LMFDB - Embedded newform 243.2.g.a.145.7

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			145.7
Character	$\chi$	$=$	243.145
Dual form			243.2.g.a.181.7

$q$-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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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	0.968529	+	0.248901i	$0.0800694\pi$
$2$	0.685792	+	1.58984i	0.484928	+	1.12419i	−0.483601	+	0.875289i	$0.660671\pi$
$3$		0			0
$3$		0			0
$4$	−0.684812	+	0.725858i	−0.342406	+	0.362929i
$5$	−0.0800683	+	1.37472i	−0.0358076	+	0.614794i	0.931900	+	0.362717i	$0.118151\pi$
$5$	−0.0800683	+	1.37472i	−0.0358076	+	0.614794i	−0.967707	+	0.252077i	$0.918886\pi$
$6$		0			0
$7$	3.19962	−	0.758323i	1.20934	−	0.286619i	0.423989	−	0.905667i	$-0.360630\pi$
$7$	3.19962	−	0.758323i	1.20934	−	0.286619i	0.785353	+	0.619048i	$0.212481\pi$
$8$	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	−0.575110	−	0.818076i	$-0.695041\pi$
$11$	−0.171563	+	0.112839i	−0.0517281	+	0.0340221i	0.523382	+	0.852098i	$0.324670\pi$
$12$		0			0
$13$	−5.21927	+	0.610045i	−1.44756	+	0.169196i	−0.803285	−	0.595595i	$-0.796916\pi$
$13$	−5.21927	+	0.610045i	−1.44756	+	0.169196i	−0.644279	+	0.764791i	$0.722842\pi$
$14$	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	0.0351981	−	0.999380i	$-0.488794\pi$
$17$	−3.88762	−	3.26210i	−0.942887	−	0.791176i	−0.978085	+	0.208204i	$0.933238\pi$
$18$		0			0
$19$	−2.25026	+	1.88819i	−0.516245	+	0.433181i	−0.863320	−	0.504656i	$-0.831619\pi$
$19$	−2.25026	+	1.88819i	−0.516245	+	0.433181i	0.347075	+	0.937837i	$0.387175\pi$
$20$	−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	0.593795	−	0.804616i	$-0.297629\pi$
$23$	3.66075	+	0.867613i	0.763318	+	0.180910i	0.169523	+	0.985526i	$0.445777\pi$
$24$		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	−0.300382	−	0.953819i	$-0.597114\pi$
$29$	3.76701	−	5.05998i	0.699517	−	0.939614i	0.999899	+	0.0142046i	$0.00452163\pi$
$30$		0			0
$31$	−1.45734	−	4.86786i	−0.261746	−	0.874293i	−0.983309	−	0.181944i	$-0.941761\pi$
$31$	−1.45734	−	4.86786i	−0.261746	−	0.874293i	0.721563	−	0.692349i	$-0.243424\pi$
$32$	−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	−0.599770	−	0.800173i	$-0.704741\pi$
$37$	1.44468	−	8.19321i	0.237505	−	1.34696i	0.837274	−	0.546783i	$-0.184148\pi$
$38$	−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	−0.811157	−	0.584829i	$-0.801162\pi$
$41$	1.09418	−	2.53659i	0.170882	−	0.396148i	0.982039	+	0.188680i	$0.0604210\pi$
$42$		0			0
$43$	−1.41783	−	0.712061i	−0.216217	−	0.108588i	0.337394	−	0.941363i	$-0.390454\pi$
$43$	−1.41783	−	0.712061i	−0.216217	−	0.108588i	−0.553611	+	0.832775i	$0.686751\pi$
$44$	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	−0.990424	−	0.138062i	$-0.955913\pi$
$47$	−0.596924	+	1.99387i	−0.0870703	+	0.290835i	0.903353	+	0.428897i	$0.141098\pi$
$48$		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	0.369003	+	0.929428i	$0.379699\pi$
$53$	−4.51663	+	7.82303i	−0.620407	+	1.07458i	−0.989410	+	0.145148i	$0.953634\pi$
$54$		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	−0.948676	−	0.316249i	$-0.897577\pi$
$59$	−12.4036	−	8.15798i	−1.61481	−	1.06208i	−0.666136	−	0.745830i	$-0.732053\pi$
$60$		0			0
$61$	1.03396	+	1.09593i	0.132385	+	0.140320i	0.790175	−	0.612882i	$-0.209990\pi$
$61$	1.03396	+	1.09593i	0.132385	+	0.140320i	−0.657790	+	0.753202i	$0.728508\pi$
$62$	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	−0.949284	−	0.314421i	$-0.898190\pi$
$67$	−8.00722	−	10.7556i	−0.978238	−	1.31400i	−0.0289544	−	0.999581i	$-0.509218\pi$
$68$	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	−0.589228	−	0.807967i	$-0.700568\pi$
$71$	−4.39214	+	1.59861i	−0.521252	+	0.189720i	0.0679763	+	0.997687i	$0.478346\pi$
$72$		0			0
$73$	15.3008	+	5.56905i	1.79083	+	0.651808i	0.999165	+	0.0408483i	$0.0130060\pi$
