LMFDB - Embedded newform 936.2.r.f.601.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(601,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.601"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.r (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.11
Character	$\chi$	$=$	936.601
Dual form			936.2.r.f.841.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.319301 + 1.70237i) q^{3} +(0.766914 + 1.32833i) q^{5} +(1.75740 + 3.04390i) q^{7} +(-2.79609 + 1.08714i) q^{9} +6.38798 q^{11} +(2.60406 - 2.49377i) q^{13} +(-2.01643 + 1.72971i) q^{15} +(-0.550501 + 0.953495i) q^{17} +(-1.13796 + 1.97100i) q^{19} +(-4.62069 + 3.96365i) q^{21} +(1.66408 - 2.88227i) q^{23} +(1.32369 - 2.29269i) q^{25} +(-2.74350 - 4.41285i) q^{27} -1.42965 q^{29} +(-1.93596 - 3.35318i) q^{31} +(2.03969 + 10.8747i) q^{33} +(-2.69554 + 4.66881i) q^{35} +(1.81670 + 3.14662i) q^{37} +(5.07678 + 3.63679i) q^{39} +(-5.99374 + 10.3815i) q^{41} +(-6.27640 - 10.8710i) q^{43} +(-3.58844 - 2.88041i) q^{45} +(-1.23298 + 2.13558i) q^{47} +(-2.67688 + 4.63648i) q^{49} +(-1.79897 - 0.632701i) q^{51} -6.18395 q^{53} +(4.89903 + 8.48537i) q^{55} +(-3.71871 - 1.30788i) q^{57} +4.85609 q^{59} +(-1.54959 - 2.68397i) q^{61} +(-8.22297 - 6.60050i) q^{63} +(5.30965 + 1.54655i) q^{65} +(3.80313 - 6.58721i) q^{67} +(5.43801 + 1.91255i) q^{69} +(2.43267 - 4.21351i) q^{71} -5.40814 q^{73} +(4.32565 + 1.52134i) q^{75} +(11.2262 + 19.4444i) q^{77} +(2.39185 - 4.14281i) q^{79} +(6.63627 - 6.07946i) q^{81} +(-3.19592 + 5.53550i) q^{83} -1.68875 q^{85} +(-0.456489 - 2.43379i) q^{87} +(-4.25286 - 7.36618i) q^{89} +(12.1671 + 3.54395i) q^{91} +(5.09018 - 4.36638i) q^{93} -3.49086 q^{95} +(1.76312 + 3.05381i) q^{97} +(-17.8614 + 6.94460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{5} + 7 q^{7} + 6 q^{9} + 11 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} - q^{23} - 23 q^{25} - 3 q^{27} - 24 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{35} + 18 q^{37} + 6 q^{39} - 3 q^{41} + 8 q^{43}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q + q^5 + 7 * q^7 + 6 * q^9 + 11 * q^15 - q^17 + 2 * q^19 - 30 * q^21 - q^23 - 23 * q^25 - 3 * q^27 - 24 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^35 + 18 * q^37 + 6 * q^39 - 3 * q^41 + 8 * q^43 + 24 * q^45 + 4 * q^47 - 23 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 + 8 * q^59 - 3 * q^61 + 10 * q^63 - 32 * q^65 + 27 * q^67 - 38 * q^69 + q^71 - 12 * q^73 + 32 * q^75 - 4 * q^77 + 13 * q^79 + 26 * q^81 - 15 * q^83 - 10 * q^85 + 25 * q^87 + 12 * q^89 - 57 * q^91 - 7 * q^93 - 2 * q^95 + 35 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.319301	+	1.70237i	0.184349	+	0.982861i
$3$	0.319301	+	1.70237i	0.184349	+	0.982861i
$4$		0			0
$5$	0.766914	+	1.32833i	0.342974	+	0.594049i	0.984984	−	0.172648i	$-0.0552323\pi$
$5$	0.766914	+	1.32833i	0.342974	+	0.594049i	−0.642009	+	0.766697i	$0.721899\pi$
$6$		0			0
$7$	1.75740	+	3.04390i	0.664233	+	1.15049i	0.979493	+	0.201480i	$0.0645750\pi$
$7$	1.75740	+	3.04390i	0.664233	+	1.15049i	−0.315260	+	0.949005i	$0.602092\pi$
$8$		0			0
$9$	−2.79609	+	1.08714i	−0.932031	+	0.362378i
$10$		0			0
$11$	6.38798			1.92605			0.963024	−	0.269414i	$-0.0868301\pi$
$11$	6.38798			1.92605			0.963024	+	0.269414i	$0.0868301\pi$
$12$		0			0
$13$	2.60406	−	2.49377i	0.722236	−	0.691647i
$13$	2.60406	−	2.49377i	0.722236	−	0.691647i
$14$		0			0
$15$	−2.01643	+	1.72971i	−0.520641	+	0.446608i
$16$		0			0
$17$	−0.550501	+	0.953495i	−0.133516	+	0.231256i	−0.925030	−	0.379895i	$-0.875960\pi$
$17$	−0.550501	+	0.953495i	−0.133516	+	0.231256i	0.791514	+	0.611152i	$0.209293\pi$
$18$		0			0
$19$	−1.13796	+	1.97100i	−0.261065	+	0.452179i	−0.966525	−	0.256571i	$-0.917407\pi$
$19$	−1.13796	+	1.97100i	−0.261065	+	0.452179i	0.705460	+	0.708750i	$0.250741\pi$
$20$		0			0
$21$	−4.62069	+	3.96365i	−1.00832	+	0.864939i
$22$		0			0
$23$	1.66408	−	2.88227i	0.346984	−	0.600994i	−0.638728	−	0.769432i	$-0.720539\pi$
$23$	1.66408	−	2.88227i	0.346984	−	0.600994i	0.985712	+	0.168439i	$0.0538725\pi$
$24$		0			0
$25$	1.32369	−	2.29269i	0.264737	−	0.458538i
$26$		0			0
$27$	−2.74350	−	4.41285i	−0.527986	−	0.849253i
$28$		0			0
$29$	−1.42965			−0.265479			−0.132740	−	0.991151i	$-0.542377\pi$
$29$	−1.42965			−0.265479			−0.132740	+	0.991151i	$0.542377\pi$
$30$		0			0
$31$	−1.93596	−	3.35318i	−0.347708	−	0.602248i	0.638134	−	0.769926i	$-0.279707\pi$
$31$	−1.93596	−	3.35318i	−0.347708	−	0.602248i	−0.985842	+	0.167677i	$0.946373\pi$
$32$		0			0
$33$	2.03969	+	10.8747i	0.355065	+	1.89304i
$34$		0			0
$35$	−2.69554	+	4.66881i	−0.455630	+	0.789174i
$36$		0			0
$37$	1.81670	+	3.14662i	0.298664	+	0.517302i	0.975831	−	0.218528i	$-0.0701256\pi$
$37$	1.81670	+	3.14662i	0.298664	+	0.517302i	−0.677166	+	0.735830i	$0.736792\pi$
$38$		0			0
$39$	5.07678	+	3.63679i	0.812936	+	0.582353i
$40$		0			0
$41$	−5.99374	+	10.3815i	−0.936065	+	1.62131i	−0.163342	+	0.986570i	$0.552227\pi$
$41$	−5.99374	+	10.3815i	−0.936065	+	1.62131i	−0.772723	+	0.634743i	$0.781106\pi$
$42$		0			0
$43$	−6.27640	−	10.8710i	−0.957142	−	1.65782i	−0.729389	−	0.684099i	$-0.760195\pi$
$43$	−6.27640	−	10.8710i	−0.957142	−	1.65782i	−0.227753	−	0.973719i	$-0.573138\pi$
$44$		0			0
$45$	−3.58844	−	2.88041i	−0.534933	−	0.429386i
$46$		0			0
$47$	−1.23298	+	2.13558i	−0.179848	+	0.311506i	−0.941828	−	0.336094i	$-0.890894\pi$
$47$	−1.23298	+	2.13558i	−0.179848	+	0.311506i	0.761980	+	0.647600i	$0.224227\pi$
$48$		0			0
$49$	−2.67688	+	4.63648i	−0.382411	+	0.662355i
$50$		0			0
$51$	−1.79897	−	0.632701i	−0.251906	−	0.0885958i
$52$		0			0
$53$	−6.18395			−0.849431			−0.424716	−	0.905327i	$-0.639626\pi$
$53$	−6.18395			−0.849431			−0.424716	+	0.905327i	$0.639626\pi$
$54$		0			0
$55$	4.89903	+	8.48537i	0.660585	+	1.14417i
$56$		0			0
$57$	−3.71871	−	1.30788i	−0.492556	−	0.173232i
$58$		0			0
$59$	4.85609			0.632209			0.316104	−	0.948724i	$-0.397625\pi$
$59$	4.85609			0.632209			0.316104	+	0.948724i	$0.397625\pi$
$60$		0			0
$61$	−1.54959	−	2.68397i	−0.198405	−	0.343647i	0.749607	−	0.661884i	$-0.230243\pi$
$61$	−1.54959	−	2.68397i	−0.198405	−	0.343647i	−0.948011	+	0.318237i	$0.896909\pi$
$62$		0			0
$63$	−8.22297	−	6.60050i	−1.03600	−	0.831584i
$64$		0			0
$65$	5.30965	+	1.54655i	0.658580	+	0.191826i
$66$		0			0
$67$	3.80313	−	6.58721i	0.464626	−	0.804756i	−0.534559	−	0.845131i	$-0.679522\pi$
$67$	3.80313	−	6.58721i	0.464626	−	0.804756i	0.999185	+	0.0403756i	$0.0128554\pi$
$68$		0			0
$69$	5.43801	+	1.91255i	0.654659	+	0.230244i
$70$		0			0
$71$	2.43267	−	4.21351i	0.288705	−	0.500051i	−0.684796	−	0.728735i	$-0.740109\pi$
