LMFDB - Embedded newform 891.2.n.k.190.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(136,891)] 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("891.136"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,2,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			190.6
Character	$\chi$	$=$	891.190
Dual form			891.2.n.k.136.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.40198 + 1.06943i) q^{2} +(3.28758 + 3.65123i) q^{4} +(-0.218849 + 0.0974376i) q^{5} +(1.15992 - 0.246548i) q^{7} +(2.36698 + 7.28482i) q^{8} -0.629874 q^{10} +(-0.139567 - 3.31369i) q^{11} +(0.631037 + 6.00392i) q^{13} +(3.04977 + 0.648249i) q^{14} +(-1.07803 + 10.2567i) q^{16} +(1.48403 + 1.07821i) q^{17} +(-1.00736 - 3.10034i) q^{19} +(-1.07525 - 0.478732i) q^{20} +(3.20853 - 8.10868i) q^{22} +(2.77520 - 4.80679i) q^{23} +(-3.30725 + 3.67308i) q^{25} +(-4.90504 + 15.0962i) q^{26} +(4.71353 + 3.42458i) q^{28} +(-6.08908 + 1.29427i) q^{29} +(-0.413671 - 3.93582i) q^{31} +(-5.89858 + 10.2166i) q^{32} +(2.41154 + 4.17691i) q^{34} +(-0.229824 + 0.166977i) q^{35} +(-1.67897 + 5.16733i) q^{37} +(0.895937 - 8.52427i) q^{38} +(-1.22783 - 1.36364i) q^{40} +(10.4325 + 2.21749i) q^{41} +(-6.07195 - 10.5169i) q^{43} +(11.6402 - 11.4036i) q^{44} +(11.8065 - 8.57795i) q^{46} +(1.10724 - 1.22972i) q^{47} +(-5.11019 + 2.27520i) q^{49} +(-11.8721 + 5.28579i) q^{50} +(-19.8471 + 22.0424i) q^{52} +(6.99142 - 5.07956i) q^{53} +(0.353422 + 0.711596i) q^{55} +(4.54157 + 7.86622i) q^{56} +(-16.0100 - 3.40303i) q^{58} +(-2.62823 - 2.91894i) q^{59} +(1.12116 - 10.6671i) q^{61} +(3.21546 - 9.89616i) q^{62} +(-8.40715 + 6.10815i) q^{64} +(-0.723109 - 1.25246i) q^{65} +(-4.61051 + 7.98564i) q^{67} +(0.942072 + 8.96322i) q^{68} +(-0.730603 + 0.155294i) q^{70} +(-5.77707 - 4.19728i) q^{71} +(-0.172710 + 0.531546i) q^{73} +(-9.55896 + 10.6163i) q^{74} +(8.00827 - 13.8707i) q^{76} +(-0.978871 - 3.80920i) q^{77} +(4.04058 + 1.79898i) q^{79} +(-0.763468 - 2.34971i) q^{80} +(22.6872 + 16.4832i) q^{82} +(1.61172 - 15.3345i) q^{83} +(-0.429835 - 0.0913643i) q^{85} +(-3.33759 - 31.7550i) q^{86} +(23.8092 - 8.86015i) q^{88} -0.0625956 q^{89} +(2.21221 + 6.80848i) q^{91} +(26.6744 - 5.66982i) q^{92} +(3.97468 - 1.76964i) q^{94} +(0.522549 + 0.580350i) q^{95} +(5.56631 + 2.47828i) q^{97} -14.7078 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} + 8 q^{4} - 4 q^{5} - 7 q^{7} + 20 q^{8} - 32 q^{10} - 5 q^{11} - 7 q^{13} - 13 q^{14} - 2 q^{16} - 10 q^{17} + 8 q^{19} - 27 q^{20} + 2 q^{22} - 6 q^{23} + 2 q^{25} - 68 q^{26} - 18 q^{28}+ \cdots + 136 q^{98}+O(q^{100}) $ 48 * q + 2 * q^2 + 8 * q^4 - 4 * q^5 - 7 * q^7 + 20 * q^8 - 32 * q^10 - 5 * q^11 - 7 * q^13 - 13 * q^14 - 2 * q^16 - 10 * q^17 + 8 * q^19 - 27 * q^20 + 2 * q^22 - 6 * q^23 + 2 * q^25 - 68 * q^26 - 18 * q^28 - 22 * q^29 - 2 * q^31 - 18 * q^32 + 42 * q^34 + 12 * q^37 + 5 * q^38 - 53 * q^40 - 10 * q^41 + 30 * q^43 + 118 * q^44 + 62 * q^46 - 4 * q^47 + 3 * q^49 - 9 * q^50 + 26 * q^52 + 34 * q^53 + 24 * q^55 + 48 * q^56 - 53 * q^58 - 11 * q^59 - 3 * q^61 - 4 * q^62 + 76 * q^64 + 68 * q^65 + 14 * q^67 - 22 * q^68 + 20 * q^70 - 72 * q^71 + 70 * q^73 - 3 * q^74 + 102 * q^76 + 88 * q^77 + 9 * q^79 - 74 * q^80 - 12 * q^82 - 32 * q^83 + 45 * q^85 + 110 * q^86 - 54 * q^88 + 68 * q^89 + 26 * q^91 + q^92 + 25 * q^94 + 84 * q^95 - 15 * q^97 + 136 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.40198	+	1.06943i	1.69846	+	0.756203i	0.999143	+	0.0413904i	$0.0131787\pi$
$2$	2.40198	+	1.06943i	1.69846	+	0.756203i	0.699316	+	0.714812i	$0.253488\pi$
$3$		0			0
$3$		0			0
$4$	3.28758	+	3.65123i	1.64379	+	1.82561i
$5$	−0.218849	+	0.0974376i	−0.0978720	+	0.0435754i	−0.455089	−	0.890446i	$-0.650392\pi$
$5$	−0.218849	+	0.0974376i	−0.0978720	+	0.0435754i	0.357217	+	0.934022i	$0.383726\pi$
$6$		0			0
$7$	1.15992	−	0.246548i	0.438408	−	0.0931865i	0.0165805	−	0.999863i	$-0.494722\pi$
$7$	1.15992	−	0.246548i	0.438408	−	0.0931865i	0.421828	+	0.906676i	$0.361389\pi$
$8$	2.36698	+	7.28482i	0.836854	+	2.57557i
$9$		0			0
$10$	−0.629874			−0.199184
$11$	−0.139567	−	3.31369i	−0.0420811	−	0.999114i
$11$	−0.139567	−	3.31369i	−0.0420811	−	0.999114i
$12$		0			0
$13$	0.631037	+	6.00392i	0.175018	+	1.66519i	0.631441	+	0.775424i	$0.282464\pi$
$13$	0.631037	+	6.00392i	0.175018	+	1.66519i	−0.456423	+	0.889763i	$0.650869\pi$
$14$	3.04977	+	0.648249i	0.815086	+	0.173252i
$15$		0			0
$16$	−1.07803	+	10.2567i	−0.269507	+	2.56419i
$17$	1.48403	+	1.07821i	0.359929	+	0.261504i	0.753023	−	0.657995i	$-0.228595\pi$
$17$	1.48403	+	1.07821i	0.359929	+	0.261504i	−0.393093	+	0.919499i	$0.628595\pi$
$18$		0			0
$19$	−1.00736	−	3.10034i	−0.231105	−	0.711267i	−0.997614	−	0.0690339i	$-0.978008\pi$
$19$	−1.00736	−	3.10034i	−0.231105	−	0.711267i	0.766510	−	0.642233i	$-0.221992\pi$
$20$	−1.07525	−	0.478732i	−0.240433	−	0.107048i
$21$		0			0
$22$	3.20853	−	8.10868i	0.684060	−	1.72878i
$23$	2.77520	−	4.80679i	0.578670	−	1.00229i	−0.416963	−	0.908924i	$-0.636905\pi$
$23$	2.77520	−	4.80679i	0.578670	−	1.00229i	0.995632	−	0.0933616i	$-0.0297613\pi$
$24$		0			0
$25$	−3.30725	+	3.67308i	−0.661450	+	0.734615i
$26$	−4.90504	+	15.0962i	−0.961958	+	2.96060i
$27$		0			0
$28$	4.71353	+	3.42458i	0.890774	+	0.647185i
$29$	−6.08908	+	1.29427i	−1.13071	+	0.240341i	−0.735022	−	0.678043i	$-0.762828\pi$
$29$	−6.08908	+	1.29427i	−1.13071	+	0.240341i	−0.395691	+	0.918384i	$0.629495\pi$
$30$		0			0
$31$	−0.413671	−	3.93582i	−0.0742975	−	0.706893i	−0.966745	−	0.255742i	$-0.917680\pi$
$31$	−0.413671	−	3.93582i	−0.0742975	−	0.706893i	0.892448	−	0.451151i	$-0.148986\pi$
$32$	−5.89858	+	10.2166i	−1.04273	+	1.80607i
$33$		0			0
$34$	2.41154	+	4.17691i	0.413575	+	0.716333i
$35$	−0.229824	+	0.166977i	−0.0388473	+	0.0282242i
$36$		0			0
$37$	−1.67897	+	5.16733i	−0.276020	+	0.849504i	0.712927	+	0.701238i	$0.247369\pi$
$37$	−1.67897	+	5.16733i	−0.276020	+	0.849504i	−0.988948	+	0.148265i	$0.952631\pi$
$38$	0.895937	−	8.52427i	0.145340	−	1.38282i
$39$		0			0
$40$	−1.22783	−	1.36364i	−0.194136	−	0.215610i
$41$	10.4325	+	2.21749i	1.62928	+	0.346313i	0.929721	−	0.368265i	$-0.120048\pi$
$41$	10.4325	+	2.21749i	1.62928	+	0.346313i	0.699556	+	0.714578i	$0.253381\pi$
$42$		0			0
$43$	−6.07195	−	10.5169i	−0.925964	−	1.60382i	−0.790003	−	0.613103i	$-0.789921\pi$
$43$	−6.07195	−	10.5169i	−0.925964	−	1.60382i	−0.135961	−	0.990714i	$-0.543412\pi$
$44$	11.6402	−	11.4036i	1.75482	−	1.71916i
$45$		0			0
$46$	11.8065	−	8.57795i	1.74078	−	1.26475i
$47$	1.10724	−	1.22972i	0.161508	−	0.179373i	−0.656959	−	0.753926i	$-0.728158\pi$
$47$	1.10724	−	1.22972i	0.161508	−	0.179373i	0.818467	+	0.574553i	$0.194824\pi$
$48$		0			0
$49$	−5.11019	+	2.27520i	−0.730027	+	0.325029i
$50$	−11.8721	+	5.28579i	−1.67896	+	0.747523i
$51$		0			0
$52$	−19.8471	+	22.0424i	−2.75230	+	3.05673i
$53$	6.99142	−	5.07956i	0.960345	−	0.697732i	0.00711436	−	0.999975i	$-0.497735\pi$
$53$	6.99142	−	5.07956i	0.960345	−	0.697732i	0.953231	+	0.302243i	$0.0977354\pi$
$54$		0			0
$55$	0.353422	+	0.711596i	0.0476554	+	0.0959516i
$56$	4.54157	+	7.86622i	0.606892	+	1.05117i
$57$		0			0
$58$	−16.0100	−	3.40303i	−2.10222	−	0.446840i
$59$	−2.62823	−	2.91894i	−0.342166	−	0.380014i	0.547361	−	0.836897i	$-0.315633\pi$
$59$	−2.62823	−	2.91894i	−0.342166	−	0.380014i	−0.889527	+	0.456883i	$0.848966\pi$
$60$		0			0
$61$	1.12116	−	10.6671i	0.143550	−	1.36579i	−0.651227	−	0.758883i	$-0.725745\pi$
$61$	1.12116	−	10.6671i	0.143550	−	1.36579i	0.794777	−	0.606902i	$-0.207588\pi$
$62$	3.21546	−	9.89616i	0.408364	−	1.25681i
$63$		0			0
$64$	−8.40715	+	6.10815i	−1.05089	+	0.763519i
$65$	−0.723109	−	1.25246i	−0.0896907	−	0.155349i
$66$		0			0
$67$	−4.61051	+	7.98564i	−0.563263	+	0.975601i	0.433946	+	0.900939i	$0.357121\pi$
$67$	−4.61051	+	7.98564i	−0.563263	+	0.975601i	−0.997209	+	0.0746617i	$0.976212\pi$
$68$	0.942072	+	8.96322i	0.114243	+	1.08695i
$69$		0			0
