LMFDB - Embedded newform 486.2.e.g.271.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [486,2,Mod(55,486)] 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("486.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(486, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.88072953823$
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} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 + 0.168222i$ of defining polynomial
Character	$\chi$	$=$	486.271
Dual form			486.2.e.g.217.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-1.59951 - 1.34215i) q^{5} +(3.77024 + 1.37225i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.04401 + 1.80828i) q^{10} +(-0.162744 + 0.136558i) q^{11} +(0.902802 - 5.12004i) q^{13} +(0.696712 - 3.95125i) q^{14} +(0.766044 - 0.642788i) q^{16} +(1.89276 - 3.27836i) q^{17} +(0.636405 + 1.10229i) q^{19} +(1.96209 + 0.714144i) q^{20} +(0.162744 + 0.136558i) q^{22} +(0.779421 - 0.283686i) q^{23} +(-0.111167 - 0.630460i) q^{25} -5.19903 q^{26} -4.01220 q^{28} +(-1.59951 - 9.07129i) q^{29} +(-3.32266 + 1.20935i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-3.55723 - 1.29473i) q^{34} +(-4.18878 - 7.25517i) q^{35} +(-1.77730 + 3.07838i) q^{37} +(0.975029 - 0.818146i) q^{38} +(0.362580 - 2.05630i) q^{40} +(-0.475691 + 2.69778i) q^{41} +(5.28305 - 4.43301i) q^{43} +(0.106223 - 0.183984i) q^{44} +(-0.414721 - 0.718318i) q^{46} +(-1.20024 - 0.436853i) q^{47} +(6.96931 + 5.84795i) q^{49} +(-0.601578 + 0.218956i) q^{50} +(0.902802 + 5.12004i) q^{52} +11.2992 q^{53} +0.443592 q^{55} +(0.696712 + 3.95125i) q^{56} +(-8.65573 + 3.15043i) q^{58} +(6.55723 + 5.50217i) q^{59} +(-2.66279 - 0.969176i) q^{61} +(1.76795 + 3.06218i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-8.31592 + 6.97788i) q^{65} +(1.69490 - 9.61227i) q^{67} +(-0.657349 + 3.72801i) q^{68} +(-6.41758 + 5.38499i) q^{70} +(-5.86207 + 10.1534i) q^{71} +(-0.375162 - 0.649800i) q^{73} +(3.34023 + 1.21575i) q^{74} +(-0.975029 - 0.818146i) q^{76} +(-0.800975 + 0.291531i) q^{77} +(-0.411161 - 2.33181i) q^{79} -2.08802 q^{80} +2.73940 q^{82} +(1.97967 + 11.2273i) q^{83} +(-7.42755 + 2.70341i) q^{85} +(-5.28305 - 4.43301i) q^{86} +(-0.199635 - 0.0726611i) q^{88} +(2.69813 + 4.67329i) q^{89} +(10.4298 - 18.0649i) q^{91} +(-0.635390 + 0.533155i) q^{92} +(-0.221796 + 1.25787i) q^{94} +(0.461496 - 2.61727i) q^{95} +(-9.62394 + 8.07544i) q^{97} +(4.54889 - 7.87892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 6 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} - 27 q^{25} - 18 q^{26} + 12 q^{28} + 3 q^{29} - 27 q^{31} + 12 q^{34}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q + 3 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^10 - 6 * q^11 - 6 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 - 27 * q^25 - 18 * q^26 + 12 * q^28 + 3 * q^29 - 27 * q^31 + 12 * q^34 - 3 * q^35 - 15 * q^37 + 15 * q^38 + 6 * q^40 - 15 * q^41 + 18 * q^43 + 3 * q^44 + 3 * q^46 + 27 * q^47 + 42 * q^49 - 36 * q^50 - 6 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 12 * q^58 + 24 * q^59 + 27 * q^61 + 12 * q^62 - 6 * q^64 - 57 * q^65 + 9 * q^67 + 15 * q^68 - 6 * q^70 - 12 * q^71 - 21 * q^73 + 3 * q^74 - 15 * q^76 + 51 * q^77 - 42 * q^79 - 6 * q^80 + 6 * q^82 - 45 * q^85 - 18 * q^86 - 12 * q^88 - 12 * q^89 - 6 * q^91 + 24 * q^92 - 9 * q^94 - 48 * q^95 - 24 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.59951	−	1.34215i	−0.715324	−	0.600228i	0.210763	−	0.977537i	$-0.432405\pi$
$5$	−1.59951	−	1.34215i	−0.715324	−	0.600228i	−0.926088	+	0.377309i	$0.876850\pi$
$6$		0			0
$7$	3.77024	+	1.37225i	1.42502	+	0.518664i	0.935499	−	0.353330i	$-0.114951\pi$
$7$	3.77024	+	1.37225i	1.42502	+	0.518664i	0.489518	+	0.871993i	$0.337173\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	−1.04401	+	1.80828i	−0.330144	+	0.571827i
$11$	−0.162744	+	0.136558i	−0.0490691	+	0.0411738i	−0.666992	−	0.745065i	$-0.732419\pi$
$11$	−0.162744	+	0.136558i	−0.0490691	+	0.0411738i	0.617923	+	0.786238i	$0.287974\pi$
$12$		0			0
$13$	0.902802	−	5.12004i	0.250392	−	1.42004i	−0.557237	−	0.830353i	$-0.688139\pi$
$13$	0.902802	−	5.12004i	0.250392	−	1.42004i	0.807629	−	0.589691i	$-0.200750\pi$
$14$	0.696712	−	3.95125i	0.186204	−	1.05602i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.89276	−	3.27836i	0.459062	−	0.795119i	−0.539850	−	0.841762i	$-0.681519\pi$
$17$	1.89276	−	3.27836i	0.459062	−	0.795119i	0.998912	+	0.0466426i	$0.0148522\pi$
$18$		0			0
$19$	0.636405	+	1.10229i	0.146001	+	0.252882i	0.929746	−	0.368201i	$-0.120026\pi$
$19$	0.636405	+	1.10229i	0.146001	+	0.252882i	−0.783745	+	0.621083i	$0.786693\pi$
$20$	1.96209	+	0.714144i	0.438738	+	0.159687i
$21$		0			0
$22$	0.162744	+	0.136558i	0.0346971	+	0.0291143i
$23$	0.779421	−	0.283686i	0.162520	−	0.0591526i	−0.259479	−	0.965749i	$-0.583551\pi$
$23$	0.779421	−	0.283686i	0.162520	−	0.0591526i	0.421999	+	0.906596i	$0.361329\pi$
$24$		0			0
$25$	−0.111167	−	0.630460i	−0.0222334	−	0.126092i
$26$	−5.19903			−1.01961
$27$		0			0
$28$	−4.01220			−0.758235
$29$	−1.59951	−	9.07129i	−0.297022	−	1.68450i	−0.658868	−	0.752259i	$-0.728964\pi$
$29$	−1.59951	−	9.07129i	−0.297022	−	1.68450i	0.361846	−	0.932238i	$-0.382147\pi$
$30$		0			0
$31$	−3.32266	+	1.20935i	−0.596768	+	0.217206i	−0.622704	−	0.782458i	$-0.713966\pi$
$31$	−3.32266	+	1.20935i	−0.596768	+	0.217206i	0.0259356	+	0.999664i	$0.491744\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$		0			0
$34$	−3.55723	−	1.29473i	−0.610060	−	0.222044i
$35$	−4.18878	−	7.25517i	−0.708032	−	1.22635i
$36$		0			0
$37$	−1.77730	+	3.07838i	−0.292187	+	0.506082i	−0.974326	−	0.225140i	$-0.927716\pi$
$37$	−1.77730	+	3.07838i	−0.292187	+	0.506082i	0.682140	+	0.731222i	$0.261049\pi$
$38$	0.975029	−	0.818146i	0.158171	−	0.132721i
$39$		0			0
$40$	0.362580	−	2.05630i	0.0573290	−	0.325129i
$41$	−0.475691	+	2.69778i	−0.0742905	+	0.421322i	0.924867	+	0.380290i	$0.124176\pi$
$41$	−0.475691	+	2.69778i	−0.0742905	+	0.421322i	−0.999158	+	0.0410323i	$0.986935\pi$
$42$		0			0
$43$	5.28305	−	4.43301i	0.805658	−	0.676027i	−0.143909	−	0.989591i	$-0.545967\pi$
$43$	5.28305	−	4.43301i	0.805658	−	0.676027i	0.949567	+	0.313564i	$0.101523\pi$
$44$	0.106223	−	0.183984i	0.0160138	−	0.0277367i
$45$		0			0
$46$	−0.414721	−	0.718318i	−0.0611473	−	0.105910i
$47$	−1.20024	−	0.436853i	−0.175074	−	0.0637216i	0.252996	−	0.967467i	$-0.418584\pi$
$47$	−1.20024	−	0.436853i	−0.175074	−	0.0637216i	−0.428070	+	0.903746i	$0.640806\pi$
$48$		0			0
$49$	6.96931	+	5.84795i	0.995616	+	0.835421i
$50$	−0.601578	+	0.218956i	−0.0850759	+	0.0309651i
$51$		0			0
$52$	0.902802	+	5.12004i	0.125196	+	0.710022i
$53$	11.2992			1.55207			0.776036	−	0.630689i	$-0.217228\pi$
$53$	11.2992			1.55207			0.776036	+	0.630689i	$0.217228\pi$
$54$		0			0
$55$	0.443592			0.0598140
$56$	0.696712	+	3.95125i	0.0931021	+	0.528008i
$57$		0			0
$58$	−8.65573	+	3.15043i	−1.13655	+	0.413671i
$59$	6.55723	+	5.50217i	0.853678	+	0.716321i	0.960597	−	0.277947i	$-0.0896538\pi$
$59$	6.55723	+	5.50217i	0.853678	+	0.716321i	−0.106918	+	0.994268i	$0.534098\pi$
$60$		0			0
$61$	−2.66279	−	0.969176i	−0.340935	−	0.124090i	0.165878	−	0.986146i	$-0.446954\pi$
$61$	−2.66279	−	0.969176i	−0.340935	−	0.124090i	−0.506813	+	0.862056i	$0.669177\pi$
$62$	1.76795	+	3.06218i	0.224530	+	0.388898i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−8.31592	+	6.97788i	−1.03146	+	0.865500i
$66$		0			0
$67$	1.69490	−	9.61227i	0.207065	−	1.17433i	−0.687091	−	0.726571i	$-0.741113\pi$
$67$	1.69490	−	9.61227i	0.207065	−	1.17433i	0.894156	−	0.447755i	$-0.147776\pi$
$68$	−0.657349	+	3.72801i	−0.0797153	+	0.452088i
$69$		0			0
$70$	−6.41758	+	5.38499i	−0.767047	+	0.643629i
$71$	−5.86207	+	10.1534i	−0.695700	+	1.20499i	0.274244	+	0.961660i	$0.411572\pi$
$71$	−5.86207	+	10.1534i	−0.695700	+	1.20499i	−0.969944	+	0.243327i	$0.921761\pi$
