LMFDB - Embedded newform 264.2.k.b.155.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(155,264)] 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("264.155"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.k (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			155.21
Character	$\chi$	$=$	264.155
Dual form			264.2.k.b.155.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.589301 - 1.28558i) q^{2} +(-1.70660 - 0.295805i) q^{3} +(-1.30545 - 1.51519i) q^{4} -2.62331 q^{5} +(-1.38599 + 2.01966i) q^{6} +2.26615i q^{7} +(-2.71721 + 0.785358i) q^{8} +(2.82500 + 1.00964i) q^{9} +(-1.54592 + 3.37249i) q^{10} +1.00000i q^{11} +(1.77968 + 2.97199i) q^{12} +3.41593i q^{13} +(2.91333 + 1.33545i) q^{14} +(4.47696 + 0.775989i) q^{15} +(-0.591610 + 3.95601i) q^{16} -5.66301i q^{17} +(2.96276 - 3.03679i) q^{18} -6.67620 q^{19} +(3.42460 + 3.97482i) q^{20} +(0.670338 - 3.86742i) q^{21} +(1.28558 + 0.589301i) q^{22} -7.70741 q^{23} +(4.86951 - 0.536534i) q^{24} +1.88177 q^{25} +(4.39146 + 2.01301i) q^{26} +(-4.52250 - 2.55871i) q^{27} +(3.43365 - 2.95834i) q^{28} -1.81910 q^{29} +(3.63587 - 5.29821i) q^{30} +8.63579i q^{31} +(4.73714 + 3.09184i) q^{32} +(0.295805 - 1.70660i) q^{33} +(-7.28027 - 3.33722i) q^{34} -5.94482i q^{35} +(-2.15809 - 5.59845i) q^{36} -7.33832i q^{37} +(-3.93430 + 8.58282i) q^{38} +(1.01045 - 5.82964i) q^{39} +(7.12808 - 2.06024i) q^{40} -0.894785i q^{41} +(-4.57686 - 3.14085i) q^{42} +4.56373 q^{43} +(1.51519 - 1.30545i) q^{44} +(-7.41086 - 2.64861i) q^{45} +(-4.54198 + 9.90851i) q^{46} -7.36576 q^{47} +(2.17985 - 6.57634i) q^{48} +1.86456 q^{49} +(1.10893 - 2.41918i) q^{50} +(-1.67515 + 9.66452i) q^{51} +(5.17579 - 4.45932i) q^{52} +3.49217 q^{53} +(-5.95455 + 4.30620i) q^{54} -2.62331i q^{55} +(-1.77974 - 6.15760i) q^{56} +(11.3936 + 1.97485i) q^{57} +(-1.07200 + 2.33861i) q^{58} +0.962971i q^{59} +(-4.66867 - 7.79646i) q^{60} -0.532187i q^{61} +(11.1020 + 5.08908i) q^{62} +(-2.28800 + 6.40187i) q^{63} +(6.76642 - 4.26796i) q^{64} -8.96105i q^{65} +(-2.01966 - 1.38599i) q^{66} +2.10323 q^{67} +(-8.58054 + 7.39277i) q^{68} +(13.1535 + 2.27989i) q^{69} +(-7.64257 - 3.50329i) q^{70} +2.27093 q^{71} +(-8.46904 - 0.524773i) q^{72} -5.89627 q^{73} +(-9.43402 - 4.32448i) q^{74} +(-3.21144 - 0.556637i) q^{75} +(8.71544 + 10.1157i) q^{76} -2.26615 q^{77} +(-6.89903 - 4.73443i) q^{78} -11.5441i q^{79} +(1.55198 - 10.3778i) q^{80} +(6.96124 + 5.70448i) q^{81} +(-1.15032 - 0.527298i) q^{82} +0.294647i q^{83} +(-6.73498 + 4.03303i) q^{84} +14.8558i q^{85} +(2.68941 - 5.86706i) q^{86} +(3.10449 + 0.538100i) q^{87} +(-0.785358 - 2.71721i) q^{88} +10.7653i q^{89} +(-7.77224 + 7.96644i) q^{90} -7.74101 q^{91} +(10.0616 + 11.6782i) q^{92} +(2.55451 - 14.7379i) q^{93} +(-4.34065 + 9.46930i) q^{94} +17.5138 q^{95} +(-7.16985 - 6.67782i) q^{96} -11.5378 q^{97} +(1.09879 - 2.39705i) q^{98} +(-1.00964 + 2.82500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} + 2 q^{6} + 8 q^{9} + 12 q^{10} - 12 q^{12} + 2 q^{18} - 32 q^{19} + 4 q^{22} + 12 q^{24} - 64 q^{27} + 40 q^{28} - 22 q^{30} - 64 q^{34} - 20 q^{36} + 32 q^{40} + 20 q^{42} - 16 q^{43} - 28 q^{46}+ \cdots - 16 q^{97}+O(q^{100}) $ 32 * q + 8 * q^3 + 2 * q^6 + 8 * q^9 + 12 * q^10 - 12 * q^12 + 2 * q^18 - 32 * q^19 + 4 * q^22 + 12 * q^24 - 64 * q^27 + 40 * q^28 - 22 * q^30 - 64 * q^34 - 20 * q^36 + 32 * q^40 + 20 * q^42 - 16 * q^43 - 28 * q^46 - 32 * q^49 + 8 * q^51 + 40 * q^52 - 8 * q^54 + 16 * q^57 - 40 * q^58 + 68 * q^60 - 14 * q^66 + 8 * q^70 - 8 * q^72 + 64 * q^73 - 16 * q^75 + 8 * q^76 + 16 * q^78 + 72 * q^81 + 88 * q^82 - 60 * q^84 + 8 * q^88 - 58 * q^90 + 80 * q^91 - 72 * q^94 - 4 * q^96 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	0.589301	−	1.28558i	0.416699	−	0.909045i
$2$	0.589301	−	1.28558i	0.416699	−	0.909045i
$3$	−1.70660	−	0.295805i	−0.985309	−	0.170783i
$3$	−1.70660	−	0.295805i	−0.985309	−	0.170783i
$4$	−1.30545	−	1.51519i	−0.652724	−	0.757596i
$5$	−2.62331			−1.17318			−0.586591	−	0.809884i	$-0.699530\pi$
$5$	−2.62331			−1.17318			−0.586591	+	0.809884i	$0.699530\pi$
$6$	−1.38599	+	2.01966i	−0.565826	+	0.824524i
$7$			2.26615i			0.856525i	0.903654	+	0.428262i	$0.140874\pi$
$7$			2.26615i			0.856525i	−0.903654	+	0.428262i	$0.859126\pi$
$8$	−2.71721	+	0.785358i	−0.960678	+	0.277666i
$9$	2.82500	+	1.00964i	0.941666	+	0.336548i
$10$	−1.54592	+	3.37249i	−0.488863	+	1.06647i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	1.77968	+	2.97199i	0.513750	+	0.857940i
$13$			3.41593i			0.947408i	0.880684	+	0.473704i	$0.157083\pi$
$13$			3.41593i			0.947408i	−0.880684	+	0.473704i	$0.842917\pi$
$14$	2.91333	+	1.33545i	0.778619	+	0.356913i
$15$	4.47696	+	0.775989i	1.15595	+	0.200359i
$16$	−0.591610	+	3.95601i	−0.147902	+	0.989002i
$17$		−	5.66301i		−	1.37348i	−0.726902	−	0.686741i	$-0.759041\pi$
$17$		−	5.66301i		−	1.37348i	0.726902	−	0.686741i	$-0.240959\pi$
$18$	2.96276	−	3.03679i	0.698328	−	0.715778i
$19$	−6.67620			−1.53163			−0.765813	−	0.643063i	$-0.777663\pi$
$19$	−6.67620			−1.53163			−0.765813	+	0.643063i	$0.777663\pi$
$20$	3.42460	+	3.97482i	0.765764	+	0.888797i
$21$	0.670338	−	3.86742i	0.146280	−	0.843941i
$22$	1.28558	+	0.589301i	0.274087	+	0.125639i
$23$	−7.70741			−1.60711			−0.803553	−	0.595234i	$-0.797059\pi$
$23$	−7.70741			−1.60711			−0.803553	+	0.595234i	$0.797059\pi$
$24$	4.86951	−	0.536534i	0.993985	−	0.109519i
$25$	1.88177			0.376355
$26$	4.39146	+	2.01301i	0.861237	+	0.394784i
$27$	−4.52250	−	2.55871i	−0.870355	−	0.492424i
$28$	3.43365	−	2.95834i	0.648899	−	0.559074i
$29$	−1.81910			−0.337799			−0.168900	−	0.985633i	$-0.554021\pi$
$29$	−1.81910			−0.337799			−0.168900	+	0.985633i	$0.554021\pi$
$30$	3.63587	−	5.29821i	0.663817	−	0.967317i
$31$			8.63579i			1.55103i	0.631327	+	0.775517i	$0.282511\pi$
$31$			8.63579i			1.55103i	−0.631327	+	0.775517i	$0.717489\pi$
$32$	4.73714	+	3.09184i	0.837416	+	0.546566i
$33$	0.295805	−	1.70660i	0.0514930	−	0.297082i
$34$	−7.28027	−	3.33722i	−1.24856	−	0.572328i
$35$		−	5.94482i		−	1.00486i
$36$	−2.15809	−	5.59845i	−0.359681	−	0.933075i
$37$		−	7.33832i		−	1.20641i	−0.797585	−	0.603206i	$-0.793890\pi$
$37$		−	7.33832i		−	1.20641i	0.797585	−	0.603206i	$-0.206110\pi$
$38$	−3.93430	+	8.58282i	−0.638227	+	1.39232i
$39$	1.01045	−	5.82964i	0.161801	−	0.933490i
$40$	7.12808	−	2.06024i	1.12705	−	0.325753i
$41$		−	0.894785i		−	0.139742i	−0.997556	−	0.0698709i	$-0.977741\pi$
$41$		−	0.894785i		−	0.139742i	0.997556	−	0.0698709i	$-0.0222587\pi$
$42$	−4.57686	−	3.14085i	−0.706225	−	0.484644i
$43$	4.56373			0.695963			0.347982	−	0.937501i	$-0.386867\pi$
$43$	4.56373			0.695963			0.347982	+	0.937501i	$0.386867\pi$
$44$	1.51519	−	1.30545i	0.228424	−	0.196804i
$45$	−7.41086	−	2.64861i	−1.10475	−	0.394832i
$46$	−4.54198	+	9.90851i	−0.669679	+	1.46093i
$47$	−7.36576			−1.07441			−0.537204	−	0.843453i	$-0.680519\pi$
$47$	−7.36576			−1.07441			−0.537204	+	0.843453i	$0.680519\pi$
$48$	2.17985	−	6.57634i	0.314634	−	0.949213i
$49$	1.86456			0.266366
$50$	1.10893	−	2.41918i	0.156827	−	0.342123i
$51$	−1.67515	+	9.66452i	−0.234567	+	1.35330i
$52$	5.17579	−	4.45932i	0.717753	−	0.618396i
$53$	3.49217			0.479686			0.239843	−	0.970812i	$-0.422904\pi$
$53$	3.49217			0.479686			0.239843	+	0.970812i	$0.422904\pi$
$54$	−5.95455	+	4.30620i	−0.810312	+	0.585999i
$55$		−	2.62331i		−	0.353728i
$56$	−1.77974	−	6.15760i	−0.237828	−	0.822844i
$57$	11.3936	+	1.97485i	1.50912	+	0.261576i
$58$	−1.07200	+	2.33861i	−0.140761	+	0.307075i
$59$			0.962971i			0.125368i	0.998033	+	0.0626841i	$0.0199661\pi$
$59$			0.962971i			0.125368i	−0.998033	+	0.0626841i	$0.980034\pi$
$60$	−4.66867	−	7.79646i	−0.602722	−	1.00652i
$61$		−	0.532187i		−	0.0681396i	−0.999419	−	0.0340698i	$-0.989153\pi$
$61$		−	0.532187i		−	0.0681396i	0.999419	−	0.0340698i	$-0.0108469\pi$
$62$	11.1020	+	5.08908i	1.40996	+	0.646314i
$63$	−2.28800	+	6.40187i	−0.288262	+	0.806560i
$64$	6.76642	−	4.26796i	0.845803	−	0.533495i
$65$		−	8.96105i		−	1.11148i
$66$	−2.01966	−	1.38599i	−0.248603	−	0.170603i
$67$	2.10323			0.256951			0.128475	−	0.991713i	$-0.458992\pi$
$67$	2.10323			0.256951			0.128475	+	0.991713i	$0.458992\pi$
$68$	−8.58054	+	7.39277i	−1.04054	+	0.896505i
$69$	13.1535	+	2.27989i	1.58349	+	0.274466i
$70$	−7.64257	−	3.50329i	−0.913461	−	0.418723i
