LMFDB - Embedded newform 648.2.t.a.37.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			37.23
Character	$\chi$	$=$	648.37
Dual form			648.2.t.a.613.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.654194 + 1.25381i) q^{2} +(-1.14406 + 1.64047i) q^{4} +(-1.15428 - 3.17134i) q^{5} +(0.593321 + 3.36489i) q^{7} +(-2.80526 - 0.361244i) q^{8} +(3.22113 - 3.52191i) q^{10} +(-0.197048 + 0.541384i) q^{11} +(-4.30199 + 5.12691i) q^{13} +(-3.83077 + 2.94520i) q^{14} +(-1.38226 - 3.75358i) q^{16} +(-1.15893 + 2.00733i) q^{17} +(0.353289 - 0.203971i) q^{19} +(6.52304 + 1.73466i) q^{20} +(-0.807698 + 0.107111i) q^{22} +(-1.15186 + 6.53250i) q^{23} +(-4.89486 + 4.10727i) q^{25} +(-9.24249 - 2.03986i) q^{26} +(-6.19878 - 2.87631i) q^{28} +(-2.24644 - 2.67721i) q^{29} +(-0.382945 + 2.17179i) q^{31} +(3.80200 - 4.18865i) q^{32} +(-3.27497 - 0.139892i) q^{34} +(9.98637 - 5.76564i) q^{35} +(1.05249 + 0.607656i) q^{37} +(0.486860 + 0.309519i) q^{38} +(2.09242 + 9.31343i) q^{40} +(-5.09057 - 4.27150i) q^{41} +(-0.442145 + 1.21478i) q^{43} +(-0.662688 - 0.942626i) q^{44} +(-8.94402 + 2.82932i) q^{46} +(0.547022 + 3.10232i) q^{47} +(-4.39261 + 1.59878i) q^{49} +(-8.35191 - 3.45024i) q^{50} +(-3.48879 - 12.9228i) q^{52} +9.35460i q^{53} +1.94436 q^{55} +(-0.448874 - 9.65374i) q^{56} +(1.88709 - 4.56802i) q^{58} +(-3.00302 - 8.25072i) q^{59} +(4.67459 - 0.824257i) q^{61} +(-2.97352 + 0.940634i) q^{62} +(7.73901 + 2.02677i) q^{64} +(21.2249 + 7.72523i) q^{65} +(9.67062 - 11.5250i) q^{67} +(-1.96707 - 4.19769i) q^{68} +(13.7620 + 8.74913i) q^{70} +(3.92323 - 6.79524i) q^{71} +(0.641809 + 1.11165i) q^{73} +(-0.0733489 + 1.71715i) q^{74} +(-0.0695752 + 0.812914i) q^{76} +(-1.93861 - 0.341829i) q^{77} +(3.84081 - 3.22282i) q^{79} +(-10.3084 + 8.71628i) q^{80} +(2.02541 - 9.17698i) q^{82} +(6.67152 + 7.95081i) q^{83} +(7.70366 + 1.35836i) q^{85} +(-1.81235 + 0.240341i) q^{86} +(0.748343 - 1.44754i) q^{88} +(2.86501 + 4.96234i) q^{89} +(-19.8040 - 11.4338i) q^{91} +(-9.39855 - 9.36314i) q^{92} +(-3.53185 + 2.71538i) q^{94} +(-1.05466 - 0.884962i) q^{95} +(10.5548 + 3.84165i) q^{97} +(-4.87818 - 4.46157i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.654194	+	1.25381i	0.462585	+	0.886575i
$2$	0.654194	+	1.25381i	0.462585	+	0.886575i
$3$		0			0
$3$		0			0
$4$	−1.14406	+	1.64047i	−0.572030	+	0.820233i
$5$	−1.15428	−	3.17134i	−0.516208	−	1.41827i	−0.874667	−	0.484723i	$-0.838920\pi$
$5$	−1.15428	−	3.17134i	−0.516208	−	1.41827i	0.358460	−	0.933545i	$-0.383302\pi$
$6$		0			0
$7$	0.593321	+	3.36489i	0.224254	+	1.27181i	0.864106	+	0.503311i	$0.167885\pi$
$7$	0.593321	+	3.36489i	0.224254	+	1.27181i	−0.639851	+	0.768499i	$0.721004\pi$
$8$	−2.80526	−	0.361244i	−0.991810	−	0.127719i
$9$		0			0
$10$	3.22113	−	3.52191i	1.01861	−	1.11373i
$11$	−0.197048	+	0.541384i	−0.0594121	+	0.163233i	−0.965848	−	0.259111i	$-0.916570\pi$
$11$	−0.197048	+	0.541384i	−0.0594121	+	0.163233i	0.906435	+	0.422344i	$0.138793\pi$
$12$		0			0
$13$	−4.30199	+	5.12691i	−1.19316	+	1.42195i	−0.311379	+	0.950286i	$0.600791\pi$
$13$	−4.30199	+	5.12691i	−1.19316	+	1.42195i	−0.881779	+	0.471664i	$0.843654\pi$
$14$	−3.83077	+	2.94520i	−1.02382	+	0.787139i
$15$		0			0
$16$	−1.38226	−	3.75358i	−0.345564	−	0.938395i
$17$	−1.15893	+	2.00733i	−0.281082	+	0.486849i	−0.971652	−	0.236417i	$-0.924027\pi$
$17$	−1.15893	+	2.00733i	−0.281082	+	0.486849i	0.690569	+	0.723266i	$0.257360\pi$
$18$		0			0
$19$	0.353289	−	0.203971i	0.0810500	−	0.0467943i	−0.458927	−	0.888474i	$-0.651766\pi$
$19$	0.353289	−	0.203971i	0.0810500	−	0.0467943i	0.539977	+	0.841680i	$0.318433\pi$
$20$	6.52304	+	1.73466i	1.45860	+	0.387881i
$21$		0			0
$22$	−0.807698	+	0.107111i	−0.172202	+	0.0228361i
$23$	−1.15186	+	6.53250i	−0.240178	+	1.36212i	0.591250	+	0.806488i	$0.298635\pi$
$23$	−1.15186	+	6.53250i	−0.240178	+	1.36212i	−0.831429	+	0.555631i	$0.812477\pi$
$24$		0			0
$25$	−4.89486	+	4.10727i	−0.978971	+	0.821454i
$26$	−9.24249	−	2.03986i	−1.81260	−	0.400050i
$27$		0			0
$28$	−6.19878	−	2.87631i	−1.17146	−	0.543572i
$29$	−2.24644	−	2.67721i	−0.417154	−	0.497145i	0.516016	−	0.856579i	$-0.327414\pi$
$29$	−2.24644	−	2.67721i	−0.417154	−	0.497145i	−0.933171	+	0.359434i	$0.882970\pi$
$30$		0			0
$31$	−0.382945	+	2.17179i	−0.0687790	+	0.390065i	0.930913	+	0.365241i	$0.119014\pi$
$31$	−0.382945	+	2.17179i	−0.0687790	+	0.390065i	−0.999692	+	0.0248236i	$0.992098\pi$
$32$	3.80200	−	4.18865i	0.672104	−	0.740456i
$33$		0			0
$34$	−3.27497	−	0.139892i	−0.561653	−	0.0239913i
$35$	9.98637	−	5.76564i	1.68801	−	0.974570i
$36$		0			0
$37$	1.05249	+	0.607656i	0.173028	+	0.0998980i	0.584013	−	0.811744i	$-0.301482\pi$
$37$	1.05249	+	0.607656i	0.173028	+	0.0998980i	−0.410985	+	0.911642i	$0.634815\pi$
$38$	0.486860	+	0.309519i	0.0789792	+	0.0502106i
$39$		0			0
$40$	2.09242	+	9.31343i	0.330840	+	1.47258i
$41$	−5.09057	−	4.27150i	−0.795014	−	0.667096i	0.151967	−	0.988386i	$-0.451439\pi$
$41$	−5.09057	−	4.27150i	−0.795014	−	0.667096i	−0.946981	+	0.321290i	$0.895884\pi$
$42$		0			0
$43$	−0.442145	+	1.21478i	−0.0674265	+	0.185253i	−0.968830	−	0.247728i	$-0.920316\pi$
$43$	−0.442145	+	1.21478i	−0.0674265	+	0.185253i	0.901403	+	0.432981i	$0.142538\pi$
$44$	−0.662688	−	0.942626i	−0.0999040	−	0.142106i
$45$		0			0
$46$	−8.94402	+	2.82932i	−1.31872	+	0.417160i
$47$	0.547022	+	3.10232i	0.0797914	+	0.452520i	0.998359	+	0.0572567i	$0.0182354\pi$
$47$	0.547022	+	3.10232i	0.0797914	+	0.452520i	−0.918568	+	0.395263i	$0.870654\pi$
$48$		0			0
$49$	−4.39261	+	1.59878i	−0.627516	+	0.228397i
$50$	−8.35191	−	3.45024i	−1.18114	−	0.487938i
$51$		0			0
$52$	−3.48879	−	12.9228i	−0.483809	−	1.79206i
$53$			9.35460i			1.28495i	0.766305	+	0.642477i	$0.222093\pi$
$53$			9.35460i			1.28495i	−0.766305	+	0.642477i	$0.777907\pi$
$54$		0			0
$55$	1.94436			0.262178
$56$	−0.448874	−	9.65374i	−0.0599833	−	1.29004i
$57$		0			0
$58$	1.88709	−	4.56802i	0.247787	−	0.599810i
$59$	−3.00302	−	8.25072i	−0.390959	−	1.07415i	−0.966564	−	0.256424i	$-0.917456\pi$
$59$	−3.00302	−	8.25072i	−0.390959	−	1.07415i	0.575605	−	0.817728i	$-0.304767\pi$
$60$		0			0
$61$	4.67459	−	0.824257i	0.598520	−	0.105535i	0.133824	−	0.991005i	$-0.457274\pi$
$61$	4.67459	−	0.824257i	0.598520	−	0.105535i	0.464697	+	0.885470i	$0.346163\pi$
$62$	−2.97352	+	0.940634i	−0.377638	+	0.119461i
$63$		0			0
$64$	7.73901	+	2.02677i	0.967376	+	0.253346i
$65$	21.2249	+	7.72523i	2.63262	+	0.958196i
$66$		0			0
$67$	9.67062	−	11.5250i	1.18145	−	1.40800i	0.288723	−	0.957413i	$-0.406769\pi$
$67$	9.67062	−	11.5250i	1.18145	−	1.40800i	0.892731	−	0.450589i	$-0.148786\pi$
$68$	−1.96707	−	4.19769i	−0.238542	−	0.509045i
$69$		0			0
$70$	13.7620	+	8.74913i	1.64488	+	1.04572i
$71$	3.92323	−	6.79524i	0.465602	−	0.806446i	−0.533627	−	0.845720i	$-0.679171\pi$
$71$	3.92323	−	6.79524i	0.465602	−	0.806446i	0.999228	+	0.0392740i	$0.0125045\pi$
$72$		0			0
$73$	0.641809	+	1.11165i	0.0751180	+	0.130108i	0.901138	−	0.433533i	$-0.142733\pi$
$73$	0.641809	+	1.11165i	0.0751180	+	0.130108i	−0.826020	+	0.563641i	$0.809400\pi$
$74$	−0.0733489	+	1.71715i	−0.00852664	+	0.199614i
$75$		0			0
$76$	−0.0695752	+	0.812914i	−0.00798082	+	0.0932476i
$77$	−1.93861	−	0.341829i	−0.220925	−	0.0389551i
$78$		0			0
$79$	3.84081	−	3.22282i	0.432125	−	0.362596i	−0.400628	−	0.916241i	$-0.631208\pi$
$79$	3.84081	−	3.22282i	0.432125	−	0.362596i	0.832753	+	0.553645i	$0.186764\pi$
$80$	−10.3084	+	8.71628i	−1.15251	+	0.974510i
$81$		0			0
$82$	2.02541	−	9.17698i	0.223669	−	1.01343i
$83$	6.67152	+	7.95081i	0.732295	+	0.872715i	0.995763	−	0.0919529i	$-0.0293109\pi$