$72$		0			0
$73$	−0.375162	−	0.649800i	−0.0439094	−	0.0760534i	0.843235	−	0.537544i	$-0.180648\pi$
$73$	−0.375162	−	0.649800i	−0.0439094	−	0.0760534i	−0.887145	+	0.461491i	$0.847315\pi$
$74$	3.34023	+	1.21575i	0.388294	+	0.141328i
$75$		0			0
$76$	−0.975029	−	0.818146i	−0.111843	−	0.0938478i
$77$	−0.800975	+	0.291531i	−0.0912796	+	0.0332231i
$78$		0			0
$79$	−0.411161	−	2.33181i	−0.0462592	−	0.262349i	0.952903	−	0.303275i	$-0.0980802\pi$
$79$	−0.411161	−	2.33181i	−0.0462592	−	0.262349i	−0.999162	+	0.0409264i	$0.986969\pi$
$80$	−2.08802			−0.233447
$81$		0			0
$82$	2.73940			0.302516
$83$	1.97967	+	11.2273i	0.217297	+	1.23236i	0.876875	+	0.480719i	$0.159624\pi$
$83$	1.97967	+	11.2273i	0.217297	+	1.23236i	−0.659577	+	0.751637i	$0.729265\pi$
$84$		0			0
$85$	−7.42755	+	2.70341i	−0.805631	+	0.293226i
$86$	−5.28305	−	4.43301i	−0.569686	−	0.478023i
$87$		0			0
$88$	−0.199635	−	0.0726611i	−0.0212811	−	0.00774570i
$89$	2.69813	+	4.67329i	0.286001	+	0.495368i	0.972851	−	0.231431i	$-0.0743407\pi$
$89$	2.69813	+	4.67329i	0.286001	+	0.495368i	−0.686851	+	0.726799i	$0.741007\pi$
$90$		0			0
$91$	10.4298	−	18.0649i	1.09334	−	1.89372i
$92$	−0.635390	+	0.533155i	−0.0662440	+	0.0555853i
$93$		0			0
$94$	−0.221796	+	1.25787i	−0.0228765	+	0.129739i
$95$	0.461496	−	2.61727i	0.0473485	−	0.268526i
$96$		0			0
$97$	−9.62394	+	8.07544i	−0.977163	+	0.819937i	−0.983659	−	0.180042i	$-0.942377\pi$
$97$	−9.62394	+	8.07544i	−0.977163	+	0.819937i	0.00649606	+	0.999979i	$0.497932\pi$
$98$	4.54889	−	7.87892i	0.459508	−	0.795891i
$99$		0			0
$100$	0.320093	+	0.554417i	0.0320093	+	0.0554417i
$101$	−2.71996	−	0.989985i	−0.270646	−	0.0985072i	0.203132	−	0.979151i	$-0.434888\pi$
$101$	−2.71996	−	0.989985i	−0.270646	−	0.0985072i	−0.473778	+	0.880644i	$0.657110\pi$
$102$		0			0
$103$	12.7853	+	10.7281i	1.25977	+	1.05708i	0.995706	+	0.0925707i	$0.0295084\pi$
$103$	12.7853	+	10.7281i	1.25977	+	1.05708i	0.264067	+	0.964504i	$0.414936\pi$
$104$	4.88549	−	1.77817i	0.479061	−	0.174364i
$105$		0			0
$106$	−1.96209	−	11.1276i	−0.190575	−	1.08081i
$107$	−0.321371			−0.0310681			−0.0155341	−	0.999879i	$-0.504945\pi$
$107$	−0.321371			−0.0310681			−0.0155341	+	0.999879i	$0.504945\pi$
$108$		0			0
$109$	0.568378			0.0544407			0.0272204	−	0.999629i	$-0.491334\pi$
$109$	0.568378			0.0544407			0.0272204	+	0.999629i	$0.491334\pi$
$110$	−0.0770290	−	0.436853i	−0.00734443	−	0.0416523i
$111$		0			0
$112$	3.77024	−	1.37225i	0.356254	−	0.129666i
$113$	1.04168	+	0.874072i	0.0979928	+	0.0822258i	0.690468	−	0.723363i	$-0.257405\pi$
$113$	1.04168	+	0.874072i	0.0979928	+	0.0822258i	−0.592475	+	0.805589i	$0.701849\pi$
$114$		0			0
$115$	−1.62744	−	0.592341i	−0.151760	−	0.0552361i
$116$	4.60562	+	7.97716i	0.427621	+	0.740661i
$117$		0			0
$118$	4.27993	−	7.41305i	0.393999	−	0.682427i
$119$	11.6349	−	9.76285i	1.06657	−	0.894959i
$120$		0			0
$121$	−1.90229	+	10.7884i	−0.172936	+	0.980767i
$122$	−0.492064	+	2.79063i	−0.0445493	+	0.252652i
$123$		0			0
$124$	2.70866	−	2.27284i	0.243245	−	0.204107i
$125$	−5.88840	+	10.1990i	−0.526675	+	0.912227i
$126$		0			0
$127$	−0.902007	−	1.56232i	−0.0800402	−	0.138634i	0.823227	−	0.567713i	$-0.192172\pi$
$127$	−0.902007	−	1.56232i	−0.0800402	−	0.138634i	−0.903267	+	0.429079i	$0.858838\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$		0			0
$130$	8.31592	+	6.97788i	0.729354	+	0.612001i
$131$	−9.12858	+	3.32253i	−0.797567	+	0.290291i	−0.708478	−	0.705733i	$-0.750618\pi$
$131$	−9.12858	+	3.32253i	−0.797567	+	0.290291i	−0.0890894	+	0.996024i	$0.528396\pi$
$132$		0			0
$133$	0.886782	+	5.02919i	0.0768937	+	0.436086i
$134$	−9.76056			−0.843184
$135$		0			0
$136$	3.78552			0.324606
$137$	1.57463	+	8.93016i	0.134530	+	0.762955i	0.975186	+	0.221387i	$0.0710583\pi$
$137$	1.57463	+	8.93016i	0.134530	+	0.762955i	−0.840657	+	0.541569i	$0.817831\pi$
$138$		0			0
$139$	9.43533	−	3.43418i	0.800294	−	0.291283i	0.0906859	−	0.995880i	$-0.471094\pi$
$139$	9.43533	−	3.43418i	0.800294	−	0.291283i	0.709608	+	0.704596i	$0.248872\pi$
$140$	6.41758	+	5.38499i	0.542384	+	0.455114i
$141$		0			0
$142$	11.0171	+	4.00989i	0.924534	+	0.336503i
$143$	0.552258	+	0.956539i	0.0461822	+	0.0799898i
$144$		0			0
$145$	−9.61660	+	16.6564i	−0.798615	+	1.38324i
$146$	−0.574782	+	0.482299i	−0.0475693	+	0.0399154i
$147$		0			0
$148$	0.617250	−	3.50060i	0.0507377	−	0.287748i
$149$	−2.75101	+	15.6018i	−0.225371	+	1.27815i	0.636602	+	0.771192i	$0.280339\pi$
$149$	−2.75101	+	15.6018i	−0.225371	+	1.27815i	−0.861974	+	0.506953i	$0.830772\pi$
$150$		0			0
$151$	4.06582	−	3.41163i	0.330872	−	0.277634i	−0.462183	−	0.886784i	$-0.652934\pi$
$151$	4.06582	−	3.41163i	0.330872	−	0.277634i	0.793055	+	0.609150i	$0.208489\pi$
$152$	−0.636405	+	1.10229i	−0.0516192	+	0.0894071i
$153$		0			0
$154$	0.426190	+	0.738183i	0.0343434	+	0.0594845i
$155$	6.93778	+	2.52514i	0.557256	+	0.202824i
$156$		0			0
$157$	−8.82256	−	7.40301i	−0.704117	−	0.590824i	0.218825	−	0.975764i	$-0.429778\pi$
$157$	−8.82256	−	7.40301i	−0.704117	−	0.590824i	−0.922942	+	0.384940i	$0.874222\pi$
$158$	−2.22499	+	0.809829i	−0.177010	+	0.0644265i
$159$		0			0
$160$	0.362580	+	2.05630i	0.0286645	+	0.162564i
$161$	3.32789			0.262275
$162$		0			0
$163$	7.66336			0.600241			0.300120	−	0.953901i	$-0.402973\pi$
$163$	7.66336			0.600241			0.300120	+	0.953901i	$0.402973\pi$
$164$	−0.475691	−	2.69778i	−0.0371452	−	0.210661i
$165$		0			0
$166$	10.7130	−	3.89920i	0.831487	−	0.302636i
$167$	−4.68053	−	3.92743i	−0.362190	−	0.303913i	0.443473	−	0.896288i	$-0.353746\pi$
$167$	−4.68053	−	3.92743i	−0.362190	−	0.303913i	−0.805663	+	0.592374i	$0.798191\pi$
$168$		0			0
$169$	−13.1838	−	4.79850i	−1.01414	−	0.369116i
$170$	3.95212	+	6.84527i	0.303114	+	0.525008i
$171$		0			0
$172$	−3.44827	+	5.97257i	−0.262928	+	0.455404i
$173$	8.65897	−	7.26574i	0.658330	−	0.552404i	−0.251256	−	0.967921i	$-0.580844\pi$
$173$	8.65897	−	7.26574i	0.658330	−	0.552404i	0.909586	+	0.415517i	$0.136399\pi$
$174$		0			0
$175$	0.446025	−	2.52953i	0.0337163	−	0.191215i
$176$	−0.0368910	+	0.209219i	−0.00278076	+	0.0157705i
$177$		0			0
$178$	4.13377	−	3.46864i	0.309839	−	0.259986i
$179$	3.46495	−	6.00147i	0.258982	−	0.448571i	−0.706987	−	0.707226i	$-0.749946\pi$
$179$	3.46495	−	6.00147i	0.258982	−	0.448571i	0.965970	+	0.258656i	$0.0832795\pi$
$180$		0			0
$181$	−1.51882	−	2.63067i	−0.112893	−	0.195536i	0.804043	−	0.594572i	$-0.202678\pi$
$181$	−1.51882	−	2.63067i	−0.112893	−	0.195536i	−0.916935	+	0.399036i	$0.869345\pi$
$182$	−19.6016	−	7.13439i	−1.45297	−	0.528836i
$183$		0			0
$184$	0.635390	+	0.533155i	0.0468415	+	0.0393047i
$185$	6.97447	−	2.53850i	0.512773	−	0.186634i
$186$		0			0
$187$	0.139652	+	0.792004i	0.0102123	+	0.0579171i
$188$	1.27727			0.0931547
$189$		0			0
$190$	−2.65765			−0.192806
$191$	0.885116	+	5.01974i	0.0640447	+	0.363216i	0.999940	+	0.0109379i	$0.00348170\pi$
$191$	0.885116	+	5.01974i	0.0640447	+	0.363216i	−0.935895	+	0.352278i	$0.885407\pi$
$192$		0			0
$193$	−17.7304	+	6.45333i	−1.27626	+	0.464521i	−0.889194	−	0.457531i	$-0.848734\pi$
$193$	−17.7304	+	6.45333i	−1.27626	+	0.464521i	−0.387066	+	0.922052i	$0.626512\pi$
$194$	9.62394	+	8.07544i	0.690959	+	0.579783i
$195$		0			0
$196$	−8.54912	−	3.11163i	−0.610652	−	0.222259i
$197$	−10.0220	−	17.3586i	−0.714036	−	1.23675i	−0.963330	−	0.268319i	$-0.913532\pi$
$197$	−10.0220	−	17.3586i	−0.714036	−	1.23675i	0.249294	−	0.968428i	$-0.419801\pi$
$198$		0			0
$199$	−2.75106	+	4.76498i	−0.195018	+	0.337780i	−0.946906	−	0.321510i	$-0.895810\pi$
$199$	−2.75106	+	4.76498i	−0.195018	+	0.337780i	0.751889	+	0.659290i	$0.229143\pi$
$200$	0.490411	−	0.411503i	0.0346773	−	0.0290977i
$201$		0			0
$202$	−0.502628	+	2.85055i	−0.0353648	+	0.200564i
$203$	6.41758	−	36.3959i	0.450426	−	2.55449i
$204$		0			0