$71$	2.27093			0.269510			0.134755	−	0.990879i	$-0.456975\pi$
$71$	2.27093			0.269510			0.134755	+	0.990879i	$0.456975\pi$
$72$	−8.46904	−	0.524773i	−0.998086	−	0.0618451i
$73$	−5.89627			−0.690106			−0.345053	−	0.938583i	$-0.612139\pi$
$73$	−5.89627			−0.690106			−0.345053	+	0.938583i	$0.612139\pi$
$74$	−9.43402	−	4.32448i	−1.09668	−	0.502711i
$75$	−3.21144	−	0.556637i	−0.370825	−	0.0642750i
$76$	8.71544	+	10.1157i	0.999730	+	1.16035i
$77$	−2.26615			−0.258252
$78$	−6.89903	−	4.73443i	−0.781161	−	0.536069i
$79$		−	11.5441i		−	1.29881i	−0.760443	−	0.649404i	$-0.775018\pi$
$79$		−	11.5441i		−	1.29881i	0.760443	−	0.649404i	$-0.224982\pi$
$80$	1.55198	−	10.3778i	0.173516	−	1.16028i
$81$	6.96124	+	5.70448i	0.773471	+	0.633832i
$82$	−1.15032	−	0.527298i	−0.127032	−	0.0582303i
$83$			0.294647i			0.0323417i	0.999869	+	0.0161709i	$0.00514757\pi$
$83$			0.294647i			0.0323417i	−0.999869	+	0.0161709i	$0.994852\pi$
$84$	−6.73498	+	4.03303i	−0.734846	+	0.440040i
$85$			14.8558i			1.61134i
$86$	2.68941	−	5.86706i	0.290007	−	0.632661i
$87$	3.10449	+	0.538100i	0.332837	+	0.0576904i
$88$	−0.785358	−	2.71721i	−0.0837195	−	0.289655i
$89$			10.7653i			1.14112i	0.821254	+	0.570562i	$0.193275\pi$
$89$			10.7653i			1.14112i	−0.821254	+	0.570562i	$0.806725\pi$
$90$	−7.77224	+	7.96644i	−0.819266	+	0.839737i
$91$	−7.74101			−0.811479
$92$	10.0616	+	11.6782i	1.04900	+	1.21754i
$93$	2.55451	−	14.7379i	0.264890	−	1.52825i
$94$	−4.34065	+	9.46930i	−0.447704	+	0.976684i
$95$	17.5138			1.79688
$96$	−7.16985	−	6.67782i	−0.731769	−	0.681552i
$97$	−11.5378			−1.17149			−0.585743	−	0.810497i	$-0.699197\pi$
$97$	−11.5378			−1.17149			−0.585743	+	0.810497i	$0.699197\pi$
$98$	1.09879	−	2.39705i	0.110994	−	0.242138i
$99$	−1.00964	+	2.82500i	−0.101473	+	0.283923i
$100$	−2.45656	−	2.85125i	−0.245656	−	0.285125i
$101$	−7.28507			−0.724891			−0.362446	−	0.932005i	$-0.618058\pi$
$101$	−7.28507			−0.724891			−0.362446	+	0.932005i	$0.618058\pi$
$102$	11.4374	+	7.84885i	1.13247	+	0.777152i
$103$		−	16.9668i		−	1.67179i	−0.548892	−	0.835893i	$-0.684950\pi$
$103$		−	16.9668i		−	1.67179i	0.548892	−	0.835893i	$-0.315050\pi$
$104$	−2.68273	−	9.28179i	−0.263063	−	0.910154i
$105$	−1.75851	+	10.1455i	−0.171613	+	0.990096i
$106$	2.05794	−	4.48947i	0.199885	−	0.436056i
$107$		−	5.97663i		−	0.577782i	−0.957362	−	0.288891i	$-0.906713\pi$
$107$		−	5.97663i		−	0.577782i	0.957362	−	0.288891i	$-0.0932866\pi$
$108$	2.02695	+	10.1927i	0.195044	+	0.980795i
$109$		−	0.680709i		−	0.0652001i	−0.999468	−	0.0326000i	$-0.989621\pi$
$109$		−	0.680709i		−	0.0652001i	0.999468	−	0.0326000i	$-0.0103788\pi$
$110$	−3.37249	−	1.54592i	−0.321554	−	0.147398i
$111$	−2.17071	+	12.5236i	−0.206035	+	1.18869i
$112$	−8.96491	−	1.34068i	−0.847105	−	0.126682i
$113$			10.5967i			0.996854i	0.866932	+	0.498427i	$0.166089\pi$
$113$			10.5967i			0.996854i	−0.866932	+	0.498427i	$0.833911\pi$
$114$	9.25312	−	13.4837i	0.866635	−	1.26286i
$115$	20.2189			1.88543
$116$	2.37475	+	2.75629i	0.220490	+	0.255915i
$117$	−3.44887	+	9.65000i	−0.318848	+	0.892143i
$118$	1.23798	+	0.567480i	0.113965	+	0.0522408i
$119$	12.8332			1.17642
$120$	−12.7743	+	1.40750i	−1.16612	+	0.128486i
$121$	−1.00000			−0.0909091
$122$	−0.684171	−	0.313619i	−0.0619419	−	0.0283937i
$123$	−0.264682	+	1.52704i	−0.0238655	+	0.137689i
$124$	13.0849	−	11.2736i	1.17506	−	1.01240i
$125$	8.18009			0.731649
$126$	6.88182	+	6.71405i	0.613081	+	0.598135i
$127$			6.12524i			0.543527i	0.962364	+	0.271763i	$0.0876068\pi$
$127$			6.12524i			0.543527i	−0.962364	+	0.271763i	$0.912393\pi$
$128$	−1.49936	−	11.2139i	−0.132526	−	0.991180i
$129$	−7.78849	−	1.34997i	−0.685738	−	0.118859i
$130$	−11.5202	−	5.28076i	−1.01039	−	0.463153i
$131$			21.7962i			1.90434i	0.305563	+	0.952172i	$0.401155\pi$
$131$			21.7962i			1.90434i	−0.305563	+	0.952172i	$0.598845\pi$
$132$	−2.97199	+	1.77968i	−0.258679	+	0.154902i
$133$		−	15.1293i		−	1.31188i
$134$	1.23944	−	2.70388i	0.107071	−	0.233580i
$135$	11.8639	+	6.71230i	1.02108	+	0.577703i
$136$	4.44749	+	15.3876i	0.381369	+	1.31947i
$137$			0.354211i			0.0302623i	0.999886	+	0.0151311i	$0.00481657\pi$
$137$			0.354211i			0.0302623i	−0.999886	+	0.0151311i	$0.995183\pi$
$138$	10.6824	−	15.5664i	0.909342	−	1.32510i
$139$	4.92521			0.417751			0.208875	−	0.977942i	$-0.433020\pi$
$139$	4.92521			0.417751			0.208875	+	0.977942i	$0.433020\pi$
$140$	−9.00755	+	7.76066i	−0.761277	+	0.655896i
$141$	12.5704	+	2.17883i	1.05862	+	0.183490i
$142$	1.33826	−	2.91947i	0.112304	−	0.244997i
$143$	−3.41593			−0.285654
$144$	−5.66545	+	10.5784i	−0.472121	+	0.881534i
$145$	4.77208			0.396300
$146$	−3.47468	+	7.58014i	−0.287566	+	0.627337i
$147$	−3.18207	−	0.551545i	−0.262452	−	0.0454907i
$148$	−11.1190	+	9.57980i	−0.913973	+	0.787455i
$149$	8.96175			0.734175			0.367088	−	0.930186i	$-0.380355\pi$
$149$	8.96175			0.734175			0.367088	+	0.930186i	$0.380355\pi$
$150$	−2.60811	+	3.80055i	−0.212951	+	0.310314i
$151$			9.80015i			0.797525i	0.917054	+	0.398762i	$0.130560\pi$
$151$			9.80015i			0.797525i	−0.917054	+	0.398762i	$0.869440\pi$
$152$	18.1406	−	5.24321i	1.47140	−	0.425281i
$153$	5.71762	−	15.9980i	0.462242	−	1.29336i
$154$	−1.33545	+	2.91333i	−0.107613	+	0.234762i
$155$		−	22.6544i		−	1.81964i
$156$	−10.1521	+	6.07927i	−0.812819	+	0.486731i
$157$			20.7120i			1.65300i	0.562936	+	0.826500i	$0.309672\pi$
$157$			20.7120i			1.65300i	−0.562936	+	0.826500i	$0.690328\pi$
$158$	−14.8409	−	6.80293i	−1.18068	−	0.541212i
$159$	−5.95975	−	1.03300i	−0.472639	−	0.0819222i
$160$	−12.4270	−	8.11087i	−0.982441	−	0.641221i
$161$		−	17.4661i		−	1.37653i
$162$	11.4359	−	5.58759i	0.898486	−	0.439003i
$163$	0.864559			0.0677175			0.0338588	−	0.999427i	$-0.489220\pi$
$163$	0.864559			0.0677175			0.0338588	+	0.999427i	$0.489220\pi$
$164$	−1.35577	+	1.16810i	−0.105868	+	0.0912129i
$165$	−0.775989	+	4.47696i	−0.0604106	+	0.348531i
$166$	0.378794	+	0.173636i	0.0294001	+	0.0134768i
$167$	−21.6643			−1.67643			−0.838216	−	0.545338i	$-0.816401\pi$
$167$	−21.6643			−1.67643			−0.838216	+	0.545338i	$0.816401\pi$
$168$	1.21587	+	11.0350i	0.0938061	+	0.851372i
$169$	1.33142			0.102417
$170$	19.0984	+	8.75457i	1.46478	+	0.671445i
$171$	−18.8603	−	6.74059i	−1.44228	−	0.515466i
$172$	−5.95772	−	6.91493i	−0.454272	−	0.527259i
$173$	−21.5677			−1.63976			−0.819882	−	0.572532i	$-0.805961\pi$
$173$	−21.5677			−1.63976			−0.819882	+	0.572532i	$0.805961\pi$
$174$	2.52125	−	3.67398i	0.191136	−	0.278524i
$175$			4.26438i			0.322357i
$176$	−3.95601	−	0.591610i	−0.298195	−	0.0445942i
$177$	0.284852	−	1.64341i	0.0214108	−	0.123526i
$178$	13.8397	+	6.34403i	1.03733	+	0.475505i
$179$			5.21948i			0.390122i	0.980791	+	0.195061i	$0.0624905\pi$
$179$			5.21948i			0.390122i	−0.980791	+	0.195061i	$0.937509\pi$
$180$	5.66134	+	14.6865i	0.421971	+	1.09467i
$181$			1.66117i			0.123474i	0.998092	+	0.0617370i	$0.0196640\pi$
$181$			1.66117i			0.123474i	−0.998092	+	0.0617370i	$0.980336\pi$
$182$	−4.56179	+	9.95172i	−0.338142	+	0.737670i
$183$	−0.157424	+	0.908233i	−0.0116371	+	0.0671385i
$184$	20.9426	−	6.05308i	1.54391	−	0.446239i
$185$			19.2507i			1.41534i
$186$	−17.4414	−	11.9691i	−1.27887	−	0.877616i
$187$	5.66301			0.414120
$188$	9.61562	+	11.1605i	0.701291	+	0.813966i
$189$	5.79842	−	10.2487i	0.421773	−	0.745481i
$190$	10.3209	−	22.5154i	0.748756	−	1.63344i
$191$	9.84970			0.712699			0.356350	−	0.934353i	$-0.384021\pi$
$191$	9.84970			0.712699			0.356350	+	0.934353i	$0.384021\pi$
$192$	−12.8101	+	5.28218i	−0.924489	+	0.381209i
$193$	−0.840647			−0.0605111			−0.0302556	−	0.999542i	$-0.509632\pi$
$193$	−0.840647			−0.0605111			−0.0302556	+	0.999542i	$0.509632\pi$
$194$	−6.79924	+	14.8328i	−0.488157	+	1.06493i
$195$	−2.65072	+	15.2930i	−0.189822	+	1.09515i
$196$	−2.43409	−	2.82516i	−0.173863	−	0.201797i
$197$	−13.7168			−0.977283			−0.488641	−	0.872485i	$-0.662507\pi$
$197$	−13.7168			−0.977283			−0.488641	+	0.872485i	$0.662507\pi$
$198$	3.03679	+	2.96276i	0.215815	+	0.210554i
$199$		−	3.67147i		−	0.260264i	−0.991497	−	0.130132i	$-0.958460\pi$
$199$		−	3.67147i		−	0.260264i	0.991497	−	0.130132i	$-0.0415401\pi$
$200$	−5.11317	+	1.47787i	−0.361555	+	0.104501i
$201$	−3.58938	−	0.622146i	−0.253176	−	0.0438828i
$202$	−4.29310	+	9.36556i	−0.302061	+	0.658958i
$203$		−	4.12237i		−	0.289333i
$204$	16.8304	−	10.0784i	1.17836	−	0.705627i
