LMFDB - Embedded newform 820.2.u.a.221.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] 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:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.6
Character	$\chi$	$=$	820.221
Dual form			820.2.u.a.141.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.42987 q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.903746 + 2.78144i) q^{7} +2.90425 q^{9} +(2.41720 - 1.75620i) q^{11} +(-1.03961 + 3.19958i) q^{13} +(-1.96580 - 1.42824i) q^{15} +(4.80955 - 3.49434i) q^{17} +(0.971064 + 2.98863i) q^{19} +(2.19598 + 6.75854i) q^{21} +(1.16123 - 3.57390i) q^{23} +(0.309017 + 0.951057i) q^{25} -0.232654 q^{27} +(2.21438 + 1.60884i) q^{29} +(-6.26976 + 4.55525i) q^{31} +(5.87348 - 4.26733i) q^{33} +(0.903746 - 2.78144i) q^{35} +(9.04450 + 6.57121i) q^{37} +(-2.52611 + 7.77456i) q^{39} +(-4.16856 - 4.86036i) q^{41} +(3.10622 - 9.55998i) q^{43} +(-2.34959 - 1.70708i) q^{45} +(-1.85022 + 5.69440i) q^{47} +(-1.25655 + 0.912939i) q^{49} +(11.6866 - 8.49078i) q^{51} +(-0.451093 - 0.327738i) q^{53} -2.98782 q^{55} +(2.35956 + 7.26197i) q^{57} +(-1.46341 + 4.50392i) q^{59} +(-3.95004 - 12.1570i) q^{61} +(2.62471 + 8.07801i) q^{63} +(2.72173 - 1.97745i) q^{65} +(-6.99129 - 5.07947i) q^{67} +(2.82164 - 8.68411i) q^{69} +(5.52700 - 4.01560i) q^{71} -10.7242 q^{73} +(0.750870 + 2.31094i) q^{75} +(7.06930 + 5.13615i) q^{77} -2.77926 q^{79} -9.27808 q^{81} -10.8048 q^{83} -5.94493 q^{85} +(5.38065 + 3.90927i) q^{87} +(1.24721 + 3.83851i) q^{89} -9.83900 q^{91} +(-15.2347 + 11.0686i) q^{93} +(0.971064 - 2.98863i) q^{95} +(-2.35673 - 1.71226i) q^{97} +(7.02016 - 5.10045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.42987			1.40288			0.701442	−	0.712726i	$-0.252540\pi$
$3$	2.42987			1.40288			0.701442	+	0.712726i	$0.252540\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	0.903746	+	2.78144i	0.341584	+	1.05129i	0.963387	+	0.268114i	$0.0864002\pi$
$7$	0.903746	+	2.78144i	0.341584	+	1.05129i	−0.621804	+	0.783173i	$0.713600\pi$
$8$		0			0
$9$	2.90425			0.968084
$10$		0			0
$11$	2.41720	−	1.75620i	0.728814	−	0.529514i	−0.160374	−	0.987056i	$-0.551270\pi$
$11$	2.41720	−	1.75620i	0.728814	−	0.529514i	0.889188	+	0.457542i	$0.151270\pi$
$12$		0			0
$13$	−1.03961	+	3.19958i	−0.288335	+	0.887405i	0.697044	+	0.717028i	$0.254498\pi$
$13$	−1.03961	+	3.19958i	−0.288335	+	0.887405i	−0.985379	+	0.170376i	$0.945502\pi$
$14$		0			0
$15$	−1.96580	−	1.42824i	−0.507568	−	0.368770i
$16$		0			0
$17$	4.80955	−	3.49434i	1.16649	−	0.847502i	0.175903	−	0.984408i	$-0.443716\pi$
$17$	4.80955	−	3.49434i	1.16649	−	0.847502i	0.990584	+	0.136905i	$0.0437156\pi$
$18$		0			0
$19$	0.971064	+	2.98863i	0.222777	+	0.685638i	0.998510	+	0.0545762i	$0.0173808\pi$
$19$	0.971064	+	2.98863i	0.222777	+	0.685638i	−0.775732	+	0.631062i	$0.782619\pi$
$20$		0			0
$21$	2.19598	+	6.75854i	0.479203	+	1.47483i
$22$		0			0
$23$	1.16123	−	3.57390i	0.242134	−	0.745210i	−0.753961	−	0.656919i	$-0.771859\pi$
$23$	1.16123	−	3.57390i	0.242134	−	0.745210i	0.996095	−	0.0882914i	$-0.0281407\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−0.232654			−0.0447743
$28$		0			0
$29$	2.21438	+	1.60884i	0.411200	+	0.298754i	0.774088	−	0.633079i	$-0.218209\pi$
$29$	2.21438	+	1.60884i	0.411200	+	0.298754i	−0.362887	+	0.931833i	$0.618209\pi$
$30$		0			0
$31$	−6.26976	+	4.55525i	−1.12608	+	0.818147i	−0.985120	−	0.171868i	$-0.945020\pi$
$31$	−6.26976	+	4.55525i	−1.12608	+	0.818147i	−0.140962	+	0.990015i	$0.545020\pi$
$32$		0			0
$33$	5.87348	−	4.26733i	1.02244	−	0.742847i
$34$		0			0
$35$	0.903746	−	2.78144i	0.152761	−	0.470150i
$36$		0			0
$37$	9.04450	+	6.57121i	1.48691	+	1.08030i	0.975249	+	0.221111i	$0.0709683\pi$
$37$	9.04450	+	6.57121i	1.48691	+	1.08030i	0.511657	+	0.859190i	$0.329032\pi$
$38$		0			0
$39$	−2.52611	+	7.77456i	−0.404501	+	1.24493i
$40$		0			0
$41$	−4.16856	−	4.86036i	−0.651020	−	0.759060i
$41$	−4.16856	−	4.86036i	−0.651020	−	0.759060i
$42$		0			0
$43$	3.10622	−	9.55998i	0.473695	−	1.45788i	−0.374015	−	0.927423i	$-0.622019\pi$
$43$	3.10622	−	9.55998i	0.473695	−	1.45788i	0.847710	−	0.530460i	$-0.177981\pi$
$44$		0			0
$45$	−2.34959	−	1.70708i	−0.350256	−	0.254476i
$46$		0			0
$47$	−1.85022	+	5.69440i	−0.269883	+	0.830614i	0.720645	+	0.693304i	$0.243846\pi$
$47$	−1.85022	+	5.69440i	−0.269883	+	0.830614i	−0.990528	+	0.137310i	$0.956154\pi$
$48$		0			0
$49$	−1.25655	+	0.912939i	−0.179508	+	0.130420i
$50$		0			0
$51$	11.6866	−	8.49078i	1.63645	−	1.18895i
$52$		0			0
$53$	−0.451093	−	0.327738i	−0.0619624	−	0.0450183i	0.556373	−	0.830933i	$-0.312193\pi$
$53$	−0.451093	−	0.327738i	−0.0619624	−	0.0450183i	−0.618335	+	0.785914i	$0.712193\pi$
$54$		0			0
$55$	−2.98782			−0.402878
$56$		0			0
$57$	2.35956	+	7.26197i	0.312531	+	0.961871i
$58$		0			0
$59$	−1.46341	+	4.50392i	−0.190520	+	0.586360i	−1.00000		0.000787735i	$-0.999749\pi$
$59$	−1.46341	+	4.50392i	−0.190520	+	0.586360i	0.809480	+	0.587148i	$0.199749\pi$
$60$		0			0
$61$	−3.95004	−	12.1570i	−0.505751	−	1.55654i	−0.799504	−	0.600661i	$-0.794904\pi$
$61$	−3.95004	−	12.1570i	−0.505751	−	1.55654i	0.293752	−	0.955882i	$-0.405096\pi$
$62$		0			0
$63$	2.62471	+	8.07801i	0.330682	+	1.01773i
$64$		0			0
$65$	2.72173	−	1.97745i	0.337589	−	0.245273i
$66$		0			0
$67$	−6.99129	−	5.07947i	−0.854122	−	0.620556i	0.0721576	−	0.997393i	$-0.477012\pi$
$67$	−6.99129	−	5.07947i	−0.854122	−	0.620556i	−0.926279	+	0.376837i	$0.877012\pi$
$68$		0			0
$69$	2.82164	−	8.68411i	0.339685	−	1.04544i
$70$		0			0
$71$	5.52700	−	4.01560i	0.655934	−	0.476564i	−0.209353	−	0.977840i	$-0.567136\pi$
$71$	5.52700	−	4.01560i	0.655934	−	0.476564i	0.865287	+	0.501276i	$0.167136\pi$
$72$		0			0
$73$	−10.7242			−1.25517			−0.627586	−	0.778547i	$-0.715957\pi$
$73$	−10.7242			−1.25517			−0.627586	+	0.778547i	$0.715957\pi$
$74$		0			0
$75$	0.750870	+	2.31094i	0.0867030	+	0.266844i
$76$		0			0
$77$	7.06930	+	5.13615i	0.805622	+	0.585319i
$78$		0			0
$79$	−2.77926			−0.312691			−0.156346	−	0.987702i	$-0.549971\pi$
$79$	−2.77926			−0.312691			−0.156346	+	0.987702i	$0.549971\pi$
$80$		0			0
$81$	−9.27808			−1.03090
$82$		0			0
$83$	−10.8048			−1.18598			−0.592989	−	0.805210i	$-0.702052\pi$
$83$	−10.8048			−1.18598			−0.592989	+	0.805210i	$0.702052\pi$
$84$		0			0
$85$	−5.94493			−0.644818
$86$		0			0
$87$	5.38065	+	3.90927i	0.576866	+	0.419118i
$88$		0			0
