LMFDB - Embedded newform 840.2.cc.c.289.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(289,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
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			289.5
Character	$\chi$	$=$	840.289
Dual form			840.2.cc.c.529.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{3} +(2.06974 - 0.846282i) q^{5} +(2.64327 - 0.114495i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-3.21893 - 5.57535i) q^{11} -3.47412i q^{13} +(-1.36930 + 1.76777i) q^{15} +(1.70960 - 0.987038i) q^{17} +(-2.21415 + 3.83501i) q^{19} +(-2.23189 + 1.42079i) q^{21} +(-1.75450 - 1.01296i) q^{23} +(3.56761 - 3.50316i) q^{25} +1.00000i q^{27} -6.25115 q^{29} +(-3.03554 - 5.25771i) q^{31} +(5.57535 + 3.21893i) q^{33} +(5.37398 - 2.47393i) q^{35} +(0.679339 + 0.392216i) q^{37} +(1.73706 + 3.00867i) q^{39} +10.2120 q^{41} +9.76386i q^{43} +(0.301966 - 2.21558i) q^{45} +(-1.48055 - 0.854794i) q^{47} +(6.97378 - 0.605281i) q^{49} +(-0.987038 + 1.70960i) q^{51} +(5.64578 - 3.25959i) q^{53} +(-11.3807 - 8.81538i) q^{55} -4.42829i q^{57} +(-5.83826 - 10.1122i) q^{59} +(2.46412 - 4.26799i) q^{61} +(1.22248 - 2.34639i) q^{63} +(-2.94008 - 7.19051i) q^{65} +(9.35985 - 5.40391i) q^{67} +2.02592 q^{69} +10.4314 q^{71} +(-4.41578 + 2.54945i) q^{73} +(-1.33806 + 4.81763i) q^{75} +(-9.14686 - 14.3686i) q^{77} +(-2.72865 + 4.72617i) q^{79} +(-0.500000 - 0.866025i) q^{81} +15.3100i q^{83} +(2.70311 - 3.48971i) q^{85} +(5.41365 - 3.12557i) q^{87} +(5.07049 - 8.78234i) q^{89} +(-0.397768 - 9.18304i) q^{91} +(5.25771 + 3.03554i) q^{93} +(-1.33719 + 9.81125i) q^{95} +9.93481i q^{97} -6.43786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$	$1$

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
$5$	2.06974	−	0.846282i	0.925614	−	0.378469i
$5$	2.06974	−	0.846282i	0.925614	−	0.378469i
$6$		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	−0.693917	−	0.720055i	$-0.744116\pi$
$11$	−3.21893	−	5.57535i	−0.970545	−	1.68103i	−0.276628	−	0.960977i	$-0.589217\pi$
$12$		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	$-0.589719\pi$
$17$	1.70960	−	0.987038i	0.414639	−	0.239392i	0.692781	+	0.721148i	$0.256385\pi$
$18$		0			0
$19$	−2.21415	+	3.83501i	−0.507960	+	0.879812i	0.491998	+	0.870596i	$0.336267\pi$
$19$	−2.21415	+	3.83501i	−0.507960	+	0.879812i	−0.999958	+	0.00921562i	$0.997067\pi$
$20$		0			0
$21$	−2.23189	+	1.42079i	−0.487039	+	0.310042i
$22$		0			0
$23$	−1.75450	−	1.01296i	−0.365839	−	0.211217i	0.305800	−	0.952096i	$-0.401076\pi$
$23$	−1.75450	−	1.01296i	−0.365839	−	0.211217i	−0.671639	+	0.740879i	$0.734409\pi$
$24$		0			0
$25$	3.56761	−	3.50316i	0.713522	−	0.700632i
$26$		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	−0.998594	−	0.0530029i	$-0.983121\pi$
$31$	−3.03554	−	5.25771i	−0.545199	−	0.944312i	0.453395	−	0.891310i	$-0.350213\pi$
$32$		0			0
$33$	5.57535	+	3.21893i	0.970545	+	0.560344i
$34$		0			0
$35$	5.37398	−	2.47393i	0.908369	−	0.418170i
$36$		0			0
$37$	0.679339	+	0.392216i	0.111683	+	0.0644800i	0.554801	−	0.831983i	$-0.312794\pi$
$37$	0.679339	+	0.392216i	0.111683	+	0.0644800i	−0.443118	+	0.896463i	$0.646128\pi$
$38$		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	$0.267306\pi$
$43$			9.76386i			1.48897i	−0.667637	+	0.744487i	$0.732694\pi$
$44$		0			0
$45$	0.301966	−	2.21558i	0.0450144	−	0.330280i
$46$		0			0
$47$	−1.48055	−	0.854794i	−0.215960	−	0.124685i	0.388118	−	0.921610i	$-0.373125\pi$
$47$	−1.48055	−	0.854794i	−0.215960	−	0.124685i	−0.604078	+	0.796925i	$0.706459\pi$
$48$		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	$-0.518896\pi$
$53$	5.64578	−	3.25959i	0.775508	−	0.447740i	0.834836	+	0.550499i	$0.185562\pi$
$54$		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	−0.942811	−	0.333328i	$-0.891828\pi$
$59$	−5.83826	−	10.1122i	−0.760076	−	1.31649i	0.182735	−	0.983162i	$-0.441505\pi$
$60$		0			0
$61$	2.46412	−	4.26799i	0.315499	−	0.546460i	−0.664045	−	0.747693i	$-0.731162\pi$
$61$	2.46412	−	4.26799i	0.315499	−	0.546460i	0.979543	+	0.201233i	$0.0644949\pi$
$62$		0			0
$63$	1.22248	−	2.34639i	0.154018	−	0.295617i
$64$		0			0
$65$	−2.94008	−	7.19051i	−0.364673	−	0.891873i
$66$		0			0
$67$	9.35985	−	5.40391i	1.14349	−	0.660193i	0.196196	−	0.980565i	$-0.437141\pi$
$67$	9.35985	−	5.40391i	1.14349	−	0.660193i	0.947292	+	0.320372i	$0.103808\pi$
$68$		0			0
$69$	2.02592			0.243893