$205$			2.34730i			0.163943i
$206$	−21.8122	−	9.99854i	−1.51973	−	0.696632i
$207$	−21.7734	−	7.78173i	−1.51336	−	0.540868i
$208$	−13.5134	−	2.02090i	−0.936989	−	0.140124i
$209$		−	6.67620i		−	0.461803i
$210$	12.0065	+	8.23944i	0.828531	+	0.568576i
$211$	8.35436			0.575138			0.287569	−	0.957760i	$-0.407153\pi$
$211$	8.35436			0.575138			0.287569	+	0.957760i	$0.407153\pi$
$212$	−4.55885	−	5.29130i	−0.313103	−	0.363408i
$213$	−3.87558	−	0.671752i	−0.265550	−	0.0460277i
$214$	−7.68345	−	3.52203i	−0.525230	−	0.240761i
$215$	−11.9721			−0.816491
$216$	14.2981	+	3.40076i	0.972860	+	0.231393i
$217$	−19.5700			−1.32850
$218$	−0.875108	−	0.401142i	−0.0592698	−	0.0271688i
$219$	10.0626	+	1.74414i	0.679967	+	0.117858i
$220$	−3.97482	+	3.42460i	−0.267982	+	0.230886i
$221$	19.3444			1.30125
$222$	14.8209	+	10.1708i	0.994717	+	0.682620i
$223$		−	15.8569i		−	1.06186i	−0.847417	−	0.530928i	$-0.821843\pi$
$223$		−	15.8569i		−	1.06186i	0.847417	−	0.530928i	$-0.178157\pi$
$224$	−7.00658	+	10.7351i	−0.468147	+	0.717268i
$225$	5.31601	+	1.89992i	0.354401	+	0.126661i
$226$	13.6229	+	6.24465i	0.906185	+	0.415388i
$227$			17.0784i			1.13354i	0.823877	+	0.566768i	$0.191806\pi$
$227$			17.0784i			1.13354i	−0.823877	+	0.566768i	$0.808194\pi$
$228$	−11.8815	−	19.8416i	−0.786874	−	1.31404i
$229$		−	13.1246i		−	0.867300i	−0.901081	−	0.433650i	$-0.857225\pi$
$229$		−	13.1246i		−	0.867300i	0.901081	−	0.433650i	$-0.142775\pi$
$230$	11.9150	−	25.9931i	0.785655	−	1.71394i
$231$	3.86742	+	0.670338i	0.254458	+	0.0441050i
$232$	4.94288	−	1.42865i	0.324516	−	0.0937954i
$233$			3.19345i			0.209210i	0.994514	+	0.104605i	$0.0333578\pi$
$233$			3.19345i			0.209210i	−0.994514	+	0.104605i	$0.966642\pi$
$234$	10.3735	+	10.1206i	0.678134	+	0.661602i
$235$	19.3227			1.26047
$236$	1.45909	−	1.25711i	0.0949784	−	0.0818309i
$237$	−3.41479	+	19.7012i	−0.221814	+	1.27973i
$238$	7.56264	−	16.4982i	0.490213	−	1.06942i
$239$	−4.69875			−0.303937			−0.151968	−	0.988385i	$-0.548561\pi$
$239$	−4.69875			−0.303937			−0.151968	+	0.988385i	$0.548561\pi$
$240$	−5.71843	+	17.2518i	−0.369123	+	1.11360i
$241$	−22.2328			−1.43214			−0.716070	−	0.698028i	$-0.754061\pi$
$241$	−22.2328			−1.43214			−0.716070	+	0.698028i	$0.754061\pi$
$242$	−0.589301	+	1.28558i	−0.0378817	+	0.0826404i
$243$	−10.1927	−	11.7945i	−0.653860	−	0.756615i
$244$	−0.806365	+	0.694743i	−0.0516223	+	0.0444764i
$245$	−4.89132			−0.312495
$246$	1.80716	+	1.24016i	0.115221	+	0.0790696i
$247$		−	22.8054i		−	1.45108i
$248$	−6.78219	−	23.4652i	−0.430669	−	1.49004i
$249$	0.0871581	−	0.502847i	0.00552342	−	0.0318666i
$250$	4.82053	−	10.5162i	0.304877	−	0.665102i
$251$		−	15.5766i		−	0.983186i	−0.870825	−	0.491593i	$-0.836415\pi$
$251$		−	15.5766i		−	0.983186i	0.870825	−	0.491593i	$-0.163585\pi$
$252$	12.6869	−	4.89055i	0.799202	−	0.308076i
$253$		−	7.70741i		−	0.484560i
$254$	7.87450	+	3.60961i	0.494090	+	0.226487i
$255$	4.39443	−	25.3531i	0.275190	−	1.58767i
$256$	−15.3000	−	4.68082i	−0.956250	−	0.292551i
$257$		−	30.2445i		−	1.88660i	−0.331943	−	0.943299i	$-0.607704\pi$
$257$		−	30.2445i		−	1.88660i	0.331943	−	0.943299i	$-0.392296\pi$
$258$	−6.32527	+	9.21721i	−0.393794	+	0.573839i
$259$	16.6297			1.03332
$260$	−13.5777	+	11.6982i	−0.842054	+	0.725491i
$261$	−5.13897	−	1.83665i	−0.318094	−	0.113686i
$262$	28.0208	+	12.8445i	1.73113	+	0.793538i
$263$	5.14939			0.317525			0.158762	−	0.987317i	$-0.449250\pi$
$263$	5.14939			0.317525			0.158762	+	0.987317i	$0.449250\pi$
$264$	0.536534	+	4.86951i	0.0330214	+	0.299698i
$265$	−9.16105			−0.562759
$266$	−19.4500	−	8.91571i	−1.19255	−	0.546657i
$267$	3.18444	−	18.3722i	0.194885	−	1.12436i
$268$	−2.74566	−	3.18680i	−0.167718	−	0.194665i
$269$	15.2250			0.928283			0.464142	−	0.885761i	$-0.346363\pi$
$269$	15.2250			0.928283			0.464142	+	0.885761i	$0.346363\pi$
$270$	15.6206	−	11.2965i	0.950642	−	0.687484i
$271$			1.73393i			0.105329i	0.998612	+	0.0526645i	$0.0167714\pi$
$271$			1.73393i			0.105329i	−0.998612	+	0.0526645i	$0.983229\pi$
$272$	22.4029	+	3.35029i	1.35838	+	0.203141i
$273$	13.2108	+	2.28983i	0.799557	+	0.138587i
$274$	0.455367	+	0.208737i	0.0275097	+	0.0126103i
$275$			1.88177i			0.113475i
$276$	−13.7167	−	22.9063i	−0.825651	−	1.37880i
$277$		−	11.9291i		−	0.716750i	−0.933578	−	0.358375i	$-0.883331\pi$
$277$		−	11.9291i		−	0.716750i	0.933578	−	0.358375i	$-0.116669\pi$
$278$	2.90243	−	6.33177i	0.174076	−	0.379754i
$279$	−8.71907	+	24.3961i	−0.521997	+	1.46056i
$280$	4.66882	+	16.1533i	0.279015	+	0.965345i
$281$			30.9171i			1.84436i	0.386761	+	0.922180i	$0.373594\pi$
$281$			30.9171i			1.84436i	−0.386761	+	0.922180i	$0.626406\pi$
$282$	10.2088	−	14.8764i	0.607928	−	0.885875i
$283$	−1.86514			−0.110871			−0.0554356	−	0.998462i	$-0.517655\pi$
$283$	−1.86514			−0.110871			−0.0554356	+	0.998462i	$0.517655\pi$
$284$	−2.96458	−	3.44089i	−0.175916	−	0.204180i
$285$	−29.8891	−	5.18066i	−1.77048	−	0.306876i
$286$	−2.01301	+	4.39146i	−0.119032	+	0.259673i
$287$	2.02772			0.119692
$288$	10.2608	+	13.5173i	0.604621	+	0.796513i
$289$	−15.0697			−0.886452
$290$	2.81219	−	6.13491i	0.165138	−	0.360254i
$291$	19.6905	+	3.41294i	1.15428	+	0.200070i
$292$	7.69727	+	8.93397i	0.450449	+	0.522821i
$293$	16.3026			0.952411			0.476205	−	0.879334i	$-0.342012\pi$
$293$	16.3026			0.952411			0.476205	+	0.879334i	$0.342012\pi$
$294$	−2.58425	+	3.76578i	−0.150717	+	0.219625i
$295$		−	2.52618i		−	0.147080i
$296$	5.76321	+	19.9397i	0.334980	+	1.15897i
$297$	2.55871	−	4.52250i	0.148471	−	0.262422i
$298$	5.28117	−	11.5211i	0.305930	−	0.667398i
$299$		−	26.3280i		−	1.52259i
$300$	3.34896	+	5.59261i	0.193352	+	0.322890i
$301$			10.3421i			0.596109i
$302$	12.5989	+	5.77524i	0.724986	+	0.332328i
$303$	12.4327	+	2.15496i	0.714242	+	0.123799i
$304$	3.94971	−	26.4111i	0.226531	−	1.51478i
$305$			1.39609i			0.0799401i
$306$	−17.1974	−	16.7781i	−0.983107	−	0.959141i
$307$	0.210110			0.0119916			0.00599580	−	0.999982i	$-0.498091\pi$
$307$	0.210110			0.0119916			0.00599580	+	0.999982i	$0.498091\pi$
$308$	2.95834	+	3.43365i	0.168567	+	0.195651i
$309$	−5.01885	+	28.9556i	−0.285513	+	1.64723i
$310$	−29.1241	−	13.3503i	−1.65414	−	0.758243i
$311$	6.71505			0.380776			0.190388	−	0.981709i	$-0.439025\pi$
$311$	6.71505			0.380776			0.190388	+	0.981709i	$0.439025\pi$
$312$	1.83276	+	16.6339i	0.103760	+	0.941709i
$313$	16.2816			0.920290			0.460145	−	0.887844i	$-0.347797\pi$
$313$	16.2816			0.920290			0.460145	+	0.887844i	$0.347797\pi$
$314$	26.6270	+	12.2056i	1.50265	+	0.688803i
$315$	6.00215	−	16.7941i	0.338183	−	0.946242i
$316$	−17.4915	+	15.0702i	−0.983972	+	0.847764i
$317$	−7.75016			−0.435293			−0.217646	−	0.976028i	$-0.569838\pi$
$317$	−7.75016			−0.435293			−0.217646	+	0.976028i	$0.569838\pi$
$318$	−4.84010	+	7.05301i	−0.271419	+	0.395513i
$319$		−	1.81910i		−	0.101850i
$320$	−17.7505	+	11.1962i	−0.992280	+	0.625887i
$321$	−1.76792	+	10.1997i	−0.0986754	+	0.569294i
$322$	−22.4542	−	10.2928i	−1.25132	−	0.573596i
$323$			37.8074i			2.10366i
$324$	−0.444154	−	17.9945i	−0.0246752	−	0.999696i
$325$			6.42801i			0.356562i
$326$	0.509486	−	1.11146i	0.0282178	−	0.0615582i
$327$	−0.201357	+	1.16170i	−0.0111351	+	0.0642422i
$328$	0.702727	+	2.43131i	0.0388016	+	0.134247i
$329$		−	16.6919i		−	0.920256i
$330$	5.29821	+	3.63587i	0.291657	+	0.200148i
$331$	1.49433			0.0821356			0.0410678	−	0.999156i	$-0.486924\pi$
$331$	1.49433			0.0821356			0.0410678	+	0.999156i	$0.486924\pi$
$332$	0.446447	−	0.384647i	0.0245020	−	0.0211102i
$333$	7.40909	−	20.7308i	0.406016	−	1.13604i
$334$	−12.7668	+	27.8512i	−0.698568	+	1.52395i
$335$	−5.51743			−0.301450
$336$	14.9030	+	4.93987i	0.813024	+	0.269492i
$337$	−29.8286			−1.62487			−0.812435	−	0.583052i	$-0.801858\pi$
$337$	−29.8286			−1.62487			−0.812435	+	0.583052i	$0.801858\pi$
$338$	0.784609	−	1.71166i	0.0426771	−	0.0931018i
$339$	3.13455	−	18.0844i	0.170246	−	0.982209i
$340$	22.5095	−	19.3935i	1.22075	−	1.05176i
$341$	−8.63579			−0.467654
$342$	−19.7800	+	20.2742i	−1.06958	+	1.09630i
$343$			20.0884i			1.08467i
$344$	−12.4006	+	3.58417i	−0.668596	+	0.193245i
$345$	−34.5057	−	5.98086i	−1.85773	−	0.321999i
$346$	−12.7099	+	27.7271i	−0.683288	+	1.49062i
$347$		−	15.3786i		−	0.825569i	−0.910829	−	0.412785i	$-0.864556\pi$
$347$		−	15.3786i		−	0.825569i	0.910829	−	0.412785i	$-0.135444\pi$