$205$	4.38170	−	3.67668i	0.306031	−	0.256791i
$206$	8.34501	−	14.4540i	0.581425	−	1.00706i
$207$		0			0
$208$	−2.59951	−	4.50249i	−0.180244	−	0.312191i
$209$	−0.254097	−	0.0924837i	−0.0175762	−	0.00639723i
$210$		0			0
$211$	−19.2623	−	16.1630i	−1.32607	−	1.11271i	−0.984979	−	0.172676i	$-0.944759\pi$
$211$	−19.2623	−	16.1630i	−1.32607	−	1.11271i	−0.341092	−	0.940030i	$-0.610797\pi$
$212$	−10.6178	+	3.86457i	−0.729235	+	0.265420i
$213$		0			0
$214$	0.0558055	+	0.316489i	0.00381479	+	0.0216347i
$215$	−14.4001			−0.982077
$216$		0			0
$217$	−14.1868			−0.963061
$218$	−0.0986977	−	0.559743i	−0.00668465	−	0.0379106i
$219$		0			0
$220$	−0.416841	+	0.151718i	−0.0281034	+	0.0102288i
$221$	−15.0766	−	12.6507i	−1.01416	−	0.850980i
$222$		0			0
$223$	3.52610	+	1.28339i	0.236125	+	0.0859424i	0.457372	−	0.889275i	$-0.348791\pi$
$223$	3.52610	+	1.28339i	0.236125	+	0.0859424i	−0.221248	+	0.975218i	$0.571013\pi$
$224$	−2.00610	−	3.47467i	−0.134038	−	0.232161i
$225$		0			0
$226$	0.679907	−	1.17763i	0.0452267	−	0.0783350i
$227$	−14.3462	+	12.0379i	−0.952193	+	0.798985i	−0.979666	−	0.200638i	$-0.935699\pi$
$227$	−14.3462	+	12.0379i	−0.952193	+	0.798985i	0.0274723	+	0.999623i	$0.491254\pi$
$228$		0			0
$229$	−0.719481	+	4.08038i	−0.0475446	+	0.269639i	−0.999308	−	0.0371938i	$-0.988158\pi$
$229$	−0.719481	+	4.08038i	−0.0475446	+	0.269639i	0.951763	+	0.306833i	$0.0992692\pi$
$230$	−0.300739	+	1.70558i	−0.0198302	+	0.112462i
$231$		0			0
$232$	7.05621	−	5.92087i	0.463263	−	0.388724i
$233$	−0.958556	+	1.66027i	−0.0627971	+	0.108768i	−0.895715	−	0.444629i	$-0.853335\pi$
$233$	−0.958556	+	1.66027i	−0.0627971	+	0.108768i	0.832918	+	0.553397i	$0.186669\pi$
$234$		0			0
$235$	1.33348	+	2.30966i	0.0869869	+	0.150666i
$236$	−8.04363	−	2.92764i	−0.523596	−	0.190573i
$237$		0			0
$238$	−11.6349	−	9.76285i	−0.754179	−	0.632831i
$239$	22.7399	−	8.27664i	1.47092	−	0.535371i	0.522570	−	0.852596i	$-0.324973\pi$
$239$	22.7399	−	8.27664i	1.47092	−	0.535371i	0.948350	+	0.317225i	$0.102751\pi$
$240$		0			0
$241$	2.29301	+	13.0043i	0.147706	+	0.837682i	0.965155	+	0.261680i	$0.0842767\pi$
$241$	2.29301	+	13.0043i	0.147706	+	0.837682i	−0.817449	+	0.576002i	$0.804612\pi$
$242$	10.9549			0.704205
$243$		0			0
$244$	2.83368			0.181408
$245$	−3.29868	−	18.7077i	−0.210745	−	1.19519i
$246$		0			0
$247$	6.21829	−	2.26327i	0.395661	−	0.144009i
$248$	−2.70866	−	2.27284i	−0.172000	−	0.144325i
$249$		0			0
$250$	11.0666	+	4.02790i	0.699912	+	0.254747i
$251$	−4.32994	−	7.49967i	−0.273303	−	0.473375i	0.696402	−	0.717652i	$-0.254783\pi$
$251$	−4.32994	−	7.49967i	−0.273303	−	0.473375i	−0.969706	+	0.244276i	$0.921450\pi$
$252$		0			0
$253$	−0.0881062	+	0.152604i	−0.00553919	+	0.00959415i
$254$	−1.38196	+	1.15960i	−0.0867116	+	0.0727597i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.79087	+	21.4991i	−0.236468	+	1.34108i	0.603031	+	0.797718i	$0.293959\pi$
$257$	−3.79087	+	21.4991i	−0.236468	+	1.34108i	−0.839500	+	0.543360i	$0.817152\pi$
$258$		0			0
$259$	−10.9252	+	9.16731i	−0.678857	+	0.569629i
$260$	5.42783	−	9.40127i	0.336620	−	0.583042i
$261$		0			0
$262$	4.85721	+	8.41294i	0.300080	+	0.519753i
$263$	−5.34453	−	1.94525i	−0.329558	−	0.119949i	0.171942	−	0.985107i	$-0.444996\pi$
$263$	−5.34453	−	1.94525i	−0.329558	−	0.119949i	−0.501500	+	0.865158i	$0.667218\pi$
$264$		0			0
$265$	−18.0733	−	15.1653i	−1.11023	−	0.931597i
$266$	4.79880	−	1.74662i	0.294233	−	0.107092i
$267$		0			0
$268$	1.69490	+	9.61227i	0.103533	+	0.587163i
$269$	22.7662			1.38808			0.694041	−	0.719936i	$-0.255829\pi$
$269$	22.7662			1.38808			0.694041	+	0.719936i	$0.255829\pi$
$270$		0			0
$271$	−19.8340			−1.20483			−0.602414	−	0.798184i	$-0.705794\pi$
$271$	−19.8340			−1.20483			−0.602414	+	0.798184i	$0.705794\pi$
$272$	−0.657349	−	3.72801i	−0.0398577	−	0.226044i
$273$		0			0
$274$	8.52106	−	3.10141i	0.514776	−	0.187363i
$275$	0.104186	+	0.0874226i	0.00628266	+	0.00527178i
$276$		0			0
$277$	22.6812	+	8.25528i	1.36278	+	0.496012i	0.916913	−	0.399087i	$-0.130673\pi$
$277$	22.6812	+	8.25528i	1.36278	+	0.496012i	0.445868	+	0.895099i	$0.352895\pi$
$278$	−5.02044	−	8.69565i	−0.301106	−	0.521530i
$279$		0			0
$280$	4.18878	−	7.25517i	0.250327	−	0.433579i
$281$	18.1210	−	15.2053i	1.08101	−	0.907073i	0.0850038	−	0.996381i	$-0.472910\pi$
$281$	18.1210	−	15.2053i	1.08101	−	0.907073i	0.996004	+	0.0893073i	$0.0284653\pi$
$282$		0			0
$283$	−2.01851	+	11.4476i	−0.119988	+	0.680487i	0.864171	+	0.503199i	$0.167844\pi$
$283$	−2.01851	+	11.4476i	−0.119988	+	0.680487i	−0.984159	+	0.177288i	$0.943268\pi$
$284$	2.03588	−	11.5460i	0.120807	−	0.685131i
$285$		0			0
$286$	0.846109	−	0.709970i	0.0500315	−	0.0419814i
$287$	−5.49551	+	9.51850i	−0.324390	+	0.561859i
$288$		0			0
$289$	1.33491	+	2.31213i	0.0785239	+	0.136007i
$290$	18.0733	+	6.57814i	1.06130	+	0.386282i
$291$		0			0
$292$	0.574782	+	0.482299i	0.0336366	+	0.0282244i
$293$	−10.0650	+	3.66335i	−0.588002	+	0.214015i	−0.618850	−	0.785509i	$-0.712401\pi$
$293$	−10.0650	+	3.66335i	−0.588002	+	0.214015i	0.0308485	+	0.999524i	$0.490179\pi$
$294$		0			0
$295$	−3.10363	−	17.6016i	−0.180701	−	1.02480i
$296$	−3.55460			−0.206607
$297$		0			0
$298$	15.8424			0.917728
$299$	−0.748822	−	4.24678i	−0.0433055	−	0.245598i
$300$		0			0
$301$	26.0016	−	9.46380i	1.49871	−	0.545484i
$302$	−4.06582	−	3.41163i	−0.233962	−	0.196317i
$303$		0			0
$304$	1.19605	+	0.435326i	0.0685981	+	0.0249677i
$305$	2.95839	+	5.12408i	0.169397	+	0.293404i
$306$		0			0
$307$	−12.3938	+	21.4667i	−0.707351	+	1.22517i	0.258485	+	0.966015i	$0.416777\pi$
$307$	−12.3938	+	21.4667i	−0.707351	+	1.22517i	−0.965836	+	0.259153i	$0.916557\pi$
$308$	0.652961	−	0.547899i	0.0372059	−	0.0312195i
$309$		0			0
$310$	1.28205	−	7.27086i	0.0728155	−	0.412957i
$311$	3.78267	−	21.4526i	0.214495	−	1.21646i	−0.667285	−	0.744803i	$-0.732543\pi$
$311$	3.78267	−	21.4526i	0.214495	−	1.21646i	0.881780	−	0.471661i	$-0.156345\pi$
$312$		0			0
$313$	−7.20270	+	6.04379i	−0.407121	+	0.341615i	−0.823238	−	0.567696i	$-0.807835\pi$
$313$	−7.20270	+	6.04379i	−0.407121	+	0.341615i	0.416117	+	0.909311i	$0.363391\pi$
$314$	−5.75852	+	9.97404i	−0.324972	+	0.562868i
$315$		0			0
$316$	1.18389	+	2.05056i	0.0665990	+	0.115353i
$317$	−13.6311	−	4.96130i	−0.765597	−	0.278654i	−0.0704431	−	0.997516i	$-0.522441\pi$
$317$	−13.6311	−	4.96130i	−0.765597	−	0.278654i	−0.695153	+	0.718861i	$0.744664\pi$
$318$		0			0
$319$	1.49907	+	1.25787i	0.0839318	+	0.0704271i
$320$	1.96209	−	0.714144i	0.109684	−	0.0399219i
$321$		0			0
$322$	−0.577882	−	3.27733i	−0.0322041	−	0.182639i
$323$	4.81825			0.268095
$324$		0			0
$325$	−3.32834			−0.184623
$326$	−1.33073	−	7.54693i	−0.0737022	−	0.417986i
$327$		0			0
$328$	−2.57419	+	0.936928i	−0.142136	+	0.0517332i
$329$	−3.92573	−	3.29408i	−0.216433	−	0.181609i
$330$		0			0
$331$	−0.758087	−	0.275921i	−0.0416682	−	0.0151660i	0.321102	−	0.947045i	$-0.395947\pi$
$331$	−0.758087	−	0.275921i	−0.0416682	−	0.0151660i	−0.362770	+	0.931879i	$0.618169\pi$
$332$	−5.70024	−	9.87311i	−0.312842	−	0.541857i
$333$		0			0
$334$	−3.05500	+	5.29141i	−0.167162	+	0.289533i
$335$	−15.6121	+	13.1001i	−0.852982	+	0.715737i
$336$		0			0
$337$	−4.63047	+	26.2607i	−0.252238	+	1.43051i	0.550827	+	0.834619i	$0.314312\pi$
$337$	−4.63047	+	26.2607i	−0.252238	+	1.43051i	−0.803065	+	0.595892i	$0.796799\pi$
$338$	−2.43626	+	13.8167i	−0.132515	+	0.751532i
$339$		0			0
$340$	6.05500	−	5.08075i	0.328378	−	0.275542i
$341$	0.375596	−	0.650551i	0.0203396	−	0.0352293i
$342$		0			0
$343$	4.20838	+	7.28912i	0.227231	+	0.393576i
$344$	6.48062	+	2.35875i	0.349412	+	0.127175i
$345$		0			0
$346$	−8.65897	−	7.26574i	−0.465509	−	0.390609i
$347$	−27.3491	+	9.95426i	−1.46818	+	0.534372i	−0.947605	−	0.319446i	$-0.896503\pi$
$347$	−27.3491	+	9.95426i	−1.46818	+	0.534372i	−0.520572	+	0.853818i	$0.674281\pi$
$348$		0			0