$70$		0			0
$71$	10.4314			1.23798			0.618989	−	0.785400i	$-0.287543\pi$
$71$	10.4314			1.23798			0.618989	+	0.785400i	$0.287543\pi$
$72$		0			0
$73$	−4.41578	+	2.54945i	−0.516828	+	0.298391i	−0.735636	−	0.677377i	$-0.763117\pi$
$73$	−4.41578	+	2.54945i	−0.516828	+	0.298391i	0.218808	+	0.975768i	$0.429783\pi$
$74$		0			0
$75$	−1.33806	+	4.81763i	−0.154506	+	0.556292i
$76$		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	$-0.932658\pi$
$79$	−2.72865	+	4.72617i	−0.306997	+	0.531735i	0.670707	+	0.741723i	$0.265991\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			15.3100i			1.68050i	0.542203	+	0.840248i	$0.317590\pi$
$83$			15.3100i			1.68050i	−0.542203	+	0.840248i	$0.682410\pi$
$84$		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	−0.461569	−	0.887104i	$-0.652713\pi$
$89$	5.07049	−	8.78234i	0.537470	−	0.930926i	0.999039	−	0.0438217i	$-0.0139534\pi$
$90$		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
$95$	−1.33719	+	9.81125i	−0.137193	+	1.00661i
$96$		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	0.778621	−	0.627494i	$-0.215919\pi$
$101$	−1.54884	−	2.68267i	−0.154115	−	0.266935i	−0.932736	+	0.360559i	$0.882586\pi$
$102$		0			0
$103$	13.2104	+	7.62702i	1.30166	+	0.751512i	0.980688	−	0.195578i	$-0.0626581\pi$
$103$	13.2104	+	7.62702i	1.30166	+	0.751512i	0.320969	+	0.947090i	$0.395991\pi$
$104$		0			0
$105$	−3.41704	+	4.82948i	−0.333469	+	0.471309i
$106$		0			0
$107$	−2.05902	−	1.18877i	−0.199053	−	0.114923i	0.397161	−	0.917749i	$-0.369995\pi$
$107$	−2.05902	−	1.18877i	−0.199053	−	0.114923i	−0.596213	+	0.802826i	$0.703329\pi$
$108$		0			0
$109$	7.20382	+	12.4774i	0.690000	+	1.19512i	0.971837	+	0.235653i	$0.0757230\pi$
$109$	7.20382	+	12.4774i	0.690000	+	1.19512i	−0.281837	+	0.959462i	$0.590944\pi$
$110$		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
$115$	−4.48861	−	0.611760i	−0.418565	−	0.0570469i
$116$		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	$0.166321\pi$
$127$			11.2482i			0.998118i	−0.866568	+	0.499059i	$0.833679\pi$
$128$		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	$-0.676663\pi$
$131$	5.40870	−	9.36814i	0.472560	−	0.818498i	0.999507	+	0.0314000i	$0.00999657\pi$
$132$		0			0
$133$	−5.41350	+	10.3905i	−0.469410	+	0.900970i
$134$		0			0
$135$	0.846282	+	2.06974i	0.0728364	+	0.178134i
$136$		0			0
$137$	1.21943	−	0.704037i	0.104183	−	0.0601500i	−0.447003	−	0.894532i	$-0.647509\pi$
$137$	1.21943	−	0.704037i	0.104183	−	0.0601500i	0.551186	+	0.834382i	$0.314175\pi$
$138$		0			0
$139$	−5.36340			−0.454917			−0.227459	−	0.973788i	$-0.573042\pi$
$139$	−5.36340			−0.454917			−0.227459	+	0.973788i	$0.573042\pi$
$140$		0			0
$141$	1.70959			0.143973
$142$		0			0
$143$	−19.3694	+	11.1829i	−1.61975	+	0.935165i
$144$		0			0
$145$	−12.9382	+	5.29024i	−1.07446	+	0.439330i
$146$		0			0
$147$	−5.73683	+	4.01108i	−0.473166	+	0.330828i
$148$		0			0
$149$	−1.46209	+	2.53241i	−0.119779	+	0.207463i	−0.919680	−	0.392669i	$-0.871552\pi$
$149$	−1.46209	+	2.53241i	−0.119779	+	0.207463i	0.799901	+	0.600132i	$0.204885\pi$
$150$		0			0
$151$	3.52450	+	6.10462i	0.286820	+	0.496787i	0.973049	−	0.230599i	$-0.0740685\pi$
$151$	3.52450	+	6.10462i	0.286820	+	0.496787i	−0.686229	+	0.727386i	$0.740735\pi$
$152$		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	$-0.710312\pi$
$157$	−2.96645	+	1.71268i	−0.236749	+	0.136687i	0.376933	+	0.926241i	$0.376979\pi$
$158$		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	0.595995	−	0.802988i	$-0.296758\pi$
$163$	2.53536	+	1.46379i	0.198584	+	0.114653i	−0.397411	+	0.917641i	$0.630091\pi$
$164$		0			0
$165$	14.2636	+	1.94402i	1.11042	+	0.151341i
$166$		0			0
$167$		−	22.1196i		−	1.71167i	−0.517250	−	0.855835i	$-0.673044\pi$
$167$		−	22.1196i		−	1.71167i	0.517250	−	0.855835i	$-0.326956\pi$
$168$		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	$-0.500184\pi$
$173$	−11.4022	−	6.58307i	−0.866894	−	0.500502i	−0.866315	+	0.499498i	$0.833518\pi$
$174$		0			0
$175$	9.02908	−	9.66828i	0.682534	−	0.730854i
$176$		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	$-0.194234\pi$
$179$	−1.15724	−	2.00439i	−0.0864960	−	0.149815i	−0.906028	+	0.423218i	$0.860900\pi$
$180$		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
$185$	1.73798	+	0.236872i	0.127779	+	0.0174152i
$186$		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	−0.133440	+	0.991057i	$0.542602\pi$