$89$	1.24721	+	3.83851i	0.132204	+	0.406882i	0.995145	−	0.0984234i	$-0.0313799\pi$
$89$	1.24721	+	3.83851i	0.132204	+	0.406882i	−0.862941	+	0.505305i	$0.831380\pi$
$90$		0			0
$91$	−9.83900			−1.03141
$92$		0			0
$93$	−15.2347	+	11.0686i	−1.57976	+	1.14777i
$94$		0			0
$95$	0.971064	−	2.98863i	0.0996291	−	0.306627i
$96$		0			0
$97$	−2.35673	−	1.71226i	−0.239289	−	0.173854i	0.461677	−	0.887048i	$-0.347248\pi$
$97$	−2.35673	−	1.71226i	−0.239289	−	0.173854i	−0.700967	+	0.713194i	$0.747248\pi$
$98$		0			0
$99$	7.02016	−	5.10045i	0.705553	−	0.512614i
$100$		0			0
$101$	0.769714	+	2.36894i	0.0765894	+	0.235718i	0.982020	−	0.188776i	$-0.0604520\pi$
$101$	0.769714	+	2.36894i	0.0765894	+	0.235718i	−0.905431	+	0.424494i	$0.860452\pi$
$102$		0			0
$103$	−5.74200	−	17.6721i	−0.565776	−	1.74128i	−0.665634	−	0.746278i	$-0.731839\pi$
$103$	−5.74200	−	17.6721i	−0.565776	−	1.74128i	0.0998582	−	0.995002i	$-0.468161\pi$
$104$		0			0
$105$	2.19598	−	6.75854i	0.214306	−	0.659566i
$106$		0			0
$107$	1.61264	+	4.96319i	0.155900	+	0.479810i	0.998251	−	0.0591190i	$-0.0188291\pi$
$107$	1.61264	+	4.96319i	0.155900	+	0.479810i	−0.842351	+	0.538929i	$0.818829\pi$
$108$		0			0
$109$	−2.68726			−0.257393			−0.128697	−	0.991684i	$-0.541079\pi$
$109$	−2.68726			−0.257393			−0.128697	+	0.991684i	$0.541079\pi$
$110$		0			0
$111$	21.9769	+	15.9672i	2.08596	+	1.51554i
$112$		0			0
$113$	5.17135	−	3.75720i	0.486479	−	0.353448i	−0.317349	−	0.948309i	$-0.602793\pi$
$113$	5.17135	−	3.75720i	0.486479	−	0.353448i	0.803829	+	0.594861i	$0.202793\pi$
$114$		0			0
$115$	−3.04014	+	2.20879i	−0.283495	+	0.205971i
$116$		0			0
$117$	−3.01928	+	9.29240i	−0.279133	+	0.859082i
$118$		0			0
$119$	14.0659	+	10.2195i	1.28942	+	0.936819i
$120$		0			0
$121$	−0.640562	+	1.97145i	−0.0582329	+	0.179223i
$122$		0			0
$123$	−10.1291	−	11.8100i	−0.913306	−	1.06487i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	15.5919	+	11.3282i	1.38356	+	1.00521i	0.996538	+	0.0831409i	$0.0264951\pi$
$127$	15.5919	+	11.3282i	1.38356	+	1.00521i	0.387019	+	0.922072i	$0.373505\pi$
$128$		0			0
$129$	7.54771	−	23.2295i	0.664539	−	2.04524i
$130$		0			0
$131$	−2.85478	+	2.07412i	−0.249423	+	0.181216i	−0.705471	−	0.708739i	$-0.749265\pi$
$131$	−2.85478	+	2.07412i	−0.249423	+	0.181216i	0.456048	+	0.889955i	$0.349265\pi$
$132$		0			0
$133$	−7.43511	+	5.40192i	−0.644705	+	0.468406i
$134$		0			0
$135$	0.188221	+	0.136751i	0.0161995	+	0.0117696i
$136$		0			0
$137$	2.02362			0.172890			0.0864448	−	0.996257i	$-0.472449\pi$
$137$	2.02362			0.172890			0.0864448	+	0.996257i	$0.472449\pi$
$138$		0			0
$139$	1.76548	+	5.43358i	0.149746	+	0.460870i	0.997591	−	0.0693742i	$-0.0221003\pi$
$139$	1.76548	+	5.43358i	0.149746	+	0.460870i	−0.847845	+	0.530244i	$0.822100\pi$
$140$		0			0
$141$	−4.49579	+	13.8366i	−0.378614	+	1.16525i
$142$		0			0
$143$	3.10616	+	9.55979i	0.259751	+	0.799430i
$144$		0			0
$145$	−0.845818	−	2.60316i	−0.0702414	−	0.216181i
$146$		0			0
$147$	−3.05326	+	2.21832i	−0.251828	+	0.182964i
$148$		0			0
$149$	−17.0902	−	12.4168i	−1.40009	−	1.01722i	−0.994672	−	0.103089i	$-0.967127\pi$
$149$	−17.0902	−	12.4168i	−1.40009	−	1.01722i	−0.405414	−	0.914133i	$-0.632873\pi$
$150$		0			0
$151$	−2.40533	+	7.40285i	−0.195743	+	0.602435i	0.804224	+	0.594326i	$0.202581\pi$
$151$	−2.40533	+	7.40285i	−0.195743	+	0.602435i	−0.999967	+	0.00810888i	$0.997419\pi$
$152$		0			0
$153$	13.9681	−	10.1484i	1.12926	−	0.820453i
$154$		0			0
$155$	7.74985			0.622483
$156$		0			0
$157$	−6.84680	−	21.0723i	−0.546434	−	1.68175i	−0.717556	−	0.696501i	$-0.754739\pi$
$157$	−6.84680	−	21.0723i	−0.546434	−	1.68175i	0.171122	−	0.985250i	$-0.445261\pi$
$158$		0			0
$159$	−1.09610	−	0.796360i	−0.0869260	−	0.0631555i
$160$		0			0
$161$	10.9901			0.866139
$162$		0			0
$163$	12.7651			0.999842			0.499921	−	0.866071i	$-0.333362\pi$
$163$	12.7651			0.999842			0.499921	+	0.866071i	$0.333362\pi$
$164$		0			0
$165$	−7.26002			−0.565191
$166$		0			0
$167$	−3.75917			−0.290894			−0.145447	−	0.989366i	$-0.546462\pi$
$167$	−3.75917			−0.290894			−0.145447	+	0.989366i	$0.546462\pi$
$168$		0			0
$169$	1.36067	+	0.988588i	0.104667	+	0.0760452i
$170$		0			0
$171$	2.82022	+	8.67973i	0.215667	+	0.663756i
$172$		0			0
$173$	−18.3229			−1.39307			−0.696534	−	0.717524i	$-0.745275\pi$
$173$	−18.3229			−1.39307			−0.696534	+	0.717524i	$0.745275\pi$
$174$		0			0
$175$	−2.36604	+	1.71903i	−0.178856	+	0.129946i
$176$		0			0
$177$	−3.55589	+	10.9439i	−0.267277	+	0.822595i
$178$		0			0
$179$	4.23445	+	3.07651i	0.316497	+	0.229949i	0.734679	−	0.678414i	$-0.237333\pi$
$179$	4.23445	+	3.07651i	0.316497	+	0.229949i	−0.418182	+	0.908363i	$0.637333\pi$
$180$		0			0
$181$	−0.691084	+	0.502102i	−0.0513679	+	0.0373210i	−0.613173	−	0.789949i	$-0.710107\pi$
$181$	−0.691084	+	0.502102i	−0.0513679	+	0.0373210i	0.561805	+	0.827270i	$0.310107\pi$
$182$		0			0
$183$	−9.59808	−	29.5399i	−0.709511	−	2.18365i
$184$		0			0
$185$	−3.45469	−	10.6324i	−0.253994	−	0.781713i
$186$		0			0
$187$	5.48889	−	16.8931i	0.401387	−	1.23534i
$188$		0			0
$189$	−0.210260	−	0.647114i	−0.0152942	−	0.0470707i
$190$		0			0
$191$	−12.8274			−0.928156			−0.464078	−	0.885794i	$-0.653614\pi$
$191$	−12.8274			−0.928156			−0.464078	+	0.885794i	$0.653614\pi$
$192$		0			0
$193$	−18.2973	−	13.2938i	−1.31707	−	0.956909i	−0.999964	−	0.00851939i	$-0.997288\pi$
$193$	−18.2973	−	13.2938i	−1.31707	−	0.956909i	−0.317108	−	0.948389i	$-0.602712\pi$
$194$		0			0
$195$	6.61344	−	4.80494i	0.473598	−	0.344089i
$196$		0			0
$197$	−0.566766	+	0.411780i	−0.0403804	+	0.0293381i	−0.607792	−	0.794096i	$-0.707945\pi$
$197$	−0.566766	+	0.411780i	−0.0403804	+	0.0293381i	0.567412	+	0.823434i	$0.307945\pi$
$198$		0			0
$199$	−0.113028	+	0.347865i	−0.00801235	+	0.0246595i	−0.954983	−	0.296661i	$-0.904127\pi$
$199$	−0.113028	+	0.347865i	−0.00801235	+	0.0246595i	0.946970	+	0.321321i	$0.104127\pi$
$200$		0			0
$201$	−16.9879	−	12.3424i	−1.19823	−	0.870568i
$202$		0			0
$203$	−2.47367	+	7.61316i	−0.173617	+	0.534339i
$204$		0			0
$205$	0.515592	+	6.38233i	0.0360105	+	0.445761i
$206$		0			0
$207$	3.37251	−	10.3795i	0.234406	−	0.721426i
$208$		0			0
$209$	7.59589	+	5.51873i	0.525418	+	0.381739i
$210$		0			0
$211$	−3.96538	+	12.2042i	−0.272988	+	0.840171i	0.716757	+	0.697323i	$0.245626\pi$
$211$	−3.96538	+	12.2042i	−0.272988	+	0.840171i	−0.989745	+	0.142847i	$0.954374\pi$
$212$		0			0
