LMFDB - Embedded newform 152.2.b.c.75.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(75,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.75"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] 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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.319794774016000000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + 2x^{8} + 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 + 2x^8 + 8x^4 - 32x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.9
Root			$1.17117 - 0.792696i$ of defining polynomial
Character	$\chi$	$=$	152.75
Dual form			152.2.b.c.75.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17117 - 0.792696i) q^{2} +1.26152i q^{3} +(0.743268 - 1.85676i) q^{4} +3.51876i q^{5} +(1.00000 + 1.47745i) q^{6} -2.23607i q^{7} +(-0.601353 - 2.76376i) q^{8} +1.40857 q^{9} +(2.78930 + 4.12105i) q^{10} +2.89511 q^{11} +(2.34234 + 0.937646i) q^{12} -6.30281 q^{13} +(-1.77252 - 2.61881i) q^{14} -4.43898 q^{15} +(-2.89511 - 2.76014i) q^{16} -4.79021 q^{17} +(1.64967 - 1.11657i) q^{18} +(0.895107 - 4.26600i) q^{19} +(6.53348 + 2.61538i) q^{20} +2.82084 q^{21} +(3.39066 - 2.29494i) q^{22} -0.524069i q^{23} +(3.48654 - 0.758618i) q^{24} -7.38164 q^{25} +(-7.38164 + 4.99621i) q^{26} +5.56149i q^{27} +(-4.15184 - 1.66200i) q^{28} +0.415427 q^{29} +(-5.19878 + 3.51876i) q^{30} +1.20271 q^{31} +(-5.57860 - 0.937646i) q^{32} +3.65223i q^{33} +(-5.61014 + 3.79718i) q^{34} +7.86818 q^{35} +(1.04695 - 2.61538i) q^{36} +5.88738 q^{37} +(-2.33332 - 5.70575i) q^{38} -7.95110i q^{39} +(9.72500 - 2.11602i) q^{40} +4.87978i q^{41} +(3.30368 - 2.23607i) q^{42} -10.6853 q^{43} +(2.15184 - 5.37551i) q^{44} +4.95642i q^{45} +(-0.415427 - 0.613773i) q^{46} -4.27737i q^{47} +(3.48196 - 3.65223i) q^{48} +2.00000 q^{49} +(-8.64514 + 5.85139i) q^{50} -6.04294i q^{51} +(-4.68467 + 11.7028i) q^{52} +6.05711 q^{53} +(4.40857 + 6.51344i) q^{54} +10.1872i q^{55} +(-6.17996 + 1.34467i) q^{56} +(5.38164 + 1.12919i) q^{57} +(0.486535 - 0.329307i) q^{58} -8.08453i q^{59} +(-3.29935 + 8.24211i) q^{60} +8.38042i q^{61} +(1.40857 - 0.953380i) q^{62} -3.14966i q^{63} +(-7.27675 + 3.32399i) q^{64} -22.1780i q^{65} +(2.89511 + 4.27737i) q^{66} +9.79353i q^{67} +(-3.56041 + 8.89427i) q^{68} +0.661123 q^{69} +(9.21495 - 6.23707i) q^{70} +10.2002 q^{71} +(-0.847049 - 3.89295i) q^{72} +7.76328 q^{73} +(6.89511 - 4.66690i) q^{74} -9.31208i q^{75} +(-7.25564 - 4.83278i) q^{76} -6.47365i q^{77} +(-6.30281 - 9.31208i) q^{78} -7.33578 q^{79} +(9.71225 - 10.1872i) q^{80} -2.79021 q^{81} +(3.86818 + 5.71504i) q^{82} +2.00000 q^{83} +(2.09664 - 5.23762i) q^{84} -16.8556i q^{85} +(-12.5143 + 8.47020i) q^{86} +0.524069i q^{87} +(-1.74098 - 8.00138i) q^{88} +12.1842i q^{89} +(3.92893 + 5.80480i) q^{90} +14.0935i q^{91} +(-0.973070 - 0.389524i) q^{92} +1.51724i q^{93} +(-3.39066 - 5.00952i) q^{94} +(15.0110 + 3.14966i) q^{95} +(1.18286 - 7.03751i) q^{96} -2.19044i q^{97} +(2.34234 - 1.58539i) q^{98} +4.07796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 12 q^{6} - 8 q^{9} + 12 q^{17} - 24 q^{19} + 4 q^{20} + 32 q^{24} - 44 q^{25} - 44 q^{26} - 20 q^{28} + 32 q^{30} + 40 q^{35} - 52 q^{36} + 4 q^{38} - 20 q^{42} - 24 q^{43} - 4 q^{44} + 24 q^{49}+ \cdots + 64 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 + 12 * q^6 - 8 * q^9 + 12 * q^17 - 24 * q^19 + 4 * q^20 + 32 * q^24 - 44 * q^25 - 44 * q^26 - 20 * q^28 + 32 * q^30 + 40 * q^35 - 52 * q^36 + 4 * q^38 - 20 * q^42 - 24 * q^43 - 4 * q^44 + 24 * q^49 + 28 * q^54 + 20 * q^57 - 4 * q^58 - 8 * q^62 - 8 * q^64 + 12 * q^68 + 4 * q^73 + 48 * q^74 - 12 * q^76 + 32 * q^80 + 36 * q^81 - 8 * q^82 + 24 * q^83 + 8 * q^92 + 64 * q^96 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.17117	−	0.792696i	0.828141	−	0.560520i
$2$	1.17117	−	0.792696i	0.828141	−	0.560520i
$3$			1.26152i			0.728338i	0.931333	+	0.364169i	$0.118647\pi$
$3$			1.26152i			0.728338i	−0.931333	+	0.364169i	$0.881353\pi$
$4$	0.743268	−	1.85676i	0.371634	−	0.928379i
$5$			3.51876i			1.57364i	0.617185	+	0.786818i	$0.288273\pi$
$5$			3.51876i			1.57364i	−0.617185	+	0.786818i	$0.711727\pi$
$6$	1.00000	+	1.47745i	0.408248	+	0.603166i
$7$		−	2.23607i		−	0.845154i	−0.906327	−	0.422577i	$-0.861126\pi$
$7$		−	2.23607i		−	0.845154i	0.906327	−	0.422577i	$-0.138874\pi$
$8$	−0.601353	−	2.76376i	−0.212611	−	0.977137i
$9$	1.40857			0.469524
$10$	2.78930	+	4.12105i	0.882055	+	1.30319i
$11$	2.89511			0.872907			0.436454	−	0.899727i	$-0.356234\pi$
$11$	2.89511			0.872907			0.436454	+	0.899727i	$0.356234\pi$
$12$	2.34234	+	0.937646i	0.676174	+	0.270675i
$13$	−6.30281			−1.74808			−0.874042	−	0.485851i	$-0.838510\pi$
$13$	−6.30281			−1.74808			−0.874042	+	0.485851i	$0.838510\pi$
$14$	−1.77252	−	2.61881i	−0.473726	−	0.699907i
$15$	−4.43898			−1.14614
$16$	−2.89511	−	2.76014i	−0.723777	−	0.690034i
$17$	−4.79021			−1.16180			−0.580899	−	0.813976i	$-0.697299\pi$
$17$	−4.79021			−1.16180			−0.580899	+	0.813976i	$0.697299\pi$
$18$	1.64967	−	1.11657i	0.388832	−	0.263178i
$19$	0.895107	−	4.26600i	0.205352	−	0.978688i
$19$	0.895107	−	4.26600i	0.205352	−	0.978688i
$20$	6.53348	+	2.61538i	1.46093	+	0.584816i
$21$	2.82084			0.615558
$22$	3.39066	−	2.29494i	0.722890	−	0.489282i
$23$		−	0.524069i		−	0.109276i	−0.998506	−	0.0546380i	$-0.982600\pi$
$23$		−	0.524069i		−	0.109276i	0.998506	−	0.0546380i	$-0.0174005\pi$
$24$	3.48654	−	0.758618i	0.711686	−	0.154852i
$25$	−7.38164			−1.47633
$26$	−7.38164	+	4.99621i	−1.44766	+	0.979836i
$27$			5.56149i			1.07031i
$28$	−4.15184	−	1.66200i	−0.784624	−	0.314088i
$29$	0.415427			0.0771429			0.0385715	−	0.999256i	$-0.487719\pi$
$29$	0.415427			0.0771429			0.0385715	+	0.999256i	$0.487719\pi$
$30$	−5.19878	+	3.51876i	−0.949164	+	0.642434i
$31$	1.20271			0.216013			0.108006	−	0.994150i	$-0.465553\pi$
$31$	1.20271			0.216013			0.108006	+	0.994150i	$0.465553\pi$
$32$	−5.57860	−	0.937646i	−0.986167	−	0.165754i
$33$			3.65223i			0.635772i
$34$	−5.61014	+	3.79718i	−0.962132	+	0.651211i
$35$	7.86818			1.32996
$36$	1.04695	−	2.61538i	0.174491	−	0.435896i
$37$	5.88738			0.967879			0.483939	−	0.875101i	$-0.339205\pi$
$37$	5.88738			0.967879			0.483939	+	0.875101i	$0.339205\pi$
$38$	−2.33332	−	5.70575i	−0.378515	−	0.925595i
$39$		−	7.95110i		−	1.27320i
$40$	9.72500	−	2.11602i	1.53766	−	0.334571i
$41$			4.87978i			0.762093i	0.924556	+	0.381047i	$0.124436\pi$
$41$			4.87978i			0.762093i	−0.924556	+	0.381047i	$0.875564\pi$
$42$	3.30368	−	2.23607i	0.509769	−	0.345033i
$43$	−10.6853			−1.62950			−0.814748	−	0.579815i	$-0.803125\pi$
$43$	−10.6853			−1.62950			−0.814748	+	0.579815i	$0.803125\pi$
$44$	2.15184	−	5.37551i	0.324402	−	0.810389i
$45$			4.95642i			0.738859i
$46$	−0.415427	−	0.613773i	−0.0612514	−	0.0904959i
$47$		−	4.27737i		−	0.623919i	−0.950095	−	0.311960i	$-0.899015\pi$
$47$		−	4.27737i		−	0.623919i	0.950095	−	0.311960i	$-0.100985\pi$
$48$	3.48196	−	3.65223i	0.502578	−	0.527154i
$49$	2.00000			0.285714
$50$	−8.64514	+	5.85139i	−1.22261	+	0.827512i
$51$		−	6.04294i		−	0.846181i
$52$	−4.68467	+	11.7028i	−0.649647	+	1.62288i
$53$	6.05711			0.832008			0.416004	−	0.909363i	$-0.363430\pi$
$53$	6.05711			0.832008			0.416004	+	0.909363i	$0.363430\pi$
$54$	4.40857	+	6.51344i	0.599931	+	0.886367i
$55$			10.1872i			1.37364i
$56$	−6.17996	+	1.34467i	−0.825832	+	0.179689i
$57$	5.38164	+	1.12919i	0.712816	+	0.149565i
$58$	0.486535	−	0.329307i	0.0638852	−	0.0432402i
$59$		−	8.08453i		−	1.05252i	−0.850325	−	0.526258i	$-0.823595\pi$
$59$		−	8.08453i		−	1.05252i	0.850325	−	0.526258i	$-0.176405\pi$
$60$	−3.29935	+	8.24211i	−0.425944	+	1.06405i
$61$			8.38042i			1.07300i	0.843900	+	0.536501i	$0.180254\pi$
$61$			8.38042i			1.07300i	−0.843900	+	0.536501i	$0.819746\pi$
$62$	1.40857	−	0.953380i	0.178889	−	0.121079i
$63$		−	3.14966i		−	0.396820i
$64$	−7.27675	+	3.32399i	−0.909594	+	0.415499i
$65$		−	22.1780i		−	2.75085i
$66$	2.89511	+	4.27737i	0.356363	+	0.526508i
$67$			9.79353i			1.19647i	0.801321	+	0.598235i	$0.204131\pi$
