$	9.04037	−	7.58577i	1.29148	−	1.08368i
$50$	0.276481	+	0.394856i	0.0391004	+	0.0558411i
$51$		0			0
$52$	−2.38913	+	1.11407i	−0.331313	+	0.154494i
$53$	−0.0572756	+	0.157363i	−0.00786740	+	0.0216155i	−0.943564	−	0.331190i	$-0.892550\pi$
$53$	−0.0572756	+	0.157363i	−0.00786740	+	0.0216155i	0.935697	+	0.352805i	$0.114772\pi$
$54$		0			0
$55$	0.535034	−	0.0468094i	0.0721439	−	0.00631178i
$56$	−4.31955	+	0.377912i	−0.577225	+	0.0505006i
$57$		0			0
$58$	−1.74299	+	4.78883i	−0.228866	+	0.628804i
$59$	8.65832	−	4.03744i	1.12722	−	0.525630i	0.232649	−	0.972561i	$-0.425261\pi$
$59$	8.65832	−	4.03744i	1.12722	−	0.525630i	0.894569	+	0.446930i	$0.147483\pi$
$60$		0			0
$61$	2.38449	+	3.40541i	0.305303	+	0.436018i	0.942260	−	0.334881i	$-0.108696\pi$
$61$	2.38449	+	3.40541i	0.305303	+	0.436018i	−0.636957	+	0.770899i	$0.719807\pi$
$62$	4.63002	−	3.88505i	0.588014	−	0.493402i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−0.972985	−	5.51807i	−0.120684	−	0.684433i
$66$		0			0
$67$	0.294563	+	0.809306i	0.0359867	+	0.0988725i	0.956385	−	0.292110i	$-0.0943574\pi$
$67$	0.294563	+	0.809306i	0.0359867	+	0.0988725i	−0.920398	+	0.390983i	$0.872135\pi$
$68$	−3.75932	−	3.75932i	−0.455885	−	0.455885i
$69$		0			0
$70$	1.60043	−	9.07649i	0.191288	−	1.08485i
$71$	10.2034	−	12.1599i	1.21092	−	1.44311i	0.348204	−	0.937419i	$-0.386792\pi$
$71$	10.2034	−	12.1599i	1.21092	−	1.44311i	0.862712	−	0.505695i	$-0.168764\pi$
$72$		0			0
$73$			15.7191i			1.83978i	0.392180	+	0.919889i	$0.371721\pi$
$73$			15.7191i			1.83978i	−0.392180	+	0.919889i	$0.628279\pi$
$74$	−6.03234	+	0.781604i	−0.701245	+	0.0908596i
$75$		0			0
$76$	−0.671402	+	7.67416i	−0.0770151	+	0.880286i
$77$	0.839294	+	0.704251i	0.0956464	+	0.0802569i
$78$		0			0
$79$	−4.40823	−	2.05559i	−0.495964	−	0.231272i	0.158508	−	0.987358i	$-0.449332\pi$
$79$	−4.40823	−	2.05559i	−0.495964	−	0.231272i	−0.654473	+	0.756086i	$0.727109\pi$
$80$	−1.50299	+	1.50299i	−0.168040	+	0.168040i
$81$		0			0
$82$	−0.854770	+	3.19004i	−0.0943935	+	0.352281i
$83$	1.24395	−	0.219342i	0.136542	−	0.0240760i	−0.104960	−	0.994476i	$-0.533471\pi$
$83$	1.24395	−	0.219342i	0.136542	−	0.0240760i	0.241501	+	0.970401i	$0.422360\pi$
$84$		0			0
$85$	9.78649	−	5.65023i	1.06149	−	0.612854i
$86$	7.85505	+	9.36128i	0.847032	+	1.00945i
$87$		0			0
$88$	−0.0653976	−	0.244067i	−0.00697140	−	0.0260176i
$89$	0.207661	+	0.445331i	0.0220120	+	0.0472050i	0.917006	−	0.398872i	$-0.130598\pi$
$89$	0.207661	+	0.445331i	0.0220120	+	0.0472050i	−0.894994	+	0.446077i	$0.852821\pi$
$90$		0			0
$91$	6.55617	−	9.36319i	0.687274	−	0.981529i
$92$	−0.363143	−	4.15075i	−0.0378603	−	0.432745i
$93$		0			0
$94$	−0.970116	−	0.679283i	−0.100060	−	0.0700627i
$95$	−15.3866	−	5.60028i	−1.57864	−	0.574577i
$96$		0			0
$97$	−9.38829	+	2.51559i	−0.953237	+	0.255419i	−0.701735	−	0.712438i	$-0.747591\pi$
$97$	−9.38829	+	2.51559i	−0.953237	+	0.255419i	−0.251502	+	0.967857i	$0.580924\pi$
$98$	9.66712	−	6.76899i	0.976526	−	0.683771i
$99$		0			0
$100$	0.241015	+	0.417451i	0.0241015	+	0.0417451i
$101$	−7.96815	+	13.8012i	−0.792860	+	1.37327i	0.131329	+	0.991339i	$0.458076\pi$
$101$	−7.96815	+	13.8012i	−0.792860	+	1.37327i	−0.924189	+	0.381935i	$0.875258\pi$
$102$		0			0
$103$	−6.78122	−	1.81702i	−0.668173	−	0.179037i	−0.0912416	−	0.995829i	$-0.529084\pi$
$103$	−6.78122	−	1.81702i	−0.668173	−	0.179037i	−0.576932	+	0.816792i	$0.695750\pi$
$104$	−2.47714	+	0.901605i	−0.242903	+	0.0884096i
$105$		0			0
$106$	−0.0707727	+	0.151773i	−0.00687405	+	0.0147415i
$107$	−11.9139	−	2.10074i	−1.15176	−	0.203087i	−0.435017	−	0.900422i	$-0.643258\pi$
$107$	−11.9139	−	2.10074i	−1.15176	−	0.203087i	−0.716745	+	0.697336i	$0.754369\pi$
$108$		0			0
$109$	0.350208	+	0.0306393i	0.0335439	+	0.00293471i	0.103915	−	0.994586i	$-0.466863\pi$
$109$	0.350208	+	0.0306393i	0.0335439	+	0.00293471i	−0.0703714	+	0.997521i	$0.522418\pi$
$110$	0.537077			0.0512083
$111$		0			0
$112$	−4.33605			−0.409719
$113$	11.2512	+	0.984352i	1.05842	+	0.0926000i	0.603052	−	0.797702i	$-0.293951\pi$
$113$	11.2512	+	0.984352i	1.05842	+	0.0926000i	0.455371	+	0.890302i	$0.349507\pi$
$114$		0			0
$115$	8.72178	+	1.53789i	0.813310	+	0.143409i
$116$	−2.15373	+	4.61869i	−0.199969	+	0.428835i
$117$		0			0
$118$	8.97726	−	3.26746i	0.826424	−	0.300794i
$119$	22.2671	+	5.96644i	2.04122	+	0.546943i
$120$		0			0
$121$	5.46808	−	9.47099i	0.497098	−	0.860999i
$122$	2.07862	+	3.60027i	0.188189	+	0.325953i
$123$		0			0
$124$	4.95101	−	3.46673i	0.444614	−	0.311322i
$125$	−11.2553	+	3.01585i	−1.00670	+	0.269746i
$126$		0			0
$127$	0.310793	+	0.113119i	0.0275784	+	0.0100377i	0.355773	−	0.934573i	$-0.384218\pi$
$127$	0.310793	+	0.113119i	0.0275784	+	0.0100377i	−0.328194	+	0.944610i	$0.606440\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$		0			0
$130$	−0.488351	−	5.58188i	−0.0428312	−	0.489563i
$131$	1.66144	−	2.37278i	0.145161	−	0.207311i	−0.739987	−	0.672621i	$-0.765168\pi$
$131$	1.66144	−	2.37278i	0.145161	−	0.207311i	0.885148	+	0.465310i	$0.154057\pi$
$132$		0			0
$133$	−14.1166	−	30.2731i	−1.22406	−	2.62501i
$134$	0.222907	+	0.831900i	0.0192562	+	0.0718652i
$135$		0			0
$136$	−3.41737	−	4.07266i	−0.293037	−	0.349228i
$137$	13.0833	−	7.55363i	1.11778	−	0.645350i	0.176946	−	0.984221i	$-0.443378\pi$
$137$	13.0833	−	7.55363i	1.11778	−	0.645350i	0.940833	+	0.338870i	$0.110045\pi$
$138$		0			0
$139$	−8.57084	+	1.51127i	−0.726969	+	0.128184i	−0.524872	−	0.851181i	$-0.675887\pi$
$139$	−8.57084	+	1.51127i	−0.726969	+	0.128184i	−0.202097	+	0.979365i	$0.564776\pi$
$140$	2.38541	−	8.90246i	0.201604	−	0.752395i
$141$		0			0
$142$	11.2243	−	11.2243i	0.941926	−	0.941926i
$143$	0.603678	+	0.281500i	0.0504821	+	0.0235402i
$144$		0			0
$145$	−8.29792	−	6.96278i	−0.689104	−	0.578227i
$146$	−1.37001	+	15.6592i	−0.113383	+	1.29597i
$147$		0			0
$148$	−6.07750	+	0.252877i	−0.499568	+	0.0207864i
$149$		−	8.31350i		−	0.681069i	−0.940232	−	0.340534i	$-0.889392\pi$
$149$		−	8.31350i		−	0.681069i	0.940232	−	0.340534i	$-0.110608\pi$
$150$		0			0
$151$	6.81227	−	8.11855i	0.554375	−	0.660678i	−0.413971	−	0.910290i	$-0.635859\pi$
$151$	6.81227	−	8.11855i	0.554375	−	0.660678i	0.968346	+	0.249612i	$0.0803031\pi$
$152$	−1.33769	+	7.58644i	−0.108501	+	0.615341i
$153$		0			0
$154$	0.774720	+	0.774720i	0.0624288	+	0.0624288i
$155$	4.39393	+	12.0722i	0.352929	+	0.969663i
$156$		0			0
$157$	−0.253515	−	1.43776i	−0.0202327	−	0.114745i	0.973019	−	0.230726i	$-0.0741101\pi$
$157$	−0.253515	−	1.43776i	−0.0202327	−	0.114745i	−0.993251	+	0.115981i	$0.962999\pi$
$158$	−4.21230	−	2.43197i	−0.335112	−	0.193477i
$159$		0			0
$160$	−1.62827	+	1.36628i	−0.128726	+	0.108014i
$161$	10.3626	+	14.7993i	0.816686	+	1.16635i
$162$		0			0
$163$	10.8893	−	5.07778i	0.852918	−	0.397722i	0.0535508	−	0.998565i	$-0.482946\pi$
$163$	10.8893	−	5.07778i	0.852918	−	0.397722i	0.799367	+	0.600843i	$0.205168\pi$
$164$	−1.12955	+	3.10341i	−0.0882028	+	0.242335i
$165$		0			0
