LMFDB - Embedded newform 171.2.u.d.100.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(28,171)] 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("171.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 57x^{8} - 182x^{6} + 423x^{4} - 408x^{2} + 289 $ x^12 - 9x^10 + 57x^8 - 182x^6 + 423x^4 - 408*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.1
Root			$0.916767 + 0.529295i$ of defining polynomial
Character	$\chi$	$=$	171.100
Dual form			171.2.u.d.118.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.95928 + 0.713118i) q^{2} +(1.79813 - 1.50881i) q^{4} +(-0.554707 - 0.465455i) q^{5} +(-0.613341 - 1.06234i) q^{7} +(-0.362059 + 0.627105i) q^{8} +(1.41875 + 0.516382i) q^{10} +(0.916767 - 1.58789i) q^{11} +(-0.641559 - 3.63846i) q^{13} +(1.95928 + 1.64403i) q^{14} +(-0.553033 + 3.13641i) q^{16} +(6.23989 - 2.27113i) q^{17} +(4.34002 + 0.405223i) q^{19} -1.69972 q^{20} +(-0.663848 + 3.76487i) q^{22} +(2.44708 - 2.05334i) q^{23} +(-0.777189 - 4.40766i) q^{25} +(3.85164 + 6.67124i) q^{26} +(-2.70574 - 0.984808i) q^{28} +(-4.72474 - 1.71967i) q^{29} +(1.40760 + 2.43804i) q^{31} +(-1.40457 - 7.96570i) q^{32} +(-10.6061 + 8.89955i) q^{34} +(-0.154245 + 0.874769i) q^{35} -7.41147 q^{37} +(-8.79227 + 2.30100i) q^{38} +(0.492726 - 0.179338i) q^{40} +(-1.75146 + 9.93303i) q^{41} +(-0.0491630 - 0.0412527i) q^{43} +(-0.747355 - 4.23846i) q^{44} +(-3.33022 + 5.76811i) q^{46} +(-9.08742 - 3.30755i) q^{47} +(2.74763 - 4.75903i) q^{49} +(4.66591 + 8.08159i) q^{50} +(-6.64337 - 5.57445i) q^{52} +(3.68223 - 3.08976i) q^{53} +(-1.24763 + 0.454099i) q^{55} +0.888263 q^{56} +10.4834 q^{58} +(-7.12815 + 2.59443i) q^{59} +(3.19459 - 2.68058i) q^{61} +(-4.49649 - 3.77301i) q^{62} +(5.24763 + 9.08916i) q^{64} +(-1.33766 + 2.31690i) q^{65} +(7.06418 + 2.57115i) q^{67} +(7.79343 - 13.4986i) q^{68} +(-0.321604 - 1.82391i) q^{70} +(11.3499 + 9.52372i) q^{71} +(0.677519 - 3.84240i) q^{73} +(14.5211 - 5.28525i) q^{74} +(8.41534 - 5.81964i) q^{76} -2.24916 q^{77} +(-1.32160 + 7.49519i) q^{79} +(1.76663 - 1.48238i) q^{80} +(-3.65183 - 20.7105i) q^{82} +(6.19622 + 10.7322i) q^{83} +(-4.51842 - 1.64457i) q^{85} +(0.125742 + 0.0457663i) q^{86} +(0.663848 + 1.14982i) q^{88} +(-2.36500 - 13.4126i) q^{89} +(-3.47178 + 2.91317i) q^{91} +(1.30206 - 7.38436i) q^{92} +20.1634 q^{94} +(-2.21883 - 2.24486i) q^{95} +(3.85844 - 1.40436i) q^{97} +(-1.98961 + 11.2836i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{4} + 6 q^{7} + 12 q^{10} - 24 q^{13} + 18 q^{16} + 12 q^{19} + 12 q^{25} - 12 q^{28} + 24 q^{31} - 78 q^{34} - 48 q^{37} - 30 q^{40} - 24 q^{43} + 6 q^{46} + 54 q^{52} + 18 q^{55} - 48 q^{58}+ \cdots + 30 q^{97}+O(q^{100}) $ 12 * q - 6 * q^4 + 6 * q^7 + 12 * q^10 - 24 * q^13 + 18 * q^16 + 12 * q^19 + 12 * q^25 - 12 * q^28 + 24 * q^31 - 78 * q^34 - 48 * q^37 - 30 * q^40 - 24 * q^43 + 6 * q^46 + 54 * q^52 + 18 * q^55 - 48 * q^58 + 30 * q^61 + 30 * q^64 + 48 * q^67 + 60 * q^70 - 42 * q^73 + 12 * q^76 + 48 * q^79 + 66 * q^82 - 78 * q^85 - 12 * q^91 - 12 * q^94 + 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.95928	+	0.713118i	−1.38542	+	0.504250i	−0.923816	−	0.382837i	$-0.874947\pi$
$2$	−1.95928	+	0.713118i	−1.38542	+	0.504250i	−0.461601	+	0.887088i	$0.652725\pi$
$3$		0			0
$3$		0			0
$4$	1.79813	−	1.50881i	0.899067	−	0.754407i
$5$	−0.554707	−	0.465455i	−0.248073	−	0.208158i	0.510269	−	0.860015i	$-0.329546\pi$
$5$	−0.554707	−	0.465455i	−0.248073	−	0.208158i	−0.758342	+	0.651857i	$0.773990\pi$
$6$		0			0
$7$	−0.613341	−	1.06234i	−0.231821	−	0.401526i	0.726523	−	0.687142i	$-0.241135\pi$
$7$	−0.613341	−	1.06234i	−0.231821	−	0.401526i	−0.958344	+	0.285616i	$0.907802\pi$
$8$	−0.362059	+	0.627105i	−0.128007	+	0.221715i
$9$		0			0
$10$	1.41875	+	0.516382i	0.448648	+	0.163294i
$11$	0.916767	−	1.58789i	0.276416	−	0.478766i	−0.694076	−	0.719902i	$-0.744187\pi$
$11$	0.916767	−	1.58789i	0.276416	−	0.478766i	0.970491	+	0.241136i	$0.0775201\pi$
$12$		0			0
$13$	−0.641559	−	3.63846i	−0.177937	−	1.00913i	−0.934700	−	0.355439i	$-0.884331\pi$
$13$	−0.641559	−	3.63846i	−0.177937	−	1.00913i	0.756763	−	0.653689i	$-0.226780\pi$
$14$	1.95928	+	1.64403i	0.523638	+	0.439385i
$15$		0			0
$16$	−0.553033	+	3.13641i	−0.138258	+	0.784102i
$17$	6.23989	−	2.27113i	1.51339	−	0.550831i	0.553906	−	0.832579i	$-0.313137\pi$
$17$	6.23989	−	2.27113i	1.51339	−	0.550831i	0.959488	+	0.281749i	$0.0909144\pi$
$18$		0			0
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$20$	−1.69972			−0.380069
$21$		0			0
$22$	−0.663848	+	3.76487i	−0.141533	+	0.802673i
$23$	2.44708	−	2.05334i	0.510251	−	0.428151i	−0.350967	−	0.936388i	$-0.614147\pi$
$23$	2.44708	−	2.05334i	0.510251	−	0.428151i	0.861217	+	0.508237i	$0.169703\pi$
$24$		0			0
$25$	−0.777189	−	4.40766i	−0.155438	−	0.881531i
$26$	3.85164	+	6.67124i	0.755370	+	1.30834i
$27$		0			0
$28$	−2.70574	−	0.984808i	−0.511336	−	0.186111i
$29$	−4.72474	−	1.71967i	−0.877362	−	0.319334i	−0.136218	−	0.990679i	$-0.543495\pi$
$29$	−4.72474	−	1.71967i	−0.877362	−	0.319334i	−0.741145	+	0.671345i	$0.765717\pi$
$30$		0			0
$31$	1.40760	+	2.43804i	0.252813	+	0.437885i	0.964299	−	0.264815i	$-0.0853109\pi$
$31$	1.40760	+	2.43804i	0.252813	+	0.437885i	−0.711486	+	0.702700i	$0.751978\pi$
$32$	−1.40457	−	7.96570i	−0.248295	−	1.40815i
$33$		0			0
$34$	−10.6061	+	8.89955i	−1.81893	+	1.52626i
$35$	−0.154245	+	0.874769i	−0.0260722	+	0.147863i
$36$		0			0
$37$	−7.41147			−1.21844			−0.609219	−	0.793002i	$-0.708517\pi$
$37$	−7.41147			−1.21844			−0.609219	+	0.793002i	$0.708517\pi$
$38$	−8.79227	+	2.30100i	−1.42629	+	0.373272i
$39$		0			0
$40$	0.492726	−	0.179338i	0.0779068	−	0.0283558i
$41$	−1.75146	+	9.93303i	−0.273532	+	1.55128i	0.470053	+	0.882638i	$0.344235\pi$
$41$	−1.75146	+	9.93303i	−0.273532	+	1.55128i	−0.743586	+	0.668641i	$0.766876\pi$
$42$		0			0
$43$	−0.0491630	−	0.0412527i	−0.00749729	−	0.00629097i	0.639031	−	0.769181i	$-0.279335\pi$
$43$	−0.0491630	−	0.0412527i	−0.00749729	−	0.00629097i	−0.646529	+	0.762890i	$0.723780\pi$
$44$	−0.747355	−	4.23846i	−0.112668	−	0.638972i
$45$		0			0
$46$	−3.33022	+	5.76811i	−0.491014	+	0.850462i
$47$	−9.08742	−	3.30755i	−1.32554	−	0.482456i	−0.420309	−	0.907381i	$-0.638078\pi$
$47$	−9.08742	−	3.30755i	−1.32554	−	0.482456i	−0.905228	+	0.424925i	$0.860300\pi$
$48$		0			0
$49$	2.74763	−	4.75903i	0.392518	−	0.679861i
$50$	4.66591	+	8.08159i	0.659859	+	1.14291i
$51$		0			0
$52$	−6.64337	−	5.57445i	−0.921270	−	0.773037i
$53$	3.68223	−	3.08976i	0.505794	−	0.424411i	−0.353852	−	0.935301i	$-0.615129\pi$
$53$	3.68223	−	3.08976i	0.505794	−	0.424411i	0.859646	+	0.510890i	$0.170684\pi$
$54$		0			0
$55$	−1.24763	+	0.454099i	−0.168230	+	0.0612307i
$56$	0.888263			0.118699
$57$		0			0
$58$	10.4834			1.37654
$59$	−7.12815	+	2.59443i	−0.928006	+	0.337767i	−0.761419	−	0.648260i	$-0.775497\pi$
$59$	−7.12815	+	2.59443i	−0.928006	+	0.337767i	−0.166587	+	0.986027i	$0.553275\pi$
$60$		0			0
$61$	3.19459	−	2.68058i	0.409026	−	0.343213i	−0.414944	−	0.909847i	$-0.636199\pi$
$61$	3.19459	−	2.68058i	0.409026	−	0.343213i	0.823970	+	0.566634i	$0.191754\pi$
$62$	−4.49649	−	3.77301i	−0.571055	−	0.479172i
$63$		0			0
$64$	5.24763	+	9.08916i	0.655953	+	1.13614i
$65$	−1.33766	+	2.31690i	−0.165917	+	0.287376i
$66$		0			0
$67$	7.06418	+	2.57115i	0.863027	+	0.314116i	0.735340	−	0.677699i	$-0.237023\pi$
$67$	7.06418	+	2.57115i	0.863027	+	0.314116i	0.127687	+	0.991815i	$0.459245\pi$
$68$	7.79343	−	13.4986i	0.945092	−	1.63695i
$69$		0			0
$70$	−0.321604	−	1.82391i	−0.0384390	−	0.217999i
$71$	11.3499	+	9.52372i	1.34699	+	1.13026i	0.979771	+	0.200122i	$0.0641338\pi$
