LMFDB - Embedded newform 567.2.be.a.503.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(62,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.62"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.be (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			503.19
Character	$\chi$	$=$	567.503
Dual form			567.2.be.a.62.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.752422 - 2.06726i) q^{2} +(-2.17534 - 1.82533i) q^{4} +(-0.562637 + 3.19087i) q^{5} +(1.24057 - 2.33688i) q^{7} +(-1.59981 + 0.923650i) q^{8} +(6.17302 + 3.56400i) q^{10} +(3.18028 - 0.560770i) q^{11} +(-1.22706 - 3.37132i) q^{13} +(-3.89751 - 4.32289i) q^{14} +(-0.280525 - 1.59093i) q^{16} +(1.49145 - 2.58328i) q^{17} +(3.49827 - 2.01973i) q^{19} +(7.04831 - 5.91424i) q^{20} +(1.23366 - 6.99641i) q^{22} +(0.441437 - 0.526084i) q^{23} +(-5.16663 - 1.88050i) q^{25} -7.89267 q^{26} +(-6.96423 + 2.81906i) q^{28} +(-3.33174 + 9.15387i) q^{29} +(0.311578 - 0.371325i) q^{31} +(-7.13842 - 1.25870i) q^{32} +(-4.21810 - 5.02694i) q^{34} +(6.75868 + 5.27330i) q^{35} +(2.82040 - 4.88507i) q^{37} +(-1.54313 - 8.75153i) q^{38} +(-2.04714 - 5.62446i) q^{40} +(1.84441 - 0.671309i) q^{41} +(1.32012 + 7.48676i) q^{43} +(-7.94179 - 4.58519i) q^{44} +(-0.755407 - 1.30840i) q^{46} +(6.71691 - 5.63616i) q^{47} +(-3.92199 - 5.79810i) q^{49} +(-7.77497 + 9.26585i) q^{50} +(-3.48449 + 9.57356i) q^{52} +3.11853i q^{53} +10.4634i q^{55} +(0.173787 + 4.88441i) q^{56} +(16.4166 + 13.7751i) q^{58} +(-1.95711 + 11.0993i) q^{59} +(3.09075 + 3.68341i) q^{61} +(-0.533187 - 0.923507i) q^{62} +(-6.35768 + 11.0118i) q^{64} +(11.4478 - 2.01856i) q^{65} +(-8.93479 + 3.25200i) q^{67} +(-7.95975 + 2.89711i) q^{68} +(15.9867 - 10.0042i) q^{70} +(2.67528 + 1.54458i) q^{71} +(-9.91831 + 5.72634i) q^{73} +(-7.97659 - 9.50613i) q^{74} +(-11.2966 - 1.99190i) q^{76} +(2.63490 - 8.12760i) q^{77} +(6.20601 + 2.25880i) q^{79} +5.23430 q^{80} -4.31797i q^{82} +(-16.4935 - 6.00315i) q^{83} +(7.40375 + 6.21249i) q^{85} +(16.4704 + 2.90417i) q^{86} +(-4.56989 + 3.83459i) q^{88} +(-3.48296 - 6.03267i) q^{89} +(-9.40061 - 1.31486i) q^{91} +(-1.92055 + 0.338646i) q^{92} +(-6.59746 - 18.1264i) q^{94} +(4.47644 + 12.2989i) q^{95} +(2.47809 - 0.436955i) q^{97} +(-14.9372 + 3.74516i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.752422	−	2.06726i	0.532042	−	1.46177i	−0.324594	−	0.945854i	$-0.605228\pi$
$2$	0.752422	−	2.06726i	0.532042	−	1.46177i	0.856636	−	0.515921i	$-0.172550\pi$
$3$		0			0
$3$		0			0
$4$	−2.17534	−	1.82533i	−1.08767	−	0.912664i
$5$	−0.562637	+	3.19087i	−0.251619	+	1.42700i	0.552986	+	0.833190i	$0.313488\pi$
$5$	−0.562637	+	3.19087i	−0.251619	+	1.42700i	−0.804605	+	0.593810i	$0.797623\pi$
$6$		0			0
$7$	1.24057	−	2.33688i	0.468890	−	0.883257i
$7$	1.24057	−	2.33688i	0.468890	−	0.883257i
$8$	−1.59981	+	0.923650i	−0.565618	+	0.326560i
$9$		0			0
$10$	6.17302	+	3.56400i	1.95208	+	1.12703i
$11$	3.18028	−	0.560770i	0.958891	−	0.169078i	0.327766	−	0.944759i	$-0.393704\pi$
$11$	3.18028	−	0.560770i	0.958891	−	0.169078i	0.631126	+	0.775681i	$0.282593\pi$
$12$		0			0
$13$	−1.22706	−	3.37132i	−0.340325	−	0.935036i	−0.985300	−	0.170832i	$-0.945354\pi$
$13$	−1.22706	−	3.37132i	−0.340325	−	0.935036i	0.644975	−	0.764204i	$-0.276868\pi$
$14$	−3.89751	−	4.32289i	−1.04165	−	1.15534i
$15$		0			0
$16$	−0.280525	−	1.59093i	−0.0701312	−	0.397734i
$17$	1.49145	−	2.58328i	0.361731	−	0.626536i	−0.626515	−	0.779409i	$-0.715519\pi$
$17$	1.49145	−	2.58328i	0.361731	−	0.626536i	0.988246	+	0.152873i	$0.0488526\pi$
$18$		0			0
$19$	3.49827	−	2.01973i	0.802559	−	0.463358i	−0.0418061	−	0.999126i	$-0.513311\pi$
$19$	3.49827	−	2.01973i	0.802559	−	0.463358i	0.844365	+	0.535768i	$0.179978\pi$
$20$	7.04831	−	5.91424i	1.57605	−	1.32246i
$21$		0			0
$22$	1.23366	−	6.99641i	0.263016	−	1.49164i
$23$	0.441437	−	0.526084i	0.0920460	−	0.109696i	−0.718055	−	0.695986i	$-0.754968\pi$
$23$	0.441437	−	0.526084i	0.0920460	−	0.109696i	0.810101	+	0.586290i	$0.199412\pi$
$24$		0			0
$25$	−5.16663	−	1.88050i	−1.03333	−	0.376100i
$26$	−7.89267			−1.54788
$27$		0			0
$28$	−6.96423	+	2.81906i	−1.31611	+	0.532753i
$29$	−3.33174	+	9.15387i	−0.618688	+	1.69983i	0.0914880	+	0.995806i	$0.470838\pi$
$29$	−3.33174	+	9.15387i	−0.618688	+	1.69983i	−0.710176	+	0.704024i	$0.751385\pi$
$30$		0			0
$31$	0.311578	−	0.371325i	0.0559611	−	0.0666919i	−0.737338	−	0.675524i	$-0.763917\pi$
$31$	0.311578	−	0.371325i	0.0559611	−	0.0666919i	0.793299	+	0.608832i	$0.208362\pi$
$32$	−7.13842	−	1.25870i	−1.26191	−	0.222508i
$33$		0			0
$34$	−4.21810	−	5.02694i	−0.723399	−	0.862113i
$35$	6.75868	+	5.27330i	1.14243	+	0.891350i
$36$		0			0
$37$	2.82040	−	4.88507i	0.463671	−	0.803101i	−0.535470	−	0.844554i	$-0.679865\pi$
$37$	2.82040	−	4.88507i	0.463671	−	0.803101i	0.999140	+	0.0414533i	$0.0131988\pi$
$38$	−1.54313	−	8.75153i	−0.250329	−	1.41969i
$39$		0			0
$40$	−2.04714	−	5.62446i	−0.323681	−	0.889306i
$41$	1.84441	−	0.671309i	0.288048	−	0.104841i	−0.193955	−	0.981010i	$-0.562132\pi$
$41$	1.84441	−	0.671309i	0.288048	−	0.104841i	0.482003	+	0.876170i	$0.339909\pi$
$42$		0			0
$43$	1.32012	+	7.48676i	0.201316	+	1.14172i	0.903132	+	0.429362i	$0.141262\pi$
$43$	1.32012	+	7.48676i	0.201316	+	1.14172i	−0.701816	+	0.712358i	$0.747627\pi$
$44$	−7.94179	−	4.58519i	−1.19727	−	0.691244i
$45$		0			0
$46$	−0.755407	−	1.30840i	−0.111379	−	0.192914i
$47$	6.71691	−	5.63616i	0.979762	−	0.822118i	−0.00429160	−	0.999991i	$-0.501366\pi$
$47$	6.71691	−	5.63616i	0.979762	−	0.822118i	0.984053	+	0.177873i	$0.0569216\pi$
$48$		0			0
$49$	−3.92199	−	5.79810i	−0.560284	−	0.828300i
$50$	−7.77497	+	9.26585i	−1.09955	+	1.31039i
$51$		0			0
$52$	−3.48449	+	9.57356i	−0.483212	+	1.32761i
$53$			3.11853i			0.428363i	0.976794	+	0.214181i	$0.0687084\pi$
$53$			3.11853i			0.428363i	−0.976794	+	0.214181i	$0.931292\pi$
$54$		0			0
$55$			10.4634i			1.41088i
$56$	0.173787	+	4.88441i	0.0232233	+	0.652706i
$57$		0			0
$58$	16.4166	+	13.7751i	2.15560	+	1.80876i
$59$	−1.95711	+	11.0993i	−0.254793	+	1.44501i	0.541809	+	0.840502i	$0.317740\pi$
$59$	−1.95711	+	11.0993i	−0.254793	+	1.44501i	−0.796602	+	0.604504i	$0.793372\pi$
$60$		0			0
$61$	3.09075	+	3.68341i	0.395730	+	0.471613i	0.926713	−	0.375770i	$-0.122622\pi$
$61$	3.09075	+	3.68341i	0.395730	+	0.471613i	−0.530983	+	0.847383i	$0.678177\pi$
$62$	−0.533187	−	0.923507i	−0.0677148	−	0.117285i
$63$		0			0
$64$	−6.35768	+	11.0118i	−0.794710	+	1.37648i
$65$	11.4478	−	2.01856i	1.41993	−	0.250372i
$66$		0			0
$67$	−8.93479	+	3.25200i	−1.09156	+	0.397295i	−0.824198	−	0.566302i	$-0.808374\pi$
$67$	−8.93479	+	3.25200i	−1.09156	+	0.397295i	−0.267360	+	0.963597i	$0.586151\pi$
$68$	−7.95975	+	2.89711i	−0.965262	+	0.351327i
$69$		0			0
$70$	15.9867	−	10.0042i	1.91077	−	1.19573i
$71$	2.67528	+	1.54458i	0.317498	+	0.183307i	0.650277	−	0.759697i	$-0.274653\pi$
$71$	2.67528	+	1.54458i	0.317498	+	0.183307i	−0.332779	+	0.943005i	$0.607986\pi$
$72$		0			0
$73$	−9.91831	+	5.72634i	−1.16085	+	0.670217i	−0.951508	−	0.307625i	$-0.900466\pi$
$73$	−9.91831	+	5.72634i	−1.16085	+	0.670217i	−0.209342	+	0.977842i	$0.567132\pi$
$74$	−7.97659	−	9.50613i	−0.927260	−	1.10507i
$75$		0			0
$76$	−11.2966	−	1.99190i	−1.29581	−	0.228486i
$77$	2.63490	−	8.12760i	0.300275	−	0.926226i
$78$		0			0
$79$	6.20601	+	2.25880i	0.698231	+	0.254135i	0.666655	−	0.745366i	$-0.267725\pi$
$79$	6.20601	+	2.25880i	0.698231	+	0.254135i	0.0315757	+	0.999501i	$0.489947\pi$
$80$	5.23430			0.585212
$81$		0			0