$67$			9.79353i			1.19647i	−0.801321	+	0.598235i	$0.795869\pi$
$68$	−3.56041	+	8.89427i	−0.431763	+	1.07859i
$69$	0.661123			0.0795899
$70$	9.21495	−	6.23707i	1.10140	−	0.745472i
$71$	10.2002			1.21054			0.605270	−	0.796020i	$-0.293065\pi$
$71$	10.2002			1.21054			0.605270	+	0.796020i	$0.293065\pi$
$72$	−0.847049	−	3.89295i	−0.0998257	−	0.458789i
$73$	7.76328			0.908624			0.454312	−	0.890843i	$-0.349885\pi$
$73$	7.76328			0.908624			0.454312	+	0.890843i	$0.349885\pi$
$74$	6.89511	−	4.66690i	0.801540	−	0.542516i
$75$		−	9.31208i		−	1.07527i
$76$	−7.25564	−	4.83278i	−0.832278	−	0.554358i
$77$		−	6.47365i		−	0.737741i
$78$	−6.30281	−	9.31208i	−0.713652	−	1.05439i
$79$	−7.33578			−0.825340			−0.412670	−	0.910881i	$-0.635404\pi$
$79$	−7.33578			−0.825340			−0.412670	+	0.910881i	$0.635404\pi$
$80$	9.71225	−	10.1872i	1.08586	−	1.13896i
$81$	−2.79021			−0.310024
$82$	3.86818	+	5.71504i	0.427169	+	0.631120i
$83$	2.00000			0.219529			0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000			0.219529			0.109764	+	0.993958i	$0.464990\pi$
$84$	2.09664	−	5.23762i	0.228762	−	0.571471i
$85$		−	16.8556i		−	1.82825i
$86$	−12.5143	+	8.47020i	−1.34945	+	0.913366i
$87$			0.524069i			0.0561861i
$88$	−1.74098	−	8.00138i	−0.185589	−	0.852950i
$89$			12.1842i			1.29153i	0.763538	+	0.645763i	$0.223461\pi$
$89$			12.1842i			1.29153i	−0.763538	+	0.645763i	$0.776539\pi$
$90$	3.92893	+	5.80480i	0.414146	+	0.611879i
$91$			14.0935i			1.47740i
$92$	−0.973070	−	0.389524i	−0.101450	−	0.0406107i
$93$			1.51724i			0.157330i
$94$	−3.39066	−	5.00952i	−0.349719	−	0.516693i
$95$	15.0110	+	3.14966i	1.54010	+	0.323148i
$96$	1.18286	−	7.03751i	0.120725	−	0.718263i
$97$		−	2.19044i		−	0.222406i	−0.993798	−	0.111203i	$-0.964530\pi$
$97$		−	2.19044i		−	0.222406i	0.993798	−	0.111203i	$-0.0354703\pi$
$98$	2.34234	−	1.58539i	0.236612	−	0.160149i
$99$	4.07796			0.409851
$100$	−5.48654	+	13.7059i	−0.548654	+	1.37059i
$101$		−	1.51724i		−	0.150971i	−0.997147	−	0.0754853i	$-0.975949\pi$
$101$		−	1.51724i		−	0.150971i	0.997147	−	0.0754853i	$-0.0240506\pi$
$102$	−4.79021	−	7.07730i	−0.474302	−	0.700757i
$103$	−0.830855			−0.0818666			−0.0409333	−	0.999162i	$-0.513033\pi$
$103$	−0.830855			−0.0818666			−0.0409333	+	0.999162i	$0.513033\pi$
$104$	3.79021	+	17.4194i	0.371661	+	1.70812i
$105$			9.92585i			0.968664i
$106$	7.09389	−	4.80144i	0.689020	−	0.466357i
$107$		−	0.780070i		−	0.0754122i	−0.999289	−	0.0377061i	$-0.987995\pi$
$107$		−	0.780070i		−	0.0754122i	0.999289	−	0.0377061i	$-0.0120051\pi$
$108$	10.3264	+	4.13368i	0.993654	+	0.397763i
$109$	−6.05711			−0.580166			−0.290083	−	0.957002i	$-0.593683\pi$
$109$	−6.05711			−0.580166			−0.290083	+	0.957002i	$0.593683\pi$
$110$	8.07533	+	11.9309i	0.769952	+	1.13757i
$111$			7.42704i			0.704943i
$112$	−6.17185	+	6.47365i	−0.583185	+	0.611703i
$113$		−	3.58429i		−	0.337181i	−0.985686	−	0.168591i	$-0.946078\pi$
$113$		−	3.58429i		−	0.337181i	0.985686	−	0.168591i	$-0.0539216\pi$
$114$	7.19791	−	2.94353i	0.674146	−	0.275687i
$115$	1.84407			0.171961
$116$	0.308774	−	0.771349i	0.0286689	−	0.0716179i
$117$	−8.87795			−0.820767
$118$	−6.40857	−	9.46834i	−0.589957	−	0.871631i
$119$			10.7112i			0.981898i
$120$	2.66939	+	12.2683i	0.243681	+	1.11993i
$121$	−2.61836			−0.238033
$122$	6.64312	+	9.81487i	0.601440	+	0.888597i
$123$	−6.15593			−0.555061
$124$	0.893933	−	2.23314i	0.0802775	−	0.200542i
$125$		−	8.38042i		−	0.749567i
$126$	−2.49672	−	3.68878i	−0.222426	−	0.328623i
$127$	17.0446			1.51246			0.756231	−	0.654305i	$-0.227039\pi$
$127$	17.0446			1.51246			0.756231	+	0.654305i	$0.227039\pi$
$128$	−5.88738	+	9.66120i	−0.520376	+	0.853938i
$129$		−	13.4797i		−	1.18682i
$130$	−17.5804	−	25.9742i	−1.54191	−	2.27809i
$131$	−11.7122			−1.02330			−0.511652	−	0.859193i	$-0.670966\pi$
$131$	−11.7122			−1.02330			−0.511652	+	0.859193i	$0.670966\pi$
$132$	6.78131	+	2.71458i	0.590237	+	0.236274i
$133$	−9.53907	−	2.00152i	−0.827143	−	0.173554i
$134$	7.76328	+	11.4699i	0.670646	+	0.990845i
$135$	−19.5695			−1.68428
$136$	2.88061	+	13.2390i	0.247010	+	1.13524i
$137$	0.946141			0.0808343			0.0404171	−	0.999183i	$-0.487131\pi$
$137$	0.946141			0.0808343			0.0404171	+	0.999183i	$0.487131\pi$
$138$	0.774286	−	0.524069i	0.0659116	−	0.0446117i
$139$	−0.841247			−0.0713537			−0.0356768	−	0.999363i	$-0.511359\pi$
$139$	−0.841247			−0.0713537			−0.0356768	+	0.999363i	$0.511359\pi$
$140$	5.84816	−	14.6093i	0.494260	−	1.23471i
$141$	5.39599			0.454424
$142$	11.9461	−	8.08565i	1.00250	−	0.678533i
$143$	−18.2473			−1.52592
$144$	−4.07796	−	3.88785i	−0.339830	−	0.323988i
$145$			1.46179i			0.121395i
$146$	9.09211	−	6.15392i	0.752468	−	0.509302i
$147$			2.52304i			0.208097i
$148$	4.37590	−	10.9314i	0.359697	−	0.898559i
$149$			11.3353i			0.928625i	0.885671	+	0.464313i	$0.153699\pi$
$149$			11.3353i			0.928625i	−0.885671	+	0.464313i	$0.846301\pi$
$150$	−7.38164	−	10.9060i	−0.602709	−	0.890471i
$151$	−9.36934			−0.762466			−0.381233	−	0.924479i	$-0.624500\pi$
$151$	−9.36934			−0.762466			−0.381233	+	0.924479i	$0.624500\pi$
$152$	−12.3285	+	0.0915151i	−0.999972	+	0.00742286i
$153$	−6.74736			−0.545491
$154$	−5.13164	−	7.58174i	−0.413519	−	0.610954i
$155$			4.23203i			0.339925i
$156$	−14.7633	−	5.90980i	−1.18201	−	0.473163i
$157$		−	17.4194i		−	1.39022i	−0.718902	−	0.695112i	$-0.755355\pi$
$157$		−	17.4194i		−	1.39022i	0.718902	−	0.695112i	$-0.244645\pi$
$158$	−8.59143	+	5.81504i	−0.683497	+	0.462620i
$159$			7.64115i			0.605983i
$160$	3.29935	−	19.6297i	0.260836	−	1.55187i
$161$	−1.17185			−0.0923551
$162$	−3.26781	+	2.21179i	−0.256743	+	0.173775i
$163$	−20.3437			−1.59344			−0.796721	−	0.604347i	$-0.793434\pi$
$163$	−20.3437			−1.59344			−0.796721	+	0.604347i	$0.793434\pi$
$164$	9.06057	+	3.62698i	0.707511	+	0.283220i
$165$	−12.8513			−1.00047
$166$	2.34234	−	1.58539i	0.181800	−	0.123050i
$167$	13.8083			1.06852			0.534260	−	0.845320i	$-0.320590\pi$
$167$	13.8083			1.06852			0.534260	+	0.845320i	$0.320590\pi$
$168$	−1.69632	−	7.79613i	−0.130874	−	0.601484i
$169$	26.7254			2.05580
$170$	−13.3614	−	19.7407i	−1.02477	−	1.51404i
$171$	1.26082	−	6.00897i	0.0964174	−	0.459517i
$172$	−7.94205	+	19.8401i	−0.605576	+	1.51279i
$173$	2.89680			0.220240			0.110120	−	0.993918i	$-0.464876\pi$
$173$	2.89680			0.220240			0.110120	+	0.993918i	$0.464876\pi$
$174$	0.415427	+	0.613773i	0.0314935	+	0.0465300i
$175$			16.5059i			1.24773i
$176$	−8.38164	−	7.99089i	−0.631790	−	0.602336i
$177$	10.1988			0.766588
$178$	9.65839	+	14.2698i	0.723927	+	1.06957i
$179$			10.6415i			0.795386i	0.917519	+	0.397693i	$0.130189\pi$
$179$			10.6415i			0.795386i	−0.917519	+	0.397693i	$0.869811\pi$
$180$	9.20287	+	3.68395i	0.685942	+	0.274585i
$181$	−2.40541			−0.178793			−0.0893965	−	0.995996i	$-0.528494\pi$
$181$	−2.40541			−0.178793			−0.0893965	+	0.995996i	$0.528494\pi$
$182$	11.1719	+	16.5059i	0.828113	+	1.22350i
$183$	−10.5720			−0.781508
$184$	−1.44840	+	0.315151i	−0.106778	+	0.0232332i
$185$			20.7162i			1.52309i
$186$	1.20271	+	1.77694i	0.0881867	+	0.130291i
$187$	−13.8682			−1.01414
$188$	−7.94205	−	3.17923i	−0.579234	−	0.231869i
$189$	12.4359			0.904577
$190$	20.0771	−	8.21039i	1.45655	−	0.595644i
$191$		−	10.0526i		−	0.727383i	−0.931520	−	0.363691i	$-0.881516\pi$
$191$		−	10.0526i		−	0.727383i	0.931520	−	0.363691i	$-0.118484\pi$
$192$	−4.19328	−	9.17975i	−0.302624	−	0.662492i
$193$			15.0399i			1.08259i	0.840832	+	0.541297i	$0.182066\pi$
$193$			15.0399i			1.08259i	−0.840832	+	0.541297i	$0.817934\pi$
$194$	−1.73635	−	2.56538i	−0.124663	−	0.184183i
$195$	27.9780			2.00355
$196$	1.48654	−	3.71352i	0.106181	−	0.265251i
$197$			13.8059i			0.983632i	0.870699	+	0.491816i	$0.163667\pi$
$197$			13.8059i			0.983632i	−0.870699	+	0.491816i	$0.836333\pi$
$198$	4.77598	−	3.23258i	0.339414	−	0.229730i
$199$			7.36682i			0.522220i	0.965309	+	0.261110i	$0.0840885\pi$
$199$			7.36682i			0.522220i	−0.965309	+	0.261110i	$0.915911\pi$
$200$	4.43898	+	20.4011i	0.313883	+	1.44258i