$70$	−0.730603	+	0.155294i	−0.0873237	+	0.0185612i
$71$	−5.77707	−	4.19728i	−0.685612	−	0.498126i	0.189603	−	0.981861i	$-0.439280\pi$
$71$	−5.77707	−	4.19728i	−0.685612	−	0.498126i	−0.875215	+	0.483735i	$0.839280\pi$
$72$		0			0
$73$	−0.172710	+	0.531546i	−0.0202141	+	0.0622127i	−0.960655	−	0.277745i	$-0.910413\pi$
$73$	−0.172710	+	0.531546i	−0.0202141	+	0.0622127i	0.940441	+	0.339958i	$0.110413\pi$
$74$	−9.55896	+	10.6163i	−1.11121	+	1.23412i
$75$		0			0
$76$	8.00827	−	13.8707i	0.918611	−	1.59108i
$77$	−0.978871	−	3.80920i	−0.111553	−	0.434098i
$78$		0			0
$79$	4.04058	+	1.79898i	0.454601	+	0.202401i	0.621246	−	0.783616i	$-0.286627\pi$
$79$	4.04058	+	1.79898i	0.454601	+	0.202401i	−0.166645	+	0.986017i	$0.553293\pi$
$80$	−0.763468	−	2.34971i	−0.0853583	−	0.262706i
$81$		0			0
$82$	22.6872	+	16.4832i	2.50538	+	1.82026i
$83$	1.61172	−	15.3345i	0.176909	−	1.68318i	−0.441455	−	0.897284i	$-0.645537\pi$
$83$	1.61172	−	15.3345i	0.176909	−	1.68318i	0.618364	−	0.785892i	$-0.287796\pi$
$84$		0			0
$85$	−0.429835	−	0.0913643i	−0.0466222	−	0.00990985i
$86$	−3.33759	−	31.7550i	−0.359902	−	3.42423i
$87$		0			0
$88$	23.8092	−	8.86015i	2.53807	−	0.944495i
$89$	−0.0625956			−0.00663512			−0.00331756	−	0.999994i	$-0.501056\pi$
$89$	−0.0625956			−0.00663512			−0.00331756	+	0.999994i	$0.501056\pi$
$90$		0			0
$91$	2.21221	+	6.80848i	0.231902	+	0.713722i
$92$	26.6744	−	5.66982i	2.78100	−	0.591119i
$93$		0			0
$94$	3.97468	−	1.76964i	0.409957	−	0.182525i
$95$	0.522549	+	0.580350i	0.0536124	+	0.0595426i
$96$		0			0
$97$	5.56631	+	2.47828i	0.565173	+	0.251631i	0.669375	−	0.742925i	$-0.266562\pi$
$97$	5.56631	+	2.47828i	0.565173	+	0.251631i	−0.104202	+	0.994556i	$0.533229\pi$
$98$	−14.7078			−1.48571
$99$		0			0
$100$	−24.2841			−2.42841
$101$	−13.9385	−	6.20580i	−1.38693	−	0.617500i	−0.428684	−	0.903454i	$-0.641023\pi$
$101$	−13.9385	−	6.20580i	−1.38693	−	0.617500i	−0.958243	+	0.285954i	$0.907689\pi$
$102$		0			0
$103$	8.36177	+	9.28669i	0.823910	+	0.915045i	0.997564	−	0.0697622i	$-0.0222240\pi$
$103$	8.36177	+	9.28669i	0.823910	+	0.915045i	−0.173654	+	0.984807i	$0.555557\pi$
$104$	−42.2438	+	18.8081i	−4.14234	+	1.84429i
$105$		0			0
$106$	22.2255	−	4.72418i	2.15873	−	0.458853i
$107$	3.33446	+	10.2624i	0.322354	+	0.992105i	0.972621	+	0.232399i	$0.0746574\pi$
$107$	3.33446	+	10.2624i	0.322354	+	0.992105i	−0.650266	+	0.759706i	$0.725343\pi$
$108$		0			0
$109$	−5.16947			−0.495146			−0.247573	−	0.968869i	$-0.579633\pi$
$109$	−5.16947			−0.495146			−0.247573	+	0.968869i	$0.579633\pi$
$110$	0.0879096	+	2.08720i	0.00838186	+	0.199007i
$111$		0			0
$112$	1.27836	+	12.1628i	0.120794	+	1.14927i
$113$	−1.99341	−	0.423712i	−0.187524	−	0.0398594i	0.113192	−	0.993573i	$-0.463892\pi$
$113$	−1.99341	−	0.423712i	−0.187524	−	0.0398594i	−0.300716	+	0.953714i	$0.597226\pi$
$114$		0			0
$115$	−0.138987	+	1.32237i	−0.0129606	+	0.123311i
$116$	−24.7440	−	17.9776i	−2.29743	−	1.66918i
$117$		0			0
$118$	−3.19135	−	9.82197i	−0.293788	−	0.904185i
$119$	1.98718	+	0.884750i	0.182165	+	0.0811049i
$120$		0			0
$121$	−10.9610	+	0.924963i	−0.996458	+	0.0840876i
$122$	14.1008	−	24.4233i	1.27662	−	2.21118i
$123$		0			0
$124$	13.0106	−	14.4497i	1.16839	−	1.29762i
$125$	0.736031	−	2.26527i	0.0658326	−	0.202612i
$126$		0			0
$127$	0.969141	+	0.704122i	0.0859974	+	0.0624808i	0.629953	−	0.776633i	$-0.283074\pi$
$127$	0.969141	+	0.704122i	0.0859974	+	0.0624808i	−0.543956	+	0.839114i	$0.683074\pi$
$128$	−3.64735	+	0.775267i	−0.322383	+	0.0685246i
$129$		0			0
$130$	−0.397474	−	3.78171i	−0.0348608	−	0.331678i
$131$	2.88350	−	4.99436i	0.251932	−	0.436359i	−0.712126	−	0.702052i	$-0.752267\pi$
$131$	2.88350	−	4.99436i	0.251932	−	0.436359i	0.964058	+	0.265693i	$0.0856007\pi$
$132$		0			0
$133$	−1.93284	−	3.34778i	−0.167599	−	0.290289i
$134$	−19.6145	+	14.2507i	−1.69443	+	1.23108i
$135$		0			0
$136$	−4.34189	+	13.3630i	−0.372314	+	1.14586i
$137$	−0.0139813	+	0.133023i	−0.00119450	+	0.0113649i	−0.995103	−	0.0988443i	$-0.968485\pi$
$137$	−0.0139813	+	0.133023i	−0.00119450	+	0.0113649i	0.993908	+	0.110209i	$0.0351521\pi$
$138$		0			0
$139$	7.45757	+	8.28247i	0.632543	+	0.702510i	0.971164	−	0.238413i	$-0.0766272\pi$
$139$	7.45757	+	8.28247i	0.632543	+	0.702510i	−0.338621	+	0.940923i	$0.609961\pi$
$140$	−1.36523	−	0.290189i	−0.115383	−	0.0245255i
$141$		0			0
$142$	−9.38771	−	16.2600i	−0.787799	−	1.36451i
$143$	19.8070	−	2.92901i	1.65635	−	0.244936i
$144$		0			0
$145$	1.20647	−	0.876555i	0.100192	−	0.0727939i
$146$	−0.983298	+	1.09206i	−0.0813784	+	0.0903798i
$147$		0			0
$148$	−24.3868	+	10.8577i	−2.00459	+	0.892499i
$149$	3.60383	−	1.60453i	0.295237	−	0.131448i	−0.253773	−	0.967264i	$-0.581672\pi$
$149$	3.60383	−	1.60453i	0.295237	−	0.131448i	0.549010	+	0.835816i	$0.315005\pi$
$150$		0			0
$151$	−1.79136	+	1.98951i	−0.145779	+	0.161904i	−0.811612	−	0.584197i	$-0.801410\pi$
$151$	−1.79136	+	1.98951i	−0.145779	+	0.161904i	0.665833	+	0.746101i	$0.268076\pi$
$152$	20.2010	−	14.6769i	1.63852	−	1.19045i
$153$		0			0
$154$	1.72245	−	10.1965i	0.138799	−	0.821655i
$155$	0.474028	+	0.821040i	0.0380748	+	0.0659476i
$156$		0			0
$157$	10.4417	+	2.21945i	0.833337	+	0.177131i	0.604773	−	0.796398i	$-0.293264\pi$
$157$	10.4417	+	2.21945i	0.833337	+	0.177131i	0.228564	+	0.973529i	$0.426597\pi$
$158$	7.78152	+	8.64226i	0.619065	+	0.687541i
$159$		0			0
$160$	0.295410	−	2.81064i	0.0233542	−	0.222201i
$161$	2.03390	−	6.25971i	0.160294	−	0.493334i
$162$		0			0
$163$	−5.97347	+	4.33998i	−0.467878	+	0.339933i	−0.796614	−	0.604489i	$-0.793378\pi$
$163$	−5.97347	+	4.33998i	−0.467878	+	0.339933i	0.328736	+	0.944422i	$0.393378\pi$
$164$	26.2010	+	45.3815i	2.04596	+	3.54370i
$165$		0			0
$166$	20.2705	−	35.1095i	1.57329	−	2.72503i
$167$	1.07893	+	10.2653i	0.0834900	+	0.794354i	0.953515	+	0.301346i	$0.0974360\pi$
$167$	1.07893	+	10.2653i	0.0834900	+	0.794354i	−0.870025	+	0.493008i	$0.835897\pi$
$168$		0			0
$169$	−22.9329	+	4.87454i	−1.76407	+	0.374964i
$170$	−0.934749	−	0.679135i	−0.0716920	−	0.0520873i
$171$		0			0
$172$	18.4377	−	56.7454i	1.40586	−	4.32679i
$173$	10.7537	−	11.9432i	0.817587	−	0.908022i	−0.179542	−	0.983750i	$-0.557461\pi$
$173$	10.7537	−	11.9432i	0.817587	−	0.908022i	0.997129	+	0.0757281i	$0.0241281\pi$
$174$		0			0
$175$	−2.93055	+	5.07587i	−0.221529	+	0.383700i
$176$	34.1381	+	2.14074i	2.57325	+	0.161364i
$177$		0			0
$178$	−0.150354	−	0.0669418i	−0.0112695	−	0.00501750i
$179$	−1.14818	−	3.53374i	−0.0858191	−	0.264124i	0.898933	−	0.438085i	$-0.144343\pi$
$179$	−1.14818	−	3.53374i	−0.0858191	−	0.264124i	−0.984752	+	0.173961i	$0.944343\pi$
$180$		0			0
$181$	12.2247	+	8.88174i	0.908652	+	0.660174i	0.940674	−	0.339313i	$-0.110195\pi$
$181$	12.2247	+	8.88174i	0.908652	+	0.660174i	−0.0320216	+	0.999487i	$0.510195\pi$
$182$	−1.96752	+	18.7197i	−0.145842	+	1.38759i
$183$		0			0
$184$	41.5854	+	8.83926i	3.06572	+	0.651639i
$185$	−0.136053	−	1.29446i	−0.0100028	−	0.0951704i
$186$		0			0
$187$	3.36572	−	5.06808i	0.246126	−	0.370615i
$188$	8.13014			0.592951
$189$		0			0
$190$	0.634510	+	1.95282i	0.0460322	+	0.141673i
$191$	−11.7220	+	2.49159i	−0.848176	+	0.180285i	−0.611442	−	0.791289i	$-0.709410\pi$
$191$	−11.7220	+	2.49159i	−0.848176	+	0.180285i	−0.236734	+	0.971575i	$0.576077\pi$
$192$		0			0
$193$	−20.5852	+	9.16514i	−1.48176	+	0.659721i	−0.978843	−	0.204615i	$-0.934406\pi$
$193$	−20.5852	+	9.16514i	−1.48176	+	0.659721i	−0.502915	+	0.864336i	$0.667739\pi$
$194$	10.7198	+	11.9056i	0.769640	+	0.854771i
$195$		0			0
$196$	−25.1075	−	11.1786i	−1.79339	−	0.798469i
$197$	−9.95308			−0.709127			−0.354564	−	0.935032i	$-0.615371\pi$
$197$	−9.95308			−0.709127			−0.354564	+	0.935032i	$0.615371\pi$
$198$		0			0
$199$	−15.5617			−1.10314			−0.551570	−	0.834128i	$-0.685971\pi$
$199$	−15.5617			−1.10314			−0.551570	+	0.834128i	$0.685971\pi$
$200$	−34.5859	−	15.3986i	−2.44559	−	1.08885i
$201$		0			0
$202$	−26.8433	−	29.8125i	−1.88869	−	2.09760i
