LMFDB - Embedded newform 1680.2.di.g.529.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(289,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.di (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,2,0,0,0,12,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.4
Character	$\chi$	$=$	1680.529
Dual form			1680.2.di.g.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{3} +(-0.301966 + 2.21558i) q^{5} +(2.64327 + 0.114495i) q^{7} +(0.500000 + 0.866025i) q^{9} +(3.21893 - 5.57535i) q^{11} -3.47412i q^{13} +(1.36930 - 1.76777i) q^{15} +(-1.70960 - 0.987038i) q^{17} +(2.21415 + 3.83501i) q^{19} +(-2.23189 - 1.42079i) q^{21} +(-1.75450 + 1.01296i) q^{23} +(-4.81763 - 1.33806i) q^{25} -1.00000i q^{27} -6.25115 q^{29} +(3.03554 - 5.25771i) q^{31} +(-5.57535 + 3.21893i) q^{33} +(-1.05185 + 5.82182i) q^{35} +(-0.679339 + 0.392216i) q^{37} +(-1.73706 + 3.00867i) q^{39} +10.2120 q^{41} -9.76386i q^{43} +(-2.06974 + 0.846282i) q^{45} +(-1.48055 + 0.854794i) q^{47} +(6.97378 + 0.605281i) q^{49} +(0.987038 + 1.70960i) q^{51} +(-5.64578 - 3.25959i) q^{53} +(11.3807 + 8.81538i) q^{55} -4.42829i q^{57} +(5.83826 - 10.1122i) q^{59} +(2.46412 + 4.26799i) q^{61} +(1.22248 + 2.34639i) q^{63} +(7.69720 + 1.04906i) q^{65} +(9.35985 + 5.40391i) q^{67} +2.02592 q^{69} -10.4314 q^{71} +(4.41578 + 2.54945i) q^{73} +(3.50316 + 3.56761i) q^{75} +(9.14686 - 14.3686i) q^{77} +(2.72865 + 4.72617i) q^{79} +(-0.500000 + 0.866025i) q^{81} -15.3100i q^{83} +(2.70311 - 3.48971i) q^{85} +(5.41365 + 3.12557i) q^{87} +(5.07049 + 8.78234i) q^{89} +(0.397768 - 9.18304i) q^{91} +(-5.25771 + 3.03554i) q^{93} +(-9.16539 + 3.74758i) q^{95} +9.93481i q^{97} +6.43786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5} + 12 q^{9} + 8 q^{11} - 8 q^{19} + 12 q^{21} + 2 q^{25} - 24 q^{29} - 4 q^{31} - 30 q^{35} - 4 q^{39} + 32 q^{41} - 2 q^{45} - 12 q^{49} + 20 q^{51} - 12 q^{55} + 4 q^{59} + 32 q^{61} + 22 q^{65}+ \cdots + 16 q^{99}+O(q^{100}) $ 24 * q + 2 * q^5 + 12 * q^9 + 8 * q^11 - 8 * q^19 + 12 * q^21 + 2 * q^25 - 24 * q^29 - 4 * q^31 - 30 * q^35 - 4 * q^39 + 32 * q^41 - 2 * q^45 - 12 * q^49 + 20 * q^51 - 12 * q^55 + 4 * q^59 + 32 * q^61 + 22 * q^65 + 56 * q^69 - 72 * q^71 + 16 * q^75 - 20 * q^79 - 12 * q^81 + 8 * q^85 + 24 * q^89 - 8 * q^91 + 18 * q^95 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	−0.301966	+	2.21558i	−0.135043	+	0.990840i
$5$	−0.301966	+	2.21558i	−0.135043	+	0.990840i
$6$		0			0
$7$	2.64327	+	0.114495i	0.999063	+	0.0432749i
$7$	2.64327	+	0.114495i	0.999063	+	0.0432749i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	3.21893	−	5.57535i	0.970545	−	1.68103i	0.276628	−	0.960977i	$-0.410783\pi$
$11$	3.21893	−	5.57535i	0.970545	−	1.68103i	0.693917	−	0.720055i	$-0.255884\pi$
$12$		0			0
$13$		−	3.47412i		−	0.963547i	−0.876296	−	0.481773i	$-0.839993\pi$
$13$		−	3.47412i		−	0.963547i	0.876296	−	0.481773i	$-0.160007\pi$
$14$		0			0
$15$	1.36930	−	1.76777i	0.353552	−	0.456436i
$16$		0			0
$17$	−1.70960	−	0.987038i	−0.414639	−	0.239392i	0.278142	−	0.960540i	$-0.410281\pi$
$17$	−1.70960	−	0.987038i	−0.414639	−	0.239392i	−0.692781	+	0.721148i	$0.743615\pi$
$18$		0			0
$19$	2.21415	+	3.83501i	0.507960	+	0.879812i	0.999958	+	0.00921562i	$0.00293346\pi$
$19$	2.21415	+	3.83501i	0.507960	+	0.879812i	−0.491998	+	0.870596i	$0.663733\pi$
$20$		0			0
$21$	−2.23189	−	1.42079i	−0.487039	−	0.310042i
$22$		0			0
$23$	−1.75450	+	1.01296i	−0.365839	+	0.211217i	−0.671639	−	0.740879i	$-0.734409\pi$
$23$	−1.75450	+	1.01296i	−0.365839	+	0.211217i	0.305800	+	0.952096i	$0.401076\pi$
$24$		0			0
$25$	−4.81763	−	1.33806i	−0.963527	−	0.267612i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−6.25115			−1.16081			−0.580405	−	0.814328i	$-0.697106\pi$
$29$	−6.25115			−1.16081			−0.580405	+	0.814328i	$0.697106\pi$
$30$		0			0
$31$	3.03554	−	5.25771i	0.545199	−	0.944312i	−0.453395	−	0.891310i	$-0.649787\pi$
$31$	3.03554	−	5.25771i	0.545199	−	0.944312i	0.998594	−	0.0530029i	$-0.0168793\pi$
$32$		0			0
$33$	−5.57535	+	3.21893i	−0.970545	+	0.560344i
$34$		0			0
$35$	−1.05185	+	5.82182i	−0.177795	+	0.984068i
$36$		0			0
$37$	−0.679339	+	0.392216i	−0.111683	+	0.0644800i	−0.554801	−	0.831983i	$-0.687206\pi$
$37$	−0.679339	+	0.392216i	−0.111683	+	0.0644800i	0.443118	+	0.896463i	$0.353872\pi$
$38$		0			0
$39$	−1.73706	+	3.00867i	−0.278152	+	0.481773i
$40$		0			0
$41$	10.2120			1.59484			0.797421	−	0.603424i	$-0.206197\pi$
$41$	10.2120			1.59484			0.797421	+	0.603424i	$0.206197\pi$
$42$		0			0
$43$		−	9.76386i		−	1.48897i	−0.667637	−	0.744487i	$-0.732694\pi$
$43$		−	9.76386i		−	1.48897i	0.667637	−	0.744487i	$-0.267306\pi$
$44$		0			0
$45$	−2.06974	+	0.846282i	−0.308538	+	0.126156i
$46$		0			0
$47$	−1.48055	+	0.854794i	−0.215960	+	0.124685i	−0.604078	−	0.796925i	$-0.706459\pi$
$47$	−1.48055	+	0.854794i	−0.215960	+	0.124685i	0.388118	+	0.921610i	$0.373125\pi$
$48$		0			0
$49$	6.97378	+	0.605281i	0.996255	+	0.0864687i
$50$		0			0
$51$	0.987038	+	1.70960i	0.138213	+	0.239392i
$52$		0			0
$53$	−5.64578	−	3.25959i	−0.775508	−	0.447740i	0.0593279	−	0.998239i	$-0.481104\pi$
$53$	−5.64578	−	3.25959i	−0.775508	−	0.447740i	−0.834836	+	0.550499i	$0.814438\pi$
$54$		0			0
$55$	11.3807	+	8.81538i	1.53457	+	1.18867i
$56$		0			0
$57$		−	4.42829i		−	0.586541i
$58$		0			0
$59$	5.83826	−	10.1122i	0.760076	−	1.31649i	−0.182735	−	0.983162i	$-0.558495\pi$
$59$	5.83826	−	10.1122i	0.760076	−	1.31649i	0.942811	−	0.333328i	$-0.108172\pi$
$60$		0			0
$61$	2.46412	+	4.26799i	0.315499	+	0.546460i	0.979543	−	0.201233i	$-0.0644949\pi$
$61$	2.46412	+	4.26799i	0.315499	+	0.546460i	−0.664045	+	0.747693i	$0.731162\pi$
$62$		0			0
$63$	1.22248	+	2.34639i	0.154018	+	0.295617i
$64$		0			0
$65$	7.69720	+	1.04906i	0.954721	+	0.130120i
$66$		0			0
$67$	9.35985	+	5.40391i	1.14349	+	0.660193i	0.947292	−	0.320372i	$-0.103808\pi$
$67$	9.35985	+	5.40391i	1.14349	+	0.660193i	0.196196	+	0.980565i	$0.437141\pi$
$68$		0			0
$69$	2.02592			0.243893
$70$		0			0
$71$	−10.4314			−1.23798			−0.618989	−	0.785400i	$-0.712457\pi$
$71$	−10.4314			−1.23798			−0.618989	+	0.785400i	$0.712457\pi$
$72$		0			0
$73$	4.41578	+	2.54945i	0.516828	+	0.298391i	0.735636	−	0.677377i	$-0.236883\pi$
$73$	4.41578	+	2.54945i	0.516828	+	0.298391i	−0.218808	+	0.975768i	$0.570217\pi$
$74$		0			0
$75$	3.50316	+	3.56761i	0.404510	+	0.411952i
$76$		0			0
$77$	9.14686	−	14.3686i	1.04238	−	1.63746i
$78$		0			0
$79$	2.72865	+	4.72617i	0.306997	+	0.531735i	0.977704	−	0.209988i	$-0.0673423\pi$
