LMFDB - Embedded newform 243.2.g.a.181.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(10,243)] 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("243.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			181.7
Character	$\chi$	$=$	243.181
Dual form			243.2.g.a.145.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.685792 - 1.58984i) q^{2} +(-0.684812 - 0.725858i) q^{4} +(-0.0800683 - 1.37472i) q^{5} +(3.19962 + 0.758323i) q^{7} +(1.63042 - 0.593424i) q^{8} +(-2.24050 - 0.815476i) q^{10} +(-0.171563 - 0.112839i) q^{11} +(-5.21927 - 0.610045i) q^{13} +(3.39989 - 4.56684i) q^{14} +(0.290724 - 4.99154i) q^{16} +(-3.88762 + 3.26210i) q^{17} +(-2.25026 - 1.88819i) q^{19} +(-0.943020 + 0.999543i) q^{20} +(-0.297052 + 0.195374i) q^{22} +(3.66075 - 0.867613i) q^{23} +(3.08275 - 0.360321i) q^{25} +(-4.54921 + 7.87946i) q^{26} +(-1.64070 - 2.84178i) q^{28} +(3.76701 + 5.05998i) q^{29} +(-1.45734 + 4.86786i) q^{31} +(-4.63538 - 2.32798i) q^{32} +(2.52014 + 8.41784i) q^{34} +(0.786294 - 4.45930i) q^{35} +(1.44468 + 8.19321i) q^{37} +(-4.54514 + 2.28266i) q^{38} +(-0.946337 - 2.19386i) q^{40} +(1.09418 + 2.53659i) q^{41} +(-1.41783 + 0.712061i) q^{43} +(0.0355834 + 0.201803i) q^{44} +(1.13114 - 6.41502i) q^{46} +(-0.596924 - 1.99387i) q^{47} +(3.40707 + 1.71109i) q^{49} +(1.54127 - 5.14819i) q^{50} +(3.13141 + 4.20621i) q^{52} +(-4.51663 - 7.82303i) q^{53} +(-0.141385 + 0.244885i) q^{55} +(5.66673 - 0.662345i) q^{56} +(10.6280 - 2.51887i) q^{58} +(-12.4036 + 8.15798i) q^{59} +(1.03396 - 1.09593i) q^{61} +(6.73971 + 5.65528i) q^{62} +(0.780406 - 0.654838i) q^{64} +(-0.420743 + 7.22388i) q^{65} +(-8.00722 + 10.7556i) q^{67} +(5.03012 + 0.587936i) q^{68} +(-6.55035 - 4.30824i) q^{70} +(-4.39214 - 1.59861i) q^{71} +(15.3008 - 5.56905i) q^{73} +(14.0167 + 3.32202i) q^{74} +(0.170445 + 2.92643i) q^{76} +(-0.463367 - 0.491140i) q^{77} +(-0.588953 + 1.36535i) q^{79} -6.88524 q^{80} +4.78316 q^{82} +(5.64471 - 13.0859i) q^{83} +(4.79576 + 5.08320i) q^{85} +(0.159730 + 2.74246i) q^{86} +(-0.346680 - 0.0821648i) q^{88} +(4.83016 - 1.75803i) q^{89} +(-16.2370 - 5.90980i) q^{91} +(-3.13669 - 2.06303i) q^{92} +(-3.57930 - 0.418360i) q^{94} +(-2.41556 + 3.24466i) q^{95} +(0.104394 - 1.79238i) q^{97} +(5.05691 - 4.24325i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	0.685792	−	1.58984i	0.484928	−	1.12419i	−0.483601	−	0.875289i	$-0.660671\pi$
$2$	0.685792	−	1.58984i	0.484928	−	1.12419i	0.968529	−	0.248901i	$-0.0800694\pi$
$3$		0			0
$3$		0			0
$4$	−0.684812	−	0.725858i	−0.342406	−	0.362929i
$5$	−0.0800683	−	1.37472i	−0.0358076	−	0.614794i	−0.967707	−	0.252077i	$-0.918886\pi$
$5$	−0.0800683	−	1.37472i	−0.0358076	−	0.614794i	0.931900	−	0.362717i	$-0.118151\pi$
$6$		0			0
$7$	3.19962	+	0.758323i	1.20934	+	0.286619i	0.785353	−	0.619048i	$-0.212481\pi$
$7$	3.19962	+	0.758323i	1.20934	+	0.286619i	0.423989	+	0.905667i	$0.360630\pi$
$8$	1.63042	−	0.593424i	0.576441	−	0.209807i
$9$		0			0
$10$	−2.24050	−	0.815476i	−0.708509	−	0.257876i
$11$	−0.171563	−	0.112839i	−0.0517281	−	0.0340221i	0.523382	−	0.852098i	$-0.324670\pi$
$11$	−0.171563	−	0.112839i	−0.0517281	−	0.0340221i	−0.575110	+	0.818076i	$0.695041\pi$
$12$		0			0
$13$	−5.21927	−	0.610045i	−1.44756	−	0.169196i	−0.644279	−	0.764791i	$-0.722842\pi$
$13$	−5.21927	−	0.610045i	−1.44756	−	0.169196i	−0.803285	+	0.595595i	$0.796916\pi$
$14$	3.39989	−	4.56684i	0.908658	−	1.22054i
$15$		0			0
$16$	0.290724	−	4.99154i	0.0726810	−	1.24788i
$17$	−3.88762	+	3.26210i	−0.942887	+	0.791176i	−0.978085	−	0.208204i	$-0.933238\pi$
$17$	−3.88762	+	3.26210i	−0.942887	+	0.791176i	0.0351981	+	0.999380i	$0.488794\pi$
$18$		0			0
$19$	−2.25026	−	1.88819i	−0.516245	−	0.433181i	0.347075	−	0.937837i	$-0.387175\pi$
$19$	−2.25026	−	1.88819i	−0.516245	−	0.433181i	−0.863320	+	0.504656i	$0.831619\pi$
$20$	−0.943020	+	0.999543i	−0.210866	+	0.223505i
$21$		0			0
$22$	−0.297052	+	0.195374i	−0.0633317	+	0.0416539i
$23$	3.66075	−	0.867613i	0.763318	−	0.180910i	0.169523	−	0.985526i	$-0.445777\pi$
$23$	3.66075	−	0.867613i	0.763318	−	0.180910i	0.593795	+	0.804616i	$0.297629\pi$
$24$		0			0
$25$	3.08275	−	0.360321i	0.616549	−	0.0720643i
$26$	−4.54921	+	7.87946i	−0.892173	+	1.54529i
$27$		0			0
$28$	−1.64070	−	2.84178i	−0.310063	−	0.537045i
$29$	3.76701	+	5.05998i	0.699517	+	0.939614i	0.999899	−	0.0142046i	$-0.00452163\pi$
$29$	3.76701	+	5.05998i	0.699517	+	0.939614i	−0.300382	+	0.953819i	$0.597114\pi$
$30$		0			0
$31$	−1.45734	+	4.86786i	−0.261746	+	0.874293i	0.721563	+	0.692349i	$0.243424\pi$
$31$	−1.45734	+	4.86786i	−0.261746	+	0.874293i	−0.983309	+	0.181944i	$0.941761\pi$
$32$	−4.63538	−	2.32798i	−0.819428	−	0.411532i
$33$		0			0
$34$	2.52014	+	8.41784i	0.432200	+	1.44365i
$35$	0.786294	−	4.45930i	0.132908	−	0.753759i
$36$		0			0
$37$	1.44468	+	8.19321i	0.237505	+	1.34696i	0.837274	+	0.546783i	$0.184148\pi$
$37$	1.44468	+	8.19321i	0.237505	+	1.34696i	−0.599770	+	0.800173i	$0.704741\pi$
$38$	−4.54514	+	2.28266i	−0.737319	+	0.370296i
$39$		0			0
$40$	−0.946337	−	2.19386i	−0.149629	−	0.346879i
$41$	1.09418	+	2.53659i	0.170882	+	0.396148i	0.982039	−	0.188680i	$-0.0604210\pi$
$41$	1.09418	+	2.53659i	0.170882	+	0.396148i	−0.811157	+	0.584829i	$0.801162\pi$
$42$		0			0
$43$	−1.41783	+	0.712061i	−0.216217	+	0.108588i	−0.553611	−	0.832775i	$-0.686751\pi$
$43$	−1.41783	+	0.712061i	−0.216217	+	0.108588i	0.337394	+	0.941363i	$0.390454\pi$
$44$	0.0355834	+	0.201803i	0.00536439	+	0.0304230i
$45$		0			0
$46$	1.13114	−	6.41502i	0.166778	−	0.945843i
$47$	−0.596924	−	1.99387i	−0.0870703	−	0.290835i	0.903353	−	0.428897i	$-0.141098\pi$
$47$	−0.596924	−	1.99387i	−0.0870703	−	0.290835i	−0.990424	+	0.138062i	$0.955913\pi$
$48$		0			0
$49$	3.40707	+	1.71109i	0.486724	+	0.244442i
$50$	1.54127	−	5.14819i	0.217968	−	0.728065i
$51$		0			0
$52$	3.13141	+	4.20621i	0.434248	+	0.583297i
$53$	−4.51663	−	7.82303i	−0.620407	−	1.07458i	−0.989410	−	0.145148i	$-0.953634\pi$
$53$	−4.51663	−	7.82303i	−0.620407	−	1.07458i	0.369003	−	0.929428i	$-0.379699\pi$
$54$		0			0
$55$	−0.141385	+	0.244885i	−0.0190643	+	0.0330203i
$56$	5.66673	−	0.662345i	0.757248	−	0.0885096i
$57$		0			0
$58$	10.6280	−	2.51887i	1.39552	−	0.330744i
$59$	−12.4036	+	8.15798i	−1.61481	+	1.06208i	−0.666136	+	0.745830i	$0.732053\pi$
$59$	−12.4036	+	8.15798i	−1.61481	+	1.06208i	−0.948676	+	0.316249i	$0.897577\pi$
$60$		0			0
$61$	1.03396	−	1.09593i	0.132385	−	0.140320i	−0.657790	−	0.753202i	$-0.728508\pi$
$61$	1.03396	−	1.09593i	0.132385	−	0.140320i	0.790175	+	0.612882i	$0.209990\pi$
$62$	6.73971	+	5.65528i	0.855943	+	0.718222i
$63$		0			0
$64$	0.780406	−	0.654838i	0.0975508	−	0.0818548i
$65$	−0.420743	+	7.22388i	−0.0521867	+	0.896012i
$66$		0			0
$67$	−8.00722	+	10.7556i	−0.978238	+	1.31400i	−0.0289544	+	0.999581i	$0.509218\pi$
$67$	−8.00722	+	10.7556i	−0.978238	+	1.31400i	−0.949284	+	0.314421i	$0.898190\pi$
$68$	5.03012	+	0.587936i	0.609991	+	0.0712977i
$69$		0			0
$70$	−6.55035	−	4.30824i	−0.782917	−	0.514933i
$71$	−4.39214	−	1.59861i	−0.521252	−	0.189720i	0.0679763	−	0.997687i	$-0.478346\pi$
$71$	−4.39214	−	1.59861i	−0.521252	−	0.189720i	−0.589228	+	0.807967i	$0.700568\pi$
$72$		0			0
$73$	15.3008	−	5.56905i	1.79083	−	0.651808i	0.791662	−	0.610960i	$-0.209216\pi$
$73$	15.3008	−	5.56905i	1.79083	−	0.651808i	0.999165	−	0.0408483i	$-0.0130060\pi$
$74$	14.0167	+	3.32202i	1.62941	+	0.386176i
$75$		0			0
$76$	0.170445	+	2.92643i	0.0195514	+	0.335684i
$77$	−0.463367	−	0.491140i	−0.0528055	−	0.0559706i
$78$		0			0
$79$	−0.588953	+	1.36535i	−0.0662624	+	0.153613i	−0.948129	−	0.317885i	$-0.897027\pi$
$79$	−0.588953	+	1.36535i	−0.0662624	+	0.153613i	0.881867	+	0.471498i	$0.156287\pi$
$80$	−6.88524			−0.769794
$81$		0			0