$191$	−12.7838	+	22.1421i	−0.925000	+	1.60215i	−0.791560	+	0.611091i	$0.790731\pi$
$192$		0			0
$193$	−18.8184	+	10.8648i	−1.35458	+	0.782065i	−0.988887	−	0.148672i	$-0.952500\pi$
$193$	−18.8184	+	10.8648i	−1.35458	+	0.782065i	−0.365690	+	0.930737i	$0.619167\pi$
$194$		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	$-0.0846327\pi$
$199$	3.59544	+	6.22748i	0.254874	+	0.441454i	−0.709987	+	0.704214i	$0.751299\pi$
$200$		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
$205$	21.1361	−	8.64221i	1.47621	−	0.603598i
$206$		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	$-0.507505\pi$
$211$	−0.684937			−0.0471530			−0.0235765	+	0.999722i	$0.507505\pi$
$212$		0			0
$213$	−9.03384	+	5.21569i	−0.618989	+	0.357373i
$214$		0			0
$215$	8.26298	+	20.2086i	0.563531	+	1.37822i
$216$		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	$-0.870187\pi$
$223$		−	11.8453i		−	0.793218i	0.917988	−	0.396609i	$-0.129813\pi$
$224$		0			0
$225$	−1.25002	−	4.84122i	−0.0833347	−	0.322748i
$226$		0			0
$227$	−18.7577	+	10.8298i	−1.24499	+	0.718798i	−0.970107	−	0.242678i	$-0.921974\pi$
$227$	−18.7577	+	10.8298i	−1.24499	+	0.718798i	−0.274888	+	0.961476i	$0.588641\pi$
$228$		0			0
$229$	−6.72719	+	11.6518i	−0.444545	+	0.769975i	−0.998020	−	0.0628908i	$-0.979968\pi$
$229$	−6.72719	+	11.6518i	−0.444545	+	0.769975i	0.553475	+	0.832866i	$0.313301\pi$
$230$		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	$-0.186688\pi$
$233$	11.7539	+	6.78613i	0.770026	+	0.444574i	−0.0628582	+	0.998022i	$0.520022\pi$
$234$		0			0
$235$	−3.78774	−	0.516237i	−0.247085	−	0.0336756i
$236$		0			0
$237$		−	5.45731i		−	0.354490i
$238$		0			0
$239$	16.0434			1.03776			0.518880	−	0.854847i	$-0.326349\pi$
$239$	16.0434			1.03776			0.518880	+	0.854847i	$0.326349\pi$
$240$		0			0
$241$	−6.72757	−	11.6525i	−0.433361	−	0.750603i	0.563800	−	0.825912i	$-0.309339\pi$
$241$	−6.72757	−	11.6525i	−0.433361	−	0.750603i	−0.997160	+	0.0753089i	$0.976006\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	13.9216	−	7.15456i	0.889421	−	0.457088i
$246$		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	$-0.343640\pi$
$251$	14.9463			0.943405			0.471703	+	0.881758i	$0.343640\pi$
$252$		0			0
$253$			13.0426i			0.819983i
$254$		0			0
$255$	−0.596104	+	4.37373i	−0.0373294	+	0.273894i
$256$		0			0
$257$	−3.78296	−	2.18409i	−0.235974	−	0.136240i	0.377351	−	0.926070i	$-0.376835\pi$
$257$	−3.78296	−	2.18409i	−0.235974	−	0.136240i	−0.613325	+	0.789831i	$0.710168\pi$
$258$		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	−0.135196	−	0.990819i	$-0.543166\pi$
$263$	10.6269	−	6.13542i	0.655280	−	0.378326i	0.790476	+	0.612493i	$0.209833\pi$
$264$		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	0.595438	−	0.803401i	$-0.296978\pi$
$269$	−6.52845	−	11.3076i	−0.398047	−	0.689437i	−0.993485	+	0.113964i	$0.963645\pi$
$270$		0			0
$271$	11.9787	−	20.7477i	0.727655	−	1.26034i	−0.230217	−	0.973139i	$-0.573943\pi$
$271$	11.9787	−	20.7477i	0.727655	−	1.26034i	0.957872	−	0.287196i	$-0.0927232\pi$
$272$		0			0
$273$	4.93600	+	7.75386i	0.298740	+	0.469285i
$274$		0			0
$275$	−31.0153	−	8.61426i	−1.87029	−	0.519459i
$276$		0			0
$277$	−10.0980	+	5.83008i	−0.606730	+	0.350296i	−0.771684	−	0.636006i	$-0.780586\pi$
$277$	−10.0980	+	5.83008i	−0.606730	+	0.350296i	0.164955	+	0.986301i	$0.447252\pi$
$278$		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	−0.315871	−	0.948802i	$-0.602297\pi$
$283$	5.85224	−	3.37879i	0.347880	−	0.200848i	0.663751	+	0.747954i	$0.268963\pi$
$284$		0			0
$285$	−3.74758	−	9.16539i	−0.221988	−	0.542911i
$286$		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
$305$	1.48816	−	10.9190i	0.0852119	−	0.625217i
$306$		0			0
$307$		−	33.0935i		−	1.88875i	−0.328878	−	0.944373i	$-0.606670\pi$
$307$		−	33.0935i		−	1.88875i	0.328878	−	0.944373i	$-0.393330\pi$
$308$		0			0
$309$	−15.2540			−0.867771
$310$		0			0
$311$	−6.09688	−	10.5601i	−0.345722	−	0.598809i	0.639762	−	0.768573i	$-0.279033\pi$
$311$	−6.09688	−	10.5601i	−0.345722	−	0.598809i	−0.985485	+	0.169764i	$0.945699\pi$
$312$		0			0
$313$	5.06300	+	2.92313i	0.286178	+	0.165225i	0.636217	−	0.771510i	$-0.280498\pi$
$313$	5.06300	+	2.92313i	0.286178	+	0.165225i	−0.350039	+	0.936735i	$0.613832\pi$
$314$		0			0
$315$	0.544505	−	5.89097i	0.0306794	−	0.331918i
$316$		0			0