$79$	2.72865	+	4.72617i	0.306997	+	0.531735i	−0.670707	+	0.741723i	$0.734009\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	15.3100i		−	1.68050i	−0.542203	−	0.840248i	$-0.682410\pi$
$83$		−	15.3100i		−	1.68050i	0.542203	−	0.840248i	$-0.317590\pi$
$84$		0			0
$85$	2.70311	−	3.48971i	0.293193	−	0.378512i
$86$		0			0
$87$	5.41365	+	3.12557i	0.580405	+	0.335097i
$88$		0			0
$89$	5.07049	+	8.78234i	0.537470	+	0.930926i	0.999039	+	0.0438217i	$0.0139534\pi$
$89$	5.07049	+	8.78234i	0.537470	+	0.930926i	−0.461569	+	0.887104i	$0.652713\pi$
$90$		0			0
$91$	0.397768	−	9.18304i	0.0416974	−	0.962644i
$92$		0			0
$93$	−5.25771	+	3.03554i	−0.545199	+	0.314771i
$94$		0			0
$95$	−9.16539	+	3.74758i	−0.940349	+	0.384494i
$96$		0			0
$97$			9.93481i			1.00873i	0.863491	+	0.504364i	$0.168273\pi$
$97$			9.93481i			1.00873i	−0.863491	+	0.504364i	$0.831727\pi$
$98$		0			0
$99$	6.43786			0.647030
$100$		0			0
$101$	−1.54884	+	2.68267i	−0.154115	+	0.266935i	−0.932736	−	0.360559i	$-0.882586\pi$
$101$	−1.54884	+	2.68267i	−0.154115	+	0.266935i	0.778621	+	0.627494i	$0.215919\pi$
$102$		0			0
$103$	13.2104	−	7.62702i	1.30166	−	0.751512i	0.320969	−	0.947090i	$-0.395991\pi$
$103$	13.2104	−	7.62702i	1.30166	−	0.751512i	0.980688	+	0.195578i	$0.0626581\pi$
$104$		0			0
$105$	3.82184	−	4.51592i	0.372973	−	0.440709i
$106$		0			0
$107$	−2.05902	+	1.18877i	−0.199053	+	0.114923i	−0.596213	−	0.802826i	$-0.703329\pi$
$107$	−2.05902	+	1.18877i	−0.199053	+	0.114923i	0.397161	+	0.917749i	$0.369995\pi$
$108$		0			0
$109$	7.20382	−	12.4774i	0.690000	−	1.19512i	−0.281837	−	0.959462i	$-0.590944\pi$
$109$	7.20382	−	12.4774i	0.690000	−	1.19512i	0.971837	−	0.235653i	$-0.0757230\pi$
$110$		0			0
$111$	0.784433			0.0744551
$112$		0			0
$113$			5.38555i			0.506630i	0.967384	+	0.253315i	$0.0815210\pi$
$113$			5.38555i			0.506630i	−0.967384	+	0.253315i	$0.918479\pi$
$114$		0			0
$115$	−1.71450	−	4.19313i	−0.159878	−	0.391011i
$116$		0			0
$117$	3.00867	−	1.73706i	0.278152	−	0.160591i
$118$		0			0
$119$	−4.40593	−	2.80475i	−0.403891	−	0.257111i
$120$		0			0
$121$	−15.2230	−	26.3671i	−1.38391	−	2.39701i
$122$		0			0
$123$	−8.84382	−	5.10598i	−0.797421	−	0.460391i
$124$		0			0
$125$	4.41935	−	10.2698i	0.395279	−	0.918561i
$126$		0			0
$127$		−	11.2482i		−	0.998118i	−0.866568	−	0.499059i	$-0.833679\pi$
$127$		−	11.2482i		−	0.998118i	0.866568	−	0.499059i	$-0.166321\pi$
$128$		0			0
$129$	−4.88193	+	8.45575i	−0.429830	+	0.744487i
$130$		0			0
$131$	−5.40870	−	9.36814i	−0.472560	−	0.818498i	0.526947	−	0.849898i	$-0.323337\pi$
$131$	−5.40870	−	9.36814i	−0.472560	−	0.818498i	−0.999507	+	0.0314000i	$0.990003\pi$
$132$		0			0
$133$	5.41350	+	10.3905i	0.469410	+	0.900970i
$134$		0			0
$135$	2.21558	+	0.301966i	0.190687	+	0.0259891i
$136$		0			0
$137$	−1.21943	−	0.704037i	−0.104183	−	0.0601500i	0.447003	−	0.894532i	$-0.352491\pi$
$137$	−1.21943	−	0.704037i	−0.104183	−	0.0601500i	−0.551186	+	0.834382i	$0.685825\pi$
$138$		0			0
$139$	5.36340			0.454917			0.227459	−	0.973788i	$-0.426958\pi$
$139$	5.36340			0.454917			0.227459	+	0.973788i	$0.426958\pi$
$140$		0			0
$141$	1.70959			0.143973
$142$		0			0
$143$	−19.3694	−	11.1829i	−1.61975	−	0.935165i
$144$		0			0
$145$	1.88763	−	13.8500i	0.156759	−	1.15018i
$146$		0			0
$147$	−5.73683	−	4.01108i	−0.473166	−	0.330828i
$148$		0			0
$149$	−1.46209	−	2.53241i	−0.119779	−	0.207463i	0.799901	−	0.600132i	$-0.204885\pi$
$149$	−1.46209	−	2.53241i	−0.119779	−	0.207463i	−0.919680	+	0.392669i	$0.871552\pi$
$150$		0			0
$151$	−3.52450	+	6.10462i	−0.286820	+	0.496787i	−0.973049	−	0.230599i	$-0.925931\pi$
$151$	−3.52450	+	6.10462i	−0.286820	+	0.496787i	0.686229	+	0.727386i	$0.259265\pi$
$152$		0			0
$153$		−	1.97408i		−	0.159595i
$154$		0			0
$155$	10.7323	+	8.31314i	0.862037	+	0.667728i
$156$		0			0
$157$	2.96645	+	1.71268i	0.236749	+	0.136687i	0.613681	−	0.789554i	$-0.289688\pi$
$157$	2.96645	+	1.71268i	0.236749	+	0.136687i	−0.376933	+	0.926241i	$0.623021\pi$
$158$		0			0
$159$	3.25959	+	5.64578i	0.258503	+	0.447740i
$160$		0			0
$161$	−4.75361	+	2.47665i	−0.374637	+	0.195188i
$162$		0			0
$163$	2.53536	−	1.46379i	0.198584	−	0.114653i	−0.397411	−	0.917641i	$-0.630091\pi$
$163$	2.53536	−	1.46379i	0.198584	−	0.114653i	0.595995	+	0.802988i	$0.296758\pi$
$164$		0			0
$165$	−5.44825	−	13.3247i	−0.424146	−	1.03732i
$166$		0			0
$167$			22.1196i			1.71167i	0.517250	+	0.855835i	$0.326956\pi$
$167$			22.1196i			1.71167i	−0.517250	+	0.855835i	$0.673044\pi$
$168$		0			0
$169$	0.930504			0.0715773
$170$		0			0
$171$	−2.21415	+	3.83501i	−0.169320	+	0.293271i
$172$		0			0
$173$	11.4022	−	6.58307i	0.866894	−	0.500502i	0.000579200	−	1.00000i	$-0.499816\pi$
$173$	11.4022	−	6.58307i	0.866894	−	0.500502i	0.866315	+	0.499498i	$0.166482\pi$
$174$		0			0
$175$	−12.5811	−	4.08846i	−0.951043	−	0.309058i
$176$		0			0
$177$	−10.1122	+	5.83826i	−0.760076	+	0.438830i
$178$		0			0
$179$	1.15724	−	2.00439i	0.0864960	−	0.149815i	−0.819532	−	0.573034i	$-0.805766\pi$
$179$	1.15724	−	2.00439i	0.0864960	−	0.149815i	0.906028	+	0.423218i	$0.139100\pi$
$180$		0			0
$181$	3.06205			0.227600			0.113800	−	0.993504i	$-0.463698\pi$
$181$	3.06205			0.227600			0.113800	+	0.993504i	$0.463698\pi$
$182$		0			0
$183$		−	4.92825i		−	0.364307i
$184$		0			0
$185$	−0.663852	−	1.62357i	−0.0488073	−	0.119367i
$186$		0			0
$187$	−11.0062	+	6.35442i	−0.804851	+	0.464681i
$188$		0			0
$189$	0.114495	−	2.64327i	0.00832826	−	0.192270i
$190$		0			0
$191$	12.7838	+	22.1421i	0.925000	+	1.60215i	0.791560	+	0.611091i	$0.209269\pi$
$191$	12.7838	+	22.1421i	0.925000	+	1.60215i	0.133440	+	0.991057i	$0.457398\pi$
$192$		0			0
$193$	18.8184	+	10.8648i	1.35458	+	0.782065i	0.988887	−	0.148672i	$-0.0474997\pi$
$193$	18.8184	+	10.8648i	1.35458	+	0.782065i	0.365690	+	0.930737i	$0.380833\pi$
$194$		0			0
$195$	−6.14144	−	4.75712i	−0.439798	−	0.340664i
$196$		0			0
$197$			11.2646i			0.802567i	0.915954	+	0.401284i	$0.131436\pi$
$197$			11.2646i			0.802567i	−0.915954	+	0.401284i	$0.868564\pi$
$198$		0			0
$199$	−3.59544	+	6.22748i	−0.254874	+	0.441454i	−0.964861	−	0.262760i	$-0.915367\pi$
$199$	−3.59544	+	6.22748i	−0.254874	+	0.441454i	0.709987	+	0.704214i	$0.248701\pi$
$200$		0			0
$201$	−5.40391	−	9.35985i	−0.381163	−	0.660193i
$202$		0			0
$203$	−16.5235	−	0.715723i	−1.15972	−	0.0502339i
$204$		0			0
$205$	−3.08367	+	22.6255i	−0.215373	+	1.58023i
$206$		0			0
$207$	−1.75450	−	1.01296i	−0.121946	−	0.0704057i
$208$		0			0
$209$	28.5087			1.97199
$210$		0			0
$211$	0.684937			0.0471530			0.0235765	−	0.999722i	$-0.492495\pi$