$201$	−12.3547			−0.871434
$202$	−1.20271	−	1.77694i	−0.0846222	−	0.125025i
$203$		−	0.928924i		−	0.0651977i
$204$	−11.2203	−	4.49152i	−0.785577	−	0.314470i
$205$	−17.1707			−1.19926
$206$	−0.973070	+	0.658615i	−0.0677970	+	0.0458879i
$207$		−	0.738189i		−	0.0513077i
$208$	18.2473	+	17.3966i	1.26522	+	1.20624i
$209$	2.59143	−	12.3505i	0.179253	−	0.854304i
$210$	7.86818	+	11.6248i	0.542956	+	0.802190i
$211$		−	15.6536i		−	1.07764i	−0.842421	−	0.538821i	$-0.818870\pi$
$211$		−	15.6536i		−	1.07764i	0.842421	−	0.538821i	$-0.181130\pi$
$212$	4.50205	−	11.2466i	0.309202	−	0.772419i
$213$			12.8677i			0.881683i
$214$	−0.618358	−	0.913593i	−0.0422701	−	0.0624519i
$215$		−	37.5990i		−	2.56423i
$216$	15.3706	−	3.34442i	1.04584	−	0.227559i
$217$		−	2.68933i		−	0.182564i
$218$	−7.09389	+	4.80144i	−0.480459	+	0.325195i
$219$			9.79353i			0.661785i
$220$	18.9151	+	7.57180i	1.27526	+	0.510490i
$221$	30.1918			2.03092
$222$	5.88738	+	8.69830i	0.395135	+	0.583792i
$223$	−11.4029			−0.763595			−0.381797	−	0.924246i	$-0.624695\pi$
$223$	−11.4029			−0.763595			−0.381797	+	0.924246i	$0.624695\pi$
$224$	−2.09664	+	12.4741i	−0.140088	+	0.833463i
$225$	−10.3976			−0.693171
$226$	−2.84125	−	4.19780i	−0.188997	−	0.279233i
$227$		−	14.4261i		−	0.957494i	−0.877953	−	0.478747i	$-0.841091\pi$
$227$		−	14.4261i		−	0.957494i	0.877953	−	0.478747i	$-0.158909\pi$
$228$	6.09664	−	9.15312i	0.403760	−	0.606180i
$229$		−	18.8419i		−	1.24511i	−0.782576	−	0.622555i	$-0.786095\pi$
$229$		−	18.8419i		−	1.24511i	0.782576	−	0.622555i	$-0.213905\pi$
$230$	2.15972	−	1.46179i	0.142408	−	0.0963874i
$231$	8.16663			0.537325
$232$	−0.249819	−	1.14814i	−0.0164014	−	0.0753792i
$233$	5.19878			0.340584			0.170292	−	0.985394i	$-0.445529\pi$
$233$	5.19878			0.340584			0.170292	+	0.985394i	$0.445529\pi$
$234$	−10.3976	+	7.03751i	−0.679710	+	0.460057i
$235$	15.0510			0.981821
$236$	−15.0110	−	6.00897i	−0.977134	−	0.391151i
$237$		−	9.25422i		−	0.601126i
$238$	8.49075	+	12.5447i	0.550374	+	0.813150i
$239$		−	12.2285i		−	0.790995i	−0.918467	−	0.395497i	$-0.870572\pi$
$239$		−	12.2285i		−	0.790995i	0.918467	−	0.395497i	$-0.129428\pi$
$240$	12.8513	+	12.2522i	0.829548	+	0.790875i
$241$		−	29.9134i		−	1.92689i	−0.267899	−	0.963447i	$-0.586329\pi$
$241$		−	29.9134i		−	1.92689i	0.267899	−	0.963447i	$-0.413671\pi$
$242$	−3.06654	+	2.07556i	−0.197124	+	0.133422i
$243$			13.1646i			0.844508i
$244$	15.5604	+	6.22889i	0.996153	+	0.398764i
$245$			7.03751i			0.449610i
$246$	−7.20962	+	4.87978i	−0.459669	+	0.311123i
$247$	−5.64168	+	26.8878i	−0.358972	+	1.71083i
$248$	−0.723252	−	3.32399i	−0.0459265	−	0.211074i
$249$			2.52304i			0.159891i
$250$	−6.64312	−	9.81487i	−0.420148	−	0.620747i
$251$	21.3947			1.35042			0.675212	−	0.737624i	$-0.264052\pi$
$251$	21.3947			1.35042			0.675212	+	0.737624i	$0.264052\pi$
$252$	−5.84816	−	2.34104i	−0.368400	−	0.147472i
$253$		−	1.51724i		−	0.0953879i
$254$	19.9621	−	13.5112i	1.25253	−	0.847766i
$255$	21.2636			1.33158
$256$	0.763283	+	15.9818i	0.0477052	+	0.998861i
$257$		−	13.5781i		−	0.846977i	−0.905901	−	0.423489i	$-0.860805\pi$
$257$		−	13.5781i		−	0.846977i	0.905901	−	0.423489i	$-0.139195\pi$
$258$	−10.6853	−	15.7870i	−0.665239	−	0.982857i
$259$		−	13.1646i		−	0.818007i
$260$	−41.1793	−	16.4842i	−2.55383	−	1.02231i
$261$	0.585159			0.0362204
$262$	−13.7170	+	9.28425i	−0.847440	+	0.573583i
$263$			12.0939i			0.745744i	0.927883	+	0.372872i	$0.121627\pi$
$263$			12.0939i			0.745744i	−0.927883	+	0.372872i	$0.878373\pi$
$264$	10.0939	−	2.19628i	0.621236	−	0.135172i
$265$			21.3135i			1.30928i
$266$	−12.7584	+	5.21747i	−0.782271	+	0.319903i
$267$	−15.3706			−0.940668
$268$	18.1842	+	7.27921i	1.11078	+	0.444649i
$269$	21.2379			1.29490			0.647448	−	0.762110i	$-0.275836\pi$
$269$	21.2379			1.29490			0.647448	+	0.762110i	$0.275836\pi$
$270$	−22.9192	+	15.5127i	−1.39482	+	0.944072i
$271$		−	16.1163i		−	0.978997i	−0.872004	−	0.489499i	$-0.837180\pi$
$271$		−	16.1163i		−	0.978997i	0.872004	−	0.489499i	$-0.162820\pi$
$272$	13.8682	+	13.2216i	0.840882	+	0.801680i
$273$	−17.7792			−1.07605
$274$	1.10809	−	0.750002i	0.0669421	−	0.0453093i
$275$	−21.3706			−1.28870
$276$	0.491391	−	1.22755i	0.0295783	−	0.0738896i
$277$			3.98785i			0.239607i	0.992798	+	0.119803i	$0.0382264\pi$
$277$			3.98785i			0.239607i	−0.992798	+	0.119803i	$0.961774\pi$
$278$	−0.985242	+	0.666853i	−0.0590909	+	0.0399952i
$279$	1.69410			0.101423
$280$	−4.73155	−	21.7458i	−0.282764	−	1.29956i
$281$			0.630302i			0.0376007i	0.999823	+	0.0188003i	$0.00598468\pi$
$281$			0.630302i			0.0376007i	−0.999823	+	0.0188003i	$0.994015\pi$
$282$	6.31960	−	4.27737i	0.376327	−	0.254714i
$283$	31.0290			1.84448			0.922242	−	0.386613i	$-0.126355\pi$
$283$	31.0290			1.84448			0.922242	+	0.386613i	$0.126355\pi$
$284$	7.58148	−	18.9393i	0.449878	−	1.12384i
$285$	−3.97336	+	18.9367i	−0.235361	+	1.12171i
$286$	−21.3706	+	14.4645i	−1.26367	+	0.855307i
$287$	10.9115			0.644086
$288$	−7.85786	−	1.32074i	−0.463029	−	0.0778254i
$289$	5.94614			0.349773
$290$	1.15875	+	1.71200i	0.0680443	+	0.100532i
$291$	2.76328			0.161987
$292$	5.77020	−	14.4145i	0.337675	−	0.843547i
$293$	−30.6832			−1.79253			−0.896265	−	0.443519i	$-0.853730\pi$
$293$	−30.6832			−1.79253			−0.896265	+	0.443519i	$0.853730\pi$
$294$	2.00000	+	2.95490i	0.116642	+	0.172333i
$295$	28.4475			1.65628
$296$	−3.54039	−	16.2713i	−0.205781	−	0.945750i
$297$			16.1011i			0.934282i
$298$	8.98545	+	13.2756i	0.520513	+	0.769032i
$299$			3.30311i			0.191024i
$300$	−17.2903	−	6.92137i	−0.998255	−	0.399605i
$301$			23.8931i			1.37718i
$302$	−10.9731	+	7.42704i	−0.631429	+	0.427378i
$303$	1.91402			0.109958
$304$	−14.3662	+	9.87992i	−0.823957	+	0.566652i
$305$	−29.4886			−1.68851
$306$	−7.90229	+	5.34860i	−0.451744	+	0.305759i
$307$		−	15.6876i		−	0.895339i	−0.894199	−	0.447670i	$-0.852254\pi$
$307$		−	15.6876i		−	0.895339i	0.894199	−	0.447670i	$-0.147746\pi$
$308$	−12.0200	−	4.81166i	−0.684904	−	0.274170i
$309$		−	1.04814i		−	0.0596265i
$310$	3.35471	+	4.95642i	0.190535	+	0.281506i
$311$		−	28.3998i		−	1.61040i	−0.593001	−	0.805202i	$-0.702057\pi$
$311$		−	28.3998i		−	1.61040i	0.593001	−	0.805202i	$-0.297943\pi$
$312$	−21.9750	+	4.78142i	−1.24409	+	0.270695i
$313$	−5.53757			−0.313002			−0.156501	−	0.987678i	$-0.550021\pi$
$313$	−5.53757			−0.313002			−0.156501	+	0.987678i	$0.550021\pi$
$314$	−13.8083	−	20.4011i	−0.779248	−	1.15130i
$315$	11.0829			0.624450
$316$	−5.45245	+	13.6208i	−0.306724	+	0.766228i
$317$	−11.9445			−0.670869			−0.335435	−	0.942063i	$-0.608883\pi$
$317$	−11.9445			−0.670869			−0.335435	+	0.942063i	$0.608883\pi$
$318$	6.05711	+	8.94907i	0.339666	+	0.501839i
$319$	1.20271			0.0673386
$320$	−11.6963	−	25.6051i	−0.653844	−	1.43137i
$321$	0.984073			0.0549256
$322$	−1.37244	+	0.928924i	−0.0764830	+	0.0517669i
$323$	−4.28775	+	20.4351i	−0.238577	+	1.13704i
$324$	−2.07387	+	5.18075i	−0.115215	+	0.287820i
$325$	46.5250			2.58075
$326$	−23.8259	+	16.1264i	−1.31959	+	0.893157i
$327$		−	7.64115i		−	0.422557i
$328$	13.4865	−	2.93447i	0.744669	−	0.162029i
$329$	−9.56450			−0.527308
$330$	−15.0510	+	10.1872i	−0.828532	+	0.560785i
$331$		−	15.5378i		−	0.854037i	−0.904243	−	0.427019i	$-0.859564\pi$
$331$		−	15.5378i		−	0.854037i	0.904243	−	0.427019i	$-0.140436\pi$
$332$	1.48654	−	3.71352i	0.0815842	−	0.203806i
$333$	8.29279			0.454442
$334$	16.1719	−	10.9458i	0.884885	−	0.598927i
$335$	−34.4610			−1.88281
$336$	−8.16663	−	7.78591i	−0.445526	−	0.424756i
$337$		−	29.4825i		−	1.60601i	−0.595970	−	0.803007i	$-0.703232\pi$
$337$		−	29.4825i		−	1.60601i	0.595970	−	0.803007i	$-0.296768\pi$
$338$	31.2999	−	21.1851i	1.70249	−	1.15232i
$339$	4.52164			0.245582
$340$	−31.2968	−	12.5282i	−1.69731	−	0.679438i
$341$	3.48196			0.188559
$342$	−3.28665	−	8.03696i	−0.177722	−	0.434589i
$343$		−	20.1246i		−	1.08663i
$344$	6.42565	+	29.5317i	0.346448	+	1.59224i
$345$			2.32633i			0.125245i
$346$	3.39264	−	2.29628i	0.182390	−	0.123449i
$347$	−19.3465			−1.03858			−0.519288	−	0.854599i	$-0.673803\pi$
