LMFDB - Embedded newform 666.2.bs.a.17.4

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			17.4
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.a.431.4

$q$-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	−0.868249	−	0.496129i	$-0.834754\pi$
$5$	−3.66079	+	0.320278i	−1.63716	+	0.143233i	−0.768906	+	0.639361i	$0.779199\pi$
$6$		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	0.999091	−	0.0426307i	$-0.0135739\pi$
$11$	1.53436	+	2.65759i	0.462626	+	0.801292i	−0.536465	+	0.843923i	$0.680241\pi$
$12$		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	−0.833180	−	0.553003i	$-0.813482\pi$
$17$	−3.89680	+	1.81711i	−0.945112	+	0.440713i	−0.111933	+	0.993716i	$0.535704\pi$
$18$		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	$0.113905\pi$
$23$	1.44170	+	5.38049i	0.300615	+	1.12191i	−0.636040	+	0.771656i	$0.719429\pi$
$24$		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	$0.255514\pi$
$29$	−1.43539	+	5.35696i	−0.266546	+	0.994763i	−0.961297	+	0.275513i	$0.911152\pi$
$30$		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	−0.662066	−	0.749446i	$-0.730320\pi$
$41$	−4.40217	+	1.60226i	−0.687503	+	0.250231i	−0.0254373	+	0.999676i	$0.508098\pi$
$42$		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	−0.0729338	−	0.997337i	$-0.523236\pi$
$47$	−6.67137	−	3.85172i	−0.973120	−	0.561831i	−0.900186	+	0.435506i	$0.856570\pi$
$48$		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	0.629321	−	0.777145i	$-0.283333\pi$
$53$	−1.78580	−	2.12823i	−0.245298	−	0.292335i	−0.874619	+	0.484810i	$0.838889\pi$
$54$		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	$-0.728130\pi$
$59$	0.929020	−	10.6187i	0.120948	−	1.38244i	0.777842	−	0.628460i	$-0.216314\pi$
$60$		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	−0.532917	−	0.846168i	$-0.678904\pi$
$71$	−11.1486	−	1.96581i	−1.32310	−	0.233298i	−0.790184	+	0.612869i	$0.790015\pi$
$72$		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	$0.229756\pi$
$83$	−2.26944	+	6.23522i	−0.249103	+	0.684404i	−0.999720	+	0.0236670i	$0.992466\pi$
$84$		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	0.832694	−	0.553733i	$-0.186797\pi$
$89$	14.6848	+	1.28475i	1.55658	+	0.136183i	0.723889	+	0.689916i	$0.242353\pi$
$90$		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	−0.640183	−	0.768223i	$-0.721141\pi$
$101$	3.46931	−	6.00902i	0.345209	−	0.597920i	0.985392	+	0.170303i	$0.0544746\pi$
$102$		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	$0.180802\pi$
$107$	5.61692	+	15.4323i	0.543008	+	1.49190i	−0.299968	+	0.953949i	$0.596976\pi$
$108$		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	$-0.527451\pi$
$113$	9.34949	−	13.3525i	0.879526	−	1.25609i	0.965660	−	0.259810i	$-0.0836600\pi$
$114$		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	0.995997	−	0.0893902i	$-0.0284918\pi$
$131$	3.28836	+	7.05191i	0.287305	+	0.616129i	−0.708691	+	0.705519i	$0.750714\pi$
$132$		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	−0.780331	−	0.625367i	$-0.784949\pi$
$137$	−7.36123	+	4.25001i	−0.628912	+	0.363103i	0.151418	+	0.988470i	$0.451616\pi$
$138$		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	$0.105706\pi$
$149$			7.95907i			0.652033i	−0.945364	+	0.326016i	$0.894294\pi$
$150$		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	0.756328	−	0.654193i	$-0.226992\pi$
$167$	−1.51316	−	2.16102i	−0.117092	−	0.167225i	−0.873420	+	0.486968i	$0.838103\pi$
$168$		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	$-0.899615\pi$
$173$	−2.14941	−	12.1899i	−0.163416	−	0.926780i	0.787266	−	0.616613i	$-0.211496\pi$
$174$		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	0.857834	−	0.513926i	$-0.171810\pi$
$179$	4.60117	+	4.60117i	0.343908	+	0.343908i	−0.513926	+	0.857834i	$0.671810\pi$
$180$		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	−0.986725	−	0.162398i	$-0.948077\pi$