$211$	0.684937			0.0471530			0.0235765	+	0.999722i	$0.492495\pi$
$212$		0			0
$213$	9.03384	+	5.21569i	0.618989	+	0.357373i
$214$		0			0
$215$	21.6327	+	2.94835i	1.47533	+	0.201076i
$216$		0			0
$217$	8.62574	−	13.5500i	0.585553	−	0.919834i
$218$		0			0
$219$	−2.54945	−	4.41578i	−0.172276	−	0.298391i
$220$		0			0
$221$	−3.42909	+	5.93935i	−0.230665	+	0.399524i
$222$		0			0
$223$			11.8453i			0.793218i	0.917988	+	0.396609i	$0.129813\pi$
$223$			11.8453i			0.793218i	−0.917988	+	0.396609i	$0.870187\pi$
$224$		0			0
$225$	−1.25002	−	4.84122i	−0.0833347	−	0.322748i
$226$		0			0
$227$	−18.7577	−	10.8298i	−1.24499	−	0.718798i	−0.274888	−	0.961476i	$-0.588641\pi$
$227$	−18.7577	−	10.8298i	−1.24499	−	0.718798i	−0.970107	+	0.242678i	$0.921974\pi$
$228$		0			0
$229$	−6.72719	−	11.6518i	−0.444545	−	0.769975i	0.553475	−	0.832866i	$-0.313301\pi$
$229$	−6.72719	−	11.6518i	−0.444545	−	0.769975i	−0.998020	+	0.0628908i	$0.979968\pi$
$230$		0			0
$231$	−15.1057	+	7.87017i	−0.993884	+	0.517819i
$232$		0			0
$233$	−11.7539	+	6.78613i	−0.770026	+	0.444574i	−0.832884	−	0.553448i	$-0.813312\pi$
$233$	−11.7539	+	6.78613i	−0.770026	+	0.444574i	0.0628582	+	0.998022i	$0.479978\pi$
$234$		0			0
$235$	−1.44679	−	3.53840i	−0.0943785	−	0.230820i
$236$		0			0
$237$		−	5.45731i		−	0.354490i
$238$		0			0
$239$	−16.0434			−1.03776			−0.518880	−	0.854847i	$-0.673651\pi$
$239$	−16.0434			−1.03776			−0.518880	+	0.854847i	$0.673651\pi$
$240$		0			0
$241$	−6.72757	+	11.6525i	−0.433361	+	0.750603i	−0.997160	−	0.0753089i	$-0.976006\pi$
$241$	−6.72757	+	11.6525i	−0.433361	+	0.750603i	0.563800	+	0.825912i	$0.309339\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−3.44690	+	15.2682i	−0.220214	+	0.975452i
$246$		0			0
$247$	13.3233	−	7.69220i	0.847740	−	0.489443i
$248$		0			0
$249$	−7.65502	+	13.2589i	−0.485117	+	0.840248i
$250$		0			0
$251$	−14.9463			−0.943405			−0.471703	−	0.881758i	$-0.656360\pi$
$251$	−14.9463			−0.943405			−0.471703	+	0.881758i	$0.656360\pi$
$252$		0			0
$253$			13.0426i			0.819983i
$254$		0			0
$255$	−4.08582	+	1.67063i	−0.255864	+	0.104619i
$256$		0			0
$257$	3.78296	−	2.18409i	0.235974	−	0.136240i	−0.377351	−	0.926070i	$-0.623165\pi$
$257$	3.78296	−	2.18409i	0.235974	−	0.136240i	0.613325	+	0.789831i	$0.289832\pi$
$258$		0			0
$259$	−1.84058	+	0.958954i	−0.114368	+	0.0595865i
$260$		0			0
$261$	−3.12557	−	5.41365i	−0.193468	−	0.335097i
$262$		0			0
$263$	10.6269	+	6.13542i	0.655280	+	0.378326i	0.790476	−	0.612493i	$-0.209833\pi$
$263$	10.6269	+	6.13542i	0.655280	+	0.378326i	−0.135196	+	0.990819i	$0.543166\pi$
$264$		0			0
$265$	8.92674	−	11.5244i	0.548365	−	0.707940i
$266$		0			0
$267$		−	10.1410i		−	0.620617i
$268$		0			0
$269$	−6.52845	+	11.3076i	−0.398047	+	0.689437i	−0.993485	−	0.113964i	$-0.963645\pi$
$269$	−6.52845	+	11.3076i	−0.398047	+	0.689437i	0.595438	+	0.803401i	$0.296978\pi$
$270$		0			0
$271$	−11.9787	−	20.7477i	−0.727655	−	1.26034i	−0.957872	−	0.287196i	$-0.907277\pi$
$271$	−11.9787	−	20.7477i	−0.727655	−	1.26034i	0.230217	−	0.973139i	$-0.426057\pi$
$272$		0			0
$273$	−4.93600	+	7.75386i	−0.298740	+	0.469285i
$274$		0			0
$275$	−22.9678	+	22.5529i	−1.38501	+	1.35999i
$276$		0			0
$277$	10.0980	+	5.83008i	0.606730	+	0.350296i	0.771684	−	0.636006i	$-0.219414\pi$
$277$	10.0980	+	5.83008i	0.606730	+	0.350296i	−0.164955	+	0.986301i	$0.552748\pi$
$278$		0			0
$279$	6.07108			0.363466
$280$		0			0
$281$	−3.15318			−0.188103			−0.0940514	−	0.995567i	$-0.529982\pi$
$281$	−3.15318			−0.188103			−0.0940514	+	0.995567i	$0.529982\pi$
$282$		0			0
$283$	5.85224	+	3.37879i	0.347880	+	0.200848i	0.663751	−	0.747954i	$-0.268963\pi$
$283$	5.85224	+	3.37879i	0.347880	+	0.200848i	−0.315871	+	0.948802i	$0.602297\pi$
$284$		0			0
$285$	9.81125	+	1.33719i	0.581168	+	0.0792084i
$286$		0			0
$287$	26.9930	+	1.16922i	1.59335	+	0.0690166i
$288$		0			0
$289$	−6.55151	−	11.3476i	−0.385383	−	0.667503i
$290$		0			0
$291$	4.96741	−	8.60380i	0.291195	−	0.504364i
$292$		0			0
$293$			23.8213i			1.39166i	0.718209	+	0.695828i	$0.244962\pi$
$293$			23.8213i			1.39166i	−0.718209	+	0.695828i	$0.755038\pi$
$294$		0			0
$295$	20.6414	+	15.9887i	1.20179	+	0.930897i
$296$		0			0
$297$	−5.57535	−	3.21893i	−0.323515	−	0.186781i
$298$		0			0
$299$	3.51915	+	6.09535i	0.203518	+	0.352503i
$300$		0			0
$301$	1.11791	−	25.8085i	0.0644352	−	1.48758i
$302$		0			0
$303$	2.68267	−	1.54884i	0.154115	−	0.0889784i
$304$		0			0
$305$	−10.2002	+	4.17069i	−0.584060	+	0.238813i
$306$		0			0
$307$			33.0935i			1.88875i	0.328878	+	0.944373i	$0.393330\pi$
$307$			33.0935i			1.88875i	−0.328878	+	0.944373i	$0.606670\pi$
$308$		0			0
$309$	−15.2540			−0.867771
$310$		0			0
$311$	6.09688	−	10.5601i	0.345722	−	0.598809i	−0.639762	−	0.768573i	$-0.720967\pi$
$311$	6.09688	−	10.5601i	0.345722	−	0.598809i	0.985485	+	0.169764i	$0.0543006\pi$
$312$		0			0
$313$	−5.06300	+	2.92313i	−0.286178	+	0.165225i	−0.636217	−	0.771510i	$-0.719502\pi$
$313$	−5.06300	+	2.92313i	−0.286178	+	0.165225i	0.350039	+	0.936735i	$0.386168\pi$
$314$		0			0
$315$	−5.56777	+	1.99998i	−0.313708	+	0.112686i
$316$		0			0
$317$	−5.53273	+	3.19432i	−0.310749	+	0.179411i	−0.647262	−	0.762268i	$-0.724086\pi$
$317$	−5.53273	+	3.19432i	−0.310749	+	0.179411i	0.336513	+	0.941679i	$0.390753\pi$
$318$		0			0
$319$	−20.1220	+	34.8524i	−1.12662	+	1.95136i
$320$		0			0
$321$	2.37755			0.132702
$322$		0			0
$323$		−	8.74178i		−	0.486406i
$324$		0			0
$325$	−4.64859	+	16.7370i	−0.257857	+	0.928403i
$326$		0			0
$327$	−12.4774	+	7.20382i	−0.690000	+	0.398372i
$328$		0			0
$329$	−4.01136	+	2.08994i	−0.221153	+	0.115222i
$330$		0			0
$331$	−11.6288	−	20.1417i	−0.639179	−	1.10709i	−0.985613	−	0.169016i	$-0.945941\pi$
$331$	−11.6288	−	20.1417i	−0.639179	−	1.10709i	0.346434	−	0.938074i	$-0.387392\pi$
$332$		0			0
$333$	−0.679339	−	0.392216i	−0.0372275	−	0.0214933i
$334$		0			0
$335$	−14.7992	+	19.1057i	−0.808566	+	1.04386i
$336$		0			0
$337$		−	26.1745i		−	1.42581i	−0.701259	−	0.712907i	$-0.747378\pi$
$337$		−	26.1745i		−	1.42581i	0.701259	−	0.712907i	$-0.252622\pi$
$338$		0			0
$339$	2.69278	−	4.66403i	0.146252	−	0.253315i
$340$		0			0
$341$	−19.5424	−	33.8484i	−1.05828	−	1.83299i
$342$		0			0
$343$	18.3643	+	2.39838i	0.991579	+	0.129501i
$344$		0			0
$345$	−0.611760	+	4.48861i	−0.0329360	+	0.241658i
$346$		0			0
$347$	−1.39822	−	0.807265i	−0.0750606	−	0.0433362i	0.462000	−	0.886880i	$-0.347132\pi$
$347$	−1.39822	−	0.807265i	−0.0750606	−	0.0433362i	−0.537061	+	0.843544i	$0.680465\pi$
$348$		0			0