$347$	−19.3465			−1.03858			−0.519288	+	0.854599i	$0.673803\pi$
$348$	0.973070	+	0.389524i	0.0521621	+	0.0208807i
$349$		−	12.4630i		−	0.667131i	−0.942727	−	0.333565i	$-0.891748\pi$
$349$		−	12.4630i		−	0.667131i	0.942727	−	0.333565i	$-0.108252\pi$
$350$	13.0841	+	19.3311i	0.699375	+	1.03329i
$351$		−	35.0530i		−	1.87099i
$352$	−16.1507	−	2.71458i	−0.860833	−	0.144688i
$353$	9.22571			0.491035			0.245518	−	0.969392i	$-0.421042\pi$
$353$	9.22571			0.491035			0.245518	+	0.969392i	$0.421042\pi$
$354$	11.9445	−	8.08453i	0.634842	−	0.429688i
$355$			35.8920i			1.90495i
$356$	22.6232	+	9.05615i	1.19903	+	0.479975i
$357$	−13.5124			−0.715154
$358$	8.43550	+	12.4630i	0.445830	+	0.658691i
$359$			18.8765i			0.996262i	0.867102	+	0.498131i	$0.165980\pi$
$359$			18.8765i			0.996262i	−0.867102	+	0.498131i	$0.834020\pi$
$360$	13.6984	−	2.98056i	0.721967	−	0.157089i
$361$	−17.3976	−	7.63705i	−0.915662	−	0.401950i
$362$	−2.81714	+	1.90676i	−0.148066	+	0.100217i
$363$		−	3.30311i		−	0.173368i
$364$	26.1682	+	10.4752i	1.37159	+	0.549052i
$365$			27.3171i			1.42984i
$366$	−12.3816	+	8.38042i	−0.647199	+	0.438051i
$367$			20.7230i			1.08173i	0.841109	+	0.540866i	$0.181903\pi$
$367$			20.7230i			1.08173i	−0.841109	+	0.540866i	$0.818097\pi$
$368$	−1.44650	+	1.51724i	−0.0754042	+	0.0790914i
$369$			6.87351i			0.357821i
$370$	16.4217	+	24.2622i	0.853722	+	1.26133i
$371$		−	13.5441i		−	0.703175i
$372$	2.81714	+	1.12771i	0.146062	+	0.0584692i
$373$	−4.23686			−0.219376			−0.109688	−	0.993966i	$-0.534985\pi$
$373$	−4.23686			−0.219376			−0.109688	+	0.993966i	$0.534985\pi$
$374$	−16.2420	+	10.9932i	−0.839852	+	0.568447i
$375$	10.5720			0.545938
$376$	−11.8216	+	2.57221i	−0.609654	+	0.132652i
$377$	−2.61836			−0.134852
$378$	14.5645	−	9.85787i	0.749117	−	0.507034i
$379$			8.91154i			0.457755i	0.973455	+	0.228877i	$0.0735055\pi$
$379$			8.91154i			0.457755i	−0.973455	+	0.228877i	$0.926494\pi$
$380$	17.0054	−	25.5308i	0.872357	−	1.30970i
$381$			21.5021i			1.10158i
$382$	−7.96867	−	11.7733i	−0.407713	−	0.602375i
$383$	−24.3480			−1.24412			−0.622062	−	0.782968i	$-0.713705\pi$
$383$	−24.3480			−1.24412			−0.622062	+	0.782968i	$0.713705\pi$
$384$	−12.1878	−	7.42704i	−0.621955	−	0.379009i
$385$	22.7792			1.16094
$386$	11.9220	+	17.6142i	0.606816	+	0.896540i
$387$	−15.0510			−0.765087
$388$	−4.06712	−	1.62808i	−0.206477	−	0.0826535i
$389$			3.04966i			0.154624i	0.997007	+	0.0773119i	$0.0246337\pi$
$389$			3.04966i			0.154624i	−0.997007	+	0.0773119i	$0.975366\pi$
$390$	32.7669	−	22.1780i	1.65922	−	1.12303i
$391$			2.51040i			0.126957i
$392$	−1.20271	−	5.52752i	−0.0607459	−	0.279182i
$393$		−	14.7752i		−	0.745311i
$394$	10.9439	+	16.1691i	0.551346	+	0.814586i
$395$		−	25.8128i		−	1.29878i
$396$	3.03102	−	7.57180i	0.152314	−	0.380497i
$397$		−	14.6389i		−	0.734704i	−0.930082	−	0.367352i	$-0.880264\pi$
$397$		−	14.6389i		−	0.734704i	0.930082	−	0.367352i	$-0.119736\pi$
$398$	5.83964	+	8.62778i	0.292715	+	0.432472i
$399$	2.52495	−	12.0337i	0.126406	−	0.602439i
$400$	21.3706	+	20.3743i	1.06853	+	1.01872i
$401$			28.6859i			1.43251i	0.697841	+	0.716253i	$0.254144\pi$
$401$			28.6859i			1.43251i	−0.697841	+	0.716253i	$0.745856\pi$
$402$	−14.4694	+	9.79353i	−0.721670	+	0.488457i
$403$	−7.58043			−0.377608
$404$	−2.81714	−	1.12771i	−0.140158	−	0.0561058i
$405$		−	9.81808i		−	0.487864i
$406$	−0.736354	−	1.08793i	−0.0365446	−	0.0539929i
$407$	17.0446			0.844869
$408$	−16.7012	+	3.63394i	−0.826835	+	0.179907i
$409$			16.0028i			0.791286i	0.918404	+	0.395643i	$0.129478\pi$
$409$			16.0028i			0.791286i	−0.918404	+	0.395643i	$0.870522\pi$
$410$	−20.1098	+	13.6112i	−0.993153	+	0.672208i
$411$			1.19357i			0.0588747i
$412$	−0.617548	+	1.54270i	−0.0304244	+	0.0760032i
$413$	−18.0776			−0.889539
$414$	−0.585159	−	0.864543i	−0.0287590	−	0.0424900i
$415$			7.03751i			0.345458i
$416$	35.1609	+	5.90980i	1.72390	+	0.289752i
$417$		−	1.06125i		−	0.0519696i
$418$	−6.75522	−	16.5188i	−0.330408	−	0.807959i
$419$	1.68814			0.0824712			0.0412356	−	0.999149i	$-0.486871\pi$
$419$	1.68814			0.0824712			0.0412356	+	0.999149i	$0.486871\pi$
$420$	18.4299	+	7.37756i	0.899288	+	0.359988i
$421$	15.9178			0.775788			0.387894	−	0.921704i	$-0.373203\pi$
$421$	15.9178			0.775788			0.387894	+	0.921704i	$0.373203\pi$
$422$	−12.4086	−	18.3330i	−0.604040	−	0.892438i
$423$		−	6.02499i		−	0.292945i
$424$	−3.64246	−	16.7404i	−0.176894	−	0.812986i
$425$	35.3596			1.71519
$426$	10.2002	+	15.0703i	0.494201	+	0.730157i
$427$	18.7392			0.906852
$428$	−1.44840	−	0.579801i	−0.0700112	−	0.0280257i
$429$		−	23.0193i		−	1.11138i
$430$	−29.8046	−	44.0348i	−1.43730	−	2.12355i
$431$	12.2661			0.590839			0.295420	−	0.955368i	$-0.404541\pi$
$431$	12.2661			0.590839			0.295420	+	0.955368i	$0.404541\pi$
$432$	15.3505	−	16.1011i	0.738551	−	0.774665i
$433$			22.2764i			1.07053i	0.844683	+	0.535267i	$0.179789\pi$
$433$			22.2764i			1.07053i	−0.844683	+	0.535267i	$0.820211\pi$
$434$	−2.13182	−	3.14966i	−0.102331	−	0.151189i
$435$	−1.84407			−0.0884165
$436$	−4.50205	+	11.2466i	−0.215609	+	0.538614i
$437$	−2.23568	−	0.469098i	−0.106947	−	0.0224400i
$438$	7.76328	+	11.4699i	0.370944	+	0.548051i
$439$	−38.1887			−1.82265			−0.911323	−	0.411692i	$-0.864938\pi$
$439$	−38.1887			−1.82265			−0.911323	+	0.411692i	$0.864938\pi$
$440$	28.1549	−	6.12609i	1.34223	−	0.292050i
$441$	2.81714			0.134150
$442$	35.3596	−	23.9329i	1.68189	−	1.13837i
$443$	9.55632			0.454035			0.227017	−	0.973891i	$-0.427103\pi$
$443$	9.55632			0.454035			0.227017	+	0.973891i	$0.427103\pi$
$444$	13.7902	+	5.52027i	0.654455	+	0.261981i
$445$	−42.8734			−2.03239
$446$	−13.3547	+	9.03903i	−0.632364	+	0.428010i
$447$	−14.2997			−0.676353
$448$	7.43268	+	16.2713i	0.351161	+	0.768747i
$449$			4.08318i			0.192697i	0.995348	+	0.0963485i	$0.0307163\pi$
$449$			4.08318i			0.192697i	−0.995348	+	0.0963485i	$0.969284\pi$
$450$	−12.1773	+	8.24211i	−0.574043	+	0.388537i
$451$			14.1275i			0.665237i
$452$	−6.65515	−	2.66408i	−0.313032	−	0.125308i
$453$		−	11.8196i		−	0.555333i
$454$	−11.4355	−	16.8954i	−0.536695	−	0.792939i
$455$	−49.5916			−2.32489
$456$	−0.115448	−	15.5526i	−0.00540635	−	0.728318i
$457$	31.4996			1.47349			0.736745	−	0.676170i	$-0.236362\pi$
$457$	31.4996			1.47349			0.736745	+	0.676170i	$0.236362\pi$
$458$	−14.9359	−	22.0671i	−0.697909	−	1.03113i
$459$		−	26.6407i		−	1.24348i
$460$	1.37064	−	3.42400i	0.0639064	−	0.159645i
$461$			11.6044i			0.540471i	0.962794	+	0.270236i	$0.0871016\pi$
$461$			11.6044i			0.540471i	−0.962794	+	0.270236i	$0.912898\pi$
$462$	9.56450	−	6.47365i	0.444981	−	0.301182i
$463$			33.7855i			1.57015i	0.619403	+	0.785073i	$0.287375\pi$
$463$			33.7855i			1.57015i	−0.619403	+	0.785073i	$0.712625\pi$
$464$	−1.20271	−	1.14664i	−0.0558343	−	0.0532313i
$465$	−5.33879			−0.247580
$466$	6.08865	−	4.12105i	0.282051	−	0.190904i
$467$	30.6853			1.41995			0.709974	−	0.704228i	$-0.248707\pi$
$467$	30.6853			1.41995			0.709974	+	0.704228i	$0.248707\pi$
$468$	−6.59869	+	16.4842i	−0.305025	+	0.761983i
$469$	21.8990			1.01120
$470$	17.6273	−	11.9309i	0.813086	−	0.550331i
$471$	21.9750			1.01255
$472$	−22.3437	+	4.86166i	−1.02845	+	0.223776i
$473$	−30.9351			−1.42240
$474$	−7.33578	−	10.8382i	−0.336944	−	0.497817i
$475$	−6.60736	+	31.4901i	−0.303166	+	1.44487i
$476$	19.8882	+	7.96132i	0.911574	+	0.364906i
$477$	8.53187			0.390648
$478$	−9.69346	−	14.3216i	−0.443369	−	0.655055i
$479$			30.4463i			1.39113i	0.718464	+	0.695564i	$0.244846\pi$
$479$			30.4463i			1.39113i	−0.718464	+	0.695564i	$0.755154\pi$
$480$	24.7633	+	4.16219i	1.13028	+	0.189977i
$481$	−37.1070			−1.69193
$482$	−23.7122	−	35.0337i	−1.08006	−	1.59574i
$483$		−	1.47832i		−	0.0672657i
$484$	−1.94614	+	4.86166i	−0.0884609	+	0.220985i
$485$	7.70763			0.349986
$486$	10.4355	+	15.4179i	0.473364	+	0.699371i
$487$	5.15029			0.233382			0.116691	−	0.993168i	$-0.462771\pi$
$487$	5.15029			0.233382			0.116691	+	0.993168i	$0.462771\pi$
$488$	23.1615	−	5.03959i	1.04847	−	0.228132i