$83$	6.67152	+	7.95081i	0.732295	+	0.872715i	−0.263468	+	0.964668i	$0.584866\pi$
$84$		0			0
$85$	7.70366	+	1.35836i	0.835580	+	0.147335i
$86$	−1.81235	+	0.240341i	−0.195431	+	0.0259166i
$87$		0			0
$88$	0.748343	−	1.44754i	0.0797736	−	0.154309i
$89$	2.86501	+	4.96234i	0.303690	+	0.526007i	0.976969	−	0.213382i	$-0.0684478\pi$
$89$	2.86501	+	4.96234i	0.303690	+	0.526007i	−0.673278	+	0.739389i	$0.735114\pi$
$90$		0			0
$91$	−19.8040	−	11.4338i	−2.07602	−	1.19859i
$92$	−9.39855	−	9.36314i	−0.979866	−	0.976175i
$93$		0			0
$94$	−3.53185	+	2.71538i	−0.364282	+	0.280070i
$95$	−1.05466	−	0.884962i	−0.108205	−	0.0907952i
$96$		0			0
$97$	10.5548	+	3.84165i	1.07168	+	0.390061i	0.816806	−	0.576913i	$-0.195743\pi$
$97$	10.5548	+	3.84165i	1.07168	+	0.390061i	0.254877	+	0.966974i	$0.417965\pi$
$98$	−4.87818	−	4.46157i	−0.492771	−	0.450687i
$99$		0			0
$100$	−1.13784	−	12.7288i	−0.113784	−	1.27288i
$101$	−12.2411	+	2.15844i	−1.21804	+	0.214773i	−0.745481	−	0.666527i	$-0.767780\pi$
$101$	−12.2411	+	2.15844i	−1.21804	+	0.214773i	−0.472557	+	0.881300i	$0.656669\pi$
$102$		0			0
$103$	−14.8537	+	5.40632i	−1.46358	+	0.532701i	−0.946350	−	0.323144i	$-0.895260\pi$
$103$	−14.8537	+	5.40632i	−1.46358	+	0.532701i	−0.517233	+	0.855844i	$0.673038\pi$
$104$	13.9203	−	12.8283i	1.36500	−	1.25792i
$105$		0			0
$106$	−11.7289	+	6.11973i	−1.13921	+	0.594401i
$107$			2.44491i			0.236359i	0.992992	+	0.118179i	$0.0377058\pi$
$107$			2.44491i			0.236359i	−0.992992	+	0.118179i	$0.962294\pi$
$108$		0			0
$109$			16.2522i			1.55668i	0.627843	+	0.778340i	$0.283938\pi$
$109$			16.2522i			1.55668i	−0.627843	+	0.778340i	$0.716062\pi$
$110$	1.27199	+	2.43785i	0.121280	+	0.232440i
$111$		0			0
$112$	11.8103	−	6.87822i	1.11597	−	0.649931i
$113$	11.4376	−	4.16294i	1.07596	−	0.391617i	0.257556	−	0.966263i	$-0.417083\pi$
$113$	11.4376	−	4.16294i	1.07596	−	0.391617i	0.818402	+	0.574646i	$0.194860\pi$
$114$		0			0
$115$	22.0464	−	3.88737i	2.05583	−	0.362499i
$116$	6.96193	−	0.622331i	0.646399	−	0.0577820i
$117$		0			0
$118$	8.38025	−	9.16278i	0.771464	−	0.843502i
$119$	−7.44207	−	2.70869i	−0.682213	−	0.248305i
$120$		0			0
$121$	8.17222	+	6.85731i	0.742929	+	0.623392i
$122$	4.09155	+	5.32181i	0.370432	+	0.481814i
$123$		0			0
$124$	−3.12463	−	3.11286i	−0.280600	−	0.279543i
$125$	4.06195	+	2.34517i	0.363312	+	0.209758i
$126$		0			0
$127$	−4.79341	−	8.30243i	−0.425346	−	0.736722i	0.571106	−	0.820876i	$-0.306514\pi$
$127$	−4.79341	−	8.30243i	−0.425346	−	0.736722i	−0.996453	+	0.0841546i	$0.973181\pi$
$128$	2.52164	+	11.0291i	0.222883	+	0.974845i
$129$		0			0
$130$	4.19927	+	31.6657i	0.368300	+	2.77726i
$131$	0.406480	+	0.0716734i	0.0355143	+	0.00626213i	0.191377	−	0.981517i	$-0.438705\pi$
$131$	0.406480	+	0.0716734i	0.0355143	+	0.00626213i	−0.155863	+	0.987779i	$0.549816\pi$
$132$		0			0
$133$	0.895956	+	1.06776i	0.0776892	+	0.0925864i
$134$	20.7766	+	4.58549i	1.79482	+	0.396126i
$135$		0			0
$136$	3.97625	−	5.21243i	0.340960	−	0.446962i
$137$	−12.0727	+	10.1302i	−1.03144	+	0.865480i	−0.991021	−	0.133703i	$-0.957313\pi$
$137$	−12.0727	+	10.1302i	−1.03144	+	0.865480i	−0.0404177	+	0.999183i	$0.512869\pi$
$138$		0			0
$139$	−2.17442	−	0.383409i	−0.184432	−	0.0325204i	0.0806691	−	0.996741i	$-0.474294\pi$
$139$	−2.17442	−	0.383409i	−0.184432	−	0.0325204i	−0.265101	+	0.964221i	$0.585405\pi$
$140$	−1.96667	+	22.9785i	−0.166214	+	1.94204i
$141$		0			0
$142$	11.0865	+	0.473565i	0.930356	+	0.0397407i
$143$	−1.92793	−	3.33928i	−0.161222	−	0.279244i
$144$		0			0
$145$	−5.89733	+	10.2145i	−0.489747	+	0.848267i
$146$	−0.973920	+	1.53194i	−0.0806022	+	0.126784i
$147$		0			0
$148$	−2.20095	+	1.03138i	−0.180917	+	0.0847790i
$149$	−4.40044	+	5.24424i	−0.360498	+	0.429625i	−0.915558	−	0.402186i	$-0.868251\pi$
$149$	−4.40044	+	5.24424i	−0.360498	+	0.429625i	0.555060	+	0.831810i	$0.312695\pi$
$150$		0			0
$151$	11.0866	+	4.03519i	0.902213	+	0.328379i	0.751139	−	0.660144i	$-0.229505\pi$
$151$	11.0866	+	4.03519i	0.902213	+	0.328379i	0.151074	+	0.988522i	$0.451727\pi$
$152$	−1.06475	+	0.444570i	−0.0863628	+	0.0360594i
$153$		0			0
$154$	−0.839641	−	2.65427i	−0.0676602	−	0.213887i
$155$	7.32952	−	1.29239i	0.588721	−	0.103807i
$156$		0			0
$157$	−4.12184	−	11.3247i	−0.328959	−	0.903808i	−0.988376	−	0.152030i	$-0.951419\pi$
$157$	−4.12184	−	11.3247i	−0.328959	−	0.903808i	0.659417	−	0.751778i	$-0.270803\pi$
$158$	6.55343	+	2.70728i	0.521363	+	0.215380i
$159$		0			0
$160$	−17.6722	−	7.22258i	−1.39711	−	0.570995i
$161$	−22.6646			−1.78622
$162$		0			0
$163$			13.3972i			1.04935i	0.851303	+	0.524675i	$0.175813\pi$
$163$			13.3972i			1.04935i	−0.851303	+	0.524675i	$0.824187\pi$
$164$	12.8312	−	3.46407i	1.00195	−	0.270498i
$165$		0			0
$166$	−5.60430	+	13.5662i	−0.434978	+	1.05294i
$167$	6.36473	−	2.31657i	0.492517	−	0.179262i	−0.0838081	−	0.996482i	$-0.526708\pi$
$167$	6.36473	−	2.31657i	0.492517	−	0.179262i	0.576325	+	0.817220i	$0.304486\pi$
$168$		0			0
$169$	−5.52068	−	31.3093i	−0.424668	−	2.40841i
$170$	3.33657	+	10.5475i	0.255903	+	0.808959i
$171$		0			0
$172$	−1.48697	−	2.11511i	−0.113380	−	0.161275i
$173$	0.576454	−	1.58380i	0.0438270	−	0.120414i	−0.915848	−	0.401524i	$-0.868481\pi$
$173$	0.576454	−	1.58380i	0.0438270	−	0.120414i	0.959675	+	0.281111i	$0.0907028\pi$
$174$		0			0
$175$	−16.7247	−	14.0337i	−1.26427	−	1.06085i
$176$	2.30450	−	0.00869789i	0.173708	−	0.000655628i
$177$		0			0
$178$	−4.34754	+	6.83850i	−0.325862	+	0.512568i
$179$	10.3190	+	5.95768i	0.771279	+	0.445298i	0.833331	−	0.552775i	$-0.186431\pi$
$179$	10.3190	+	5.95768i	0.771279	+	0.445298i	−0.0620517	+	0.998073i	$0.519764\pi$
$180$		0			0
$181$	−14.3027	+	8.25769i	−1.06311	+	0.613789i	−0.926292	−	0.376806i	$-0.877022\pi$
$181$	−14.3027	+	8.25769i	−1.06311	+	0.613789i	−0.136822	+	0.990596i	$0.543689\pi$
$182$	1.38015	−	32.3103i	0.102304	−	2.39500i
$183$		0			0
$184$	5.59109	−	17.9093i	0.412180	−	1.32029i
$185$	0.712223	−	4.03922i	0.0523636	−	0.296969i
$186$		0			0
$187$	−0.858372	−	1.02297i	−0.0627703	−	0.0748068i
$188$	−5.71507	−	2.65186i	−0.416815	−	0.193407i
$189$		0			0
$190$	0.419620	−	1.90127i	0.0304424	−	0.137933i
$191$	10.1267	−	8.49734i	0.732745	−	0.614846i	−0.198134	−	0.980175i	$-0.563488\pi$
$191$	10.1267	−	8.49734i	0.732745	−	0.614846i	0.930878	+	0.365329i	$0.119044\pi$
$192$		0			0
$193$	−0.0307325	+	0.174293i	−0.00221218	+	0.0125459i	−0.985894	−	0.167372i	$-0.946472\pi$
$193$	−0.0307325	+	0.174293i	−0.00221218	+	0.0125459i	0.983682	+	0.179918i	$0.0575831\pi$
$194$	2.08824	+	15.7469i	0.149927	+	1.13056i
$195$		0			0
$196$	2.40266	−	9.03503i	0.171619	−	0.645359i
$197$	−0.841221	+	0.485679i	−0.0599345	+	0.0346032i	−0.529668	−	0.848205i	$-0.677683\pi$
$197$	−0.841221	+	0.485679i	−0.0599345	+	0.0346032i	0.469733	+	0.882808i	$0.344350\pi$
$198$		0			0
$199$	2.04926	−	3.54942i	0.145268	−	0.251612i	−0.784205	−	0.620502i	$-0.786929\pi$
$199$	2.04926	−	3.54942i	0.145268	−	0.251612i	0.929473	+	0.368890i	$0.120262\pi$
$200$	15.2151	−	9.75374i	1.07587	−	0.689693i
$201$		0			0
$202$	−10.7143	−	13.9360i	−0.753858	−	0.980530i
$203$	7.67565	−	9.14748i	0.538725	−	0.642027i
$204$		0			0
$205$	−7.67047	+	21.0745i	−0.535729	+	1.47190i
$206$	−16.4957	−	15.0869i	−1.14931	−	1.05116i
$207$		0			0
$208$	25.1907	+	9.06115i	1.74666	+	0.628278i
$209$	0.0408121	+	0.231457i	0.00282303	+	0.0160102i
$210$		0			0
$211$	−1.28341	−	3.52613i	−0.0883534	−	0.242749i	0.887644	−	0.460530i	$-0.152340\pi$
$211$	−1.28341	−	3.52613i	−0.0883534	−	0.242749i	−0.975998	+	0.217781i	$0.930118\pi$
$212$	−15.3459	−	10.7022i	−1.05396	−	0.735031i
$213$		0			0
$214$	−3.06545	+	1.59945i	−0.209550	+	0.109336i