$349$	9.09023			0.486589			0.243294	−	0.969953i	$-0.421772\pi$
$349$	9.09023			0.486589			0.243294	+	0.969953i	$0.421772\pi$
$350$		0			0
$351$	−3.47412			−0.185435
$352$		0			0
$353$	6.37068	+	3.67811i	0.339077	+	0.195766i	0.659864	−	0.751385i	$-0.270614\pi$
$353$	6.37068	+	3.67811i	0.339077	+	0.195766i	−0.320787	+	0.947151i	$0.603947\pi$
$354$		0			0
$355$	3.14992	−	23.1116i	0.167180	−	1.22664i
$356$		0			0
$357$	2.41327	+	4.63195i	0.127724	+	0.245149i
$358$		0			0
$359$	1.03562	+	1.79375i	0.0546580	+	0.0946705i	0.892060	−	0.451917i	$-0.149260\pi$
$359$	1.03562	+	1.79375i	0.0546580	+	0.0946705i	−0.837402	+	0.546588i	$0.815926\pi$
$360$		0			0
$361$	−0.304877	+	0.528063i	−0.0160462	+	0.0277928i
$362$		0			0
$363$			30.4461i			1.59801i
$364$		0			0
$365$	−6.98195	+	9.01370i	−0.365452	+	0.471798i
$366$		0			0
$367$	5.28141	+	3.04922i	0.275687	+	0.159168i	0.631469	−	0.775401i	$-0.282452\pi$
$367$	5.28141	+	3.04922i	0.275687	+	0.159168i	−0.355782	+	0.934569i	$0.615785\pi$
$368$		0			0
$369$	5.10598	+	8.84382i	0.265807	+	0.460391i
$370$		0			0
$371$	−14.5501	−	9.26241i	−0.755406	−	0.480880i
$372$		0			0
$373$	−22.6143	+	13.0564i	−1.17092	+	0.676033i	−0.953897	−	0.300133i	$-0.902969\pi$
$373$	−22.6143	+	13.0564i	−1.17092	+	0.676033i	−0.217026	+	0.976166i	$0.569636\pi$
$374$		0			0
$375$	−8.96218	+	6.68426i	−0.462805	+	0.345173i
$376$		0			0
$377$			21.7172i			1.11849i
$378$		0			0
$379$	18.9893			0.975414			0.487707	−	0.873007i	$-0.337833\pi$
$379$	18.9893			0.975414			0.487707	+	0.873007i	$0.337833\pi$
$380$		0			0
$381$	−5.62411	+	9.74125i	−0.288132	+	0.499059i
$382$		0			0
$383$	25.2815	−	14.5963i	1.29183	−	0.745836i	0.312847	−	0.949803i	$-0.398717\pi$
$383$	25.2815	−	14.5963i	1.29183	−	0.745836i	0.978978	+	0.203968i	$0.0653838\pi$
$384$		0			0
$385$	29.0729	+	24.6045i	1.48169	+	1.25396i
$386$		0			0
$387$	8.45575	−	4.88193i	0.429830	−	0.248162i
$388$		0			0
$389$	−12.1922	+	21.1175i	−0.618168	+	1.07070i	0.371651	+	0.928372i	$0.378792\pi$
$389$	−12.1922	+	21.1175i	−0.618168	+	1.07070i	−0.989820	+	0.142327i	$0.954542\pi$
$390$		0			0
$391$	3.99933			0.202255
$392$		0			0
$393$			10.8174i			0.545666i
$394$		0			0
$395$	−11.2952	+	4.61842i	−0.568322	+	0.232378i
$396$		0			0
$397$	−5.97866	+	3.45178i	−0.300060	+	0.173240i	−0.642470	−	0.766311i	$-0.722090\pi$
$397$	−5.97866	+	3.45178i	−0.300060	+	0.173240i	0.342410	+	0.939551i	$0.388757\pi$
$398$		0			0
$399$	0.507016	−	11.7052i	0.0253825	−	0.585992i
$400$		0			0
$401$	−16.6242	−	28.7940i	−0.830173	−	1.43790i	−0.897901	−	0.440198i	$-0.854908\pi$
$401$	−16.6242	−	28.7940i	−0.830173	−	1.43790i	0.0677277	−	0.997704i	$-0.478425\pi$
$402$		0			0
$403$	−18.2659	−	10.5458i	−0.909889	−	0.525325i
$404$		0			0
$405$	−1.76777	−	1.36930i	−0.0878412	−	0.0680412i
$406$		0			0
$407$			5.05007i			0.250323i
$408$		0			0
$409$	8.81071	−	15.2606i	0.435662	−	0.754588i	−0.561688	−	0.827349i	$-0.689848\pi$
$409$	8.81071	−	15.2606i	0.435662	−	0.754588i	0.997349	+	0.0727612i	$0.0231811\pi$
$410$		0			0
$411$	0.704037	+	1.21943i	0.0347276	+	0.0601500i
$412$		0			0
$413$	16.5899	−	26.0607i	0.816335	−	1.28236i
$414$		0			0
$415$	33.9207	+	4.62311i	1.66510	+	0.226939i
$416$		0			0
$417$	−4.64484	−	2.68170i	−0.227459	−	0.131323i
$418$		0			0
$419$	17.7842			0.868813			0.434406	−	0.900717i	$-0.356958\pi$
$419$	17.7842			0.868813			0.434406	+	0.900717i	$0.356958\pi$
$420$		0			0
$421$	−16.0439			−0.781934			−0.390967	−	0.920405i	$-0.627859\pi$
$421$	−16.0439			−0.781934			−0.390967	+	0.920405i	$0.627859\pi$
$422$		0			0
$423$	−1.48055	−	0.854794i	−0.0719867	−	0.0415615i
$424$		0			0
$425$	6.91551	+	7.04274i	0.335451	+	0.341623i
$426$		0			0
$427$	6.02469	+	11.5636i	0.291555	+	0.559601i
$428$		0			0
$429$	11.1829	+	19.3694i	0.539918	+	0.935165i
$430$		0			0
$431$	−4.27652	+	7.40715i	−0.205993	+	0.356790i	−0.950449	−	0.310882i	$-0.899376\pi$
$431$	−4.27652	+	7.40715i	−0.205993	+	0.356790i	0.744456	+	0.667672i	$0.232709\pi$
$432$		0			0
$433$			17.5573i			0.843751i	0.906654	+	0.421876i	$0.138628\pi$
$433$			17.5573i			0.843751i	−0.906654	+	0.421876i	$0.861372\pi$
$434$		0			0
$435$	−8.55971	+	11.0506i	−0.410407	+	0.529835i
$436$		0			0
$437$	−7.76944	−	4.48569i	−0.371663	−	0.214580i
$438$		0			0
$439$	−6.77536	−	11.7353i	−0.323370	−	0.560093i	0.657811	−	0.753183i	$-0.271483\pi$
$439$	−6.77536	−	11.7353i	−0.323370	−	0.560093i	−0.981181	+	0.193090i	$0.938149\pi$
$440$		0			0
$441$	2.96270	+	6.34211i	0.141081	+	0.302005i
$442$		0			0
$443$	12.0290	−	6.94496i	0.571516	−	0.329965i	−0.186238	−	0.982505i	$-0.559630\pi$
$443$	12.0290	−	6.94496i	0.571516	−	0.329965i	0.757755	+	0.652539i	$0.226296\pi$
$444$		0			0
$445$	−20.9891	+	8.58213i	−0.994980	+	0.406832i
$446$		0			0
$447$			2.92417i			0.138309i
$448$		0			0
$449$	−38.9144			−1.83648			−0.918241	−	0.396022i	$-0.870390\pi$
$449$	−38.9144			−1.83648			−0.918241	+	0.396022i	$0.870390\pi$
$450$		0			0
$451$	32.8716	−	56.9353i	1.54786	−	2.68098i
$452$		0			0
$453$	6.10462	−	3.52450i	0.286820	−	0.165596i
$454$		0			0
$455$	20.2257	+	3.65425i	0.948195	+	0.171314i
$456$		0			0
$457$	2.29331	−	1.32404i	0.107276	−	0.0619360i	−0.445402	−	0.895331i	$-0.646939\pi$
$457$	2.29331	−	1.32404i	0.107276	−	0.0619360i	0.552678	+	0.833395i	$0.313606\pi$
$458$		0			0
$459$	−0.987038	+	1.70960i	−0.0460710	+	0.0797973i
$460$		0			0
$461$	−20.4079			−0.950493			−0.475246	−	0.879853i	$-0.657641\pi$
$461$	−20.4079			−0.950493			−0.475246	+	0.879853i	$0.657641\pi$
$462$		0			0
$463$			21.0475i			0.978160i	0.872239	+	0.489080i	$0.162667\pi$
$463$			21.0475i			0.978160i	−0.872239	+	0.489080i	$0.837333\pi$
$464$		0			0
$465$	−5.13785	−	12.5655i	−0.238262	−	0.582713i
$466$		0			0
$467$	8.33062	−	4.80968i	0.385495	−	0.222566i	−0.294711	−	0.955586i	$-0.595223\pi$
$467$	8.33062	−	4.80968i	0.385495	−	0.222566i	0.680206	+	0.733021i	$0.261890\pi$
$468$		0			0
$469$	24.1219	+	15.3557i	1.11385	+	0.709059i
$470$		0			0
$471$	−1.71268	−	2.96645i	−0.0789162	−	0.136687i
$472$		0			0
$473$	−54.4370	−	31.4292i	−2.50301	−	1.44512i
$474$		0			0
$475$	−5.53546	−	21.4383i	−0.253984	−	0.983659i
$476$		0			0
$477$		−	6.51919i		−	0.298493i
$478$		0			0
$479$	−14.5152	+	25.1410i	−0.663215	+	1.14872i	0.316551	+	0.948575i	$0.397475\pi$
$479$	−14.5152	+	25.1410i	−0.663215	+	1.14872i	−0.979766	+	0.200146i	$0.935858\pi$
$480$		0			0
$481$	1.36261	+	2.36010i	0.0621295	+	0.107611i
$482$		0			0
$483$	5.35507	+	0.231957i	0.243664	+	0.0105544i
$484$		0			0
$485$	−22.0114	−	2.99997i	−0.999487	−	0.136222i
$486$		0			0