$349$	−5.13104	−	29.0996i	−0.274659	−	1.55767i	−0.740044	−	0.672558i	$-0.765196\pi$
$349$	−5.13104	−	29.0996i	−0.274659	−	1.55767i	0.465386	−	0.885108i	$-0.345916\pi$
$350$	−2.56856			−0.137295
$351$		0			0
$352$	0.212447			0.0113235
$353$	−1.08575	−	6.15757i	−0.0577884	−	0.327734i	0.942185	−	0.335095i	$-0.108768\pi$
$353$	−1.08575	−	6.15757i	−0.0577884	−	0.327734i	−0.999973	+	0.00736024i	$0.997657\pi$
$354$		0			0
$355$	23.0039	−	8.37272i	1.22092	−	0.444378i
$356$	−4.13377	−	3.46864i	−0.219089	−	0.183838i
$357$		0			0
$358$	−6.51197	−	2.37016i	−0.344169	−	0.125267i
$359$	−1.29314	−	2.23979i	−0.0682495	−	0.118212i	0.829881	−	0.557940i	$-0.188408\pi$
$359$	−1.29314	−	2.23979i	−0.0682495	−	0.118212i	−0.898131	+	0.439728i	$0.855075\pi$
$360$		0			0
$361$	8.68998	−	15.0515i	0.457367	−	0.792183i
$362$	−2.32696	+	1.95255i	−0.122302	+	0.102624i
$363$		0			0
$364$	−3.62223	+	20.5427i	−0.189856	+	1.07673i
$365$	−0.272053	+	1.54289i	−0.0142399	+	0.0807585i
$366$		0			0
$367$	14.3106	−	12.0080i	0.747009	−	0.626815i	−0.187701	−	0.982226i	$-0.560104\pi$
$367$	14.3106	−	12.0080i	0.747009	−	0.626815i	0.934710	+	0.355411i	$0.115659\pi$
$368$	0.414721	−	0.718318i	0.0216188	−	0.0374449i
$369$		0			0
$370$	−3.71104	−	6.42770i	−0.192928	−	0.334160i
$371$	42.6009	+	15.5054i	2.21173	+	0.805003i
$372$		0			0
$373$	10.3616	+	8.69443i	0.536505	+	0.450181i	0.870340	−	0.492450i	$-0.163899\pi$
$373$	10.3616	+	8.69443i	0.536505	+	0.450181i	−0.333836	+	0.942631i	$0.608343\pi$
$374$	0.755722	−	0.275060i	0.0390774	−	0.0142230i
$375$		0			0
$376$	−0.221796	−	1.25787i	−0.0114383	−	0.0648696i
$377$	−47.8894			−2.46643
$378$		0			0
$379$	30.2178			1.55218			0.776092	−	0.630620i	$-0.217199\pi$
$379$	30.2178			1.55218			0.776092	+	0.630620i	$0.217199\pi$
$380$	0.461496	+	2.61727i	0.0236742	+	0.134263i
$381$		0			0
$382$	4.78978	−	1.74334i	0.245067	−	0.0891969i
$383$	29.5609	+	24.8046i	1.51049	+	1.26745i	0.862791	+	0.505560i	$0.168714\pi$
$383$	29.5609	+	24.8046i	1.51049	+	1.26745i	0.647702	+	0.761894i	$0.275730\pi$
$384$		0			0
$385$	1.67245	+	0.608722i	0.0852359	+	0.0310233i
$386$	9.43413	+	16.3404i	0.480185	+	0.831704i
$387$		0			0
$388$	6.28158	−	10.8800i	0.318899	−	0.552349i
$389$	4.30990	−	3.61644i	0.218521	−	0.183361i	−0.526955	−	0.849893i	$-0.676667\pi$
$389$	4.30990	−	3.61644i	0.218521	−	0.183361i	0.745476	+	0.666532i	$0.232222\pi$
$390$		0			0
$391$	0.545233	−	3.09217i	0.0275736	−	0.156378i
$392$	−1.57981	+	8.95957i	−0.0797927	+	0.452527i
$393$		0			0
$394$	−15.3546	+	12.8840i	−0.773551	+	0.649087i
$395$	−2.47198	+	4.28160i	−0.124379	+	0.215431i
$396$		0			0
$397$	−3.85809	−	6.68240i	−0.193632	−	0.335380i	0.752819	−	0.658227i	$-0.228693\pi$
$397$	−3.85809	−	6.68240i	−0.193632	−	0.335380i	−0.946451	+	0.322847i	$0.895360\pi$
$398$	5.17030	+	1.88184i	0.259164	+	0.0943279i
$399$		0			0
$400$	−0.490411	−	0.411503i	−0.0245205	−	0.0205752i
$401$	34.1854	−	12.4425i	1.70714	−	0.621347i	0.710532	−	0.703665i	$-0.248455\pi$
$401$	34.1854	−	12.4425i	1.70714	−	0.621347i	0.996606	+	0.0823180i	$0.0262323\pi$
$402$		0			0
$403$	3.19222	+	18.1040i	0.159016	+	0.901823i
$404$	2.89452			0.144008
$405$		0			0
$406$	−36.9574			−1.83416
$407$	−0.131133	−	0.743691i	−0.00650001	−	0.0368634i
$408$		0			0
$409$	−5.51381	+	2.00686i	−0.272640	+	0.0992330i	−0.474722	−	0.880136i	$-0.657452\pi$
$409$	−5.51381	+	2.00686i	−0.272640	+	0.0992330i	0.202082	+	0.979369i	$0.435229\pi$
$410$	−4.38170	−	3.67668i	−0.216397	−	0.181578i
$411$		0			0
$412$	−15.6835	−	5.70832i	−0.772670	−	0.281229i
$413$	17.1719	+	29.7427i	0.844976	+	1.46354i
$414$		0			0
$415$	11.9022	−	20.6152i	0.584256	−	1.01196i
$416$	−3.98269	+	3.34187i	−0.195267	+	0.163849i
$417$		0			0
$418$	−0.0469552	+	0.266296i	−0.00229665	+	0.0130250i
$419$	−3.67016	+	20.8145i	−0.179299	+	1.01685i	0.753765	+	0.657144i	$0.228236\pi$
$419$	−3.67016	+	20.8145i	−0.179299	+	1.01685i	−0.933064	+	0.359710i	$0.882876\pi$
$420$		0			0
$421$	5.70160	−	4.78421i	0.277879	−	0.233168i	−0.493187	−	0.869923i	$-0.664168\pi$
$421$	5.70160	−	4.78421i	0.277879	−	0.233168i	0.771066	+	0.636755i	$0.219724\pi$
$422$	−12.5726	+	21.7763i	−0.612023	+	1.06005i
$423$		0			0
$424$	5.64962	+	9.78544i	0.274370	+	0.475223i
$425$	−2.27729	−	0.828865i	−0.110465	−	0.0402058i
$426$		0			0
$427$	−8.70940	−	7.30805i	−0.421477	−	0.353661i
$428$	0.301990	−	0.109915i	0.0145972	−	0.00531296i
$429$		0			0
$430$	2.50055	+	14.1813i	0.120587	+	0.683883i
$431$	13.0502			0.628607			0.314303	−	0.949323i	$-0.398229\pi$
$431$	13.0502			0.628607			0.314303	+	0.949323i	$0.398229\pi$
$432$		0			0
$433$	0.143533			0.00689775			0.00344887	−	0.999994i	$-0.498902\pi$
$433$	0.143533			0.00689775			0.00344887	+	0.999994i	$0.498902\pi$
$434$	2.46351	+	13.9712i	0.118252	+	0.670641i
$435$		0			0
$436$	−0.534100	+	0.194397i	−0.0255788	+	0.00930991i
$437$	0.808730	+	0.678605i	0.0386868	+	0.0324621i
$438$		0			0
$439$	−12.7390	−	4.63660i	−0.607997	−	0.221293i	0.0196295	−	0.999807i	$-0.493751\pi$
$439$	−12.7390	−	4.63660i	−0.607997	−	0.221293i	−0.627627	+	0.778514i	$0.715974\pi$
$440$	0.221796	+	0.384162i	0.0105737	+	0.0183142i
$441$		0			0
$442$	−9.84052	+	17.0443i	−0.468066	+	0.810714i
$443$	−9.40800	+	7.89425i	−0.446988	+	0.375067i	−0.838317	−	0.545184i	$-0.816460\pi$
$443$	−9.40800	+	7.89425i	−0.446988	+	0.375067i	0.391329	+	0.920251i	$0.372015\pi$
$444$		0			0
$445$	1.95657	−	11.0963i	0.0927505	−	0.526014i
$446$	0.651596	−	3.69539i	0.0308540	−	0.174982i
$447$		0			0
$448$	−3.07353	+	2.57900i	−0.145211	+	0.121846i
$449$	20.3323	−	35.2165i	0.959540	−	1.66197i	0.235920	−	0.971772i	$-0.424190\pi$
$449$	20.3323	−	35.2165i	0.959540	−	1.66197i	0.723620	−	0.690199i	$-0.242477\pi$
$450$		0			0
$451$	−0.290988	−	0.504006i	−0.0137021	−	0.0237327i
$452$	−1.27781	−	0.465084i	−0.0601030	−	0.0218757i
$453$		0			0
$454$	14.3462	+	12.0379i	0.673302	+	0.564968i
$455$	−40.9284	+	14.8967i	−1.91875	+	0.698369i
$456$		0			0
$457$	5.65936	+	32.0958i	0.264734	+	1.50138i	0.769792	+	0.638295i	$0.220360\pi$
$457$	5.65936	+	32.0958i	0.264734	+	1.50138i	−0.505058	+	0.863085i	$0.668529\pi$
$458$	4.14333			0.193605
$459$		0			0
$460$	1.73189			0.0807498
$461$	4.74414	+	26.9054i	0.220957	+	1.25311i	0.870265	+	0.492583i	$0.163947\pi$
$461$	4.74414	+	26.9054i	0.220957	+	1.25311i	−0.649308	+	0.760525i	$0.724942\pi$
$462$		0			0
$463$	3.19419	−	1.16259i	0.148447	−	0.0540301i	−0.266728	−	0.963772i	$-0.585943\pi$
$463$	3.19419	−	1.16259i	0.148447	−	0.0540301i	0.415175	+	0.909742i	$0.363720\pi$
$464$	−7.05621	−	5.92087i	−0.327576	−	0.274869i
$465$		0			0
$466$	1.80150	+	0.655691i	0.0834527	+	0.0303743i
$467$	16.4988	+	28.5767i	0.763473	+	1.32237i	0.941050	+	0.338267i	$0.109841\pi$
$467$	16.4988	+	28.5767i	0.763473	+	1.32237i	−0.177577	+	0.984107i	$0.556826\pi$
$468$		0			0
$469$	19.5807	−	33.9147i	0.904152	−	1.56604i
$470$	2.04302	−	1.71429i	0.0942373	−	0.0790745i
$471$		0			0
$472$	−1.48640	+	8.42981i	−0.0684172	+	0.388013i
$473$	−0.254420	+	1.44289i	−0.0116982	+	0.0663440i
$474$		0			0
$475$	0.624199	−	0.523765i	0.0286402	−	0.0240320i
$476$	−7.59415	+	13.1534i	−0.348077	+	0.602887i
$477$		0			0
$478$	−12.0996	−	20.9572i	−0.553424	−	0.958559i
$479$	−21.6536	−	7.88126i	−0.989378	−	0.360104i	−0.203898	−	0.978992i	$-0.565361\pi$
$479$	−21.6536	−	7.88126i	−0.989378	−	0.360104i	−0.785479	+	0.618888i	$0.787583\pi$
$480$		0			0
$481$	14.1569	+	11.8790i	0.645498	+	0.541637i
$482$	12.4086	−	4.51635i	0.565195	−	0.205714i
$483$		0			0
$484$	−1.90229	−	10.7884i	−0.0864678	−	0.490384i
$485$	26.2321			1.19114
$486$		0			0
$487$	26.9315			1.22038			0.610192	−	0.792254i	$-0.291092\pi$
$487$	26.9315			1.22038			0.610192	+	0.792254i	$0.291092\pi$
$488$	−0.492064	−	2.79063i	−0.0222747	−	0.126326i
$489$		0			0
$490$	−17.8507	+	6.49713i	−0.806413	+	0.293510i