$71$	11.3499	+	9.52372i	1.34699	+	1.13026i	0.367217	+	0.930135i	$0.380311\pi$
$72$		0			0
$73$	0.677519	−	3.84240i	0.0792976	−	0.449719i	−0.919145	−	0.393921i	$-0.871119\pi$
$73$	0.677519	−	3.84240i	0.0792976	−	0.449719i	0.998442	−	0.0557983i	$-0.0177704\pi$
$74$	14.5211	−	5.28525i	1.68805	−	0.614398i
$75$		0			0
$76$	8.41534	−	5.81964i	0.965306	−	0.667558i
$77$	−2.24916			−0.256316
$78$		0			0
$79$	−1.32160	+	7.49519i	−0.148692	+	0.843275i	0.815636	+	0.578565i	$0.196387\pi$
$79$	−1.32160	+	7.49519i	−0.148692	+	0.843275i	−0.964328	+	0.264709i	$0.914724\pi$
$80$	1.76663	−	1.48238i	0.197515	−	0.165735i
$81$		0			0
$82$	−3.65183	−	20.7105i	−0.403277	−	2.28710i
$83$	6.19622	+	10.7322i	0.680123	+	1.17801i	0.974943	+	0.222455i	$0.0714070\pi$
$83$	6.19622	+	10.7322i	0.680123	+	1.17801i	−0.294820	+	0.955553i	$0.595260\pi$
$84$		0			0
$85$	−4.51842	−	1.64457i	−0.490091	−	0.178379i
$86$	0.125742	+	0.0457663i	0.0135591	+	0.00493511i
$87$		0			0
$88$	0.663848	+	1.14982i	0.0707664	+	0.122571i
$89$	−2.36500	−	13.4126i	−0.250690	−	1.42173i	−0.806898	−	0.590690i	$-0.798855\pi$
$89$	−2.36500	−	13.4126i	−0.250690	−	1.42173i	0.556208	−	0.831043i	$-0.312256\pi$
$90$		0			0
$91$	−3.47178	+	2.91317i	−0.363942	+	0.305383i
$92$	1.30206	−	7.38436i	0.135749	−	0.769873i
$93$		0			0
$94$	20.1634			2.07970
$95$	−2.21883	−	2.24486i	−0.227647	−	0.230318i
$96$		0			0
$97$	3.85844	−	1.40436i	0.391765	−	0.142591i	−0.138624	−	0.990345i	$-0.544268\pi$
$97$	3.85844	−	1.40436i	0.391765	−	0.142591i	0.530389	+	0.847754i	$0.322046\pi$
$98$	−1.98961	+	11.2836i	−0.200981	+	1.13982i
$99$		0			0
$100$	−8.04782	−	6.75292i	−0.804782	−	0.675292i
$101$	1.84870	+	10.4845i	0.183952	+	1.04325i	0.927294	+	0.374334i	$0.122129\pi$
$101$	1.84870	+	10.4845i	0.183952	+	1.04325i	−0.743341	+	0.668912i	$0.766760\pi$
$102$		0			0
$103$	−0.432419	+	0.748971i	−0.0426075	+	0.0737983i	−0.886543	−	0.462647i	$-0.846900\pi$
$103$	−0.432419	+	0.748971i	−0.0426075	+	0.0737983i	0.843935	+	0.536445i	$0.180233\pi$
$104$	2.51398	+	0.915015i	0.246516	+	0.0897246i
$105$		0			0
$106$	−5.01114	+	8.67956i	−0.486725	+	0.843033i
$107$	−2.80914	−	4.86557i	−0.271569	−	0.470372i	0.697694	−	0.716395i	$-0.254209\pi$
$107$	−2.80914	−	4.86557i	−0.271569	−	0.470372i	−0.969264	+	0.246023i	$0.920876\pi$
$108$		0			0
$109$	−6.07398	−	5.09667i	−0.581782	−	0.488173i	0.303750	−	0.952752i	$-0.401761\pi$
$109$	−6.07398	−	5.09667i	−0.581782	−	0.488173i	−0.885532	+	0.464579i	$0.846206\pi$
$110$	2.12062	−	1.77941i	0.202193	−	0.169660i
$111$		0			0
$112$	3.67112	−	1.33618i	0.346888	−	0.126257i
$113$	−9.28534			−0.873491			−0.436746	−	0.899585i	$-0.643869\pi$
$113$	−9.28534			−0.873491			−0.436746	+	0.899585i	$0.643869\pi$
$114$		0			0
$115$	−2.31315			−0.215702
$116$	−11.0904	+	4.03656i	−1.02971	+	0.374786i
$117$		0			0
$118$	12.1159	−	10.1664i	1.11536	−	0.935895i
$119$	−6.23989	−	5.23589i	−0.572009	−	0.479973i
$120$		0			0
$121$	3.81908	+	6.61484i	0.347189	+	0.601349i
$122$	−4.34752	+	7.53012i	−0.393606	+	0.681745i
$123$		0			0
$124$	6.20961	+	2.26011i	0.557639	+	0.202964i
$125$	−3.43075	+	5.94223i	−0.306856	+	0.531489i
$126$		0			0
$127$	3.31268	+	18.7871i	0.293953	+	1.66709i	0.671428	+	0.741070i	$0.265681\pi$
$127$	3.31268	+	18.7871i	0.293953	+	1.66709i	−0.377475	+	0.926020i	$0.623208\pi$
$128$	−4.37075	−	3.66750i	−0.386324	−	0.324164i
$129$		0			0
$130$	0.968626	−	5.49335i	0.0849541	−	0.481799i
$131$	7.04608	−	2.56456i	0.615619	−	0.224067i	−0.0153413	−	0.999882i	$-0.504883\pi$
$131$	7.04608	−	2.56456i	0.615619	−	0.224067i	0.630960	+	0.775815i	$0.282661\pi$
$132$		0			0
$133$	−2.23143	−	4.85911i	−0.193489	−	0.421338i
$134$	−15.6742			−1.35404
$135$		0			0
$136$	−0.834970	+	4.73535i	−0.0715981	+	0.406053i
$137$	9.13109	−	7.66190i	0.780122	−	0.654600i	−0.163157	−	0.986600i	$-0.552168\pi$
$137$	9.13109	−	7.66190i	0.780122	−	0.654600i	0.943279	+	0.332000i	$0.107723\pi$
$138$		0			0
$139$	1.75284	+	9.94085i	0.148674	+	0.843172i	0.964343	+	0.264654i	$0.0852577\pi$
$139$	1.75284	+	9.94085i	0.148674	+	0.843172i	−0.815669	+	0.578518i	$0.803631\pi$
$140$	1.04251	+	1.80568i	0.0881081	+	0.152608i
$141$		0			0
$142$	−29.0292	−	10.5657i	−2.43607	−	0.886658i
$143$	−6.36563	−	2.31690i	−0.532320	−	0.193749i
$144$		0			0
$145$	1.82042	+	3.15306i	0.151178	+	0.261848i
$146$	1.41264	+	8.01147i	0.116911	+	0.663034i
$147$		0			0
$148$	−13.3268	+	11.1825i	−1.09546	+	0.919198i
$149$	−0.911499	+	5.16937i	−0.0746729	+	0.423491i	0.924438	+	0.381332i	$0.124535\pi$
$149$	−0.911499	+	5.16937i	−0.0746729	+	0.423491i	−0.999111	+	0.0421589i	$0.986576\pi$
$150$		0			0
$151$	8.87258			0.722040			0.361020	−	0.932558i	$-0.382429\pi$
$151$	8.87258			0.722040			0.361020	+	0.932558i	$0.382429\pi$
$152$	−1.82546	+	2.57494i	−0.148065	+	0.208855i
$153$		0			0
$154$	4.40673	−	1.60392i	0.355104	−	0.129247i
$155$	0.353990	−	2.00757i	0.0284331	−	0.161252i
$156$		0			0
$157$	−14.3589	−	12.0486i	−1.14597	−	0.961579i	−0.146348	−	0.989233i	$-0.546752\pi$
$157$	−14.3589	−	12.0486i	−1.14597	−	0.961579i	−0.999618	+	0.0276539i	$0.991196\pi$
$158$	−2.75557	−	15.6276i	−0.219221	−	1.24326i
$159$		0			0
$160$	−2.92855	+	5.07239i	−0.231522	+	0.401008i
$161$	−3.68223	−	1.34022i	−0.290201	−	0.105624i
$162$		0			0
$163$	−11.2096	+	19.4156i	−0.878004	+	1.52075i	−0.0244765	+	0.999700i	$0.507792\pi$
$163$	−11.2096	+	19.4156i	−0.878004	+	1.52075i	−0.853528	+	0.521048i	$0.825541\pi$
$164$	11.8377	+	20.5035i	0.924371	+	1.60106i
$165$		0			0
$166$	−19.7934	−	16.6086i	−1.53626	−	1.28908i
$167$	2.21883	−	1.86182i	0.171698	−	0.144072i	−0.552889	−	0.833255i	$-0.686475\pi$
$167$	2.21883	−	1.86182i	0.171698	−	0.144072i	0.724587	+	0.689183i	$0.242030\pi$
$168$		0			0
$169$	−0.610815	+	0.222318i	−0.0469857	+	0.0171014i
$170$	10.0256			0.768928
$171$		0			0
$172$	−0.150644			−0.0114865
$173$	14.4390	−	5.25538i	1.09778	−	0.399559i	0.271283	−	0.962500i	$-0.412552\pi$
$173$	14.4390	−	5.25538i	1.09778	−	0.399559i	0.826498	+	0.562940i	$0.190330\pi$
$174$		0			0
$175$	−4.20574	+	3.52903i	−0.317924	+	0.266770i
$176$	4.47326	+	3.75351i	0.337184	+	0.282931i
$177$		0			0
$178$	14.1985	+	24.5925i	1.06422	+	1.84328i
$179$	11.4373	−	19.8099i	0.854861	−	1.48066i	−0.0219128	−	0.999760i	$-0.506976\pi$
$179$	11.4373	−	19.8099i	0.854861	−	1.48066i	0.876774	−	0.480903i	$-0.159691\pi$
$180$		0			0
$181$	−13.2369	−	4.81786i	−0.983895	−	0.358108i	−0.200541	−	0.979685i	$-0.564270\pi$
$181$	−13.2369	−	4.81786i	−0.983895	−	0.358108i	−0.783353	+	0.621577i	$0.786492\pi$
$182$	4.72474	−	8.18349i	0.350221	−	0.606601i
$183$		0			0
$184$	0.401674	+	2.27801i	0.0296118	+	0.167937i
$185$	4.11120	+	3.44970i	0.302261	+	0.253627i
$186$		0			0
$187$	2.11422	−	11.9903i	0.154607	−	0.876820i
$188$	−21.3309	+	7.76380i	−1.55571	+	0.566234i
$189$		0			0
$190$	5.94815	+	2.81602i	0.431524	+	0.204295i
$191$	23.4078			1.69373			0.846865	−	0.531807i	$-0.178487\pi$
$191$	23.4078			1.69373			0.846865	+	0.531807i	$0.178487\pi$
$192$		0			0
$193$	−3.85591	+	21.8680i	−0.277555	+	1.57409i	0.453173	+	0.891423i	$0.350292\pi$
$193$	−3.85591	+	21.8680i	−0.277555	+	1.57409i	−0.730728	+	0.682669i	$0.760819\pi$
$194$	−6.55827	+	5.50305i	−0.470857	+	0.395096i
$195$		0			0
$196$	−2.23989	−	12.7030i	−0.159992	−	0.907359i
$197$	−0.207814	−	0.359945i	−0.0148061	−	0.0256450i	0.858527	−	0.512768i	$-0.171380\pi$
$197$	−0.207814	−	0.359945i	−0.0148061	−	0.0256450i	−0.873334	+	0.487123i	$0.838046\pi$
$198$		0			0
$199$	14.7233	+	5.35883i	1.04371	+	0.379878i	0.806284	−	0.591529i	$-0.201475\pi$
$199$	14.7233	+	5.35883i	1.04371	+	0.379878i	0.237422	+	0.971407i	$0.423698\pi$
$200$	3.04545	+	1.10845i	0.215346	+	0.0783796i
$201$		0			0