$487$	−9.37294	−	5.41147i	−0.424729	−	0.245217i	0.272370	−	0.962193i	$-0.412193\pi$
$487$	−9.37294	−	5.41147i	−0.424729	−	0.245217i	−0.697098	+	0.716975i	$0.745526\pi$
$488$		0			0
$489$	−2.92758			−0.132390
$490$		0			0
$491$	−25.0455			−1.13029			−0.565143	−	0.824993i	$-0.691179\pi$
$491$	−25.0455			−1.13029			−0.565143	+	0.824993i	$0.691179\pi$
$492$		0			0
$493$	10.6870	+	6.17012i	0.481317	+	0.277888i
$494$		0			0
$495$	−1.94402	+	14.2636i	−0.0873770	+	0.641103i
$496$		0			0
$497$	−27.5730	−	1.19434i	−1.23682	−	0.0535734i
$498$		0			0
$499$	−2.12900	−	3.68753i	−0.0953069	−	0.165076i	0.814430	−	0.580262i	$-0.197050\pi$
$499$	−2.12900	−	3.68753i	−0.0953069	−	0.165076i	−0.909737	+	0.415186i	$0.863717\pi$
$500$		0			0
$501$	11.0598	−	19.1562i	0.494116	−	0.855835i
$502$		0			0
$503$		−	31.2478i		−	1.39327i	−0.717425	−	0.696636i	$-0.754679\pi$
$503$		−	31.2478i		−	1.39327i	0.717425	−	0.696636i	$-0.245321\pi$
$504$		0			0
$505$	−5.47598	−	4.24166i	−0.243678	−	0.188751i
$506$		0			0
$507$	−0.805840	−	0.465252i	−0.0357886	−	0.0206626i
$508$		0			0
$509$	4.84131	+	8.38539i	0.214587	+	0.371676i	0.953145	−	0.302514i	$-0.0978261\pi$
$509$	4.84131	+	8.38539i	0.214587	+	0.371676i	−0.738558	+	0.674190i	$0.764493\pi$
$510$		0			0
$511$	11.3802	+	7.24449i	0.503431	+	0.320477i
$512$		0			0
$513$	3.83501	−	2.21415i	0.169320	−	0.0977569i
$514$		0			0
$515$	12.9092	+	31.5718i	0.568848	+	1.39122i
$516$		0			0
$517$			11.0061i			0.484048i
$518$		0			0
$519$	−13.1661			−0.577929
$520$		0			0
$521$	−10.5451	+	18.2647i	−0.461990	+	0.800190i	−0.999060	−	0.0433477i	$-0.986198\pi$
$521$	−10.5451	+	18.2647i	−0.461990	+	0.800190i	0.537070	+	0.843538i	$0.319531\pi$
$522$		0			0
$523$	−22.5910	+	13.0429i	−0.987837	+	0.570328i	−0.904627	−	0.426204i	$-0.859850\pi$
$523$	−22.5910	+	13.0429i	−0.987837	+	0.570328i	−0.0832098	+	0.996532i	$0.526517\pi$
$524$		0			0
$525$	8.85134	+	9.83127i	0.386304	+	0.429072i
$526$		0			0
$527$	−10.3791	+	5.99239i	−0.452121	+	0.261032i
$528$		0			0
$529$	−9.44782	+	16.3641i	−0.410775	+	0.711482i
$530$		0			0
$531$	11.6765			0.506717
$532$		0			0
$533$		−	35.4776i		−	1.53670i
$534$		0			0
$535$	−2.01208	−	4.92089i	−0.0869896	−	0.212749i
$536$		0			0
$537$	−2.00439	+	1.15724i	−0.0864960	+	0.0499385i
$538$		0			0
$539$	25.8228	−	36.9329i	1.11227	−	1.59081i
$540$		0			0
$541$	19.0706	+	33.0312i	0.819907	+	1.42012i	0.905750	+	0.423812i	$0.139308\pi$
$541$	19.0706	+	33.0312i	0.819907	+	1.42012i	−0.0858430	+	0.996309i	$0.527358\pi$
$542$		0			0
$543$	−2.65181	−	1.53103i	−0.113800	−	0.0657026i
$544$		0			0
$545$	25.4694	+	19.7284i	1.09099	+	0.845072i
$546$		0			0
$547$		−	30.7904i		−	1.31650i	−0.752798	−	0.658252i	$-0.771296\pi$
$547$		−	30.7904i		−	1.31650i	0.752798	−	0.658252i	$-0.228704\pi$
$548$		0			0
$549$	−2.46412	+	4.26799i	−0.105166	+	0.182153i
$550$		0			0
$551$	−13.8410	−	23.9732i	−0.589644	−	1.02129i
$552$		0			0
$553$	6.67145	+	12.8050i	0.283699	+	0.544522i
$554$		0			0
$555$	−0.236872	+	1.73798i	−0.0100547	+	0.0737730i
$556$		0			0
$557$	−15.6082	−	9.01142i	−0.661342	−	0.381826i	0.131446	−	0.991323i	$-0.458038\pi$
$557$	−15.6082	−	9.01142i	−0.661342	−	0.381826i	−0.792788	+	0.609497i	$0.791371\pi$
$558$		0			0
$559$	−33.9208			−1.43470
$560$		0			0
$561$	12.7088			0.536567
$562$		0			0
$563$	5.78357	+	3.33914i	0.243748	+	0.140728i	0.616898	−	0.787043i	$-0.288389\pi$
$563$	5.78357	+	3.33914i	0.243748	+	0.140728i	−0.373150	+	0.927771i	$0.621722\pi$
$564$		0			0
$565$	−11.9322	−	1.62625i	−0.501989	−	0.0684170i
$566$		0			0
$567$	−1.42079	+	2.23189i	−0.0596676	+	0.0937307i
$568$		0			0
$569$	−8.52169	−	14.7600i	−0.357248	−	0.618771i	0.630252	−	0.776390i	$-0.282951\pi$
$569$	−8.52169	−	14.7600i	−0.357248	−	0.618771i	−0.987500	+	0.157619i	$0.949618\pi$
$570$		0			0
$571$	−19.4492	+	33.6870i	−0.813923	+	1.40976i	0.0961751	+	0.995364i	$0.469339\pi$
$571$	−19.4492	+	33.6870i	−0.813923	+	1.40976i	−0.910098	+	0.414392i	$0.863994\pi$
$572$		0			0
$573$		−	25.5675i		−	1.06810i
$574$		0			0
$575$	9.80795	−	2.53245i	0.409020	−	0.105610i
$576$		0			0
$577$	3.42639	+	1.97823i	0.142643	+	0.0823547i	0.569623	−	0.821906i	$-0.307089\pi$
$577$	3.42639	+	1.97823i	0.142643	+	0.0823547i	−0.426980	+	0.904261i	$0.640423\pi$
$578$		0			0
$579$	−10.8648	−	18.8184i	−0.451526	−	0.782065i
$580$		0			0
$581$	1.75292	−	40.4686i	0.0727233	−	1.67892i
$582$		0			0
$583$	−36.3468	+	20.9848i	−1.50533	+	0.869103i
$584$		0			0
$585$	2.94008	+	7.19051i	0.121558	+	0.297291i
$586$		0			0
$587$		−	8.33774i		−	0.344135i	−0.985085	−	0.172068i	$-0.944955\pi$
$587$		−	8.33774i		−	0.344135i	0.985085	−	0.172068i	$-0.0550448\pi$
$588$		0			0
$589$	26.8845			1.10776
$590$		0			0
$591$	5.63229	−	9.75540i	0.231681	−	0.401284i
$592$		0			0
$593$	20.8547	−	12.0405i	0.856400	−	0.494442i	−0.00640542	−	0.999979i	$-0.502039\pi$
$593$	20.8547	−	12.0405i	0.856400	−	0.494442i	0.862805	+	0.505537i	$0.168706\pi$
$594$		0			0
$595$	7.54460	−	8.91477i	0.309299	−	0.365470i
$596$		0			0
$597$	6.22748	−	3.59544i	0.254874	−	0.147151i
$598$		0			0
$599$	7.92587	−	13.7280i	0.323842	−	0.560912i	−0.657435	−	0.753511i	$-0.728359\pi$
$599$	7.92587	−	13.7280i	0.323842	−	0.560912i	0.981277	+	0.192600i	$0.0616919\pi$
$600$		0			0
$601$	−43.7845			−1.78601			−0.893003	−	0.450050i	$-0.851406\pi$
$601$	−43.7845			−1.78601			−0.893003	+	0.450050i	$0.851406\pi$
$602$		0			0
$603$			10.8078i			0.440129i
$604$		0			0
$605$	63.0154	−	25.7660i	2.56194	−	1.04754i
$606$		0			0
$607$	−9.07478	+	5.23933i	−0.368334	+	0.212658i	−0.672730	−	0.739888i	$-0.734879\pi$
$607$	−9.07478	+	5.23933i	−0.368334	+	0.212658i	0.304396	+	0.952545i	$0.401545\pi$
$608$		0			0
$609$	13.9519	+	8.88158i	0.565360	+	0.359900i
$610$		0			0
$611$	2.96966	+	5.14360i	0.120139	+	0.208088i
$612$		0			0
$613$	−14.4808	−	8.36052i	−0.584876	−	0.337678i	0.178193	−	0.983996i	$-0.442975\pi$
$613$	−14.4808	−	8.36052i	−0.584876	−	0.337678i	−0.763069	+	0.646317i	$0.776308\pi$
$614$		0			0
$615$	13.9833	−	18.0524i	0.563860	−	0.727943i
$616$		0			0
$617$			44.5830i			1.79485i	0.441172	+	0.897423i	$0.354563\pi$
$617$			44.5830i			1.79485i	−0.441172	+	0.897423i	$0.645437\pi$
$618$		0			0
$619$	−13.3076	+	23.0495i	−0.534879	+	0.926438i	0.464290	+	0.885683i	$0.346310\pi$
$619$	−13.3076	+	23.0495i	−0.534879	+	0.926438i	−0.999169	+	0.0407546i	$0.987024\pi$
$620$		0			0
$621$	1.01296	+	1.75450i	0.0406488	+	0.0704057i
$622$		0			0
$623$	12.3971	+	23.7947i	0.496681	+	0.953313i
$624$		0			0
$625$	21.4192	+	12.8926i	0.856767	+	0.515703i
$626$		0			0