$73$	15.3008	+	5.56905i	1.79083	+	0.651808i	0.791662	+	0.610960i	$0.209216\pi$
$74$	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	0.881867	−	0.471498i	$-0.156287\pi$
$79$	−0.588953	−	1.36535i	−0.0662624	−	0.153613i	−0.948129	+	0.317885i	$0.897027\pi$
$80$	−6.88524			−0.769794
$81$		0			0
$82$	4.78316			0.528211
$83$	5.64471	+	13.0859i	0.619587	+	1.43636i	0.881926	+	0.471388i	$0.156247\pi$
$83$	5.64471	+	13.0859i	0.619587	+	1.43636i	−0.262339	+	0.964976i	$0.584494\pi$
$84$		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	0.585082	−	0.810974i	$-0.301062\pi$
$89$	4.83016	+	1.75803i	0.511996	+	0.186351i	−0.0730859	+	0.997326i	$0.523285\pi$
$90$		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	0.999452	+	0.0330916i	$0.0105353\pi$
$97$	0.104394	+	1.79238i	0.0105996	+	0.181989i	−0.988853	+	0.148897i	$0.952428\pi$
$98$	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	0.205406	−	0.978677i	$-0.434149\pi$
$101$	−7.87467	−	8.34666i	−0.783559	−	0.830524i	−0.988964	+	0.148153i	$0.952667\pi$
$102$		0			0
$103$	−0.417908	−	0.274862i	−0.0411777	−	0.0270830i	0.528753	−	0.848776i	$-0.322660\pi$
$103$	−0.417908	−	0.274862i	−0.0411777	−	0.0270830i	−0.569931	+	0.821693i	$0.693030\pi$
$104$	−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	0.967072	−	0.254504i	$-0.0819123\pi$
$107$	2.72183	+	4.71434i	0.263129	+	0.455752i	−0.703943	+	0.710257i	$0.748579\pi$
$108$		0			0
$109$	−8.38980	+	14.5316i	−0.803597	+	1.39187i	0.113637	+	0.993522i	$0.463750\pi$
$109$	−8.38980	+	14.5316i	−0.803597	+	1.39187i	−0.917234	+	0.398348i	$0.869584\pi$
$110$	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	−0.0369833	−	0.999316i	$-0.511775\pi$
$113$	7.89295	−	3.96399i	0.742506	−	0.372901i	0.779490	+	0.626415i	$0.215479\pi$
$114$		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	−0.990183	−	0.139775i	$-0.955362\pi$
$127$	−1.21170	−	6.87190i	−0.107521	−	0.609783i	0.882662	−	0.470008i	$-0.155749\pi$
$128$	−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	0.999120	−	0.0419413i	$-0.0133542\pi$
$131$	1.61749	+	5.40278i	0.141320	+	0.472043i	−0.857800	+	0.513984i	$0.828169\pi$
$132$		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	0.0686757	−	0.997639i	$-0.478123\pi$
$137$	−1.10693	−	0.129381i	−0.0945712	−	0.0110538i	−0.163247	+	0.986585i	$0.552197\pi$
$138$		0			0
$139$	−4.62972	−	1.09726i	−0.392688	−	0.0930687i	0.0295282	−	0.999564i	$-0.490600\pi$
$139$	−4.62972	−	1.09726i	−0.392688	−	0.0930687i	−0.422216	+	0.906495i	$0.638748\pi$
$140$	−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	0.202155	−	0.979354i	$-0.435206\pi$
$149$	7.62562	−	0.891307i	0.624715	−	0.0730187i	0.422560	+	0.906335i	$0.361132\pi$
$150$		0			0
$151$	−2.58058	+	1.69727i	−0.210005	+	0.138122i	−0.650154	−	0.759802i	$-0.725296\pi$
$151$	−2.58058	+	1.69727i	−0.210005	+	0.138122i	0.440150	+	0.897924i	$0.354925\pi$
$152$	−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	0.953747	+	0.300609i	$0.0971900\pi$
$157$	−0.356474	+	6.12042i	−0.0284497	+	0.488463i	−0.982197	+	0.187853i	$0.939847\pi$
$158$	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	−0.998906	−	0.0467721i	$-0.985107\pi$
$167$	−0.0171142	+	0.293839i	−0.00132434	+	0.0227380i	0.997581	+	0.0695100i	$0.0221436\pi$
$168$		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	−0.631974	−	0.774990i	$-0.717755\pi$
$173$	−2.24492	+	1.47651i	−0.170678	+	0.112257i	0.461296	+	0.887246i	$0.347385\pi$
$174$		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	0.708734	−	0.705476i	$-0.249267\pi$
$179$	1.83356	+	1.53854i	0.137047	+	0.114996i	−0.571687	+	0.820471i	$0.693711\pi$
$180$		0			0
$181$	12.8278	−	10.7638i	0.953481	−	0.800065i	−0.0263995	−	0.999651i	$-0.508404\pi$
$181$	12.8278	−	10.7638i	0.953481	−	0.800065i	0.979880	+	0.199586i	$0.0639598\pi$
$182$	−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	−0.994923	−	0.100636i	$-0.967912\pi$
