LMFDB - Embedded newform 1008.2.bf.g.943.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(31,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-3,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			943.9
Character	$\chi$	$=$	1008.943
Dual form			1008.2.bf.g.31.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.823206 + 1.52392i) q^{3} -0.280665i q^{5} +(-0.164674 + 2.64062i) q^{7} +(-1.64466 + 2.50900i) q^{9} -2.82201i q^{11} +(-4.06955 + 2.34956i) q^{13} +(0.427710 - 0.231045i) q^{15} +(-7.00051 + 4.04175i) q^{17} +(0.474304 - 0.821518i) q^{19} +(-4.15966 + 1.92282i) q^{21} +0.392466i q^{23} +4.92123 q^{25} +(-5.17741 - 0.440916i) q^{27} +(1.51148 - 2.61795i) q^{29} +(-1.06355 + 1.84211i) q^{31} +(4.30052 - 2.32310i) q^{33} +(0.741129 + 0.0462181i) q^{35} +(-2.43458 + 4.21681i) q^{37} +(-6.93061 - 4.26750i) q^{39} +(-0.478990 + 0.276545i) q^{41} +(4.28515 + 2.47404i) q^{43} +(0.704187 + 0.461599i) q^{45} +(-1.39435 - 2.41508i) q^{47} +(-6.94577 - 0.869682i) q^{49} +(-11.9222 - 7.34103i) q^{51} +(6.21935 + 10.7722i) q^{53} -0.792039 q^{55} +(1.64238 + 0.0465226i) q^{57} +(5.70053 - 9.87361i) q^{59} +(-9.67619 + 5.58655i) q^{61} +(-6.35448 - 4.75610i) q^{63} +(0.659437 + 1.14218i) q^{65} +(7.85871 + 4.53723i) q^{67} +(-0.598086 + 0.323080i) q^{69} +1.54594i q^{71} +(-0.542172 + 0.313023i) q^{73} +(4.05118 + 7.49956i) q^{75} +(7.45187 + 0.464711i) q^{77} +(-13.3691 + 7.71866i) q^{79} +(-3.59015 - 8.25293i) q^{81} +(5.30821 - 9.19409i) q^{83} +(1.13438 + 1.96480i) q^{85} +(5.23381 + 0.148255i) q^{87} +(9.90157 + 5.71667i) q^{89} +(-5.53414 - 11.1331i) q^{91} +(-3.68275 - 0.104319i) q^{93} +(-0.230571 - 0.133120i) q^{95} +(-13.6260 - 7.86698i) q^{97} +(7.08043 + 4.64126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 8 q^{7} - q^{9} + 3 q^{13} - 6 q^{15} - 3 q^{17} + 4 q^{19} - 20 q^{21} - 30 q^{25} - 9 q^{27} + 18 q^{29} + 17 q^{31} - 12 q^{33} + 42 q^{35} - 3 q^{37} - 42 q^{39} - 36 q^{41} + 24 q^{43}+ \cdots + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 8 * q^7 - q^9 + 3 * q^13 - 6 * q^15 - 3 * q^17 + 4 * q^19 - 20 * q^21 - 30 * q^25 - 9 * q^27 + 18 * q^29 + 17 * q^31 - 12 * q^33 + 42 * q^35 - 3 * q^37 - 42 * q^39 - 36 * q^41 + 24 * q^43 + 12 * q^45 - 21 * q^47 - 24 * q^49 + 18 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 - 6 * q^59 - 48 * q^61 - 6 * q^63 + 42 * q^67 - 6 * q^69 + 48 * q^73 - 33 * q^75 + 36 * q^77 - 30 * q^79 + 23 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 - 8 * q^93 - 33 * q^95 - 3 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.823206	+	1.52392i	0.475278	+	0.879836i
$3$	0.823206	+	1.52392i	0.475278	+	0.879836i
$4$		0			0
$5$		−	0.280665i		−	0.125517i	−0.998029	−	0.0627585i	$-0.980010\pi$
$5$		−	0.280665i		−	0.125517i	0.998029	−	0.0627585i	$-0.0199898\pi$
$6$		0			0
$7$	−0.164674	+	2.64062i	−0.0622408	+	0.998061i
$7$	−0.164674	+	2.64062i	−0.0622408	+	0.998061i
$8$		0			0
$9$	−1.64466	+	2.50900i	−0.548222	+	0.836333i
$10$		0			0
$11$		−	2.82201i		−	0.850869i	−0.904989	−	0.425434i	$-0.860121\pi$
$11$		−	2.82201i		−	0.850869i	0.904989	−	0.425434i	$-0.139879\pi$
$12$		0			0
$13$	−4.06955	+	2.34956i	−1.12869	+	0.651650i	−0.943605	−	0.331073i	$-0.892589\pi$
$13$	−4.06955	+	2.34956i	−1.12869	+	0.651650i	−0.185085	+	0.982722i	$0.559256\pi$
$14$		0			0
$15$	0.427710	−	0.231045i	0.110434	−	0.0596555i
$16$		0			0
$17$	−7.00051	+	4.04175i	−1.69787	+	0.980268i	−0.750100	+	0.661324i	$0.769995\pi$
$17$	−7.00051	+	4.04175i	−1.69787	+	0.980268i	−0.947774	+	0.318944i	$0.896672\pi$
$18$		0			0
$19$	0.474304	−	0.821518i	0.108813	−	0.188469i	−0.806477	−	0.591266i	$-0.798628\pi$
$19$	0.474304	−	0.821518i	0.108813	−	0.188469i	0.915290	+	0.402797i	$0.131962\pi$
$20$		0			0
$21$	−4.15966	+	1.92282i	−0.907712	+	0.419595i
$22$		0			0
$23$			0.392466i			0.0818348i	0.999163	+	0.0409174i	$0.0130280\pi$
$23$			0.392466i			0.0818348i	−0.999163	+	0.0409174i	$0.986972\pi$
$24$		0			0
$25$	4.92123			0.984245
$26$		0			0
$27$	−5.17741	−	0.440916i	−0.996393	−	0.0848543i
$28$		0			0
$29$	1.51148	−	2.61795i	0.280674	−	0.486142i	−0.690877	−	0.722973i	$-0.742775\pi$
$29$	1.51148	−	2.61795i	0.280674	−	0.486142i	0.971551	+	0.236831i	$0.0761086\pi$
$30$		0			0
$31$	−1.06355	+	1.84211i	−0.191018	+	0.330854i	−0.945588	−	0.325366i	$-0.894512\pi$
$31$	−1.06355	+	1.84211i	−0.191018	+	0.330854i	0.754570	+	0.656220i	$0.227846\pi$
$32$		0			0
$33$	4.30052	−	2.32310i	0.748625	−	0.404399i
$34$		0			0
$35$	0.741129	+	0.0462181i	0.125274	+	0.00781229i
$36$		0			0
$37$	−2.43458	+	4.21681i	−0.400242	+	0.693240i	−0.993755	−	0.111585i	$-0.964407\pi$
$37$	−2.43458	+	4.21681i	−0.400242	+	0.693240i	0.593513	+	0.804825i	$0.297741\pi$
$38$		0			0
$39$	−6.93061	−	4.26750i	−1.10979	−	0.683347i
$40$		0			0
$41$	−0.478990	+	0.276545i	−0.0748057	+	0.0431891i	−0.536936	−	0.843623i	$-0.680418\pi$
$41$	−0.478990	+	0.276545i	−0.0748057	+	0.0431891i	0.462131	+	0.886812i	$0.347085\pi$
$42$		0			0
$43$	4.28515	+	2.47404i	0.653480	+	0.377287i	0.789788	−	0.613380i	$-0.210190\pi$
$43$	4.28515	+	2.47404i	0.653480	+	0.377287i	−0.136308	+	0.990666i	$0.543524\pi$
$44$		0			0
$45$	0.704187	+	0.461599i	0.104974	+	0.0688112i
$46$		0			0
$47$	−1.39435	−	2.41508i	−0.203387	−	0.352276i	0.746231	−	0.665687i	$-0.231862\pi$
$47$	−1.39435	−	2.41508i	−0.203387	−	0.352276i	−0.949618	+	0.313411i	$0.898528\pi$
$48$		0			0
$49$	−6.94577	−	0.869682i	−0.992252	−	0.124240i
$50$		0			0
$51$	−11.9222	−	7.34103i	−1.66944	−	1.02795i
$52$		0			0
$53$	6.21935	+	10.7722i	0.854293	+	1.47968i	0.877300	+	0.479943i	$0.159343\pi$
$53$	6.21935	+	10.7722i	0.854293	+	1.47968i	−0.0230067	+	0.999735i	$0.507324\pi$
$54$		0			0
$55$	−0.792039			−0.106799
$56$		0			0
$57$	1.64238	+	0.0465226i	0.217538	+	0.00616207i
$58$		0			0
$59$	5.70053	−	9.87361i	0.742146	−	1.28543i	−0.209371	−	0.977836i	$-0.567141\pi$
$59$	5.70053	−	9.87361i	0.742146	−	1.28543i	0.951516	−	0.307598i	$-0.0995252\pi$
$60$		0			0
$61$	−9.67619	+	5.58655i	−1.23891	+	0.715284i	−0.968871	−	0.247565i	$-0.920370\pi$
$61$	−9.67619	+	5.58655i	−1.23891	+	0.715284i	−0.270038	+	0.962850i	$0.587036\pi$
$62$		0			0
$63$	−6.35448	−	4.75610i	−0.800590	−	0.599213i
$64$		0			0
$65$	0.659437	+	1.14218i	0.0817932	+	0.141670i
$66$		0			0
$67$	7.85871	+	4.53723i	0.960095	+	0.554311i	0.896202	−	0.443646i	$-0.146315\pi$
$67$	7.85871	+	4.53723i	0.960095	+	0.554311i	0.0638926	+	0.997957i	$0.479648\pi$
$68$		0			0
$69$	−0.598086	+	0.323080i	−0.0720011	+	0.0388943i
$70$		0			0
$71$			1.54594i			0.183469i	0.995784	+	0.0917344i	$0.0292411\pi$
$71$			1.54594i			0.183469i	−0.995784	+	0.0917344i	$0.970759\pi$
$72$		0			0
$73$	−0.542172	+	0.313023i	−0.0634564	+	0.0366366i	−0.531393	−	0.847126i	$-0.678331\pi$