$627$	−24.6893	−	14.2544i	−0.985995	−	0.569265i
$628$		0			0
$629$	1.54853			0.0617439
$630$		0			0
$631$	−44.2904			−1.76317			−0.881586	−	0.472023i	$-0.843524\pi$
$631$	−44.2904			−1.76317			−0.881586	+	0.472023i	$0.843524\pi$
$632$		0			0
$633$	−0.593173	−	0.342468i	−0.0235765	−	0.0136119i
$634$		0			0
$635$	24.9214	+	3.39658i	0.988975	+	0.134789i
$636$		0			0
$637$	2.10282	−	24.2277i	0.0833167	−	0.959938i
$638$		0			0
$639$	−5.21569	−	9.03384i	−0.206330	−	0.357373i
$640$		0			0
$641$	1.38352	−	2.39632i	0.0546457	−	0.0946491i	−0.837409	−	0.546577i	$-0.815930\pi$
$641$	1.38352	−	2.39632i	0.0546457	−	0.0946491i	0.892054	+	0.451928i	$0.149264\pi$
$642$		0			0
$643$			37.1906i			1.46665i	0.679876	+	0.733327i	$0.262034\pi$
$643$			37.1906i			1.46665i	−0.679876	+	0.733327i	$0.737966\pi$
$644$		0			0
$645$	−17.2603	−	13.3697i	−0.679622	−	0.526430i
$646$		0			0
$647$	10.0673	+	5.81235i	0.395786	+	0.228507i	0.684664	−	0.728859i	$-0.259949\pi$
$647$	10.0673	+	5.81235i	0.395786	+	0.228507i	−0.288878	+	0.957366i	$0.593282\pi$
$648$		0			0
$649$	−37.5859	−	65.1007i	−1.47538	−	2.55543i
$650$		0			0
$651$	−14.2451	+	7.42178i	−0.558310	+	0.290883i
$652$		0			0
$653$	17.2759	−	9.97424i	0.676058	−	0.390322i	−0.122310	−	0.992492i	$-0.539030\pi$
$653$	17.2759	−	9.97424i	0.676058	−	0.390322i	0.798368	+	0.602170i	$0.205697\pi$
$654$		0			0
$655$	22.3892	−	9.15457i	0.874817	−	0.357699i
$656$		0			0
$657$			5.09891i			0.198927i
$658$		0			0
$659$	38.7827			1.51076			0.755380	−	0.655287i	$-0.227452\pi$
$659$	38.7827			1.51076			0.755380	+	0.655287i	$0.227452\pi$
$660$		0			0
$661$	6.42009	−	11.1199i	0.249713	−	0.432515i	−0.713733	−	0.700417i	$-0.752997\pi$
$661$	6.42009	−	11.1199i	0.249713	−	0.432515i	0.963446	+	0.267903i	$0.0863305\pi$
$662$		0			0
$663$	5.93935	−	3.42909i	0.230665	−	0.133175i
$664$		0			0
$665$	−24.6557	+	8.85650i	−0.956107	+	0.343440i
$666$		0			0
$667$	10.9677	−	6.33218i	0.424669	−	0.245183i
$668$		0			0
$669$	5.92263	−	10.2583i	0.228982	−	0.396609i
$670$		0			0
$671$	31.7274			1.22482
$672$		0			0
$673$		−	42.8349i		−	1.65116i	−0.564282	−	0.825582i	$-0.690847\pi$
$673$		−	42.8349i		−	1.65116i	0.564282	−	0.825582i	$-0.309153\pi$
$674$		0			0
$675$	−1.33806	+	4.81763i	−0.0515020	+	0.185431i
$676$		0			0
$677$	−19.0937	+	11.0237i	−0.733830	+	0.423677i	−0.819822	−	0.572619i	$-0.805928\pi$
$677$	−19.0937	+	11.0237i	−0.733830	+	0.423677i	0.0859916	+	0.996296i	$0.472594\pi$
$678$		0			0
$679$	−1.13748	+	26.2604i	−0.0436526	+	1.00778i
$680$		0			0
$681$	10.8298	+	18.7577i	0.414998	+	0.718798i
$682$		0			0
$683$	−16.8976	−	9.75586i	−0.646571	−	0.373298i	0.140570	−	0.990071i	$-0.455106\pi$
$683$	−16.8976	−	9.75586i	−0.646571	−	0.373298i	−0.787141	+	0.616773i	$0.788440\pi$
$684$		0			0
$685$	1.92808	−	2.48915i	0.0736682	−	0.0951056i
$686$		0			0
$687$			13.4544i			0.513317i
$688$		0			0
$689$	−11.3242	+	19.6141i	−0.431418	+	0.747238i
$690$		0			0
$691$	3.88472	+	6.72854i	0.147782	+	0.255966i	0.930407	−	0.366527i	$-0.119453\pi$
$691$	3.88472	+	6.72854i	0.147782	+	0.255966i	−0.782625	+	0.622493i	$0.786120\pi$
$692$		0			0
$693$	17.0170	+	0.737101i	0.646424	+	0.0280002i
$694$		0			0
$695$	−1.61956	+	11.8831i	−0.0614335	+	0.450750i
$696$		0			0
$697$	−17.4584	−	10.0796i	−0.661283	−	0.381792i
$698$		0			0
$699$	13.5723			0.513350
$700$		0			0
$701$	44.9618			1.69818			0.849091	−	0.528246i	$-0.177150\pi$
$701$	44.9618			1.69818			0.849091	+	0.528246i	$0.177150\pi$
$702$		0			0
$703$	−3.00831	−	1.73685i	−0.113461	−	0.0655065i
$704$		0			0
$705$	−0.516237	+	3.78774i	−0.0194426	+	0.142655i
$706$		0			0
$707$	−4.40115	+	6.91368i	−0.165522	+	0.260016i
$708$		0			0
$709$	7.35513	+	12.7395i	0.276228	+	0.478441i	0.970444	−	0.241326i	$-0.0775822\pi$
$709$	7.35513	+	12.7395i	0.276228	+	0.478441i	−0.694216	+	0.719766i	$0.744249\pi$
$710$		0			0
$711$	−2.72865	+	4.72617i	−0.102332	+	0.177245i
$712$		0			0
$713$			12.2995i			0.460622i
$714$		0			0
$715$	30.6257	−	39.5378i	1.14534	−	1.47863i
$716$		0			0
$717$	13.8940	+	8.02169i	0.518880	+	0.299575i
$718$		0			0
$719$	8.07036	+	13.9783i	0.300974	+	0.521302i	0.976357	−	0.216165i	$-0.0693550\pi$
$719$	8.07036	+	13.9783i	0.300974	+	0.521302i	−0.675383	+	0.737467i	$0.736022\pi$
$720$		0			0
$721$	35.7919	−	18.6478i	1.33296	−	0.694479i
$722$		0			0
$723$	11.6525	−	6.72757i	0.433361	−	0.250201i
$724$		0			0
$725$	30.1157	+	8.36442i	1.11847	+	0.310647i
$726$		0			0
$727$			12.7937i			0.474492i	0.971450	+	0.237246i	$0.0762447\pi$
$727$			12.7937i			0.474492i	−0.971450	+	0.237246i	$0.923755\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−9.63730	+	16.6923i	−0.356448	+	0.617387i
$732$		0			0
$733$	−2.98687	+	1.72447i	−0.110323	+	0.0636949i	−0.554146	−	0.832419i	$-0.686955\pi$
$733$	−2.98687	+	1.72447i	−0.110323	+	0.0636949i	0.443823	+	0.896114i	$0.353622\pi$
$734$		0			0
$735$	10.6192	−	11.4992i	0.391696	−	0.424155i
$736$		0			0
$737$	60.2574	−	34.7897i	2.21961	−	1.28149i
$738$		0			0
$739$	−0.415306	+	0.719331i	−0.0152773	+	0.0264610i	−0.873563	−	0.486711i	$-0.838196\pi$
$739$	−0.415306	+	0.719331i	−0.0152773	+	0.0264610i	0.858286	+	0.513172i	$0.171530\pi$
$740$		0			0
$741$	−15.3844			−0.565160
$742$		0			0
$743$		−	44.6351i		−	1.63750i	−0.574149	−	0.818751i	$-0.694667\pi$
$743$		−	44.6351i		−	1.63750i	0.574149	−	0.818751i	$-0.305333\pi$
$744$		0			0
$745$	6.05226	−	2.47468i	0.221738	−	0.0906651i
$746$		0			0
$747$	13.2589	−	7.65502i	0.485117	−	0.280083i
$748$		0			0
$749$	−5.57865	+	2.90651i	−0.203839	+	0.106201i
$750$		0			0
$751$	1.90845	+	3.30554i	0.0696404	+	0.120621i	0.898743	−	0.438476i	$-0.144481\pi$
$751$	1.90845	+	3.30554i	0.0696404	+	0.120621i	−0.829103	+	0.559096i	$0.811148\pi$
$752$		0			0
$753$	12.9439	+	7.47317i	0.471703	+	0.272338i
$754$		0			0
$755$	−12.4610	−	9.65222i	−0.453503	−	0.351280i
$756$		0			0
$757$			27.5200i			1.00023i	0.865958	+	0.500116i	$0.166709\pi$
$757$			27.5200i			1.00023i	−0.865958	+	0.500116i	$0.833291\pi$
$758$		0			0
$759$	6.52131	−	11.2952i	0.236709	−	0.409991i
$760$		0			0
$761$	12.0646	+	20.8964i	0.437340	+	0.757495i	0.997483	−	0.0709007i	$-0.0225873\pi$
$761$	12.0646	+	20.8964i	0.437340	+	0.757495i	−0.560143	+	0.828396i	$0.689254\pi$
$762$		0			0
$763$	20.4702	−	32.1563i	0.741072	−	1.16414i
$764$		0			0
$765$	4.37373	+	0.596104i	0.158133	+	0.0215522i
$766$		0			0
$767$	−35.1308	−	20.2828i	−1.26850	−	0.732369i
$768$		0			0
$769$	48.2761			1.74088			0.870441	−	0.492273i	$-0.163834\pi$
$769$	48.2761			1.74088			0.870441	+	0.492273i	$0.163834\pi$