$203$	−6.74374	+	3.00250i	−0.473317	+	0.210735i
$204$		0			0
$205$	−2.49920	+	0.531220i	−0.174551	+	0.0371020i
$206$	10.1534	+	31.2488i	0.707418	+	2.17721i
$207$		0			0
$208$	−62.2609			−4.31702
$209$	−10.1330	+	3.77078i	−0.700911	+	0.260831i
$210$		0			0
$211$	0.250333	+	2.38176i	0.0172337	+	0.163967i	0.999754	−	0.0221891i	$-0.00706358\pi$
$211$	0.250333	+	2.38176i	0.0172337	+	0.163967i	−0.982520	+	0.186156i	$0.940397\pi$
$212$	41.5315	+	8.82779i	2.85240	+	0.606295i
$213$		0			0
$214$	−2.96564	+	28.2161i	−0.202727	+	1.92882i
$215$	2.35358	+	1.70998i	0.160513	+	0.116620i
$216$		0			0
$217$	−1.45019	−	4.46324i	−0.0984456	−	0.302984i
$218$	−12.4170	−	5.52840i	−0.840985	−	0.374430i
$219$		0			0
$220$	−1.43630	+	3.62986i	−0.0968352	+	0.244725i
$221$	−5.53700	+	9.59036i	−0.372459	+	0.645118i
$222$		0			0
$223$	8.68791	−	9.64890i	0.581785	−	0.646138i	−0.378354	−	0.925661i	$-0.623510\pi$
$223$	8.68791	−	9.64890i	0.581785	−	0.646138i	0.960139	+	0.279523i	$0.0901763\pi$
$224$	−4.32298	+	13.3048i	−0.288841	+	0.888962i
$225$		0			0
$226$	−4.33500	−	3.14956i	−0.288360	−	0.209506i
$227$	−18.0474	+	3.83610i	−1.19785	+	0.254611i	−0.763305	−	0.646039i	$-0.776424\pi$
$227$	−18.0474	+	3.83610i	−1.19785	+	0.254611i	−0.434546	+	0.900650i	$0.643091\pi$
$228$		0			0
$229$	−2.10518	−	20.0294i	−0.139114	−	1.32358i	−0.811922	−	0.583765i	$-0.801579\pi$
$229$	−2.10518	−	20.0294i	−0.139114	−	1.32358i	0.672808	−	0.739817i	$-0.265088\pi$
$230$	−1.74803	+	3.02767i	−0.115261	+	0.199639i
$231$		0			0
$232$	−23.8413	−	41.2943i	−1.56526	−	2.71110i
$233$	5.95367	−	4.32560i	0.390038	−	0.283379i	−0.375433	−	0.926850i	$-0.622506\pi$
$233$	5.95367	−	4.32560i	0.390038	−	0.283379i	0.765471	+	0.643470i	$0.222506\pi$
$234$		0			0
$235$	−0.122498	+	0.377009i	−0.00799087	+	0.0245934i
$236$	2.01722	−	19.1925i	0.131310	−	1.24933i
$237$		0			0
$238$	3.82700	+	4.25031i	0.248067	+	0.275507i
$239$	−9.41547	−	2.00132i	−0.609036	−	0.129455i	−0.106939	−	0.994266i	$-0.534105\pi$
$239$	−9.41547	−	2.00132i	−0.609036	−	0.129455i	−0.502098	+	0.864811i	$0.667438\pi$
$240$		0			0
$241$	13.2816	+	23.0043i	0.855540	+	1.48184i	0.876143	+	0.482052i	$0.160108\pi$
$241$	13.2816	+	23.0043i	0.855540	+	1.48184i	−0.0206023	+	0.999788i	$0.506558\pi$
$242$	−27.3174	−	9.50034i	−1.75603	−	0.610705i
$243$		0			0
$244$	42.6340	−	30.9754i	2.72936	−	1.98300i
$245$	0.896668	−	0.995850i	0.0572860	−	0.0636225i
$246$		0			0
$247$	17.9785	−	8.00454i	1.14394	−	0.509317i
$248$	27.6925	−	12.3295i	1.75848	−	0.782925i
$249$		0			0
$250$	4.19049	−	4.65401i	0.265030	−	0.294345i
$251$	−20.1137	+	14.6135i	−1.26957	+	0.922394i	−0.999185	−	0.0403590i	$-0.987150\pi$
$251$	−20.1137	+	14.6135i	−1.26957	+	0.922394i	−0.270382	+	0.962753i	$0.587150\pi$
$252$		0			0
$253$	−16.3155	−	8.52528i	−1.02575	−	0.535980i
$254$	1.57485	+	2.72772i	0.0988149	+	0.171152i
$255$		0			0
$256$	10.7395	+	2.28275i	0.671217	+	0.142672i
$257$	8.97309	+	9.96563i	0.559726	+	0.621639i	0.954886	−	0.296974i	$-0.0959774\pi$
$257$	8.97309	+	9.96563i	0.559726	+	0.621639i	−0.395160	+	0.918612i	$0.629311\pi$
$258$		0			0
$259$	−0.673469	+	6.40763i	−0.0418473	+	0.398151i
$260$	2.19574	−	6.75781i	0.136174	−	0.419101i
$261$		0			0
$262$	12.2672	−	8.91267i	0.757873	−	0.550627i
$263$	0.390951	+	0.677147i	0.0241071	+	0.0417546i	0.877827	−	0.478977i	$-0.158992\pi$
$263$	0.390951	+	0.677147i	0.0241071	+	0.0417546i	−0.853720	+	0.520732i	$0.825659\pi$
$264$		0			0
$265$	−1.03512	+	1.79288i	−0.0635870	+	0.110136i
$266$	−1.06243	−	10.1084i	−0.0651418	−	0.619783i
$267$		0			0
$268$	−44.3148	+	9.41940i	−2.70696	+	0.575382i
$269$	8.62814	+	6.26871i	0.526067	+	0.382210i	0.818884	−	0.573958i	$-0.194593\pi$
$269$	8.62814	+	6.26871i	0.526067	+	0.382210i	−0.292818	+	0.956168i	$0.594593\pi$
$270$		0			0
$271$	−7.60141	+	23.3947i	−0.461753	+	1.42113i	0.401268	+	0.915961i	$0.368570\pi$
$271$	−7.60141	+	23.3947i	−0.461753	+	1.42113i	−0.863021	+	0.505168i	$0.831430\pi$
$272$	−12.6587	+	14.0589i	−0.767548	+	0.852448i
$273$		0			0
$274$	−0.175842	+	0.304567i	−0.0106230	+	0.0183996i
$275$	12.6330	+	10.4466i	0.761799	+	0.629951i
$276$		0			0
$277$	−8.19654	−	3.64933i	−0.492482	−	0.219267i	0.145441	−	0.989367i	$-0.453540\pi$
$277$	−8.19654	−	3.64933i	−0.492482	−	0.219267i	−0.637924	+	0.770100i	$0.720206\pi$
$278$	9.05542	+	27.8697i	0.543108	+	1.67151i
$279$		0			0
$280$	−1.76038	−	1.27899i	−0.105203	−	0.0764344i
$281$	−1.74835	+	16.6345i	−0.104298	+	0.992330i	0.809764	+	0.586756i	$0.199595\pi$
$281$	−1.74835	+	16.6345i	−0.104298	+	0.992330i	−0.914062	+	0.405574i	$0.867072\pi$
$282$		0			0
$283$	5.72409	+	1.21669i	0.340262	+	0.0723249i	0.374874	−	0.927076i	$-0.377686\pi$
$283$	5.72409	+	1.21669i	0.340262	+	0.0723249i	−0.0346116	+	0.999401i	$0.511019\pi$
$284$	−3.66733	−	34.8923i	−0.217616	−	2.07048i
$285$		0			0
$286$	50.7086	+	14.1468i	2.99846	+	0.836520i
$287$	12.6475			0.746560
$288$		0			0
$289$	−4.21349	−	12.9678i	−0.247852	−	0.762811i
$290$	3.83535	−	0.815229i	0.225219	−	0.0478719i
$291$		0			0
$292$	−2.50859	+	1.11690i	−0.146804	+	0.0653615i
$293$	10.0255	+	11.1344i	0.585695	+	0.650480i	0.961041	−	0.276404i	$-0.0891429\pi$
$293$	10.0255	+	11.1344i	0.585695	+	0.650480i	−0.375346	+	0.926885i	$0.622476\pi$
$294$		0			0
$295$	0.859599	+	0.382718i	0.0500478	+	0.0222827i
$296$	−41.6171			−2.41895
$297$		0			0
$298$	10.3723			0.600850
$299$	30.6108	+	13.6288i	1.77027	+	0.788175i
$300$		0			0
$301$	−9.63591	−	10.7018i	−0.555404	−	0.616839i
$302$	−6.43047	+	2.86303i	−0.370032	+	0.164749i
$303$		0			0
$304$	32.8853	−	6.98999i	1.88610	−	0.400904i
$305$	0.794015	+	2.44373i	0.0454652	+	0.139927i
$306$		0			0
$307$	6.52424			0.372358			0.186179	−	0.982516i	$-0.440390\pi$
$307$	6.52424			0.372358			0.186179	+	0.982516i	$0.440390\pi$
$308$	10.6901	−	16.0971i	0.609127	−	0.917219i
$309$		0			0
$310$	0.260560	+	2.47907i	0.0147988	+	0.140802i
$311$	−14.0999	−	2.99703i	−0.799534	−	0.169946i	−0.210012	−	0.977699i	$-0.567350\pi$
$311$	−14.0999	−	2.99703i	−0.799534	−	0.169946i	−0.589522	+	0.807753i	$0.700684\pi$
$312$		0			0
$313$	−1.64511	+	15.6522i	−0.0929873	+	0.884715i	0.844233	+	0.535977i	$0.180057\pi$
$313$	−1.64511	+	15.6522i	−0.0929873	+	0.884715i	−0.937220	+	0.348738i	$0.886610\pi$
$314$	22.7072	+	16.4978i	1.28144	+	0.931022i
$315$		0			0
$316$	6.71524	+	20.6674i	0.377762	+	1.16263i
$317$	26.7830	+	11.9245i	1.50428	+	0.669749i	0.982995	−	0.183633i	$-0.0587859\pi$
$317$	26.7830	+	11.9245i	1.50428	+	0.669749i	0.521286	+	0.853382i	$0.325453\pi$
$318$		0			0
$319$	5.13865	+	19.9967i	0.287709	+	1.11960i
$320$	1.24473	−	2.15593i	0.0695824	−	0.120520i
$321$		0			0
$322$	11.5797	−	12.8606i	0.645314	−	0.716693i
$323$	1.84786	−	5.68713i	0.102818	−	0.316440i
$324$		0			0
$325$	−24.1398	−	17.5386i	−1.33904	−	0.972868i
$326$	−18.9895	+	4.03634i	−1.05173	+	0.223552i
$327$		0			0
$328$	8.53944	+	81.2473i	0.471512	+	4.48613i
$329$	0.981128	−	1.69936i	0.0540913	−	0.0936889i
$330$		0			0
$331$	−6.70580	−	11.6148i	−0.368584	−	0.638407i	0.620760	−	0.784001i	$-0.286824\pi$
$331$	−6.70580	−	11.6148i	−0.368584	−	0.638407i	−0.989344	+	0.145594i	$0.953491\pi$
$332$	61.2883	−	44.5285i	3.36363	−	2.44382i
$333$		0			0
$334$	−8.38649	+	25.8110i	−0.458888	+	1.41231i
$335$	0.230902	−	2.19688i	0.0126155	−	0.120028i
$336$		0			0
$337$	8.64664	+	9.60307i	0.471012	+	0.523112i	0.931101	−	0.364761i	$-0.118849\pi$
$337$	8.64664	+	9.60307i	0.471012	+	0.523112i	−0.460089	+	0.887873i	$0.652182\pi$
$338$	−60.2974	−	12.8166i	−3.27975	−	0.697132i
$339$		0			0
$340$	−1.07953	−	1.86979i	−0.0585455	−	0.101404i
$341$	−12.9843	+	1.92009i	−0.703141	+	0.103979i
$342$		0			0
$343$	−12.0820	+	8.77807i	−0.652365	+	0.473971i
$344$	62.2417	−	69.1264i	3.35585	−	3.72705i
$345$		0			0
$346$	38.6026	−	17.1870i	2.07529	−	0.923977i
$347$	−31.8790	+	14.1935i	−1.71136	+	0.761945i	−0.713219	+	0.700941i	$0.752763\pi$