$166$	1.25834	−	0.110090i	0.0976658	−	0.00854465i
$167$	12.4432	−	1.08864i	0.962885	−	0.0842415i	0.405140	−	0.914254i	$-0.367223\pi$
$167$	12.4432	−	1.08864i	0.962885	−	0.0842415i	0.557744	+	0.830013i	$0.311667\pi$
$168$		0			0
$169$	−2.06953	+	5.68598i	−0.159194	+	0.437383i
$170$	10.2417	−	4.77578i	0.785502	−	0.366286i
$171$		0			0
$172$	7.00927	+	10.0103i	0.534452	+	0.763276i
$173$	−5.79005	+	4.85843i	−0.440209	+	0.369380i	−0.835788	−	0.549053i	$-0.814989\pi$
$173$	−5.79005	+	4.85843i	−0.440209	+	0.369380i	0.395578	+	0.918432i	$0.370544\pi$
$174$		0			0
$175$	−1.81009	−	1.04506i	−0.136830	−	0.0789987i
$176$	−0.0438769	−	0.248838i	−0.00330734	−	0.0187569i
$177$		0			0
$178$	0.168058	+	0.461735i	0.0125965	+	0.0346085i
$179$	17.0585	+	17.0585i	1.27501	+	1.27501i	0.943426	+	0.331583i	$0.107583\pi$
$179$	17.0585	+	17.0585i	1.27501	+	1.27501i	0.331583	+	0.943426i	$0.392417\pi$
$180$		0			0
$181$	−0.880474	+	4.99342i	−0.0654451	+	0.371158i	0.934442	+	0.356116i	$0.115899\pi$
$181$	−0.880474	+	4.99342i	−0.0654451	+	0.371158i	−0.999887	+	0.0150417i	$0.995212\pi$
$182$	7.34728	−	8.75615i	0.544617	−	0.649049i
$183$		0			0
$184$		−	4.16660i		−	0.307166i
$185$	2.82425	−	12.6170i	0.207643	−	0.927620i
$186$		0			0
$187$	−0.117081	+	1.33824i	−0.00856180	+	0.0978618i
$188$	−0.907221	−	0.761249i	−0.0661659	−	0.0555198i
$189$		0			0
$190$	−14.8400	−	6.92001i	−1.07661	−	0.502030i
$191$	−17.0814	+	17.0814i	−1.23597	+	1.23597i	−0.274333	+	0.961635i	$0.588457\pi$
$191$	−17.0814	+	17.0814i	−1.23597	+	1.23597i	−0.961635	+	0.274333i	$0.911543\pi$
$192$		0			0
$193$	3.67398	−	13.7115i	0.264459	−	0.986973i	−0.698122	−	0.715979i	$-0.745981\pi$
$193$	3.67398	−	13.7115i	0.264459	−	0.986973i	0.962581	−	0.270994i	$-0.0873525\pi$
$194$	−9.57182	+	1.68777i	−0.687216	+	0.121175i
$195$		0			0
$196$	10.2203	−	5.90068i	0.730020	−	0.421477i
$197$	−7.07764	−	8.43481i	−0.504261	−	0.600955i	0.452523	−	0.891753i	$-0.350524\pi$
$197$	−7.07764	−	8.43481i	−0.504261	−	0.600955i	−0.956785	+	0.290797i	$0.906079\pi$
$198$		0			0
$199$	2.98518	+	11.1408i	0.211614	+	0.789754i	0.987331	+	0.158673i	$0.0507216\pi$
$199$	2.98518	+	11.1408i	0.211614	+	0.789754i	−0.775717	+	0.631081i	$0.782612\pi$
$200$	0.203715	+	0.436868i	0.0144048	+	0.0308912i
$201$		0			0
$202$	−9.14068	+	13.0542i	−0.643136	+	0.918494i
$203$	−1.92590	−	22.0132i	−0.135172	−	1.54502i
$204$		0			0
$205$	−5.75028	−	4.02639i	−0.401617	−	0.281215i
$206$	−6.59705	−	2.40113i	−0.459638	−	0.167295i
$207$		0			0
$208$	−2.54629	+	0.682277i	−0.176554	+	0.0473074i
$209$	1.59447	−	1.11646i	0.110292	−	0.0772271i
$210$		0			0
$211$	5.62565	+	9.74391i	0.387286	+	0.670799i	0.992083	−	0.125581i	$-0.0400794\pi$
$211$	5.62565	+	9.74391i	0.387286	+	0.670799i	−0.604798	+	0.796379i	$0.706746\pi$
$212$	−0.0837313	+	0.145027i	−0.00575069	+	0.00996048i
$213$		0			0
$214$	−11.6855	−	3.13112i	−0.798803	−	0.214039i
$215$	−24.4084	+	8.88392i	−1.66464	+	0.605878i
$216$		0			0
$217$	−11.0757	+	23.7520i	−0.751870	+	1.61239i
$218$	0.346205	+	0.0610453i	0.0234480	+	0.00413451i
$219$		0			0
$220$	0.535034	+	0.0468094i	0.0360720	+	0.00315589i
$221$	14.0149			0.942742
$222$		0			0
$223$	−12.4704			−0.835077			−0.417538	−	0.908659i	$-0.637107\pi$
$223$	−12.4704			−0.835077			−0.417538	+	0.908659i	$0.637107\pi$
$224$	−4.31955	−	0.377912i	−0.288612	−	0.0252503i
$225$		0			0
$226$	11.1226	+	1.96121i	0.739863	+	0.130458i
$227$	9.42390	−	20.2096i	0.625486	−	1.34136i	−0.296832	−	0.954930i	$-0.595930\pi$
$227$	9.42390	−	20.2096i	0.625486	−	1.34136i	0.922319	−	0.386430i	$-0.126292\pi$
$228$		0			0
$229$	−3.18431	+	1.15900i	−0.210425	+	0.0765886i	−0.445082	−	0.895490i	$-0.646826\pi$
$229$	−3.18431	+	1.15900i	−0.210425	+	0.0765886i	0.234657	+	0.972078i	$0.424603\pi$
$230$	8.55456	+	2.29219i	0.564071	+	0.151142i
$231$		0			0
$232$	−2.54808	+	4.41341i	−0.167290	+	0.289754i
$233$	7.08146	+	12.2655i	0.463922	+	0.803537i	0.999152	−	0.0411696i	$-0.0131084\pi$
$233$	7.08146	+	12.2655i	0.463922	+	0.803537i	−0.535230	+	0.844706i	$0.679775\pi$
$234$		0			0
$235$	2.06203	−	1.44385i	0.134512	−	0.0941864i
$236$	9.22788	−	2.47260i	0.600684	−	0.160953i
$237$		0			0
$238$	21.6623	+	7.88444i	1.40416	+	0.511073i
$239$	−15.4504	−	10.8185i	−0.999403	−	0.699789i	−0.0452087	−	0.998978i	$-0.514395\pi$
$239$	−15.4504	−	10.8185i	−0.999403	−	0.699789i	−0.954194	+	0.299188i	$0.903284\pi$
$240$		0			0
$241$	1.64247	+	18.7735i	0.105801	+	1.20931i	0.844606	+	0.535389i	$0.179835\pi$
$241$	1.64247	+	18.7735i	0.105801	+	1.20931i	−0.738805	+	0.673919i	$0.764610\pi$
$242$	6.27272	−	8.95837i	0.403226	−	0.575866i
$243$		0			0
$244$	1.75692	+	3.76773i	0.112475	+	0.241204i
$245$	6.49233	+	24.2297i	0.414779	+	1.54798i
$246$		0			0
$247$	−13.0532	−	15.5563i	−0.830558	−	0.989821i
$248$	5.23432	−	3.02203i	0.332379	−	0.191899i
$249$		0			0
$250$	−11.4753	+	2.02341i	−0.725763	+	0.127972i
$251$	−5.19638	+	19.3931i	−0.327992	+	1.22408i	0.583277	+	0.812273i	$0.301770\pi$
$251$	−5.19638	+	19.3931i	−0.327992	+	1.22408i	−0.911269	+	0.411811i	$0.864896\pi$
$252$		0			0
$253$	−0.744445	+	0.744445i	−0.0468028	+	0.0468028i
$254$	0.299752	+	0.139776i	0.0188081	+	0.00877035i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−1.06034	+	12.1198i	−0.0661423	+	0.756010i	0.888621	+	0.458643i	$0.151664\pi$
$257$	−1.06034	+	12.1198i	−0.0661423	+	0.756010i	−0.954763	+	0.297367i	$0.903891\pi$
$258$		0			0
$259$	22.2736	−	14.1258i	1.38401	−	0.877733i
$260$		−	5.60320i		−	0.347496i
$261$		0			0
$262$	1.86192	−	2.21895i	0.115030	−	0.137087i
$263$	−2.44537	+	13.8684i	−0.150788	+	0.855161i	0.811748	+	0.584008i	$0.198516\pi$
$263$	−2.44537	+	13.8684i	−0.150788	+	0.855161i	−0.962536	+	0.271153i	$0.912595\pi$
$264$		0			0
$265$	−0.251695	−	0.251695i	−0.0154615	−	0.0154615i
$266$	−11.4244	−	31.3882i	−0.700474	−	1.92454i
$267$		0			0
$268$	0.149554	+	0.848162i	0.00913545	+	0.0518097i
$269$	−7.10505	−	4.10210i	−0.433203	−	0.250110i	0.267507	−	0.963556i	$-0.413800\pi$
$269$	−7.10505	−	4.10210i	−0.433203	−	0.250110i	−0.700710	+	0.713446i	$0.747133\pi$
$270$		0			0
$271$	12.3228	−	10.3401i	0.748558	−	0.628115i	−0.186563	−	0.982443i	$-0.559735\pi$
$271$	12.3228	−	10.3401i	0.748558	−	0.628115i	0.935121	+	0.354328i	$0.115290\pi$
$272$	−3.04941	−	4.35501i	−0.184898	−	0.264061i
$273$		0			0
$274$	13.6918	−	6.38460i	0.827154	−	0.385708i
$275$	0.0416573	−	0.114453i	0.00251203	−	0.00690175i
$276$		0			0
$277$	−8.33395	+	0.729126i	−0.500738	+	0.0438089i	−0.334727	−	0.942315i	$-0.608644\pi$
$277$	−8.33395	+	0.729126i	−0.500738	+	0.0438089i	−0.166011	+	0.986124i	$0.553089\pi$
$278$	−8.66994	+	0.758522i	−0.519989	+	0.0454931i
$279$		0			0
$280$	3.15223	−	8.66068i	0.188382	−	0.517575i
$281$	−29.1652	+	13.6000i	−1.73985	+	0.811305i	−0.751383	+	0.659867i	$0.770613\pi$
$281$	−29.1652	+	13.6000i	−1.73985	+	0.811305i	−0.988467	+	0.151438i	$0.951610\pi$
$282$		0			0
$283$	4.74744	+	6.78005i	0.282206	+	0.403032i	0.935081	−	0.354434i	$-0.115326\pi$