$73$	−0.542172	+	0.313023i	−0.0634564	+	0.0366366i	0.467936	+	0.883762i	$0.344998\pi$
$74$		0			0
$75$	4.05118	+	7.49956i	0.467790	+	0.865974i
$76$		0			0
$77$	7.45187	+	0.464711i	0.849219	+	0.0529588i
$78$		0			0
$79$	−13.3691	+	7.71866i	−1.50414	+	0.868417i	−0.504153	+	0.863614i	$0.668195\pi$
$79$	−13.3691	+	7.71866i	−1.50414	+	0.868417i	−0.999988	+	0.00480263i	$0.998471\pi$
$80$		0			0
$81$	−3.59015	−	8.25293i	−0.398906	−	0.916992i
$82$		0			0
$83$	5.30821	−	9.19409i	0.582652	−	1.00918i	−0.412512	−	0.910952i	$-0.635348\pi$
$83$	5.30821	−	9.19409i	0.582652	−	1.00918i	0.995164	−	0.0982303i	$-0.0313182\pi$
$84$		0			0
$85$	1.13438	+	1.96480i	0.123040	+	0.213112i
$86$		0			0
$87$	5.23381	+	0.148255i	0.561123	+	0.0158946i
$88$		0			0
$89$	9.90157	+	5.71667i	1.04956	+	0.605966i	0.922527	−	0.385932i	$-0.126120\pi$
$89$	9.90157	+	5.71667i	1.04956	+	0.605966i	0.127037	+	0.991898i	$0.459453\pi$
$90$		0			0
$91$	−5.53414	−	11.1331i	−0.580136	−	1.16706i
$92$		0			0
$93$	−3.68275	−	0.104319i	−0.381884	−	0.0108174i
$94$		0			0
$95$	−0.230571	−	0.133120i	−0.0236561	−	0.0136579i
$96$		0			0
$97$	−13.6260	−	7.86698i	−1.38351	−	0.798770i	−0.390937	−	0.920417i	$-0.627849\pi$
$97$	−13.6260	−	7.86698i	−1.38351	−	0.798770i	−0.992573	+	0.121647i	$0.961182\pi$
$98$		0			0
$99$	7.08043	+	4.64126i	0.711610	+	0.466465i
$100$		0			0
$101$			7.01091i			0.697611i	0.937195	+	0.348806i	$0.113413\pi$
$101$			7.01091i			0.697611i	−0.937195	+	0.348806i	$0.886587\pi$
$102$		0			0
$103$	5.63248			0.554985			0.277493	−	0.960728i	$-0.410497\pi$
$103$	5.63248			0.554985			0.277493	+	0.960728i	$0.410497\pi$
$104$		0			0
$105$	0.539669	+	1.16747i	0.0526663	+	0.113933i
$106$		0			0
$107$	5.00552	+	2.88994i	0.483902	+	0.279381i	0.722041	−	0.691850i	$-0.243204\pi$
$107$	5.00552	+	2.88994i	0.483902	+	0.279381i	−0.238139	+	0.971231i	$0.576537\pi$
$108$		0			0
$109$	4.12859	+	7.15092i	0.395447	+	0.684934i	0.993158	−	0.116777i	$-0.0372564\pi$
$109$	4.12859	+	7.15092i	0.395447	+	0.684934i	−0.597711	+	0.801712i	$0.703923\pi$
$110$		0			0
$111$	−8.43025	−	0.238798i	−0.800164	−	0.0226657i
$112$		0			0
$113$	−6.47539	−	11.2157i	−0.609154	−	1.05508i	−0.991380	−	0.131016i	$-0.958176\pi$
$113$	−6.47539	−	11.2157i	−0.609154	−	1.05508i	0.382227	−	0.924069i	$-0.375157\pi$
$114$		0			0
$115$	0.110151			0.0102717
$116$		0			0
$117$	0.798013	−	14.0747i	0.0737763	−	1.30121i
$118$		0			0
$119$	−9.51993	−	19.1513i	−0.872690	−	1.75559i
$120$		0			0
$121$	3.03625			0.276023
$122$		0			0
$123$	−0.815740	−	0.502289i	−0.0735528	−	0.0452899i
$124$		0			0
$125$		−	2.78454i		−	0.249057i
$126$		0			0
$127$			7.77236i			0.689685i	0.938660	+	0.344843i	$0.112068\pi$
$127$			7.77236i			0.689685i	−0.938660	+	0.344843i	$0.887932\pi$
$128$		0			0
$129$	−0.242668	+	8.56687i	−0.0213658	+	0.754271i
$130$		0			0
$131$	−7.98542			−0.697690			−0.348845	−	0.937180i	$-0.613426\pi$
$131$	−7.98542			−0.697690			−0.348845	+	0.937180i	$0.613426\pi$
$132$		0			0
$133$	2.09121	+	1.38774i	0.181331	+	0.120332i
$134$		0			0
$135$	−0.123749	+	1.45312i	−0.0106507	+	0.125064i
$136$		0			0
$137$	8.64941			0.738969			0.369484	−	0.929237i	$-0.379534\pi$
$137$	8.64941			0.738969			0.369484	+	0.929237i	$0.379534\pi$
$138$		0			0
$139$	7.19469	+	12.4616i	0.610246	+	1.05698i	0.991199	+	0.132383i	$0.0422627\pi$
$139$	7.19469	+	12.4616i	0.610246	+	1.05698i	−0.380953	+	0.924595i	$0.624404\pi$
$140$		0			0
$141$	2.53256	−	4.11299i	0.213280	−	0.346376i
$142$		0			0
$143$	6.63048	+	11.4843i	0.554468	+	0.960367i
$144$		0			0
$145$	−0.734767	−	0.424218i	−0.0610191	−	0.0352294i
$146$		0			0
$147$	−4.39247	−	11.3007i	−0.362285	−	0.932068i
$148$		0			0
$149$	−1.06764			−0.0874644			−0.0437322	−	0.999043i	$-0.513925\pi$
$149$	−1.06764			−0.0874644			−0.0437322	+	0.999043i	$0.513925\pi$
$150$		0			0
$151$		−	12.9439i		−	1.05336i	−0.850064	−	0.526679i	$-0.823437\pi$
$151$		−	12.9439i		−	1.05336i	0.850064	−	0.526679i	$-0.176563\pi$
$152$		0			0
$153$	1.37276	−	24.2116i	0.110981	−	1.95739i
$154$		0			0
$155$	0.517016	+	0.298500i	0.0415278	+	0.0239761i
$156$		0			0
$157$	7.01702	+	4.05128i	0.560019	+	0.323327i	0.753153	−	0.657845i	$-0.228532\pi$
$157$	7.01702	+	4.05128i	0.560019	+	0.323327i	−0.193134	+	0.981172i	$0.561865\pi$
$158$		0			0
$159$	−11.2962	+	18.3455i	−0.895847	+	1.45490i
$160$		0			0
$161$	−1.03635	−	0.0646288i	−0.0816761	−	0.00509346i
$162$		0			0
$163$	15.8164	+	9.13162i	1.23884	+	0.715244i	0.968857	−	0.247621i	$-0.0796489\pi$
$163$	15.8164	+	9.13162i	1.23884	+	0.715244i	0.269982	+	0.962865i	$0.412982\pi$
$164$		0			0
$165$	−0.652011	−	1.20700i	−0.0507590	−	0.0939651i
$166$		0			0
$167$	8.41991	+	14.5837i	0.651553	+	1.12852i	0.982746	+	0.184959i	$0.0592153\pi$
$167$	8.41991	+	14.5837i	0.651553	+	1.12852i	−0.331194	+	0.943563i	$0.607451\pi$
$168$		0			0
$169$	4.54083	−	7.86496i	0.349295	−	0.604997i
$170$		0			0
$171$	1.28112	+	2.54115i	0.0979695	+	0.194327i
$172$		0			0
$173$	−17.1823	+	9.92020i	−1.30635	+	0.754219i	−0.981484	−	0.191543i	$-0.938651\pi$
$173$	−17.1823	+	9.92020i	−1.30635	+	0.754219i	−0.324861	+	0.945762i	$0.605318\pi$
$174$		0			0
$175$	−0.810397	+	12.9951i	−0.0612603	+	0.982337i
$176$		0			0
$177$	19.7393	+	0.559143i	1.48370	+	0.0420278i
$178$		0			0
$179$	21.5488	−	12.4412i	1.61063	−	0.929899i	0.621409	−	0.783486i	$-0.286561\pi$
$179$	21.5488	−	12.4412i	1.61063	−	0.929899i	0.989224	−	0.146413i	$-0.0467728\pi$
$180$		0			0
$181$		−	7.30569i		−	0.543027i	−0.962435	−	0.271514i	$-0.912476\pi$
$181$		−	7.30569i		−	0.543027i	0.962435	−	0.271514i	$-0.0875242\pi$
$182$		0			0
$183$	−16.4789	−	10.1469i	−1.21816	−	0.750077i
$184$		0			0
$185$	1.18351	+	0.683300i	0.0870134	+	0.0502372i
$186$		0			0
$187$	11.4059	+	19.7555i	0.834079	+	1.44467i
$188$		0			0
$189$	2.01688	−	13.5990i	0.146706	−	0.989180i
$190$		0			0
$191$	7.11844	−	4.10983i	0.515072	−	0.297377i	−0.219844	−	0.975535i	$-0.570555\pi$
$191$	7.11844	−	4.10983i	0.515072	−	0.297377i	0.734916	+	0.678158i	$0.237222\pi$
$192$		0			0
$193$	−9.78487	+	16.9479i	−0.704331	+	1.21994i	0.262602	+	0.964904i	$0.415419\pi$
$193$	−9.78487	+	16.9479i	−0.704331	+	1.21994i	−0.966933	+	0.255032i	$0.917914\pi$
$194$		0			0
$195$	−1.19774	+	1.94518i	−0.0857717	+	0.139297i
$196$		0			0
$197$	16.3933			1.16797			0.583987	−	0.811763i	$-0.301492\pi$
$197$	16.3933			1.16797			0.583987	+	0.811763i	$0.301492\pi$
$198$		0			0
$199$	7.86905	+	13.6296i	0.557822	+	0.966176i	0.997678	+	0.0681077i	$0.0216961\pi$
$199$	7.86905	+	13.6296i	0.557822	+	0.966176i	−0.439856	+	0.898068i	$0.644971\pi$
$200$		0			0
$201$	−0.445039	+	15.7111i	−0.0313907	+	1.10818i
$202$		0			0
$203$	6.66413	+	4.42235i	0.467730	+	0.310388i
$204$		0			0
$205$	0.0776164	+	0.134436i	0.00542097	+	0.00938939i
$206$		0			0
$207$	−0.984696	−	0.645475i	−0.0684411	−	0.0448636i