$82$		−	4.31797i		−	0.476841i
$83$	−16.4935	−	6.00315i	−1.81040	−	0.658932i	−0.997015	−	0.0772059i	$-0.975400\pi$
$83$	−16.4935	−	6.00315i	−1.81040	−	0.658932i	−0.813385	−	0.581726i	$-0.802378\pi$
$84$		0			0
$85$	7.40375	+	6.21249i	0.803050	+	0.673839i
$86$	16.4704	+	2.90417i	1.77605	+	0.313165i
$87$		0			0
$88$	−4.56989	+	3.83459i	−0.487152	+	0.408769i
$89$	−3.48296	−	6.03267i	−0.369193	−	0.639462i	0.620246	−	0.784407i	$-0.287033\pi$
$89$	−3.48296	−	6.03267i	−0.369193	−	0.639462i	−0.989440	+	0.144945i	$0.953699\pi$
$90$		0			0
$91$	−9.40061	−	1.31486i	−0.985452	−	0.137835i
$92$	−1.92055	+	0.338646i	−0.200232	+	0.0353062i
$93$		0			0
$94$	−6.59746	−	18.1264i	−0.680476	−	1.86959i
$95$	4.47644	+	12.2989i	0.459273	+	1.26184i
$96$		0			0
$97$	2.47809	−	0.436955i	0.251612	−	0.0443660i	−0.0464193	−	0.998922i	$-0.514781\pi$
$97$	2.47809	−	0.436955i	0.251612	−	0.0443660i	0.298032	+	0.954556i	$0.403670\pi$
$98$	−14.9372	+	3.74516i	−1.50888	+	0.378318i
$99$		0			0
$100$	7.80666	+	13.5215i	0.780666	+	1.35215i
$101$	−8.81458	+	7.39631i	−0.877083	+	0.735960i	−0.965577	−	0.260117i	$-0.916239\pi$
$101$	−8.81458	+	7.39631i	−0.877083	+	0.735960i	0.0884942	+	0.996077i	$0.471795\pi$
$102$		0			0
$103$	17.5678	+	3.09768i	1.73101	+	0.305223i	0.948349	−	0.317229i	$-0.102752\pi$
$103$	17.5678	+	3.09768i	1.73101	+	0.305223i	0.782658	+	0.622452i	$0.213863\pi$
$104$	5.07698	+	4.26009i	0.497839	+	0.417737i
$105$		0			0
$106$	6.44681	+	2.34645i	0.626170	+	0.227907i
$107$			2.99079i			0.289131i	0.989495	+	0.144565i	$0.0461784\pi$
$107$			2.99079i			0.289131i	−0.989495	+	0.144565i	$0.953822\pi$
$108$		0			0
$109$	2.85397			0.273361			0.136681	−	0.990615i	$-0.456357\pi$
$109$	2.85397			0.273361			0.136681	+	0.990615i	$0.456357\pi$
$110$	21.6305	+	7.87287i	2.06239	+	0.750649i
$111$		0			0
$112$	−4.06583	−	1.31811i	−0.384185	−	0.124550i
$113$	−3.48822	−	0.615067i	−0.328144	−	0.0578607i	0.00714917	−	0.999974i	$-0.497724\pi$
$113$	−3.48822	−	0.615067i	−0.328144	−	0.0578607i	−0.335293	+	0.942114i	$0.608835\pi$
$114$		0			0
$115$	1.43030	+	1.70456i	0.133376	+	0.158951i
$116$	23.9565	−	13.8313i	2.22430	−	1.28420i
$117$		0			0
$118$	21.4726	+	12.3972i	1.97671	+	1.14125i
$119$	−4.18655	−	6.69007i	−0.383780	−	0.613278i
$120$		0			0
$121$	−0.536887	+	0.195411i	−0.0488080	+	0.0177646i
$122$	9.94013	−	3.61791i	0.899937	−	0.327550i
$123$		0			0
$124$	−1.35558	+	0.239025i	−0.121735	+	0.0214651i
$125$	0.807133	−	1.39800i	0.0721922	−	0.125041i
$126$		0			0
$127$	−7.37491	−	12.7737i	−0.654418	−	1.13348i	−0.982039	−	0.188676i	$-0.939580\pi$
$127$	−7.37491	−	12.7737i	−0.654418	−	1.13348i	0.327622	−	0.944809i	$-0.393753\pi$
$128$	8.66211	+	10.3231i	0.765630	+	0.912442i
$129$		0			0
$130$	4.44070	−	25.1845i	0.389475	−	2.20883i
$131$	6.97748	+	5.85480i	0.609625	+	0.511536i	0.894523	−	0.447021i	$-0.147515\pi$
$131$	6.97748	+	5.85480i	0.609625	+	0.511536i	−0.284898	+	0.958558i	$0.591960\pi$
$132$		0			0
$133$	−0.380017	−	10.6806i	−0.0329517	−	0.926129i
$134$			20.9174i			1.80699i
$135$		0			0
$136$			5.51033i			0.472507i
$137$	3.43127	−	9.42733i	0.293153	−	0.805431i	−0.702448	−	0.711735i	$-0.747910\pi$
$137$	3.43127	−	9.42733i	0.293153	−	0.805431i	0.995601	−	0.0936959i	$-0.0298681\pi$
$138$		0			0
$139$	−2.61949	+	3.12178i	−0.222182	+	0.264786i	−0.865608	−	0.500722i	$-0.833068\pi$
$139$	−2.61949	+	3.12178i	−0.222182	+	0.264786i	0.643426	+	0.765508i	$0.277512\pi$
$140$	−5.07694	−	23.8081i	−0.429080	−	2.01215i
$141$		0			0
$142$	5.20598	−	4.36834i	0.436876	−	0.366583i
$143$	−5.79293	−	10.0337i	−0.484429	−	0.839056i
$144$		0			0
$145$	−27.3343	−	15.7814i	−2.26999	−	1.31058i
$146$	4.37509	+	24.8123i	0.362085	+	2.05348i
$147$		0			0
$148$	−15.0522	+	5.47855i	−1.23728	+	0.450334i
$149$	−3.33221	−	9.15518i	−0.272985	−	0.750021i	−0.998113	−	0.0614066i	$-0.980441\pi$
$149$	−3.33221	−	9.15518i	−0.272985	−	0.750021i	0.725127	−	0.688615i	$-0.241781\pi$
$150$		0			0
$151$	3.65868	+	20.7494i	0.297739	+	1.68856i	0.655855	+	0.754887i	$0.272308\pi$
$151$	3.65868	+	20.7494i	0.297739	+	1.68856i	−0.358116	+	0.933677i	$0.616581\pi$
$152$	−3.73105	+	6.46236i	−0.302628	+	0.524167i
$153$		0			0
$154$	−14.8193	−	11.5624i	−1.19417	−	0.931726i
$155$	1.00954	+	1.20313i	0.0810885	+	0.0966375i
$156$		0			0
$157$	10.0273	+	1.76809i	0.800269	+	0.141109i	0.558803	−	0.829300i	$-0.311261\pi$
$157$	10.0273	+	1.76809i	0.800269	+	0.141109i	0.241466	+	0.970409i	$0.422372\pi$
$158$	9.33908	−	11.1299i	0.742977	−	0.885446i
$159$		0			0
$160$	8.03267	−	22.0696i	0.635039	−	1.74475i
$161$	−0.681762	−	1.68423i	−0.0537304	−	0.132736i
$162$		0			0
$163$	−10.1031			−0.791340			−0.395670	−	0.918393i	$-0.629488\pi$
$163$	−10.1031			−0.791340			−0.395670	+	0.918393i	$0.629488\pi$
$164$	−5.23757	−	1.90632i	−0.408986	−	0.148859i
$165$		0			0
$166$	−24.8202	+	29.5795i	−1.92642	+	2.29582i
$167$	−2.21093	+	12.5388i	−0.171087	+	0.970284i	0.771477	+	0.636258i	$0.219518\pi$
$167$	−2.21093	+	12.5388i	−0.171087	+	0.970284i	−0.942564	+	0.334026i	$0.891593\pi$
$168$		0			0
$169$	0.0984525	−	0.0826114i	0.00757327	−	0.00635473i
$170$	18.4136	−	10.6311i	1.41226	−	0.815367i
$171$		0			0
$172$	10.7941	−	18.6959i	0.823042	−	1.42555i
$173$	1.25238	+	7.10260i	0.0952167	+	0.540001i	0.994681	+	0.103006i	$0.0328461\pi$
$173$	1.25238	+	7.10260i	0.0952167	+	0.540001i	−0.899464	+	0.436995i	$0.856043\pi$
$174$		0			0
$175$	−10.8041	+	9.74090i	−0.816709	+	0.736343i
$176$	−1.78430	−	4.90231i	−0.134496	−	0.369526i
$177$		0			0
$178$	−15.0918	+	2.66109i	−1.13118	+	0.199457i
$179$	−6.14419	−	3.54735i	−0.459238	−	0.265141i	0.252486	−	0.967601i	$-0.418752\pi$
$179$	−6.14419	−	3.54735i	−0.459238	−	0.265141i	−0.711724	+	0.702459i	$0.752085\pi$
$180$		0			0
$181$	4.46843	−	2.57985i	0.332136	−	0.191759i	−0.324653	−	0.945833i	$-0.605248\pi$
$181$	4.46843	−	2.57985i	0.332136	−	0.191759i	0.656789	+	0.754074i	$0.271914\pi$
$182$	−9.79138	+	18.4442i	−0.725785	+	1.36717i
$183$		0			0
$184$	−0.220297	+	1.24937i	−0.0162405	+	0.0921046i
$185$	14.0008	+	11.7480i	1.02936	+	0.863734i
$186$		0			0
$187$	3.29462	−	9.05191i	0.240927	−	0.661941i
$188$	−24.8994			−1.81598
$189$		0			0
$190$	28.7932			2.08888
$191$	−1.36266	+	3.74387i	−0.0985984	+	0.270897i	−0.979179	−	0.203000i	$-0.934931\pi$
$191$	−1.36266	+	3.74387i	−0.0985984	+	0.270897i	0.880580	+	0.473897i	$0.157153\pi$
$192$		0			0
$193$	5.82741	+	4.88978i	0.419466	+	0.351974i	0.827960	−	0.560787i	$-0.189501\pi$
$193$	5.82741	+	4.88978i	0.419466	+	0.351974i	−0.408494	+	0.912761i	$0.633946\pi$
$194$	0.961271	−	5.45164i	0.0690152	−	0.391405i
$195$		0			0
$196$	−2.05178	+	19.7718i	−0.146556	+	1.41227i
$197$	3.24083	−	1.87109i	0.230899	−	0.133310i	−0.380087	−	0.924951i	$-0.624106\pi$
$197$	3.24083	−	1.87109i	0.230899	−	0.133310i	0.610987	+	0.791641i	$0.290773\pi$
$198$		0			0
$199$	1.91984	+	1.10842i	0.136094	+	0.0785736i	0.566501	−	0.824061i	$-0.308297\pi$
$199$	1.91984	+	1.10842i	0.136094	+	0.0785736i	−0.430407	+	0.902635i	$0.641630\pi$
$200$	10.0025	−	1.76372i	0.707287	−	0.124714i
$201$		0			0
$202$	8.65782	+	23.7872i	0.609162	+	1.67366i
$203$	17.2582	+	19.1418i	1.21129	+	1.34349i
$204$		0			0
$205$	1.10433	+	6.26296i	0.0771297	+	0.437424i
$206$	19.6221	−	33.9865i	1.36714	−	2.36795i
$207$		0			0
$208$	−5.01933	+	2.89791i	−0.348028	+	0.200934i
$209$	9.99289	−	8.38503i	0.691223	−	0.580005i
$210$		0			0
$211$	−0.591357	+	3.35375i	−0.0407107	+	0.230882i	−0.998374	−	0.0570100i	$-0.981843\pi$