$213$	13.4299	−	9.75737i	0.920200	−	0.668564i
$214$		0			0
$215$	−8.13220	+	5.90839i	−0.554612	+	0.402949i
$216$		0			0
$217$	−18.3364	−	13.3222i	−1.24476	−	0.904370i
$218$		0			0
$219$	−26.0584			−1.76086
$220$		0			0
$221$	6.18039	+	19.0213i	0.415738	+	1.27951i
$222$		0			0
$223$	−1.12789	+	3.47128i	−0.0755290	+	0.232454i	−0.981692	−	0.190474i	$-0.938998\pi$
$223$	−1.12789	+	3.47128i	−0.0755290	+	0.232454i	0.906163	+	0.422928i	$0.138998\pi$
$224$		0			0
$225$	0.897463	+	2.76211i	0.0598309	+	0.184141i
$226$		0			0
$227$	−2.34934	−	7.23054i	−0.155931	−	0.479908i	0.842323	−	0.538974i	$-0.181188\pi$
$227$	−2.34934	−	7.23054i	−0.155931	−	0.479908i	−0.998254	+	0.0590660i	$0.981188\pi$
$228$		0			0
$229$	−1.32391	+	0.961880i	−0.0874867	+	0.0635628i	−0.630669	−	0.776052i	$-0.717219\pi$
$229$	−1.32391	+	0.961880i	−0.0874867	+	0.0635628i	0.543182	+	0.839615i	$0.317219\pi$
$230$		0			0
$231$	17.1775	+	12.4802i	1.13019	+	0.821134i
$232$		0			0
$233$	3.76293	−	11.5811i	0.246517	−	0.758703i	−0.748866	−	0.662722i	$-0.769401\pi$
$233$	3.76293	−	11.5811i	0.246517	−	0.758703i	0.995383	−	0.0959810i	$-0.0305988\pi$
$234$		0			0
$235$	4.84395	−	3.51933i	0.315984	−	0.229576i
$236$		0			0
$237$	−6.75323			−0.438669
$238$		0			0
$239$	8.99150	+	27.6730i	0.581612	+	1.79002i	0.612471	+	0.790493i	$0.290176\pi$
$239$	8.99150	+	27.6730i	0.581612	+	1.79002i	−0.0308587	+	0.999524i	$0.509824\pi$
$240$		0			0
$241$	7.04891	+	5.12133i	0.454060	+	0.329894i	0.791197	−	0.611562i	$-0.209458\pi$
$241$	7.04891	+	5.12133i	0.454060	+	0.329894i	−0.337137	+	0.941456i	$0.609458\pi$
$242$		0			0
$243$	−21.8465			−1.40146
$244$		0			0
$245$	1.55318			0.0992293
$246$		0			0
$247$	−10.5719			−0.672673
$248$		0			0
$249$	−26.2542			−1.66379
$250$		0			0
$251$	17.1585	+	12.4664i	1.08304	+	0.786871i	0.978210	−	0.207619i	$-0.0665715\pi$
$251$	17.1585	+	12.4664i	1.08304	+	0.786871i	0.104826	+	0.994491i	$0.466572\pi$
$252$		0			0
$253$	−3.46956	−	10.6782i	−0.218129	−	0.671332i
$254$		0			0
$255$	−14.4454			−0.904605
$256$		0			0
$257$	−19.0601	+	13.8480i	−1.18894	+	0.863814i	−0.993152	−	0.116833i	$-0.962726\pi$
$257$	−19.0601	+	13.8480i	−1.18894	+	0.863814i	−0.195786	+	0.980647i	$0.562726\pi$
$258$		0			0
$259$	−10.1035	+	31.0955i	−0.627803	+	1.93218i
$260$		0			0
$261$	6.43112	+	4.67248i	0.398076	+	0.289219i
$262$		0			0
$263$	−7.57870	+	5.50624i	−0.467322	+	0.339530i	−0.796397	−	0.604774i	$-0.793263\pi$
$263$	−7.57870	+	5.50624i	−0.467322	+	0.339530i	0.329074	+	0.944304i	$0.393263\pi$
$264$		0			0
$265$	0.172302	+	0.530292i	0.0105844	+	0.0325756i
$266$		0			0
$267$	3.03055	+	9.32708i	0.185467	+	0.570808i
$268$		0			0
$269$	8.06023	−	24.8068i	0.491441	−	1.51250i	−0.330991	−	0.943634i	$-0.607383\pi$
$269$	8.06023	−	24.8068i	0.491441	−	1.51250i	0.822431	−	0.568865i	$-0.192617\pi$
$270$		0			0
$271$	3.25433	+	10.0158i	0.197687	+	0.608417i	0.999935	+	0.0114262i	$0.00363715\pi$
$271$	3.25433	+	10.0158i	0.197687	+	0.608417i	−0.802248	+	0.596991i	$0.796363\pi$
$272$		0			0
$273$	−23.9075			−1.44695
$274$		0			0
$275$	2.41720	+	1.75620i	0.145763	+	0.105903i
$276$		0			0
$277$	−9.59857	+	6.97377i	−0.576722	+	0.419013i	−0.837541	−	0.546375i	$-0.816008\pi$
$277$	−9.59857	+	6.97377i	−0.576722	+	0.419013i	0.260819	+	0.965388i	$0.416008\pi$
$278$		0			0
$279$	−18.2090	+	13.2296i	−1.09014	+	0.792035i
$280$		0			0
$281$	9.14679	−	28.1509i	0.545652	−	1.67934i	−0.173783	−	0.984784i	$-0.555599\pi$
$281$	9.14679	−	28.1509i	0.545652	−	1.67934i	0.719435	−	0.694560i	$-0.244401\pi$
$282$		0			0
$283$	−10.7044	−	7.77720i	−0.636310	−	0.462306i	0.222270	−	0.974985i	$-0.428653\pi$
$283$	−10.7044	−	7.77720i	−0.636310	−	0.462306i	−0.858581	+	0.512679i	$0.828653\pi$
$284$		0			0
$285$	2.35956	−	7.26197i	0.139768	−	0.430162i
$286$		0			0
$287$	9.75149	−	15.9872i	0.575612	−	0.943692i
$288$		0			0
$289$	5.66804	−	17.4444i	0.333414	−	1.02614i
$290$		0			0
$291$	−5.72653	−	4.16057i	−0.335695	−	0.243897i
$292$		0			0
$293$	9.33102	−	28.7179i	0.545124	−	1.67772i	−0.175572	−	0.984467i	$-0.556177\pi$
$293$	9.33102	−	28.7179i	0.545124	−	1.67772i	0.720696	−	0.693252i	$-0.243823\pi$
$294$		0			0
$295$	3.83126	−	2.78357i	0.223065	−	0.162066i
$296$		0			0
$297$	−0.562372	+	0.408587i	−0.0326321	+	0.0237086i
$298$		0			0
$299$	10.2278	+	7.43091i	0.591487	+	0.429741i
$300$		0			0
$301$	29.3978			1.69446
$302$		0			0
$303$	1.87030	+	5.75620i	0.107446	+	0.330685i
$304$		0			0
$305$	−3.95004	+	12.1570i	−0.226179	+	0.696107i
$306$		0			0
$307$	−9.61293	−	29.5856i	−0.548639	−	1.68854i	−0.712177	−	0.702000i	$-0.752291\pi$
$307$	−9.61293	−	29.5856i	−0.548639	−	1.68854i	0.163539	−	0.986537i	$-0.447709\pi$
$308$		0			0
$309$	−13.9523	−	42.9408i	−0.793718	−	2.44281i
$310$		0			0
$311$	9.92227	−	7.20895i	0.562640	−	0.408782i	−0.269784	−	0.962921i	$-0.586952\pi$
$311$	9.92227	−	7.20895i	0.562640	−	0.408782i	0.832424	+	0.554139i	$0.186952\pi$
$312$		0			0
$313$	11.1573	+	8.10627i	0.630649	+	0.458194i	0.856625	−	0.515939i	$-0.172557\pi$
$313$	11.1573	+	8.10627i	0.630649	+	0.458194i	−0.225976	+	0.974133i	$0.572557\pi$
$314$		0			0
$315$	2.62471	−	8.07801i	0.147885	−	0.455145i
$316$		0			0
$317$	−1.52629	+	1.10891i	−0.0857248	+	0.0622827i	−0.629822	−	0.776739i	$-0.716872\pi$
$317$	−1.52629	+	1.10891i	−0.0857248	+	0.0622827i	0.544097	+	0.839022i	$0.316872\pi$
$318$		0			0
$319$	8.17805			0.457883
$320$		0			0
$321$	3.91850	+	12.0599i	0.218709	+	0.673118i
$322$		0			0
$323$	15.1137	+	10.9807i	0.840947	+	0.610984i
$324$		0			0
$325$	−3.36424			−0.186614
$326$		0			0
$327$	−6.52970			−0.361093
$328$		0			0
$329$	−17.5108			−0.965401
$330$		0			0
$331$	2.63183			0.144658			0.0723292	−	0.997381i	$-0.476957\pi$
$331$	2.63183			0.144658			0.0723292	+	0.997381i	$0.476957\pi$
$332$		0			0
$333$	26.2675	+	19.0845i	1.43945	+	1.04582i
$334$		0			0
$335$	2.67043	+	8.21875i	0.145901	+	0.449038i
$336$		0			0
$337$	14.3912			0.783937			0.391968	−	0.919979i	$-0.371794\pi$
$337$	14.3912			0.783937			0.391968	+	0.919979i	$0.371794\pi$
$338$		0			0
$339$	12.5657	−	9.12950i	0.682474	−	0.495846i
$340$		0			0
$341$	−7.15535	+	22.0219i	−0.387484	+	1.19255i
$342$		0			0
$343$	12.8874	+	9.36322i	0.695852	+	0.505566i
$344$		0			0
$345$	−7.38714	+	5.36707i	−0.397710	+	0.288954i
$346$		0			0
$347$	−1.57802	−	4.85665i	−0.0847126	−	0.260719i	0.899724	−	0.436460i	$-0.143768\pi$
$347$	−1.57802	−	4.85665i	−0.0847126	−	0.260719i	−0.984436	+	0.175741i	$0.943768\pi$