$191$	−8.47415	+	11.3828i	−0.613168	+	0.823627i	0.381755	+	0.924263i	$0.375320\pi$
$192$		0			0
$193$	1.19766	+	4.00046i	0.0862094	+	0.287959i	0.990213	−	0.139566i	$-0.0445707\pi$
$193$	1.19766	+	4.00046i	0.0862094	+	0.287959i	−0.904003	+	0.427525i	$0.859386\pi$
$194$	−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	−0.792650	−	0.609677i	$-0.791299\pi$
$197$	−3.59768	−	20.4035i	−0.256324	−	1.45369i	0.536326	−	0.844011i	$-0.319812\pi$
$198$		0			0
$199$	0.499478	−	2.83268i	0.0354071	−	0.200803i	−0.961973	−	0.273145i	$-0.911936\pi$
$199$	0.499478	−	2.83268i	0.0354071	−	0.200803i	0.997380	+	0.0723417i	$0.0230472\pi$
$200$	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	−0.744259	−	0.667891i	$-0.767197\pi$
$211$	−9.48492	+	4.76351i	−0.652969	+	0.327933i	0.0912903	+	0.995824i	$0.470901\pi$
$212$	−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	0.987399	+	0.158248i	$0.0505844\pi$
$223$	16.2468	+	17.2206i	1.08797	+	1.15318i	0.100568	+	0.994930i	$0.467934\pi$
$224$	−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	0.999078	−	0.0429309i	$-0.0136695\pi$
$227$	0.0266893	+	0.458237i	0.00177143	+	0.0304143i	−0.997307	+	0.0733452i	$0.976633\pi$
$228$		0			0
$229$	9.55048	+	12.8285i	0.631113	+	0.847732i	0.996541	−	0.0831075i	$-0.0264845\pi$
$229$	9.55048	+	12.8285i	0.631113	+	0.847732i	−0.365427	+	0.930840i	$0.619077\pi$
$230$	−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	−0.0855784	−	0.996331i	$-0.527274\pi$
$233$	7.46875	−	2.71840i	0.489294	−	0.178089i	0.574873	+	0.818243i	$0.305052\pi$
$234$		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	−1.00000		2.70339e-5i	$-0.999991\pi$
$239$	−14.5603	+	15.4330i	−0.941828	+	0.998280i	0.0581718	+	0.998307i	$0.481473\pi$
$240$		0			0
$241$	−7.15707	−	16.5920i	−0.461028	−	1.06878i	−0.977205	−	0.212300i	$-0.931905\pi$
$241$	−7.15707	−	16.5920i	−0.461028	−	1.06878i	0.516177	−	0.856482i	$-0.327355\pi$
$242$	−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	0.0912569	−	0.995827i	$-0.470912\pi$
$251$	−7.58786	−	2.76176i	−0.478942	−	0.174321i	−0.570199	+	0.821507i	$0.693134\pi$
$252$		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	0.379317	−	0.925267i	$-0.376159\pi$
$257$	−9.87311	−	13.2619i	−0.615868	−	0.827254i	−0.995185	+	0.0980126i	$0.968751\pi$
$258$		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	0.727018	−	0.686618i	$-0.240906\pi$
$263$	−0.0115217	−	0.0122123i	−0.000710459	−	0.000753043i	−0.727729	+	0.685865i	$0.759424\pi$
$264$		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	0.946202	−	0.323578i	$-0.104886\pi$
$269$	3.16338	+	5.47913i	0.192874	+	0.334068i	−0.753327	+	0.657646i	$0.771552\pi$
$270$		0			0
$271$	−9.98751	+	17.2989i	−0.606698	+	1.05083i	0.385082	+	0.922882i	$0.374173\pi$
$271$	−9.98751	+	17.2989i	−0.606698	+	1.05083i	−0.991781	+	0.127950i	$0.959160\pi$
$272$	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	−0.994820	−	0.101652i	$-0.967587\pi$
$277$	−1.79418	+	5.99296i	−0.107802	+	0.360082i	0.887019	+	0.461734i	$0.152772\pi$
$278$	−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	0.597154	−	0.802126i	$-0.296298\pi$
$281$	5.20235	+	2.61272i	0.310346	+	0.155862i	−0.286808	+	0.957988i	$0.592594\pi$
$282$		0			0
$283$	−3.40508	+	7.89386i	−0.202411	+	0.469241i	−0.988941	−	0.148311i	$-0.952616\pi$
$283$	−3.40508	+	7.89386i	−0.202411	+	0.469241i	0.786530	+	0.617552i	$0.211876\pi$
$284$	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	0.994826	−	0.101594i	$-0.0323944\pi$
$293$	1.84582	+	6.16547i	0.107834	+	0.360190i	−0.886992	+	0.461785i	$0.847209\pi$
$294$		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	0.995349	−	0.0963370i	$-0.0307127\pi$
$307$	18.8060	+	15.7801i	1.07332	+	0.900619i	0.0779670	+	0.996956i	$0.475157\pi$
$308$	−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	−0.473653	−	0.880711i	$-0.657065\pi$
