LMFDB - Embedded newform 864.2.bn.a.611.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(35,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			611.39
Character	$\chi$	$=$	864.611
Dual form			864.2.bn.a.683.39

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26591 + 0.630463i) q^{2} +(1.20503 + 1.59621i) q^{4} +(-0.00886053 + 0.0673024i) q^{5} +(0.666754 - 2.48836i) q^{7} +(0.519104 + 2.78038i) q^{8} +(-0.0536483 + 0.0796122i) q^{10} +(-0.332332 - 0.255007i) q^{11} +(3.75972 + 4.89976i) q^{13} +(2.41287 - 2.72966i) q^{14} +(-1.09579 + 3.84698i) q^{16} -3.64897 q^{17} +(3.97733 + 1.64746i) q^{19} +(-0.118106 + 0.0669583i) q^{20} +(-0.259928 - 0.532338i) q^{22} +(8.77221 - 2.35051i) q^{23} +(4.82518 + 1.29290i) q^{25} +(1.67033 + 8.57300i) q^{26} +(4.77541 - 1.93427i) q^{28} +(-7.27433 + 0.957684i) q^{29} +(1.77380 + 1.02410i) q^{31} +(-3.81255 + 4.17905i) q^{32} +(-4.61925 - 2.30054i) q^{34} +(0.161565 + 0.0669223i) q^{35} +(-3.36655 - 8.12758i) q^{37} +(3.99625 + 4.59309i) q^{38} +(-0.191726 + 0.0103013i) q^{40} +(-1.45472 - 5.42911i) q^{41} +(-2.16028 + 2.81533i) q^{43} +(0.00657510 - 0.837765i) q^{44} +(12.5867 + 2.55503i) q^{46} +(-2.05961 + 1.18912i) q^{47} +(0.314804 + 0.181752i) q^{49} +(5.29309 + 4.67879i) q^{50} +(-3.29048 + 11.9057i) q^{52} +(0.0730018 + 0.176242i) q^{53} +(0.0201073 - 0.0201073i) q^{55} +(7.26471 + 0.562114i) q^{56} +(-9.81240 - 3.37386i) q^{58} +(-5.21160 - 0.686120i) q^{59} +(0.357730 + 2.71723i) q^{61} +(1.59980 + 2.41473i) q^{62} +(-7.46106 + 2.88662i) q^{64} +(-0.363079 + 0.209624i) q^{65} +(-0.969906 - 1.26401i) q^{67} +(-4.39712 - 5.82453i) q^{68} +(0.162334 + 0.186578i) q^{70} +(-7.18803 + 7.18803i) q^{71} +(-6.62149 - 6.62149i) q^{73} +(0.862401 - 12.4112i) q^{74} +(2.16311 + 8.33390i) q^{76} +(-0.856134 + 0.656935i) q^{77} +(-4.97251 - 8.61265i) q^{79} +(-0.249202 - 0.107836i) q^{80} +(1.58131 - 7.78988i) q^{82} +(4.26191 - 0.561091i) q^{83} +(0.0323318 - 0.245584i) q^{85} +(-4.50967 + 2.20197i) q^{86} +(0.536503 - 1.05639i) q^{88} +(-2.46723 - 2.46723i) q^{89} +(14.6992 - 6.08860i) q^{91} +(14.3227 + 11.1699i) q^{92} +(-3.35696 + 0.206801i) q^{94} +(-0.146119 + 0.253086i) q^{95} +(-7.74713 - 13.4184i) q^{97} +(0.283924 + 0.428554i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.26591	+	0.630463i	0.895130	+	0.445805i
$2$	1.26591	+	0.630463i	0.895130	+	0.445805i
$3$		0			0
$3$		0			0
$4$	1.20503	+	1.59621i	0.602516	+	0.798107i
$5$	−0.00886053	+	0.0673024i	−0.00396255	+	0.0300986i	−0.993312	−	0.115462i	$-0.963165\pi$
$5$	−0.00886053	+	0.0673024i	−0.00396255	+	0.0300986i	0.989349	+	0.145560i	$0.0464985\pi$
$6$		0			0
$7$	0.666754	−	2.48836i	0.252009	−	0.940512i	−0.717721	−	0.696331i	$-0.754814\pi$
$7$	0.666754	−	2.48836i	0.252009	−	0.940512i	0.969730	−	0.244180i	$-0.0785189\pi$
$8$	0.519104	+	2.78038i	0.183531	+	0.983014i
$9$		0			0
$10$	−0.0536483	+	0.0796122i	−0.0169651	+	0.0251756i
$11$	−0.332332	−	0.255007i	−0.100202	−	0.0768876i	0.557445	−	0.830214i	$-0.311782\pi$
$11$	−0.332332	−	0.255007i	−0.100202	−	0.0768876i	−0.657647	+	0.753326i	$0.728448\pi$
$12$		0			0
$13$	3.75972	+	4.89976i	1.04276	+	1.35895i	0.930920	+	0.365223i	$0.119007\pi$
$13$	3.75972	+	4.89976i	1.04276	+	1.35895i	0.111838	+	0.993726i	$0.464326\pi$
$14$	2.41287	−	2.72966i	0.644866	−	0.729533i
$15$		0			0
$16$	−1.09579	+	3.84698i	−0.273948	+	0.961744i
$17$	−3.64897			−0.885004			−0.442502	−	0.896767i	$-0.645909\pi$
$17$	−3.64897			−0.885004			−0.442502	+	0.896767i	$0.645909\pi$
$18$		0			0
$19$	3.97733	+	1.64746i	0.912461	+	0.377954i	0.788998	−	0.614395i	$-0.210600\pi$
$19$	3.97733	+	1.64746i	0.912461	+	0.377954i	0.123463	+	0.992349i	$0.460600\pi$
$20$	−0.118106	+	0.0669583i	−0.0264094	+	0.0149723i
$21$		0			0
$22$	−0.259928	−	0.532338i	−0.0554169	−	0.113495i
$23$	8.77221	−	2.35051i	1.82913	−	0.490114i	0.831293	−	0.555834i	$-0.187601\pi$
$23$	8.77221	−	2.35051i	1.82913	−	0.490114i	0.997838	+	0.0657198i	$0.0209344\pi$
$24$		0			0
$25$	4.82518	+	1.29290i	0.965036	+	0.258581i
$26$	1.67033	+	8.57300i	0.327579	+	1.68130i
$27$		0			0
$28$	4.77541	−	1.93427i	0.902468	−	0.365543i
$29$	−7.27433	+	0.957684i	−1.35081	+	0.177837i	−0.770959	−	0.636885i	$-0.780222\pi$
$29$	−7.27433	+	0.957684i	−1.35081	+	0.177837i	−0.579851	+	0.814723i	$0.696889\pi$
$30$		0			0
$31$	1.77380	+	1.02410i	0.318584	+	0.183935i	0.650761	−	0.759282i	$-0.274450\pi$
$31$	1.77380	+	1.02410i	0.318584	+	0.183935i	−0.332177	+	0.943217i	$0.607783\pi$
$32$	−3.81255	+	4.17905i	−0.673969	+	0.738759i
$33$		0			0
$34$	−4.61925	−	2.30054i	−0.792194	−	0.394539i
$35$	0.161565	+	0.0669223i	0.0273094	+	0.0113119i
$36$		0			0
$37$	−3.36655	−	8.12758i	−0.553458	−	1.33617i	−0.914866	−	0.403758i	$-0.867704\pi$
$37$	−3.36655	−	8.12758i	−0.553458	−	1.33617i	0.361408	−	0.932408i	$-0.382296\pi$
$38$	3.99625	+	4.59309i	0.648278	+	0.745097i
$39$		0			0
$40$	−0.191726	+	0.0103013i	−0.0303145	+	0.00162877i
$41$	−1.45472	−	5.42911i	−0.227190	−	0.847884i	−0.981515	−	0.191383i	$-0.938703\pi$
$41$	−1.45472	−	5.42911i	−0.227190	−	0.847884i	0.754326	−	0.656501i	$-0.227964\pi$
$42$		0			0
$43$	−2.16028	+	2.81533i	−0.329440	+	0.429334i	−0.928479	−	0.371386i	$-0.878883\pi$
$43$	−2.16028	+	2.81533i	−0.329440	+	0.429334i	0.599039	+	0.800720i	$0.295549\pi$
$44$	0.00657510	−	0.837765i	0.000991233	−	0.126298i
$45$		0			0
$46$	12.5867	+	2.55503i	1.85581	+	0.376719i
$47$	−2.05961	+	1.18912i	−0.300425	+	0.173450i	−0.642634	−	0.766173i	$-0.722158\pi$
$47$	−2.05961	+	1.18912i	−0.300425	+	0.173450i	0.342209	+	0.939624i	$0.388825\pi$
$48$		0			0
$49$	0.314804	+	0.181752i	0.0449720	+	0.0259646i
$50$	5.29309	+	4.67879i	0.748556	+	0.661681i
$51$		0			0
$52$	−3.29048	+	11.9057i	−0.456307	+	1.65102i
$53$	0.0730018	+	0.176242i	0.0100276	+	0.0242087i	0.928814	−	0.370546i	$-0.120829\pi$
$53$	0.0730018	+	0.176242i	0.0100276	+	0.0242087i	−0.918786	+	0.394755i	$0.870829\pi$
$54$		0			0
$55$	0.0201073	−	0.0201073i	0.00271126	−	0.00271126i
$56$	7.26471	+	0.562114i	0.970788	+	0.0751157i
$57$		0			0
$58$	−9.81240	−	3.37386i	−1.28843	−	0.443009i
$59$	−5.21160	−	0.686120i	−0.678493	−	0.0893252i	−0.216599	−	0.976261i	$-0.569496\pi$
$59$	−5.21160	−	0.686120i	−0.678493	−	0.0893252i	−0.461893	+	0.886935i	$0.652830\pi$
$60$		0			0
$61$	0.357730	+	2.71723i	0.0458026	+	0.347905i	0.998967	+	0.0454512i	$0.0144725\pi$
$61$	0.357730	+	2.71723i	0.0458026	+	0.347905i	−0.953164	+	0.302454i	$0.902194\pi$
$62$	1.59980	+	2.41473i	0.203175	+	0.306672i
$63$		0			0
$64$	−7.46106	+	2.88662i	−0.932633	+	0.360827i
$65$	−0.363079	+	0.209624i	−0.0450344	+	0.0260006i
$66$		0			0
$67$	−0.969906	−	1.26401i	−0.118493	−	0.154423i	0.730341	−	0.683083i	$-0.239361\pi$
$67$	−0.969906	−	1.26401i	−0.118493	−	0.154423i	−0.848834	+	0.528660i	$0.822695\pi$
$68$	−4.39712	−	5.82453i	−0.533230	−	0.706328i
$69$		0			0
$70$	0.162334	+	0.186578i	0.0194026	+	0.0223003i
$71$	−7.18803	+	7.18803i	−0.853063	+	0.853063i	−0.990509	−	0.137446i	$-0.956111\pi$
$71$	−7.18803	+	7.18803i	−0.853063	+	0.853063i	0.137446	+	0.990509i	$0.456111\pi$
$72$		0			0
$73$	−6.62149	−	6.62149i	−0.774986	−	0.774986i	0.203987	−	0.978974i	$-0.434610\pi$
$73$	−6.62149	−	6.62149i	−0.774986	−	0.774986i	−0.978974	+	0.203987i	$0.934610\pi$
$74$	0.862401	−	12.4112i	0.100252	−	1.44278i
$75$		0			0
$76$	2.16311	+	8.33390i	0.248125	+	0.955964i
$77$	−0.856134	+	0.656935i	−0.0975655	+	0.0748647i
$78$		0			0
$79$	−4.97251	−	8.61265i	−0.559452	−	0.968999i	−0.997542	−	0.0700678i	$-0.977678\pi$
$79$	−4.97251	−	8.61265i	−0.559452	−	0.968999i	0.438091	−	0.898931i	$-0.355655\pi$
$80$	−0.249202	−	0.107836i	−0.0278616	−	0.0120564i
$81$		0			0
$82$	1.58131	−	7.78988i	0.174626	−	0.860249i