$82$	4.78316			0.528211
$83$	5.64471	−	13.0859i	0.619587	−	1.43636i	−0.262339	−	0.964976i	$-0.584494\pi$
$83$	5.64471	−	13.0859i	0.619587	−	1.43636i	0.881926	−	0.471388i	$-0.156247\pi$
$84$		0			0
$85$	4.79576	+	5.08320i	0.520173	+	0.551351i
$86$	0.159730	+	2.74246i	0.0172241	+	0.295727i
$87$		0			0
$88$	−0.346680	−	0.0821648i	−0.0369562	−	0.00875879i
$89$	4.83016	−	1.75803i	0.511996	−	0.186351i	−0.0730859	−	0.997326i	$-0.523285\pi$
$89$	4.83016	−	1.75803i	0.511996	−	0.186351i	0.585082	+	0.810974i	$0.301062\pi$
$90$		0			0
$91$	−16.2370	−	5.90980i	−1.70210	−	0.619515i
$92$	−3.13669	−	2.06303i	−0.327022	−	0.215086i
$93$		0			0
$94$	−3.57930	−	0.418360i	−0.369177	−	0.0431506i
$95$	−2.41556	+	3.24466i	−0.247831	+	0.332895i
$96$		0			0
$97$	0.104394	−	1.79238i	0.0105996	−	0.181989i	−0.988853	−	0.148897i	$-0.952428\pi$
$97$	0.104394	−	1.79238i	0.0105996	−	0.181989i	0.999452	−	0.0330916i	$-0.0105353\pi$
$98$	5.05691	−	4.24325i	0.510825	−	0.428633i
$99$		0			0
$100$	−2.37264	−	1.99088i	−0.237264	−	0.199088i
$101$	−7.87467	+	8.34666i	−0.783559	+	0.830524i	−0.988964	−	0.148153i	$-0.952667\pi$
$101$	−7.87467	+	8.34666i	−0.783559	+	0.830524i	0.205406	+	0.978677i	$0.434149\pi$
$102$		0			0
$103$	−0.417908	+	0.274862i	−0.0411777	+	0.0270830i	−0.569931	−	0.821693i	$-0.693030\pi$
$103$	−0.417908	+	0.274862i	−0.0411777	+	0.0270830i	0.528753	+	0.848776i	$0.322660\pi$
$104$	−8.87161	+	2.10261i	−0.869933	+	0.206178i
$105$		0			0
$106$	−15.5349	+	1.81577i	−1.50888	+	0.176363i
$107$	2.72183	−	4.71434i	0.263129	−	0.455752i	−0.703943	−	0.710257i	$-0.748579\pi$
$107$	2.72183	−	4.71434i	0.263129	−	0.455752i	0.967072	+	0.254504i	$0.0819123\pi$
$108$		0			0
$109$	−8.38980	−	14.5316i	−0.803597	−	1.39187i	−0.917234	−	0.398348i	$-0.869584\pi$
$109$	−8.38980	−	14.5316i	−0.803597	−	1.39187i	0.113637	−	0.993522i	$-0.463750\pi$
$110$	0.292369	+	0.392720i	0.0278763	+	0.0374444i
$111$		0			0
$112$	4.71540	−	15.7505i	0.445564	−	1.48829i
$113$	7.89295	+	3.96399i	0.742506	+	0.372901i	0.779490	−	0.626415i	$-0.215479\pi$
$113$	7.89295	+	3.96399i	0.742506	+	0.372901i	−0.0369833	+	0.999316i	$0.511775\pi$
$114$		0			0
$115$	−1.48583	−	4.96303i	−0.138555	−	0.462805i
$116$	1.09313	−	6.19945i	0.101495	−	0.575604i
$117$		0			0
$118$	4.46363	+	25.3145i	0.410910	+	2.33039i
$119$	−14.9126	+	7.48941i	−1.36704	+	0.686553i
$120$		0			0
$121$	−4.34018	−	10.0617i	−0.394561	−	0.914696i
$122$	−1.03328	−	2.39542i	−0.0935490	−	0.216871i
$123$		0			0
$124$	4.53138	−	2.27574i	0.406930	−	0.204368i
$125$	−1.93778	−	10.9897i	−0.173321	−	0.982950i
$126$		0			0
$127$	−1.21170	+	6.87190i	−0.107521	+	0.609783i	0.882662	+	0.470008i	$0.155749\pi$
$127$	−1.21170	+	6.87190i	−0.107521	+	0.609783i	−0.990183	+	0.139775i	$0.955362\pi$
$128$	−3.48126	−	11.6282i	−0.307703	−	1.02780i
$129$		0			0
$130$	11.1963	+	5.62299i	0.981980	+	0.493169i
$131$	1.61749	−	5.40278i	0.141320	−	0.472043i	−0.857800	−	0.513984i	$-0.828169\pi$
$131$	1.61749	−	5.40278i	0.141320	−	0.472043i	0.999120	+	0.0419413i	$0.0133542\pi$
$132$		0			0
$133$	−5.76811	−	7.74792i	−0.500159	−	0.671829i
$134$	11.6084	+	20.1063i	1.00281	+	1.73692i
$135$		0			0
$136$	−4.40265	+	7.62561i	−0.377524	+	0.653891i
$137$	−1.10693	+	0.129381i	−0.0945712	+	0.0110538i	−0.163247	−	0.986585i	$-0.552197\pi$
$137$	−1.10693	+	0.129381i	−0.0945712	+	0.0110538i	0.0686757	+	0.997639i	$0.478123\pi$
$138$		0			0
$139$	−4.62972	+	1.09726i	−0.392688	+	0.0930687i	−0.422216	−	0.906495i	$-0.638748\pi$
$139$	−4.62972	+	1.09726i	−0.392688	+	0.0930687i	0.0295282	+	0.999564i	$0.490600\pi$
$140$	−3.77528	+	2.48304i	−0.319069	+	0.209855i
$141$		0			0
$142$	−5.55364	+	5.88651i	−0.466051	+	0.493985i
$143$	0.826595	+	0.693595i	0.0691233	+	0.0580014i
$144$		0			0
$145$	6.65443	−	5.58373i	0.552621	−	0.463704i
$146$	1.63927	−	28.1452i	0.135667	−	2.32931i
$147$		0			0
$148$	4.95777	−	6.65944i	0.407526	−	0.547403i
$149$	7.62562	+	0.891307i	0.624715	+	0.0730187i	0.422560	−	0.906335i	$-0.361132\pi$
$149$	7.62562	+	0.891307i	0.624715	+	0.0730187i	0.202155	+	0.979354i	$0.435206\pi$
$150$		0			0
$151$	−2.58058	−	1.69727i	−0.210005	−	0.138122i	0.440150	−	0.897924i	$-0.354925\pi$
$151$	−2.58058	−	1.69727i	−0.210005	−	0.138122i	−0.650154	+	0.759802i	$0.725296\pi$
$152$	−4.78937	−	1.74319i	−0.388469	−	0.141391i
$153$		0			0
$154$	−1.09861	+	0.399861i	−0.0885285	+	0.0322217i
$155$	6.80863	+	1.61367i	0.546882	+	0.129613i
$156$		0			0
$157$	−0.356474	−	6.12042i	−0.0284497	−	0.488463i	−0.982197	−	0.187853i	$-0.939847\pi$
$157$	−0.356474	−	6.12042i	−0.0284497	−	0.488463i	0.953747	−	0.300609i	$-0.0971900\pi$
$158$	1.76679	+	1.87269i	0.140558	+	0.148983i
$159$		0			0
$160$	−2.82917	+	6.55875i	−0.223666	+	0.518515i
$161$	12.3709			0.974965
$162$		0			0
$163$	−0.171894			−0.0134638			−0.00673188	−	0.999977i	$-0.502143\pi$
$163$	−0.171894			−0.0134638			−0.00673188	+	0.999977i	$0.502143\pi$
$164$	1.09190	−	2.53130i	0.0852628	−	0.197661i
$165$		0			0
$166$	−16.9335	−	17.9484i	−1.31429	−	1.39307i
$167$	−0.0171142	−	0.293839i	−0.00132434	−	0.0227380i	0.997581	−	0.0695100i	$-0.0221436\pi$
$167$	−0.0171142	−	0.293839i	−0.00132434	−	0.0227380i	−0.998906	+	0.0467721i	$0.985107\pi$
$168$		0			0
$169$	14.2190	+	3.36997i	1.09377	+	0.259228i
$170$	11.3704	−	4.13849i	0.872069	−	0.317407i
$171$		0			0
$172$	1.48780	+	0.541516i	0.113444	+	0.0412902i
$173$	−2.24492	−	1.47651i	−0.170678	−	0.112257i	0.461296	−	0.887246i	$-0.347385\pi$
$173$	−2.24492	−	1.47651i	−0.170678	−	0.112257i	−0.631974	+	0.774990i	$0.717755\pi$
$174$		0			0
$175$	10.1369	+	1.18483i	0.766274	+	0.0895646i
$176$	−0.613115	+	0.823556i	−0.0462153	+	0.0620779i
$177$		0			0
$178$	0.517483	−	8.88485i	0.0387870	−	0.665947i
$179$	1.83356	−	1.53854i	0.137047	−	0.114996i	−0.571687	−	0.820471i	$-0.693711\pi$
$179$	1.83356	−	1.53854i	0.137047	−	0.114996i	0.708734	+	0.705476i	$0.249267\pi$
$180$		0			0
$181$	12.8278	+	10.7638i	0.953481	+	0.800065i	0.979880	−	0.199586i	$-0.0639598\pi$
$181$	12.8278	+	10.7638i	0.953481	+	0.800065i	−0.0263995	+	0.999651i	$0.508404\pi$
$182$	−20.5309	+	21.7615i	−1.52185	+	1.61307i
$183$		0			0
$184$	5.45369	−	3.58695i	0.402051	−	0.264433i
$185$	11.1477	−	2.64205i	0.819595	−	0.194248i
$186$		0			0
$187$	1.03506	−	0.120981i	0.0756912	−	0.00884704i
$188$	−1.03848	+	1.79870i	−0.0757391	+	0.131184i
$189$		0			0
$190$	3.50193	+	6.06553i	0.254057	+	0.440040i
$191$	−8.47415	−	11.3828i	−0.613168	−	0.823627i	0.381755	−	0.924263i	$-0.375320\pi$
$191$	−8.47415	−	11.3828i	−0.613168	−	0.823627i	−0.994923	+	0.100636i	$0.967912\pi$
$192$		0			0
$193$	1.19766	−	4.00046i	0.0862094	−	0.287959i	−0.904003	−	0.427525i	$-0.859386\pi$
$193$	1.19766	−	4.00046i	0.0862094	−	0.287959i	0.990213	+	0.139566i	$0.0445707\pi$
$194$	−2.77802	−	1.39517i	−0.199450	−	0.100168i
$195$		0			0
$196$	−1.09119	−	3.64483i	−0.0779421	−	0.260345i
$197$	−3.59768	+	20.4035i	−0.256324	+	1.45369i	0.536326	+	0.844011i	$0.319812\pi$
$197$	−3.59768	+	20.4035i	−0.256324	+	1.45369i	−0.792650	+	0.609677i	$0.791299\pi$
$198$		0			0
$199$	0.499478	+	2.83268i	0.0354071	+	0.200803i	0.997380	−	0.0723417i	$-0.0230472\pi$
$199$	0.499478	+	2.83268i	0.0354071	+	0.200803i	−0.961973	+	0.273145i	$0.911936\pi$
$200$	4.81235	−	2.41685i	0.340285	−	0.170897i
$201$		0			0
$202$	7.86951	+	18.2436i	0.553697	+	1.28361i
$203$	8.21590	+	19.0466i	0.576643	+	1.33681i
$204$		0			0
$205$	3.39949	−	1.70729i	0.237431	−	0.119242i
$206$	0.150390	+	0.852907i	0.0104782	+	0.0594248i
$207$		0			0
$208$	−4.56243	+	25.8748i	−0.316347	+	1.79409i
$209$	0.173000	+	0.577859i	0.0119666	+	0.0399714i
$210$		0			0
$211$	−9.48492	−	4.76351i	−0.652969	−	0.327933i	0.0912903	−	0.995824i	$-0.470901\pi$
$211$	−9.48492	−	4.76351i	−0.652969	−	0.327933i	−0.744259	+	0.667891i	$0.767197\pi$