$317$	5.53273	+	3.19432i	0.310749	+	0.179411i	0.647262	−	0.762268i	$-0.275914\pi$
$317$	5.53273	+	3.19432i	0.310749	+	0.179411i	−0.336513	+	0.941679i	$0.609247\pi$
$318$		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
$325$	−12.1704	−	12.3943i	−0.675092	−	0.687512i
$326$		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	−0.346434	−	0.938074i	$-0.612608\pi$
$331$	11.6288	−	20.1417i	0.639179	−	1.10709i	0.985613	−	0.169016i	$-0.0540590\pi$
$332$		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
$345$	4.19313	−	1.71450i	0.225750	−	0.0923058i
$346$		0			0
$347$	−1.39822	+	0.807265i	−0.0750606	+	0.0433362i	−0.537061	−	0.843544i	$-0.680465\pi$
$347$	−1.39822	+	0.807265i	−0.0750606	+	0.0433362i	0.462000	+	0.886880i	$0.347132\pi$
$348$		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	$-0.729386\pi$
$353$	−6.37068	+	3.67811i	−0.339077	+	0.195766i	0.320787	+	0.947151i	$0.396053\pi$
$354$		0			0
$355$	21.5902	−	8.82790i	1.14589	−	0.468536i
$356$		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	$-0.850740\pi$
$359$	−1.03562	+	1.79375i	−0.0546580	+	0.0946705i	0.837402	+	0.546588i	$0.184074\pi$
$360$		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	−0.355782	−	0.934569i	$-0.615785\pi$
$367$	5.28141	−	3.04922i	0.275687	−	0.159168i	0.631469	+	0.775401i	$0.282452\pi$
$368$		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	$-0.0970311\pi$
$373$	22.6143	+	13.0564i	1.17092	+	0.676033i	0.217026	+	0.976166i	$0.430364\pi$
$374$		0			0
$375$	1.30764	+	11.1036i	0.0675264	+	0.573388i
$376$		0			0
$377$			21.7172i			1.11849i
$378$		0			0
$379$	−18.9893			−0.975414			−0.487707	−	0.873007i	$-0.662167\pi$
$379$	−18.9893			−0.975414			−0.487707	+	0.873007i	$0.662167\pi$
$380$		0			0
$381$	−5.62411	−	9.74125i	−0.288132	−	0.499059i
$382$		0			0
$383$	25.2815	+	14.5963i	1.29183	+	0.745836i	0.978978	−	0.203968i	$-0.0653838\pi$
$383$	25.2815	+	14.5963i	1.29183	+	0.745836i	0.312847	+	0.949803i	$0.398717\pi$
$384$		0			0
$385$	−31.0915	−	21.9984i	−1.58457	−	1.12114i
$386$		0			0
$387$	8.45575	+	4.88193i	0.429830	+	0.248162i
$388$		0			0
$389$	−12.1922	−	21.1175i	−0.618168	−	1.07070i	−0.989820	−	0.142327i	$-0.954542\pi$
$389$	−12.1922	−	21.1175i	−0.618168	−	1.07070i	0.371651	−	0.928372i	$-0.378792\pi$
$390$		0			0
$391$	−3.99933			−0.202255
$392$		0			0
$393$			10.8174i			0.545666i
$394$		0			0
$395$	−1.64792	+	12.0911i	−0.0829159	+	0.608371i
$396$		0			0
$397$	5.97866	+	3.45178i	0.300060	+	0.173240i	0.642470	−	0.766311i	$-0.277910\pi$
$397$	5.97866	+	3.45178i	0.300060	+	0.173240i	−0.342410	+	0.939551i	$0.611243\pi$
$398$		0			0
$399$	−0.507016	−	11.7052i	−0.0253825	−	0.585992i
$400$		0			0
$401$	−16.6242	+	28.7940i	−0.830173	+	1.43790i	0.0677277	+	0.997704i	$0.478425\pi$
$401$	−16.6242	+	28.7940i	−0.830173	+	1.43790i	−0.897901	+	0.440198i	$0.854908\pi$
$402$		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	0.997349	−	0.0727612i	$-0.0231811\pi$
$409$	8.81071	+	15.2606i	0.435662	+	0.754588i	−0.561688	+	0.827349i	$0.689848\pi$
$410$		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
$415$	12.9566	+	31.6877i	0.636015	+	1.55549i
$416$		0			0
$417$	4.64484	−	2.68170i	0.227459	−	0.131323i
$418$		0			0
$419$	−17.7842			−0.868813			−0.434406	−	0.900717i	$-0.643042\pi$
$419$	−17.7842			−0.868813			−0.434406	+	0.900717i	$0.643042\pi$
$420$		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
$425$	2.64144	−	9.51037i	0.128128	−	0.461321i
$426$		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	$-0.100624\pi$
$431$	4.27652	+	7.40715i	0.205993	+	0.356790i	−0.744456	+	0.667672i	$0.767291\pi$
$432$		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	$-0.728517\pi$
$439$	6.77536	−	11.7353i	0.323370	−	0.560093i	0.981181	+	0.193090i	$0.0618508\pi$
$440$		0			0
$441$	2.96270	−	6.34211i	0.141081	−	0.302005i
$442$		0			0
$443$	12.0290	+	6.94496i	0.571516	+	0.329965i	0.757755	−	0.652539i	$-0.226296\pi$
$443$	12.0290	+	6.94496i	0.571516	+	0.329965i	−0.186238	+	0.982505i	$0.559630\pi$
$444$		0			0
$445$	3.06223	−	22.4682i	0.145163	−	1.06509i
$446$		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
$455$	−8.59472	−	18.6698i	−0.402927	−	0.875256i
$456$		0			0
$457$	−2.29331	−	1.32404i	−0.107276	−	0.0619360i	0.445402	−	0.895331i	$-0.353061\pi$
$457$	−2.29331	−	1.32404i	−0.107276	−	0.0619360i	−0.552678	+	0.833395i	$0.686394\pi$