$202$	−11.0988	−	19.2237i	−0.780908	−	1.35257i
$203$	1.07101	+	6.07401i	0.0751703	+	0.426312i
$204$		0			0
$205$	5.59492	−	4.69470i	0.390766	−	0.327892i
$206$	0.313123	−	1.77581i	0.0218163	−	0.123726i
$207$		0			0
$208$	11.7665			0.815861
$209$	4.62224	−	6.51997i	0.319727	−	0.450996i
$210$		0			0
$211$	12.7023	−	4.62327i	0.874465	−	0.318279i	0.134491	−	0.990915i	$-0.457060\pi$
$211$	12.7023	−	4.62327i	0.874465	−	0.318279i	0.739974	+	0.672636i	$0.234838\pi$
$212$	1.95928	−	11.1116i	0.134564	−	0.763148i
$213$		0			0
$214$	8.97359	+	7.52974i	0.613422	+	0.514722i
$215$	0.00806984	+	0.0457663i	0.000550358	+	0.00312124i
$216$		0			0
$217$	1.72668	−	2.99070i	0.117215	−	0.203022i
$218$	15.5351	+	5.65432i	1.05217	+	0.382959i
$219$		0			0
$220$	−1.55825	+	2.69896i	−0.105057	+	0.181964i
$221$	−12.2667	−	21.2465i	−0.825147	−	1.42920i
$222$		0			0
$223$	−5.99794	−	5.03287i	−0.401652	−	0.337026i	0.419480	−	0.907765i	$-0.362212\pi$
$223$	−5.99794	−	5.03287i	−0.401652	−	0.337026i	−0.821132	+	0.570739i	$0.806657\pi$
$224$	−7.60078	+	6.37781i	−0.507849	+	0.426136i
$225$		0			0
$226$	18.1925	−	6.62154i	1.21015	−	0.440458i
$227$	−19.1666			−1.27213			−0.636066	−	0.771635i	$-0.719439\pi$
$227$	−19.1666			−1.27213			−0.636066	+	0.771635i	$0.719439\pi$
$228$		0			0
$229$	−5.45336			−0.360368			−0.180184	−	0.983633i	$-0.557669\pi$
$229$	−5.45336			−0.360368			−0.180184	+	0.983633i	$0.557669\pi$
$230$	4.53209	−	1.64955i	0.298837	−	0.108768i
$231$		0			0
$232$	2.78905	−	2.34029i	0.183110	−	0.153648i
$233$	9.10786	+	7.64240i	0.596676	+	0.500670i	0.890375	−	0.455228i	$-0.150442\pi$
$233$	9.10786	+	7.64240i	0.596676	+	0.500670i	−0.293700	+	0.955898i	$0.594887\pi$
$234$		0			0
$235$	3.50134	+	6.06451i	0.228403	+	0.395605i
$236$	−8.90285	+	15.4202i	−0.579526	+	1.00377i
$237$		0			0
$238$	15.9595	+	5.80877i	1.03450	+	0.376526i
$239$	−14.7726	+	25.5869i	−0.955560	+	1.65508i	−0.222479	+	0.974937i	$0.571415\pi$
$239$	−14.7726	+	25.5869i	−0.955560	+	1.65508i	−0.733081	+	0.680141i	$0.761918\pi$
$240$		0			0
$241$	0.241230	+	1.36808i	0.0155390	+	0.0881258i	0.991591	−	0.129411i	$-0.0413088\pi$
$241$	0.241230	+	1.36808i	0.0155390	+	0.0881258i	−0.976052	+	0.217537i	$0.930198\pi$
$242$	−12.1998	−	10.2368i	−0.784232	−	0.658049i
$243$		0			0
$244$	1.69981	−	9.64009i	0.108819	−	0.617143i
$245$	−3.73924	+	1.36097i	−0.238891	+	0.0869493i
$246$		0			0
$247$	−1.30999	−	16.0510i	−0.0833529	−	1.02130i
$248$	−2.03854			−0.129448
$249$		0			0
$250$	2.48427	−	14.0890i	0.157119	−	0.891066i
$251$	−12.2354	+	10.2667i	−0.772291	+	0.648029i	−0.941294	−	0.337587i	$-0.890389\pi$
$251$	−12.2354	+	10.2667i	−0.772291	+	0.648029i	0.169004	+	0.985615i	$0.445945\pi$
$252$		0			0
$253$	−1.01707	−	5.76811i	−0.0639429	−	0.362638i
$254$	−19.8879	−	34.4469i	−1.24788	−	2.16139i
$255$		0			0
$256$	−8.54576	−	3.11040i	−0.534110	−	0.194400i
$257$	0.164144	+	0.0597437i	0.0102390	+	0.00372671i	0.347135	−	0.937815i	$-0.387155\pi$
$257$	0.164144	+	0.0597437i	0.0102390	+	0.00372671i	−0.336896	+	0.941542i	$0.609377\pi$
$258$		0			0
$259$	4.54576	+	7.87349i	0.282460	+	0.489235i
$260$	1.09047	+	6.18437i	0.0676282	+	0.383539i
$261$		0			0
$262$	−11.9764	+	10.0494i	−0.739902	+	0.620852i
$263$	−1.13975	+	6.46383i	−0.0702798	+	0.398577i	0.929293	+	0.369344i	$0.120418\pi$
$263$	−1.13975	+	6.46383i	−0.0702798	+	0.398577i	−0.999573	+	0.0292328i	$0.990694\pi$
$264$		0			0
$265$	−3.48070			−0.213818
$266$	7.83710	+	7.92906i	0.480523	+	0.486162i
$267$		0			0
$268$	16.5817	−	6.03525i	1.01289	−	0.368662i
$269$	−0.0873394	+	0.495326i	−0.00532518	+	0.0302006i	−0.987355	−	0.158527i	$-0.949325\pi$
$269$	−0.0873394	+	0.495326i	−0.00532518	+	0.0302006i	0.982029	+	0.188728i	$0.0604365\pi$
$270$		0			0
$271$	−4.85117	−	4.07061i	−0.294687	−	0.247272i	0.483442	−	0.875377i	$-0.339387\pi$
$271$	−4.85117	−	4.07061i	−0.294687	−	0.247272i	−0.778129	+	0.628105i	$0.783831\pi$
$272$	3.67233	+	20.8268i	0.222668	+	1.26281i
$273$		0			0
$274$	−12.4265	+	21.5233i	−0.750712	+	1.30027i
$275$	−7.71136	−	2.80671i	−0.465012	−	0.169251i
$276$		0			0
$277$	8.07444	−	13.9853i	0.485146	−	0.840298i	−0.514708	−	0.857366i	$-0.672100\pi$
$277$	8.07444	−	13.9853i	0.485146	−	0.840298i	0.999854	+	0.0170674i	$0.00543299\pi$
$278$	−10.5233	−	18.2269i	−0.631145	−	1.09318i
$279$		0			0
$280$	−0.492726	−	0.413446i	−0.0294460	−	0.0247081i
$281$	−9.25684	+	7.76741i	−0.552216	+	0.463365i	−0.875691	−	0.482872i	$-0.839594\pi$
$281$	−9.25684	+	7.76741i	−0.552216	+	0.463365i	0.323474	+	0.946237i	$0.395149\pi$
$282$		0			0
$283$	−7.41787	+	2.69988i	−0.440947	+	0.160491i	−0.552946	−	0.833217i	$-0.686497\pi$
$283$	−7.41787	+	2.69988i	−0.440947	+	0.160491i	0.112000	+	0.993708i	$0.464274\pi$
$284$	34.7782			2.06371
$285$		0			0
$286$	14.1242			0.835184
$287$	11.6265	−	4.23169i	0.686289	−	0.249789i
$288$		0			0
$289$	20.7554	−	17.4158i	1.22090	−	1.02446i
$290$	−5.81521	−	4.87954i	−0.341481	−	0.286537i
$291$		0			0
$292$	−4.57919	−	7.93139i	−0.267977	−	0.464150i
$293$	4.04429	−	7.00492i	0.236270	−	0.409232i	−0.723371	−	0.690460i	$-0.757408\pi$
$293$	4.04429	−	7.00492i	0.236270	−	0.409232i	0.959641	+	0.281228i	$0.0907417\pi$
$294$		0			0
$295$	5.16163	+	1.87868i	0.300522	+	0.109381i
$296$	2.68339	−	4.64777i	0.155969	−	0.270146i
$297$		0			0
$298$	−1.90049	−	10.7782i	−0.110093	−	0.624366i
$299$	−9.04095	−	7.58626i	−0.522852	−	0.438725i
$300$		0			0
$301$	−0.0136706	+	0.0775297i	−0.000787959	+	0.00446874i
$302$	−17.3838	+	6.32719i	−1.00033	+	0.364089i
$303$		0			0
$304$	−3.67112	+	13.3880i	−0.210553	+	0.767853i
$305$	−3.01975			−0.172911
$306$		0			0
$307$	0.737359	−	4.18177i	0.0420833	−	0.238666i	−0.956509	−	0.291702i	$-0.905779\pi$
$307$	0.737359	−	4.18177i	0.0420833	−	0.238666i	0.998593	+	0.0530355i	$0.0168896\pi$
$308$	−4.04429	+	3.39356i	−0.230445	+	0.193366i
$309$		0			0
$310$	0.738074	+	4.18583i	0.0419198	+	0.237739i
$311$	−6.36563	−	11.0256i	−0.360962	−	0.625204i	0.627158	−	0.778892i	$-0.284218\pi$
$311$	−6.36563	−	11.0256i	−0.360962	−	0.625204i	−0.988119	+	0.153688i	$0.950885\pi$
$312$		0			0
$313$	13.6348	+	4.96264i	0.770682	+	0.280505i	0.697282	−	0.716797i	$-0.254393\pi$
$313$	13.6348	+	4.96264i	0.770682	+	0.280505i	0.0734002	+	0.997303i	$0.476615\pi$
$314$	36.7251	+	13.3668i	2.07252	+	0.754334i
$315$		0			0
$316$	8.93242	+	15.4714i	0.502488	+	0.870334i
$317$	3.81078	+	21.6120i	0.214035	+	1.21385i	0.882574	+	0.470174i	$0.155809\pi$
$317$	3.81078	+	21.6120i	0.214035	+	1.21385i	−0.668539	+	0.743677i	$0.733080\pi$
$318$		0			0
$319$	−7.06212	+	5.92582i	−0.395403	+	0.331782i
$320$	1.31969	−	7.48435i	0.0737731	−	0.418388i
$321$		0			0
$322$	8.17024			0.455310
$323$	28.0016	−	7.32822i	1.55805	−	0.407753i
$324$		0			0
$325$	−15.5385	+	5.65555i	−0.861920	+	0.313713i
$326$	8.11709	−	46.0343i	0.449564	−	2.54960i
$327$		0			0
$328$	−5.59492	−	4.69470i	−0.308928	−	0.259221i
$329$	2.05995	+	11.6826i	0.113569	+	0.644081i
$330$		0			0
$331$	7.92855	−	13.7326i	0.435792	−	0.754815i	−0.561568	−	0.827431i	$-0.689802\pi$
$331$	7.92855	−	13.7326i	0.435792	−	0.754815i	0.997360	+	0.0726163i	$0.0231348\pi$
$332$	27.3344	+	9.94892i	1.50017	+	0.546018i
$333$		0			0
$334$	−3.01960	+	5.23010i	−0.165225	+	0.286178i
$335$	−2.72180	−	4.71429i	−0.148708	−	0.257569i
$336$		0			0
$337$	11.9802	+	10.0526i	0.652605	+	0.547601i	0.907860	−	0.419273i	$-0.137715\pi$
$337$	11.9802	+	10.0526i	0.652605	+	0.547601i	−0.255255	+	0.966874i	$0.582159\pi$
$338$	1.03821	−	0.871166i	0.0564714	−	0.0473852i
$339$		0			0
$340$	−10.6061	+	3.86029i	−0.575195	+	0.209354i
$341$	5.16178			0.279526
$342$		0			0
$343$	−15.3277			−0.827618
