LMFDB - Embedded newform 666.2.bs.a.17.3

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:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.a.431.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.66079 - 0.320278i) q^{5} +(-1.19170 - 0.999952i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.66079 - 0.320278i) q^{5} +(-1.19170 - 0.999952i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-1.83739 + 3.18245i) q^{10} +(-1.53436 - 2.65759i) q^{11} +(4.68016 + 2.18239i) q^{13} +(1.50264 - 0.402632i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(3.89680 - 1.81711i) q^{17} +(-3.65122 + 2.55661i) q^{19} +(-1.55303 - 3.33048i) q^{20} +(3.05704 + 0.267456i) q^{22} +(-1.44170 - 5.38049i) q^{23} +(8.37477 - 1.47670i) q^{25} +(-4.47214 + 2.58199i) q^{26} +(-0.532063 + 1.46183i) q^{28} +(1.43539 - 5.35696i) q^{29} +(0.808501 - 0.808501i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-0.746625 + 4.23432i) q^{34} +(-4.68281 - 3.27894i) q^{35} +(-5.10126 + 3.31317i) q^{37} -4.45732i q^{38} +(3.61895 + 0.638118i) q^{40} +(4.40217 - 1.60226i) q^{41} +(2.81097 + 2.81097i) q^{43} +(-1.97253 + 2.35077i) q^{44} +(5.23437 + 1.90515i) q^{46} +(6.67137 + 3.85172i) q^{47} +(-0.795301 - 4.51038i) q^{49} +(-3.59393 + 7.70721i) q^{50} +(0.450071 - 5.14433i) q^{52} +(1.78580 + 2.12823i) q^{53} +(-6.46813 - 9.23744i) q^{55} +(-0.892284 - 1.27431i) q^{56} +(3.56486 + 4.24843i) q^{58} +(-0.929020 + 10.6187i) q^{59} +(-2.73579 + 5.86693i) q^{61} +(0.198548 + 1.12602i) q^{62} +(0.866025 + 0.500000i) q^{64} +(17.8320 + 6.49033i) q^{65} +(6.26523 - 7.46661i) q^{67} +(-3.04031 - 3.04031i) q^{68} +(5.37190 - 1.95521i) q^{70} +(11.1486 + 1.96581i) q^{71} +2.09637i q^{73} +(0.211973 - 6.07907i) q^{74} +(3.65122 + 2.55661i) q^{76} +(-0.828969 + 4.70132i) q^{77} +(1.21429 + 13.8793i) q^{79} +(-2.59846 + 2.59846i) q^{80} +(-1.21249 + 4.52506i) q^{82} +(2.26944 - 6.23522i) q^{83} +(13.6834 - 7.90010i) q^{85} +(-3.91492 + 0.690306i) q^{86} +(-0.794242 - 2.96415i) q^{88} +(-14.6848 - 1.28475i) q^{89} +(-3.39504 - 7.28068i) q^{91} +(-4.56292 + 3.19499i) q^{92} +(-6.98169 + 3.25561i) q^{94} +(-12.5475 + 10.5286i) q^{95} +(-14.4814 + 3.88029i) q^{97} +(4.15085 + 1.93557i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{7}{36}\right)$

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 $

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$		0			0
$3$		0			0
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$	3.66079	−	0.320278i	1.63716	−	0.143233i	0.768906	−	0.639361i	$-0.220801\pi$
$5$	3.66079	−	0.320278i	1.63716	−	0.143233i	0.868249	+	0.496129i	$0.165246\pi$
$6$		0			0
$7$	−1.19170	−	0.999952i	−0.450419	−	0.377946i	0.389172	−	0.921165i	$-0.372761\pi$
$7$	−1.19170	−	0.999952i	−0.450419	−	0.377946i	−0.839591	+	0.543219i	$0.817205\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	−1.83739	+	3.18245i	−0.581033	+	1.00638i
$11$	−1.53436	−	2.65759i	−0.462626	−	0.801292i	0.536465	−	0.843923i	$-0.319759\pi$
$11$	−1.53436	−	2.65759i	−0.462626	−	0.801292i	−0.999091	+	0.0426307i	$0.986426\pi$
$12$		0			0
$13$	4.68016	+	2.18239i	1.29804	+	0.605287i	0.944001	−	0.329943i	$-0.107030\pi$
$13$	4.68016	+	2.18239i	1.29804	+	0.605287i	0.354041	+	0.935230i	$0.384807\pi$
$14$	1.50264	−	0.402632i	0.401598	−	0.107608i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	3.89680	−	1.81711i	0.945112	−	0.440713i	0.111933	−	0.993716i	$-0.464296\pi$
$17$	3.89680	−	1.81711i	0.945112	−	0.440713i	0.833180	+	0.553003i	$0.186518\pi$
$18$		0			0
$19$	−3.65122	+	2.55661i	−0.837648	+	0.586527i	−0.911760	−	0.410723i	$-0.865276\pi$
$19$	−3.65122	+	2.55661i	−0.837648	+	0.586527i	0.0741127	+	0.997250i	$0.476388\pi$
$20$	−1.55303	−	3.33048i	−0.347267	−	0.744717i
$21$		0			0
$22$	3.05704	+	0.267456i	0.651763	+	0.0570218i
$23$	−1.44170	−	5.38049i	−0.300615	−	1.12191i	−0.936655	−	0.350254i	$-0.886095\pi$
$23$	−1.44170	−	5.38049i	−0.300615	−	1.12191i	0.636040	−	0.771656i	$-0.280571\pi$
$24$		0			0
$25$	8.37477	−	1.47670i	1.67495	−	0.295340i
$26$	−4.47214	+	2.58199i	−0.877059	+	0.506370i
$27$		0			0
$28$	−0.532063	+	1.46183i	−0.100551	+	0.276260i
$29$	1.43539	−	5.35696i	0.266546	−	0.994763i	−0.694751	−	0.719250i	$-0.744486\pi$
$29$	1.43539	−	5.35696i	0.266546	−	0.994763i	0.961297	−	0.275513i	$-0.0888478\pi$
$30$		0			0
$31$	0.808501	−	0.808501i	0.145211	−	0.145211i	−0.630764	−	0.775975i	$-0.717258\pi$
$31$	0.808501	−	0.808501i	0.145211	−	0.145211i	0.775975	+	0.630764i	$0.217258\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$		0			0
$34$	−0.746625	+	4.23432i	−0.128045	+	0.726180i
$35$	−4.68281	−	3.27894i	−0.791540	−	0.554242i
$36$		0			0
$37$	−5.10126	+	3.31317i	−0.838643	+	0.544682i
$37$	−5.10126	+	3.31317i	−0.838643	+	0.544682i
$38$		−	4.45732i		−	0.723073i
$39$		0			0
$40$	3.61895	+	0.638118i	0.572206	+	0.100895i
$41$	4.40217	−	1.60226i	0.687503	−	0.250231i	0.0254373	−	0.999676i	$-0.491902\pi$
$41$	4.40217	−	1.60226i	0.687503	−	0.250231i	0.662066	+	0.749446i	$0.269680\pi$
$42$		0			0
$43$	2.81097	+	2.81097i	0.428669	+	0.428669i	0.888175	−	0.459506i	$-0.151973\pi$
$43$	2.81097	+	2.81097i	0.428669	+	0.428669i	−0.459506	+	0.888175i	$0.651973\pi$
$44$	−1.97253	+	2.35077i	−0.297370	+	0.354392i
$45$		0			0
$46$	5.23437	+	1.90515i	0.771765	+	0.280900i
$47$	6.67137	+	3.85172i	0.973120	+	0.561831i	0.900186	−	0.435506i	$-0.143430\pi$
$47$	6.67137	+	3.85172i	0.973120	+	0.561831i	0.0729338	+	0.997337i	$0.476764\pi$
$48$		0			0
$49$	−0.795301	−	4.51038i	−0.113614	−	0.644339i
$50$	−3.59393	+	7.70721i	−0.508258	+	1.08996i
$51$		0			0
$52$	0.450071	−	5.14433i	0.0624136	−	0.713390i
$53$	1.78580	+	2.12823i	0.245298	+	0.292335i	0.874619	−	0.484810i	$-0.161111\pi$
$53$	1.78580	+	2.12823i	0.245298	+	0.292335i	−0.629321	+	0.777145i	$0.716667\pi$
$54$		0			0
$55$	−6.46813	−	9.23744i	−0.872162	−	1.24558i
$56$	−0.892284	−	1.27431i	−0.119236	−	0.170287i
$57$		0			0
$58$	3.56486	+	4.24843i	0.468089	+	0.557847i
$59$	−0.929020	+	10.6187i	−0.120948	+	1.38244i	0.656894	+	0.753983i	$0.271870\pi$
$59$	−0.929020	+	10.6187i	−0.120948	+	1.38244i	−0.777842	+	0.628460i	$0.783686\pi$
$60$		0			0
$61$	−2.73579	+	5.86693i	−0.350282	+	0.751183i	−0.999959	−	0.00902754i	$-0.997126\pi$
$61$	−2.73579	+	5.86693i	−0.350282	+	0.751183i	0.649677	+	0.760210i	$0.274904\pi$
$62$	0.198548	+	1.12602i	0.0252156	+	0.143005i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	17.8320	+	6.49033i	2.21179	+	0.805027i
$66$		0			0
$67$	6.26523	−	7.46661i	0.765419	−	0.912191i	−0.232758	−	0.972535i	$-0.574775\pi$
$67$	6.26523	−	7.46661i	0.765419	−	0.912191i	0.998178	+	0.0603433i	$0.0192196\pi$
$68$	−3.04031	−	3.04031i	−0.368691	−	0.368691i
$69$		0			0
$70$	5.37190	−	1.95521i	0.642065	−	0.233693i
$71$	11.1486	+	1.96581i	1.32310	+	0.233298i	0.790184	−	0.612869i	$-0.209985\pi$
$71$	11.1486	+	1.96581i	1.32310	+	0.233298i	0.532917	+	0.846168i	$0.321096\pi$
$72$		0			0
$73$			2.09637i			0.245362i	0.992446	+	0.122681i	$0.0391491\pi$
$73$			2.09637i			0.245362i	−0.992446	+	0.122681i	$0.960851\pi$
$74$	0.211973	−	6.07907i	0.0246413	−	0.706677i
$75$		0			0
$76$	3.65122	+	2.55661i	0.418824	+	0.293264i
$77$	−0.828969	+	4.70132i	−0.0944698	+	0.535765i
$78$		0			0
$79$	1.21429	+	13.8793i	0.136618	+	1.56155i	0.687014	+	0.726645i	$0.258921\pi$
$79$	1.21429	+	13.8793i	0.136618	+	1.56155i	−0.550396	+	0.834904i	$0.685523\pi$
$80$	−2.59846	+	2.59846i	−0.290516	+	0.290516i
$81$		0			0
$82$	−1.21249	+	4.52506i	−0.133897	+	0.499709i
$83$	2.26944	−	6.23522i	0.249103	−	0.684404i	−0.750617	−	0.660738i	$-0.770244\pi$