$458$		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	$-0.837333\pi$
$463$		−	21.0475i		−	0.978160i	0.872239	−	0.489080i	$-0.162667\pi$
$464$		0			0
$465$	13.4510	+	1.83326i	0.623775	+	0.0850153i
$466$		0			0
$467$	8.33062	+	4.80968i	0.385495	+	0.222566i	0.680206	−	0.733021i	$-0.261890\pi$
$467$	8.33062	+	4.80968i	0.385495	+	0.222566i	−0.294711	+	0.955586i	$0.595223\pi$
$468$		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	0.979766	+	0.200146i	$0.0641418\pi$
$479$	14.5152	+	25.1410i	0.663215	+	1.14872i	−0.316551	+	0.948575i	$0.602525\pi$
$480$		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
$485$	8.40766	+	20.5624i	0.381772	+	0.933692i
$486$		0			0
$487$	−9.37294	+	5.41147i	−0.424729	+	0.245217i	−0.697098	−	0.716975i	$-0.745526\pi$
$487$	−9.37294	+	5.41147i	−0.424729	+	0.245217i	0.272370	+	0.962193i	$0.412193\pi$
$488$		0			0
$489$	−2.92758			−0.132390
$490$		0			0
$491$	25.0455			1.13029			0.565143	−	0.824993i	$-0.308821\pi$
$491$	25.0455			1.13029			0.565143	+	0.824993i	$0.308821\pi$
$492$		0			0
$493$	−10.6870	+	6.17012i	−0.481317	+	0.277888i
$494$		0			0
$495$	−13.3247	+	5.44825i	−0.598900	+	0.244881i
$496$		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	$-0.802950\pi$
$499$	2.12900	−	3.68753i	0.0953069	−	0.165076i	0.909737	+	0.415186i	$0.136283\pi$
$500$		0			0
$501$	11.0598	+	19.1562i	0.494116	+	0.855835i
$502$		0			0
$503$			31.2478i			1.39327i	0.717425	+	0.696636i	$0.245321\pi$
$503$			31.2478i			1.39327i	−0.717425	+	0.696636i	$0.754679\pi$
$504$		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	−0.738558	−	0.674190i	$-0.764493\pi$
$509$	4.84131	−	8.38539i	0.214587	−	0.371676i	0.953145	+	0.302514i	$0.0978261\pi$
$510$		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
$515$	33.7966	+	4.60620i	1.48926	+	0.202973i
$516$		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	0.537070	−	0.843538i	$-0.319531\pi$
$521$	−10.5451	−	18.2647i	−0.461990	−	0.800190i	−0.999060	+	0.0433477i	$0.986198\pi$
$522$		0			0
$523$	−22.5910	−	13.0429i	−0.987837	−	0.570328i	−0.0832098	−	0.996532i	$-0.526517\pi$
$523$	−22.5910	−	13.0429i	−0.987837	−	0.570328i	−0.904627	+	0.426204i	$0.859850\pi$
$524$		0			0
$525$	−2.98527	+	12.8875i	−0.130288	+	0.562457i
$526$		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
$535$	−5.26766	−	0.717938i	−0.227741	−	0.0310392i
$536$		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	−0.0858430	−	0.996309i	$-0.527358\pi$
$541$	19.0706	−	33.0312i	0.819907	−	1.42012i	0.905750	−	0.423812i	$-0.139308\pi$
$542$		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	$0.228704\pi$
$547$			30.7904i			1.31650i	−0.752798	+	0.658252i	$0.771296\pi$
$548$		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
$555$	−1.62357	+	0.663852i	−0.0689167	+	0.0281789i
$556$		0			0
$557$	15.6082	−	9.01142i	0.661342	−	0.381826i	−0.131446	−	0.991323i	$-0.541962\pi$
$557$	15.6082	−	9.01142i	0.661342	−	0.381826i	0.792788	+	0.609497i	$0.208629\pi$
$558$		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	−0.373150	−	0.927771i	$-0.621722\pi$
$563$	5.78357	−	3.33914i	0.243748	−	0.140728i	0.616898	+	0.787043i	$0.288389\pi$
$564$		0			0
$565$	4.55770	+	11.1467i	0.191744	+	0.468944i
$566$		0			0
$567$	−1.42079	−	2.23189i	−0.0596676	−	0.0937307i
$568$		0			0
$569$	−8.52169	+	14.7600i	−0.357248	+	0.618771i	−0.987500	−	0.157619i	$-0.949618\pi$
$569$	−8.52169	+	14.7600i	−0.357248	+	0.618771i	0.630252	+	0.776390i	$0.282951\pi$
$570$		0			0
$571$	19.4492	+	33.6870i	0.813923	+	1.40976i	0.910098	+	0.414392i	$0.136006\pi$
$571$	19.4492	+	33.6870i	0.813923	+	1.40976i	−0.0961751	+	0.995364i	$0.530661\pi$
$572$		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	$-0.692911\pi$
$577$	−3.42639	+	1.97823i	−0.142643	+	0.0823547i	0.426980	+	0.904261i	$0.359577\pi$
$578$		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
$585$	−7.69720	−	1.04906i	−0.318240	−	0.0433735i
$586$		0			0
$587$			8.33774i			0.344135i	0.985085	+	0.172068i	$0.0550448\pi$
$587$			8.33774i			0.344135i	−0.985085	+	0.172068i	$0.944955\pi$
$588$		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	$-0.497961\pi$
$593$	−20.8547	−	12.0405i	−0.856400	−	0.494442i	−0.862805	+	0.505537i	$0.831294\pi$
$594$		0			0
$595$	6.74550	−	9.53375i	0.276538	−	0.390846i
$596$		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	$-0.271641\pi$