$348$	−3.23743	−	5.40636i	−0.173544	−	0.289811i
$349$			18.2307i			0.975866i	0.872881	+	0.487933i	$0.162249\pi$
$349$			18.2307i			0.975866i	−0.872881	+	0.487933i	$0.837751\pi$
$350$	5.48222	+	2.51301i	0.293037	+	0.134326i
$351$	8.74038	−	15.4485i	0.466527	−	0.824582i
$352$	−3.09184	+	4.73714i	−0.164796	+	0.252490i
$353$			22.3922i			1.19181i	0.803053	+	0.595907i	$0.203207\pi$
$353$			22.3922i			1.19181i	−0.803053	+	0.595907i	$0.796793\pi$
$354$	−1.94488	−	1.33466i	−0.103369	−	0.0709366i
$355$	−5.95736			−0.316184
$356$	16.3116	−	14.0536i	0.864511	−	0.744839i
$357$	−21.9013	−	3.79613i	−1.15914	−	0.200913i
$358$	6.71007	+	3.07584i	0.354638	+	0.162563i
$359$	−3.73476			−0.197113			−0.0985566	−	0.995131i	$-0.531423\pi$
$359$	−3.73476			−0.197113			−0.0985566	+	0.995131i	$0.531423\pi$
$360$	22.2169	+	1.37665i	1.17094	+	0.0725556i
$361$	25.5717			1.34588
$362$	2.13558	+	0.978931i	0.112243	+	0.0514515i
$363$	1.70660	+	0.295805i	0.0895735	+	0.0155257i
$364$	10.1055	+	11.7291i	0.529672	+	0.614773i
$365$	15.4678			0.809620
$366$	1.07484	+	0.737604i	0.0561828	+	0.0385552i
$367$		−	9.68922i		−	0.505773i	−0.967496	−	0.252887i	$-0.918620\pi$
$367$		−	9.68922i		−	0.505773i	0.967496	−	0.252887i	$-0.0813800\pi$
$368$	4.55977	−	30.4906i	0.237695	−	1.58943i
$369$	0.903414	−	2.52777i	0.0470298	−	0.131590i
$370$	24.7484	+	11.3445i	1.28661	+	0.589771i
$371$			7.91378i			0.410863i
$372$	−25.6655	+	15.3690i	−1.33069	+	0.796844i
$373$			29.1125i			1.50739i	0.657226	+	0.753694i	$0.271730\pi$
$373$			29.1125i			1.50739i	−0.657226	+	0.753694i	$0.728270\pi$
$374$	3.33722	−	7.28027i	0.172563	−	0.376454i
$375$	−13.9602	−	2.41971i	−0.720900	−	0.124953i
$376$	20.0143	−	5.78476i	1.03216	−	0.298326i
$377$		−	6.21393i		−	0.320034i
$378$	−9.75850	−	13.4939i	−0.501923	−	0.694052i
$379$	−19.3350			−0.993170			−0.496585	−	0.867988i	$-0.665413\pi$
$379$	−19.3350			−0.993170			−0.496585	+	0.867988i	$0.665413\pi$
$380$	−22.8633	−	26.5367i	−1.17286	−	1.36131i
$381$	1.81187	−	10.4534i	0.0928251	−	0.535542i
$382$	5.80444	−	12.6626i	0.296981	−	0.647875i
$383$	2.48690			0.127075			0.0635374	−	0.997979i	$-0.479762\pi$
$383$	2.48690			0.127075			0.0635374	+	0.997979i	$0.479762\pi$
$384$	−0.758317	+	19.5812i	−0.0386977	+	0.999251i
$385$	5.94482			0.302976
$386$	−0.495395	+	1.08072i	−0.0252149	+	0.0550073i
$387$	12.8925	+	4.60775i	0.655365	+	0.234225i
$388$	15.0620	+	17.4820i	0.764657	+	0.887513i
$389$	−23.1594			−1.17423			−0.587113	−	0.809505i	$-0.699736\pi$
$389$	−23.1594			−1.17423			−0.587113	+	0.809505i	$0.699736\pi$
$390$	18.0983	+	12.4199i	0.916444	+	0.628906i
$391$			43.6471i			2.20733i
$392$	−5.06639	+	1.46435i	−0.255891	+	0.0739607i
$393$	6.44742	−	37.1975i	0.325229	−	1.87637i
$394$	−8.08334	+	17.6341i	−0.407233	+	0.888394i
$395$			30.2837i			1.52374i
$396$	5.59845	−	2.15809i	0.281333	−	0.108448i
$397$			16.4907i			0.827645i	0.910358	+	0.413822i	$0.135807\pi$
$397$			16.4907i			0.827645i	−0.910358	+	0.413822i	$0.864193\pi$
$398$	−4.71999	−	2.16360i	−0.236592	−	0.108452i
$399$	−4.47532	+	25.8197i	−0.224046	+	1.29260i
$400$	−1.11327	+	7.44431i	−0.0556637	+	0.372215i
$401$			30.0042i			1.49834i	0.662379	+	0.749169i	$0.269547\pi$
$401$			30.0042i			1.49834i	−0.662379	+	0.749169i	$0.730453\pi$
$402$	−2.91505	+	4.24782i	−0.145389	+	0.211862i
$403$	−29.4993			−1.46946
$404$	9.51028	+	11.0383i	0.473154	+	0.549174i
$405$	−18.2615	−	14.9646i	−0.907422	−	0.743599i
$406$	−5.29964	−	2.42932i	−0.263017	−	0.120565i
$407$	7.33832			0.363747
$408$	−3.03840	−	27.5761i	−0.150423	−	1.36522i
$409$	−3.02003			−0.149331			−0.0746655	−	0.997209i	$-0.523789\pi$
$409$	−3.02003			−0.149331			−0.0746655	+	0.997209i	$0.523789\pi$
$410$	3.01765	+	1.38327i	0.149031	+	0.0683147i
$411$	0.104777	−	0.604498i	0.00516828	−	0.0298177i
$412$	−25.7079	+	22.1493i	−1.26654	+	1.09122i
$413$	−2.18224			−0.107381
$414$	−22.8352	+	23.4058i	−1.12229	+	1.15033i
$415$		−	0.772952i		−	0.0379427i
$416$	−10.5615	+	16.1817i	−0.517821	+	0.793375i
$417$	−8.40539	−	1.45690i	−0.411614	−	0.0713447i
$418$	−8.58282	−	3.93430i	−0.419799	−	0.192433i
$419$			10.4164i			0.508873i	0.967090	+	0.254436i	$0.0818899\pi$
$419$			10.4164i			0.508873i	−0.967090	+	0.254436i	$0.918110\pi$
$420$	17.6680	−	10.5799i	0.862108	−	0.516247i
$421$		−	7.24700i		−	0.353197i	−0.984283	−	0.176599i	$-0.943491\pi$
$421$		−	7.24700i		−	0.353197i	0.984283	−	0.176599i	$-0.0565094\pi$
$422$	4.92323	−	10.7402i	0.239659	−	0.522826i
$423$	−20.8083	−	7.43680i	−1.01173	−	0.361589i
$424$	−9.48894	+	2.74260i	−0.460824	+	0.133193i
$425$		−	10.6565i		−	0.516916i
$426$	−3.14748	+	4.58652i	−0.152496	+	0.222217i
$427$	1.20602			0.0583632
$428$	−9.05574	+	7.80218i	−0.437725	+	0.377133i
$429$	5.82964	+	1.01045i	0.281458	+	0.0487849i
$430$	−7.05518	+	15.3911i	−0.340231	+	0.742227i
$431$	−3.50855			−0.169001			−0.0845005	−	0.996423i	$-0.526929\pi$
$431$	−3.50855			−0.169001			−0.0845005	+	0.996423i	$0.526929\pi$
$432$	12.7978	−	16.3773i	0.615736	−	0.787953i
$433$	41.2801			1.98380			0.991898	−	0.127040i	$-0.0405476\pi$
$433$	41.2801			1.98380			0.991898	+	0.127040i	$0.0405476\pi$
$434$	−11.5326	+	25.1589i	−0.553584	+	1.20766i
$435$	−8.14406	−	1.41160i	−0.390478	−	0.0676813i
$436$	−1.03140	+	0.888630i	−0.0493953	+	0.0425577i
$437$	51.4562			2.46148
$438$	8.17214	−	11.9085i	0.390480	−	0.569009i
$439$		−	12.2339i		−	0.583891i	−0.956435	−	0.291945i	$-0.905697\pi$
$439$		−	12.2339i		−	0.583891i	0.956435	−	0.291945i	$-0.0943026\pi$
$440$	2.06024	+	7.12808i	0.0982181	+	0.339818i
$441$	5.26738	+	1.88254i	0.250828	+	0.0896448i
$442$	11.3997	−	24.8689i	0.542229	−	1.18289i
$443$		−	21.5894i		−	1.02574i	−0.858466	−	0.512871i	$-0.828582\pi$
$443$		−	21.5894i		−	1.02574i	0.858466	−	0.512871i	$-0.171418\pi$
$444$	21.8094	−	13.0599i	1.03503	−	0.619795i
$445$		−	28.2409i		−	1.33875i
$446$	−20.3854	−	9.34449i	−0.965275	−	0.442475i
$447$	−15.2942	−	2.65093i	−0.723389	−	0.125385i
$448$	9.67185	+	15.3337i	0.456952	+	0.724451i
$449$		−	13.9011i		−	0.656033i	−0.944672	−	0.328017i	$-0.893620\pi$
$449$		−	13.9011i		−	0.656033i	0.944672	−	0.328017i	$-0.106380\pi$
$450$	5.57523	−	5.71454i	0.262819	−	0.269386i
$451$	0.894785			0.0421338
$452$	16.0560	−	13.8334i	0.755212	−	0.650671i
$453$	2.89893	−	16.7250i	0.136204	−	0.785808i
$454$	21.9558	+	10.0643i	1.03043	+	0.472343i
$455$	20.3071			0.952012
$456$	−32.5098	+	3.58201i	−1.52241	+	0.167743i
$457$	−17.8607			−0.835489			−0.417744	−	0.908565i	$-0.637179\pi$
$457$	−17.8607			−0.835489			−0.417744	+	0.908565i	$0.637179\pi$
$458$	−16.8728	−	7.73436i	−0.788414	−	0.361403i
$459$	−14.4900	+	25.6110i	−0.676335	+	1.19542i
$460$	−26.3948	−	30.6356i	−1.23066	−	1.42839i
$461$	27.2690			1.27004			0.635022	−	0.772494i	$-0.280991\pi$
$461$	27.2690			1.27004			0.635022	+	0.772494i	$0.280991\pi$
$462$	3.14085	−	4.57686i	0.146126	−	0.212935i
$463$		−	2.17027i		−	0.100861i	−0.998728	−	0.0504306i	$-0.983941\pi$
$463$		−	2.17027i		−	0.100861i	0.998728	−	0.0504306i	$-0.0160594\pi$
$464$	1.07620	−	7.19639i	0.0499613	−	0.334084i
$465$	−6.70127	+	38.6621i	−0.310764	+	1.79291i
$466$	4.10545	+	1.88190i	0.190181	+	0.0871776i
$467$		−	42.7049i		−	1.97615i	−0.153976	−	0.988075i	$-0.549208\pi$
$467$		−	42.7049i		−	1.97615i	0.153976	−	0.988075i	$-0.450792\pi$
$468$	19.1239	−	7.37187i	0.884003	−	0.340765i
$469$			4.76624i			0.220084i
$470$	11.3869	−	24.8409i	0.525238	−	1.14583i
$471$	6.12672	−	35.3473i	0.282304	−	1.62872i
$472$	−0.756278	−	2.61659i	−0.0348105	−	0.120438i
$473$			4.56373i			0.209841i
$474$	23.3151	+	15.9999i	1.07090	+	0.734900i
$475$	−12.5631			−0.576435
$476$	−16.7531	−	19.4448i	−0.767878	−	0.891251i
$477$	9.86537	+	3.52585i	0.451704	+	0.161437i
$478$	−2.76898	+	6.04063i	−0.126650	+	0.276292i
$479$	−17.2409			−0.787757			−0.393878	−	0.919163i	$-0.628867\pi$
$479$	−17.2409			−0.787757			−0.393878	+	0.919163i	$0.628867\pi$
$480$	18.8088	+	17.5180i	0.858498	+	0.799585i
$481$	25.0672			1.14297
$482$	−13.1018	+	28.5821i	−0.596771	+	1.30188i
$483$	−5.16657	+	29.8078i	−0.235087	+	1.35630i
$484$	1.30545	+	1.51519i	0.0593386	+	0.0688723i
$485$	30.2673			1.37437
$486$	−21.1693	+	6.15303i	−0.960260	+	0.279107i
$487$			31.0591i			1.40742i	0.710485	+	0.703712i	$0.248476\pi$
$487$			31.0591i			1.40742i	−0.710485	+	0.703712i	$0.751524\pi$
$488$	0.417958	+	1.44606i	0.0189201	+	0.0654602i