$489$		−	25.6640i		−	1.16056i
$490$	5.57860	+	8.24211i	0.252016	+	0.372340i
$491$	20.3437			0.918099			0.459049	−	0.888411i	$-0.348190\pi$
$491$	20.3437			0.918099			0.459049	+	0.888411i	$0.348190\pi$
$492$	−4.57550	+	11.4301i	−0.206280	+	0.515307i
$493$	−1.98999			−0.0896245
$494$	14.7065	+	35.9622i	0.661675	+	1.61802i
$495$			14.3494i			0.644956i
$496$	−3.48196	−	3.31964i	−0.156345	−	0.149056i
$497$		−	22.8083i		−	1.02309i
$498$	2.00000	+	2.95490i	0.0896221	+	0.132412i
$499$	−18.5776			−0.831648			−0.415824	−	0.909445i	$-0.636507\pi$
$499$	−18.5776			−0.831648			−0.415824	+	0.909445i	$0.636507\pi$
$500$	−15.5604	−	6.22889i	−0.695883	−	0.278564i
$501$			17.4194i			0.778243i
$502$	25.0568	−	16.9595i	1.11834	−	0.756940i
$503$			28.6741i			1.27852i	0.768993	+	0.639258i	$0.220758\pi$
$503$			28.6741i			1.27852i	−0.768993	+	0.639258i	$0.779242\pi$
$504$	−8.70491	+	1.89406i	−0.387748	+	0.0843681i
$505$	5.33879			0.237573
$506$	−1.20271	−	1.77694i	−0.0534668	−	0.0789946i
$507$			33.7145i			1.49731i
$508$	12.6687	−	31.6477i	0.562082	−	1.40414i
$509$	−26.8729			−1.19112			−0.595561	−	0.803310i	$-0.703070\pi$
$509$	−26.8729			−1.19112			−0.595561	+	0.803310i	$0.703070\pi$
$510$	24.9033	−	16.8556i	1.10274	−	0.746378i
$511$		−	17.3592i		−	0.767927i
$512$	13.5626	+	18.1123i	0.599389	+	0.800458i
$513$	23.7254	+	4.97813i	1.04750	+	0.219790i
$514$	−10.7633	−	15.9022i	−0.474748	−	0.701416i
$515$		−	2.92358i		−	0.128828i
$516$	−25.0286	−	10.0190i	−1.10182	−	0.441064i
$517$		−	12.3835i		−	0.544624i
$518$	−10.4355	−	15.4179i	−0.458510	−	0.677425i
$519$			3.65437i			0.160409i
$520$	−61.2948	+	13.3368i	−2.68795	+	0.584859i
$521$			19.3528i			0.847862i	0.905695	+	0.423931i	$0.139350\pi$
$521$			19.3528i			0.847862i	−0.905695	+	0.423931i	$0.860650\pi$
$522$	0.685320	−	0.463853i	0.0299956	−	0.0203023i
$523$		−	33.6806i		−	1.47275i	−0.676575	−	0.736374i	$-0.736536\pi$
$523$		−	33.6806i		−	1.47275i	0.676575	−	0.736374i	$-0.263464\pi$
$524$	−8.70534	+	21.7468i	−0.380294	+	0.950014i
$525$	−20.8224			−0.908766
$526$	9.58681	+	14.1640i	0.418005	+	0.617581i
$527$	−5.76122			−0.250963
$528$	10.0807	−	10.5736i	0.438704	−	0.460157i
$529$	22.7254			0.988059
$530$	16.8951	+	24.9617i	0.733877	+	1.08427i
$531$		−	11.3876i		−	0.494181i
$532$	−10.8064	+	16.2241i	−0.468518	+	0.703404i
$533$		−	30.7563i		−	1.33220i
$534$	−18.0016	+	12.1842i	−0.779005	+	0.527263i
$535$	2.74488			0.118671
$536$	27.0670	−	5.88937i	1.16911	−	0.254382i
$537$	−13.4245			−0.579310
$538$	24.8731	−	16.8352i	1.07236	−	0.725815i
$539$	5.79021			0.249402
$540$	−14.5454	+	36.3359i	−0.625935	+	1.56365i
$541$		−	17.2043i		−	0.739669i	−0.929098	−	0.369834i	$-0.879414\pi$
$541$		−	17.2043i		−	0.739669i	0.929098	−	0.369834i	$-0.120586\pi$
$542$	−12.7753	−	18.8749i	−0.548748	−	0.810747i
$543$		−	3.03447i		−	0.130222i
$544$	26.7227	+	4.49152i	1.14573	+	0.192572i
$545$		−	21.3135i		−	0.912970i
$546$	−20.8224	+	14.0935i	−0.891118	+	0.603146i
$547$		−	12.4185i		−	0.530976i	−0.964114	−	0.265488i	$-0.914467\pi$
$547$		−	12.4185i		−	0.530976i	0.964114	−	0.265488i	$-0.0855330\pi$
$548$	0.703236	−	1.75676i	0.0300407	−	0.0750449i
$549$			11.8044i			0.503800i
$550$	−25.0286	+	16.9404i	−1.06722	+	0.722342i
$551$	0.371852	−	1.77221i	0.0158414	−	0.0754989i
$552$	−0.397569	−	1.82719i	−0.0169216	−	0.0777702i
$553$			16.4033i			0.697539i
$554$	3.16115	+	4.67045i	0.134305	+	0.198428i
$555$	−26.1339			−1.10932
$556$	−0.625272	+	1.56199i	−0.0265174	+	0.0662433i
$557$		−	23.8931i		−	1.01238i	−0.862421	−	0.506192i	$-0.831053\pi$
$557$		−	23.8931i		−	1.01238i	0.862421	−	0.506192i	$-0.168947\pi$
$558$	1.98407	−	1.34290i	0.0839925	−	0.0568497i
$559$	67.3475			2.84850
$560$	−22.7792	−	21.7172i	−0.962597	−	0.917721i
$561$		−	17.4950i		−	0.738638i
$562$	0.499637	+	0.738189i	0.0210759	+	0.0311386i
$563$			5.26287i			0.221804i	0.993831	+	0.110902i	$0.0353739\pi$
$563$			5.26287i			0.221804i	−0.993831	+	0.110902i	$0.964626\pi$
$564$	4.01066	−	10.0190i	0.168879	−	0.421878i
$565$	12.6122			0.530600
$566$	36.3402	−	24.5966i	1.52749	−	1.03387i
$567$			6.23911i			0.262018i
$568$	−6.13392	−	28.1909i	−0.257374	−	1.18286i
$569$			42.6949i			1.78986i	0.446202	+	0.894932i	$0.352776\pi$
$569$			42.6949i			1.78986i	−0.446202	+	0.894932i	$0.647224\pi$
$570$	10.3576	+	25.3277i	0.433830	+	1.06086i
$571$	−16.0539			−0.671833			−0.335917	−	0.941892i	$-0.609046\pi$
$571$	−16.0539			−0.671833			−0.335917	+	0.941892i	$0.609046\pi$
$572$	−13.5626	+	33.8808i	−0.567082	+	1.41663i
$573$	12.6816			0.529780
$574$	12.7792	−	8.64951i	0.533394	−	0.361023i
$575$			3.86849i			0.161327i
$576$	−10.2498	+	4.68208i	−0.427076	+	0.195087i
$577$	8.58043			0.357208			0.178604	−	0.983921i	$-0.442842\pi$
$577$	8.58043			0.357208			0.178604	+	0.983921i	$0.442842\pi$
$578$	6.96393	−	4.71348i	0.289661	−	0.196055i
$579$	−18.9731			−0.788494
$580$	2.71419	+	1.08650i	0.112700	+	0.0451144i
$581$		−	4.47214i		−	0.185535i
$582$	3.23627	−	2.19044i	0.134148	−	0.0907968i
$583$	17.5360			0.726266
$584$	−4.66848	−	21.4559i	−0.193183	−	0.887850i
$585$		−	31.2393i		−	1.29159i
$586$	−35.9351	+	24.3224i	−1.48447	+	1.00475i
$587$	−32.9213			−1.35881			−0.679404	−	0.733764i	$-0.737762\pi$
$587$	−32.9213			−1.35881			−0.679404	+	0.733764i	$0.737762\pi$
$588$	4.68467	+	1.87529i	0.193193	+	0.0773357i
$589$	1.07655	−	5.13075i	0.0443585	−	0.211409i
$590$	33.3168	−	22.5502i	1.37163	−	0.928377i
$591$	−17.4164			−0.716416
$592$	−17.0446	−	16.2500i	−0.700528	−	0.667870i
$593$	12.9731			0.532740			0.266370	−	0.963871i	$-0.414176\pi$
$593$	12.9731			0.532740			0.266370	+	0.963871i	$0.414176\pi$
$594$	12.7633	+	18.8571i	0.523684	+	0.773717i
$595$	−37.6902			−1.54515
$596$	21.0469	+	8.42517i	0.862116	+	0.345109i
$597$	−9.29338			−0.380353
$598$	2.61836	+	3.86849i	0.107073	+	0.158194i
$599$	12.9775			0.530245			0.265122	−	0.964215i	$-0.414588\pi$
$599$	12.9775			0.530245			0.265122	+	0.964215i	$0.414588\pi$
$600$	−25.7364	+	5.59985i	−1.05068	+	0.228613i
$601$			0.135889i			0.00554301i	0.999996	+	0.00277150i	$0.000882198\pi$
$601$			0.135889i			0.00554301i	−0.999996	+	0.00277150i	$0.999118\pi$
$602$	18.9400	+	27.9828i	0.771935	+	1.14049i
$603$			13.7949i			0.561771i
$604$	−6.96393	+	17.3966i	−0.283358	+	0.707858i
$605$		−	9.21336i		−	0.374576i
$606$	2.24164	−	1.51724i	0.0910604	−	0.0616335i
$607$	−31.1052			−1.26252			−0.631261	−	0.775571i	$-0.717462\pi$
$607$	−31.1052			−1.26252			−0.631261	+	0.775571i	$0.717462\pi$
$608$	−8.99344	+	22.9590i	−0.364732	+	0.931112i
$609$	1.17185			0.0474860
$610$	−34.5361	+	23.3755i	−1.39833	+	0.946447i
$611$			26.9595i			1.09066i
$612$	−5.01509	+	12.5282i	−0.202723	+	0.506423i
$613$			21.4073i			0.864633i	0.901722	+	0.432316i	$0.142304\pi$
$613$			21.4073i			0.864633i	−0.901722	+	0.432316i	$0.857696\pi$
$614$	−12.4355	−	18.3728i	−0.501856	−	0.741467i
$615$		−	21.6612i		−	0.873464i
$616$	−17.8916	+	3.89295i	−0.720874	+	0.156852i
$617$	−1.30650			−0.0525978			−0.0262989	−	0.999654i	$-0.508372\pi$
$617$	−1.30650			−0.0525978			−0.0262989	+	0.999654i	$0.508372\pi$
$618$	−0.830855	−	1.22755i	−0.0334219	−	0.0493792i
$619$	−33.9780			−1.36569			−0.682845	−	0.730563i	$-0.739258\pi$
$619$	−33.9780			−1.36569			−0.682845	+	0.730563i	$0.739258\pi$
$620$	7.85786	+	3.14553i	0.315579	+	0.126328i
$621$	2.91461			0.116959
$622$	−22.5124	−	33.2609i	−0.902664	−	1.33364i
$623$	27.2448			1.09154
$624$	−21.9461	+	23.0193i	−0.878549	+	0.921509i
$625$	−7.41957			−0.296783
$626$	−6.48542	+	4.38961i	−0.259210	+	0.175444i
$627$	15.5804	+	3.26914i	0.622222	+	0.130557i
$628$	−32.3437	−	12.9473i	−1.29065	−	0.516654i
$629$	−28.2018			−1.12448
$630$	12.9799	−	8.78536i	0.517132	−	0.350017i
$631$		−	7.50136i		−	0.298625i	−0.988790	−	0.149312i	$-0.952294\pi$
$631$		−	7.50136i		−	0.298625i	0.988790	−	0.149312i	$-0.0477060\pi$
$632$	4.41140	+	20.2743i	0.175476	+	0.806470i
$633$	19.7474			0.784887
$634$	−13.9890	+	9.46834i	−0.555574	+	0.376036i
$635$			59.9757i			2.38006i
$636$	14.1878	+	5.67942i	0.562582	+	0.225204i