$215$	4.36285			0.297544
$216$		0			0
$217$	−7.53504			−0.511512
$218$	−20.3771	+	10.6321i	−1.38011	+	0.720097i
$219$		0			0
$220$	−2.22447	+	3.18966i	−0.149973	+	0.215047i
$221$	−5.30569	−	14.5773i	−0.356899	−	0.980572i
$222$		0			0
$223$	0.680991	+	3.86209i	0.0456025	+	0.258625i	0.999082	−	0.0428323i	$-0.0136381\pi$
$223$	0.680991	+	3.86209i	0.0456025	+	0.258625i	−0.953480	+	0.301457i	$0.902527\pi$
$224$	16.3502	+	10.3081i	1.09244	+	0.688738i
$225$		0			0
$226$	12.7019	+	11.6171i	0.844920	+	0.772761i
$227$	−4.04735	+	11.1200i	−0.268632	+	0.738061i	0.729882	+	0.683573i	$0.239575\pi$
$227$	−4.04735	+	11.1200i	−0.268632	+	0.738061i	−0.998514	+	0.0544879i	$0.982647\pi$
$228$		0			0
$229$	6.81207	−	8.11831i	0.450154	−	0.536473i	−0.492470	−	0.870330i	$-0.663906\pi$
$229$	6.81207	−	8.11831i	0.450154	−	0.536473i	0.942624	+	0.333857i	$0.108350\pi$
$230$	19.2966	+	25.0988i	1.27238	+	1.65496i
$231$		0			0
$232$	5.33474	+	8.32179i	0.350243	+	0.546352i
$233$	0.565006	−	0.978619i	0.0370148	−	0.0641115i	−0.846925	−	0.531713i	$-0.821548\pi$
$233$	0.565006	−	0.978619i	0.0370148	−	0.0641115i	0.883939	+	0.467602i	$0.154882\pi$
$234$		0			0
$235$	9.20711	−	5.31572i	0.600605	−	0.346760i
$236$	16.9707	+	4.51296i	1.10470	+	0.293769i
$237$		0			0
$238$	−1.47239	−	11.1029i	−0.0954406	−	0.719695i
$239$	−1.00787	+	5.71591i	−0.0651936	+	0.369731i	0.934704	+	0.355427i	$0.115665\pi$
$239$	−1.00787	+	5.71591i	−0.0651936	+	0.369731i	−0.999898	+	0.0143045i	$0.995447\pi$
$240$		0			0
$241$	22.5974	−	18.9615i	1.45563	−	1.22142i	0.527286	−	0.849688i	$-0.323210\pi$
$241$	22.5974	−	18.9615i	1.45563	−	1.22142i	0.928342	−	0.371728i	$-0.121235\pi$
$242$	−3.25151	+	14.7324i	−0.209015	+	0.947034i
$243$		0			0
$244$	−3.99585	+	8.61151i	−0.255808	+	0.551295i
$245$	10.1406	+	12.0851i	0.647857	+	0.772086i
$246$		0			0
$247$	−0.474102	+	2.68876i	−0.0301664	+	0.171082i
$248$	1.85881	−	5.95410i	0.118034	−	0.378086i
$249$		0			0
$250$	−0.283080	+	6.62709i	−0.0179036	+	0.419134i
$251$	−5.20730	+	3.00644i	−0.328682	+	0.189765i	−0.655256	−	0.755407i	$-0.727439\pi$
$251$	−5.20730	+	3.00644i	−0.328682	+	0.189765i	0.326574	+	0.945172i	$0.394106\pi$
$252$		0			0
$253$	−3.30962	−	1.91081i	−0.208074	−	0.120132i
$254$	7.27381	−	11.4414i	0.456400	−	0.717898i
$255$		0			0
$256$	−12.1787	+	10.3768i	−0.761171	+	0.648552i
$257$	−19.8936	−	16.6927i	−1.24093	−	1.04126i	−0.997451	−	0.0713589i	$-0.977266\pi$
$257$	−19.8936	−	16.6927i	−1.24093	−	1.04126i	−0.243480	−	0.969906i	$-0.578289\pi$
$258$		0			0
$259$	−1.42023	+	3.90205i	−0.0882489	+	0.242462i
$260$	−36.9555	+	25.9806i	−2.29188	+	1.61125i
$261$		0			0
$262$	0.176052	+	0.556535i	0.0108766	+	0.0343829i
$263$	2.41565	+	13.6998i	0.148956	+	0.844769i	0.964106	+	0.265519i	$0.0855433\pi$
$263$	2.41565	+	13.6998i	0.148956	+	0.844769i	−0.815150	+	0.579250i	$0.803346\pi$
$264$		0			0
$265$	29.6667	−	10.7978i	1.82241	−	0.663303i
$266$	−0.752633	+	1.82188i	−0.0461469	+	0.111706i
$267$		0			0
$268$	7.84260	+	29.0496i	0.479063	+	1.77449i
$269$			3.89404i			0.237424i	0.992929	+	0.118712i	$0.0378765\pi$
$269$			3.89404i			0.237424i	−0.992929	+	0.118712i	$0.962123\pi$
$270$		0			0
$271$	27.1005			1.64624			0.823119	−	0.567869i	$-0.192232\pi$
$271$	27.1005			1.64624			0.823119	+	0.567869i	$0.192232\pi$
$272$	9.13662	+	1.57550i	0.553989	+	0.0955287i
$273$		0			0
$274$	−20.5992	−	8.50969i	−1.24444	−	0.514089i
$275$	−1.25909	−	3.45933i	−0.0759261	−	0.208605i
$276$		0			0
$277$	7.05421	−	1.24385i	0.423847	−	0.0747356i	0.0423435	−	0.999103i	$-0.486518\pi$
$277$	7.05421	−	1.24385i	0.423847	−	0.0747356i	0.381503	+	0.924368i	$0.375407\pi$
$278$	−0.941775	−	2.97713i	−0.0564839	−	0.178556i
$279$		0			0
$280$	−30.0972	+	12.5666i	−1.79865	+	0.750998i
$281$	0.728892	+	0.265295i	0.0434820	+	0.0158262i	0.363670	−	0.931528i	$-0.381524\pi$
$281$	0.728892	+	0.265295i	0.0434820	+	0.0158262i	−0.320188	+	0.947354i	$0.603746\pi$
$282$		0			0
$283$	−0.982704	+	1.17114i	−0.0584157	+	0.0696171i	−0.794461	−	0.607315i	$-0.792247\pi$
$283$	−0.982704	+	1.17114i	−0.0584157	+	0.0696171i	0.736045	+	0.676932i	$0.236691\pi$
$284$	6.65895	+	14.2101i	0.395136	+	0.843213i
$285$		0			0
$286$	2.92556	−	4.60179i	0.172992	−	0.272109i
$287$	11.3528	−	19.6636i	0.670134	−	1.16071i
$288$		0			0
$289$	5.81375	+	10.0697i	0.341985	+	0.592336i
$290$	−16.6650	−	0.711855i	−0.978601	−	0.0418016i
$291$		0			0
$292$	−2.55788	−	0.218923i	−0.149689	−	0.0128115i
$293$	−15.6621	−	2.76164i	−0.914987	−	0.161337i	−0.303720	−	0.952761i	$-0.598229\pi$
$293$	−15.6621	−	2.76164i	−0.914987	−	0.161337i	−0.611267	+	0.791424i	$0.709340\pi$
$294$		0			0
$295$	−22.6996	+	19.0472i	−1.32162	+	1.10897i
$296$	−2.73300	−	2.08484i	−0.158853	−	0.121179i
$297$		0			0
$298$	−9.45399	−	2.08654i	−0.547655	−	0.120870i
$299$	−28.5363	−	34.0082i	−1.65029	−	1.96674i
$300$		0			0
$301$	−4.34995	−	0.767013i	−0.250727	−	0.0442099i
$302$	2.19344	+	16.5402i	0.126218	+	0.951783i
$303$		0			0
$304$	−1.25396	−	1.04416i	−0.0719195	−	0.0598865i
$305$	−8.00977	−	13.8733i	−0.458638	−	0.794385i
$306$		0			0
$307$	−0.370582	−	0.213955i	−0.0211502	−	0.0122111i	0.489388	−	0.872066i	$-0.337220\pi$
$307$	−0.370582	−	0.213955i	−0.0211502	−	0.0122111i	−0.510538	+	0.859855i	$0.670554\pi$
$308$	2.77865	−	2.78915i	0.158328	−	0.158927i
$309$		0			0
$310$	6.41534	+	8.34432i	0.364367	+	0.473925i
$311$	−8.46179	−	7.10028i	−0.479824	−	0.402620i	0.370539	−	0.928817i	$-0.379173\pi$
$311$	−8.46179	−	7.10028i	−0.479824	−	0.402620i	−0.850363	+	0.526197i	$0.823617\pi$
$312$		0			0
$313$	−26.1193	−	9.50664i	−1.47635	−	0.537347i	−0.526533	−	0.850155i	$-0.676508\pi$
$313$	−26.1193	−	9.50664i	−1.47635	−	0.537347i	−0.949817	+	0.312807i	$0.898731\pi$
$314$	11.5025	−	12.5765i	0.649121	−	0.709735i
$315$		0			0
$316$	0.892817	+	9.98782i	0.0502249	+	0.561859i
$317$	−3.46040	+	0.610163i	−0.194356	+	0.0342701i	−0.269979	−	0.962866i	$-0.587017\pi$
$317$	−3.46040	+	0.610163i	−0.194356	+	0.0342701i	0.0756229	+	0.997136i	$0.475905\pi$
$318$		0			0
$319$	1.89205	−	0.688651i	0.105935	−	0.0385571i
$320$	−2.50535	−	26.8825i	−0.140053	−	1.50278i
$321$		0			0
$322$	−14.8270	−	28.4170i	−0.826278	−	1.58362i
$323$			0.945557i			0.0526122i
$324$		0			0
$325$		−	42.7649i		−	2.37217i
$326$	−16.7975	+	8.76438i	−0.930327	+	0.485414i
$327$		0			0
$328$	12.7373	+	13.8216i	0.703302	+	0.763171i
$329$	−10.1144	+	3.68134i	−0.557625	+	0.202959i
$330$		0			0
$331$	−17.1533	+	3.02459i	−0.942832	+	0.166247i	−0.623876	−	0.781523i	$-0.714443\pi$
$331$	−17.1533	+	3.02459i	−0.942832	+	0.166247i	−0.318956	+	0.947770i	$0.603332\pi$
$332$	−20.6757	+	1.84821i	−1.13472	+	0.101434i
$333$		0			0
$334$	7.06830	+	6.46465i	0.386760	+	0.353730i
$335$	−47.7123	−	17.3659i	−2.60680	−	0.948798i
$336$		0			0
$337$	−2.18023	−	1.82943i	−0.118765	−	0.0996554i	0.581471	−	0.813567i	$-0.302477\pi$
$337$	−2.18023	−	1.82943i	−0.118765	−	0.0996554i	−0.700236	+	0.713912i	$0.746922\pi$
$338$	35.6442	−	27.4043i	1.93879	−	1.49060i
$339$		0			0
$340$	−11.0418	+	11.0835i	−0.598825	+	0.601090i
$341$	−1.10031	−	0.635266i	−0.0595853	−	0.0344016i
$342$		0			0
$343$	3.97285	+	6.88117i	0.214514	+	0.371548i
$344$	1.67917	−	3.24806i	0.0905346	−	0.175124i
$345$		0			0
$346$	2.36289	−	0.313348i	0.127029	−	0.0168457i
$347$	25.7859	+	4.54675i	1.38426	+	0.244082i	0.815659	−	0.578533i	$-0.196374\pi$
$347$	25.7859	+	4.54675i	1.38426	+	0.244082i	0.568599	+	0.822615i	$0.307486\pi$
$348$		0			0
$349$	3.27963	+	3.90851i	0.175555	+	0.209218i	0.846646	−	0.532157i	$-0.178618\pi$
$349$	3.27963	+	3.90851i	0.175555	+	0.209218i	−0.671091	+	0.741375i	$0.734174\pi$