$211$	−0.591357	+	3.35375i	−0.0407107	+	0.230882i	0.957663	+	0.287892i	$0.0929544\pi$
$212$	5.69234	−	6.78386i	0.390951	−	0.465918i
$213$		0			0
$214$	6.18275	+	2.25034i	0.422644	+	0.153830i
$215$	−24.6320			−1.67989
$216$		0			0
$217$	−0.481206	−	1.18877i	−0.0326664	−	0.0806992i
$218$	2.14739	−	5.89991i	0.145440	−	0.399592i
$219$		0			0
$220$	19.0991	−	22.7614i	1.28766	−	1.53458i
$221$	−10.5392	−	1.85834i	−0.708940	−	0.125005i
$222$		0			0
$223$	3.08075	+	3.67150i	0.206302	+	0.245862i	0.859268	−	0.511526i	$-0.170920\pi$
$223$	3.08075	+	3.67150i	0.206302	+	0.245862i	−0.652965	+	0.757388i	$0.726475\pi$
$224$	−11.7971	+	15.1201i	−0.788227	+	1.01026i
$225$		0			0
$226$	−3.89612	+	6.74827i	−0.259166	+	0.448888i
$227$	−1.47843	−	8.38458i	−0.0981267	−	0.556504i	−0.993744	−	0.111679i	$-0.964377\pi$
$227$	−1.47843	−	8.38458i	−0.0981267	−	0.556504i	0.895618	−	0.444825i	$-0.146734\pi$
$228$		0			0
$229$	7.67684	+	21.0920i	0.507300	+	1.39380i	0.884012	+	0.467465i	$0.154833\pi$
$229$	7.67684	+	21.0920i	0.507300	+	1.39380i	−0.376712	+	0.926331i	$0.622945\pi$
$230$	4.59997	−	1.67425i	0.303313	−	0.110397i
$231$		0			0
$232$	−3.12483	−	17.7218i	−0.205155	−	1.16349i
$233$	4.77720	+	2.75812i	0.312965	+	0.180690i	0.648252	−	0.761426i	$-0.275500\pi$
$233$	4.77720	+	2.75812i	0.312965	+	0.180690i	−0.335288	+	0.942116i	$0.608833\pi$
$234$		0			0
$235$	14.2051	+	24.6039i	0.926636	+	1.60498i
$236$	24.5172	−	20.5724i	1.59594	−	1.33915i
$237$		0			0
$238$	−16.9802	+	3.62093i	−1.10066	+	0.234710i
$239$	−17.7886	+	21.1996i	−1.15065	+	1.37129i	−0.233687	+	0.972312i	$0.575079\pi$
$239$	−17.7886	+	21.1996i	−1.15065	+	1.37129i	−0.916961	+	0.398977i	$0.869365\pi$
$240$		0			0
$241$	0.237543	−	0.652643i	0.0153015	−	0.0420404i	−0.931807	−	0.362955i	$-0.881768\pi$
$241$	0.237543	−	0.652643i	0.0153015	−	0.0420404i	0.947108	+	0.320914i	$0.103990\pi$
$242$			1.25692i			0.0807978i
$243$		0			0
$244$		−	13.6543i		−	0.874128i
$245$	20.7077	−	9.25233i	1.32296	−	0.591110i
$246$		0			0
$247$	−11.1017	−	9.31547i	−0.706387	−	0.592729i
$248$	−0.155492	+	0.881838i	−0.00987374	+	0.0559968i
$249$		0			0
$250$	−2.28272	−	2.72044i	−0.144372	−	0.172056i
$251$	−2.14378	−	3.71314i	−0.135314	−	0.234371i	0.790403	−	0.612587i	$-0.209871\pi$
$251$	−2.14378	−	3.71314i	−0.135314	−	0.234371i	−0.925717	+	0.378216i	$0.876538\pi$
$252$		0			0
$253$	1.10888	−	1.92064i	0.0697149	−	0.120750i
$254$	−31.9557	+	5.63465i	−2.00508	+	0.353549i
$255$		0			0
$256$	3.96106	−	1.44171i	0.247566	−	0.0901067i
$257$	−9.32291	+	3.39326i	−0.581547	+	0.211666i	−0.616007	−	0.787740i	$-0.711251\pi$
$257$	−9.32291	+	3.39326i	−0.581547	+	0.211666i	0.0344606	+	0.999406i	$0.489029\pi$
$258$		0			0
$259$	−7.91692	−	12.6512i	−0.491934	−	0.786106i
$260$	−28.5875	−	16.5050i	−1.77292	−	1.02360i
$261$		0			0
$262$	17.3534	−	10.0190i	1.07210	−	0.618976i
$263$	−2.88623	−	3.43967i	−0.177973	−	0.212099i	0.669682	−	0.742648i	$-0.266430\pi$
$263$	−2.88623	−	3.43967i	−0.177973	−	0.212099i	−0.847655	+	0.530549i	$0.821986\pi$
$264$		0			0
$265$	−9.95082	−	1.75460i	−0.611274	−	0.107784i
$266$	−22.3656	−	7.25075i	−1.37132	−	0.444572i
$267$		0			0
$268$	25.3722	+	9.23472i	1.54985	+	0.564100i
$269$	3.30722			0.201645			0.100823	−	0.994904i	$-0.467853\pi$
$269$	3.30722			0.201645			0.100823	+	0.994904i	$0.467853\pi$
$270$		0			0
$271$		−	27.4022i		−	1.66457i	−0.554351	−	0.832283i	$-0.687034\pi$
$271$		−	27.4022i		−	1.66457i	0.554351	−	0.832283i	$-0.312966\pi$
$272$	−4.52821	−	1.64813i	−0.274563	−	0.0999328i
$273$		0			0
$274$	−16.9070	−	14.1866i	−1.02139	−	0.857047i
$275$	−17.4859	−	3.08323i	−1.05444	−	0.185926i
$276$		0			0
$277$	15.3342	−	12.8670i	0.921346	−	0.773101i	−0.0528977	−	0.998600i	$-0.516846\pi$
$277$	15.3342	−	12.8670i	0.921346	−	0.773101i	0.974243	+	0.225499i	$0.0724013\pi$
$278$	4.48259	+	7.76407i	0.268848	+	0.465658i
$279$		0			0
$280$	−15.6833	−	2.19361i	−0.937256	−	0.131093i
$281$	−22.5838	+	3.98212i	−1.34723	+	0.237554i	−0.800289	−	0.599615i	$-0.795320\pi$
$281$	−22.5838	+	3.98212i	−1.34723	+	0.237554i	−0.546945	+	0.837169i	$0.684209\pi$
$282$		0			0
$283$	−7.62218	−	20.9418i	−0.453091	−	1.24486i	−0.930537	−	0.366197i	$-0.880660\pi$
$283$	−7.62218	−	20.9418i	−0.453091	−	1.24486i	0.477446	−	0.878661i	$-0.341563\pi$
$284$	−3.00030	−	8.24325i	−0.178035	−	0.489147i
$285$		0			0
$286$	−25.1009	+	4.42597i	−1.48425	+	0.261713i
$287$	0.719342	−	5.14295i	0.0424614	−	0.303579i
$288$		0			0
$289$	4.05112	+	7.01675i	0.238301	+	0.412750i
$290$	−53.1912	+	44.6327i	−3.12350	+	2.62093i
$291$		0			0
$292$	32.0282	+	5.64743i	1.87431	+	0.330491i
$293$	10.6534	+	8.93928i	0.622379	+	0.522238i	0.898550	−	0.438870i	$-0.144621\pi$
$293$	10.6534	+	8.93928i	0.622379	+	0.522238i	−0.276171	+	0.961108i	$0.589066\pi$
$294$		0			0
$295$	−34.3153	−	12.4897i	−1.99791	−	0.727181i
$296$			10.4202i			0.605664i
$297$		0			0
$298$	−21.4334			−1.24160
$299$	−2.31527	−	0.842689i	−0.133895	−	0.0487340i
$300$		0			0
$301$	19.1333	+	6.20287i	1.10283	+	0.357528i
$302$	45.6474	+	8.04886i	2.62671	+	0.463160i
$303$		0			0
$304$	−4.19461	−	4.99894i	−0.240577	−	0.286709i
$305$	−13.4923	+	7.78977i	−0.772565	+	0.446041i
$306$		0			0
$307$	−4.06170	−	2.34502i	−0.231813	−	0.133837i	0.379595	−	0.925153i	$-0.376063\pi$
$307$	−4.06170	−	2.34502i	−0.231813	−	0.133837i	−0.611408	+	0.791315i	$0.709397\pi$
$308$	−20.5674	+	12.8707i	−1.17193	+	0.733379i
$309$		0			0
$310$	3.24678	−	1.18173i	0.184405	−	0.0671178i
$311$	−0.145456	+	0.0529415i	−0.00824803	+	0.00300204i	−0.346141	−	0.938183i	$-0.612508\pi$
$311$	−0.145456	+	0.0529415i	−0.00824803	+	0.00300204i	0.337893	+	0.941185i	$0.390286\pi$
$312$		0			0
$313$	23.8814	−	4.21093i	1.34986	−	0.238016i	0.548473	−	0.836168i	$-0.315209\pi$
$313$	23.8814	−	4.21093i	1.34986	−	0.238016i	0.801383	+	0.598152i	$0.204098\pi$
$314$	11.1999	−	19.3988i	0.632047	−	1.09474i
$315$		0			0
$316$	−9.37714	−	16.2417i	−0.527505	−	0.913666i
$317$	3.59159	+	4.28029i	0.201724	+	0.240405i	0.857417	−	0.514623i	$-0.172068\pi$
$317$	3.59159	+	4.28029i	0.201724	+	0.240405i	−0.655693	+	0.755027i	$0.727624\pi$
$318$		0			0
$319$	−5.46265	+	30.9802i	−0.305850	+	1.73456i
$320$	−31.5602	−	26.4822i	−1.76427	−	1.48040i
$321$		0			0
$322$	−3.99471	+	0.142132i	−0.222617	+	0.00792070i
$323$		−	12.0493i		−	0.670443i
$324$		0			0
$325$			19.7259i			1.09419i
$326$	−7.60183	+	20.8858i	−0.421026	+	1.15676i
$327$		0			0
$328$	−2.33064	+	2.77755i	−0.128688	+	0.153365i
$329$	−4.83823	−	22.6886i	−0.266740	−	1.25086i
$330$		0			0
$331$	−6.72476	+	5.64274i	−0.369626	+	0.310153i	−0.808614	−	0.588340i	$-0.799782\pi$
$331$	−6.72476	+	5.64274i	−0.369626	+	0.310153i	0.438987	+	0.898493i	$0.355337\pi$
$332$	24.9213	+	43.1650i	1.36774	+	2.36899i
$333$		0			0
$334$	24.2575	+	14.0051i	1.32731	+	0.766323i
$335$	−5.34966	−	30.3394i	−0.292283	−	1.65762i
$336$		0			0
$337$	16.3526	−	5.95186i	0.890783	−	0.324218i	0.144230	−	0.989544i	$-0.453930\pi$
$337$	16.3526	−	5.95186i	0.890783	−	0.324218i	0.746553	+	0.665326i	$0.231707\pi$
$338$	−0.0967017	−	0.265686i	−0.00525988	−	0.0144514i
$339$		0			0
$340$	−4.76586	−	27.0286i	−0.258465	−	1.46583i
$341$	0.782680	−	1.35564i	0.0423845	−	0.0734121i
$342$		0			0
$343$	−18.4149	+	1.97227i	−0.994313	+	0.106493i
$344$	−9.02708	−	10.7581i	−0.486708	−	0.580036i
$345$		0			0
$346$	15.6252	+	2.75515i	0.840018	+	0.148118i
$347$	−1.81114	+	2.15843i	−0.0972268	+	0.115870i	−0.812464	−	0.583011i	$-0.801874\pi$
$347$	−1.81114	+	2.15843i	−0.0972268	+	0.115870i	0.715237	+	0.698882i	$0.246319\pi$