$348$		0			0
$349$	5.18691	+	15.9637i	0.277649	+	0.854515i	0.988506	+	0.151179i	$0.0483071\pi$
$349$	5.18691	+	15.9637i	0.277649	+	0.854515i	−0.710857	+	0.703336i	$0.751693\pi$
$350$		0			0
$351$	0.241869	−	0.744396i	0.0129100	−	0.0397329i
$352$		0			0
$353$	−1.02191	−	3.14512i	−0.0543908	−	0.167398i	0.920171	−	0.391517i	$-0.128050\pi$
$353$	−1.02191	−	3.14512i	−0.0543908	−	0.167398i	−0.974562	+	0.224119i	$0.928050\pi$
$354$		0			0
$355$	−6.83175			−0.362592
$356$		0			0
$357$	34.1783	+	24.8320i	1.80891	+	1.31425i
$358$		0			0
$359$	8.48454	−	6.16438i	0.447797	−	0.325343i	−0.340929	−	0.940089i	$-0.610741\pi$
$359$	8.48454	−	6.16438i	0.447797	−	0.325343i	0.788725	+	0.614746i	$0.210741\pi$
$360$		0			0
$361$	7.38239	−	5.36362i	0.388547	−	0.282296i
$362$		0			0
$363$	−1.55648	+	4.79036i	−0.0816941	+	0.251428i
$364$		0			0
$365$	8.67606	+	6.30353i	0.454126	+	0.329942i
$366$		0			0
$367$	−6.24762	+	19.2282i	−0.326123	+	1.00370i	0.644808	+	0.764345i	$0.276937\pi$
$367$	−6.24762	+	19.2282i	−0.326123	+	1.00370i	−0.970931	+	0.239359i	$0.923063\pi$
$368$		0			0
$369$	−12.1066	−	14.1157i	−0.630242	−	0.734834i
$370$		0			0
$371$	0.503912	−	1.55088i	0.0261618	−	0.0805178i
$372$		0			0
$373$	15.9753	+	11.6067i	0.827168	+	0.600973i	0.918757	−	0.394824i	$-0.129194\pi$
$373$	15.9753	+	11.6067i	0.827168	+	0.600973i	−0.0915885	+	0.995797i	$0.529194\pi$
$374$		0			0
$375$	0.750870	−	2.31094i	0.0387748	−	0.119336i
$376$		0			0
$377$	−7.44971	+	5.41253i	−0.383680	+	0.278760i
$378$		0			0
$379$	18.1388	−	13.1786i	0.931725	−	0.676938i	−0.0146895	−	0.999892i	$-0.504676\pi$
$379$	18.1388	−	13.1786i	0.931725	−	0.676938i	0.946415	+	0.322954i	$0.104676\pi$
$380$		0			0
$381$	37.8862	+	27.5259i	1.94097	+	1.41020i
$382$		0			0
$383$	17.4033			0.889267			0.444633	−	0.895713i	$-0.353334\pi$
$383$	17.4033			0.889267			0.444633	+	0.895713i	$0.353334\pi$
$384$		0			0
$385$	−2.70023	−	8.31047i	−0.137617	−	0.423541i
$386$		0			0
$387$	9.02126	−	27.7646i	0.458576	−	1.41135i
$388$		0			0
$389$	−2.02795	−	6.24139i	−0.102821	−	0.316451i	0.886392	−	0.462936i	$-0.153204\pi$
$389$	−2.02795	−	6.24139i	−0.102821	−	0.316451i	−0.989213	+	0.146485i	$0.953204\pi$
$390$		0			0
$391$	−6.90344	−	21.2466i	−0.349122	−	1.07449i
$392$		0			0
$393$	−6.93673	+	5.03983i	−0.349912	+	0.254226i
$394$		0			0
$395$	2.24847	+	1.63361i	0.113133	+	0.0821957i
$396$		0			0
$397$	−1.76964	+	5.44640i	−0.0888158	+	0.273347i	−0.985593	−	0.169136i	$-0.945902\pi$
$397$	−1.76964	+	5.44640i	−0.0888158	+	0.273347i	0.896777	+	0.442483i	$0.145902\pi$
$398$		0			0
$399$	−18.0663	+	13.1259i	−0.904447	+	0.657119i
$400$		0			0
$401$	27.3307			1.36483			0.682416	−	0.730964i	$-0.260929\pi$
$401$	27.3307			1.36483			0.682416	+	0.730964i	$0.260929\pi$
$402$		0			0
$403$	−8.05680	−	24.7963i	−0.401338	−	1.23519i
$404$		0			0
$405$	7.50612	+	5.45352i	0.372982	+	0.270987i
$406$		0			0
$407$	33.4027			1.65571
$408$		0			0
$409$	23.6163			1.16775			0.583875	−	0.811844i	$-0.301536\pi$
$409$	23.6163			1.16775			0.583875	+	0.811844i	$0.301536\pi$
$410$		0			0
$411$	4.91713			0.242544
$412$		0			0
$413$	−13.8499			−0.681511
$414$		0			0
$415$	8.74125	+	6.35089i	0.429091	+	0.311753i
$416$		0			0
$417$	4.28987	+	13.2029i	0.210076	+	0.646547i
$418$		0			0
$419$	5.20618			0.254339			0.127169	−	0.991881i	$-0.459411\pi$
$419$	5.20618			0.254339			0.127169	+	0.991881i	$0.459411\pi$
$420$		0			0
$421$	−29.2568	+	21.2563i	−1.42589	+	1.03597i	−0.435123	+	0.900371i	$0.643295\pi$
$421$	−29.2568	+	21.2563i	−1.42589	+	1.03597i	−0.990764	+	0.135597i	$0.956705\pi$
$422$		0			0
$423$	−5.37351	+	16.5380i	−0.261269	+	0.804104i
$424$		0			0
$425$	4.80955	+	3.49434i	0.233297	+	0.169500i
$426$		0			0
$427$	30.2441	−	21.9737i	1.46362	−	1.06338i
$428$		0			0
$429$	7.54757	+	23.2290i	0.364400	+	1.12151i
$430$		0			0
$431$	9.00463	+	27.7134i	0.433738	+	1.33491i	0.894375	+	0.447319i	$0.147621\pi$
$431$	9.00463	+	27.7134i	0.433738	+	1.33491i	−0.460637	+	0.887589i	$0.652379\pi$
$432$		0			0
$433$	−3.90455	+	12.0170i	−0.187640	+	0.577498i	−0.999984	−	0.00568143i	$-0.998192\pi$
$433$	−3.90455	+	12.0170i	−0.187640	+	0.577498i	0.812343	+	0.583179i	$0.198192\pi$
$434$		0			0
$435$	−2.05523	−	6.32533i	−0.0985405	−	0.303277i
$436$		0			0
$437$	11.8087			0.564887
$438$		0			0
$439$	14.1868	+	10.3073i	0.677097	+	0.491940i	0.872393	−	0.488804i	$-0.162567\pi$
$439$	14.1868	+	10.3073i	0.677097	+	0.491940i	−0.195296	+	0.980744i	$0.562567\pi$
$440$		0			0
$441$	−3.64935	+	2.65141i	−0.173778	+	0.126257i
$442$		0			0
$443$	29.5266	−	21.4523i	1.40285	−	1.01923i	0.408538	−	0.912741i	$-0.366039\pi$
$443$	29.5266	−	21.4523i	1.40285	−	1.01923i	0.994314	−	0.106490i	$-0.0339612\pi$
$444$		0			0
$445$	1.24721	−	3.83851i	0.0591234	−	0.181963i
$446$		0			0
$447$	−41.5270	−	30.1711i	−1.96416	−	1.42704i
$448$		0			0
$449$	−3.46321	+	10.6586i	−0.163439	+	0.503013i	−0.998918	−	0.0465095i	$-0.985190\pi$
$449$	−3.46321	+	10.6586i	−0.163439	+	0.503013i	0.835479	+	0.549522i	$0.185190\pi$
$450$		0			0
$451$	−18.6120	−	4.42763i	−0.876405	−	0.208489i
$452$		0			0
$453$	−5.84463	+	17.9879i	−0.274605	+	0.845147i
$454$		0			0
$455$	7.95992	+	5.78322i	0.373167	+	0.271121i
$456$		0			0
$457$	−4.01464	+	12.3558i	−0.187797	+	0.577979i	−0.999985	−	0.00541588i	$-0.998276\pi$
$457$	−4.01464	+	12.3558i	−0.187797	+	0.577979i	0.812189	+	0.583395i	$0.198276\pi$
$458$		0			0
$459$	−1.11896	+	0.812973i	−0.0522287	+	0.0379463i
$460$		0			0
$461$	−15.9984	+	11.6236i	−0.745122	+	0.541363i	−0.894311	−	0.447446i	$-0.852334\pi$
$461$	−15.9984	+	11.6236i	−0.745122	+	0.541363i	0.149189	+	0.988809i	$0.452334\pi$
$462$		0			0
$463$	−1.65610	−	1.20323i	−0.0769654	−	0.0559186i	0.548637	−	0.836061i	$-0.315147\pi$
$463$	−1.65610	−	1.20323i	−0.0769654	−	0.0559186i	−0.625603	+	0.780142i	$0.715147\pi$
$464$		0			0
$465$	18.8311			0.873272
$466$		0			0
$467$	3.91612	+	12.0526i	0.181217	+	0.557727i	0.999863	−	0.0165710i	$-0.00527496\pi$
$467$	3.91612	+	12.0526i	0.181217	+	0.557727i	−0.818646	+	0.574298i	$0.805275\pi$
$468$		0			0
$469$	7.80991	−	24.0364i	0.360628	−	1.10990i
$470$		0			0
$471$	−16.6368	−	51.2028i	−0.766584	−	2.35930i
$472$		0			0
$473$	−9.28085	−	28.5635i	−0.426734	−	1.31335i
$474$		0			0
$475$	−2.54228	+	1.84707i	−0.116648	+	0.0847496i
$476$		0			0
$477$	−1.31009	−	0.951834i	−0.0599848	−	0.0435815i