$489$	−1.47546	−	0.255741i	−0.0667226	−	0.0115650i
$490$	−2.88246	+	6.28820i	−0.130216	+	0.284072i
$491$			24.5591i			1.10834i	0.832404	+	0.554169i	$0.186964\pi$
$491$			24.5591i			1.10834i	−0.832404	+	0.554169i	$0.813036\pi$
$492$	2.65929	−	1.59243i	0.119890	−	0.0717924i
$493$			10.3016i			0.463961i
$494$	−29.3183	−	13.4393i	−1.31909	−	0.604662i
$495$	2.64861	−	7.41086i	0.119046	−	0.333093i
$496$	−34.1633	−	5.10902i	−1.53398	−	0.229402i
$497$			5.14627i			0.230842i
$498$	−0.595089	−	0.408377i	−0.0266666	−	0.0182998i
$499$	2.12362			0.0950665			0.0475332	−	0.998870i	$-0.484864\pi$
$499$	2.12362			0.0950665			0.0475332	+	0.998870i	$0.484864\pi$
$500$	−10.6787	−	12.3944i	−0.477565	−	0.554294i
$501$	36.9724	+	6.40840i	1.65180	+	0.286306i
$502$	−20.0250	−	9.17930i	−0.893760	−	0.409692i
$503$	22.2580			0.992437			0.496218	−	0.868198i	$-0.334722\pi$
$503$	22.2580			0.992437			0.496218	+	0.868198i	$0.334722\pi$
$504$	1.18922	−	19.1921i	0.0529719	−	0.854885i
$505$	19.1110			0.850429
$506$	−9.90851	−	4.54198i	−0.440487	−	0.201916i
$507$	−2.27221	−	0.393841i	−0.100913	−	0.0174911i
$508$	9.28090	−	7.99618i	0.411774	−	0.354773i
$509$	−29.0384			−1.28711			−0.643553	−	0.765402i	$-0.722540\pi$
$509$	−29.0384			−1.28711			−0.643553	+	0.765402i	$0.722540\pi$
$510$	−30.0038	−	20.5900i	−1.32859	−	0.911740i
$511$		−	13.3618i		−	0.591093i
$512$	−15.0339	+	16.9110i	−0.664411	+	0.747368i
$513$	30.1931	+	17.0825i	1.33306	+	0.754210i
$514$	−38.8818	−	17.8231i	−1.71500	−	0.786144i
$515$			44.5092i			1.96131i
$516$	8.12200	+	13.5634i	0.357551	+	0.597094i
$517$		−	7.36576i		−	0.323946i
$518$	9.79993	−	21.3789i	0.430584	−	0.939336i
$519$	36.8076	+	6.37984i	1.61567	+	0.280044i
$520$	7.03764	+	24.3490i	0.308621	+	1.06778i
$521$		−	23.1068i		−	1.01233i	−0.862437	−	0.506164i	$-0.831063\pi$
$521$		−	23.1068i		−	1.01233i	0.862437	−	0.506164i	$-0.168937\pi$
$522$	−5.38956	+	5.52423i	−0.235895	+	0.241789i
$523$	−32.3423			−1.41423			−0.707115	−	0.707099i	$-0.750004\pi$
$523$	−32.3423			−1.41423			−0.707115	+	0.707099i	$0.750004\pi$
$524$	33.0254	−	28.4538i	1.44272	−	1.24301i
$525$	1.26142	−	7.27761i	0.0550531	−	0.317621i
$526$	3.03454	−	6.61996i	0.132312	−	0.288644i
$527$	48.9046			2.13032
$528$	6.57634	+	2.17985i	0.286198	+	0.0948658i
$529$	36.4041			1.58279
$530$	−5.39862	+	11.7773i	−0.234501	+	0.511573i
$531$	−0.972258	+	2.72039i	−0.0421924	+	0.118055i
$532$	−22.9238	+	19.7505i	−0.993871	+	0.856293i
$533$	3.05652			0.132393
$534$	−21.7424	−	14.9206i	−0.940885	−	0.645678i
$535$			15.6786i			0.677844i
$536$	−5.71491	+	1.65179i	−0.246847	+	0.0713465i
$537$	1.54395	−	8.90759i	0.0666262	−	0.384391i
$538$	8.97210	−	19.5730i	0.386815	−	0.843851i
$539$			1.86456i			0.0803123i
$540$	−5.31733	−	26.7387i	−0.228822	−	1.15065i
$541$		−	13.6061i		−	0.584972i	−0.956270	−	0.292486i	$-0.905518\pi$
$541$		−	13.6061i		−	0.584972i	0.956270	−	0.292486i	$-0.0944825\pi$
$542$	2.22912	+	1.02181i	0.0957487	+	0.0438905i
$543$	0.491383	−	2.83496i	0.0210873	−	0.121660i
$544$	17.5091	−	26.8265i	0.750698	−	1.15018i
$545$			1.78571i			0.0764915i
$546$	10.7289	−	15.6342i	0.459156	−	0.669084i
$547$	17.5887			0.752039			0.376019	−	0.926612i	$-0.377293\pi$
$547$	17.5887			0.752039			0.376019	+	0.926612i	$0.377293\pi$
$548$	0.536697	−	0.462404i	0.0229266	−	0.0197529i
$549$	0.537319	−	1.50343i	0.0229322	−	0.0641648i
$550$	2.41918	+	1.10893i	0.103154	+	0.0472850i
$551$	12.1447			0.517382
$552$	−37.5313	+	4.13528i	−1.59744	+	0.176009i
$553$	26.1606			1.11246
$554$	−15.3358	−	7.02983i	−0.651557	−	0.298669i
$555$	5.69445	−	32.8534i	0.241716	−	1.39455i
$556$	−6.42961	−	7.46263i	−0.272676	−	0.316486i
$557$	−45.4801			−1.92705			−0.963527	−	0.267613i	$-0.913765\pi$
$557$	−45.4801			−1.92705			−0.963527	+	0.267613i	$0.913765\pi$
$558$	26.2251	+	25.5857i	1.11020	+	1.08313i
$559$			15.5894i			0.659361i
$560$	23.5178	+	3.51701i	0.993807	+	0.148621i
$561$	−9.66452	−	1.67515i	−0.408036	−	0.0707247i
$562$	39.7465	+	18.2195i	1.67661	+	0.768542i
$563$			31.9538i			1.34669i	0.739327	+	0.673346i	$0.235144\pi$
$563$			31.9538i			1.34669i	−0.739327	+	0.673346i	$0.764856\pi$
$564$	−13.1087	−	21.8910i	−0.551977	−	0.921777i
$565$		−	27.7985i		−	1.16949i
$566$	−1.09913	+	2.39780i	−0.0461999	+	0.100787i
$567$	−12.9272	+	15.7752i	−0.542892	+	0.662497i
$568$	−6.17059	+	1.78349i	−0.258912	+	0.0748338i
$569$			22.5764i			0.946450i	0.880942	+	0.473225i	$0.156910\pi$
$569$			22.5764i			0.946450i	−0.880942	+	0.473225i	$0.843090\pi$
$570$	−24.2738	+	35.3719i	−1.01672	+	1.48157i
$571$	−37.2738			−1.55986			−0.779930	−	0.625867i	$-0.784745\pi$
$571$	−37.2738			−1.55986			−0.779930	+	0.625867i	$0.784745\pi$
$572$	4.45932	+	5.17579i	0.186454	+	0.216411i
$573$	−16.8095	−	2.91359i	−0.702229	−	0.121717i
$574$	1.19494	−	2.60680i	0.0498757	−	0.108806i
$575$	−14.5036			−0.604842
$576$	23.4243	−	5.22531i	0.976011	−	0.217721i
$577$	37.3835			1.55629			0.778147	−	0.628082i	$-0.216160\pi$
$577$	37.3835			1.55629			0.778147	+	0.628082i	$0.216160\pi$
$578$	−8.88058	+	19.3733i	−0.369383	+	0.805824i
$579$	1.43465	+	0.248668i	0.0596221	+	0.0103343i
$580$	−6.22971	−	7.23062i	−0.258674	−	0.300235i
$581$	−0.667715			−0.0277015
$582$	15.9912	−	23.3025i	0.662858	−	0.965919i
$583$			3.49217i			0.144631i
$584$	16.0214	−	4.63068i	0.662969	−	0.191619i
$585$	9.04747	−	25.3150i	0.374067	−	1.04665i
$586$	9.60717	−	20.9584i	0.396868	−	0.865784i
$587$			10.6158i			0.438161i	0.975707	+	0.219081i	$0.0703058\pi$
$587$			10.6158i			0.438161i	−0.975707	+	0.219081i	$0.929694\pi$
$588$	3.31833	+	5.54145i	0.136845	+	0.228526i
$589$		−	57.6543i		−	2.37560i
$590$	−3.24761	−	1.48868i	−0.133702	−	0.0612879i
$591$	23.4092	+	4.05750i	0.962925	+	0.166903i
$592$	29.0305	+	4.34142i	1.19314	+	0.178431i
$593$		−	26.7250i		−	1.09747i	−0.835998	−	0.548733i	$-0.815110\pi$
$593$		−	26.7250i		−	1.09747i	0.835998	−	0.548733i	$-0.184890\pi$
$594$	−4.30620	−	5.95455i	−0.176685	−	0.244318i
$595$	−33.6656			−1.38015
$596$	−11.6991	−	13.5788i	−0.479214	−	0.556208i
$597$	−1.08604	+	6.26576i	−0.0444486	+	0.256440i
$598$	−33.8468	−	15.5151i	−1.38410	−	0.634459i
$599$	−2.73919			−0.111920			−0.0559601	−	0.998433i	$-0.517822\pi$
$599$	−2.73919			−0.111920			−0.0559601	+	0.998433i	$0.517822\pi$
$600$	9.16331	−	1.00963i	0.374091	−	0.0412182i
$601$	9.15738			0.373537			0.186769	−	0.982404i	$-0.440199\pi$
$601$	9.15738			0.373537			0.186769	+	0.982404i	$0.440199\pi$
$602$	13.2956	+	6.09462i	0.541890	+	0.248398i
$603$	5.94163	+	2.12351i	0.241962	+	0.0864762i
$604$	14.8491	−	12.7936i	0.604201	−	0.520564i
$605$	2.62331			0.106653
$606$	10.0970	−	14.7134i	0.410162	−	0.597690i
$607$			30.3172i			1.23054i	0.788317	+	0.615269i	$0.210953\pi$
$607$			30.3172i			1.23054i	−0.788317	+	0.615269i	$0.789047\pi$
$608$	−31.6261	−	20.6418i	−1.28261	−	0.837135i
$609$	−1.21942	+	7.03525i	−0.0494132	+	0.285083i
$610$	1.79479	+	0.822720i	0.0726691	+	0.0333109i
$611$		−	25.1609i		−	1.01790i
$612$	−31.7041	+	12.2213i	−1.28156	+	0.494015i
$613$		−	36.6401i		−	1.47988i	−0.672673	−	0.739940i	$-0.734854\pi$
$613$		−	36.6401i		−	1.47988i	0.672673	−	0.739940i	$-0.265146\pi$
$614$	0.123818	−	0.270114i	0.00499689	−	0.0109009i
$615$	0.694343	−	4.00591i	0.0279986	−	0.161534i
$616$	6.15760	−	1.77974i	0.248097	−	0.0717078i
$617$			32.0784i			1.29143i	0.763580	+	0.645713i	$0.223440\pi$
$617$			32.0784i			1.29143i	−0.763580	+	0.645713i	$0.776560\pi$
$618$	34.2672	+	23.5157i	1.37843	+	0.945941i
$619$	−2.26988			−0.0912340			−0.0456170	−	0.998959i	$-0.514525\pi$
$619$	−2.26988			−0.0912340			−0.0456170	+	0.998959i	$0.514525\pi$
$620$	−34.3257	+	29.5741i	−1.37855	+	1.18773i
$621$	34.8567	+	19.7210i	1.39875	+	0.791377i
$622$	3.95719	−	8.63276i	0.158669	−	0.346142i
$623$	−24.3959			−0.977401
$624$	22.4643	+	7.44621i	0.899292	+	0.298087i
$625$	−30.8678			−1.23471
$626$	9.59476	−	20.9313i	0.383484	−	0.836585i
$627$	−1.97485	+	11.3936i	−0.0788680	+	0.455018i
$628$	31.3827	−	27.0385i	1.25231	−	1.07895i
$629$	−41.5570			−1.65699
$630$	−18.0532	−	17.6131i	−0.719255	−	0.701721i
$631$		−	10.6837i		−	0.425311i	−0.977127	−	0.212655i	$-0.931789\pi$
$631$		−	10.6837i		−	0.425311i	0.977127	−	0.212655i	$-0.0682112\pi$
$632$	9.06623	+	31.3676i	0.360635	+	1.24774i
$633$	−14.2576	−	2.47126i	−0.566688	−	0.0982237i
$634$	−4.56718	+	9.96348i	−0.181386	+	0.395700i