$348$		0			0
$349$	−7.28167	+	20.0062i	−0.389779	+	1.07091i	0.577323	+	0.816516i	$0.304098\pi$
$349$	−7.28167	+	20.0062i	−0.389779	+	1.07091i	−0.967101	+	0.254392i	$0.918125\pi$
$350$	12.0078	+	29.6641i	0.641843	+	1.58561i
$351$		0			0
$352$	−23.4080			−1.24765
$353$	−20.7113	−	7.53828i	−1.10235	−	0.401222i	−0.274167	−	0.961682i	$-0.588402\pi$
$353$	−20.7113	−	7.53828i	−1.10235	−	0.401222i	−0.828182	+	0.560460i	$0.810624\pi$
$354$		0			0
$355$	−6.43375	+	7.66745i	−0.341468	+	0.406946i
$356$	−3.43497	+	19.4807i	−0.182053	+	1.03247i
$357$		0			0
$358$	−11.9563	+	10.0325i	−0.631911	+	0.530236i
$359$	17.6192	−	10.1725i	0.929908	−	0.536883i	0.0431257	−	0.999070i	$-0.486268\pi$
$359$	17.6192	−	10.1725i	0.929908	−	0.536883i	0.886783	+	0.462187i	$0.152935\pi$
$360$		0			0
$361$	−1.34139	+	2.32335i	−0.0705993	+	0.122282i
$362$	−1.97108	−	11.1786i	−0.103598	−	0.587532i
$363$		0			0
$364$	18.0495	+	20.0195i	0.946051	+	1.04931i
$365$	−12.6916	−	34.8699i	−0.664309	−	1.82517i
$366$		0			0
$367$	−23.5883	+	4.15925i	−1.23130	+	0.217111i	−0.751183	−	0.660094i	$-0.770517\pi$
$367$	−23.5883	+	4.15925i	−1.23130	+	0.217111i	−0.480116	+	0.877205i	$0.659405\pi$
$368$	−0.960800	−	0.554718i	−0.0500852	−	0.0289167i
$369$		0			0
$370$	34.8208	−	20.1038i	1.81025	−	1.04515i
$371$	7.28762	+	3.86874i	0.378354	+	0.200855i
$372$		0			0
$373$	3.20352	−	18.1680i	0.165872	−	0.940706i	−0.782289	−	0.622915i	$-0.785948\pi$
$373$	3.20352	−	18.1680i	0.165872	−	0.940706i	0.948161	−	0.317790i	$-0.102941\pi$
$374$	−16.2337	−	13.6217i	−0.839425	−	0.704361i
$375$		0			0
$376$	−5.53993	+	15.2208i	−0.285700	+	0.784955i
$377$	34.9489			1.79996
$378$		0			0
$379$	−14.2916			−0.734112			−0.367056	−	0.930199i	$-0.619634\pi$
$379$	−14.2916			−0.734112			−0.367056	+	0.930199i	$0.619634\pi$
$380$	12.7118	−	34.9253i	0.652100	−	1.79163i
$381$		0			0
$382$	6.71427	+	5.63394i	0.343532	+	0.288257i
$383$	3.96910	−	22.5099i	0.202812	−	1.15020i	−0.698035	−	0.716064i	$-0.745942\pi$
$383$	3.96910	−	22.5099i	0.202812	−	1.15020i	0.900846	−	0.434138i	$-0.142947\pi$
$384$		0			0
$385$	24.4516	+	12.9805i	1.24617	+	0.661548i
$386$	14.4931	−	8.36760i	0.737680	−	0.425900i
$387$		0			0
$388$	−6.18829	−	3.57281i	−0.314163	−	0.181382i
$389$	2.40905	−	0.424780i	0.122143	−	0.0215372i	−0.112242	−	0.993681i	$-0.535803\pi$
$389$	2.40905	−	0.424780i	0.122143	−	0.0215372i	0.234386	+	0.972144i	$0.424692\pi$
$390$		0			0
$391$	−0.700637	−	1.92499i	−0.0354328	−	0.0973507i
$392$	11.6299	+	5.65331i	0.587396	+	0.285535i
$393$		0			0
$394$	−1.42957	−	8.10749i	−0.0720207	−	0.408449i
$395$	−10.6993	+	18.5317i	−0.538339	+	0.932431i
$396$		0			0
$397$	−11.7575	+	6.78822i	−0.590094	+	0.340691i	−0.765135	−	0.643870i	$-0.777328\pi$
$397$	−11.7575	+	6.78822i	−0.590094	+	0.340691i	0.175041	+	0.984561i	$0.443994\pi$
$398$	3.73591	−	3.13480i	0.187264	−	0.157134i
$399$		0			0
$400$	−1.54239	+	8.74730i	−0.0771193	+	0.437365i
$401$	12.2624	−	14.6138i	0.612356	−	0.729777i	−0.367380	−	0.930071i	$-0.619745\pi$
$401$	12.2624	−	14.6138i	0.612356	−	0.729777i	0.979736	+	0.200294i	$0.0641897\pi$
$402$		0			0
$403$	−1.63418	−	0.594793i	−0.0814043	−	0.0296287i
$404$	32.6754			1.62566
$405$		0			0
$406$	52.5566	−	21.2745i	2.60834	−	1.05584i
$407$	6.23026	−	17.1175i	0.308823	−	0.848483i
$408$		0			0
$409$	21.1128	−	25.1612i	1.04396	−	1.24414i	0.0749336	−	0.997189i	$-0.476126\pi$
$409$	21.1128	−	25.1612i	1.04396	−	1.24414i	0.969027	−	0.246955i	$-0.0794300\pi$
$410$	13.7781	+	2.42945i	0.680452	+	0.119982i
$411$		0			0
$412$	−32.5617	−	38.8055i	−1.60420	−	1.91181i
$413$	23.5098	+	18.3429i	1.15684	+	0.902597i
$414$		0			0
$415$	28.4352	−	49.2511i	1.39583	−	2.41764i
$416$	4.51580	+	25.6104i	0.221406	+	1.25565i
$417$		0			0
$418$	−9.81519	−	26.9670i	−0.480076	−	1.31900i
$419$	−24.1055	+	8.77369i	−1.17763	+	0.428623i	−0.855365	−	0.518026i	$-0.826667\pi$
$419$	−24.1055	+	8.77369i	−1.17763	+	0.428623i	−0.322267	+	0.946649i	$0.604445\pi$
$420$		0			0
$421$	−2.00087	−	11.3475i	−0.0975165	−	0.553044i	−0.993947	−	0.109860i	$-0.964960\pi$
$421$	−2.00087	−	11.3475i	−0.0975165	−	0.553044i	0.896431	−	0.443184i	$-0.146151\pi$
$422$	6.48814	+	3.74593i	0.315838	+	0.182349i
$423$		0			0
$424$	−2.88043	−	4.98905i	−0.139886	−	0.242290i
$425$	−12.5637	+	10.5422i	−0.609427	+	0.511370i
$426$		0			0
$427$	12.4420	−	2.65319i	0.602109	−	0.128397i
$428$	5.45918	−	6.50600i	0.263880	−	0.314479i
$429$		0			0
$430$	−18.5337	+	50.9208i	−0.893773	+	2.45562i
$431$			27.5891i			1.32892i	0.747323	+	0.664461i	$0.231339\pi$
$431$			27.5891i			1.32892i	−0.747323	+	0.664461i	$0.768661\pi$
$432$		0			0
$433$			1.08018i			0.0519102i	0.999663	+	0.0259551i	$0.00826269\pi$
$433$			1.08018i			0.0519102i	−0.999663	+	0.0259551i	$0.991737\pi$
$434$	−2.81958	+	0.100320i	−0.135344	+	0.00481554i
$435$		0			0
$436$	−6.20837	−	5.20944i	−0.297327	−	0.249487i
$437$	0.481720	−	2.73197i	0.0230438	−	0.130688i
$438$		0			0
$439$	−1.70073	−	2.02686i	−0.0811716	−	0.0967365i	0.723930	−	0.689873i	$-0.242334\pi$
$439$	−1.70073	−	2.02686i	−0.0811716	−	0.0967365i	−0.805102	+	0.593137i	$0.797889\pi$
$440$	−9.66450	−	16.7394i	−0.460737	−	0.798020i
$441$		0			0
$442$	−11.7716	+	20.3889i	−0.559916	+	0.969803i
$443$	15.9507	−	2.81254i	0.757840	−	0.133628i	0.218640	−	0.975806i	$-0.429838\pi$
$443$	15.9507	−	2.81254i	0.757840	−	0.133628i	0.539200	+	0.842178i	$0.318727\pi$
$444$		0			0
$445$	21.2091	−	7.71949i	1.00541	−	0.365939i
$446$	9.90797	−	3.60621i	0.469156	−	0.170759i
$447$		0			0
$448$	17.8462	+	28.5180i	0.843151	+	1.34735i
$449$	−16.4077	−	9.47299i	−0.774327	−	0.447058i	0.0600887	−	0.998193i	$-0.480862\pi$
$449$	−16.4077	−	9.47299i	−0.774327	−	0.447058i	−0.834416	+	0.551135i	$0.814195\pi$
$450$		0			0
$451$	5.48928	−	3.16924i	0.258480	−	0.149234i
$452$	6.46537	+	7.70513i	0.304106	+	0.362419i
$453$		0			0
$454$	−18.4455	−	3.25244i	−0.865691	−	0.152645i
$455$	9.48467	−	29.2563i	0.444648	−	1.37156i
$456$		0			0
$457$	−27.2962	−	9.93500i	−1.27686	−	0.464740i	−0.387468	−	0.921883i	$-0.626650\pi$
$457$	−27.2962	−	9.93500i	−1.27686	−	0.464740i	−0.889393	+	0.457143i	$0.848873\pi$
$458$	49.3788			2.30732
$459$		0			0
$460$		−	6.31877i		−	0.294614i
$461$	39.9292	+	14.5330i	1.85969	+	0.676870i	0.979233	+	0.202737i	$0.0649836\pi$
$461$	39.9292	+	14.5330i	1.85969	+	0.676870i	0.880453	+	0.474134i	$0.157239\pi$
$462$		0			0
$463$	−10.3324	−	8.66991i	−0.480187	−	0.402925i	0.370307	−	0.928909i	$-0.379252\pi$
$463$	−10.3324	−	8.66991i	−0.480187	−	0.402925i	−0.850494	+	0.525985i	$0.823697\pi$
$464$	15.4978	+	2.73269i	0.719469	+	0.126862i
$465$		0			0
$466$	9.29622	−	7.80045i	0.430639	−	0.361349i
$467$	12.0023	+	20.7886i	0.555401	+	0.961983i	0.997872	+	0.0652000i	$0.0207685\pi$
$467$	12.0023	+	20.7886i	0.555401	+	0.961983i	−0.442471	+	0.896783i	$0.645898\pi$
$468$		0			0
$469$	−3.48468	+	24.9138i	−0.160908	+	1.15041i
$470$	61.5509	−	10.8531i	2.83913	−	0.500615i
$471$		0			0
$472$	−7.12087	−	19.5644i	−0.327765	−	0.900526i
$473$	8.39669	+	23.0697i	0.386080	+	1.06075i
$474$		0			0
$475$	−21.8724	+	3.85669i	−1.00357	+	0.176957i
$476$	−3.10441	+	22.1950i	−0.142290	+	1.01731i
$477$		0			0
$478$	30.4406	+	52.7247i	1.39232	+	2.41157i
$479$	17.1728	−	14.4097i	0.784647	−	0.658397i	−0.159767	−	0.987155i	$-0.551074\pi$
$479$	17.1728	−	14.4097i	0.784647	−	0.658397i	0.944414	+	0.328758i	$0.106630\pi$
$480$		0			0
$481$	−19.9299	−	3.51419i	−0.908727	−	0.160233i
$482$	−1.17045	−	0.982126i	−0.0533126	−	0.0447346i
$483$		0			0