$83$	4.26191	−	0.561091i	0.467805	−	0.0615877i	0.107061	−	0.994252i	$-0.465856\pi$
$83$	4.26191	−	0.561091i	0.467805	−	0.0615877i	0.360744	+	0.932665i	$0.382523\pi$
$84$		0			0
$85$	0.0323318	−	0.245584i	0.00350687	−	0.0266373i
$86$	−4.50967	+	2.20197i	−0.486291	+	0.237444i
$87$		0			0
$88$	0.536503	−	1.05639i	0.0571915	−	0.112611i
$89$	−2.46723	−	2.46723i	−0.261526	−	0.261526i	0.564148	−	0.825674i	$-0.309205\pi$
$89$	−2.46723	−	2.46723i	−0.261526	−	0.261526i	−0.825674	+	0.564148i	$0.809205\pi$
$90$		0			0
$91$	14.6992	−	6.08860i	1.54089	−	0.638259i
$92$	14.3227	+	11.1699i	1.49324	+	1.16454i
$93$		0			0
$94$	−3.35696	+	0.206801i	−0.346244	+	0.0213299i
$95$	−0.146119	+	0.253086i	−0.0149915	+	0.0259661i
$96$		0			0
$97$	−7.74713	−	13.4184i	−0.786602	−	1.36243i	−0.928038	−	0.372486i	$-0.878505\pi$
$97$	−7.74713	−	13.4184i	−0.786602	−	1.36243i	0.141436	−	0.989947i	$-0.454828\pi$
$98$	0.283924	+	0.428554i	0.0286807	+	0.0432905i
$99$		0			0
$100$	3.75075	+	9.26000i	0.375075	+	0.926000i
$101$	3.40929	+	2.61604i	0.339237	+	0.260306i	0.764304	−	0.644856i	$-0.223083\pi$
$101$	3.40929	+	2.61604i	0.339237	+	0.260306i	−0.425067	+	0.905162i	$0.639749\pi$
$102$		0			0
$103$	−1.69436	+	0.454001i	−0.166950	+	0.0447341i	−0.341326	−	0.939945i	$-0.610876\pi$
$103$	−1.69436	+	0.454001i	−0.166950	+	0.0447341i	0.174376	+	0.984679i	$0.444209\pi$
$104$	−11.6715	+	12.9969i	−1.14449	+	1.27446i
$105$		0			0
$106$	−0.0187007	+	0.269131i	−0.00181637	+	0.0261403i
$107$	6.52327	−	2.70203i	0.630628	−	0.261215i	−0.0443917	−	0.999014i	$-0.514135\pi$
$107$	6.52327	−	2.70203i	0.630628	−	0.261215i	0.675020	+	0.737799i	$0.264135\pi$
$108$		0			0
$109$	−2.14998	+	5.19051i	−0.205931	+	0.497161i	−0.992775	−	0.119991i	$-0.961713\pi$
$109$	−2.14998	+	5.19051i	−0.205931	+	0.497161i	0.786844	+	0.617152i	$0.211713\pi$
$110$	0.0381308	−	0.0127770i	0.00363563	−	0.00121824i
$111$		0			0
$112$	8.84204	+	5.29171i	0.835494	+	0.500020i
$113$	6.18560	−	10.7138i	0.581893	−	1.00787i	−0.413362	−	0.910567i	$-0.635646\pi$
$113$	6.18560	−	10.7138i	0.581893	−	1.00787i	0.995255	−	0.0973009i	$-0.0310209\pi$
$114$		0			0
$115$	0.0804683	+	0.611217i	0.00750371	+	0.0569963i
$116$	−10.2945	−	10.4573i	−0.955818	−	0.970940i
$117$		0			0
$118$	−6.16482	−	4.15428i	−0.567518	−	0.382433i
$119$	−2.43296	+	9.07994i	−0.223029	+	0.832357i
$120$		0			0
$121$	−2.80159	−	10.4557i	−0.254690	−	0.950517i
$122$	−1.26026	+	3.66529i	−0.114098	+	0.331840i
$123$		0			0
$124$	0.502799	+	4.06544i	0.0451527	+	0.365087i
$125$	−0.259658	+	0.626870i	−0.0232245	+	0.0560689i
$126$		0			0
$127$		−	6.09879i		−	0.541180i	−0.962695	−	0.270590i	$-0.912781\pi$
$127$		−	6.09879i		−	0.541180i	0.962695	−	0.270590i	$-0.0872188\pi$
$128$	−11.2649	−	1.04974i	−0.995686	−	0.0927850i
$129$		0			0
$130$	−0.591783	+	0.0364559i	−0.0519028	+	0.00319740i
$131$	10.9721	−	8.41920i	0.958638	−	0.735589i	−0.00577685	−	0.999983i	$-0.501839\pi$
$131$	10.9721	−	8.41920i	0.958638	−	0.735589i	0.964415	+	0.264395i	$0.0851722\pi$
$132$		0			0
$133$	6.75138	−	8.79856i	0.585419	−	0.762932i
$134$	−0.430900	−	2.21160i	−0.0372241	−	0.191053i
$135$		0			0
$136$	−1.89419	−	10.1455i	−0.162426	−	0.869972i
$137$	−19.6939	−	5.27697i	−1.68256	−	0.450842i	−0.714110	−	0.700033i	$-0.753169\pi$
$137$	−19.6939	−	5.27697i	−1.68256	−	0.450842i	−0.968454	+	0.249191i	$0.919835\pi$
$138$		0			0
$139$	22.2105	+	2.92407i	1.88387	+	0.248017i	0.982668	−	0.185374i	$-0.0593498\pi$
$139$	22.2105	+	2.92407i	1.88387	+	0.248017i	0.901206	+	0.433391i	$0.142683\pi$
$140$	0.0878686	+	0.338535i	0.00742625	+	0.0286115i
$141$		0			0
$142$	−13.6312	+	4.56758i	−1.14390	+	0.383303i
$143$		−	2.58710i		−	0.216345i
$144$		0			0
$145$		−	0.498066i		−	0.0413621i
$146$	−4.20757	−	12.5568i	−0.348221	−	1.03921i
$147$		0			0
$148$	8.91654	−	15.1677i	0.732935	−	1.24678i
$149$	−9.26048	−	1.21916i	−0.758648	−	0.0998779i	−0.258729	−	0.965950i	$-0.583304\pi$
$149$	−9.26048	−	1.21916i	−0.758648	−	0.0998779i	−0.499919	+	0.866072i	$0.666637\pi$
$150$		0			0
$151$	−4.46253	−	1.19573i	−0.363155	−	0.0973071i	0.0726273	−	0.997359i	$-0.476862\pi$
$151$	−4.46253	−	1.19573i	−0.363155	−	0.0973071i	−0.435782	+	0.900052i	$0.643528\pi$
$152$	−2.51593	+	11.9137i	−0.204069	+	0.966328i
$153$		0			0
$154$	−1.49796	+	0.291856i	−0.120709	+	0.0235185i
$155$	−0.0846415	+	0.110307i	−0.00679857	+	0.00886007i
$156$		0			0
$157$	−3.89270	+	2.98697i	−0.310671	+	0.238386i	−0.752314	−	0.658804i	$-0.771062\pi$
$157$	−3.89270	+	2.98697i	−0.310671	+	0.238386i	0.441643	+	0.897191i	$0.354396\pi$
$158$	−0.864777	−	14.0378i	−0.0687979	−	1.11679i
$159$		0			0
$160$	−0.247479	−	0.293622i	−0.0195649	−	0.0232129i
$161$		−	23.3956i		−	1.84383i
$162$		0			0
$163$	−2.68046	+	6.47120i	−0.209950	+	0.506863i	−0.993415	−	0.114572i	$-0.963450\pi$
$163$	−2.68046	+	6.47120i	−0.209950	+	0.506863i	0.783465	+	0.621436i	$0.213450\pi$
$164$	6.91302	−	8.86430i	0.539816	−	0.692186i
$165$		0			0
$166$	5.74892	+	1.97669i	0.446203	+	0.153421i
$167$	5.28563	+	19.7262i	0.409014	+	1.52646i	0.796530	+	0.604599i	$0.206667\pi$
$167$	5.28563	+	19.7262i	0.409014	+	1.52646i	−0.387516	+	0.921863i	$0.626667\pi$
$168$		0			0
$169$	−6.50753	+	24.2864i	−0.500579	+	1.86819i
$170$	0.195761	−	0.290502i	0.0150142	−	0.0222805i
$171$		0			0
$172$	−7.09708	−	0.0557006i	−0.541147	−	0.00424713i
$173$	1.17706	+	8.94067i	0.0894903	+	0.679747i	0.976115	+	0.217256i	$0.0697107\pi$
$173$	1.17706	+	8.94067i	0.0894903	+	0.679747i	−0.886624	+	0.462490i	$0.846956\pi$
$174$		0			0
$175$	6.43441	−	11.1447i	0.486396	−	0.842462i
$176$	1.34517	−	0.999039i	0.101396	−	0.0753054i
$177$		0			0
$178$	−1.56778	−	4.67878i	−0.117510	−	0.350690i
$179$	3.79147	−	9.15342i	0.283388	−	0.684159i	−0.716522	−	0.697564i	$-0.754267\pi$
$179$	3.79147	−	9.15342i	0.283388	−	0.684159i	0.999910	+	0.0134054i	$0.00426720\pi$
$180$		0			0
$181$	−19.1915	+	7.94937i	−1.42649	+	0.590872i	−0.956482	−	0.291790i	$-0.905749\pi$
$181$	−19.1915	+	7.94937i	−1.42649	+	0.590872i	−0.470009	+	0.882662i	$0.655749\pi$
$182$	22.4464	+	1.55970i	1.66384	+	0.115613i
$183$		0			0
$184$	11.0890	+	23.1699i	0.817491	+	1.70811i
$185$	0.576835	−	0.154563i	0.0424098	−	0.0113637i
$186$		0			0
$187$	1.21267	+	0.930513i	0.0886791	+	0.0680459i
$188$	−4.37998	−	1.85465i	−0.319443	−	0.135264i
$189$		0			0
$190$	−0.344535	+	0.228260i	−0.0249952	+	0.0165597i
$191$	−4.73817	−	8.20675i	−0.342842	−	0.593820i	0.642117	−	0.766606i	$-0.278056\pi$
$191$	−4.73817	−	8.20675i	−0.342842	−	0.593820i	−0.984959	+	0.172787i	$0.944723\pi$
$192$		0			0
$193$	−8.97329	+	15.5422i	−0.645912	+	1.11875i	0.338178	+	0.941082i	$0.390189\pi$
$193$	−8.97329	+	15.5422i	−0.645912	+	1.11875i	−0.984090	+	0.177670i	$0.943144\pi$
$194$	−1.34731	−	21.8707i	−0.0967314	−	1.57023i
$195$		0			0
$196$	0.0892340	+	0.721512i	0.00637386	+	0.0515366i
$197$	4.82042	−	1.99668i	0.343441	−	0.142258i	−0.204295	−	0.978909i	$-0.565490\pi$
$197$	4.82042	−	1.99668i	0.343441	−	0.142258i	0.547735	+	0.836652i	$0.315490\pi$
$198$		0			0
$199$	−14.2378	−	14.2378i	−1.00929	−	1.00929i	−0.999956	−	0.00933576i	$-0.997028\pi$
$199$	−14.2378	−	14.2378i	−1.00929	−	1.00929i	−0.00933576	−	0.999956i	$-0.502972\pi$
$200$	−1.09000	+	14.0870i	−0.0770743	+	0.996101i
$201$		0			0
$202$	2.66652	+	5.46109i	0.187616	+	0.384241i
$203$	−2.46713	+	18.7397i	−0.173158	+	1.31527i
$204$		0			0
$205$	0.378282	−	0.0498017i	0.0264203	−	0.00347830i
$206$	−2.43113	−	0.493506i	−0.169385	−	0.0343842i
$207$		0			0
$208$	−22.9691	+	9.09444i	−1.59262	+	0.630586i
$209$	−0.901678	−	1.56175i	−0.0623704	−	0.108029i
$210$		0			0
$211$	5.21165	−	3.99904i	0.358785	−	0.275305i	−0.413602	−	0.910458i	$-0.635729\pi$