$347$	−31.8790	+	14.1935i	−1.71136	+	0.761945i	−0.998138	+	0.0610035i	$0.980570\pi$
$348$		0			0
$349$	−2.48935	+	2.76470i	−0.133252	+	0.147991i	−0.806078	−	0.591810i	$-0.798414\pi$
$349$	−2.48935	+	2.76470i	−0.133252	+	0.147991i	0.672826	+	0.739801i	$0.265080\pi$
$350$	−12.4674	+	9.05813i	−0.666413	+	0.484177i
$351$		0			0
$352$	34.6780	+	18.1202i	1.84834	+	0.965807i
$353$	1.97626	+	3.42298i	0.105186	+	0.182187i	0.913814	−	0.406133i	$-0.133123\pi$
$353$	1.97626	+	3.42298i	0.105186	+	0.182187i	−0.808628	+	0.588320i	$0.799790\pi$
$354$		0			0
$355$	1.67328	+	0.355666i	0.0888083	+	0.0188768i
$356$	−0.205788	−	0.228551i	−0.0109068	−	0.0121132i
$357$		0			0
$358$	1.02118	−	9.71588i	0.0539711	−	0.513500i
$359$	−2.28796	+	7.04162i	−0.120754	+	0.371643i	−0.993104	−	0.117240i	$-0.962595\pi$
$359$	−2.28796	+	7.04162i	−0.120754	+	0.371643i	0.872350	+	0.488883i	$0.162595\pi$
$360$		0			0
$361$	6.77400	−	4.92160i	0.356526	−	0.259031i
$362$	19.8650	+	34.4072i	1.04408	+	1.80840i
$363$		0			0
$364$	−17.5865	+	30.4607i	−0.921783	+	1.59657i
$365$	−0.0139953	−	0.133156i	−0.000732548	−	0.00696973i
$366$		0			0
$367$	24.8605	−	5.28426i	1.29771	−	0.275836i	0.493272	−	0.869875i	$-0.335801\pi$
$367$	24.8605	−	5.28426i	1.29771	−	0.275836i	0.804436	+	0.594039i	$0.202468\pi$
$368$	46.3103	+	33.6464i	2.41409	+	1.75394i
$369$		0			0
$370$	1.05754	−	3.25476i	0.0549787	−	0.169207i
$371$	6.85712	−	7.61561i	0.356004	−	0.395383i
$372$		0			0
$373$	2.38737	−	4.13505i	0.123614	−	0.214105i	−0.797577	−	0.603218i	$-0.793885\pi$
$373$	2.38737	−	4.13505i	0.123614	−	0.214105i	0.921190	+	0.389113i	$0.127218\pi$
$374$	13.5044	−	8.57404i	0.698295	−	0.443353i
$375$		0			0
$376$	11.5791	+	5.15535i	0.597146	+	0.265867i
$377$	−11.6131	−	35.7416i	−0.598107	−	1.84079i
$378$		0			0
$379$	14.1162	+	10.2560i	0.725100	+	0.526816i	0.888009	−	0.459825i	$-0.152088\pi$
$379$	14.1162	+	10.2560i	0.725100	+	0.526816i	−0.162910	+	0.986641i	$0.552088\pi$
$380$	−0.401067	+	3.81589i	−0.0205743	+	0.195751i
$381$		0			0
$382$	−30.8207	−	6.55115i	−1.57693	−	0.335186i
$383$	−0.354156	−	3.36957i	−0.0180965	−	0.172177i	0.981741	−	0.190225i	$-0.0609216\pi$
$383$	−0.354156	−	3.36957i	−0.0180965	−	0.172177i	−0.999837	+	0.0180477i	$0.994255\pi$
$384$		0			0
$385$	0.585384	+	0.738259i	0.0298339	+	0.0376251i
$386$	−59.2469			−3.01559
$387$		0			0
$388$	9.25093	+	28.4714i	0.469645	+	1.44542i
$389$	−18.3444	+	3.89923i	−0.930099	+	0.197699i	−0.647960	−	0.761675i	$-0.724377\pi$
$389$	−18.3444	+	3.89923i	−0.930099	+	0.197699i	−0.282139	+	0.959373i	$0.591044\pi$
$390$		0			0
$391$	9.30120	−	4.14116i	0.470382	−	0.209427i
$392$	−28.6702	−	31.8414i	−1.44806	−	1.60824i
$393$		0			0
$394$	−23.9071	−	10.6441i	−1.20442	−	0.536244i
$395$	−1.05956			−0.0533125
$396$		0			0
$397$	10.7157			0.537806			0.268903	−	0.963167i	$-0.413339\pi$
$397$	10.7157			0.537806			0.268903	+	0.963167i	$0.413339\pi$
$398$	−37.3790	−	16.6422i	−1.87364	−	0.834198i
$399$		0			0
$400$	−34.1085	−	37.8813i	−1.70542	−	1.89407i
$401$	2.58776	−	1.15214i	0.129226	−	0.0575353i	−0.341105	−	0.940025i	$-0.610801\pi$
$401$	2.58776	−	1.15214i	0.129226	−	0.0575353i	0.470331	+	0.882490i	$0.344134\pi$
$402$		0			0
$403$	23.3693	−	4.96729i	1.16411	−	0.247438i
$404$	−23.1650	−	71.2945i	−1.15250	−	3.54704i
$405$		0			0
$406$	−19.4093			−0.963268
$407$	17.3572	+	4.84238i	0.860366	+	0.240028i
$408$		0			0
$409$	−2.46099	−	23.4148i	−0.121688	−	1.15779i	−0.869520	−	0.493897i	$-0.835572\pi$
$409$	−2.46099	−	23.4148i	−0.121688	−	1.15779i	0.747832	−	0.663888i	$-0.231095\pi$
$410$	−6.57113	−	1.39674i	−0.324525	−	0.0689799i
$411$		0			0
$412$	−6.41782	+	61.0615i	−0.316183	+	3.00828i
$413$	−3.76819	−	2.73775i	−0.185421	−	0.134716i
$414$		0			0
$415$	1.14143	+	3.51297i	0.0560307	+	0.172445i
$416$	−65.0621	−	28.9675i	−3.18993	−	1.42025i
$417$		0			0
$418$	−28.3718	−	1.77915i	−1.38771	−	0.0870209i
$419$	−10.5587	+	18.2882i	−0.515826	+	0.893437i	0.484005	+	0.875065i	$0.339182\pi$
$419$	−10.5587	+	18.2882i	−0.515826	+	0.893437i	−0.999831	+	0.0183715i	$0.994152\pi$
$420$		0			0
$421$	−15.7361	+	17.4767i	−0.766930	+	0.851763i	−0.992472	−	0.122471i	$-0.960918\pi$
$421$	−15.7361	+	17.4767i	−0.766930	+	0.851763i	0.225542	+	0.974234i	$0.427585\pi$
$422$	−1.94584	+	5.98867i	−0.0947218	+	0.291524i
$423$		0			0
$424$	53.5522	+	38.9080i	2.60073	+	1.88954i
$425$	−8.86839	+	1.88503i	−0.430180	+	0.0914376i
$426$		0			0
$427$	−1.32951	−	12.6494i	−0.0643394	−	0.612148i
$428$	−26.5081	+	45.9134i	−1.28132	+	2.21931i
$429$		0			0
$430$	3.82456	+	6.62434i	0.184437	+	0.319454i
$431$	4.02881	−	2.92710i	0.194061	−	0.140994i	−0.486512	−	0.873674i	$-0.661731\pi$
$431$	4.02881	−	2.92710i	0.194061	−	0.140994i	0.680573	+	0.732680i	$0.261731\pi$
$432$		0			0
$433$	−7.90629	+	24.3331i	−0.379952	+	1.16937i	0.560124	+	0.828409i	$0.310753\pi$
$433$	−7.90629	+	24.3331i	−0.379952	+	1.16937i	−0.940076	+	0.340964i	$0.889247\pi$
$434$	1.28979	−	12.2715i	0.0619118	−	0.589051i
$435$		0			0
$436$	−16.9951	−	18.8749i	−0.813916	−	0.903945i
$437$	−17.6983	−	3.76189i	−0.846625	−	0.179956i
$438$		0			0
$439$	2.33003	+	4.03572i	0.111206	+	0.192615i	0.916257	−	0.400591i	$-0.131195\pi$
$439$	2.33003	+	4.03572i	0.111206	+	0.192615i	−0.805051	+	0.593206i	$0.797862\pi$
$440$	−4.34731	+	4.25895i	−0.207250	+	0.203037i
$441$		0			0
$442$	−23.5560	+	17.1145i	−1.12045	+	0.814052i
$443$	−15.4728	+	17.1843i	−0.735135	+	0.816450i	−0.988548	−	0.150908i	$-0.951780\pi$
$443$	−15.4728	+	17.1843i	−0.735135	+	0.816450i	0.253413	+	0.967358i	$0.418447\pi$
$444$		0			0
$445$	0.0136990	−	0.00609917i	0.000649393	−	0.000289128i
$446$	31.1871	−	13.8854i	1.47675	−	0.657492i
$447$		0			0
$448$	−8.24566	+	9.15773i	−0.389571	+	0.432662i
$449$	−11.1354	+	8.09035i	−0.525512	+	0.381807i	−0.818676	−	0.574255i	$-0.805292\pi$
$449$	−11.1354	+	8.09035i	−0.525512	+	0.381807i	0.293164	+	0.956062i	$0.405292\pi$
$450$		0			0
$451$	5.89203	−	34.8794i	0.277445	−	1.64241i
$452$	−5.00642	−	8.67137i	−0.235482	−	0.407867i
$453$		0			0
$454$	−47.4521	−	10.0863i	−2.22704	−	0.473372i
$455$	−1.14754	−	1.27447i	−0.0537975	−	0.0597482i
$456$		0			0
$457$	−1.13304	+	10.7801i	−0.0530013	+	0.504274i	0.935529	+	0.353250i	$0.114924\pi$
$457$	−1.13304	+	10.7801i	−0.0530013	+	0.504274i	−0.988530	+	0.151023i	$0.951743\pi$
$458$	16.3635	−	50.3617i	0.764617	−	2.35325i
$459$		0			0
$460$	−5.28520	+	3.83992i	−0.246424	+	0.179037i
$461$	−1.46396	−	2.53565i	−0.0681833	−	0.118097i	0.829918	−	0.557885i	$-0.188387\pi$
$461$	−1.46396	−	2.53565i	−0.0681833	−	0.118097i	−0.898102	+	0.439788i	$0.855054\pi$
$462$		0			0
$463$	13.5417	−	23.4550i	0.629337	−	1.09004i	−0.358347	−	0.933588i	$-0.616660\pi$
$463$	13.5417	−	23.4550i	0.629337	−	1.09004i	0.987685	−	0.156456i	$-0.0500070\pi$
$464$	−6.71084	−	63.8493i	−0.311543	−	2.96413i
$465$		0			0
$466$	18.9266	−	4.02296i	0.876756	−	0.186360i
$467$	9.14721	+	6.64584i	0.423282	+	0.307533i	0.778957	−	0.627077i	$-0.215749\pi$
$467$	9.14721	+	6.64584i	0.423282	+	0.307533i	−0.355675	+	0.934610i	$0.615749\pi$
$468$		0			0
$469$	−3.37897	+	10.3994i	−0.156026	+	0.480200i
$470$	−0.697424	+	0.774567i	−0.0321697	+	0.0357281i
$471$		0			0
$472$	15.0430	−	26.0552i	0.692410	−	1.19929i
$473$	−34.0024	+	21.5884i	−1.56343	+	0.992634i
$474$		0			0
$475$	14.7194	+	6.55349i	0.675371	+	0.300695i
$476$	3.30259	+	10.1643i	0.151374	+	0.465882i
$477$		0			0
$478$	−20.4755	−	14.8764i	−0.936530	−	0.680429i
$479$	3.17618	−	30.2193i	0.145123	−	1.38076i	−0.643296	−	0.765618i	$-0.722433\pi$
$479$	3.17618	−	30.2193i	0.145123	−	1.38076i	0.788419	−	0.615138i	$-0.210900\pi$
$480$		0			0
$481$	−32.0837	−	6.81960i	−1.46289	−	0.310947i
$482$	7.30052	+	69.4598i	0.332529	+	3.16381i
$483$		0			0
$484$	−39.4126	−	36.9804i	−1.79148	−	1.68093i
$485$	−1.45966			−0.0662796
$486$		0			0
$487$	−0.988742	−	3.04303i	−0.0448042	−	0.137893i	0.926152	−	0.377150i	$-0.123096\pi$