$484$	1.52460	+	0.554910i	0.0693002	+	0.0252232i
$485$			8.15312i			0.370214i
$486$		0			0
$487$	6.87495			0.311534			0.155767	−	0.987794i	$-0.450215\pi$
$487$	6.87495			0.311534			0.155767	+	0.987794i	$0.450215\pi$
$488$	−8.34680	−	3.03799i	−0.377842	−	0.137523i
$489$		0			0
$490$	−3.54611	−	49.7698i	−0.160197	−	2.24837i
$491$	5.85169	+	1.03181i	0.264083	+	0.0465650i	0.304122	−	0.952633i	$-0.401637\pi$
$491$	5.85169	+	1.03181i	0.264083	+	0.0465650i	−0.0400387	+	0.999198i	$0.512748\pi$
$492$		0			0
$493$	18.6778	+	22.2594i	0.841207	+	1.00251i
$494$	−27.6107	+	15.9411i	−1.24226	+	0.717222i
$495$		0			0
$496$	−0.678159	−	0.391535i	−0.0304502	−	0.0175804i
$497$	6.92835	−	4.33566i	0.310779	−	0.194481i
$498$		0			0
$499$	8.89086	−	3.23601i	0.398010	−	0.144864i	−0.135258	−	0.990810i	$-0.543186\pi$
$499$	8.89086	−	3.23601i	0.398010	−	0.144864i	0.533267	+	0.845947i	$0.320964\pi$
$500$	−4.30759	+	1.56784i	−0.192641	+	0.0701158i
$501$		0			0
$502$	−9.28905	+	1.63791i	−0.414590	+	0.0731035i
$503$	−8.03207	+	13.9120i	−0.358132	+	0.620303i	−0.987649	−	0.156684i	$-0.949920\pi$
$503$	−8.03207	+	13.9120i	−0.358132	+	0.620303i	0.629517	+	0.776987i	$0.283253\pi$
$504$		0			0
$505$	−18.6413	−	32.2876i	−0.829525	−	1.43678i
$506$	−3.13612	−	3.73748i	−0.139418	−	0.166151i
$507$		0			0
$508$	−7.27329	+	41.2489i	−0.322700	+	1.83012i
$509$	−7.79226	−	6.53848i	−0.345386	−	0.289813i	0.453548	−	0.891232i	$-0.350158\pi$
$509$	−7.79226	−	6.53848i	−0.345386	−	0.289813i	−0.798934	+	0.601419i	$0.794602\pi$
$510$		0			0
$511$	1.07743	+	30.2818i	0.0476625	+	1.33959i
$512$			17.6784i			0.781282i
$513$		0			0
$514$			21.8260i			0.962705i
$515$	−19.7686	+	54.3137i	−0.871108	+	2.39335i
$516$		0			0
$517$	18.2011	−	21.6912i	0.800483	−	0.953978i
$518$	−32.1102	+	6.84733i	−1.41084	+	0.300854i
$519$		0			0
$520$	−16.4499	+	13.8031i	−0.721376	+	0.605306i
$521$	−18.8534	−	32.6550i	−0.825982	−	1.43064i	−0.901166	−	0.433474i	$-0.857288\pi$
$521$	−18.8534	−	32.6550i	−0.825982	−	1.43064i	0.0751836	−	0.997170i	$-0.476046\pi$
$522$		0			0
$523$	1.29357	+	0.746842i	0.0565638	+	0.0326571i	0.528015	−	0.849235i	$-0.322936\pi$
$523$	1.29357	+	0.746842i	0.0565638	+	0.0326571i	−0.471451	+	0.881892i	$0.656270\pi$
$524$	−4.49147	−	25.4724i	−0.196211	−	1.11277i
$525$		0			0
$526$	−9.28237	+	3.37851i	−0.404730	+	0.147310i
$527$	−0.494529	−	1.35871i	−0.0215420	−	0.0591862i
$528$		0			0
$529$	3.91201	+	22.1861i	0.170087	+	0.964614i
$530$	−11.1144	+	19.2507i	−0.482780	+	0.836199i
$531$		0			0
$532$	−18.6690	+	23.9277i	−0.809405	+	1.03740i
$533$	−4.52639	−	5.39435i	−0.196060	−	0.233655i
$534$		0			0
$535$	−9.54324	−	1.68273i	−0.412590	−	0.0727508i
$536$	11.2902	−	13.4552i	0.487664	−	0.581176i
$537$		0			0
$538$	2.48843	−	6.83690i	0.107284	−	0.294760i
$539$	−15.7244	−	16.2403i	−0.677299	−	0.699518i
$540$		0			0
$541$	3.68188			0.158297			0.0791483	−	0.996863i	$-0.474780\pi$
$541$	3.68188			0.158297			0.0791483	+	0.996863i	$0.474780\pi$
$542$	−56.6475	−	20.6180i	−2.43322	−	0.885620i
$543$		0			0
$544$	−13.8982	+	16.5632i	−0.595880	+	0.710142i
$545$	−1.60575	+	9.10666i	−0.0687828	+	0.390087i
$546$		0			0
$547$	28.1372	−	23.6099i	1.20306	−	1.00949i	0.203523	−	0.979070i	$-0.434761\pi$
$547$	28.1372	−	23.6099i	1.20306	−	1.00949i	0.999537	−	0.0304178i	$-0.00968377\pi$
$548$	−24.6722	+	14.2445i	−1.05394	+	0.608494i
$549$		0			0
$550$	−19.5306	+	33.8280i	−0.832787	+	1.44243i
$551$	6.83301	+	38.7519i	0.291096	+	1.65089i
$552$		0			0
$553$	12.9775	−	11.7005i	0.551860	−	0.497556i
$554$	−15.0616	−	41.3813i	−0.639904	−	1.75812i
$555$		0			0
$556$	11.3966	−	2.00952i	0.483322	−	0.0852227i
$557$	−2.40680	−	1.38957i	−0.101979	−	0.0588778i	0.448143	−	0.893962i	$-0.352086\pi$
$557$	−2.40680	−	1.38957i	−0.101979	−	0.0588778i	−0.550122	+	0.835084i	$0.685419\pi$
$558$		0			0
$559$	23.6204	−	13.6372i	0.999036	−	0.576794i
$560$	6.49350	−	12.2319i	0.274400	−	0.516893i
$561$		0			0
$562$	−8.76041	+	49.6827i	−0.369536	+	2.09574i
$563$	25.7160	+	21.5783i	1.08380	+	0.909415i	0.996231	−	0.0867435i	$-0.0276461\pi$
$563$	25.7160	+	21.5783i	1.08380	+	0.909415i	0.0875679	+	0.996159i	$0.472091\pi$
$564$		0			0
$565$	3.92520	−	10.7844i	0.165134	−	0.453703i
$566$	−49.0272			−2.06077
$567$		0			0
$568$	−5.70659			−0.239443
$569$	12.7217	−	34.9527i	0.533323	−	1.46529i	−0.321771	−	0.946818i	$-0.604278\pi$
$569$	12.7217	−	34.9527i	0.533323	−	1.46529i	0.855093	−	0.518474i	$-0.173500\pi$
$570$		0			0
$571$	−6.22425	−	5.22276i	−0.260477	−	0.218566i	0.503191	−	0.864175i	$-0.332159\pi$
$571$	−6.22425	−	5.22276i	−0.260477	−	0.218566i	−0.763668	+	0.645609i	$0.776604\pi$
$572$	−5.71311	+	32.4006i	−0.238877	+	1.35474i
$573$		0			0
$574$	−10.0906	−	5.35674i	−0.421173	−	0.223586i
$575$	−3.27005	+	1.88796i	−0.136370	+	0.0787335i
$576$		0			0
$577$	15.4017	+	8.89220i	0.641183	+	0.370187i	0.785070	−	0.619407i	$-0.212627\pi$
$577$	15.4017	+	8.89220i	0.641183	+	0.370187i	−0.143887	+	0.989594i	$0.545960\pi$
$578$	17.5536	−	3.09518i	0.730134	−	0.128742i
$579$		0			0
$580$	30.6550	+	84.2240i	1.27288	+	3.49721i
$581$	−34.4900	+	31.0960i	−1.43088	+	1.29008i
$582$		0			0
$583$	1.74878	+	9.91780i	0.0724269	+	0.410753i
$584$	10.5783	−	18.3221i	0.437732	−	0.758173i
$585$		0			0
$586$	26.4957	−	15.2973i	1.09453	−	0.631925i
$587$	14.9687	−	12.5602i	0.617822	−	0.518415i	−0.279296	−	0.960205i	$-0.590101\pi$
$587$	14.9687	−	12.5602i	0.617822	−	0.518415i	0.897118	+	0.441791i	$0.145657\pi$
$588$		0			0
$589$	0.340011	−	1.92830i	0.0140099	−	0.0794542i
$590$	−51.6391	+	61.5411i	−2.12595	+	2.53361i
$591$		0			0
$592$	−8.56302	−	3.11669i	−0.351938	−	0.128095i
$593$	−20.8572			−0.856502			−0.428251	−	0.903660i	$-0.640870\pi$
$593$	−20.8572			−0.856502			−0.428251	+	0.903660i	$0.640870\pi$
$594$		0			0
$595$	23.7027	−	9.59466i	0.971714	−	0.393343i
$596$	−9.46251	+	25.9980i	−0.387599	+	1.06492i
$597$		0			0
$598$	−3.48412	+	4.15221i	−0.142476	+	0.169796i
$599$	−15.9702	−	2.81598i	−0.652526	−	0.115058i	−0.162421	−	0.986722i	$-0.551930\pi$
$599$	−15.9702	−	2.81598i	−0.652526	−	0.115058i	−0.490105	+	0.871664i	$0.663041\pi$
$600$		0			0
$601$	−22.4423	−	26.7456i	−0.915439	−	1.09098i	−0.995554	−	0.0941916i	$-0.969973\pi$
$601$	−22.4423	−	26.7456i	−0.915439	−	1.09098i	0.0801156	−	0.996786i	$-0.474471\pi$
$602$	27.2193	−	34.8864i	1.10938	−	1.42186i
$603$		0			0
$604$	29.9156	−	51.8154i	1.21725	−	2.10834i
$605$	−0.321459	−	1.82308i	−0.0130692	−	0.0741189i
$606$		0			0
$607$	−1.32209	−	3.63240i	−0.0536618	−	0.147435i	0.909966	−	0.414683i	$-0.136108\pi$
$607$	−1.32209	−	3.63240i	−0.0536618	−	0.147435i	−0.963628	+	0.267249i	$0.913885\pi$
$608$	−27.5144	+	10.0144i	−1.11586	+	0.406138i
$609$		0			0
$610$	5.95161	+	33.7532i	0.240973	+	1.36663i
$611$	−27.2433	−	15.7289i	−1.10215	−	0.636325i
$612$		0			0
$613$	−1.60472	−	2.77946i	−0.0648142	−	0.112261i	0.831797	−	0.555079i	$-0.187312\pi$
$613$	−1.60472	−	2.77946i	−0.0648142	−	0.112261i	−0.896612	+	0.442818i	$0.853979\pi$
$614$	−7.90388	+	6.63214i	−0.318975	+	0.267651i
$615$		0			0
$616$	3.29172	+	15.4363i	0.132627	+	0.621948i
$617$	3.37702	−	4.02458i	0.135954	−	0.162024i	−0.693772	−	0.720195i	$-0.744052\pi$
$617$	3.37702	−	4.02458i	0.135954	−	0.162024i	0.829726	+	0.558171i	$0.188497\pi$
$618$		0			0
$619$	9.02167	−	24.7868i	0.362611	−	0.996267i	−0.615491	−	0.788144i	$-0.711042\pi$
$619$	9.02167	−	24.7868i	0.362611	−	0.996267i	0.978103	−	0.208123i	$-0.0667355\pi$
$620$		−	4.45996i		−	0.179116i
$621$		0			0