$208$		0			0
$209$	−2.31833	−	1.33849i	−0.160363	−	0.0925854i
$210$		0			0
$211$	7.41442	−	4.28072i	0.510430	−	0.294697i	−0.222581	−	0.974914i	$-0.571448\pi$
$211$	7.41442	−	4.28072i	0.510430	−	0.294697i	0.733010	+	0.680218i	$0.238115\pi$
$212$		0			0
$213$	−2.35588	+	1.27262i	−0.161422	+	0.0871987i
$214$		0			0
$215$	0.694374	−	1.20269i	0.0473559	−	0.0820229i
$216$		0			0
$217$	−4.68919	−	3.11177i	−0.318323	−	0.211241i
$218$		0			0
$219$	−0.923341	−	0.568544i	−0.0623936	−	0.0384187i
$220$		0			0
$221$	18.9926	−	32.8962i	1.27758	−	2.21284i
$222$		0			0
$223$	−9.63167	+	16.6825i	−0.644984	+	1.11715i	0.339321	+	0.940671i	$0.389803\pi$
$223$	−9.63167	+	16.6825i	−0.644984	+	1.11715i	−0.984305	+	0.176475i	$0.943531\pi$
$224$		0			0
$225$	−8.09377	+	12.3474i	−0.539585	+	0.823157i
$226$		0			0
$227$	20.6399			1.36992			0.684960	−	0.728581i	$-0.259820\pi$
$227$	20.6399			1.36992			0.684960	+	0.728581i	$0.259820\pi$
$228$		0			0
$229$		−	21.1950i		−	1.40060i	−0.713848	−	0.700301i	$-0.753049\pi$
$229$		−	21.1950i		−	1.40060i	0.713848	−	0.700301i	$-0.246951\pi$
$230$		0			0
$231$	5.42624	+	11.7386i	0.357020	+	0.772343i
$232$		0			0
$233$	−7.78510	+	13.4842i	−0.510019	+	0.883378i	0.489914	+	0.871771i	$0.337028\pi$
$233$	−7.78510	+	13.4842i	−0.510019	+	0.883378i	−0.999933	+	0.0116076i	$0.996305\pi$
$234$		0			0
$235$	−0.677828	+	0.391344i	−0.0442167	+	0.0255285i
$236$		0			0
$237$	−22.7681	−	14.0194i	−1.47895	−	0.910658i
$238$		0			0
$239$	6.36686	−	3.67591i	0.411838	−	0.237775i	−0.279741	−	0.960075i	$-0.590249\pi$
$239$	6.36686	−	3.67591i	0.411838	−	0.237775i	0.691579	+	0.722301i	$0.256915\pi$
$240$		0			0
$241$		−	5.75441i		−	0.370674i	−0.982675	−	0.185337i	$-0.940662\pi$
$241$		−	5.75441i		−	0.370674i	0.982675	−	0.185337i	$-0.0593376\pi$
$242$		0			0
$243$	9.62136	−	12.2650i	0.617211	−	0.786798i
$244$		0			0
$245$	−0.244089	+	1.94943i	−0.0155943	+	0.124545i
$246$		0			0
$247$			4.45762i			0.283631i
$248$		0			0
$249$	18.3808	+	0.520662i	1.16484	+	0.0329956i
$250$		0			0
$251$	−21.9997			−1.38861			−0.694305	−	0.719681i	$-0.744288\pi$
$251$	−21.9997			−1.38861			−0.694305	+	0.719681i	$0.744288\pi$
$252$		0			0
$253$	1.10754			0.0696306
$254$		0			0
$255$	−2.06037	+	3.34613i	−0.129025	+	0.209543i
$256$		0			0
$257$		−	1.45564i		−	0.0908000i	−0.998969	−	0.0454000i	$-0.985544\pi$
$257$		−	1.45564i		−	0.0908000i	0.998969	−	0.0454000i	$-0.0144562\pi$
$258$		0			0
$259$	−10.7341	−	7.12320i	−0.666985	−	0.442614i
$260$		0			0
$261$	4.08257	+	8.09795i	0.252705	+	0.501251i
$262$		0			0
$263$		−	21.2421i		−	1.30984i	−0.755696	−	0.654922i	$-0.772701\pi$
$263$		−	21.2421i		−	1.30984i	0.755696	−	0.654922i	$-0.227299\pi$
$264$		0			0
$265$	3.02338	−	1.74555i	0.185725	−	0.107228i
$266$		0			0
$267$	−0.560726	+	19.7952i	−0.0343159	+	1.21145i
$268$		0			0
$269$	17.4754	−	10.0894i	1.06549	−	0.615162i	0.138546	−	0.990356i	$-0.455757\pi$
$269$	17.4754	−	10.0894i	1.06549	−	0.615162i	0.926946	+	0.375194i	$0.122424\pi$
$270$		0			0
$271$	8.69232	−	15.0555i	0.528021	−	0.914559i	−0.471445	−	0.881895i	$-0.656268\pi$
$271$	8.69232	−	15.0555i	0.528021	−	0.914559i	0.999466	−	0.0326639i	$-0.0103991\pi$
$272$		0			0
$273$	12.4102	−	17.5984i	0.751097	−	1.06510i
$274$		0			0
$275$		−	13.8878i		−	0.837464i
$276$		0			0
$277$	1.13376			0.0681208			0.0340604	−	0.999420i	$-0.489156\pi$
$277$	1.13376			0.0681208			0.0340604	+	0.999420i	$0.489156\pi$
$278$		0			0
$279$	−2.87269	−	5.69810i	−0.171983	−	0.341136i
$280$		0			0
$281$	−6.37564	+	11.0429i	−0.380339	+	0.658766i	−0.991111	−	0.133040i	$-0.957526\pi$
$281$	−6.37564	+	11.0429i	−0.380339	+	0.658766i	0.610772	+	0.791807i	$0.290859\pi$
$282$		0			0
$283$	3.38500	−	5.86300i	0.201218	−	0.348519i	−0.747703	−	0.664033i	$-0.768844\pi$
$283$	3.38500	−	5.86300i	0.201218	−	0.348519i	0.948921	+	0.315514i	$0.102177\pi$
$284$		0			0
$285$	0.0130573	−	0.460957i	0.000773445	−	0.0273048i
$286$		0			0
$287$	−0.651374	−	1.31037i	−0.0384494	−	0.0773488i
$288$		0			0
$289$	24.1715	−	41.8662i	1.42185	−	2.46272i
$290$		0			0
$291$	0.771641	−	27.2411i	0.0452344	−	1.59690i
$292$		0			0
$293$	10.5242	−	6.07616i	0.614831	−	0.354973i	−0.160023	−	0.987113i	$-0.551157\pi$
$293$	10.5242	−	6.07616i	0.614831	−	0.354973i	0.774854	+	0.632140i	$0.217823\pi$
$294$		0			0
$295$	−2.77117	−	1.59994i	−0.161344	−	0.0931519i
$296$		0			0
$297$	−1.24427	+	14.6107i	−0.0721998	+	0.847800i
$298$		0			0
$299$	−0.922120	−	1.59716i	−0.0533276	−	0.0923661i
$300$		0			0
$301$	−7.23864	+	10.9081i	−0.417228	+	0.628730i
$302$		0			0
$303$	−10.6841	+	5.77142i	−0.613783	+	0.331559i
$304$		0			0
$305$	1.56795	+	2.71576i	0.0897804	+	0.155504i
$306$		0			0
$307$	−17.3006			−0.987396			−0.493698	−	0.869634i	$-0.664355\pi$
$307$	−17.3006			−0.987396			−0.493698	+	0.869634i	$0.664355\pi$
$308$		0			0
$309$	4.63669	+	8.58346i	0.263772	+	0.488296i
$310$		0			0
$311$	−13.2379	+	22.9288i	−0.750655	+	1.30017i	0.196850	+	0.980434i	$0.436929\pi$
$311$	−13.2379	+	22.9288i	−0.750655	+	1.30017i	−0.947505	+	0.319739i	$0.896405\pi$
$312$		0			0
$313$	−3.86883	+	2.23367i	−0.218679	+	0.126255i	−0.605339	−	0.795968i	$-0.706962\pi$
$313$	−3.86883	+	2.23367i	−0.218679	+	0.126255i	0.386659	+	0.922223i	$0.373629\pi$
$314$		0			0
$315$	−1.33487	+	1.78348i	−0.0752114	+	0.100488i
$316$		0			0
$317$	−14.7017	−	25.4640i	−0.825728	−	1.43020i	−0.901362	−	0.433067i	$-0.857431\pi$
$317$	−14.7017	−	25.4640i	−0.825728	−	1.43020i	0.0756338	−	0.997136i	$-0.475902\pi$
$318$		0			0
$319$	−7.38790	−	4.26541i	−0.413643	−	0.238817i
$320$		0			0
$321$	−0.283463	+	10.0070i	−0.0158213	+	0.558538i
$322$		0			0
$323$			7.66807i			0.426663i
$324$		0			0
$325$	−20.0272	+	11.5627i	−1.11091	+	0.641383i
$326$		0			0
$327$	−7.49876	+	12.1783i	−0.414682	+	0.673463i
$328$		0			0
$329$	6.60693	−	3.28425i	0.364252	−	0.181066i
$330$		0			0
$331$	−0.850295	+	0.490918i	−0.0467364	+	0.0269833i	−0.523186	−	0.852218i	$-0.675257\pi$
$331$	−0.850295	+	0.490918i	−0.0467364	+	0.0269833i	0.476450	+	0.879202i	$0.341923\pi$
$332$		0			0
$333$	−6.57592	−	13.0436i	−0.360358	−	0.714785i
$334$		0			0
$335$	1.27344	−	2.20566i	0.0695755	−	0.120508i
$336$		0			0
$337$	5.58390	+	9.67160i	0.304174	+	0.526846i	0.977077	−	0.212885i	$-0.0682861\pi$
$337$	5.58390	+	9.67160i	0.304174	+	0.526846i	−0.672903	+	0.739731i	$0.734953\pi$
$338$		0			0
$339$	11.7613	−	19.1008i	0.638784	−	1.03741i
$340$		0			0
$341$	5.19847	+	3.00134i	0.281513	+	0.162532i
$342$		0			0
$343$	3.44029	−	18.1979i	0.185758	−	0.982596i
$344$		0			0
$345$	0.0906771	+	0.167862i	0.00488189	+	0.00903737i
$346$		0			0
$347$	7.61089	+	4.39415i	0.408574	+	0.235890i	0.690177	−	0.723641i	$-0.257533\pi$
$347$	7.61089	+	4.39415i	0.408574	+	0.235890i	−0.281603	+	0.959531i	$0.590866\pi$
$348$		0			0