$487$	−0.988742	−	3.04303i	−0.0448042	−	0.137893i	−0.970956	+	0.239257i	$0.923096\pi$
$488$	80.3618	−	17.0814i	3.63781	−	0.773240i
$489$		0			0
$490$	3.21878	−	1.43309i	0.145409	−	0.0647405i
$491$	−4.00249	−	4.44522i	−0.180630	−	0.200610i	0.646029	−	0.763312i	$-0.276428\pi$
$491$	−4.00249	−	4.44522i	−0.180630	−	0.200610i	−0.826659	+	0.562703i	$0.809762\pi$
$492$		0			0
$493$	−10.4318	−	4.64456i	−0.469827	−	0.209180i
$494$	51.7444			2.32809
$495$		0			0
$496$	40.8146			1.83263
$497$	−7.73576	−	3.44418i	−0.346996	−	0.154493i
$498$		0			0
$499$	19.6572	+	21.8316i	0.879979	+	0.977316i	0.999880	−	0.0154701i	$-0.00492449\pi$
$499$	19.6572	+	21.8316i	0.879979	+	0.977316i	−0.119901	+	0.992786i	$0.538258\pi$
$500$	10.6908	−	4.75985i	0.478107	−	0.212867i
$501$		0			0
$502$	−63.9410	+	13.5911i	−2.85382	+	0.606599i
$503$	−4.45188	−	13.7015i	−0.198500	−	0.610919i	−0.999918	−	0.0128145i	$-0.995921\pi$
$503$	−4.45188	−	13.7015i	−0.198500	−	0.610919i	0.801418	−	0.598104i	$-0.204079\pi$
$504$		0			0
$505$	3.65509			0.162649
$506$	−30.0724	−	37.9259i	−1.33688	−	1.68601i
$507$		0			0
$508$	0.615219	+	5.85342i	0.0272959	+	0.259703i
$509$	42.8833	+	9.11513i	1.90077	+	0.404021i	0.999568	−	0.0293818i	$-0.00935386\pi$
$509$	42.8833	+	9.11513i	1.90077	+	0.404021i	0.901200	+	0.433403i	$0.142687\pi$
$510$		0			0
$511$	−0.0692775	+	0.659132i	−0.00306466	+	0.0291583i
$512$	29.3882	+	21.3518i	1.29879	+	0.943624i
$513$		0			0
$514$	10.8957	+	33.5334i	0.480587	+	1.47909i
$515$	−2.73483	−	1.21763i	−0.120511	−	0.0536550i
$516$		0			0
$517$	−4.22944	−	3.49743i	−0.186010	−	0.153817i
$518$	−8.47019	+	14.6708i	−0.372159	+	0.644598i
$519$		0			0
$520$	7.41237	−	8.23227i	0.325054	−	0.361009i
$521$	6.23122	−	19.1777i	0.272995	−	0.840191i	−0.716748	−	0.697332i	$-0.754370\pi$
$521$	6.23122	−	19.1777i	0.272995	−	0.840191i	0.989743	−	0.142859i	$-0.0456296\pi$
$522$		0			0
$523$	−31.6906	−	23.0245i	−1.38573	−	1.00679i	−0.996318	−	0.0857293i	$-0.972678\pi$
$523$	−31.6906	−	23.0245i	−1.38573	−	1.00679i	−0.389413	−	0.921063i	$-0.627322\pi$
$524$	27.7153	−	5.89107i	1.21075	−	0.257352i
$525$		0			0
$526$	0.214895	+	2.04459i	0.00936987	+	0.0891484i
$527$	3.62973	−	6.28688i	0.158114	−	0.273861i
$528$		0			0
$529$	−3.90349	−	6.76105i	−0.169717	−	0.293959i
$530$	−4.40371	+	3.19948i	−0.191285	+	0.138977i
$531$		0			0
$532$	5.86914	−	18.0633i	0.254459	−	0.783145i
$533$	−6.73035	+	64.0350i	−0.291524	+	2.77366i
$534$		0			0
$535$	−1.72969	−	1.92101i	−0.0747809	−	0.0830526i
$536$	−69.0869	−	14.6849i	−2.98410	−	0.634290i
$537$		0			0
$538$	14.0207	+	24.2845i	0.604475	+	1.04698i
$539$	8.25253	+	16.6160i	0.355462	+	0.715703i
$540$		0			0
$541$	−14.5837	+	10.5957i	−0.627002	+	0.455544i	−0.855360	−	0.518034i	$-0.826664\pi$
$541$	−14.5837	+	10.5957i	−0.627002	+	0.455544i	0.228358	+	0.973577i	$0.426664\pi$
$542$	−43.2776	+	48.0646i	−1.85893	+	2.06455i
$543$		0			0
$544$	−19.7693	+	8.80187i	−0.847603	+	0.377377i
$545$	1.13133	−	0.503701i	0.0484609	−	0.0215762i
$546$		0			0
$547$	−0.0599338	+	0.0665633i	−0.00256259	+	0.00284604i	−0.744425	−	0.667706i	$-0.767276\pi$
$547$	−0.0599338	+	0.0665633i	−0.00256259	+	0.00284604i	0.741862	+	0.670552i	$0.233943\pi$
$548$	−0.531662	+	0.386275i	−0.0227115	+	0.0165008i
$549$		0			0
$550$	19.1724	+	38.6026i	0.817514	+	1.64602i
$551$	10.1466	+	17.5744i	0.432259	+	0.748695i
$552$		0			0
$553$	5.13028	+	1.09048i	0.218162	+	0.0463717i
$554$	−15.7852	−	17.5313i	−0.670651	−	0.744833i
$555$		0			0
$556$	−5.72383	+	54.4586i	−0.242744	+	2.30956i
$557$	−0.950270	+	2.92463i	−0.0402642	+	0.123921i	−0.969168	−	0.246400i	$-0.920752\pi$
$557$	−0.950270	+	2.92463i	−0.0402642	+	0.123921i	0.928904	+	0.370321i	$0.120752\pi$
$558$		0			0
$559$	59.3112	−	43.0921i	2.50859	−	1.82260i
$560$	−1.46488	−	2.53725i	−0.0619024	−	0.107218i
$561$		0			0
$562$	−21.9890	+	38.0860i	−0.927548	+	1.60656i
$563$	−1.86208	−	17.7165i	−0.0784773	−	0.746662i	−0.961029	−	0.276447i	$-0.910843\pi$
$563$	−1.86208	−	17.7165i	−0.0784773	−	0.746662i	0.882552	−	0.470215i	$-0.155824\pi$
$564$		0			0
$565$	0.477540	−	0.101504i	0.0200902	−	0.00427031i
$566$	12.4480	+	9.04401i	0.523229	+	0.380148i
$567$		0			0
$568$	16.9022	−	52.0197i	0.709202	−	2.18270i
$569$	−2.84313	+	3.15761i	−0.119190	+	0.132374i	−0.799787	−	0.600284i	$-0.795054\pi$
$569$	−2.84313	+	3.15761i	−0.119190	+	0.132374i	0.680596	+	0.732658i	$0.261721\pi$
$570$		0			0
$571$	22.5287	−	39.0208i	0.942795	−	1.63297i	0.182688	−	0.983171i	$-0.441520\pi$
$571$	22.5287	−	39.0208i	0.942795	−	1.63297i	0.760107	−	0.649798i	$-0.225146\pi$
$572$	75.8117	+	62.6907i	3.16985	+	2.62123i
$573$		0			0
$574$	30.3792	+	13.5257i	1.26800	+	0.564551i
$575$	8.47741	+	26.0908i	0.353533	+	1.08806i
$576$		0			0
$577$	12.3578	+	8.97845i	0.514461	+	0.373778i	0.814513	−	0.580145i	$-0.197004\pi$
$577$	12.3578	+	8.97845i	0.514461	+	0.373778i	−0.300052	+	0.953923i	$0.597004\pi$
$578$	3.74743	−	35.6544i	0.155873	−	1.48303i
$579$		0			0
$580$	7.16689	+	1.52337i	0.297589	+	0.0632545i
$581$	−1.91123	−	18.1841i	−0.0792910	−	0.754404i
$582$		0			0
$583$	−17.8079	−	22.4584i	−0.737526	−	0.930133i
$584$	−4.28101			−0.177150
$585$		0			0
$586$	12.1735	+	37.4663i	0.502884	+	1.54772i
$587$	41.6554	−	8.85413i	1.71930	−	0.365449i	0.760460	−	0.649385i	$-0.224974\pi$
$587$	41.6554	−	8.85413i	1.71930	−	0.365449i	0.958843	+	0.283936i	$0.0916404\pi$
$588$		0			0
$589$	−11.7856	+	5.24731i	−0.485619	+	0.216212i
$590$	1.65545	+	1.83857i	0.0681539	+	0.0756925i
$591$		0			0
$592$	−51.1900	−	22.7912i	−2.10389	−	0.936714i
$593$	−10.6230			−0.436236			−0.218118	−	0.975922i	$-0.569992\pi$
$593$	−10.6230			−0.436236			−0.218118	+	0.975922i	$0.569992\pi$
$594$		0			0
$595$	−0.521100			−0.0213630
$596$	17.7064	+	7.88339i	0.725282	+	0.322916i
$597$		0			0
$598$	58.9516	+	65.4724i	2.41071	+	2.67737i
$599$	31.7620	−	14.1414i	1.29776	−	0.577801i	0.362575	−	0.931955i	$-0.381898\pi$
$599$	31.7620	−	14.1414i	1.29776	−	0.577801i	0.935187	+	0.354154i	$0.115231\pi$
$600$		0			0
$601$	−8.88904	+	1.88942i	−0.362592	+	0.0770712i	−0.385605	−	0.922664i	$-0.626007\pi$
$601$	−8.88904	+	1.88942i	−0.362592	+	0.0770712i	0.0230134	+	0.999735i	$0.492674\pi$
$602$	−11.7005	−	36.0104i	−0.476876	−	1.46767i
$603$		0			0
$604$	−13.1534			−0.535204
$605$	2.30868	−	1.27045i	0.0938613	−	0.0516509i
$606$		0			0
$607$	1.63024	+	15.5107i	0.0661696	+	0.629561i	0.976476	+	0.215626i	$0.0691793\pi$
$607$	1.63024	+	15.5107i	0.0661696	+	0.629561i	−0.910306	+	0.413935i	$0.864154\pi$
$608$	37.6171	+	7.99576i	1.52557	+	0.324271i
$609$		0			0
$610$	−0.706189	+	6.71894i	−0.0285928	+	0.272042i
$611$	8.08184	+	5.87180i	0.326956	+	0.237548i
$612$		0			0
$613$	−8.59141	−	26.4417i	−0.347004	−	1.06797i	−0.960502	−	0.278272i	$-0.910238\pi$
$613$	−8.59141	−	26.4417i	−0.347004	−	1.06797i	0.613498	−	0.789696i	$-0.289762\pi$
$614$	15.6711	+	6.97723i	0.632435	+	0.281578i
$615$		0			0
$616$	25.4323	−	16.1472i	1.02470	−	0.650589i
$617$	4.01690	−	6.95747i	0.161714	−	0.280097i	−0.773769	−	0.633467i	$-0.781631\pi$
$617$	4.01690	−	6.95747i	0.161714	−	0.280097i	0.935484	+	0.353370i	$0.114964\pi$
$618$		0			0
$619$	2.40894	−	2.67540i	0.0968236	−	0.107533i	−0.692785	−	0.721144i	$-0.743617\pi$
$619$	2.40894	−	2.67540i	0.0968236	−	0.107533i	0.789609	+	0.613610i	$0.210283\pi$
$620$	−1.43940	+	4.43002i	−0.0578078	+	0.177914i
$621$		0			0
$622$	−30.6627	−	22.2777i	−1.22946	−	0.893256i
$623$	−0.0726059	+	0.0154329i	−0.00290889	+	0.000618304i
$624$		0			0
$625$	−2.52357	−	24.0102i	−0.100943	−	0.960408i
$626$	−20.6905	+	35.8370i	−0.826959	+	1.43234i
$627$		0			0
$628$	26.2242	+	45.4216i	1.04646	+	1.81252i
$629$	−8.06309	+	5.85818i	−0.321496	+	0.233581i
$630$		0			0
$631$	−6.25432	+	19.2488i	−0.248981	+	0.766283i	0.745976	+	0.665973i	$0.231984\pi$
$631$	−6.25432	+	19.2488i	−0.248981	+	0.766283i	−0.994956	+	0.100310i	$0.968016\pi$
$632$	−3.54128	+	33.6931i	−0.140865	+	1.34024i
$633$		0			0