$622$			0.340529i			0.0136540i
$623$	−18.4185	+	0.655329i	−0.737920	+	0.0262552i
$624$		0			0
$625$	−17.0527	−	14.3089i	−0.682107	−	0.572356i
$626$	9.26377	−	52.5375i	0.370255	−	2.09982i
$627$		0			0
$628$	−18.5856	−	22.1494i	−0.741645	−	0.883858i
$629$	−8.41299	−	14.5717i	−0.335448	−	0.581013i
$630$		0			0
$631$	−21.3850	+	37.0399i	−0.851324	+	1.47454i	0.0286891	+	0.999588i	$0.490867\pi$
$631$	−21.3850	+	37.0399i	−0.851324	+	1.47454i	−0.880013	+	0.474949i	$0.842467\pi$
$632$	−12.0148	+	2.11853i	−0.477922	+	0.0842706i
$633$		0			0
$634$	11.5509	−	4.20417i	0.458743	−	0.166969i
$635$	44.9087	−	16.3454i	1.78215	−	0.648649i
$636$		0			0
$637$	−14.7347	+	20.3369i	−0.583812	+	0.805777i
$638$	59.9340	+	34.6029i	2.37281	+	1.36994i
$639$		0			0
$640$	−37.8133	+	21.8315i	−1.49470	+	0.862967i
$641$	0.504295	+	0.600995i	0.0199185	+	0.0237379i	0.775912	−	0.630842i	$-0.217290\pi$
$641$	0.504295	+	0.600995i	0.0199185	+	0.0237379i	−0.755993	+	0.654579i	$0.772846\pi$
$642$		0			0
$643$	10.7345	+	1.89279i	0.423329	+	0.0746443i	0.381254	−	0.924470i	$-0.375492\pi$
$643$	10.7345	+	1.89279i	0.423329	+	0.0746443i	0.0420745	+	0.999114i	$0.486603\pi$
$644$	−1.59120	+	4.90821i	−0.0627022	+	0.193411i
$645$		0			0
$646$	−24.9091	−	9.06618i	−0.980037	−	0.356704i
$647$	8.04220			0.316172			0.158086	−	0.987425i	$-0.449468\pi$
$647$	8.04220			0.316172			0.158086	+	0.987425i	$0.449468\pi$
$648$		0			0
$649$			36.3964i			1.42868i
$650$	40.7785	+	14.8422i	1.59946	+	0.582158i
$651$		0			0
$652$	21.9778	+	18.4416i	0.860717	+	0.722228i
$653$	10.0845	+	1.77817i	0.394638	+	0.0695853i	0.367446	−	0.930045i	$-0.380232\pi$
$653$	10.0845	+	1.77817i	0.394638	+	0.0695853i	0.0271920	+	0.999630i	$0.491343\pi$
$654$		0			0
$655$	−22.6077	+	18.9701i	−0.883356	+	0.741224i
$656$	−1.58541	−	2.74601i	−0.0618998	−	0.107214i
$657$		0			0
$658$	−50.5437	−	7.06952i	−1.97040	−	0.275599i
$659$	−20.5607	+	3.62540i	−0.800930	+	0.141226i	−0.559108	−	0.829095i	$-0.688856\pi$
$659$	−20.5607	+	3.62540i	−0.800930	+	0.141226i	−0.241822	+	0.970321i	$0.577745\pi$
$660$		0			0
$661$	1.62538	+	4.46570i	0.0632200	+	0.173696i	0.967281	−	0.253708i	$-0.0816504\pi$
$661$	1.62538	+	4.46570i	0.0632200	+	0.173696i	−0.904061	+	0.427404i	$0.859428\pi$
$662$	6.60517	+	18.1476i	0.256717	+	0.705325i
$663$		0			0
$664$	31.9313	−	5.63035i	1.23918	−	0.218500i
$665$	34.2944	+	4.79674i	1.32988	+	0.186009i
$666$		0			0
$667$	3.34496	+	5.79363i	0.129517	+	0.224330i
$668$	27.6970	−	23.2406i	1.07163	−	0.899204i
$669$		0			0
$670$	−66.7448	−	11.7689i	−2.57857	−	0.454672i
$671$	11.8950	+	9.98110i	0.459202	+	0.385316i
$672$		0			0
$673$	30.7990	+	11.2099i	1.18721	+	0.432110i	0.858744	−	0.512404i	$-0.171245\pi$
$673$	30.7990	+	11.2099i	1.18721	+	0.432110i	0.328469	+	0.944515i	$0.393467\pi$
$674$		−	38.2834i		−	1.47462i
$675$		0			0
$676$	−0.364961			−0.0140370
$677$	−3.36060	−	1.22316i	−0.129158	−	0.0470098i	0.276632	−	0.960976i	$-0.410782\pi$
$677$	−3.36060	−	1.22316i	−0.129158	−	0.0470098i	−0.405791	+	0.913966i	$0.633004\pi$
$678$		0			0
$679$	2.05313	−	6.33307i	0.0787919	−	0.243041i
$680$	−17.5827	−	3.10031i	−0.674268	−	0.118892i
$681$		0			0
$682$	−2.21356	−	2.63802i	−0.0847615	−	0.101015i
$683$	6.89711	−	3.98205i	0.263910	−	0.152369i	−0.362207	−	0.932098i	$-0.617977\pi$
$683$	6.89711	−	3.98205i	0.263910	−	0.152369i	0.626117	+	0.779729i	$0.284643\pi$
$684$		0			0
$685$	28.1508	+	16.2529i	1.07559	+	0.620991i
$686$	−9.77860	+	39.5525i	−0.373349	+	1.51012i
$687$		0			0
$688$	11.5406	−	4.20044i	0.439982	−	0.160140i
$689$	10.5136	−	3.82662i	0.400535	−	0.145783i
$690$		0			0
$691$	10.8617	−	1.91522i	0.413200	−	0.0728583i	0.0368159	−	0.999322i	$-0.488278\pi$
$691$	10.8617	−	1.91522i	0.413200	−	0.0728583i	0.376384	+	0.926464i	$0.377167\pi$
$692$	10.2402	−	17.7366i	0.389275	−	0.674244i
$693$		0			0
$694$	3.09929	+	5.36814i	0.117648	+	0.203772i
$695$	−8.48739	−	10.1149i	−0.321945	−	0.383679i
$696$		0			0
$697$	1.01667	−	5.76583i	0.0385092	−	0.218397i
$698$	35.8792	+	30.1062i	1.35805	+	1.13954i
$699$		0			0
$700$	41.2828	−	1.46884i	1.56035	−	0.0555171i
$701$		−	38.5950i		−	1.45771i	−0.684665	−	0.728857i	$-0.740052\pi$
$701$		−	38.5950i		−	1.45771i	0.684665	−	0.728857i	$-0.259948\pi$
$702$		0			0
$703$		−	22.7858i		−	0.859381i
$704$	−14.0441	+	38.5859i	−0.529308	+	1.45426i
$705$		0			0
$706$	−31.1672	+	37.1436i	−1.17299	+	1.39792i
$707$	6.34919	+	29.7742i	0.238786	+	1.11977i
$708$		0			0
$709$	25.2492	−	21.1866i	0.948253	−	0.795679i	−0.0307495	−	0.999527i	$-0.509789\pi$
$709$	25.2492	−	21.1866i	0.948253	−	0.795679i	0.979002	+	0.203848i	$0.0653450\pi$
$710$	11.0097	+	19.0694i	0.413188	+	0.715662i
$711$		0			0
$712$	11.1442	+	6.43408i	0.417645	+	0.241127i
$713$	−0.0578058	−	0.327833i	−0.00216484	−	0.0122774i
$714$		0			0
$715$	35.2754	−	12.8392i	1.31923	−	0.480159i
$716$	6.89064	+	18.9319i	0.257515	+	0.707517i
$717$		0			0
$718$	−7.77207	−	44.0776i	−0.290051	−	1.64496i
$719$	9.13910	−	15.8294i	0.340831	−	0.590336i	−0.643756	−	0.765231i	$-0.722625\pi$
$719$	9.13910	−	15.8294i	0.340831	−	0.590336i	0.984587	+	0.174894i	$0.0559583\pi$
$720$		0			0
$721$	29.0329	−	37.2109i	1.08124	−	1.38581i
$722$	3.79368	+	4.52114i	0.141186	+	0.168259i
$723$		0			0
$724$	−14.4294	−	2.54430i	−0.536266	−	0.0945582i
$725$	34.4277	−	41.0293i	1.27861	−	1.52379i
$726$		0			0
$727$	−13.0156	+	35.7602i	−0.482723	+	1.32627i	0.424426	+	0.905462i	$0.360476\pi$
$727$	−13.0156	+	35.7602i	−0.482723	+	1.32627i	−0.907150	+	0.420808i	$0.861746\pi$
$728$	16.2537	−	6.57935i	0.602400	−	0.243847i
$729$		0			0
$730$	−81.6346			−3.02143
$731$	21.3093	+	7.75594i	0.788151	+	0.286864i
$732$		0			0
$733$	−12.2043	+	14.5445i	−0.450776	+	0.537214i	−0.942796	−	0.333370i	$-0.891814\pi$
$733$	−12.2043	+	14.5445i	−0.450776	+	0.537214i	0.492020	+	0.870584i	$0.336259\pi$
$734$	−9.15008	+	51.8927i	−0.337736	+	1.91539i
$735$		0			0
$736$	−3.81335	+	3.19978i	−0.140562	+	0.117945i
$737$	−26.5915	+	15.3526i	−0.979511	+	0.565521i
$738$		0			0
$739$	−0.674129	+	1.16763i	−0.0247982	+	0.0429518i	−0.878158	−	0.478370i	$-0.841228\pi$
$739$	−0.674129	+	1.16763i	−0.0247982	+	0.0429518i	0.853360	+	0.521322i	$0.174561\pi$
$740$	−9.01243	−	51.1120i	−0.331304	−	1.87892i
$741$		0			0
$742$	13.4811	−	12.1545i	0.494905	−	0.446205i
$743$	14.7521	+	40.5311i	0.541203	+	1.48694i	0.845295	+	0.534301i	$0.179425\pi$
$743$	14.7521	+	40.5311i	0.541203	+	1.48694i	−0.304091	+	0.952643i	$0.598353\pi$
$744$		0			0
$745$	31.0878	−	5.48162i	1.13897	−	0.200831i
$746$	−35.1477	−	20.2925i	−1.28685	−	0.742962i
$747$		0			0
$748$	−23.6896	+	13.6772i	−0.866179	+	0.500089i
$749$	6.98912	+	3.71028i	0.255377	+	0.135571i
$750$		0			0
$751$	−1.49167	+	8.45970i	−0.0544319	+	0.308699i	−0.999853	−	0.0171527i	$-0.994540\pi$
$751$	−1.49167	+	8.45970i	−0.0544319	+	0.308699i	0.945421	+	0.325852i	$0.105651\pi$
$752$	−10.8510	−	9.10508i	−0.395696	−	0.332028i
$753$		0			0
$754$	26.2963	−	72.2484i	0.957654	−	2.63113i
$755$	−68.2672			−2.48450
$756$		0			0
$757$	42.8160			1.55618			0.778088	−	0.628156i	$-0.216190\pi$
$757$	42.8160			1.55618			0.778088	+	0.628156i	$0.216190\pi$
$758$	−10.7533	+	29.5446i	−0.390579	+	1.07311i
$759$		0			0
$760$	−18.5213	−	15.5412i	−0.671840	−	0.563740i
$761$	7.33501	−	41.5989i	0.265894	−	1.50796i	−0.500583	−	0.865688i	$-0.666881\pi$
$761$	7.33501	−	41.5989i	0.265894	−	1.50796i	0.766477	−	0.642271i	$-0.222008\pi$
$762$		0			0
$763$	3.54055	−	6.66939i	0.128176	−	0.241448i
$764$	9.79804	−	5.65690i	0.354481	−	0.204659i