$349$	18.2265	+	10.5231i	0.975644	+	0.563288i	0.900952	−	0.433919i	$-0.142869\pi$
$349$	18.2265	+	10.5231i	0.975644	+	0.563288i	0.0746915	+	0.997207i	$0.476203\pi$
$350$		0			0
$351$	22.1057	−	10.3703i	1.17992	−	0.553525i
$352$		0			0
$353$			2.64279i			0.140661i	0.997524	+	0.0703307i	$0.0224055\pi$
$353$			2.64279i			0.140661i	−0.997524	+	0.0703307i	$0.977595\pi$
$354$		0			0
$355$	0.433889			0.0230285
$356$		0			0
$357$	21.3482	−	30.2730i	1.12986	−	1.60222i
$358$		0			0
$359$	−20.5571	−	11.8687i	−1.08496	−	0.626405i	−0.152733	−	0.988267i	$-0.548808\pi$
$359$	−20.5571	−	11.8687i	−1.08496	−	0.626405i	−0.932231	+	0.361863i	$0.882141\pi$
$360$		0			0
$361$	9.05007	+	15.6752i	0.476320	+	0.825010i
$362$		0			0
$363$	2.49946	+	4.62700i	0.131187	+	0.242854i
$364$		0			0
$365$	0.0878545	+	0.152168i	0.00459852	+	0.00796486i
$366$		0			0
$367$	30.6820			1.60159			0.800793	−	0.598942i	$-0.204412\pi$
$367$	30.6820			1.60159			0.800793	+	0.598942i	$0.204412\pi$
$368$		0			0
$369$	0.0939269	−	1.65661i	0.00488964	−	0.0862397i
$370$		0			0
$371$	−29.4695	+	14.6490i	−1.52998	+	0.760540i
$372$		0			0
$373$	6.58921			0.341176			0.170588	−	0.985342i	$-0.445433\pi$
$373$	6.58921			0.341176			0.170588	+	0.985342i	$0.445433\pi$
$374$		0			0
$375$	4.24341	−	2.29225i	0.219129	−	0.118371i
$376$		0			0
$377$			14.2052i			0.731605i
$378$		0			0
$379$		−	0.316910i		−	0.0162786i	−0.999967	−	0.00813930i	$-0.997409\pi$
$379$		−	0.316910i		−	0.0162786i	0.999967	−	0.00813930i	$-0.00259085\pi$
$380$		0			0
$381$	−11.8445	+	6.39825i	−0.606810	+	0.327792i
$382$		0			0
$383$	−3.69711			−0.188913			−0.0944567	−	0.995529i	$-0.530111\pi$
$383$	−3.69711			−0.188913			−0.0944567	+	0.995529i	$0.530111\pi$
$384$		0			0
$385$	0.130428	−	2.09148i	0.00664723	−	0.106591i
$386$		0			0
$387$	−13.2550	+	6.68249i	−0.673789	+	0.339690i
$388$		0			0
$389$	−8.59629			−0.435849			−0.217925	−	0.975966i	$-0.569929\pi$
$389$	−8.59629			−0.435849			−0.217925	+	0.975966i	$0.569929\pi$
$390$		0			0
$391$	−1.58625	−	2.74746i	−0.0802200	−	0.138945i
$392$		0			0
$393$	−6.57365	−	12.1691i	−0.331597	−	0.613852i
$394$		0			0
$395$	2.16635	+	3.75224i	0.109001	+	0.188795i
$396$		0			0
$397$	−10.9255	−	6.30783i	−0.548334	−	0.316581i	0.200116	−	0.979772i	$-0.435868\pi$
$397$	−10.9255	−	6.30783i	−0.548334	−	0.316581i	−0.748450	+	0.663192i	$0.769201\pi$
$398$		0			0
$399$	−0.393305	+	4.32924i	−0.0196899	+	0.216733i
$400$		0			0
$401$	−26.1292			−1.30483			−0.652414	−	0.757862i	$-0.726244\pi$
$401$	−26.1292			−1.30483			−0.652414	+	0.757862i	$0.726244\pi$
$402$		0			0
$403$		−	9.99544i		−	0.497908i
$404$		0			0
$405$	−2.31630	+	1.00763i	−0.115098	+	0.0500695i
$406$		0			0
$407$	11.8999	+	6.87041i	0.589856	+	0.340554i
$408$		0			0
$409$	−0.249796	−	0.144220i	−0.0123516	−	0.00713121i	0.493811	−	0.869569i	$-0.335603\pi$
$409$	−0.249796	−	0.144220i	−0.0123516	−	0.00713121i	−0.506163	+	0.862438i	$0.668937\pi$
$410$		0			0
$411$	7.12024	+	13.1810i	0.351216	+	0.650171i
$412$		0			0
$413$	25.1337	+	16.6789i	1.23675	+	0.820713i
$414$		0			0
$415$	−2.58046	−	1.48983i	−0.126670	−	0.0731327i
$416$		0			0
$417$	−13.0677	+	21.2226i	−0.639930	+	1.03927i
$418$		0			0
$419$	9.56824	+	16.5727i	0.467439	+	0.809629i	0.999308	−	0.0371983i	$-0.0118433\pi$
$419$	9.56824	+	16.5727i	0.467439	+	0.809629i	−0.531869	+	0.846827i	$0.678510\pi$
$420$		0			0
$421$	−11.5319	+	19.9738i	−0.562030	+	0.973465i	0.435289	+	0.900291i	$0.356646\pi$
$421$	−11.5319	+	19.9738i	−0.562030	+	0.973465i	−0.997319	+	0.0731740i	$0.976687\pi$
$422$		0			0
$423$	8.35268	+	0.473582i	0.406121	+	0.0230264i
$424$		0			0
$425$	−34.4511	+	19.8904i	−1.67112	+	0.964824i
$426$		0			0
$427$	−13.1585	−	26.4711i	−0.636787	−	1.28103i
$428$		0			0
$429$	−12.0429	+	19.5583i	−0.581439	+	0.944283i
$430$		0			0
$431$	−13.2196	+	7.63235i	−0.636766	+	0.367637i	−0.783368	−	0.621558i	$-0.786500\pi$
$431$	−13.2196	+	7.63235i	−0.636766	+	0.367637i	0.146601	+	0.989196i	$0.453167\pi$
$432$		0			0
$433$			24.5275i			1.17871i	0.807873	+	0.589357i	$0.200619\pi$
$433$			24.5275i			1.17871i	−0.807873	+	0.589357i	$0.799381\pi$
$434$		0			0
$435$	0.0416099	−	1.46895i	0.00199504	−	0.0704305i
$436$		0			0
$437$	0.322418	+	0.186148i	0.0154233	+	0.00890467i
$438$		0			0
$439$	−9.14003	−	15.8310i	−0.436230	−	0.755572i	0.561165	−	0.827704i	$-0.310353\pi$
$439$	−9.14003	−	15.8310i	−0.436230	−	0.755572i	−0.997395	+	0.0721316i	$0.977020\pi$
$440$		0			0
$441$	13.6055	−	15.9966i	0.647880	−	0.761742i
$442$		0			0
$443$	−4.51333	+	2.60578i	−0.214435	+	0.123804i	−0.603371	−	0.797461i	$-0.706176\pi$
$443$	−4.51333	+	2.60578i	−0.214435	+	0.123804i	0.388936	+	0.921265i	$0.372843\pi$
$444$		0			0
$445$	1.60447	−	2.77902i	0.0760591	−	0.131738i
$446$		0			0
$447$	−0.878887	−	1.62700i	−0.0415699	−	0.0769543i
$448$		0			0
$449$	−9.38031			−0.442684			−0.221342	−	0.975196i	$-0.571044\pi$
$449$	−9.38031			−0.442684			−0.221342	+	0.975196i	$0.571044\pi$
$450$		0			0
$451$	0.780414	+	1.35172i	0.0367482	+	0.0636498i
$452$		0			0
$453$	19.7254	−	10.6555i	0.926782	−	0.500638i
$454$		0			0
$455$	−3.12466	+	1.55324i	−0.146486	+	0.0728169i
$456$		0			0
$457$	−14.6810	−	25.4283i	−0.686749	−	1.18948i	−0.972884	−	0.231295i	$-0.925704\pi$
$457$	−14.6810	−	25.4283i	−0.686749	−	1.18948i	0.286134	−	0.958190i	$-0.407630\pi$
$458$		0			0
$459$	38.0266	−	17.8392i	1.77493	−	0.832661i
$460$		0			0
$461$	1.10606	+	0.638584i	0.0515144	+	0.0297418i	0.525536	−	0.850771i	$-0.323865\pi$
$461$	1.10606	+	0.638584i	0.0515144	+	0.0297418i	−0.474022	+	0.880513i	$0.657198\pi$
$462$		0			0
$463$	−23.8988	+	13.7980i	−1.11067	+	0.641247i	−0.939004	−	0.343907i	$-0.888249\pi$
$463$	−23.8988	+	13.7980i	−1.11067	+	0.641247i	−0.171669	+	0.985155i	$0.554916\pi$
$464$		0			0
$465$	−0.0292787	+	1.03362i	−0.00135777	+	0.0479329i
$466$		0			0
$467$	−5.00656	+	8.67162i	−0.231676	+	0.401275i	−0.958301	−	0.285759i	$-0.907754\pi$
$467$	−5.00656	+	8.67162i	−0.231676	+	0.401275i	0.726625	+	0.687034i	$0.241088\pi$
$468$		0			0
$469$	−13.2752	+	20.0047i	−0.612993	+	0.923733i
$470$		0			0
$471$	−0.397374	+	14.0284i	−0.0183100	+	0.646395i
$472$		0			0
$473$	6.98176	−	12.0928i	0.321022	−	0.556026i
$474$		0			0
$475$	2.33416	−	4.04288i	0.107098	−	0.185500i
$476$		0			0
$477$	−37.2562	−	2.11236i	−1.70585	−	0.0967185i
$478$		0			0
$479$	14.7895			0.675749			0.337874	−	0.941191i	$-0.390292\pi$
$479$	14.7895			0.675749			0.337874	+	0.941191i	$0.390292\pi$
$480$		0			0
$481$		−	22.8807i		−	1.04327i
$482$		0			0
$483$	−0.754643	−	1.63252i	−0.0343374	−	0.0742824i
$484$		0			0
$485$	−2.20798	+	3.82434i	−0.100259	+	0.173654i
$486$		0			0
$487$	−12.8101	+	7.39589i	−0.580479	+	0.335140i	−0.761324	−	0.648372i	$-0.775450\pi$
$487$	−12.8101	+	7.39589i	−0.580479	+	0.335140i	0.180845	+	0.983512i	$0.442117\pi$