$634$	51.5797	+	57.2851i	2.04849	+	2.27508i
$635$	−0.280703	−	0.0596653i	−0.0111394	−	0.00236775i
$636$		0			0
$637$	−16.8849	−	29.2454i	−0.669002	−	1.15875i
$638$	−9.04211	+	53.5271i	−0.357981	+	2.11916i
$639$		0			0
$640$	0.722676	−	0.525055i	0.0285663	−	0.0207546i
$641$	18.6545	−	20.7179i	0.736809	−	0.818310i	−0.251963	−	0.967737i	$-0.581076\pi$
$641$	18.6545	−	20.7179i	0.736809	−	0.818310i	0.988773	+	0.149427i	$0.0477429\pi$
$642$		0			0
$643$	0.0817314	−	0.0363892i	0.00322317	−	0.00143505i	−0.405124	−	0.914262i	$-0.632772\pi$
$643$	0.0817314	−	0.0363892i	0.00322317	−	0.00143505i	0.408348	+	0.912827i	$0.366105\pi$
$644$	29.5423	−	13.1531i	1.16413	−	0.518303i
$645$		0			0
$646$	10.5205	−	11.6842i	0.413925	−	0.459710i
$647$	−38.1698	+	27.7320i	−1.50061	+	1.09026i	−0.530473	+	0.847702i	$0.677986\pi$
$647$	−38.1698	+	27.7320i	−1.50061	+	1.09026i	−0.970137	+	0.242556i	$0.922014\pi$
$648$		0			0
$649$	−9.30565	+	9.11651i	−0.365279	+	0.357854i
$650$	−39.2272	−	67.9434i	−1.53862	−	2.66496i
$651$		0			0
$652$	−35.4845	−	7.54247i	−1.38968	−	0.295386i
$653$	−11.5631	−	12.8421i	−0.452499	−	0.502551i	0.473125	−	0.880995i	$-0.343126\pi$
$653$	−11.5631	−	12.8421i	−0.452499	−	0.502551i	−0.925624	+	0.378444i	$0.876459\pi$
$654$		0			0
$655$	−0.144410	+	1.37397i	−0.00564257	+	0.0536854i
$656$	−33.9907	+	104.613i	−1.32711	+	4.08443i
$657$		0			0
$658$	4.17401	−	3.03259i	0.162720	−	0.118223i
$659$	−6.04319	−	10.4671i	−0.235409	−	0.407741i	0.723982	−	0.689818i	$-0.242310\pi$
$659$	−6.04319	−	10.4671i	−0.235409	−	0.407741i	−0.959391	+	0.282078i	$0.908976\pi$
$660$		0			0
$661$	−19.2915	+	33.4139i	−0.750353	+	1.29965i	0.197299	+	0.980343i	$0.436783\pi$
$661$	−19.2915	+	33.4139i	−0.750353	+	1.29965i	−0.947652	+	0.319306i	$0.896550\pi$
$662$	−3.68600	−	35.0700i	−0.143260	−	1.36303i
$663$		0			0
$664$	115.524	−	24.5553i	4.48319	−	0.952931i
$665$	0.749199	+	0.544325i	0.0290527	+	0.0211080i
$666$		0			0
$667$	−10.6771	+	32.8608i	−0.413420	+	1.27237i
$668$	−33.9340	+	37.6875i	−1.31294	+	1.45817i
$669$		0			0
$670$	2.90404	−	5.02994i	0.112193	−	0.194324i
$671$	−35.5040	−	2.22639i	−1.37062	−	0.0859490i
$672$		0			0
$673$	26.3490	+	11.7313i	1.01568	+	0.452210i	0.845940	−	0.533279i	$-0.179040\pi$
$673$	26.3490	+	11.7313i	1.01568	+	0.452210i	0.169741	+	0.985489i	$0.445707\pi$
$674$	10.4993	+	32.3134i	0.404416	+	1.24467i
$675$		0			0
$676$	−93.1918	−	67.7078i	−3.58430	−	2.60415i
$677$	−0.736623	+	7.00850i	−0.0283107	+	0.269359i	0.971205	+	0.238245i	$0.0765721\pi$
$677$	−0.736623	+	7.00850i	−0.0283107	+	0.269359i	−0.999516	+	0.0311137i	$0.990095\pi$
$678$		0			0
$679$	7.06749	+	1.50224i	0.271225	+	0.0576507i
$680$	−0.351839	−	3.34753i	−0.0134924	−	0.128372i
$681$		0			0
$682$	−33.2416	−	9.27384i	−1.27288	−	0.355114i
$683$	−32.5733			−1.24638			−0.623191	−	0.782070i	$-0.714164\pi$
$683$	−32.5733			−1.24638			−0.623191	+	0.782070i	$0.714164\pi$
$684$		0			0
$685$	−0.00990166	−	0.0304742i	−0.000378323	−	0.00116436i
$686$	−38.4082	+	8.16393i	−1.46643	+	0.311700i
$687$		0			0
$688$	114.415	−	50.9409i	4.36204	−	1.94210i
$689$	34.9091	+	38.7705i	1.32993	+	1.47704i
$690$		0			0
$691$	39.4477	+	17.5632i	1.50066	+	0.668137i	0.982349	−	0.187055i	$-0.0598942\pi$
$691$	39.4477	+	17.5632i	1.50066	+	0.668137i	0.518311	+	0.855192i	$0.326561\pi$
$692$	78.9608			3.00164
$693$		0			0
$694$	−91.7519			−3.48285
$695$	−2.43910	−	1.08596i	−0.0925204	−	0.0411927i
$696$		0			0
$697$	13.0911	+	14.5392i	0.495862	+	0.550711i
$698$	−8.93604	+	3.97858i	−0.338234	+	0.150592i
$699$		0			0
$700$	−28.1676	+	5.98721i	−1.06463	+	0.226295i
$701$	−8.39620	−	25.8408i	−0.317120	−	0.975995i	−0.974873	−	0.222761i	$-0.928493\pi$
$701$	−8.39620	−	25.8408i	−0.317120	−	0.975995i	0.657753	−	0.753234i	$-0.271507\pi$
$702$		0			0
$703$	17.7118			0.668013
$704$	21.4139	+	27.0062i	0.807065	+	1.01783i
$705$		0			0
$706$	1.08630	+	10.3354i	0.0408833	+	0.388979i
$707$	−17.6975	−	3.76172i	−0.665583	−	0.141474i
$708$		0			0
$709$	2.24331	−	21.3437i	0.0842493	−	0.801578i	−0.868063	−	0.496454i	$-0.834635\pi$
$709$	2.24331	−	21.3437i	0.0842493	−	0.801578i	0.952312	−	0.305125i	$-0.0986981\pi$
$710$	3.63882	+	2.64376i	0.136563	+	0.0992185i
$711$		0			0
$712$	−0.148163	−	0.455998i	−0.00555263	−	0.0170892i
$713$	−20.0667	−	8.93426i	−0.751503	−	0.334590i
$714$		0			0
$715$	−4.04934	+	2.57096i	−0.151437	+	0.0961484i
$716$	9.12775	−	15.8097i	0.341120	−	0.590837i
$717$		0			0
$718$	−13.0262	+	14.4670i	−0.486133	+	0.539905i
$719$	−5.61293	+	17.2748i	−0.209327	+	0.644242i	0.790181	+	0.612874i	$0.209987\pi$
$719$	−5.61293	+	17.2748i	−0.209327	+	0.644242i	−0.999508	+	0.0313684i	$0.990013\pi$
$720$		0			0
$721$	11.9886	+	8.71023i	0.446479	+	0.324386i
$722$	21.5343	−	4.57727i	0.801426	−	0.170348i
$723$		0			0
$724$	7.76032	+	73.8345i	0.288410	+	2.74404i
$725$	15.3842	−	26.6461i	0.571353	−	0.989612i
$726$		0			0
$727$	12.7753	+	22.1275i	0.473810	+	0.820662i	0.999550	−	0.0299825i	$-0.00954516\pi$
$727$	12.7753	+	22.1275i	0.473810	+	0.820662i	−0.525741	+	0.850645i	$0.676212\pi$
$728$	−44.3622	+	32.2311i	−1.64417	+	1.19456i
$729$		0			0
$730$	0.108785	−	0.334807i	0.00402633	−	0.0123918i
$731$	2.32850	−	22.1542i	0.0861228	−	0.819404i
$732$		0			0
$733$	−27.2582	−	30.2734i	−1.00681	−	1.11817i	−0.992982	−	0.118267i	$-0.962266\pi$
$733$	−27.2582	−	30.2734i	−1.00681	−	1.11817i	−0.0138245	−	0.999904i	$-0.504401\pi$
$734$	65.3657	+	13.8939i	2.41269	+	0.512834i
$735$		0			0
$736$	32.7395	+	56.7065i	1.20679	+	2.09023i
$737$	27.1054	+	14.1633i	0.998439	+	0.521710i
$738$		0			0
$739$	25.9774	−	18.8737i	0.955596	−	0.694281i	0.00347186	−	0.999994i	$-0.498895\pi$
$739$	25.9774	−	18.8737i	0.955596	−	0.694281i	0.952124	+	0.305713i	$0.0988949\pi$
$740$	4.27907	−	4.75239i	0.157302	−	0.174701i
$741$		0			0
$742$	24.6151	−	10.9593i	0.903648	−	0.402330i
$743$	16.4094	−	7.30594i	0.602003	−	0.268029i	−0.0830233	−	0.996548i	$-0.526458\pi$
$743$	16.4094	−	7.30594i	0.602003	−	0.268029i	0.685026	+	0.728519i	$0.259791\pi$
$744$		0			0
$745$	−0.632352	+	0.702298i	−0.0231676	+	0.0257302i
$746$	10.1566	−	7.37920i	0.371859	−	0.270172i
$747$		0			0
$748$	29.5698	−	4.37270i	1.08118	−	0.159882i
$749$	6.39789	+	11.0815i	0.233774	+	0.404908i
$750$		0			0
$751$	24.3399	+	5.17361i	0.888176	+	0.188788i	0.629337	−	0.777133i	$-0.283327\pi$
$751$	24.3399	+	5.17361i	0.888176	+	0.188788i	0.258839	+	0.965920i	$0.416660\pi$
$752$	11.4193	+	12.6824i	0.416418	+	0.462479i
$753$		0			0
$754$	10.3286	−	98.2702i	0.376146	−	3.57879i
$755$	0.198184	−	0.609947i	0.00721265	−	0.0221983i
$756$		0			0
$757$	26.3079	−	19.1138i	0.956178	−	0.694704i	0.00391833	−	0.999992i	$-0.498753\pi$
$757$	26.3079	−	19.1138i	0.956178	−	0.694704i	0.952260	+	0.305288i	$0.0987528\pi$
$758$	22.9387	+	39.7311i	0.833173	+	1.44310i
$759$		0			0
$760$	−2.99088	+	5.18035i	−0.108491	+	0.187911i
$761$	0.922270	+	8.77482i	0.0334323	+	0.318087i	0.998439	+	0.0558602i	$0.0177901\pi$
$761$	0.922270	+	8.77482i	0.0334323	+	0.318087i	−0.965006	+	0.262227i	$0.915543\pi$
$762$		0			0
$763$	−5.99617	+	1.27452i	−0.217076	+	0.0461409i
$764$	−47.6345	−	34.6085i	−1.72336	−	1.25209i
$765$		0			0
$766$	2.75285	−	8.47239i	0.0994644	−	0.306120i
$767$	15.8666	−	17.6216i	0.572909	−	0.636280i
$768$		0			0
$769$	13.4824	−	23.3523i	0.486189	−	0.842104i	−0.513685	−	0.857979i	$-0.671720\pi$
$769$	13.4824	−	23.3523i	0.486189	−	0.842104i	0.999874	+	0.0158750i	$0.00505339\pi$
$770$	0.616565	+	2.39931i	0.0222195	+	0.0864653i
$771$		0			0
$772$	−101.140	−	45.0303i	−3.64010	−	1.62068i
$773$	−8.24081	−	25.3626i	−0.296401	−	0.912230i	−0.982747	−	0.184954i	$-0.940786\pi$
$773$	−8.24081	−	25.3626i	−0.296401	−	0.912230i	0.686346	−	0.727276i	$-0.259214\pi$
$774$		0			0
$775$	15.8247	+	11.4973i	0.568439	+	0.412995i
$776$	−4.87848	+	46.4156i	−0.175127	+	1.66622i
$777$		0			0
$778$	−48.2330	−	10.2522i	−1.72924	−	0.367560i
$779$	−3.63429	−	34.5780i	−0.130212	−	1.23888i