$350$	6.65433	−	30.1504i	0.355689	−	1.61160i
$351$		0			0
$352$	1.51850	+	2.88371i	0.0809361	+	0.153702i
$353$	11.4022	−	9.56754i	0.606875	−	0.509229i	−0.286772	−	0.957999i	$-0.592582\pi$
$353$	11.4022	−	9.56754i	0.606875	−	0.509229i	0.893647	+	0.448770i	$0.148138\pi$
$354$		0			0
$355$	−26.0785	−	4.59835i	−1.38410	−	0.244055i
$356$	−11.4183	−	0.977262i	−0.605168	−	0.0517948i
$357$		0			0
$358$	−0.719139	+	16.8355i	−0.0380077	+	0.889785i
$359$	7.74329	+	13.4118i	0.408675	+	0.707846i	0.994742	−	0.102417i	$-0.0326575\pi$
$359$	7.74329	+	13.4118i	0.408675	+	0.707846i	−0.586066	+	0.810263i	$0.699324\pi$
$360$		0			0
$361$	−9.41679	+	16.3104i	−0.495621	+	0.858440i
$362$	−19.7103	−	12.5307i	−1.03595	−	0.658600i
$363$		0			0
$364$	41.4137	−	19.4068i	2.17067	−	1.01719i
$365$	2.78459	−	3.31854i	0.145752	−	0.173700i
$366$		0			0
$367$	24.0744	+	8.76237i	1.25667	+	0.457392i	0.882652	−	0.470027i	$-0.155756\pi$
$367$	24.0744	+	8.76237i	1.25667	+	0.457392i	0.374023	+	0.927419i	$0.377978\pi$
$368$	26.1124	−	4.70601i	1.36120	−	0.245318i
$369$		0			0
$370$	5.53032	−	1.74944i	0.287508	−	0.0909492i
$371$	−31.4772	+	5.55028i	−1.63422	+	0.288156i
$372$		0			0
$373$	−4.86012	−	13.3531i	−0.251648	−	0.691396i	−0.999617	−	0.0276634i	$-0.991193\pi$
$373$	−4.86012	−	13.3531i	−0.251648	−	0.691396i	0.747970	−	0.663733i	$-0.231029\pi$
$374$	0.721061	−	1.74545i	0.0372852	−	0.0902551i
$375$		0			0
$376$	−0.413847	−	8.90043i	−0.0213425	−	0.459004i
$377$	23.3900			1.20465
$378$		0			0
$379$			1.93137i			0.0992080i	0.998769	+	0.0496040i	$0.0157959\pi$
$379$			1.93137i			0.0992080i	−0.998769	+	0.0496040i	$0.984204\pi$
$380$	2.65834	−	0.717680i	0.136370	−	0.0368162i
$381$		0			0
$382$	17.2789	+	7.13805i	0.884064	+	0.365214i
$383$	−12.4377	+	4.52695i	−0.635537	+	0.231317i	−0.639639	−	0.768675i	$-0.720916\pi$
$383$	−12.4377	+	4.52695i	−0.635537	+	0.231317i	0.00410258	+	0.999992i	$0.498694\pi$
$384$		0			0
$385$	1.15363	+	6.54257i	0.0587945	+	0.333440i
$386$	−0.238634	+	0.0754888i	−0.0121462	+	0.00384228i
$387$		0			0
$388$	−18.3775	+	12.9198i	−0.932975	+	0.655903i
$389$	−8.22522	+	22.5986i	−0.417035	+	1.14579i	0.536339	+	0.844003i	$0.319807\pi$
$389$	−8.22522	+	22.5986i	−0.417035	+	1.14579i	−0.953374	+	0.301792i	$0.902415\pi$
$390$		0			0
$391$	−11.7780	−	9.88288i	−0.595637	−	0.499799i
$392$	12.9000	−	2.89819i	0.651548	−	0.146381i
$393$		0			0
$394$	−1.15927	−	0.736999i	−0.0584032	−	0.0371295i
$395$	−14.6540	−	8.46051i	−0.737325	−	0.425695i
$396$		0			0
$397$	−28.6833	+	16.5603i	−1.43957	+	0.831137i	−0.997820	−	0.0659997i	$-0.978976\pi$
$397$	−28.6833	+	16.5603i	−1.43957	+	0.831137i	−0.441752	+	0.897137i	$0.645643\pi$
$398$	5.79090	+	0.247362i	0.290272	+	0.0123991i
$399$		0			0
$400$	22.1829	+	12.6959i	1.10915	+	0.634796i
$401$	−1.94567	+	11.0344i	−0.0971620	+	0.551033i	0.896901	+	0.442231i	$0.145813\pi$
$401$	−1.94567	+	11.0344i	−0.0971620	+	0.551033i	−0.994063	+	0.108802i	$0.965298\pi$
$402$		0			0
$403$	−9.48715	−	11.3063i	−0.472588	−	0.563209i
$404$	10.4637	−	22.5505i	0.520590	−	1.12193i
$405$		0			0
$406$	16.4905	+	3.63954i	0.818412	+	0.180627i
$407$	−0.536366	+	0.450065i	−0.0265867	+	0.0223089i
$408$		0			0
$409$	1.95004	−	11.0592i	0.0964233	−	0.546844i	−0.897879	−	0.440243i	$-0.854892\pi$
$409$	1.95004	−	11.0592i	0.0964233	−	0.546844i	0.994302	−	0.106601i	$-0.0339966\pi$
$410$	−31.4413	+	4.16950i	−1.55277	+	0.205917i
$411$		0			0
$412$	8.12468	−	30.5522i	0.400274	−	1.50520i
$413$	25.9810	−	15.0001i	1.27844	−	0.738109i
$414$		0			0
$415$	17.5140	−	30.3351i	0.859728	−	1.48909i
$416$	5.11871	+	37.5120i	0.250966	+	1.83918i
$417$		0			0
$418$	−0.263503	+	0.202589i	−0.0128884	+	0.00990893i
$419$	−8.95678	+	10.6743i	−0.437567	+	0.521472i	−0.939090	−	0.343672i	$-0.888329\pi$
$419$	−8.95678	+	10.6743i	−0.437567	+	0.521472i	0.501522	+	0.865145i	$0.332774\pi$
$420$		0			0
$421$	−4.06687	+	11.1736i	−0.198207	+	0.544570i	−0.998483	−	0.0550623i	$-0.982464\pi$
$421$	−4.06687	+	11.1736i	−0.198207	+	0.544570i	0.800276	+	0.599632i	$0.204686\pi$
$422$	3.58149	−	3.91592i	0.174344	−	0.190624i
$423$		0			0
$424$	3.37930	−	26.2421i	0.164113	−	1.27443i
$425$	−2.57184	−	14.5856i	−0.124753	−	0.707507i
$426$		0			0
$427$	5.54707	+	15.2404i	0.268442	+	0.737537i
$428$	−4.01080	−	2.79713i	−0.193869	−	0.135204i
$429$		0			0
$430$	2.85415	+	5.47017i	0.137640	+	0.263795i
$431$	28.2506			1.36079			0.680393	−	0.732848i	$-0.261809\pi$
$431$	28.2506			1.36079			0.680393	+	0.732848i	$0.261809\pi$
$432$		0			0
$433$	−27.8524			−1.33850			−0.669251	−	0.743036i	$-0.733385\pi$
$433$	−27.8524			−1.33850			−0.669251	+	0.743036i	$0.733385\pi$
$434$	−4.92938	−	9.44748i	−0.236618	−	0.453494i
$435$		0			0
$436$	−26.6612	−	18.5935i	−1.27684	−	0.890467i
$437$	0.925505	+	2.54280i	0.0442729	+	0.121639i
$438$		0			0
$439$	−2.13242	−	12.0935i	−0.101775	−	0.577193i	−0.992460	−	0.122572i	$-0.960886\pi$
$439$	−2.13242	−	12.0935i	−0.101775	−	0.577193i	0.890685	−	0.454621i	$-0.150225\pi$
$440$	−5.45445	−	0.702390i	−0.260031	−	0.0334851i
$441$		0			0
$442$	14.8061	−	16.1887i	0.704254	−	0.770016i
$443$	−7.22670	+	19.8552i	−0.343351	+	0.943348i	0.641064	+	0.767487i	$0.278493\pi$
$443$	−7.22670	+	19.8552i	−0.343351	+	0.943348i	−0.984415	+	0.175861i	$0.943729\pi$
$444$		0			0
$445$	12.4303	−	14.8138i	0.589252	−	0.702243i
$446$	−4.39681	+	3.38039i	−0.208195	+	0.160066i
$447$		0			0
$448$	−2.22815	+	27.2434i	−0.105270	+	1.28713i
$449$	−13.8708	+	24.0249i	−0.654604	+	1.13381i	0.327389	+	0.944890i	$0.393831\pi$
$449$	−13.8708	+	24.0249i	−0.654604	+	1.13381i	−0.981993	+	0.188917i	$0.939502\pi$
$450$		0			0
$451$	3.31561	−	1.91427i	0.156126	−	0.0901393i
$452$	−6.25612	+	23.5256i	−0.294263	+	1.10655i
$453$		0			0
$454$	−16.5901	+	2.20005i	−0.778611	+	0.103254i
$455$	−13.4014	+	76.0030i	−0.628266	+	3.56307i
$456$		0			0
$457$	−26.0906	+	21.8926i	−1.22047	+	1.02409i	−0.221668	+	0.975122i	$0.571150\pi$
$457$	−26.0906	+	21.8926i	−1.22047	+	1.02409i	−0.998800	+	0.0489720i	$0.984405\pi$
$458$	14.6352	+	3.23006i	0.683858	+	0.150931i
$459$		0			0
$460$	−18.8452	+	40.6137i	−0.878664	+	1.89362i
$461$	−8.93591	−	10.6494i	−0.416187	−	0.495992i	0.516698	−	0.856168i	$-0.327161\pi$
$461$	−8.93591	−	10.6494i	−0.416187	−	0.495992i	−0.932884	+	0.360176i	$0.882717\pi$
$462$		0			0
$463$	3.22751	−	18.3041i	0.149995	−	0.850665i	−0.813224	−	0.581950i	$-0.802290\pi$
$463$	3.22751	−	18.3041i	0.149995	−	0.850665i	0.963220	−	0.268715i	$-0.0865991\pi$
$464$	−6.94395	+	12.1328i	−0.322365	+	0.563251i
$465$		0			0
$466$	1.59662	+	0.0682007i	0.0739621	+	0.00315934i
$467$	−8.34116	+	4.81577i	−0.385983	+	0.222847i	−0.680418	−	0.732824i	$-0.738202\pi$
$467$	−8.34116	+	4.81577i	−0.385983	+	0.222847i	0.294435	+	0.955671i	$0.404868\pi$
$468$		0			0
$469$	44.5181	+	25.7026i	2.05566	+	1.18683i
$470$	12.6881	+	8.06641i	0.585260	+	0.372076i
$471$		0			0
$472$	5.44373	+	24.2303i	0.250568	+	1.11529i
$473$	−0.570541	−	0.478741i	−0.0262335	−	0.0220125i
$474$		0			0
$475$	−0.891532	+	2.44946i	−0.0409063	+	0.112389i
$476$	12.9577	−	9.10955i	0.593914	−	0.417536i
$477$		0			0
$478$	−7.82598	+	2.47564i	−0.357952	+	0.113233i
$479$	−5.05443	−	28.6651i	−0.230943	−	1.30974i	−0.850992	−	0.525179i	$-0.823998\pi$
$479$	−5.05443	−	28.6651i	−0.230943	−	1.30974i	0.620049	−	0.784563i	$-0.287113\pi$
$480$		0			0
$481$	−7.64321	+	2.78190i	−0.348500	+	0.126844i
$482$	38.5571	+	15.9283i	1.75623	+	0.725513i
$483$		0			0
$484$	−20.5987	+	5.56108i	−0.936304	+	0.252777i
$485$		−	37.9074i		−	1.72129i
$486$		0			0
$487$	−13.1429			−0.595563			−0.297782	−	0.954634i	$-0.596247\pi$