$283$	4.74744	+	6.78005i	0.282206	+	0.403032i	−0.652875	+	0.757465i	$0.726437\pi$
$284$	12.1599	−	10.2034i	0.721557	−	0.605458i
$285$		0			0
$286$	0.576847	+	0.333043i	0.0341097	+	0.0196932i
$287$	−2.48667	−	14.1026i	−0.146783	−	0.832450i
$288$		0			0
$289$	3.85286	+	10.5856i	0.226639	+	0.622685i
$290$	−7.65949	−	7.65949i	−0.449781	−	0.449781i
$291$		0			0
$292$	−2.72959	+	15.4803i	−0.159737	+	0.905913i
$293$	−11.7263	+	13.9749i	−0.685059	+	0.816421i	−0.990749	−	0.135710i	$-0.956669\pi$
$293$	−11.7263	+	13.9749i	−0.685059	+	0.816421i	0.305690	+	0.952131i	$0.401113\pi$
$294$		0			0
$295$			20.3063i			1.18228i
$296$	−6.07642	−	0.277775i	−0.353185	−	0.0161453i
$297$		0			0
$298$	0.724569	−	8.28187i	0.0419732	−	0.479756i
$299$	8.41396	+	7.06015i	0.486592	+	0.408299i
$300$		0			0
$301$	−48.0233	−	22.3936i	−2.76802	−	1.29075i
$302$	7.49393	−	7.49393i	0.431227	−	0.431227i
$303$		0			0
$304$	−1.99381	+	7.44098i	−0.114353	+	0.426770i
$305$	−8.70217	+	1.53443i	−0.498285	+	0.0878611i
$306$		0			0
$307$	7.68710	−	4.43815i	0.438726	−	0.253298i	−0.264331	−	0.964432i	$-0.585151\pi$
$307$	7.68710	−	4.43815i	0.438726	−	0.253298i	0.703057	+	0.711134i	$0.251818\pi$
$308$	0.704251	+	0.839294i	0.0401284	+	0.0478232i
$309$		0			0
$310$	3.32504	+	12.4092i	0.188850	+	0.704797i
$311$	−4.14969	−	8.89904i	−0.235307	−	0.504618i	0.752825	−	0.658220i	$-0.228690\pi$
$311$	−4.14969	−	8.89904i	−0.235307	−	0.504618i	−0.988133	+	0.153602i	$0.950913\pi$
$312$		0			0
$313$	10.2316	−	14.6123i	0.578325	−	0.825934i	−0.418275	−	0.908320i	$-0.637365\pi$
$313$	10.2316	−	14.6123i	0.578325	−	0.825934i	0.996600	+	0.0823863i	$0.0262541\pi$
$314$	−0.127242	−	1.45438i	−0.00718067	−	0.0820754i
$315$		0			0
$316$	−3.98431	−	2.78984i	−0.224135	−	0.156941i
$317$	−21.1931	−	7.71366i	−1.19032	−	0.433242i	−0.330486	−	0.943811i	$-0.607213\pi$
$317$	−21.1931	−	7.71366i	−1.19032	−	0.433242i	−0.859837	+	0.510569i	$0.829435\pi$
$318$		0			0
$319$	1.24381	−	0.333277i	0.0696397	−	0.0186599i
$320$	−1.74115	+	1.21917i	−0.0973332	+	0.0681535i
$321$		0			0
$322$	9.03331	+	15.6461i	0.503407	+	0.871926i
$323$	20.4777	−	35.4684i	1.13941	−	1.97352i
$324$		0			0
$325$	−1.22739	−	0.328878i	−0.0680834	−	0.0182429i
$326$	11.2904	−	4.10939i	0.625320	−	0.227598i
$327$		0			0
$328$	−1.39573	+	2.99315i	−0.0770662	+	0.165269i
$329$	5.05715	+	0.891711i	0.278809	+	0.0491616i
$330$		0			0
$331$	0.341962	+	0.0299178i	0.0187959	+	0.00164443i	0.0965498	−	0.995328i	$-0.469219\pi$
$331$	0.341962	+	0.0299178i	0.0187959	+	0.00164443i	−0.0777539	+	0.996973i	$0.524775\pi$
$332$	1.26314			0.0693239
$333$		0			0
$334$	12.4907			0.683463
$335$	−1.82366	−	0.159549i	−0.0996370	−	0.00871711i
$336$		0			0
$337$	−4.09969	−	0.722887i	−0.223325	−	0.0393781i	0.0608661	−	0.998146i	$-0.480614\pi$
$337$	−4.09969	−	0.722887i	−0.223325	−	0.0393781i	−0.284191	+	0.958768i	$0.591725\pi$
$338$	−2.55722	+	5.48397i	−0.139094	+	0.298289i
$339$		0			0
$340$	10.6190	−	3.86499i	0.575894	−	0.209608i
$341$	−1.47516	−	0.395267i	−0.0798843	−	0.0214049i
$342$		0			0
$343$	−10.4095	+	18.0298i	−0.562060	+	0.973517i
$344$	6.11014	+	10.5831i	0.329437	+	0.570601i
$345$		0			0
$346$	−6.19146	+	4.33531i	−0.332855	+	0.233067i
$347$	−10.8884	+	2.91753i	−0.584518	+	0.156621i	−0.538947	−	0.842340i	$-0.681178\pi$
$347$	−10.8884	+	2.91753i	−0.584518	+	0.156621i	−0.0455717	+	0.998961i	$0.514511\pi$
$348$		0			0
$349$	26.3588	+	9.59381i	1.41095	+	0.513545i	0.931410	−	0.363973i	$-0.118580\pi$
$349$	26.3588	+	9.59381i	1.41095	+	0.513545i	0.479544	+	0.877518i	$0.340802\pi$
$350$	−1.71212	−	1.19884i	−0.0915166	−	0.0640806i
$351$		0			0
$352$	−0.0220222	−	0.251715i	−0.00117379	−	0.0134165i
$353$	−16.6940	+	23.8415i	−0.888531	+	1.26895i	0.0738555	+	0.997269i	$0.476470\pi$
$353$	−16.6940	+	23.8415i	−0.888531	+	1.26895i	−0.962386	+	0.271685i	$0.912419\pi$
$354$		0			0
$355$	14.2592	+	30.5790i	0.756801	+	1.62296i
$356$	0.127175	+	0.474625i	0.00674028	+	0.0251551i
$357$		0			0
$358$	15.5068	+	18.4803i	0.819560	+	0.976714i
$359$	29.1472	−	16.8282i	1.53833	−	0.888156i	0.539395	−	0.842053i	$-0.318653\pi$
$359$	29.1472	−	16.8282i	1.53833	−	0.888156i	0.998937	−	0.0461029i	$-0.0146802\pi$
$360$		0			0
$361$	−39.7306	+	7.00557i	−2.09108	+	0.368714i
$362$	−1.31233	+	4.89768i	−0.0689745	+	0.257416i
$363$		0			0
$364$	8.08247	−	8.08247i	0.423637	−	0.423637i
$365$	−30.2813	−	14.1204i	−1.58499	−	0.739095i
$366$		0			0
$367$	−0.757220	−	0.635383i	−0.0395266	−	0.0331667i	0.622810	−	0.782373i	$-0.285991\pi$
$367$	−0.757220	−	0.635383i	−0.0395266	−	0.0331667i	−0.662337	+	0.749206i	$0.730435\pi$
$368$	0.363143	−	4.15075i	0.0189302	−	0.216373i
$369$		0			0
$370$	3.91314	−	12.3228i	0.203435	−	0.640633i
$371$		−	0.726127i		−	0.0376986i
$372$		0			0
$373$	−14.9246	+	17.7864i	−0.772766	+	0.920947i	−0.998583	−	0.0532232i	$-0.983051\pi$
$373$	−14.9246	+	17.7864i	−0.772766	+	0.920947i	0.225817	+	0.974170i	$0.427495\pi$
$374$	−0.233271	+	1.32294i	−0.0120621	+	0.0684078i
$375$		0			0
$376$	−0.837422	−	0.837422i	−0.0431867	−	0.0431867i
$377$	−4.59473	−	12.6239i	−0.236640	−	0.650164i
$378$		0			0
$379$	0.553908	+	3.14137i	0.0284523	+	0.161361i	0.995723	−	0.0923838i	$-0.0294487\pi$
$379$	0.553908	+	3.14137i	0.0284523	+	0.161361i	−0.967271	+	0.253745i	$0.918338\pi$
$380$	−14.1804	−	8.18706i	−0.727440	−	0.419988i
$381$		0			0
$382$	−18.5052	+	15.5277i	−0.946806	+	0.794465i
$383$	7.82942	+	11.1816i	0.400065	+	0.571352i	0.967756	−	0.251890i	$-0.0810521\pi$
$383$	7.82942	+	11.1816i	0.400065	+	0.571352i	−0.567691	+	0.823242i	$0.692163\pi$
$384$		0			0
$385$	−2.11061	+	0.984192i	−0.107566	+	0.0501591i
$386$	4.85503	−	13.3391i	0.247114	−	0.678941i
$387$		0			0
$388$	−9.68249	+	0.847108i	−0.491554	+	0.0430054i
$389$	28.4894	−	2.49250i	1.44447	−	0.126375i	0.662207	−	0.749321i	$-0.269620\pi$
$389$	28.4894	−	2.49250i	1.44447	−	0.126375i	0.782265	+	0.622946i	$0.214064\pi$
$390$		0			0
$391$	−7.57632	+	20.8158i	−0.383151	+	1.05270i
$392$	10.6957	−	4.98747i	0.540213	−	0.251905i
$393$		0			0
$394$	−6.31557	−	9.01957i	−0.318174	−	0.454399i
$395$	7.91979	−	6.64550i	0.398488	−	0.334371i
$396$		0			0
$397$	32.6255	+	18.8363i	1.63742	+	0.945367i	0.981716	+	0.190354i	$0.0609634\pi$
$397$	32.6255	+	18.8363i	1.63742	+	0.945367i	0.655709	+	0.755014i	$0.272370\pi$
$398$	2.00283	+	11.3586i	0.100393	+	0.569357i
$399$		0			0
$400$	0.164864	+	0.452960i	0.00824321	+	0.0226480i
$401$	−11.8875	−	11.8875i	−0.593634	−	0.593634i	0.344977	−	0.938611i	$-0.387887\pi$
$401$	−11.8875	−	11.8875i	−0.593634	−	0.593634i	−0.938611	+	0.344977i	$0.887887\pi$
$402$		0			0
$403$	−2.76671	+	15.6908i	−0.137820	+	0.781615i
$404$	−10.2437	+	12.2079i	−0.509641	+	0.607366i
$405$		0			0
$406$		−	22.0972i		−	1.09667i
$407$	1.03604	+	1.13530i	0.0513546	+	0.0562747i
$408$		0			0
$409$	2.70426	−	30.9098i	0.133717	−	1.52839i	−0.572211	−	0.820106i	$-0.693914\pi$