$344$	0.0436697	−	0.0158945i	0.00235451	−	0.000856973i
$345$		0			0
$346$	−24.5424	+	20.5935i	−1.31941	+	1.10711i
$347$	16.5705	+	13.9043i	0.889553	+	0.746424i	0.968120	−	0.250485i	$-0.0805902\pi$
$347$	16.5705	+	13.9043i	0.889553	+	0.746424i	−0.0785675	+	0.996909i	$0.525035\pi$
$348$		0			0
$349$	−7.77332	−	13.4638i	−0.416096	−	0.720700i	0.579447	−	0.815010i	$-0.303269\pi$
$349$	−7.77332	−	13.4638i	−0.416096	−	0.720700i	−0.995543	+	0.0943104i	$0.969935\pi$
$350$	5.72358	−	9.91353i	0.305938	−	0.529901i
$351$		0			0
$352$	−13.9363	−	5.07239i	−0.742807	−	0.270360i
$353$	−9.19273	+	15.9223i	−0.489280	+	0.847457i	−0.999924	−	0.0123348i	$-0.996074\pi$
$353$	−9.19273	+	15.9223i	−0.489280	+	0.847457i	0.510644	+	0.859792i	$0.329407\pi$
$354$		0			0
$355$	−1.86303	−	10.5657i	−0.0988792	−	0.560772i
$356$	−24.4897	−	20.5493i	−1.29795	−	1.08911i
$357$		0			0
$358$	−8.28194	+	46.9692i	−0.437714	+	2.48240i
$359$	−22.2913	+	8.11337i	−1.17649	+	0.428208i	−0.854961	−	0.518692i	$-0.826419\pi$
$359$	−22.2913	+	8.11337i	−1.17649	+	0.428208i	−0.321529	+	0.946900i	$0.604197\pi$
$360$		0			0
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$	29.3705			1.54368
$363$		0			0
$364$	−1.84730	+	10.4765i	−0.0968246	+	0.549120i
$365$	−2.16429	+	1.81605i	−0.113284	+	0.0950565i
$366$		0			0
$367$	−2.11216	−	11.9786i	−0.110254	−	0.625280i	−0.988991	−	0.147975i	$-0.952725\pi$
$367$	−2.11216	−	11.9786i	−0.110254	−	0.625280i	0.878737	−	0.477306i	$-0.158387\pi$
$368$	5.08680	+	8.81060i	0.265168	+	0.459284i
$369$		0			0
$370$	−10.5150	−	3.82715i	−0.546650	−	0.198964i
$371$	−5.54083	−	2.01670i	−0.287666	−	0.104702i
$372$		0			0
$373$	−2.59627	−	4.49687i	−0.134430	−	0.232839i	0.790950	−	0.611881i	$-0.209587\pi$
$373$	−2.59627	−	4.49687i	−0.134430	−	0.232839i	−0.925379	+	0.379042i	$0.876254\pi$
$374$	4.40818	+	25.0000i	0.227942	+	1.29272i
$375$		0			0
$376$	5.36437	−	4.50124i	0.276646	−	0.232134i
$377$	−3.22574	+	18.2941i	−0.166134	+	0.942192i
$378$		0			0
$379$	−32.7128			−1.68034			−0.840171	−	0.542322i	$-0.817545\pi$
$379$	−32.7128			−1.68034			−0.840171	+	0.542322i	$0.817545\pi$
$380$	−7.37683	−	0.688766i	−0.378423	−	0.0353330i
$381$		0			0
$382$	−45.8624	+	16.6925i	−2.34652	+	0.854064i
$383$	2.51398	−	14.2575i	0.128459	−	0.728524i	−0.850735	−	0.525595i	$-0.823843\pi$
$383$	2.51398	−	14.2575i	0.128459	−	0.728524i	0.979193	−	0.202929i	$-0.0650462\pi$
$384$		0			0
$385$	1.24763	+	1.04688i	0.0635849	+	0.0533541i
$386$	−8.03965	−	45.5951i	−0.409207	−	2.32073i
$387$		0			0
$388$	4.81908	−	8.34689i	0.244652	−	0.423749i
$389$	−27.4299	−	9.98365i	−1.39075	−	0.506191i	−0.465330	−	0.885137i	$-0.654064\pi$
$389$	−27.4299	−	9.98365i	−1.39075	−	0.506191i	−0.925419	+	0.378946i	$0.876287\pi$
$390$		0			0
$391$	10.6061	−	18.3702i	0.536372	−	0.929023i
$392$	1.98961	+	3.44610i	0.100490	+	0.174054i
$393$		0			0
$394$	0.663848	+	0.557035i	0.0334442	+	0.0280630i
$395$	4.22177	−	3.54249i	0.212420	−	0.178242i
$396$		0			0
$397$	−29.2246	+	10.6369i	−1.46674	+	0.533850i	−0.947214	−	0.320603i	$-0.896114\pi$
$397$	−29.2246	+	10.6369i	−1.46674	+	0.533850i	−0.519528	+	0.854453i	$0.673892\pi$
$398$	−32.6684			−1.63752
$399$		0			0
$400$	14.2540			0.712701
$401$	22.4555	−	8.17312i	1.12137	−	0.408146i	0.286219	−	0.958164i	$-0.407601\pi$
$401$	22.4555	−	8.17312i	1.12137	−	0.408146i	0.835153	+	0.550018i	$0.185379\pi$
$402$		0			0
$403$	7.96766	−	6.68566i	0.396898	−	0.333037i
$404$	19.1434	+	16.0632i	0.952417	+	0.799173i
$405$		0			0
$406$	−6.42989	−	11.1369i	−0.319110	−	0.552715i
$407$	−6.79459	+	11.7686i	−0.336795	+	0.583347i
$408$		0			0
$409$	21.6339	+	7.87409i	1.06973	+	0.389349i	0.816074	−	0.577947i	$-0.196146\pi$
$409$	21.6339	+	7.87409i	1.06973	+	0.389349i	0.253652	+	0.967296i	$0.418368\pi$
$410$	−7.61412	+	13.1880i	−0.376035	+	0.651311i
$411$		0			0
$412$	0.352511	+	1.99919i	0.0173670	+	0.0984930i
$413$	7.12815	+	5.98123i	0.350753	+	0.294317i
$414$		0			0
$415$	1.55825	−	8.83726i	0.0764914	−	0.433804i
$416$	−28.0818	+	10.2209i	−1.37682	+	0.501123i
$417$		0			0
$418$	−4.40673	+	16.0706i	−0.215540	+	0.786039i
$419$	−9.38882			−0.458674			−0.229337	−	0.973347i	$-0.573656\pi$
$419$	−9.38882			−0.458674			−0.229337	+	0.973347i	$0.573656\pi$
$420$		0			0
$421$	−3.51889	+	19.9566i	−0.171500	+	0.972625i	0.770607	+	0.637311i	$0.219953\pi$
$421$	−3.51889	+	19.9566i	−0.171500	+	0.972625i	−0.942107	+	0.335314i	$0.891158\pi$
$422$	−21.5904	+	18.1165i	−1.05101	+	0.881898i
$423$		0			0
$424$	0.604418	+	3.42782i	0.0293531	+	0.166470i
$425$	−14.8599	−	25.7382i	−0.720813	−	1.24848i
$426$		0			0
$427$	−4.80706	−	1.74963i	−0.232630	−	0.0846703i
$428$	−12.3924	−	4.51048i	−0.599011	−	0.218022i
$429$		0			0
$430$	−0.0484478	−	0.0839141i	−0.00233636	−	0.00404670i
$431$	−1.82300	−	10.3387i	−0.0878108	−	0.498000i	−0.996715	−	0.0809938i	$-0.974191\pi$
$431$	−1.82300	−	10.3387i	−0.0878108	−	0.498000i	0.908904	−	0.417006i	$-0.136921\pi$
$432$		0			0
$433$	9.56805	−	8.02855i	0.459811	−	0.385827i	−0.383250	−	0.923644i	$-0.625195\pi$
$433$	9.56805	−	8.02855i	0.459811	−	0.385827i	0.843061	+	0.537817i	$0.180751\pi$
$434$	−1.25032	+	7.09093i	−0.0600174	+	0.340376i
$435$		0			0
$436$	−18.6117			−0.891341
$437$	11.4524	−	7.91993i	0.547844	−	0.378862i
$438$		0			0
$439$	18.6805	−	6.79915i	0.891572	−	0.324506i	0.144702	−	0.989475i	$-0.453778\pi$
$439$	18.6805	−	6.79915i	0.891572	−	0.324506i	0.746870	+	0.664970i	$0.231556\pi$
$440$	0.166947	−	0.946804i	0.00795889	−	0.0451371i
$441$		0			0
$442$	39.1851	+	32.8802i	1.86385	+	1.56395i
$443$	3.98729	+	22.6130i	0.189442	+	1.07438i	0.920115	+	0.391649i	$0.128095\pi$
$443$	3.98729	+	22.6130i	0.189442	+	1.07438i	−0.730673	+	0.682728i	$0.760794\pi$
$444$		0			0
$445$	−4.93107	+	8.54087i	−0.233755	+	0.404876i
$446$	15.3406	+	5.58354i	0.726401	+	0.264388i
$447$		0			0
$448$	6.43717	−	11.1495i	0.304128	−	0.526764i
$449$	−4.19327	−	7.26296i	−0.197893	−	0.342760i	0.749952	−	0.661492i	$-0.230076\pi$
$449$	−4.19327	−	7.26296i	−0.197893	−	0.342760i	−0.947845	+	0.318732i	$0.896743\pi$
$450$		0			0
$451$	14.1668	+	11.8874i	0.667090	+	0.559755i
$452$	−16.6963	+	14.0098i	−0.785327	+	0.658967i
$453$		0			0
$454$	37.5526	−	13.6680i	1.76243	−	0.641473i
$455$	3.28177			0.153852
$456$		0			0
$457$	25.5885			1.19698			0.598490	−	0.801130i	$-0.295767\pi$
$457$	25.5885			1.19698			0.598490	+	0.801130i	$0.295767\pi$
$458$	10.6846	−	3.88889i	0.499260	−	0.181716i
$459$		0			0
$460$	−4.15935	+	3.49011i	−0.193931	+	0.162727i
$461$	−1.36090	−	1.14193i	−0.0633834	−	0.0531849i	0.610546	−	0.791981i	$-0.290950\pi$
$461$	−1.36090	−	1.14193i	−0.0633834	−	0.0531849i	−0.673929	+	0.738796i	$0.735395\pi$
$462$		0			0
$463$	−18.1668	−	31.4659i	−0.844285	−	1.46234i	−0.886241	−	0.463225i	$-0.846692\pi$
$463$	−18.1668	−	31.4659i	−0.844285	−	1.46234i	0.0419562	−	0.999119i	$-0.486641\pi$
$464$	8.00651	−	13.8677i	0.371693	−	0.643791i
$465$		0			0
$466$	−23.2947	−	8.47859i	−1.07911	−	0.392763i
$467$	−10.9879	+	19.0315i	−0.508458	+	0.880674i	0.491494	+	0.870881i	$0.336451\pi$
$467$	−10.9879	+	19.0315i	−0.508458	+	0.880674i	−0.999952	+	0.00979373i	$0.996883\pi$
$468$		0			0
$469$	−1.60132	−	9.08153i	−0.0739420	−	0.419346i
$470$	−11.1848	−	9.38517i	−0.515917	−	0.432905i
$471$		0			0
$472$	0.953830	−	5.40944i	0.0439036	−	0.248990i
$473$	−0.110576	+	0.0402462i	−0.00508427	+	0.00185052i
$474$		0			0
$475$	−1.58693	−	19.4443i	−0.0728135	−	0.892164i
$476$	−19.1201			−0.876369
$477$		0			0
$478$	10.6971	−	60.6664i	0.489275	−	2.77482i
$479$	31.7052	−	26.6038i	1.44865	−	1.21556i	0.515088	−	0.857138i	$-0.327759\pi$
$479$	31.7052	−	26.6038i	1.44865	−	1.21556i	0.933560	−	0.358422i	$-0.116685\pi$