$311$	−12.8990	+	1.50767i	−0.731433	+	0.0854923i	−0.257780	+	0.966204i	$0.582991\pi$
$312$		0			0
$313$	−4.36800	+	2.87288i	−0.246894	+	0.162385i	−0.666925	−	0.745125i	$-0.732390\pi$
$313$	−4.36800	+	2.87288i	−0.246894	+	0.162385i	0.420031	+	0.907510i	$0.362019\pi$
$314$	−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	0.716582	−	0.697502i	$-0.245705\pi$
$317$	29.7332	−	7.04690i	1.66998	−	0.395793i	0.953400	+	0.301709i	$0.0975572\pi$
$318$		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	−0.144595	−	0.989491i	$-0.546188\pi$
$331$	3.09786	−	0.734205i	0.170274	−	0.0403556i	0.314868	+	0.949135i	$0.398040\pi$
$332$	−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	0.834216	−	0.551438i	$-0.185921\pi$
$337$	32.5501	−	3.80456i	1.77312	−	0.207247i	0.938900	+	0.344191i	$0.111847\pi$
$338$	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	0.769472	−	0.638681i	$-0.220519\pi$
$347$	21.8032	+	5.16746i	1.17046	+	0.277404i	0.400986	+	0.916084i	$0.368668\pi$
$348$		0			0
$349$	−21.9185	−	2.56190i	−1.17327	−	0.137136i	−0.492955	−	0.870055i	$-0.664083\pi$
$349$	−21.9185	−	2.56190i	−1.17327	−	0.137136i	−0.680315	+	0.732919i	$0.738157\pi$
$350$	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	−0.594039	−	0.804436i	$-0.702467\pi$
$353$	6.51907	−	8.75663i	0.346975	−	0.466068i	0.941014	+	0.338368i	$0.109875\pi$
$354$		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	0.858457	+	0.512885i	$0.171423\pi$
$359$	4.30460	+	24.4126i	0.227188	+	1.28845i	−0.631269	+	0.775564i	$0.717466\pi$
$360$		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	0.123137	−	0.992390i	$-0.460705\pi$
$367$	−11.4819	−	5.76642i	−0.599350	−	0.301005i	−0.722487	+	0.691385i	$0.757001\pi$
$368$	−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	−0.396443	−	0.918059i	$-0.629756\pi$
$373$	1.99340	−	1.00112i	0.103214	−	0.0518362i	0.499657	+	0.866223i	$0.333459\pi$
$374$	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	0.944918	−	0.327308i	$-0.106142\pi$
$379$	3.67947	+	6.37302i	0.189001	+	0.327360i	−0.755916	+	0.654668i	$0.772808\pi$
$380$	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	0.819233	−	0.573461i	$-0.194400\pi$
$383$	12.0779	+	7.94378i	0.617154	+	0.405908i	−0.202079	+	0.979369i	$0.564770\pi$
$384$		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	−0.987368	−	0.158446i	$-0.949352\pi$
$389$	−0.494471	−	8.48974i	−0.0250707	−	0.430447i	0.962297	−	0.272001i	$-0.0876854\pi$
$390$		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	0.209243	−	0.977864i	$-0.432900\pi$
$397$	−5.16106	−	1.87847i	−0.259026	−	0.0942779i	−0.468269	+	0.883586i	$0.655122\pi$
$398$	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	−0.545799	−	0.837916i	$-0.683774\pi$
$401$	6.45676	−	6.84377i	0.322435	−	0.341762i	0.868234	+	0.496155i	$0.165255\pi$
$402$		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	−0.410780	−	0.911735i	$-0.634743\pi$
$409$	10.5830	−	11.2174i	0.523297	−	0.554663i	0.934077	+	0.357072i	$0.116225\pi$
$410$	−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	−0.999969	−	0.00787086i	$-0.997495\pi$
$419$	−14.7527	−	19.8163i	−0.720715	−	0.968088i	0.279254	−	0.960217i	$-0.409913\pi$
$420$		0			0
$421$	0.0108029	+	0.185479i	0.000526502	+	0.00903969i	0.998561	−	0.0536244i	$-0.0170774\pi$
$421$	0.0108029	+	0.185479i	0.000526502	+	0.00903969i	−0.998035	+	0.0626641i	$0.980040\pi$
$422$	−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	0.635855	−	0.771808i	$-0.280648\pi$
$431$	−7.27612	−	12.6026i	−0.350478	−	0.607046i	−0.986333	+	0.164762i	$0.947314\pi$
$432$		0			0
$433$	17.3096	−	29.9811i	0.831846	−	1.44080i	−0.0647264	−	0.997903i	$-0.520617\pi$
$433$	17.3096	−	29.9811i	0.831846	−	1.44080i	0.896573	−	0.442897i	$-0.146049\pi$
$434$	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	−0.943480	−	0.331428i	$-0.892470\pi$