$191$	−11.3924	+	11.3924i	−0.824328	+	0.824328i	0.162398	+	0.986725i	$0.448077\pi$
$192$		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	0.611245	−	0.791442i	$-0.290669\pi$
$197$	20.4404	−	3.60419i	1.45632	−	0.256788i	0.845071	+	0.534654i	$0.179558\pi$
$198$		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	0.636141	−	0.771573i	$-0.280530\pi$
$227$	21.0419	−	1.84093i	1.39660	−	0.122187i	0.760459	+	0.649386i	$0.224974\pi$
$228$		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	0.936414	−	0.350896i	$-0.114123\pi$
$233$	2.50827	+	4.34445i	0.164322	+	0.284615i	−0.772092	+	0.635511i	$0.780790\pi$
$234$		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	−0.130705	−	0.991421i	$-0.541724\pi$
$239$	8.42166	−	3.92709i	0.544752	−	0.254022i	0.675457	+	0.737399i	$0.263946\pi$
$240$		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	$-0.561956\pi$
$251$	7.36138	−	27.4730i	0.464646	−	1.73408i	0.658060	−	0.752966i	$-0.271377\pi$
$252$		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	0.553709	−	0.832711i	$-0.313212\pi$
$257$	−0.631694	−	0.442317i	−0.0394040	−	0.0275910i	−0.593112	+	0.805120i	$0.702101\pi$
$258$		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	−0.922051	−	0.387068i	$-0.873488\pi$
$263$	−22.3730	+	8.14312i	−1.37958	+	0.502126i	−0.457530	+	0.889194i	$0.651266\pi$
$264$		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	0.362903	−	0.931827i	$-0.381786\pi$
$269$	−4.30748	−	2.48692i	−0.262631	−	0.151630i	−0.625534	+	0.780197i	$0.715119\pi$
$270$		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	$-0.695978\pi$
$281$	2.22930	−	25.4810i	0.132989	−	1.52007i	0.710505	−	0.703692i	$-0.248466\pi$
$282$		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	−0.289627	−	0.957140i	$-0.593531\pi$
$293$	−15.2198	−	2.68365i	−0.889148	−	0.156781i	−0.599521	+	0.800359i	$0.704642\pi$
$294$		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	0.763032	−	0.646361i	$-0.223710\pi$
$311$	24.7286	+	2.16348i	1.40223	+	0.122679i	0.639200	+	0.769040i	$0.279265\pi$
$312$		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	$-0.281689\pi$
$317$	26.8034	−	22.4907i	1.50543	−	1.26321i	0.872103	−	0.489323i	$-0.162756\pi$
$318$		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	−0.306126	−	0.951991i	$-0.599033\pi$
$347$	−1.77419	+	0.475393i	−0.0952436	+	0.0255205i	0.210882	+	0.977511i	$0.432366\pi$
$348$		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	$0.0932102\pi$
$353$	10.5803	+	22.6896i	0.563134	+	1.20764i	−0.394297	+	0.918983i	$0.629012\pi$
$354$		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	−0.997044	−	0.0768359i	$-0.975518\pi$
$359$	−27.0761	+	15.6324i	−1.42902	+	0.825047i	−0.431980	+	0.901883i	$0.642185\pi$
$360$		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	−0.993102	−	0.117257i	$-0.962590\pi$
$383$	−5.18467	+	11.1186i	−0.264924	+	0.568132i	0.728177	+	0.685389i	$0.240368\pi$
$384$		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	0.865513	−	0.500886i	$-0.166993\pi$
$389$	1.94886	+	2.78325i	0.0988109	+	0.141117i	−0.766702	+	0.642003i	$0.778104\pi$
$390$		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	0.277179	−	0.960818i	$-0.410601\pi$
$401$	−13.6899	−	13.6899i	−0.683639	−	0.683639i	−0.960818	+	0.277179i	$0.910601\pi$
$402$		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	0.474167	−	0.880435i	$-0.342749\pi$
$419$	24.9905	−	4.40649i	1.22086	−	0.215271i	0.746697	+	0.665164i	$0.231638\pi$
$420$		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	0.952636	−	0.304112i	$-0.0983598\pi$
$431$	27.6534	+	12.8950i	1.33202	+	0.621129i	0.379379	+	0.925241i	$0.376138\pi$
$432$		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	$-0.410910\pi$
$443$	11.6286			0.552490			0.276245	+	0.961087i	$0.410910\pi$
$444$		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	−0.0564065	−	0.998408i	$-0.517964\pi$