$637$	−12.6056			−0.499452
$638$	1.40857	−	0.953380i	0.0557659	−	0.0377447i
$639$	14.3677			0.568378
$640$	−33.9954	−	20.7162i	−1.34379	−	0.818881i
$641$		−	1.22755i		−	0.0484852i	−0.999706	−	0.0242426i	$-0.992283\pi$
$641$		−	1.22755i		−	0.0484852i	0.999706	−	0.0242426i	$-0.00771741\pi$
$642$	1.15251	−	0.780070i	0.0454861	−	0.0307869i
$643$	24.4755			0.965221			0.482610	−	0.875835i	$-0.339689\pi$
$643$	24.4755			0.965221			0.482610	+	0.875835i	$0.339689\pi$
$644$	−0.871002	+	2.17585i	−0.0343223	+	0.0857406i
$645$	47.4319			1.86763
$646$	11.1771	+	27.3318i	0.439757	+	1.07535i
$647$		−	0.598399i		−	0.0235255i	−0.999931	−	0.0117627i	$-0.996256\pi$
$647$		−	0.598399i		−	0.0235255i	0.999931	−	0.0117627i	$-0.00374428\pi$
$648$	1.67790	+	7.71148i	0.0659143	+	0.302936i
$649$		−	23.4056i		−	0.918749i
$650$	54.4886	−	36.8802i	2.13722	−	1.44656i
$651$	3.39264			0.132968
$652$	−15.1208	+	37.7734i	−0.592177	+	1.47932i
$653$		−	34.6646i		−	1.35653i	−0.734818	−	0.678265i	$-0.762732\pi$
$653$		−	34.6646i		−	1.35653i	0.734818	−	0.678265i	$-0.237268\pi$
$654$	−6.05711	−	8.94907i	−0.236852	−	0.349936i
$655$		−	41.2125i		−	1.61031i
$656$	13.4689	−	14.1275i	0.525870	−	0.551585i
$657$	10.9351			0.426620
$658$	−11.2016	+	7.58174i	−0.436685	+	0.295567i
$659$		−	11.5705i		−	0.450721i	−0.974275	−	0.225361i	$-0.927644\pi$
$659$		−	11.5705i		−	0.450721i	0.974275	−	0.225361i	$-0.0723560\pi$
$660$	−9.55196	+	23.8618i	−0.371810	+	0.928818i
$661$	10.3699			0.403343			0.201672	−	0.979453i	$-0.435363\pi$
$661$	10.3699			0.403343			0.201672	+	0.979453i	$0.435363\pi$
$662$	−12.3168	−	18.1974i	−0.478705	−	0.707263i
$663$			38.0875i			1.47920i
$664$	−1.20271	−	5.52752i	−0.0466741	−	0.214509i
$665$	7.04286	−	33.5657i	0.273110	−	1.30162i
$666$	9.71225	−	6.57366i	0.376342	−	0.254724i
$667$		−	0.217713i		−	0.00842987i
$668$	10.2633	−	25.6387i	0.397098	−	0.991992i
$669$		−	14.3850i		−	0.556155i
$670$	−40.3596	+	27.3171i	−1.55923	+	1.05535i
$671$			24.2622i			0.936632i
$672$	−15.7364	−	2.64495i	−0.607043	−	0.102031i
$673$			9.16231i			0.353181i	0.984284	+	0.176591i	$0.0565068\pi$
$673$			9.16231i			0.353181i	−0.984284	+	0.176591i	$0.943493\pi$
$674$	−23.3706	−	34.5289i	−0.900203	−	1.33001i
$675$		−	41.0530i		−	1.58013i
$676$	19.8641	−	49.6225i	0.764003	−	1.90856i
$677$	30.1852			1.16011			0.580055	−	0.814577i	$-0.303031\pi$
$677$	30.1852			1.16011			0.580055	+	0.814577i	$0.303031\pi$
$678$	5.29560	−	3.58429i	0.203376	−	0.137654i
$679$	−4.89798			−0.187967
$680$	−46.5848	+	10.1362i	−1.78645	+	0.388704i
$681$	18.1988			0.697379
$682$	4.07796	−	2.76014i	0.156153	−	0.105691i
$683$		−	21.2151i		−	0.811775i	−0.913923	−	0.405887i	$-0.866963\pi$
$683$		−	21.2151i		−	0.811775i	0.913923	−	0.405887i	$-0.133037\pi$
$684$	−10.2201	−	6.80731i	−0.390775	−	0.260284i
$685$			3.32924i			0.127204i
$686$	−15.9527	−	23.5693i	−0.609077	−	0.899880i
$687$	23.7694			0.906860
$688$	30.9351	+	29.4929i	1.17939	+	1.12441i
$689$	−38.1768			−1.45442
$690$	1.84407	+	2.72452i	0.0702026	+	0.103721i
$691$	−9.52447			−0.362328			−0.181164	−	0.983453i	$-0.557986\pi$
$691$	−9.52447			−0.362328			−0.181164	+	0.983453i	$0.557986\pi$
$692$	2.15310	−	5.37867i	0.0818486	−	0.204466i
$693$		−	9.11860i		−	0.346387i
$694$	−22.6580	+	15.3359i	−0.860087	+	0.582143i
$695$		−	2.96014i		−	0.112285i
$696$	1.44840	−	0.315151i	0.0549016	−	0.0119458i
$697$		−	23.3752i		−	0.885398i
$698$	−9.87939	−	14.5963i	−0.373940	−	0.552478i
$699$			6.55836i			0.248060i
$700$	30.6474	+	12.2683i	1.15836	+	0.463697i
$701$			28.7291i			1.08508i	0.840029	+	0.542541i	$0.182538\pi$
$701$			28.7291i			1.08508i	−0.840029	+	0.542541i	$0.817462\pi$
$702$	−27.7864	−	41.0530i	−1.04873	−	1.54944i
$703$	5.26983	−	25.1156i	0.198755	−	0.947252i
$704$	−21.0670	+	9.62332i	−0.793991	+	0.362692i
$705$			18.9872i			0.715098i
$706$	10.8049	−	7.31318i	0.406646	−	0.275235i
$707$	−3.39264			−0.127594
$708$	7.58043	−	18.9367i	0.284890	−	0.711684i
$709$			16.3713i			0.614837i	0.951574	+	0.307419i	$0.0994652\pi$
$709$			16.3713i			0.614837i	−0.951574	+	0.307419i	$0.900535\pi$
$710$	28.4514	+	42.0356i	1.06776	+	1.57757i
$711$	−10.3330			−0.387517
$712$	33.6743	−	7.32703i	1.26200	−	0.274592i
$713$		−	0.630302i		−	0.0236050i
$714$	−15.8253	+	10.7112i	−0.592248	+	0.400858i
$715$		−	64.2078i		−	2.40123i
$716$	19.7588	+	7.90951i	0.738420	+	0.295592i
$717$	15.4265			0.576111
$718$	14.9633	+	22.1075i	0.558425	+	0.825045i
$719$		−	7.75634i		−	0.289263i	−0.989486	−	0.144631i	$-0.953800\pi$
$719$		−	7.75634i		−	0.289263i	0.989486	−	0.144631i	$-0.0461996\pi$
$720$	13.6804	−	14.3494i	0.509838	−	0.534769i
$721$			1.85785i			0.0691899i
$722$	−26.4293	+	4.84670i	−0.983598	+	0.180376i
$723$	37.7364			1.40343
$724$	−1.78787	+	4.46627i	−0.0664455	+	0.165988i
$725$	−3.06654			−0.113888
$726$	−2.61836	−	3.86849i	−0.0971764	−	0.143573i
$727$			34.3892i			1.27542i	0.770275	+	0.637712i	$0.220119\pi$
$727$			34.3892i			1.27542i	−0.770275	+	0.637712i	$0.779881\pi$
$728$	38.9511	−	8.47517i	1.44362	−	0.314111i
$729$	−24.9780			−0.925111
$730$	21.6541	+	31.9929i	0.801456	+	1.18411i
$731$	51.1850			1.89314
$732$	−7.85786	+	19.6297i	−0.290435	+	0.725536i
$733$			42.5350i			1.57107i	0.618819	+	0.785533i	$0.287611\pi$
$733$			42.5350i			1.57107i	−0.618819	+	0.785533i	$0.712389\pi$
$734$	16.4270	+	24.2701i	0.606333	+	0.895827i
$735$	−8.87795			−0.327468
$736$	−0.491391	+	2.92358i	−0.0181129	+	0.107764i
$737$			28.3533i			1.04441i
$738$	5.44860	+	8.05004i	0.200566	+	0.296326i
$739$	8.23389			0.302889			0.151444	−	0.988466i	$-0.451608\pi$
$739$	8.23389			0.302889			0.151444	+	0.988466i	$0.451608\pi$
$740$	38.4651	+	15.3977i	1.41400	+	0.566031i
$741$	−33.9194	−	7.11709i	−1.24606	−	0.261453i
$742$	−10.7364	−	15.8624i	−0.394144	−	0.582328i
$743$	0.459003			0.0168392			0.00841960	−	0.999965i	$-0.497320\pi$
$743$	0.459003			0.0168392			0.00841960	+	0.999965i	$0.497320\pi$
$744$	4.19328	−	0.912395i	0.153733	−	0.0334500i
$745$	−39.8862			−1.46132
$746$	−4.96207	+	3.35854i	−0.181674	+	0.122965i
$747$	2.81714			0.103074
$748$	−10.3078	+	25.7499i	−0.376889	+	0.941508i
$749$	−1.74429			−0.0637350
$750$	12.3816	−	8.38042i	0.452114	−	0.306010i
$751$	4.47136			0.163162			0.0815812	−	0.996667i	$-0.474003\pi$
$751$	4.47136			0.163162			0.0815812	+	0.996667i	$0.474003\pi$
$752$	−11.8061	+	12.3835i	−0.430526	+	0.451578i
$753$			26.9899i			0.983565i
$754$	−3.06654	+	2.07556i	−0.111677	+	0.0755875i
$755$		−	32.9684i		−	1.19984i
$756$	9.24319	−	23.0904i	0.336171	−	0.839791i
$757$		−	21.8764i		−	0.795111i	−0.917578	−	0.397556i	$-0.869859\pi$
$757$		−	21.8764i		−	0.795111i	0.917578	−	0.397556i	$-0.130141\pi$
$758$	7.06414	+	10.4369i	0.256581	+	0.379085i
$759$	1.91402			0.0694746
$760$	−0.322019	−	43.3809i	−0.0116809	−	1.57359i
$761$	13.2416			0.480009			0.240005	−	0.970772i	$-0.422851\pi$
$761$	13.2416			0.480009			0.240005	+	0.970772i	$0.422851\pi$
$762$	17.0446	+	25.1825i	0.617460	+	0.912266i
$763$			13.5441i			0.490330i
$764$	−18.6653	−	7.47179i	−0.675287	−	0.270320i
$765$		−	23.7423i		−	0.858405i
$766$	−28.5156	+	19.3005i	−1.03031	+	0.697357i
$767$			50.9552i			1.83989i
$768$	−20.1613	+	0.962896i	−0.727509	+	0.0347455i
$769$	−4.84407			−0.174682			−0.0873409	−	0.996178i	$-0.527837\pi$
$769$	−4.84407			−0.174682			−0.0873409	+	0.996178i	$0.527837\pi$
$770$	26.6783	−	18.0570i	0.961418	−	0.650728i
$771$	17.1290			0.616886
$772$	27.9254	+	11.1786i	1.00506	+	0.402328i
$773$	−40.0525			−1.44059			−0.720294	−	0.693669i	$-0.755993\pi$
$773$	−40.0525			−1.44059			−0.720294	+	0.693669i	$0.755993\pi$
$774$	−17.6273	+	11.9309i	−0.633600	+	0.428847i
$775$	−8.87795			−0.318905
$776$	−6.05386	+	1.31723i	−0.217321	+	0.0472858i
$777$	16.6074			0.595786
$778$	2.41745	+	3.57166i	0.0866698	+	0.128050i
$779$	20.8171	+	4.36792i	0.745852	+	0.156497i
$780$	20.7951	−	51.9484i	0.744585	−	1.86005i
$781$	29.5307			1.05669
$782$	1.98999	+	2.94010i	0.0711618	+	0.105138i
$783$			2.31040i			0.0825669i
$784$	−5.79021	−	5.52027i	−0.206793	−	0.197153i