$765$		0			0
$766$	−43.5474	−	25.1421i	−1.57343	−	0.908421i
$767$	39.8208	−	7.02148i	1.43784	−	0.253531i
$768$		0			0
$769$	−7.08056	−	19.4537i	−0.255331	−	0.701517i	−0.999440	−	0.0334587i	$-0.989348\pi$
$769$	−7.08056	−	19.4537i	−0.255331	−	0.701517i	0.744109	−	0.668059i	$-0.232874\pi$
$770$	45.2321	−	40.7811i	1.63005	−	1.46965i
$771$		0			0
$772$	−3.75116	−	21.2739i	−0.135007	−	0.765663i
$773$	−5.17350	+	8.96077i	−0.186078	+	0.322296i	−0.943939	−	0.330119i	$-0.892911\pi$
$773$	−5.17350	+	8.96077i	−0.186078	+	0.322296i	0.757861	+	0.652416i	$0.226244\pi$
$774$		0			0
$775$	−2.30809	+	1.33257i	−0.0829089	+	0.0478675i
$776$	−3.56088	+	2.98793i	−0.127828	+	0.107261i
$777$		0			0
$778$	0.934487	−	5.29974i	0.0335030	−	0.190005i
$779$	5.09637	−	6.07362i	0.182597	−	0.217610i
$780$		0			0
$781$	9.37431	+	3.41197i	0.335439	+	0.122090i
$782$	−4.50662			−0.161156
$783$		0			0
$784$	−8.12419	+	7.86614i	−0.290150	+	0.280933i
$785$	−11.2835	+	31.0012i	−0.402726	+	1.10648i
$786$		0			0
$787$	−23.3874	+	27.8721i	−0.833673	+	0.993532i	0.166300	+	0.986075i	$0.446818\pi$
$787$	−23.3874	+	27.8721i	−0.833673	+	0.993532i	−0.999972	+	0.00745697i	$0.997626\pi$
$788$	−10.4653	−	1.84531i	−0.372810	−	0.0657364i
$789$		0			0
$790$	30.2595	+	36.0619i	1.07658	+	1.28302i
$791$	−5.76471	+	7.38851i	−0.204969	+	0.262705i
$792$		0			0
$793$	8.62543	−	14.9397i	0.306298	−	0.530524i
$794$	5.18640	+	29.4135i	0.184058	+	1.04385i
$795$		0			0
$796$	−2.15307	−	5.91552i	−0.0763136	−	0.209670i
$797$	3.95939	−	1.44110i	0.140249	−	0.0510464i	−0.270942	−	0.962596i	$-0.587335\pi$
$797$	3.95939	−	1.44110i	0.140249	−	0.0510464i	0.411191	+	0.911549i	$0.365113\pi$
$798$		0			0
$799$	−4.54178	−	25.7577i	−0.160677	−	0.911242i
$800$	34.5146	+	19.9270i	1.22028	+	0.704527i
$801$		0			0
$802$	−20.9840	−	36.3453i	−0.740970	−	1.28340i
$803$	−28.3319	+	23.7733i	−0.999810	+	0.838940i
$804$		0			0
$805$	5.75774	−	1.22781i	0.202934	−	0.0432745i
$806$	−2.45918	+	2.93074i	−0.0866211	+	0.103231i
$807$		0			0
$808$	7.27004	−	19.9743i	0.255759	−	0.702692i
$809$		−	41.1433i		−	1.44652i	−0.690574	−	0.723261i	$-0.742642\pi$
$809$		−	41.1433i		−	1.44652i	0.690574	−	0.723261i	$-0.257358\pi$
$810$		0			0
$811$		−	25.7104i		−	0.902815i	−0.892318	−	0.451407i	$-0.850922\pi$
$811$		−	25.7104i		−	0.902815i	0.892318	−	0.451407i	$-0.149078\pi$
$812$	−2.60239	−	73.1420i	−0.0913260	−	2.56678i
$813$		0			0
$814$	−30.6986	−	25.7592i	−1.07598	−	0.902858i
$815$	5.68440	−	32.2378i	0.199116	−	1.12924i
$816$		0			0
$817$	19.7394	+	23.5245i	0.690593	+	0.823016i
$818$	−36.1292	−	62.5775i	−1.26323	−	2.18797i
$819$		0			0
$820$	9.02967	−	15.6398i	0.315330	−	0.546167i
$821$	−34.7029	+	6.11906i	−1.21114	+	0.213557i	−0.742508	−	0.669837i	$-0.766364\pi$
$821$	−34.7029	+	6.11906i	−1.21114	+	0.213557i	−0.468632	+	0.883394i	$0.655253\pi$
$822$		0			0
$823$	−11.0749	+	4.03095i	−0.386048	+	0.140510i	−0.527751	−	0.849399i	$-0.676964\pi$
$823$	−11.0749	+	4.03095i	−0.386048	+	0.140510i	0.141703	+	0.989909i	$0.454742\pi$
$824$	−30.9663	+	11.2708i	−1.07876	+	0.392637i
$825$		0			0
$826$	55.6089	−	34.7992i	1.93488	−	1.21082i
$827$	−4.77748	−	2.75828i	−0.166129	−	0.0959148i	0.414630	−	0.909990i	$-0.363911\pi$
$827$	−4.77748	−	2.75828i	−0.166129	−	0.0959148i	−0.580759	+	0.814075i	$0.697244\pi$
$828$		0			0
$829$	−33.5706	+	19.3820i	−1.16595	+	0.673164i	−0.952724	−	0.303837i	$-0.901732\pi$
$829$	−33.5706	+	19.3820i	−1.16595	+	0.673164i	−0.213231	+	0.977002i	$0.568399\pi$
$830$	−80.4197	−	95.8405i	−2.79141	−	3.32667i
$831$		0			0
$832$	44.9256	+	7.92160i	1.55752	+	0.274632i
$833$	−20.8276	+	1.48397i	−0.721632	+	0.0514165i
$834$		0			0
$835$	−38.7658	−	14.1096i	−1.34155	−	0.488283i
$836$	−37.0434			−1.28117
$837$		0			0
$838$			56.4339i			1.94948i
$839$	35.0483	+	12.7566i	1.21000	+	0.440405i	0.866705	−	0.498821i	$-0.166234\pi$
$839$	35.0483	+	12.7566i	1.21000	+	0.440405i	0.343298	+	0.939226i	$0.388456\pi$
$840$		0			0
$841$	−50.4775	−	42.3557i	−1.74061	−	1.46054i
$842$	−24.9638	−	4.40178i	−0.860308	−	0.151696i
$843$		0			0
$844$	7.40811	−	6.21614i	0.254998	−	0.213968i
$845$	0.208209	+	0.360629i	0.00716262	+	0.0124060i
$846$		0			0
$847$	−0.209393	+	1.49706i	−0.00719483	+	0.0514396i
$848$	4.96137	−	0.874824i	0.170374	−	0.0300416i
$849$		0			0
$850$	12.3402	+	33.9045i	0.423266	+	1.16291i
$851$	−1.32493	−	3.64022i	−0.0454181	−	0.124785i
$852$		0			0
$853$	4.83719	−	0.852926i	0.165622	−	0.0292036i	−0.0902221	−	0.995922i	$-0.528758\pi$
$853$	4.83719	−	0.852926i	0.165622	−	0.0292036i	0.255844	+	0.966718i	$0.417647\pi$
$854$	3.87678	−	27.7171i	0.132661	−	0.948460i
$855$		0			0
$856$	−2.76245	−	4.78470i	−0.0944185	−	0.163538i
$857$	9.53580	−	8.00148i	0.325737	−	0.273325i	−0.465223	−	0.885193i	$-0.654026\pi$
$857$	9.53580	−	8.00148i	0.325737	−	0.273325i	0.790960	+	0.611868i	$0.209582\pi$
$858$		0			0
$859$	48.9734	+	8.63533i	1.67095	+	0.294634i	0.927407	−	0.374054i	$-0.122032\pi$
$859$	48.9734	+	8.63533i	1.67095	+	0.294634i	0.743544	+	0.668687i	$0.233144\pi$
$860$	53.5831	+	44.9615i	1.82717	+	1.53318i
$861$		0			0
$862$	57.0339	+	20.7587i	1.94258	+	0.707043i
$863$			7.82559i			0.266386i	0.991090	+	0.133193i	$0.0425230\pi$
$863$			7.82559i			0.266386i	−0.991090	+	0.133193i	$0.957477\pi$
$864$		0			0
$865$	−23.3681			−0.794540
$866$	2.23301	+	0.812751i	0.0758809	+	0.0276184i
$867$		0			0
$868$	−1.12311	+	3.46435i	−0.0381210	+	0.117588i
$869$	21.0035	+	3.70349i	0.712496	+	0.125632i
$870$		0			0
$871$	21.9270	+	26.1316i	0.742970	+	0.885437i
$872$	−4.56581	+	2.63607i	−0.154618	+	0.0892687i
$873$		0			0
$874$	−5.28524	−	3.05144i	−0.178776	−	0.103216i
$875$	−2.26564	−	3.62048i	−0.0765927	−	0.122395i
$876$		0			0
$877$	−38.6291	+	14.0598i	−1.30441	+	0.474767i	−0.898431	−	0.439115i	$-0.855292\pi$
$877$	−38.6291	+	14.0598i	−1.30441	+	0.474767i	−0.405980	+	0.913882i	$0.633070\pi$
$878$	−5.46971	+	1.99081i	−0.184594	+	0.0671866i
$879$		0			0
$880$	16.6465	−	2.93524i	0.561155	−	0.0989468i
$881$	−13.4109	+	23.2283i	−0.451824	+	0.782582i	−0.998499	−	0.0547623i	$-0.982560\pi$
$881$	−13.4109	+	23.2283i	−0.451824	+	0.782582i	0.546675	+	0.837345i	$0.315893\pi$
$882$		0			0
$883$	15.7111	+	27.2125i	0.528722	+	0.915773i	0.999439	+	0.0334889i	$0.0106618\pi$
$883$	15.7111	+	27.2125i	0.528722	+	0.915773i	−0.470717	+	0.882284i	$0.656005\pi$
$884$	19.5342	+	23.2799i	0.657006	+	0.782989i
$885$		0			0
$886$	6.18739	−	35.0905i	0.207870	−	1.17889i
$887$	8.61019	+	7.22481i	0.289102	+	0.242585i	0.775791	−	0.630990i	$-0.217351\pi$
$887$	8.61019	+	7.22481i	0.289102	+	0.242585i	−0.486689	+	0.873575i	$0.661796\pi$
$888$		0			0
$889$	−38.9997	+	1.38761i	−1.30801	+	0.0465389i
$890$		−	49.6531i		−	1.66438i
$891$		0			0
$892$		−	13.6102i		−	0.455702i
$893$	12.1141	−	33.2832i	0.405382	−	1.11378i
$894$		0			0
$895$	14.7761	−	17.6094i	0.493910	−	0.588619i
$896$	34.8698	−	7.43579i	1.16492	−	0.248412i
$897$		0			0
$898$	−31.9287	+	26.7913i	−1.06547	+	0.894038i
$899$	2.36096	+	4.08930i	0.0787424	+	0.136386i
$900$		0			0
$901$	8.05602	+	4.65114i	0.268385	+	0.154952i
$902$	−2.42139	−	13.7324i	−0.0806234	−	0.457238i
$903$		0			0
$904$	6.14859	−	2.23791i	0.204499	−	0.0744316i
$905$	5.71787	+	15.7097i	0.190068	+	0.522209i
$906$		0			0
$907$	0.449186	+	2.54746i	0.0149150	+	0.0845870i	0.991357	−	0.131194i	$-0.0418812\pi$
$907$	0.449186	+	2.54746i	0.0149150	+	0.0845870i	−0.976442	+	0.215781i	$0.930770\pi$
$908$	−12.0885	+	20.9379i	−0.401172	+	0.694850i
$909$		0			0