$211$	5.21165	−	3.99904i	0.358785	−	0.275305i	0.772387	+	0.635153i	$0.219063\pi$
$212$	−0.193350	+	0.328904i	−0.0132793	+	0.0225892i
$213$		0			0
$214$	9.96137	+	0.692171i	0.680945	+	0.0473158i
$215$	−0.170337	−	0.170337i	−0.0116169	−	0.0116169i
$216$		0			0
$217$	3.73103	−	3.73103i	0.253279	−	0.253279i
$218$	−5.99410	+	5.21521i	−0.405971	+	0.353219i
$219$		0			0
$220$	0.0563254	+	0.00786556i	0.00379745	+	0.000530296i
$221$	−13.7191	−	17.8791i	−0.922846	−	1.20268i
$222$		0			0
$223$	−2.03938	+	1.17744i	−0.136567	+	0.0788471i	−0.566727	−	0.823906i	$-0.691791\pi$
$223$	−2.03938	+	1.17744i	−0.136567	+	0.0788471i	0.430160	+	0.902753i	$0.358457\pi$
$224$	7.85696	+	12.2734i	0.524965	+	0.820050i
$225$		0			0
$226$	14.5850	−	9.66283i	0.970182	−	0.642762i
$227$	−2.07726	−	15.7783i	−0.137872	−	1.04725i	−0.910828	−	0.412786i	$-0.864556\pi$
$227$	−2.07726	−	15.7783i	−0.137872	−	1.04725i	0.772956	−	0.634460i	$-0.218777\pi$
$228$		0			0
$229$	−15.3299	−	2.01822i	−1.01303	−	0.133368i	−0.394307	−	0.918979i	$-0.629015\pi$
$229$	−15.3299	−	2.01822i	−1.01303	−	0.133368i	−0.618720	+	0.785611i	$0.712349\pi$
$230$	−0.283485	+	0.824476i	−0.0186924	+	0.0543643i
$231$		0			0
$232$	−6.43886	−	19.7283i	−0.422732	−	1.29523i
$233$	5.49432	−	5.49432i	0.359945	−	0.359945i	−0.503848	−	0.863793i	$-0.668083\pi$
$233$	5.49432	−	5.49432i	0.359945	−	0.359945i	0.863793	+	0.503848i	$0.168083\pi$
$234$		0			0
$235$	−0.0617812	−	0.149153i	−0.00403016	−	0.00972966i
$236$	−5.18495	−	9.14562i	−0.337512	−	0.595329i
$237$		0			0
$238$	−8.80447	+	9.96045i	−0.570709	+	0.645640i
$239$	17.3751	+	10.0315i	1.12390	+	0.648883i	0.942393	−	0.334507i	$-0.108570\pi$
$239$	17.3751	+	10.0315i	1.12390	+	0.648883i	0.181506	+	0.983390i	$0.441903\pi$
$240$		0			0
$241$	9.35807	−	5.40288i	0.602806	−	0.348030i	−0.167339	−	0.985899i	$-0.553517\pi$
$241$	9.35807	−	5.40288i	0.602806	−	0.348030i	0.770145	+	0.637869i	$0.220184\pi$
$242$	3.04537	−	15.0022i	0.195764	−	0.964379i
$243$		0			0
$244$	−3.90620	+	3.84536i	−0.250069	+	0.246174i
$245$	−0.0150217	+	0.0195767i	−0.000959701	+	0.00125071i
$246$		0			0
$247$	6.88146	+	25.6819i	0.437857	+	1.63410i
$248$	−1.92662	+	5.46346i	−0.122340	+	0.346930i
$249$		0			0
$250$	−0.723920	+	0.629853i	−0.0457847	+	0.0398354i
$251$	−3.41749	−	8.25055i	−0.215710	−	0.520770i	0.778572	−	0.627555i	$-0.215944\pi$
$251$	−3.41749	−	8.25055i	−0.215710	−	0.520770i	−0.994282	+	0.106785i	$0.965944\pi$
$252$		0			0
$253$	−3.51468	−	1.45583i	−0.220966	−	0.0915272i
$254$	3.84506	−	7.72050i	0.241261	−	0.484427i
$255$		0			0
$256$	−13.5985	−	8.43098i	−0.849905	−	0.526936i
$257$	23.7599	+	13.7178i	1.48210	+	0.855692i	0.999794	−	0.0203099i	$-0.00646527\pi$
$257$	23.7599	+	13.7178i	1.48210	+	0.855692i	0.482308	+	0.876002i	$0.339799\pi$
$258$		0			0
$259$	−22.4690	+	2.95810i	−1.39616	+	0.183807i
$260$	−0.772126	−	0.326948i	−0.0478852	−	0.0202764i
$261$		0			0
$262$	19.1976	−	3.74040i	1.18603	−	0.231082i
$263$	−21.9440	−	5.87988i	−1.35313	−	0.362569i	−0.491838	−	0.870686i	$-0.663675\pi$
$263$	−21.9440	−	5.87988i	−1.35313	−	0.362569i	−0.861288	+	0.508117i	$0.830342\pi$
$264$		0			0
$265$	−0.0125083	+	0.00335160i	−0.000768381	+	0.000205887i
$266$	14.0938	−	6.88166i	0.864145	−	0.421941i
$267$		0			0
$268$	0.848855	−	3.07135i	0.0518521	−	0.187612i
$269$	26.9125	+	11.1475i	1.64088	+	0.679677i	0.996387	−	0.0849297i	$-0.0270666\pi$
$269$	26.9125	+	11.1475i	1.64088	+	0.679677i	0.644498	+	0.764606i	$0.277067\pi$
$270$		0			0
$271$	4.68410			0.284539			0.142269	−	0.989828i	$-0.454560\pi$
$271$	4.68410			0.284539			0.142269	+	0.989828i	$0.454560\pi$
$272$	3.99851	−	14.0375i	0.242445	−	0.851148i
$273$		0			0
$274$	−21.6037	−	19.0964i	−1.30513	−	1.15366i
$275$	−1.27386	−	1.66013i	−0.0768168	−	0.100110i
$276$		0			0
$277$	−9.86942	−	7.57307i	−0.592996	−	0.455022i	0.268152	−	0.963377i	$-0.413587\pi$
$277$	−9.86942	−	7.57307i	−0.592996	−	0.455022i	−0.861148	+	0.508355i	$0.830254\pi$
$278$	26.2729	+	17.7045i	1.57575	+	1.06185i
$279$		0			0
$280$	−0.102201	+	0.483952i	−0.00610767	+	0.0289216i
$281$	−3.14266	+	11.7286i	−0.187475	+	0.699668i	0.806612	+	0.591082i	$0.201299\pi$
$281$	−3.14266	+	11.7286i	−0.187475	+	0.699668i	−0.994087	+	0.108586i	$0.965368\pi$
$282$		0			0
$283$	−1.06070	+	8.05683i	−0.0630522	+	0.478929i	0.930565	+	0.366126i	$0.119316\pi$
$283$	−1.06070	+	8.05683i	−0.0630522	+	0.478929i	−0.993617	+	0.112803i	$0.964017\pi$
$284$	−20.1355	−	2.81182i	−1.19482	−	0.166851i
$285$		0			0
$286$	1.63107	−	3.27503i	0.0964474	−	0.193657i
$287$	−14.4795			−0.854699
$288$		0			0
$289$	−3.68505			−0.216767
$290$	0.314012	−	0.630504i	0.0184394	−	0.0370245i
$291$		0			0
$292$	2.59020	−	18.5484i	0.151580	−	1.08546i
$293$	−1.06313	+	8.07531i	−0.0621090	+	0.471764i	0.931921	+	0.362660i	$0.118131\pi$
$293$	−1.06313	+	8.07531i	−0.0621090	+	0.471764i	−0.994030	+	0.109104i	$0.965202\pi$
$294$		0			0
$295$	0.0923551	−	0.344674i	0.00537712	−	0.0200677i
$296$	20.8502	−	13.5794i	1.21189	−	0.789285i
$297$		0			0
$298$	−10.9542	−	7.38173i	−0.634562	−	0.427612i
$299$	44.4979	+	34.1445i	2.57338	+	1.97463i
$300$		0			0
$301$	5.56519	+	7.25269i	0.320772	+	0.418038i
$302$	−4.89527	−	4.32714i	−0.281691	−	0.248999i
$303$		0			0
$304$	−10.6961	+	13.4954i	−0.613462	+	0.774015i
$305$	−0.186046			−0.0106529
$306$		0			0
$307$	30.9448	+	12.8178i	1.76611	+	0.731549i	0.995555	+	0.0941803i	$0.0300230\pi$
$307$	30.9448	+	12.8178i	1.76611	+	0.731549i	0.770559	+	0.637368i	$0.219977\pi$
$308$	−2.08028	−	0.574944i	−0.118535	−	0.0327605i
$309$		0			0
$310$	−0.176693	+	0.0862748i	−0.0100355	+	0.00490008i
$311$	−15.3848	+	4.12235i	−0.872393	+	0.233757i	−0.667122	−	0.744948i	$-0.732474\pi$
$311$	−15.3848	+	4.12235i	−0.872393	+	0.233757i	−0.205270	+	0.978705i	$0.565807\pi$
$312$		0			0
$313$	26.6925	+	7.15224i	1.50875	+	0.404268i	0.916020	−	0.401132i	$-0.131383\pi$
$313$	26.6925	+	7.15224i	1.50875	+	0.404268i	0.592730	+	0.805401i	$0.298050\pi$
$314$	−6.81096	+	1.32702i	−0.384365	+	0.0748882i
$315$		0			0
$316$	7.75558	−	18.3157i	0.436285	−	1.03034i
$317$	0.823543	−	0.108422i	0.0462548	−	0.00608956i	−0.107363	−	0.994220i	$-0.534241\pi$
$317$	0.823543	−	0.108422i	0.0462548	−	0.00608956i	0.153618	+	0.988130i	$0.450907\pi$
$318$		0			0
$319$	2.66171	+	1.53674i	0.149027	+	0.0860409i
$320$	−0.128167	−	0.527724i	−0.00716477	−	0.0295007i
$321$		0			0
$322$	14.7501	−	29.6166i	0.821989	−	1.65047i
$323$	−14.5131	−	6.01153i	−0.807532	−	0.334491i
$324$		0			0
$325$	11.8064	+	28.5032i	0.654901	+	1.58107i
$326$	−7.47305	+	6.50199i	−0.413894	+	0.360112i
$327$		0			0
$328$	14.3398	−	6.86296i	0.791785	−	0.378944i
$329$	1.58570	+	5.91790i	0.0874222	+	0.326264i
$330$		0			0
$331$	9.14211	−	11.9142i	0.502496	−	0.654866i	−0.471384	−	0.881928i	$-0.656245\pi$
$331$	9.14211	−	11.9142i	0.502496	−	0.654866i	0.973880	+	0.227062i	$0.0729121\pi$
$332$	6.03136	+	6.12678i	0.331014	+	0.336251i
$333$		0			0
$334$	−5.74556	+	28.3039i	−0.314383	+	1.54872i
$335$	0.0936646	−	0.0540773i	0.00511744	−	0.00295456i
$336$		0			0
$337$	−17.1129	−	9.88013i	−0.932198	−	0.538205i	−0.0446921	−	0.999001i	$-0.514231\pi$
$337$	−17.1129	−	9.88013i	−0.932198	−	0.538205i	−0.887506	+	0.460796i	$0.847564\pi$
$338$	−23.5496	+	26.6416i	−1.28093	+	1.44911i
$339$		0			0
$340$	0.430966	−	0.244329i	0.0233724	−	0.0132506i
$341$	−0.328337	−	0.792675i	−0.0177804	−	0.0429258i
$342$		0			0
$343$	13.4134	−	13.4134i	0.724256	−	0.724256i
$344$	−8.94911	−	4.54496i	−0.482504	−	0.245048i
$345$		0			0
$346$	−4.14671	+	12.0601i	−0.222929	+	0.648357i
$347$	11.6853	+	1.53839i	0.627298	+	0.0825853i	0.437471	−	0.899232i	$-0.355874\pi$
$347$	11.6853	+	1.53839i	0.627298	+	0.0825853i	0.189826	+	0.981818i	$0.439207\pi$
$348$		0			0