$491$	0.189974	+	0.159407i	0.00857340	+	0.00719394i	0.647064	−	0.762435i	$-0.275997\pi$
$491$	0.189974	+	0.159407i	0.00857340	+	0.00719394i	−0.638491	+	0.769629i	$0.720441\pi$
$492$		0			0
$493$	−32.7665	−	11.9260i	−1.47573	−	0.537121i
$494$	−3.30869	−	5.73081i	−0.148865	−	0.257841i
$495$		0			0
$496$	−1.76795	+	3.06218i	−0.0793834	+	0.137496i
$497$	−36.0345	+	30.2365i	−1.61637	+	1.35629i
$498$		0			0
$499$	−4.63958	+	26.3124i	−0.207696	+	1.17790i	0.685444	+	0.728125i	$0.259608\pi$
$499$	−4.63958	+	26.3124i	−0.207696	+	1.17790i	−0.893140	+	0.449778i	$0.851503\pi$
$500$	2.04502	−	11.5979i	0.0914561	−	0.518673i
$501$		0			0
$502$	−6.63385	+	5.56646i	−0.296083	+	0.248443i
$503$	13.0871	−	22.6676i	0.583527	−	1.01070i	−0.411530	−	0.911396i	$-0.635006\pi$
$503$	13.0871	−	22.6676i	0.583527	−	1.01070i	0.995057	−	0.0993022i	$-0.0316611\pi$
$504$		0			0
$505$	3.02190	+	5.23409i	0.134473	+	0.232914i
$506$	0.165585	+	0.0602682i	0.00736117	+	0.00267925i
$507$		0			0
$508$	1.38196	+	1.15960i	0.0613144	+	0.0514489i
$509$	5.12867	−	1.86668i	0.227324	−	0.0827392i	−0.225847	−	0.974163i	$-0.572515\pi$
$509$	5.12867	−	1.86668i	0.227324	−	0.0827392i	0.453171	+	0.891424i	$0.350293\pi$
$510$		0			0
$511$	−0.522760	−	2.96472i	−0.0231256	−	0.131152i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	21.8308			0.962914
$515$	−6.05147	−	34.3196i	−0.266660	−	1.51230i
$516$		0			0
$517$	0.254988	−	0.0928081i	0.0112144	−	0.00408169i
$518$	10.9252	+	9.16731i	0.480024	+	0.402788i
$519$		0			0
$520$	−10.2010	−	3.71285i	−0.447343	−	0.162819i
$521$	−13.0596	−	22.6199i	−0.572151	−	0.990995i	−0.996345	−	0.0854234i	$-0.972776\pi$
$521$	−13.0596	−	22.6199i	−0.572151	−	0.990995i	0.424194	−	0.905572i	$-0.360558\pi$
$522$		0			0
$523$	−3.70382	+	6.41521i	−0.161957	+	0.280518i	−0.935570	−	0.353140i	$-0.885114\pi$
$523$	−3.70382	+	6.41521i	−0.161957	+	0.280518i	0.773614	+	0.633658i	$0.218447\pi$
$524$	7.44168	−	6.24431i	0.325091	−	0.272784i
$525$		0			0
$526$	−0.987629	+	5.60112i	−0.0430627	+	0.244221i
$527$	−2.32432	+	13.1819i	−0.101249	+	0.574212i
$528$		0			0
$529$	−17.0920	+	14.3419i	−0.743131	+	0.623561i
$530$	−11.7965	+	20.4322i	−0.512408	+	0.887516i
$531$		0			0
$532$	−2.55339	−	4.42259i	−0.110703	−	0.191744i
$533$	13.3833	+	4.87112i	0.579694	+	0.210991i
$534$		0			0
$535$	0.514038	+	0.431329i	0.0222238	+	0.0186480i
$536$	9.17192	−	3.33831i	0.396167	−	0.144193i
$537$		0			0
$538$	−3.95331	−	22.4204i	−0.170440	−	0.966610i
$539$	−1.93280			−0.0832514
$540$		0			0
$541$	11.3209			0.486725			0.243362	−	0.969935i	$-0.421750\pi$
$541$	11.3209			0.486725			0.243362	+	0.969935i	$0.421750\pi$
$542$	3.44413	+	19.5326i	0.147938	+	0.838998i
$543$		0			0
$544$	−3.55723	+	1.29473i	−0.152515	+	0.0555109i
$545$	−0.909128	−	0.762849i	−0.0389428	−	0.0326769i
$546$		0			0
$547$	9.99614	+	3.63830i	0.427404	+	0.155562i	0.546760	−	0.837289i	$-0.315861\pi$
$547$	9.99614	+	3.63830i	0.427404	+	0.155562i	−0.119356	+	0.992851i	$0.538083\pi$
$548$	−4.53396	−	7.85305i	−0.193681	−	0.335466i
$549$		0			0
$550$	0.0680027	−	0.117784i	0.00289964	−	0.00502233i
$551$	8.98121	−	7.53613i	0.382613	−	0.321050i
$552$		0			0
$553$	1.64966	−	9.35569i	0.0701507	−	0.397845i
$554$	4.19132	−	23.7701i	0.178072	−	1.00990i
$555$		0			0
$556$	−7.69175	+	6.45415i	−0.326203	+	0.273717i
$557$	−5.92385	+	10.2604i	−0.251001	+	0.434747i	−0.963802	−	0.266620i	$-0.914093\pi$
$557$	−5.92385	+	10.2604i	−0.251001	+	0.434747i	0.712800	+	0.701367i	$0.247427\pi$
$558$		0			0
$559$	−17.9276	−	31.0516i	−0.758258	−	1.31334i
$560$	−7.87232	−	2.86529i	−0.332666	−	0.121081i
$561$		0			0
$562$	−18.1210	−	15.2053i	−0.764388	−	0.641398i
$563$	5.64562	−	2.05484i	0.237935	−	0.0866012i	−0.220301	−	0.975432i	$-0.570704\pi$
$563$	5.64562	−	2.05484i	0.237935	−	0.0866012i	0.458235	+	0.888831i	$0.348482\pi$
$564$		0			0
$565$	−0.493042	−	2.79618i	−0.0207424	−	0.117636i
$566$	11.6242			0.488600
$567$		0			0
$568$	−11.7241			−0.491934
$569$	5.06851	+	28.7449i	0.212483	+	1.20505i	0.885221	+	0.465170i	$0.154007\pi$
$569$	5.06851	+	28.7449i	0.212483	+	1.20505i	−0.672739	+	0.739880i	$0.734882\pi$
$570$		0			0
$571$	−20.4985	+	7.46085i	−0.857836	+	0.312227i	−0.733231	−	0.679980i	$-0.761989\pi$
$571$	−20.4985	+	7.46085i	−0.857836	+	0.312227i	−0.124605	+	0.992206i	$0.539766\pi$
$572$	−0.846109	−	0.709970i	−0.0353776	−	0.0296853i
$573$		0			0
$574$	10.3282	+	3.75915i	0.431090	+	0.156904i
$575$	−0.265499	−	0.459857i	−0.0110721	−	0.0191774i
$576$		0			0
$577$	−20.0399	+	34.7102i	−0.834273	+	1.44500i	0.0603476	+	0.998177i	$0.480779\pi$
$577$	−20.0399	+	34.7102i	−0.834273	+	1.44500i	−0.894621	+	0.446826i	$0.852554\pi$
$578$	2.04520	−	1.71612i	0.0850689	−	0.0713813i
$579$		0			0
$580$	3.33981	−	18.9410i	0.138678	−	0.786483i
$581$	−7.94286	+	45.0462i	−0.329525	+	1.86883i
$582$		0			0
$583$	−1.83888	+	1.54300i	−0.0761587	+	0.0639047i
$584$	0.375162	−	0.649800i	0.0155243	−	0.0268889i
$585$		0			0
$586$	5.35546	+	9.27593i	0.221232	+	0.383185i
$587$	−25.2455	−	9.18861i	−1.04199	−	0.379255i	−0.236358	−	0.971666i	$-0.575954\pi$
$587$	−25.2455	−	9.18861i	−1.04199	−	0.379255i	−0.805636	+	0.592411i	$0.798176\pi$
$588$		0			0
$589$	−3.44761	−	2.89289i	−0.142056	−	0.119199i
$590$	−16.7952	+	6.11297i	−0.691449	+	0.251667i
$591$		0			0
$592$	0.617250	+	3.50060i	0.0253688	+	0.143874i
$593$	−30.4609			−1.25088			−0.625440	−	0.780272i	$-0.715081\pi$
$593$	−30.4609			−1.25088			−0.625440	+	0.780272i	$0.715081\pi$
$594$		0			0
$595$	−31.7134			−1.30012
$596$	−2.75101	−	15.6018i	−0.112686	−	0.639073i
$597$		0			0
$598$	−4.05223	+	1.47489i	−0.165708	+	0.0603128i
$599$	22.3600	+	18.7622i	0.913603	+	0.766604i	0.972801	−	0.231642i	$-0.0744099\pi$
$599$	22.3600	+	18.7622i	0.913603	+	0.766604i	−0.0591981	+	0.998246i	$0.518854\pi$
$600$		0			0
$601$	21.8214	+	7.94233i	0.890113	+	0.323975i	0.746284	−	0.665628i	$-0.231836\pi$
$601$	21.8214	+	7.94233i	0.890113	+	0.323975i	0.143829	+	0.989603i	$0.454058\pi$
$602$	−13.8352	−	23.9632i	−0.563879	−	0.976667i
$603$		0			0
$604$	−2.65377	+	4.59647i	−0.107981	+	0.187028i
$605$	17.5225	−	14.7031i	0.712389	−	0.597766i
$606$		0			0
$607$	7.40980	−	42.0231i	0.300754	−	1.70566i	−0.342091	−	0.939667i	$-0.611135\pi$
$607$	7.40980	−	42.0231i	0.300754	−	1.70566i	0.642845	−	0.765996i	$-0.277754\pi$
$608$	0.221021	−	1.25347i	0.00896359	−	0.0508350i
$609$		0			0
$610$	4.53251	−	3.80323i	0.183516	−	0.153988i
$611$	−3.32029	+	5.75091i	−0.134325	+	0.232657i
$612$		0			0
$613$	6.80411	+	11.7851i	0.274815	+	0.475994i	0.970089	−	0.242752i	$-0.0780500\pi$
$613$	6.80411	+	11.7851i	0.274815	+	0.475994i	−0.695273	+	0.718746i	$0.744717\pi$
$614$	23.2927	+	8.47785i	0.940017	+	0.342138i
$615$		0			0
$616$	−0.652961	−	0.547899i	−0.0263085	−	0.0220755i
$617$	26.4322	−	9.62052i	1.06412	−	0.387308i	0.250145	−	0.968209i	$-0.419522\pi$
$617$	26.4322	−	9.62052i	1.06412	−	0.387308i	0.813974	+	0.580901i	$0.197300\pi$
$618$		0			0
$619$	−3.38559	−	19.2007i	−0.136079	−	0.771740i	−0.974103	−	0.226106i	$-0.927400\pi$
$619$	−3.38559	−	19.2007i	−0.136079	−	0.771740i	0.838024	−	0.545633i	$-0.183711\pi$
$620$	−7.38303			−0.296510
$621$		0			0
$622$	−21.7835			−0.873439
$623$	3.75963	+	21.3219i	0.150626	+	0.854245i
$624$		0			0
$625$	20.0993	−	7.31555i	0.803972	−	0.292622i
$626$	7.20270	+	6.04379i	0.287878	+	0.241558i
$627$		0			0
$628$	10.8225	+	3.93906i	0.431864	+	0.157185i
$629$	6.72802	+	11.6533i	0.268264	+	0.464646i
$630$		0			0
$631$	−6.27471	+	10.8681i	−0.249792	+	0.432653i	−0.963468	−	0.267823i	$-0.913696\pi$
$631$	−6.27471	+	10.8681i	−0.249792	+	0.432653i	0.713676	+	0.700476i	$0.247029\pi$
$632$	1.81383	−	1.52198i	0.0721501	−	0.0605411i
$633$		0			0
$634$	−2.51892	+	14.2855i	−0.100039	+	0.567349i
$635$	−0.654100	+	3.70959i	−0.0259572	+	0.147210i
$636$		0			0
$637$	36.2336	−	30.4036i	1.43563	−	1.20464i