$488$		0			0
$489$	−0.895686	+	31.6202i	−0.0405043	+	1.42991i
$490$		0			0
$491$	12.5410	−	7.24053i	0.565966	−	0.326760i	−0.189571	−	0.981867i	$-0.560710\pi$
$491$	12.5410	−	7.24053i	0.565966	−	0.326760i	0.755536	+	0.655107i	$0.227376\pi$
$492$		0			0
$493$			24.4360i			1.10054i
$494$		0			0
$495$	1.30264	−	1.98723i	0.0585493	−	0.0893191i
$496$		0			0
$497$	−4.08223	−	0.254575i	−0.183113	−	0.0114193i
$498$		0			0
$499$			8.69119i			0.389071i	0.980895	+	0.194536i	$0.0623200\pi$
$499$			8.69119i			0.389071i	−0.980895	+	0.194536i	$0.937680\pi$
$500$		0			0
$501$	−15.2931	+	24.8367i	−0.683245	+	1.10962i
$502$		0			0
$503$	−40.3239			−1.79795			−0.898977	−	0.437995i	$-0.855689\pi$
$503$	−40.3239			−1.79795			−0.898977	+	0.437995i	$0.855689\pi$
$504$		0			0
$505$	1.96771			0.0875621
$506$		0			0
$507$	15.7236	+	0.445393i	0.698310	+	0.0197806i
$508$		0			0
$509$			3.37858i			0.149753i	0.997193	+	0.0748764i	$0.0238562\pi$
$509$			3.37858i			0.149753i	−0.997193	+	0.0748764i	$0.976144\pi$
$510$		0			0
$511$	−0.737294	−	1.48322i	−0.0326160	−	0.0656137i
$512$		0			0
$513$	−2.81789	+	4.04421i	−0.124413	+	0.178556i
$514$		0			0
$515$		−	1.58084i		−	0.0696601i
$516$		0			0
$517$	−6.81539	+	3.93487i	−0.299741	+	0.173055i
$518$		0			0
$519$	−29.2621	−	18.0181i	−1.28447	−	0.790906i
$520$		0			0
$521$	−34.6315	+	19.9945i	−1.51723	+	0.875976i	−0.517440	+	0.855719i	$0.673115\pi$
$521$	−34.6315	+	19.9945i	−1.51723	+	0.875976i	−0.999795	+	0.0202566i	$0.993552\pi$
$522$		0			0
$523$	−6.43351	+	11.1432i	−0.281318	+	0.487257i	−0.971710	−	0.236179i	$-0.924105\pi$
$523$	−6.43351	+	11.1432i	−0.281318	+	0.487257i	0.690392	+	0.723436i	$0.257438\pi$
$524$		0			0
$525$	−20.4706	+	9.46266i	−0.893411	+	0.412984i
$526$		0			0
$527$		−	17.1943i		−	0.748997i
$528$		0			0
$529$	22.8460			0.993303
$530$		0			0
$531$	15.3974	+	30.5414i	0.668191	+	1.32538i
$532$		0			0
$533$	1.29952	−	2.25083i	0.0562883	−	0.0974942i
$534$		0			0
$535$	0.811103	−	1.40487i	0.0350671	−	0.0607379i
$536$		0			0
$537$	36.6985	+	22.5970i	1.58366	+	0.975131i
$538$		0			0
$539$	−2.45425	+	19.6010i	−0.105712	+	0.844276i
$540$		0			0
$541$	−2.79138	+	4.83481i	−0.120011	+	0.207865i	−0.919772	−	0.392454i	$-0.871626\pi$
$541$	−2.79138	+	4.83481i	−0.120011	+	0.207865i	0.799761	+	0.600319i	$0.204960\pi$
$542$		0			0
$543$	11.1333	−	6.01408i	0.477775	−	0.258089i
$544$		0			0
$545$	2.00701	−	1.15875i	0.0859709	−	0.0496353i
$546$		0			0
$547$	−9.37486	−	5.41258i	−0.400840	−	0.231425i	0.286006	−	0.958228i	$-0.407672\pi$
$547$	−9.37486	−	5.41258i	−0.400840	−	0.231425i	−0.686846	+	0.726803i	$0.741006\pi$
$548$		0			0
$549$	1.89744	−	33.4656i	0.0809807	−	1.42827i
$550$		0			0
$551$	−1.43380	−	2.48341i	−0.0610819	−	0.105797i
$552$		0			0
$553$	−18.1805	−	36.5738i	−0.773114	−	1.55528i
$554$		0			0
$555$	−0.0670223	+	2.36607i	−0.00284494	+	0.100434i
$556$		0			0
$557$	8.38879	+	14.5298i	0.355445	+	0.615648i	0.987194	−	0.159525i	$-0.0509961\pi$
$557$	8.38879	+	14.5298i	0.355445	+	0.615648i	−0.631749	+	0.775173i	$0.717663\pi$
$558$		0			0
$559$	−23.2515			−0.983436
$560$		0			0
$561$	−20.7165	+	33.6445i	−0.874651	+	1.42047i
$562$		0			0
$563$	14.3360	−	24.8307i	0.604192	−	1.04649i	−0.387987	−	0.921665i	$-0.626829\pi$
$563$	14.3360	−	24.8307i	0.604192	−	1.04649i	0.992179	−	0.124826i	$-0.0398374\pi$
$564$		0			0
$565$	−3.14785	+	1.81741i	−0.132431	+	0.0764592i
$566$		0			0
$567$	22.3841	−	8.12120i	0.940042	−	0.341058i
$568$		0			0
$569$	−16.6286	−	28.8015i	−0.697106	−	1.20742i	−0.969466	−	0.245227i	$-0.921137\pi$
$569$	−16.6286	−	28.8015i	−0.697106	−	1.20742i	0.272360	−	0.962195i	$-0.412196\pi$
$570$		0			0
$571$	−28.2309	−	16.2991i	−1.18143	−	0.682097i	−0.225082	−	0.974340i	$-0.572265\pi$
$571$	−28.2309	−	16.2991i	−1.18143	−	0.682097i	−0.956344	+	0.292243i	$0.905598\pi$
$572$		0			0
$573$	12.1230	+	7.46469i	0.506445	+	0.311842i
$574$		0			0
$575$			1.93141i			0.0805455i
$576$		0			0
$577$	11.6155	−	6.70622i	0.483560	−	0.279183i	−0.238339	−	0.971182i	$-0.576603\pi$
$577$	11.6155	−	6.70622i	0.483560	−	0.279183i	0.721899	+	0.691999i	$0.243270\pi$
$578$		0			0
$579$	−33.8822	−	0.959760i	−1.40810	−	0.0398863i
$580$		0			0
$581$	23.4040	+	15.5310i	0.970961	+	0.644334i
$582$		0			0
$583$	30.3993	−	17.5511i	1.25901	−	0.726891i
$584$		0			0
$585$	−3.95028	−	0.223974i	−0.163324	−	0.00926019i
$586$		0			0
$587$	−17.2883	+	29.9443i	−0.713566	+	1.23593i	0.249943	+	0.968260i	$0.419588\pi$
$587$	−17.2883	+	29.9443i	−0.713566	+	1.23593i	−0.963510	+	0.267673i	$0.913745\pi$
$588$		0			0
$589$	1.00889	+	1.74744i	0.0415705	+	0.0720022i
$590$		0			0
$591$	13.4951	+	24.9821i	0.555112	+	1.02763i
$592$		0			0
$593$	16.9169	+	9.76697i	0.694693	+	0.401081i	0.805368	−	0.592775i	$-0.201968\pi$
$593$	16.9169	+	9.76697i	0.694693	+	0.401081i	−0.110675	+	0.993857i	$0.535301\pi$
$594$		0			0
$595$	−5.37509	+	2.67191i	−0.220357	+	0.109538i
$596$		0			0
$597$	−14.2926	+	23.2118i	−0.584956	+	0.949994i
$598$		0			0
$599$	14.5524	+	8.40186i	0.594597	+	0.343291i	0.766913	−	0.641751i	$-0.221792\pi$
$599$	14.5524	+	8.40186i	0.594597	+	0.343291i	−0.172316	+	0.985042i	$0.555125\pi$
$600$		0			0
$601$	−6.18993	−	3.57376i	−0.252492	−	0.145777i	0.368413	−	0.929662i	$-0.379901\pi$
$601$	−6.18993	−	3.57376i	−0.252492	−	0.145777i	−0.620905	+	0.783886i	$0.713235\pi$
$602$		0			0
$603$	−24.3089	+	12.2553i	−0.989933	+	0.499074i
$604$		0			0
$605$		−	0.852167i		−	0.0346455i
$606$		0			0
$607$	17.8635			0.725058			0.362529	−	0.931972i	$-0.381913\pi$
$607$	17.8635			0.725058			0.362529	+	0.931972i	$0.381913\pi$
$608$		0			0
$609$	−1.25336	+	13.7961i	−0.0507886	+	0.559046i
$610$		0			0
$611$	11.3488	+	6.55220i	0.459121	+	0.265074i
$612$		0			0
$613$	9.85193	+	17.0640i	0.397916	+	0.689210i	0.993469	−	0.114106i	$-0.0364003\pi$
$613$	9.85193	+	17.0640i	0.397916	+	0.689210i	−0.595553	+	0.803316i	$0.703067\pi$
$614$		0			0
$615$	−0.140975	+	0.228949i	−0.00568465	+	0.00923213i
$616$		0			0
$617$	−15.2946	−	26.4910i	−0.615738	−	1.06649i	−0.990255	−	0.139269i	$-0.955525\pi$
$617$	−15.2946	−	26.4910i	−0.615738	−	1.06649i	0.374517	−	0.927220i	$-0.377809\pi$
$618$		0			0
$619$	12.8995			0.518475			0.259237	−	0.965814i	$-0.416529\pi$
$619$	12.8995			0.518475			0.259237	+	0.965814i	$0.416529\pi$
$620$		0			0
$621$	0.173044	−	2.03196i	0.00694403	−	0.0815396i
$622$		0			0
$623$	−16.7261	+	25.2049i	−0.670117	+	1.00981i
$624$		0			0
$625$	23.8246			0.952985
$626$		0			0
$627$	0.131287	−	4.63481i	0.00524311	−	0.185096i
$628$		0			0
$629$		−	39.3598i		−	1.56938i
$630$		0			0
$631$		−	16.8826i		−	0.672085i	−0.941847	−	0.336042i	$-0.890911\pi$
$631$		−	16.8826i		−	0.672085i	0.941847	−	0.336042i	$-0.109089\pi$
$632$		0			0
$633$	12.6271	+	7.77507i	0.501881	+	0.309031i