$635$		−	16.0684i		−	0.637656i
$636$	6.21495	+	10.3787i	0.246439	+	0.411542i
$637$			6.36920i			0.252357i
$638$	−2.33861	−	1.07200i	−0.0925865	−	0.0424409i
$639$	6.41538	+	2.29283i	0.253788	+	0.0907030i
$640$	3.93329	+	29.4176i	0.155477	+	1.16283i
$641$		−	7.85931i		−	0.310424i	−0.987881	−	0.155212i	$-0.950394\pi$
$641$		−	7.85931i		−	0.310424i	0.987881	−	0.155212i	$-0.0496061\pi$
$642$	12.0708	+	8.28352i	0.476396	+	0.326925i
$643$	−28.1749			−1.11111			−0.555555	−	0.831480i	$-0.687494\pi$
$643$	−28.1749			−1.11111			−0.555555	+	0.831480i	$0.687494\pi$
$644$	−26.4646	+	22.8012i	−1.04285	+	0.898491i
$645$	20.4317	+	3.54141i	0.804496	+	0.139443i
$646$	48.6046	+	22.2800i	1.91232	+	0.876593i
$647$	−19.1067			−0.751160			−0.375580	−	0.926790i	$-0.622556\pi$
$647$	−19.1067			−0.751160			−0.375580	+	0.926790i	$0.622556\pi$
$648$	−23.3952	−	10.0332i	−0.919050	−	0.394141i
$649$	−0.962971			−0.0377999
$650$	8.26374	+	3.78803i	0.324130	+	0.148579i
$651$	33.3983	+	5.78890i	1.30898	+	0.226885i
$652$	−1.12864	−	1.30997i	−0.0442008	−	0.0513025i
$653$	−43.6738			−1.70909			−0.854545	−	0.519378i	$-0.826164\pi$
$653$	−43.6738			−1.70909			−0.854545	+	0.519378i	$0.826164\pi$
$654$	1.37480	+	0.943453i	0.0537591	+	0.0368919i
$655$		−	57.1783i		−	2.23414i
$656$	3.53977	+	0.529363i	0.138205	+	0.0206682i
$657$	−16.6570	−	5.95313i	−0.649850	−	0.232254i
$658$	−21.4589	−	9.83658i	−0.836554	−	0.383470i
$659$		−	13.2237i		−	0.515122i	−0.966262	−	0.257561i	$-0.917081\pi$
$659$		−	13.2237i		−	0.515122i	0.966262	−	0.257561i	$-0.0829189\pi$
$660$	7.79646	−	4.66867i	0.303477	−	0.181728i
$661$		−	5.14037i		−	0.199937i	−0.994991	−	0.0999685i	$-0.968126\pi$
$661$		−	5.14037i		−	0.199937i	0.994991	−	0.0999685i	$-0.0318742\pi$
$662$	0.880608	−	1.92108i	0.0342258	−	0.0746649i
$663$	−33.0133	−	5.72218i	−1.28213	−	0.222231i
$664$	−0.231404	−	0.800618i	−0.00898021	−	0.0310700i
$665$			39.6889i			1.53907i
$666$	−22.2849	−	21.7417i	−0.863523	−	0.842472i
$667$	14.0206			0.542879
$668$	28.2816	+	32.8255i	1.09425	+	1.27006i
$669$	−4.69055	+	27.0615i	−0.181347	+	1.04626i
$670$	−3.25143	+	7.09312i	−0.125614	+	0.274031i
$671$	0.532187			0.0205449
$672$	15.1330	−	16.2480i	0.583766	−	0.626778i
$673$	−14.5565			−0.561112			−0.280556	−	0.959838i	$-0.590519\pi$
$673$	−14.5565			−0.561112			−0.280556	+	0.959838i	$0.590519\pi$
$674$	−17.5781	+	38.3472i	−0.677081	+	1.47708i
$675$	−8.51032	−	4.81491i	−0.327562	−	0.185326i
$676$	−1.73810	−	2.01736i	−0.0668502	−	0.0775908i
$677$	−20.1577			−0.774722			−0.387361	−	0.921928i	$-0.626613\pi$
$677$	−20.1577			−0.774722			−0.387361	+	0.921928i	$0.626613\pi$
$678$	−21.4018	−	14.6869i	−0.821930	−	0.564046i
$679$		−	26.1464i		−	1.00341i
$680$	−11.6672	−	40.3664i	−0.447415	−	1.54798i
$681$	5.05188	−	29.1461i	0.193589	−	1.11688i
$682$	−5.08908	+	11.1020i	−0.194871	+	0.425119i
$683$		−	34.0428i		−	1.30261i	−0.758815	−	0.651306i	$-0.774221\pi$
$683$		−	34.0428i		−	1.30261i	0.758815	−	0.651306i	$-0.225779\pi$
$684$	14.4078	+	37.3764i	0.550897	+	1.42912i
$685$		−	0.929206i		−	0.0355031i
$686$	25.8253	+	11.8381i	0.986016	+	0.451982i
$687$	−3.88233	+	22.3985i	−0.148120	+	0.854558i
$688$	−2.69995	+	18.0542i	−0.102935	+	0.688309i
$689$			11.9290i			0.454459i
$690$	−28.0232	+	40.8355i	−1.06682	+	1.55458i
$691$	−4.45349			−0.169419			−0.0847095	−	0.996406i	$-0.526996\pi$
$691$	−4.45349			−0.169419			−0.0847095	+	0.996406i	$0.526996\pi$
$692$	28.1556	+	32.6792i	1.07031	+	1.24228i
$693$	−6.40187	−	2.28800i	−0.243187	−	0.0869141i
$694$	−19.7705	−	9.06266i	−0.750479	−	0.344014i
$695$	−12.9204			−0.490098
$696$	−8.85815	+	0.976011i	−0.335767	+	0.0369956i
$697$	−5.06717			−0.191933
$698$	23.4371	+	10.7434i	0.887106	+	0.406642i
$699$	0.944638	−	5.44996i	0.0357295	−	0.206136i
$700$	6.46136	−	5.56693i	0.244216	−	0.210410i
$701$	−21.6957			−0.819436			−0.409718	−	0.912212i	$-0.634373\pi$
$701$	−21.6957			−0.819436			−0.409718	+	0.912212i	$0.634373\pi$
$702$	−14.7097	−	20.3403i	−0.555181	−	0.767696i
$703$			48.9921i			1.84777i
$704$	4.26796	+	6.76642i	0.160855	+	0.255019i
$705$	−32.9762	−	5.71575i	−1.24196	−	0.215268i
$706$	28.7870	+	13.1957i	1.08341	+	0.496628i
$707$		−	16.5091i		−	0.620887i
$708$	−2.86194	+	1.71378i	−0.107558	+	0.0644080i
$709$			16.8944i			0.634482i	0.948345	+	0.317241i	$0.102756\pi$
$709$			16.8944i			0.634482i	−0.948345	+	0.317241i	$0.897244\pi$
$710$	−3.51068	+	7.65869i	−0.131754	+	0.287425i
$711$	11.6554	−	32.6120i	0.437111	−	1.22304i
$712$	−8.45465	−	29.2517i	−0.316852	−	1.09625i
$713$		−	66.5595i		−	2.49267i
$714$	−17.7867	+	25.9188i	−0.665650	+	0.969988i
$715$	8.96105			0.335124
$716$	7.90851	−	6.81376i	0.295555	−	0.254642i
$717$	8.01890	+	1.38991i	0.299471	+	0.0519072i
$718$	−2.20090	+	4.80135i	−0.0821369	+	0.179185i
$719$	−28.8671			−1.07656			−0.538281	−	0.842765i	$-0.680926\pi$
$719$	−28.8671			−1.07656			−0.538281	+	0.842765i	$0.680926\pi$
$720$	14.8623	−	27.7505i	0.553884	−	1.03420i
$721$	38.4493			1.43193
$722$	15.0694	−	32.8746i	0.560826	−	1.22346i
$723$	37.9426	+	6.57657i	1.41110	+	0.244585i
$724$	2.51699	−	2.16857i	0.0935433	−	0.0805944i
$725$	−3.42314			−0.127132
$726$	1.38599	−	2.01966i	0.0514388	−	0.0749568i
$727$		−	25.4333i		−	0.943267i	−0.881795	−	0.471634i	$-0.843664\pi$
$727$		−	25.4333i		−	0.943267i	0.881795	−	0.471634i	$-0.156336\pi$
$728$	21.0339	−	6.07947i	0.779569	−	0.225320i
$729$	13.9060	+	23.1435i	0.515037	+	0.857168i
$730$	9.11517	−	19.8851i	0.337368	−	0.735980i
$731$		−	25.8445i		−	0.955892i
$732$	1.58166	−	0.947125i	0.0584597	−	0.0350067i
$733$			16.9853i			0.627365i	0.949528	+	0.313682i	$0.101563\pi$
$733$			16.9853i			0.627365i	−0.949528	+	0.313682i	$0.898437\pi$
$734$	−12.4563	−	5.70987i	−0.459771	−	0.210755i
$735$	8.34755	+	1.44688i	0.307904	+	0.0533688i
$736$	−36.5111	−	23.8301i	−1.34582	−	0.878389i
$737$			2.10323i			0.0774735i
$738$	−2.71727	−	2.65103i	−0.100024	−	0.0975857i
$739$	−31.4425			−1.15663			−0.578316	−	0.815813i	$-0.696290\pi$
$739$	−31.4425			−1.15663			−0.578316	+	0.815813i	$0.696290\pi$
$740$	29.1685	−	25.1308i	1.07226	−	0.923827i
$741$	−6.74596	+	38.9199i	−0.247819	+	1.42976i
$742$	10.1738	+	4.66360i	0.373493	+	0.171206i
$743$	29.5341			1.08350			0.541750	−	0.840540i	$-0.317762\pi$
$743$	29.5341			1.08350			0.541750	+	0.840540i	$0.317762\pi$
$744$	4.63339	+	42.0521i	0.169868	+	1.54170i
$745$	−23.5095			−0.861321
$746$	37.4265	+	17.1560i	1.37028	+	0.628126i
$747$	−0.297489	+	0.832379i	−0.0108845	+	0.0304551i
$748$	−7.39277	−	8.58054i	−0.270306	−	0.313736i
$749$	13.5439			0.494885
$750$	−11.3375	+	16.5210i	−0.413986	+	0.603263i
$751$		−	6.19019i		−	0.225883i	−0.993602	−	0.112942i	$-0.963973\pi$
$751$		−	6.19019i		−	0.225883i	0.993602	−	0.112942i	$-0.0360273\pi$
$752$	4.35766	−	29.1390i	0.158907	−	1.06259i
$753$	−4.60763	+	26.5831i	−0.167911	+	0.968741i
$754$	−7.98853	−	3.66188i	−0.290925	−	0.133358i
$755$		−	25.7089i		−	0.935641i
$756$	−23.0982	+	4.59338i	−0.840075	+	0.167060i
$757$			30.8328i			1.12064i	0.828277	+	0.560319i	$0.189321\pi$
$757$			30.8328i			1.12064i	−0.828277	+	0.560319i	$0.810679\pi$
$758$	−11.3941	+	24.8567i	−0.413853	+	0.902836i
$759$	−2.27989	+	13.1535i	−0.0827547	+	0.477442i
$760$	−47.5886	+	13.7546i	−1.72622	+	0.498931i
$761$			11.8303i			0.428847i	0.976741	+	0.214424i	$0.0687873\pi$
$761$			11.8303i			0.428847i	−0.976741	+	0.214424i	$0.931213\pi$
$762$	−12.3709	−	8.48949i	−0.448151	−	0.307542i
$763$	1.54259			0.0558455
$764$	−12.8583	−	14.9242i	−0.465196	−	0.539938i
$765$	−14.9991	+	41.9678i	−0.542294	+	1.51735i
$766$	1.46554	−	3.19712i	0.0529519	−	0.115517i
$767$	−3.28944			−0.118775
$768$	24.7264	+	12.5141i	0.892238	+	0.451565i
$769$	0.159860			0.00576471			0.00288235	−	0.999996i	$-0.499083\pi$
$769$	0.159860			0.00576471			0.00288235	+	0.999996i	$0.499083\pi$
$770$	3.50329	−	7.64257i	0.126250	−	0.275419i
$771$	−8.94646	+	51.6154i	−0.322199	+	1.85888i
$772$	1.09742	+	1.27374i	0.0394971	+	0.0458430i
$773$	40.5052			1.45687			0.728435	−	0.685115i	$-0.240248\pi$
$773$	40.5052			1.45687			0.728435	+	0.685115i	$0.240248\pi$
$774$	13.5212	−	13.8591i	0.486011	−	0.498155i
$775$			16.2506i			0.583739i
$776$	31.3506	−	9.06131i	1.12542	−	0.325282i
$777$	−28.3804	−	4.91916i	−1.01814	−	0.176474i
$778$	−13.6478	+	29.7733i	−0.489299	+	1.06742i
$779$			5.97377i			0.214032i