$638$	0.978448	−	1.69472i	0.0387371	−	0.0670947i
$639$		0			0
$640$	−1.04401	−	1.80828i	−0.0412681	−	0.0714784i
$641$	−13.1114	−	4.77215i	−0.517868	−	0.188488i	0.0698453	−	0.997558i	$-0.477749\pi$
$641$	−13.1114	−	4.77215i	−0.517868	−	0.188488i	−0.587713	+	0.809069i	$0.699972\pi$
$642$		0			0
$643$	31.4470	+	26.3871i	1.24015	+	1.04061i	0.997513	+	0.0704893i	$0.0224561\pi$
$643$	31.4470	+	26.3871i	1.24015	+	1.04061i	0.242635	+	0.970118i	$0.421988\pi$
$644$	−3.12720	+	1.13821i	−0.123229	+	0.0448516i
$645$		0			0
$646$	−0.836680	−	4.74505i	−0.0329187	−	0.186691i
$647$	−0.303995			−0.0119513			−0.00597563	−	0.999982i	$-0.501902\pi$
$647$	−0.303995			−0.0119513			−0.00597563	+	0.999982i	$0.501902\pi$
$648$		0			0
$649$	−1.81851			−0.0713829
$650$	0.577961	+	3.27778i	0.0226695	+	0.128565i
$651$		0			0
$652$	−7.20120	+	2.62102i	−0.282021	+	0.102647i
$653$	−36.0937	−	30.2862i	−1.41246	−	1.18519i	−0.955239	−	0.295835i	$-0.904402\pi$
$653$	−36.0937	−	30.2862i	−1.41246	−	1.18519i	−0.457216	−	0.889356i	$-0.651153\pi$
$654$		0			0
$655$	19.0606	+	6.93750i	0.744760	+	0.271071i
$656$	1.36970	+	2.37239i	0.0534777	+	0.0926261i
$657$		0			0
$658$	−2.56234	+	4.43811i	−0.0998905	+	0.173015i
$659$	32.9137	−	27.6179i	1.28214	−	1.07584i	0.289190	−	0.957272i	$-0.406614\pi$
$659$	32.9137	−	27.6179i	1.28214	−	1.07584i	0.992946	−	0.118568i	$-0.0378302\pi$
$660$		0			0
$661$	4.77987	−	27.1080i	0.185915	−	1.05438i	−0.738858	−	0.673861i	$-0.764635\pi$
$661$	4.77987	−	27.1080i	0.185915	−	1.05438i	0.924774	−	0.380518i	$-0.124254\pi$
$662$	−0.140089	+	0.794483i	−0.00544471	+	0.0308785i
$663$		0			0
$664$	−8.73328	+	7.32809i	−0.338917	+	0.284385i
$665$	5.33151	−	9.23445i	0.206747	−	0.358097i
$666$		0			0
$667$	−3.82009	−	6.61659i	−0.147915	−	0.256196i
$668$	5.74151	+	2.08974i	0.222146	+	0.0808545i
$669$		0			0
$670$	15.6121	+	13.1001i	0.603150	+	0.506103i
$671$	0.565701	−	0.205898i	0.0218386	−	0.00794862i
$672$		0			0
$673$	−5.84201	−	33.1317i	−0.225193	−	1.27713i	−0.862316	−	0.506370i	$-0.830987\pi$
$673$	−5.84201	−	33.1317i	−0.225193	−	1.27713i	0.637123	−	0.770762i	$-0.280124\pi$
$674$	26.6658			1.02713
$675$		0			0
$676$	14.0299			0.539611
$677$	−5.91951	−	33.5712i	−0.227505	−	1.29025i	−0.857838	−	0.513921i	$-0.828192\pi$
$677$	−5.91951	−	33.5712i	−0.227505	−	1.29025i	0.630332	−	0.776325i	$-0.282919\pi$
$678$		0			0
$679$	−47.3661	+	17.2399i	−1.81774	+	0.661605i
$680$	−6.05500	−	5.08075i	−0.232199	−	0.194838i
$681$		0			0
$682$	−0.705889	−	0.256923i	−0.0270299	−	0.00983807i
$683$	−8.22650	−	14.2487i	−0.314778	−	0.545212i	0.664612	−	0.747189i	$-0.268597\pi$
$683$	−8.22650	−	14.2487i	−0.314778	−	0.545212i	−0.979390	+	0.201976i	$0.935264\pi$
$684$		0			0
$685$	9.46699	−	16.3973i	0.361715	−	0.626509i
$686$	6.44761	−	5.41018i	0.246171	−	0.206562i
$687$		0			0
$688$	1.19757	−	6.79176i	0.0456569	−	0.258933i
$689$	10.2010	−	57.8526i	0.388626	−	2.20401i
$690$		0			0
$691$	−10.9308	+	9.17202i	−0.415827	+	0.348920i	−0.826573	−	0.562830i	$-0.809713\pi$
$691$	−10.9308	+	9.17202i	−0.415827	+	0.348920i	0.410746	+	0.911750i	$0.365268\pi$
$692$	−5.65174	+	9.78911i	−0.214847	+	0.372126i
$693$		0			0
$694$	14.5521	+	25.2051i	0.552392	+	0.956771i
$695$	−19.7011	−	7.17063i	−0.747307	−	0.271997i
$696$		0			0
$697$	7.94392	+	6.66574i	0.300897	+	0.252483i
$698$	−27.7665	+	10.1062i	−1.05098	+	0.382525i
$699$		0			0
$700$	0.446025	+	2.52953i	0.0168582	+	0.0956074i
$701$	−15.8891			−0.600123			−0.300062	−	0.953920i	$-0.597007\pi$
$701$	−15.8891			−0.600123			−0.300062	+	0.953920i	$0.597007\pi$
$702$		0			0
$703$	−4.52433			−0.170638
$704$	−0.0368910	−	0.209219i	−0.00139038	−	0.00788525i
$705$		0			0
$706$	−5.87548	+	2.13850i	−0.221127	+	0.0804835i
$707$	−8.89639	−	7.46496i	−0.334583	−	0.280749i
$708$		0			0
$709$	7.74476	+	2.81886i	0.290860	+	0.105865i	0.483330	−	0.875438i	$-0.339427\pi$
$709$	7.74476	+	2.81886i	0.290860	+	0.105865i	−0.192469	+	0.981303i	$0.561650\pi$
$710$	−12.2401	−	21.2005i	−0.459363	−	0.795640i
$711$		0			0
$712$	−2.69813	+	4.67329i	−0.101117	+	0.175139i
$713$	−2.24668	+	1.88519i	−0.0841387	+	0.0706008i
$714$		0			0
$715$	0.400476	−	2.27121i	0.0149770	−	0.0849385i
$716$	−1.20336	+	6.82462i	−0.0449718	+	0.255048i
$717$		0			0
$718$	−1.98121	+	1.66243i	−0.0739382	+	0.0620415i
$719$	10.9348	−	18.9397i	0.407801	−	0.706331i	−0.586842	−	0.809701i	$-0.699629\pi$
$719$	10.9348	−	18.9397i	0.407801	−	0.706331i	0.994643	+	0.103370i	$0.0329625\pi$
$720$		0			0
$721$	33.4819	+	57.9923i	1.24693	+	2.15975i
$722$	−16.3318	−	5.94430i	−0.607807	−	0.221224i
$723$		0			0
$724$	2.32696	+	1.95255i	0.0864808	+	0.0725660i
$725$	−5.54127	+	2.01686i	−0.205798	+	0.0749042i
$726$		0			0
$727$	8.44938	+	47.9188i	0.313370	+	1.77721i	0.581216	+	0.813749i	$0.302577\pi$
$727$	8.44938	+	47.9188i	0.313370	+	1.77721i	−0.267846	+	0.963462i	$0.586312\pi$
$728$	20.8596			0.773107
$729$		0			0
$730$	1.56669			0.0579858
$731$	−4.53343	−	25.7104i	−0.167675	−	0.950932i
$732$		0			0
$733$	24.5995	−	8.95349i	0.908603	−	0.330705i	0.154908	−	0.987929i	$-0.450492\pi$
$733$	24.5995	−	8.95349i	0.908603	−	0.330705i	0.753695	+	0.657224i	$0.228270\pi$
$734$	−14.3106	−	12.0080i	−0.528215	−	0.443225i
$735$		0			0
$736$	−0.779421	−	0.283686i	−0.0287298	−	0.0104568i
$737$	1.03680	+	1.79579i	0.0381910	+	0.0661487i
$738$		0			0
$739$	−1.28655	+	2.22838i	−0.0473267	+	0.0819722i	−0.888718	−	0.458454i	$-0.848404\pi$
$739$	−1.28655	+	2.22838i	−0.0473267	+	0.0819722i	0.841392	+	0.540426i	$0.181737\pi$
$740$	−5.68564	+	4.77082i	−0.209008	+	0.175379i
$741$		0			0
$742$	7.87232	−	44.6462i	0.289002	−	1.63901i
$743$	8.50824	−	48.2527i	0.312137	−	1.77022i	−0.275705	−	0.961242i	$-0.588911\pi$
$743$	8.50824	−	48.2527i	0.312137	−	1.77022i	0.587842	−	0.808976i	$-0.299978\pi$
$744$		0			0
$745$	25.3402	−	21.2629i	0.928393	−	0.779014i
$746$	6.76307	−	11.7140i	0.247614	−	0.428879i
$747$		0			0
$748$	−0.402111	−	0.696477i	−0.0147026	−	0.0254657i
$749$	−1.21165	−	0.441003i	−0.0442726	−	0.0161139i
$750$		0			0
$751$	6.51971	+	5.47068i	0.237908	+	0.199628i	0.753944	−	0.656938i	$-0.228149\pi$
$751$	6.51971	+	5.47068i	0.237908	+	0.199628i	−0.516037	+	0.856566i	$0.672593\pi$
$752$	−1.20024	+	0.436853i	−0.0437684	+	0.0159304i
$753$		0			0
$754$	8.31592	+	47.1619i	0.302848	+	1.71754i
$755$	−11.0822			−0.403324
$756$		0			0
$757$	17.3242			0.629658			0.314829	−	0.949148i	$-0.398053\pi$
$757$	17.3242			0.629658			0.314829	+	0.949148i	$0.398053\pi$
$758$	−5.24726	−	29.7587i	−0.190589	−	1.08088i
$759$		0			0
$760$	2.49737	−	0.908969i	0.0905892	−	0.0329718i
$761$	−8.00268	−	6.71504i	−0.290097	−	0.243420i	0.486111	−	0.873897i	$-0.338415\pi$
$761$	−8.00268	−	6.71504i	−0.290097	−	0.243420i	−0.776208	+	0.630477i	$0.782859\pi$
$762$		0			0
$763$	2.14292	+	0.779959i	0.0775789	+	0.0282364i
$764$	−2.54859	−	4.41429i	−0.0922047	−	0.159703i
$765$		0			0
$766$	19.2945	−	33.4191i	0.697140	−	1.20748i
$767$	34.0912	−	28.6059i	1.23096	−	1.03290i
$768$		0			0
$769$	6.85036	−	38.8503i	0.247030	−	1.40098i	−0.568700	−	0.822545i	$-0.692553\pi$
$769$	6.85036	−	38.8503i	0.247030	−	1.40098i	0.815730	−	0.578433i	$-0.196335\pi$
$770$	0.309056	−	1.75274i	0.0111376	−	0.0631645i
$771$		0			0
$772$	14.4539	−	12.1283i	0.520208	−	0.436507i
$773$	−11.6713	+	20.2152i	−0.419786	+	0.727091i	−0.995918	−	0.0902659i	$-0.971228\pi$
$773$	−11.6713	+	20.2152i	−0.419786	+	0.727091i	0.576131	+	0.817357i	$0.304562\pi$
$774$		0			0
$775$	1.13182	+	1.96037i	0.0406561	+	0.0704184i
$776$	−11.8055	−	4.29685i	−0.423793	−	0.154248i
$777$		0			0
$778$	−4.30990	−	3.61644i	−0.154518	−	0.129656i
$779$	−3.27645	+	1.19253i	−0.117391	+	0.0427269i
$780$		0			0
$781$	−0.432515	−	2.45292i	−0.0154766	−	0.0877722i
$782$	−3.13987			−0.112282
$783$		0			0
$784$	9.09779			0.324921
$785$	4.17585	+	23.6824i	0.149042	+	0.845262i