$71$	2.43267	−	4.21351i	0.288705	−	0.500051i	0.973501	+	0.228683i	$0.0734421\pi$
$72$		0			0
$73$	−5.40814			−0.632975			−0.316487	−	0.948597i	$-0.602504\pi$
$73$	−5.40814			−0.632975			−0.316487	+	0.948597i	$0.602504\pi$
$74$		0			0
$75$	4.32565	+	1.52134i	0.499483	+	0.175669i
$76$		0			0
$77$	11.2262	+	19.4444i	1.27934	+	2.21589i
$78$		0			0
$79$	2.39185	−	4.14281i	0.269104	−	0.466102i	−0.699527	−	0.714607i	$-0.746606\pi$
$79$	2.39185	−	4.14281i	0.269104	−	0.466102i	0.968631	+	0.248505i	$0.0799391\pi$
$80$		0			0
$81$	6.63627	−	6.07946i	0.737364	−	0.675496i
$82$		0			0
$83$	−3.19592	+	5.53550i	−0.350798	+	0.607600i	−0.986390	−	0.164425i	$-0.947423\pi$
$83$	−3.19592	+	5.53550i	−0.350798	+	0.607600i	0.635591	+	0.772026i	$0.280756\pi$
$84$		0			0
$85$	−1.68875			−0.183170
$86$		0			0
$87$	−0.456489	−	2.43379i	−0.0489408	−	0.260929i
$88$		0			0
$89$	−4.25286	−	7.36618i	−0.450803	−	0.780813i	0.547633	−	0.836718i	$-0.315529\pi$
$89$	−4.25286	−	7.36618i	−0.450803	−	0.780813i	−0.998436	+	0.0559053i	$0.982196\pi$
$90$		0			0
$91$	12.1671	+	3.54395i	1.27546	+	0.371507i
$92$		0			0
$93$	5.09018	−	4.36638i	0.527827	−	0.452773i
$94$		0			0
$95$	−3.49086			−0.358155
$96$		0			0
$97$	1.76312	+	3.05381i	0.179017	+	0.310067i	0.941544	−	0.336889i	$-0.109375\pi$
$97$	1.76312	+	3.05381i	0.179017	+	0.310067i	−0.762527	+	0.646956i	$0.776042\pi$
$98$		0			0
$99$	−17.8614	+	6.94460i	−1.79514	+	0.697958i
$100$		0			0
$101$	−14.8681			−1.47943			−0.739717	−	0.672918i	$-0.765041\pi$
$101$	−14.8681			−1.47943			−0.739717	+	0.672918i	$0.765041\pi$
$102$		0			0
$103$	−5.76469	−	9.98474i	−0.568012	−	0.983826i	−0.996762	−	0.0804029i	$-0.974379\pi$
$103$	−5.76469	−	9.98474i	−0.568012	−	0.983826i	0.428750	−	0.903423i	$-0.358954\pi$
$104$		0			0
$105$	−8.80872	−	3.09804i	−0.859643	−	0.302337i
$106$		0			0
$107$	4.41074	+	7.63962i	0.426402	+	0.738550i	0.996550	−	0.0829919i	$-0.0264476\pi$
$107$	4.41074	+	7.63962i	0.426402	+	0.738550i	−0.570148	+	0.821542i	$0.693114\pi$
$108$		0			0
$109$	−9.26955			−0.887862			−0.443931	−	0.896061i	$-0.646416\pi$
$109$	−9.26955			−0.887862			−0.443931	+	0.896061i	$0.646416\pi$
$110$		0			0
$111$	−4.77663	+	4.09742i	−0.453377	+	0.388909i
$112$		0			0
$113$	−6.72485			−0.632621			−0.316310	−	0.948656i	$-0.602444\pi$
$113$	−6.72485			−0.632621			−0.316310	+	0.948656i	$0.602444\pi$
$114$		0			0
$115$	5.10481			0.476026
$116$		0			0
$117$	−4.57012	+	9.80377i	−0.422508	+	0.906359i
$118$		0			0
$119$	−3.86979			−0.354743
$120$		0			0
$121$	29.8063			2.70966
$122$		0			0
$123$	−19.5869	−	6.88872i	−1.76609	−	0.621135i
$124$		0			0
$125$	11.7298			1.04914
$126$		0			0
$127$	7.61299	+	13.1861i	0.675544	+	1.17008i	0.976310	+	0.216378i	$0.0694245\pi$
$127$	7.61299	+	13.1861i	0.675544	+	1.17008i	−0.300766	+	0.953698i	$0.597242\pi$
$128$		0			0
$129$	16.5024	−	14.1559i	1.45296	−	1.24635i
$130$		0			0
$131$	5.89951	+	10.2183i	0.515443	+	0.892773i	0.999839	+	0.0179247i	$0.00570593\pi$
$131$	5.89951	+	10.2183i	0.515443	+	0.892773i	−0.484396	+	0.874849i	$0.660961\pi$
$132$		0			0
$133$	−7.99937			−0.693633
$134$		0			0
$135$	3.75771	−	7.02855i	0.323412	−	0.604922i
$136$		0			0
$137$	7.00266	+	12.1290i	0.598277	+	1.03625i	0.993075	+	0.117479i	$0.0374812\pi$
$137$	7.00266	+	12.1290i	0.598277	+	1.03625i	−0.394798	+	0.918768i	$0.629185\pi$
$138$		0			0
$139$	−8.28707			−0.702900			−0.351450	−	0.936207i	$-0.614311\pi$
$139$	−8.28707			−0.702900			−0.351450	+	0.936207i	$0.614311\pi$
$140$		0			0
$141$	−4.02922	−	1.41708i	−0.339322	−	0.119340i
$142$		0			0
$143$	16.6347	−	15.9301i	1.39106	−	1.33215i
$144$		0			0
$145$	−1.09642	−	1.89905i	−0.0910526	−	0.157708i
$146$		0			0
$147$	−8.74772	−	3.07658i	−0.721500	−	0.253752i
$148$		0			0
$149$	3.93701			0.322533			0.161266	−	0.986911i	$-0.448442\pi$
$149$	3.93701			0.322533			0.161266	+	0.986911i	$0.448442\pi$
$150$		0			0
$151$	10.1395	−	17.5621i	0.825138	−	1.42918i	−0.0766753	−	0.997056i	$-0.524430\pi$
$151$	10.1395	−	17.5621i	0.825138	−	1.42918i	0.901814	−	0.432125i	$-0.142236\pi$
$152$		0			0
$153$	0.502673	−	3.26453i	0.0406387	−	0.263922i
$154$		0			0
$155$	2.96943	−	5.14320i	0.238510	−	0.413111i
$156$		0			0
$157$	−11.7247	−	20.3078i	−0.935735	−	1.62074i	−0.773319	−	0.634017i	$-0.781405\pi$
$157$	−11.7247	−	20.3078i	−0.935735	−	1.62074i	−0.162416	−	0.986722i	$-0.551929\pi$
$158$		0			0
$159$	−1.97454	−	10.5273i	−0.156592	−	0.834873i
$160$		0			0
$161$	11.6978			0.921913
$162$		0			0
$163$	−1.54310	+	2.67272i	−0.120865	+	0.209344i	−0.920109	−	0.391663i	$-0.871900\pi$
$163$	−1.54310	+	2.67272i	−0.120865	+	0.209344i	0.799244	+	0.601006i	$0.205233\pi$
$164$		0			0
$165$	−12.8809	+	11.0493i	−1.00278	+	0.860189i
$166$		0			0
$167$	9.75344	−	16.8935i	0.754744	−	1.30726i	−0.190757	−	0.981637i	$-0.561094\pi$
$167$	9.75344	−	16.8935i	0.754744	−	1.30726i	0.945501	−	0.325618i	$-0.105572\pi$
$168$		0			0
$169$	0.562232	−	12.9878i	0.0432486	−	0.999064i
$170$		0			0
$171$	1.03909	−	6.74822i	0.0794614	−	0.516049i
$172$		0			0
$173$	5.35024	+	9.26689i	0.406771	+	0.704549i	0.994526	−	0.104491i	$-0.0333212\pi$
$173$	5.35024	+	9.26689i	0.406771	+	0.704549i	−0.587754	+	0.809039i	$0.699988\pi$
$174$		0			0
$175$	9.30496			0.703389
$176$		0			0
$177$	1.55056	+	8.26684i	0.116547	+	0.621373i
$178$		0			0
$179$	1.14067	+	1.97569i	0.0852574	+	0.147670i	0.905501	−	0.424344i	$-0.139495\pi$
$179$	1.14067	+	1.97569i	0.0852574	+	0.147670i	−0.820243	+	0.572015i	$0.806162\pi$
$180$		0			0
$181$	10.2756			0.763780			0.381890	−	0.924208i	$-0.375273\pi$
$181$	10.2756			0.763780			0.381890	+	0.924208i	$0.375273\pi$
$182$		0			0
$183$	4.07431	−	3.49496i	0.301182	−	0.258355i
$184$		0			0
$185$	−2.78651	+	4.82638i	−0.204868	+	0.354842i
$186$		0			0
$187$	−3.51659	+	6.09091i	−0.257158	+	0.445411i
$188$		0			0
$189$	8.61085	−	16.1060i	0.626347	−	1.17154i
$190$		0			0
$191$	−11.8139	−	20.4623i	−0.854826	−	1.48060i	−0.876806	−	0.480844i	$-0.840330\pi$
$191$	−11.8139	−	20.4623i	−0.854826	−	1.48060i	0.0219799	−	0.999758i	$-0.493003\pi$
$192$		0			0
$193$	−5.51975	+	9.56048i	−0.397320	+	0.688178i	−0.993394	−	0.114751i	$-0.963393\pi$
$193$	−5.51975	+	9.56048i	−0.397320	+	0.688178i	0.596074	+	0.802929i	$0.296726\pi$
$194$		0			0
$195$	−0.937418	+	9.53277i	−0.0671299	+	0.682656i
$196$		0			0
$197$	4.47677	+	7.75399i	0.318957	+	0.552449i	0.980271	−	0.197660i	$-0.0633342\pi$
$197$	4.47677	+	7.75399i	0.318957	+	0.552449i	−0.661314	+	0.750109i	$0.730001\pi$
$198$		0			0
$199$	11.6750	−	20.2217i	0.827620	−	1.43348i	−0.0722797	−	0.997384i	$-0.523027\pi$
$199$	11.6750	−	20.2217i	0.827620	−	1.43348i	0.899900	−	0.436096i	$-0.143639\pi$
$200$		0			0
