LMFDB - Embedded newform 891.2.n.j.190.1

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			190.1
Character	$\chi$	$=$	891.190
Dual form			891.2.n.j.136.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.40198 - 1.06943i) q^{2} +(3.28758 + 3.65123i) q^{4} +(0.218849 - 0.0974376i) q^{5} +(1.15992 - 0.246548i) q^{7} +(-2.36698 - 7.28482i) q^{8} -0.629874 q^{10} +(0.139567 + 3.31369i) q^{11} +(0.631037 + 6.00392i) q^{13} +(-3.04977 - 0.648249i) q^{14} +(-1.07803 + 10.2567i) q^{16} +(-1.48403 - 1.07821i) q^{17} +(-1.00736 - 3.10034i) q^{19} +(1.07525 + 0.478732i) q^{20} +(3.20853 - 8.10868i) q^{22} +(-2.77520 + 4.80679i) q^{23} +(-3.30725 + 3.67308i) q^{25} +(4.90504 - 15.0962i) q^{26} +(4.71353 + 3.42458i) q^{28} +(6.08908 - 1.29427i) q^{29} +(-0.413671 - 3.93582i) q^{31} +(5.89858 - 10.2166i) q^{32} +(2.41154 + 4.17691i) q^{34} +(0.229824 - 0.166977i) q^{35} +(-1.67897 + 5.16733i) q^{37} +(-0.895937 + 8.52427i) q^{38} +(-1.22783 - 1.36364i) q^{40} +(-10.4325 - 2.21749i) q^{41} +(-6.07195 - 10.5169i) q^{43} +(-11.6402 + 11.4036i) q^{44} +(11.8065 - 8.57795i) q^{46} +(-1.10724 + 1.22972i) q^{47} +(-5.11019 + 2.27520i) q^{49} +(11.8721 - 5.28579i) q^{50} +(-19.8471 + 22.0424i) q^{52} +(-6.99142 + 5.07956i) q^{53} +(0.353422 + 0.711596i) q^{55} +(-4.54157 - 7.86622i) q^{56} +(-16.0100 - 3.40303i) q^{58} +(2.62823 + 2.91894i) q^{59} +(1.12116 - 10.6671i) q^{61} +(-3.21546 + 9.89616i) q^{62} +(-8.40715 + 6.10815i) q^{64} +(0.723109 + 1.25246i) q^{65} +(-4.61051 + 7.98564i) q^{67} +(-0.942072 - 8.96322i) q^{68} +(-0.730603 + 0.155294i) q^{70} +(5.77707 + 4.19728i) q^{71} +(-0.172710 + 0.531546i) q^{73} +(9.55896 - 10.6163i) q^{74} +(8.00827 - 13.8707i) q^{76} +(0.978871 + 3.80920i) q^{77} +(4.04058 + 1.79898i) q^{79} +(0.763468 + 2.34971i) q^{80} +(22.6872 + 16.4832i) q^{82} +(-1.61172 + 15.3345i) q^{83} +(-0.429835 - 0.0913643i) q^{85} +(3.33759 + 31.7550i) q^{86} +(23.8092 - 8.86015i) q^{88} +0.0625956 q^{89} +(2.21221 + 6.80848i) q^{91} +(-26.6744 + 5.66982i) q^{92} +(3.97468 - 1.76964i) q^{94} +(-0.522549 - 0.580350i) q^{95} +(5.56631 + 2.47828i) q^{97} +14.7078 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.986821\pi$
$2$	−2.40198	−	1.06943i	−1.69846	−	0.756203i	−0.699316	−	0.714812i	$-0.746512\pi$
$3$		0			0
$3$		0			0
$4$	3.28758	+	3.65123i	1.64379	+	1.82561i
$5$	0.218849	−	0.0974376i	0.0978720	−	0.0435754i	−0.357217	−	0.934022i	$-0.616274\pi$
$5$	0.218849	−	0.0974376i	0.0978720	−	0.0435754i	0.455089	+	0.890446i	$0.349608\pi$
$6$		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	0.393093	−	0.919499i	$-0.371405\pi$
$17$	−1.48403	−	1.07821i	−0.359929	−	0.261504i	−0.753023	+	0.657995i	$0.771405\pi$
$18$		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	$0.363095\pi$
$23$	−2.77520	+	4.80679i	−0.578670	+	1.00229i	−0.995632	+	0.0933616i	$0.970239\pi$
$24$		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	0.395691	−	0.918384i	$-0.370505\pi$
$29$	6.08908	−	1.29427i	1.13071	−	0.240341i	0.735022	+	0.678043i	$0.237172\pi$
$30$		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	−0.699556	−	0.714578i	$-0.746619\pi$
$41$	−10.4325	−	2.21749i	−1.62928	−	0.346313i	−0.929721	+	0.368265i	$0.879952\pi$
$42$		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	−0.818467	−	0.574553i	$-0.805176\pi$
$47$	−1.10724	+	1.22972i	−0.161508	+	0.179373i	0.656959	+	0.753926i	$0.271842\pi$
$48$		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	−0.953231	−	0.302243i	$-0.902265\pi$
$53$	−6.99142	+	5.07956i	−0.960345	+	0.697732i	−0.00711436	+	0.999975i	$0.502265\pi$