$786$		0			0
$787$	−35.6045	+	12.9590i	−1.26916	+	0.461938i	−0.886834	−	0.462088i	$-0.847101\pi$
$787$	−35.6045	+	12.9590i	−1.26916	+	0.461938i	−0.382330	+	0.924026i	$0.624878\pi$
$788$	15.3546	+	12.8840i	0.546983	+	0.458974i
$789$		0			0
$790$	4.64581	+	1.69094i	0.165290	+	0.0601608i
$791$	2.72793	+	4.72491i	0.0969939	+	0.167998i
$792$		0			0
$793$	−7.36619	+	12.7586i	−0.261581	+	0.453072i
$794$	−5.91093	+	4.95986i	−0.209771	+	0.176019i
$795$		0			0
$796$	0.955433	−	5.41853i	0.0338644	−	0.192055i
$797$	0.469629	−	2.66340i	0.0166351	−	0.0943423i	−0.975360	−	0.220620i	$-0.929192\pi$
$797$	0.469629	−	2.66340i	0.0166351	−	0.0943423i	0.991995	+	0.126278i	$0.0403030\pi$
$798$		0			0
$799$	−3.70394	+	3.10797i	−0.131036	+	0.109952i
$800$	−0.320093	+	0.554417i	−0.0113170	+	0.0196016i
$801$		0			0
$802$	−18.1897	−	31.5054i	−0.642300	−	1.11250i
$803$	0.149791	+	0.0545194i	0.00528600	+	0.00192395i
$804$		0			0
$805$	−5.32301	−	4.46654i	−0.187611	−	0.157425i
$806$	17.2746	−	6.28745i	0.608472	−	0.221466i
$807$		0			0
$808$	−0.502628	−	2.85055i	−0.0176824	−	0.100282i
$809$	22.3977			0.787460			0.393730	−	0.919226i	$-0.371185\pi$
$809$	22.3977			0.787460			0.393730	+	0.919226i	$0.371185\pi$
$810$		0			0
$811$	−35.0916			−1.23223			−0.616117	−	0.787655i	$-0.711295\pi$
$811$	−35.0916			−1.23223			−0.616117	+	0.787655i	$0.711295\pi$
$812$	6.41758	+	36.3959i	0.225213	+	1.27725i
$813$		0			0
$814$	−0.709622	+	0.258281i	−0.0248722	+	0.00905275i
$815$	−12.2576	−	10.2854i	−0.429367	−	0.360281i
$816$		0			0
$817$	8.24860	+	3.00224i	0.288582	+	0.105035i
$818$	2.93384	+	5.08156i	0.102579	+	0.177672i
$819$		0			0
$820$	−2.85995	+	4.95358i	−0.0998739	+	0.172987i
$821$	−10.8533	+	9.10696i	−0.378781	+	0.317835i	−0.812224	−	0.583346i	$-0.801743\pi$
$821$	−10.8533	+	9.10696i	−0.378781	+	0.317835i	0.433443	+	0.901181i	$0.357299\pi$
$822$		0			0
$823$	−6.00820	+	34.0742i	−0.209433	+	1.18775i	0.680877	+	0.732397i	$0.261599\pi$
$823$	−6.00820	+	34.0742i	−0.209433	+	1.18775i	−0.890310	+	0.455355i	$0.849512\pi$
$824$	−2.89819	+	16.4365i	−0.100963	+	0.572591i
$825$		0			0
$826$	26.3089	−	22.0758i	0.915405	−	0.768116i
$827$	25.3847	−	43.9676i	0.882713	−	1.52890i	0.0344011	−	0.999408i	$-0.489048\pi$
$827$	25.3847	−	43.9676i	0.882713	−	1.52890i	0.848312	−	0.529496i	$-0.177619\pi$
$828$		0			0
$829$	−27.2911	−	47.2695i	−0.947859	−	1.64174i	−0.749924	−	0.661524i	$-0.769910\pi$
$829$	−27.2911	−	47.2695i	−0.947859	−	1.64174i	−0.197935	−	0.980215i	$-0.563423\pi$
$830$	−22.3688	−	8.14159i	−0.776433	−	0.282599i
$831$		0			0
$832$	3.98269	+	3.34187i	0.138075	+	0.115859i
$833$	32.3629	−	11.7791i	1.12131	−	0.408123i
$834$		0			0
$835$	2.21536	+	12.5639i	0.0766658	+	0.434793i
$836$	0.270404			0.00935213
$837$		0			0
$838$	21.1356			0.730117
$839$	1.92376	+	10.9102i	0.0664155	+	0.376661i	0.999840	+	0.0178872i	$0.00569397\pi$
$839$	1.92376	+	10.9102i	0.0664155	+	0.376661i	−0.933425	+	0.358774i	$0.883195\pi$
$840$		0			0
$841$	−52.4788	+	19.1007i	−1.80961	+	0.658646i
$842$	−5.70160	−	4.78421i	−0.196490	−	0.164875i
$843$		0			0
$844$	23.6287	+	8.60014i	0.813333	+	0.296029i
$845$	14.6473	+	25.3699i	0.503883	+	0.872751i
$846$		0			0
$847$	−21.9766	+	38.0646i	−0.755124	+	1.30791i
$848$	8.65573	−	7.26302i	0.297239	−	0.249413i
$849$		0			0
$850$	−0.420826	+	2.38662i	−0.0144342	+	0.0818604i
$851$	−0.511974	+	2.90355i	−0.0175502	+	0.0995323i
$852$		0			0
$853$	−19.4866	+	16.3512i	−0.667210	+	0.559856i	−0.912238	−	0.409660i	$-0.865647\pi$
$853$	−19.4866	+	16.3512i	−0.667210	+	0.559856i	0.245028	+	0.969516i	$0.421203\pi$
$854$	−5.68465	+	9.84611i	−0.194525	+	0.336927i
$855$		0			0
$856$	−0.160686	−	0.278316i	−0.00549212	−	0.00951263i
$857$	44.3515	+	16.1426i	1.51502	+	0.551422i	0.959899	−	0.280348i	$-0.0904498\pi$
$857$	44.3515	+	16.1426i	1.51502	+	0.551422i	0.555121	+	0.831770i	$0.312672\pi$
$858$		0			0
$859$	−18.7963	−	15.7720i	−0.641323	−	0.538134i	0.263101	−	0.964768i	$-0.415255\pi$
$859$	−18.7963	−	15.7720i	−0.641323	−	0.538134i	−0.904424	+	0.426634i	$0.859699\pi$
$860$	13.5316	−	4.92512i	0.461425	−	0.167945i
$861$		0			0
$862$	−2.26615	−	12.8519i	−0.0771852	−	0.437739i
$863$	−28.4215			−0.967479			−0.483740	−	0.875212i	$-0.660722\pi$
$863$	−28.4215			−0.967479			−0.483740	+	0.875212i	$0.660722\pi$
$864$		0			0
$865$	−23.6019			−0.802488
$866$	−0.0249242	−	0.141352i	−0.000846959	−	0.00480335i
$867$		0			0
$868$	13.3312	−	4.85216i	0.452491	−	0.164693i
$869$	0.385341	+	0.323340i	0.0130718	+	0.0109685i
$870$		0			0
$871$	−47.6851	−	17.3559i	−1.61575	−	0.588084i
$872$	0.284189	+	0.492229i	0.00962385	+	0.0166690i
$873$		0			0
$874$	0.527861	−	0.914282i	0.0178552	−	0.0309261i
$875$	−36.1963	+	30.3723i	−1.22366	+	1.02677i
$876$		0			0
$877$	7.51049	−	42.5941i	0.253611	−	1.43830i	−0.546001	−	0.837784i	$-0.683851\pi$
$877$	7.51049	−	42.5941i	0.253611	−	1.43830i	0.799612	−	0.600516i	$-0.205038\pi$
$878$	−2.35406	+	13.3506i	−0.0794458	+	0.450560i
$879$		0			0
$880$	0.339811	−	0.285136i	0.0114550	−	0.00961192i
$881$	−10.2218	+	17.7047i	−0.344381	+	0.596485i	−0.985241	−	0.171173i	$-0.945244\pi$
$881$	−10.2218	+	17.7047i	−0.344381	+	0.596485i	0.640860	+	0.767658i	$0.278578\pi$
$882$		0			0
$883$	14.1469	+	24.5031i	0.476080	+	0.824595i	0.999624	−	0.0274033i	$-0.00872385\pi$
$883$	14.1469	+	24.5031i	0.476080	+	0.824595i	−0.523544	+	0.851999i	$0.675391\pi$
$884$	18.4941	+	6.73131i	0.622025	+	0.226399i
$885$		0			0
$886$	9.40800	+	7.89425i	0.316068	+	0.265212i
$887$	−53.9771	+	19.6461i	−1.81237	+	0.659650i	−0.815670	+	0.578517i	$0.803632\pi$
$887$	−53.9771	+	19.6461i	−1.81237	+	0.659650i	−0.996703	+	0.0811331i	$0.974146\pi$
$888$		0			0
$889$	−1.25688	−	7.12811i	−0.0421544	−	0.239069i
$890$	−11.2675			−0.377686
$891$		0			0
$892$	−3.75239			−0.125639
$893$	−0.282304	−	1.60103i	−0.00944695	−	0.0535763i
$894$		0			0
$895$	−13.5971	+	4.94894i	−0.454501	+	0.165425i
$896$	3.07353	+	2.57900i	0.102679	+	0.0861582i
$897$		0			0
$898$	−38.2122	−	13.9081i	−1.27516	−	0.464119i
$899$	16.2850	+	28.2065i	0.543136	+	0.940739i
$900$		0			0
$901$	21.3868	−	37.0430i	0.712497	−	1.23408i
$902$	−0.445819	+	0.374087i	−0.0148442	+	0.0124557i
$903$		0			0
$904$	−0.236129	+	1.33916i	−0.00785354	+	0.0445397i
$905$	−1.10139	+	6.24627i	−0.0366113	+	0.207633i
$906$		0			0
$907$	−21.8237	+	18.3123i	−0.724644	+	0.608049i	−0.928666	−	0.370918i	$-0.879043\pi$
$907$	−21.8237	+	18.3123i	−0.724644	+	0.608049i	0.204022	+	0.978966i	$0.434599\pi$
$908$	9.36384	−	16.2186i	0.310750	−	0.538235i
$909$		0			0
$910$	21.7776	+	37.7198i	0.721919	+	1.25040i
$911$	−17.8340	−	6.49106i	−0.590868	−	0.215058i	0.0292430	−	0.999572i	$-0.490690\pi$
$911$	−17.8340	−	6.49106i	−0.590868	−	0.215058i	−0.620111	+	0.784514i	$0.712913\pi$
$912$		0			0
$913$	−1.85536	−	1.55683i	−0.0614034	−	0.0515235i
$914$	30.6255	−	11.1468i	1.01300	−	0.368702i
$915$		0			0
$916$	−0.719481	−	4.08038i	−0.0237723	−	0.134820i
$917$	−38.9763			−1.28711
$918$		0			0
$919$	−13.1481			−0.433715			−0.216857	−	0.976203i	$-0.569581\pi$
$919$	−13.1481			−0.433715			−0.216857	+	0.976203i	$0.569581\pi$
$920$	−0.300739	−	1.70558i	−0.00991509	−	0.0562312i
$921$		0			0
$922$	25.6728	−	9.34414i	0.845489	−	0.307733i
$923$	46.6936	+	39.1806i	1.53694	+	1.28964i
$924$		0			0
$925$	2.13837	+	0.778303i	0.0703092	+	0.0255904i
$926$	−1.69959	−	2.94378i	−0.0558521	−	0.0967386i
$927$		0			0
$928$	−4.60562	+	7.97716i	−0.151187	+	0.261863i
$929$	−20.9758	+	17.6008i	−0.688194	+	0.577463i	−0.918388	−	0.395682i	$-0.870508\pi$
$929$	−20.9758	+	17.6008i	−0.688194	+	0.577463i	0.230194	+	0.973145i	$0.426064\pi$
$930$		0			0
$931$	−2.01080	+	11.4038i	−0.0659014	+	0.373745i
$932$	0.332903	−	1.88799i	0.0109046	−	0.0618430i
$933$		0			0
$934$	25.2776	−	21.2104i	0.827109	−	0.694027i
$935$	0.839615	−	1.45426i	0.0274583	−	0.0475592i