$201$	12.4282	+	4.37101i	0.876616	+	0.308307i
$202$		0			0
$203$	−2.51246	−	4.35171i	−0.176340	−	0.305430i
$204$		0			0
$205$	−18.3867			−1.28419
$206$		0			0
$207$	−1.51950	+	9.86816i	−0.105613	+	0.685884i
$208$		0			0
$209$	−7.26925	+	12.5907i	−0.502825	+	0.870918i
$210$		0			0
$211$	0.0859803	−	0.148922i	0.00591913	−	0.0102522i	−0.863051	−	0.505117i	$-0.831449\pi$
$211$	0.0859803	−	0.148922i	0.00591913	−	0.0102522i	0.868970	+	0.494865i	$0.164783\pi$
$212$		0			0
$213$	7.94968	+	2.79591i	0.544703	+	0.191573i
$214$		0			0
$215$	9.62691	−	16.6743i	0.656550	−	1.13718i
$216$		0			0
$217$	6.80449	−	11.7857i	0.461919	−	0.800066i
$218$		0			0
$219$	−1.72683	−	9.20663i	−0.116688	−	0.622126i
$220$		0			0
$221$	0.944261	+	3.85578i	0.0635179	+	0.259368i
$222$		0			0
$223$	−1.62625			−0.108902			−0.0544510	−	0.998516i	$-0.517341\pi$
$223$	−1.62625			−0.108902			−0.0544510	+	0.998516i	$0.517341\pi$
$224$		0			0
$225$	−1.20868	+	7.84961i	−0.0805790	+	0.523307i
$226$		0			0
$227$	11.2694	+	19.5192i	0.747979	+	1.29554i	0.948790	+	0.315908i	$0.102309\pi$
$227$	11.2694	+	19.5192i	0.747979	+	1.29554i	−0.200811	+	0.979630i	$0.564358\pi$
$228$		0			0
$229$	−12.0818	−	20.9263i	−0.798389	−	1.38285i	−0.920665	−	0.390354i	$-0.872353\pi$
$229$	−12.0818	−	20.9263i	−0.798389	−	1.38285i	0.122276	−	0.992496i	$-0.460981\pi$
$230$		0			0
$231$	−29.5169	+	25.3197i	−1.94207	+	1.66591i
$232$		0			0
$233$	16.4919			1.08042			0.540211	−	0.841530i	$-0.318344\pi$
$233$	16.4919			1.08042			0.540211	+	0.841530i	$0.318344\pi$
$234$		0			0
$235$	−3.78235			−0.246733
$236$		0			0
$237$	7.81629	+	2.74900i	0.507723	+	0.178567i
$238$		0			0
$239$	−5.24014	−	9.07618i	−0.338956	−	0.587089i	0.645280	−	0.763946i	$-0.276741\pi$
$239$	−5.24014	−	9.07618i	−0.338956	−	0.587089i	−0.984237	+	0.176856i	$0.943407\pi$
$240$		0			0
$241$	−11.5900	−	20.0745i	−0.746577	−	1.29311i	−0.949454	−	0.313905i	$-0.898363\pi$
$241$	−11.5900	−	20.0745i	−0.746577	−	1.29311i	0.202877	−	0.979204i	$-0.434971\pi$
$242$		0			0
$243$	12.4684	+	9.35618i	0.799850	+	0.600199i
$244$		0			0
$245$	−8.21173			−0.524628
$246$		0			0
$247$	1.95191	+	7.97040i	0.124197	+	0.507145i
$248$		0			0
$249$	−10.4439	−	3.67313i	−0.661856	−	0.232775i
$250$		0			0
$251$	−10.1392	+	17.5616i	−0.639979	+	1.10848i	0.345458	+	0.938434i	$0.387724\pi$
$251$	−10.1392	+	17.5616i	−0.639979	+	1.10848i	−0.985437	+	0.170042i	$0.945610\pi$
$252$		0			0
$253$	10.6301	−	18.4119i	0.668308	−	1.15754i
$254$		0			0
$255$	−0.539219	−	2.87486i	−0.0337672	−	0.180031i
$256$		0			0
$257$	0.362989	−	0.628715i	0.0226426	−	0.0392182i	−0.854482	−	0.519481i	$-0.826125\pi$
$257$	0.362989	−	0.628715i	0.0226426	−	0.0392182i	0.877125	+	0.480263i	$0.159459\pi$
$258$		0			0
$259$	−6.38534	+	11.0597i	−0.396765	+	0.687218i
$260$		0			0
$261$	3.99743	−	1.55422i	0.247435	−	0.0962040i
$262$		0			0
$263$	−9.62127			−0.593273			−0.296637	−	0.954990i	$-0.595865\pi$
$263$	−9.62127			−0.593273			−0.296637	+	0.954990i	$0.595865\pi$
$264$		0			0
$265$	−4.74256	−	8.21435i	−0.291333	−	0.504604i
$266$		0			0
$267$	11.1820	−	9.59196i	0.684326	−	0.587018i
$268$		0			0
$269$	−6.12405	+	10.6072i	−0.373390	+	0.646731i	−0.990085	−	0.140472i	$-0.955138\pi$
$269$	−6.12405	+	10.6072i	−0.373390	+	0.646731i	0.616695	+	0.787202i	$0.288471\pi$
$270$		0			0
$271$	2.64462	+	4.58062i	0.160650	+	0.278253i	0.935102	−	0.354379i	$-0.115308\pi$
$271$	2.64462	+	4.58062i	0.160650	+	0.278253i	−0.774452	+	0.632632i	$0.781974\pi$
$272$		0			0
$273$	−2.14811	+	21.8445i	−0.130009	+	1.32209i
$274$		0			0
$275$	8.45568	−	14.6457i	0.509897	−	0.883167i
$276$		0			0
$277$	−2.96456	−	5.13476i	−0.178123	−	0.308518i	0.763115	−	0.646263i	$-0.223669\pi$
$277$	−2.96456	−	5.13476i	−0.178123	−	0.308518i	−0.941238	+	0.337745i	$0.890336\pi$
$278$		0			0
$279$	9.05847	+	7.27115i	0.542317	+	0.435312i
$280$		0			0
$281$	16.2879	−	28.2115i	0.971654	−	1.68295i	0.281094	−	0.959680i	$-0.409303\pi$
$281$	16.2879	−	28.2115i	0.971654	−	1.68295i	0.690561	−	0.723275i	$-0.257364\pi$
$282$		0			0
$283$	−9.27398	+	16.0630i	−0.551281	+	0.954847i	0.446902	+	0.894583i	$0.352527\pi$
$283$	−9.27398	+	16.0630i	−0.551281	+	0.954847i	−0.998183	+	0.0602634i	$0.980806\pi$
$284$		0			0
$285$	−1.11464	−	5.94272i	−0.0660254	−	0.352016i
$286$		0			0
$287$	−42.1335			−2.48706
$288$		0			0
$289$	7.89390	+	13.6726i	0.464347	+	0.804273i
$290$		0			0
$291$	−4.63573	+	3.97655i	−0.271751	+	0.233110i
$292$		0			0
$293$	−17.9848			−1.05069			−0.525343	−	0.850891i	$-0.676063\pi$
$293$	−17.9848			−1.05069			−0.525343	+	0.850891i	$0.676063\pi$
$294$		0			0
$295$	3.72420	+	6.45051i	0.216831	+	0.375563i
$296$		0			0
$297$	−17.5254	−	28.1892i	−1.01693	−	1.63570i
$298$		0			0
$299$	−2.85435	−	11.6554i	−0.165071	−	0.674050i
$300$		0			0
$301$	22.0602	−	38.2094i	1.27153	−	2.20236i
$302$		0			0
$303$	−4.74741	−	25.3110i	−0.272732	−	1.45408i
$304$		0			0
$305$	2.37680	−	4.11675i	0.136095	−	0.235724i
$306$		0			0
$307$	14.0831			0.803768			0.401884	−	0.915691i	$-0.368356\pi$
$307$	14.0831			0.803768			0.401884	+	0.915691i	$0.368356\pi$
$308$		0			0
$309$	15.1570	−	13.0018i	0.862252	−	0.739644i
$310$		0			0
$311$	15.3440	+	26.5767i	0.870081	+	1.50702i	0.861912	+	0.507058i	$0.169267\pi$
$311$	15.3440	+	26.5767i	0.870081	+	1.50702i	0.00816904	+	0.999967i	$0.497400\pi$
$312$		0			0
$313$	−5.48343	+	9.49757i	−0.309942	+	0.536835i	−0.978349	−	0.206961i	$-0.933643\pi$
$313$	−5.48343	+	9.49757i	−0.309942	+	0.536835i	0.668408	+	0.743795i	$0.266976\pi$
$314$		0			0
$315$	2.46135	−	15.9849i	0.138682	−	0.900645i
$316$		0			0
$317$	−1.15353	+	1.99797i	−0.0647885	+	0.112217i	−0.896600	−	0.442841i	$-0.853971\pi$
$317$	−1.15353	+	1.99797i	−0.0647885	+	0.112217i	0.831812	+	0.555058i	$0.187304\pi$
$318$		0			0
$319$	−9.13258			−0.511326
$320$		0			0
$321$	−11.5971	+	9.94802i	−0.647285	+	0.555245i
$322$		0			0
$323$	−1.25289	−	2.17007i	−0.0697128	−	0.120746i
$324$		0			0
$325$	−2.27049	−	9.27127i	−0.125944	−	0.514278i
$326$		0			0
$327$	−2.95978	−	15.7802i	−0.163676	−	0.872645i
$328$		0			0
$329$	−8.66730			−0.477844
$330$		0			0
$331$	16.8249	+	29.1416i	0.924780	+	1.60177i	0.791914	+	0.610632i	$0.209085\pi$
$331$	16.8249	+	29.1416i	0.924780	+	1.60177i	0.132866	+	0.991134i	$0.457582\pi$
$332$		0			0
$333$	−8.50048	−	6.82325i	−0.465823	−	0.373912i
$334$		0			0
$335$	11.6667			0.637419
$336$		0			0
$337$	6.88906	+	11.9322i	0.375271	+	0.649988i	0.990368	−	0.138464i	$-0.0442164\pi$
$337$	6.88906	+	11.9322i	0.375271	+	0.649988i	−0.615097	+	0.788452i	$0.710883\pi$
$338$		0			0
$339$	−2.14725	−	11.4481i	−0.116623	−	0.621778i
$340$		0			0