$54$		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	0.889527	−	0.456883i	$-0.151034\pi$
$59$	2.62823	+	2.91894i	0.342166	+	0.380014i	−0.547361	+	0.836897i	$0.684367\pi$
$60$		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	0.875215	−	0.483735i	$-0.160720\pi$
$71$	5.77707	+	4.19728i	0.685612	+	0.498126i	−0.189603	+	0.981861i	$0.560720\pi$
$72$		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	$0.354463\pi$
$83$	−1.61172	+	15.3345i	−0.176909	+	1.68318i	−0.618364	+	0.785892i	$0.712204\pi$
$84$		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	$-0.498944\pi$
$89$	0.0625956			0.00663512			0.00331756	+	0.999994i	$0.498944\pi$
$90$		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	0.958243	−	0.285954i	$-0.0923106\pi$
$101$	13.9385	+	6.20580i	1.38693	+	0.617500i	0.428684	+	0.903454i	$0.358977\pi$
$102$		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	$-0.925343\pi$
$107$	−3.33446	−	10.2624i	−0.322354	−	0.992105i	0.650266	−	0.759706i	$-0.274657\pi$
$108$		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	0.300716	−	0.953714i	$-0.402774\pi$
$113$	1.99341	+	0.423712i	0.187524	+	0.0398594i	−0.113192	+	0.993573i	$0.536108\pi$
$114$		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	−0.964058	−	0.265693i	$-0.914399\pi$
$131$	−2.88350	+	4.99436i	−0.251932	+	0.436359i	0.712126	+	0.702052i	$0.247733\pi$
$132$		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	−0.993908	−	0.110209i	$-0.964848\pi$
$137$	0.0139813	−	0.133023i	0.00119450	−	0.0113649i	0.995103	+	0.0988443i	$0.0315146\pi$
$138$		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	−0.549010	−	0.835816i	$-0.684995\pi$
$149$	−3.60383	+	1.60453i	−0.295237	+	0.131448i	0.253773	+	0.967264i	$0.418328\pi$
$150$		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	$-0.902564\pi$
$167$	−1.07893	−	10.2653i	−0.0834900	−	0.794354i	0.870025	−	0.493008i	$-0.164103\pi$
$168$		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	−0.997129	−	0.0757281i	$-0.975872\pi$
$173$	−10.7537	+	11.9432i	−0.817587	+	0.908022i	0.179542	+	0.983750i	$0.442539\pi$
$174$		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	0.984752	−	0.173961i	$-0.0556568\pi$
$179$	1.14818	+	3.53374i	0.0858191	+	0.264124i	−0.898933	+	0.438085i	$0.855657\pi$
$180$		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	0.236734	−	0.971575i	$-0.423923\pi$
$191$	11.7220	−	2.49159i	0.848176	−	0.180285i	0.611442	+	0.791289i	$0.290590\pi$
$192$		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	$-0.384629\pi$
$197$	9.95308			0.709127			0.354564	+	0.935032i	$0.384629\pi$
$198$		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	0.434546	−	0.900650i	$-0.356909\pi$
$227$	18.0474	−	3.83610i	1.19785	−	0.254611i	0.763305	+	0.646039i	$0.223576\pi$
$228$		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	−0.765471	−	0.643470i	$-0.777494\pi$
$233$	−5.95367	+	4.32560i	−0.390038	+	0.283379i	0.375433	+	0.926850i	$0.377494\pi$
$234$		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	0.502098	−	0.864811i	$-0.332562\pi$
$239$	9.41547	+	2.00132i	0.609036	+	0.129455i	0.106939	+	0.994266i	$0.465895\pi$
$240$		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	0.270382	−	0.962753i	$-0.412850\pi$
$251$	20.1137	−	14.6135i	1.26957	−	0.922394i	0.999185	+	0.0403590i	$0.0128502\pi$
$252$		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	0.395160	−	0.918612i	$-0.370689\pi$
$257$	−8.97309	−	9.96563i	−0.559726	−	0.621639i	−0.954886	+	0.296974i	$0.904023\pi$
$258$		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	0.853720	−	0.520732i	$-0.174341\pi$