$83$	2.26944	−	6.23522i	0.249103	−	0.684404i	0.999720	−	0.0236670i	$-0.00753413\pi$
$84$		0			0
$85$	13.6834	−	7.90010i	1.48417	−	0.856887i
$86$	−3.91492	+	0.690306i	−0.422157	+	0.0744376i
$87$		0			0
$88$	−0.794242	−	2.96415i	−0.0846665	−	0.315980i
$89$	−14.6848	−	1.28475i	−1.55658	−	0.136183i	−0.723889	−	0.689916i	$-0.757647\pi$
$89$	−14.6848	−	1.28475i	−1.55658	−	0.136183i	−0.832694	+	0.553733i	$0.813203\pi$
$90$		0			0
$91$	−3.39504	−	7.28068i	−0.355897	−	0.763223i
$92$	−4.56292	+	3.19499i	−0.475717	+	0.333101i
$93$		0			0
$94$	−6.98169	+	3.25561i	−0.720106	+	0.335791i
$95$	−12.5475	+	10.5286i	−1.28735	+	1.08021i
$96$		0			0
$97$	−14.4814	+	3.88029i	−1.47037	+	0.393983i	−0.903057	−	0.429521i	$-0.858682\pi$
$97$	−14.4814	+	3.88029i	−1.47037	+	0.393983i	−0.567309	+	0.823505i	$0.692016\pi$
$98$	4.15085	+	1.93557i	0.419299	+	0.195522i
$99$		0			0
$100$	−4.25198	−	7.36465i	−0.425198	−	0.736465i
$101$	−3.46931	+	6.00902i	−0.345209	+	0.597920i	−0.985392	−	0.170303i	$-0.945525\pi$
$101$	−3.46931	+	6.00902i	−0.345209	+	0.597920i	0.640183	+	0.768223i	$0.278859\pi$
$102$		0			0
$103$	−0.728310	−	0.195150i	−0.0717626	−	0.0192287i	0.222759	−	0.974874i	$-0.428494\pi$
$103$	−0.728310	−	0.195150i	−0.0717626	−	0.0192287i	−0.294522	+	0.955645i	$0.595160\pi$
$104$	3.95584	+	3.31934i	0.387902	+	0.325488i
$105$		0			0
$106$	−2.76764	+	0.242137i	−0.268817	+	0.0235184i
$107$	−5.61692	−	15.4323i	−0.543008	−	1.49190i	−0.842975	−	0.537952i	$-0.819198\pi$
$107$	−5.61692	−	15.4323i	−0.543008	−	1.49190i	0.299968	−	0.953949i	$-0.403024\pi$
$108$		0			0
$109$	3.45094	−	4.92845i	0.330540	−	0.472060i	−0.619140	−	0.785280i	$-0.712519\pi$
$109$	3.45094	−	4.92845i	0.330540	−	0.472060i	0.949681	+	0.313220i	$0.101408\pi$
$110$	11.2768			1.07520
$111$		0			0
$112$	1.55565			0.146995
$113$	−9.34949	+	13.3525i	−0.879526	+	1.25609i	0.0861333	+	0.996284i	$0.472549\pi$
$113$	−9.34949	+	13.3525i	−0.879526	+	1.25609i	−0.965660	+	0.259810i	$0.916340\pi$
$114$		0			0
$115$	−7.00101	−	19.2351i	−0.652847	−	1.79368i
$116$	−5.52483	+	0.483360i	−0.512968	+	0.0448789i
$117$		0			0
$118$	−8.16551	−	6.85167i	−0.751696	−	0.630748i
$119$	−6.46082	−	1.73117i	−0.592262	−	0.158696i
$120$		0			0
$121$	0.791494	−	1.37091i	0.0719540	−	0.124628i
$122$	−3.23672	−	5.60616i	−0.293039	−	0.507558i
$123$		0			0
$124$	−1.03627	−	0.483219i	−0.0930594	−	0.0433943i
$125$	12.4375	−	3.33262i	1.11245	−	0.298079i
$126$		0			0
$127$	−17.0656	+	14.3197i	−1.51433	+	1.27067i	−0.659572	+	0.751641i	$0.729263\pi$
$127$	−17.0656	+	14.3197i	−1.51433	+	1.27067i	−0.854755	+	0.519031i	$0.826293\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$		0			0
$130$	−15.5446	+	10.8845i	−1.36335	+	0.954630i
$131$	−3.28836	−	7.05191i	−0.287305	−	0.616129i	0.708691	−	0.705519i	$-0.249286\pi$
$131$	−3.28836	−	7.05191i	−0.287305	−	0.616129i	−0.995997	+	0.0893902i	$0.971508\pi$
$132$		0			0
$133$	6.90764	+	0.604340i	0.598968	+	0.0524029i
$134$	2.52270	+	9.41484i	0.217928	+	0.813319i
$135$		0			0
$136$	4.23432	−	0.746625i	0.363090	−	0.0640226i
$137$	7.36123	−	4.25001i	0.628912	−	0.363103i	−0.151418	−	0.988470i	$-0.548384\pi$
$137$	7.36123	−	4.25001i	0.628912	−	0.363103i	0.780331	+	0.625367i	$0.215051\pi$
$138$		0			0
$139$	−1.92381	+	5.28564i	−0.163176	+	0.448322i	−0.994152	−	0.107985i	$-0.965560\pi$
$139$	−1.92381	+	5.28564i	−0.163176	+	0.448322i	0.830977	+	0.556307i	$0.187782\pi$
$140$	−1.47958	+	5.52187i	−0.125047	+	0.466683i
$141$		0			0
$142$	−8.00490	+	8.00490i	−0.671756	+	0.671756i
$143$	−1.38114	−	15.7865i	−0.115497	−	1.32013i
$144$		0			0
$145$	3.53896	−	20.0704i	0.293895	−	1.66676i
$146$	−1.71725	−	1.20243i	−0.142120	−	0.0995137i
$147$		0			0
$148$	4.85810	+	3.66045i	0.399333	+	0.300887i
$149$		−	7.95907i		−	0.652033i	−0.945364	−	0.326016i	$-0.894294\pi$
$149$		−	7.95907i		−	0.652033i	0.945364	−	0.326016i	$-0.105706\pi$
$150$		0			0
$151$	11.7722	+	2.07576i	0.958010	+	0.168923i	0.630728	−	0.776004i	$-0.282756\pi$
$151$	11.7722	+	2.07576i	0.958010	+	0.168923i	0.327282	+	0.944927i	$0.393867\pi$
$152$	−4.18851	+	1.52449i	−0.339733	+	0.123653i
$153$		0			0
$154$	−3.37562	−	3.37562i	−0.272015	−	0.272015i
$155$	2.70081	−	3.21870i	0.216934	−	0.258532i
$156$		0			0
$157$	−22.6665	−	8.24992i	−1.80898	−	0.658415i	−0.997227	−	0.0744136i	$-0.976291\pi$
$157$	−22.6665	−	8.24992i	−1.80898	−	0.658415i	−0.811753	−	0.584001i	$-0.801486\pi$
$158$	−12.0658	−	6.96618i	−0.959902	−	0.554200i
$159$		0			0
$160$	−0.638118	−	3.61895i	−0.0504476	−	0.286103i
$161$	−3.66217	+	7.85354i	−0.288619	+	0.618946i
$162$		0			0
$163$	−0.0266854	+	0.305015i	−0.00209016	+	0.0238907i	−0.997168	−	0.0752041i	$-0.976039\pi$
$163$	−0.0266854	+	0.305015i	−0.00209016	+	0.0238907i	0.995078	+	0.0990948i	$0.0315947\pi$
$164$	−3.01126	−	3.58868i	−0.235140	−	0.280229i
$165$		0			0
$166$	3.80590	+	5.43539i	0.295395	+	0.421868i
$167$	1.51316	+	2.16102i	0.117092	+	0.167225i	0.873420	−	0.486968i	$-0.161897\pi$
$167$	1.51316	+	2.16102i	0.117092	+	0.167225i	−0.756328	+	0.654193i	$0.773008\pi$
$168$		0			0
$169$	8.78479	+	10.4693i	0.675753	+	0.805331i
$170$	−1.37708	+	15.7401i	−0.105617	+	1.20721i
$171$		0			0
$172$	1.68004	−	3.60286i	0.128102	−	0.274715i
$173$	2.14941	+	12.1899i	0.163416	+	0.926780i	0.950682	+	0.310166i	$0.100385\pi$
$173$	2.14941	+	12.1899i	0.163416	+	0.926780i	−0.787266	+	0.616613i	$0.788504\pi$
$174$		0			0
$175$	−11.4568	−	6.61459i	−0.866053	−	0.500016i
$176$	2.88365	+	1.04956i	0.217363	+	0.0791137i
$177$		0			0
$178$	9.47525	−	11.2922i	0.710200	−	0.846383i
$179$	−4.60117	−	4.60117i	−0.343908	−	0.343908i	0.513926	−	0.857834i	$-0.328190\pi$
$179$	−4.60117	−	4.60117i	−0.343908	−	0.343908i	−0.857834	+	0.513926i	$0.828190\pi$
$180$		0			0
$181$	−11.8555	+	4.31504i	−0.881210	+	0.320734i	−0.742698	−	0.669627i	$-0.766454\pi$
$181$	−11.8555	+	4.31504i	−0.881210	+	0.320734i	−0.138512	+	0.990361i	$0.544232\pi$
$182$	7.91130	+	1.39498i	0.586425	+	0.103402i
$183$		0			0
$184$		−	5.57030i		−	0.410648i
$185$	−17.6135	+	13.7626i	−1.29497	+	1.01185i
$186$		0			0
$187$	−10.8082	−	7.56798i	−0.790374	−	0.553426i
$188$	1.33769	−	7.58641i	0.0975609	−	0.553295i
$189$		0			0
$190$	−1.42758	−	16.3173i	−0.103567	−	1.18378i
$191$	11.3924	−	11.3924i	0.824328	−	0.824328i	−0.162398	−	0.986725i	$-0.551923\pi$
$191$	11.3924	−	11.3924i	0.824328	−	0.824328i	0.986725	+	0.162398i	$0.0519228\pi$
$192$		0			0
$193$	4.03122	−	15.0447i	0.290173	−	1.08294i	−0.654802	−	0.755801i	$-0.727248\pi$
$193$	4.03122	−	15.0447i	0.290173	−	1.08294i	0.944975	−	0.327142i	$-0.106085\pi$
$194$	5.12766	−	14.0881i	0.368145	−	1.01147i
$195$		0			0
$196$	−3.96636	+	2.28998i	−0.283311	+	0.163570i
$197$	−20.4404	+	3.60419i	−1.45632	+	0.256788i	−0.845071	−	0.534654i	$-0.820442\pi$
$197$	−20.4404	+	3.60419i	−1.45632	+	0.256788i	−0.611245	+	0.791442i	$0.709331\pi$
$198$		0			0
$199$	2.36433	+	8.82379i	0.167603	+	0.625502i	0.997694	+	0.0678743i	$0.0216217\pi$
$199$	2.36433	+	8.82379i	0.167603	+	0.625502i	−0.830091	+	0.557628i	$0.811712\pi$
$200$	8.47160	+	0.741169i	0.599033	+	0.0524086i
$201$		0			0
$202$	−2.93239	−	6.28853i	−0.206322	−	0.442459i
$203$	−7.06726	+	4.94855i	−0.496025	+	0.347320i
$204$		0			0
$205$	15.6022	−	7.27545i	1.08971	−	0.508139i
$206$	0.577599	−	0.484663i	0.0402433	−	0.0337681i
$207$		0			0
$208$	−4.98802	+	1.33654i	−0.345857	+	0.0926721i
$209$	12.3967	+	5.78067i	0.857497	+	0.399858i
$210$		0			0
$211$	11.2198	+	19.4332i	0.772402	+	1.33784i	0.936243	+	0.351353i	$0.114278\pi$
$211$	11.2198	+	19.4332i	0.772402	+	1.33784i	−0.163841	+	0.986487i	$0.552388\pi$