$910$	−53.3440	−	41.6204i	−1.76834	−	1.37970i
$911$	−12.1000	−	14.4203i	−0.400892	−	0.477765i	0.527399	−	0.849617i	$-0.323167\pi$
$911$	−12.1000	−	14.4203i	−0.400892	−	0.477765i	−0.928292	+	0.371852i	$0.878723\pi$
$912$		0			0
$913$	−55.8205	−	9.84265i	−1.84739	−	0.325744i
$914$	−41.0765	+	48.9530i	−1.35869	+	1.61922i
$915$		0			0
$916$	21.8000	−	59.8950i	0.720292	−	1.97899i
$917$	22.3380	−	9.04224i	0.737665	−	0.298601i
$918$		0			0
$919$	−28.9423			−0.954719			−0.477359	−	0.878708i	$-0.658406\pi$
$919$	−28.9423			−0.954719			−0.477359	+	0.878708i	$0.658406\pi$
$920$	−3.86262	−	1.40588i	−0.127347	−	0.0463505i
$921$		0			0
$922$	60.0871	−	71.6090i	1.97886	−	2.35832i
$923$	1.92453	−	10.9145i	0.0633465	−	0.359256i
$924$		0			0
$925$	−23.7583	+	19.9356i	−0.781170	+	0.655479i
$926$	−25.6973	+	14.8363i	−0.844465	+	0.487552i
$927$		0			0
$928$	35.3053	−	61.1505i	1.15895	−	2.00736i
$929$	2.16578	+	12.2827i	0.0710569	+	0.402983i	0.999503	+	0.0315170i	$0.0100338\pi$
$929$	2.16578	+	12.2827i	0.0710569	+	0.402983i	−0.928446	+	0.371467i	$0.878855\pi$
$930$		0			0
$931$	−25.4308	−	12.3620i	−0.833460	−	0.405148i
$932$	−5.35757	−	14.7198i	−0.175493	−	0.482163i
$933$		0			0
$934$	52.0063	−	9.17012i	1.70170	−	0.300055i
$935$	27.0298	+	15.6057i	0.883969	+	0.510360i
$936$		0			0
$937$	−36.9165	+	21.3137i	−1.20601	+	0.696290i	−0.961885	−	0.273454i	$-0.911834\pi$
$937$	−36.9165	+	21.3137i	−1.20601	+	0.696290i	−0.244124	+	0.969744i	$0.578500\pi$
$938$	48.8814	+	25.9494i	1.59603	+	0.847279i
$939$		0			0
$940$	14.0093	−	79.4508i	0.456934	−	2.59140i
$941$	−37.0819	−	31.1154i	−1.20884	−	1.01433i	−0.999333	−	0.0365255i	$-0.988371\pi$
$941$	−37.0819	−	31.1154i	−1.20884	−	1.01433i	−0.209503	−	0.977808i	$-0.567185\pi$
$942$		0			0
$943$	0.461024	−	1.26665i	0.0150130	−	0.0412479i
$944$	18.2073			0.592596
$945$		0			0
$946$	54.0090			1.75598
$947$	−9.84660	+	27.0533i	−0.319972	+	0.879115i	0.670563	+	0.741852i	$0.266053\pi$
$947$	−9.84660	+	27.0533i	−0.319972	+	0.879115i	−0.990535	+	0.137262i	$0.956170\pi$
$948$		0			0
$949$	31.4757	+	26.4112i	1.02174	+	0.857345i
$950$	−8.48447	+	48.1178i	−0.275273	+	1.56115i
$951$		0			0
$952$	12.8770	+	6.83593i	0.417345	+	0.221554i
$953$	−29.6982	+	17.1463i	−0.962020	+	0.555422i	−0.896794	−	0.442448i	$-0.854110\pi$
$953$	−29.6982	+	17.1463i	−0.962020	+	0.555422i	−0.0652258	+	0.997871i	$0.520777\pi$
$954$		0			0
$955$	−11.1795	−	6.45450i	−0.361761	−	0.208863i
$956$	77.3925	−	13.6464i	2.50305	−	0.441356i
$957$		0			0
$958$	−16.8674	−	46.3429i	−0.544962	−	1.49727i
$959$	−17.7738	−	19.7137i	−0.573946	−	0.636588i
$960$		0			0
$961$	5.34229	+	30.2976i	0.172332	+	0.977343i
$962$	−22.2605	+	38.5563i	−0.717706	+	1.24310i
$963$		0			0
$964$	−1.70802	+	0.986129i	−0.0550118	+	0.0317611i
$965$	−18.8814	+	15.8433i	−0.607812	+	0.510015i
$966$		0			0
$967$	−8.18346	+	46.4107i	−0.263162	+	1.49247i	0.511055	+	0.859548i	$0.329255\pi$
$967$	−8.18346	+	46.4107i	−0.263162	+	1.49247i	−0.774218	+	0.632919i	$0.781856\pi$
$968$	0.678426	−	0.808517i	0.0218054	−	0.0259867i
$969$		0			0
$970$	16.8546	+	6.13458i	0.541170	+	0.196970i
$971$	8.35204			0.268030			0.134015	−	0.990979i	$-0.457213\pi$
$971$	8.35204			0.268030			0.134015	+	0.990979i	$0.457213\pi$
$972$		0			0
$973$	4.04558	+	9.99421i	0.129695	+	0.320400i
$974$	5.17286	−	14.2123i	0.165749	−	0.455392i
$975$		0			0
$976$	4.99304	−	5.95047i	0.159823	−	0.190470i
$977$	−55.1882	−	9.73116i	−1.76563	−	0.311327i	−0.805855	−	0.592113i	$-0.798294\pi$
$977$	−55.1882	−	9.73116i	−1.76563	−	0.311327i	−0.959771	+	0.280785i	$0.909405\pi$
$978$		0			0
$979$	−14.4597	−	17.2325i	−0.462135	−	0.550752i
$980$	−61.9348	−	17.6713i	−1.97843	−	0.564488i
$981$		0			0
$982$	6.53596	−	11.3206i	0.208571	−	0.361255i
$983$	1.87543	+	10.6361i	0.0598170	+	0.339239i	0.999999	−	0.00143367i	$-0.000456353\pi$
$983$	1.87543	+	10.6361i	0.0598170	+	0.339239i	−0.940182	+	0.340673i	$0.889345\pi$
$984$		0			0
$985$	4.14701	+	11.3938i	0.132135	+	0.363037i
$986$	60.0695	−	21.8635i	1.91300	−	0.696276i
$987$		0			0
$988$	7.14630	+	40.5287i	0.227354	+	1.28939i
$989$	4.52142	+	2.61044i	0.143773	+	0.0830072i
$990$		0			0
$991$	−5.25786	−	9.10688i	−0.167021	−	0.289290i	0.770350	−	0.637621i	$-0.220082\pi$
$991$	−5.25786	−	9.10688i	−0.167021	−	0.289290i	−0.937371	+	0.348332i	$0.886748\pi$
$992$	−2.69156	+	2.25849i	−0.0854572	+	0.0717071i
$993$		0			0
$994$	−3.74990	−	17.5850i	−0.118940	−	0.557761i
$995$	−4.61699	+	5.50231i	−0.146368	+	0.174435i
$996$		0			0
$997$	19.0094	−	52.2279i	0.602034	−	1.65407i	−0.145113	−	0.989415i	$-0.546354\pi$
$997$	19.0094	−	52.2279i	0.602034	−	1.65407i	0.747146	−	0.664659i	$-0.231423\pi$
$998$		−	20.8146i		−	0.658874i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.503.19		132
3.2	odd	2		189.2.be.a.104.3	yes	132
7.6	odd	2	inner	567.2.be.a.503.20		132
21.20	even	2		189.2.be.a.104.4	yes	132
27.7	even	9		189.2.be.a.20.4	yes	132
27.20	odd	18	inner	567.2.be.a.62.20		132
189.20	even	18	inner	567.2.be.a.62.19		132
189.34	odd	18		189.2.be.a.20.3	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.3	✓	132	189.34	odd	18
189.2.be.a.20.4	yes	132	27.7	even	9
189.2.be.a.104.3	yes	132	3.2	odd	2
189.2.be.a.104.4	yes	132	21.20	even	2
567.2.be.a.62.19		132	189.20	even	18	inner
567.2.be.a.62.20		132	27.20	odd	18	inner
567.2.be.a.503.19		132	1.1	even	1	trivial
567.2.be.a.503.20		132	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.be (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.752422 - 2.06726i) q^{2} +(-2.17534 - 1.82533i) q^{4} +(-0.562637 + 3.19087i) q^{5} +(1.24057 - 2.33688i) q^{7} +(-1.59981 + 0.923650i) q^{8} +(6.17302 + 3.56400i) q^{10} +(3.18028 - 0.560770i) q^{11} +(-1.22706 - 3.37132i) q^{13} +(-3.89751 - 4.32289i) q^{14} +(-0.280525 - 1.59093i) q^{16} +(1.49145 - 2.58328i) q^{17} +(3.49827 - 2.01973i) q^{19} +(7.04831 - 5.91424i) q^{20} +(1.23366 - 6.99641i) q^{22} +(0.441437 - 0.526084i) q^{23} +(-5.16663 - 1.88050i) q^{25} -7.89267 q^{26} +(-6.96423 + 2.81906i) q^{28} +(-3.33174 + 9.15387i) q^{29} +(0.311578 - 0.371325i) q^{31} +(-7.13842 - 1.25870i) q^{32} +(-4.21810 - 5.02694i) q^{34} +(6.75868 + 5.27330i) q^{35} +(2.82040 - 4.88507i) q^{37} +(-1.54313 - 8.75153i) q^{38} +(-2.04714 - 5.62446i) q^{40} +(1.84441 - 0.671309i) q^{41} +(1.32012 + 7.48676i) q^{43} +(-7.94179 - 4.58519i) q^{44} +(-0.755407 - 1.30840i) q^{46} +(6.71691 - 5.63616i) q^{47} +(-3.92199 - 5.79810i) q^{49} +(-7.77497 + 9.26585i) q^{50} +(-3.48449 + 9.57356i) q^{52} +3.11853i q^{53} +10.4634i q^{55} +(0.173787 + 4.88441i) q^{56} +(16.4166 + 13.7751i) q^{58} +(-1.95711 + 11.0993i) q^{59} +(3.09075 + 3.68341i) q^{61} +(-0.533187 - 0.923507i) q^{62} +(-6.35768 + 11.0118i) q^{64} +(11.4478 - 2.01856i) q^{65} +(-8.93479 + 3.25200i) q^{67} +(-7.95975 + 2.89711i) q^{68} +(15.9867 - 10.0042i) q^{70} +(2.67528 + 1.54458i) q^{71} +(-9.91831 + 5.72634i) q^{73} +(-7.97659 - 9.50613i) q^{74} +(-11.2966 - 1.99190i) q^{76} +(2.63490 - 8.12760i) q^{77} +(6.20601 + 2.25880i) q^{79} +5.23430 q^{80} -4.31797i q^{82} +(-16.4935 - 6.00315i) q^{83} +(7.40375 + 6.21249i) q^{85} +(16.4704 + 2.90417i) q^{86} +(-4.56989 + 3.83459i) q^{88} +(-3.48296 - 6.03267i) q^{89} +(-9.40061 - 1.31486i) q^{91} +(-1.92055 + 0.338646i) q^{92} +(-6.59746 - 18.1264i) q^{94} +(4.47644 + 12.2989i) q^{95} +(2.47809 - 0.436955i) q^{97} +(-14.9372 + 3.74516i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Introduction

L-functions

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