$212$	−2.58537	+	8.63574i	−0.177564	+	0.593105i
$213$		0			0
$214$	−5.62846	−	7.56034i	−0.384754	−	0.516814i
$215$	1.09241	+	1.89211i	0.0745016	+	0.129041i
$216$		0			0
$217$	−8.35434	+	14.4701i	−0.567130	+	0.982298i
$218$	−28.8566	+	3.37285i	−1.95441	+	0.228438i
$219$		0			0
$220$	0.274574	−	0.0650752i	0.0185118	−	0.00438737i
$221$	22.2806	−	14.6542i	1.49875	−	0.985746i
$222$		0			0
$223$	16.2468	−	17.2206i	1.08797	−	1.15318i	0.100568	−	0.994930i	$-0.467934\pi$
$223$	16.2468	−	17.2206i	1.08797	−	1.15318i	0.987399	−	0.158248i	$-0.0505844\pi$
$224$	−13.0661	−	10.9638i	−0.873015	−	0.732547i
$225$		0			0
$226$	11.7150	−	9.83009i	0.779273	−	0.653888i
$227$	0.0266893	−	0.458237i	0.00177143	−	0.0304143i	−0.997307	−	0.0733452i	$-0.976633\pi$
$227$	0.0266893	−	0.458237i	0.00177143	−	0.0304143i	0.999078	+	0.0429309i	$0.0136695\pi$
$228$		0			0
$229$	9.55048	−	12.8285i	0.631113	−	0.847732i	−0.365427	−	0.930840i	$-0.619077\pi$
$229$	9.55048	−	12.8285i	0.631113	−	0.847732i	0.996541	+	0.0831075i	$0.0264845\pi$
$230$	−8.90942	−	1.04136i	−0.587470	−	0.0686654i
$231$		0			0
$232$	9.14453	+	6.01445i	0.600368	+	0.394868i
$233$	7.46875	+	2.71840i	0.489294	+	0.178089i	0.574873	−	0.818243i	$-0.305052\pi$
$233$	7.46875	+	2.71840i	0.489294	+	0.178089i	−0.0855784	+	0.996331i	$0.527274\pi$
$234$		0			0
$235$	−2.69321	+	0.980249i	−0.175686	+	0.0639444i
$236$	14.4157	+	3.41658i	0.938381	+	0.222400i
$237$		0			0
$238$	1.68003	+	28.8450i	0.108900	+	1.86974i
$239$	−14.5603	−	15.4330i	−0.941828	−	0.998280i	0.0581718	−	0.998307i	$-0.481473\pi$
$239$	−14.5603	−	15.4330i	−0.941828	−	0.998280i	−1.00000		2.70339e-5i	$0.999991\pi$
$240$		0			0
$241$	−7.15707	+	16.5920i	−0.461028	+	1.06878i	0.516177	+	0.856482i	$0.327355\pi$
$241$	−7.15707	+	16.5920i	−0.461028	+	1.06878i	−0.977205	+	0.212300i	$0.931905\pi$
$242$	−18.9729			−1.21963
$243$		0			0
$244$	−1.50356			−0.0962556
$245$	2.07948	−	4.82077i	0.132853	−	0.307988i
$246$		0			0
$247$	10.5928	+	11.2277i	0.674005	+	0.714404i
$248$	0.512628	+	8.80148i	0.0325519	+	0.558894i
$249$		0			0
$250$	−18.8008	−	4.45588i	−1.18907	−	0.281815i
$251$	−7.58786	+	2.76176i	−0.478942	+	0.174321i	−0.570199	−	0.821507i	$-0.693134\pi$
$251$	−7.58786	+	2.76176i	−0.478942	+	0.174321i	0.0912569	+	0.995827i	$0.470912\pi$
$252$		0			0
$253$	−0.725947	−	0.264223i	−0.0456399	−	0.0166116i
$254$	10.0943	+	6.63911i	0.633371	+	0.416575i
$255$		0			0
$256$	−18.8508	−	2.20334i	−1.17817	−	0.137709i
$257$	−9.87311	+	13.2619i	−0.615868	+	0.827254i	−0.995185	−	0.0980126i	$-0.968751\pi$
$257$	−9.87311	+	13.2619i	−0.615868	+	0.827254i	0.379317	+	0.925267i	$0.376159\pi$
$258$		0			0
$259$	−1.59067	+	27.3107i	−0.0988392	+	1.69700i
$260$	5.53164	−	4.64160i	0.343058	−	0.287860i
$261$		0			0
$262$	−7.48032	−	6.27673i	−0.462135	−	0.387778i
$263$	−0.0115217	+	0.0122123i	−0.000710459	+	0.000753043i	−0.727729	−	0.685865i	$-0.759424\pi$
$263$	−0.0115217	+	0.0122123i	−0.000710459	+	0.000753043i	0.727018	+	0.686618i	$0.240906\pi$
$264$		0			0
$265$	−10.3928	+	6.83548i	−0.638427	+	0.419900i
$266$	−16.2737	+	3.85694i	−0.997805	+	0.236484i
$267$		0			0
$268$	13.2905	−	1.55343i	0.811844	−	0.0948909i
$269$	3.16338	−	5.47913i	0.192874	−	0.334068i	−0.753327	−	0.657646i	$-0.771552\pi$
$269$	3.16338	−	5.47913i	0.192874	−	0.334068i	0.946202	+	0.323578i	$0.104886\pi$
$270$		0			0
$271$	−9.98751	−	17.2989i	−0.606698	−	1.05083i	−0.991781	−	0.127950i	$-0.959160\pi$
$271$	−9.98751	−	17.2989i	−0.606698	−	1.05083i	0.385082	−	0.922882i	$-0.374173\pi$
$272$	15.1527	+	20.3536i	0.918766	+	1.23412i
$273$		0			0
$274$	−0.553426	+	1.84857i	−0.0334337	+	0.111676i
$275$	−0.569542	−	0.286035i	−0.0343447	−	0.0172486i
$276$		0			0
$277$	−1.79418	−	5.99296i	−0.107802	−	0.360082i	0.887019	−	0.461734i	$-0.152772\pi$
$277$	−1.79418	−	5.99296i	−0.107802	−	0.360082i	−0.994820	+	0.101652i	$0.967587\pi$
$278$	−1.43055	+	8.11303i	−0.0857985	+	0.486587i
$279$		0			0
$280$	−1.36427	−	7.73713i	−0.0815304	−	0.462382i
$281$	5.20235	−	2.61272i	0.310346	−	0.155862i	−0.286808	−	0.957988i	$-0.592594\pi$
$281$	5.20235	−	2.61272i	0.310346	−	0.155862i	0.597154	+	0.802126i	$0.296298\pi$
$282$		0			0
$283$	−3.40508	−	7.89386i	−0.202411	−	0.469241i	0.786530	−	0.617552i	$-0.211876\pi$
$283$	−3.40508	−	7.89386i	−0.202411	−	0.469241i	−0.988941	+	0.148311i	$0.952616\pi$
$284$	1.84743	+	4.28282i	0.109625	+	0.254139i
$285$		0			0
$286$	1.66958	−	0.838495i	0.0987244	−	0.0495812i
$287$	1.57739	+	8.94585i	0.0931106	+	0.528057i
$288$		0			0
$289$	1.52028	−	8.62194i	0.0894282	−	0.507173i
$290$	−4.31371	−	14.4088i	−0.253310	−	0.846114i
$291$		0			0
$292$	−14.5205	−	7.29248i	−0.849750	−	0.426760i
$293$	1.84582	−	6.16547i	0.107834	−	0.360190i	−0.886992	−	0.461785i	$-0.847209\pi$
$293$	1.84582	−	6.16547i	0.107834	−	0.360190i	0.994826	+	0.101594i	$0.0323944\pi$
$294$		0			0
$295$	12.2081	+	16.3983i	0.710782	+	0.954746i
$296$	7.21749	+	12.5011i	0.419508	+	0.726610i
$297$		0			0
$298$	6.64663	−	11.5123i	0.385029	−	0.666889i
$299$	−19.6357	+	2.29508i	−1.13556	+	0.132728i
$300$		0			0
$301$	−5.07649	+	1.20315i	−0.292604	+	0.0693484i
$302$	−4.46814	+	2.93874i	−0.257113	+	0.169106i
$303$		0			0
$304$	−10.0792	+	10.6833i	−0.578081	+	0.612730i
$305$	−1.58939	−	1.33366i	−0.0910082	−	0.0763649i
$306$		0			0
$307$	18.8060	−	15.7801i	1.07332	−	0.900619i	0.0779670	−	0.996956i	$-0.475157\pi$
$307$	18.8060	−	15.7801i	1.07332	−	0.900619i	0.995349	+	0.0963370i	$0.0307127\pi$
$308$	−0.0391790	+	0.672677i	−0.00223243	+	0.0383293i
$309$		0			0
$310$	7.23480	−	9.71802i	0.410909	−	0.551946i
$311$	−12.8990	−	1.50767i	−0.731433	−	0.0854923i	−0.257780	−	0.966204i	$-0.582991\pi$
$311$	−12.8990	−	1.50767i	−0.731433	−	0.0854923i	−0.473653	+	0.880711i	$0.657065\pi$
$312$		0			0
$313$	−4.36800	−	2.87288i	−0.246894	−	0.162385i	0.420031	−	0.907510i	$-0.362019\pi$
$313$	−4.36800	−	2.87288i	−0.246894	−	0.162385i	−0.666925	+	0.745125i	$0.732390\pi$
$314$	−9.97498	−	3.63060i	−0.562921	−	0.204886i
$315$		0			0
$316$	1.39437	−	0.507509i	0.0784394	−	0.0285496i
$317$	29.7332	+	7.04690i	1.66998	+	0.395793i	0.953400	−	0.301709i	$-0.0975572\pi$
$317$	29.7332	+	7.04690i	1.66998	+	0.395793i	0.716582	+	0.697502i	$0.245705\pi$
$318$		0			0
$319$	−0.0753184	−	1.29317i	−0.00421702	−	0.0724035i
$320$	−0.962705	−	1.02041i	−0.0538169	−	0.0570425i
$321$		0			0
$322$	8.48388	−	19.6678i	0.472788	−	1.09605i
$323$	14.9076			0.829483
$324$		0			0
$325$	−16.3095			−0.904688
$326$	−0.117883	+	0.273284i	−0.00652896	+	0.0151358i
$327$		0			0
$328$	3.28924	+	3.48639i	0.181618	+	0.192504i
$329$	−0.397934	−	6.83227i	−0.0219388	−	0.376675i
$330$		0			0
$331$	3.09786	+	0.734205i	0.170274	+	0.0403556i	0.314868	−	0.949135i	$-0.398040\pi$
$331$	3.09786	+	0.734205i	0.170274	+	0.0403556i	−0.144595	+	0.989491i	$0.546188\pi$
$332$	−13.3641	+	4.86412i	−0.733449	+	0.266953i
$333$		0			0
$334$	−0.478896	−	0.174304i	−0.0262040	−	0.00953748i
$335$	15.4270	+	10.1465i	0.842868	+	0.554363i
$336$		0			0
$337$	32.5501	+	3.80456i	1.77312	+	0.207247i	0.938900	−	0.344191i	$-0.111847\pi$
$337$	32.5501	+	3.80456i	1.77312	+	0.207247i	0.834216	+	0.551438i	$0.185921\pi$
$338$	15.1090	−	20.2949i	0.821821	−	1.10390i
$339$		0			0
$340$	0.405495	−	6.96208i	0.0219910	−	0.377572i
$341$	0.799307	−	0.670699i	0.0432849	−	0.0363204i
$342$		0			0
$343$	−8.02888	−	6.73703i	−0.433519	−	0.363765i
$344$	−1.88910	+	2.00233i	−0.101854	+	0.107959i
$345$		0			0
$346$	−3.88696	+	2.55649i	−0.208964	+	0.137438i
$347$	21.8032	−	5.16746i	1.17046	−	0.277404i	0.400986	−	0.916084i	$-0.368668\pi$
$347$	21.8032	−	5.16746i	1.17046	−	0.277404i	0.769472	+	0.638681i	$0.220519\pi$
$348$		0			0
$349$	−21.9185	+	2.56190i	−1.17327	+	0.137136i	−0.680315	−	0.732919i	$-0.738157\pi$