$480$		0			0
$481$	4.75490	+	26.9664i	0.216805	+	1.22956i
$482$	−1.44824	−	2.50842i	−0.0659654	−	0.114255i
$483$		0			0
$484$	16.8478	+	6.13208i	0.765807	+	0.278731i
$485$	−2.79397	−	1.01692i	−0.126868	−	0.0461760i
$486$		0			0
$487$	17.8097	+	30.8474i	0.807037	+	1.39783i	0.914908	+	0.403663i	$0.132263\pi$
$487$	17.8097	+	30.8474i	0.807037	+	1.39783i	−0.107871	+	0.994165i	$0.534403\pi$
$488$	0.524375	+	2.97388i	0.0237373	+	0.134621i
$489$		0			0
$490$	6.35567	−	5.33304i	0.287120	−	0.240922i
$491$	2.00575	−	11.3752i	0.0905181	−	0.513354i	−0.905511	−	0.424323i	$-0.860512\pi$
$491$	2.00575	−	11.3752i	0.0905181	−	0.513354i	0.996029	−	0.0890305i	$-0.0283769\pi$
$492$		0			0
$493$	−33.3874			−1.50369
$494$	14.0129	+	30.5141i	0.630469	+	1.37290i
$495$		0			0
$496$	−8.42514	+	3.06650i	−0.378300	+	0.137690i
$497$	3.15603	−	17.8987i	0.141567	−	0.802868i
$498$		0			0
$499$	−13.5608	−	11.3788i	−0.607064	−	0.509387i	0.286644	−	0.958037i	$-0.407460\pi$
$499$	−13.5608	−	11.3788i	−0.607064	−	0.509387i	−0.893707	+	0.448650i	$0.851905\pi$
$500$	2.79677	+	15.8613i	0.125075	+	0.709338i
$501$		0			0
$502$	16.6511	−	28.8406i	0.743175	−	1.28722i
$503$	23.0003	+	8.37141i	1.02553	+	0.373263i	0.799378	−	0.600829i	$-0.205163\pi$
$503$	23.0003	+	8.37141i	1.02553	+	0.373263i	0.226153	+	0.974092i	$0.427385\pi$
$504$		0			0
$505$	3.85457	−	6.67631i	0.171526	−	0.297092i
$506$	6.10607	+	10.5760i	0.271448	+	0.470162i
$507$		0			0
$508$	34.3029	+	28.7836i	1.52195	+	1.27706i
$509$	5.22491	−	4.38422i	0.231590	−	0.194327i	−0.519607	−	0.854406i	$-0.673921\pi$
$509$	5.22491	−	4.38422i	0.231590	−	0.194327i	0.751197	+	0.660079i	$0.229477\pi$
$510$		0			0
$511$	−4.49747	+	1.63695i	−0.198957	+	0.0724143i
$512$	30.3728			1.34230
$513$		0			0
$514$	−0.364208			−0.0160645
$515$	0.588478	−	0.214188i	0.0259314	−	0.00943827i
$516$		0			0
$517$	−13.5831	+	11.3975i	−0.597382	+	0.501263i
$518$	−14.5211	−	12.1847i	−0.638021	−	0.535363i
$519$		0			0
$520$	−0.968626	−	1.67771i	−0.0424771	−	0.0735725i
$521$	10.2021	−	17.6706i	0.446962	−	0.774161i	−0.551224	−	0.834357i	$-0.685839\pi$
$521$	10.2021	−	17.6706i	0.446962	−	0.774161i	0.998187	+	0.0601956i	$0.0191725\pi$
$522$		0			0
$523$	−5.67112	−	2.06412i	−0.247981	−	0.0902576i	0.215039	−	0.976605i	$-0.431012\pi$
$523$	−5.67112	−	2.06412i	−0.247981	−	0.0902576i	−0.463020	+	0.886348i	$0.653234\pi$
$524$	8.80034	−	15.2426i	0.384445	−	0.665878i
$525$		0			0
$526$	−2.37639	−	13.4772i	−0.103616	−	0.587633i
$527$	14.3204	+	12.0162i	0.623806	+	0.523436i
$528$		0			0
$529$	−2.22193	+	12.6012i	−0.0966058	+	0.547879i
$530$	6.81966	−	2.48215i	0.296227	−	0.107818i
$531$		0			0
$532$	−11.3439	−	5.37051i	−0.491820	−	0.232841i
$533$	37.2646			1.61411
$534$		0			0
$535$	−0.706452	+	4.00649i	−0.0305426	+	0.173216i
$536$	−4.17003	+	3.49907i	−0.180118	+	0.151137i
$537$		0			0
$538$	−0.182104	−	1.03276i	−0.00785107	−	0.0445256i
$539$	−5.03786	−	8.72584i	−0.216996	−	0.375848i
$540$		0			0
$541$	26.7567	+	9.73865i	1.15036	+	0.418697i	0.845645	−	0.533746i	$-0.179216\pi$
$541$	26.7567	+	9.73865i	1.15036	+	0.418697i	0.304716	+	0.952443i	$0.401438\pi$
$542$	12.4076	+	4.51600i	0.532952	+	0.193979i
$543$		0			0
$544$	−26.8555	−	46.5151i	−1.15142	−	1.99432i
$545$	0.997010	+	5.65432i	0.0427072	+	0.242205i
$546$		0			0
$547$	16.9834	−	14.2508i	0.726157	−	0.609318i	−0.202924	−	0.979195i	$-0.565044\pi$
$547$	16.9834	−	14.2508i	0.726157	−	0.609318i	0.929081	+	0.369876i	$0.120600\pi$
$548$	4.85855	−	27.5542i	0.207547	−	1.17706i
$549$		0			0
$550$	17.1102			0.729581
$551$	−19.8086	−	9.37796i	−0.843876	−	0.399514i
$552$		0			0
$553$	8.77301	−	3.19312i	0.373066	−	0.135785i
$554$	−5.84686	+	33.1592i	−0.248409	+	1.40880i
$555$		0			0
$556$	18.1507	+	15.2303i	0.769762	+	0.645907i
$557$	−2.34704	−	13.3107i	−0.0994471	−	0.563992i	−0.993294	−	0.115619i	$-0.963115\pi$
$557$	−2.34704	−	13.3107i	−0.0994471	−	0.563992i	0.893847	−	0.448373i	$-0.147996\pi$
$558$		0			0
$559$	−0.118555	+	0.205344i	−0.00501436	+	0.00868512i
$560$	−2.65833	−	0.967552i	−0.112335	−	0.0408866i
$561$		0			0
$562$	12.5976	−	21.8197i	0.531398	−	0.920409i
$563$	−8.53798	−	14.7882i	−0.359833	−	0.623249i	0.628100	−	0.778133i	$-0.283833\pi$
$563$	−8.53798	−	14.7882i	−0.359833	−	0.623249i	−0.987933	+	0.154884i	$0.950500\pi$
$564$		0			0
$565$	5.15064	+	4.32190i	0.216689	+	0.181824i
$566$	12.6083	−	10.5796i	0.529967	−	0.444695i
$567$		0			0
$568$	−10.0817	+	3.66945i	−0.423020	+	0.153967i
$569$	−0.262018			−0.0109844			−0.00549219	−	0.999985i	$-0.501748\pi$
$569$	−0.262018			−0.0109844			−0.00549219	+	0.999985i	$0.501748\pi$
$570$		0			0
$571$	−29.2253			−1.22304			−0.611519	−	0.791229i	$-0.709441\pi$
$571$	−29.2253			−1.22304			−0.611519	+	0.791229i	$0.709441\pi$
$572$	−14.9420	+	5.43845i	−0.624757	+	0.227393i
$573$		0			0
$574$	−19.7618	+	16.5821i	−0.824840	+	0.692123i
$575$	−10.9523	−	9.19004i	−0.456741	−	0.383251i
$576$		0			0
$577$	14.6288	+	25.3379i	0.609006	+	1.05483i	0.991405	+	0.130832i	$0.0417647\pi$
$577$	14.6288	+	25.3379i	0.609006	+	1.05483i	−0.382399	+	0.923997i	$0.624902\pi$
$578$	−28.2459	+	48.9234i	−1.17488	+	2.03495i
$579$		0			0
$580$	8.03074	+	2.92295i	0.333459	+	0.121369i
$581$	7.60078	−	13.1649i	0.315334	−	0.546174i
$582$		0			0
$583$	−1.53044	−	8.67956i	−0.0633843	−	0.359471i
$584$	2.16429	+	1.81605i	0.0895588	+	0.0751488i
$585$		0			0
$586$	−2.92855	+	16.6086i	−0.120977	+	0.686096i
$587$	32.5987	−	11.8650i	1.34549	−	0.489720i	0.433955	−	0.900935i	$-0.357118\pi$
$587$	32.5987	−	11.8650i	1.34549	−	0.489720i	0.911538	+	0.411215i	$0.134895\pi$
$588$		0			0
$589$	5.12108	+	11.1515i	0.211010	+	0.459491i
$590$	−11.4528			−0.471503
$591$		0			0
$592$	4.09879	−	23.2454i	0.168459	−	0.955380i
$593$	−33.5743	+	28.1722i	−1.37873	+	1.15689i	−0.409054	+	0.912510i	$0.634141\pi$
$593$	−33.5743	+	28.1722i	−1.37873	+	1.15689i	−0.969679	+	0.244384i	$0.921414\pi$
$594$		0			0
$595$	1.02424	+	5.80877i	0.0419898	+	0.238136i
$596$	6.16062	+	10.6705i	0.252349	+	0.437081i
$597$		0			0
$598$	23.1236	+	8.41630i	0.945595	+	0.344168i
$599$	9.59846	+	3.49355i	0.392182	+	0.142743i	0.530582	−	0.847634i	$-0.321973\pi$
$599$	9.59846	+	3.49355i	0.392182	+	0.142743i	−0.138399	+	0.990377i	$0.544196\pi$
$600$		0			0
$601$	4.99138	+	8.64533i	0.203603	+	0.352650i	0.949687	−	0.313202i	$-0.101402\pi$
$601$	4.99138	+	8.64533i	0.203603	+	0.352650i	−0.746084	+	0.665852i	$0.768068\pi$
$602$	−0.0285034	−	0.161651i	−0.00116171	−	0.00658839i
$603$		0			0
$604$	15.9541	−	13.3871i	0.649162	−	0.544712i
$605$	0.960436	−	5.44691i	0.0390473	−	0.221448i
$606$		0			0
$607$	3.25166			0.131981			0.0659904	−	0.997820i	$-0.478979\pi$
$607$	3.25166			0.131981			0.0659904	+	0.997820i	$0.478979\pi$
$608$	−2.86797	−	35.1405i	−0.116312	−	1.42513i
$609$		0			0
$610$	5.91653	−	2.15344i	0.239553	−	0.0871902i
$611$	−6.20429	+	35.1862i	−0.250999	+	1.42348i
$612$		0			0
$613$	−11.2424	−	9.43350i	−0.454077	−	0.381016i	0.386869	−	0.922135i	$-0.373556\pi$
$613$	−11.2424	−	9.43350i	−0.454077	−	0.381016i	−0.840946	+	0.541119i	$0.818001\pi$
$614$	1.53741	+	8.71906i	0.0620447	+	0.351873i
$615$		0			0
$616$	0.814330	−	1.41046i	0.0328103	−	0.0568291i
$617$	−8.03502	−	2.92451i	−0.323478	−	0.117736i	0.175177	−	0.984537i	$-0.443950\pi$
$617$	−8.03502	−	2.92451i	−0.323478	−	0.117736i	−0.498655	+	0.866801i	$0.666172\pi$
$618$		0			0
$619$	−17.0069	+	29.4568i	−0.683564	+	1.18397i	0.290322	+	0.956929i	$0.406237\pi$
$619$	−17.0069	+	29.4568i	−0.683564	+	1.18397i	−0.973886	+	0.227038i	$0.927096\pi$
$620$	−2.39253	−	4.14399i	−0.0960865	−	0.166427i
$621$		0			0
$622$	20.3346	+	17.0627i	0.815342	+	0.684153i