$263$	−0.390951	−	0.677147i	−0.0241071	−	0.0417546i	−0.877827	+	0.478977i	$0.841008\pi$
$264$		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	0.292818	−	0.956168i	$-0.405407\pi$
$269$	−8.62814	−	6.26871i	−0.526067	−	0.382210i	−0.818884	+	0.573958i	$0.805407\pi$
$270$		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	$-0.800405\pi$
$281$	1.74835	−	16.6345i	0.104298	−	0.992330i	0.914062	−	0.405574i	$-0.132928\pi$
$282$		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	0.375346	−	0.926885i	$-0.377524\pi$
$293$	−10.0255	−	11.1344i	−0.585695	−	0.650480i	−0.961041	+	0.276404i	$0.910857\pi$
$294$		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	0.589522	−	0.807753i	$-0.299316\pi$
$311$	14.0999	+	2.99703i	0.799534	+	0.169946i	0.210012	+	0.977699i	$0.432650\pi$
$312$		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	−0.521286	−	0.853382i	$-0.674547\pi$
$317$	−26.7830	−	11.9245i	−1.50428	−	0.669749i	−0.982995	+	0.183633i	$0.941214\pi$
$318$		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	$-0.247237\pi$
$347$	31.8790	−	14.1935i	1.71136	−	0.761945i	0.998138	−	0.0610035i	$-0.0194301\pi$
$348$		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	0.808628	−	0.588320i	$-0.200210\pi$
$353$	−1.97626	−	3.42298i	−0.105186	−	0.182187i	−0.913814	+	0.406133i	$0.866877\pi$
$354$		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	−0.872350	−	0.488883i	$-0.837405\pi$
$359$	2.28796	−	7.04162i	0.120754	−	0.371643i	0.993104	+	0.117240i	$0.0374046\pi$
$360$		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	0.999837	−	0.0180477i	$-0.00574507\pi$
$383$	0.354156	+	3.36957i	0.0180965	+	0.172177i	−0.981741	+	0.190225i	$0.939078\pi$
$384$		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	0.282139	−	0.959373i	$-0.408956\pi$
$389$	18.3444	−	3.89923i	0.930099	−	0.197699i	0.647960	+	0.761675i	$0.275623\pi$
$390$		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	−0.470331	−	0.882490i	$-0.655866\pi$
$401$	−2.58776	+	1.15214i	−0.129226	+	0.0575353i	0.341105	+	0.940025i	$0.389199\pi$
$402$		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	$-0.660818\pi$
$419$	10.5587	−	18.2882i	0.515826	−	0.893437i	0.999831	−	0.0183715i	$-0.00584817\pi$
$420$		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	−0.680573	−	0.732680i	$-0.738269\pi$
$431$	−4.02881	+	2.92710i	−0.194061	+	0.140994i	0.486512	+	0.873674i	$0.338269\pi$
$432$		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	−0.253413	−	0.967358i	$-0.581553\pi$
$443$	15.4728	−	17.1843i	0.735135	−	0.816450i	0.988548	+	0.150908i	$0.0482198\pi$
$444$		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	−0.293164	−	0.956062i	$-0.594708\pi$
$449$	11.1354	−	8.09035i	0.525512	−	0.381807i	0.818676	+	0.574255i	$0.194708\pi$
$450$		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	0.898102	−	0.439788i	$-0.144946\pi$
$461$	1.46396	+	2.53565i	0.0681833	+	0.118097i	−0.829918	+	0.557885i	$0.811613\pi$
$462$		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	0.355675	−	0.934610i	$-0.384251\pi$
$467$	−9.14721	−	6.64584i	−0.423282	−	0.307533i	−0.778957	+	0.627077i	$0.784251\pi$
$468$		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	$0.277567\pi$
$479$	−3.17618	+	30.2193i	−0.145123	+	1.38076i	−0.788419	+	0.615138i	$0.789100\pi$
$480$		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	0.826659	−	0.562703i	$-0.190238\pi$
$491$	4.00249	+	4.44522i	0.180630	+	0.200610i	−0.646029	+	0.763312i	$0.723572\pi$
$492$		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	$0.00407911\pi$