$349$	−21.9185	+	2.56190i	−1.17327	+	0.137136i	−0.492955	+	0.870055i	$0.664083\pi$
$350$	8.83546	−	15.3035i	0.472275	−	0.818005i
$351$		0			0
$352$	0.532573	+	0.922444i	0.0283863	+	0.0491664i
$353$	6.51907	+	8.75663i	0.346975	+	0.466068i	0.941014	−	0.338368i	$-0.109875\pi$
$353$	6.51907	+	8.75663i	0.346975	+	0.466068i	−0.594039	+	0.804436i	$0.702467\pi$
$354$		0			0
$355$	−1.84597	+	6.16597i	−0.0979739	+	0.327256i
$356$	−4.58383	−	2.30209i	−0.242943	−	0.122010i
$357$		0			0
$358$	−1.18860	−	3.97019i	−0.0628194	−	0.209831i
$359$	4.30460	−	24.4126i	0.227188	−	1.28845i	−0.631269	−	0.775564i	$-0.717466\pi$
$359$	4.30460	−	24.4126i	0.227188	−	1.28845i	0.858457	−	0.512885i	$-0.171423\pi$
$360$		0			0
$361$	−1.80092	−	10.2135i	−0.0947851	−	0.537553i
$362$	25.9099	−	13.0125i	1.36180	−	0.683919i
$363$		0			0
$364$	6.82964	+	15.8329i	0.357971	+	0.829869i
$365$	−8.88099	−	20.5885i	−0.464853	−	1.07765i
$366$		0			0
$367$	−11.4819	+	5.76642i	−0.599350	+	0.301005i	−0.722487	−	0.691385i	$-0.757001\pi$
$367$	−11.4819	+	5.76642i	−0.599350	+	0.301005i	0.123137	+	0.992390i	$0.460705\pi$
$368$	−3.26645	−	18.5250i	−0.170276	−	0.965681i
$369$		0			0
$370$	3.44455	−	19.5350i	0.179074	−	1.01558i
$371$	−8.51910	−	28.4558i	−0.442290	−	1.47735i
$372$		0			0
$373$	1.99340	+	1.00112i	0.103214	+	0.0518362i	0.499657	−	0.866223i	$-0.333459\pi$
$373$	1.99340	+	1.00112i	0.103214	+	0.0518362i	−0.396443	+	0.918059i	$0.629756\pi$
$374$	0.517496	−	1.72856i	0.0267591	−	0.0893815i
$375$		0			0
$376$	−2.15645	−	2.89661i	−0.111210	−	0.149381i
$377$	−16.5742	−	28.7074i	−0.853617	−	1.47851i
$378$		0			0
$379$	3.67947	−	6.37302i	0.189001	−	0.327360i	−0.755916	−	0.654668i	$-0.772808\pi$
$379$	3.67947	−	6.37302i	0.189001	−	0.327360i	0.944918	+	0.327308i	$0.106142\pi$
$380$	4.00937	−	0.468628i	0.205676	−	0.0240401i
$381$		0			0
$382$	−23.9083	+	5.66638i	−1.22326	+	0.289917i
$383$	12.0779	−	7.94378i	0.617154	−	0.405908i	−0.202079	−	0.979369i	$-0.564770\pi$
$383$	12.0779	−	7.94378i	0.617154	−	0.405908i	0.819233	+	0.573461i	$0.194400\pi$
$384$		0			0
$385$	−0.638079	+	0.676324i	−0.0325195	+	0.0344687i
$386$	−5.53876	−	4.64757i	−0.281916	−	0.236555i
$387$		0			0
$388$	−1.37251	+	1.15167i	−0.0696784	+	0.0584671i
$389$	−0.494471	+	8.48974i	−0.0250707	+	0.430447i	0.962297	+	0.272001i	$0.0876854\pi$
$389$	−0.494471	+	8.48974i	−0.0250707	+	0.430447i	−0.987368	+	0.158446i	$0.949352\pi$
$390$		0			0
$391$	−11.4014	+	15.3147i	−0.576592	+	0.774497i
$392$	6.57036	+	0.767965i	0.331853	+	0.0387881i
$393$		0			0
$394$	29.9711	+	19.7123i	1.50992	+	0.993091i
$395$	1.92413	+	0.700325i	0.0968133	+	0.0352372i
$396$		0			0
$397$	−5.16106	+	1.87847i	−0.259026	+	0.0942779i	−0.468269	−	0.883586i	$-0.655122\pi$
$397$	−5.16106	+	1.87847i	−0.259026	+	0.0942779i	0.209243	+	0.977864i	$0.432900\pi$
$398$	4.84606	+	1.14854i	0.242911	+	0.0575710i
$399$		0			0
$400$	−0.902330	−	15.4924i	−0.0451165	−	0.774620i
$401$	6.45676	+	6.84377i	0.322435	+	0.341762i	0.868234	−	0.496155i	$-0.165255\pi$
$401$	6.45676	+	6.84377i	0.322435	+	0.341762i	−0.545799	+	0.837916i	$0.683774\pi$
$402$		0			0
$403$	10.5759	−	24.5176i	0.526821	−	1.22131i
$404$	11.4512			0.569716
$405$		0			0
$406$	35.9155			1.78246
$407$	0.676656	−	1.56867i	0.0335406	−	0.0777558i
$408$		0			0
$409$	10.5830	+	11.2174i	0.523297	+	0.554663i	0.934077	−	0.357072i	$-0.116225\pi$
$409$	10.5830	+	11.2174i	0.523297	+	0.554663i	−0.410780	+	0.911735i	$0.634743\pi$
$410$	−0.382979	−	6.57550i	−0.0189140	−	0.324741i
$411$		0			0
$412$	0.485699	+	0.115113i	0.0239287	+	0.00567120i
$413$	−45.8732	+	16.6965i	−2.25727	+	0.821580i
$414$		0			0
$415$	−18.4414	−	6.71212i	−0.905253	−	0.329485i
$416$	22.7731	+	14.9781i	1.11654	+	0.734363i
$417$		0			0
$418$	1.03735	+	0.121249i	0.0507384	+	0.00593046i
$419$	−14.7527	+	19.8163i	−0.720715	+	0.968088i	0.279254	+	0.960217i	$0.409913\pi$
$419$	−14.7527	+	19.8163i	−0.720715	+	0.968088i	−0.999969	+	0.00787086i	$0.997495\pi$
$420$		0			0
$421$	0.0108029	−	0.185479i	0.000526502	−	0.00903969i	−0.998035	−	0.0626641i	$-0.980040\pi$
$421$	0.0108029	−	0.185479i	0.000526502	−	0.00903969i	0.998561	+	0.0536244i	$0.0170774\pi$
$422$	−14.0779	+	11.8128i	−0.685302	+	0.575037i
$423$		0			0
$424$	−12.0064	−	10.0746i	−0.583082	−	0.489264i
$425$	−10.8092	+	11.4570i	−0.524321	+	0.555748i
$426$		0			0
$427$	4.13935	−	2.72249i	0.200317	−	0.131751i
$428$	−5.28588	+	1.25278i	−0.255503	+	0.0605552i
$429$		0			0
$430$	3.75732	−	0.439168i	0.181194	−	0.0211785i
$431$	−7.27612	+	12.6026i	−0.350478	+	0.607046i	−0.986333	−	0.164762i	$-0.947314\pi$
$431$	−7.27612	+	12.6026i	−0.350478	+	0.607046i	0.635855	+	0.771808i	$0.280648\pi$
$432$		0			0
$433$	17.3096	+	29.9811i	0.831846	+	1.44080i	0.896573	+	0.442897i	$0.146049\pi$
$433$	17.3096	+	29.9811i	0.831846	+	1.44080i	−0.0647264	+	0.997903i	$0.520617\pi$
$434$	17.2759	+	23.2056i	0.829272	+	1.11391i
$435$		0			0
$436$	−4.80242	+	16.0412i	−0.229994	+	0.768233i
$437$	−9.87585	−	4.95984i	−0.472426	−	0.237261i
$438$		0			0
$439$	0.563799	+	1.88322i	0.0269087	+	0.0898812i	0.970389	−	0.241547i	$-0.0776548\pi$
$439$	0.563799	+	1.88322i	0.0269087	+	0.0898812i	−0.943480	+	0.331428i	$0.892470\pi$
$440$	−0.0851954	+	0.483167i	−0.00406153	+	0.0230341i
$441$		0			0
$442$	−8.01800	−	45.4724i	−0.381378	−	2.16290i
$443$	−28.4252	+	14.2757i	−1.35052	+	0.678257i	−0.969220	−	0.246195i	$-0.920820\pi$
$443$	−28.4252	+	14.2757i	−1.35052	+	0.678257i	−0.381300	+	0.924451i	$0.624523\pi$
$444$		0			0
$445$	−2.80355	−	6.49935i	−0.132901	−	0.308099i
$446$	−16.2362	−	37.6397i	−0.768805	−	1.78229i
$447$		0			0
$448$	2.99358	−	1.50343i	0.141433	−	0.0710305i
$449$	5.17251	+	29.3348i	0.244106	+	1.38439i	0.822560	+	0.568679i	$0.192545\pi$
$449$	5.17251	+	29.3348i	0.244106	+	1.38439i	−0.578454	+	0.815715i	$0.696344\pi$
$450$		0			0
$451$	0.0985049	−	0.558649i	0.00463841	−	0.0263057i
$452$	−2.52789	−	8.44375i	−0.118902	−	0.397160i
$453$		0			0
$454$	−0.710223	−	0.356687i	−0.0333324	−	0.0167402i
$455$	−6.82425	+	22.7946i	−0.319926	+	1.06863i
$456$		0			0
$457$	7.61163	+	10.2242i	0.356057	+	0.478267i	0.943676	−	0.330870i	$-0.107342\pi$
$457$	7.61163	+	10.2242i	0.356057	+	0.478267i	−0.587619	+	0.809137i	$0.699935\pi$
$458$	−13.8457	−	23.9815i	−0.646968	−	1.12058i
$459$		0			0
$460$	−2.58494	+	4.47725i	−0.120523	+	0.208753i
$461$	20.5283	−	2.39941i	0.956097	−	0.111752i	0.376287	−	0.926503i	$-0.377201\pi$
$461$	20.5283	−	2.39941i	0.956097	−	0.111752i	0.579810	+	0.814752i	$0.303127\pi$
$462$		0			0
$463$	−16.2014	+	3.83980i	−0.752943	+	0.178451i	−0.589127	−	0.808040i	$-0.700528\pi$
$463$	−16.2014	+	3.83980i	−0.752943	+	0.178451i	−0.163816	+	0.986491i	$0.552380\pi$
$464$	26.3522	−	17.3321i	1.22337	−	0.804624i
$465$		0			0
$466$	9.44385	−	10.0099i	0.437478	−	0.463700i
$467$	22.4416	+	18.8308i	1.03848	+	0.871384i	0.991835	−	0.127527i	$-0.0407041\pi$
$467$	22.4416	+	18.8308i	1.03848	+	0.871384i	0.0466403	+	0.998912i	$0.485149\pi$
$468$		0			0
$469$	−33.7762	+	28.3416i	−1.55964	+	1.30870i
$470$	−0.288540	+	4.95403i	−0.0133093	+	0.228513i
$471$		0			0
$472$	−15.3819	+	20.6615i	−0.708012	+	0.951025i
$473$	0.323595	+	0.0378228i	0.0148789	+	0.00173909i
$474$		0			0
$475$	−7.61734	−	5.01000i	−0.349507	−	0.229875i
$476$	15.6486	+	5.69562i	0.717252	+	0.261059i
$477$		0			0
$478$	−34.5215	+	12.5648i	−1.57897	+	0.574700i
$479$	−21.7592	−	5.15702i	−0.994201	−	0.235630i	−0.298850	−	0.954300i	$-0.596603\pi$
$479$	−21.7592	−	5.15702i	−0.994201	−	0.235630i	−0.695351	+	0.718670i	$0.744751\pi$
$480$		0			0
$481$	−2.54197	−	43.6439i	−0.115904	−	1.98999i
$482$	21.4704	+	22.7573i	0.977949	+	1.03657i
$483$		0			0
$484$	−4.33113	+	10.0407i	−0.196870	+	0.456395i
$485$	−2.47238			−0.112265