$623$	−12.7982	+	10.7389i	−0.512747	+	0.430246i
$624$		0			0
$625$	−16.3598	+	5.95447i	−0.654391	+	0.238179i
$626$	−30.2532			−1.20916
$627$		0			0
$628$	−43.9982			−1.75572
$629$	−46.2467	+	16.8324i	−1.84398	+	0.671153i
$630$		0			0
$631$	−7.41329	+	6.22048i	−0.295118	+	0.247634i	−0.778309	−	0.627882i	$-0.783922\pi$
$631$	−7.41329	+	6.22048i	−0.295118	+	0.247634i	0.483191	+	0.875515i	$0.339478\pi$
$632$	−4.22177	−	3.54249i	−0.167933	−	0.140913i
$633$		0			0
$634$	−22.8783	−	39.6263i	−0.908612	−	1.57376i
$635$	6.90700	−	11.9633i	0.274096	−	0.474748i
$636$		0			0
$637$	−19.0783	−	6.94394i	−0.755910	−	0.275129i
$638$	9.61082	−	16.6464i	0.380496	−	0.659039i
$639$		0			0
$640$	0.717435	+	4.06877i	0.0283591	+	0.160832i
$641$	2.22312	+	1.86542i	0.0878081	+	0.0736797i	0.685635	−	0.727945i	$-0.259525\pi$
$641$	2.22312	+	1.86542i	0.0878081	+	0.0736797i	−0.597827	+	0.801625i	$0.703969\pi$
$642$		0			0
$643$	4.91194	−	27.8570i	0.193708	−	1.09857i	−0.720539	−	0.693415i	$-0.756105\pi$
$643$	4.91194	−	27.8570i	0.193708	−	1.09857i	0.914247	−	0.405158i	$-0.132784\pi$
$644$	−8.64329	+	3.14590i	−0.340593	+	0.123966i
$645$		0			0
$646$	−49.6369	+	34.3264i	−1.95294	+	1.35055i
$647$	−37.0738			−1.45752			−0.728761	−	0.684768i	$-0.759903\pi$
$647$	−37.0738			−1.45752			−0.728761	+	0.684768i	$0.759903\pi$
$648$		0			0
$649$	−2.41518	+	13.6972i	−0.0948042	+	0.537661i
$650$	26.4111	−	22.1615i	1.03593	−	0.869247i
$651$		0			0
$652$	9.13816	+	51.8251i	0.357878	+	2.02963i
$653$	17.7511	+	30.7459i	0.694656	+	1.20318i	0.970296	+	0.241919i	$0.0777768\pi$
$653$	17.7511	+	30.7459i	0.694656	+	1.20318i	−0.275640	+	0.961261i	$0.588890\pi$
$654$		0			0
$655$	−5.10220	−	1.85705i	−0.199359	−	0.0725609i
$656$	−30.1854	−	10.9866i	−1.17854	−	0.428954i
$657$		0			0
$658$	−12.3671	−	21.4204i	−0.482118	−	0.835053i
$659$	−0.734653	−	4.16643i	−0.0286180	−	0.162301i	0.967150	−	0.254208i	$-0.0818148\pi$
$659$	−0.734653	−	4.16643i	−0.0286180	−	0.162301i	−0.995768	+	0.0919072i	$0.970704\pi$
$660$		0			0
$661$	19.5633	−	16.4156i	0.760924	−	0.638491i	−0.177443	−	0.984131i	$-0.556783\pi$
$661$	19.5633	−	16.4156i	0.760924	−	0.638491i	0.938367	+	0.345640i	$0.112338\pi$
$662$	−5.74121	+	32.5600i	−0.223139	+	1.26548i
$663$		0			0
$664$	−8.97359			−0.348243
$665$	−1.02390	+	3.73401i	−0.0397053	+	0.144799i
$666$		0			0
$667$	−15.0929	+	5.49335i	−0.584398	+	0.212703i
$668$	1.18061	−	6.69560i	0.0456793	−	0.259060i
$669$		0			0
$670$	8.69459	+	7.29563i	0.335901	+	0.281855i
$671$	−1.32776	−	7.53012i	−0.0512577	−	0.290697i
$672$		0			0
$673$	−10.6887	+	18.5133i	−0.412018	+	0.713636i	−0.995110	−	0.0987702i	$-0.968509\pi$
$673$	−10.6887	+	18.5133i	−0.412018	+	0.713636i	0.583093	+	0.812406i	$0.301842\pi$
$674$	−30.6413	−	11.1525i	−1.18026	−	0.429579i
$675$		0			0
$676$	−0.762889	+	1.32136i	−0.0293419	+	0.0508217i
$677$	17.4257	+	30.1821i	0.669723	+	1.15999i	0.977982	+	0.208691i	$0.0669203\pi$
$677$	17.4257	+	30.1821i	0.669723	+	1.15999i	−0.308259	+	0.951302i	$0.599746\pi$
$678$		0			0
$679$	−3.85844	−	3.23762i	−0.148073	−	0.124248i
$680$	2.66725	−	2.23809i	0.102285	−	0.0858269i
$681$		0			0
$682$	−10.1133	+	3.68096i	−0.387260	+	0.140951i
$683$	−10.8977			−0.416990			−0.208495	−	0.978023i	$-0.566856\pi$
$683$	−10.8977			−0.416990			−0.208495	+	0.978023i	$0.566856\pi$
$684$		0			0
$685$	−8.63135			−0.329787
$686$	30.0312	−	10.9305i	1.14660	−	0.417327i
$687$		0			0
$688$	0.156574	−	0.131381i	0.00596933	−	0.00500886i
$689$	−13.6044	−	11.4154i	−0.518284	−	0.434892i
$690$		0			0
$691$	−4.09627	−	7.09494i	−0.155829	−	0.269904i	0.777531	−	0.628844i	$-0.216472\pi$
$691$	−4.09627	−	7.09494i	−0.155829	−	0.269904i	−0.933361	+	0.358940i	$0.883138\pi$
$692$	18.0339	−	31.2357i	0.685547	−	1.18740i
$693$		0			0
$694$	−42.3817	−	15.4257i	−1.60879	−	0.585550i
$695$	3.65470	−	6.33013i	0.138631	−	0.240116i
$696$		0			0
$697$	11.6303	+	65.9588i	0.440529	+	2.49837i
$698$	24.8313	+	20.8360i	0.939880	+	0.788653i
$699$		0			0
$700$	−2.23783	+	12.6913i	−0.0845819	+	0.479688i
$701$	11.0653	−	4.02744i	0.417931	−	0.152114i	−0.124491	−	0.992221i	$-0.539730\pi$
$701$	11.0653	−	4.02744i	0.417931	−	0.152114i	0.542422	+	0.840106i	$0.317508\pi$
$702$		0			0
$703$	−32.1660	−	3.00330i	−1.21316	−	0.113272i
$704$	19.2434			0.725263
$705$		0			0
$706$	6.65663	−	37.7516i	0.250526	−	1.42080i
$707$	10.0042	−	8.39451i	0.376246	−	0.315708i
$708$		0			0
$709$	4.50908	+	25.5723i	0.169342	+	0.960388i	0.944474	+	0.328587i	$0.106573\pi$
$709$	4.50908	+	25.5723i	0.169342	+	0.960388i	−0.775131	+	0.631800i	$0.782316\pi$
$710$	11.1848	+	19.3726i	0.419758	+	0.727043i
$711$		0			0
$712$	9.26739	+	3.37305i	0.347310	+	0.126411i
$713$	8.45064	+	3.07578i	0.316479	+	0.115189i
$714$		0			0
$715$	2.45265	+	4.24811i	0.0917238	+	0.158870i
$716$	−9.32374	−	52.8776i	−0.348445	−	1.97613i
$717$		0			0
$718$	37.8890	−	31.7927i	1.41401	−	1.18649i
$719$	−2.80387	+	15.9015i	−0.104567	+	0.593027i	0.886826	+	0.462104i	$0.152905\pi$
$719$	−2.80387	+	15.9015i	−0.104567	+	0.593027i	−0.991393	+	0.130923i	$0.958206\pi$
$720$		0			0
$721$	1.06088			0.0395092
$722$	−39.0911	+	6.42358i	−1.45482	+	0.239061i
$723$		0			0
$724$	−31.0710	+	11.3089i	−1.15475	+	0.420293i
$725$	−3.90768	+	22.1615i	−0.145128	+	0.823059i
$726$		0			0
$727$	−1.22075	−	1.02433i	−0.0452752	−	0.0379904i	0.619869	−	0.784705i	$-0.287186\pi$
$727$	−1.22075	−	1.02433i	−0.0452752	−	0.0379904i	−0.665144	+	0.746715i	$0.731630\pi$
$728$	−0.569874	−	3.23191i	−0.0211209	−	0.119783i
$729$		0			0
$730$	2.94537	−	5.10154i	0.109013	−	0.188816i
$731$	−0.400462	−	0.145756i	−0.0148116	−	0.00539099i
$732$		0			0
$733$	−5.99154	+	10.3777i	−0.221303	+	0.383308i	−0.955204	−	0.295949i	$-0.904364\pi$
$733$	−5.99154	+	10.3777i	−0.221303	+	0.383308i	0.733901	+	0.679256i	$0.237698\pi$
$734$	12.6805	+	21.9632i	0.468045	+	0.810678i
$735$		0			0
$736$	−19.7934	−	16.6086i	−0.729594	−	0.612202i
$737$	10.5589	−	8.85997i	0.388942	−	0.326361i
$738$		0			0
$739$	31.3387	−	11.4064i	1.15281	−	0.419590i	0.306289	−	0.951939i	$-0.400913\pi$
$739$	31.3387	−	11.4064i	1.15281	−	0.419590i	0.846525	+	0.532349i	$0.178690\pi$
$740$	12.5974			0.463091
$741$		0			0
$742$	12.2942			0.451333
$743$	8.18399	−	2.97873i	0.300242	−	0.109279i	−0.187507	−	0.982263i	$-0.560041\pi$
$743$	8.18399	−	2.97873i	0.300242	−	0.109279i	0.487748	+	0.872984i	$0.337818\pi$
$744$		0			0
$745$	2.91172	−	2.44323i	0.106677	−	0.0895128i
$746$	8.29360	+	6.95915i	0.303650	+	0.254793i
$747$		0			0
$748$	−14.2895	−	24.7502i	−0.522476	−	0.904956i
$749$	−3.44592	+	5.96850i	−0.125911	+	0.218084i
$750$		0			0
$751$	17.7233	+	6.45075i	0.646732	+	0.235391i	0.644497	−	0.764606i	$-0.277067\pi$
$751$	17.7233	+	6.45075i	0.646732	+	0.235391i	0.00223414	+	0.999998i	$0.499289\pi$
$752$	15.3995	−	26.6727i	0.561561	−	0.972653i
$753$		0			0
$754$	−6.72572	−	38.1434i	−0.244936	−	1.38910i
$755$	−4.92168	−	4.12978i	−0.179118	−	0.150298i
$756$		0			0
$757$	1.74123	−	9.87500i	0.0632861	−	0.358913i	−0.936676	−	0.350197i	$-0.886115\pi$
$757$	1.74123	−	9.87500i	0.0632861	−	0.358913i	0.999962	−	0.00871579i	$-0.00277436\pi$
$758$	64.0933	−	23.3281i	2.32797	−	0.847313i
$759$		0			0
$760$	2.21111	−	0.578665i	0.0802055	−	0.0209904i
$761$	−10.0398			−0.363942			−0.181971	−	0.983304i	$-0.558248\pi$
$761$	−10.0398			−0.363942			−0.181971	+	0.983304i	$0.558248\pi$
$762$		0			0
$763$	−1.68897	+	9.57861i	−0.0611447	+	0.346769i
$764$	42.0904	−	35.3180i	1.52278	−	1.27776i
$765$		0			0
$766$	5.24170	+	29.7271i	0.189390	+	1.07409i
$767$	14.0129	+	24.2710i	0.505976	+	0.876376i
$768$		0			0
$769$	37.6930	+	13.7191i	1.35924	+	0.494724i	0.915821	−	0.401588i	$-0.131541\pi$