$409$	2.70426	−	30.9098i	0.133717	−	1.52839i	0.705928	−	0.708284i	$-0.250530\pi$
$410$	−5.37748	−	4.51224i	−0.265575	−	0.222844i
$411$		0			0
$412$	−6.36268	−	2.96696i	−0.313467	−	0.146172i
$413$	−29.2912	+	29.2912i	−1.44133	+	1.44133i
$414$		0			0
$415$	−0.694897	+	2.59339i	−0.0341111	+	0.127304i
$416$	−2.59607	+	0.457757i	−0.127283	+	0.0224434i
$417$		0			0
$418$	1.68571	−	0.973244i	0.0824507	−	0.0476029i
$419$	−10.1607	−	12.1091i	−0.496384	−	0.591568i	0.458445	−	0.888723i	$-0.348407\pi$
$419$	−10.1607	−	12.1091i	−0.496384	−	0.591568i	−0.954829	+	0.297155i	$0.903962\pi$
$420$		0			0
$421$	−0.281698	−	1.05131i	−0.0137291	−	0.0512378i	0.958721	−	0.284347i	$-0.0917767\pi$
$421$	−0.281698	−	1.05131i	−0.0137291	−	0.0512378i	−0.972451	+	0.233109i	$0.925110\pi$
$422$	4.75500	+	10.1971i	0.231470	+	0.496389i
$423$		0			0
$424$	−0.0960526	+	0.137177i	−0.00466472	+	0.00666192i
$425$	−0.223355	−	2.55296i	−0.0108343	−	0.123837i
$426$		0			0
$427$	−14.7660	−	10.3393i	−0.714578	−	0.500353i
$428$	−11.3681	−	4.13766i	−0.549499	−	0.200001i
$429$		0			0
$430$	−25.0898	+	6.72279i	−1.20994	+	0.324202i
$431$	19.5025	−	13.6558i	0.939401	−	0.657776i	−0.000217195	−	1.00000i	$-0.500069\pi$
$431$	19.5025	−	13.6558i	0.939401	−	0.657776i	0.939618	+	0.342224i	$0.111180\pi$
$432$		0			0
$433$	−9.79455	−	16.9647i	−0.470696	−	0.815269i	0.528742	−	0.848782i	$-0.322664\pi$
$433$	−9.79455	−	16.9647i	−0.470696	−	0.815269i	−0.999438	+	0.0335132i	$0.989330\pi$
$434$	−13.1037	+	22.6963i	−0.628998	+	1.08946i
$435$		0			0
$436$	0.339567	+	0.0909868i	0.0162623	+	0.00435748i
$437$	30.1616	−	10.9779i	1.44283	−	0.525145i
$438$		0			0
$439$	−8.85417	+	18.9878i	−0.422587	+	0.906240i	0.573612	+	0.819127i	$0.305542\pi$
$439$	−8.85417	+	18.9878i	−0.422587	+	0.906240i	−0.996198	+	0.0871126i	$0.972236\pi$
$440$	0.528918	+	0.0932625i	0.0252152	+	0.00444612i
$441$		0			0
$442$	13.9615	+	1.22148i	0.664083	+	0.0580997i
$443$	−8.80849			−0.418504			−0.209252	−	0.977862i	$-0.567103\pi$
$443$	−8.80849			−0.418504			−0.209252	+	0.977862i	$0.567103\pi$
$444$		0			0
$445$	−1.04443			−0.0495106
$446$	−12.4229	−	1.08686i	−0.588242	−	0.0514645i
$447$		0			0
$448$	−4.27018	−	0.752948i	−0.201747	−	0.0355734i
$449$	−3.11614	+	6.68258i	−0.147060	+	0.315370i	−0.966015	−	0.258487i	$-0.916776\pi$
$449$	−3.11614	+	6.68258i	−0.147060	+	0.315370i	0.818955	+	0.573858i	$0.194554\pi$
$450$		0			0
$451$	0.784159	−	0.285410i	0.0369246	−	0.0134394i
$452$	10.9093	+	2.92315i	0.513132	+	0.137493i
$453$		0			0
$454$	11.1494	−	19.3114i	0.523268	−	0.906327i
$455$	12.1479	+	21.0408i	0.569502	+	0.986406i
$456$		0			0
$457$	−10.0562	+	7.04142i	−0.470409	+	0.329384i	−0.784628	−	0.619967i	$-0.787146\pi$
$457$	−10.0562	+	7.04142i	−0.470409	+	0.329384i	0.314220	+	0.949350i	$0.398257\pi$
$458$	−3.27321	+	0.877054i	−0.152947	+	0.0409820i
$459$		0			0
$460$	8.32223	+	3.02904i	0.388026	+	0.141230i
$461$	26.3115	+	18.4235i	1.22545	+	0.858070i	0.993408	−	0.114636i	$-0.0365701\pi$
$461$	26.3115	+	18.4235i	1.22545	+	0.858070i	0.232043	+	0.972706i	$0.425459\pi$
$462$		0			0
$463$	1.25012	+	14.2889i	0.0580980	+	0.664064i	0.968282	+	0.249860i	$0.0803845\pi$
$463$	1.25012	+	14.2889i	0.0580980	+	0.664064i	−0.910184	+	0.414204i	$0.864060\pi$
$464$	−2.92304	+	4.17453i	−0.135699	+	0.193798i
$465$		0			0
$466$	5.98551	+	12.8360i	0.277274	+	0.594615i
$467$	−4.52335	−	16.8814i	−0.209316	−	0.781177i	−0.988091	−	0.153874i	$-0.950825\pi$
$467$	−4.52335	−	16.8814i	−0.209316	−	0.781177i	0.778775	−	0.627304i	$-0.215842\pi$
$468$		0			0
$469$	−2.40043	−	2.86072i	−0.110842	−	0.132096i
$470$	2.18003	−	1.25864i	0.100557	−	0.0580567i
$471$		0			0
$472$	9.40827	−	1.65893i	0.433051	−	0.0763585i
$473$	0.799177	−	2.98257i	0.0367462	−	0.137139i
$474$		0			0
$475$	−2.62571	+	2.62571i	−0.120476	+	0.120476i
$476$	20.8927	+	9.74244i	0.957616	+	0.446544i
$477$		0			0
$478$	−14.4487	−	12.1239i	−0.660868	−	0.554534i
$479$	−1.24170	+	14.1927i	−0.0567347	+	0.648480i	0.913584	+	0.406650i	$0.133303\pi$
$479$	−1.24170	+	14.1927i	−0.0567347	+	0.648480i	−0.970319	+	0.241830i	$0.922252\pi$
$480$		0			0
$481$	10.8572	−	11.7999i	0.495045	−	0.538030i
$482$			18.8452i			0.858376i
$483$		0			0
$484$	7.02962	−	8.37758i	0.319528	−	0.380799i
$485$	3.58744	−	20.3454i	0.162897	−	0.923837i
$486$		0			0
$487$	−1.37132	−	1.37132i	−0.0621402	−	0.0621402i	0.675354	−	0.737494i	$-0.263991\pi$
$487$	−1.37132	−	1.37132i	−0.0621402	−	0.0621402i	−0.737494	+	0.675354i	$0.763991\pi$
$488$	1.42186	+	3.90652i	0.0643645	+	0.176840i
$489$		0			0
$490$	4.35586	+	24.7033i	0.196778	+	1.11598i
$491$	−1.55584	−	0.898263i	−0.0702139	−	0.0405380i	0.464482	−	0.885583i	$-0.346241\pi$
$491$	−1.55584	−	0.898263i	−0.0702139	−	0.0405380i	−0.534696	+	0.845045i	$0.679574\pi$
$492$		0			0
$493$	20.7550	−	17.4155i	0.934756	−	0.784354i
$494$	−11.6478	−	16.6347i	−0.524057	−	0.748431i
$495$		0			0
$496$	5.47779	−	2.55433i	0.245960	−	0.114693i
$497$	−23.5409	+	64.6780i	−1.05595	+	2.90120i
$498$		0			0
$499$	36.6663	−	3.20788i	1.64141	−	0.143605i	0.771302	−	0.636470i	$-0.219606\pi$
$499$	36.6663	−	3.20788i	1.64141	−	0.143605i	0.870106	+	0.492865i	$0.164050\pi$
$500$	−11.6080	+	1.01557i	−0.519125	+	0.0454176i
$501$		0			0
$502$	−6.86683	+	18.8665i	−0.306481	+	0.842051i
$503$	−1.60035	+	0.746255i	−0.0713561	+	0.0332739i	−0.457969	−	0.888968i	$-0.651423\pi$
$503$	−1.60035	+	0.746255i	−0.0713561	+	0.0332739i	0.386613	+	0.922242i	$0.373645\pi$
$504$		0			0
$505$	−19.4290	−	27.7475i	−0.864579	−	1.23475i
$506$	−0.806494	+	0.676729i	−0.0358530	+	0.0300843i
$507$		0			0
$508$	0.286429	+	0.165370i	0.0127082	+	0.00733709i
$509$	2.94615	+	16.7085i	0.130586	+	0.740589i	0.977832	+	0.209389i	$0.0671476\pi$
$509$	2.94615	+	16.7085i	0.130586	+	0.740589i	−0.847247	+	0.531200i	$0.821741\pi$
$510$		0			0
$511$	−23.3117	−	64.0482i	−1.03125	−	2.83333i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−2.11261	+	11.9812i	−0.0931834	+	0.528469i
$515$	9.59187	−	11.4311i	0.422668	−	0.503716i
$516$		0			0
$517$			0.299243i			0.0131607i
$518$	23.4200	−	12.1308i	1.02901	−	0.532995i
$519$		0			0
$520$	0.488351	−	5.58188i	0.0214156	−	0.244782i
$521$	−14.0942	−	11.8264i	−0.617477	−	0.518125i	0.279532	−	0.960136i	$-0.409821\pi$
$521$	−14.0942	−	11.8264i	−0.617477	−	0.518125i	−0.897009	+	0.442011i	$0.854265\pi$
$522$		0			0
$523$	34.5290	+	16.1011i	1.50985	+	0.704054i	0.988769	−	0.149454i	$-0.0477517\pi$
$523$	34.5290	+	16.1011i	1.50985	+	0.704054i	0.521080	+	0.853508i	$0.325529\pi$
$524$	2.04823	−	2.04823i	0.0894772	−	0.0894772i
$525$		0			0
$526$	−3.64477	+	13.6025i	−0.158920	+	0.593096i
$527$	−31.6450	+	5.57987i	−1.37848	+	0.243063i
$528$		0			0
$529$	4.88388	−	2.81971i	0.212343	−	0.122596i
$530$	−0.228800	−	0.272674i	−0.00993845	−	0.0118442i
$531$		0			0
$532$	−8.64525	−	32.2645i	−0.374819	−	1.39884i
$533$	−3.67930	−	7.89029i	−0.159368	−	0.341766i
$534$		0			0
$535$	14.7491	−	21.0639i	0.637660	−	0.910672i