$599$	−7.92587	−	13.7280i	−0.323842	−	0.560912i	−0.981277	+	0.192600i	$0.938308\pi$
$600$		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
$605$	−9.19368	+	67.4559i	−0.373776	+	2.74247i
$606$		0			0
$607$	−9.07478	−	5.23933i	−0.368334	−	0.212658i	0.304396	−	0.952545i	$-0.401545\pi$
$607$	−9.07478	−	5.23933i	−0.368334	−	0.212658i	−0.672730	+	0.739888i	$0.734879\pi$
$608$		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	$-0.557025\pi$
$613$	14.4808	−	8.36052i	0.584876	−	0.337678i	0.763069	+	0.646317i	$0.223692\pi$
$614$		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	0.999169	+	0.0407546i	$0.0129762\pi$
$619$	13.3076	+	23.0495i	0.534879	+	0.926438i	−0.464290	+	0.885683i	$0.653690\pi$
$620$		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
$625$	0.455714	−	24.9958i	0.0182286	−	0.999834i
$626$		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	$-0.156476\pi$
$631$	44.2904			1.76317			0.881586	+	0.472023i	$0.156476\pi$
$632$		0			0
$633$	0.593173	−	0.342468i	0.0235765	−	0.0136119i
$634$		0			0
$635$	9.51917	+	23.2808i	0.377757	+	0.923872i
$636$		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	0.892054	−	0.451928i	$-0.149264\pi$
$641$	1.38352	+	2.39632i	0.0546457	+	0.0946491i	−0.837409	+	0.546577i	$0.815930\pi$
$642$		0			0
$643$		−	37.1906i		−	1.46665i	−0.679876	−	0.733327i	$-0.737966\pi$
$643$		−	37.1906i		−	1.46665i	0.679876	−	0.733327i	$-0.262034\pi$
$644$		0			0
$645$	−17.2603	−	13.3697i	−0.679622	−	0.526430i
$646$		0			0
$647$	10.0673	−	5.81235i	0.395786	−	0.228507i	−0.288878	−	0.957366i	$-0.593282\pi$
$647$	10.0673	−	5.81235i	0.395786	−	0.228507i	0.684664	+	0.728859i	$0.259949\pi$
$648$		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	$-0.460970\pi$
$653$	−17.2759	−	9.97424i	−0.676058	−	0.390322i	−0.798368	+	0.602170i	$0.794303\pi$
$654$		0			0
$655$	3.26648	−	23.9669i	0.127632	−	0.936463i
$656$		0			0
$657$			5.09891i			0.198927i
$658$		0			0
$659$	−38.7827			−1.51076			−0.755380	−	0.655287i	$-0.772548\pi$
$659$	−38.7827			−1.51076			−0.755380	+	0.655287i	$0.772548\pi$
$660$		0			0
$661$	6.42009	+	11.1199i	0.249713	+	0.432515i	0.963446	−	0.267903i	$-0.0863305\pi$
$661$	6.42009	+	11.1199i	0.249713	+	0.432515i	−0.713733	+	0.700417i	$0.752997\pi$
$662$		0			0
$663$	5.93935	+	3.42909i	0.230665	+	0.133175i
$664$		0			0
$665$	−2.41123	+	26.0869i	−0.0935034	+	1.01161i
$666$		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
$675$	3.50316	+	3.56761i	0.134837	+	0.137317i
$676$		0			0
$677$	19.0937	+	11.0237i	0.733830	+	0.423677i	0.819822	−	0.572619i	$-0.194072\pi$
$677$	19.0937	+	11.0237i	0.733830	+	0.423677i	−0.0859916	+	0.996296i	$0.527406\pi$
$678$		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	−0.787141	−	0.616773i	$-0.788440\pi$
$683$	−16.8976	+	9.75586i	−0.646571	+	0.373298i	0.140570	+	0.990071i	$0.455106\pi$
$684$		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	$-0.880547\pi$
$691$	−3.88472	+	6.72854i	−0.147782	+	0.255966i	0.782625	+	0.622493i	$0.213880\pi$
$692$		0			0
$693$	−17.0170	+	0.737101i	−0.646424	+	0.0280002i
$694$		0			0
$695$	−11.1008	+	4.53895i	−0.421078	+	0.172172i
$696$		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
$705$	3.53840	−	1.44679i	0.133264	−	0.0544894i
$706$		0			0
$707$	−4.40115	−	6.91368i	−0.165522	−	0.260016i
$708$		0			0
$709$	7.35513	−	12.7395i	0.276228	−	0.478441i	−0.694216	−	0.719766i	$-0.744249\pi$
$709$	7.35513	−	12.7395i	0.276228	−	0.478441i	0.970444	+	0.241326i	$0.0775822\pi$
$710$		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	$-0.930645\pi$
$719$	−8.07036	+	13.9783i	−0.300974	+	0.521302i	0.675383	+	0.737467i	$0.263978\pi$
$720$		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
$725$	−22.3017	+	21.8988i	−0.828263	+	0.813301i
$726$		0			0
$727$		−	12.7937i		−	0.474492i	−0.971450	−	0.237246i	$-0.923755\pi$
$727$		−	12.7937i		−	0.474492i	0.971450	−	0.237246i	$-0.0762447\pi$
$728$		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	$-0.313045\pi$
$733$	2.98687	+	1.72447i	0.110323	+	0.0636949i	−0.443823	+	0.896114i	$0.646378\pi$
$734$		0			0
$735$	−8.47922	+	13.1569i	−0.312761	+	0.485298i
$736$		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	$-0.161804\pi$
$739$	0.415306	+	0.719331i	0.0152773	+	0.0264610i	−0.858286	+	0.513172i	$0.828470\pi$
$740$		0			0
$741$	−15.3844			−0.565160
$742$		0			0