$785$	61.2948			2.18770
$786$	−11.7122	−	17.3043i	−0.417762	−	0.617222i
$787$			1.18061i			0.0420842i	0.999779	+	0.0210421i	$0.00669840\pi$
$787$			1.18061i			0.0420842i	−0.999779	+	0.0210421i	$0.993302\pi$
$788$	25.6343	+	10.2615i	0.913184	+	0.365551i
$789$	−15.2567			−0.543154
$790$	−20.4617	−	30.2311i	−0.727995	−	1.07558i
$791$	−8.01471			−0.284970
$792$	−2.45230	−	11.2705i	−0.0871386	−	0.400480i
$793$		−	52.8201i		−	1.87570i
$794$	−11.6042	−	17.1446i	−0.411817	−	0.608438i
$795$	−26.8874			−0.953596
$796$	13.6784	+	5.47552i	0.484818	+	0.194075i
$797$	47.0231			1.66564			0.832821	−	0.553542i	$-0.186724\pi$
$797$	47.0231			1.66564			0.832821	+	0.553542i	$0.186724\pi$
$798$	−6.58193	−	16.0950i	−0.232998	−	0.569758i
$799$			20.4895i			0.724868i
$800$	41.1793	+	6.92137i	1.45591	+	0.244707i
$801$			17.1624i			0.606402i
$802$	22.7392	+	33.5960i	0.802948	+	1.18632i
$803$	22.4755			0.793144
$804$	−9.18286	+	22.9397i	−0.323854	+	0.809022i
$805$		−	4.12347i		−	0.145333i
$806$	−8.87795	+	6.00897i	−0.312712	+	0.211657i
$807$			26.7920i			0.943122i
$808$	−4.19328	+	0.912395i	−0.147519	+	0.0320980i
$809$	−22.8923			−0.804850			−0.402425	−	0.915453i	$-0.631833\pi$
$809$	−22.8923			−0.804850			−0.402425	+	0.915453i	$0.631833\pi$
$810$	−7.78275	−	11.4986i	−0.273458	−	0.404020i
$811$			7.45423i			0.261753i	0.991399	+	0.130877i	$0.0417792\pi$
$811$			7.45423i			0.261753i	−0.991399	+	0.130877i	$0.958221\pi$
$812$	−1.72479	−	0.690439i	−0.0605282	−	0.0242297i
$813$	20.3310			0.713041
$814$	19.9621	−	13.5112i	0.699670	−	0.473566i
$815$		−	71.5845i		−	2.50750i
$816$	−16.6793	+	17.4950i	−0.583894	+	0.612446i
$817$	−9.56450	+	45.5836i	−0.334619	+	1.59477i
$818$	12.6853	+	18.7419i	0.443532	+	0.655296i
$819$			19.8517i			0.693675i
$820$	−12.7625	+	31.8819i	−0.445684	+	1.11337i
$821$		−	51.2254i		−	1.78778i	−0.448288	−	0.893889i	$-0.647966\pi$
$821$		−	51.2254i		−	1.78778i	0.448288	−	0.893889i	$-0.352034\pi$
$822$	0.946141	+	1.39788i	0.0330005	+	0.0487565i
$823$		−	35.1273i		−	1.22446i	−0.790679	−	0.612231i	$-0.790272\pi$
$823$		−	35.1273i		−	1.22446i	0.790679	−	0.612231i	$-0.209728\pi$
$824$	0.499637	+	2.29628i	0.0174057	+	0.0799949i
$825$		−	26.9595i		−	0.938608i
$826$	−21.1719	+	14.3300i	−0.736663	+	0.498605i
$827$			20.5839i			0.715773i	0.933765	+	0.357886i	$0.116503\pi$
$827$			20.5839i			0.715773i	−0.933765	+	0.357886i	$0.883497\pi$
$828$	−1.37064	−	0.548672i	−0.0476330	−	0.0190677i
$829$	25.0415			0.869727			0.434863	−	0.900496i	$-0.356797\pi$
$829$	25.0415			0.869727			0.434863	+	0.900496i	$0.356797\pi$
$830$	5.57860	+	8.24211i	0.193636	+	0.286088i
$831$	−5.03075			−0.174515
$832$	45.8639	−	20.9505i	1.59005	−	0.726327i
$833$	−9.58043			−0.331942
$834$	−0.841247	−	1.24290i	−0.0291300	−	0.0430381i
$835$			48.5881i			1.68146i
$836$	−21.0058	−	13.9914i	−0.726502	−	0.483903i
$837$			6.68885i			0.231200i
$838$	1.97710	−	1.33818i	0.0682978	−	0.0462268i
$839$	−40.2222			−1.38863			−0.694313	−	0.719673i	$-0.744292\pi$
$839$	−40.2222			−1.38863			−0.694313	+	0.719673i	$0.744292\pi$
$840$	27.4327	−	5.96894i	0.946517	−	0.205948i
$841$	−28.8274			−0.994049
$842$	18.6425	−	12.6180i	0.642462	−	0.434845i
$843$	−0.795137			−0.0273860
$844$	−29.0650	−	11.6348i	−1.00046	−	0.400488i
$845$			94.0400i			3.23507i
$846$	−4.77598	−	7.05627i	−0.164202	−	0.242600i
$847$			5.85483i			0.201174i
$848$	−17.5360	−	16.7185i	−0.602188	−	0.574114i
$849$			39.1437i			1.34341i
$850$	41.4121	−	28.0294i	1.42042	−	0.961401i
$851$		−	3.08539i		−	0.105766i
$852$	23.8923	+	9.56417i	0.818536	+	0.327663i
$853$			29.2390i			1.00113i	0.865700	+	0.500563i	$0.166874\pi$
$853$			29.2390i			1.00113i	−0.865700	+	0.500563i	$0.833126\pi$
$854$	21.9467	−	14.8545i	0.751001	−	0.508309i
$855$	21.1441	+	4.43652i	0.723113	+	0.151726i
$856$	−2.15593	+	0.469098i	−0.0736881	+	0.0160334i
$857$			34.2639i			1.17043i	0.810877	+	0.585217i	$0.198990\pi$
$857$			34.2639i			1.17043i	−0.810877	+	0.585217i	$0.801010\pi$
$858$	−18.2473	−	26.9595i	−0.622952	−	0.920381i
$859$	1.50246			0.0512633			0.0256317	−	0.999671i	$-0.491840\pi$
$859$	1.50246			0.0512633			0.0256317	+	0.999671i	$0.491840\pi$
$860$	−69.8123	−	27.9461i	−2.38058	−	0.952955i
$861$			13.7651i			0.469112i
$862$	14.3657	−	9.72332i	0.489298	−	0.331178i
$863$	−53.5392			−1.82249			−0.911247	−	0.411860i	$-0.864879\pi$
$863$	−53.5392			−1.82249			−0.911247	+	0.411860i	$0.864879\pi$
$864$	5.21471	−	31.0254i	0.177408	−	1.05550i
$865$			10.1931i			0.346577i
$866$	17.6584	+	26.0894i	0.600057	+	0.886553i
$867$			7.50117i			0.254753i
$868$	−4.99344	−	1.99889i	−0.169489	−	0.0678469i
$869$	−21.2379			−0.720445
$870$	−2.15972	+	1.46179i	−0.0732213	+	0.0495592i
$871$		−	61.7267i		−	2.09153i
$872$	3.64246	+	16.7404i	0.123349	+	0.566902i
$873$		−	3.08539i		−	0.104425i
$874$	−2.99021	+	1.22282i	−0.101145	+	0.0413626i
$875$	−18.7392			−0.633500
$876$	18.1842	+	7.27921i	0.614388	+	0.245942i
$877$	−7.96451			−0.268943			−0.134471	−	0.990917i	$-0.542934\pi$
$877$	−7.96451			−0.268943			−0.134471	+	0.990917i	$0.542934\pi$
$878$	−44.7254	+	30.2720i	−1.50941	+	1.02163i
$879$		−	38.7074i		−	1.30557i
$880$	28.1180	−	29.4929i	0.947857	−	0.994207i
$881$	−0.779210			−0.0262523			−0.0131261	−	0.999914i	$-0.504178\pi$
$881$	−0.779210			−0.0262523			−0.0131261	+	0.999914i	$0.504178\pi$
$882$	3.29935	−	2.23314i	0.111095	−	0.0751936i
$883$	4.42167			0.148801			0.0744006	−	0.997228i	$-0.476296\pi$
$883$	4.42167			0.148801			0.0744006	+	0.997228i	$0.476296\pi$
$884$	22.4406	−	56.0589i	0.754758	−	1.88546i
$885$			35.8870i			1.20633i
$886$	11.1921	−	7.57525i	0.376004	−	0.254496i
$887$	15.3505			0.515419			0.257709	−	0.966222i	$-0.417032\pi$
$887$	15.3505			0.515419			0.257709	+	0.966222i	$0.417032\pi$
$888$	20.5265	−	4.46627i	0.688826	−	0.149878i
$889$		−	38.1129i		−	1.27826i
$890$	−50.2119	+	33.9855i	−1.68311	+	1.13920i
$891$	−8.07796			−0.270622
$892$	−8.47541	+	21.1724i	−0.283778	+	0.708906i
$893$	−18.2473	−	3.82871i	−0.610622	−	0.128123i
$894$	−16.7474	+	11.3353i	−0.560115	+	0.379110i
$895$	−37.4450			−1.25165
$896$	21.6031	+	13.1646i	0.721709	+	0.439798i
$897$	−4.16693			−0.139130
$898$	3.23672	+	4.78209i	0.108011	+	0.159580i
$899$	0.499637			0.0166638
$900$	−7.72818	+	19.3058i	−0.257606	+	0.643526i
$901$	−29.0148			−0.966625
$902$	11.1988	+	16.5456i	0.372879	+	0.550910i
$903$	−30.1416			−1.00305
$904$	−9.90611	+	2.15542i	−0.329472	+	0.0716883i
$905$		−	8.46406i		−	0.281355i
$906$	−9.36934	−	13.8427i	−0.311276	−	0.459894i
$907$		−	21.6756i		−	0.719726i	−0.933005	−	0.359863i	$-0.882823\pi$
$907$		−	21.6756i		−	0.719726i	0.933005	−	0.359863i	$-0.117177\pi$
$908$	−26.7858	−	10.7224i	−0.888917	−	0.355837i
$909$		−	2.13714i		−	0.0708843i
$910$	−58.0801	+	39.3110i	−1.92534	+	1.30315i
$911$	20.9922			0.695502			0.347751	−	0.937587i	$-0.386946\pi$
$911$	20.9922			0.695502			0.347751	+	0.937587i	$0.386946\pi$
$912$	−12.4637	−	18.1232i	−0.412714	−	0.600119i
$913$	5.79021			0.191628
$914$	36.8914	−	24.9696i	1.22026	−	0.825922i
$915$		−	37.2005i		−	1.22981i
$916$	−34.9849	−	14.0046i	−1.15593	−	0.462725i
$917$			26.1894i			0.864850i
$918$	−21.1180	−	31.2008i	−0.696998	−	1.02978i
$919$		−	12.7719i		−	0.421306i	−0.977561	−	0.210653i	$-0.932441\pi$
$919$		−	12.7719i		−	0.421306i	0.977561	−	0.210653i	$-0.0675591\pi$
$920$	−1.10894	−	5.09657i	−0.0365606	−	0.168029i
$921$	19.7902			0.652110
$922$	9.19876	+	13.5907i	0.302945	+	0.447586i
$923$	−64.2899			−2.11613
$924$	6.07000	−	15.1635i	0.199688	−	0.498842i
$925$	−43.4585			−1.42891
$926$	26.7816	+	39.5685i	0.880099	+	1.30030i
$927$	−1.17032			−0.0384383
$928$	−2.31751	−	0.389524i	−0.0760758	−	0.0127867i
$929$	−9.11800			−0.299152			−0.149576	−	0.988750i	$-0.547791\pi$
$929$	−9.11800			−0.299152			−0.149576	+	0.988750i	$0.547791\pi$
$930$	−6.25261	+	4.23203i	−0.205031	+	0.138774i
$931$	1.79021	−	8.53201i	0.0586719	−	0.279625i
$932$	3.86409	−	9.65289i	0.126572	−	0.316191i
$933$	35.8268			1.17292
$934$	35.9377	−	24.3241i	1.17592	−	0.795909i