$770$		0			0
$771$	−4.36818			−0.157316
$772$		0			0
$773$	0.220383	+	0.127238i	0.00792664	+	0.00457645i	0.503958	−	0.863728i	$-0.331877\pi$
$773$	0.220383	+	0.127238i	0.00792664	+	0.00457645i	−0.496031	+	0.868305i	$0.665210\pi$
$774$		0			0
$775$	−21.6593	+	21.2680i	−0.778024	+	0.763968i
$776$		0			0
$777$	2.07347	+	0.0898134i	0.0743853	+	0.00322204i
$778$		0			0
$779$	22.6108	+	39.1630i	0.810115	+	1.40316i
$780$		0			0
$781$	−33.5779	+	58.1586i	−1.20151	+	2.08108i
$782$		0			0
$783$			6.25115i			0.223398i
$784$		0			0
$785$	−4.69036	+	6.05525i	−0.167406	+	0.216121i
$786$		0			0
$787$	−13.9417	−	8.04923i	−0.496967	−	0.286924i	0.230493	−	0.973074i	$-0.425966\pi$
$787$	−13.9417	−	8.04923i	−0.496967	−	0.286924i	−0.727460	+	0.686150i	$0.759299\pi$
$788$		0			0
$789$	−6.13542	−	10.6269i	−0.218427	−	0.378326i
$790$		0			0
$791$	−0.616617	+	14.2355i	−0.0219244	+	0.506156i
$792$		0			0
$793$	14.8275	−	8.56066i	0.526540	−	0.303998i
$794$		0			0
$795$	−13.4930	+	5.51708i	−0.478547	+	0.195670i
$796$		0			0
$797$			36.0791i			1.27799i	0.769212	+	0.638993i	$0.220649\pi$
$797$			36.0791i			1.27799i	−0.769212	+	0.638993i	$0.779351\pi$
$798$		0			0
$799$	3.37486			0.119394
$800$		0			0
$801$	−5.07049	+	8.78234i	−0.179157	+	0.310309i
$802$		0			0
$803$	28.4282	−	16.4130i	1.00321	−	0.579204i
$804$		0			0
$805$	−4.05181	−	11.2799i	−0.142808	−	0.397564i
$806$		0			0
$807$	11.3076	−	6.52845i	0.398047	−	0.229812i
$808$		0			0
$809$	15.6052	−	27.0291i	0.548651	−	0.950291i	−0.449717	−	0.893171i	$-0.648475\pi$
$809$	15.6052	−	27.0291i	0.548651	−	0.950291i	0.998367	−	0.0571195i	$-0.0181916\pi$
$810$		0			0
$811$	−6.91344			−0.242764			−0.121382	−	0.992606i	$-0.538733\pi$
$811$	−6.91344			−0.242764			−0.121382	+	0.992606i	$0.538733\pi$
$812$		0			0
$813$			23.9574i			0.840224i
$814$		0			0
$815$	2.47756	+	6.05931i	0.0867850	+	0.212248i
$816$		0			0
$817$	37.4445	−	21.6186i	1.31002	−	0.756339i
$818$		0			0
$819$	8.15163	−	4.24704i	0.284841	−	0.148404i
$820$		0			0
$821$	−2.05513	−	3.55959i	−0.0717245	−	0.124230i	0.827933	−	0.560827i	$-0.189517\pi$
$821$	−2.05513	−	3.55959i	−0.0717245	−	0.124230i	−0.899657	+	0.436597i	$0.856184\pi$
$822$		0			0
$823$	25.6619	+	14.8159i	0.894516	+	0.516449i	0.875417	−	0.483368i	$-0.160587\pi$
$823$	25.6619	+	14.8159i	0.894516	+	0.516449i	0.0190992	+	0.999818i	$0.493920\pi$
$824$		0			0
$825$	31.1671	−	8.04747i	1.08510	−	0.280177i
$826$		0			0
$827$			1.19658i			0.0416093i	0.999784	+	0.0208046i	$0.00662280\pi$
$827$			1.19658i			0.0416093i	−0.999784	+	0.0208046i	$0.993377\pi$
$828$		0			0
$829$	0.860027	−	1.48961i	0.0298700	−	0.0517363i	−0.850704	−	0.525645i	$-0.823824\pi$
$829$	0.860027	−	1.48961i	0.0298700	−	0.0517363i	0.880574	+	0.473909i	$0.157157\pi$
$830$		0			0
$831$	−5.83008	−	10.0980i	−0.202243	−	0.350296i
$832$		0			0
$833$	−11.3249	−	7.91818i	−0.392386	−	0.274349i
$834$		0			0
$835$	−49.0079	−	6.67938i	−1.69599	−	0.231149i
$836$		0			0
$837$	−5.25771	−	3.03554i	−0.181733	−	0.104924i
$838$		0			0
$839$	−14.6942			−0.507299			−0.253650	−	0.967296i	$-0.581631\pi$
$839$	−14.6942			−0.507299			−0.253650	+	0.967296i	$0.581631\pi$
$840$		0			0
$841$	10.0769			0.347478
$842$		0			0
$843$	2.73073	+	1.57659i	0.0940514	+	0.0543006i
$844$		0			0
$845$	−0.280981	+	2.06161i	−0.00966602	+	0.0709216i
$846$		0			0
$847$	−37.2198	−	71.4384i	−1.27889	−	2.45465i
$848$		0			0
$849$	−3.37879	−	5.85224i	−0.115960	−	0.200848i
$850$		0			0
$851$	0.794601	−	1.37629i	0.0272386	−	0.0471786i
$852$		0			0
$853$		−	10.3635i		−	0.354839i	−0.984135	−	0.177420i	$-0.943225\pi$
$853$		−	10.3635i		−	0.354839i	0.984135	−	0.177420i	$-0.0567750\pi$
$854$		0			0
$855$	−7.82820	−	6.06367i	−0.267719	−	0.207373i
$856$		0			0
$857$	10.2373	+	5.91051i	0.349699	+	0.201899i	0.664553	−	0.747241i	$-0.268622\pi$
$857$	10.2373	+	5.91051i	0.349699	+	0.201899i	−0.314853	+	0.949140i	$0.601955\pi$
$858$		0			0
$859$	6.63018	+	11.4838i	0.226219	+	0.391822i	0.956684	−	0.291127i	$-0.0940302\pi$
$859$	6.63018	+	11.4838i	0.226219	+	0.391822i	−0.730466	+	0.682949i	$0.760697\pi$
$860$		0			0
$861$	−22.7920	−	14.5091i	−0.776750	−	0.494468i
$862$		0			0
$863$	−41.8247	+	24.1475i	−1.42373	+	0.821990i	−0.996615	−	0.0822074i	$-0.973803\pi$
$863$	−41.8247	+	24.1475i	−1.42373	+	0.821990i	−0.427114	+	0.904198i	$0.640470\pi$
$864$		0			0
$865$	11.1423	+	27.2504i	0.378849	+	0.926542i
$866$		0			0
$867$			13.1030i			0.445002i
$868$		0			0
$869$	35.1334			1.19182
$870$		0			0
$871$	18.7738	−	32.5172i	0.636127	−	1.10180i
$872$		0			0
$873$	−8.60380	+	4.96741i	−0.291195	+	0.168121i
$874$		0			0
$875$	12.8574	−	26.6400i	0.434659	−	0.900595i
$876$		0			0
$877$	−45.4274	+	26.2275i	−1.53397	+	0.885640i	−0.534801	+	0.844978i	$0.679613\pi$
$877$	−45.4274	+	26.2275i	−1.53397	+	0.885640i	−0.999173	+	0.0406624i	$0.987053\pi$
$878$		0			0
$879$	11.9107	−	20.6299i	0.401736	−	0.695828i
$880$		0			0
$881$	39.9109			1.34463			0.672316	−	0.740264i	$-0.265300\pi$
$881$	39.9109			1.34463			0.672316	+	0.740264i	$0.265300\pi$
$882$		0			0
$883$			16.5805i			0.557977i	0.960294	+	0.278988i	$0.0899991\pi$
$883$			16.5805i			0.557977i	−0.960294	+	0.278988i	$0.910001\pi$
$884$		0			0
$885$	−9.88163	−	24.1673i	−0.332167	−	0.812375i
$886$		0			0
$887$	2.68503	−	1.55020i	0.0901546	−	0.0520508i	−0.454245	−	0.890877i	$-0.650091\pi$
$887$	2.68503	−	1.55020i	0.0901546	−	0.0520508i	0.544399	+	0.838826i	$0.316758\pi$
$888$		0			0
$889$	1.28786	−	29.7321i	0.0431935	−	0.997183i
$890$		0			0
$891$	3.21893	+	5.57535i	0.107838	+	0.186781i
$892$		0			0
$893$	−6.55629	−	3.78528i	−0.219398	−	0.126669i
$894$		0			0
$895$	4.09146	+	3.16922i	0.136762	+	0.105935i
$896$		0			0
$897$		−	7.03830i		−	0.235002i
$898$		0			0
$899$	−18.9756	+	32.8667i	−0.632872	+	1.09617i
$900$		0			0
$901$	6.43469	+	11.1452i	0.214371	+	0.371301i
$902$		0			0
$903$	−13.8724	+	21.7919i	−0.461645	+	0.725189i
$904$		0			0
$905$	−0.924635	+	6.78423i	−0.0307359	+	0.225516i
$906$		0			0
$907$	−46.7805	−	27.0087i	−1.55332	−	0.896810i	−0.997868	−	0.0652613i	$-0.979212\pi$
$907$	−46.7805	−	27.0087i	−1.55332	−	0.896810i	−0.555452	−	0.831549i	$-0.687455\pi$
$908$		0			0
$909$	−3.09768			−0.102743
$910$		0			0
$911$	37.7405			1.25040			0.625199	−	0.780466i	$-0.285018\pi$
$911$	37.7405			1.25040			0.625199	+	0.780466i	$0.285018\pi$
$912$		0			0
$913$	−85.3589	−	49.2820i	−2.82497	−	1.63100i
$914$		0			0
$915$	10.9190	+	1.48816i	0.360969	+	0.0491971i
$916$		0			0
$917$	−13.2241	−	25.3818i	−0.436697	−	0.838182i
$918$		0			0