$780$		0			0
$781$	−13.1022	+	19.7292i	−0.468833	+	0.705966i
$782$	26.7700			0.957294
$783$		0			0
$784$	−17.8273	−	54.8666i	−0.636688	−	1.95952i
$785$	−2.50140	+	0.531690i	−0.0892790	+	0.0189768i
$786$		0			0
$787$	−15.1150	+	6.72964i	−0.538792	+	0.239886i	−0.658046	−	0.752978i	$-0.728617\pi$
$787$	−15.1150	+	6.72964i	−0.538792	+	0.239886i	0.119253	+	0.992864i	$0.461950\pi$
$788$	−32.7216	−	36.3410i	−1.16566	−	1.29459i
$789$		0			0
$790$	−2.54506	−	1.13313i	−0.0905490	−	0.0403150i
$791$	−2.41666			−0.0859264
$792$		0			0
$793$	64.7520			2.29941
$794$	25.7389	+	11.4597i	0.913441	+	0.406690i
$795$		0			0
$796$	−51.1604	−	56.8194i	−1.81333	−	2.01391i
$797$	40.6697	−	18.1073i	1.44059	−	0.641394i	0.470121	−	0.882602i	$-0.344210\pi$
$797$	40.6697	−	18.1073i	1.44059	−	0.641394i	0.970473	+	0.241209i	$0.0775438\pi$
$798$		0			0
$799$	2.96907	−	0.631096i	0.105038	−	0.0223266i
$800$	−18.0184	−	55.4550i	−0.637047	−	1.96063i
$801$		0			0
$802$	7.44789			0.262994
$803$	1.78548	+	0.498120i	0.0630083	+	0.0175783i
$804$		0			0
$805$	0.164815	+	1.56811i	0.00580896	+	0.0552685i
$806$	61.4448	+	13.0605i	2.16430	+	0.460036i
$807$		0			0
$808$	12.2161	−	116.228i	0.429759	−	4.08889i
$809$	39.7013	+	28.8447i	1.39582	+	1.01413i	0.995198	+	0.0978851i	$0.0312078\pi$
$809$	39.7013	+	28.8447i	1.39582	+	1.01413i	0.400627	+	0.916241i	$0.368792\pi$
$810$		0			0
$811$	−13.2047	−	40.6400i	−0.463681	−	1.42706i	−0.860634	−	0.509224i	$-0.829933\pi$
$811$	−13.2047	−	40.6400i	−0.463681	−	1.42706i	0.396953	−	0.917839i	$-0.370067\pi$
$812$	−33.1334	−	14.7519i	−1.16275	−	0.517692i
$813$		0			0
$814$	36.5132	+	30.1937i	1.27979	+	1.05829i
$815$	0.884408	−	1.53184i	0.0309795	−	0.0536580i
$816$		0			0
$817$	−26.4894	+	29.4195i	−0.926747	+	1.02926i
$818$	19.1292	−	58.8737i	0.668838	−	2.05847i
$819$		0			0
$820$	−10.1559	−	7.37871i	−0.354660	−	0.257676i
$821$	−28.3438	+	6.02466i	−0.989205	+	0.210262i	−0.673976	−	0.738753i	$-0.735415\pi$
$821$	−28.3438	+	6.02466i	−0.989205	+	0.210262i	−0.315229	+	0.949015i	$0.602081\pi$
$822$		0			0
$823$	−2.01003	−	19.1241i	−0.0700652	−	0.666626i	−0.972036	−	0.234830i	$-0.924547\pi$
$823$	−2.01003	−	19.1241i	−0.0700652	−	0.666626i	0.901971	−	0.431796i	$-0.142120\pi$
$824$	−47.8597	+	82.8954i	−1.66727	+	2.88780i
$825$		0			0
$826$	−6.12330	−	10.6059i	−0.213057	−	0.369025i
$827$	35.2773	−	25.6305i	1.22671	−	0.891259i	0.230074	−	0.973173i	$-0.426103\pi$
$827$	35.2773	−	25.6305i	1.22671	−	0.891259i	0.996639	+	0.0819138i	$0.0261032\pi$
$828$		0			0
$829$	6.68209	−	20.5654i	0.232078	−	0.714264i	−0.765417	−	0.643535i	$-0.777467\pi$
$829$	6.68209	−	20.5654i	0.232078	−	0.714264i	0.997496	−	0.0707296i	$-0.0225327\pi$
$830$	−1.01518	+	9.65877i	−0.0352373	+	0.335261i
$831$		0			0
$832$	−41.9781	−	46.6214i	−1.45533	−	1.61630i
$833$	−10.0368	−	2.13339i	−0.347755	−	0.0739175i
$834$		0			0
$835$	−1.23635	−	2.14142i	−0.0427857	−	0.0741069i
$836$	−47.0809	−	24.6010i	−1.62833	−	0.850843i
$837$		0			0
$838$	−44.9198	+	32.6361i	−1.55173	+	1.12740i
$839$	14.8571	−	16.5005i	0.512925	−	0.569660i	−0.429931	−	0.902862i	$-0.641462\pi$
$839$	14.8571	−	16.5005i	0.512925	−	0.569660i	0.942856	+	0.333201i	$0.108129\pi$
$840$		0			0
$841$	8.90890	−	3.96650i	0.307203	−	0.136776i
$842$	−56.4880	+	25.1501i	−1.94671	+	0.866729i
$843$		0			0
$844$	−7.87337	+	8.74426i	−0.271012	+	0.300990i
$845$	4.54387	−	3.30131i	0.156314	−	0.113569i
$846$		0			0
$847$	−12.4859	+	3.77531i	−0.429020	+	0.129721i
$848$	44.5628	+	77.1851i	1.53029	+	2.65055i
$849$		0			0
$850$	−23.3177	−	4.95632i	−0.799789	−	0.170000i
$851$	20.1788	+	22.4108i	0.691720	+	0.768233i
$852$		0			0
$853$	−2.75078	+	26.1720i	−0.0941850	+	0.896111i	0.840781	+	0.541375i	$0.182096\pi$
$853$	−2.75078	+	26.1720i	−0.0941850	+	0.896111i	−0.934966	+	0.354736i	$0.884571\pi$
$854$	10.3342	−	31.8055i	0.353630	−	1.08836i
$855$		0			0
$856$	−66.8672	+	48.5819i	−2.28547	+	1.66049i
$857$	−13.9851	−	24.2229i	−0.477721	−	0.827437i	0.521953	−	0.852974i	$-0.325204\pi$
$857$	−13.9851	−	24.2229i	−0.477721	−	0.827437i	−0.999674	+	0.0255371i	$0.991870\pi$
$858$		0			0
$859$	−7.69037	+	13.3201i	−0.262392	+	0.454476i	−0.966877	−	0.255243i	$-0.917845\pi$
$859$	−7.69037	+	13.3201i	−0.262392	+	0.454476i	0.704485	+	0.709719i	$0.251178\pi$
$860$	1.49407	+	14.2152i	0.0509475	+	0.484733i
$861$		0			0
$862$	12.8075	−	2.72231i	0.436225	−	0.0927224i
$863$	−26.5699	−	19.3041i	−0.904449	−	0.657121i	0.0351559	−	0.999382i	$-0.488807\pi$
$863$	−26.5699	−	19.3041i	−0.904449	−	0.657121i	−0.939605	+	0.342261i	$0.888807\pi$
$864$		0			0
$865$	−1.18971	+	3.66156i	−0.0404514	+	0.124497i
$866$	−45.0134	+	49.9924i	−1.52962	+	1.69881i
$867$		0			0
$868$	11.5287	−	19.9682i	0.391309	−	0.677767i
$869$	5.39733	−	13.6403i	0.183092	−	0.462716i
$870$		0			0
$871$	−50.8545	−	22.6419i	−1.72314	−	0.767191i
$872$	−12.2360	−	37.6586i	−0.414364	−	1.27528i
$873$		0			0
$874$	−38.4880	−	27.9632i	−1.30188	−	0.945868i
$875$	0.295238	−	2.80900i	0.00998086	−	0.0949615i
$876$		0			0
$877$	−48.9243	−	10.3992i	−1.65206	−	0.351155i	−0.714674	−	0.699457i	$-0.753425\pi$
$877$	−48.9243	−	10.3992i	−1.65206	−	0.351155i	−0.937382	+	0.348302i	$0.886758\pi$
$878$	1.28075	+	12.1855i	0.0432233	+	0.411242i
$879$		0			0
$880$	−7.67966	+	2.85784i	−0.258881	+	0.0963377i
$881$	32.0798			1.08080			0.540399	−	0.841409i	$-0.318273\pi$
$881$	32.0798			1.08080			0.540399	+	0.841409i	$0.318273\pi$
$882$		0			0
$883$	14.4035	+	44.3294i	0.484716	+	1.49180i	0.832392	+	0.554188i	$0.186971\pi$
$883$	14.4035	+	44.3294i	0.484716	+	1.49180i	−0.347676	+	0.937615i	$0.613029\pi$
$884$	−53.2199	+	11.3122i	−1.78998	+	0.380472i
$885$		0			0
$886$	−55.5428	+	24.7293i	−1.86600	+	0.830796i
$887$	−19.6390	−	21.8113i	−0.659414	−	0.732353i	0.316961	−	0.948439i	$-0.397338\pi$
$887$	−19.6390	−	21.8113i	−0.659414	−	0.732353i	−0.976374	+	0.216086i	$0.930671\pi$
$888$		0			0
$889$	1.29773	+	0.577785i	0.0435243	+	0.0193783i
$890$	0.0394273			0.00132161
$891$		0			0
$892$	63.7925			2.13593
$893$	−4.92794	−	2.19406i	−0.164907	−	0.0734214i
$894$		0			0
$895$	0.595597	+	0.661477i	0.0199086	+	0.0221107i
$896$	−4.03949	+	1.79849i	−0.134950	+	0.0600835i
$897$		0			0
$898$	−35.3991	+	7.52432i	−1.18128	+	0.251090i
$899$	7.61290	+	23.4301i	0.253904	+	0.781437i
$900$		0			0
$901$	15.8523			0.528116
$902$	51.4537	−	77.4786i	1.71322	−	2.57976i
$903$		0			0
$904$	−1.63169	−	15.5245i	−0.0542693	−	0.516338i
$905$	−3.54077	−	0.752613i	−0.117699	−	0.0250177i
$906$		0			0
$907$	2.62571	−	24.9819i	0.0871852	−	0.829512i	−0.860316	−	0.509761i	$-0.829734\pi$
$907$	2.62571	−	24.9819i	0.0871852	−	0.829512i	0.947502	−	0.319751i	$-0.103599\pi$
$908$	−73.3389	−	53.2838i	−2.43384	−	1.76829i
$909$		0			0
$910$	−1.39341	−	4.28848i	−0.0461912	−	0.142162i
$911$	−2.52956	−	1.12623i	−0.0838079	−	0.0373137i	0.364405	−	0.931241i	$-0.381273\pi$
$911$	−2.52956	−	1.12623i	−0.0838079	−	0.0373137i	−0.448212	+	0.893927i	$0.647939\pi$
$912$		0			0
$913$	−51.0385	−	3.20054i	−1.68913	−	0.105922i
$914$	−14.2502	+	24.6820i	−0.471354	+	0.816408i
$915$		0			0
$916$	66.2111	−	73.5349i	2.18768	−	2.42966i
$917$	2.11327	−	6.50398i	0.0697863	−	0.214780i
$918$		0			0
$919$	−9.58156	−	6.96141i	−0.316066	−	0.229636i	0.418429	−	0.908250i	$-0.362581\pi$
$919$	−9.58156	−	6.96141i	−0.316066	−	0.229636i	−0.734495	+	0.678614i	$0.762581\pi$
$920$	−9.96219	+	2.11753i	−0.328444	+	0.0698128i
$921$		0			0
$922$	−0.804698	−	7.65619i	−0.0265013	−	0.252143i
$923$	21.5546	−	37.3337i	0.709478	−	1.22885i
$924$		0			0
$925$	−13.4272	−	23.2566i	−0.441484	−	0.764673i
$926$	57.6105	−	41.8565i	1.89320	−	1.37549i
$927$		0			0
$928$	22.6938	−	69.8443i	0.744960	−	2.29275i
$929$	1.17684	−	11.1968i	0.0386107	−	0.367356i	−0.958108	−	0.286408i	$-0.907539\pi$
$929$	1.17684	−	11.1968i	0.0386107	−	0.367356i	0.996718	−	0.0809480i	$-0.0257948\pi$
$930$		0			0
$931$	12.2017	+	13.5514i	0.399895	+	0.444128i