$487$	−13.1429			−0.595563			−0.297782	+	0.954634i	$0.596247\pi$
$488$	−13.4112	+	0.623587i	−0.607098	+	0.0282285i
$489$		0			0
$490$	−8.51842	+	20.6203i	−0.384823	+	0.931530i
$491$	4.01945	+	11.0433i	0.181395	+	0.498379i	0.996748	−	0.0805856i	$-0.0256791\pi$
$491$	4.01945	+	11.0433i	0.181395	+	0.498379i	−0.815352	+	0.578965i	$0.803457\pi$
$492$		0			0
$493$	7.97752	−	1.40665i	0.359289	−	0.0633524i
$494$	−3.68134	+	1.16454i	−0.165631	+	0.0523953i
$495$		0			0
$496$	8.68131	−	1.56456i	0.389802	−	0.0702507i
$497$	25.1930	+	9.16949i	1.13006	+	0.411308i
$498$		0			0
$499$	−23.2598	+	27.7199i	−1.04125	+	1.24091i	−0.0713387	+	0.997452i	$0.522727\pi$
$499$	−23.2598	+	27.7199i	−1.04125	+	1.24091i	−0.969911	+	0.243461i	$0.921717\pi$
$500$	−8.49427	+	3.98048i	−0.379875	+	0.178012i
$501$		0			0
$502$	−7.17608	−	4.56215i	−0.320284	−	0.203619i
$503$	−1.18773	+	2.05720i	−0.0529581	+	0.0917261i	−0.891289	−	0.453435i	$-0.850198\pi$
$503$	−1.18773	+	2.05720i	−0.0529581	+	0.0917261i	0.838331	+	0.545161i	$0.183532\pi$
$504$		0			0
$505$	20.9748	+	36.3294i	0.933366	+	1.61664i
$506$	0.230650	−	5.39966i	0.0102536	−	0.240044i
$507$		0			0
$508$	19.1038	+	1.63504i	0.847594	+	0.0725434i
$509$	40.5051	+	7.14215i	1.79536	+	0.316570i	0.969090	−	0.246706i	$-0.0793482\pi$
$509$	40.5051	+	7.14215i	1.79536	+	0.316570i	0.826269	+	0.563276i	$0.190459\pi$
$510$		0			0
$511$	−3.35977	+	2.81918i	−0.148627	+	0.124713i
$512$	−20.9778	−	8.48130i	−0.927096	−	0.374824i
$513$		0			0
$514$	7.91515	−	35.8631i	0.349123	−	1.58185i
$515$	34.2906	+	40.8660i	1.51103	+	1.80077i
$516$		0			0
$517$	−1.78734	−	0.315155i	−0.0786069	−	0.0138605i
$518$	−5.82153	+	0.772007i	−0.255783	+	0.0339201i
$519$		0			0
$520$	−56.7507	−	29.3387i	−2.48868	−	1.28659i
$521$	5.21530	+	9.03316i	0.228486	+	0.395750i	0.957360	−	0.288899i	$-0.0932890\pi$
$521$	5.21530	+	9.03316i	0.228486	+	0.395750i	−0.728873	+	0.684649i	$0.759956\pi$
$522$		0			0
$523$	14.6626	+	8.46543i	0.641149	+	0.370167i	0.785057	−	0.619424i	$-0.212634\pi$
$523$	14.6626	+	8.46543i	0.641149	+	0.370167i	−0.143908	+	0.989591i	$0.545967\pi$
$524$	−0.582615	+	0.584818i	−0.0254516	+	0.0255479i
$525$		0			0
$526$	−15.5966	+	11.9911i	−0.680046	+	0.522838i
$527$	−3.91569	−	3.28565i	−0.170570	−	0.143125i
$528$		0			0
$529$	−19.7338	−	7.18252i	−0.857992	−	0.312283i
$530$	32.9461	+	30.1324i	1.43109	+	1.30887i
$531$		0			0
$532$	−2.77665	+	0.248206i	−0.120383	+	0.0107611i
$533$	43.7992	−	7.72298i	1.89715	−	0.334519i
$534$		0			0
$535$	7.75366	−	2.82210i	0.335220	−	0.122010i
$536$	−31.2920	+	28.8372i	−1.35161	+	1.24558i
$537$		0			0
$538$	−4.88238	+	2.54746i	−0.210494	+	0.109829i
$539$		−	2.69313i		−	0.116001i
$540$		0			0
$541$		−	29.4745i		−	1.26721i	−0.773658	−	0.633603i	$-0.781575\pi$
$541$		−	29.4745i		−	1.26721i	0.773658	−	0.633603i	$-0.218425\pi$
$542$	17.7290	+	33.9788i	0.761526	+	1.45951i
$543$		0			0
$544$	4.00175	+	12.4862i	0.171574	+	0.535343i
$545$	51.5414	−	18.7595i	2.20779	−	0.803570i
$546$		0			0
$547$	31.4846	−	5.55158i	1.34618	−	0.237369i	0.546333	−	0.837568i	$-0.316023\pi$
$547$	31.4846	−	5.55158i	1.34618	−	0.237369i	0.799850	+	0.600199i	$0.204912\pi$
$548$	−2.80636	−	31.3944i	−0.119882	−	1.34110i
$549$		0			0
$550$	3.51363	−	3.84173i	0.149822	−	0.163812i
$551$	−1.33972	−	0.487617i	−0.0570739	−	0.0207732i
$552$		0			0
$553$	13.1233	+	11.0117i	0.558059	+	0.468267i
$554$	6.17437	+	8.03090i	0.262324	+	0.341200i
$555$		0			0
$556$	3.11664	−	3.12842i	0.132175	−	0.132675i
$557$	7.19468	+	4.15385i	0.304849	+	0.176004i	0.644619	−	0.764504i	$-0.277016\pi$
$557$	7.19468	+	4.15385i	0.304849	+	0.176004i	−0.339770	+	0.940508i	$0.610349\pi$
$558$		0			0
$559$	−4.32598	−	7.49282i	−0.182970	−	0.316913i
$560$	−35.4455	−	29.5151i	−1.49785	−	1.24724i
$561$		0			0
$562$	0.144209	+	1.08744i	0.00608307	+	0.0458710i
$563$	−6.57453	−	1.15927i	−0.277083	−	0.0488573i	0.0333796	−	0.999443i	$-0.489373\pi$
$563$	−6.57453	−	1.15927i	−0.277083	−	0.0488573i	−0.310463	+	0.950585i	$0.600484\pi$
$564$		0			0
$565$	−26.4043	−	31.4674i	−1.11084	−	1.32384i
$566$	−2.11126	−	0.465966i	−0.0887430	−	0.0195860i
$567$		0			0
$568$	−13.4604	+	17.6452i	−0.564787	+	0.740375i
$569$	24.2709	−	20.3657i	1.01749	−	0.853775i	0.0281798	−	0.999603i	$-0.491029\pi$
$569$	24.2709	−	20.3657i	1.01749	−	0.853775i	0.989310	+	0.145827i	$0.0465844\pi$
$570$		0			0
$571$	32.6020	+	5.74861i	1.36435	+	0.240572i	0.807416	−	0.589983i	$-0.200866\pi$
$571$	32.6020	+	5.74861i	1.36435	+	0.240572i	0.556936	+	0.830555i	$0.311977\pi$
$572$	7.68363	+	0.657622i	0.321269	+	0.0274966i
$573$		0			0
$574$	32.0813	+	1.37037i	1.33905	+	0.0571982i
$575$	−21.1926	−	36.7066i	−0.883791	−	1.53077i
$576$		0			0
$577$	15.0611	−	26.0866i	0.627001	−	1.08600i	−0.361149	−	0.932508i	$-0.617615\pi$
$577$	15.0611	−	26.0866i	0.627001	−	1.08600i	0.988150	−	0.153490i	$-0.0490512\pi$
$578$	−8.82214	+	13.8769i	−0.366953	+	0.577202i
$579$		0			0
$580$	−10.0096	−	21.3603i	−0.415627	−	0.886940i
$581$	−22.7953	+	27.1663i	−0.945707	+	1.12705i
$582$		0			0
$583$	−5.06443	−	1.84330i	−0.209747	−	0.0763418i
$584$	−1.39887	−	3.35031i	−0.0578855	−	0.138637i
$585$		0			0
$586$	−6.78347	−	21.4438i	−0.280222	−	0.885837i
$587$	15.0318	−	2.65051i	0.620427	−	0.109398i	0.145406	−	0.989372i	$-0.453551\pi$
$587$	15.0318	−	2.65051i	0.620427	−	0.109398i	0.475022	+	0.879974i	$0.342440\pi$
$588$		0			0
$589$	0.307693	+	0.845379i	0.0126783	+	0.0348332i
$590$	−38.7314	−	16.0003i	−1.59455	−	0.658721i
$591$		0			0
$592$	0.826072	−	4.79055i	0.0339513	−	0.196890i
$593$	−27.1813			−1.11620			−0.558101	−	0.829773i	$-0.688470\pi$
$593$	−27.1813			−1.11620			−0.558101	+	0.829773i	$0.688470\pi$
$594$		0			0
$595$			26.7279i			1.09574i
$596$	−3.56863	−	13.2185i	−0.146177	−	0.541450i
$597$		0			0
$598$	23.9714	−	58.0269i	0.980264	−	2.37290i
$599$	39.7660	−	14.4737i	1.62480	−	0.591378i	0.640509	−	0.767951i	$-0.278723\pi$
$599$	39.7660	−	14.4737i	1.62480	−	0.591378i	0.984288	+	0.176573i	$0.0565012\pi$
$600$		0			0
$601$	−0.648834	−	3.67972i	−0.0264665	−	0.150099i	0.968711	−	0.248193i	$-0.0798366\pi$
$601$	−0.648834	−	3.67972i	−0.0264665	−	0.150099i	−0.995177	+	0.0980937i	$0.968726\pi$
$602$	−1.88403	−	5.95577i	−0.0767872	−	0.242739i
$603$		0			0
$604$	−19.3033	+	13.5707i	−0.785440	+	0.552183i
$605$	12.3139	−	33.8321i	0.500631	−	1.37547i
$606$		0			0
$607$	35.5497	+	29.8298i	1.44292	+	1.21075i	0.937550	+	0.347850i	$0.113088\pi$
$607$	35.5497	+	29.8298i	1.44292	+	1.21075i	0.505370	+	0.862903i	$0.331356\pi$
$608$	0.488837	−	2.25530i	0.0198250	−	0.0914647i
$609$		0			0
$610$	12.1545	−	19.1186i	0.492122	−	0.774088i
$611$	−18.2586	−	10.5416i	−0.738664	−	0.426468i
$612$		0			0
$613$	21.9670	−	12.6827i	0.887239	−	0.512248i	0.0142005	−	0.999899i	$-0.495480\pi$
$613$	21.9670	−	12.6827i	0.887239	−	0.512248i	0.873038	+	0.487652i	$0.162146\pi$
$614$	0.0258261	−	0.604606i	0.00104226	−	0.0243999i
$615$		0			0
$616$	5.31483	+	1.65923i	0.214141	+	0.0668524i
$617$	−1.23909	+	7.02722i	−0.0498838	+	0.282905i	−0.999538	−	0.0303950i	$-0.990323\pi$
$617$	−1.23909	+	7.02722i	−0.0498838	+	0.282905i	0.949654	+	0.313300i	$0.101435\pi$
$618$		0			0
$619$	17.2889	+	20.6041i	0.694900	+	0.828149i	0.991939	−	0.126716i	$-0.0404437\pi$
$619$	17.2889	+	20.6041i	0.694900	+	0.828149i	−0.297039	+	0.954865i	$0.595999\pi$
$620$	−6.26528	+	13.5024i	−0.251620	+	0.542269i
$621$		0			0
$622$	3.36672	−	15.2544i	0.134993	−	0.611646i
$623$	−14.9979	+	12.5847i	−0.600877	+	0.504196i
$624$		0			0
$625$	−2.79914	+	15.8747i	−0.111966	+	0.634989i
$626$	−5.16761	−	38.9677i	−0.206539	−	1.55746i
$627$		0			0