$449$	1.30137	−	0.113855i	0.0614156	−	0.00537317i	0.117822	+	0.993035i	$0.462409\pi$
$450$		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	−0.604841	−	0.796346i	$-0.706763\pi$
$461$	−8.23601	+	3.84051i	−0.383589	+	0.178870i	0.221252	+	0.975217i	$0.428986\pi$
$462$		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	$-0.995382\pi$
$467$	−3.05167	−	11.3890i	−0.141214	−	0.527019i	0.858680	−	0.512511i	$-0.171285\pi$
$468$		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	0.490351	−	0.871525i	$-0.336869\pi$
$479$	−3.52158	−	2.46584i	−0.160905	−	0.112667i	−0.651256	+	0.758858i	$0.725758\pi$
$480$		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	0.858556	−	0.512720i	$-0.171362\pi$
$491$	18.6975	+	10.7950i	0.843806	+	0.487172i	−0.0147501	+	0.999891i	$0.504695\pi$
$492$		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	$0.217131\pi$
$503$	−2.19084	+	25.0414i	−0.0976846	+	1.11654i	−0.873911	+	0.486086i	$0.838424\pi$
$504$		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	0.241551	−	0.970388i	$-0.422344\pi$
$509$	−4.44824	−	1.61903i	−0.197165	−	0.0717620i	−0.438715	+	0.898626i	$0.644566\pi$
$510$		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	$-0.855141\pi$
$521$	2.19494	−	12.4481i	0.0961622	−	0.545363i	0.994385	−	0.105822i	$-0.0337475\pi$
$522$		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	−0.799421	−	0.600771i	$-0.794860\pi$
$557$	0.909499	−	1.29890i	0.0385367	−	0.0550361i	0.837958	+	0.545735i	$0.183749\pi$
$558$		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	−0.150612	−	0.988593i	$-0.548125\pi$
$563$	−18.3970	−	4.92947i	−0.775343	−	0.207752i	−0.624731	+	0.780840i	$0.714791\pi$
$564$		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	−0.999956	−	0.00939572i	$-0.997009\pi$
$569$	−44.3976	+	11.8963i	−1.86125	+	0.498719i	−0.861289	+	0.508115i	$0.830343\pi$
$570$		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	0.999855	−	0.0170283i	$-0.00542055\pi$
$587$	0.296385	+	3.38769i	0.0122331	+	0.139825i	−0.987622	+	0.156853i	$0.949865\pi$
$588$		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	$-0.796075\pi$
$593$		−	29.1107i		−	1.19543i	0.801708	−	0.597716i	$-0.203925\pi$
$594$		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	−0.485962	−	0.873980i	$-0.661531\pi$
$599$	11.2369	−	13.3916i	0.459126	−	0.547165i	0.945089	+	0.326814i	$0.105975\pi$
$600$		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	$-0.956938\pi$
$617$	−2.63013	−	14.9162i	−0.105885	−	0.600505i	0.884978	−	0.465633i	$-0.154173\pi$
$618$		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	−0.0990072	−	0.995087i	$-0.531567\pi$
$641$	3.75456	−	0.662030i	0.148296	−	0.0261486i	0.247303	+	0.968938i	$0.420456\pi$
$642$		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	−0.531094	−	0.847313i	$-0.678219\pi$
$647$	2.12326	−	1.48672i	0.0834740	−	0.0584491i	0.614568	+	0.788864i	$0.289330\pi$
$648$		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	0.425878	−	0.904780i	$-0.359965\pi$
$653$	0.166760	+	0.0777616i	0.00652583	+	0.00304304i	−0.419353	+	0.907823i	$0.637743\pi$
$654$		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	0.414847	−	0.909891i	$-0.363835\pi$
$659$	−10.5041	−	8.81401i	−0.409183	−	0.343345i	−0.824030	+	0.566546i	$0.808279\pi$
$660$		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	0.985047	−	0.172289i	$-0.0551161\pi$
$677$	8.93284	+	15.4721i	0.343317	+	0.594643i	−0.641730	+	0.766931i	$0.721783\pi$
$678$		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	−0.767105	−	0.641522i	$-0.778303\pi$
$683$	−20.0909	+	9.36854i	−0.768756	+	0.358477i	−0.00165152	+	0.999999i	$0.500526\pi$
$684$		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	0.547791	−	0.836615i	$-0.315469\pi$
$701$	−1.35069	−	0.945762i	−0.0510148	−	0.0357209i	−0.598806	+	0.800894i	$0.704358\pi$
$702$		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	0.681978	−	0.731373i	$-0.261120\pi$