$478$		0			0
$479$	5.11786	−	15.7511i	0.233841	−	0.719688i	−0.763432	−	0.645888i	$-0.776487\pi$
$479$	5.11786	−	15.7511i	0.233841	−	0.719688i	0.997273	−	0.0738001i	$-0.0235127\pi$
$480$		0			0
$481$	−30.4279	+	22.1071i	−1.38739	+	1.00800i
$482$		0			0
$483$	26.7044			1.21509
$484$		0			0
$485$	0.900190	+	2.77050i	0.0408755	+	0.125802i
$486$		0			0
$487$	6.81614	+	4.95221i	0.308869	+	0.224406i	0.731411	−	0.681937i	$-0.238862\pi$
$487$	6.81614	+	4.95221i	0.308869	+	0.224406i	−0.422542	+	0.906343i	$0.638862\pi$
$488$		0			0
$489$	31.0176			1.40266
$490$		0			0
$491$	39.6606			1.78986			0.894928	−	0.446210i	$-0.147227\pi$
$491$	39.6606			1.78986			0.894928	+	0.446210i	$0.147227\pi$
$492$		0			0
$493$	16.2720			0.732855
$494$		0			0
$495$	−8.67740			−0.390020
$496$		0			0
$497$	16.1642	+	11.7440i	0.725062	+	0.526788i
$498$		0			0
$499$	7.18321	+	22.1076i	0.321564	+	0.989674i	0.972968	+	0.230942i	$0.0741807\pi$
$499$	7.18321	+	22.1076i	0.321564	+	0.989674i	−0.651403	+	0.758732i	$0.725819\pi$
$500$		0			0
$501$	−9.13429			−0.408090
$502$		0			0
$503$	−21.7517	+	15.8036i	−0.969861	+	0.704646i	−0.955420	−	0.295250i	$-0.904597\pi$
$503$	−21.7517	+	15.8036i	−0.969861	+	0.704646i	−0.0144415	+	0.999896i	$0.504597\pi$
$504$		0			0
$505$	0.769714	−	2.36894i	0.0342518	−	0.105416i
$506$		0			0
$507$	3.30626	+	2.40214i	0.146836	+	0.106683i
$508$		0			0
$509$	−6.64686	+	4.82923i	−0.294617	+	0.214052i	−0.725268	−	0.688467i	$-0.758284\pi$
$509$	−6.64686	+	4.82923i	−0.294617	+	0.214052i	0.430651	+	0.902519i	$0.358284\pi$
$510$		0			0
$511$	−9.69195	−	29.8288i	−0.428747	−	1.31955i
$512$		0			0
$513$	−0.225922	−	0.695317i	−0.00997471	−	0.0306990i
$514$		0			0
$515$	−5.74200	+	17.6721i	−0.253023	+	0.778724i
$516$		0			0
$517$	5.52814	+	17.0139i	0.243127	+	0.748269i
$518$		0			0
$519$	−44.5223			−1.95431
$520$		0			0
$521$	13.0467	+	9.47895i	0.571584	+	0.415280i	0.835680	−	0.549216i	$-0.185074\pi$
$521$	13.0467	+	9.47895i	0.571584	+	0.415280i	−0.264096	+	0.964496i	$0.585074\pi$
$522$		0			0
$523$	−11.5433	+	8.38671i	−0.504754	+	0.366725i	−0.810830	−	0.585282i	$-0.800984\pi$
$523$	−11.5433	+	8.38671i	−0.504754	+	0.366725i	0.306076	+	0.952007i	$0.400984\pi$
$524$		0			0
$525$	−5.74916	+	4.17701i	−0.250914	+	0.182299i
$526$		0			0
$527$	−14.2371	+	43.8174i	−0.620179	+	1.90871i
$528$		0			0
$529$	7.18306	+	5.21880i	0.312307	+	0.226904i
$530$		0			0
$531$	−4.25012	+	13.0805i	−0.184439	+	0.567646i
$532$		0			0
$533$	19.8848	−	8.28480i	0.861306	−	0.358854i
$534$		0			0
$535$	1.61264	−	4.96319i	0.0697205	−	0.214578i
$536$		0			0
$537$	10.2891	+	7.47550i	0.444009	+	0.322592i
$538$		0			0
$539$	−1.43404	+	4.41351i	−0.0617684	+	0.190104i
$540$		0			0
$541$	−9.42529	+	6.84788i	−0.405225	+	0.294413i	−0.771666	−	0.636028i	$-0.780576\pi$
$541$	−9.42529	+	6.84788i	−0.405225	+	0.294413i	0.366441	+	0.930441i	$0.380576\pi$
$542$		0			0
$543$	−1.67924	+	1.22004i	−0.0720632	+	0.0523570i
$544$		0			0
$545$	2.17404	+	1.57953i	0.0931258	+	0.0676598i
$546$		0			0
$547$	−42.4768			−1.81618			−0.908089	−	0.418778i	$-0.862459\pi$
$547$	−42.4768			−1.81618			−0.908089	+	0.418778i	$0.862459\pi$
$548$		0			0
$549$	−11.4719	−	35.3070i	−0.489610	−	1.50686i
$550$		0			0
$551$	−2.65792	+	8.18025i	−0.113231	+	0.348490i
$552$		0			0
$553$	−2.51174	−	7.73035i	−0.106810	−	0.328728i
$554$		0			0
$555$	−8.39444	−	25.8354i	−0.356324	−	1.09665i
$556$		0			0
$557$	32.8452	−	23.8634i	1.39170	−	1.01113i	0.396018	−	0.918243i	$-0.370392\pi$
$557$	32.8452	−	23.8634i	1.39170	−	1.01113i	0.995677	−	0.0928833i	$-0.0296084\pi$
$558$		0			0
$559$	27.3587	+	19.8772i	1.15715	+	0.840718i
$560$		0			0
$561$	13.3373	−	41.0479i	0.563100	−	1.73304i
$562$		0			0
$563$	2.24203	−	1.62893i	0.0944904	−	0.0686513i	−0.539537	−	0.841962i	$-0.681401\pi$
$563$	2.24203	−	1.62893i	0.0944904	−	0.0686513i	0.634027	+	0.773311i	$0.281401\pi$
$564$		0			0
$565$	−6.39213			−0.268919
$566$		0			0
$567$	−8.38502	−	25.8064i	−0.352138	−	1.08377i
$568$		0			0
$569$	11.7266	+	8.51988i	0.491605	+	0.357172i	0.805801	−	0.592186i	$-0.201735\pi$
$569$	11.7266	+	8.51988i	0.491605	+	0.357172i	−0.314196	+	0.949358i	$0.601735\pi$
$570$		0			0
$571$	−20.9078			−0.874965			−0.437482	−	0.899227i	$-0.644130\pi$
$571$	−20.9078			−0.874965			−0.437482	+	0.899227i	$0.644130\pi$
$572$		0			0
$573$	−31.1688			−1.30210
$574$		0			0
$575$	3.75782			0.156712
$576$		0			0
$577$	−16.9709			−0.706510			−0.353255	−	0.935527i	$-0.614925\pi$
$577$	−16.9709			−0.706510			−0.353255	+	0.935527i	$0.614925\pi$
$578$		0			0
$579$	−44.4601	−	32.3022i	−1.84770	−	1.34243i
$580$		0			0
$581$	−9.76478	−	30.0529i	−0.405111	−	1.24680i
$582$		0			0
$583$	−1.66596			−0.0689968
$584$		0			0
$585$	7.90458	−	5.74302i	0.326814	−	0.237444i
$586$		0			0
$587$	10.3437	−	31.8347i	0.426932	−	1.31396i	−0.474201	−	0.880417i	$-0.657263\pi$
$587$	10.3437	−	31.8347i	0.426932	−	1.31396i	0.901132	−	0.433544i	$-0.142737\pi$
$588$		0			0
$589$	−19.7023	−	14.3145i	−0.811819	−	0.589821i
$590$		0			0
$591$	−1.37717	+	1.00057i	−0.0566490	+	0.0411579i
$592$		0			0
$593$	−7.94846	−	24.4628i	−0.326404	−	1.00457i	−0.970803	−	0.239879i	$-0.922892\pi$
$593$	−7.94846	−	24.4628i	−0.326404	−	1.00457i	0.644399	−	0.764690i	$-0.277108\pi$
$594$		0			0
$595$	−5.37270	−	16.5355i	−0.220259	−	0.677889i
$596$		0			0
$597$	−0.274643	+	0.845265i	−0.0112404	+	0.0345944i
$598$		0			0
$599$	7.26133	+	22.3481i	0.296690	+	0.913118i	0.982649	+	0.185477i	$0.0593831\pi$
$599$	7.26133	+	22.3481i	0.296690	+	0.913118i	−0.685959	+	0.727641i	$0.740617\pi$
$600$		0			0
$601$	9.25090			0.377352			0.188676	−	0.982039i	$-0.439580\pi$
$601$	9.25090			0.377352			0.188676	+	0.982039i	$0.439580\pi$
$602$		0			0
$603$	−20.3045	−	14.7521i	−0.826862	−	0.600750i
$604$		0			0
$605$	1.67701	−	1.21842i	0.0681803	−	0.0495359i
$606$		0			0
$607$	−15.8204	+	11.4942i	−0.642131	+	0.466535i	−0.860582	−	0.509313i	$-0.829900\pi$
$607$	−15.8204	+	11.4942i	−0.642131	+	0.466535i	0.218451	+	0.975848i	$0.429900\pi$
$608$		0			0
$609$	−6.01068	+	18.4990i	−0.243565	+	0.749616i
$610$		0			0
$611$	−16.2962	−	11.8399i	−0.659274	−	0.478990i
$612$		0			0
$613$	−14.7455	+	45.3819i	−0.595564	+	1.83296i	−0.0436666	+	0.999046i	$0.513904\pi$
$613$	−14.7455	+	45.3819i	−0.595564	+	1.83296i	−0.551898	+	0.833912i	$0.686096\pi$
$614$		0			0
$615$	1.25282	+	15.5082i	0.0505185	+	0.625352i
$616$		0			0