$349$	2.27090	+	17.2492i	0.121558	+	0.923327i	0.938178	+	0.346152i	$0.112512\pi$
$349$	2.27090	+	17.2492i	0.121558	+	0.923327i	−0.816620	+	0.577176i	$0.804155\pi$
$350$	15.1717	−	10.0515i	0.810961	−	0.537276i
$351$		0			0
$352$	2.33272	−	0.416606i	0.124334	−	0.0222052i
$353$	10.1154	−	5.84016i	0.538391	−	0.310840i	−0.206036	−	0.978544i	$-0.566056\pi$
$353$	10.1154	−	5.84016i	0.538391	−	0.310840i	0.744427	+	0.667704i	$0.232723\pi$
$354$		0			0
$355$	−0.420082	−	0.547462i	−0.0222957	−	0.0290563i
$356$	0.965133	−	6.91133i	0.0511520	−	0.366300i
$357$		0			0
$358$	10.5705	−	9.19698i	0.558670	−	0.486076i
$359$	5.22831	−	5.22831i	0.275939	−	0.275939i	−0.555546	−	0.831486i	$-0.687491\pi$
$359$	5.22831	−	5.22831i	0.275939	−	0.275939i	0.831486	+	0.555546i	$0.187491\pi$
$360$		0			0
$361$	−0.330044	−	0.330044i	−0.0173707	−	0.0173707i
$362$	−29.3064	−	2.03637i	−1.54031	−	0.107029i
$363$		0			0
$364$	27.4317	+	16.1261i	1.43781	+	0.845235i
$365$	0.504312	−	0.386972i	0.0263969	−	0.0202550i
$366$		0			0
$367$	−0.612755	−	1.06132i	−0.0319855	−	0.0554006i	0.849590	−	0.527444i	$-0.176850\pi$
$367$	−0.612755	−	1.06132i	−0.0319855	−	0.0554006i	−0.881575	+	0.472044i	$0.843516\pi$
$368$	−0.570175	+	36.3221i	−0.0297224	+	1.89342i
$369$		0			0
$370$	0.827665	+	0.168012i	0.0430282	+	0.00873452i
$371$	0.487228	−	0.0641447i	0.0252956	−	0.00333023i
$372$		0			0
$373$	2.19784	−	16.6943i	0.113800	−	0.864396i	−0.835382	−	0.549669i	$-0.814754\pi$
$373$	2.19784	−	16.6943i	0.113800	−	0.864396i	0.949182	−	0.314727i	$-0.101913\pi$
$374$	0.948469	+	1.94248i	0.0490442	+	0.100443i
$375$		0			0
$376$	−4.37535	−	5.10923i	−0.225641	−	0.263488i
$377$	−32.0419	−	32.0419i	−1.65024	−	1.65024i
$378$		0			0
$379$	10.2546	−	4.24759i	0.526742	−	0.218184i	−0.103433	−	0.994636i	$-0.532983\pi$
$379$	10.2546	−	4.24759i	0.526742	−	0.218184i	0.630176	+	0.776453i	$0.282983\pi$
$380$	−0.580058	+	0.0717395i	−0.0297564	+	0.00368016i
$381$		0			0
$382$	−0.824021	−	13.3762i	−0.0421606	−	0.684387i
$383$	−2.90214	+	5.02665i	−0.148292	+	0.256850i	−0.930596	−	0.366047i	$-0.880711\pi$
$383$	−2.90214	+	5.02665i	−0.148292	+	0.256850i	0.782304	+	0.622897i	$0.214044\pi$
$384$		0			0
$385$	−0.0366275	−	0.0634407i	−0.00186671	−	0.00323324i
$386$	−21.1581	+	14.0176i	−1.07692	+	0.713478i
$387$		0			0
$388$	12.0831	−	28.5357i	0.613427	−	1.44868i
$389$	−3.23589	−	2.48298i	−0.164066	−	0.125892i	0.523465	−	0.852047i	$-0.324639\pi$
$389$	−3.23589	−	2.48298i	−0.164066	−	0.125892i	−0.687531	+	0.726155i	$0.741306\pi$
$390$		0			0
$391$	−32.0095	+	8.57692i	−1.61879	+	0.433753i
$392$	−0.341925	+	0.969625i	−0.0172698	+	0.0489734i
$393$		0			0
$394$	7.36103	+	0.511485i	0.370843	+	0.0257682i
$395$	0.623711	−	0.258350i	0.0313823	−	0.0129990i
$396$		0			0
$397$	−10.8114	+	26.1011i	−0.542610	+	1.30998i	0.380266	+	0.924877i	$0.375833\pi$
$397$	−10.8114	+	26.1011i	−0.542610	+	1.30998i	−0.922875	+	0.385099i	$0.874167\pi$
$398$	−9.04731	−	27.0001i	−0.453501	−	1.35340i
$399$		0			0
$400$	−10.2612	+	17.1456i	−0.513058	+	0.857280i
$401$	−13.2637	+	22.9733i	−0.662355	+	1.14723i	0.317640	+	0.948211i	$0.397110\pi$
$401$	−13.2637	+	22.9733i	−0.662355	+	1.14723i	−0.979995	+	0.199022i	$0.936224\pi$
$402$		0			0
$403$	1.65113	+	12.5415i	0.0822484	+	0.624739i
$404$	−0.0674519	+	8.59437i	−0.00335586	+	0.427586i
$405$		0			0
$406$	−14.9378	+	22.1672i	−0.741352	+	1.10014i
$407$	−0.953779	+	3.55955i	−0.0472771	+	0.176440i
$408$		0			0
$409$	−7.12609	−	26.5949i	−0.352362	−	1.31503i	−0.883771	−	0.467919i	$-0.845004\pi$
$409$	−7.12609	−	26.5949i	−0.352362	−	1.31503i	0.531409	−	0.847116i	$-0.321663\pi$
$410$	0.510267	+	0.175448i	0.0252003	+	0.00866477i
$411$		0			0
$412$	−2.76644	−	2.15747i	−0.136293	−	0.106291i
$413$	−5.18217	+	12.5109i	−0.254998	+	0.615619i
$414$		0			0
$415$			0.291808i			0.0143243i
$416$	−34.8105	−	2.96850i	−1.70672	−	0.145543i
$417$		0			0
$418$	−0.156812	−	2.54550i	−0.00766992	−	0.124505i
$419$	4.67711	−	3.58887i	0.228492	−	0.175328i	−0.488170	−	0.872748i	$-0.662336\pi$
$419$	4.67711	−	3.58887i	0.228492	−	0.175328i	0.716662	+	0.697420i	$0.245669\pi$
$420$		0			0
$421$	−22.3387	+	29.1124i	−1.08872	+	1.41885i	−0.189221	+	0.981935i	$0.560596\pi$
$421$	−22.3387	+	29.1124i	−1.08872	+	1.41885i	−0.899502	+	0.436917i	$0.856070\pi$
$422$	9.11870	−	1.77665i	0.443892	−	0.0864861i
$423$		0			0
$424$	−0.452125	+	0.294461i	−0.0219571	+	0.0143003i
$425$	−17.6069	−	4.71776i	−0.854061	−	0.228845i
$426$		0			0
$427$	6.99996	+	0.921562i	0.338752	+	0.0445975i
$428$	12.1738	+	7.15650i	0.588441	+	0.345922i
$429$		0			0
$430$	−0.108240	−	0.323023i	−0.00521978	−	0.0155775i
$431$		−	5.39534i		−	0.259884i	−0.991522	−	0.129942i	$-0.958521\pi$
$431$		−	5.39534i		−	0.259884i	0.991522	−	0.129942i	$-0.0414792\pi$
$432$		0			0
$433$			1.07138i			0.0514873i	0.999669	+	0.0257436i	$0.00819536\pi$
$433$			1.07138i			0.0514873i	−0.999669	+	0.0257436i	$0.991805\pi$
$434$	7.07540	−	2.37085i	0.339630	−	0.113805i
$435$		0			0
$436$	−10.8760	+	2.82291i	−0.520864	+	0.135193i
$437$	38.7623	+	5.10315i	1.85425	+	0.244117i
$438$		0			0
$439$	−6.10948	−	1.63703i	−0.291589	−	0.0781312i	0.110059	−	0.993925i	$-0.464896\pi$
$439$	−6.10948	−	1.63703i	−0.291589	−	0.0781312i	−0.401649	+	0.915794i	$0.631563\pi$
$440$	0.0663436	+	0.0454681i	0.00316281	+	0.00216761i
$441$		0			0
$442$	−6.09498	−	31.2826i	−0.289909	−	1.48796i
$443$	−12.2735	+	15.9952i	−0.583133	+	0.759954i	−0.988005	−	0.154419i	$-0.950649\pi$
$443$	−12.2735	+	15.9952i	−0.583133	+	0.759954i	0.404872	+	0.914373i	$0.367316\pi$
$444$		0			0
$445$	0.187912	−	0.144190i	0.00890787	−	0.00683525i
$446$	−3.32400	+	0.204770i	−0.157396	+	0.00969614i
$447$		0			0
$448$	2.20825	+	20.4905i	0.104330	+	0.968084i
$449$		−	2.03680i		−	0.0961223i	−0.998844	−	0.0480612i	$-0.984696\pi$
$449$		−	2.03680i		−	0.0961223i	0.998844	−	0.0480612i	$-0.0153042\pi$
$450$		0			0
$451$	−0.901011	+	2.17523i	−0.0424269	+	0.102428i
$452$	24.5553	−	3.03691i	1.15499	−	0.142844i
$453$		0			0
$454$	7.31805	−	21.2835i	0.343453	−	0.998885i
$455$	0.279535	+	1.04324i	0.0131048	+	0.0489078i
$456$		0			0
$457$	−2.86574	+	10.6951i	−0.134054	+	0.500295i	0.865946	+	0.500137i	$0.166717\pi$
$457$	−2.86574	+	10.6951i	−0.134054	+	0.500295i	−1.00000		0.000158032i	$0.999950\pi$
$458$	−18.1338	−	12.2198i	−0.847335	−	0.570994i
$459$		0			0
$460$	−0.878666	+	0.864981i	−0.0409680	+	0.0403300i
$461$	3.77317	+	28.6601i	0.175734	+	1.33483i	0.821023	+	0.570895i	$0.193404\pi$
$461$	3.77317	+	28.6601i	0.175734	+	1.33483i	−0.645289	+	0.763939i	$0.723263\pi$
$462$		0			0
$463$	−3.25725	+	5.64172i	−0.151377	+	0.262193i	−0.931734	−	0.363142i	$-0.881704\pi$
$463$	−3.25725	+	5.64172i	−0.151377	+	0.262193i	0.780357	+	0.625334i	$0.215037\pi$
$464$	4.28697	−	29.0336i	0.199018	−	1.34785i
$465$		0			0
$466$	10.4193	−	3.49132i	0.482663	−	0.161732i
$467$	−8.14793	+	19.6708i	−0.377041	+	0.910258i	0.615476	+	0.788156i	$0.288964\pi$
$467$	−8.14793	+	19.6708i	−0.377041	+	0.910258i	−0.992517	+	0.122103i	$0.961036\pi$
$468$		0			0
$469$	−3.79199	+	1.57069i	−0.175098	+	0.0725279i
$470$	0.0158263	−	0.227764i	0.000730013	−	0.0105060i
$471$		0			0
$472$	−0.797685	−	14.8464i	−0.0367164	−	0.683362i
$473$	1.43586	−	0.384738i	0.0660210	−	0.0176903i
$474$		0			0
$475$	17.0613	+	13.0916i	0.782826	+	0.600683i
$476$	−17.4253	+	7.05810i	−0.798688	+	0.323507i
$477$		0			0
$478$	15.6707	+	23.6533i	0.716761	+	1.08187i
$479$	−0.238327	−	0.412794i	−0.0108894	−	0.0188611i	0.860529	−	0.509401i	$-0.170133\pi$
$479$	−0.238327	−	0.412794i	−0.0108894	−	0.0188611i	−0.871419	+	0.490540i	$0.836800\pi$
$480$		0			0
$481$	27.1659	−	47.0527i	1.23866	−	2.14542i
$482$	15.2527	−	0.939622i	0.694744	−	0.0427986i
$483$		0			0