$769$	37.6930	+	13.7191i	1.35924	+	0.494724i	0.443424	+	0.896312i	$0.353764\pi$
$770$	−3.19099	−	1.16143i	−0.114995	−	0.0418549i
$771$		0			0
$772$	26.0612	+	45.1394i	0.937965	+	1.62460i
$773$	−7.00767	−	39.7425i	−0.252048	−	1.42944i	−0.803537	−	0.595255i	$-0.797051\pi$
$773$	−7.00767	−	39.7425i	−0.252048	−	1.42944i	0.551488	−	0.834183i	$-0.314060\pi$
$774$		0			0
$775$	9.65207	−	8.09905i	0.346713	−	0.290927i
$776$	−0.516305	+	2.92811i	−0.0185343	+	0.105113i
$777$		0			0
$778$	60.8621			2.18201
$779$	−11.6265	+	42.3998i	−0.416562	+	1.51913i
$780$		0			0
$781$	25.5278	−	9.29136i	0.913457	−	0.332471i
$782$	−7.68005	+	43.5557i	−0.274638	+	1.55755i
$783$		0			0
$784$	13.4067	+	11.2496i	0.478812	+	0.401771i
$785$	2.35693	+	13.3668i	0.0841226	+	0.477083i
$786$		0			0
$787$	24.4183	−	42.2938i	0.870420	−	1.50761i	0.00885659	−	0.999961i	$-0.497181\pi$
$787$	24.4183	−	42.2938i	0.870420	−	1.50761i	0.861563	−	0.507650i	$-0.169486\pi$
$788$	−0.916767	−	0.333676i	−0.0326585	−	0.0118867i
$789$		0			0
$790$	−5.74540	+	9.95133i	−0.204412	+	0.354053i
$791$	5.69508	+	9.86416i	0.202494	+	0.350729i
$792$		0			0
$793$	−11.8027	−	9.90366i	−0.419127	−	0.351689i
$794$	49.6737	−	41.6812i	1.76285	−	1.47921i
$795$		0			0
$796$	34.5599	−	12.5788i	1.22494	−	0.445843i
$797$	−12.7171			−0.450461			−0.225231	−	0.974305i	$-0.572314\pi$
$797$	−12.7171			−0.450461			−0.225231	+	0.974305i	$0.572314\pi$
$798$		0			0
$799$	−64.2164			−2.27181
$800$	−34.0185	+	12.3817i	−1.20273	+	0.437759i
$801$		0			0
$802$	−38.1680	+	32.0268i	−1.34776	+	1.13090i
$803$	−5.48017	−	4.59841i	−0.193391	−	0.162274i
$804$		0			0
$805$	1.41875	+	2.45734i	0.0500043	+	0.0866100i
$806$	−10.8432	+	18.7809i	−0.381935	+	0.661530i
$807$		0			0
$808$	−7.24422	−	2.63668i	−0.254851	−	0.0927581i
$809$	5.52567	−	9.57073i	0.194272	−	0.336489i	−0.752390	−	0.658718i	$-0.771099\pi$
$809$	5.52567	−	9.57073i	0.194272	−	0.336489i	0.946662	+	0.322229i	$0.104432\pi$
$810$		0			0
$811$	1.94238	+	11.0158i	0.0682062	+	0.386817i	0.999732	+	0.0231419i	$0.00736695\pi$
$811$	1.94238	+	11.0158i	0.0682062	+	0.386817i	−0.931526	+	0.363675i	$0.881522\pi$
$812$	11.0904	+	9.30592i	0.389196	+	0.326574i
$813$		0			0
$814$	4.92009	−	27.9032i	0.172449	−	0.978008i
$815$	15.2551	−	5.55242i	0.534364	−	0.194493i
$816$		0			0
$817$	−0.196652	−	0.198960i	−0.00687999	−	0.00696071i
$818$	−48.0019			−1.67835
$819$		0			0
$820$	2.97700	−	16.8834i	0.103961	−	0.589593i
$821$	1.06294	−	0.891914i	0.0370969	−	0.0311280i	−0.624051	−	0.781384i	$-0.714514\pi$
$821$	1.06294	−	0.891914i	0.0370969	−	0.0311280i	0.661148	+	0.750256i	$0.270070\pi$
$822$		0			0
$823$	1.76904	+	10.0327i	0.0616648	+	0.349718i	0.999992	+	0.00397014i	$0.00126374\pi$
$823$	1.76904	+	10.0327i	0.0616648	+	0.349718i	−0.938327	+	0.345748i	$0.887625\pi$
$824$	−0.313123	−	0.542344i	−0.0109081	−	0.0188935i
$825$		0			0
$826$	−18.2313	−	6.63566i	−0.634349	−	0.230884i
$827$	−22.6044	−	8.22734i	−0.786033	−	0.286093i	−0.0823471	−	0.996604i	$-0.526242\pi$
$827$	−22.6044	−	8.22734i	−0.786033	−	0.286093i	−0.703686	+	0.710511i	$0.748464\pi$
$828$		0			0
$829$	−23.2212	−	40.2203i	−0.806506	−	1.39691i	−0.915269	−	0.402842i	$-0.868022\pi$
$829$	−23.2212	−	40.2203i	−0.806506	−	1.39691i	0.108763	−	0.994068i	$-0.465311\pi$
$830$	3.24897	+	18.4258i	0.112774	+	0.639570i
$831$		0			0
$832$	29.7039	−	24.9245i	1.02980	−	0.864103i
$833$	6.33649	−	35.9360i	0.219546	−	1.24511i
$834$		0			0
$835$	−2.09739			−0.0725833
$836$	−1.52602	−	18.6979i	−0.0527784	−	0.646679i
$837$		0			0
$838$	18.3953	−	6.69533i	0.635454	−	0.231286i
$839$	1.57678	−	8.94238i	0.0544366	−	0.308725i	−0.945417	−	0.325864i	$-0.894345\pi$
$839$	1.57678	−	8.94238i	0.0544366	−	0.308725i	0.999853	+	0.0171392i	$0.00545585\pi$
$840$		0			0
$841$	−2.84936	−	2.39089i	−0.0982536	−	0.0824446i
$842$	−7.33694	−	41.6098i	−0.252848	−	1.43397i
$843$		0			0
$844$	15.8648	−	27.4787i	0.546090	−	0.945856i
$845$	0.442302	+	0.160985i	0.0152157	+	0.00553805i
$846$		0			0
$847$	4.68479	−	8.11430i	0.160971	−	0.278811i
$848$	7.65435	+	13.2577i	0.262852	+	0.455272i
$849$		0			0
$850$	47.4691	+	39.8313i	1.62818	+	1.36620i
$851$	−18.1364	+	15.2183i	−0.621709	+	0.521676i
$852$		0			0
$853$	−35.0001	+	12.7390i	−1.19838	+	0.436174i	−0.862658	−	0.505787i	$-0.831202\pi$
$853$	−35.0001	+	12.7390i	−1.19838	+	0.436174i	−0.335721	+	0.941962i	$0.608980\pi$
$854$	10.6660			0.364984
$855$		0			0
$856$	4.06830			0.139052
$857$	−19.9362	+	7.25619i	−0.681008	+	0.247867i	−0.659280	−	0.751897i	$-0.729139\pi$
$857$	−19.9362	+	7.25619i	−0.681008	+	0.247867i	−0.0217277	+	0.999764i	$0.506917\pi$
$858$		0			0
$859$	5.86618	−	4.92231i	0.200152	−	0.167947i	−0.537203	−	0.843453i	$-0.680519\pi$
$859$	5.86618	−	4.92231i	0.200152	−	0.167947i	0.737355	+	0.675506i	$0.236075\pi$
$860$	0.0835635	+	0.0701181i	0.00284949	+	0.00239101i
$861$		0			0
$862$	10.9445	+	18.9564i	0.372771	+	0.645658i
$863$	−16.8477	+	29.1811i	−0.573503	+	0.993336i	0.422699	+	0.906270i	$0.361083\pi$
$863$	−16.8477	+	29.1811i	−0.573503	+	0.993336i	−0.996203	+	0.0870665i	$0.972251\pi$
$864$		0			0
$865$	−10.4556	−	3.80552i	−0.355501	−	0.129392i
$866$	−13.0211	+	22.5533i	−0.442476	+	0.766392i
$867$		0			0
$868$	−1.40760	−	7.98292i	−0.0477772	−	0.270958i
$869$	10.6899	+	8.96990i	0.362630	+	0.304283i
$870$		0			0
$871$	4.82295	−	27.3523i	0.163419	−	0.926797i
$872$	5.39529	−	1.96373i	0.182708	−	0.0665001i
$873$		0			0
$874$	−16.7906	+	23.6843i	−0.567951	+	0.801132i
$875$	8.41687			0.284542
$876$		0			0
$877$	0.917242	−	5.20194i	0.0309731	−	0.175657i	−0.965397	−	0.260785i	$-0.916019\pi$
$877$	0.917242	−	5.20194i	0.0309731	−	0.175657i	0.996370	+	0.0851278i	$0.0271298\pi$
$878$	−31.7517	+	26.6428i	−1.07157	+	0.899151i
$879$		0			0
$880$	−0.734260	−	4.16420i	−0.0247519	−	0.140375i
$881$	25.3903	+	43.9773i	0.855422	+	1.48163i	0.876253	+	0.481852i	$0.160036\pi$
$881$	25.3903	+	43.9773i	0.855422	+	1.48163i	−0.0208308	+	0.999783i	$0.506631\pi$
$882$		0			0
$883$	9.18897	+	3.34451i	0.309233	+	0.112552i	0.491975	−	0.870609i	$-0.336275\pi$
$883$	9.18897	+	3.34451i	0.309233	+	0.112552i	−0.182742	+	0.983161i	$0.558497\pi$
$884$	−54.1142	−	19.6960i	−1.82006	−	0.662447i
$885$		0			0
$886$	−23.9379	−	41.4617i	−0.804211	−	1.39293i
$887$	−3.61813	−	20.5194i	−0.121485	−	0.688975i	−0.983334	−	0.181810i	$-0.941804\pi$
$887$	−3.61813	−	20.5194i	−0.121485	−	0.688975i	0.861849	−	0.507165i	$-0.169307\pi$
$888$		0			0
$889$	17.9265	−	15.0421i	0.601235	−	0.504496i
$890$	3.57068	−	20.2504i	0.119690	−	0.678793i
$891$		0			0
$892$	−18.3788			−0.615366
$893$	−38.0993	−	18.0373i	−1.27495	−	0.603595i
$894$		0			0
$895$	−15.5649	+	5.66518i	−0.520279	+	0.189366i
$896$	−1.21536	+	6.89264i	−0.0406023	+	0.230267i
$897$		0			0
$898$	13.3951	+	11.2398i	0.447001	+	0.375078i
$899$	−2.45795	−	13.9397i	−0.0819772	−	0.464916i
$900$		0			0
$901$	15.9595	−	27.6426i	0.531687	−	0.920908i
$902$	−36.2339	−	13.1880i	−1.20646	−	0.439114i
$903$		0			0
$904$	3.36184	−	5.82289i	0.111813	−	0.193666i
$905$	5.10014	+	8.83370i	0.169534	+	0.293642i
$906$		0			0
$907$	25.7442	+	21.6020i	0.854823	+	0.717282i	0.960846	−	0.277082i	$-0.0893674\pi$
$907$	25.7442	+	21.6020i	0.854823	+	0.717282i	−0.106023	+	0.994364i	$0.533812\pi$
$908$	−34.4641	+	28.9188i	−1.14373	+	0.959704i
$909$		0			0
$910$	−6.42989	+	2.34029i	−0.213149	+	0.0775798i
$911$	−0.821993			−0.0272338			−0.0136169	−	0.999907i	$-0.504335\pi$
$911$	−0.821993			−0.0272338			−0.0136169	+	0.999907i	$0.504335\pi$
$912$		0			0
$913$	22.7219			0.751986
$914$	−50.1350	+	18.2476i	−1.65832	+	0.603578i
$915$		0			0
$916$	−9.80587	+	8.22811i	−0.323995	+	0.271864i