$617$	−5.07963	+	15.6335i	−0.204498	+	0.629381i	0.795235	+	0.606301i	$0.207347\pi$
$617$	−5.07963	+	15.6335i	−0.204498	+	0.629381i	−0.999734	+	0.0230802i	$0.992653\pi$
$618$		0			0
$619$	31.0324	+	22.5464i	1.24730	+	0.906215i	0.998062	−	0.0622283i	$-0.0198207\pi$
$619$	31.0324	+	22.5464i	1.24730	+	0.906215i	0.249235	+	0.968443i	$0.419821\pi$
$620$		0			0
$621$	−0.270165	+	0.831484i	−0.0108414	+	0.0333663i
$622$		0			0
$623$	−9.54945	+	6.93808i	−0.382591	+	0.277968i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	18.4570	+	13.4098i	0.737101	+	0.535535i
$628$		0			0
$629$	66.4620			2.65001
$630$		0			0
$631$	−12.2655	−	37.7492i	−0.488280	−	1.50277i	−0.827173	−	0.561948i	$-0.810052\pi$
$631$	−12.2655	−	37.7492i	−0.488280	−	1.50277i	0.338892	−	0.940825i	$-0.389948\pi$
$632$		0			0
$633$	−9.63534	+	29.6545i	−0.382971	+	1.17866i
$634$		0			0
$635$	−5.95557	−	18.3294i	−0.236340	−	0.727379i
$636$		0			0
$637$	−1.61470	−	4.96954i	−0.0639768	−	0.196900i
$638$		0			0
$639$	16.0518	−	11.6623i	0.635000	−	0.461354i
$640$		0			0
$641$	7.34918	+	5.33949i	0.290275	+	0.210897i	0.723387	−	0.690443i	$-0.242584\pi$
$641$	7.34918	+	5.33949i	0.290275	+	0.210897i	−0.433112	+	0.901340i	$0.642584\pi$
$642$		0			0
$643$	6.75698	−	20.7959i	0.266469	−	0.820108i	−0.724882	−	0.688873i	$-0.758106\pi$
$643$	6.75698	−	20.7959i	0.266469	−	0.820108i	0.991351	−	0.131235i	$-0.0418943\pi$
$644$		0			0
$645$	−19.7602	+	14.3566i	−0.778056	+	0.565291i
$646$		0			0
$647$	16.0803			0.632182			0.316091	−	0.948729i	$-0.397629\pi$
$647$	16.0803			0.632182			0.316091	+	0.948729i	$0.397629\pi$
$648$		0			0
$649$	4.37242	+	13.4569i	0.171632	+	0.528230i
$650$		0			0
$651$	−44.5551	−	32.3712i	−1.74625	−	1.26873i
$652$		0			0
$653$	−2.15603			−0.0843718			−0.0421859	−	0.999110i	$-0.513432\pi$
$653$	−2.15603			−0.0843718			−0.0421859	+	0.999110i	$0.513432\pi$
$654$		0			0
$655$	3.52870			0.137878
$656$		0			0
$657$	−31.1458			−1.21511
$658$		0			0
$659$	−35.5478			−1.38475			−0.692373	−	0.721540i	$-0.743435\pi$
$659$	−35.5478			−1.38475			−0.692373	+	0.721540i	$0.743435\pi$
$660$		0			0
$661$	−0.662322	−	0.481205i	−0.0257613	−	0.0187167i	0.574830	−	0.818273i	$-0.305068\pi$
$661$	−0.662322	−	0.481205i	−0.0257613	−	0.0187167i	−0.600591	+	0.799556i	$0.705068\pi$
$662$		0			0
$663$	15.0175	+	46.2192i	0.583233	+	1.79501i
$664$		0			0
$665$	9.19030			0.356384
$666$		0			0
$667$	8.32125	−	6.04575i	0.322200	−	0.234092i
$668$		0			0
$669$	−2.74062	+	8.43476i	−0.105958	+	0.326107i
$670$		0			0
$671$	−30.8981	−	22.4488i	−1.19281	−	0.866627i
$672$		0			0
$673$	12.4809	−	9.06789i	0.481102	−	0.349541i	−0.320650	−	0.947198i	$-0.603901\pi$
$673$	12.4809	−	9.06789i	0.481102	−	0.349541i	0.801752	+	0.597656i	$0.203901\pi$
$674$		0			0
$675$	−0.0718941	−	0.221267i	−0.00276721	−	0.00851658i
$676$		0			0
$677$	−8.65310	−	26.6315i	−0.332566	−	1.02353i	−0.967909	−	0.251302i	$-0.919141\pi$
$677$	−8.65310	−	26.6315i	−0.332566	−	1.02353i	0.635343	−	0.772230i	$-0.280859\pi$
$678$		0			0
$679$	2.63268	−	8.10255i	0.101033	−	0.310947i
$680$		0			0
$681$	−5.70859	−	17.5692i	−0.218754	−	0.673255i
$682$		0			0
$683$	14.5474			0.556639			0.278320	−	0.960488i	$-0.410223\pi$
$683$	14.5474			0.556639			0.278320	+	0.960488i	$0.410223\pi$
$684$		0			0
$685$	−1.63714	−	1.18945i	−0.0625520	−	0.0454467i
$686$		0			0
$687$	−3.21694	+	2.33724i	−0.122734	+	0.0891713i
$688$		0			0
$689$	1.51759	−	1.10259i	0.0578154	−	0.0420053i
$690$		0			0
$691$	−2.39129	+	7.35963i	−0.0909689	+	0.279973i	−0.986182	−	0.165665i	$-0.947023\pi$
$691$	−2.39129	+	7.35963i	−0.0909689	+	0.279973i	0.895213	+	0.445638i	$0.147023\pi$
$692$		0			0
$693$	20.5310	+	14.9167i	0.779910	+	0.566638i
$694$		0			0
$695$	1.76548	−	5.43358i	0.0669683	−	0.206107i
$696$		0			0
$697$	−37.0327	−	8.80974i	−1.40271	−	0.333693i
$698$		0			0
$699$	9.14341	−	28.1405i	0.345836	−	1.06437i
$700$		0			0
$701$	−29.1893	−	21.2072i	−1.10246	−	0.800987i	−0.121003	−	0.992652i	$-0.538611\pi$
$701$	−29.1893	−	21.2072i	−1.10246	−	0.800987i	−0.981460	+	0.191665i	$0.938611\pi$
$702$		0			0
$703$	−10.8561	+	33.4117i	−0.409446	+	1.26015i
$704$		0			0
$705$	11.7701	−	8.55151i	0.443289	−	0.322068i
$706$		0			0
$707$	−5.89344	+	4.28183i	−0.221646	+	0.161035i
$708$		0			0
$709$	12.6064	+	9.15909i	0.473443	+	0.343977i	0.798782	−	0.601621i	$-0.205478\pi$
$709$	12.6064	+	9.15909i	0.473443	+	0.343977i	−0.325338	+	0.945598i	$0.605478\pi$
$710$		0			0
$711$	−8.07167			−0.302711
$712$		0			0
$713$	8.99937	+	27.6972i	0.337029	+	1.03727i
$714$		0			0
$715$	3.10616	−	9.55979i	0.116164	−	0.357516i
$716$		0			0
$717$	21.8481	+	67.2417i	0.815934	+	2.51119i
$718$		0			0
$719$	2.89718	+	8.91660i	0.108047	+	0.332533i	0.990433	−	0.137992i	$-0.0440647\pi$
$719$	2.89718	+	8.91660i	0.108047	+	0.332533i	−0.882387	+	0.470525i	$0.844065\pi$
$720$		0			0
$721$	43.9645	−	31.9421i	1.63732	−	1.18959i
$722$		0			0
$723$	17.1279	+	12.4442i	0.636994	+	0.462803i
$724$		0			0
$725$	−0.845818	+	2.60316i	−0.0314129	+	0.0966790i
$726$		0			0
$727$	13.9172	−	10.1114i	0.516160	−	0.375012i	−0.298995	−	0.954255i	$-0.596652\pi$
$727$	13.9172	−	10.1114i	0.516160	−	0.375012i	0.815155	+	0.579242i	$0.196652\pi$
$728$		0			0
$729$	−25.2499			−0.935182
$730$		0			0
$731$	−18.4663	−	56.8334i	−0.683000	−	2.10206i
$732$		0			0
$733$	12.8489	+	9.33530i	0.474587	+	0.344807i	0.799226	−	0.601031i	$-0.205243\pi$
$733$	12.8489	+	9.33530i	0.474587	+	0.344807i	−0.324640	+	0.945838i	$0.605243\pi$
$734$		0			0
$735$	3.77403			0.139207
$736$		0			0
$737$	−25.8199			−0.951089
$738$		0			0
$739$	−33.0056			−1.21413			−0.607065	−	0.794652i	$-0.707653\pi$
$739$	−33.0056			−1.21413			−0.607065	+	0.794652i	$0.707653\pi$
$740$		0			0
$741$	−25.6883			−0.943683
$742$		0			0
$743$	13.1267	+	9.53707i	0.481570	+	0.349881i	0.801933	−	0.597414i	$-0.203805\pi$
$743$	13.1267	+	9.53707i	0.481570	+	0.349881i	−0.320363	+	0.947295i	$0.603805\pi$
$744$		0			0
$745$	6.52789	+	20.0908i	0.239163	+	0.736069i
$746$		0			0
$747$	−31.3798			−1.14813
$748$		0			0
$749$	−12.3474	+	8.97093i	−0.451165	+	0.327791i
$750$		0			0
$751$	−5.11879	+	15.7540i	−0.186787	+	0.574873i	−0.999975	−	0.00712965i	$-0.997731\pi$
$751$	−5.11879	+	15.7540i	−0.186787	+	0.574873i	0.813187	+	0.582002i	$0.197731\pi$
$752$		0			0
$753$	41.6929	+	30.2917i	1.51937	+	1.10389i
$754$		0			0
$755$	6.29724	−	4.57521i	0.229180	−	0.166509i
$756$		0			0