$503$	4.45188	+	13.7015i	0.198500	+	0.610919i	−0.801418	+	0.598104i	$0.795921\pi$
$504$		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	−0.901200	−	0.433403i	$-0.857313\pi$
$509$	−42.8833	−	9.11513i	−1.90077	−	0.404021i	−0.999568	+	0.0293818i	$0.990646\pi$
$510$		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	$0.245630\pi$
$521$	−6.23122	+	19.1777i	−0.272995	+	0.840191i	−0.989743	+	0.142859i	$0.954370\pi$
$522$		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	−0.928904	−	0.370321i	$-0.879248\pi$
$557$	0.950270	−	2.92463i	0.0402642	−	0.123921i	0.969168	+	0.246400i	$0.0792478\pi$
$558$		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	$0.0891570\pi$
$563$	1.86208	+	17.7165i	0.0784773	+	0.746662i	−0.882552	+	0.470215i	$0.844176\pi$
$564$		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	−0.680596	−	0.732658i	$-0.738279\pi$
$569$	2.84313	−	3.15761i	0.119190	−	0.132374i	0.799787	+	0.600284i	$0.204946\pi$
$570$		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	−0.958843	−	0.283936i	$-0.908360\pi$
$587$	−41.6554	+	8.85413i	−1.71930	+	0.365449i	−0.760460	+	0.649385i	$0.775026\pi$
$588$		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	$-0.430008\pi$
$593$	10.6230			0.436236			0.218118	+	0.975922i	$0.430008\pi$
$594$		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	−0.935187	−	0.354154i	$-0.884769\pi$
$599$	−31.7620	+	14.1414i	−1.29776	+	0.577801i	−0.362575	+	0.931955i	$0.618102\pi$
$600$		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	−0.935484	−	0.353370i	$-0.885036\pi$
$617$	−4.01690	+	6.95747i	−0.161714	+	0.280097i	0.773769	+	0.633467i	$0.218369\pi$
$618$		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	−0.988773	−	0.149427i	$-0.952257\pi$
$641$	−18.6545	+	20.7179i	−0.736809	+	0.818310i	0.251963	+	0.967737i	$0.418924\pi$
$642$		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	$-0.322014\pi$
$647$	38.1698	−	27.7320i	1.50061	−	1.09026i	0.970137	−	0.242556i	$-0.0779857\pi$
$648$		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	0.925624	−	0.378444i	$-0.123541\pi$
$653$	11.5631	+	12.8421i	0.452499	+	0.502551i	−0.473125	+	0.880995i	$0.656874\pi$
$654$		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	0.959391	−	0.282078i	$-0.0910237\pi$
$659$	6.04319	+	10.4671i	0.235409	+	0.407741i	−0.723982	+	0.689818i	$0.757690\pi$
$660$		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	$-0.923428\pi$
$677$	0.736623	−	7.00850i	0.0283107	−	0.269359i	0.999516	−	0.0311137i	$-0.00990540\pi$
$678$		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	$-0.285836\pi$
$683$	32.5733			1.24638			0.623191	+	0.782070i	$0.285836\pi$
$684$		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	$0.0715070\pi$
$701$	8.39620	+	25.8408i	0.317120	+	0.975995i	−0.657753	+	0.753234i	$0.728493\pi$
$702$		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	$-0.790013\pi$
$719$	5.61293	−	17.2748i	0.209327	−	0.644242i	0.999508	−	0.0313684i	$-0.00998651\pi$
$720$		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	−0.685026	−	0.728519i	$-0.740209\pi$
$743$	−16.4094	+	7.30594i	−0.602003	+	0.268029i	0.0830233	+	0.996548i	$0.473542\pi$
$744$		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	$-0.982210\pi$
$761$	−0.922270	−	8.77482i	−0.0334323	−	0.318087i	0.965006	−	0.262227i	$-0.0844568\pi$
$762$		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	$0.0592138\pi$
$773$	8.24081	+	25.3626i	0.296401	+	0.912230i	−0.686346	+	0.727276i	$0.740786\pi$
$774$		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	−0.970473	−	0.241209i	$-0.922456\pi$