$212$	1.38910	−	2.40600i	0.0954041	−	0.165245i
$213$		0			0
$214$	15.8632	+	4.25052i	1.08438	+	0.290560i
$215$	11.1907	+	9.39009i	0.763198	+	0.640399i
$216$		0			0
$217$	−1.77195	+	0.155026i	−0.120288	+	0.0105238i
$218$	2.05777	+	5.65369i	0.139370	+	0.382916i
$219$		0			0
$220$	−6.46813	+	9.23744i	−0.436081	+	0.622788i
$221$	22.2033			1.49355
$222$		0			0
$223$	−13.6153			−0.911749			−0.455874	−	0.890044i	$-0.650673\pi$
$223$	−13.6153			−0.911749			−0.455874	+	0.890044i	$0.650673\pi$
$224$	−0.892284	+	1.27431i	−0.0596182	+	0.0851436i
$225$		0			0
$226$	−5.57505	−	15.3173i	−0.370847	−	1.01889i
$227$	−21.0419	+	1.84093i	−1.39660	+	0.122187i	−0.760459	−	0.649386i	$-0.775026\pi$
$227$	−21.0419	+	1.84093i	−1.39660	+	0.122187i	−0.636141	+	0.771573i	$0.719470\pi$
$228$		0			0
$229$	−6.86936	−	5.76408i	−0.453940	−	0.380901i	0.386955	−	0.922098i	$-0.373527\pi$
$229$	−6.86936	−	5.76408i	−0.453940	−	0.380901i	−0.840896	+	0.541197i	$0.817971\pi$
$230$	19.7721	+	5.29792i	1.30373	+	0.349334i
$231$		0			0
$232$	2.77297	−	4.80292i	0.182054	−	0.315327i
$233$	−2.50827	−	4.34445i	−0.164322	−	0.284615i	0.772092	−	0.635511i	$-0.219210\pi$
$233$	−2.50827	−	4.34445i	−0.164322	−	0.284615i	−0.936414	+	0.350896i	$0.885877\pi$
$234$		0			0
$235$	25.6561	+	11.9636i	1.67362	+	0.780422i
$236$	10.2961	−	2.75883i	0.670219	−	0.179585i
$237$		0			0
$238$	5.12387	−	4.29943i	0.332131	−	0.278691i
$239$	−8.42166	+	3.92709i	−0.544752	+	0.254022i	−0.675457	−	0.737399i	$-0.736054\pi$
$239$	−8.42166	+	3.92709i	−0.544752	+	0.254022i	0.130705	+	0.991421i	$0.458276\pi$
$240$		0			0
$241$	5.07704	−	3.55498i	0.327041	−	0.228996i	−0.398512	−	0.917163i	$-0.630473\pi$
$241$	5.07704	−	3.55498i	0.327041	−	0.228996i	0.725553	+	0.688167i	$0.241584\pi$
$242$	0.668999	+	1.43467i	0.0430049	+	0.0922243i
$243$		0			0
$244$	6.44880	+	0.564197i	0.412842	+	0.0361190i
$245$	−4.35600	−	16.2568i	−0.278295	−	1.03861i
$246$		0			0
$247$	−22.6678	+	3.99695i	−1.44232	+	0.254320i
$248$	0.990207	−	0.571696i	0.0628782	−	0.0363028i
$249$		0			0
$250$	−4.40394	+	12.0997i	−0.278530	+	0.765255i
$251$	−7.36138	+	27.4730i	−0.464646	+	1.73408i	0.193414	+	0.981117i	$0.438044\pi$
$251$	−7.36138	+	27.4730i	−0.464646	+	1.73408i	−0.658060	+	0.752966i	$0.728623\pi$
$252$		0			0
$253$	−12.0870	+	12.0870i	−0.759905	+	0.759905i
$254$	−1.94162	−	22.1928i	−0.121828	−	1.39250i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	0.631694	+	0.442317i	0.0394040	+	0.0275910i	0.593112	−	0.805120i	$-0.297899\pi$
$257$	0.631694	+	0.442317i	0.0394040	+	0.0275910i	−0.553709	+	0.832711i	$0.686788\pi$
$258$		0			0
$259$	9.39217	+	1.15272i	0.583601	+	0.0716267i
$260$		−	18.9765i		−	1.17687i
$261$		0			0
$262$	7.66272	+	1.35114i	0.473404	+	0.0834739i
$263$	22.3730	−	8.14312i	1.37958	−	0.502126i	0.457530	−	0.889194i	$-0.348734\pi$
$263$	22.3730	−	8.14312i	1.37958	−	0.502126i	0.922051	+	0.387068i	$0.126512\pi$
$264$		0			0
$265$	7.21906	+	7.21906i	0.443463	+	0.443463i
$266$	−4.45710	+	5.31177i	−0.273283	+	0.325686i
$267$		0			0
$268$	−9.15915	−	3.33366i	−0.559484	−	0.203636i
$269$	4.30748	+	2.48692i	0.262631	+	0.151630i	0.625534	−	0.780197i	$-0.284881\pi$
$269$	4.30748	+	2.48692i	0.262631	+	0.151630i	−0.362903	+	0.931827i	$0.618214\pi$
$270$		0			0
$271$	2.38022	+	13.4989i	0.144588	+	0.819999i	0.967697	+	0.252116i	$0.0811264\pi$
$271$	2.38022	+	13.4989i	0.144588	+	0.819999i	−0.823109	+	0.567883i	$0.807762\pi$
$272$	−1.81711	+	3.89680i	−0.110178	+	0.236278i
$273$		0			0
$274$	−0.740825	+	8.46767i	−0.0447549	+	0.511551i
$275$	−16.7743	−	19.9909i	−1.01153	−	1.20550i
$276$		0			0
$277$	−0.863214	−	1.23280i	−0.0518655	−	0.0740716i	0.792382	−	0.610026i	$-0.208841\pi$
$277$	−0.863214	−	1.23280i	−0.0518655	−	0.0740716i	−0.844247	+	0.535954i	$0.819952\pi$
$278$	−3.22629	−	4.60761i	−0.193500	−	0.276346i
$279$		0			0
$280$	−3.67460	−	4.37922i	−0.219599	−	0.261708i
$281$	−2.22930	+	25.4810i	−0.132989	+	1.52007i	0.577516	+	0.816379i	$0.304022\pi$
$281$	−2.22930	+	25.4810i	−0.132989	+	1.52007i	−0.710505	+	0.703692i	$0.751534\pi$
$282$		0			0
$283$	−4.89533	+	10.4981i	−0.290997	+	0.624045i	−0.996401	−	0.0847600i	$-0.972988\pi$
$283$	−4.89533	+	10.4981i	−0.290997	+	0.624045i	0.705404	+	0.708805i	$0.250765\pi$
$284$	−1.96581	−	11.1486i	−0.116649	−	0.661550i
$285$		0			0
$286$	13.7237	+	7.92339i	0.811501	+	0.468520i
$287$	−6.84823	−	2.49255i	−0.404238	−	0.147131i
$288$		0			0
$289$	0.955769	−	1.13904i	0.0562217	−	0.0670024i
$290$	14.4109	+	14.4109i	0.846236	+	0.846236i
$291$		0			0
$292$	1.96994	−	0.717001i	0.115282	−	0.0419593i
$293$	15.2198	+	2.68365i	0.889148	+	0.156781i	0.599521	−	0.800359i	$-0.295358\pi$
$293$	15.2198	+	2.68365i	0.889148	+	0.156781i	0.289627	+	0.957140i	$0.406469\pi$
$294$		0			0
$295$			39.1706i			2.28060i
$296$	−5.78495	+	1.87997i	−0.336244	+	0.109271i
$297$		0			0
$298$	6.51969	+	4.56514i	0.377676	+	0.264451i
$299$	4.99497	−	28.3279i	0.288867	−	1.63824i
$300$		0			0
$301$	−0.538988	−	6.16066i	−0.0310668	−	0.355095i
$302$	−8.45263	+	8.45263i	−0.486394	+	0.486394i
$303$		0			0
$304$	1.15364	−	4.30544i	0.0661657	−	0.246934i
$305$	−8.13612	+	22.3538i	−0.465873	+	1.27997i
$306$		0			0
$307$	7.57872	−	4.37558i	0.432540	−	0.249727i	−0.267888	−	0.963450i	$-0.586326\pi$
$307$	7.57872	−	4.37558i	0.432540	−	0.249727i	0.700428	+	0.713723i	$0.252992\pi$
$308$	4.70132	−	0.828969i	0.267883	−	0.0472349i
$309$		0			0
$310$	1.08748	+	4.05854i	0.0617649	+	0.230510i
$311$	−24.7286	−	2.16348i	−1.40223	−	0.122679i	−0.639200	−	0.769040i	$-0.720735\pi$
$311$	−24.7286	−	2.16348i	−1.40223	−	0.122679i	−0.763032	+	0.646361i	$0.776290\pi$
$312$		0			0
$313$	−4.98918	−	10.6993i	−0.282005	−	0.604762i	0.713374	−	0.700784i	$-0.247166\pi$
$313$	−4.98918	−	10.6993i	−0.282005	−	0.604762i	−0.995379	+	0.0960211i	$0.969388\pi$
$314$	19.7589	−	13.8353i	1.11506	−	0.780772i
$315$		0			0
$316$	12.6270	−	5.88807i	0.710325	−	0.331230i
$317$	−26.8034	+	22.4907i	−1.50543	+	1.26321i	−0.633328	+	0.773884i	$0.718311\pi$
$317$	−26.8034	+	22.4907i	−1.50543	+	1.26321i	−0.872103	+	0.489323i	$0.837244\pi$
$318$		0			0
$319$	−16.4390	+	4.40482i	−0.920407	+	0.246622i
$320$	3.33048	+	1.55303i	0.186179	+	0.0868168i
$321$		0			0
$322$	−4.33271	−	7.50448i	−0.241453	−	0.418208i
$323$	−9.58243	+	16.5973i	−0.533181	+	0.923496i
$324$		0			0
$325$	42.4180	+	11.3659i	2.35293	+	0.630464i
$326$	−0.234548	−	0.196809i	−0.0129904	−	0.0109002i
$327$		0			0
$328$	4.66686	−	0.408297i	0.257684	−	0.0225445i
$329$	−4.09872	−	11.2611i	−0.225970	−	0.620846i
$330$		0			0
$331$	0.937171	−	1.33842i	0.0515116	−	0.0735662i	−0.792570	−	0.609781i	$-0.791257\pi$
$331$	0.937171	−	1.33842i	0.0515116	−	0.0735662i	0.844082	+	0.536215i	$0.180146\pi$
$332$	−6.63538			−0.364164
$333$		0			0
$334$	−2.63812			−0.144351
$335$	20.5443	−	29.3403i	1.12245	−	1.60303i
$336$		0			0
$337$	1.59401	+	4.37950i	0.0868311	+	0.238566i	0.975507	−	0.219970i	$-0.0705960\pi$
$337$	1.59401	+	4.37950i	0.0868311	+	0.238566i	−0.888676	+	0.458537i	$0.848374\pi$
$338$	−13.6147	+	1.19113i	−0.740542	+	0.0647890i
$339$		0			0
$340$	−12.1037	−	10.1562i	−0.656413	−	0.550796i
$341$	−3.38919	−	0.908130i	−0.183535	−	0.0491780i
$342$		0			0
$343$	−9.00717	+	15.6009i	−0.486342	+	0.842369i
$344$	1.98766	+	3.44272i	0.107167	+	0.185619i
$345$		0			0
$346$	−11.2182	−	5.23114i	−0.603095	−	0.281228i
$347$	1.77419	−	0.475393i	0.0952436	−	0.0255205i	−0.210882	−	0.977511i	$-0.567634\pi$
$347$	1.77419	−	0.475393i	0.0952436	−	0.0255205i	0.306126	+	0.951991i	$0.400967\pi$
$348$		0			0