$536$	0.0750625	+	0.857969i	0.00324221	+	0.0370586i
$537$		0			0
$538$	−6.72049	−	4.70574i	−0.289741	−	0.202879i
$539$	−2.80210	−	1.01988i	−0.120695	−	0.0439294i
$540$		0			0
$541$	1.27055	−	0.340444i	0.0546254	−	0.0146368i	−0.231403	−	0.972858i	$-0.574332\pi$
$541$	1.27055	−	0.340444i	0.0546254	−	0.0146368i	0.286028	+	0.958221i	$0.407665\pi$
$542$	13.1771	−	9.22672i	0.566006	−	0.396322i
$543$		0			0
$544$	−2.65824	−	4.60421i	−0.113971	−	0.197404i
$545$	−0.373615	+	0.647120i	−0.0160039	+	0.0277196i
$546$		0			0
$547$	−20.7268	−	5.55373i	−0.886214	−	0.237460i	−0.213128	−	0.977024i	$-0.568365\pi$
$547$	−20.7268	−	5.55373i	−0.886214	−	0.237460i	−0.673086	+	0.739564i	$0.735032\pi$
$548$	14.1962	−	5.16699i	0.606431	−	0.220723i
$549$		0			0
$550$	0.0514740	−	0.110386i	0.00219486	−	0.00470689i
$551$	−38.6617	−	6.81711i	−1.64705	−	0.290419i
$552$		0			0
$553$	21.0101	+	1.83814i	0.893439	+	0.0781657i
$554$	−8.36578			−0.355428
$555$		0			0
$556$	−8.70306			−0.369092
$557$	19.7764	+	1.73021i	0.837951	+	0.0733112i	0.498048	−	0.867149i	$-0.334050\pi$
$557$	19.7764	+	1.73021i	0.837951	+	0.0733112i	0.339903	+	0.940461i	$0.389606\pi$
$558$		0			0
$559$	−31.7247	−	5.59392i	−1.34181	−	0.236598i
$560$	3.89506	−	8.35299i	0.164597	−	0.352978i
$561$		0			0
$562$	−30.2395	+	11.0063i	−1.27558	+	0.464272i
$563$	16.8985	+	4.52794i	0.712186	+	0.190830i	0.596683	−	0.802477i	$-0.296485\pi$
$563$	16.8985	+	4.52794i	0.712186	+	0.190830i	0.115504	+	0.993307i	$0.463152\pi$
$564$		0			0
$565$	−12.0032	+	20.7901i	−0.504977	+	0.874646i
$566$	4.13845	+	7.16801i	0.173952	+	0.301294i
$567$		0			0
$568$	13.0029	−	9.10473i	0.545590	−	0.382026i
$569$	17.5472	−	4.70176i	0.735618	−	0.197108i	0.128488	−	0.991711i	$-0.458988\pi$
$569$	17.5472	−	4.70176i	0.735618	−	0.197108i	0.607130	+	0.794603i	$0.292321\pi$
$570$		0			0
$571$	−26.6104	−	9.68540i	−1.11361	−	0.405321i	−0.281294	−	0.959622i	$-0.590764\pi$
$571$	−26.6104	−	9.68540i	−1.11361	−	0.405321i	−0.832317	+	0.554300i	$0.812986\pi$
$572$	0.545625	+	0.382051i	0.0228137	+	0.0159743i
$573$		0			0
$574$	−1.24808	−	14.2657i	−0.0520940	−	0.595437i
$575$	1.15199	−	1.64521i	0.0480412	−	0.0686100i
$576$		0			0
$577$	−6.95604	−	14.9173i	−0.289584	−	0.621015i	0.706665	−	0.707548i	$-0.250199\pi$
$577$	−6.95604	−	14.9173i	−0.289584	−	0.621015i	−0.996249	+	0.0865336i	$0.972421\pi$
$578$	2.91560	+	10.8812i	0.121273	+	0.452597i
$579$		0			0
$580$	−6.96278	−	8.29792i	−0.289114	−	0.344552i
$581$	−4.74327	+	2.73853i	−0.196784	+	0.113613i
$582$		0			0
$583$	0.0416710	−	0.00734773i	0.00172584	−	0.000304312i
$584$	−4.06839	+	15.1834i	−0.168351	+	0.628296i
$585$		0			0
$586$	−12.8997	+	12.8997i	−0.532881	+	0.532881i
$587$	7.43057	+	3.46493i	0.306692	+	0.143013i	0.569871	−	0.821734i	$-0.306993\pi$
$587$	7.43057	+	3.46493i	0.306692	+	0.143013i	−0.263179	+	0.964747i	$0.584771\pi$
$588$		0			0
$589$	35.6673	+	29.9284i	1.46964	+	1.23318i
$590$	−1.76981	+	20.2290i	−0.0728618	+	0.832814i
$591$		0			0
$592$	−6.02908	−	0.806312i	−0.247794	−	0.0331392i
$593$		−	23.7534i		−	0.975437i	−0.873001	−	0.487718i	$-0.837829\pi$
$593$		−	23.7534i		−	0.975437i	0.873001	−	0.487718i	$-0.162171\pi$
$594$		0			0
$595$	−31.4962	+	37.5357i	−1.29122	+	1.53882i
$596$	1.44362	−	8.18720i	0.0591332	−	0.335361i
$597$		0			0
$598$	7.76661	+	7.76661i	0.317600	+	0.317600i
$599$	5.18796	+	14.2538i	0.211974	+	0.582394i	0.999422	−	0.0339866i	$-0.0108204\pi$
$599$	5.18796	+	14.2538i	0.211974	+	0.582394i	−0.787448	+	0.616381i	$0.788598\pi$
$600$		0			0
$601$	5.85890	+	33.2275i	0.238989	+	1.35538i	0.834047	+	0.551693i	$0.186018\pi$
$601$	5.85890	+	33.2275i	0.238989	+	1.35538i	−0.595058	+	0.803683i	$0.702871\pi$
$602$	−45.8888	−	26.4939i	−1.87029	−	1.07981i
$603$		0			0
$604$	8.11855	−	6.81227i	0.330339	−	0.277187i
$605$	13.3330	+	19.0415i	0.542063	+	0.774146i
$606$		0			0
$607$	35.2398	−	16.4326i	1.43034	−	0.666978i	0.455571	−	0.890200i	$-0.349435\pi$
$607$	35.2398	−	16.4326i	1.43034	−	0.666978i	0.974768	+	0.223222i	$0.0716575\pi$
$608$	−2.63474	+	7.23890i	−0.106853	+	0.293576i
$609$		0			0
$610$	−8.80279	+	0.770144i	−0.356415	+	0.0311822i
$611$	3.11005	−	0.272094i	0.125819	−	0.0110078i
$612$		0			0
$613$	5.21940	−	14.3402i	0.210810	−	0.579195i	−0.788550	−	0.614970i	$-0.789168\pi$
$613$	5.21940	−	14.3402i	0.210810	−	0.579195i	0.999360	+	0.0357757i	$0.0113902\pi$
$614$	8.04465	−	3.75128i	0.324656	−	0.151389i
$615$		0			0
$616$	0.628422	+	0.897479i	0.0253198	+	0.0361605i
$617$	21.2890	−	17.8636i	0.857063	−	0.719162i	−0.104270	−	0.994549i	$-0.533251\pi$
$617$	21.2890	−	17.8636i	0.857063	−	0.719162i	0.961333	+	0.275387i	$0.0888061\pi$
$618$		0			0
$619$	15.0804	+	8.70667i	0.606132	+	0.349951i	0.771450	−	0.636290i	$-0.219532\pi$
$619$	15.0804	+	8.70667i	0.606132	+	0.349951i	−0.165318	+	0.986240i	$0.552865\pi$
$620$	2.23085	+	12.6518i	0.0895933	+	0.508109i
$621$		0			0
$622$	−3.35830	−	9.22685i	−0.134655	−	0.369963i
$623$	−1.50656	−	1.50656i	−0.0603591	−	0.0603591i
$624$		0			0
$625$	3.88234	−	22.0178i	0.155294	−	0.880713i
$626$	11.4662	−	13.6649i	0.458283	−	0.546160i
$627$		0			0
$628$		−	1.45994i		−	0.0582578i
$629$	29.8518	+	12.4367i	1.19027	+	0.495885i
$630$		0			0
$631$	1.74755	−	19.9746i	0.0695688	−	0.795176i	−0.878631	−	0.477501i	$-0.841543\pi$
$631$	1.74755	−	19.9746i	0.0695688	−	0.795176i	0.948200	−	0.317674i	$-0.102902\pi$
$632$	−3.72599	−	3.12648i	−0.148212	−	0.124365i
$633$		0			0
$634$	−20.4402	−	9.53140i	−0.811782	−	0.378540i
$635$	−0.497098	+	0.497098i	−0.0197267	+	0.0197267i
$636$		0			0
$637$	−8.05180	+	30.0497i	−0.319024	+	1.19061i
$638$	1.26812	−	0.223604i	0.0502053	−	0.00885255i
$639$		0			0
$640$	−1.84078	+	1.06278i	−0.0727633	+	0.0420099i
$641$	−18.1389	−	21.6171i	−0.716444	−	0.853825i	0.277836	−	0.960629i	$-0.410383\pi$
$641$	−18.1389	−	21.6171i	−0.716444	−	0.853825i	−0.994280	+	0.106804i	$0.965938\pi$
$642$		0			0
$643$	−11.2196	−	41.8723i	−0.442460	−	1.65128i	−0.722558	−	0.691310i	$-0.757034\pi$
$643$	−11.2196	−	41.8723i	−0.442460	−	1.65128i	0.280099	−	0.959971i	$-0.409633\pi$
$644$	7.63528	+	16.3739i	0.300872	+	0.645223i
$645$		0			0
$646$	23.4910	−	33.5487i	0.924243	−	1.31996i
$647$	1.64148	+	18.7623i	0.0645334	+	0.737620i	0.957676	+	0.287847i	$0.0929396\pi$
$647$	1.64148	+	18.7623i	0.0645334	+	0.737620i	−0.893143	+	0.449773i	$0.851505\pi$
$648$		0			0
$649$	−1.97737	−	1.38457i	−0.0776186	−	0.0543491i
$650$	−1.19406	−	0.434601i	−0.0468347	−	0.0170465i
$651$		0			0
$652$	11.6056	−	3.10972i	0.454512	−	0.121786i
$653$	32.1143	−	22.4867i	1.25673	−	0.879972i	0.260394	−	0.965502i	$-0.416147\pi$
$653$	32.1143	−	22.4867i	1.25673	−	0.879972i	0.996336	+	0.0855307i	$0.0272586\pi$
$654$		0			0
$655$	3.07847	+	5.33206i	0.120286	+	0.208341i
$656$	−1.65129	+	2.86011i	−0.0644720	+	0.111669i
$657$		0			0
$658$	4.96018	+	1.32908i	0.193368	+	0.0518128i
$659$	21.6562	−	7.88221i	0.843606	−	0.307047i	0.116175	−	0.993229i	$-0.462937\pi$