$780$	26.6322	−	15.9478i	0.953585	−	0.571024i
$781$			2.27093i			0.0812603i
$782$	56.1120	+	25.7213i	2.00656	+	0.919792i
$783$	8.22690	+	4.65456i	0.294005	+	0.166340i
$784$	−1.10309	+	7.37621i	−0.0393961	+	0.263436i
$785$		−	54.3342i		−	1.93927i
$786$	−44.0210	−	30.2092i	−1.57018	−	1.07753i
$787$	49.5411			1.76595			0.882975	−	0.469420i	$-0.155537\pi$
$787$	49.5411			1.76595			0.882975	+	0.469420i	$0.155537\pi$
$788$	17.9066	+	20.7836i	0.637896	+	0.740385i
$789$	−8.78797	−	1.52321i	−0.312860	−	0.0542278i
$790$	38.9322	+	17.8462i	1.38515	+	0.634940i
$791$	−24.0137			−0.853830
$792$	0.524773	−	8.46904i	0.0186470	−	0.300934i
$793$	1.81791			0.0645560
$794$	21.2002	+	9.71799i	0.752366	+	0.344879i
$795$	15.6343	+	2.70988i	0.554491	+	0.0961096i
$796$	−5.56299	+	4.79292i	−0.197175	+	0.169881i
$797$	48.1713			1.70632			0.853158	−	0.521653i	$-0.174685\pi$
$797$	48.1713			1.70632			0.853158	+	0.521653i	$0.174685\pi$
$798$	30.5561	+	20.9690i	1.08167	+	0.742294i
$799$			41.7124i			1.47568i
$800$	8.91423	+	5.81815i	0.315165	+	0.205703i
$801$	−10.8692	+	30.4121i	−0.384043	+	1.07456i
$802$	38.5729	+	17.6815i	1.36206	+	0.624355i
$803$		−	5.89627i		−	0.208075i
$804$	3.74309	+	6.25078i	0.132008	+	0.220448i
$805$			45.8192i			1.61491i
$806$	−17.3839	+	37.9237i	−0.612323	+	1.33581i
$807$	−25.9830	−	4.50362i	−0.914646	−	0.158535i
$808$	19.7950	−	5.72139i	0.696387	−	0.201278i
$809$		−	18.5277i		−	0.651398i	−0.945474	−	0.325699i	$-0.894400\pi$
$809$		−	18.5277i		−	0.651398i	0.945474	−	0.325699i	$-0.105600\pi$
$810$	−29.9998	+	14.6580i	−1.05409	+	0.515030i
$811$	−33.4335			−1.17401			−0.587004	−	0.809584i	$-0.699693\pi$
$811$	−33.4335			−1.17401			−0.587004	+	0.809584i	$0.699693\pi$
$812$	−6.24617	+	5.38154i	−0.219198	+	0.188855i
$813$	0.512906	−	2.95914i	0.0179884	−	0.103782i
$814$	4.32448	−	9.43402i	0.151573	−	0.330662i
$815$	−2.26801			−0.0794449
$816$	−37.2419	−	12.3445i	−1.30373	−	0.432144i
$817$	−30.4684			−1.06596
$818$	−1.77971	+	3.88250i	−0.0622260	+	0.135749i
$819$	−21.8684	−	7.81566i	−0.764142	−	0.273101i
$820$	3.55661	−	3.06428i	0.124202	−	0.107009i
$821$	−7.23244			−0.252414			−0.126207	−	0.992004i	$-0.540280\pi$
$821$	−7.23244			−0.252414			−0.126207	+	0.992004i	$0.540280\pi$
$822$	−0.715387	−	0.490931i	−0.0249520	−	0.0171232i
$823$			1.91133i			0.0666247i	0.999445	+	0.0333123i	$0.0106056\pi$
$823$			1.91133i			0.0666247i	−0.999445	+	0.0333123i	$0.989394\pi$
$824$	13.3250	+	46.1022i	0.464198	+	1.60605i
$825$	0.556637	−	3.21144i	0.0193796	−	0.111808i
$826$	−1.28600	+	2.80545i	−0.0447455	+	0.0976141i
$827$		−	11.1784i		−	0.388713i	−0.980931	−	0.194356i	$-0.937738\pi$
$827$		−	11.1784i		−	0.388713i	0.980931	−	0.194356i	$-0.0622618\pi$
$828$	16.6333	+	43.1495i	0.578046	+	1.49955i
$829$		−	30.1331i		−	1.04657i	−0.852159	−	0.523283i	$-0.824707\pi$
$829$		−	30.1331i		−	1.04657i	0.852159	−	0.523283i	$-0.175293\pi$
$830$	−0.993695	−	0.455502i	−0.0344916	−	0.0158107i
$831$	−3.52868	+	20.3582i	−0.122409	+	0.706220i
$832$	14.5791	+	23.1136i	0.505438	+	0.801321i
$833$		−	10.5590i		−	0.365848i
$834$	−6.82627	+	9.94727i	−0.236374	+	0.344446i
$835$	56.8322			1.96676
$836$	−10.1157	+	8.71544i	−0.349860	+	0.301430i
$837$	22.0965	−	39.0554i	0.763766	−	1.34995i
$838$	13.3911	+	6.13837i	0.462588	+	0.212047i
$839$	−41.2510			−1.42414			−0.712072	−	0.702107i	$-0.752243\pi$
$839$	−41.2510			−1.42414			−0.712072	+	0.702107i	$0.752243\pi$
$840$	−3.18960	−	28.9484i	−0.110052	−	0.998814i
$841$	−25.6909			−0.885892
$842$	−9.31662	−	4.27067i	−0.321072	−	0.147177i
$843$	9.14543	−	52.7633i	0.314985	−	1.81726i
$844$	−10.9062	−	12.6585i	−0.375406	−	0.435722i
$845$	−3.49274			−0.120154
$846$	−21.8230	+	22.3683i	−0.750289	+	0.769037i
$847$		−	2.26615i		−	0.0778659i
$848$	−2.06600	+	13.8150i	−0.0709467	+	0.474411i
$849$	3.18306	+	0.551718i	0.109242	+	0.0189349i
$850$	−13.6998	−	6.27989i	−0.469900	−	0.215398i
$851$			56.5594i			1.93883i
$852$	4.04154	+	6.74918i	0.138461	+	0.231223i
$853$		−	18.2920i		−	0.626306i	−0.949703	−	0.313153i	$-0.898615\pi$
$853$		−	18.2920i		−	0.626306i	0.949703	−	0.313153i	$-0.101385\pi$
$854$	0.710707	−	1.55043i	0.0243199	−	0.0530548i
$855$	49.4764	+	17.6827i	1.69206	+	0.604735i
$856$	4.69380	+	16.2397i	0.160431	+	0.555063i
$857$		−	4.23009i		−	0.144497i	−0.997387	−	0.0722486i	$-0.976982\pi$
$857$		−	4.23009i		−	0.144497i	0.997387	−	0.0722486i	$-0.0230175\pi$
$858$	4.73443	−	6.89903i	0.161631	−	0.235529i
$859$	54.2336			1.85043			0.925213	−	0.379449i	$-0.123886\pi$
$859$	54.2336			1.85043			0.925213	+	0.379449i	$0.123886\pi$
$860$	15.6290	+	18.1400i	0.532943	+	0.618570i
$861$	−3.46051	−	0.599808i	−0.117934	−	0.0204414i
$862$	−2.06759	+	4.51054i	−0.0704226	+	0.153630i
$863$	−23.9858			−0.816488			−0.408244	−	0.912873i	$-0.633859\pi$
$863$	−23.9858			−0.816488			−0.408244	+	0.912873i	$0.633859\pi$
$864$	−13.5126	−	26.1038i	−0.459707	−	0.888070i
$865$	56.5789			1.92374
$866$	24.3264	−	53.0690i	0.826645	−	1.80336i
$867$	25.7180	+	4.45768i	0.873428	+	0.151391i
$868$	25.5476	+	29.6523i	0.867143	+	1.00646i
$869$	11.5441			0.391606
$870$	−6.61404	+	9.63800i	−0.224237	+	0.326759i
$871$			7.18449i			0.243437i
$872$	0.534600	+	1.84963i	0.0181039	+	0.0626362i
$873$	−32.5943	−	11.6491i	−1.10315	−	0.394261i
$874$	30.3232	−	66.1513i	1.02570	−	2.23760i
$875$			18.5373i			0.626675i
$876$	−10.4935	−	17.5237i	−0.354542	−	0.592069i
$877$			12.4093i			0.419033i	0.977805	+	0.209516i	$0.0671890\pi$
$877$			12.4093i			0.419033i	−0.977805	+	0.209516i	$0.932811\pi$
$878$	−15.7277	−	7.20943i	−0.530783	−	0.243307i
$879$	−27.8222	−	4.82240i	−0.938418	−	0.162655i
$880$	10.3778	+	1.55198i	0.349837	+	0.0523171i
$881$			4.72245i			0.159103i	0.996831	+	0.0795516i	$0.0253489\pi$
$881$			4.72245i			0.159103i	−0.996831	+	0.0795516i	$0.974651\pi$
$882$	5.52423	−	5.66227i	0.186011	−	0.190659i
$883$	−30.2745			−1.01882			−0.509409	−	0.860525i	$-0.670136\pi$
$883$	−30.2745			−1.01882			−0.509409	+	0.860525i	$0.670136\pi$
$884$	−25.2532	−	29.3105i	−0.849356	−	0.985820i
$885$	−0.747255	+	4.31118i	−0.0251187	+	0.144919i
$886$	−27.7549	−	12.7226i	−0.932444	−	0.427425i
$887$	−1.86952			−0.0627723			−0.0313862	−	0.999507i	$-0.509992\pi$
$887$	−1.86952			−0.0627723			−0.0313862	+	0.999507i	$0.509992\pi$
$888$	−3.93726	−	35.7340i	−0.132126	−	1.19916i
$889$	−13.8807			−0.465544
$890$	−36.3060	−	16.6424i	−1.21698	−	0.557854i
$891$	−5.70448	+	6.96124i	−0.191107	+	0.233210i
$892$	−24.0262	+	20.7004i	−0.804458	+	0.693100i
$893$	49.1753			1.64559
$894$	−12.4209	+	18.0997i	−0.415416	+	0.605345i
$895$		−	13.6923i		−	0.457684i
$896$	25.4124	−	3.39777i	0.848970	−	0.113512i
$897$	−7.78794	+	44.9314i	−0.260032	+	1.50022i
$898$	−17.8710	−	8.19193i	−0.596364	−	0.273368i
$899$		−	15.7094i		−	0.523938i
$900$	−4.06103	−	10.5350i	−0.135368	−	0.351167i
$901$		−	19.7762i		−	0.658840i
$902$	0.527298	−	1.15032i	0.0175571	−	0.0383015i
$903$	3.05925	−	17.6499i	0.101805	−	0.587352i
$904$	−8.32221	−	28.7934i	−0.276793	−	0.957655i
$905$		−	4.35778i		−	0.144857i
$906$	−19.7930	−	13.5829i	−0.657579	−	0.451261i
$907$	11.2376			0.373138			0.186569	−	0.982442i	$-0.440263\pi$
$907$	11.2376			0.373138			0.186569	+	0.982442i	$0.440263\pi$
$908$	25.8771	−	22.2950i	0.858762	−	0.739886i
$909$	−20.5803	−	7.35532i	−0.682606	−	0.243961i
$910$	11.9670	−	26.1065i	0.396702	−	0.865421i
$911$	35.7926			1.18586			0.592930	−	0.805254i	$-0.297971\pi$
$911$	35.7926			1.18586			0.592930	+	0.805254i	$0.297971\pi$
$912$	−14.5531	+	43.9050i	−0.481902	+	1.45384i
$913$	−0.294647			−0.00975140
$914$	−10.5253	+	22.9614i	−0.348147	+	0.759497i
$915$	0.412971	−	2.38258i	0.0136524	−	0.0787657i
$916$	−19.8863	+	17.1335i	−0.657063	+	0.566107i
$917$	−49.3935			−1.63112
$918$	24.3860	+	33.7207i	0.804859	+	1.11295i
$919$		−	56.2605i		−	1.85586i	−0.372750	−	0.927932i	$-0.621585\pi$
$919$		−	56.2605i		−	1.85586i	0.372750	−	0.927932i	$-0.378415\pi$
$920$	−54.9390	+	15.8791i	−1.81129	+	0.523519i
$921$	−0.358575	−	0.0621515i	−0.0118154	−	0.00204796i
$922$	16.0696	−	35.0566i	0.529226	−	1.15453i
$923$			7.75734i			0.255336i
$924$	−4.03303	−	6.73498i	−0.132677	−	0.221565i
$925$		−	13.8091i		−	0.454039i
$926$	−2.79007	−	1.27894i	−0.0916873	−	0.0420287i
$927$	17.1304	−	47.9311i	0.562636	−	1.57427i
$928$	−8.61736	−	5.62439i	−0.282879	−	0.184630i