$628$	23.2934	+	6.19435i	0.929507	+	0.247182i
$629$	−2.43953	+	1.40846i	−0.0972705	+	0.0561592i
$630$		0			0
$631$	−11.7466	+	20.3457i	−0.467624	+	0.809949i	−0.999316	−	0.0369893i	$-0.988223\pi$
$631$	−11.7466	+	20.3457i	−0.467624	+	0.809949i	0.531691	+	0.846938i	$0.321557\pi$
$632$	−11.9387	+	7.65340i	−0.474897	+	0.304436i
$633$		0			0
$634$	−3.02880	−	3.93951i	−0.120289	−	0.156458i
$635$	−20.7970	+	24.7848i	−0.825302	+	0.983557i
$636$		0			0
$637$	10.7002	−	29.3985i	0.423956	−	1.16481i
$638$	2.10121	+	1.92176i	0.0831876	+	0.0760831i
$639$		0			0
$640$	32.0665	−	20.7276i	1.26754	−	0.819331i
$641$	7.57282	+	42.9476i	0.299108	+	1.69633i	0.650019	+	0.759918i	$0.274761\pi$
$641$	7.57282	+	42.9476i	0.299108	+	1.69633i	−0.350911	+	0.936409i	$0.614128\pi$
$642$		0			0
$643$	0.120739	+	0.331727i	0.00476148	+	0.0130820i	0.942051	−	0.335471i	$-0.108895\pi$
$643$	0.120739	+	0.331727i	0.00476148	+	0.0130820i	−0.937289	+	0.348553i	$0.886673\pi$
$644$	25.9296	−	37.1804i	1.02177	−	1.46511i
$645$		0			0
$646$	−1.18554	+	0.618578i	−0.0466446	+	0.0243376i
$647$	26.0967			1.02597			0.512984	−	0.858398i	$-0.328540\pi$
$647$	26.0967			1.02597			0.512984	+	0.858398i	$0.328540\pi$
$648$		0			0
$649$	5.05855			0.198565
$650$	53.6189	−	27.9766i	2.10311	−	1.09733i
$651$		0			0
$652$	−21.9777	−	15.3272i	−0.860711	−	0.600259i
$653$	0.281991	+	0.774764i	0.0110352	+	0.0303189i	0.945088	−	0.326816i	$-0.105976\pi$
$653$	0.281991	+	0.774764i	0.0110352	+	0.0303189i	−0.934053	+	0.357135i	$0.883754\pi$
$654$		0			0
$655$	−0.241889	−	1.37182i	−0.00945137	−	0.0536014i
$656$	−8.99693	+	25.0122i	−0.351271	+	0.976562i
$657$		0			0
$658$	−11.2325	−	10.2732i	−0.437887	−	0.400490i
$659$	14.2971	−	39.2809i	0.556935	−	1.53017i	−0.267123	−	0.963662i	$-0.586073\pi$
$659$	14.2971	−	39.2809i	0.556935	−	1.53017i	0.824058	−	0.566505i	$-0.191705\pi$
$660$		0			0
$661$	−1.06741	+	1.27208i	−0.0415173	+	0.0494784i	−0.786404	−	0.617713i	$-0.788059\pi$
$661$	−1.06741	+	1.27208i	−0.0415173	+	0.0494784i	0.744886	+	0.667192i	$0.232504\pi$
$662$	−15.0139	−	19.5283i	−0.583530	−	0.758988i
$663$		0			0
$664$	−15.8432	−	24.7142i	−0.614835	−	0.959096i
$665$	2.35205	−	4.07387i	0.0912086	−	0.157978i
$666$		0			0
$667$	20.0764	−	11.5911i	0.777362	−	0.448810i
$668$	−3.48137	+	13.0914i	−0.134698	+	0.506522i
$669$		0			0
$670$	−9.43970	−	71.1826i	−0.364688	−	2.75002i
$671$	−0.474878	+	2.69317i	−0.0183325	+	0.103969i
$672$		0			0
$673$	−4.23311	+	3.55200i	−0.163175	+	0.136920i	−0.720719	−	0.693227i	$-0.756188\pi$
$673$	−4.23311	+	3.55200i	−0.163175	+	0.136920i	0.557544	+	0.830147i	$0.311744\pi$
$674$	0.867456	−	3.93039i	0.0334132	−	0.151393i
$675$		0			0
$676$	57.6779	+	26.7632i	2.21838	+	1.02936i
$677$	−2.08429	−	2.48396i	−0.0801056	−	0.0954662i	0.724503	−	0.689272i	$-0.242069\pi$
$677$	−2.08429	−	2.48396i	−0.0801056	−	0.0954662i	−0.804609	+	0.593805i	$0.797625\pi$
$678$		0			0
$679$	−6.66432	+	37.7952i	−0.255753	+	1.45045i
$680$	−21.1201	−	6.59347i	−0.809919	−	0.252848i
$681$		0			0
$682$	0.0766817	−	1.79517i	0.00293629	−	0.0687405i
$683$	−22.4547	+	12.9642i	−0.859206	+	0.496063i	−0.863746	−	0.503927i	$-0.831888\pi$
$683$	−22.4547	+	12.9642i	−0.859206	+	0.496063i	0.00454025	+	0.999990i	$0.498555\pi$
$684$		0			0
$685$	46.0615	+	26.5936i	1.75992	+	1.01609i
$686$	−6.02864	+	9.48281i	−0.230175	+	0.362055i
$687$		0			0
$688$	5.17094	−	0.0195167i	0.197140	−	0.000744069i
$689$	−47.9602	−	40.2434i	−1.82714	−	1.53315i
$690$		0			0
$691$	−10.2247	+	28.0920i	−0.388964	+	1.06867i	0.578504	+	0.815679i	$0.303637\pi$
$691$	−10.2247	+	28.0920i	−0.388964	+	1.06867i	−0.967469	+	0.252991i	$0.918586\pi$
$692$	1.93866	+	2.75761i	0.0736970	+	0.104829i
$693$		0			0
$694$	11.1682	+	35.3049i	0.423941	+	1.34016i
$695$	1.29396	+	7.33841i	0.0490827	+	0.278362i
$696$		0			0
$697$	14.4739	−	5.26808i	0.548240	−	0.199543i
$698$	−2.75500	+	6.66895i	−0.104278	+	0.252423i
$699$		0			0
$700$	42.1559	−	11.3810i	1.59334	−	0.430160i
$701$			24.6223i			0.929973i	0.885318	+	0.464987i	$0.153941\pi$
$701$			24.6223i			0.929973i	−0.885318	+	0.464987i	$0.846059\pi$
$702$		0			0
$703$	0.495778			0.0186986
$704$	−2.62221	+	3.79040i	−0.0988284	+	0.142856i
$705$		0			0
$706$	19.4551	+	8.03705i	0.732201	+	0.302479i
$707$	−14.5258	−	39.9094i	−0.546300	−	1.50095i
$708$		0			0
$709$	−26.4148	+	4.65765i	−0.992030	+	0.174922i	−0.646029	−	0.763313i	$-0.723572\pi$
$709$	−26.4148	+	4.65765i	−0.992030	+	0.174922i	−0.346001	+	0.938234i	$0.612460\pi$
$710$	−11.2950	−	35.7056i	−0.423894	−	1.34001i
$711$		0			0
$712$	−6.24449	−	14.9556i	−0.234022	−	0.560487i
$713$	−13.7461	−	5.00317i	−0.514796	−	0.187370i
$714$		0			0
$715$	−8.36463	+	9.96858i	−0.312819	+	0.372804i
$716$	−21.5789	+	10.1120i	−0.806443	+	0.377905i
$717$		0			0
$718$	−11.7501	+	18.4825i	−0.438512	+	0.689761i
$719$	−9.26666	+	16.0503i	−0.345588	+	0.598576i	−0.985460	−	0.169905i	$-0.945654\pi$
$719$	−9.26666	+	16.0503i	−0.345588	+	0.598576i	0.639872	+	0.768481i	$0.278987\pi$
$720$		0			0
$721$	−27.0047	−	46.7736i	−1.00571	−	1.74194i
$722$	−26.6104	−	1.13668i	−0.990338	−	0.0423029i
$723$		0			0
$724$	2.81672	−	32.9105i	0.104683	−	1.22311i
$725$	21.9920	+	3.87779i	0.816764	+	0.144017i
$726$		0			0
$727$	4.82234	−	4.04643i	0.178851	−	0.150074i	−0.548967	−	0.835844i	$-0.684979\pi$
$727$	4.82234	−	4.04643i	0.178851	−	0.150074i	0.727818	+	0.685770i	$0.240534\pi$
$728$	51.4249	+	39.2290i	1.90593	+	1.45392i
$729$		0			0
$730$	5.98247	+	1.32036i	0.221421	+	0.0488687i
$731$	−1.92605	−	2.29538i	−0.0712377	−	0.0848978i
$732$		0			0
$733$	−22.4113	−	3.95172i	−0.827781	−	0.145960i	−0.256323	−	0.966591i	$-0.582511\pi$
$733$	−22.4113	−	3.95172i	−0.827781	−	0.145960i	−0.571458	+	0.820631i	$0.693622\pi$
$734$	4.76304	+	35.9170i	0.175807	+	1.32572i
$735$		0			0
$736$	22.9830	+	29.6612i	0.847165	+	1.09333i
$737$	4.33388	+	7.50649i	0.159640	+	0.276505i
$738$		0			0
$739$	−37.2940	−	21.5317i	−1.37188	−	0.792056i	−0.380717	−	0.924692i	$-0.624323\pi$
$739$	−37.2940	−	21.5317i	−1.37188	−	0.792056i	−0.991165	+	0.132636i	$0.957656\pi$
$740$	5.81137	+	5.78948i	0.213630	+	0.212825i
$741$		0			0
$742$	−27.5512	−	35.8354i	−1.01144	−	1.31556i
$743$	27.0616	+	22.7074i	0.992794	+	0.833053i	0.985970	−	0.166924i	$-0.0533834\pi$
$743$	27.0616	+	22.7074i	0.992794	+	0.833053i	0.00682406	+	0.999977i	$0.497828\pi$
$744$		0			0
$745$	21.7106	+	7.90201i	0.795415	+	0.289507i
$746$	13.5627	−	14.8292i	0.496566	−	0.542934i
$747$		0			0
$748$	2.66017	−	0.237794i	0.0972655	−	0.00869462i
$749$	−8.22687	+	1.45062i	−0.300603	+	0.0530045i
$750$		0			0
$751$	−23.5008	+	8.55359i	−0.857557	+	0.312125i	−0.733117	−	0.680102i	$-0.761935\pi$
$751$	−23.5008	+	8.55359i	−0.857557	+	0.312125i	−0.124439	+	0.992227i	$0.539713\pi$
$752$	10.8887	−	6.34149i	0.397069	−	0.231250i
$753$		0			0
$754$	15.3016	+	29.3265i	0.557251	+	1.06801i
$755$		−	39.8171i		−	1.44909i
$756$		0			0
$757$		−	31.3025i		−	1.13771i	−0.822439	−	0.568853i	$-0.807387\pi$
$757$		−	31.3025i		−	1.13771i	0.822439	−	0.568853i	$-0.192613\pi$
$758$	−2.42157	+	1.26349i	−0.0879553	+	0.0458922i
$759$		0			0
$760$	2.63890	+	2.86354i	0.0957230	+	0.103872i
$761$	2.59308	−	0.943805i	0.0939992	−	0.0342129i	−0.294592	−	0.955623i	$-0.595184\pi$
$761$	2.59308	−	0.943805i	0.0939992	−	0.0342129i	0.388592	+	0.921410i	$0.372962\pi$
$762$		0			0
$763$	−54.6869	+	9.64278i	−1.97980	+	0.349092i
$764$	2.35401	+	26.3340i	0.0851652	+	0.952732i
$765$		0			0
$766$	−13.8126	−	12.6330i	−0.499069	−	0.456447i
$767$	55.2197	+	20.0983i	1.99387	+	0.725708i
$768$		0			0
$769$	3.61913	+	3.03681i	0.130509	+	0.109510i	0.705706	−	0.708505i	$-0.250630\pi$