$935$		−	48.7987i		−	1.59589i
$936$	5.33879	+	24.5365i	0.174504	+	0.802002i
$937$	6.18286			0.201985			0.100993	−	0.994887i	$-0.467798\pi$
$937$	6.18286			0.201985			0.100993	+	0.994887i	$0.467798\pi$
$938$	25.6474	−	17.3592i	0.837417	−	0.566799i
$939$		−	6.98575i		−	0.227971i
$940$	11.1869	−	27.9461i	0.364878	−	0.911503i
$941$	18.9084			0.616397			0.308198	−	0.951322i	$-0.400274\pi$
$941$	18.9084			0.616397			0.308198	+	0.951322i	$0.400274\pi$
$942$	25.7364	−	17.4194i	0.838536	−	0.567556i
$943$	2.55734			0.0832785
$944$	−22.3144	+	23.4056i	−0.726272	+	0.761787i
$945$			43.7588i			1.42347i
$946$	−36.2302	+	24.5221i	−1.17795	+	0.797284i
$947$	−33.2409			−1.08018			−0.540092	−	0.841606i	$-0.681611\pi$
$947$	−33.2409			−1.08018			−0.540092	+	0.841606i	$0.681611\pi$
$948$	−17.1829	−	6.87836i	−0.558073	−	0.223399i
$949$	−48.9305			−1.58835
$950$	17.2237	+	42.1178i	0.558812	+	1.36648i
$951$		−	15.0682i		−	0.488620i
$952$	29.6033	−	6.44124i	0.959449	−	0.208762i
$953$		−	43.2269i		−	1.40026i	−0.714018	−	0.700128i	$-0.753126\pi$
$953$		−	43.2269i		−	1.40026i	0.714018	−	0.700128i	$-0.246874\pi$
$954$	9.99225	−	6.76318i	0.323511	−	0.218966i
$955$	35.3727			1.14463
$956$	−22.7053	−	9.08903i	−0.734343	−	0.293960i
$957$			1.51724i			0.0490453i
$958$	24.1347	+	35.6578i	0.779756	+	1.15205i
$959$		−	2.11564i		−	0.0683174i
$960$	32.3013	−	14.7551i	1.04252	−	0.476220i
$961$	−29.5535			−0.953339
$962$	−43.4585	+	29.4145i	−1.40116	+	0.948363i
$963$		−	1.09878i		−	0.0354078i
$964$	−55.5420	−	22.2337i	−1.78889	−	0.716099i
$965$	−52.9216			−1.70361
$966$	−1.17185	−	1.73136i	−0.0377038	−	0.0557055i
$967$		−	24.5774i		−	0.790356i	−0.918605	−	0.395178i	$-0.870683\pi$
$967$		−	24.5774i		−	0.790356i	0.918605	−	0.395178i	$-0.129317\pi$
$968$	1.57456	+	7.23652i	0.0506082	+	0.232590i
$969$	−25.7792	−	5.40908i	−0.828148	−	0.173765i
$970$	9.02693	−	6.10981i	0.289837	−	0.196174i
$971$		−	31.4083i		−	1.00794i	−0.863721	−	0.503970i	$-0.831872\pi$
$971$		−	31.4083i		−	1.00794i	0.863721	−	0.503970i	$-0.168128\pi$
$972$	24.4434	+	9.78480i	0.784024	+	0.313848i
$973$			1.88109i			0.0603049i
$974$	6.03185	−	4.08261i	0.193273	−	0.130815i
$975$			58.6922i			1.87965i
$976$	23.1311	−	24.2622i	0.740408	−	0.776614i
$977$		−	36.9532i		−	1.18224i	−0.806584	−	0.591120i	$-0.798686\pi$
$977$		−	36.9532i		−	1.18224i	0.806584	−	0.591120i	$-0.201314\pi$
$978$	−20.3437	−	30.0568i	−0.650520	−	0.961111i
$979$			35.2747i			1.12738i
$980$	13.0670	+	5.23075i	0.417409	+	0.167090i
$981$	−8.53187			−0.272402
$982$	23.8259	−	16.1264i	0.760315	−	0.514613i
$983$	31.1924			0.994882			0.497441	−	0.867498i	$-0.334273\pi$
$983$	31.1924			0.994882			0.497441	+	0.867498i	$0.334273\pi$
$984$	3.70189	+	17.0135i	0.118012	+	0.542371i
$985$	−48.5797			−1.54788
$986$	−2.33061	+	1.57745i	−0.0742217	+	0.0502363i
$987$		−	12.0658i		−	0.384058i
$988$	45.7309	+	30.4601i	1.45489	+	0.969064i
$989$			5.59985i			0.178065i
$990$	11.3747	+	16.8055i	0.361511	+	0.534114i
$991$	−44.0827			−1.40033			−0.700166	−	0.713980i	$-0.746891\pi$
$991$	−44.0827			−1.40033			−0.700166	+	0.713980i	$0.746891\pi$
$992$	−6.70942	−	1.12771i	−0.213024	−	0.0358049i
$993$	19.6013			0.622028
$994$	−18.0801	−	26.7124i	−0.573465	−	0.847265i
$995$	−25.9220			−0.821784
$996$	4.68467	+	1.87529i	0.148439	+	0.0594209i
$997$			20.9382i			0.663119i	0.943434	+	0.331560i	$0.107575\pi$
$997$			20.9382i			0.663119i	−0.943434	+	0.331560i	$0.892425\pi$
$998$	−21.7575	+	14.7264i	−0.688721	+	0.466155i
$999$			32.7426i			1.03593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.b.c.75.9	yes	12
3.2	odd	2		1368.2.e.e.379.4		12
4.3	odd	2		608.2.b.c.303.4		12
8.3	odd	2	inner	152.2.b.c.75.3	✓	12
8.5	even	2		608.2.b.c.303.3		12
12.11	even	2		5472.2.e.e.5167.1		12
19.18	odd	2	inner	152.2.b.c.75.4	yes	12
24.5	odd	2		5472.2.e.e.5167.12		12
24.11	even	2		1368.2.e.e.379.10		12
57.56	even	2		1368.2.e.e.379.9		12
76.75	even	2		608.2.b.c.303.10		12
152.37	odd	2		608.2.b.c.303.9		12
152.75	even	2	inner	152.2.b.c.75.10	yes	12
228.227	odd	2		5472.2.e.e.5167.2		12
456.227	odd	2		1368.2.e.e.379.3		12
456.341	even	2		5472.2.e.e.5167.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.b.c.75.3	✓	12	8.3	odd	2	inner
152.2.b.c.75.4	yes	12	19.18	odd	2	inner
152.2.b.c.75.9	yes	12	1.1	even	1	trivial
152.2.b.c.75.10	yes	12	152.75	even	2	inner
608.2.b.c.303.3		12	8.5	even	2
608.2.b.c.303.4		12	4.3	odd	2
608.2.b.c.303.9		12	152.37	odd	2
608.2.b.c.303.10		12	76.75	even	2
1368.2.e.e.379.3		12	456.227	odd	2
1368.2.e.e.379.4		12	3.2	odd	2
1368.2.e.e.379.9		12	57.56	even	2
1368.2.e.e.379.10		12	24.11	even	2
5472.2.e.e.5167.1		12	12.11	even	2
5472.2.e.e.5167.2		12	228.227	odd	2
5472.2.e.e.5167.11		12	456.341	even	2
5472.2.e.e.5167.12		12	24.5	odd	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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17117 - 0.792696i) q^{2} +1.26152i q^{3} +(0.743268 - 1.85676i) q^{4} +3.51876i q^{5} +(1.00000 + 1.47745i) q^{6} -2.23607i q^{7} +(-0.601353 - 2.76376i) q^{8} +1.40857 q^{9} +(2.78930 + 4.12105i) q^{10} +2.89511 q^{11} +(2.34234 + 0.937646i) q^{12} -6.30281 q^{13} +(-1.77252 - 2.61881i) q^{14} -4.43898 q^{15} +(-2.89511 - 2.76014i) q^{16} -4.79021 q^{17} +(1.64967 - 1.11657i) q^{18} +(0.895107 - 4.26600i) q^{19} +(6.53348 + 2.61538i) q^{20} +2.82084 q^{21} +(3.39066 - 2.29494i) q^{22} -0.524069i q^{23} +(3.48654 - 0.758618i) q^{24} -7.38164 q^{25} +(-7.38164 + 4.99621i) q^{26} +5.56149i q^{27} +(-4.15184 - 1.66200i) q^{28} +0.415427 q^{29} +(-5.19878 + 3.51876i) q^{30} +1.20271 q^{31} +(-5.57860 - 0.937646i) q^{32} +3.65223i q^{33} +(-5.61014 + 3.79718i) q^{34} +7.86818 q^{35} +(1.04695 - 2.61538i) q^{36} +5.88738 q^{37} +(-2.33332 - 5.70575i) q^{38} -7.95110i q^{39} +(9.72500 - 2.11602i) q^{40} +4.87978i q^{41} +(3.30368 - 2.23607i) q^{42} -10.6853 q^{43} +(2.15184 - 5.37551i) q^{44} +4.95642i q^{45} +(-0.415427 - 0.613773i) q^{46} -4.27737i q^{47} +(3.48196 - 3.65223i) q^{48} +2.00000 q^{49} +(-8.64514 + 5.85139i) q^{50} -6.04294i q^{51} +(-4.68467 + 11.7028i) q^{52} +6.05711 q^{53} +(4.40857 + 6.51344i) q^{54} +10.1872i q^{55} +(-6.17996 + 1.34467i) q^{56} +(5.38164 + 1.12919i) q^{57} +(0.486535 - 0.329307i) q^{58} -8.08453i q^{59} +(-3.29935 + 8.24211i) q^{60} +8.38042i q^{61} +(1.40857 - 0.953380i) q^{62} -3.14966i q^{63} +(-7.27675 + 3.32399i) q^{64} -22.1780i q^{65} +(2.89511 + 4.27737i) q^{66} +9.79353i q^{67} +(-3.56041 + 8.89427i) q^{68} +0.661123 q^{69} +(9.21495 - 6.23707i) q^{70} +10.2002 q^{71} +(-0.847049 - 3.89295i) q^{72} +7.76328 q^{73} +(6.89511 - 4.66690i) q^{74} -9.31208i q^{75} +(-7.25564 - 4.83278i) q^{76} -6.47365i q^{77} +(-6.30281 - 9.31208i) q^{78} -7.33578 q^{79} +(9.71225 - 10.1872i) q^{80} -2.79021 q^{81} +(3.86818 + 5.71504i) q^{82} +2.00000 q^{83} +(2.09664 - 5.23762i) q^{84} -16.8556i q^{85} +(-12.5143 + 8.47020i) q^{86} +0.524069i q^{87} +(-1.74098 - 8.00138i) q^{88} +12.1842i q^{89} +(3.92893 + 5.80480i) q^{90} +14.0935i q^{91} +(-0.973070 - 0.389524i) q^{92} +1.51724i q^{93} +(-3.39066 - 5.00952i) q^{94} +(15.0110 + 3.14966i) q^{95} +(1.18286 - 7.03751i) q^{96} -2.19044i q^{97} +(2.34234 - 1.58539i) q^{98} +4.07796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 12 q^{6} - 8 q^{9} + 12 q^{17} - 24 q^{19} + 4 q^{20} + 32 q^{24} - 44 q^{25} - 44 q^{26} - 20 q^{28} + 32 q^{30} + 40 q^{35} - 52 q^{36} + 4 q^{38} - 20 q^{42} - 24 q^{43} - 4 q^{44} + 24 q^{49}+ \cdots + 64 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 + 12 * q^6 - 8 * q^9 + 12 * q^17 - 24 * q^19 + 4 * q^20 + 32 * q^24 - 44 * q^25 - 44 * q^26 - 20 * q^28 + 32 * q^30 + 40 * q^35 - 52 * q^36 + 4 * q^38 - 20 * q^42 - 24 * q^43 - 4 * q^44 + 24 * q^49 + 28 * q^54 + 20 * q^57 - 4 * q^58 - 8 * q^62 - 8 * q^64 + 12 * q^68 + 4 * q^73 + 48 * q^74 - 12 * q^76 + 32 * q^80 + 36 * q^81 - 8 * q^82 + 24 * q^83 + 8 * q^92 + 64 * q^96 + 64 * q^99

Introduction

L-functions

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