$929$		−	8.63508i		−	0.283308i	−0.989916	−	0.141654i	$-0.954758\pi$
$929$		−	8.63508i		−	0.283308i	0.989916	−	0.141654i	$-0.0452420\pi$
$930$	45.7542	+	31.3987i	1.50034	+	1.02960i
$931$	−12.4482			−0.407973
$932$	4.83869	−	4.16889i	0.158497	−	0.136556i
$933$	−11.4599	−	1.98634i	−0.375182	−	0.0650300i
$934$	−54.9008	−	25.1661i	−1.79641	−	0.823459i
$935$	−14.8558			−0.485838
$936$	1.79259	−	28.9296i	0.0585926	−	0.945595i
$937$	−33.8018			−1.10426			−0.552128	−	0.833759i	$-0.686184\pi$
$937$	−33.8018			−1.10426			−0.552128	+	0.833759i	$0.686184\pi$
$938$	6.12740	+	2.80875i	0.200067	+	0.0917090i
$939$	−27.7862	−	4.81617i	−0.906770	−	0.157170i
$940$	−25.2248	−	29.2776i	−0.822742	−	0.954930i
$941$	−9.13576			−0.297817			−0.148909	−	0.988851i	$-0.547576\pi$
$941$	−9.13576			−0.297817			−0.148909	+	0.988851i	$0.547576\pi$
$942$	−41.8314	−	28.7066i	−1.36294	−	0.935311i
$943$			6.89647i			0.224580i
$944$	−3.80952	−	0.569703i	−0.123989	−	0.0185423i
$945$	−15.2111	+	26.8855i	−0.494817	+	0.874584i
$946$	5.86706	+	2.68941i	0.190755	+	0.0874404i
$947$		−	28.9161i		−	0.939647i	−0.882760	−	0.469823i	$-0.844318\pi$
$947$		−	28.9161i		−	0.939647i	0.882760	−	0.469823i	$-0.155682\pi$
$948$	34.3089	−	20.5448i	1.11430	−	0.667263i
$949$		−	20.1412i		−	0.653812i
$950$	−7.40345	+	16.1509i	−0.240200	+	0.524005i
$951$	13.2265	+	2.29254i	0.428898	+	0.0743405i
$952$	−34.8706	+	10.0787i	−1.13016	+	0.326652i
$953$			34.6544i			1.12257i	0.827624	+	0.561284i	$0.189692\pi$
$953$			34.6544i			1.12257i	−0.827624	+	0.561284i	$0.810308\pi$
$954$	10.3464	−	10.6050i	0.334978	−	0.343349i
$955$	−25.8388			−0.836125
$956$	6.13397	+	7.11950i	0.198387	+	0.230261i
$957$	−0.538100	+	3.10449i	−0.0173943	+	0.100354i
$958$	−10.1601	+	22.1646i	−0.328257	+	0.716106i
$959$	−0.802695			−0.0259204
$960$	33.6049	−	13.8568i	1.08459	−	0.447227i
$961$	−43.5769			−1.40571
$962$	14.7721	−	32.2260i	0.476272	−	1.03901i
$963$	6.03426	−	16.8840i	0.194451	−	0.544078i
$964$	29.0238	+	33.6869i	0.934793	+	1.08498i
$965$	2.20528			0.0709905
$966$	35.2758	+	24.2078i	1.13498	+	0.778874i
$967$		−	47.7447i		−	1.53537i	−0.640829	−	0.767684i	$-0.721409\pi$
$967$		−	47.7447i		−	1.53537i	0.640829	−	0.767684i	$-0.278591\pi$
$968$	2.71721	−	0.785358i	0.0873343	−	0.0252424i
$969$	11.1836	−	64.5223i	0.359269	−	2.07276i
$970$	17.8365	−	38.9111i	0.572697	−	1.24936i
$971$			1.75054i			0.0561774i	0.999605	+	0.0280887i	$0.00894208\pi$
$971$			1.75054i			0.0561774i	−0.999605	+	0.0280887i	$0.991058\pi$
$972$	−4.56487	+	30.8409i	−0.146418	+	0.989223i
$973$			11.1613i			0.357814i
$974$	39.9291	+	18.3032i	1.27941	+	0.586472i
$975$	1.90143	−	10.9701i	0.0608946	−	0.351323i
$976$	2.10534	+	0.314847i	0.0673902	+	0.0100780i
$977$		−	10.9073i		−	0.348957i	−0.984661	−	0.174478i	$-0.944176\pi$
$977$		−	10.9073i		−	0.348957i	0.984661	−	0.174478i	$-0.0558239\pi$
$978$	−1.19827	+	1.74612i	−0.0383163	+	0.0558347i
$979$	−10.7653			−0.344062
$980$	6.38537	+	7.41129i	0.203973	+	0.236745i
$981$	0.687273	−	1.92300i	0.0219429	−	0.0613967i
$982$	31.5728	+	14.4727i	1.00753	+	0.461843i
$983$	59.4277			1.89545			0.947725	−	0.319087i	$-0.103376\pi$
$983$	59.4277			1.89545			0.947725	+	0.319087i	$0.103376\pi$
$984$	−0.480082	−	4.35716i	−0.0153045	−	0.138901i
$985$	35.9835			1.14653
$986$	13.2436	+	6.07075i	0.421761	+	0.193332i
$987$	−4.93755	+	28.4865i	−0.157164	+	0.906736i
$988$	−34.5546	+	29.7713i	−1.09933	+	0.947152i
$989$	−35.1746			−1.11849
$990$	−7.96644	−	7.77224i	−0.253190	−	0.247018i
$991$			12.9007i			0.409803i	0.978783	+	0.204902i	$0.0656874\pi$
$991$			12.9007i			0.409803i	−0.978783	+	0.204902i	$0.934313\pi$
$992$	−26.7005	+	40.9090i	−0.847742	+	1.29886i
$993$	−2.55022	−	0.442029i	−0.0809289	−	0.0140274i
$994$	6.61596	+	3.03270i	0.209846	+	0.0961915i
$995$			9.63143i			0.305337i
$996$	−0.875689	+	0.524379i	−0.0277473	+	0.0166156i
$997$			19.1672i			0.607033i	0.952826	+	0.303516i	$0.0981607\pi$
$997$			19.1672i			0.607033i	−0.952826	+	0.303516i	$0.901839\pi$
$998$	1.25145	−	2.73010i	0.0396141	−	0.0864197i
$999$	−18.7766	+	33.1876i	−0.594067	+	1.05001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.k.b.155.21	yes	32
3.2	odd	2	inner	264.2.k.b.155.12	yes	32
4.3	odd	2		1056.2.k.b.815.31		32
8.3	odd	2	inner	264.2.k.b.155.11	✓	32
8.5	even	2		1056.2.k.b.815.32		32
12.11	even	2		1056.2.k.b.815.30		32
24.5	odd	2		1056.2.k.b.815.29		32
24.11	even	2	inner	264.2.k.b.155.22	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.k.b.155.11	✓	32	8.3	odd	2	inner
264.2.k.b.155.12	yes	32	3.2	odd	2	inner
264.2.k.b.155.21	yes	32	1.1	even	1	trivial
264.2.k.b.155.22	yes	32	24.11	even	2	inner
1056.2.k.b.815.29		32	24.5	odd	2
1056.2.k.b.815.30		32	12.11	even	2
1056.2.k.b.815.31		32	4.3	odd	2
1056.2.k.b.815.32		32	8.5	even	2

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:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.589301 - 1.28558i) q^{2} +(-1.70660 - 0.295805i) q^{3} +(-1.30545 - 1.51519i) q^{4} -2.62331 q^{5} +(-1.38599 + 2.01966i) q^{6} +2.26615i q^{7} +(-2.71721 + 0.785358i) q^{8} +(2.82500 + 1.00964i) q^{9} +(-1.54592 + 3.37249i) q^{10} +1.00000i q^{11} +(1.77968 + 2.97199i) q^{12} +3.41593i q^{13} +(2.91333 + 1.33545i) q^{14} +(4.47696 + 0.775989i) q^{15} +(-0.591610 + 3.95601i) q^{16} -5.66301i q^{17} +(2.96276 - 3.03679i) q^{18} -6.67620 q^{19} +(3.42460 + 3.97482i) q^{20} +(0.670338 - 3.86742i) q^{21} +(1.28558 + 0.589301i) q^{22} -7.70741 q^{23} +(4.86951 - 0.536534i) q^{24} +1.88177 q^{25} +(4.39146 + 2.01301i) q^{26} +(-4.52250 - 2.55871i) q^{27} +(3.43365 - 2.95834i) q^{28} -1.81910 q^{29} +(3.63587 - 5.29821i) q^{30} +8.63579i q^{31} +(4.73714 + 3.09184i) q^{32} +(0.295805 - 1.70660i) q^{33} +(-7.28027 - 3.33722i) q^{34} -5.94482i q^{35} +(-2.15809 - 5.59845i) q^{36} -7.33832i q^{37} +(-3.93430 + 8.58282i) q^{38} +(1.01045 - 5.82964i) q^{39} +(7.12808 - 2.06024i) q^{40} -0.894785i q^{41} +(-4.57686 - 3.14085i) q^{42} +4.56373 q^{43} +(1.51519 - 1.30545i) q^{44} +(-7.41086 - 2.64861i) q^{45} +(-4.54198 + 9.90851i) q^{46} -7.36576 q^{47} +(2.17985 - 6.57634i) q^{48} +1.86456 q^{49} +(1.10893 - 2.41918i) q^{50} +(-1.67515 + 9.66452i) q^{51} +(5.17579 - 4.45932i) q^{52} +3.49217 q^{53} +(-5.95455 + 4.30620i) q^{54} -2.62331i q^{55} +(-1.77974 - 6.15760i) q^{56} +(11.3936 + 1.97485i) q^{57} +(-1.07200 + 2.33861i) q^{58} +0.962971i q^{59} +(-4.66867 - 7.79646i) q^{60} -0.532187i q^{61} +(11.1020 + 5.08908i) q^{62} +(-2.28800 + 6.40187i) q^{63} +(6.76642 - 4.26796i) q^{64} -8.96105i q^{65} +(-2.01966 - 1.38599i) q^{66} +2.10323 q^{67} +(-8.58054 + 7.39277i) q^{68} +(13.1535 + 2.27989i) q^{69} +(-7.64257 - 3.50329i) q^{70} +2.27093 q^{71} +(-8.46904 - 0.524773i) q^{72} -5.89627 q^{73} +(-9.43402 - 4.32448i) q^{74} +(-3.21144 - 0.556637i) q^{75} +(8.71544 + 10.1157i) q^{76} -2.26615 q^{77} +(-6.89903 - 4.73443i) q^{78} -11.5441i q^{79} +(1.55198 - 10.3778i) q^{80} +(6.96124 + 5.70448i) q^{81} +(-1.15032 - 0.527298i) q^{82} +0.294647i q^{83} +(-6.73498 + 4.03303i) q^{84} +14.8558i q^{85} +(2.68941 - 5.86706i) q^{86} +(3.10449 + 0.538100i) q^{87} +(-0.785358 - 2.71721i) q^{88} +10.7653i q^{89} +(-7.77224 + 7.96644i) q^{90} -7.74101 q^{91} +(10.0616 + 11.6782i) q^{92} +(2.55451 - 14.7379i) q^{93} +(-4.34065 + 9.46930i) q^{94} +17.5138 q^{95} +(-7.16985 - 6.67782i) q^{96} -11.5378 q^{97} +(1.09879 - 2.39705i) q^{98} +(-1.00964 + 2.82500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} + 2 q^{6} + 8 q^{9} + 12 q^{10} - 12 q^{12} + 2 q^{18} - 32 q^{19} + 4 q^{22} + 12 q^{24} - 64 q^{27} + 40 q^{28} - 22 q^{30} - 64 q^{34} - 20 q^{36} + 32 q^{40} + 20 q^{42} - 16 q^{43} - 28 q^{46}+ \cdots - 16 q^{97}+O(q^{100}) \) 32 * q + 8 * q^3 + 2 * q^6 + 8 * q^9 + 12 * q^10 - 12 * q^12 + 2 * q^18 - 32 * q^19 + 4 * q^22 + 12 * q^24 - 64 * q^27 + 40 * q^28 - 22 * q^30 - 64 * q^34 - 20 * q^36 + 32 * q^40 + 20 * q^42 - 16 * q^43 - 28 * q^46 - 32 * q^49 + 8 * q^51 + 40 * q^52 - 8 * q^54 + 16 * q^57 - 40 * q^58 + 68 * q^60 - 14 * q^66 + 8 * q^70 - 8 * q^72 + 64 * q^73 - 16 * q^75 + 8 * q^76 + 16 * q^78 + 72 * q^81 + 88 * q^82 - 60 * q^84 + 8 * q^88 - 58 * q^90 + 80 * q^91 - 72 * q^94 - 4 * q^96 - 16 * q^97

Introduction

L-functions

Modular forms

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Database

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