$932$	35.3669	+	7.51747i	1.15848	+	0.246243i
$933$		0			0
$934$	14.8642	+	25.7455i	0.486371	+	0.842419i
$935$	−0.242762	+	1.43709i	−0.00793916	+	0.0469979i
$936$		0			0
$937$	25.6860	−	18.6619i	0.839123	−	0.609659i	−0.0830022	−	0.996549i	$-0.526451\pi$
$937$	25.6860	−	18.6619i	0.839123	−	0.609659i	0.922126	+	0.386891i	$0.126451\pi$
$938$	−19.2377	+	21.3656i	−0.628133	+	0.697612i
$939$		0			0
$940$	−1.77927	+	0.792181i	−0.0580333	+	0.0258381i
$941$	−11.5197	+	5.12890i	−0.375532	+	0.167197i	−0.585818	−	0.810442i	$-0.699227\pi$
$941$	−11.5197	+	5.12890i	−0.375532	+	0.167197i	0.210287	+	0.977640i	$0.432560\pi$
$942$		0			0
$943$	39.6112	−	43.9927i	1.28992	−	1.43260i
$944$	32.7721	−	23.8104i	1.06664	−	0.774961i
$945$		0			0
$946$	−104.760	+	15.4917i	−3.40606	+	0.503678i
$947$	−0.184885	−	0.320230i	−0.00600796	−	0.0104061i	0.863006	−	0.505194i	$-0.168579\pi$
$947$	−0.184885	−	0.320230i	−0.00600796	−	0.0104061i	−0.869014	+	0.494788i	$0.835246\pi$
$948$		0			0
$949$	−3.30034	−	0.701510i	−0.107134	−	0.0227720i
$950$	28.3472	+	31.4828i	0.919705	+	1.02144i
$951$		0			0
$952$	−1.74162	+	16.5704i	−0.0564463	+	0.537051i
$953$	−5.23478	+	16.1110i	−0.169571	+	0.521886i	−0.999344	−	0.0362151i	$-0.988470\pi$
$953$	−5.23478	+	16.1110i	−0.169571	+	0.521886i	0.829773	+	0.558101i	$0.188470\pi$
$954$		0			0
$955$	2.32257	−	1.68745i	0.0751567	−	0.0546046i
$956$	−23.6469	−	40.9576i	−0.764794	−	1.32466i
$957$		0			0
$958$	39.9467	−	69.1896i	1.29062	−	2.23542i
$959$	0.0165794	+	0.157743i	0.000535378	+	0.00509378i
$960$		0			0
$961$	15.0031	−	3.18900i	0.483969	−	0.102871i
$962$	−69.7714	−	50.6919i	−2.24952	−	1.63437i
$963$		0			0
$964$	−40.3299	+	124.123i	−1.29894	+	3.99772i
$965$	3.61202	−	4.01155i	0.116275	−	0.129137i
$966$		0			0
$967$	−12.4080	+	21.4914i	−0.399016	+	0.691115i	−0.993605	−	0.112914i	$-0.963981\pi$
$967$	−12.4080	+	21.4914i	−0.399016	+	0.691115i	0.594589	+	0.804030i	$0.297315\pi$
$968$	−32.6828	−	77.6598i	−1.05046	−	2.49608i
$969$		0			0
$970$	−3.50607	−	1.56100i	−0.112573	−	0.0501208i
$971$	−3.75006	−	11.5415i	−0.120345	−	0.370384i	0.872679	−	0.488294i	$-0.162381\pi$
$971$	−3.75006	−	11.5415i	−0.120345	−	0.370384i	−0.993024	+	0.117910i	$0.962381\pi$
$972$		0			0
$973$	10.6922	+	7.76834i	0.342776	+	0.249042i
$974$	0.879377	−	8.36671i	0.0281771	−	0.268087i
$975$		0			0
$976$	108.201	+	22.9989i	3.46344	+	0.736176i
$977$	−3.69784	−	35.1826i	−0.118305	−	1.12559i	−0.879112	−	0.476615i	$-0.841864\pi$
$977$	−3.69784	−	35.1826i	−0.118305	−	1.12559i	0.760808	−	0.648978i	$-0.224803\pi$
$978$		0			0
$979$	0.00873629	+	0.207422i	0.000279213	+	0.00662925i
$980$	6.58394			0.210316
$981$		0			0
$982$	−4.86006	−	14.9577i	−0.155091	−	0.477321i
$983$	−21.9946	+	4.67509i	−0.701518	+	0.149112i	−0.544843	−	0.838538i	$-0.683411\pi$
$983$	−21.9946	+	4.67509i	−0.701518	+	0.149112i	−0.156675	+	0.987650i	$0.550077\pi$
$984$		0			0
$985$	2.17822	−	0.969805i	0.0694038	−	0.0309005i
$986$	−20.0901	−	22.3123i	−0.639799	−	0.710569i
$987$		0			0
$988$	88.3322	+	39.3280i	2.81022	+	1.25119i
$989$	−67.4036			−2.14331
$990$		0			0
$991$	16.2761			0.517028			0.258514	−	0.966008i	$-0.416767\pi$
$991$	16.2761			0.517028			0.258514	+	0.966008i	$0.416767\pi$
$992$	42.6509	+	18.9894i	1.35417	+	0.602914i
$993$		0			0
$994$	−14.8979	−	16.5457i	−0.472531	−	0.524799i
$995$	3.40566	−	1.51630i	0.107967	−	0.0480698i
$996$		0			0
$997$	−4.52313	+	0.961421i	−0.143249	+	0.0304485i	−0.278978	−	0.960297i	$-0.589996\pi$
$997$	−4.52313	+	0.961421i	−0.143249	+	0.0304485i	0.135729	+	0.990746i	$0.456662\pi$
$998$	23.8690	+	73.4612i	0.755560	+	2.32537i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.k.190.6		48
3.2	odd	2		891.2.n.j.190.1		48
9.2	odd	6		891.2.n.j.784.6		48
9.4	even	3		891.2.f.c.487.1	✓	24
9.5	odd	6		891.2.f.d.487.6	yes	24
9.7	even	3	inner	891.2.n.k.784.1		48
11.4	even	5	inner	891.2.n.k.433.1		48
33.26	odd	10		891.2.n.j.433.6		48
99.4	even	15		891.2.f.c.730.1	yes	24
99.13	odd	30		9801.2.a.cl.1.1		12
99.31	even	15		9801.2.a.cg.1.12		12
99.59	odd	30		891.2.f.d.730.6	yes	24
99.68	even	30		9801.2.a.cf.1.12		12
99.70	even	15	inner	891.2.n.k.136.6		48
99.86	odd	30		9801.2.a.ck.1.1		12
99.92	odd	30		891.2.n.j.136.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.c.487.1	✓	24	9.4	even	3
891.2.f.c.730.1	yes	24	99.4	even	15
891.2.f.d.487.6	yes	24	9.5	odd	6
891.2.f.d.730.6	yes	24	99.59	odd	30
891.2.n.j.136.1		48	99.92	odd	30
891.2.n.j.190.1		48	3.2	odd	2
891.2.n.j.433.6		48	33.26	odd	10
891.2.n.j.784.6		48	9.2	odd	6
891.2.n.k.136.6		48	99.70	even	15	inner
891.2.n.k.190.6		48	1.1	even	1	trivial
891.2.n.k.433.1		48	11.4	even	5	inner
891.2.n.k.784.1		48	9.7	even	3	inner
9801.2.a.cf.1.12		12	99.68	even	30
9801.2.a.cg.1.12		12	99.31	even	15
9801.2.a.ck.1.1		12	99.86	odd	30
9801.2.a.cl.1.1		12	99.13	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.40198 + 1.06943i) q^{2} +(3.28758 + 3.65123i) q^{4} +(-0.218849 + 0.0974376i) q^{5} +(1.15992 - 0.246548i) q^{7} +(2.36698 + 7.28482i) q^{8} -0.629874 q^{10} +(-0.139567 - 3.31369i) q^{11} +(0.631037 + 6.00392i) q^{13} +(3.04977 + 0.648249i) q^{14} +(-1.07803 + 10.2567i) q^{16} +(1.48403 + 1.07821i) q^{17} +(-1.00736 - 3.10034i) q^{19} +(-1.07525 - 0.478732i) q^{20} +(3.20853 - 8.10868i) q^{22} +(2.77520 - 4.80679i) q^{23} +(-3.30725 + 3.67308i) q^{25} +(-4.90504 + 15.0962i) q^{26} +(4.71353 + 3.42458i) q^{28} +(-6.08908 + 1.29427i) q^{29} +(-0.413671 - 3.93582i) q^{31} +(-5.89858 + 10.2166i) q^{32} +(2.41154 + 4.17691i) q^{34} +(-0.229824 + 0.166977i) q^{35} +(-1.67897 + 5.16733i) q^{37} +(0.895937 - 8.52427i) q^{38} +(-1.22783 - 1.36364i) q^{40} +(10.4325 + 2.21749i) q^{41} +(-6.07195 - 10.5169i) q^{43} +(11.6402 - 11.4036i) q^{44} +(11.8065 - 8.57795i) q^{46} +(1.10724 - 1.22972i) q^{47} +(-5.11019 + 2.27520i) q^{49} +(-11.8721 + 5.28579i) q^{50} +(-19.8471 + 22.0424i) q^{52} +(6.99142 - 5.07956i) q^{53} +(0.353422 + 0.711596i) q^{55} +(4.54157 + 7.86622i) q^{56} +(-16.0100 - 3.40303i) q^{58} +(-2.62823 - 2.91894i) q^{59} +(1.12116 - 10.6671i) q^{61} +(3.21546 - 9.89616i) q^{62} +(-8.40715 + 6.10815i) q^{64} +(-0.723109 - 1.25246i) q^{65} +(-4.61051 + 7.98564i) q^{67} +(0.942072 + 8.96322i) q^{68} +(-0.730603 + 0.155294i) q^{70} +(-5.77707 - 4.19728i) q^{71} +(-0.172710 + 0.531546i) q^{73} +(-9.55896 + 10.6163i) q^{74} +(8.00827 - 13.8707i) q^{76} +(-0.978871 - 3.80920i) q^{77} +(4.04058 + 1.79898i) q^{79} +(-0.763468 - 2.34971i) q^{80} +(22.6872 + 16.4832i) q^{82} +(1.61172 - 15.3345i) q^{83} +(-0.429835 - 0.0913643i) q^{85} +(-3.33759 - 31.7550i) q^{86} +(23.8092 - 8.86015i) q^{88} -0.0625956 q^{89} +(2.21221 + 6.80848i) q^{91} +(26.6744 - 5.66982i) q^{92} +(3.97468 - 1.76964i) q^{94} +(0.522549 + 0.580350i) q^{95} +(5.56631 + 2.47828i) q^{97} -14.7078 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} + 8 q^{4} - 4 q^{5} - 7 q^{7} + 20 q^{8} - 32 q^{10} - 5 q^{11} - 7 q^{13} - 13 q^{14} - 2 q^{16} - 10 q^{17} + 8 q^{19} - 27 q^{20} + 2 q^{22} - 6 q^{23} + 2 q^{25} - 68 q^{26} - 18 q^{28}+ \cdots + 136 q^{98}+O(q^{100}) \) 48 * q + 2 * q^2 + 8 * q^4 - 4 * q^5 - 7 * q^7 + 20 * q^8 - 32 * q^10 - 5 * q^11 - 7 * q^13 - 13 * q^14 - 2 * q^16 - 10 * q^17 + 8 * q^19 - 27 * q^20 + 2 * q^22 - 6 * q^23 + 2 * q^25 - 68 * q^26 - 18 * q^28 - 22 * q^29 - 2 * q^31 - 18 * q^32 + 42 * q^34 + 12 * q^37 + 5 * q^38 - 53 * q^40 - 10 * q^41 + 30 * q^43 + 118 * q^44 + 62 * q^46 - 4 * q^47 + 3 * q^49 - 9 * q^50 + 26 * q^52 + 34 * q^53 + 24 * q^55 + 48 * q^56 - 53 * q^58 - 11 * q^59 - 3 * q^61 - 4 * q^62 + 76 * q^64 + 68 * q^65 + 14 * q^67 - 22 * q^68 + 20 * q^70 - 72 * q^71 + 70 * q^73 - 3 * q^74 + 102 * q^76 + 88 * q^77 + 9 * q^79 - 74 * q^80 - 12 * q^82 - 32 * q^83 + 45 * q^85 + 110 * q^86 - 54 * q^88 + 68 * q^89 + 26 * q^91 + q^92 + 25 * q^94 + 84 * q^95 - 15 * q^97 + 136 * q^98

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