$634$		0			0
$635$	2.18143			0.0865673
$636$		0			0
$637$	30.3095	−	12.7803i	1.20091	−	0.506372i
$638$		0			0
$639$	−3.87875	−	2.54255i	−0.153441	−	0.100582i
$640$		0			0
$641$	12.2901			0.485429			0.242715	−	0.970098i	$-0.421962\pi$
$641$	12.2901			0.485429			0.242715	+	0.970098i	$0.421962\pi$
$642$		0			0
$643$	−20.2664	−	35.1024i	−0.799228	−	1.38430i	−0.920119	−	0.391638i	$-0.871909\pi$
$643$	−20.2664	−	35.1024i	−0.799228	−	1.38430i	0.120891	−	0.992666i	$-0.461425\pi$
$644$		0			0
$645$	2.40442	+	0.0681085i	0.0946739	+	0.00268177i
$646$		0			0
$647$	−12.3850	−	21.4515i	−0.486905	−	0.843344i	0.512982	−	0.858400i	$-0.328541\pi$
$647$	−12.3850	−	21.4515i	−0.486905	−	0.843344i	−0.999887	+	0.0150552i	$0.995208\pi$
$648$		0			0
$649$	−27.8634	−	16.0870i	−1.09374	−	0.631469i
$650$		0			0
$651$	0.881920	−	9.70758i	0.0345652	−	0.380470i
$652$		0			0
$653$	−18.6715			−0.730671			−0.365335	−	0.930876i	$-0.619046\pi$
$653$	−18.6715			−0.730671			−0.365335	+	0.930876i	$0.619046\pi$
$654$		0			0
$655$			2.24123i			0.0875719i
$656$		0			0
$657$	0.106316	−	1.87513i	0.00414780	−	0.0731557i
$658$		0			0
$659$	−39.5720	−	22.8469i	−1.54150	−	0.889988i	−0.998744	−	0.0501010i	$-0.984046\pi$
$659$	−39.5720	−	22.8469i	−1.54150	−	0.889988i	−0.542761	−	0.839887i	$-0.682621\pi$
$660$		0			0
$661$	25.4400	+	14.6878i	0.989501	+	0.571289i	0.905125	−	0.425145i	$-0.139777\pi$
$661$	25.4400	+	14.6878i	0.989501	+	0.571289i	0.0843762	+	0.996434i	$0.473110\pi$
$662$		0			0
$663$	65.7660	+	1.86291i	2.55414	+	0.0723496i
$664$		0			0
$665$	0.389489	−	0.586930i	0.0151038	−	0.0227602i
$666$		0			0
$667$	1.02746	+	0.593203i	0.0397833	+	0.0229689i
$668$		0			0
$669$	−33.3517	−	0.944733i	−1.28945	−	0.0365255i
$670$		0			0
$671$	15.7653	+	27.3063i	0.608613	+	1.05415i
$672$		0			0
$673$	13.3294	−	23.0872i	0.513810	−	0.889945i	−0.486062	−	0.873925i	$-0.661567\pi$
$673$	13.3294	−	23.0872i	0.513810	−	0.889945i	0.999872	−	0.0160205i	$-0.00509972\pi$
$674$		0			0
$675$	−25.4792	−	2.16985i	−0.980696	−	0.0835174i
$676$		0			0
$677$	−40.9678	+	23.6528i	−1.57452	+	0.909050i	−0.578917	+	0.815387i	$0.696524\pi$
$677$	−40.9678	+	23.6528i	−1.57452	+	0.909050i	−0.995604	+	0.0936633i	$0.970142\pi$
$678$		0			0
$679$	23.0176	−	34.6856i	0.883333	−	1.33111i
$680$		0			0
$681$	16.9909	+	31.4536i	0.651093	+	1.20530i
$682$		0			0
$683$	−23.6562	+	13.6579i	−0.905178	+	0.522605i	−0.878877	−	0.477049i	$-0.841706\pi$
$683$	−23.6562	+	13.6579i	−0.905178	+	0.522605i	−0.0263018	+	0.999654i	$0.508373\pi$
$684$		0			0
$685$		−	2.42758i		−	0.0927532i
$686$		0			0
$687$	32.2994	−	17.4478i	1.23230	−	0.665675i
$688$		0			0
$689$	−50.6199	−	29.2254i	−1.92846	−	1.11340i
$690$		0			0
$691$	−19.8841	−	34.4403i	−0.756427	−	1.31017i	−0.944662	−	0.328046i	$-0.893610\pi$
$691$	−19.8841	−	34.4403i	−0.756427	−	1.31017i	0.188235	−	0.982124i	$-0.439723\pi$
$692$		0			0
$693$	−13.4218	+	17.9324i	−0.509851	+	0.681197i
$694$		0			0
$695$	3.49752	−	2.01930i	0.132669	−	0.0765963i
$696$		0			0
$697$	2.23545	−	3.87192i	0.0846738	−	0.146659i
$698$		0			0
$699$	−26.9576	−	0.763610i	−1.01963	−	0.0288824i
$700$		0			0
$701$	−33.5286			−1.26636			−0.633180	−	0.774005i	$-0.718251\pi$
$701$	−33.5286			−1.26636			−0.633180	+	0.774005i	$0.718251\pi$
$702$		0			0
$703$	2.30946	+	4.00010i	0.0871029	+	0.150867i
$704$		0			0
$705$	−1.15437	−	0.710799i	−0.0434761	−	0.0267703i
$706$		0			0
$707$	−18.5132	−	1.15451i	−0.696259	−	0.0434199i
$708$		0			0
$709$	15.1763	+	26.2860i	0.569956	+	0.987193i	0.996570	+	0.0827589i	$0.0263732\pi$
$709$	15.1763	+	26.2860i	0.569956	+	0.987193i	−0.426613	+	0.904434i	$0.640294\pi$
$710$		0			0
$711$	2.62160	−	46.2377i	0.0983175	−	1.73405i
$712$		0			0
$713$	−0.722967	−	0.417405i	−0.0270753	−	0.0156319i
$714$		0			0
$715$	3.22324	−	1.86094i	0.120542	−	0.0695952i
$716$		0			0
$717$	10.8430	+	6.67656i	0.404940	+	0.249341i
$718$		0			0
$719$	−17.8512	+	30.9192i	−0.665737	+	1.15309i	0.313348	+	0.949638i	$0.398549\pi$
$719$	−17.8512	+	30.9192i	−0.665737	+	1.15309i	−0.979085	+	0.203452i	$0.934784\pi$
$720$		0			0
$721$	−0.927523	+	14.8733i	−0.0345427	+	0.553909i
$722$		0			0
$723$	8.76925	−	4.73706i	0.326132	−	0.176173i
$724$		0			0
$725$	7.43832	−	12.8835i	0.276252	−	0.478483i
$726$		0			0
$727$	4.33546	−	7.50924i	0.160793	−	0.278502i	−0.774360	−	0.632745i	$-0.781928\pi$
$727$	4.33546	−	7.50924i	0.160793	−	0.278502i	0.935153	+	0.354243i	$0.115261\pi$
$728$		0			0
$729$	26.6112	+	4.56560i	0.985600	+	0.169096i
$730$		0			0
$731$	−39.9977			−1.47937
$732$		0			0
$733$			4.04828i			0.149527i	0.997201	+	0.0747633i	$0.0238201\pi$
$733$			4.04828i			0.149527i	−0.997201	+	0.0747633i	$0.976180\pi$
$734$		0			0
$735$	−3.17171	+	1.23281i	−0.116990	+	0.0454729i
$736$		0			0
$737$	12.8041	−	22.1774i	0.471646	−	0.816915i
$738$		0			0
$739$	18.5401	−	10.7042i	0.682010	−	0.393759i	−0.118602	−	0.992942i	$-0.537841\pi$
$739$	18.5401	−	10.7042i	0.682010	−	0.393759i	0.800612	+	0.599183i	$0.204508\pi$
$740$		0			0
$741$	−6.79305	+	3.66953i	−0.249549	+	0.134804i
$742$		0			0
$743$	43.3251	−	25.0137i	1.58944	−	0.917665i	0.596044	−	0.802952i	$-0.296738\pi$
$743$	43.3251	−	25.0137i	1.58944	−	0.917665i	0.993399	−	0.114714i	$-0.0365951\pi$
$744$		0			0
$745$			0.299649i			0.0109783i
$746$		0			0
$747$	14.3377	+	28.4395i	0.524590	+	1.04055i
$748$		0			0
$749$	−8.45551	+	12.7418i	−0.308958	+	0.465575i
$750$		0			0
$751$		−	21.3074i		−	0.777516i	−0.921340	−	0.388758i	$-0.872904\pi$
$751$		−	21.3074i		−	0.777516i	0.921340	−	0.388758i	$-0.127096\pi$
$752$		0			0
$753$	−18.1103	−	33.5258i	−0.659976	−	1.22175i
$754$		0			0
$755$	−3.63289			−0.132214
$756$		0			0
$757$	13.2589			0.481904			0.240952	−	0.970537i	$-0.422540\pi$
$757$	13.2589			0.481904			0.240952	+	0.970537i	$0.422540\pi$
$758$		0			0
$759$	0.911736	+	1.68781i	0.0330939	+	0.0612635i
$760$		0			0
$761$			40.2650i			1.45961i	0.683658	+	0.729803i	$0.260388\pi$
$761$			40.2650i			1.45961i	−0.683658	+	0.729803i	$0.739612\pi$
$762$		0			0
$763$	−19.5628	+	9.72447i	−0.708219	+	0.352049i
$764$		0			0
$765$	−6.79534	−	0.385284i	−0.245686	−	0.0139300i
$766$		0			0
$767$			53.5749i			1.93448i
$768$		0			0
$769$	−5.51138	+	3.18199i	−0.198745	+	0.114746i	−0.596070	−	0.802932i	$-0.703272\pi$
$769$	−5.51138	+	3.18199i	−0.198745	+	0.114746i	0.397325	+	0.917678i	$0.369939\pi$
$770$		0			0
$771$	2.21827	−	1.19829i	0.0798891	−	0.0431553i
$772$		0			0
$773$	42.9373	−	24.7899i	1.54435	−	0.891629i	0.545790	−	0.837922i	$-0.316230\pi$
$773$	42.9373	−	24.7899i	1.54435	−	0.891629i	0.998557	−	0.0537073i	$-0.0171038\pi$
$774$		0			0
$775$	−5.23395	+	9.06546i	−0.188009	+	0.325641i
$776$		0			0
$777$	2.01882	−	22.2218i	0.0724247	−	0.797202i
$778$		0			0
$779$			0.524666i			0.0187981i
$780$		0			0