$349$	21.7511	−	18.2513i	1.16431	−	0.976970i	0.164352	−	0.986402i	$-0.447447\pi$
$349$	21.7511	−	18.2513i	1.16431	−	0.976970i	0.999956	+	0.00943165i	$0.00300223\pi$
$350$	11.9897	−	5.59089i	0.640877	−	0.298846i
$351$		0			0
$352$	−2.51374	+	1.76014i	−0.133983	+	0.0938159i
$353$	−10.5803	−	22.6896i	−0.563134	−	1.20764i	−0.957431	−	0.288662i	$-0.906790\pi$
$353$	−10.5803	−	22.6896i	−0.563134	−	1.20764i	0.394297	−	0.918983i	$-0.370988\pi$
$354$		0			0
$355$	41.4425	+	3.62575i	2.19954	+	0.192435i
$356$	3.81522	+	14.2386i	0.202206	+	0.754644i
$357$		0			0
$358$	6.40818	−	1.12994i	0.338683	−	0.0597190i
$359$	27.0761	−	15.6324i	1.42902	−	0.825047i	0.431980	−	0.901883i	$-0.357815\pi$
$359$	27.0761	−	15.6324i	1.42902	−	0.825047i	0.997044	+	0.0768359i	$0.0244818\pi$
$360$		0			0
$361$	0.296766	−	0.815359i	0.0156193	−	0.0429136i
$362$	3.26534	−	12.1864i	0.171623	−	0.640505i
$363$		0			0
$364$	−5.68043	+	5.68043i	−0.297736	+	0.297736i
$365$	0.671420	+	7.67437i	0.0351438	+	0.401695i
$366$		0			0
$367$	1.93772	−	10.9893i	0.101148	−	0.573639i	−0.891541	−	0.452940i	$-0.850375\pi$
$367$	1.93772	−	10.9893i	0.101148	−	0.573639i	0.992689	−	0.120699i	$-0.0385136\pi$
$368$	4.56292	+	3.19499i	0.237859	+	0.166550i
$369$		0			0
$370$	−1.17100	−	22.3221i	−0.0608775	−	1.16047i
$371$		−	4.32192i		−	0.224383i
$372$		0			0
$373$	26.1895	+	4.61792i	1.35604	+	0.239107i	0.803960	−	0.594683i	$-0.202723\pi$
$373$	26.1895	+	4.61792i	1.35604	+	0.239107i	0.552082	+	0.833790i	$0.313834\pi$
$374$	12.3987	−	4.51274i	0.641119	−	0.233348i
$375$		0			0
$376$	5.44715	+	5.44715i	0.280915	+	0.280915i
$377$	18.4089	−	21.9388i	0.948105	−	1.12991i
$378$		0			0
$379$	32.4178	+	11.7991i	1.66519	+	0.606081i	0.991166	−	0.132626i	$-0.0423411\pi$
$379$	32.4178	+	11.7991i	1.66519	+	0.606081i	0.674027	+	0.738707i	$0.264563\pi$
$380$	14.1852	+	8.18982i	0.727684	+	0.420129i
$381$		0			0
$382$	2.79770	+	15.8666i	0.143143	+	0.811804i
$383$	5.18467	−	11.1186i	0.264924	−	0.568132i	−0.728177	−	0.685389i	$-0.759632\pi$
$383$	5.18467	−	11.1186i	0.264924	−	0.568132i	0.993102	+	0.117257i	$0.0374100\pi$
$384$		0			0
$385$	−1.52896	+	17.4760i	−0.0779228	+	0.890662i
$386$	10.0117	+	11.9315i	0.509582	+	0.607296i
$387$		0			0
$388$	8.59922	+	12.2810i	0.436559	+	0.623471i
$389$	−1.94886	−	2.78325i	−0.0988109	−	0.141117i	0.766702	−	0.642003i	$-0.221896\pi$
$389$	−1.94886	−	2.78325i	−0.0988109	−	0.141117i	−0.865513	+	0.500886i	$0.833007\pi$
$390$		0			0
$391$	−15.3949	−	18.3470i	−0.778555	−	0.927846i
$392$	0.399169	−	4.56253i	0.0201611	−	0.230442i
$393$		0			0
$394$	8.77173	−	18.8110i	0.441914	−	0.947687i
$395$	8.89049	+	50.4205i	0.447329	+	2.53693i
$396$		0			0
$397$	−2.26379	−	1.30700i	−0.113616	−	0.0655964i	0.442115	−	0.896958i	$-0.354228\pi$
$397$	−2.26379	−	1.30700i	−0.113616	−	0.0655964i	−0.555731	+	0.831362i	$0.687562\pi$
$398$	−8.58415	−	3.12438i	−0.430285	−	0.156611i
$399$		0			0
$400$	−5.46624	+	6.51441i	−0.273312	+	0.325721i
$401$	13.6899	+	13.6899i	0.683639	+	0.683639i	0.960818	−	0.277179i	$-0.0893995\pi$
$401$	13.6899	+	13.6899i	0.683639	+	0.683639i	−0.277179	+	0.960818i	$0.589399\pi$
$402$		0			0
$403$	5.54838	−	2.01944i	0.276384	−	0.100596i
$404$	6.83321	+	1.20488i	0.339965	+	0.0599450i
$405$		0			0
$406$		−	8.62753i		−	0.428177i
$407$	16.6322	+	8.47345i	0.824428	+	0.420013i
$408$		0			0
$409$	32.7972	+	22.9648i	1.62172	+	1.13554i	0.892271	+	0.451500i	$0.149111\pi$
$409$	32.7972	+	22.9648i	1.62172	+	1.13554i	0.729446	+	0.684038i	$0.239778\pi$
$410$	−2.98938	+	16.9536i	−0.147635	+	0.837280i
$411$		0			0
$412$	0.0657156	+	0.751133i	0.00323758	+	0.0370057i
$413$	11.7253	−	11.7253i	0.576967	−	0.576967i
$414$		0			0
$415$	6.31092	−	23.5527i	0.309791	−	1.15616i
$416$	1.76619	−	4.85256i	0.0865944	−	0.237916i
$417$		0			0
$418$	−11.8457	+	6.83912i	−0.579392	+	0.334512i
$419$	−24.9905	+	4.40649i	−1.22086	+	0.215271i	−0.746697	−	0.665164i	$-0.768362\pi$
$419$	−24.9905	+	4.40649i	−1.22086	+	0.215271i	−0.474167	+	0.880435i	$0.657251\pi$
$420$		0			0
$421$	1.25480	+	4.68297i	0.0611551	+	0.228234i	0.989739	−	0.142890i	$-0.0456394\pi$
$421$	1.25480	+	4.68297i	0.0611551	+	0.228234i	−0.928584	+	0.371123i	$0.878973\pi$
$422$	−22.3542	−	1.95574i	−1.08818	−	0.0952038i
$423$		0			0
$424$	1.17412	+	2.51791i	0.0570204	+	0.122281i
$425$	29.9515	−	20.9722i	1.45286	−	1.01730i
$426$		0			0
$427$	9.12688	−	4.25593i	0.441681	−	0.205959i
$428$	−12.5806	+	10.5563i	−0.608105	+	0.510260i
$429$		0			0
$430$	−14.1106	+	3.78093i	−0.680474	+	0.182333i
$431$	−27.6534	−	12.8950i	−1.33202	−	0.621129i	−0.379379	−	0.925241i	$-0.623862\pi$
$431$	−27.6534	−	12.8950i	−1.33202	−	0.621129i	−0.952636	+	0.304112i	$0.901640\pi$
$432$		0			0
$433$	0.0554427	+	0.0960295i	0.00266440	+	0.00461488i	0.867355	−	0.497691i	$-0.165819\pi$
$433$	0.0554427	+	0.0960295i	0.00266440	+	0.00461488i	−0.864690	+	0.502306i	$0.832485\pi$
$434$	0.889359	−	1.54042i	0.0426906	−	0.0739423i
$435$		0			0
$436$	−5.81152	−	1.55719i	−0.278321	−	0.0745760i
$437$	19.0198	+	15.9595i	0.909840	+	0.763447i
$438$		0			0
$439$	−21.8124	+	1.90834i	−1.04105	+	0.0910799i	−0.594836	−	0.803847i	$-0.702783\pi$
$439$	−21.8124	+	1.90834i	−1.04105	+	0.0910799i	−0.446212	+	0.894927i	$0.647227\pi$
$440$	−3.85690	−	10.5968i	−0.183871	−	0.505181i
$441$		0			0
$442$	−12.7353	+	18.1879i	−0.605755	+	0.865108i
$443$	−11.6286			−0.552490			−0.276245	−	0.961087i	$-0.589090\pi$
$443$	−11.6286			−0.552490			−0.276245	+	0.961087i	$0.589090\pi$
$444$		0			0
$445$	−54.1694			−2.56787
$446$	7.80942	−	11.1530i	0.369787	−	0.528110i
$447$		0			0
$448$	−0.532063	−	1.46183i	−0.0251376	−	0.0690651i
$449$	−1.30137	+	0.113855i	−0.0614156	+	0.00537317i	−0.117822	−	0.993035i	$-0.537591\pi$
$449$	−1.30137	+	0.113855i	−0.0614156	+	0.00537317i	0.0564065	+	0.998408i	$0.482036\pi$
$450$		0			0
$451$	−11.0126	−	9.24070i	−0.518565	−	0.435127i
$452$	15.7449	+	4.21884i	0.740579	+	0.198438i
$453$		0			0
$454$	10.5611	−	18.2924i	0.495659	−	0.858506i
$455$	−14.7604	−	25.5657i	−0.691976	−	1.19854i
$456$		0			0
$457$	26.3447	+	12.2847i	1.23235	+	0.574655i	0.926094	−	0.377293i	$-0.123145\pi$
$457$	26.3447	+	12.2847i	1.23235	+	0.574655i	0.306259	+	0.951948i	$0.400923\pi$
$458$	8.66176	−	2.32091i	0.404737	−	0.108449i
$459$		0			0
$460$	−15.6806	+	13.1576i	−0.731112	+	0.613476i
$461$	8.23601	−	3.84051i	0.383589	−	0.178870i	−0.221252	−	0.975217i	$-0.571014\pi$
$461$	8.23601	−	3.84051i	0.383589	−	0.178870i	0.604841	+	0.796346i	$0.293237\pi$
$462$		0			0
$463$	18.6726	−	13.0747i	0.867790	−	0.607633i	−0.0526080	−	0.998615i	$-0.516753\pi$
$463$	18.6726	−	13.0747i	0.867790	−	0.607633i	0.920398	+	0.390982i	$0.127865\pi$
$464$	2.34381	+	5.02633i	0.108809	+	0.233341i
$465$		0			0
$466$	4.99745	+	0.437220i	0.231503	+	0.0202538i
$467$	3.05167	+	11.3890i	0.141214	+	0.527019i	0.999895	+	0.0145077i	$0.00461809\pi$
$467$	3.05167	+	11.3890i	0.141214	+	0.527019i	−0.858680	+	0.512511i	$0.828715\pi$
$468$		0			0
$469$	−14.9325	+	2.63300i	−0.689519	+	0.121581i
$470$	−24.5158	+	14.1542i	−1.13083	+	0.652884i
$471$		0			0
$472$	−3.64570	+	10.0165i	−0.167807	+	0.461046i
$473$	3.15736	−	11.7834i	0.145176	−	0.541803i
$474$		0			0
$475$	−26.8028	+	26.8028i	−1.22980	+	1.22980i
$476$	0.582962	+	6.66328i	0.0267200	+	0.305411i
$477$		0			0
$478$	1.61359	−	9.15111i	0.0738038	−	0.418562i
$479$	3.52158	+	2.46584i	0.160905	+	0.112667i	0.651256	−	0.758858i	$-0.274242\pi$
$479$	3.52158	+	2.46584i	0.160905	+	0.112667i	−0.490351	+	0.871525i	$0.663131\pi$
$480$		0			0
$481$	−31.1054	+	4.37320i	−1.41828	+	0.199401i
$482$			6.19792i			0.282307i