$486$		0			0
$487$	3.73936			0.169447			0.0847233	−	0.996405i	$-0.472999\pi$
$487$	3.73936			0.169447			0.0847233	+	0.996405i	$0.472999\pi$
$488$	1.03544	−	2.40041i	0.0468720	−	0.108661i
$489$		0			0
$490$	−6.23819	−	6.61209i	−0.281813	−	0.298704i
$491$	−0.0701629	−	1.20465i	−0.00316641	−	0.0543651i	0.996355	−	0.0853058i	$-0.0271867\pi$
$491$	−0.0701629	−	1.20465i	−0.00316641	−	0.0543651i	−0.999521	+	0.0309407i	$0.990150\pi$
$492$		0			0
$493$	−31.1509	−	7.38290i	−1.40297	−	0.332509i
$494$	25.1148	−	9.14105i	1.12997	−	0.411275i
$495$		0			0
$496$	23.8744	+	8.68957i	1.07199	+	0.390173i
$497$	−12.8409	−	8.44560i	−0.575994	−	0.378837i
$498$		0			0
$499$	−3.31533	−	0.387506i	−0.148415	−	0.0173472i	0.0415612	−	0.999136i	$-0.486767\pi$
$499$	−3.31533	−	0.387506i	−0.148415	−	0.0173472i	−0.189976	+	0.981789i	$0.560841\pi$
$500$	−6.64995	+	8.93244i	−0.297395	+	0.399471i
$501$		0			0
$502$	−0.812933	+	13.9575i	−0.0362830	+	0.622954i
$503$	−18.7108	+	15.7002i	−0.834274	+	0.700039i	−0.956268	−	0.292492i	$-0.905516\pi$
$503$	−18.7108	+	15.7002i	−0.834274	+	0.700039i	0.121994	+	0.992531i	$0.461071\pi$
$504$		0			0
$505$	12.1048	+	10.1572i	0.538658	+	0.451988i
$506$	−0.917923	+	0.972941i	−0.0408066	+	0.0432525i
$507$		0			0
$508$	5.81781	−	3.82643i	0.258124	−	0.169771i
$509$	−30.1051	+	7.13503i	−1.33438	+	0.316255i	−0.835059	−	0.550160i	$-0.814567\pi$
$509$	−30.1051	+	7.13503i	−1.33438	+	0.316255i	−0.499325	+	0.866415i	$0.666418\pi$
$510$		0			0
$511$	53.1800	−	6.21585i	2.35254	−	0.274973i
$512$	−4.29252	+	7.43487i	−0.189705	+	0.328578i
$513$		0			0
$514$	14.3134	+	24.7916i	0.631339	+	1.09351i
$515$	0.411320	+	0.552499i	0.0181249	+	0.0243460i
$516$		0			0
$517$	−0.122575	+	0.409429i	−0.00539084	+	0.0180067i
$518$	42.3289	+	21.2584i	1.85982	+	0.934039i
$519$		0			0
$520$	3.60084	+	12.0276i	0.157907	+	0.527447i
$521$	−2.47495	+	14.0361i	−0.108430	+	0.614934i	0.881365	+	0.472435i	$0.156625\pi$
$521$	−2.47495	+	14.0361i	−0.108430	+	0.614934i	−0.989795	+	0.142499i	$0.954486\pi$
$522$		0			0
$523$	0.234960	+	1.33253i	0.0102741	+	0.0582673i	0.989514	−	0.144439i	$-0.0461376\pi$
$523$	0.234960	+	1.33253i	0.0102741	+	0.0582673i	−0.979240	+	0.202706i	$0.935026\pi$
$524$	−5.02932	+	2.52582i	−0.219707	+	0.110341i
$525$		0			0
$526$	0.0115142	+	0.0266928i	0.000502042	+	0.00116386i
$527$	−10.2139	−	23.6784i	−0.444923	−	1.03145i
$528$		0			0
$529$	−7.90524	+	3.97016i	−0.343706	+	0.172616i
$530$	3.74002	+	21.2107i	0.162456	+	0.921335i
$531$		0			0
$532$	−1.67382	+	9.49269i	−0.0725692	+	0.411560i
$533$	−4.16337	−	13.9066i	−0.180335	−	0.602362i
$534$		0			0
$535$	−6.69883	−	3.36428i	−0.289616	−	0.145450i
$536$	−6.67252	+	22.2878i	−0.288209	+	0.962685i
$537$		0			0
$538$	−6.54154	−	8.78682i	−0.282026	−	0.378827i
$539$	−0.391448	−	0.678008i	−0.0168609	−	0.0292039i
$540$		0			0
$541$	12.5060	−	21.6611i	0.537676	−	0.931283i	−0.461352	−	0.887217i	$-0.652636\pi$
$541$	12.5060	−	21.6611i	0.537676	−	0.931283i	0.999029	−	0.0440659i	$-0.0140312\pi$
$542$	−34.3519	+	4.01516i	−1.47554	+	0.172466i
$543$		0			0
$544$	25.6147	−	6.07080i	1.09822	−	0.260284i
$545$	−19.3051	+	12.6971i	−0.826938	+	0.543886i
$546$		0			0
$547$	−19.4886	+	20.6567i	−0.833273	+	0.883218i	−0.994611	−	0.103681i	$-0.966938\pi$
$547$	−19.4886	+	20.6567i	−0.833273	+	0.883218i	0.161337	+	0.986899i	$0.448419\pi$
$548$	0.851950	+	0.714871i	0.0363935	+	0.0305378i
$549$		0			0
$550$	−0.845339	+	0.709324i	−0.0360454	+	0.0302457i
$551$	1.07745	−	18.4991i	0.0459009	−	0.788089i
$552$		0			0
$553$	−2.91980	+	3.92197i	−0.124162	+	0.166779i
$554$	−10.7583	−	1.25747i	−0.457077	−	0.0534246i
$555$		0			0
$556$	3.96695	+	2.60910i	0.168236	+	0.110651i
$557$	34.6621	+	12.6160i	1.46868	+	0.534556i	0.947742	−	0.319039i	$-0.103360\pi$
$557$	34.6621	+	12.6160i	1.46868	+	0.534556i	0.520938	+	0.853594i	$0.325582\pi$
$558$		0			0
$559$	7.83442	−	2.85150i	0.331361	−	0.120605i
$560$	−22.0301	−	5.22124i	−0.930943	−	0.220638i
$561$		0			0
$562$	−0.586086	−	10.0627i	−0.0247226	−	0.424470i
$563$	15.2051	+	16.1164i	0.640817	+	0.679226i	0.963631	−	0.267236i	$-0.0861104\pi$
$563$	15.2051	+	16.1164i	0.640817	+	0.679226i	−0.322814	+	0.946462i	$0.604629\pi$
$564$		0			0
$565$	4.81740	−	11.1680i	0.202670	−	0.469841i
$566$	−14.8852			−0.625671
$567$		0			0
$568$	−8.10969			−0.340275
$569$	−2.53616	+	5.87948i	−0.106321	+	0.246480i	−0.963069	−	0.269256i	$-0.913222\pi$
$569$	−2.53616	+	5.87948i	−0.106321	+	0.246480i	0.856747	+	0.515736i	$0.172482\pi$
$570$		0			0
$571$	3.79067	+	4.01787i	0.158634	+	0.168143i	0.801816	−	0.597571i	$-0.203867\pi$
$571$	3.79067	+	4.01787i	0.158634	+	0.168143i	−0.643182	+	0.765714i	$0.722386\pi$
$572$	−0.0626100	−	1.07497i	−0.00261786	−	0.0449469i
$573$		0			0
$574$	15.3043	+	3.62718i	0.638788	+	0.151395i
$575$	10.9725	−	3.99368i	0.457586	−	0.166548i
$576$		0			0
$577$	36.7599	+	13.3795i	1.53033	+	0.556996i	0.963703	−	0.266977i	$-0.0860246\pi$
$577$	36.7599	+	13.3795i	1.53033	+	0.556996i	0.566630	+	0.823972i	$0.308247\pi$
$578$	−12.6649	−	8.32986i	−0.526792	−	0.346477i
$579$		0			0
$580$	−8.61003	−	1.00637i	−0.357512	−	0.0417872i
$581$	27.9842	−	37.5894i	1.16098	−	1.55947i
$582$		0			0
$583$	−0.107855	+	1.85179i	−0.00446688	+	0.0766933i
$584$	21.6420	−	18.1598i	0.895551	−	0.751457i
$585$		0			0
$586$	−8.53628	−	7.16279i	−0.352631	−	0.295892i
$587$	9.54436	−	10.1164i	0.393938	−	0.417550i	−0.499799	−	0.866141i	$-0.666593\pi$
$587$	9.54436	−	10.1164i	0.393938	−	0.417550i	0.893737	+	0.448592i	$0.148074\pi$
$588$		0			0
$589$	12.4708	−	8.20221i	0.513852	−	0.337966i
$590$	34.4429	−	8.16313i	1.41799	−	0.336071i
$591$		0			0
$592$	41.3167	−	4.82923i	1.69811	−	0.198480i
$593$	−8.67989	+	15.0340i	−0.356441	+	0.617373i	−0.987363	−	0.158472i	$-0.949343\pi$
$593$	−8.67989	+	15.0340i	−0.356441	+	0.617373i	0.630923	+	0.775846i	$0.282676\pi$
$594$		0			0
$595$	11.4899	+	19.9010i	0.471039	+	0.815863i
$596$	−4.57515	−	6.14549i	−0.187405	−	0.251729i
$597$		0			0
$598$	−9.81717	+	32.7916i	−0.401454	+	1.34095i
$599$	−37.1512	−	18.6580i	−1.51796	−	0.762346i	−0.522065	−	0.852906i	$-0.674838\pi$
$599$	−37.1512	−	18.6580i	−1.51796	−	0.762346i	−0.995891	+	0.0905596i	$0.971134\pi$
$600$		0			0
$601$	2.64850	+	8.84660i	0.108035	+	0.360860i	0.994862	−	0.101240i	$-0.0322811\pi$
$601$	2.64850	+	8.84660i	0.108035	+	0.360860i	−0.886827	+	0.462101i	$0.847096\pi$
$602$	−1.56859	+	8.89594i	−0.0639311	+	0.362571i
$603$		0			0
$604$	0.535232	+	3.03545i	0.0217783	+	0.123511i
$605$	−13.4845	+	6.77215i	−0.548221	+	0.275327i
$606$		0			0
$607$	−5.34301	−	12.3865i	−0.216866	−	0.502752i	0.774704	−	0.632324i	$-0.217899\pi$
$607$	−5.34301	−	12.3865i	−0.216866	−	0.502752i	−0.991570	+	0.129572i	$0.958640\pi$
$608$	6.03515	+	13.9910i	0.244758	+	0.567412i
$609$		0			0
$610$	−3.21030	+	1.61227i	−0.129981	+	0.0652790i
$611$	1.89916	+	10.7707i	0.0768317	+	0.435734i
$612$		0			0
$613$	−0.675007	+	3.82815i	−0.0272633	+	0.154618i	−0.995400	−	0.0958034i	$-0.969458\pi$
$613$	−0.675007	+	3.82815i	−0.0272633	+	0.154618i	0.968137	+	0.250421i	$0.0805691\pi$
$614$	−12.1909	−	40.7205i	−0.491986	−	1.64335i
$615$		0			0
$616$	−1.04694	−	0.525792i	−0.0421823	−	0.0211847i
$617$	6.88741	−	23.0055i	0.277276	−	0.926168i	−0.699990	−	0.714153i	$-0.746812\pi$
$617$	6.88741	−	23.0055i	0.277276	−	0.926168i	0.977266	−	0.212015i	$-0.0680026\pi$
$618$		0			0
$619$	−6.07827	−	8.16453i	−0.244306	−	0.328160i	0.663009	−	0.748612i	$-0.269279\pi$
$619$	−6.07827	−	8.16453i	−0.244306	−	0.328160i	−0.907315	+	0.420451i	$0.861872\pi$
$620$	−3.49133	−	6.04716i	−0.140215	−	0.242860i
$621$		0			0
$622$	−11.2430	+	19.4734i	−0.450802	+	0.780812i
$623$	16.7878	−	1.96221i	0.672590	−	0.0786144i
$624$		0			0