$341$	−12.3669	−	21.4200i	−0.669703	−	1.15996i
$342$		0			0
$343$	5.78622			0.312427
$344$		0			0
$345$	1.62997	+	8.69026i	0.0877548	+	0.467868i
$346$		0			0
$347$	6.32520			0.339555			0.169777	−	0.985482i	$-0.445695\pi$
$347$	6.32520			0.339555			0.169777	+	0.985482i	$0.445695\pi$
$348$		0			0
$349$	13.3337			0.713736			0.356868	−	0.934155i	$-0.383845\pi$
$349$	13.3337			0.713736			0.356868	+	0.934155i	$0.383845\pi$
$350$		0			0
$351$	−18.1488	−	4.64966i	−0.968714	−	0.248181i
$352$		0			0
$353$	−25.2494			−1.34389			−0.671945	−	0.740601i	$-0.734541\pi$
$353$	−25.2494			−1.34389			−0.671945	+	0.740601i	$0.734541\pi$
$354$		0			0
$355$	7.46259			0.396073
$356$		0			0
$357$	−1.23563	−	6.58779i	−0.0653964	−	0.348663i
$358$		0			0
$359$	1.22423			0.0646123			0.0323062	−	0.999478i	$-0.489715\pi$
$359$	1.22423			0.0646123			0.0323062	+	0.999478i	$0.489715\pi$
$360$		0			0
$361$	6.91010	+	11.9687i	0.363690	+	0.629929i
$362$		0			0
$363$	9.51719	+	50.7412i	0.499523	+	2.66322i
$364$		0			0
$365$	−4.14758	−	7.18381i	−0.217094	−	0.376018i
$366$		0			0
$367$	−14.2000			−0.741233			−0.370617	−	0.928786i	$-0.620854\pi$
$367$	−14.2000			−0.741233			−0.370617	+	0.928786i	$0.620854\pi$
$368$		0			0
$369$	5.47301	−	35.5436i	0.284913	−	1.85032i
$370$		0			0
$371$	−10.8676	−	18.8233i	−0.564220	−	0.977258i
$372$		0			0
$373$	−16.7767			−0.868666			−0.434333	−	0.900752i	$-0.643016\pi$
$373$	−16.7767			−0.868666			−0.434333	+	0.900752i	$0.643016\pi$
$374$		0			0
$375$	3.74533	+	19.9683i	0.193408	+	1.03116i
$376$		0			0
$377$	−3.72289	+	3.56522i	−0.191739	+	0.183618i
$378$		0			0
$379$	18.3934	+	31.8583i	0.944807	+	1.63645i	0.756138	+	0.654413i	$0.227084\pi$
$379$	18.3934	+	31.8583i	0.944807	+	1.63645i	0.188669	+	0.982041i	$0.439583\pi$
$380$		0			0
$381$	−20.0167	+	17.1704i	−1.02549	+	0.879668i
$382$		0			0
$383$	15.3260			0.783121			0.391561	−	0.920152i	$-0.371935\pi$
$383$	15.3260			0.783121			0.391561	+	0.920152i	$0.371935\pi$
$384$		0			0
$385$	−17.2191	+	29.8243i	−0.877565	+	1.51999i
$386$		0			0
$387$	29.3677	+	23.5732i	1.49284	+	1.19829i
$388$		0			0
$389$	4.10671	−	7.11304i	0.208219	−	0.360645i	−0.742935	−	0.669364i	$-0.766567\pi$
$389$	4.10671	−	7.11304i	0.208219	−	0.360645i	0.951153	+	0.308718i	$0.0999001\pi$
$390$		0			0
$391$	1.83215	+	3.17338i	0.0926558	+	0.160485i
$392$		0			0
$393$	−15.5115	+	13.3058i	−0.782451	+	0.671190i
$394$		0			0
$395$	7.33737			0.369183
$396$		0			0
$397$	−12.3499	+	21.3906i	−0.619822	+	1.07356i	0.369695	+	0.929153i	$0.379462\pi$
$397$	−12.3499	+	21.3906i	−0.619822	+	1.07356i	−0.989518	+	0.144411i	$0.953871\pi$
$398$		0			0
$399$	−2.55421	−	13.6178i	−0.127870	−	0.681745i
$400$		0			0
$401$	−6.92365	+	11.9921i	−0.345750	+	0.598857i	−0.985490	−	0.169735i	$-0.945709\pi$
$401$	−6.92365	+	11.9921i	−0.345750	+	0.598857i	0.639739	+	0.768592i	$0.279042\pi$
$402$		0			0
$403$	−13.4034	−	3.90404i	−0.667671	−	0.194474i
$404$		0			0
$405$	13.1650	+	4.15276i	0.654174	+	0.206353i
$406$		0			0
$407$	11.6051	+	20.1006i	0.575242	+	0.996349i
$408$		0			0
$409$	18.6508			0.922222			0.461111	−	0.887342i	$-0.347451\pi$
$409$	18.6508			0.922222			0.461111	+	0.887342i	$0.347451\pi$
$410$		0			0
$411$	−18.4120	+	15.7939i	−0.908195	+	0.779054i
$412$		0			0
$413$	8.53407	+	14.7814i	0.419934	+	0.727347i
$414$		0			0
$415$	−9.80399			−0.481259
$416$		0			0
$417$	−2.64607	−	14.1076i	−0.129579	−	0.690853i
$418$		0			0
$419$	7.87761	−	13.6444i	0.384846	−	0.666574i	−0.606901	−	0.794777i	$-0.707588\pi$
$419$	7.87761	−	13.6444i	0.384846	−	0.666574i	0.991748	+	0.128203i	$0.0409211\pi$
$420$		0			0
$421$	−7.16989	+	12.4186i	−0.349439	+	0.605246i	−0.986150	−	0.165856i	$-0.946961\pi$
$421$	−7.16989	+	12.4186i	−0.349439	+	0.605246i	0.636711	+	0.771103i	$0.280295\pi$
$422$		0			0
$423$	1.12586	−	7.31168i	0.0547410	−	0.355506i
$424$		0			0
$425$	1.45738	+	2.52426i	0.0706933	+	0.122444i
$426$		0			0
$427$	5.44648	−	9.43359i	0.263574	−	0.456523i
$428$		0			0
$429$	32.4304	+	23.2318i	1.56575	+	1.12164i
$430$		0			0
$431$	4.49274	+	7.78165i	0.216408	+	0.374829i	0.953707	−	0.300737i	$-0.0972327\pi$
$431$	4.49274	+	7.78165i	0.216408	+	0.374829i	−0.737300	+	0.675566i	$0.763899\pi$
$432$		0			0
$433$	−13.8669	+	24.0182i	−0.666401	+	1.15424i	0.312503	+	0.949917i	$0.398833\pi$
$433$	−13.8669	+	24.0182i	−0.666401	+	1.15424i	−0.978904	+	0.204323i	$0.934501\pi$
$434$		0			0
$435$	2.88279	−	2.47287i	0.138219	−	0.118565i
$436$		0			0
$437$	3.78730	+	6.55979i	0.181171	+	0.313797i
$438$		0			0
$439$	5.95194			0.284071			0.142035	−	0.989862i	$-0.454635\pi$
$439$	5.95194			0.284071			0.142035	+	0.989862i	$0.454635\pi$
$440$		0			0
$441$	2.44431	−	15.8742i	0.116396	−	0.755913i
$442$		0			0
$443$	−5.66685	+	9.81526i	−0.269240	+	0.466337i	−0.968666	−	0.248368i	$-0.920106\pi$
$443$	−5.66685	+	9.81526i	−0.269240	+	0.466337i	0.699426	+	0.714705i	$0.253439\pi$
$444$		0			0
$445$	6.52316	−	11.2984i	0.309227	−	0.535598i
$446$		0			0
$447$	1.25709	+	6.70223i	0.0594585	+	0.317005i
$448$		0			0
$449$	6.47394	−	11.2132i	0.305524	−	0.529183i	−0.671854	−	0.740684i	$-0.734502\pi$
$449$	6.47394	−	11.2132i	0.305524	−	0.529183i	0.977378	+	0.211501i	$0.0678350\pi$
$450$		0			0
$451$	−38.2879	+	66.3166i	−1.80291	+	3.12273i
$452$		0			0
$453$	33.1346	+	11.6535i	1.55680	+	0.547528i
$454$		0			0
$455$	4.62360	+	18.8799i	0.216758	+	0.885104i
$456$		0			0
$457$	−19.3479			−0.905058			−0.452529	−	0.891750i	$-0.649478\pi$
$457$	−19.3479			−0.905058			−0.452529	+	0.891750i	$0.649478\pi$
$458$		0			0
$459$	5.71792	−	0.186636i	0.266890	−	0.00871140i
$460$		0			0
$461$	−17.3986	−	30.1353i	−0.810334	−	1.40354i	−0.912631	−	0.408785i	$-0.865953\pi$
$461$	−17.3986	−	30.1353i	−0.810334	−	1.40354i	0.102297	−	0.994754i	$-0.467381\pi$
$462$		0			0
$463$	13.0277	+	22.5647i	0.605450	+	1.04867i	0.991980	+	0.126394i	$0.0403402\pi$
$463$	13.0277	+	22.5647i	0.605450	+	1.04867i	−0.386530	+	0.922277i	$0.626326\pi$
$464$		0			0
$465$	9.70374	+	3.41282i	0.450000	+	0.158266i
$466$		0			0
$467$	−39.3170			−1.81937			−0.909686	−	0.415296i	$-0.863678\pi$
$467$	−39.3170			−1.81937			−0.909686	+	0.415296i	$0.863678\pi$
$468$		0			0
$469$	26.7344			1.23448
$470$		0			0
$471$	30.8276	−	26.4441i	1.42046	−	1.21848i
$472$		0			0
$473$	−40.0935	−	69.4440i	−1.84350	−	3.19304i
$474$		0			0
$475$	3.01260	+	5.21797i	0.138228	+	0.239417i
$476$		0			0
$477$	17.2909	−	6.72279i	0.791696	−	0.307815i
$478$		0			0
$479$	24.7294			1.12991			0.564957	−	0.825120i	$-0.308893\pi$
$479$	24.7294			1.12991			0.564957	+	0.825120i	$0.308893\pi$
$480$		0			0
$481$	12.5778	+	3.66355i	0.573496	+	0.167044i
$482$		0			0