$483$		0			0
$484$	−1.55894	−	0.274883i	−0.0708608	−	0.0124947i
$485$	−51.7707	+	18.8430i	−2.35079	+	0.855616i
$486$		0			0
$487$	−28.8514	−	28.8514i	−1.30738	−	1.30738i	−0.923300	−	0.384080i	$-0.874519\pi$
$487$	−28.8514	−	28.8514i	−1.30738	−	1.30738i	−0.384080	−	0.923300i	$-0.625481\pi$
$488$	−4.16104	+	4.95894i	−0.188362	+	0.224481i
$489$		0			0
$490$	15.8153	+	5.75630i	0.714463	+	0.260043i
$491$	−18.6975	−	10.7950i	−0.843806	−	0.487172i	0.0147501	−	0.999891i	$-0.495305\pi$
$491$	−18.6975	−	10.7950i	−0.843806	−	0.487172i	−0.858556	+	0.512720i	$0.828638\pi$
$492$		0			0
$493$	−4.14073	−	23.4833i	−0.186489	−	1.05763i
$494$	9.72762	−	20.8609i	0.437666	−	0.938578i
$495$		0			0
$496$	−0.0996532	+	1.13904i	−0.00447456	+	0.0511445i
$497$	−11.3201	−	13.4908i	−0.507775	−	0.605143i
$498$		0			0
$499$	−4.87713	−	6.96527i	−0.218330	−	0.311808i	0.695014	−	0.718996i	$-0.255398\pi$
$499$	−4.87713	−	6.96527i	−0.218330	−	0.311808i	−0.913344	+	0.407188i	$0.866509\pi$
$500$	−7.38553	−	10.5476i	−0.330291	−	0.471704i
$501$		0			0
$502$	−18.2823	−	21.7880i	−0.815978	−	0.972445i
$503$	2.19084	−	25.0414i	0.0976846	−	1.11654i	−0.776226	−	0.630454i	$-0.782869\pi$
$503$	2.19084	−	25.0414i	0.0976846	−	1.11654i	0.873911	−	0.486086i	$-0.161576\pi$
$504$		0			0
$505$	−10.7759	+	23.1089i	−0.479520	+	1.02833i
$506$	−2.96828	−	16.8340i	−0.131956	−	0.748361i
$507$		0			0
$508$	19.2929	+	11.1388i	0.855986	+	0.494204i
$509$	4.44824	+	1.61903i	0.197165	+	0.0717620i	0.438715	−	0.898626i	$-0.355434\pi$
$509$	4.44824	+	1.61903i	0.197165	+	0.0717620i	−0.241551	+	0.970388i	$0.577656\pi$
$510$		0			0
$511$	2.09627	−	2.49824i	0.0927335	−	0.110515i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−0.724649	+	0.263751i	−0.0319629	+	0.0116335i
$515$	−2.72869	−	0.481142i	−0.120241	−	0.0212017i
$516$		0			0
$517$		−	23.6397i		−	1.03967i
$518$	−6.33138	+	7.03244i	−0.278185	+	0.308988i
$519$		0			0
$520$	15.5446	+	10.8845i	0.681676	+	0.477315i
$521$	−2.19494	+	12.4481i	−0.0961622	+	0.545363i	0.898223	+	0.439540i	$0.144859\pi$
$521$	−2.19494	+	12.4481i	−0.0961622	+	0.545363i	−0.994385	+	0.105822i	$0.966252\pi$
$522$		0			0
$523$	3.06422	+	35.0242i	0.133989	+	1.53150i	0.704199	+	0.710002i	$0.251306\pi$
$523$	3.06422	+	35.0242i	0.133989	+	1.53150i	−0.570210	+	0.821499i	$0.693138\pi$
$524$	−5.50195	+	5.50195i	−0.240354	+	0.240354i
$525$		0			0
$526$	−6.16220	+	22.9976i	−0.268685	+	1.00274i
$527$	1.68143	−	4.61970i	0.0732443	−	0.201237i
$528$		0			0
$529$	−6.95262	+	4.01410i	−0.302288	+	0.174526i
$530$	−10.0542	+	1.77283i	−0.436726	+	0.0770066i
$531$		0			0
$532$	−1.79466	−	6.69775i	−0.0778083	−	0.290384i
$533$	24.0996	+	2.10844i	1.04387	+	0.0913267i
$534$		0			0
$535$	−25.5050	−	54.6956i	−1.10268	−	2.36470i
$536$	7.98425	−	5.59063i	0.344867	−	0.241478i
$537$		0			0
$538$	−4.50783	+	2.10204i	−0.194347	+	0.0906253i
$539$	−10.7664	+	9.03411i	−0.463743	+	0.389127i
$540$		0			0
$541$	10.0160	−	2.68378i	0.430621	−	0.115385i	−0.0369965	−	0.999315i	$-0.511779\pi$
$541$	10.0160	−	2.68378i	0.430621	−	0.115385i	0.467618	+	0.883931i	$0.345112\pi$
$542$	−12.4229	−	5.79289i	−0.533609	−	0.248826i
$543$		0			0
$544$	−2.14982	−	3.72360i	−0.0921728	−	0.159648i
$545$	11.0547	−	19.1473i	0.473531	−	0.820180i
$546$		0			0
$547$	−20.3902	−	5.46354i	−0.871822	−	0.233604i	−0.204946	−	0.978773i	$-0.565702\pi$
$547$	−20.3902	−	5.46354i	−0.871822	−	0.233604i	−0.666875	+	0.745169i	$0.732369\pi$
$548$	−6.51139	−	5.46370i	−0.278153	−	0.233398i
$549$		0			0
$550$	25.9969	−	2.27444i	1.10851	−	0.0969823i
$551$	8.45474	+	23.2292i	0.360184	+	0.989598i
$552$		0			0
$553$	12.4316	−	17.7542i	0.528646	−	0.754985i
$554$	1.50497			0.0639400
$555$		0			0
$556$	5.62486			0.238547
$557$	−0.909499	+	1.29890i	−0.0385367	+	0.0550361i	−0.837958	−	0.545735i	$-0.816251\pi$
$557$	−0.909499	+	1.29890i	−0.0385367	+	0.0550361i	0.799421	+	0.600771i	$0.205140\pi$
$558$		0			0
$559$	7.02114	+	19.2904i	0.296963	+	0.815899i
$560$	5.69491	−	0.498240i	0.240654	−	0.0210545i
$561$		0			0
$562$	−19.5942	−	16.4415i	−0.826530	−	0.693541i
$563$	18.3970	+	4.92947i	0.775343	+	0.207752i	0.624731	−	0.780840i	$-0.285209\pi$
$563$	18.3970	+	4.92947i	0.775343	+	0.207752i	0.150612	+	0.988593i	$0.451875\pi$
$564$		0			0
$565$	−29.9500	+	51.8750i	−1.26001	+	2.18240i
$566$	−5.79167	−	10.0315i	−0.243442	−	0.421654i
$567$		0			0
$568$	10.2600	+	4.78431i	0.430499	+	0.200745i
$569$	44.3976	−	11.8963i	1.86125	−	0.498719i	0.861289	−	0.508115i	$-0.169657\pi$
$569$	44.3976	−	11.8963i	1.86125	−	0.498719i	0.999956	+	0.00939572i	$0.00299079\pi$
$570$		0			0
$571$	23.2410	−	19.5015i	0.972604	−	0.816112i	−0.0103531	−	0.999946i	$-0.503296\pi$
$571$	23.2410	−	19.5015i	0.972604	−	0.816112i	0.982957	+	0.183835i	$0.0588511\pi$
$572$	−14.3621	+	6.69714i	−0.600508	+	0.280022i
$573$		0			0
$574$	5.96976	−	4.18007i	0.249173	−	0.174473i
$575$	−20.0193	−	42.9314i	−0.834861	−	1.79036i
$576$		0			0
$577$	−38.5127	−	3.36942i	−1.60330	−	0.140271i	−0.749910	−	0.661539i	$-0.769903\pi$
$577$	−38.5127	−	3.36942i	−1.60330	−	0.140271i	−0.853393	+	0.521269i	$0.825459\pi$
$578$	0.384841	+	1.43625i	0.0160073	+	0.0597400i
$579$		0			0
$580$	−20.0704	+	3.53896i	−0.833380	+	0.146947i
$581$	−8.93940	+	5.16117i	−0.370869	+	0.214121i
$582$		0			0
$583$	2.91590	−	8.01138i	0.120764	−	0.331798i
$584$	−0.542581	+	2.02494i	−0.0224521	+	0.0837925i
$585$		0			0
$586$	−10.9280	+	10.9280i	−0.451432	+	0.451432i
$587$	−0.296385	−	3.38769i	−0.0122331	−	0.139825i	0.987622	−	0.156853i	$-0.0501350\pi$
$587$	−0.296385	−	3.38769i	−0.0122331	−	0.139825i	−0.999855	+	0.0170283i	$0.994579\pi$
$588$		0			0
$589$	−0.884992	+	5.01904i	−0.0364655	+	0.206806i
$590$	−32.0866	−	22.4673i	−1.32099	−	0.924964i
$591$		0			0
$592$	1.77813	−	5.81707i	0.0730806	−	0.239080i
$593$			29.1107i			1.19543i	0.801708	+	0.597716i	$0.203925\pi$
$593$			29.1107i			1.19543i	−0.801708	+	0.597716i	$0.796075\pi$
$594$		0			0
$595$	−24.2062	−	4.26820i	−0.992356	−	0.174979i
$596$	−7.47908	+	2.72216i	−0.306355	+	0.111504i
$597$		0			0
$598$	20.3399	+	20.3399i	0.831759	+	0.831759i
$599$	−11.2369	+	13.3916i	−0.459126	+	0.547165i	−0.945089	−	0.326814i	$-0.894025\pi$
$599$	−11.2369	+	13.3916i	−0.459126	+	0.547165i	0.485962	+	0.873980i	$0.338469\pi$
$600$		0			0
$601$	17.2945	+	6.29469i	0.705458	+	0.256766i	0.669739	−	0.742596i	$-0.266406\pi$
$601$	17.2945	+	6.29469i	0.705458	+	0.256766i	0.0357183	+	0.999362i	$0.488628\pi$
$602$	5.35567	+	3.09210i	0.218281	+	0.126025i
$603$		0			0
$604$	−2.07576	−	11.7722i	−0.0844615	−	0.479005i
$605$	2.45842	−	5.27210i	0.0999491	−	0.214341i
$606$		0			0
$607$	0.637978	−	7.29212i	0.0258947	−	0.295978i	−0.972194	−	0.234178i	$-0.924760\pi$
$607$	0.637978	−	7.29212i	0.0258947	−	0.295978i	0.998089	−	0.0618003i	$-0.0196842\pi$
$608$	2.86511	+	3.41450i	0.116196	+	0.138476i
$609$		0			0
$610$	−13.6445	−	19.4863i	−0.552449	−	0.788978i
$611$	22.8171	+	32.5862i	0.923081	+	1.31830i
$612$		0			0
$613$	−10.3404	−	12.3232i	−0.417644	−	0.497728i	0.515672	−	0.856786i	$-0.327542\pi$
$613$	−10.3404	−	12.3232i	−0.417644	−	0.497728i	−0.933315	+	0.359058i	$0.883098\pi$
$614$	−0.762713	+	8.71785i	−0.0307806	+	0.351824i
$615$		0			0
$616$	−2.01751	+	4.32657i	−0.0812879	+	0.174323i
$617$	2.63013	+	14.9162i	0.105885	+	0.600505i	0.990863	+	0.134872i	$0.0430622\pi$
$617$	2.63013	+	14.9162i	0.105885	+	0.600505i	−0.884978	+	0.465633i	$0.845827\pi$
$618$		0			0
$619$	−9.39100	−	5.42190i	−0.377456	−	0.217924i	0.299255	−	0.954173i	$-0.403262\pi$
$619$	−9.39100	−	5.42190i	−0.377456	−	0.217924i	−0.676711	+	0.736249i	$0.736595\pi$