$936$		0			0
$937$	−20.0466	−	34.7218i	−0.654895	−	1.13431i	−0.981920	−	0.189296i	$-0.939380\pi$
$937$	−20.0466	−	34.7218i	−0.654895	−	1.13431i	0.327025	−	0.945016i	$-0.393954\pi$
$938$	−36.7996	−	13.3940i	−1.20155	−	0.437329i
$939$		0			0
$940$	−2.04302	−	1.71429i	−0.0666358	−	0.0559141i
$941$	−3.20347	+	1.16597i	−0.104430	+	0.0380095i	−0.393707	−	0.919236i	$-0.628807\pi$
$941$	−3.20347	+	1.16597i	−0.104430	+	0.0380095i	0.289277	+	0.957246i	$0.406585\pi$
$942$		0			0
$943$	0.394558	+	2.23765i	0.0128486	+	0.0728679i
$944$	8.55985			0.278600
$945$		0			0
$946$	1.46515			0.0476360
$947$	−0.665952	−	3.77680i	−0.0216405	−	0.122730i	0.972074	−	0.234675i	$-0.0754027\pi$
$947$	−0.665952	−	3.77680i	−0.0216405	−	0.122730i	−0.993714	+	0.111946i	$0.964292\pi$
$948$		0			0
$949$	−3.66570	+	1.33421i	−0.118994	+	0.0433102i
$950$	−0.624199	−	0.523765i	−0.0202517	−	0.0169932i
$951$		0			0
$952$	14.2723	+	5.19470i	0.462569	+	0.168361i
$953$	−26.3964	−	45.7200i	−0.855065	−	1.48102i	−0.876585	−	0.481247i	$-0.840184\pi$
$953$	−26.3964	−	45.7200i	−0.855065	−	1.48102i	0.0215205	−	0.999768i	$-0.493149\pi$
$954$		0			0
$955$	5.32150	−	9.21711i	0.172200	−	0.298259i
$956$	−18.5377	+	15.5550i	−0.599553	+	0.503084i
$957$		0			0
$958$	−4.00142	+	22.6932i	−0.129280	+	0.733184i
$959$	−6.31773	+	35.8296i	−0.204010	+	1.15700i
$960$		0			0
$961$	−14.1698	+	11.8899i	−0.457091	+	0.383545i
$962$	9.24024	−	16.0046i	0.297917	−	0.516008i
$963$		0			0
$964$	−6.60247	−	11.4358i	−0.212651	−	0.368323i
$965$	37.0213	+	13.4747i	1.19176	+	0.433764i
$966$		0			0
$967$	7.69394	+	6.45598i	0.247420	+	0.207610i	0.758061	−	0.652184i	$-0.226147\pi$
$967$	7.69394	+	6.45598i	0.247420	+	0.207610i	−0.510640	+	0.859795i	$0.670592\pi$
$968$	−10.2942	+	3.74678i	−0.330868	+	0.120426i
$969$		0			0
$970$	−4.55515	−	25.8336i	−0.146257	−	0.829466i
$971$	−4.06174			−0.130348			−0.0651738	−	0.997874i	$-0.520760\pi$
$971$	−4.06174			−0.130348			−0.0651738	+	0.997874i	$0.520760\pi$
$972$		0			0
$973$	40.2860			1.29151
$974$	−4.67661	−	26.5224i	−0.149848	−	0.849832i
$975$		0			0
$976$	−2.66279	+	0.969176i	−0.0852338	+	0.0310226i
$977$	−13.9642	−	11.7174i	−0.446756	−	0.374873i	0.391475	−	0.920189i	$-0.371965\pi$
$977$	−13.9642	−	11.7174i	−0.446756	−	0.374873i	−0.838230	+	0.545316i	$0.816410\pi$
$978$		0			0
$979$	−1.07728	−	0.392097i	−0.0344300	−	0.0125315i
$980$	9.49817	+	16.4513i	0.303408	+	0.525518i
$981$		0			0
$982$	0.123997	−	0.214768i	0.00395689	−	0.00685354i
$983$	32.2069	−	27.0248i	1.02724	−	0.861957i	0.0367208	−	0.999326i	$-0.488309\pi$
$983$	32.2069	−	27.0248i	1.02724	−	0.861957i	0.990520	+	0.137368i	$0.0438643\pi$
$984$		0			0
$985$	−7.26754	+	41.2163i	−0.231563	+	1.31326i
$986$	−6.05500	+	34.3396i	−0.192830	+	1.09360i
$987$		0			0
$988$	−5.06920	+	4.25356i	−0.161273	+	0.135324i
$989$	2.86014	−	4.95391i	0.0909471	−	0.157525i
$990$		0			0
$991$	15.9365	+	27.6029i	0.506241	+	0.876834i	0.999974	+	0.00722097i	$0.00229853\pi$
$991$	15.9365	+	27.6029i	0.506241	+	0.876834i	−0.493733	+	0.869613i	$0.664368\pi$
$992$	3.32266	+	1.20935i	0.105495	+	0.0383969i
$993$		0			0
$994$	36.0345	+	30.2365i	1.14294	+	0.959044i
$995$	10.7957	−	3.92931i	0.342246	−	0.124567i
$996$		0			0
$997$	−5.55670	−	31.5136i	−0.175982	−	0.998045i	−0.937004	−	0.349319i	$-0.886413\pi$
$997$	−5.55670	−	31.5136i	−0.175982	−	0.998045i	0.761022	−	0.648727i	$-0.224698\pi$
$998$	26.7183			0.845753
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.e.g.271.1		12
3.2	odd	2		486.2.e.f.271.2		12
9.2	odd	6		54.2.e.b.49.2	yes	12
9.4	even	3		486.2.e.e.433.1		12
9.5	odd	6		486.2.e.h.433.2		12
9.7	even	3		162.2.e.b.37.2		12
27.2	odd	18		486.2.e.f.217.2		12
27.4	even	9		1458.2.c.g.487.4		12
27.5	odd	18		1458.2.a.g.1.4		6
27.7	even	9		162.2.e.b.127.2		12
27.11	odd	18		486.2.e.h.55.2		12
27.13	even	9		1458.2.c.g.973.4		12
27.14	odd	18		1458.2.c.f.973.3		12
27.16	even	9		486.2.e.e.55.1		12
27.20	odd	18		54.2.e.b.43.2	✓	12
27.22	even	9		1458.2.a.f.1.3		6
27.23	odd	18		1458.2.c.f.487.3		12
27.25	even	9	inner	486.2.e.g.217.1		12
36.11	even	6		432.2.u.b.49.1		12
108.47	even	18		432.2.u.b.97.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.2	✓	12	27.20	odd	18
54.2.e.b.49.2	yes	12	9.2	odd	6
162.2.e.b.37.2		12	9.7	even	3
162.2.e.b.127.2		12	27.7	even	9
432.2.u.b.49.1		12	36.11	even	6
432.2.u.b.97.1		12	108.47	even	18
486.2.e.e.55.1		12	27.16	even	9
486.2.e.e.433.1		12	9.4	even	3
486.2.e.f.217.2		12	27.2	odd	18
486.2.e.f.271.2		12	3.2	odd	2
486.2.e.g.217.1		12	27.25	even	9	inner
486.2.e.g.271.1		12	1.1	even	1	trivial
486.2.e.h.55.2		12	27.11	odd	18
486.2.e.h.433.2		12	9.5	odd	6
1458.2.a.f.1.3		6	27.22	even	9
1458.2.a.g.1.4		6	27.5	odd	18
1458.2.c.f.487.3		12	27.23	odd	18
1458.2.c.f.973.3		12	27.14	odd	18
1458.2.c.g.487.4		12	27.4	even	9
1458.2.c.g.973.4		12	27.13	even	9

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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-1.59951 - 1.34215i) q^{5} +(3.77024 + 1.37225i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.04401 + 1.80828i) q^{10} +(-0.162744 + 0.136558i) q^{11} +(0.902802 - 5.12004i) q^{13} +(0.696712 - 3.95125i) q^{14} +(0.766044 - 0.642788i) q^{16} +(1.89276 - 3.27836i) q^{17} +(0.636405 + 1.10229i) q^{19} +(1.96209 + 0.714144i) q^{20} +(0.162744 + 0.136558i) q^{22} +(0.779421 - 0.283686i) q^{23} +(-0.111167 - 0.630460i) q^{25} -5.19903 q^{26} -4.01220 q^{28} +(-1.59951 - 9.07129i) q^{29} +(-3.32266 + 1.20935i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-3.55723 - 1.29473i) q^{34} +(-4.18878 - 7.25517i) q^{35} +(-1.77730 + 3.07838i) q^{37} +(0.975029 - 0.818146i) q^{38} +(0.362580 - 2.05630i) q^{40} +(-0.475691 + 2.69778i) q^{41} +(5.28305 - 4.43301i) q^{43} +(0.106223 - 0.183984i) q^{44} +(-0.414721 - 0.718318i) q^{46} +(-1.20024 - 0.436853i) q^{47} +(6.96931 + 5.84795i) q^{49} +(-0.601578 + 0.218956i) q^{50} +(0.902802 + 5.12004i) q^{52} +11.2992 q^{53} +0.443592 q^{55} +(0.696712 + 3.95125i) q^{56} +(-8.65573 + 3.15043i) q^{58} +(6.55723 + 5.50217i) q^{59} +(-2.66279 - 0.969176i) q^{61} +(1.76795 + 3.06218i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-8.31592 + 6.97788i) q^{65} +(1.69490 - 9.61227i) q^{67} +(-0.657349 + 3.72801i) q^{68} +(-6.41758 + 5.38499i) q^{70} +(-5.86207 + 10.1534i) q^{71} +(-0.375162 - 0.649800i) q^{73} +(3.34023 + 1.21575i) q^{74} +(-0.975029 - 0.818146i) q^{76} +(-0.800975 + 0.291531i) q^{77} +(-0.411161 - 2.33181i) q^{79} -2.08802 q^{80} +2.73940 q^{82} +(1.97967 + 11.2273i) q^{83} +(-7.42755 + 2.70341i) q^{85} +(-5.28305 - 4.43301i) q^{86} +(-0.199635 - 0.0726611i) q^{88} +(2.69813 + 4.67329i) q^{89} +(10.4298 - 18.0649i) q^{91} +(-0.635390 + 0.533155i) q^{92} +(-0.221796 + 1.25787i) q^{94} +(0.461496 - 2.61727i) q^{95} +(-9.62394 + 8.07544i) q^{97} +(4.54889 - 7.87892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 6 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} - 27 q^{25} - 18 q^{26} + 12 q^{28} + 3 q^{29} - 27 q^{31} + 12 q^{34}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q + 3 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^10 - 6 * q^11 - 6 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 - 27 * q^25 - 18 * q^26 + 12 * q^28 + 3 * q^29 - 27 * q^31 + 12 * q^34 - 3 * q^35 - 15 * q^37 + 15 * q^38 + 6 * q^40 - 15 * q^41 + 18 * q^43 + 3 * q^44 + 3 * q^46 + 27 * q^47 + 42 * q^49 - 36 * q^50 - 6 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 12 * q^58 + 24 * q^59 + 27 * q^61 + 12 * q^62 - 6 * q^64 - 57 * q^65 + 9 * q^67 + 15 * q^68 - 6 * q^70 - 12 * q^71 - 21 * q^73 + 3 * q^74 - 15 * q^76 + 51 * q^77 - 42 * q^79 - 6 * q^80 + 6 * q^82 - 45 * q^85 - 18 * q^86 - 12 * q^88 - 12 * q^89 - 6 * q^91 + 24 * q^92 - 9 * q^94 - 48 * q^95 - 24 * q^97 + 12 * q^98

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