$757$	−14.8886	−	45.8225i	−0.541137	−	1.66545i	−0.730001	−	0.683446i	$-0.760481\pi$
$757$	−14.8886	−	45.8225i	−0.541137	−	1.66545i	0.188864	−	0.982003i	$-0.439519\pi$
$758$		0			0
$759$	−8.43056	−	25.9466i	−0.306010	−	0.941802i
$760$		0			0
$761$	−9.06638	+	27.9034i	−0.328656	+	1.01150i	0.641107	+	0.767451i	$0.278475\pi$
$761$	−9.06638	+	27.9034i	−0.328656	+	1.01150i	−0.969763	+	0.244048i	$0.921525\pi$
$762$		0			0
$763$	−2.42860	−	7.47448i	−0.0879214	−	0.270594i
$764$		0			0
$765$	−17.2656			−0.624238
$766$		0			0
$767$	−12.8893	−	9.36461i	−0.465405	−	0.338137i
$768$		0			0
$769$	−14.5237	+	10.5521i	−0.523737	+	0.380517i	−0.818010	−	0.575204i	$-0.804923\pi$
$769$	−14.5237	+	10.5521i	−0.523737	+	0.380517i	0.294273	+	0.955721i	$0.404923\pi$
$770$		0			0
$771$	−46.3135	+	33.6488i	−1.66794	+	1.21183i
$772$		0			0
$773$	10.9987	−	33.8505i	0.395595	−	1.21752i	−0.532902	−	0.846177i	$-0.678898\pi$
$773$	10.9987	−	33.8505i	0.395595	−	1.21752i	0.928497	−	0.371340i	$-0.121102\pi$
$774$		0			0
$775$	−6.26976	−	4.55525i	−0.225216	−	0.163629i
$776$		0			0
$777$	−24.5502	+	75.5578i	−0.880734	+	2.71062i
$778$		0			0
$779$	10.4779	−	17.1780i	0.375408	−	0.615466i
$780$		0			0
$781$	6.30768	−	19.4130i	0.225706	−	0.694653i
$782$		0			0
$783$	−0.515185	−	0.374304i	−0.0184112	−	0.0133765i
$784$		0			0
$785$	−6.84680	+	21.0723i	−0.244373	+	0.752102i
$786$		0			0
$787$	25.0188	−	18.1772i	0.891822	−	0.647947i	−0.0445303	−	0.999008i	$-0.514179\pi$
$787$	25.0188	−	18.1772i	0.891822	−	0.647947i	0.936352	+	0.351061i	$0.114179\pi$
$788$		0			0
$789$	−18.4152	+	13.3794i	−0.655599	+	0.476321i
$790$		0			0
$791$	15.1240	+	10.9883i	0.537749	+	0.390697i
$792$		0			0
$793$	43.0038			1.52711
$794$		0			0
$795$	0.418671	+	1.28854i	0.0148487	+	0.0456997i
$796$		0			0
$797$	1.29656	−	3.99039i	0.0459264	−	0.141347i	−0.925464	−	0.378836i	$-0.876324\pi$
$797$	1.29656	−	3.99039i	0.0459264	−	0.141347i	0.971390	+	0.237489i	$0.0763244\pi$
$798$		0			0
$799$	10.9994	+	33.8528i	0.389132	+	1.19763i
$800$		0			0
$801$	3.62221	+	11.1480i	0.127984	+	0.393896i
$802$		0			0
$803$	−25.9225	+	18.8338i	−0.914787	+	0.664632i
$804$		0			0
$805$	−8.89115	−	6.45980i	−0.313372	−	0.227678i
$806$		0			0
$807$	19.5853	−	60.2773i	0.689434	−	2.12186i
$808$		0			0
$809$	25.2978	−	18.3800i	0.889425	−	0.646205i	−0.0463034	−	0.998927i	$-0.514744\pi$
$809$	25.2978	−	18.3800i	0.889425	−	0.646205i	0.935728	+	0.352723i	$0.114744\pi$
$810$		0			0
$811$	12.4807			0.438256			0.219128	−	0.975696i	$-0.429679\pi$
$811$	12.4807			0.438256			0.219128	+	0.975696i	$0.429679\pi$
$812$		0			0
$813$	7.90760	+	24.3371i	0.277332	+	0.853539i
$814$		0			0
$815$	−10.3272	−	7.50315i	−0.361746	−	0.262824i
$816$		0			0
$817$	31.5876			1.10511
$818$		0			0
$819$	−28.5749			−0.998489
$820$		0			0
$821$	−36.9369			−1.28911			−0.644553	−	0.764559i	$-0.722957\pi$
$821$	−36.9369			−1.28911			−0.644553	+	0.764559i	$0.722957\pi$
$822$		0			0
$823$	−49.2807			−1.71782			−0.858909	−	0.512128i	$-0.828857\pi$
$823$	−49.2807			−1.71782			−0.858909	+	0.512128i	$0.828857\pi$
$824$		0			0
$825$	5.87348	+	4.26733i	0.204488	+	0.148569i
$826$		0			0
$827$	17.4761	+	53.7860i	0.607705	+	1.87032i	0.477006	+	0.878900i	$0.341722\pi$
$827$	17.4761	+	53.7860i	0.607705	+	1.87032i	0.130699	+	0.991422i	$0.458278\pi$
$828$		0			0
$829$	7.76797			0.269793			0.134896	−	0.990860i	$-0.456930\pi$
$829$	7.76797			0.269793			0.134896	+	0.990860i	$0.456930\pi$
$830$		0			0
$831$	−23.3233	+	16.9453i	−0.809075	+	0.587827i
$832$		0			0
$833$	−2.85333	+	8.78165i	−0.0988620	+	0.304266i
$834$		0			0
$835$	3.04124	+	2.20959i	0.105246	+	0.0764659i
$836$		0			0
$837$	1.45869	−	1.05980i	0.0504196	−	0.0366320i
$838$		0			0
$839$	−4.87384	−	15.0001i	−0.168264	−	0.517862i	0.830998	−	0.556275i	$-0.187770\pi$
$839$	−4.87384	−	15.0001i	−0.168264	−	0.517862i	−0.999262	+	0.0384127i	$0.987770\pi$
$840$		0			0
$841$	−6.64638	−	20.4555i	−0.229186	−	0.705361i
$842$		0			0
$843$	22.2255	−	68.4030i	0.765487	−	2.35593i
$844$		0			0
$845$	−0.519732	−	1.59957i	−0.0178793	−	0.0550269i
$846$		0			0
$847$	−6.06238			−0.208306
$848$		0			0
$849$	−26.0102	−	18.8976i	−0.892669	−	0.648562i
$850$		0			0
$851$	33.9876	−	24.6935i	1.16508	−	0.846481i
$852$		0			0
$853$	41.4138	−	30.0889i	1.41798	−	1.03022i	0.425883	−	0.904778i	$-0.359964\pi$
$853$	41.4138	−	30.0889i	1.41798	−	1.03022i	0.992100	−	0.125447i	$-0.0400364\pi$
$854$		0			0
$855$	2.82022	−	8.67973i	0.0964493	−	0.296841i
$856$		0			0
$857$	43.5442	+	31.6367i	1.48744	+	1.08069i	0.975062	+	0.221931i	$0.0712359\pi$
$857$	43.5442	+	31.6367i	1.48744	+	1.08069i	0.512380	+	0.858759i	$0.328764\pi$
$858$		0			0
$859$	−14.3645	+	44.2093i	−0.490110	+	1.50840i	0.334331	+	0.942456i	$0.391490\pi$
$859$	−14.3645	+	44.2093i	−0.490110	+	1.50840i	−0.824441	+	0.565948i	$0.808510\pi$
$860$		0			0
$861$	23.6948	−	38.8466i	0.807517	−	1.32389i
$862$		0			0
$863$	−15.9126	+	48.9738i	−0.541670	+	1.66709i	0.187109	+	0.982339i	$0.440088\pi$
$863$	−15.9126	+	48.9738i	−0.541670	+	1.66709i	−0.728779	+	0.684749i	$0.759912\pi$
$864$		0			0
$865$	14.8236	+	10.7700i	0.504017	+	0.366190i
$866$		0			0
$867$	13.7726	−	42.3877i	0.467742	−	1.43956i
$868$		0			0
$869$	−6.71803	+	4.88093i	−0.227893	+	0.165574i
$870$		0			0
$871$	23.5204	−	17.0886i	0.796958	−	0.579024i
$872$		0			0
$873$	−6.84453	−	4.97284i	−0.231652	−	0.168305i
$874$		0			0
$875$	2.92458			0.0988689
$876$		0			0
$877$	−10.7577	−	33.1088i	−0.363262	−	1.11801i	−0.951062	−	0.308999i	$-0.900006\pi$
$877$	−10.7577	−	33.1088i	−0.363262	−	1.11801i	0.587800	−	0.809006i	$-0.299994\pi$
$878$		0			0
$879$	22.6731	−	69.7807i	0.764745	−	2.35364i
$880$		0			0
$881$	−13.6750	−	42.0874i	−0.460723	−	1.41796i	−0.864282	−	0.503007i	$-0.832227\pi$
$881$	−13.6750	−	42.0874i	−0.460723	−	1.41796i	0.403559	−	0.914954i	$-0.367773\pi$
$882$		0			0
$883$	−0.562347	−	1.73073i	−0.0189245	−	0.0582435i	0.941148	−	0.337994i	$-0.109748\pi$
$883$	−0.562347	−	1.73073i	−0.0189245	−	0.0582435i	−0.960073	+	0.279750i	$0.909748\pi$
$884$		0			0
$885$	9.30945	−	6.76371i	0.312934	−	0.227360i
$886$		0			0
$887$	19.4665	+	14.1433i	0.653622	+	0.474884i	0.864503	−	0.502628i	$-0.167633\pi$
$887$	19.4665	+	14.1433i	0.653622	+	0.474884i	−0.210881	+	0.977512i	$0.567633\pi$
$888$		0			0
$889$	−17.4176	+	53.6058i	−0.584166	+	1.79788i
$890$		0			0
$891$	−22.4270	+	16.2942i	−0.751332	+	0.545875i