$483$	3.73511	+	19.9139i	0.169953	+	0.906112i
$484$		0			0
$485$	−2.70432	+	4.68401i	−0.122797	+	0.212690i
$486$		0			0
$487$	15.5768	−	26.9798i	0.705853	−	1.22257i	−0.260530	−	0.965466i	$-0.583897\pi$
$487$	15.5768	−	26.9798i	0.705853	−	1.22257i	0.966383	−	0.257107i	$-0.0827694\pi$
$488$		0			0
$489$	−5.04266	−	1.77351i	−0.228037	−	0.0802009i
$490$		0			0
$491$	0.824435	−	1.42796i	0.0372062	−	0.0644431i	−0.846823	−	0.531875i	$-0.821487\pi$
$491$	0.824435	−	1.42796i	0.0372062	−	0.0644431i	0.884029	+	0.467432i	$0.154821\pi$
$492$		0			0
$493$	0.787023	−	1.36316i	0.0354457	−	0.0613938i
$494$		0			0
$495$	−22.9229	−	18.4000i	−1.03031	−	0.827018i
$496$		0			0
$497$	17.1006			0.767069
$498$		0			0
$499$	−21.3882	−	37.0455i	−0.957468	−	1.65838i	−0.728618	−	0.684921i	$-0.759837\pi$
$499$	−21.3882	−	37.0455i	−0.957468	−	1.65838i	−0.228850	−	0.973462i	$-0.573496\pi$
$500$		0			0
$501$	31.8731	+	11.2098i	1.42399	+	0.500818i
$502$		0			0
$503$	−19.6416	+	34.0203i	−0.875777	+	1.51689i	−0.0198439	+	0.999803i	$0.506317\pi$
$503$	−19.6416	+	34.0203i	−0.875777	+	1.51689i	−0.855933	+	0.517087i	$0.827016\pi$
$504$		0			0
$505$	−11.4026	−	19.7498i	−0.507408	−	0.878856i
$506$		0			0
$507$	22.2896	−	3.18991i	0.989914	−	0.141669i
$508$		0			0
$509$	−6.02885	+	10.4423i	−0.267224	+	0.462846i	−0.968144	−	0.250394i	$-0.919440\pi$
$509$	−6.02885	+	10.4423i	−0.267224	+	0.462846i	0.700920	+	0.713240i	$0.252773\pi$
$510$		0			0
$511$	−9.50424	−	16.4618i	−0.420443	−	0.728228i
$512$		0			0
$513$	11.8197	−	0.385800i	0.521853	−	0.0170335i
$514$		0			0
$515$	8.84205	−	15.3149i	0.389627	−	0.674854i
$516$		0			0
$517$	−7.87623	+	13.6420i	−0.346396	+	0.599976i
$518$		0			0
$519$	−14.0673	+	12.0670i	−0.617486	+	0.529682i
$520$		0			0
$521$	16.6196			0.728116			0.364058	−	0.931376i	$-0.381391\pi$
$521$	16.6196			0.728116			0.364058	+	0.931376i	$0.381391\pi$
$522$		0			0
$523$	−0.621458	−	1.07640i	−0.0271745	−	0.0470676i	0.852118	−	0.523349i	$-0.175318\pi$
$523$	−0.621458	−	1.07640i	−0.0271745	−	0.0470676i	−0.879293	+	0.476282i	$0.841984\pi$
$524$		0			0
$525$	2.97109	+	15.8404i	0.129669	+	0.691333i
$526$		0			0
$527$	4.26298			0.185698
$528$		0			0
$529$	5.96170	+	10.3260i	0.259204	+	0.448955i
$530$		0			0
$531$	−13.5781	+	5.27922i	−0.589238	+	0.229099i
$532$		0			0
$533$	10.2809	+	41.9809i	0.445316	+	1.81840i
$534$		0			0
$535$	−6.76531	+	11.7179i	−0.292490	+	0.506607i
$536$		0			0
$537$	−2.99913	+	2.57267i	−0.129422	+	0.111019i
$538$		0			0
$539$	−17.0998	+	29.6178i	−0.736542	+	1.27573i
$540$		0			0
$541$	−41.8105			−1.79757			−0.898787	−	0.438386i	$-0.855550\pi$
$541$	−41.8105			−1.79757			−0.898787	+	0.438386i	$0.855550\pi$
$542$		0			0
$543$	3.28102	+	17.4928i	0.140802	+	0.750690i
$544$		0			0
$545$	−7.10895	−	12.3131i	−0.304514	−	0.527433i
$546$		0			0
$547$	−0.266912	+	0.462305i	−0.0114123	+	0.0197668i	−0.871675	−	0.490084i	$-0.836966\pi$
$547$	−0.266912	+	0.462305i	−0.0114123	+	0.0197668i	0.860263	+	0.509851i	$0.170299\pi$
$548$		0			0
$549$	7.25063	+	5.82001i	0.309450	+	0.248392i
$550$		0			0
$551$	1.62688	−	2.81784i	0.0693075	−	0.120044i
$552$		0			0
$553$	16.8137			0.714991
$554$		0			0
$555$	−9.10600	−	3.20259i	−0.386528	−	0.135942i
$556$		0			0
$557$	3.96368	+	6.86530i	0.167947	+	0.290892i	0.937698	−	0.347452i	$-0.112953\pi$
$557$	3.96368	+	6.86530i	0.167947	+	0.290892i	−0.769751	+	0.638344i	$0.779620\pi$
$558$		0			0
$559$	−43.4540	−	12.6569i	−1.83791	−	0.535331i
$560$		0			0
$561$	−11.4918	−	4.04168i	−0.485184	−	0.170640i
$562$		0			0
$563$	31.1732			1.31379			0.656897	−	0.753980i	$-0.271869\pi$
$563$	31.1732			1.31379			0.656897	+	0.753980i	$0.271869\pi$
$564$		0			0
$565$	−5.15738	−	8.93284i	−0.216973	−	0.375808i
$566$		0			0
$567$	30.1678	+	9.51612i	1.26693	+	0.399640i
$568$		0			0
$569$	21.0506			0.882488			0.441244	−	0.897387i	$-0.354537\pi$
$569$	21.0506			0.882488			0.441244	+	0.897387i	$0.354537\pi$
$570$		0			0
$571$	−2.80025	−	4.85017i	−0.117187	−	0.202973i	0.801465	−	0.598042i	$-0.204054\pi$
$571$	−2.80025	−	4.85017i	−0.117187	−	0.202973i	−0.918652	+	0.395068i	$0.870721\pi$
$572$		0			0
$573$	31.0622	−	26.6453i	1.29764	−	1.11312i
$574$		0			0
$575$	−4.40543	−	7.63043i	−0.183719	−	0.318211i
$576$		0			0
$577$	−30.6676			−1.27671			−0.638355	−	0.769742i	$-0.720385\pi$
$577$	−30.6676			−1.27671			−0.638355	+	0.769742i	$0.720385\pi$
$578$		0			0
$579$	−18.0379	−	6.34395i	−0.749629	−	0.263645i
$580$		0			0
$581$	−22.4660			−0.932047
$582$		0			0
$583$	−39.5030			−1.63605
$584$		0			0
$585$	−16.5276	+	1.44800i	−0.683331	+	0.0598674i
$586$		0			0
$587$	−31.4657			−1.29873			−0.649364	−	0.760477i	$-0.724965\pi$
$587$	−31.4657			−1.29873			−0.649364	+	0.760477i	$0.724965\pi$
$588$		0			0
$589$	8.81215			0.363098
$590$		0			0
$591$	−11.7707	+	10.0970i	−0.484181	+	0.415333i
$592$		0			0
$593$	0.583862			0.0239763			0.0119882	−	0.999928i	$-0.496184\pi$
$593$	0.583862			0.0239763			0.0119882	+	0.999928i	$0.496184\pi$
$594$		0			0
$595$	−2.96779	−	5.14037i	−0.121668	−	0.210735i
$596$		0			0
$597$	38.1526	+	13.4183i	1.56148	+	0.549175i
$598$		0			0
$599$	−12.5346	−	21.7106i	−0.512150	−	0.887069i	−0.999901	−	0.0140866i	$-0.995516\pi$
$599$	−12.5346	−	21.7106i	−0.512150	−	0.887069i	0.487751	−	0.872983i	$-0.337817\pi$
$600$		0			0
$601$	15.5243			0.633249			0.316625	−	0.948551i	$-0.397450\pi$
$601$	15.5243			0.633249			0.316625	+	0.948551i	$0.397450\pi$
$602$		0			0
$603$	−3.47271	+	22.5530i	−0.141420	+	0.918428i
$604$		0			0
$605$	22.8589	+	39.5927i	0.929345	+	1.60967i
$606$		0			0
$607$	30.8883			1.25372			0.626858	−	0.779134i	$-0.284341\pi$
$607$	30.8883			1.25372			0.626858	+	0.779134i	$0.284341\pi$
$608$		0			0
$609$	6.60596	−	5.66663i	0.267687	−	0.229623i
$610$		0			0
$611$	2.11490	+	8.63592i	0.0855595	+	0.349372i
$612$		0			0
$613$	15.1558	+	26.2506i	0.612138	+	1.06025i	0.990879	+	0.134751i	$0.0430235\pi$
$613$	15.1558	+	26.2506i	0.612138	+	1.06025i	−0.378742	+	0.925502i	$0.623643\pi$
$614$		0			0
$615$	−5.87091	−	31.3009i	−0.236738	−	1.26218i
$616$		0			0
$617$	11.9498			0.481083			0.240541	−	0.970639i	$-0.422675\pi$
$617$	11.9498			0.481083			0.240541	+	0.970639i	$0.422675\pi$
$618$		0			0
$619$	−11.3093	+	19.5884i	−0.454561	+	0.787323i	−0.998663	−	0.0516965i	$-0.983537\pi$
$619$	−11.3093	+	19.5884i	−0.454561	+	0.787323i	0.544102	+	0.839019i	$0.316870\pi$
$620$		0			0
$621$	−17.2844	+	0.564170i	−0.693599	+	0.0226394i
$622$		0			0
$623$	14.9479	−	25.8906i	0.598876	−	1.03728i
$624$		0			0
$625$	2.37728	+	4.11756i	0.0950911	+	0.164703i
$626$		0			0
$627$	−23.7551	−	8.35469i	−0.948686	−	0.333654i
$628$		0			0
$629$	−4.00039			−0.159506