$620$	−3.94832	−	1.43707i	−0.158568	−	0.0577141i
$621$		0			0
$622$	15.9560	−	19.0156i	0.639776	−	0.762456i
$623$	16.2151	+	16.2151i	0.649645	+	0.649645i
$624$		0			0
$625$	4.50825	−	1.64087i	0.180330	−	0.0656347i
$626$	11.6261	+	2.04999i	0.464671	+	0.0819340i
$627$		0			0
$628$			24.1211i			0.962538i
$629$	−13.8582	+	22.1803i	−0.552563	+	0.884387i
$630$		0			0
$631$	10.8272	+	7.58128i	0.431024	+	0.301806i	0.768882	−	0.639391i	$-0.220813\pi$
$631$	10.8272	+	7.58128i	0.431024	+	0.301806i	−0.337858	+	0.941197i	$0.609702\pi$
$632$	−2.41933	+	13.7207i	−0.0962358	+	0.545780i
$633$		0			0
$634$	−3.04953	−	34.8562i	−0.121112	−	1.38432i
$635$	−57.8873	+	57.8873i	−2.29719	+	2.29719i
$636$		0			0
$637$	6.12128	−	22.8449i	0.242534	−	0.905149i
$638$	5.82081	−	15.9925i	0.230448	−	0.633151i
$639$		0			0
$640$	−3.18245	+	1.83739i	−0.125797	+	0.0726291i
$641$	−3.75456	+	0.662030i	−0.148296	+	0.0261486i	−0.247303	−	0.968938i	$-0.579544\pi$
$641$	−3.75456	+	0.662030i	−0.148296	+	0.0261486i	0.0990072	+	0.995087i	$0.468433\pi$
$642$		0			0
$643$	0.126462	+	0.471963i	0.00498718	+	0.0186124i	0.968375	−	0.249501i	$-0.0802665\pi$
$643$	0.126462	+	0.471963i	0.00498718	+	0.0186124i	−0.963387	+	0.268113i	$0.913600\pi$
$644$	8.63245	+	0.755242i	0.340166	+	0.0297607i
$645$		0			0
$646$	−8.09942	−	17.3693i	−0.318668	−	0.683385i
$647$	−2.12326	+	1.48672i	−0.0834740	+	0.0584491i	−0.614568	−	0.788864i	$-0.710670\pi$
$647$	−2.12326	+	1.48672i	−0.0834740	+	0.0584491i	0.531094	+	0.847313i	$0.321781\pi$
$648$		0			0
$649$	29.6457	−	13.8240i	1.16369	−	0.542640i
$650$	−33.6403	+	28.2276i	−1.31948	+	1.10718i
$651$		0			0
$652$	0.295748	−	0.0792454i	0.0115824	−	0.00310349i
$653$	−0.166760	−	0.0777616i	−0.00652583	−	0.00304304i	0.419353	−	0.907823i	$-0.362257\pi$
$653$	−0.166760	−	0.0777616i	−0.00652583	−	0.00304304i	−0.425878	+	0.904780i	$0.640035\pi$
$654$		0			0
$655$	−14.2966	−	24.7624i	−0.558613	−	0.967547i
$656$	−2.34234	+	4.05706i	−0.0914532	+	0.158402i
$657$		0			0
$658$	11.5755	+	3.10165i	0.451260	+	0.120915i
$659$	10.5041	+	8.81401i	0.409183	+	0.343345i	0.824030	−	0.566546i	$-0.191721\pi$
$659$	10.5041	+	8.81401i	0.409183	+	0.343345i	−0.414847	+	0.909891i	$0.636165\pi$
$660$		0			0
$661$	37.1727	−	3.25219i	1.44585	−	0.126495i	0.662960	−	0.748655i	$-0.269300\pi$
$661$	37.1727	−	3.25219i	1.44585	−	0.126495i	0.782890	+	0.622160i	$0.213745\pi$
$662$	0.558829	+	1.53537i	0.0217195	+	0.0596739i
$663$		0			0
$664$	3.80590	−	5.43539i	0.147698	−	0.210934i
$665$	25.4810			0.988110
$666$		0			0
$667$	−30.8925			−1.19616
$668$	1.51316	−	2.16102i	0.0585460	−	0.0836124i
$669$		0			0
$670$	12.2504	+	33.6578i	0.473276	+	1.30031i
$671$	19.7895	−	1.73136i	0.763967	−	0.0668384i
$672$		0			0
$673$	−37.3561	−	31.3454i	−1.43997	−	1.20828i	−0.939511	−	0.342518i	$-0.888720\pi$
$673$	−37.3561	−	31.3454i	−1.43997	−	1.20828i	−0.500459	−	0.865760i	$-0.666835\pi$
$674$	−4.50176	−	1.20624i	−0.173401	−	0.0464627i
$675$		0			0
$676$	6.83335	−	11.8357i	0.262821	−	0.455220i
$677$	−8.93284	−	15.4721i	−0.343317	−	0.594643i	0.641730	−	0.766931i	$-0.278217\pi$
$677$	−8.93284	−	15.4721i	−0.343317	−	0.594643i	−0.985047	+	0.172289i	$0.944884\pi$
$678$		0			0
$679$	21.1376	+	9.85661i	0.811185	+	0.378262i
$680$	15.2618	−	4.08939i	0.585264	−	0.156821i
$681$		0			0
$682$	2.68786	−	2.25538i	0.102923	−	0.0863629i
$683$	20.0909	−	9.36854i	0.768756	−	0.358477i	0.00165152	−	0.999999i	$-0.499474\pi$
$683$	20.0909	−	9.36854i	0.768756	−	0.358477i	0.767105	+	0.641522i	$0.221697\pi$
$684$		0			0
$685$	25.5867	−	17.9160i	0.977619	−	0.684536i
$686$	−7.61319	−	16.3265i	−0.290673	−	0.623350i
$687$		0			0
$688$	−3.96019	−	0.346472i	−0.150981	−	0.0132091i
$689$	3.71318	+	13.8578i	0.141461	+	0.527939i
$690$		0			0
$691$	−36.2174	+	6.38610i	−1.37777	+	0.242939i	−0.812979	−	0.582293i	$-0.802156\pi$
$691$	−36.2174	+	6.38610i	−1.37777	+	0.242939i	−0.564794	+	0.825232i	$0.691045\pi$
$692$	10.7196	−	6.18897i	0.407498	−	0.235269i
$693$		0			0
$694$	−0.628215	+	1.72601i	−0.0238467	+	0.0655184i
$695$	−5.34981	+	19.9658i	−0.202930	+	0.757345i
$696$		0			0
$697$	14.2429	−	14.2429i	0.539488	−	0.539488i
$698$	2.47470	+	28.2859i	0.0936688	+	1.07064i
$699$		0			0
$700$	−2.29722	+	13.0282i	−0.0868269	+	0.492420i
$701$	1.35069	+	0.945762i	0.0510148	+	0.0357209i	0.598806	−	0.800894i	$-0.295642\pi$
$701$	1.35069	+	0.945762i	0.0510148	+	0.0357209i	−0.547791	+	0.836615i	$0.684531\pi$
$702$		0			0
$703$	10.1553	−	25.1391i	0.383016	−	0.948138i
$704$		−	3.06872i		−	0.115657i
$705$		0			0
$706$	24.6548	+	4.34731i	0.927897	+	0.163613i
$707$	10.1431	−	3.69179i	0.381470	−	0.138844i
$708$		0			0
$709$	5.15695	+	5.15695i	0.193673	+	0.193673i	0.797281	−	0.603608i	$-0.206271\pi$
$709$	5.15695	+	5.15695i	0.193673	+	0.193673i	−0.603608	+	0.797281i	$0.706271\pi$
$710$	−26.7405	+	31.8680i	−1.00355	+	1.19599i
$711$		0			0
$712$	−13.8519	−	5.04168i	−0.519122	−	0.188945i
$713$	−5.51575	−	3.18452i	−0.206566	−	0.119261i
$714$		0			0
$715$	−10.1121	−	57.3487i	−0.378172	−	2.14472i
$716$	−2.74999	+	5.89738i	−0.102772	+	0.220396i
$717$		0			0
$718$	−2.72491	+	31.1459i	−0.101693	+	1.16235i
$719$	4.20199	+	5.00774i	0.156708	+	0.186757i	0.838686	−	0.544616i	$-0.183324\pi$
$719$	4.20199	+	5.00774i	0.156708	+	0.186757i	−0.681978	+	0.731373i	$0.738880\pi$
$720$		0			0
$721$	0.672784	+	0.960835i	0.0250558	+	0.0357834i
$722$	0.497685	+	0.710767i	0.0185219	+	0.0264520i
$723$		0			0
$724$	8.10962	+	9.66466i	0.301391	+	0.359184i
$725$	4.11048	−	46.9830i	0.152659	−	1.74490i
$726$		0			0
$727$	−10.9210	+	23.4201i	−0.405036	+	0.868603i	0.592954	+	0.805236i	$0.297962\pi$
$727$	−10.9210	+	23.4201i	−0.405036	+	0.868603i	−0.997990	+	0.0633670i	$0.979816\pi$
$728$	−1.39498	−	7.91130i	−0.0517012	−	0.293212i
$729$		0			0
$730$	−6.67159	−	3.85184i	−0.246927	−	0.142563i
$731$	16.0616	+	5.84595i	0.594061	+	0.216220i
$732$		0			0
$733$	−1.25385	+	1.49428i	−0.0463119	+	0.0551924i	−0.788703	−	0.614774i	$-0.789247\pi$
$733$	−1.25385	+	1.49428i	−0.0463119	+	0.0551924i	0.742391	+	0.669967i	$0.233692\pi$
$734$	7.89051	+	7.89051i	0.291244	+	0.291244i
$735$		0			0
$736$	−5.23437	+	1.90515i	−0.192941	+	0.0702249i
$737$	−29.4562	−	5.19393i	−1.08503	−	0.191321i
$738$		0			0
$739$			29.5395i			1.08663i	0.839530	+	0.543314i	$0.182831\pi$
$739$			29.5395i			1.08663i	−0.839530	+	0.543314i	$0.817169\pi$
$740$	18.9568	+	11.8442i	0.696867	+	0.435401i
$741$		0			0
$742$	3.54031	+	2.47895i	0.129969	+	0.0910052i
$743$	6.54308	−	37.1076i	0.240042	−	1.36135i	−0.591688	−	0.806167i	$-0.701538\pi$
$743$	6.54308	−	37.1076i	0.240042	−	1.36135i	0.831730	−	0.555180i	$-0.187351\pi$
$744$		0			0
$745$	−2.54911	−	29.1365i	−0.0933923	−	1.06748i
$746$	−18.8045	+	18.8045i	−0.688480	+	0.688480i
$747$		0			0
$748$	−3.41496	+	12.7448i	−0.124863	+	0.465996i
$749$	−8.73795	+	24.0073i	−0.319278	+	0.877208i
$750$		0			0
$751$	43.2976	−	24.9979i	1.57995	−	0.912186i	0.585089	−	0.810969i	$-0.301060\pi$
$751$	43.2976	−	24.9979i	1.57995	−	0.912186i	0.994864	−	0.101217i	$-0.0322737\pi$
$752$	−7.58641	+	1.33769i	−0.276648	+	0.0487805i
$753$		0			0
$754$	7.41235	+	27.6633i	0.269942	+	1.00744i
$755$	43.7605	+	3.82854i	1.59261	+	0.139335i
$756$		0			0
$757$	18.0312	+	38.6681i	0.655356	+	1.40541i	0.900038	+	0.435812i	$0.143539\pi$
$757$	18.0312	+	38.6681i	0.655356	+	1.40541i	−0.244682	+	0.969603i	$0.578684\pi$
$758$	−28.2594	+	19.7874i	−1.02643	+	0.718712i
$759$		0			0
$760$	−14.8450	+	6.92233i	−0.538484	+	0.251099i
$761$	31.9664	−	26.8230i	1.15878	−	0.972333i	0.158894	−	0.987296i	$-0.449207\pi$