$439$	0.563799	−	1.88322i	0.0269087	−	0.0898812i	0.970389	+	0.241547i	$0.0776548\pi$
$440$	−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	−0.381300	−	0.924451i	$-0.624523\pi$
$443$	−28.4252	−	14.2757i	−1.35052	−	0.678257i	−0.969220	+	0.246195i	$0.920820\pi$
$444$		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	−0.578454	−	0.815715i	$-0.696344\pi$
$449$	5.17251	−	29.3348i	0.244106	−	1.38439i	0.822560	−	0.568679i	$-0.192545\pi$
$450$		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	−0.587619	−	0.809137i	$-0.699935\pi$
$457$	7.61163	−	10.2242i	0.356057	−	0.478267i	0.943676	+	0.330870i	$0.107342\pi$
$458$	−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	0.579810	−	0.814752i	$-0.303127\pi$
$461$	20.5283	+	2.39941i	0.956097	+	0.111752i	0.376287	+	0.926503i	$0.377201\pi$
$462$		0			0
$463$	−16.2014	−	3.83980i	−0.752943	−	0.178451i	−0.163816	−	0.986491i	$-0.552380\pi$
$463$	−16.2014	−	3.83980i	−0.752943	−	0.178451i	−0.589127	+	0.808040i	$0.700528\pi$
$464$	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	0.0466403	−	0.998912i	$-0.485149\pi$
$467$	22.4416	−	18.8308i	1.03848	−	0.871384i	0.991835	+	0.127527i	$0.0407041\pi$
$468$		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	−0.695351	−	0.718670i	$-0.744751\pi$
$479$	−21.7592	+	5.15702i	−0.994201	+	0.235630i	−0.298850	+	0.954300i	$0.596603\pi$
$480$		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	−0.999521	−	0.0309407i	$-0.990150\pi$
$491$	−0.0701629	+	1.20465i	−0.00316641	+	0.0543651i	0.996355	+	0.0853058i	$0.0271867\pi$
$492$		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	−0.189976	−	0.981789i	$-0.560841\pi$
$499$	−3.31533	+	0.387506i	−0.148415	+	0.0173472i	0.0415612	+	0.999136i	$0.486767\pi$
$500$	−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	0.121994	−	0.992531i	$-0.461071\pi$
$503$	−18.7108	−	15.7002i	−0.834274	−	0.700039i	−0.956268	+	0.292492i	$0.905516\pi$
$504$		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	−0.499325	−	0.866415i	$-0.666418\pi$
$509$	−30.1051	−	7.13503i	−1.33438	−	0.316255i	−0.835059	+	0.550160i	$0.814567\pi$
$510$		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	−0.989795	−	0.142499i	$-0.954486\pi$
$521$	−2.47495	−	14.0361i	−0.108430	−	0.614934i	0.881365	−	0.472435i	$-0.156625\pi$
$522$		0			0
$523$	0.234960	−	1.33253i	0.0102741	−	0.0582673i	−0.979240	−	0.202706i	$-0.935026\pi$
$523$	0.234960	−	1.33253i	0.0102741	−	0.0582673i	0.989514	+	0.144439i	$0.0461376\pi$
$524$	−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	0.999029	+	0.0440659i	$0.0140312\pi$
$541$	12.5060	+	21.6611i	0.537676	+	0.931283i	−0.461352	+	0.887217i	$0.652636\pi$
$542$	−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	0.161337	−	0.986899i	$-0.448419\pi$
$547$	−19.4886	−	20.6567i	−0.833273	−	0.883218i	−0.994611	+	0.103681i	$0.966938\pi$
$548$	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	0.520938	−	0.853594i	$-0.325582\pi$
$557$	34.6621	−	12.6160i	1.46868	−	0.534556i	0.947742	+	0.319039i	$0.103360\pi$
$558$		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	−0.322814	−	0.946462i	$-0.604629\pi$
$563$	15.2051	−	16.1164i	0.640817	−	0.679226i	0.963631	+	0.267236i	$0.0861104\pi$
$564$		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	0.856747	−	0.515736i	$-0.172482\pi$
$569$	−2.53616	−	5.87948i	−0.106321	−	0.246480i	−0.963069	+	0.269256i	$0.913222\pi$
$570$		0			0
$571$	3.79067	−	4.01787i	0.158634	−	0.168143i	−0.643182	−	0.765714i	$-0.722386\pi$
$571$	3.79067	−	4.01787i	0.158634	−	0.168143i	0.801816	+	0.597571i	$0.203867\pi$
$572$	−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	0.566630	−	0.823972i	$-0.308247\pi$
$577$	36.7599	−	13.3795i	1.53033	−	0.556996i	0.963703	+	0.266977i	$0.0860246\pi$
$578$	−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	0.893737	−	0.448592i	$-0.148074\pi$