$630$		0			0
$631$	2.92924	−	5.07359i	0.116611	−	0.201976i	−0.801811	−	0.597577i	$-0.796130\pi$
$631$	2.92924	−	5.07359i	0.116611	−	0.201976i	0.918423	+	0.395601i	$0.129464\pi$
$632$		0			0
$633$	0.280974	+	0.0988188i	0.0111677	+	0.00392769i
$634$		0			0
$635$	−11.6770	+	20.2252i	−0.463388	+	0.802612i
$636$		0			0
$637$	4.59158	+	18.7492i	0.181925	+	0.742870i
$638$		0			0
$639$	−2.22132	+	14.4260i	−0.0878741	+	0.570684i
$640$		0			0
$641$	6.94265	+	12.0250i	0.274218	+	0.474960i	0.969938	−	0.243354i	$-0.0782476\pi$
$641$	6.94265	+	12.0250i	0.274218	+	0.474960i	−0.695719	+	0.718314i	$0.744914\pi$
$642$		0			0
$643$	27.9811			1.10347			0.551734	−	0.834020i	$-0.313966\pi$
$643$	27.9811			1.10347			0.551734	+	0.834020i	$0.313966\pi$
$644$		0			0
$645$	31.4596	+	11.0644i	1.23872	+	0.435660i
$646$		0			0
$647$	13.4477	+	23.2920i	0.528682	+	0.915705i	0.999441	+	0.0334425i	$0.0106471\pi$
$647$	13.4477	+	23.2920i	0.528682	+	0.915705i	−0.470758	+	0.882262i	$0.656020\pi$
$648$		0			0
$649$	31.0206			1.21767
$650$		0			0
$651$	22.2363	+	7.82052i	0.871508	+	0.306510i
$652$		0			0
$653$	9.69819	−	16.7978i	0.379519	−	0.657347i	−0.611473	−	0.791265i	$-0.709423\pi$
$653$	9.69819	−	16.7978i	0.379519	−	0.657347i	0.990992	+	0.133918i	$0.0427560\pi$
$654$		0			0
$655$	−9.04884	+	15.6730i	−0.353567	+	0.612397i
$656$		0			0
$657$	15.1217	−	5.87938i	0.589952	−	0.229376i
$658$		0			0
$659$	−19.9251	−	34.5112i	−0.776171	−	1.34437i	−0.934134	−	0.356922i	$-0.883826\pi$
$659$	−19.9251	−	34.5112i	−0.776171	−	1.34437i	0.157963	−	0.987445i	$-0.449507\pi$
$660$		0			0
$661$	−5.73725	+	9.93720i	−0.223153	+	0.386512i	−0.955764	−	0.294136i	$-0.904968\pi$
$661$	−5.73725	+	9.93720i	−0.223153	+	0.386512i	0.732611	+	0.680648i	$0.238302\pi$
$662$		0			0
$663$	−6.26244	+	2.83863i	−0.243213	+	0.110243i
$664$		0			0
$665$	−6.13482	−	10.6258i	−0.237898	−	0.412052i
$666$		0			0
$667$	−2.37905	+	4.12063i	−0.0921171	+	0.159551i
$668$		0			0
$669$	−0.519265	−	2.76848i	−0.0200759	−	0.107036i
$670$		0			0
$671$	−9.89875	−	17.1451i	−0.382137	−	0.661881i
$672$		0			0
$673$	−36.7086			−1.41501			−0.707506	−	0.706707i	$-0.750180\pi$
$673$	−36.7086			−1.41501			−0.707506	+	0.706707i	$0.750180\pi$
$674$		0			0
$675$	−13.7488	+	0.448768i	−0.529193	+	0.0172731i
$676$		0			0
$677$	−3.57943	+	6.19976i	−0.137569	+	0.238276i	−0.926576	−	0.376108i	$-0.877262\pi$
$677$	−3.57943	+	6.19976i	−0.137569	+	0.238276i	0.789007	+	0.614384i	$0.210595\pi$
$678$		0			0
$679$	−6.19698	+	10.7335i	−0.237818	+	0.411914i
$680$		0			0
$681$	−29.6305	+	25.4172i	−1.13544	+	0.973990i
$682$		0			0
$683$	13.2982	−	23.0331i	0.508841	−	0.881338i	−0.491107	−	0.871099i	$-0.663408\pi$
$683$	13.2982	−	23.0331i	0.508841	−	0.881338i	0.999948	−	0.0102387i	$-0.00325912\pi$
$684$		0			0
$685$	−10.7409	+	18.6037i	−0.410387	+	0.710812i
$686$		0			0
$687$	31.7665	−	27.2495i	1.21197	−	1.03963i
$688$		0			0
$689$	−16.1034	+	15.4214i	−0.613490	+	0.587507i
$690$		0			0
$691$	−31.1162			−1.18372			−0.591858	−	0.806042i	$-0.701605\pi$
$691$	−31.1162			−1.18372			−0.591858	+	0.806042i	$0.701605\pi$
$692$		0			0
$693$	−52.5282	−	42.1638i	−1.99538	−	1.60167i
$694$		0			0
$695$	−6.35547	−	11.0080i	−0.241077	−	0.417557i
$696$		0			0
$697$	−6.59912	−	11.4300i	−0.249959	−	0.432942i
$698$		0			0
$699$	5.26589	+	28.0753i	0.199174	+	1.06190i
$700$		0			0
$701$	−38.5419			−1.45571			−0.727854	−	0.685732i	$-0.759482\pi$
$701$	−38.5419			−1.45571			−0.727854	+	0.685732i	$0.759482\pi$
$702$		0			0
$703$	−8.26933			−0.311884
$704$		0			0
$705$	−1.20771	−	6.43893i	−0.0454849	−	0.242504i
$706$		0			0
$707$	−26.1292	−	45.2570i	−0.982688	−	1.70207i
$708$		0			0
$709$	−0.920397	−	1.59417i	−0.0345662	−	0.0598705i	0.848225	−	0.529636i	$-0.177672\pi$
$709$	−0.920397	−	1.59417i	−0.0345662	−	0.0598705i	−0.882791	+	0.469766i	$0.844338\pi$
$710$		0			0
$711$	−2.18405	+	14.1839i	−0.0819081	+	0.531939i
$712$		0			0
$713$	−12.8863			−0.482597
$714$		0			0
$715$	33.9179	+	9.87934i	1.26846	+	0.369466i
$716$		0			0
$717$	13.7778	−	11.8187i	0.514541	−	0.441376i
$718$		0			0
$719$	9.15519	−	15.8573i	0.341431	−	0.591376i	−0.643268	−	0.765641i	$-0.722422\pi$
$719$	9.15519	−	15.8573i	0.341431	−	0.591376i	0.984699	+	0.174265i	$0.0557551\pi$
$720$		0			0
$721$	20.2617	−	35.0943i	0.754585	−	1.30698i
$722$		0			0
$723$	30.4734	−	26.1402i	1.13332	−	0.972164i
$724$		0			0
$725$	−1.89241	+	3.27775i	−0.0702823	+	0.121732i
$726$		0			0
$727$	−11.6183	+	20.1235i	−0.430900	+	0.746340i	−0.996951	−	0.0780300i	$-0.975137\pi$
$727$	−11.6183	+	20.1235i	−0.430900	+	0.746340i	0.566051	+	0.824370i	$0.308470\pi$
$728$		0			0
$729$	−11.9464	+	24.2133i	−0.442461	+	0.896788i
$730$		0			0
$731$	13.8206			0.511175
$732$		0			0
$733$	−9.62013	−	16.6626i	−0.355328	−	0.615446i	0.631846	−	0.775094i	$-0.282297\pi$
$733$	−9.62013	−	16.6626i	−0.355328	−	0.615446i	−0.987174	+	0.159648i	$0.948964\pi$
$734$		0			0
$735$	−2.62202	−	13.9794i	−0.0967145	−	0.515637i
$736$		0			0
$737$	24.2943	−	42.0790i	0.894892	−	1.55000i
$738$		0			0
$739$	−1.98535	−	3.43873i	−0.0730324	−	0.126496i	0.827197	−	0.561913i	$-0.189934\pi$
$739$	−1.98535	−	3.43873i	−0.0730324	−	0.126496i	−0.900229	+	0.435417i	$0.856601\pi$
$740$		0			0
$741$	−12.9453	+	5.86783i	−0.475557	+	0.215560i
$742$		0			0
$743$	2.87589	−	4.98118i	0.105506	−	0.182742i	−0.808439	−	0.588580i	$-0.799687\pi$
$743$	2.87589	−	4.98118i	0.105506	−	0.182742i	0.913945	+	0.405838i	$0.133020\pi$
$744$		0			0
$745$	3.01935	+	5.22966i	0.110620	+	0.191600i
$746$		0			0
$747$	2.91826	−	18.9522i	0.106774	−	0.693424i
$748$		0			0
$749$	−15.5028	+	26.8517i	−0.566460	+	0.981138i
$750$		0			0
$751$	22.6801	−	39.2831i	0.827610	−	1.43346i	−0.0722986	−	0.997383i	$-0.523033\pi$
$751$	22.6801	−	39.2831i	0.827610	−	1.43346i	0.899908	−	0.436079i	$-0.143633\pi$
$752$		0			0
$753$	−33.1337	−	11.6531i	−1.20746	−	0.424664i
$754$		0			0
$755$	31.1044			1.13200
$756$		0			0
$757$	6.54346	+	11.3336i	0.237826	+	0.411927i	0.960090	−	0.279691i	$-0.0902319\pi$
$757$	6.54346	+	11.3336i	0.237826	+	0.411927i	−0.722264	+	0.691617i	$0.756899\pi$
$758$		0			0
$759$	34.7379	+	12.2174i	1.26091	+	0.443462i
$760$		0			0
$761$	−27.0183			−0.979411			−0.489706	−	0.871888i	$-0.662896\pi$
$761$	−27.0183			−0.979411			−0.489706	+	0.871888i	$0.662896\pi$
$762$		0			0
$763$	−16.2903	−	28.2156i	−0.589747	−	1.02147i
$764$		0			0
$765$	4.72189	−	1.83589i	0.170720	−	0.0663769i
$766$		0			0
$767$	12.6455	−	12.1100i	0.456604	−	0.437265i
$768$		0			0
$769$	−23.1288	+	40.0602i	−0.834045	+	1.44461i	0.0607607	+	0.998152i	$0.480647\pi$
$769$	−23.1288	+	40.0602i	−0.834045	+	1.44461i	−0.894806	+	0.446456i	$0.852686\pi$