$659$	21.6562	−	7.88221i	0.843606	−	0.307047i	0.727431	+	0.686181i	$0.240714\pi$
$660$		0			0
$661$	15.1253	−	32.4363i	0.588305	−	1.26162i	−0.356593	−	0.934260i	$-0.616062\pi$
$661$	15.1253	−	32.4363i	0.588305	−	1.26162i	0.944898	−	0.327365i	$-0.106161\pi$
$662$	0.338053	+	0.0596079i	0.0131388	+	0.00231673i
$663$		0			0
$664$	1.25834	+	0.110090i	0.0488329	+	0.00427232i
$665$	70.9991			2.75323
$666$		0			0
$667$	21.2337			0.822172
$668$	12.4432	+	1.08864i	0.481442	+	0.0421207i
$669$		0			0
$670$	−1.80281	−	0.317884i	−0.0696487	−	0.0122809i
$671$	0.443934	−	0.952019i	0.0171379	−	0.0367523i
$672$		0			0
$673$	42.3428	−	15.4115i	1.63220	−	0.594071i	0.646546	−	0.762875i	$-0.276213\pi$
$673$	42.3428	−	15.4115i	1.63220	−	0.594071i	0.985650	+	0.168804i	$0.0539905\pi$
$674$	−4.02109	−	1.07745i	−0.154887	−	0.0415017i
$675$		0			0
$676$	−3.02545	+	5.24023i	−0.116363	+	0.201547i
$677$	−22.6797	−	39.2823i	−0.871650	−	1.50974i	−0.860289	−	0.509807i	$-0.829717\pi$
$677$	−22.6797	−	39.2823i	−0.871650	−	1.50974i	−0.0113617	−	0.999935i	$-0.503617\pi$
$678$		0			0
$679$	34.5225	−	24.1729i	1.32485	−	0.927671i
$680$	10.9154	−	2.92477i	0.418587	−	0.112160i
$681$		0			0
$682$	−1.43509	−	0.522332i	−0.0549526	−	0.0200011i
$683$	25.9549	+	18.1738i	0.993135	+	0.695401i	0.952741	−	0.303783i	$-0.0982499\pi$
$683$	25.9549	+	18.1738i	0.993135	+	0.695401i	0.0403938	+	0.999184i	$0.487139\pi$
$684$		0			0
$685$	2.79868	+	31.9891i	0.106932	+	1.22224i
$686$	−11.9413	+	17.0539i	−0.455921	+	0.651122i
$687$		0			0
$688$	5.16452	+	11.0753i	0.196895	+	0.422243i
$689$	−0.114256	−	0.426409i	−0.00435280	−	0.0162449i
$690$		0			0
$691$	−13.7101	−	16.3390i	−0.521555	−	0.621566i	0.439392	−	0.898295i	$-0.355194\pi$
$691$	−13.7101	−	16.3390i	−0.521555	−	0.621566i	−0.960948	+	0.276730i	$0.910749\pi$
$692$	−6.54574	+	3.77919i	−0.248832	+	0.143663i
$693$		0			0
$694$	−11.1012	+	1.95744i	−0.421396	+	0.0743036i
$695$	4.78784	−	17.8685i	0.181613	−	0.677790i
$696$		0			0
$697$	12.4154	−	12.4154i	0.470269	−	0.470269i
$698$	25.4223	+	11.8546i	0.962249	+	0.448704i
$699$		0			0
$700$	−1.60112	−	1.34350i	−0.0605166	−	0.0507794i
$701$	1.26431	−	14.4512i	0.0477525	−	0.545813i	−0.934208	−	0.356728i	$-0.883892\pi$
$701$	1.26431	−	14.4512i	0.0477525	−	0.545813i	0.981961	−	0.189085i	$-0.0605522\pi$
$702$		0			0
$703$	−13.9990	−	44.7184i	−0.527983	−	1.68659i
$704$		−	0.252677i		−	0.00952311i
$705$		0			0
$706$	−18.7084	+	22.2958i	−0.704099	+	0.839112i
$707$	11.9992	−	68.0508i	0.451276	−	2.55932i
$708$		0			0
$709$	23.9807	+	23.9807i	0.900613	+	0.900613i	0.995489	−	0.0948759i	$-0.0302454\pi$
$709$	23.9807	+	23.9807i	0.900613	+	0.900613i	−0.0948759	+	0.995489i	$0.530245\pi$
$710$	11.5398	+	31.7054i	0.433082	+	1.18988i
$711$		0			0
$712$	0.0853252	+	0.483903i	0.00319770	+	0.0181350i
$713$	−21.8093	−	12.5916i	−0.816765	−	0.471560i
$714$		0			0
$715$	−1.08456	+	0.910058i	−0.0405604	+	0.0340342i
$716$	13.8371	+	19.7615i	0.517118	+	0.738521i
$717$		0			0
$718$	30.5030	−	14.2238i	1.13836	−	0.530826i
$719$	−13.4026	+	36.8234i	−0.499833	+	1.37328i	0.391603	+	0.920134i	$0.371921\pi$
$719$	−13.4026	+	36.8234i	−0.499833	+	1.37328i	−0.891436	+	0.453146i	$0.850302\pi$
$720$		0			0
$721$	30.3252	−	2.65311i	1.12937	−	0.0988069i
$722$	−40.1900	+	3.51617i	−1.49572	+	0.130858i
$723$		0			0
$724$	−1.73420	+	4.76466i	−0.0644509	+	0.177077i
$725$	−2.22635	+	1.03816i	−0.0826846	+	0.0385565i
$726$		0			0
$727$	−6.03333	−	8.61649i	−0.223764	−	0.319568i	0.691535	−	0.722343i	$-0.256935\pi$
$727$	−6.03333	−	8.61649i	−0.223764	−	0.319568i	−0.915299	+	0.402775i	$0.868046\pi$
$728$	8.75615	−	7.34728i	0.324524	−	0.272308i
$729$		0			0
$730$	−28.9354	−	16.7058i	−1.07095	−	0.618311i
$731$	−11.2817	−	63.9819i	−0.417270	−	2.36646i
$732$		0			0
$733$	−0.882266	−	2.42401i	−0.0325872	−	0.0895327i	0.922332	−	0.386398i	$-0.126281\pi$
$733$	−0.882266	−	2.42401i	−0.0325872	−	0.0895327i	−0.954919	+	0.296865i	$0.904059\pi$
$734$	−0.698961	−	0.698961i	−0.0257991	−	0.0257991i
$735$		0			0
$736$	0.723523	−	4.10330i	0.0266694	−	0.151250i
$737$	0.139881	−	0.166704i	0.00515260	−	0.00614063i
$738$		0			0
$739$		−	20.4153i		−	0.750988i	−0.926825	−	0.375494i	$-0.877473\pi$
$739$		−	20.4153i		−	0.750988i	0.926825	−	0.375494i	$-0.122527\pi$
$740$	4.97226	−	11.9349i	0.182784	−	0.438735i
$741$		0			0
$742$	0.0632861	−	0.723364i	0.00232331	−	0.0265555i
$743$	23.3544	+	19.5966i	0.856788	+	0.718931i	0.961274	−	0.275596i	$-0.0888751\pi$
$743$	23.3544	+	19.5966i	0.856788	+	0.718931i	−0.104485	+	0.994526i	$0.533320\pi$
$744$		0			0
$745$	16.0152	+	7.46799i	0.586750	+	0.273606i
$746$	−16.4180	+	16.4180i	−0.601105	+	0.601105i
$747$		0			0
$748$	−0.347685	+	1.29758i	−0.0127126	+	0.0474442i
$749$	51.6594	−	9.10894i	1.88759	−	0.332833i
$750$		0			0
$751$	−17.4379	+	10.0677i	−0.636316	+	0.367377i	−0.783194	−	0.621777i	$-0.786411\pi$
$751$	−17.4379	+	10.0677i	−0.636316	+	0.367377i	0.146878	+	0.989155i	$0.453078\pi$
$752$	−0.761249	−	0.907221i	−0.0277599	−	0.0330830i
$753$		0			0
$754$	−3.47700	−	12.9763i	−0.126625	−	0.472570i
$755$	9.52016	+	20.4160i	0.346474	+	0.743016i
$756$		0			0
$757$	−0.904586	+	1.29188i	−0.0328777	+	0.0469543i	−0.835254	−	0.549864i	$-0.814680\pi$
$757$	−0.904586	+	1.29188i	−0.0328777	+	0.0469543i	0.802377	+	0.596818i	$0.203569\pi$
$758$	0.278012	+	3.17769i	0.0100978	+	0.115419i
$759$		0			0
$760$	−13.4129	−	9.39181i	−0.486537	−	0.340677i
$761$	2.59738	+	0.945367i	0.0941548	+	0.0342695i	0.388668	−	0.921378i	$-0.372935\pi$
$761$	2.59738	+	0.945367i	0.0941548	+	0.0342695i	−0.294513	+	0.955647i	$0.595158\pi$
$762$		0			0
$763$	−1.47238	+	0.394524i	−0.0533038	+	0.0142827i
$764$	−19.7881	+	13.8558i	−0.715907	+	0.501284i
$765$		0			0
$766$	6.82509	+	11.8214i	0.246600	+	0.427125i
$767$	−12.5919	+	21.8099i	−0.454669	+	0.787509i
$768$		0			0
$769$	21.6922	+	5.81240i	0.782240	+	0.209601i	0.627772	−	0.778397i	$-0.283967\pi$
$769$	21.6922	+	5.81240i	0.782240	+	0.209601i	0.154468	+	0.987998i	$0.450634\pi$
$770$	−2.18835	+	0.796496i	−0.0788628	+	0.0287037i
$771$		0			0
$772$	5.99913	−	12.8652i	0.215913	−	0.463028i
$773$	−15.7222	−	2.77225i	−0.565488	−	0.0997107i	−0.116406	−	0.993202i	$-0.537138\pi$
$773$	−15.7222	−	2.77225i	−0.565488	−	0.0997107i	−0.449081	+	0.893491i	$0.648249\pi$
$774$		0			0
$775$	2.90234	+	0.253922i	0.104255	+	0.00912114i
$776$	−9.71948			−0.348909
$777$		0			0
$778$	28.5983			1.02530
$779$	−25.3445	−	2.21736i	−0.908061	−	0.0794450i
$780$		0			0
$781$	−3.94996	−	0.696484i	−0.141341	−	0.0249222i
$782$	−9.36170	+	20.0762i	−0.334774	+	0.717925i
$783$		0			0
$784$	11.0897	−	4.03631i	0.396059	−	0.144154i
$785$	2.99743	+	0.803159i	0.106983	+	0.0286660i
$786$		0			0
$787$	−25.0149	+	43.3271i	−0.891686	+	1.54445i	−0.0538333	+	0.998550i	$0.517144\pi$
$787$	−25.0149	+	43.3271i	−0.891686	+	1.54445i	−0.837853	+	0.545896i	$0.816189\pi$
$788$	−5.50543	−	9.53568i	−0.196123	−	0.339695i
$789$		0			0