$761$	31.9664	−	26.8230i	1.15878	−	0.972333i	0.999888	+	0.0149622i	$0.00476278\pi$
$762$		0			0
$763$	−9.04069	+	2.42245i	−0.327295	+	0.0876984i
$764$	−14.6018	−	6.80894i	−0.528276	−	0.246339i
$765$		0			0
$766$	6.13399	+	10.6244i	0.221630	+	0.383874i
$767$	−27.5222	+	47.6699i	−0.993770	+	1.72126i
$768$		0			0
$769$	−29.7533	−	7.97238i	−1.07293	−	0.287492i	−0.321235	−	0.946999i	$-0.604098\pi$
$769$	−29.7533	−	7.97238i	−1.07293	−	0.287492i	−0.751698	+	0.659508i	$0.770765\pi$
$770$	−13.4386	−	11.2763i	−0.484292	−	0.406369i
$771$		0			0
$772$	−15.5162	+	1.35749i	−0.558439	+	0.0488571i
$773$	−11.5209	−	31.6535i	−0.414379	−	1.13850i	−0.954838	−	0.297127i	$-0.903971\pi$
$773$	−11.5209	−	31.6535i	−0.414379	−	1.13850i	0.540459	−	0.841371i	$-0.318251\pi$
$774$		0			0
$775$	5.57710	−	7.96492i	0.200335	−	0.286108i
$776$	−14.9923			−0.538191
$777$		0			0
$778$	3.39773			0.121814
$779$	−11.9769	+	17.1048i	−0.429118	+	0.612844i
$780$		0			0
$781$	−11.8817	−	32.6447i	−0.425161	−	1.16812i
$782$	23.8591	−	2.08740i	0.853201	−	0.0746454i
$783$		0			0
$784$	3.50845	+	2.94394i	0.125302	+	0.105141i
$785$	−85.6194	−	22.9417i	−3.05589	−	0.818823i
$786$		0			0
$787$	4.20143	−	7.27709i	0.149765	−	0.259400i	−0.781376	−	0.624061i	$-0.785482\pi$
$787$	4.20143	−	7.27709i	0.149765	−	0.259400i	0.931140	+	0.364661i	$0.118815\pi$
$788$	10.3778	+	17.9750i	0.369695	+	0.640331i
$789$		0			0
$790$	−46.4014	−	21.6373i	−1.65089	−	0.769822i
$791$	24.4936	−	6.56303i	0.870891	−	0.233355i
$792$		0			0
$793$	−25.6079	+	21.4876i	−0.909362	+	0.763046i
$794$	2.36909	−	1.10472i	0.0840757	−	0.0392051i
$795$		0			0
$796$	7.48300	−	5.23966i	0.265228	−	0.185715i
$797$	7.46727	+	16.0136i	0.264504	+	0.567231i	0.993040	−	0.117777i	$-0.0375767\pi$
$797$	7.46727	+	16.0136i	0.264504	+	0.567231i	−0.728536	+	0.685008i	$0.759799\pi$
$798$		0			0
$799$	32.9960	+	2.88677i	1.16731	+	0.102127i
$800$	−2.20099	−	8.21420i	−0.0778167	−	0.290416i
$801$		0			0
$802$	−19.0663	+	3.36190i	−0.673253	+	0.118713i
$803$	5.57128	−	3.21658i	0.196606	−	0.113511i
$804$		0			0
$805$	−10.8911	+	29.9231i	−0.383861	+	1.05465i
$806$	−1.52819	+	5.70327i	−0.0538281	+	0.200889i
$807$		0			0
$808$	−4.90635	+	4.90635i	−0.172605	+	0.172605i
$809$	−1.93848	−	22.1569i	−0.0681534	−	0.778996i	−0.950971	−	0.309280i	$-0.899912\pi$
$809$	−1.93848	−	22.1569i	−0.0681534	−	0.778996i	0.882818	−	0.469716i	$-0.155644\pi$
$810$		0			0
$811$	−6.84579	+	38.8244i	−0.240388	+	1.36331i	0.590575	+	0.806983i	$0.298901\pi$
$811$	−6.84579	+	38.8244i	−0.240388	+	1.36331i	−0.830963	+	0.556327i	$0.812210\pi$
$812$	7.06726	+	4.94855i	0.248012	+	0.173660i
$813$		0			0
$814$	−16.4809	+	8.76413i	−0.577655	+	0.307183i
$815$			1.12514i			0.0394121i
$816$		0			0
$817$	−17.4501	−	3.07691i	−0.610500	−	0.107648i
$818$	−37.6234	+	13.6938i	−1.31547	+	0.478792i
$819$		0			0
$820$	−12.1730	−	12.1730i	−0.425098	−	0.425098i
$821$	14.3587	−	17.1121i	0.501123	−	0.597215i	−0.454887	−	0.890549i	$-0.650320\pi$
$821$	14.3587	−	17.1121i	0.501123	−	0.597215i	0.956010	+	0.293334i	$0.0947649\pi$
$822$		0			0
$823$	4.11015	+	1.49597i	0.143271	+	0.0521463i	0.412660	−	0.910885i	$-0.364600\pi$
$823$	4.11015	+	1.49597i	0.143271	+	0.0521463i	−0.269389	+	0.963031i	$0.586822\pi$
$824$	−0.652985	−	0.377001i	−0.0227478	−	0.0131335i
$825$		0			0
$826$	2.87946	+	16.3302i	0.100189	+	0.568201i
$827$	11.2970	−	24.2265i	0.392836	−	0.842439i	−0.606058	−	0.795420i	$-0.707250\pi$
$827$	11.2970	−	24.2265i	0.392836	−	0.842439i	0.998894	−	0.0470190i	$-0.0149721\pi$
$828$		0			0
$829$	−3.04022	+	34.7498i	−0.105591	+	1.20691i	0.739824	+	0.672801i	$0.234909\pi$
$829$	−3.04022	+	34.7498i	−0.105591	+	1.20691i	−0.845415	+	0.534111i	$0.820647\pi$
$830$	15.6734	+	18.6789i	0.544033	+	0.648353i
$831$		0			0
$832$	2.96194	+	4.23009i	0.102687	+	0.146652i
$833$	−11.2950	−	16.1309i	−0.391347	−	0.558902i
$834$		0			0
$835$	6.23150	+	7.42641i	0.215650	+	0.257001i
$836$	1.19214	−	13.6262i	0.0412309	−	0.471272i
$837$		0			0
$838$	10.7244	−	22.9984i	0.370467	−	0.794468i
$839$	−7.10849	−	40.3142i	−0.245412	−	1.39180i	−0.819533	−	0.573031i	$-0.805767\pi$
$839$	−7.10849	−	40.3142i	−0.245412	−	1.39180i	0.574121	−	0.818770i	$-0.305344\pi$
$840$		0			0
$841$	−1.52197	−	0.878711i	−0.0524818	−	0.0303004i
$842$	−4.55578	−	1.65817i	−0.157003	−	0.0571443i
$843$		0			0
$844$	14.4239	−	17.1897i	0.496490	−	0.591694i
$845$	35.5123	+	35.5123i	1.22166	+	1.22166i
$846$		0			0
$847$	−2.31406	+	0.842250i	−0.0795121	+	0.0289400i
$848$	−2.73600	−	0.482431i	−0.0939547	−	0.0165668i
$849$		0			0
$850$			36.5640i			1.25413i
$851$	25.1810	+	22.6707i	0.863193	+	0.777142i
$852$		0			0
$853$	27.7788	+	19.4509i	0.951127	+	0.665986i	0.942581	−	0.333977i	$-0.108391\pi$
$853$	27.7788	+	19.4509i	0.951127	+	0.665986i	0.00854567	+	0.999963i	$0.497280\pi$
$854$	−1.74871	+	9.91741i	−0.0598395	+	0.339367i
$855$		0			0
$856$	−1.43134	−	16.3603i	−0.0489221	−	0.559182i
$857$	−13.2439	+	13.2439i	−0.452402	+	0.452402i	−0.896151	−	0.443749i	$-0.853648\pi$
$857$	−13.2439	+	13.2439i	−0.452402	+	0.452402i	0.443749	+	0.896151i	$0.353648\pi$
$858$		0			0
$859$	−11.5883	+	43.2482i	−0.395388	+	1.47561i	0.425729	+	0.904851i	$0.360018\pi$
$859$	−11.5883	+	43.2482i	−0.395388	+	1.47561i	−0.821118	+	0.570759i	$0.806649\pi$
$860$	4.99636	−	13.7274i	0.170375	−	0.468100i
$861$		0			0
$862$	26.4243	−	15.2561i	0.900014	−	0.519623i
$863$	29.6144	−	5.22182i	1.00809	−	0.177753i	0.354864	−	0.934918i	$-0.384527\pi$
$863$	29.6144	−	5.22182i	1.00809	−	0.177753i	0.653224	+	0.757165i	$0.273416\pi$
$864$		0			0
$865$	11.7727	+	43.9362i	0.400283	+	1.49388i
$866$	−0.110463	−	0.00966429i	−0.00375370	−	0.000328406i
$867$		0			0
$868$	0.751719	+	1.61207i	0.0255150	+	0.0547171i
$869$	35.0224	−	24.5229i	1.18805	−	0.831884i
$870$		0			0
$871$	45.6173	−	21.2717i	1.54568	−	0.720764i
$872$	4.60893	−	3.86735i	0.156078	−	0.130965i
$873$		0			0
$874$	−23.9826	+	6.42611i	−0.811222	+	0.217366i
$875$	−18.1542	−	8.46545i	−0.613725	−	0.286184i
$876$		0			0
$877$	−19.0393	−	32.9770i	−0.642911	−	1.11355i	−0.984780	−	0.173807i	$-0.944393\pi$
$877$	−19.0393	−	32.9770i	−0.642911	−	1.11355i	0.341869	−	0.939748i	$-0.388940\pi$
$878$	10.9478	−	18.9622i	0.369472	−	0.639944i
$879$		0			0
$880$	10.8926	+	2.91866i	0.367189	+	0.0983880i
$881$	−28.1096	−	23.5868i	−0.947038	−	0.794659i	0.0317586	−	0.999496i	$-0.489889\pi$
$881$	−28.1096	−	23.5868i	−0.947038	−	0.794659i	−0.978796	+	0.204837i	$0.934334\pi$
$882$		0			0
$883$	47.6331	−	4.16736i	1.60298	−	0.140243i	0.749731	−	0.661743i	$-0.230183\pi$
$883$	47.6331	−	4.16736i	1.60298	−	0.140243i	0.853251	+	0.521500i	$0.174627\pi$
$884$	−7.59396	−	20.8642i	−0.255413	−	0.701740i
$885$		0			0
$886$	6.66987	−	9.52556i	0.224079	−	0.320017i
$887$	45.1191			1.51495			0.757475	−	0.652864i	$-0.226433\pi$
$887$	45.1191			1.51495			0.757475	+	0.652864i	$0.226433\pi$
$888$		0			0
$889$	34.6561			1.16233
$890$	31.0703	−	44.3730i	1.04148	−	1.48738i
$891$		0			0
$892$	4.65671	+	12.7942i	0.155918	+	0.428382i
$893$	−34.2060	+	2.99264i	−1.14466	+	0.100145i
$894$		0			0
$895$	−18.3176	−	15.3703i	−0.612289	−	0.513772i
$896$	1.50264	+	0.402632i	0.0501997	+	0.0134510i
$897$		0			0
$898$	0.653172	−	1.13133i	0.0217966	−	0.0377529i
$899$	−3.17059	−	5.49163i	−0.105745	−	0.183156i
$900$		0			0
$901$	10.8261	+	5.04830i	0.360670	+	0.168183i
$902$	13.8861	−	3.72078i	0.462357	−	0.123888i
$903$		0			0
$904$	−12.4868	+	10.4777i	−0.415304	+	0.348482i
$905$	−42.0184	+	19.5935i	−1.39674	+	0.651309i
$906$		0			0