$484$	13.3135	−	17.0714i	0.605159	−	0.775972i
$485$	0.971735	−	0.402506i	0.0441242	−	0.0182769i
$486$		0			0
$487$	19.6952	+	19.6952i	0.892476	+	0.892476i	0.994756	−	0.102280i	$-0.0326138\pi$
$487$	19.6952	+	19.6952i	0.892476	+	0.892476i	−0.102280	+	0.994756i	$0.532614\pi$
$488$	−7.36923	+	2.40515i	−0.333589	+	0.108876i
$489$		0			0
$490$	−0.0313584	+	0.0153116i	−0.00141663	+	0.000691706i
$491$	3.97996	−	30.2308i	0.179613	−	1.36430i	−0.629664	−	0.776868i	$-0.716807\pi$
$491$	3.97996	−	30.2308i	0.179613	−	1.36430i	0.809277	−	0.587428i	$-0.199859\pi$
$492$		0			0
$493$	26.5438	−	3.49456i	1.19547	−	0.157387i
$494$	−7.48024	+	36.8494i	−0.336552	+	1.65793i
$495$		0			0
$496$	−5.88342	+	5.70157i	−0.264173	+	0.256008i
$497$	13.0938	+	22.6791i	0.587336	+	1.01730i
$498$		0			0
$499$	−26.8949	+	20.6372i	−1.20398	+	0.923846i	−0.998497	−	0.0548147i	$-0.982543\pi$
$499$	−26.8949	+	20.6372i	−1.20398	+	0.923846i	−0.205483	+	0.978661i	$0.565877\pi$
$500$	−1.31351	+	0.340929i	−0.0587421	+	0.0152468i
$501$		0			0
$502$	0.875448	−	12.5990i	0.0390732	−	0.562321i
$503$	24.6072	+	24.6072i	1.09718	+	1.09718i	0.994739	+	0.102441i	$0.0326652\pi$
$503$	24.6072	+	24.6072i	1.09718	+	1.09718i	0.102441	+	0.994739i	$0.467335\pi$
$504$		0			0
$505$	−0.206274	+	0.206274i	−0.00917908	+	0.00917908i
$506$	−3.53141	−	4.05882i	−0.156990	−	0.180437i
$507$		0			0
$508$	9.73498	−	7.34925i	0.431920	−	0.326070i
$509$	11.3991	+	14.8556i	0.505258	+	0.658465i	0.974443	−	0.224635i	$-0.0721189\pi$
$509$	11.3991	+	14.8556i	0.505258	+	0.658465i	−0.469185	+	0.883100i	$0.655452\pi$
$510$		0			0
$511$	−20.8915	+	12.0617i	−0.924188	+	0.533580i
$512$	−11.8990	−	19.2462i	−0.525865	−	0.850568i
$513$		0			0
$514$	21.4292	+	32.3452i	0.945203	+	1.42668i
$515$	−0.0155425	−	0.118057i	−0.000684884	−	0.00520221i
$516$		0			0
$517$	0.987708	+	0.130034i	0.0434393	+	0.00571890i
$518$	−30.3086	−	10.4212i	−1.33168	−	0.457881i
$519$		0			0
$520$	−0.771310	−	0.900682i	−0.0338242	−	0.0394975i
$521$	−26.8438	+	26.8438i	−1.17605	+	1.17605i	−0.195305	+	0.980743i	$0.562570\pi$
$521$	−26.8438	+	26.8438i	−1.17605	+	1.17605i	−0.980743	+	0.195305i	$0.937430\pi$
$522$		0			0
$523$	−8.96802	−	21.6507i	−0.392144	−	0.946720i	−0.989472	−	0.144723i	$-0.953771\pi$
$523$	−8.96802	−	21.6507i	−0.392144	−	0.946720i	0.597328	−	0.801997i	$-0.296229\pi$
$524$	26.6606	+	7.36842i	1.16467	+	0.321891i
$525$		0			0
$526$	−24.0720	−	21.2783i	−1.04959	−	0.927777i
$527$	−6.47254	−	3.73692i	−0.281948	−	0.162783i
$528$		0			0
$529$	51.5081	−	29.7382i	2.23948	−	1.29297i
$530$	−0.0179474	−	0.00364324i	−0.000779587	−	0.000158252i
$531$		0			0
$532$	22.1800	+	0.174077i	0.961625	+	0.00754720i
$533$	21.1320	−	27.5397i	0.915327	−	1.19288i
$534$		0			0
$535$	0.124053	+	0.462973i	0.00536329	+	0.0200161i
$536$	3.01094	−	3.35286i	0.130053	−	0.144822i
$537$		0			0
$538$	27.0406	+	31.0791i	1.16580	+	1.33991i
$539$	−0.0582714	−	0.140680i	−0.00250993	−	0.00605950i
$540$		0			0
$541$	−8.00916	−	3.31750i	−0.344341	−	0.142631i	0.203809	−	0.979011i	$-0.434668\pi$
$541$	−8.00916	−	3.31750i	−0.344341	−	0.142631i	−0.548150	+	0.836380i	$0.684668\pi$
$542$	5.92963	+	2.95315i	0.254699	+	0.126849i
$543$		0			0
$544$	13.9119	−	15.2492i	0.596466	−	0.653805i
$545$	−0.330284	−	0.190689i	−0.0141478	−	0.00816824i
$546$		0			0
$547$	−45.1314	+	5.94166i	−1.92968	+	0.254047i	−0.994874	−	0.101119i	$-0.967758\pi$
$547$	−45.1314	+	5.94166i	−1.92968	+	0.254047i	−0.934803	+	0.355166i	$0.884424\pi$
$548$	−15.3086	−	37.7946i	−0.653953	−	1.61451i
$549$		0			0
$550$	−0.565939	−	2.90469i	−0.0241317	−	0.123856i
$551$	−30.5101	−	8.17516i	−1.29978	−	0.348274i
$552$		0			0
$553$	−24.7468	+	6.63089i	−1.05234	+	0.281974i
$554$	−7.71921	−	15.8091i	−0.327958	−	0.671664i
$555$		0			0
$556$	22.0970	+	38.9764i	0.937121	+	1.65297i
$557$	19.9105	+	8.24722i	0.843637	+	0.349446i	0.762286	−	0.647240i	$-0.224077\pi$
$557$	19.9105	+	8.24722i	0.843637	+	0.349446i	0.0813502	+	0.996686i	$0.474077\pi$
$558$		0			0
$559$	−21.9165			−0.926970
$560$	−0.434490	+	0.548203i	−0.0183606	+	0.0231658i
$561$		0			0
$562$	−11.3727	+	12.8659i	−0.479730	+	0.542717i
$563$	4.05452	+	5.28396i	0.170878	+	0.222692i	0.870940	−	0.491390i	$-0.163511\pi$
$563$	4.05452	+	5.28396i	0.170878	+	0.222692i	−0.700062	+	0.714082i	$0.746844\pi$
$564$		0			0
$565$	0.666255	+	0.511236i	0.0280296	+	0.0215078i
$566$	−6.42228	+	9.53045i	−0.269949	+	0.400595i
$567$		0			0
$568$	−23.7168	−	16.2542i	−0.995136	−	0.682009i
$569$	−1.77871	+	6.63825i	−0.0745676	+	0.278290i	−0.993135	−	0.116975i	$-0.962680\pi$
$569$	−1.77871	+	6.63825i	−0.0745676	+	0.278290i	0.918567	+	0.395265i	$0.129347\pi$
$570$		0			0
$571$	4.59351	−	34.8912i	0.192233	−	1.46015i	−0.574669	−	0.818386i	$-0.694869\pi$
$571$	4.59351	−	34.8912i	0.192233	−	1.46015i	0.766901	−	0.641765i	$-0.221798\pi$
$572$	4.12957	−	3.11755i	0.172666	−	0.130351i
$573$		0			0
$574$	−18.3297	−	9.12880i	−0.765067	−	0.381029i
$575$	45.3664			1.89191
$576$		0			0
$577$	27.6999			1.15316			0.576580	−	0.817041i	$-0.304387\pi$
$577$	27.6999			1.15316			0.576580	+	0.817041i	$0.304387\pi$
$578$	−4.66492	−	2.32328i	−0.194035	−	0.0966359i
$579$		0			0
$580$	0.795019	−	0.600185i	0.0330114	−	0.0249213i
$581$	1.44545	−	10.9793i	0.0599673	−	0.455497i
$582$		0			0
$583$	0.0206822	−	0.0771869i	0.000856567	−	0.00319675i
$584$	14.9730	−	21.8475i	0.619588	−	0.904056i
$585$		0			0
$586$	−6.43701	+	9.55231i	−0.265910	+	0.394602i
$587$	5.48578	+	4.20938i	0.226422	+	0.173740i	0.715743	−	0.698364i	$-0.246088\pi$
$587$	5.48578	+	4.20938i	0.226422	+	0.173740i	−0.489320	+	0.872104i	$0.662755\pi$
$588$		0			0
$589$	5.36781	+	6.99546i	0.221177	+	0.288243i
$590$	0.334217	−	0.378098i	0.0137595	−	0.0155660i
$591$		0			0
$592$	34.9557	−	4.04492i	1.43667	−	0.166245i
$593$	−0.448752			−0.0184280			−0.00921401	−	0.999958i	$-0.502933\pi$
$593$	−0.448752			−0.0184280			−0.00921401	+	0.999958i	$0.502933\pi$
$594$		0			0
$595$	−0.589545	−	0.244197i	−0.0241690	−	0.0100111i
$596$	−9.21313	−	16.2508i	−0.377384	−	0.665660i
$597$		0			0
$598$	34.8034	+	71.2780i	1.42322	+	2.91477i
$599$	−17.6744	+	4.73585i	−0.722157	+	0.193501i	−0.601134	−	0.799148i	$-0.705284\pi$
$599$	−17.6744	+	4.73585i	−0.722157	+	0.193501i	−0.121023	+	0.992650i	$0.538618\pi$
$600$		0			0
$601$	−4.76933	−	1.27794i	−0.194545	−	0.0521282i	0.160231	−	0.987080i	$-0.448776\pi$
$601$	−4.76933	−	1.27794i	−0.194545	−	0.0521282i	−0.354776	+	0.934951i	$0.615443\pi$
$602$	2.47244	+	12.6899i	0.100769	+	0.517200i
$603$		0			0
$604$	−3.46885	−	8.56404i	−0.141145	−	0.348466i
$605$	0.728517	−	0.0959110i	0.0296184	−	0.00389934i
$606$		0			0
$607$	11.1380	+	6.43050i	0.452075	+	0.261006i	0.708706	−	0.705504i	$-0.249279\pi$
$607$	11.1380	+	6.43050i	0.452075	+	0.261006i	−0.256631	+	0.966509i	$0.582612\pi$
$608$	−22.0486	+	10.3404i	−0.894188	+	0.419360i
$609$		0			0
$610$	−0.235516	−	0.117295i	−0.00953577	−	0.00474913i
$611$	−13.5699	−	5.62085i	−0.548981	−	0.227395i
$612$		0			0
$613$	1.29501	+	3.12642i	0.0523048	+	0.126275i	0.947872	−	0.318651i	$-0.103230\pi$
$613$	1.29501	+	3.12642i	0.0523048	+	0.126275i	−0.895567	+	0.444926i	$0.853230\pi$
$614$	31.0921	+	35.7356i	1.25477	+	1.44217i
$615$		0			0
$616$	−2.27095	−	2.03936i	−0.0914993	−	0.0821683i
$617$	−3.73222	−	13.9289i	−0.150254	−	0.560755i	−0.999465	−	0.0327016i	$-0.989589\pi$
$617$	−3.73222	−	13.9289i	−0.150254	−	0.560755i	0.849211	−	0.528053i	$-0.177078\pi$
$618$		0			0
$619$	−2.66294	+	3.47042i	−0.107033	+	0.139488i	−0.843798	−	0.536661i	$-0.819686\pi$
$619$	−2.66294	+	3.47042i	−0.107033	+	0.139488i	0.736765	+	0.676148i	$0.236352\pi$
$620$	−0.278069	−	0.00218239i	−0.0111675	−	8.76469e-5i
$621$		0			0
$622$	−22.0747	−	4.48105i	−0.885115	−	0.179674i