$770$		0			0
$771$	1.18621	+	0.417190i	0.0427202	+	0.0150247i
$772$		0			0
$773$	20.9744	−	36.3287i	0.754397	−	1.30665i	−0.191276	−	0.981536i	$-0.561263\pi$
$773$	20.9744	−	36.3287i	0.754397	−	1.30665i	0.945673	−	0.325118i	$-0.105404\pi$
$774$		0			0
$775$	−10.2504			−0.368205
$776$		0			0
$777$	−20.8665	−	7.33879i	−0.748583	−	0.263277i
$778$		0			0
$779$	−13.6413	−	23.6273i	−0.488749	−	0.846537i
$780$		0			0
$781$	15.5398	−	26.9158i	0.556059	−	0.963123i
$782$		0			0
$783$	3.92224	+	6.30883i	0.140169	+	0.225459i
$784$		0			0
$785$	17.9837	−	31.1487i	0.641866	−	1.11174i
$786$		0			0
$787$	41.0216			1.46226			0.731131	−	0.682237i	$-0.238993\pi$
$787$	41.0216			1.46226			0.731131	+	0.682237i	$0.238993\pi$
$788$		0			0
$789$	−3.07209	−	16.3789i	−0.109369	−	0.583105i
$790$		0			0
$791$	−11.8182	−	20.4698i	−0.420207	−	0.727821i
$792$		0			0
$793$	−10.7284	−	3.12489i	−0.380977	−	0.110968i
$794$		0			0
$795$	12.4695	−	10.6964i	0.442248	−	0.379363i
$796$		0			0
$797$	16.5621			0.586660			0.293330	−	0.956011i	$-0.405236\pi$
$797$	16.5621			0.586660			0.293330	+	0.956011i	$0.405236\pi$
$798$		0			0
$799$	−1.35751	−	2.35127i	−0.0480252	−	0.0831821i
$800$		0			0
$801$	19.8994	+	15.9731i	0.703112	+	0.564381i
$802$		0			0
$803$	−34.5471			−1.21914
$804$		0			0
$805$	8.97117	+	15.5385i	0.316192	+	0.547661i
$806$		0			0
$807$	−20.0127	−	7.03849i	−0.704480	−	0.247767i
$808$		0			0
$809$	−25.0672	−	43.4176i	−0.881314	−	1.52648i	−0.849880	−	0.526976i	$-0.823326\pi$
$809$	−25.0672	−	43.4176i	−0.881314	−	1.52648i	−0.0314339	−	0.999506i	$-0.510007\pi$
$810$		0			0
$811$	−15.2618			−0.535914			−0.267957	−	0.963431i	$-0.586349\pi$
$811$	−15.2618			−0.535914			−0.267957	+	0.963431i	$0.586349\pi$
$812$		0			0
$813$	−6.95346	+	5.96472i	−0.243869	+	0.209192i
$814$		0			0
$815$	−4.73369			−0.165814
$816$		0			0
$817$	28.5691			0.999507
$818$		0			0
$819$	−37.8732	+	3.31811i	−1.32340	+	0.115944i
$820$		0			0
$821$	−5.12150			−0.178742			−0.0893708	−	0.995998i	$-0.528486\pi$
$821$	−5.12150			−0.178742			−0.0893708	+	0.995998i	$0.528486\pi$
$822$		0			0
$823$	−14.9031			−0.519490			−0.259745	−	0.965677i	$-0.583638\pi$
$823$	−14.9031			−0.519490			−0.259745	+	0.965677i	$0.583638\pi$
$824$		0			0
$825$	27.6322	+	9.71828i	0.962029	+	0.338347i
$826$		0			0
$827$	−18.5879			−0.646364			−0.323182	−	0.946337i	$-0.604753\pi$
$827$	−18.5879			−0.646364			−0.323182	+	0.946337i	$0.604753\pi$
$828$		0			0
$829$	−10.4298	−	18.0650i	−0.362243	−	0.627422i	0.626087	−	0.779753i	$-0.284655\pi$
$829$	−10.4298	−	18.0650i	−0.362243	−	0.627422i	−0.988330	+	0.152331i	$0.951322\pi$
$830$		0			0
$831$	7.79465	−	6.68629i	0.270393	−	0.231945i
$832$		0			0
$833$	−2.94724	−	5.10477i	−0.102116	−	0.176870i
$834$		0			0
$835$	29.9202			1.03543
$836$		0			0
$837$	−9.48577	+	17.7425i	−0.327876	+	0.613271i
$838$		0			0
$839$	−18.0229	−	31.2165i	−0.622219	−	1.07771i	−0.989072	−	0.147436i	$-0.952898\pi$
$839$	−18.0229	−	31.2165i	−0.622219	−	1.07771i	0.366853	−	0.930279i	$-0.380435\pi$
$840$		0			0
$841$	−26.9561			−0.929521
$842$		0			0
$843$	53.2270	+	18.7200i	1.83323	+	0.644751i
$844$		0			0
$845$	17.6834	−	9.21372i	0.608326	−	0.316962i
$846$		0			0
$847$	52.3814	+	90.7273i	1.79985	+	3.11743i
$848$		0			0
$849$	−30.3063	−	10.6588i	−1.04011	−	0.365808i
$850$		0			0
$851$	12.0925			0.414527
$852$		0			0
$853$	6.97776	−	12.0858i	0.238914	−	0.413811i	−0.721489	−	0.692426i	$-0.756542\pi$
$853$	6.97776	−	12.0858i	0.238914	−	0.413811i	0.960403	+	0.278615i	$0.0898753\pi$
$854$		0			0
$855$	9.76078	−	3.79504i	0.333812	−	0.129788i
$856$		0			0
$857$	8.73939	−	15.1371i	0.298532	−	0.517073i	−0.677268	−	0.735736i	$-0.736836\pi$
$857$	8.73939	−	15.1371i	0.298532	−	0.517073i	0.975800	+	0.218664i	$0.0701697\pi$
$858$		0			0
$859$	−4.17576	−	7.23263i	−0.142475	−	0.246774i	0.785953	−	0.618286i	$-0.212173\pi$
$859$	−4.17576	−	7.23263i	−0.142475	−	0.246774i	−0.928428	+	0.371512i	$0.878839\pi$
$860$		0			0
$861$	−13.4533	−	71.7266i	−0.458487	−	2.44444i
$862$		0			0
$863$	4.11501			0.140077			0.0700384	−	0.997544i	$-0.477688\pi$
$863$	4.11501			0.140077			0.0700384	+	0.997544i	$0.477688\pi$
$864$		0			0
$865$	−8.20635	+	14.2138i	−0.279024	+	0.483284i
$866$		0			0
$867$	−20.7553	+	17.8040i	−0.704886	+	0.604655i
$868$		0			0
$869$	15.2791	−	26.4642i	0.518308	−	0.897735i
$870$		0			0
$871$	−6.52342	−	26.6376i	−0.221038	−	0.902581i
$872$		0			0
$873$	−8.24974	−	6.62198i	−0.279211	−	0.224120i
$874$		0			0
$875$	20.6138	+	35.7042i	0.696874	+	1.20702i
$876$		0			0
$877$	10.6198			0.358606			0.179303	−	0.983794i	$-0.442616\pi$
$877$	10.6198			0.358606			0.179303	+	0.983794i	$0.442616\pi$
$878$		0			0
$879$	−5.74258	−	30.6168i	−0.193693	−	1.03268i
$880$		0			0
$881$	15.0048	+	25.9891i	0.505525	+	0.875595i	0.999980	+	0.00639173i	$0.00203456\pi$
$881$	15.0048	+	25.9891i	0.505525	+	0.875595i	−0.494454	+	0.869204i	$0.664632\pi$
$882$		0			0
$883$	21.3674			0.719072			0.359536	−	0.933131i	$-0.382935\pi$
$883$	21.3674			0.719072			0.359536	+	0.933131i	$0.382935\pi$
$884$		0			0
$885$	−9.79197	+	8.39961i	−0.329154	+	0.282350i
$886$		0			0
$887$	−20.1581	+	34.9148i	−0.676841	+	1.17232i	0.299086	+	0.954226i	$0.403318\pi$
$887$	−20.1581	+	34.9148i	−0.676841	+	1.17232i	−0.975927	+	0.218097i	$0.930015\pi$
$888$		0			0
$889$	−26.7581	+	46.3464i	−0.897437	+	1.55441i
$890$		0			0
$891$	42.3924	−	38.8355i	1.42020	−	1.30104i
$892$		0			0
$893$	−2.80615	−	4.86039i	−0.0939042	−	0.162647i
$894$		0			0
$895$	−1.74959	+	3.03037i	−0.0584822	+	0.101294i
$896$		0			0
$897$	18.9304	−	8.58074i	0.632066	−	0.286502i
$898$		0			0
$899$	2.76774	+	4.79387i	0.0923094	+	0.159884i
$900$		0			0
$901$	3.40427	−	5.89637i	0.113413	−	0.196436i
$902$		0			0
$903$	72.0903	+	25.3542i	2.39901	+	0.843736i
$904$		0			0
$905$	7.88051	+	13.6494i	0.261957	+	0.453723i
$906$		0			0
$907$	14.7911			0.491131			0.245566	−	0.969380i	$-0.421026\pi$
$907$	14.7911			0.491131			0.245566	+	0.969380i	$0.421026\pi$
$908$		0			0
$909$	41.5727	−	16.1637i	1.37888	−	0.536115i
$910$		0			0
$911$	−16.1529	+	27.9777i	−0.535170	+	0.926942i	0.463985	+	0.885843i	$0.346419\pi$
$911$	−16.1529	+	27.9777i	−0.535170	+	0.926942i	−0.999155	+	0.0410987i	$0.986914\pi$
$912$		0			0
$913$	−20.4155	+	35.3607i	−0.675654	+	1.17027i
$914$		0			0
$915$	7.76712	+	2.73171i	0.256773	+	0.0903074i
$916$		0			0
$917$	−20.7356	+	35.9150i	−0.684748	+	1.18602i
$918$		0			0
$919$	18.5950	−	32.2075i	0.613392	−	1.06243i	−0.377272	−	0.926103i	$-0.623138\pi$
$919$	18.5950	−	32.2075i	0.613392	−	1.06243i	0.990664	−	0.136324i	$-0.0435289\pi$
$920$		0			0