$892$		0			0
$893$	−18.8151			−0.629624
$894$		0			0
$895$	−1.61742	−	4.97789i	−0.0540642	−	0.166393i
$896$		0			0
$897$	24.8521	+	18.0561i	0.829788	+	0.602877i
$898$		0			0
$899$	−21.2123			−0.707470
$900$		0			0
$901$	−3.31478			−0.110431
$902$		0			0
$903$	71.4327			2.37713
$904$		0			0
$905$	0.854227			0.0283955
$906$		0			0
$907$	−35.0673	−	25.4779i	−1.16439	−	0.845979i	−0.174064	−	0.984734i	$-0.555690\pi$
$907$	−35.0673	−	25.4779i	−1.16439	−	0.845979i	−0.990327	+	0.138755i	$0.955690\pi$
$908$		0			0
$909$	2.23544	+	6.87999i	0.0741450	+	0.228195i
$910$		0			0
$911$	1.76735			0.0585550			0.0292775	−	0.999571i	$-0.490679\pi$
$911$	1.76735			0.0585550			0.0292775	+	0.999571i	$0.490679\pi$
$912$		0			0
$913$	−26.1173	+	18.9753i	−0.864357	+	0.627992i
$914$		0			0
$915$	−9.59808	+	29.5399i	−0.317303	+	0.976558i
$916$		0			0
$917$	−8.34903	−	6.06593i	−0.275709	−	0.200315i
$918$		0			0
$919$	−25.3440	+	18.4135i	−0.836020	+	0.607404i	−0.921256	−	0.388956i	$-0.872836\pi$
$919$	−25.3440	+	18.4135i	−0.836020	+	0.607404i	0.0852357	+	0.996361i	$0.472836\pi$
$920$		0			0
$921$	−23.3581	−	71.8889i	−0.769677	−	2.36882i
$922$		0			0
$923$	7.10234	+	21.8587i	0.233776	+	0.719489i
$924$		0			0
$925$	−3.45469	+	10.6324i	−0.113590	+	0.349593i
$926$		0			0
$927$	−16.6762	−	51.3241i	−0.547719	−	1.68571i
$928$		0			0
$929$	−30.5027			−1.00076			−0.500381	−	0.865805i	$-0.666807\pi$
$929$	−30.5027			−1.00076			−0.500381	+	0.865805i	$0.666807\pi$
$930$		0			0
$931$	−3.94863	−	2.86885i	−0.129411	−	0.0940227i
$932$		0			0
$933$	24.1098	−	17.5168i	0.789319	−	0.573474i
$934$		0			0
$935$	−14.3701	+	10.4405i	−0.469952	+	0.341440i
$936$		0			0
$937$	−1.00408	+	3.09024i	−0.0328018	+	0.100954i	−0.966117	−	0.258105i	$-0.916902\pi$
$937$	−1.00408	+	3.09024i	−0.0328018	+	0.100954i	0.933315	+	0.359058i	$0.116902\pi$
$938$		0			0
$939$	27.1108	+	19.6972i	0.884728	+	0.642792i
$940$		0			0
$941$	0.0182408	−	0.0561394i	0.000594633	−	0.00183009i	−0.950759	−	0.309932i	$-0.899694\pi$
$941$	0.0182408	−	0.0561394i	0.000594633	−	0.00183009i	0.951353	+	0.308102i	$0.0996937\pi$
$942$		0			0
$943$	−22.2111	+	9.25404i	−0.723294	+	0.301353i
$944$		0			0
$945$	−0.210260	+	0.647114i	−0.00683977	+	0.0210506i
$946$		0			0
$947$	24.3058	+	17.6592i	0.789831	+	0.573846i	0.907913	−	0.419158i	$-0.137675\pi$
$947$	24.3058	+	17.6592i	0.789831	+	0.573846i	−0.118082	+	0.993004i	$0.537675\pi$
$948$		0			0
$949$	11.1490	−	34.3130i	0.361910	−	1.11385i
$950$		0			0
$951$	−3.70867	+	2.69451i	−0.120262	+	0.0873754i
$952$		0			0
$953$	8.16589	−	5.93287i	0.264519	−	0.192184i	−0.447618	−	0.894225i	$-0.647727\pi$
$953$	8.16589	−	5.93287i	0.264519	−	0.192184i	0.712137	+	0.702041i	$0.247727\pi$
$954$		0			0
$955$	10.3776	+	7.53974i	0.335810	+	0.243980i
$956$		0			0
$957$	19.8716			0.642357
$958$		0			0
$959$	1.82884	+	5.62859i	0.0590563	+	0.181757i
$960$		0			0
$961$	8.98009	−	27.6379i	0.289680	−	0.891545i
$962$		0			0
$963$	4.68351	+	14.4144i	0.150924	+	0.464496i
$964$		0			0
$965$	6.98896	+	21.5098i	0.224983	+	0.692426i
$966$		0			0
$967$	−26.5254	+	19.2718i	−0.852999	+	0.619740i	−0.925971	−	0.377594i	$-0.876752\pi$
$967$	−26.5254	+	19.2718i	−0.852999	+	0.619740i	0.0729721	+	0.997334i	$0.476752\pi$
$968$		0			0
$969$	36.7242	+	26.6817i	1.17975	+	0.857140i
$970$		0			0
$971$	5.77964	−	17.7879i	0.185477	−	0.570840i	−0.814479	−	0.580193i	$-0.802977\pi$
$971$	5.77964	−	17.7879i	0.185477	−	0.570840i	0.999956	+	0.00935262i	$0.00297708\pi$
$972$		0			0
$973$	−13.5176	+	9.82114i	−0.433356	+	0.314851i
$974$		0			0
$975$	−8.17466			−0.261799
$976$		0			0
$977$	17.5509	+	54.0162i	0.561504	+	1.72813i	0.678117	+	0.734954i	$0.262796\pi$
$977$	17.5509	+	54.0162i	0.561504	+	1.72813i	−0.116614	+	0.993177i	$0.537204\pi$
$978$		0			0
$979$	9.75595	+	7.08811i	0.311802	+	0.226537i
$980$		0			0
$981$	−7.80450			−0.249178
$982$		0			0
$983$	0.416676			0.0132899			0.00664495	−	0.999978i	$-0.497885\pi$
$983$	0.416676			0.0132899			0.00664495	+	0.999978i	$0.497885\pi$
$984$		0			0
$985$	0.700561			0.0223217
$986$		0			0
$987$	−42.5489			−1.35435
$988$		0			0
$989$	−30.5594	−	22.2027i	−0.971732	−	0.706005i
$990$		0			0
$991$	14.3813	+	44.2611i	0.456837	+	1.40600i	0.868965	+	0.494874i	$0.164786\pi$
$991$	14.3813	+	44.2611i	0.456837	+	1.40600i	−0.412128	+	0.911126i	$0.635214\pi$
$992$		0			0
$993$	6.39499			0.202939
$994$		0			0
$995$	0.295911	−	0.214992i	0.00938102	−	0.00681571i
$996$		0			0
$997$	8.93664	−	27.5041i	0.283026	−	0.871065i	−0.703957	−	0.710242i	$-0.748585\pi$
$997$	8.93664	−	27.5041i	0.283026	−	0.871065i	0.986983	−	0.160823i	$-0.0514147\pi$
$998$		0			0
$999$	−2.10424	−	1.52882i	−0.0665752	−	0.0483697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.a.221.6	yes	24
41.18	even	5	inner	820.2.u.a.141.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.a.141.6	✓	24	41.18	even	5	inner
820.2.u.a.221.6	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.42987 q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.903746 + 2.78144i) q^{7} +2.90425 q^{9} +(2.41720 - 1.75620i) q^{11} +(-1.03961 + 3.19958i) q^{13} +(-1.96580 - 1.42824i) q^{15} +(4.80955 - 3.49434i) q^{17} +(0.971064 + 2.98863i) q^{19} +(2.19598 + 6.75854i) q^{21} +(1.16123 - 3.57390i) q^{23} +(0.309017 + 0.951057i) q^{25} -0.232654 q^{27} +(2.21438 + 1.60884i) q^{29} +(-6.26976 + 4.55525i) q^{31} +(5.87348 - 4.26733i) q^{33} +(0.903746 - 2.78144i) q^{35} +(9.04450 + 6.57121i) q^{37} +(-2.52611 + 7.77456i) q^{39} +(-4.16856 - 4.86036i) q^{41} +(3.10622 - 9.55998i) q^{43} +(-2.34959 - 1.70708i) q^{45} +(-1.85022 + 5.69440i) q^{47} +(-1.25655 + 0.912939i) q^{49} +(11.6866 - 8.49078i) q^{51} +(-0.451093 - 0.327738i) q^{53} -2.98782 q^{55} +(2.35956 + 7.26197i) q^{57} +(-1.46341 + 4.50392i) q^{59} +(-3.95004 - 12.1570i) q^{61} +(2.62471 + 8.07801i) q^{63} +(2.72173 - 1.97745i) q^{65} +(-6.99129 - 5.07947i) q^{67} +(2.82164 - 8.68411i) q^{69} +(5.52700 - 4.01560i) q^{71} -10.7242 q^{73} +(0.750870 + 2.31094i) q^{75} +(7.06930 + 5.13615i) q^{77} -2.77926 q^{79} -9.27808 q^{81} -10.8048 q^{83} -5.94493 q^{85} +(5.38065 + 3.90927i) q^{87} +(1.24721 + 3.83851i) q^{89} -9.83900 q^{91} +(-15.2347 + 11.0686i) q^{93} +(0.971064 - 2.98863i) q^{95} +(-2.35673 - 1.71226i) q^{97} +(7.02016 - 5.10045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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