$623$	−7.78440	+	4.49433i	−0.311875	+	0.180061i
$624$		0			0
$625$	21.5908	+	12.4654i	0.863632	+	0.498618i
$626$	29.2810	+	25.8827i	1.17030	+	1.03448i
$627$		0			0
$628$	−9.45868	−	2.61418i	−0.377442	−	0.104317i
$629$	12.2844	+	29.6573i	0.489813	+	1.18251i
$630$		0			0
$631$	−10.5738	+	10.5738i	−0.420937	+	0.420937i	−0.885526	−	0.464589i	$-0.846202\pi$
$631$	−10.5738	+	10.5738i	−0.420937	+	0.420937i	0.464589	+	0.885526i	$0.346202\pi$
$632$	21.3652	−	18.2964i	0.849862	−	0.727790i
$633$		0			0
$634$	1.11088	+	0.381962i	0.0441188	+	0.0151697i
$635$	0.410464	+	0.0540386i	0.0162887	+	0.00214445i
$636$		0			0
$637$	0.293033	+	2.22580i	0.0116104	+	0.0881895i
$638$	2.40062	+	3.62348i	0.0950413	+	0.143455i
$639$		0			0
$640$	0.170463	−	0.748854i	0.00673815	−	0.0296010i
$641$	25.9177	−	14.9636i	1.02369	−	0.591027i	0.108519	−	0.994094i	$-0.465389\pi$
$641$	25.9177	−	14.9636i	1.02369	−	0.591027i	0.915170	+	0.403067i	$0.132056\pi$
$642$		0			0
$643$	3.48073	+	4.53618i	0.137267	+	0.178889i	0.856928	−	0.515435i	$-0.172370\pi$
$643$	3.48073	+	4.53618i	0.137267	+	0.178889i	−0.719662	+	0.694325i	$0.755703\pi$
$644$	37.3444	−	28.1925i	1.47157	−	1.11094i
$645$		0			0
$646$	−14.5822	−	16.7600i	−0.573729	−	0.659414i
$647$	5.34200	−	5.34200i	0.210016	−	0.210016i	−0.594258	−	0.804274i	$-0.702554\pi$
$647$	5.34200	−	5.34200i	0.210016	−	0.210016i	0.804274	+	0.594258i	$0.202554\pi$
$648$		0			0
$649$	1.55702	+	1.55702i	0.0611182	+	0.0611182i
$650$	−3.02441	+	43.5258i	−0.118627	+	1.70722i
$651$		0			0
$652$	−13.5594	+	3.51942i	−0.531029	+	0.137831i
$653$	−30.0734	+	23.0761i	−1.17686	+	0.903038i	−0.996746	−	0.0806079i	$-0.974314\pi$
$653$	−30.0734	+	23.0761i	−1.17686	+	0.903038i	−0.180116	+	0.983645i	$0.557647\pi$
$654$		0			0
$655$	0.469413	+	0.813048i	0.0183415	+	0.0317684i
$656$	22.4797	+	0.352880i	0.877686	+	0.0137777i
$657$		0			0
$658$	−1.72367	+	8.49122i	−0.0671958	+	0.331022i
$659$	28.1151	−	3.70142i	1.09521	−	0.144187i	0.438795	−	0.898587i	$-0.355406\pi$
$659$	28.1151	−	3.70142i	1.09521	−	0.144187i	0.656415	+	0.754400i	$0.272072\pi$
$660$		0			0
$661$	3.64650	−	27.6979i	0.141832	−	1.07732i	−0.761434	−	0.648243i	$-0.775504\pi$
$661$	3.64650	−	27.6979i	0.141832	−	1.07732i	0.903266	−	0.429081i	$-0.141163\pi$
$662$	19.0845	−	9.31853i	0.741742	−	0.362175i
$663$		0			0
$664$	3.77242	+	11.5585i	0.146398	+	0.448556i
$665$	0.532344	+	0.532344i	0.0206434	+	0.0206434i
$666$		0			0
$667$	−61.5609	+	25.4994i	−2.38365	+	0.987339i
$668$	−25.1179	+	32.2077i	−0.971841	+	1.24616i
$669$		0			0
$670$	0.152664	−	0.00940465i	0.00589793	−	0.000363333i
$671$	0.574028	−	0.994245i	0.0221601	−	0.0383824i
$672$		0			0
$673$	0.577904	+	1.00096i	0.0222766	+	0.0385841i	0.876949	−	0.480584i	$-0.159575\pi$
$673$	0.577904	+	1.00096i	0.0222766	+	0.0385841i	−0.854672	+	0.519168i	$0.826242\pi$
$674$	−15.4342	−	23.2963i	−0.594505	−	0.897342i
$675$		0			0
$676$	−46.6081	+	18.8785i	−1.79262	+	0.726097i
$677$	−14.2749	−	10.9535i	−0.548628	−	0.420977i	0.296900	−	0.954909i	$-0.404047\pi$
$677$	−14.2749	−	10.9535i	−0.548628	−	0.420977i	−0.845528	+	0.533932i	$0.820714\pi$
$678$		0			0
$679$	−38.5553	+	10.3309i	−1.47962	+	0.396462i
$680$	0.699602	−	0.0375890i	0.0268285	−	0.00144147i
$681$		0			0
$682$	0.0841091	−	1.21046i	0.00322070	−	0.0463507i
$683$	10.9938	−	4.55377i	0.420665	−	0.174245i	−0.162302	−	0.986741i	$-0.551892\pi$
$683$	10.9938	−	4.55377i	0.420665	−	0.174245i	0.582967	+	0.812496i	$0.301892\pi$
$684$		0			0
$685$	0.529651	−	1.27869i	0.0202369	−	0.0488563i
$686$	25.4368	−	8.52344i	0.971180	−	0.325427i
$687$		0			0
$688$	−8.46330	−	11.3956i	−0.322660	−	0.434452i
$689$	−0.589077	+	1.02031i	−0.0224421	+	0.0388708i
$690$		0			0
$691$	−6.21944	−	47.2413i	−0.236599	−	1.79714i	−0.537263	−	0.843415i	$-0.680542\pi$
$691$	−6.21944	−	47.2413i	−0.236599	−	1.79714i	0.300664	−	0.953730i	$-0.402792\pi$
$692$	−12.8528	+	12.6526i	−0.488591	+	0.480981i
$693$		0			0
$694$	13.8225	+	9.31459i	0.524696	+	0.353577i
$695$	−0.393594	+	1.46891i	−0.0149299	+	0.0557191i
$696$		0			0
$697$	5.30824	+	19.8106i	0.201064	+	0.750381i
$698$	−8.00023	+	23.2675i	−0.302813	+	0.880690i
$699$		0			0
$700$	25.5430	−	3.15907i	0.965436	−	0.119402i
$701$	4.28366	−	10.3417i	0.161792	−	0.390599i	−0.822106	−	0.569335i	$-0.807201\pi$
$701$	4.28366	−	10.3417i	0.161792	−	0.390599i	0.983897	+	0.178736i	$0.0572007\pi$
$702$		0			0
$703$		−	37.8723i		−	1.42838i
$704$	3.21566	+	0.943311i	0.121195	+	0.0355524i
$705$		0			0
$706$	16.4872	−	1.01567i	0.620504	−	0.0382252i
$707$	8.78281	−	6.73929i	0.330312	−	0.253457i
$708$		0			0
$709$	22.2568	−	29.0056i	0.835872	−	1.08933i	−0.158909	−	0.987293i	$-0.550798\pi$
$709$	22.2568	−	29.0056i	0.835872	−	1.08933i	0.994781	−	0.102036i	$-0.0325356\pi$
$710$	−0.186630	−	0.957881i	−0.00700410	−	0.0359486i
$711$		0			0
$712$	5.57910	−	8.14060i	0.209086	−	0.305082i
$713$	17.9673	+	4.81432i	0.672881	+	0.180298i
$714$		0			0
$715$	0.174118	+	0.0229231i	0.00651166	+	0.000857276i
$716$	19.1797	−	4.97818i	0.716777	−	0.186043i
$717$		0			0
$718$	9.91480	−	3.32229i	0.370017	−	0.123987i
$719$		−	35.9890i		−	1.34216i	−0.741383	−	0.671082i	$-0.765830\pi$
$719$		−	35.9890i		−	1.34216i	0.741383	−	0.671082i	$-0.234170\pi$
$720$		0			0
$721$			4.51888i			0.168292i
$722$	−0.209724	−	0.625885i	−0.00780511	−	0.0232930i
$723$		0			0
$724$	−35.8152	−	21.0544i	−1.33106	−	0.782482i
$725$	−36.3381	−	4.78401i	−1.34956	−	0.177674i
$726$		0			0
$727$	47.5511	+	12.7413i	1.76357	+	0.472548i	0.987436	−	0.158017i	$-0.0505100\pi$
$727$	47.5511	+	12.7413i	1.76357	+	0.472548i	0.776137	+	0.630565i	$0.217177\pi$
$728$	24.5590	+	37.7087i	0.910219	+	1.39758i
$729$		0			0
$730$	0.882383	−	0.171920i	0.0326585	−	0.00636305i
$731$	7.88279	−	10.2731i	0.291556	−	0.379963i
$732$		0			0
$733$	9.72530	−	7.46248i	0.359212	−	0.275633i	−0.413350	−	0.910572i	$-0.635641\pi$
$733$	9.72530	−	7.46248i	0.359212	−	0.275633i	0.772562	+	0.634939i	$0.218975\pi$
$734$	−0.106565	−	1.72985i	−0.00393339	−	0.0638501i
$735$		0			0
$736$	−23.6216	+	45.6209i	−0.870702	+	1.68161i
$737$			0.667403i			0.0245841i
$738$		0			0
$739$	15.0548	−	36.3454i	0.553798	−	1.33699i	−0.360807	−	0.932640i	$-0.617499\pi$
$739$	15.0548	−	36.3454i	0.553798	−	1.33699i	0.914606	−	0.404347i	$-0.132501\pi$
$740$	0.941820	+	0.734499i	0.0346220	+	0.0270007i
$741$		0			0
$742$	0.657225	+	0.225978i	0.0241275	+	0.00829591i
$743$	−12.7934	−	47.7455i	−0.469344	−	1.75161i	−0.642072	−	0.766644i	$-0.721925\pi$
$743$	−12.7934	−	47.7455i	−0.469344	−	1.75161i	0.172728	−	0.984969i	$-0.444742\pi$
$744$		0			0
$745$	0.164105	−	0.612450i	0.00601236	−	0.0224384i
$746$	13.3074	−	19.7477i	0.487217	−	0.723014i
$747$		0			0
$748$	−0.0239923	+	3.05698i	−0.000877246	+	0.111774i
$749$	−2.37420	−	18.0338i	−0.0867514	−	0.658942i
$750$		0			0
$751$	19.0194	−	32.9426i	0.694028	−	1.20209i	−0.276479	−	0.961020i	$-0.589168\pi$
$751$	19.0194	−	32.9426i	0.694028	−	1.20209i	0.970507	−	0.241073i	$-0.0774992\pi$
$752$	−2.31760	−	9.22630i	−0.0845141	−	0.336448i
$753$		0			0
$754$	−20.3608	−	60.7632i	−0.741495	−	2.21286i
$755$	0.120016	−	0.289744i	0.00436782	−	0.0105449i
$756$		0			0
$757$	−13.4464	+	5.56969i	−0.488718	+	0.202434i	−0.613414	−	0.789761i	$-0.710204\pi$
$757$	−13.4464	+	5.56969i	−0.488718	+	0.202434i	0.124696	+	0.992195i	$0.460204\pi$
$758$	15.6593	+	1.08809i	0.568770	+	0.0395213i
$759$		0			0
$760$	−0.779528	−	0.274890i	−0.0282764	−	0.00997130i
$761$	23.0675	−	6.18093i	0.836197	−	0.224058i	0.184782	−	0.982780i	$-0.440842\pi$
$761$	23.0675	−	6.18093i	0.836197	−	0.224058i	0.651415	+	0.758721i	$0.274176\pi$
$762$		0			0
$763$	11.4823	+	8.81072i	0.415689	+	0.318969i