$587$	9.54436	+	10.1164i	0.393938	+	0.417550i	−0.499799	+	0.866141i	$0.666593\pi$
$588$		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	0.630923	−	0.775846i	$-0.282676\pi$
$593$	−8.67989	−	15.0340i	−0.356441	−	0.617373i	−0.987363	+	0.158472i	$0.949343\pi$
$594$		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	−0.995891	−	0.0905596i	$-0.971134\pi$
$599$	−37.1512	+	18.6580i	−1.51796	+	0.762346i	−0.522065	+	0.852906i	$0.674838\pi$
$600$		0			0
$601$	2.64850	−	8.84660i	0.108035	−	0.360860i	−0.886827	−	0.462101i	$-0.847096\pi$
$601$	2.64850	−	8.84660i	0.108035	−	0.360860i	0.994862	+	0.101240i	$0.0322811\pi$
$602$	−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	−0.991570	−	0.129572i	$-0.958640\pi$
$607$	−5.34301	+	12.3865i	−0.216866	+	0.502752i	0.774704	+	0.632324i	$0.217899\pi$
$608$	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	0.968137	−	0.250421i	$-0.0805691\pi$
$613$	−0.675007	−	3.82815i	−0.0272633	−	0.154618i	−0.995400	+	0.0958034i	$0.969458\pi$
$614$	−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	0.977266	+	0.212015i	$0.0680026\pi$
$617$	6.88741	+	23.0055i	0.277276	+	0.926168i	−0.699990	+	0.714153i	$0.746812\pi$
$618$		0			0
$619$	−6.07827	+	8.16453i	−0.244306	+	0.328160i	−0.907315	−	0.420451i	$-0.861872\pi$
$619$	−6.07827	+	8.16453i	−0.244306	+	0.328160i	0.663009	+	0.748612i	$0.269279\pi$
$620$	−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	−0.878621	−	0.477520i	$-0.841536\pi$
$631$	−37.7162	−	31.6476i	−1.50146	−	1.25987i	−0.622836	−	0.782352i	$-0.714020\pi$
$632$	−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	0.484314	−	0.874894i	$-0.339069\pi$
$641$	33.1606	−	7.85921i	1.30976	−	0.310420i	0.825451	+	0.564474i	$0.190921\pi$
$642$		0			0
$643$	1.15570	−	19.8426i	0.0455764	−	0.782516i	−0.895654	−	0.444751i	$-0.853292\pi$
$643$	1.15570	−	19.8426i	0.0455764	−	0.782516i	0.941230	−	0.337765i	$-0.109671\pi$
$644$	−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	0.986229	+	0.165387i	$0.0528874\pi$
$653$	−0.320235	+	5.49823i	−0.0125318	+	0.215162i	−0.998760	+	0.0497749i	$0.984150\pi$
$654$		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	0.251194	−	0.967937i	$-0.419177\pi$
$659$	31.8182	−	20.9272i	1.23946	−	0.815207i	0.988268	+	0.152730i	$0.0488065\pi$
$660$		0			0
$661$	27.9872	−	3.27123i	1.08857	−	0.127236i	0.447177	−	0.894445i	$-0.352429\pi$
$661$	27.9872	−	3.27123i	1.08857	−	0.127236i	0.641397	+	0.767209i	$0.278355\pi$
$662$	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	−0.373702	−	0.927549i	$-0.621912\pi$
$673$	−24.6772	−	2.88436i	−0.951238	−	0.111184i	−0.577536	+	0.816365i	$0.695986\pi$
$674$	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	0.184663	+	0.982802i	$0.440881\pi$
$677$	−21.0707	+	28.3029i	−0.809813	+	1.08777i	−0.994476	+	0.104965i	$0.966527\pi$
$678$		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	0.775483	+	0.631369i	$0.217507\pi$
$683$	6.86569	+	38.9372i	0.262708	+	1.48989i	−0.512774	+	0.858523i	$0.671382\pi$
$684$		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	0.135908	−	0.990721i	$-0.456605\pi$
$691$	−15.1837	−	7.62552i	−0.577613	−	0.290088i	−0.713522	+	0.700633i	$0.752901\pi$
$692$	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	0.371328	+	0.928502i	$0.378903\pi$
$701$	−16.3741	+	28.3608i	−0.618442	+	1.07117i	−0.989770	+	0.142672i	$0.954431\pi$
$702$		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	0.149913	−	0.988699i	$-0.452101\pi$
$709$	−22.5220	−	23.8719i	−0.845830	−	0.896527i	−0.995743	+	0.0921719i	$0.970619\pi$
$710$	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	−0.0296323	−	0.999561i	$-0.509434\pi$
$719$	15.8250	−	5.75983i	0.590173	−	0.214806i	0.619806	+	0.784755i	$0.287211\pi$
$720$		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	0.845282	−	0.534320i	$-0.179432\pi$
$727$	−3.32819	−	7.71562i	−0.123436	−	0.286157i	−0.968718	+	0.248163i	$0.920173\pi$