$907$	11.5329	−	8.07540i	0.382943	−	0.268139i	−0.366216	−	0.930530i	$-0.619347\pi$
$907$	11.5329	−	8.07540i	0.382943	−	0.268139i	0.749159	+	0.662391i	$0.230458\pi$
$908$	8.92666	+	19.1433i	0.296242	+	0.635292i
$909$		0			0
$910$	29.4084	+	2.57290i	0.974879	+	0.0852908i
$911$	−1.81698	−	6.78107i	−0.0601993	−	0.224667i	0.929272	−	0.369396i	$-0.120435\pi$
$911$	−1.81698	−	6.78107i	−0.0601993	−	0.224667i	−0.989471	+	0.144729i	$0.953769\pi$
$912$		0			0
$913$	−20.0528	+	3.53584i	−0.663649	+	0.117019i
$914$	−25.1738	+	14.5341i	−0.832674	+	0.480744i
$915$		0			0
$916$	−3.06700	+	8.42652i	−0.101337	+	0.278420i
$917$	−3.13285	+	11.6919i	−0.103456	+	0.386102i
$918$		0			0
$919$	27.3677	−	27.3677i	0.902776	−	0.902776i	−0.0928998	−	0.995675i	$-0.529614\pi$
$919$	27.3677	−	27.3677i	0.902776	−	0.902776i	0.995675	+	0.0928998i	$0.0296136\pi$
$920$	−1.78404	−	20.3917i	−0.0588181	−	0.672294i
$921$		0			0
$922$	−1.57802	+	8.94937i	−0.0519692	+	0.294732i
$923$	47.8872	+	33.5310i	1.57623	+	1.10369i
$924$		0			0
$925$	−37.8293	+	35.2801i	−1.24382	+	1.16000i
$926$			22.7951i			0.749092i
$927$		0			0
$928$	−5.46168	−	0.963042i	−0.179289	−	0.0316134i
$929$	−29.2774	+	10.6561i	−0.960561	+	0.349616i	−0.774253	−	0.632876i	$-0.781874\pi$
$929$	−29.2774	+	10.6561i	−0.960561	+	0.349616i	−0.186308	+	0.982491i	$0.559652\pi$
$930$		0			0
$931$	14.4351	+	14.4351i	0.473091	+	0.473091i
$932$	−3.22457	+	3.84289i	−0.105624	+	0.125878i
$933$		0			0
$934$	−11.0797	−	4.03267i	−0.362538	−	0.131953i
$935$	−41.9904	−	24.2432i	−1.37323	−	0.792836i
$936$		0			0
$937$	−8.97280	−	50.8873i	−0.293129	−	1.66241i	−0.674713	−	0.738081i	$-0.735732\pi$
$937$	−8.97280	−	50.8873i	−0.293129	−	1.66241i	0.381584	−	0.924334i	$-0.375379\pi$
$938$	6.40810	−	13.7422i	0.209232	−	0.448699i
$939$		0			0
$940$	2.46724	−	28.2007i	0.0804725	−	0.919804i
$941$	12.0288	+	14.3354i	0.392128	+	0.467320i	0.925603	−	0.378496i	$-0.123559\pi$
$941$	12.0288	+	14.3354i	0.392128	+	0.467320i	−0.533475	+	0.845816i	$0.679114\pi$
$942$		0			0
$943$	−14.9675	−	21.3759i	−0.487410	−	0.696094i
$944$	−6.11393	−	8.73160i	−0.198991	−	0.284189i
$945$		0			0
$946$	7.84144	+	9.34506i	0.254947	+	0.303834i
$947$	−1.41994	+	16.2300i	−0.0461418	+	0.527404i	0.937588	+	0.347749i	$0.113054\pi$
$947$	−1.41994	+	16.2300i	−0.0461418	+	0.527404i	−0.983730	+	0.179655i	$0.942502\pi$
$948$		0			0
$949$	−4.57510	+	9.81134i	−0.148514	+	0.318490i
$950$	−6.58211	−	37.3290i	−0.213552	−	1.21111i
$951$		0			0
$952$	−5.79261	−	3.34437i	−0.187740	−	0.108392i
$953$	33.0765	+	12.0389i	1.07145	+	0.389977i	0.816720	−	0.577035i	$-0.195790\pi$
$953$	33.0765	+	12.0389i	1.07145	+	0.389977i	0.254733	+	0.967011i	$0.418012\pi$
$954$		0			0
$955$	38.0566	−	45.3541i	1.23148	−	1.46762i
$956$	6.57063	+	6.57063i	0.212509	+	0.212509i
$957$		0			0
$958$	−4.03979	+	1.47036i	−0.130520	+	0.0475053i
$959$	−13.0222	−	2.29616i	−0.420507	−	0.0741468i
$960$		0			0
$961$			29.6927i			0.957828i
$962$	14.2590	−	27.9884i	0.459728	−	0.902382i
$963$		0			0
$964$	−5.07704	−	3.55498i	−0.163520	−	0.114498i
$965$	9.93896	−	56.3667i	0.319946	−	1.81451i
$966$		0			0
$967$	−2.85383	−	32.6194i	−0.0917730	−	1.04897i	−0.892834	−	0.450387i	$-0.851286\pi$
$967$	−2.85383	−	32.6194i	−0.0917730	−	1.04897i	0.801061	−	0.598583i	$-0.204269\pi$
$968$	1.11934	−	1.11934i	0.0359770	−	0.0359770i
$969$		0			0
$970$	14.2592	−	53.2160i	0.457835	−	1.70866i
$971$	10.6104	−	29.1517i	0.340503	−	0.935524i	−0.644746	−	0.764397i	$-0.723037\pi$
$971$	10.6104	−	29.1517i	0.340503	−	0.935524i	0.985249	−	0.171127i	$-0.0547408\pi$
$972$		0			0
$973$	7.57799	−	4.37515i	0.242939	−	0.140261i
$974$	40.1821	−	7.08519i	1.28752	−	0.227024i
$975$		0			0
$976$	−1.67545	−	6.25286i	−0.0536298	−	0.200149i
$977$	18.6931	+	1.63544i	0.598046	+	0.0523222i	0.382160	−	0.924096i	$-0.375180\pi$
$977$	18.6931	+	1.63544i	0.598046	+	0.0523222i	0.215886	+	0.976419i	$0.430736\pi$
$978$		0			0
$979$	19.1174	+	40.9973i	0.610994	+	1.31028i
$980$	−13.7866	+	9.65346i	−0.440396	+	0.308369i
$981$		0			0
$982$	19.5672	−	9.12433i	0.624414	−	0.291169i
$983$	25.4374	−	21.3445i	0.811328	−	0.680785i	−0.139597	−	0.990208i	$-0.544581\pi$
$983$	25.4374	−	21.3445i	0.811328	−	0.680785i	0.950924	+	0.309424i	$0.100136\pi$
$984$		0			0
$985$	−73.6735	+	19.7408i	−2.34743	+	0.628993i
$986$	21.6114	+	10.0776i	0.688247	+	0.320935i
$987$		0			0
$988$	11.5088	+	19.9337i	0.366142	+	0.634177i
$989$	11.0718	−	19.1770i	0.352064	−	0.609793i
$990$		0			0
$991$	2.31736	+	0.620935i	0.0736134	+	0.0197247i	0.295438	−	0.955362i	$-0.404534\pi$
$991$	2.31736	+	0.620935i	0.0736134	+	0.0197247i	−0.221824	+	0.975087i	$0.571201\pi$
$992$	−0.875890	−	0.734959i	−0.0278095	−	0.0233350i
$993$		0			0
$994$	17.5439	−	1.53489i	0.556459	−	0.0486839i
$995$	11.4814	+	31.5448i	0.363984	+	1.00004i
$996$		0			0
$997$	0.727994	−	1.03968i	0.0230558	−	0.0329271i	−0.807459	−	0.589924i	$-0.799158\pi$
$997$	0.727994	−	1.03968i	0.0230558	−	0.0329271i	0.830514	+	0.556997i	$0.188047\pi$
$998$	8.50302			0.269158
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.a.17.3	✓	72
3.2	odd	2	inner	666.2.bs.a.17.4	yes	72
37.24	odd	36	inner	666.2.bs.a.431.4	yes	72
111.98	even	36	inner	666.2.bs.a.431.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.a.17.3	✓	72	1.1	even	1	trivial
666.2.bs.a.17.4	yes	72	3.2	odd	2	inner
666.2.bs.a.431.3	yes	72	111.98	even	36	inner
666.2.bs.a.431.4	yes	72	37.24	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.66079 - 0.320278i) q^{5} +(-1.19170 - 0.999952i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.66079 - 0.320278i) q^{5} +(-1.19170 - 0.999952i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-1.83739 + 3.18245i) q^{10} +(-1.53436 - 2.65759i) q^{11} +(4.68016 + 2.18239i) q^{13} +(1.50264 - 0.402632i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(3.89680 - 1.81711i) q^{17} +(-3.65122 + 2.55661i) q^{19} +(-1.55303 - 3.33048i) q^{20} +(3.05704 + 0.267456i) q^{22} +(-1.44170 - 5.38049i) q^{23} +(8.37477 - 1.47670i) q^{25} +(-4.47214 + 2.58199i) q^{26} +(-0.532063 + 1.46183i) q^{28} +(1.43539 - 5.35696i) q^{29} +(0.808501 - 0.808501i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-0.746625 + 4.23432i) q^{34} +(-4.68281 - 3.27894i) q^{35} +(-5.10126 + 3.31317i) q^{37} -4.45732i q^{38} +(3.61895 + 0.638118i) q^{40} +(4.40217 - 1.60226i) q^{41} +(2.81097 + 2.81097i) q^{43} +(-1.97253 + 2.35077i) q^{44} +(5.23437 + 1.90515i) q^{46} +(6.67137 + 3.85172i) q^{47} +(-0.795301 - 4.51038i) q^{49} +(-3.59393 + 7.70721i) q^{50} +(0.450071 - 5.14433i) q^{52} +(1.78580 + 2.12823i) q^{53} +(-6.46813 - 9.23744i) q^{55} +(-0.892284 - 1.27431i) q^{56} +(3.56486 + 4.24843i) q^{58} +(-0.929020 + 10.6187i) q^{59} +(-2.73579 + 5.86693i) q^{61} +(0.198548 + 1.12602i) q^{62} +(0.866025 + 0.500000i) q^{64} +(17.8320 + 6.49033i) q^{65} +(6.26523 - 7.46661i) q^{67} +(-3.04031 - 3.04031i) q^{68} +(5.37190 - 1.95521i) q^{70} +(11.1486 + 1.96581i) q^{71} +2.09637i q^{73} +(0.211973 - 6.07907i) q^{74} +(3.65122 + 2.55661i) q^{76} +(-0.828969 + 4.70132i) q^{77} +(1.21429 + 13.8793i) q^{79} +(-2.59846 + 2.59846i) q^{80} +(-1.21249 + 4.52506i) q^{82} +(2.26944 - 6.23522i) q^{83} +(13.6834 - 7.90010i) q^{85} +(-3.91492 + 0.690306i) q^{86} +(-0.794242 - 2.96415i) q^{88} +(-14.6848 - 1.28475i) q^{89} +(-3.39504 - 7.28068i) q^{91} +(-4.56292 + 3.19499i) q^{92} +(-6.98169 + 3.25561i) q^{94} +(-12.5475 + 10.5286i) q^{95} +(-14.4814 + 3.88029i) q^{97} +(4.15085 + 1.93557i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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