$625$	0.147739	−	0.0350147i	0.00590955	−	0.00140059i
$626$	−7.56297	+	4.97425i	−0.302277	+	0.198811i
$627$		0			0
$628$	−4.19844	+	4.45009i	−0.167536	+	0.177578i
$629$	−32.3435	−	27.1394i	−1.28962	−	1.08212i
$630$		0			0
$631$	−37.7162	+	31.6476i	−1.50146	+	1.25987i	−0.622836	+	0.782352i	$0.714020\pi$
$631$	−37.7162	+	31.6476i	−1.50146	+	1.25987i	−0.878621	+	0.477520i	$0.841536\pi$
$632$	−0.150011	+	2.57559i	−0.00596711	+	0.102451i
$633$		0			0
$634$	31.5943	−	42.4384i	1.25477	−	1.68545i
$635$	9.54396	+	1.11553i	0.378740	+	0.0442684i
$636$		0			0
$637$	−16.7386	−	11.0091i	−0.663206	−	0.436197i
$638$	−2.10759	−	0.767099i	−0.0834402	−	0.0303698i
$639$		0			0
$640$	−15.7068	+	5.71682i	−0.620867	+	0.225977i
$641$	33.1606	+	7.85921i	1.30976	+	0.310420i	0.825451	−	0.564474i	$-0.190921\pi$
$641$	33.1606	+	7.85921i	1.30976	+	0.310420i	0.484314	+	0.874894i	$0.339069\pi$
$642$		0			0
$643$	1.15570	+	19.8426i	0.0455764	+	0.782516i	0.941230	+	0.337765i	$0.109671\pi$
$643$	1.15570	+	19.8426i	0.0455764	+	0.782516i	−0.895654	+	0.444751i	$0.853292\pi$
$644$	−8.47175	−	8.97953i	−0.333834	−	0.353843i
$645$		0			0
$646$	10.2235	−	23.7008i	0.402240	−	0.932497i
$647$	37.1636			1.46105			0.730525	−	0.682886i	$-0.239275\pi$
$647$	37.1636			1.46105			0.730525	+	0.682886i	$0.239275\pi$
$648$		0			0
$649$	3.04853			0.119665
$650$	−11.1849	+	25.9296i	−0.438709	+	1.01704i
$651$		0			0
$652$	0.117715	+	0.124771i	0.00461007	+	0.00488639i
$653$	−0.320235	−	5.49823i	−0.0125318	−	0.215162i	−0.998760	−	0.0497749i	$-0.984150\pi$
$653$	−0.320235	−	5.49823i	−0.0125318	−	0.215162i	0.986229	−	0.165387i	$-0.0528874\pi$
$654$		0			0
$655$	−7.55681	−	1.79100i	−0.295269	−	0.0699801i
$656$	12.9796	−	4.72418i	0.506767	−	0.184448i
$657$		0			0
$658$	−11.1351	−	4.05286i	−0.434093	−	0.157997i
$659$	31.8182	+	20.9272i	1.23946	+	0.815207i	0.988268	−	0.152730i	$-0.0488065\pi$
$659$	31.8182	+	20.9272i	1.23946	+	0.815207i	0.251194	+	0.967937i	$0.419177\pi$
$660$		0			0
$661$	27.9872	+	3.27123i	1.08857	+	0.127236i	0.641397	−	0.767209i	$-0.278355\pi$
$661$	27.9872	+	3.27123i	1.08857	+	0.127236i	0.447177	+	0.894445i	$0.352429\pi$
$662$	3.29176	−	4.42160i	0.127938	−	0.171850i
$663$		0			0
$664$	1.43775	−	24.6852i	0.0557955	−	0.957972i
$665$	−10.1894	+	8.54990i	−0.395127	+	0.331551i
$666$		0			0
$667$	18.1802	+	15.2550i	0.703939	+	0.590675i
$668$	−0.201566	+	0.213647i	−0.00779881	+	0.00826626i
$669$		0			0
$670$	26.7111	−	17.5682i	1.03194	−	0.678718i
$671$	−0.301053	+	0.0713508i	−0.0116220	+	0.00275447i
$672$		0			0
$673$	−24.6772	+	2.88436i	−0.951238	+	0.111184i	−0.577536	−	0.816365i	$-0.695986\pi$
$673$	−24.6772	+	2.88436i	−0.951238	+	0.111184i	−0.373702	+	0.927549i	$0.621912\pi$
$674$	28.3712	−	49.1404i	1.09282	−	1.89282i
$675$		0			0
$676$	−7.29123	−	12.6288i	−0.280432	−	0.485722i
$677$	−21.0707	−	28.3029i	−0.809813	−	1.08777i	−0.994476	−	0.104965i	$-0.966527\pi$
$677$	−21.0707	−	28.3029i	−0.809813	−	1.08777i	0.184663	−	0.982802i	$-0.440881\pi$
$678$		0			0
$679$	1.69323	−	5.65577i	0.0649801	−	0.217049i
$680$	10.8356	+	5.44184i	0.415526	+	0.208685i
$681$		0			0
$682$	−0.518148	−	1.73073i	−0.0198409	−	0.0662732i
$683$	6.86569	−	38.9372i	0.262708	−	1.48989i	−0.512774	−	0.858523i	$-0.671382\pi$
$683$	6.86569	−	38.9372i	0.262708	−	1.48989i	0.775483	−	0.631369i	$-0.217507\pi$
$684$		0			0
$685$	0.266493	+	1.51136i	0.0101822	+	0.0577460i
$686$	−16.2170	+	8.14447i	−0.619167	+	0.310957i
$687$		0			0
$688$	3.14208	+	7.28417i	0.119791	+	0.277706i
$689$	18.8011	+	43.5859i	0.716265	+	1.66049i
$690$		0			0
$691$	−15.1837	+	7.62552i	−0.577613	+	0.290088i	−0.713522	−	0.700633i	$-0.752901\pi$
$691$	−15.1837	+	7.62552i	−0.577613	+	0.290088i	0.135908	+	0.990721i	$0.456605\pi$
$692$	0.465612	+	2.64062i	0.0176999	+	0.100381i
$693$		0			0
$694$	6.73702	−	38.2075i	0.255734	−	1.45034i
$695$	1.87913	+	6.27672i	0.0712793	+	0.238089i
$696$		0			0
$697$	−12.5284	−	6.29198i	−0.474545	−	0.238326i
$698$	−10.9585	+	36.6039i	−0.414785	+	1.38548i
$699$		0			0
$700$	−6.08182	−	8.16930i	−0.229871	−	0.308771i
$701$	−16.3741	−	28.3608i	−0.618442	−	1.07117i	−0.989770	−	0.142672i	$-0.954431\pi$
$701$	−16.3741	−	28.3608i	−0.618442	−	1.07117i	0.371328	−	0.928502i	$-0.378903\pi$
$702$		0			0
$703$	12.2194	−	21.1647i	0.460865	−	0.798241i
$704$	−0.207780	+	0.0242859i	−0.00783099	+	0.000915311i
$705$		0			0
$706$	18.3924	−	4.35908i	0.692207	−	0.164056i
$707$	−31.5254	+	20.7346i	−1.18563	+	0.779804i
$708$		0			0
$709$	−22.5220	+	23.8719i	−0.845830	+	0.896527i	−0.995743	−	0.0921719i	$-0.970619\pi$
$709$	−22.5220	+	23.8719i	−0.845830	+	0.896527i	0.149913	+	0.988699i	$0.452101\pi$
$710$	8.53698	+	7.16337i	0.320387	+	0.268837i
$711$		0			0
$712$	6.83193	−	5.73267i	0.256037	−	0.214841i
$713$	−1.11154	+	19.0844i	−0.0416275	+	0.714716i
$714$		0			0
$715$	0.887315	−	1.19187i	0.0331837	−	0.0445735i
$716$	−2.37241	−	0.277294i	−0.0886610	−	0.0103630i
$717$		0			0
$718$	−35.8602	−	23.5856i	−1.33829	−	0.880208i
$719$	15.8250	+	5.75983i	0.590173	+	0.214806i	0.619806	−	0.784755i	$-0.287211\pi$
$719$	15.8250	+	5.75983i	0.590173	+	0.214806i	−0.0296323	+	0.999561i	$0.509434\pi$
$720$		0			0
$721$	−1.54558	+	0.562545i	−0.0575604	+	0.0209503i
$722$	−17.4729	−	4.14116i	−0.650275	−	0.154118i
$723$		0			0
$724$	−0.971634	−	16.6823i	−0.0361105	−	0.619993i
$725$	13.4360	+	14.2413i	0.498999	+	0.528908i
$726$		0			0
$727$	−3.32819	+	7.71562i	−0.123436	+	0.286157i	−0.968718	−	0.248163i	$-0.920173\pi$
$727$	−3.32819	+	7.71562i	−0.123436	+	0.286157i	0.845282	+	0.534320i	$0.179432\pi$
$728$	−29.9802			−1.11114
$729$		0			0
$730$	−38.8230			−1.43690
$731$	3.18917	−	7.39334i	0.117956	−	0.273452i
$732$		0			0
$733$	−8.47275	−	8.98059i	−0.312948	−	0.331705i	0.551739	−	0.834017i	$-0.313965\pi$
$733$	−8.47275	−	8.98059i	−0.312948	−	0.331705i	−0.864687	+	0.502312i	$0.832483\pi$
$734$	1.29353	+	22.2090i	0.0477449	+	0.819749i
$735$		0			0
$736$	−18.9887	−	4.50042i	−0.699934	−	0.165888i
$737$	2.58738	−	0.941730i	0.0953075	−	0.0346891i
$738$		0			0
$739$	37.3973	+	13.6115i	1.37568	+	0.500707i	0.920866	−	0.389879i	$-0.127483\pi$
$739$	37.3973	+	13.6115i	1.37568	+	0.500707i	0.454815	+	0.890586i	$0.349705\pi$
$740$	−9.55183	−	6.28234i	−0.351132	−	0.230943i
$741$		0			0
$742$	−51.0826	−	5.97070i	−1.87530	−	0.219191i
$743$	−11.8466	+	15.9127i	−0.434608	+	0.583780i	−0.964433	−	0.264327i	$-0.914850\pi$
$743$	−11.8466	+	15.9127i	−0.434608	+	0.583780i	0.529825	+	0.848107i	$0.322258\pi$
$744$		0			0
$745$	0.614727	−	10.5545i	0.0225219	−	0.386685i
$746$	2.95869	−	2.48263i	0.108325	−	0.0908957i
$747$		0			0
$748$	−0.796638	−	0.668459i	−0.0291280	−	0.0244413i
$749$	12.2838	−	13.0201i	0.448840	−	0.475743i
$750$		0			0
$751$	−32.0641	+	21.0889i	−1.17004	+	0.769545i	−0.977332	−	0.211712i	$-0.932096\pi$
$751$	−32.0641	+	21.0889i	−1.17004	+	0.769545i	−0.192704	+	0.981257i	$0.561726\pi$
$752$	−10.1260	+	2.39990i	−0.369257	+	0.0875155i
$753$		0			0
$754$	−57.0068	+	6.66314i	−2.07607	+	0.242657i
$755$	−2.12665	+	3.68347i	−0.0773969	+	0.134055i
$756$		0			0
$757$	7.07444	+	12.2533i	0.257125	+	0.445353i	0.965470	−	0.260513i	$-0.0838915\pi$
$757$	7.07444	+	12.2533i	0.257125	+	0.445353i	−0.708346	+	0.705866i	$0.750558\pi$
$758$	−7.60877	−	10.2203i	−0.276363	−	0.371220i
$759$		0			0
$760$	−2.01292	+	6.72361i	−0.0730162	+	0.243891i
$761$	−8.47080	−	4.25420i	−0.307066	−	0.154215i	0.288593	−	0.957452i	$-0.406813\pi$
$761$	−8.47080	−	4.25420i	−0.307066	−	0.154215i	−0.595659	+	0.803237i	$0.703109\pi$
$762$		0			0
$763$	−15.8245	−	52.8576i	−0.572886	−	1.91357i
$764$	−2.45907	+	13.9461i	−0.0889660	+	0.504551i
$765$		0			0
$766$	−4.34643	−	24.6498i	−0.157043	−	0.890634i
$767$	69.7145	−	35.0119i	2.51724	−	1.26421i
$768$		0			0