$728$	−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	−0.864687	−	0.502312i	$-0.832483\pi$
$733$	−8.47275	+	8.98059i	−0.312948	+	0.331705i	0.551739	+	0.834017i	$0.313965\pi$
$734$	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	0.454815	−	0.890586i	$-0.349705\pi$
$739$	37.3973	−	13.6115i	1.37568	−	0.500707i	0.920866	+	0.389879i	$0.127483\pi$
$740$	−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	0.529825	−	0.848107i	$-0.322258\pi$
$743$	−11.8466	−	15.9127i	−0.434608	−	0.583780i	−0.964433	+	0.264327i	$0.914850\pi$
$744$		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	−0.192704	−	0.981257i	$-0.561726\pi$
$751$	−32.0641	−	21.0889i	−1.17004	−	0.769545i	−0.977332	+	0.211712i	$0.932096\pi$
$752$	−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	−0.708346	−	0.705866i	$-0.750558\pi$
$757$	7.07444	−	12.2533i	0.257125	−	0.445353i	0.965470	+	0.260513i	$0.0838915\pi$
$758$	−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	−0.595659	−	0.803237i	$-0.703109\pi$
$761$	−8.47080	+	4.25420i	−0.307066	+	0.154215i	0.288593	+	0.957452i	$0.406813\pi$
$762$		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	−0.983930	−	0.178553i	$-0.942858\pi$
$769$	−4.95943	+	11.4972i	−0.178841	+	0.414601i	0.805089	+	0.593154i	$0.202118\pi$
$770$	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	0.639882	+	0.768474i	$0.278983\pi$
$773$	−6.23462	+	35.3583i	−0.224244	+	1.27175i	−0.864125	+	0.503277i	$0.832128\pi$
$774$		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	0.854781	−	0.518989i	$-0.173691\pi$
$787$	38.8743	+	9.21338i	1.38572	+	0.328421i	0.530938	+	0.847411i	$0.321840\pi$
$788$	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	−0.692165	−	0.721739i	$-0.743343\pi$
$797$	−33.8557	+	3.95716i	−1.19923	+	0.140170i	−0.507063	+	0.861909i	$0.669269\pi$
$798$		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	−0.909672	−	0.415328i	$-0.863667\pi$
$821$	−25.4615	+	16.7463i	−0.888613	+	0.584450i	0.0210583	+	0.999778i	$0.493296\pi$
$822$		0			0
$823$	22.1674	−	2.59100i	0.772707	−	0.0903165i	0.279404	−	0.960174i	$-0.409863\pi$
$823$	22.1674	−	2.59100i	0.772707	−	0.0903165i	0.493304	+	0.869857i	$0.335789\pi$
$824$	−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	0.978893	−	0.204374i	$-0.0655159\pi$
$827$	27.2509	+	22.8662i	0.947606	+	0.795136i	−0.0312864	+	0.999510i	$0.509960\pi$
$828$		0			0
$829$	−13.4520	+	11.2875i	−0.467206	+	0.392032i	−0.845774	−	0.533541i	$-0.820861\pi$
$829$	−13.4520	+	11.2875i	−0.467206	+	0.392032i	0.378568	+	0.925573i	$0.376416\pi$
$830$	−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	−0.206298	−	0.978489i	$-0.566142\pi$
$839$	22.8900	−	30.7466i	0.790251	−	1.06149i	0.996549	−	0.0830022i	$-0.0264509\pi$
$840$		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	0.572568	−	0.819857i	$-0.305947\pi$
$853$	7.50175	+	3.76752i	0.256855	+	0.128997i	−0.315713	+	0.948855i	$0.602244\pi$
$854$	−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	−0.309977	−	0.950744i	$-0.600321\pi$
$857$	13.8014	−	46.0999i	0.471447	−	1.57474i	0.781424	−	0.624000i	$-0.214493\pi$
$858$		0			0
$859$	45.6471	−	22.9248i	1.55746	−	0.782185i	0.558575	−	0.829454i	$-0.311348\pi$
$859$	45.6471	−	22.9248i	1.55746	−	0.782185i	0.998882	+	0.0472690i	$0.0150518\pi$
$860$	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	−0.362403	−	0.932022i	$-0.618043\pi$
$863$	18.3885	−	31.8499i	0.625953	−	1.08418i	0.988356	−	0.152161i	$-0.0486232\pi$
$864$		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	0.759304	−	0.650736i	$-0.225540\pi$
$877$	−2.42437	−	3.25649i	−0.0818651	−	0.109964i	−0.841169	+	0.540772i	$0.818132\pi$
$878$	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	−0.892986	−	0.450085i	$-0.851394\pi$
$881$	−38.2223	+	13.9118i	−1.28774	+	0.468700i	−0.394758	+	0.918785i	$0.629171\pi$
$882$		0			0