$769$	3.61913	+	3.03681i	0.130509	+	0.109510i	−0.575197	+	0.818015i	$0.695074\pi$
$770$	−7.44841	+	5.72654i	−0.268422	+	0.206370i
$771$		0			0
$772$	−0.250762	−	0.249817i	−0.00902511	−	0.00899111i
$773$	17.3435	+	10.0133i	0.623803	+	0.360153i	0.778348	−	0.627833i	$-0.216058\pi$
$773$	17.3435	+	10.0133i	0.623803	+	0.360153i	−0.154545	+	0.987986i	$0.549391\pi$
$774$		0			0
$775$	−7.04567	−	12.2035i	−0.253088	−	0.438361i
$776$	−28.2214	−	14.5897i	−1.01309	−	0.523741i
$777$		0			0
$778$	−33.7152	+	4.47105i	−1.20875	+	0.160295i
$779$	−2.66971	−	0.470742i	−0.0956522	−	0.0168661i
$780$		0			0
$781$	2.90577	+	3.46296i	0.103977	+	0.123914i
$782$	4.68614	−	21.2326i	0.167576	−	0.759276i
$783$		0			0
$784$	12.0729	+	14.2781i	0.431174	+	0.509932i
$785$	−31.1567	+	26.1436i	−1.11203	+	0.933105i
$786$		0			0
$787$	41.5062	+	7.31867i	1.47954	+	0.260882i	0.854393	−	0.519627i	$-0.173929\pi$
$787$	41.5062	+	7.31867i	1.47954	+	0.260882i	0.625144	+	0.780510i	$0.285040\pi$
$788$	0.165666	−	1.93564i	0.00590162	−	0.0689543i
$789$		0			0
$790$	1.02125	−	23.9081i	0.0363345	−	0.850613i
$791$	20.7940	+	36.0163i	0.739350	+	1.28059i
$792$		0			0
$793$	−15.8842	+	27.5122i	−0.564063	+	0.976986i
$794$	−39.5278	−	25.1296i	−1.40279	−	0.891816i
$795$		0			0
$796$	3.47823	+	7.42249i	0.123283	+	0.263083i
$797$	32.1711	−	38.3400i	1.13956	−	1.35807i	0.215189	−	0.976572i	$-0.430963\pi$
$797$	32.1711	−	38.3400i	1.13956	−	1.35807i	0.924369	−	0.381500i	$-0.124592\pi$
$798$		0			0
$799$	−6.86134	−	2.49732i	−0.242737	−	0.0883489i
$800$	−1.40628	+	36.1187i	−0.0497196	+	1.27699i
$801$		0			0
$802$	−15.1079	+	4.77917i	−0.533478	+	0.168758i
$803$	−0.728294	+	0.128418i	−0.0257009	+	0.00453177i
$804$		0			0
$805$	26.1611	+	71.8771i	0.922059	+	2.53334i
$806$	7.96952	−	19.2916i	0.280714	−	0.679517i
$807$		0			0
$808$	35.1193	−	1.63296i	1.23549	−	0.0574472i
$809$	−7.89082			−0.277426			−0.138713	−	0.990333i	$-0.544297\pi$
$809$	−7.89082			−0.277426			−0.138713	+	0.990333i	$0.544297\pi$
$810$		0			0
$811$			16.9433i			0.594960i	0.954728	+	0.297480i	$0.0961461\pi$
$811$			16.9433i			0.594960i	−0.954728	+	0.297480i	$0.903854\pi$
$812$	6.22474	+	23.0569i	0.218445	+	0.809139i
$813$		0			0
$814$	−0.915182	−	0.378069i	−0.0320771	−	0.0132513i
$815$	42.4871	−	15.4641i	1.48826	−	0.541682i
$816$		0			0
$817$	0.0915762	+	0.519355i	0.00320385	+	0.0181699i
$818$	15.1418	−	4.78992i	0.529422	−	0.167475i
$819$		0			0
$820$	−25.7964	−	36.6936i	−0.900851	−	1.28140i
$821$	16.2209	−	44.5665i	0.566112	−	1.55538i	−0.244410	−	0.969672i	$-0.578594\pi$
$821$	16.2209	−	44.5665i	0.566112	−	1.55538i	0.810522	−	0.585708i	$-0.199184\pi$
$822$		0			0
$823$	−3.65996	−	3.07107i	−0.127578	−	0.107051i	0.576766	−	0.816909i	$-0.304314\pi$
$823$	−3.65996	−	3.07107i	−0.127578	−	0.107051i	−0.704344	+	0.709858i	$0.748759\pi$
$824$	43.6217	−	9.80032i	1.51963	−	0.341410i
$825$		0			0
$826$	35.8039	+	22.7621i	1.24578	+	0.791996i
$827$	25.0451	+	14.4598i	0.870903	+	0.502816i	0.867648	−	0.497179i	$-0.165631\pi$
$827$	25.0451	+	14.4598i	0.870903	+	0.502816i	0.00325451	+	0.999995i	$0.498964\pi$
$828$		0			0
$829$	−17.1833	+	9.92077i	−0.596800	+	0.344563i	−0.767782	−	0.640711i	$-0.778639\pi$
$829$	−17.1833	+	9.92077i	−0.596800	+	0.344563i	0.170982	+	0.985274i	$0.445306\pi$
$830$	49.4919	+	2.11408i	1.71789	+	0.0733807i
$831$		0			0
$832$	−43.6842	+	30.9580i	−1.51448	+	1.07328i
$833$	1.88146	−	10.6703i	0.0651888	−	0.369704i
$834$		0			0
$835$	−14.6933	−	17.5108i	−0.508482	−	0.605986i
$836$	−0.426389	−	0.197850i	−0.0147470	−	0.00684278i
$837$		0			0
$838$	−19.2429	−	4.24701i	−0.664737	−	0.146711i
$839$	−26.2638	+	22.0379i	−0.906725	+	0.760833i	−0.971493	−	0.237067i	$-0.923814\pi$
$839$	−26.2638	+	22.0379i	−0.906725	+	0.760833i	0.0647677	+	0.997900i	$0.479369\pi$
$840$		0			0
$841$	2.91487	−	16.5310i	0.100513	−	0.570036i
$842$	−16.6701	+	2.21066i	−0.574490	+	0.0761845i
$843$		0			0
$844$	7.25279	+	1.92872i	0.249651	+	0.0663892i
$845$	−92.9203	+	53.6476i	−3.19656	+	1.84553i
$846$		0			0
$847$	−18.2253	+	31.5672i	−0.626230	+	1.08466i
$848$	35.1133	−	12.9305i	1.20579	−	0.444034i
$849$		0			0
$850$	16.6051	−	12.7664i	0.569549	−	0.437885i
$851$	−5.18183	+	6.17546i	−0.177631	+	0.211692i
$852$		0			0
$853$	11.5939	−	31.8539i	0.396967	−	1.09066i	−0.566787	−	0.823865i	$-0.691814\pi$
$853$	11.5939	−	31.8539i	0.396967	−	1.09066i	0.963754	−	0.266793i	$-0.0859641\pi$
$854$	−15.4797	+	16.9252i	−0.529705	+	0.579167i
$855$		0			0
$856$	0.883211	−	6.85863i	0.0301875	−	0.234423i
$857$	−0.670084	−	3.80024i	−0.0228896	−	0.129814i	0.971222	−	0.238177i	$-0.0765500\pi$
$857$	−0.670084	−	3.80024i	−0.0228896	−	0.129814i	−0.994111	+	0.108364i	$0.965439\pi$
$858$		0			0
$859$	−7.37600	−	20.2654i	−0.251666	−	0.691446i	−0.999617	−	0.0276917i	$-0.991184\pi$
$859$	−7.37600	−	20.2654i	−0.251666	−	0.691446i	0.747951	−	0.663754i	$-0.231038\pi$
$860$	−4.99136	+	7.15711i	−0.170204	+	0.244056i
$861$		0			0
$862$	18.4814	+	35.4208i	0.629480	+	1.20644i
$863$	−30.2497			−1.02971			−0.514857	−	0.857276i	$-0.672155\pi$
$863$	−30.2497			−1.02971			−0.514857	+	0.857276i	$0.672155\pi$
$864$		0			0
$865$	−5.68815			−0.193403
$866$	−18.2209	−	34.9216i	−0.619172	−	1.18668i
$867$		0			0
$868$	8.62053	−	12.3610i	0.292600	−	0.419559i
$869$	0.987962	+	2.71440i	0.0335143	+	0.0920799i
$870$		0			0
$871$	17.4847	+	99.1608i	0.592447	+	3.35994i
$872$	5.87102	−	45.5917i	0.198818	−	1.54393i
$873$		0			0
$874$	−2.58272	+	2.82389i	−0.0873619	+	0.0955196i
$875$	−5.48119	+	15.0594i	−0.185298	+	0.509102i
$876$		0			0
$877$	−10.0265	+	11.9491i	−0.338571	+	0.403493i	−0.908286	−	0.418349i	$-0.862609\pi$
$877$	−10.0265	+	11.9491i	−0.338571	+	0.403493i	0.569715	+	0.821842i	$0.307053\pi$
$878$	13.7679	−	10.5852i	0.464645	−	0.357232i
$879$		0			0
$880$	−2.68761	−	7.29832i	−0.0905993	−	0.246026i
$881$	−18.2832	+	31.6674i	−0.615977	+	1.06690i	0.374235	+	0.927334i	$0.377905\pi$
$881$	−18.2832	+	31.6674i	−0.615977	+	1.06690i	−0.990212	+	0.139569i	$0.955428\pi$
$882$		0			0
$883$	26.1355	−	15.0893i	0.879529	−	0.507796i	0.00902592	−	0.999959i	$-0.497127\pi$
$883$	26.1355	−	15.0893i	0.879529	−	0.507796i	0.870503	+	0.492163i	$0.163794\pi$
$884$	29.9835	+	7.97344i	1.00845	+	0.268176i
$885$		0			0
$886$	−29.6222	+	3.92828i	−0.995178	+	0.131973i
$887$	7.16882	−	40.6564i	0.240705	−	1.36511i	−0.589553	−	0.807730i	$-0.700696\pi$
$887$	7.16882	−	40.6564i	0.240705	−	1.36511i	0.830258	−	0.557379i	$-0.188193\pi$
$888$		0			0
$889$	25.0927	−	21.0553i	0.841584	−	0.706172i
$890$	26.7055	+	5.89404i	0.895171	+	0.197569i
$891$		0			0
$892$	−7.11472	−	3.30132i	−0.238219	−	0.110536i
$893$	0.826041	+	0.984438i	0.0276424	+	0.0329430i
$894$		0			0
$895$	6.98289	−	39.6019i	0.233412	−	1.32375i
$896$	−35.6156	+	15.0288i	−1.18983	+	0.502078i
$897$		0			0
$898$	−39.1968	−	1.67432i	−1.30801	−	0.0558726i
$899$	6.67459	−	3.85358i	0.222610	−	0.128524i
$900$		0			0
$901$	−18.7778	−	10.8414i	−0.625578	−	0.361178i
$902$	4.56917	+	2.90483i	0.152137	+	0.0967201i
$903$		0			0
$904$	−33.5893	+	7.54639i	−1.11716	+	0.250989i
$905$	42.6973	+	35.8273i	1.41931	+	1.19094i
$906$		0			0
$907$	13.9229	−	38.2529i	0.462303	−	1.27017i	−0.461446	−	0.887168i	$-0.652669\pi$
$907$	13.9229	−	38.2529i	0.462303	−	1.27017i	0.923749	−	0.382999i	$-0.125109\pi$
$908$	−13.6116	−	19.3615i	−0.451716	−	0.642533i
$909$		0			0
$910$	−104.060	+	32.9180i	−3.44956	+	1.09122i
$911$	−7.42318	−	42.0989i	−0.245941	−	1.39480i	−0.818298	−	0.574795i	$-0.805082\pi$
$911$	−7.42318	−	42.0989i	−0.245941	−	1.39480i	0.572357	−	0.820005i	$-0.306029\pi$
$912$		0			0