$917$	−7.04608	−	5.91236i	−0.232682	−	0.195243i
$918$		0			0
$919$	−3.07057	−	5.31839i	−0.101289	−	0.175438i	0.810927	−	0.585147i	$-0.198963\pi$
$919$	−3.07057	−	5.31839i	−0.101289	−	0.175438i	−0.912216	+	0.409710i	$0.865630\pi$
$920$	0.837497	−	1.45059i	0.0276115	−	0.0478245i
$921$		0			0
$922$	3.48070	+	1.26687i	0.114631	+	0.0417222i
$923$	27.3700	−	47.4063i	0.900896	−	1.56040i
$924$		0			0
$925$	5.76011	+	32.6672i	0.189391	+	1.07409i
$926$	58.0327	+	48.6952i	1.90707	+	1.60022i
$927$		0			0
$928$	−7.06212	+	40.0513i	−0.231825	+	1.31475i
$929$	6.66885	−	2.42726i	0.218798	−	0.0796359i	−0.230295	−	0.973121i	$-0.573969\pi$
$929$	6.66885	−	2.42726i	0.218798	−	0.0796359i	0.449093	+	0.893485i	$0.351747\pi$
$930$		0			0
$931$	13.8532	−	19.5409i	0.454021	−	0.640427i
$932$	27.9081			0.914160
$933$		0			0
$934$	7.95652	−	45.1237i	0.260345	−	1.47649i
$935$	−6.75373	+	5.66705i	−0.220870	+	0.185332i
$936$		0			0
$937$	−2.04529	−	11.5994i	−0.0668168	−	0.378937i	−0.999818	−	0.0190643i	$-0.993931\pi$
$937$	−2.04529	−	11.5994i	−0.0668168	−	0.378937i	0.933001	−	0.359873i	$-0.117180\pi$
$938$	9.61363	+	16.6513i	0.313896	+	0.543684i
$939$		0			0
$940$	15.4461	+	5.62192i	0.503796	+	0.183367i
$941$	16.8425	+	6.13015i	0.549048	+	0.199837i	0.601624	−	0.798780i	$-0.294521\pi$
$941$	16.8425	+	6.13015i	0.549048	+	0.199837i	−0.0525753	+	0.998617i	$0.516743\pi$
$942$		0			0
$943$	16.1099	+	27.9032i	0.524612	+	0.908654i
$944$	−4.19510	−	23.7916i	−0.136539	−	0.774350i
$945$		0			0
$946$	0.187948	−	0.157707i	0.00611071	−	0.00512749i
$947$	6.77943	−	38.4480i	0.220302	−	1.24939i	−0.651164	−	0.758937i	$-0.725719\pi$
$947$	6.77943	−	38.4480i	0.220302	−	1.24939i	0.871466	−	0.490456i	$-0.163170\pi$
$948$		0			0
$949$	−14.4151			−0.467934
$950$	16.9753	+	36.9650i	0.550751	+	1.19930i
$951$		0			0
$952$	5.54266	−	2.01736i	0.179639	−	0.0653831i
$953$	−1.34046	+	7.60215i	−0.0434219	+	0.246258i	−0.998791	−	0.0491566i	$-0.984347\pi$
$953$	−1.34046	+	7.60215i	−0.0434219	+	0.246258i	0.955369	+	0.295415i	$0.0954578\pi$
$954$		0			0
$955$	−12.9845	−	10.8953i	−0.420168	−	0.352563i
$956$	12.0427	+	68.2977i	0.389490	+	2.20891i
$957$		0			0
$958$	−43.1475	+	74.7337i	−1.39403	+	2.41454i
$959$	−13.7400	−	5.00095i	−0.443687	−	0.161489i
$960$		0			0
$961$	11.5373	−	19.9832i	0.372171	−	0.644619i
$962$	−28.5464	−	49.4438i	−0.920372	−	1.59413i
$963$		0			0
$964$	2.49794	+	2.09602i	0.0804532	+	0.0675083i
$965$	12.3175	−	10.3356i	0.396513	−	0.332714i
$966$		0			0
$967$	33.0749	−	12.0383i	1.06362	−	0.387125i	0.249831	−	0.968289i	$-0.419625\pi$
$967$	33.0749	−	12.0383i	1.06362	−	0.387125i	0.813786	+	0.581164i	$0.197403\pi$
$968$	−5.53093			−0.177771
$969$		0			0
$970$	6.19934			0.199049
$971$	1.31723	−	0.479432i	0.0422719	−	0.0153857i	−0.320798	−	0.947148i	$-0.603951\pi$
$971$	1.31723	−	0.479432i	0.0422719	−	0.0153857i	0.363070	+	0.931762i	$0.381729\pi$
$972$		0			0
$973$	9.48545	−	7.95924i	0.304090	−	0.255161i
$974$	−56.8920	−	47.7381i	−1.82294	−	1.52963i
$975$		0			0
$976$	6.64068	+	11.5020i	0.212563	+	0.368170i
$977$	−8.03685	+	13.9202i	−0.257121	+	0.445347i	−0.965470	−	0.260516i	$-0.916107\pi$
$977$	−8.03685	+	13.9202i	−0.257121	+	0.445347i	0.708348	+	0.705863i	$0.249441\pi$
$978$		0			0
$979$	−23.4659	−	8.54087i	−0.749972	−	0.272967i
$980$	−4.67020	+	8.08902i	−0.149184	+	0.258394i
$981$		0			0
$982$	4.18202	+	23.7174i	0.133454	+	0.756853i
$983$	−1.71059	−	1.43536i	−0.0545595	−	0.0457808i	0.615100	−	0.788449i	$-0.289116\pi$
$983$	−1.71059	−	1.43536i	−0.0545595	−	0.0457808i	−0.669660	+	0.742668i	$0.733560\pi$
$984$		0			0
$985$	−0.0522619	+	0.296392i	−0.00166520	+	0.00944383i
$986$	65.4152	−	23.8092i	2.08324	−	0.758239i
$987$		0			0
$988$	−26.5735	−	26.8853i	−0.845415	−	0.855335i
$989$	−0.205012			−0.00651899
$990$		0			0
$991$	−3.40538	+	19.3129i	−0.108176	+	0.613494i	0.881729	+	0.471757i	$0.156380\pi$
$991$	−3.40538	+	19.3129i	−0.108176	+	0.613494i	−0.989904	+	0.141737i	$0.954731\pi$
$992$	17.4436	−	14.6369i	0.553836	−	0.464723i
$993$		0			0
$994$	6.58037	+	37.3192i	0.208717	+	1.18369i
$995$	−5.67281	−	9.82560i	−0.179840	−	0.311493i
$996$		0			0
$997$	−7.44831	−	2.71096i	−0.235890	−	0.0858571i	0.221370	−	0.975190i	$-0.428947\pi$
$997$	−7.44831	−	2.71096i	−0.235890	−	0.0858571i	−0.457261	+	0.889333i	$0.651169\pi$
$998$	34.6837	+	12.6239i	1.09789	+	0.399601i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.u.d.100.1	✓	12
3.2	odd	2	inner	171.2.u.d.100.2	yes	12
19.2	odd	18		3249.2.a.bj.1.2		6
19.4	even	9	inner	171.2.u.d.118.1	yes	12
19.17	even	9		3249.2.a.bi.1.5		6
57.2	even	18		3249.2.a.bj.1.5		6
57.17	odd	18		3249.2.a.bi.1.2		6
57.23	odd	18	inner	171.2.u.d.118.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.u.d.100.1	✓	12	1.1	even	1	trivial
171.2.u.d.100.2	yes	12	3.2	odd	2	inner
171.2.u.d.118.1	yes	12	19.4	even	9	inner
171.2.u.d.118.2	yes	12	57.23	odd	18	inner
3249.2.a.bi.1.2		6	57.17	odd	18
3249.2.a.bi.1.5		6	19.17	even	9
3249.2.a.bj.1.2		6	19.2	odd	18
3249.2.a.bj.1.5		6	57.2	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95928 + 0.713118i) q^{2} +(1.79813 - 1.50881i) q^{4} +(-0.554707 - 0.465455i) q^{5} +(-0.613341 - 1.06234i) q^{7} +(-0.362059 + 0.627105i) q^{8} +(1.41875 + 0.516382i) q^{10} +(0.916767 - 1.58789i) q^{11} +(-0.641559 - 3.63846i) q^{13} +(1.95928 + 1.64403i) q^{14} +(-0.553033 + 3.13641i) q^{16} +(6.23989 - 2.27113i) q^{17} +(4.34002 + 0.405223i) q^{19} -1.69972 q^{20} +(-0.663848 + 3.76487i) q^{22} +(2.44708 - 2.05334i) q^{23} +(-0.777189 - 4.40766i) q^{25} +(3.85164 + 6.67124i) q^{26} +(-2.70574 - 0.984808i) q^{28} +(-4.72474 - 1.71967i) q^{29} +(1.40760 + 2.43804i) q^{31} +(-1.40457 - 7.96570i) q^{32} +(-10.6061 + 8.89955i) q^{34} +(-0.154245 + 0.874769i) q^{35} -7.41147 q^{37} +(-8.79227 + 2.30100i) q^{38} +(0.492726 - 0.179338i) q^{40} +(-1.75146 + 9.93303i) q^{41} +(-0.0491630 - 0.0412527i) q^{43} +(-0.747355 - 4.23846i) q^{44} +(-3.33022 + 5.76811i) q^{46} +(-9.08742 - 3.30755i) q^{47} +(2.74763 - 4.75903i) q^{49} +(4.66591 + 8.08159i) q^{50} +(-6.64337 - 5.57445i) q^{52} +(3.68223 - 3.08976i) q^{53} +(-1.24763 + 0.454099i) q^{55} +0.888263 q^{56} +10.4834 q^{58} +(-7.12815 + 2.59443i) q^{59} +(3.19459 - 2.68058i) q^{61} +(-4.49649 - 3.77301i) q^{62} +(5.24763 + 9.08916i) q^{64} +(-1.33766 + 2.31690i) q^{65} +(7.06418 + 2.57115i) q^{67} +(7.79343 - 13.4986i) q^{68} +(-0.321604 - 1.82391i) q^{70} +(11.3499 + 9.52372i) q^{71} +(0.677519 - 3.84240i) q^{73} +(14.5211 - 5.28525i) q^{74} +(8.41534 - 5.81964i) q^{76} -2.24916 q^{77} +(-1.32160 + 7.49519i) q^{79} +(1.76663 - 1.48238i) q^{80} +(-3.65183 - 20.7105i) q^{82} +(6.19622 + 10.7322i) q^{83} +(-4.51842 - 1.64457i) q^{85} +(0.125742 + 0.0457663i) q^{86} +(0.663848 + 1.14982i) q^{88} +(-2.36500 - 13.4126i) q^{89} +(-3.47178 + 2.91317i) q^{91} +(1.30206 - 7.38436i) q^{92} +20.1634 q^{94} +(-2.21883 - 2.24486i) q^{95} +(3.85844 - 1.40436i) q^{97} +(-1.98961 + 11.2836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{4} + 6 q^{7} + 12 q^{10} - 24 q^{13} + 18 q^{16} + 12 q^{19} + 12 q^{25} - 12 q^{28} + 24 q^{31} - 78 q^{34} - 48 q^{37} - 30 q^{40} - 24 q^{43} + 6 q^{46} + 54 q^{52} + 18 q^{55} - 48 q^{58}+ \cdots + 30 q^{97}+O(q^{100}) \) 12 * q - 6 * q^4 + 6 * q^7 + 12 * q^10 - 24 * q^13 + 18 * q^16 + 12 * q^19 + 12 * q^25 - 12 * q^28 + 24 * q^31 - 78 * q^34 - 48 * q^37 - 30 * q^40 - 24 * q^43 + 6 * q^46 + 54 * q^52 + 18 * q^55 - 48 * q^58 + 30 * q^61 + 30 * q^64 + 48 * q^67 + 60 * q^70 - 42 * q^73 + 12 * q^76 + 48 * q^79 + 66 * q^82 - 78 * q^85 - 12 * q^91 - 12 * q^94 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more