$790$	8.46885	−	5.92995i	0.301308	−	0.210978i
$791$	−47.3034	+	12.6749i	−1.68192	+	0.450668i
$792$		0			0
$793$	−10.2980	−	3.74818i	−0.365694	−	0.133102i
$794$	30.8596	+	21.6081i	1.09517	+	0.766844i
$795$		0			0
$796$	1.00524	+	11.4900i	0.0356299	+	0.407251i
$797$	21.4649	−	30.6550i	0.760325	−	1.08586i	−0.233220	−	0.972424i	$-0.574926\pi$
$797$	21.4649	−	30.6550i	0.760325	−	1.08586i	0.993546	−	0.113433i	$-0.0361848\pi$
$798$		0			0
$799$	2.66092	+	5.70636i	0.0941366	+	0.201877i
$800$	0.124759	+	0.465606i	0.00441088	+	0.0164616i
$801$		0			0
$802$	−10.8062	−	12.8783i	−0.381580	−	0.454750i
$803$	3.43972	−	1.98592i	0.121385	−	0.0700816i
$804$		0			0
$805$	−37.8181	+	6.66836i	−1.33291	+	0.235029i
$806$	−4.12373	+	15.3900i	−0.145252	+	0.542088i
$807$		0			0
$808$	−11.2687	+	11.2687i	−0.396430	+	0.396430i
$809$	−50.3455	−	23.4765i	−1.77005	−	0.825390i	−0.976072	−	0.217448i	$-0.930227\pi$
$809$	−50.3455	−	23.4765i	−1.77005	−	0.825390i	−0.793982	−	0.607942i	$-0.791995\pi$
$810$		0			0
$811$	18.5766	+	15.5876i	0.652312	+	0.547355i	0.907771	−	0.419465i	$-0.137782\pi$
$811$	18.5766	+	15.5876i	0.652312	+	0.547355i	−0.255460	+	0.966820i	$0.582227\pi$
$812$	1.92590	−	22.0132i	0.0675859	−	0.772510i
$813$		0			0
$814$	0.933150	+	1.22128i	0.0327069	+	0.0428057i
$815$			25.5386i			0.894578i
$816$		0			0
$817$	−60.5112	+	72.1144i	−2.11702	+	2.52296i
$818$	5.38793	−	30.5565i	0.188385	−	1.06838i
$819$		0			0
$820$	−4.96374	−	4.96374i	−0.173341	−	0.173341i
$821$	−8.92852	−	24.5309i	−0.311607	−	0.856134i	−0.992333	−	0.123595i	$-0.960558\pi$
$821$	−8.92852	−	24.5309i	−0.311607	−	0.856134i	0.680725	−	0.732539i	$-0.261665\pi$
$822$		0			0
$823$	0.160279	+	0.908989i	0.00558699	+	0.0316854i	0.987474	−	0.157783i	$-0.0504347\pi$
$823$	0.160279	+	0.908989i	0.00558699	+	0.0316854i	−0.981887	+	0.189468i	$0.939324\pi$
$824$	−6.07988	−	3.51022i	−0.211802	−	0.122284i
$825$		0			0
$826$	−31.7327	+	26.6269i	−1.10412	+	0.926468i
$827$	−26.0590	−	37.2161i	−0.906161	−	1.29413i	−0.955391	−	0.295344i	$-0.904566\pi$
$827$	−26.0590	−	37.2161i	−0.906161	−	1.29413i	0.0492301	−	0.998787i	$-0.484323\pi$
$828$		0			0
$829$	40.5356	−	18.9021i	1.40786	−	0.656496i	0.437736	−	0.899104i	$-0.355781\pi$
$829$	40.5356	−	18.9021i	1.40786	−	0.656496i	0.970124	+	0.242608i	$0.0780028\pi$
$830$	−0.918281	+	2.52296i	−0.0318740	+	0.0875731i
$831$		0			0
$832$	−2.62608	+	0.229753i	−0.0910431	+	0.00796524i
$833$	−62.5030	+	5.46831i	−2.16560	+	0.189466i
$834$		0			0
$835$	−9.08054	+	24.9486i	−0.314245	+	0.863381i
$836$	1.76412	−	0.822622i	0.0610133	−	0.0284510i
$837$		0			0
$838$	−9.06669	−	12.9486i	−0.313204	−	0.447301i
$839$	−20.9211	+	17.5549i	−0.722275	+	0.606061i	−0.928014	−	0.372546i	$-0.878485\pi$
$839$	−20.9211	+	17.5549i	−0.722275	+	0.606061i	0.205738	+	0.978607i	$0.434040\pi$
$840$		0			0
$841$	2.62329	+	1.51456i	0.0904582	+	0.0522261i
$842$	−0.188998	−	1.07186i	−0.00651331	−	0.0369388i
$843$		0			0
$844$	3.84817	+	10.5728i	0.132460	+	0.363930i
$845$	−9.09444	−	9.09444i	−0.312858	−	0.312858i
$846$		0			0
$847$	−8.23436	+	46.6994i	−0.282936	+	1.60461i
$848$	−0.107643	+	0.128284i	−0.00369647	+	0.00440528i
$849$		0			0
$850$		−	2.56271i		−	0.0879001i
$851$	11.6567	+	22.5047i	0.399586	+	0.771452i
$852$		0			0
$853$	0.711142	−	8.12838i	0.0243490	−	0.278311i	−0.974253	−	0.225457i	$-0.927613\pi$
$853$	0.711142	−	8.12838i	0.0243490	−	0.278311i	0.998602	−	0.0528541i	$-0.0168318\pi$
$854$	−13.8087	−	11.5869i	−0.472525	−	0.396495i
$855$		0			0
$856$	−10.9642	−	5.11271i	−0.374750	−	0.174749i
$857$	37.3232	−	37.3232i	1.27494	−	1.27494i	0.331470	−	0.943466i	$-0.392455\pi$
$857$	37.3232	−	37.3232i	1.27494	−	1.27494i	0.943466	−	0.331470i	$-0.107545\pi$
$858$		0			0
$859$	10.5361	−	39.3211i	0.359486	−	1.34162i	−0.515259	−	0.857035i	$-0.672304\pi$
$859$	10.5361	−	39.3211i	0.359486	−	1.34162i	0.874744	−	0.484585i	$-0.161029\pi$
$860$	−25.5802	+	4.51049i	−0.872279	+	0.153806i
$861$		0			0
$862$	20.6184	−	11.9041i	0.702267	−	0.405454i
$863$	3.78310	+	4.50852i	0.128778	+	0.153472i	0.826580	−	0.562819i	$-0.190283\pi$
$863$	3.78310	+	4.50852i	0.128778	+	0.153472i	−0.697802	+	0.716290i	$0.745839\pi$
$864$		0			0
$865$	−4.15811	−	15.5183i	−0.141380	−	0.527638i
$866$	−8.27871	−	17.7537i	−0.281322	−	0.603297i
$867$		0			0
$868$	−15.0320	+	21.4679i	−0.510218	+	0.728666i
$869$	0.107115	+	1.22433i	0.00363362	+	0.0415325i
$870$		0			0
$871$	−1.85976	−	1.30222i	−0.0630155	−	0.0441239i
$872$	0.330345	+	0.120236i	0.0111869	+	0.00407170i
$873$		0			0
$874$	31.0036	−	8.30740i	1.04871	−	0.281002i
$875$	41.3878	−	28.9801i	1.39916	−	0.979705i
$876$		0			0
$877$	−7.45673	−	12.9154i	−0.251796	−	0.436123i	0.712225	−	0.701952i	$-0.247688\pi$
$877$	−7.45673	−	12.9154i	−0.251796	−	0.436123i	−0.964020	+	0.265829i	$0.914354\pi$
$878$	−10.4754	+	18.1439i	−0.353527	+	0.612327i
$879$		0			0
$880$	0.518777	+	0.139006i	0.0174880	+	0.00468589i
$881$	−20.4248	+	7.43403i	−0.688130	+	0.250459i	−0.662334	−	0.749208i	$-0.730434\pi$
$881$	−20.4248	+	7.43403i	−0.688130	+	0.250459i	−0.0257959	+	0.999667i	$0.508212\pi$
$882$		0			0
$883$	−16.2671	+	34.8849i	−0.547432	+	1.17397i	0.416821	+	0.908989i	$0.363144\pi$
$883$	−16.2671	+	34.8849i	−0.547432	+	1.17397i	−0.964253	+	0.264983i	$0.914634\pi$
$884$	13.8020	+	2.43366i	0.464210	+	0.0818527i
$885$		0			0
$886$	−8.77497	−	0.767711i	−0.294801	−	0.0257917i
$887$	−19.6596			−0.660104			−0.330052	−	0.943963i	$-0.607066\pi$
$887$	−19.6596			−0.660104			−0.330052	+	0.943963i	$0.607066\pi$
$888$		0			0
$889$	−1.43410			−0.0480983
$890$	−1.04045	−	0.0910279i	−0.0348761	−	0.00305126i
$891$		0			0
$892$	−12.2809	−	2.16545i	−0.411195	−	0.0725048i
$893$	3.85562	−	8.26840i	0.129023	−	0.276691i
$894$		0			0
$895$	−48.1850	+	17.5379i	−1.61065	+	0.586228i
$896$	−4.18831	−	1.12225i	−0.139922	−	0.0374919i
$897$		0			0
$898$	−3.68670	+	6.38556i	−0.123027	+	0.213089i
$899$	15.4008	+	26.6749i	0.513645	+	0.889659i
$900$		0			0
$901$	0.729301	−	0.510662i	0.0242965	−	0.0170126i
$902$	0.806050	−	0.215980i	0.0268385	−	0.00719136i
$903$		0			0
$904$	10.6130	+	3.86283i	0.352985	+	0.128476i
$905$	−8.82841	−	6.18172i	−0.293466	−	0.205487i
$906$		0			0
$907$	0.879937	+	10.0577i	0.0292178	+	0.333961i	0.996709	+	0.0810580i	$0.0258299\pi$
$907$	0.879937	+	10.0577i	0.0292178	+	0.333961i	−0.967492	+	0.252903i	$0.918615\pi$
$908$	12.7901	−	18.2661i	0.424454	−	0.606183i
$909$		0			0
$910$	10.2678	+	22.0195i	0.340376	+	0.729938i
$911$	13.1401	+	49.0396i	0.435351	+	1.62475i	0.740224	+	0.672360i	$0.234719\pi$
$911$	13.1401	+	49.0396i	0.435351	+	1.62475i	−0.304872	+	0.952393i	$0.598614\pi$
$912$		0			0
$913$	−0.205156	−	0.244496i	−0.00678969	−	0.00809163i
$914$	−10.6316	+	6.13817i	−0.351663	+	0.203033i
$915$		0			0
$916$	−3.33719	+	0.588437i	−0.110264	+	0.0194425i
$917$	−3.25075	+	12.1320i	−0.107349	+	0.400633i
$918$		0			0
$919$	18.1992	−	18.1992i	0.600335	−	0.600335i	−0.340066	−	0.940401i	$-0.610450\pi$