$913$	−5.61905	+	2.04517i	−0.185963	+	0.0676852i
$914$	−44.5175	−	18.3905i	−1.47251	−	0.608305i
$915$		0			0
$916$	5.52440	+	20.4628i	0.182531	+	0.676110i
$917$			1.41029i			0.0465717i
$918$		0			0
$919$	−4.00742			−0.132193			−0.0660963	−	0.997813i	$-0.521054\pi$
$919$	−4.00742			−0.132193			−0.0660963	+	0.997813i	$0.521054\pi$
$920$	−63.2501	+	2.94097i	−2.08529	+	0.0969608i
$921$		0			0
$922$	7.50646	−	18.1707i	0.247212	−	0.598419i
$923$	17.9609	+	49.3471i	0.591189	+	1.62428i
$924$		0			0
$925$	−7.64760	+	1.34848i	−0.251452	+	0.0443377i
$926$	25.0613	−	7.92779i	0.823564	−	0.260523i
$927$		0			0
$928$	−19.7549	−	0.769156i	−0.648485	−	0.0252488i
$929$	−46.5451	−	16.9410i	−1.52710	−	0.555818i	−0.564188	−	0.825646i	$-0.690811\pi$
$929$	−46.5451	−	16.9410i	−1.52710	−	0.555818i	−0.962908	+	0.269829i	$0.913033\pi$
$930$		0			0
$931$	−1.22576	+	1.46080i	−0.0401725	+	0.0478758i
$932$	0.958991	+	2.04647i	0.0314128	+	0.0670344i
$933$		0			0
$934$	−11.4948	−	7.30774i	−0.376121	−	0.239117i
$935$	−2.25339	+	3.90298i	−0.0736936	+	0.127641i
$936$		0			0
$937$	4.84280	+	8.38798i	0.158207	+	0.274023i	0.934222	−	0.356691i	$-0.116095\pi$
$937$	4.84280	+	8.38798i	0.158207	+	0.274023i	−0.776015	+	0.630715i	$0.782762\pi$
$938$	−3.10250	+	72.6316i	−0.101300	+	2.37150i
$939$		0			0
$940$	−1.81321	+	21.1854i	−0.0591403	+	0.690993i
$941$	5.10500	+	0.900150i	0.166418	+	0.0293440i	0.256236	−	0.966614i	$-0.417517\pi$
$941$	5.10500	+	0.900150i	0.166418	+	0.0293440i	−0.0898181	+	0.995958i	$0.528629\pi$
$942$		0			0
$943$	33.7672	−	28.3340i	1.09961	−	0.922682i
$944$	−26.8188	+	22.6767i	−0.872877	+	0.738063i
$945$		0			0
$946$	0.227003	−	1.02854i	0.00738051	−	0.0334406i
$947$	−19.6357	−	23.4009i	−0.638075	−	0.760428i	0.345990	−	0.938238i	$-0.387543\pi$
$947$	−19.6357	−	23.4009i	−0.638075	−	0.760428i	−0.984065	+	0.177811i	$0.943099\pi$
$948$		0			0
$949$	−8.46036	−	1.49179i	−0.274635	−	0.0484256i
$950$	−3.65439	+	0.484618i	−0.118564	+	0.0157231i
$951$		0			0
$952$	19.8985	+	10.2870i	0.644913	+	0.333403i
$953$	−8.71927	−	15.1022i	−0.282445	−	0.489209i	0.689542	−	0.724246i	$-0.257812\pi$
$953$	−8.71927	−	15.1022i	−0.282445	−	0.489209i	−0.971986	+	0.235037i	$0.924479\pi$
$954$		0			0
$955$	−38.6370	−	22.3071i	−1.25027	−	0.721841i
$956$	−8.22369	−	8.19271i	−0.265973	−	0.264971i
$957$		0			0
$958$	32.6339	−	25.0898i	1.05435	−	0.810616i
$959$	−41.2500	−	34.6128i	−1.33203	−	1.11771i
$960$		0			0
$961$	24.5605	+	8.93927i	0.792273	+	0.288364i
$962$	−8.48811	−	7.76319i	−0.273667	−	0.250295i
$963$		0			0
$964$	5.25289	+	58.7633i	0.169184	+	1.89264i
$965$	0.588217	−	0.103718i	0.0189354	−	0.00333882i
$966$		0			0
$967$	−46.2859	+	16.8467i	−1.48845	+	0.541752i	−0.953042	−	0.302839i	$-0.902065\pi$
$967$	−46.2859	+	16.8467i	−1.48845	+	0.541752i	−0.535411	+	0.844592i	$0.679843\pi$
$968$	−20.4481	−	22.1887i	−0.657226	−	0.713172i
$969$		0			0
$970$	47.5285	−	24.7988i	1.52605	−	0.796242i
$971$			13.2201i			0.424253i	0.977242	+	0.212126i	$0.0680388\pi$
$971$			13.2201i			0.424253i	−0.977242	+	0.212126i	$0.931961\pi$
$972$		0			0
$973$		−	7.54418i		−	0.241855i
$974$	−8.59804	−	16.4787i	−0.275499	−	0.528011i
$975$		0			0
$976$	−9.55541	−	16.4071i	−0.305861	−	0.525179i
$977$	22.1311	−	8.05506i	0.708037	−	0.257704i	0.0371983	−	0.999308i	$-0.488157\pi$
$977$	22.1311	−	8.05506i	0.708037	−	0.257704i	0.670838	+	0.741604i	$0.265934\pi$
$978$		0			0
$979$	−3.25108	+	0.573253i	−0.103905	+	0.0183212i
$980$	−31.4265	+	2.80924i	−1.00388	+	0.0897378i
$981$		0			0
$982$	−11.2167	+	12.2641i	−0.357940	+	0.391363i
$983$	44.1620	+	16.0737i	1.40855	+	0.512670i	0.930704	−	0.365773i	$-0.119195\pi$
$983$	44.1620	+	16.0737i	1.40855	+	0.512670i	0.477846	+	0.878444i	$0.341418\pi$
$984$		0			0
$985$	2.51126	+	2.10719i	0.0800153	+	0.0671408i
$986$	6.98251	+	9.08203i	0.222369	+	0.289231i
$987$		0			0
$988$	−3.86843	−	3.85385i	−0.123071	−	0.122607i
$989$	−7.42628	−	4.28756i	−0.236142	−	0.136337i
$990$		0			0
$991$	−10.5119	−	18.2072i	−0.333922	−	0.578370i	0.649355	−	0.760486i	$-0.275039\pi$
$991$	−10.5119	−	18.2072i	−0.333922	−	0.578370i	−0.983277	+	0.182115i	$0.941706\pi$
$992$	7.64092	+	9.86116i	0.242599	+	0.313092i
$993$		0			0
$994$	4.98434	+	37.5857i	0.158094	+	1.19215i
$995$	−13.6219	−	2.40190i	−0.431842	−	0.0761454i
$996$		0			0
$997$	1.15413	+	1.37543i	0.0365515	+	0.0435604i	0.784011	−	0.620748i	$-0.213171\pi$
$997$	1.15413	+	1.37543i	0.0365515	+	0.0435604i	−0.747459	+	0.664308i	$0.768726\pi$
$998$	−49.9718	−	11.0290i	−1.58183	−	0.349117i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.37.23		204
3.2	odd	2		216.2.t.a.157.12	✓	204
8.5	even	2	inner	648.2.t.a.37.8		204
12.11	even	2		864.2.bf.a.49.22		204
24.5	odd	2		216.2.t.a.157.27	yes	204
24.11	even	2		864.2.bf.a.49.13		204
27.11	odd	18		216.2.t.a.205.27	yes	204
27.16	even	9	inner	648.2.t.a.613.8		204
108.11	even	18		864.2.bf.a.529.13		204
216.11	even	18		864.2.bf.a.529.22		204
216.173	odd	18		216.2.t.a.205.12	yes	204
216.205	even	18	inner	648.2.t.a.613.23		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.12	✓	204	3.2	odd	2
216.2.t.a.157.27	yes	204	24.5	odd	2
216.2.t.a.205.12	yes	204	216.173	odd	18
216.2.t.a.205.27	yes	204	27.11	odd	18
648.2.t.a.37.8		204	8.5	even	2	inner
648.2.t.a.37.23		204	1.1	even	1	trivial
648.2.t.a.613.8		204	27.16	even	9	inner
648.2.t.a.613.23		204	216.205	even	18	inner
864.2.bf.a.49.13		204	24.11	even	2
864.2.bf.a.49.22		204	12.11	even	2
864.2.bf.a.529.13		204	108.11	even	18
864.2.bf.a.529.22		204	216.11	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.654194 + 1.25381i) q^{2} +(-1.14406 + 1.64047i) q^{4} +(-1.15428 - 3.17134i) q^{5} +(0.593321 + 3.36489i) q^{7} +(-2.80526 - 0.361244i) q^{8} +(3.22113 - 3.52191i) q^{10} +(-0.197048 + 0.541384i) q^{11} +(-4.30199 + 5.12691i) q^{13} +(-3.83077 + 2.94520i) q^{14} +(-1.38226 - 3.75358i) q^{16} +(-1.15893 + 2.00733i) q^{17} +(0.353289 - 0.203971i) q^{19} +(6.52304 + 1.73466i) q^{20} +(-0.807698 + 0.107111i) q^{22} +(-1.15186 + 6.53250i) q^{23} +(-4.89486 + 4.10727i) q^{25} +(-9.24249 - 2.03986i) q^{26} +(-6.19878 - 2.87631i) q^{28} +(-2.24644 - 2.67721i) q^{29} +(-0.382945 + 2.17179i) q^{31} +(3.80200 - 4.18865i) q^{32} +(-3.27497 - 0.139892i) q^{34} +(9.98637 - 5.76564i) q^{35} +(1.05249 + 0.607656i) q^{37} +(0.486860 + 0.309519i) q^{38} +(2.09242 + 9.31343i) q^{40} +(-5.09057 - 4.27150i) q^{41} +(-0.442145 + 1.21478i) q^{43} +(-0.662688 - 0.942626i) q^{44} +(-8.94402 + 2.82932i) q^{46} +(0.547022 + 3.10232i) q^{47} +(-4.39261 + 1.59878i) q^{49} +(-8.35191 - 3.45024i) q^{50} +(-3.48879 - 12.9228i) q^{52} +9.35460i q^{53} +1.94436 q^{55} +(-0.448874 - 9.65374i) q^{56} +(1.88709 - 4.56802i) q^{58} +(-3.00302 - 8.25072i) q^{59} +(4.67459 - 0.824257i) q^{61} +(-2.97352 + 0.940634i) q^{62} +(7.73901 + 2.02677i) q^{64} +(21.2249 + 7.72523i) q^{65} +(9.67062 - 11.5250i) q^{67} +(-1.96707 - 4.19769i) q^{68} +(13.7620 + 8.74913i) q^{70} +(3.92323 - 6.79524i) q^{71} +(0.641809 + 1.11165i) q^{73} +(-0.0733489 + 1.71715i) q^{74} +(-0.0695752 + 0.812914i) q^{76} +(-1.93861 - 0.341829i) q^{77} +(3.84081 - 3.22282i) q^{79} +(-10.3084 + 8.71628i) q^{80} +(2.02541 - 9.17698i) q^{82} +(6.67152 + 7.95081i) q^{83} +(7.70366 + 1.35836i) q^{85} +(-1.81235 + 0.240341i) q^{86} +(0.748343 - 1.44754i) q^{88} +(2.86501 + 4.96234i) q^{89} +(-19.8040 - 11.4338i) q^{91} +(-9.39855 - 9.36314i) q^{92} +(-3.53185 + 2.71538i) q^{94} +(-1.05466 - 0.884962i) q^{95} +(10.5548 + 3.84165i) q^{97} +(-4.87818 - 4.46157i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

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