$797$	−40.6697	+	18.1073i	−1.44059	+	0.641394i	−0.470121	+	0.882602i	$0.655790\pi$
$798$		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	$-0.968792\pi$
$809$	−39.7013	−	28.8447i	−1.39582	−	1.01413i	−0.400627	−	0.916241i	$-0.631208\pi$
$810$		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	0.315229	−	0.949015i	$-0.397919\pi$
$821$	28.3438	−	6.02466i	0.989205	−	0.210262i	0.673976	+	0.738753i	$0.264585\pi$
$822$		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	−0.996639	−	0.0819138i	$-0.973897\pi$
$827$	−35.2773	+	25.6305i	−1.22671	+	0.891259i	−0.230074	+	0.973173i	$0.573897\pi$
$828$		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	−0.942856	−	0.333201i	$-0.891871\pi$
$839$	−14.8571	+	16.5005i	−0.512925	+	0.569660i	0.429931	+	0.902862i	$0.358538\pi$
$840$		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	0.999674	−	0.0255371i	$-0.00812959\pi$
$857$	13.9851	+	24.2229i	0.477721	+	0.827437i	−0.521953	+	0.852974i	$0.674796\pi$
$858$		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	0.939605	−	0.342261i	$-0.111193\pi$
$863$	26.5699	+	19.3041i	0.904449	+	0.657121i	−0.0351559	+	0.999382i	$0.511193\pi$
$864$		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	$-0.681727\pi$
$881$	−32.0798			−1.08080			−0.540399	+	0.841409i	$0.681727\pi$
$882$		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	0.976374	−	0.216086i	$-0.0693290\pi$
$887$	19.6390	+	21.8113i	0.659414	+	0.732353i	−0.316961	+	0.948439i	$0.602662\pi$
$888$		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	0.448212	−	0.893927i	$-0.352061\pi$
$911$	2.52956	+	1.12623i	0.0838079	+	0.0373137i	−0.364405	+	0.931241i	$0.618727\pi$
$912$		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	$0.0924614\pi$
$929$	−1.17684	+	11.1968i	−0.0386107	+	0.367356i	−0.996718	+	0.0809480i	$0.974205\pi$
$930$		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	−0.210287	−	0.977640i	$-0.567440\pi$
$941$	11.5197	−	5.12890i	0.375532	−	0.167197i	0.585818	+	0.810442i	$0.300773\pi$
$942$		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	0.869014	−	0.494788i	$-0.164754\pi$
$947$	0.184885	+	0.320230i	0.00600796	+	0.0104061i	−0.863006	+	0.505194i	$0.831421\pi$
$948$		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	−0.829773	−	0.558101i	$-0.811530\pi$
$953$	5.23478	−	16.1110i	0.169571	−	0.521886i	0.999344	+	0.0362151i	$0.0115301\pi$
$954$		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	0.993024	−	0.117910i	$-0.0376194\pi$
$971$	3.75006	+	11.5415i	0.120345	+	0.370384i	−0.872679	+	0.488294i	$0.837619\pi$
$972$		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	$0.158136\pi$
$977$	3.69784	+	35.1826i	0.118305	+	1.12559i	−0.760808	+	0.648978i	$0.775197\pi$
$978$		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	0.156675	−	0.987650i	$-0.449923\pi$
$983$	21.9946	−	4.67509i	0.701518	−	0.149112i	0.544843	+	0.838538i	$0.316589\pi$
$984$		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.j.190.1		48
3.2	odd	2		891.2.n.k.190.6		48
9.2	odd	6		891.2.n.k.784.1		48
9.4	even	3		891.2.f.d.487.6	yes	24
9.5	odd	6		891.2.f.c.487.1	✓	24
9.7	even	3	inner	891.2.n.j.784.6		48
11.4	even	5	inner	891.2.n.j.433.6		48
33.26	odd	10		891.2.n.k.433.1		48
99.4	even	15		891.2.f.d.730.6	yes	24
99.13	odd	30		9801.2.a.cf.1.12		12
99.31	even	15		9801.2.a.ck.1.1		12
99.59	odd	30		891.2.f.c.730.1	yes	24
99.68	even	30		9801.2.a.cl.1.1		12
99.70	even	15	inner	891.2.n.j.136.1		48
99.86	odd	30		9801.2.a.cg.1.12		12
99.92	odd	30		891.2.n.k.136.6		48

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