$781$	4.36265			0.156108
$782$		0			0
$783$	−8.97983	+	12.8878i	−0.320913	+	0.460572i
$784$		0			0
$785$	1.13705	−	1.96943i	0.0405831	−	0.0702919i
$786$		0			0
$787$	−14.1133	+	24.4450i	−0.503086	+	0.871370i	0.496908	+	0.867803i	$0.334469\pi$
$787$	−14.1133	+	24.4450i	−0.503086	+	0.871370i	−0.999994	+	0.00356700i	$0.998865\pi$
$788$		0			0
$789$	32.3713	−	17.4866i	1.15245	−	0.622540i
$790$		0			0
$791$	30.6828	−	15.2521i	1.09095	−	0.542303i
$792$		0			0
$793$	26.2518	−	45.4695i	0.932230	−	1.61467i
$794$		0			0
$795$	5.14894	+	3.17045i	0.182614	+	0.112444i
$796$		0			0
$797$	15.6877	−	9.05731i	0.555688	−	0.320826i	−0.195725	−	0.980659i	$-0.562706\pi$
$797$	15.6877	−	9.05731i	0.555688	−	0.320826i	0.751413	+	0.659832i	$0.229373\pi$
$798$		0			0
$799$	19.5223	+	11.2712i	0.690650	+	0.398747i
$800$		0			0
$801$	−30.6279	+	15.4410i	−1.08218	+	0.545582i
$802$		0			0
$803$	0.883355	+	1.53002i	0.0311729	+	0.0539931i
$804$		0			0
$805$	−0.0181390	+	0.290868i	−0.000639317	+	0.0102517i
$806$		0			0
$807$	29.7613	+	18.3254i	1.04765	+	0.645085i
$808$		0			0
$809$	−1.56171	−	2.70496i	−0.0549067	−	0.0951012i	0.837266	−	0.546796i	$-0.184153\pi$
$809$	−1.56171	−	2.70496i	−0.0549067	−	0.0951012i	−0.892172	+	0.451695i	$0.850819\pi$
$810$		0			0
$811$	9.66660			0.339440			0.169720	−	0.985492i	$-0.445714\pi$
$811$	9.66660			0.339440			0.169720	+	0.985492i	$0.445714\pi$
$812$		0			0
$813$	30.0990	+	0.852596i	1.05562	+	0.0299019i
$814$		0			0
$815$	2.56292	−	4.43911i	0.0897753	−	0.155495i
$816$		0			0
$817$	4.06493	−	2.34689i	0.142214	−	0.0821072i
$818$		0			0
$819$	37.0346	+	4.42499i	1.29410	+	0.154622i
$820$		0			0
$821$	−14.4777	−	25.0761i	−0.505275	−	0.875162i	−0.999981	−	0.00610201i	$-0.998058\pi$
$821$	−14.4777	−	25.0761i	−0.505275	−	0.875162i	0.494706	−	0.869060i	$-0.335276\pi$
$822$		0			0
$823$	−34.4646	−	19.8981i	−1.20136	−	0.693605i	−0.240502	−	0.970649i	$-0.577312\pi$
$823$	−34.4646	−	19.8981i	−1.20136	−	0.693605i	−0.960857	+	0.277043i	$0.910645\pi$
$824$		0			0
$825$	21.1638	−	11.4325i	0.736830	−	0.398028i
$826$		0			0
$827$			37.9694i			1.32033i	0.751123	+	0.660163i	$0.229513\pi$
$827$			37.9694i			1.32033i	−0.751123	+	0.660163i	$0.770487\pi$
$828$		0			0
$829$	38.3383	−	22.1346i	1.33154	−	0.768766i	0.346006	−	0.938232i	$-0.387538\pi$
$829$	38.3383	−	22.1346i	1.33154	−	0.768766i	0.985536	+	0.169466i	$0.0542042\pi$
$830$		0			0
$831$	0.933314	+	1.72775i	0.0323763	+	0.0599351i
$832$		0			0
$833$	52.1390	−	21.9848i	1.80651	−	0.761729i
$834$		0			0
$835$	4.09313	−	2.36317i	0.141649	−	0.0817809i
$836$		0			0
$837$	6.31863	−	9.06845i	0.218404	−	0.313452i
$838$		0			0
$839$	16.3128	−	28.2547i	0.563182	−	0.975460i	−0.434034	−	0.900896i	$-0.642910\pi$
$839$	16.3128	−	28.2547i	0.563182	−	0.975460i	0.997216	−	0.0745634i	$-0.0237563\pi$
$840$		0			0
$841$	9.93088	+	17.2008i	0.342444	+	0.593130i
$842$		0			0
$843$	−22.0770	−	0.625362i	−0.760373	−	0.0215386i
$844$		0			0
$845$	−2.20741	−	1.27445i	−0.0759374	−	0.0438425i
$846$		0			0
$847$	−0.499990	+	8.01758i	−0.0171799	+	0.275487i
$848$		0			0
$849$	11.7213	+	0.332022i	0.402274	+	0.0113950i
$850$		0			0
$851$	−1.65495	−	0.955489i	−0.0567311	−	0.0327537i
$852$		0			0
$853$	9.50254	+	5.48629i	0.325361	+	0.187847i	0.653779	−	0.756685i	$-0.273182\pi$
$853$	9.50254	+	5.48629i	0.325361	+	0.187847i	−0.328419	+	0.944532i	$0.606516\pi$
$854$		0			0
$855$	0.713211	−	0.359565i	0.0243913	−	0.0122968i
$856$		0			0
$857$			3.51579i			0.120097i	0.998195	+	0.0600485i	$0.0191255\pi$
$857$			3.51579i			0.120097i	−0.998195	+	0.0600485i	$0.980874\pi$
$858$		0			0
$859$	15.1768			0.517827			0.258913	−	0.965901i	$-0.416636\pi$
$859$	15.1768			0.517827			0.258913	+	0.965901i	$0.416636\pi$
$860$		0			0
$861$	1.46069	−	2.07135i	0.0497801	−	0.0705913i
$862$		0			0
$863$	−29.7041	−	17.1496i	−1.01114	−	0.583781i	−0.0996133	−	0.995026i	$-0.531761\pi$
$863$	−29.7041	−	17.1496i	−1.01114	−	0.583781i	−0.911525	+	0.411245i	$0.865094\pi$
$864$		0			0
$865$	2.78425	+	4.82246i	0.0946673	+	0.163969i
$866$		0			0
$867$	83.6988	+	2.37088i	2.84256	+	0.0805195i
$868$		0			0
$869$	21.7821	+	37.7278i	0.738909	+	1.27983i
$870$		0			0
$871$	−42.6419			−1.44487
$872$		0			0
$873$	42.1484	−	21.2491i	1.42651	−	0.719173i
$874$		0			0
$875$	7.35291	+	0.458540i	0.248574	+	0.0155015i
$876$		0			0
$877$	21.2826			0.718664			0.359332	−	0.933210i	$-0.383005\pi$
$877$	21.2826			0.718664			0.359332	+	0.933210i	$0.383005\pi$
$878$		0			0
$879$	17.9232	+	11.0361i	0.604534	+	0.372240i
$880$		0			0
$881$			20.5029i			0.690761i	0.938463	+	0.345380i	$0.112250\pi$
$881$			20.5029i			0.690761i	−0.938463	+	0.345380i	$0.887750\pi$
$882$		0			0
$883$			39.9687i			1.34506i	0.740072	+	0.672528i	$0.234791\pi$
$883$			39.9687i			1.34506i	−0.740072	+	0.672528i	$0.765209\pi$
$884$		0			0
$885$	0.156932	−	5.54012i	0.00527520	−	0.186229i
$886$		0			0
$887$	−33.3020			−1.11817			−0.559085	−	0.829110i	$-0.688848\pi$
$887$	−33.3020			−1.11817			−0.559085	+	0.829110i	$0.688848\pi$
$888$		0			0
$889$	−20.5239	−	1.27990i	−0.688348	−	0.0429266i
$890$		0			0
$891$	−23.2899	+	10.1315i	−0.780240	+	0.339417i
$892$		0			0
$893$	−2.64538			−0.0885243
$894$		0			0
$895$	−3.49181	−	6.04798i	−0.116718	−	0.202162i
$896$		0			0
$897$	1.67485	−	2.72003i	0.0559216	−	0.0908191i
$898$		0			0
$899$	3.21505	+	5.56863i	0.107228	+	0.185724i
$900$		0			0
$901$	−87.0772	−	50.2741i	−2.90096	−	1.67487i
$902$		0			0
$903$	−22.5819	−	2.05154i	−0.751479	−	0.0682708i
$904$		0			0
$905$	−2.05045			−0.0681592
$906$		0			0
$907$			1.71137i			0.0568250i	0.999596	+	0.0284125i	$0.00904519\pi$
$907$			1.71137i			0.0568250i	−0.999596	+	0.0284125i	$0.990955\pi$
$908$		0			0
$909$	−17.5904	−	11.5306i	−0.583435	−	0.382446i
$910$		0			0
$911$	−7.22479	−	4.17123i	−0.239368	−	0.138199i	0.375518	−	0.926815i	$-0.377465\pi$
$911$	−7.22479	−	4.17123i	−0.239368	−	0.138199i	−0.614886	+	0.788616i	$0.710798\pi$
$912$		0			0
$913$	−25.9458	−	14.9798i	−0.858682	−	0.495760i
$914$		0			0
$915$	−2.84786	+	4.62506i	−0.0941475	+	0.152900i
$916$		0			0
$917$	1.31499	−	21.0865i	0.0434248	−	0.696337i
$918$		0			0
$919$	13.4897	+	7.78828i	0.444984	+	0.256911i	0.705709	−	0.708501i	$-0.250628\pi$
$919$	13.4897	+	7.78828i	0.444984	+	0.256911i	−0.260726	+	0.965413i	$0.583962\pi$
$920$		0			0
$921$	−14.2419	−	26.3647i	−0.469287	−	0.868746i
$922$		0			0
$923$	−3.63226	−	6.29126i	−0.119557	−	0.207079i
$924$		0			0
$925$	−11.9811	+	20.7519i	−0.393937	+	0.682318i
$926$		0			0
$927$	−9.26355	+	14.1319i	−0.304255	+	0.464152i
$928$		0			0
$929$	2.11736	−	1.22246i	0.0694684	−	0.0401076i	−0.464863	−	0.885382i	$-0.653897\pi$
$929$	2.11736	−	1.22246i	0.0694684	−	0.0401076i	0.534332	+	0.845275i	$0.320563\pi$
$930$		0			0
$931$	−4.00886	+	5.29358i	−0.131385	+	0.173490i