$769$	−4.95943	−	11.4972i	−0.178841	−	0.414601i	0.805089	−	0.593154i	$-0.202118\pi$
$769$	−4.95943	−	11.4972i	−0.178841	−	0.414601i	−0.983930	+	0.178553i	$0.942858\pi$
$770$	0.637661	+	1.47826i	0.0229797	+	0.0532730i
$771$		0			0
$772$	−3.72394	+	1.87023i	−0.134027	+	0.0673111i
$773$	−6.23462	−	35.3583i	−0.224244	−	1.27175i	−0.864125	−	0.503277i	$-0.832128\pi$
$773$	−6.23462	−	35.3583i	−0.224244	−	1.27175i	0.639882	−	0.768474i	$-0.278983\pi$
$774$		0			0
$775$	−2.73862	+	15.5315i	−0.0983742	+	0.557908i
$776$	−0.893437	−	2.98429i	−0.0320725	−	0.107130i
$777$		0			0
$778$	13.1583	+	6.60833i	0.471747	+	0.236920i
$779$	2.32738	−	7.77399i	0.0833871	−	0.278532i
$780$		0			0
$781$	0.573143	+	0.769865i	0.0205087	+	0.0275479i
$782$	16.5290	+	28.6291i	0.591076	+	1.02377i
$783$		0			0
$784$	9.53150	−	16.5091i	0.340411	−	0.589609i
$785$	−8.38532	+	0.980104i	−0.299285	+	0.0349814i
$786$		0			0
$787$	38.8743	−	9.21338i	1.38572	−	0.328421i	0.530938	−	0.847411i	$-0.321840\pi$
$787$	38.8743	−	9.21338i	1.38572	−	0.328421i	0.854781	+	0.518989i	$0.173691\pi$
$788$	17.2738	−	11.3611i	0.615352	−	0.404724i
$789$		0			0
$790$	2.43296	−	2.57878i	0.0865607	−	0.0917490i
$791$	22.2484	+	18.6687i	0.791063	+	0.663781i
$792$		0			0
$793$	−6.06508	+	5.08921i	−0.215377	+	0.180723i
$794$	−0.552935	+	9.49353i	−0.0196229	+	0.336913i
$795$		0			0
$796$	1.71408	−	2.30240i	0.0607538	−	0.0816065i
$797$	−33.8557	−	3.95716i	−1.19923	−	0.140170i	−0.507063	−	0.861909i	$-0.669269\pi$
$797$	−33.8557	−	3.95716i	−1.19923	−	0.140170i	−0.692165	+	0.721739i	$0.743343\pi$
$798$		0			0
$799$	8.82481	+	5.80417i	0.312199	+	0.205337i
$800$	−15.1285	−	5.50634i	−0.534875	−	0.194678i
$801$		0			0
$802$	15.3085	−	5.57185i	0.540563	−	0.196749i
$803$	−3.25346	−	0.771083i	−0.114812	−	0.0272109i
$804$		0			0
$805$	−0.990519	−	17.0065i	−0.0349112	−	0.599402i
$806$	−31.7263	−	33.6280i	−1.11751	−	1.18449i
$807$		0			0
$808$	−7.88590	+	18.2816i	−0.277425	+	0.643144i
$809$	−7.57622			−0.266366			−0.133183	−	0.991091i	$-0.542520\pi$
$809$	−7.57622			−0.266366			−0.133183	+	0.991091i	$0.542520\pi$
$810$		0			0
$811$	20.5558			0.721810			0.360905	−	0.932602i	$-0.382468\pi$
$811$	20.5558			0.721810			0.360905	+	0.932602i	$0.382468\pi$
$812$	8.19879	−	19.0069i	0.287721	−	0.667012i
$813$		0			0
$814$	−2.02989	−	2.15156i	−0.0711475	−	0.0754120i
$815$	0.0137632	+	0.236306i	0.000482106	+	0.00827743i
$816$		0			0
$817$	4.53499	+	1.07481i	0.158659	+	0.0376030i
$818$	25.0916	−	9.13260i	0.877308	−	0.319314i
$819$		0			0
$820$	−3.56726	−	1.29838i	−0.124574	−	0.0453412i
$821$	−25.4615	−	16.7463i	−0.888613	−	0.584450i	0.0210583	−	0.999778i	$-0.493296\pi$
$821$	−25.4615	−	16.7463i	−0.888613	−	0.584450i	−0.909672	+	0.415328i	$0.863667\pi$
$822$		0			0
$823$	22.1674	+	2.59100i	0.772707	+	0.0903165i	0.493304	−	0.869857i	$-0.335789\pi$
$823$	22.1674	+	2.59100i	0.772707	+	0.0903165i	0.279404	+	0.960174i	$0.409863\pi$
$824$	−0.518255	+	0.696138i	−0.0180543	+	0.0242511i
$825$		0			0
$826$	−4.91467	+	84.3816i	−0.171003	+	2.93601i
$827$	27.2509	−	22.8662i	0.947606	−	0.795136i	−0.0312864	−	0.999510i	$-0.509960\pi$
$827$	27.2509	−	22.8662i	0.947606	−	0.795136i	0.978893	+	0.204374i	$0.0655159\pi$
$828$		0			0
$829$	−13.4520	−	11.2875i	−0.467206	−	0.392032i	0.378568	−	0.925573i	$-0.376416\pi$
$829$	−13.4520	−	11.2875i	−0.467206	−	0.392032i	−0.845774	+	0.533541i	$0.820861\pi$
$830$	−23.3182	+	24.7159i	−0.809387	+	0.857900i
$831$		0			0
$832$	−4.47263	+	2.94169i	−0.155060	+	0.101985i
$833$	−18.8272	+	4.46212i	−0.652323	+	0.154603i
$834$		0			0
$835$	−0.402577	+	0.0470545i	−0.0139317	+	0.00162839i
$836$	0.300972	−	0.521298i	0.0104093	−	0.0180295i
$837$		0			0
$838$	21.3875	+	37.0443i	0.738820	+	1.27967i
$839$	22.8900	+	30.7466i	0.790251	+	1.06149i	0.996549	+	0.0830022i	$0.0264509\pi$
$839$	22.8900	+	30.7466i	0.790251	+	1.06149i	−0.206298	+	0.978489i	$0.566142\pi$
$840$		0			0
$841$	−3.09569	+	10.3403i	−0.106748	+	0.356563i
$842$	−0.287474	−	0.144375i	−0.00990701	−	0.00497549i
$843$		0			0
$844$	3.03776	+	10.1468i	0.104564	+	0.349268i
$845$	3.49427	−	19.8170i	0.120206	−	0.681725i
$846$		0			0
$847$	−6.25691	−	35.4847i	−0.214990	−	1.21927i
$848$	−40.3621	+	20.2706i	−1.38604	+	0.696095i
$849$		0			0
$850$	10.8021	+	25.0420i	0.370508	+	0.858934i
$851$	12.3972	+	28.7398i	0.424969	+	0.985189i
$852$		0			0
$853$	7.50175	−	3.76752i	0.256855	−	0.128997i	−0.315713	−	0.948855i	$-0.602244\pi$
$853$	7.50175	−	3.76752i	0.256855	−	0.128997i	0.572568	+	0.819857i	$0.305947\pi$
$854$	−1.48961	−	8.44799i	−0.0509733	−	0.289084i
$855$		0			0
$856$	1.64011	−	9.30155i	0.0560580	−	0.317920i
$857$	13.8014	+	46.0999i	0.471447	+	1.57474i	0.781424	+	0.624000i	$0.214493\pi$
$857$	13.8014	+	46.0999i	0.471447	+	1.57474i	−0.309977	+	0.950744i	$0.600321\pi$
$858$		0			0
$859$	45.6471	+	22.9248i	1.55746	+	0.782185i	0.998882	−	0.0472690i	$-0.0150518\pi$
$859$	45.6471	+	22.9248i	1.55746	+	0.782185i	0.558575	+	0.829454i	$0.311348\pi$
$860$	0.625307	−	2.08867i	0.0213228	−	0.0712231i
$861$		0			0
$862$	15.0463	+	20.2107i	0.512478	+	0.688378i
$863$	18.3885	+	31.8499i	0.625953	+	1.08418i	0.988356	+	0.152161i	$0.0486232\pi$
$863$	18.3885	+	31.8499i	0.625953	+	1.08418i	−0.362403	+	0.932022i	$0.618043\pi$
$864$		0			0
$865$	−1.85003	+	3.20435i	−0.0629031	+	0.108951i
$866$	59.5361	−	6.95877i	2.02312	−	0.236469i
$867$		0			0
$868$	16.2244	−	3.84526i	0.550693	−	0.130517i
$869$	0.255106	−	0.167786i	0.00865388	−	0.00569175i
$870$		0			0
$871$	48.3532	−	51.2514i	1.63839	−	1.73659i
$872$	−22.3023	−	18.7138i	−0.755250	−	0.633730i
$873$		0			0
$874$	−14.6581	+	12.2996i	−0.495819	+	0.416042i
$875$	2.13359	−	36.6323i	0.0721285	−	1.23840i
$876$		0			0
$877$	−2.42437	+	3.25649i	−0.0818651	+	0.109964i	−0.841169	−	0.540772i	$-0.818132\pi$
$877$	−2.42437	+	3.25649i	−0.0818651	+	0.109964i	0.759304	+	0.650736i	$0.225540\pi$
$878$	3.38068	+	0.395144i	0.114092	+	0.0133355i
$879$		0			0
$880$	1.18125	+	0.776921i	0.0398200	+	0.0261900i
$881$	−38.2223	−	13.9118i	−1.28774	−	0.468700i	−0.394758	−	0.918785i	$-0.629171\pi$
$881$	−38.2223	−	13.9118i	−1.28774	−	0.468700i	−0.892986	+	0.450085i	$0.851394\pi$
$882$		0			0
$883$	−24.6043	+	8.95523i	−0.828000	+	0.301367i	−0.721038	−	0.692896i	$-0.756335\pi$
$883$	−24.6043	+	8.95523i	−0.828000	+	0.301367i	−0.106962	+	0.994263i	$0.534112\pi$
$884$	−25.8948	−	6.13719i	−0.870938	−	0.206416i
$885$		0			0
$886$	3.20232	+	54.9817i	0.107584	+	1.84715i
$887$	14.9184	+	15.8126i	0.500910	+	0.530933i	0.927655	−	0.373438i	$-0.121821\pi$
$887$	14.9184	+	15.8126i	0.500910	+	0.530933i	−0.426745	+	0.904372i	$0.640340\pi$
$888$		0			0
$889$	−9.08810	+	21.0686i	−0.304805	+	0.706618i
$890$	−12.2556			−0.410809
$891$		0			0
$892$	−23.6257			−0.791048
$893$	−2.42157	+	5.61382i	−0.0810346	+	0.187859i
$894$		0			0
$895$	−2.26187	−	2.39744i	−0.0756060	−	0.0801377i
$896$	−2.32075	−	39.8458i	−0.0775310	−	1.33116i
$897$		0			0
$898$	50.1850	+	11.8941i	1.67470	+	0.396910i
$899$	−30.1211	+	10.9632i	−1.00459	+	0.365642i
$900$		0			0
$901$	43.0785	+	15.6793i	1.43515	+	0.522353i
$902$	−0.820611	−	0.539724i	−0.0273234	−	0.0179709i
$903$		0			0
$904$	15.2212	+	1.77910i	0.506248	+	0.0591719i
$905$	13.7701	−	18.4964i	0.457733	−	0.614842i
$906$		0			0
$907$	3.06495	−	52.6232i	0.101770	−	1.74733i	−0.432160	−	0.901797i	$-0.642248\pi$
$907$	3.06495	−	52.6232i	0.101770	−	1.74733i	0.533930	−	0.845529i	$-0.320714\pi$
$908$	−0.350892	+	0.294434i	−0.0116448	+	0.00977113i
$909$		0			0
$910$	31.5598	+	26.4818i	1.04620	+	0.877864i
$911$	29.5444	−	31.3152i	0.978850	−	1.03752i	−0.0204380	−	0.999791i	$-0.506506\pi$
$911$	29.5444	−	31.3152i	0.978850	−	1.03752i	0.999288	−	0.0377293i	$-0.0120125\pi$
$912$		0			0