$764$	7.39007	−	17.4525i	0.267364	−	0.631410i
$765$		0			0
$766$	−6.84295	+	4.53357i	−0.247246	+	0.163805i
$767$	−16.2323	−	28.1152i	−0.586115	−	1.01518i
$768$		0			0
$769$	−1.73319	+	3.00198i	−0.0625005	+	0.108254i	−0.895583	−	0.444895i	$-0.853241\pi$
$769$	−1.73319	+	3.00198i	−0.0625005	+	0.108254i	0.833082	+	0.553149i	$0.186574\pi$
$770$	−0.00636993	−	0.103402i	−0.000229556	−	0.00372636i
$771$		0			0
$772$	−35.6218	+	4.40557i	−1.28206	+	0.158560i
$773$	−17.9811	+	7.44800i	−0.646734	+	0.267886i	−0.681844	−	0.731497i	$-0.738822\pi$
$773$	−17.9811	+	7.44800i	−0.646734	+	0.267886i	0.0351102	+	0.999383i	$0.488822\pi$
$774$		0			0
$775$	7.23484	+	7.23484i	0.259883	+	0.259883i
$776$	33.2868	−	28.5055i	1.19493	−	1.02329i
$777$		0			0
$778$	−2.53090	−	5.18333i	−0.0907370	−	0.185831i
$779$	3.15833	−	23.9899i	0.113159	−	0.859528i
$780$		0			0
$781$	4.22182	−	0.555813i	0.151068	−	0.0198885i
$782$	−45.9284	−	9.32323i	−1.64240	−	0.333398i
$783$		0			0
$784$	−1.04416	+	1.01188i	−0.0372913	+	0.0361386i
$785$	−0.166539	−	0.288454i	−0.00594404	−	0.0102954i
$786$		0			0
$787$	−18.9960	+	14.5761i	−0.677133	+	0.519583i	−0.889111	−	0.457692i	$-0.848676\pi$
$787$	−18.9960	+	14.5761i	−0.677133	+	0.519583i	0.211977	+	0.977275i	$0.432010\pi$
$788$	8.99590	+	5.28835i	0.320466	+	0.188390i
$789$		0			0
$790$	0.952439	+	0.0661807i	0.0338863	+	0.00235460i
$791$	−22.5355	−	22.5355i	−0.801269	−	0.801269i
$792$		0			0
$793$	−11.9688	+	11.9688i	−0.425025	+	0.425025i
$794$	−30.1420	+	26.2253i	−1.06970	+	0.930701i
$795$		0			0
$796$	5.56956	−	39.8836i	0.197408	−	1.41364i
$797$	6.61805	+	8.62481i	0.234423	+	0.305507i	0.895721	−	0.444618i	$-0.146660\pi$
$797$	6.61805	+	8.62481i	0.234423	+	0.305507i	−0.661297	+	0.750124i	$0.729994\pi$
$798$		0			0
$799$	7.51545	−	4.33904i	0.265877	−	0.153504i
$800$	−23.7993	+	15.2354i	−0.841433	+	0.538654i
$801$		0			0
$802$	−31.2744	+	20.7198i	−1.10434	+	0.731642i
$803$	0.512005	+	3.88906i	0.0180683	+	0.137242i
$804$		0			0
$805$	1.57458	+	0.207298i	0.0554967	+	0.00730628i
$806$	−5.81681	+	16.9174i	−0.204888	+	0.595889i
$807$		0			0
$808$	−5.50382	+	10.8371i	−0.193624	+	0.381249i
$809$	−11.2197	+	11.2197i	−0.394464	+	0.394464i	−0.876275	−	0.481811i	$-0.839979\pi$
$809$	−11.2197	+	11.2197i	−0.394464	+	0.394464i	0.481811	+	0.876275i	$0.339979\pi$
$810$		0			0
$811$	15.3654	+	37.0955i	0.539554	+	1.30260i	0.925035	+	0.379882i	$0.124036\pi$
$811$	15.3654	+	37.0955i	0.539554	+	1.30260i	−0.385481	+	0.922716i	$0.625964\pi$
$812$	−32.8855	+	18.6439i	−1.15406	+	0.654272i
$813$		0			0
$814$	−3.45156	+	3.90473i	−0.120977	+	0.136861i
$815$	−0.411777	−	0.237739i	−0.0144239	−	0.00832765i
$816$		0			0
$817$	−13.2303	+	7.63851i	−0.462869	+	0.267238i
$818$	7.74617	−	38.1594i	0.270838	−	1.33421i
$819$		0			0
$820$	0.535336	+	0.543805i	0.0186947	+	0.0189905i
$821$	14.6379	−	19.0765i	0.510867	−	0.665774i	−0.464703	−	0.885467i	$-0.653839\pi$
$821$	14.6379	−	19.0765i	0.510867	−	0.665774i	0.975569	+	0.219693i	$0.0705054\pi$
$822$		0			0
$823$	1.70474	+	6.36218i	0.0594236	+	0.221772i	0.989252	−	0.146222i	$-0.0467114\pi$
$823$	1.70474	+	6.36218i	0.0594236	+	0.221772i	−0.929828	+	0.367994i	$0.880045\pi$
$824$	−2.14185	−	4.47529i	−0.0746147	−	0.155904i
$825$		0			0
$826$	−14.4478	+	12.5704i	−0.502702	+	0.437380i
$827$	12.8972	+	31.1365i	0.448478	+	1.08272i	0.972892	+	0.231259i	$0.0742843\pi$
$827$	12.8972	+	31.1365i	0.448478	+	1.08272i	−0.524414	+	0.851463i	$0.675716\pi$
$828$		0			0
$829$	21.8417	+	9.04712i	0.758593	+	0.314220i	0.728242	−	0.685320i	$-0.240338\pi$
$829$	21.8417	+	9.04712i	0.758593	+	0.314220i	0.0303508	+	0.999539i	$0.490338\pi$
$830$	−0.183974	+	0.369402i	−0.00638584	+	0.0128221i
$831$		0			0
$832$	−42.1952	−	25.7046i	−1.46286	−	0.891145i
$833$	−1.14871	−	0.663208i	−0.0398004	−	0.0229788i
$834$		0			0
$835$	−1.37446	+	0.180951i	−0.0475650	+	0.00626205i
$836$	1.40634	−	3.32123i	0.0486392	−	0.114867i
$837$		0			0
$838$	8.18343	−	1.59443i	0.282692	−	0.0550786i
$839$	−28.6548	−	7.67802i	−0.989272	−	0.265075i	−0.272328	−	0.962205i	$-0.587793\pi$
$839$	−28.6548	−	7.67802i	−0.989272	−	0.265075i	−0.716945	+	0.697130i	$0.754460\pi$
$840$		0			0
$841$	23.9869	−	6.42726i	0.827134	−	0.221630i
$842$	−46.6330	+	22.7698i	−1.60708	+	0.784699i
$843$		0			0
$844$	12.6635	+	3.49993i	0.435897	+	0.120473i
$845$	−1.57687	−	0.653163i	−0.0542461	−	0.0224695i
$846$		0			0
$847$	−27.8855			−0.958157
$848$	−0.757994	+	0.0877117i	−0.0260296	+	0.00301203i
$849$		0			0
$850$	−19.3143	−	17.0727i	−0.662475	−	0.585590i
$851$	−48.6360	−	63.3837i	−1.66722	−	2.17277i
$852$		0			0
$853$	−4.26787	−	3.27486i	−0.146129	−	0.112129i	0.533110	−	0.846046i	$-0.321023\pi$
$853$	−4.26787	−	3.27486i	−0.146129	−	0.112129i	−0.679239	+	0.733917i	$0.737690\pi$
$854$	8.28027	+	5.57982i	0.283345	+	0.190938i
$855$		0			0
$856$	10.8989	+	16.7346i	0.372518	+	0.571976i
$857$	6.94395	−	25.9152i	0.237201	−	0.885246i	−0.739943	−	0.672669i	$-0.765148\pi$
$857$	6.94395	−	25.9152i	0.237201	−	0.885246i	0.977144	−	0.212577i	$-0.0681856\pi$
$858$		0			0
$859$	−5.20582	+	39.5421i	−0.177620	+	1.34916i	0.637760	+	0.770235i	$0.279861\pi$
$859$	−5.20582	+	39.5421i	−0.177620	+	1.34916i	−0.815381	+	0.578925i	$0.803472\pi$
$860$	0.0666327	−	0.477157i	0.00227216	−	0.0162709i
$861$		0			0
$862$	3.40156	−	6.82999i	0.115858	−	0.232630i
$863$	−31.8190			−1.08313			−0.541566	−	0.840658i	$-0.682169\pi$
$863$	−31.8190			−1.08313			−0.541566	+	0.840658i	$0.682169\pi$
$864$		0			0
$865$	−0.612158			−0.0208140
$866$	−0.675466	+	1.35627i	−0.0229533	+	0.0460878i
$867$		0			0
$868$	10.4515	+	1.45951i	0.354748	+	0.0495388i
$869$	−0.543763	+	4.13029i	−0.0184459	+	0.140110i
$870$		0			0
$871$	2.54676	−	9.50462i	0.0862935	−	0.322052i
$872$	−15.5477	−	3.28335i	−0.526510	−	0.111188i
$873$		0			0
$874$	45.8520	+	30.8983i	1.55097	+	1.04515i
$875$	1.38675	+	1.06409i	0.0468807	+	0.0359728i
$876$		0			0
$877$	16.0161	+	20.8726i	0.540825	+	0.704817i	0.981199	−	0.192998i	$-0.0618209\pi$
$877$	16.0161	+	20.8726i	0.540825	+	0.704817i	−0.440374	+	0.897814i	$0.645154\pi$
$878$	−6.70193	−	5.92412i	−0.226179	−	0.199930i
$879$		0			0
$880$	0.0553188	+	0.0993855i	0.00186480	+	0.00335029i
$881$	−28.0517			−0.945086			−0.472543	−	0.881308i	$-0.656664\pi$
$881$	−28.0517			−0.945086			−0.472543	+	0.881308i	$0.656664\pi$
$882$		0			0
$883$	−19.5098	−	8.08123i	−0.656558	−	0.271955i	0.0294315	−	0.999567i	$-0.490630\pi$
$883$	−19.5098	−	8.08123i	−0.656558	−	0.271955i	−0.685989	+	0.727612i	$0.740630\pi$
$884$	12.0068	−	43.4434i	0.403834	−	1.46116i
$885$		0			0
$886$	−25.6215	+	12.5104i	−0.860772	+	0.420294i
$887$	5.16774	−	1.38469i	0.173516	−	0.0464934i	−0.171015	−	0.985268i	$-0.554705\pi$
$887$	5.16774	−	1.38469i	0.173516	−	0.0464934i	0.344531	+	0.938775i	$0.388038\pi$
$888$		0			0
$889$	−15.1760	−	4.06640i	−0.508987	−	0.136383i
$890$	0.328785	−	0.0640592i	0.0110209	−	0.00214727i
$891$		0			0
$892$	−4.33697	−	1.83644i	−0.145212	−	0.0614885i
$893$	−10.1508	+	1.33637i	−0.339682	+	0.0447200i
$894$		0			0
$895$	0.582453	+	0.336279i	0.0194693	+	0.0112406i
$896$	−10.1231	+	27.3312i	−0.338188	+	0.913072i
$897$		0			0
$898$	1.28412	−	2.57839i	0.0428518	−	0.0860420i
$899$	−13.8840	−	5.75093i	−0.463057	−	0.191804i
$900$		0			0
$901$	−0.266381	−	0.643101i	−0.00887444	−	0.0214248i
$902$	−2.51200	+	2.18558i	−0.0836404	+	0.0727720i
$903$		0			0
$904$	32.9994	+	11.6368i	1.09754	+	0.387034i
$905$	−0.364965	−	1.36207i	−0.0121318	−	0.0452767i
$906$		0			0
$907$	24.5568	−	32.0031i	0.815396	−	1.06264i	−0.181459	−	0.983399i	$-0.558082\pi$
$907$	24.5568	−	32.0031i	0.815396	−	1.06264i	0.996855	−	0.0792463i	$-0.0252514\pi$
$908$	22.6824	−	22.3292i	0.752743	−	0.741019i
$909$		0			0