$743$			44.6351i			1.63750i	0.574149	+	0.818751i	$0.305333\pi$
$743$			44.6351i			1.63750i	−0.574149	+	0.818751i	$0.694667\pi$
$744$		0			0
$745$	−0.883000	+	6.47875i	−0.0323506	+	0.237363i
$746$		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	$-0.855519\pi$
$751$	−1.90845	+	3.30554i	−0.0696404	+	0.120621i	0.829103	+	0.559096i	$0.188852\pi$
$752$		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	−0.560143	−	0.828396i	$-0.689254\pi$
$761$	12.0646	−	20.8964i	0.437340	−	0.757495i	0.997483	+	0.0709007i	$0.0225873\pi$
$762$		0			0
$763$	20.4702	+	32.1563i	0.741072	+	1.16414i
$764$		0			0
$765$	−1.67063	−	4.08582i	−0.0604016	−	0.147723i
$766$		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	$-0.668123\pi$
$773$	−0.220383	+	0.127238i	−0.00792664	+	0.00457645i	0.496031	+	0.868305i	$0.334790\pi$
$774$		0			0
$775$	−29.2482	−	8.12348i	−1.05063	−	0.291804i
$776$		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	−0.727460	−	0.686150i	$-0.759299\pi$
$787$	−13.9417	+	8.04923i	−0.496967	+	0.286924i	0.230493	+	0.973074i	$0.425966\pi$
$788$		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
$795$	−1.96857	+	14.4438i	−0.0698181	+	0.512269i
$796$		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
$805$	−11.9347	−	1.10313i	−0.420641	−	0.0388801i
$806$		0			0
$807$	11.3076	+	6.52845i	0.398047	+	0.229812i
$808$		0			0
$809$	15.6052	+	27.0291i	0.548651	+	0.950291i	0.998367	+	0.0571195i	$0.0181916\pi$
$809$	15.6052	+	27.0291i	0.548651	+	0.950291i	−0.449717	+	0.893171i	$0.648475\pi$
$810$		0			0
$811$	6.91344			0.242764			0.121382	−	0.992606i	$-0.461267\pi$
$811$	6.91344			0.242764			0.121382	+	0.992606i	$0.461267\pi$
$812$		0			0
$813$			23.9574i			0.840224i
$814$		0			0
$815$	6.48629	+	0.884028i	0.227205	+	0.0309662i
$816$		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	−0.899657	−	0.436597i	$-0.856184\pi$
$821$	−2.05513	+	3.55959i	−0.0717245	+	0.124230i	0.827933	+	0.560827i	$0.189517\pi$
$822$		0			0
$823$	25.6619	−	14.8159i	0.894516	−	0.516449i	0.0190992	−	0.999818i	$-0.493920\pi$
$823$	25.6619	−	14.8159i	0.894516	−	0.516449i	0.875417	+	0.483368i	$0.160587\pi$
$824$		0			0
$825$	31.1671	−	8.04747i	1.08510	−	0.280177i
$826$		0			0
$827$		−	1.19658i		−	0.0416093i	−0.999784	−	0.0208046i	$-0.993377\pi$
$827$		−	1.19658i		−	0.0416093i	0.999784	−	0.0208046i	$-0.00662280\pi$
$828$		0			0
$829$	0.860027	+	1.48961i	0.0298700	+	0.0517363i	0.880574	−	0.473909i	$-0.157157\pi$
$829$	0.860027	+	1.48961i	0.0298700	+	0.0517363i	−0.850704	+	0.525645i	$0.823824\pi$
$830$		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
$835$	−18.7195	−	45.7818i	−0.647814	−	1.58434i
$836$		0			0
$837$	5.25771	−	3.03554i	0.181733	−	0.104924i
$838$		0			0
$839$	14.6942			0.507299			0.253650	−	0.967296i	$-0.418369\pi$
$839$	14.6942			0.507299			0.253650	+	0.967296i	$0.418369\pi$
$840$		0			0
$841$	10.0769			0.347478
$842$		0			0
$843$	2.73073	−	1.57659i	0.0940514	−	0.0543006i
$844$		0			0
$845$	1.92590	−	0.787469i	0.0662529	−	0.0270898i
$846$		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	$-0.731378\pi$
$857$	−10.2373	+	5.91051i	−0.349699	+	0.201899i	0.314853	+	0.949140i	$0.398045\pi$
$858$		0			0
$859$	−6.63018	+	11.4838i	−0.226219	+	0.391822i	−0.956684	−	0.291127i	$-0.905970\pi$
$859$	−6.63018	+	11.4838i	−0.226219	+	0.391822i	0.730466	+	0.682949i	$0.239303\pi$
$860$		0			0
$861$	−22.7920	+	14.5091i	−0.776750	+	0.494468i
$862$		0			0
$863$	−41.8247	−	24.1475i	−1.42373	−	0.821990i	−0.427114	−	0.904198i	$-0.640470\pi$
$863$	−41.8247	−	24.1475i	−1.42373	−	0.821990i	−0.996615	+	0.0822074i	$0.973803\pi$
$864$		0			0
$865$	−29.1707	−	3.97572i	−0.991834	−	0.135179i
$866$		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
$875$	10.5057	−	27.6519i	0.355158	−	0.934806i
$876$		0			0
$877$	45.4274	+	26.2275i	1.53397	+	0.885640i	0.999173	+	0.0406624i	$0.0129468\pi$
$877$	45.4274	+	26.2275i	1.53397	+	0.885640i	0.534801	+	0.844978i	$0.320387\pi$
$878$		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	$-0.910001\pi$
$883$		−	16.5805i		−	0.557977i	0.960294	−	0.278988i	$-0.0899991\pi$
$884$		0			0
$885$	25.8703	+	3.52591i	0.869621	+	0.118522i
$886$		0			0
$887$	2.68503	+	1.55020i	0.0901546	+	0.0520508i	0.544399	−	0.838826i	$-0.316758\pi$
$887$	2.68503	+	1.55020i	0.0901546	+	0.0520508i	−0.454245	+	0.890877i	$0.650091\pi$
$888$		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