$921$	4.49677	+	23.9747i	0.148174	+	0.789992i
$922$		0			0
$923$	−4.17270	−	17.0387i	−0.137346	−	0.560837i
$924$		0			0
$925$	9.61899			0.316270
$926$		0			0
$927$	26.9734	+	21.6513i	0.885922	+	0.711121i
$928$		0			0
$929$	−7.60222	−	13.1674i	−0.249421	−	0.432009i	0.713944	−	0.700202i	$-0.246907\pi$
$929$	−7.60222	−	13.1674i	−0.249421	−	0.432009i	−0.963365	+	0.268193i	$0.913574\pi$
$930$		0			0
$931$	−6.09234	−	10.5522i	−0.199668	−	0.345836i
$932$		0			0
$933$	−40.3438	+	34.6071i	−1.32080	+	1.13299i
$934$		0			0
$935$	−10.7877			−0.352795
$936$		0			0
$937$	56.1934			1.83576			0.917880	−	0.396859i	$-0.129900\pi$
$937$	56.1934			1.83576			0.917880	+	0.396859i	$0.129900\pi$
$938$		0			0
$939$	−17.9192	−	6.30220i	−0.584771	−	0.205665i
$940$		0			0
$941$	15.6111	+	27.0393i	0.508909	+	0.881455i	0.999947	+	0.0103174i	$0.00328419\pi$
$941$	15.6111	+	27.0393i	0.508909	+	0.881455i	−0.491038	+	0.871138i	$0.663382\pi$
$942$		0			0
$943$	19.9481	+	34.5511i	0.649599	+	1.12514i
$944$		0			0
$945$	27.9980	−	0.913866i	0.910774	−	0.0297281i
$946$		0			0
$947$	−40.6727			−1.32169			−0.660843	−	0.750524i	$-0.729801\pi$
$947$	−40.6727			−1.32169			−0.660843	+	0.750524i	$0.729801\pi$
$948$		0			0
$949$	−14.0831	+	13.4867i	−0.457157	+	0.437795i
$950$		0			0
$951$	−3.76959	−	1.32577i	−0.122237	−	0.0429910i
$952$		0			0
$953$	1.35525	−	2.34736i	0.0439008	−	0.0760384i	−0.843240	−	0.537537i	$-0.819355\pi$
$953$	1.35525	−	2.34736i	0.0439008	−	0.0760384i	0.887141	+	0.461499i	$0.152688\pi$
$954$		0			0
$955$	18.1205	−	31.3857i	0.586367	−	1.01562i
$956$		0			0
$957$	−2.91604	−	15.5470i	−0.0942623	−	0.502562i
$958$		0			0
$959$	−24.6129	+	42.6307i	−0.794791	+	1.37662i
$960$		0			0
$961$	8.00414	−	13.8636i	0.258198	−	0.447212i
$962$		0			0
$963$	−20.6381	−	16.5660i	−0.665054	−	0.533833i
$964$		0			0
$965$	−16.9327			−0.545082
$966$		0			0
$967$	−2.04491	−	3.54189i	−0.0657600	−	0.113900i	0.831271	−	0.555868i	$-0.187614\pi$
$967$	−2.04491	−	3.54189i	−0.0657600	−	0.113900i	−0.897031	+	0.441968i	$0.854280\pi$
$968$		0			0
$969$	3.29421	−	2.82579i	0.105825	−	0.0907774i
$970$		0			0
$971$	−6.04999	+	10.4789i	−0.194153	+	0.336283i	−0.946623	−	0.322344i	$-0.895529\pi$
$971$	−6.04999	+	10.4789i	−0.194153	+	0.336283i	0.752469	+	0.658627i	$0.228863\pi$
$972$		0			0
$973$	−14.5637	−	25.2250i	−0.466890	−	0.808677i
$974$		0			0
$975$	15.0581	−	6.82553i	0.482246	−	0.218592i
$976$		0			0
$977$	−3.82475	+	6.62467i	−0.122365	+	0.211942i	−0.920700	−	0.390272i	$-0.872381\pi$
$977$	−3.82475	+	6.62467i	−0.122365	+	0.211942i	0.798335	+	0.602214i	$0.205714\pi$
$978$		0			0
$979$	−27.1672	−	47.0550i	−0.868268	−	1.50388i
$980$		0			0
$981$	25.9185	−	10.0773i	0.827515	−	0.321742i
$982$		0			0
$983$	25.0980	−	43.4711i	0.800503	−	1.38651i	−0.118783	−	0.992920i	$-0.537899\pi$
$983$	25.0980	−	43.4711i	0.800503	−	1.38651i	0.919286	−	0.393591i	$-0.128767\pi$
$984$		0			0
$985$	−6.86659	+	11.8933i	−0.218788	+	0.378952i
$986$		0			0
$987$	−2.76748	−	14.7549i	−0.0880899	−	0.469654i
$988$		0			0
$989$	−41.7776			−1.32845
$990$		0			0
$991$	−21.7547	−	37.6803i	−0.691062	−	1.19695i	−0.971490	−	0.237079i	$-0.923810\pi$
$991$	−21.7547	−	37.6803i	−0.691062	−	1.19695i	0.280428	−	0.959875i	$-0.409523\pi$
$992$		0			0
$993$	−44.2374	+	37.9471i	−1.40383	+	1.20421i
$994$		0			0
$995$	35.8149			1.13541
$996$		0			0
$997$	15.1014	+	26.1564i	0.478266	+	0.828381i	0.999690	−	0.0249170i	$-0.00793213\pi$
$997$	15.1014	+	26.1564i	0.478266	+	0.828381i	−0.521423	+	0.853298i	$0.674599\pi$
$998$		0			0
$999$	8.90145	−	16.6496i	0.281629	−	0.526770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.r.f.601.11	✓	40
3.2	odd	2		2808.2.r.f.289.8		40
9.4	even	3		936.2.s.f.913.17	yes	40
9.5	odd	6		2808.2.s.f.1225.8		40
13.9	even	3		936.2.s.f.529.17	yes	40
39.35	odd	6		2808.2.s.f.1153.8		40
117.22	even	3	inner	936.2.r.f.841.11	yes	40
117.113	odd	6		2808.2.r.f.2089.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.11	✓	40	1.1	even	1	trivial
936.2.r.f.841.11	yes	40	117.22	even	3	inner
936.2.s.f.529.17	yes	40	13.9	even	3
936.2.s.f.913.17	yes	40	9.4	even	3
2808.2.r.f.289.8		40	3.2	odd	2
2808.2.r.f.2089.8		40	117.113	odd	6
2808.2.s.f.1153.8		40	39.35	odd	6
2808.2.s.f.1225.8		40	9.5	odd	6

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.319301 + 1.70237i) q^{3} +(0.766914 + 1.32833i) q^{5} +(1.75740 + 3.04390i) q^{7} +(-2.79609 + 1.08714i) q^{9} +6.38798 q^{11} +(2.60406 - 2.49377i) q^{13} +(-2.01643 + 1.72971i) q^{15} +(-0.550501 + 0.953495i) q^{17} +(-1.13796 + 1.97100i) q^{19} +(-4.62069 + 3.96365i) q^{21} +(1.66408 - 2.88227i) q^{23} +(1.32369 - 2.29269i) q^{25} +(-2.74350 - 4.41285i) q^{27} -1.42965 q^{29} +(-1.93596 - 3.35318i) q^{31} +(2.03969 + 10.8747i) q^{33} +(-2.69554 + 4.66881i) q^{35} +(1.81670 + 3.14662i) q^{37} +(5.07678 + 3.63679i) q^{39} +(-5.99374 + 10.3815i) q^{41} +(-6.27640 - 10.8710i) q^{43} +(-3.58844 - 2.88041i) q^{45} +(-1.23298 + 2.13558i) q^{47} +(-2.67688 + 4.63648i) q^{49} +(-1.79897 - 0.632701i) q^{51} -6.18395 q^{53} +(4.89903 + 8.48537i) q^{55} +(-3.71871 - 1.30788i) q^{57} +4.85609 q^{59} +(-1.54959 - 2.68397i) q^{61} +(-8.22297 - 6.60050i) q^{63} +(5.30965 + 1.54655i) q^{65} +(3.80313 - 6.58721i) q^{67} +(5.43801 + 1.91255i) q^{69} +(2.43267 - 4.21351i) q^{71} -5.40814 q^{73} +(4.32565 + 1.52134i) q^{75} +(11.2262 + 19.4444i) q^{77} +(2.39185 - 4.14281i) q^{79} +(6.63627 - 6.07946i) q^{81} +(-3.19592 + 5.53550i) q^{83} -1.68875 q^{85} +(-0.456489 - 2.43379i) q^{87} +(-4.25286 - 7.36618i) q^{89} +(12.1671 + 3.54395i) q^{91} +(5.09018 - 4.36638i) q^{93} -3.49086 q^{95} +(1.76312 + 3.05381i) q^{97} +(-17.8614 + 6.94460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{5} + 7 q^{7} + 6 q^{9} + 11 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} - q^{23} - 23 q^{25} - 3 q^{27} - 24 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{35} + 18 q^{37} + 6 q^{39} - 3 q^{41} + 8 q^{43}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q + q^5 + 7 * q^7 + 6 * q^9 + 11 * q^15 - q^17 + 2 * q^19 - 30 * q^21 - q^23 - 23 * q^25 - 3 * q^27 - 24 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^35 + 18 * q^37 + 6 * q^39 - 3 * q^41 + 8 * q^43 + 24 * q^45 + 4 * q^47 - 23 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 + 8 * q^59 - 3 * q^61 + 10 * q^63 - 32 * q^65 + 27 * q^67 - 38 * q^69 + q^71 - 12 * q^73 + 32 * q^75 - 4 * q^77 + 13 * q^79 + 26 * q^81 - 15 * q^83 - 10 * q^85 + 25 * q^87 + 12 * q^89 - 57 * q^91 - 7 * q^93 - 2 * q^95 + 35 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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