$910$	−0.303859	+	1.49688i	−0.0100728	+	0.0496210i
$911$	46.5326	−	26.8656i	1.54169	−	0.890097i	0.542961	−	0.839758i	$-0.317303\pi$
$911$	46.5326	−	26.8656i	1.54169	−	0.890097i	0.998732	−	0.0503391i	$-0.0160302\pi$
$912$		0			0
$913$	−1.55945	−	0.900350i	−0.0516103	−	0.0297972i
$914$	−10.3706	+	11.7322i	−0.343029	+	0.388067i
$915$		0			0
$916$	−15.2515	−	26.9018i	−0.503924	−	0.888860i
$917$	−13.6343	−	32.9161i	−0.450244	−	1.08699i
$918$		0			0
$919$	−18.7622	+	18.7622i	−0.618909	+	0.618909i	−0.945252	−	0.326343i	$-0.894184\pi$
$919$	−18.7622	+	18.7622i	−0.618909	+	0.618909i	0.326343	+	0.945252i	$0.394184\pi$
$920$	−1.65765	+	0.541018i	−0.0546510	+	0.0178368i
$921$		0			0
$922$	−13.2926	+	38.6598i	−0.437770	+	1.27319i
$923$	−62.2447	−	8.19466i	−2.04881	−	0.269731i
$924$		0			0
$925$	−5.73605	−	43.5697i	−0.188600	−	1.43256i
$926$	−7.68026	+	5.08831i	−0.252389	+	0.167212i
$927$		0			0
$928$	23.7315	−	34.0510i	0.779025	−	1.11778i
$929$	−38.2126	+	22.0621i	−1.25371	+	0.723832i	−0.971845	−	0.235620i	$-0.924288\pi$
$929$	−38.2126	+	22.0621i	−1.25371	+	0.723832i	−0.281869	+	0.959453i	$0.590954\pi$
$930$		0			0
$931$	0.952649	+	1.24152i	0.0312218	+	0.0406890i
$932$	15.3909	+	2.14927i	0.504147	+	0.0704017i
$933$		0			0
$934$	−22.7163	+	19.7645i	−0.743299	+	0.646713i
$935$	−0.0733707	+	0.0733707i	−0.00239948	+	0.00239948i
$936$		0			0
$937$	−17.0883	−	17.0883i	−0.558251	−	0.558251i	0.370558	−	0.928809i	$-0.379166\pi$
$937$	−17.0883	−	17.0883i	−0.558251	−	0.558251i	−0.928809	+	0.370558i	$0.879166\pi$
$938$	−5.79057	−	0.402360i	−0.189069	−	0.0131375i
$939$		0			0
$940$	0.163631	−	0.278350i	0.00533707	−	0.00907878i
$941$	7.02586	−	5.39113i	0.229037	−	0.175746i	−0.487868	−	0.872918i	$-0.662225\pi$
$941$	7.02586	−	5.39113i	0.229037	−	0.175746i	0.716904	+	0.697172i	$0.245558\pi$
$942$		0			0
$943$	−25.5223	−	44.2059i	−0.831120	−	1.43954i
$944$	8.35032	−	19.2971i	0.271780	−	0.628066i
$945$		0			0
$946$	2.06023	+	0.418216i	0.0669838	+	0.0135974i
$947$	−44.1003	+	5.80592i	−1.43307	+	0.188667i	−0.806747	−	0.590897i	$-0.798774\pi$
$947$	−44.1003	+	5.80592i	−1.43307	+	0.188667i	−0.626322	+	0.779565i	$0.715440\pi$
$948$		0			0
$949$	7.54878	−	57.3386i	0.245044	−	1.86129i
$950$	13.3442	+	27.3292i	0.432944	+	0.886677i
$951$		0			0
$952$	−26.5087	−	2.05114i	−0.859151	−	0.0664777i
$953$	31.3869	+	31.3869i	1.01672	+	1.01672i	0.999858	+	0.0168649i	$0.00536852\pi$
$953$	31.3869	+	31.3869i	1.01672	+	1.01672i	0.0168649	+	0.999858i	$0.494631\pi$
$954$		0			0
$955$	0.594317	−	0.246174i	0.0192316	−	0.00796601i
$956$	4.92511	+	39.8226i	0.159289	+	1.28795i
$957$		0			0
$958$	−0.0414477	−	0.672815i	−0.00133912	−	0.0217377i
$959$	−26.2620	+	45.4871i	−0.848044	+	1.46886i
$960$		0			0
$961$	−13.4024	−	23.2137i	−0.432336	−	0.748828i
$962$	64.0545	−	42.4372i	2.06520	−	1.36823i
$963$		0			0
$964$	19.9009	+	8.42682i	0.640966	+	0.271410i
$965$	−0.966519	−	0.741636i	−0.0311134	−	0.0238741i
$966$		0			0
$967$	3.02217	−	0.809787i	0.0971863	−	0.0260410i	−0.209898	−	0.977723i	$-0.567313\pi$
$967$	3.02217	−	0.809787i	0.0971863	−	0.0260410i	0.307084	+	0.951682i	$0.400647\pi$
$968$	27.6165	−	13.2171i	0.887628	−	0.424813i
$969$		0			0
$970$	1.48389	+	0.103109i	0.0476448	+	0.00331062i
$971$	−38.1764	+	15.8132i	−1.22514	+	0.507470i	−0.899040	−	0.437866i	$-0.855735\pi$
$971$	−38.1764	+	15.8132i	−1.22514	+	0.507470i	−0.326100	+	0.945335i	$0.605735\pi$
$972$		0			0
$973$	22.0851	−	53.3182i	0.708016	−	1.70930i
$974$	12.5152	+	37.3494i	0.401012	+	1.19675i
$975$		0			0
$976$	−10.8451	−	1.60134i	−0.347143	−	0.0512576i
$977$	15.1894	−	26.3088i	0.485951	−	0.841692i	−0.513919	−	0.857839i	$-0.671807\pi$
$977$	15.1894	−	26.3088i	0.485951	−	0.841692i	0.999870	+	0.0161471i	$0.00513999\pi$
$978$		0			0
$979$	0.190778	+	1.44910i	0.00609729	+	0.0463135i
$980$	−0.0493502		0.000387319i	−0.00157643		1.23724e-5i
$981$		0			0
$982$	24.0976	−	35.7601i	0.768986	−	1.14115i
$983$	−9.55477	+	35.6589i	−0.304750	+	1.13734i	0.628411	+	0.777882i	$0.283706\pi$
$983$	−9.55477	+	35.6589i	−0.304750	+	1.13734i	−0.933161	+	0.359460i	$0.882961\pi$
$984$		0			0
$985$	0.0916701	+	0.342118i	0.00292085	+	0.0109008i
$986$	35.8051	+	12.3111i	1.14027	+	0.392065i
$987$		0			0
$988$	−32.7015	+	41.9318i	−1.04037	+	1.33403i
$989$	−12.3330	+	29.7744i	−0.392166	+	0.946772i
$990$		0			0
$991$		−	43.6720i		−	1.38729i	−0.720319	−	0.693643i	$-0.756005\pi$
$991$		−	43.6720i		−	1.38729i	0.720319	−	0.693643i	$-0.243995\pi$
$992$	−11.0425	+	3.50836i	−0.350599	+	0.111391i
$993$		0			0
$994$	2.27715	+	36.9647i	0.0722269	+	1.17245i
$995$	1.08439	−	0.832085i	0.0343776	−	0.0263789i
$996$		0			0
$997$	−1.33100	+	1.73459i	−0.0421532	+	0.0549352i	−0.813954	−	0.580929i	$-0.802689\pi$
$997$	−1.33100	+	1.73459i	−0.0421532	+	0.0549352i	0.771801	+	0.635864i	$0.219356\pi$
$998$	−47.0573	+	9.16847i	−1.48957	+	0.290223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.611.39		368
3.2	odd	2		288.2.bf.a.131.8	yes	368
9.2	odd	6	inner	864.2.bn.a.35.23		368
9.7	even	3		288.2.bf.a.227.24	yes	368
32.11	odd	8	inner	864.2.bn.a.395.23		368
96.11	even	8		288.2.bf.a.203.24	yes	368
288.11	even	24	inner	864.2.bn.a.683.39		368
288.43	odd	24		288.2.bf.a.11.8	✓	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.8	✓	368	288.43	odd	24
288.2.bf.a.131.8	yes	368	3.2	odd	2
288.2.bf.a.203.24	yes	368	96.11	even	8
288.2.bf.a.227.24	yes	368	9.7	even	3
864.2.bn.a.35.23		368	9.2	odd	6	inner
864.2.bn.a.395.23		368	32.11	odd	8	inner
864.2.bn.a.611.39		368	1.1	even	1	trivial
864.2.bn.a.683.39		368	288.11	even	24	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26591 + 0.630463i) q^{2} +(1.20503 + 1.59621i) q^{4} +(-0.00886053 + 0.0673024i) q^{5} +(0.666754 - 2.48836i) q^{7} +(0.519104 + 2.78038i) q^{8} +(-0.0536483 + 0.0796122i) q^{10} +(-0.332332 - 0.255007i) q^{11} +(3.75972 + 4.89976i) q^{13} +(2.41287 - 2.72966i) q^{14} +(-1.09579 + 3.84698i) q^{16} -3.64897 q^{17} +(3.97733 + 1.64746i) q^{19} +(-0.118106 + 0.0669583i) q^{20} +(-0.259928 - 0.532338i) q^{22} +(8.77221 - 2.35051i) q^{23} +(4.82518 + 1.29290i) q^{25} +(1.67033 + 8.57300i) q^{26} +(4.77541 - 1.93427i) q^{28} +(-7.27433 + 0.957684i) q^{29} +(1.77380 + 1.02410i) q^{31} +(-3.81255 + 4.17905i) q^{32} +(-4.61925 - 2.30054i) q^{34} +(0.161565 + 0.0669223i) q^{35} +(-3.36655 - 8.12758i) q^{37} +(3.99625 + 4.59309i) q^{38} +(-0.191726 + 0.0103013i) q^{40} +(-1.45472 - 5.42911i) q^{41} +(-2.16028 + 2.81533i) q^{43} +(0.00657510 - 0.837765i) q^{44} +(12.5867 + 2.55503i) q^{46} +(-2.05961 + 1.18912i) q^{47} +(0.314804 + 0.181752i) q^{49} +(5.29309 + 4.67879i) q^{50} +(-3.29048 + 11.9057i) q^{52} +(0.0730018 + 0.176242i) q^{53} +(0.0201073 - 0.0201073i) q^{55} +(7.26471 + 0.562114i) q^{56} +(-9.81240 - 3.37386i) q^{58} +(-5.21160 - 0.686120i) q^{59} +(0.357730 + 2.71723i) q^{61} +(1.59980 + 2.41473i) q^{62} +(-7.46106 + 2.88662i) q^{64} +(-0.363079 + 0.209624i) q^{65} +(-0.969906 - 1.26401i) q^{67} +(-4.39712 - 5.82453i) q^{68} +(0.162334 + 0.186578i) q^{70} +(-7.18803 + 7.18803i) q^{71} +(-6.62149 - 6.62149i) q^{73} +(0.862401 - 12.4112i) q^{74} +(2.16311 + 8.33390i) q^{76} +(-0.856134 + 0.656935i) q^{77} +(-4.97251 - 8.61265i) q^{79} +(-0.249202 - 0.107836i) q^{80} +(1.58131 - 7.78988i) q^{82} +(4.26191 - 0.561091i) q^{83} +(0.0323318 - 0.245584i) q^{85} +(-4.50967 + 2.20197i) q^{86} +(0.536503 - 1.05639i) q^{88} +(-2.46723 - 2.46723i) q^{89} +(14.6992 - 6.08860i) q^{91} +(14.3227 + 11.1699i) q^{92} +(-3.35696 + 0.206801i) q^{94} +(-0.146119 + 0.253086i) q^{95} +(-7.74713 - 13.4184i) q^{97} +(0.283924 + 0.428554i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

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