$883$	−24.6043	−	8.95523i	−0.828000	−	0.301367i	−0.106962	−	0.994263i	$-0.534112\pi$
$883$	−24.6043	−	8.95523i	−0.828000	−	0.301367i	−0.721038	+	0.692896i	$0.756335\pi$
$884$	−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	−0.426745	−	0.904372i	$-0.640340\pi$
$887$	14.9184	−	15.8126i	0.500910	−	0.530933i	0.927655	+	0.373438i	$0.121821\pi$
$888$		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	0.533930	+	0.845529i	$0.320714\pi$
$907$	3.06495	+	52.6232i	0.101770	+	1.74733i	−0.432160	+	0.901797i	$0.642248\pi$
$908$	−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	0.999288	+	0.0377293i	$0.0120125\pi$
$911$	29.5444	+	31.3152i	0.978850	+	1.03752i	−0.0204380	+	0.999791i	$0.506506\pi$
$912$		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	0.0649552	+	0.997888i	$0.479310\pi$
$919$	−25.2136	+	43.6712i	−0.831719	+	1.44058i	−0.896674	+	0.442691i	$0.854024\pi$
$920$	−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	0.666226	−	0.745750i	$-0.267909\pi$
$929$	14.2000	+	7.13149i	0.465886	+	0.233977i	−0.200340	+	0.979726i	$0.564205\pi$
$930$		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	0.978179	+	0.207765i	$0.0666189\pi$
$937$	3.98093	+	22.5770i	0.130051	+	0.737557i	−0.848128	+	0.529792i	$0.822270\pi$
$938$	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	0.998299	−	0.0582943i	$-0.0185662\pi$
$941$	4.05531	+	13.5457i	0.132199	+	0.441576i	−0.866100	+	0.499870i	$0.833381\pi$
$942$		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	−0.877940	−	0.478771i	$-0.841082\pi$
$947$	−56.7038	−	6.62773i	−1.84263	−	0.215372i	−0.964687	+	0.263399i	$0.915156\pi$
$948$		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	−0.395740	−	0.918363i	$-0.629512\pi$
$953$	13.5816	−	11.3963i	0.439951	−	0.369163i	0.835691	+	0.549200i	$0.185067\pi$
$954$		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	−0.912365	−	0.409378i	$-0.865746\pi$
$967$	1.28606	−	22.0808i	0.0413568	−	0.710070i	0.953722	−	0.300691i	$-0.0972174\pi$
$968$	−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	−0.905198	−	0.424991i	$-0.860277\pi$
$977$	1.35086	−	23.1934i	0.0432178	−	0.742022i	0.948415	−	0.317030i	$-0.102686\pi$
$978$		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	−0.753851	−	0.657045i	$-0.771806\pi$
$983$	−14.0814	+	9.26149i	−0.449127	+	0.295396i	0.304724	+	0.952441i	$0.401436\pi$
$984$		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	−0.647800	−	0.761810i	$-0.724311\pi$
$991$	−0.316451	+	0.265534i	−0.0100524	+	0.00843496i	0.637748	+	0.770245i	$0.279866\pi$
$992$	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	0.0237143	−	0.999719i	$-0.492451\pi$
$997$	−5.80233	−	0.678195i	−0.183762	−	0.0214787i	−0.207476	+	0.978240i	$0.566525\pi$
$998$	−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.145.7		144
3.2	odd	2		81.2.g.a.31.2	✓	144
9.2	odd	6		729.2.g.d.190.2		144
9.4	even	3		729.2.g.b.433.2		144
9.5	odd	6		729.2.g.c.433.7		144
9.7	even	3		729.2.g.a.190.7		144
81.7	even	27		729.2.g.b.298.2		144
81.14	odd	54		6561.2.a.c.1.17		72
81.20	odd	54		729.2.g.d.541.2		144
81.34	even	27	inner	243.2.g.a.181.7		144
81.47	odd	54		81.2.g.a.34.2	yes	144
81.61	even	27		729.2.g.a.541.7		144
81.67	even	27		6561.2.a.d.1.56		72
81.74	odd	54		729.2.g.c.298.7		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.31.2	✓	144	3.2	odd	2
81.2.g.a.34.2	yes	144	81.47	odd	54
243.2.g.a.145.7		144	1.1	even	1	trivial
243.2.g.a.181.7		144	81.34	even	27	inner
729.2.g.a.190.7		144	9.7	even	3
729.2.g.a.541.7		144	81.61	even	27
729.2.g.b.298.2		144	81.7	even	27
729.2.g.b.433.2		144	9.4	even	3
729.2.g.c.298.7		144	81.74	odd	54
729.2.g.c.433.7		144	9.5	odd	6
729.2.g.d.190.2		144	9.2	odd	6
729.2.g.d.541.2		144	81.20	odd	54
6561.2.a.c.1.17		72	81.14	odd	54
6561.2.a.d.1.56		72	81.67	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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