$719$	−4.20199	−	5.00774i	−0.156708	−	0.186757i	−0.838686	+	0.544616i	$0.816676\pi$
$720$		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	$0.298462\pi$
$743$	−6.54308	+	37.1076i	−0.240042	+	1.36135i	−0.831730	+	0.555180i	$0.812649\pi$
$744$		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	−0.999888	−	0.0149622i	$-0.995237\pi$
$761$	−31.9664	+	26.8230i	−1.15878	+	0.972333i	−0.158894	+	0.987296i	$0.550793\pi$
$762$		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	$0.0960285\pi$
$773$	11.5209	+	31.6535i	0.414379	+	1.13850i	−0.540459	+	0.841371i	$0.681749\pi$
$774$		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	0.728536	−	0.685008i	$-0.240201\pi$
$797$	−7.46727	−	16.0136i	−0.264504	−	0.567231i	−0.993040	+	0.117777i	$0.962423\pi$
$798$		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	$0.100088\pi$
$809$	1.93848	+	22.1569i	0.0681534	+	0.778996i	−0.882818	+	0.469716i	$0.844356\pi$
$810$		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	−0.956010	−	0.293334i	$-0.905235\pi$
$821$	−14.3587	+	17.1121i	−0.501123	+	0.597215i	0.454887	+	0.890549i	$0.349680\pi$
$822$		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	$0.292750\pi$
$827$	−11.2970	+	24.2265i	−0.392836	+	0.842439i	−0.998894	+	0.0470190i	$0.985028\pi$
$828$		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	$0.194233\pi$
$839$	7.10849	+	40.3142i	0.245412	+	1.39180i	−0.574121	+	0.818770i	$0.694656\pi$
$840$		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	−0.443749	−	0.896151i	$-0.646352\pi$
$857$	13.2439	−	13.2439i	0.452402	−	0.452402i	0.896151	+	0.443749i	$0.146352\pi$
$858$		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	−0.653224	−	0.757165i	$-0.726584\pi$
$863$	−29.6144	+	5.22182i	−1.00809	+	0.177753i	−0.354864	+	0.934918i	$0.615473\pi$
$864$		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	0.978796	−	0.204837i	$-0.0656663\pi$
$881$	28.1096	+	23.5868i	0.947038	+	0.794659i	−0.0317586	+	0.999496i	$0.510111\pi$
$882$		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	$-0.773567\pi$
$887$	−45.1191			−1.51495			−0.757475	+	0.652864i	$0.773567\pi$
$888$		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	0.989471	−	0.144729i	$-0.0462312\pi$
$911$	1.81698	+	6.78107i	0.0601993	+	0.224667i	−0.929272	+	0.369396i	$0.879565\pi$
$912$		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	0.186308	−	0.982491i	$-0.440348\pi$
$929$	29.2774	−	10.6561i	0.960561	−	0.349616i	0.774253	+	0.632876i	$0.218126\pi$
$930$		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	0.533475	−	0.845816i	$-0.320886\pi$
$941$	−12.0288	−	14.3354i	−0.392128	−	0.467320i	−0.925603	+	0.378496i	$0.876441\pi$
$942$		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	$-0.886946\pi$
$947$	1.41994	−	16.2300i	0.0461418	−	0.527404i	0.983730	−	0.179655i	$-0.0574982\pi$
$948$		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	−0.254733	−	0.967011i	$-0.581988\pi$
$953$	−33.0765	−	12.0389i	−1.07145	−	0.389977i	−0.816720	+	0.577035i	$0.804210\pi$
$954$		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	$0.276963\pi$
$971$	−10.6104	+	29.1517i	−0.340503	+	0.935524i	−0.985249	+	0.171127i	$0.945259\pi$
$972$		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	−0.215886	−	0.976419i	$-0.569264\pi$
$977$	−18.6931	−	1.63544i	−0.598046	−	0.0523222i	−0.382160	+	0.924096i	$0.624820\pi$
$978$		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	−0.950924	−	0.309424i	$-0.899864\pi$
$983$	−25.4374	+	21.3445i	−0.811328	+	0.680785i	0.139597	+	0.990208i	$0.455419\pi$
$984$		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.17.4	yes	72
3.2	odd	2	inner	666.2.bs.a.17.3	✓	72
37.24	odd	36	inner	666.2.bs.a.431.3	yes	72
111.98	even	36	inner	666.2.bs.a.431.4	yes	72

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

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

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