$919$	2.96944	+	5.14321i	0.0979527	+	0.169659i	0.910837	−	0.412766i	$-0.135437\pi$
$919$	2.96944	+	5.14321i	0.0979527	+	0.169659i	−0.812884	+	0.582425i	$0.802104\pi$
$920$		0			0
$921$	16.5467	−	28.6598i	0.545234	−	0.944373i
$922$		0			0
$923$			36.2399i			1.19285i
$924$		0			0
$925$	3.79761	−	0.980558i	0.124865	−	0.0322405i
$926$		0			0
$927$	13.2104	+	7.62702i	0.433886	+	0.250504i
$928$		0			0
$929$	17.4419	+	30.2102i	0.572249	+	0.991164i	0.996335	+	0.0855421i	$0.0272622\pi$
$929$	17.4419	+	30.2102i	0.572249	+	0.991164i	−0.424086	+	0.905622i	$0.639404\pi$
$930$		0			0
$931$	13.1197	+	28.0847i	0.429981	+	0.920439i
$932$		0			0
$933$	−10.5601	+	6.09688i	−0.345722	+	0.199603i
$934$		0			0
$935$	−10.7553	−	26.3039i	−0.351735	−	0.860230i
$936$		0			0
$937$			0.324265i			0.0105933i	0.999986	+	0.00529664i	$0.00168598\pi$
$937$			0.324265i			0.0105933i	−0.999986	+	0.00529664i	$0.998314\pi$
$938$		0			0
$939$	5.84625			0.190785
$940$		0			0
$941$	2.05593	−	3.56098i	0.0670214	−	0.116085i	−0.830567	−	0.556918i	$-0.811984\pi$
$941$	2.05593	−	3.56098i	0.0670214	−	0.116085i	0.897589	+	0.440834i	$0.145317\pi$
$942$		0			0
$943$	−17.9169	+	10.3443i	−0.583455	+	0.336858i
$944$		0			0
$945$	5.82182	+	1.05185i	0.189384	+	0.0342167i
$946$		0			0
$947$	−0.839535	+	0.484706i	−0.0272812	+	0.0157508i	−0.513579	−	0.858043i	$-0.671681\pi$
$947$	−0.839535	+	0.484706i	−0.0272812	+	0.0157508i	0.486297	+	0.873793i	$0.338347\pi$
$948$		0			0
$949$	8.85710	−	15.3410i	0.287514	−	0.497988i
$950$		0			0
$951$	6.38865			0.207166
$952$		0			0
$953$		−	46.5994i		−	1.50950i	−0.656011	−	0.754752i	$-0.727757\pi$
$953$		−	46.5994i		−	1.50950i	0.656011	−	0.754752i	$-0.272243\pi$
$954$		0			0
$955$	−52.9180	+	21.6373i	−1.71239	+	0.700168i
$956$		0			0
$957$	34.8524	−	20.1220i	1.12662	−	0.650453i
$958$		0			0
$959$	−3.14267	−	2.00058i	−0.101482	−	0.0646021i
$960$		0			0
$961$	−2.92900	−	5.07318i	−0.0944840	−	0.163651i
$962$		0			0
$963$	−2.05902	−	1.18877i	−0.0663508	−	0.0383077i
$964$		0			0
$965$	−29.7544	+	38.4129i	−0.957828	+	1.23656i
$966$		0			0
$967$			11.3945i			0.366421i	0.983074	+	0.183211i	$0.0586490\pi$
$967$			11.3945i			0.366421i	−0.983074	+	0.183211i	$0.941351\pi$
$968$		0			0
$969$	−4.37089	+	7.57060i	−0.140413	+	0.243203i
$970$		0			0
$971$	−21.4249	−	37.1091i	−0.687558	−	1.19089i	−0.972625	−	0.232379i	$-0.925349\pi$
$971$	−21.4249	−	37.1091i	−0.687558	−	1.19089i	0.285067	−	0.958508i	$-0.407984\pi$
$972$		0			0
$973$	14.1769	+	0.614080i	0.454491	+	0.0196865i
$974$		0			0
$975$	12.3943	−	12.1704i	0.396935	−	0.389765i
$976$		0			0
$977$	−10.9311	−	6.31107i	−0.349717	−	0.201909i	0.314844	−	0.949144i	$-0.398048\pi$
$977$	−10.9311	−	6.31107i	−0.349717	−	0.201909i	−0.664561	+	0.747234i	$0.731381\pi$
$978$		0			0
$979$	65.2862			2.08656
$980$		0			0
$981$	14.4076			0.460000
$982$		0			0
$983$	−24.7997	−	14.3181i	−0.790988	−	0.456677i	0.0493222	−	0.998783i	$-0.484294\pi$
$983$	−24.7997	−	14.3181i	−0.790988	−	0.456677i	−0.840310	+	0.542106i	$0.817627\pi$
$984$		0			0
$985$	−24.9576	−	3.40152i	−0.795216	−	0.108381i
$986$		0			0
$987$	4.51891	+	0.195739i	0.143838	+	0.00623043i
$988$		0			0
$989$	9.89042	+	17.1307i	0.314497	+	0.544725i
$990$		0			0
$991$	21.5883	−	37.3921i	0.685776	−	1.18780i	−0.287417	−	0.957806i	$-0.592796\pi$
$991$	21.5883	−	37.3921i	0.685776	−	1.18780i	0.973192	−	0.229993i	$-0.0738703\pi$
$992$		0			0
$993$			23.2577i			0.738060i
$994$		0			0
$995$	−12.7118	−	9.84648i	−0.402992	−	0.312155i
$996$		0			0
$997$	−7.47512	−	4.31576i	−0.236739	−	0.136682i	0.376938	−	0.926239i	$-0.376977\pi$
$997$	−7.47512	−	4.31576i	−0.236739	−	0.136682i	−0.613677	+	0.789557i	$0.710310\pi$
$998$		0			0
$999$	0.392216	+	0.679339i	0.0124092	+	0.0214933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.di.g.529.4		24
4.3	odd	2		840.2.cc.c.529.9	yes	24
5.4	even	2	inner	1680.2.di.g.529.8		24
7.2	even	3	inner	1680.2.di.g.289.8		24
20.19	odd	2		840.2.cc.c.529.5	yes	24
28.23	odd	6		840.2.cc.c.289.5	✓	24
35.9	even	6	inner	1680.2.di.g.289.4		24
140.79	odd	6		840.2.cc.c.289.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cc.c.289.5	✓	24	28.23	odd	6
840.2.cc.c.289.9	yes	24	140.79	odd	6
840.2.cc.c.529.5	yes	24	20.19	odd	2
840.2.cc.c.529.9	yes	24	4.3	odd	2
1680.2.di.g.289.4		24	35.9	even	6	inner
1680.2.di.g.289.8		24	7.2	even	3	inner
1680.2.di.g.529.4		24	1.1	even	1	trivial
1680.2.di.g.529.8		24	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.di (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-0.301966 + 2.21558i) q^{5} +(2.64327 + 0.114495i) q^{7} +(0.500000 + 0.866025i) q^{9} +(3.21893 - 5.57535i) q^{11} -3.47412i q^{13} +(1.36930 - 1.76777i) q^{15} +(-1.70960 - 0.987038i) q^{17} +(2.21415 + 3.83501i) q^{19} +(-2.23189 - 1.42079i) q^{21} +(-1.75450 + 1.01296i) q^{23} +(-4.81763 - 1.33806i) q^{25} -1.00000i q^{27} -6.25115 q^{29} +(3.03554 - 5.25771i) q^{31} +(-5.57535 + 3.21893i) q^{33} +(-1.05185 + 5.82182i) q^{35} +(-0.679339 + 0.392216i) q^{37} +(-1.73706 + 3.00867i) q^{39} +10.2120 q^{41} -9.76386i q^{43} +(-2.06974 + 0.846282i) q^{45} +(-1.48055 + 0.854794i) q^{47} +(6.97378 + 0.605281i) q^{49} +(0.987038 + 1.70960i) q^{51} +(-5.64578 - 3.25959i) q^{53} +(11.3807 + 8.81538i) q^{55} -4.42829i q^{57} +(5.83826 - 10.1122i) q^{59} +(2.46412 + 4.26799i) q^{61} +(1.22248 + 2.34639i) q^{63} +(7.69720 + 1.04906i) q^{65} +(9.35985 + 5.40391i) q^{67} +2.02592 q^{69} -10.4314 q^{71} +(4.41578 + 2.54945i) q^{73} +(3.50316 + 3.56761i) q^{75} +(9.14686 - 14.3686i) q^{77} +(2.72865 + 4.72617i) q^{79} +(-0.500000 + 0.866025i) q^{81} -15.3100i q^{83} +(2.70311 - 3.48971i) q^{85} +(5.41365 + 3.12557i) q^{87} +(5.07049 + 8.78234i) q^{89} +(0.397768 - 9.18304i) q^{91} +(-5.25771 + 3.03554i) q^{93} +(-9.16539 + 3.74758i) q^{95} +9.93481i q^{97} +6.43786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5} + 12 q^{9} + 8 q^{11} - 8 q^{19} + 12 q^{21} + 2 q^{25} - 24 q^{29} - 4 q^{31} - 30 q^{35} - 4 q^{39} + 32 q^{41} - 2 q^{45} - 12 q^{49} + 20 q^{51} - 12 q^{55} + 4 q^{59} + 32 q^{61} + 22 q^{65}+ \cdots + 16 q^{99}+O(q^{100}) \) 24 * q + 2 * q^5 + 12 * q^9 + 8 * q^11 - 8 * q^19 + 12 * q^21 + 2 * q^25 - 24 * q^29 - 4 * q^31 - 30 * q^35 - 4 * q^39 + 32 * q^41 - 2 * q^45 - 12 * q^49 + 20 * q^51 - 12 * q^55 + 4 * q^59 + 32 * q^61 + 22 * q^65 + 56 * q^69 - 72 * q^71 + 16 * q^75 - 20 * q^79 - 12 * q^81 + 8 * q^85 + 24 * q^89 - 8 * q^91 + 18 * q^95 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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