$919$	18.1992	−	18.1992i	0.600335	−	0.600335i	0.940401	+	0.340066i	$0.110450\pi$
$920$	8.02656	+	3.74285i	0.264628	+	0.123398i
$921$		0			0
$922$	24.6057	+	20.6466i	0.810346	+	0.679961i
$923$	−3.64700	+	41.6855i	−0.120043	+	1.37209i
$924$		0			0
$925$	−2.32251	−	1.78970i	−0.0763637	−	0.0588449i
$926$			14.3435i			0.471358i
$927$		0			0
$928$	−3.27575	+	3.90389i	−0.107532	+	0.128151i
$929$	5.93772	−	33.6745i	0.194810	−	1.10482i	−0.717878	−	0.696169i	$-0.754886\pi$
$929$	5.93772	−	33.6745i	0.194810	−	1.10482i	0.912688	−	0.408656i	$-0.134002\pi$
$930$		0			0
$931$	64.2842	+	64.2842i	2.10683	+	2.10683i
$932$	4.84401	+	13.3088i	0.158671	+	0.435944i
$933$		0			0
$934$	−3.03483	−	17.2114i	−0.0993027	−	0.563174i
$935$	−2.47282	−	1.42768i	−0.0808698	−	0.0466902i
$936$		0			0
$937$	−24.5179	+	20.5730i	−0.800966	+	0.672091i	−0.948433	−	0.316976i	$-0.897332\pi$
$937$	−24.5179	+	20.5730i	−0.800966	+	0.672091i	0.147467	+	0.989067i	$0.452888\pi$
$938$	−2.14197	−	3.05905i	−0.0699378	−	0.0998815i
$939$		0			0
$940$	2.28143	−	1.06385i	0.0744120	−	0.0346989i
$941$	−2.79863	+	7.68919i	−0.0912329	+	0.250660i	−0.976914	−	0.213634i	$-0.931470\pi$
$941$	−2.79863	+	7.68919i	−0.0912329	+	0.250660i	0.885681	+	0.464295i	$0.153692\pi$
$942$		0			0
$943$	13.7082	−	1.19931i	0.446399	−	0.0390549i
$944$	9.51705	−	0.832634i	0.309754	−	0.0270999i
$945$		0			0
$946$	1.05608	−	2.90157i	0.0343362	−	0.0943381i
$947$	0.0260460	−	0.0121455i	0.000846383	−	0.000394675i	−0.422195	−	0.906505i	$-0.638740\pi$
$947$	0.0260460	−	0.0121455i	0.000846383	−	0.000394675i	0.423041	+	0.906110i	$0.360962\pi$
$948$		0			0
$949$	−23.7674	−	33.9434i	−0.771524	−	1.10185i
$950$	−2.84456	+	2.38687i	−0.0922897	+	0.0774402i
$951$		0			0
$952$	19.9641	+	11.5263i	0.647041	+	0.373569i
$953$	9.20179	+	52.1859i	0.298075	+	1.69047i	0.654434	+	0.756119i	$0.272907\pi$
$953$	9.20179	+	52.1859i	0.298075	+	1.69047i	−0.356359	+	0.934349i	$0.615982\pi$
$954$		0			0
$955$	−17.5615	−	48.2499i	−0.568278	−	1.56133i
$956$	−13.3371	−	13.3371i	−0.431351	−	0.431351i
$957$		0			0
$958$	−2.47395	+	14.0305i	−0.0799296	+	0.453304i
$959$	−42.1064	+	50.1804i	−1.35969	+	1.62041i
$960$		0			0
$961$		−	5.53076i		−	0.178412i
$962$	11.8443	−	10.8088i	0.381876	−	0.348488i
$963$		0			0
$964$	−1.64247	+	18.7735i	−0.0529004	+	0.604654i
$965$	23.1135	+	19.3945i	0.744050	+	0.624332i
$966$		0			0
$967$	−12.7866	−	5.96248i	−0.411189	−	0.191740i	0.206006	−	0.978551i	$-0.433953\pi$
$967$	−12.7866	−	5.96248i	−0.411189	−	0.191740i	−0.617195	+	0.786810i	$0.711731\pi$
$968$	7.73303	−	7.73303i	0.248549	−	0.248549i
$969$		0			0
$970$	5.34701	−	19.9553i	0.171682	−	0.640726i
$971$	−38.9085	+	6.86061i	−1.24863	+	0.220168i	−0.758612	−	0.651543i	$-0.774122\pi$
$971$	−38.9085	+	6.86061i	−1.24863	+	0.220168i	−0.490021	+	0.871711i	$0.663011\pi$
$972$		0			0
$973$	32.6812	−	18.8685i	1.04771	−	0.604895i
$974$	−1.24658	−	1.48562i	−0.0399430	−	0.0476022i
$975$		0			0
$976$	1.07597	+	4.01558i	0.0344410	+	0.128536i
$977$	21.1372	+	45.3289i	0.676240	+	1.45020i	0.881832	+	0.471564i	$0.156310\pi$
$977$	21.1372	+	45.3289i	0.676240	+	1.45020i	−0.205592	+	0.978638i	$0.565912\pi$
$978$		0			0
$979$	0.0712137	−	0.101704i	0.00227600	−	0.00325046i
$980$	2.18625	+	24.9890i	0.0698372	+	0.798243i
$981$		0			0
$982$	−1.47163	−	1.03044i	−0.0469615	−	0.0328828i
$983$	−37.5145	−	13.6542i	−1.19653	−	0.435500i	−0.334516	−	0.942390i	$-0.608573\pi$
$983$	−37.5145	−	13.6542i	−1.19653	−	0.435500i	−0.862011	+	0.506890i	$0.830795\pi$
$984$		0			0
$985$	22.6067	−	6.05744i	0.720308	−	0.193006i
$986$	22.1938	−	15.5403i	0.706796	−	0.494904i
$987$		0			0
$988$	−10.1536	−	17.5866i	−0.323030	−	0.559504i
$989$	25.4585	−	44.0955i	0.809534	−	1.40215i
$990$		0			0
$991$	−38.1552	−	10.2236i	−1.21204	−	0.324765i	−0.404477	−	0.914548i	$-0.632547\pi$
$991$	−38.1552	−	10.2236i	−1.21204	−	0.324765i	−0.807562	+	0.589783i	$0.799213\pi$
$992$	5.67957	−	2.06719i	0.180326	−	0.0656334i
$993$		0			0
$994$	−29.0883	+	62.3801i	−0.922626	+	1.97858i
$995$	−24.1434	−	4.25713i	−0.765396	−	0.134960i
$996$		0			0
$997$	−24.1259	−	2.11074i	−0.764074	−	0.0668478i	−0.301545	−	0.953452i	$-0.597502\pi$
$997$	−24.1259	−	2.11074i	−0.764074	−	0.0668478i	−0.462529	+	0.886604i	$0.653058\pi$
$998$	36.8063			1.16508
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.35.6	yes	96
3.2	odd	2	inner	666.2.bs.b.35.3	✓	96
37.18	odd	36	inner	666.2.bs.b.647.3	yes	96
111.92	even	36	inner	666.2.bs.b.647.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.35.3	✓	96	3.2	odd	2	inner
666.2.bs.b.35.6	yes	96	1.1	even	1	trivial
666.2.bs.b.647.3	yes	96	37.18	odd	36	inner
666.2.bs.b.647.6	yes	96	111.92	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.898297 + 1.92640i) q^{5} +(-4.07456 + 1.48302i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-0.898297 + 1.92640i) q^{5} +(-4.07456 + 1.48302i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-1.06278 + 1.84078i) q^{10} +(-0.126338 - 0.218824i) q^{11} +(-2.15938 + 1.51201i) q^{13} +(-4.18831 + 1.12225i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-4.35501 - 3.04941i) q^{17} +(0.671402 + 7.67416i) q^{19} +(-1.21917 + 1.74115i) q^{20} +(-0.106786 - 0.229003i) q^{22} +(-1.07840 - 4.02463i) q^{23} +(0.309843 + 0.369257i) q^{25} +(-2.28294 + 1.31806i) q^{26} +(-4.27018 + 0.752948i) q^{28} +(-1.31898 + 4.92252i) q^{29} +(4.27380 - 4.27380i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-4.07266 - 3.41737i) q^{34} +(0.803272 - 9.18144i) q^{35} +(-5.94126 + 1.30438i) q^{37} +7.70347i q^{38} +(-1.36628 + 1.62827i) q^{40} +(-0.573486 + 3.25240i) q^{41} +(8.64105 + 8.64105i) q^{43} +(-0.0864205 - 0.237438i) q^{44} +(-0.723523 - 4.10330i) q^{46} +(-1.02563 - 0.592147i) q^{47} +(9.04037 - 7.58577i) q^{49} +(0.276481 + 0.394856i) q^{50} +(-2.38913 + 1.11407i) q^{52} +(-0.0572756 + 0.157363i) q^{53} +(0.535034 - 0.0468094i) q^{55} +(-4.31955 + 0.377912i) q^{56} +(-1.74299 + 4.78883i) q^{58} +(8.65832 - 4.03744i) q^{59} +(2.38449 + 3.40541i) q^{61} +(4.63002 - 3.88505i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.972985 - 5.51807i) q^{65} +(0.294563 + 0.809306i) q^{67} +(-3.75932 - 3.75932i) q^{68} +(1.60043 - 9.07649i) q^{70} +(10.2034 - 12.1599i) q^{71} +15.7191i q^{73} +(-6.03234 + 0.781604i) q^{74} +(-0.671402 + 7.67416i) q^{76} +(0.839294 + 0.704251i) q^{77} +(-4.40823 - 2.05559i) q^{79} +(-1.50299 + 1.50299i) q^{80} +(-0.854770 + 3.19004i) q^{82} +(1.24395 - 0.219342i) q^{83} +(9.78649 - 5.65023i) q^{85} +(7.85505 + 9.36128i) q^{86} +(-0.0653976 - 0.244067i) q^{88} +(0.207661 + 0.445331i) q^{89} +(6.55617 - 9.36319i) q^{91} +(-0.363143 - 4.15075i) q^{92} +(-0.970116 - 0.679283i) q^{94} +(-15.3866 - 5.60028i) q^{95} +(-9.38829 + 2.51559i) q^{97} +(9.66712 - 6.76899i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

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Database

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