$913$	−2.44501	+	1.60811i	−0.0809182	+	0.0532207i
$914$	21.4749	−	5.08964i	0.710325	−	0.168350i
$915$		0			0
$916$	−15.8520	+	1.85283i	−0.523764	+	0.0612192i
$917$	9.27238	−	16.0602i	0.306201	−	0.530356i
$918$		0			0
$919$	−25.2136	−	43.6712i	−0.831719	−	1.44058i	−0.896674	−	0.442691i	$-0.854024\pi$
$919$	−25.2136	−	43.6712i	−0.831719	−	1.44058i	0.0649552	−	0.997888i	$-0.479310\pi$
$920$	−5.36772	−	7.21010i	−0.176968	−	0.237710i
$921$		0			0
$922$	10.2634	−	34.2823i	0.338008	−	1.12903i
$923$	21.9485	+	11.0230i	0.722445	+	0.362826i
$924$		0			0
$925$	7.40579	+	24.7370i	0.243501	+	0.813349i
$926$	−5.00610	+	28.3910i	−0.164511	+	0.932987i
$927$		0			0
$928$	−5.68204	−	32.2245i	−0.186522	−	1.05782i
$929$	14.2000	−	7.13149i	0.465886	−	0.233977i	−0.200340	−	0.979726i	$-0.564205\pi$
$929$	14.2000	−	7.13149i	0.465886	−	0.233977i	0.666226	+	0.745750i	$0.267909\pi$
$930$		0			0
$931$	−4.43591	−	10.2836i	−0.145381	−	0.337032i
$932$	−3.14152	−	7.28285i	−0.102904	−	0.238558i
$933$		0			0
$934$	45.3283	−	22.7647i	1.48319	−	0.744885i
$935$	−0.249191	−	1.41323i	−0.00814943	−	0.0462177i
$936$		0			0
$937$	3.98093	−	22.5770i	0.130051	−	0.737557i	−0.848128	−	0.529792i	$-0.822270\pi$
$937$	3.98093	−	22.5770i	0.130051	−	0.737557i	0.978179	−	0.207765i	$-0.0666189\pi$
$938$	21.8953	+	73.1355i	0.714907	+	2.38796i
$939$		0			0
$940$	2.55586	+	1.28360i	0.0833631	+	0.0418665i
$941$	4.05531	−	13.5457i	0.132199	−	0.441576i	−0.866100	−	0.499870i	$-0.833381\pi$
$941$	4.05531	−	13.5457i	0.132199	−	0.441576i	0.998299	+	0.0582943i	$0.0185662\pi$
$942$		0			0
$943$	6.20628	+	8.33648i	0.202104	+	0.271473i
$944$	37.1148	+	64.2848i	1.20799	+	2.09229i
$945$		0			0
$946$	0.282051	−	0.488527i	0.00917027	−	0.0158834i
$947$	−56.7038	+	6.62773i	−1.84263	+	0.215372i	−0.964687	−	0.263399i	$-0.915156\pi$
$947$	−56.7038	+	6.62773i	−1.84263	+	0.215372i	−0.877940	+	0.478771i	$0.841082\pi$
$948$		0			0
$949$	−83.2565	+	19.7322i	−2.70262	+	0.640533i
$950$	−13.1890	+	8.67456i	−0.427909	+	0.281440i
$951$		0			0
$952$	−19.8695	+	21.0604i	−0.643973	+	0.682572i
$953$	13.5816	+	11.3963i	0.439951	+	0.369163i	0.835691	−	0.549200i	$-0.185067\pi$
$953$	13.5816	+	11.3963i	0.439951	+	0.369163i	−0.395740	+	0.918363i	$0.629512\pi$
$954$		0			0
$955$	−14.9696	+	12.5610i	−0.484405	+	0.406464i
$956$	−1.23112	+	21.1374i	−0.0398171	+	0.683634i
$957$		0			0
$958$	−23.1211	+	31.0570i	−0.747009	+	1.00341i
$959$	−3.63986	−	0.425438i	−0.117537	−	0.0137381i
$960$		0			0
$961$	4.32792	+	2.84652i	0.139610	+	0.0918231i
$962$	−71.1302	−	25.8893i	−2.29333	−	0.834704i
$963$		0			0
$964$	16.9447	−	6.16735i	0.545751	−	0.198637i
$965$	−5.59541	−	1.32614i	−0.180122	−	0.0426898i
$966$		0			0
$967$	1.28606	+	22.0808i	0.0413568	+	0.710070i	0.953722	+	0.300691i	$0.0972174\pi$
$967$	1.28606	+	22.0808i	0.0413568	+	0.710070i	−0.912365	+	0.409378i	$0.865746\pi$
$968$	−13.0471	−	13.8292i	−0.419351	−	0.444486i
$969$		0			0
$970$	−1.69554	+	3.93070i	−0.0544405	+	0.126207i
$971$	5.09901			0.163635			0.0818176	−	0.996647i	$-0.473928\pi$
$971$	5.09901			0.163635			0.0818176	+	0.996647i	$0.473928\pi$
$972$		0			0
$973$	−15.6454			−0.501569
$974$	2.56442	−	5.94500i	0.0821694	−	0.190490i
$975$		0			0
$976$	−5.16980	−	5.47966i	−0.165481	−	0.175400i
$977$	1.35086	+	23.1934i	0.0432178	+	0.742022i	0.948415	+	0.317030i	$0.102686\pi$
$977$	1.35086	+	23.1934i	0.0432178	+	0.742022i	−0.905198	+	0.424991i	$0.860277\pi$
$978$		0			0
$979$	−1.02705	−	0.243415i	−0.0328246	−	0.00777958i
$980$	−4.92325	+	1.79191i	−0.157267	+	0.0572406i
$981$		0			0
$982$	−1.96332	−	0.714592i	−0.0626522	−	0.0228035i
$983$	−14.0814	−	9.26149i	−0.449127	−	0.295396i	0.304724	−	0.952441i	$-0.401436\pi$
$983$	−14.0814	−	9.26149i	−0.449127	−	0.295396i	−0.753851	+	0.657045i	$0.771806\pi$
$984$		0			0
$985$	28.3371	+	3.31214i	0.902896	+	0.105533i
$986$	−33.1007	+	44.4620i	−1.05414	+	1.41596i
$987$		0			0
$988$	0.895653	−	15.3778i	0.0284945	−	0.489232i
$989$	−4.57252	+	3.83680i	−0.145398	+	0.122003i
$990$		0			0
$991$	−0.316451	−	0.265534i	−0.0100524	−	0.00843496i	0.637748	−	0.770245i	$-0.279866\pi$
$991$	−0.316451	−	0.265534i	−0.0100524	−	0.00843496i	−0.647800	+	0.761810i	$0.724311\pi$
$992$	18.0876	−	19.1717i	0.574282	−	0.608703i
$993$		0			0
$994$	−22.2334	+	14.6231i	−0.705200	+	0.463818i
$995$	3.85415	−	0.913450i	0.122185	−	0.0289583i
$996$		0			0
$997$	−5.80233	+	0.678195i	−0.183762	+	0.0214787i	−0.207476	−	0.978240i	$-0.566525\pi$
$997$	−5.80233	+	0.678195i	−0.183762	+	0.0214787i	0.0237143	+	0.999719i	$0.492451\pi$
$998$	−2.88970	+	5.00511i	−0.0914719	+	0.158434i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.181.7		144
3.2	odd	2		81.2.g.a.34.2	yes	144
9.2	odd	6		729.2.g.c.298.7		144
9.4	even	3		729.2.g.a.541.7		144
9.5	odd	6		729.2.g.d.541.2		144
9.7	even	3		729.2.g.b.298.2		144
81.4	even	27		729.2.g.a.190.7		144
81.23	odd	54		729.2.g.c.433.7		144
81.29	odd	54		6561.2.a.c.1.17		72
81.31	even	27	inner	243.2.g.a.145.7		144
81.50	odd	54		81.2.g.a.31.2	✓	144
81.52	even	27		6561.2.a.d.1.56		72
81.58	even	27		729.2.g.b.433.2		144
81.77	odd	54		729.2.g.d.190.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.31.2	✓	144	81.50	odd	54
81.2.g.a.34.2	yes	144	3.2	odd	2
243.2.g.a.145.7		144	81.31	even	27	inner
243.2.g.a.181.7		144	1.1	even	1	trivial
729.2.g.a.190.7		144	81.4	even	27
729.2.g.a.541.7		144	9.4	even	3
729.2.g.b.298.2		144	9.7	even	3
729.2.g.b.433.2		144	81.58	even	27
729.2.g.c.298.7		144	9.2	odd	6
729.2.g.c.433.7		144	81.23	odd	54
729.2.g.d.190.2		144	81.77	odd	54
729.2.g.d.541.2		144	9.5	odd	6
6561.2.a.c.1.17		72	81.29	odd	54
6561.2.a.d.1.56		72	81.52	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.685792 - 1.58984i) q^{2} +(-0.684812 - 0.725858i) q^{4} +(-0.0800683 - 1.37472i) q^{5} +(3.19962 + 0.758323i) q^{7} +(1.63042 - 0.593424i) q^{8} +(-2.24050 - 0.815476i) q^{10} +(-0.171563 - 0.112839i) q^{11} +(-5.21927 - 0.610045i) q^{13} +(3.39989 - 4.56684i) q^{14} +(0.290724 - 4.99154i) q^{16} +(-3.88762 + 3.26210i) q^{17} +(-2.25026 - 1.88819i) q^{19} +(-0.943020 + 0.999543i) q^{20} +(-0.297052 + 0.195374i) q^{22} +(3.66075 - 0.867613i) q^{23} +(3.08275 - 0.360321i) q^{25} +(-4.54921 + 7.87946i) q^{26} +(-1.64070 - 2.84178i) q^{28} +(3.76701 + 5.05998i) q^{29} +(-1.45734 + 4.86786i) q^{31} +(-4.63538 - 2.32798i) q^{32} +(2.52014 + 8.41784i) q^{34} +(0.786294 - 4.45930i) q^{35} +(1.44468 + 8.19321i) q^{37} +(-4.54514 + 2.28266i) q^{38} +(-0.946337 - 2.19386i) q^{40} +(1.09418 + 2.53659i) q^{41} +(-1.41783 + 0.712061i) q^{43} +(0.0355834 + 0.201803i) q^{44} +(1.13114 - 6.41502i) q^{46} +(-0.596924 - 1.99387i) q^{47} +(3.40707 + 1.71109i) q^{49} +(1.54127 - 5.14819i) q^{50} +(3.13141 + 4.20621i) q^{52} +(-4.51663 - 7.82303i) q^{53} +(-0.141385 + 0.244885i) q^{55} +(5.66673 - 0.662345i) q^{56} +(10.6280 - 2.51887i) q^{58} +(-12.4036 + 8.15798i) q^{59} +(1.03396 - 1.09593i) q^{61} +(6.73971 + 5.65528i) q^{62} +(0.780406 - 0.654838i) q^{64} +(-0.420743 + 7.22388i) q^{65} +(-8.00722 + 10.7556i) q^{67} +(5.03012 + 0.587936i) q^{68} +(-6.55035 - 4.30824i) q^{70} +(-4.39214 - 1.59861i) q^{71} +(15.3008 - 5.56905i) q^{73} +(14.0167 + 3.32202i) q^{74} +(0.170445 + 2.92643i) q^{76} +(-0.463367 - 0.491140i) q^{77} +(-0.588953 + 1.36535i) q^{79} -6.88524 q^{80} +4.78316 q^{82} +(5.64471 - 13.0859i) q^{83} +(4.79576 + 5.08320i) q^{85} +(0.159730 + 2.74246i) q^{86} +(-0.346680 - 0.0821648i) q^{88} +(4.83016 - 1.75803i) q^{89} +(-16.2370 - 5.90980i) q^{91} +(-3.13669 - 2.06303i) q^{92} +(-3.57930 - 0.418360i) q^{94} +(-2.41556 + 3.24466i) q^{95} +(0.104394 - 1.79238i) q^{97} +(5.05691 - 4.24325i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

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