$932$		0			0
$933$	−45.8392	−	1.29846i	−1.50071	−	0.0425096i
$934$		0			0
$935$	5.54468	−	3.20122i	0.181330	−	0.104691i
$936$		0			0
$937$			2.32069i			0.0758137i	0.999281	+	0.0379069i	$0.0120690\pi$
$937$			2.32069i			0.0758137i	−0.999281	+	0.0379069i	$0.987931\pi$
$938$		0			0
$939$	−6.58878	−	4.05702i	−0.215017	−	0.132396i
$940$		0			0
$941$	13.7718	+	7.95114i	0.448947	+	0.259200i	0.707386	−	0.706828i	$-0.249875\pi$
$941$	13.7718	+	7.95114i	0.448947	+	0.259200i	−0.258438	+	0.966028i	$0.583208\pi$
$942$		0			0
$943$	−0.108534	−	0.187987i	−0.00353437	−	0.00612171i
$944$		0			0
$945$	−3.81675	−	0.566066i	−0.124159	−	0.0184141i
$946$		0			0
$947$	31.4689	−	18.1686i	1.02260	−	0.590400i	0.107746	−	0.994178i	$-0.465637\pi$
$947$	31.4689	−	18.1686i	1.02260	−	0.590400i	0.914857	+	0.403778i	$0.132303\pi$
$948$		0			0
$949$	1.47093	−	2.54773i	0.0477484	−	0.0827027i
$950$		0			0
$951$	26.7027	−	43.3663i	0.865893	−	1.40625i
$952$		0			0
$953$	−10.1790			−0.329730			−0.164865	−	0.986316i	$-0.552719\pi$
$953$	−10.1790			−0.329730			−0.164865	+	0.986316i	$0.552719\pi$
$954$		0			0
$955$	−1.15348	−	1.99789i	−0.0373259	−	0.0646503i
$956$		0			0
$957$	0.418377	−	14.7699i	0.0135242	−	0.477442i
$958$		0			0
$959$	−1.42433	+	22.8398i	−0.0459940	+	0.737536i
$960$		0			0
$961$	13.2377	+	22.9284i	0.427024	+	0.739627i
$962$		0			0
$963$	−15.4833	+	7.80586i	−0.498941	+	0.251540i
$964$		0			0
$965$	4.75668	+	2.74627i	0.153123	+	0.0884055i
$966$		0			0
$967$	−17.1689	+	9.91247i	−0.552115	+	0.318764i	−0.749974	−	0.661467i	$-0.769934\pi$
$967$	−17.1689	+	9.91247i	−0.552115	+	0.318764i	0.197860	+	0.980230i	$0.436601\pi$
$968$		0			0
$969$	−11.6855	+	6.31240i	−0.375393	+	0.202783i
$970$		0			0
$971$	12.7738	−	22.1249i	0.409931	−	0.710021i	−0.584951	−	0.811069i	$-0.698886\pi$
$971$	12.7738	−	22.1249i	0.409931	−	0.710021i	0.994882	+	0.101048i	$0.0322196\pi$
$972$		0			0
$973$	−34.0911	+	16.9464i	−1.09291	+	0.543276i
$974$		0			0
$975$	−34.1071	−	21.0014i	−1.09230	−	0.672582i
$976$		0			0
$977$	11.3985	−	19.7428i	0.364671	−	0.631629i	−0.624052	−	0.781383i	$-0.714515\pi$
$977$	11.3985	−	19.7428i	0.364671	−	0.631629i	0.988723	+	0.149754i	$0.0478480\pi$
$978$		0			0
$979$	16.1325	−	27.9424i	0.515598	−	0.893041i
$980$		0			0
$981$	−24.7318	−	1.40225i	−0.789626	−	0.0447704i
$982$		0			0
$983$	55.9907			1.78583			0.892914	−	0.450228i	$-0.148657\pi$
$983$	55.9907			1.78583			0.892914	+	0.450228i	$0.148657\pi$
$984$		0			0
$985$		−	4.60102i		−	0.146601i
$986$		0			0
$987$	10.4438	+	7.36483i	0.332430	+	0.234425i
$988$		0			0
$989$	−0.970974	+	1.68178i	−0.0308752	+	0.0534774i
$990$		0			0
$991$	−21.3062	+	12.3011i	−0.676814	+	0.390759i	−0.798653	−	0.601791i	$-0.794454\pi$
$991$	−21.3062	+	12.3011i	−0.676814	+	0.390759i	0.121840	+	0.992550i	$0.461121\pi$
$992$		0			0
$993$	−1.44809	−	0.891655i	−0.0459537	−	0.0282958i
$994$		0			0
$995$	3.82534	−	2.20856i	0.121272	−	0.0700162i
$996$		0			0
$997$		−	40.4343i		−	1.28057i	−0.768139	−	0.640283i	$-0.778817\pi$
$997$		−	40.4343i		−	1.28057i	0.768139	−	0.640283i	$-0.221183\pi$
$998$		0			0
$999$	14.4641	−	20.7587i	0.457623	−	0.656777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bf.g.943.9	yes	24
3.2	odd	2		3024.2.bf.h.2287.6		24
4.3	odd	2		1008.2.bf.h.943.4	yes	24
7.3	odd	6		1008.2.cz.g.367.5	yes	24
9.4	even	3		1008.2.cz.h.607.8	yes	24
9.5	odd	6		3024.2.cz.g.1279.6		24
12.11	even	2		3024.2.bf.g.2287.6		24
21.17	even	6		3024.2.cz.h.2719.6		24
28.3	even	6		1008.2.cz.h.367.8	yes	24
36.23	even	6		3024.2.cz.h.1279.6		24
36.31	odd	6		1008.2.cz.g.607.5	yes	24
63.31	odd	6		1008.2.bf.h.31.4	yes	24
63.59	even	6		3024.2.bf.g.1711.7		24
84.59	odd	6		3024.2.cz.g.2719.6		24
252.31	even	6	inner	1008.2.bf.g.31.9	✓	24
252.59	odd	6		3024.2.bf.h.1711.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.9	✓	24	252.31	even	6	inner
1008.2.bf.g.943.9	yes	24	1.1	even	1	trivial
1008.2.bf.h.31.4	yes	24	63.31	odd	6
1008.2.bf.h.943.4	yes	24	4.3	odd	2
1008.2.cz.g.367.5	yes	24	7.3	odd	6
1008.2.cz.g.607.5	yes	24	36.31	odd	6
1008.2.cz.h.367.8	yes	24	28.3	even	6
1008.2.cz.h.607.8	yes	24	9.4	even	3
3024.2.bf.g.1711.7		24	63.59	even	6
3024.2.bf.g.2287.6		24	12.11	even	2
3024.2.bf.h.1711.7		24	252.59	odd	6
3024.2.bf.h.2287.6		24	3.2	odd	2
3024.2.cz.g.1279.6		24	9.5	odd	6
3024.2.cz.g.2719.6		24	84.59	odd	6
3024.2.cz.h.1279.6		24	36.23	even	6
3024.2.cz.h.2719.6		24	21.17	even	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.823206 + 1.52392i) q^{3} -0.280665i q^{5} +(-0.164674 + 2.64062i) q^{7} +(-1.64466 + 2.50900i) q^{9} -2.82201i q^{11} +(-4.06955 + 2.34956i) q^{13} +(0.427710 - 0.231045i) q^{15} +(-7.00051 + 4.04175i) q^{17} +(0.474304 - 0.821518i) q^{19} +(-4.15966 + 1.92282i) q^{21} +0.392466i q^{23} +4.92123 q^{25} +(-5.17741 - 0.440916i) q^{27} +(1.51148 - 2.61795i) q^{29} +(-1.06355 + 1.84211i) q^{31} +(4.30052 - 2.32310i) q^{33} +(0.741129 + 0.0462181i) q^{35} +(-2.43458 + 4.21681i) q^{37} +(-6.93061 - 4.26750i) q^{39} +(-0.478990 + 0.276545i) q^{41} +(4.28515 + 2.47404i) q^{43} +(0.704187 + 0.461599i) q^{45} +(-1.39435 - 2.41508i) q^{47} +(-6.94577 - 0.869682i) q^{49} +(-11.9222 - 7.34103i) q^{51} +(6.21935 + 10.7722i) q^{53} -0.792039 q^{55} +(1.64238 + 0.0465226i) q^{57} +(5.70053 - 9.87361i) q^{59} +(-9.67619 + 5.58655i) q^{61} +(-6.35448 - 4.75610i) q^{63} +(0.659437 + 1.14218i) q^{65} +(7.85871 + 4.53723i) q^{67} +(-0.598086 + 0.323080i) q^{69} +1.54594i q^{71} +(-0.542172 + 0.313023i) q^{73} +(4.05118 + 7.49956i) q^{75} +(7.45187 + 0.464711i) q^{77} +(-13.3691 + 7.71866i) q^{79} +(-3.59015 - 8.25293i) q^{81} +(5.30821 - 9.19409i) q^{83} +(1.13438 + 1.96480i) q^{85} +(5.23381 + 0.148255i) q^{87} +(9.90157 + 5.71667i) q^{89} +(-5.53414 - 11.1331i) q^{91} +(-3.68275 - 0.104319i) q^{93} +(-0.230571 - 0.133120i) q^{95} +(-13.6260 - 7.86698i) q^{97} +(7.08043 + 4.64126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 8 q^{7} - q^{9} + 3 q^{13} - 6 q^{15} - 3 q^{17} + 4 q^{19} - 20 q^{21} - 30 q^{25} - 9 q^{27} + 18 q^{29} + 17 q^{31} - 12 q^{33} + 42 q^{35} - 3 q^{37} - 42 q^{39} - 36 q^{41} + 24 q^{43}+ \cdots + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 8 * q^7 - q^9 + 3 * q^13 - 6 * q^15 - 3 * q^17 + 4 * q^19 - 20 * q^21 - 30 * q^25 - 9 * q^27 + 18 * q^29 + 17 * q^31 - 12 * q^33 + 42 * q^35 - 3 * q^37 - 42 * q^39 - 36 * q^41 + 24 * q^43 + 12 * q^45 - 21 * q^47 - 24 * q^49 + 18 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 - 6 * q^59 - 48 * q^61 - 6 * q^63 + 42 * q^67 - 6 * q^69 + 48 * q^73 - 33 * q^75 + 36 * q^77 - 30 * q^79 + 23 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 - 8 * q^93 - 33 * q^95 - 3 * q^97 + 30 * q^99

Introduction

L-functions

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