$905$	6.33764	−	2.59136i	0.210670	−	0.0861397i
$906$		0			0
$907$	−46.7805	+	27.0087i	−1.55332	+	0.896810i	−0.555452	+	0.831549i	$0.687455\pi$
$907$	−46.7805	+	27.0087i	−1.55332	+	0.896810i	−0.997868	+	0.0652613i	$0.979212\pi$
$908$		0			0
$909$	−3.09768			−0.102743
$910$		0			0
$911$	−37.7405			−1.25040			−0.625199	−	0.780466i	$-0.714982\pi$
$911$	−37.7405			−1.25040			−0.625199	+	0.780466i	$0.714982\pi$
$912$		0			0
$913$	85.3589	−	49.2820i	2.82497	−	1.63100i
$914$		0			0
$915$	4.17069	+	10.2002i	0.137879	+	0.337207i
$916$		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	$-0.864563\pi$
$919$	−2.96944	+	5.14321i	−0.0979527	+	0.169659i	0.812884	+	0.582425i	$0.197896\pi$
$920$		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	−0.424086	−	0.905622i	$-0.639404\pi$
$929$	17.4419	−	30.2102i	0.572249	−	0.991164i	0.996335	−	0.0855421i	$-0.0272622\pi$
$930$		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
$935$	−28.1575	−	3.83763i	−0.920849	−	0.125504i
$936$		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	0.897589	−	0.440834i	$-0.145317\pi$
$941$	2.05593	+	3.56098i	0.0670214	+	0.116085i	−0.830567	+	0.556918i	$0.811984\pi$
$942$		0			0
$943$	−17.9169	−	10.3443i	−0.583455	−	0.336858i
$944$		0			0
$945$	2.47393	+	5.37398i	0.0804769	+	0.174816i
$946$		0			0
$947$	−0.839535	−	0.484706i	−0.0272812	−	0.0157508i	0.486297	−	0.873793i	$-0.338347\pi$
$947$	−0.839535	−	0.484706i	−0.0272812	−	0.0157508i	−0.513579	+	0.858043i	$0.671681\pi$
$948$		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
$955$	−7.72052	+	56.6470i	−0.249830	+	1.83305i
$956$		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	$-0.941351\pi$
$967$		−	11.3945i		−	0.366421i	0.983074	−	0.183211i	$-0.0586490\pi$
$968$		0			0
$969$	−4.37089	−	7.57060i	−0.140413	−	0.243203i
$970$		0			0
$971$	21.4249	−	37.1091i	0.687558	−	1.19089i	−0.285067	−	0.958508i	$-0.592016\pi$
$971$	21.4249	−	37.1091i	0.687558	−	1.19089i	0.972625	−	0.232379i	$-0.0746508\pi$
$972$		0			0
$973$	−14.1769	+	0.614080i	−0.454491	+	0.0196865i
$974$		0			0
$975$	16.7370	+	4.64859i	0.536014	+	0.148874i
$976$		0			0
$977$	10.9311	−	6.31107i	0.349717	−	0.201909i	−0.314844	−	0.949144i	$-0.601952\pi$
$977$	10.9311	−	6.31107i	0.349717	−	0.201909i	0.664561	+	0.747234i	$0.268619\pi$
$978$		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	−0.840310	−	0.542106i	$-0.817627\pi$
$983$	−24.7997	+	14.3181i	−0.790988	+	0.456677i	0.0493222	+	0.998783i	$0.484294\pi$
$984$		0			0
$985$	9.53301	+	23.3147i	0.303747	+	0.742868i
$986$		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	−0.973192	−	0.229993i	$-0.926130\pi$
$991$	−21.5883	−	37.3921i	−0.685776	−	1.18780i	0.287417	−	0.957806i	$-0.407204\pi$
$992$		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	$-0.623023\pi$
$997$	7.47512	−	4.31576i	0.236739	−	0.136682i	0.613677	+	0.789557i	$0.289690\pi$
$998$		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	840.2.cc.c.289.5	✓	24
4.3	odd	2		1680.2.di.g.289.8		24
5.4	even	2	inner	840.2.cc.c.289.9	yes	24
7.4	even	3	inner	840.2.cc.c.529.9	yes	24
20.19	odd	2		1680.2.di.g.289.4		24
28.11	odd	6		1680.2.di.g.529.4		24
35.4	even	6	inner	840.2.cc.c.529.5	yes	24
140.39	odd	6		1680.2.di.g.529.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cc.c.289.5	✓	24	1.1	even	1	trivial
840.2.cc.c.289.9	yes	24	5.4	even	2	inner
840.2.cc.c.529.5	yes	24	35.4	even	6	inner
840.2.cc.c.529.9	yes	24	7.4	even	3	inner
1680.2.di.g.289.4		24	20.19	odd	2
1680.2.di.g.289.8		24	4.3	odd	2
1680.2.di.g.529.4		24	28.11	odd	6
1680.2.di.g.529.8		24	140.39	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(2.06974 - 0.846282i) q^{5} +(2.64327 - 0.114495i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-3.21893 - 5.57535i) q^{11} -3.47412i q^{13} +(-1.36930 + 1.76777i) q^{15} +(1.70960 - 0.987038i) q^{17} +(-2.21415 + 3.83501i) q^{19} +(-2.23189 + 1.42079i) q^{21} +(-1.75450 - 1.01296i) q^{23} +(3.56761 - 3.50316i) q^{25} +1.00000i q^{27} -6.25115 q^{29} +(-3.03554 - 5.25771i) q^{31} +(5.57535 + 3.21893i) q^{33} +(5.37398 - 2.47393i) q^{35} +(0.679339 + 0.392216i) q^{37} +(1.73706 + 3.00867i) q^{39} +10.2120 q^{41} +9.76386i q^{43} +(0.301966 - 2.21558i) q^{45} +(-1.48055 - 0.854794i) q^{47} +(6.97378 - 0.605281i) q^{49} +(-0.987038 + 1.70960i) q^{51} +(5.64578 - 3.25959i) q^{53} +(-11.3807 - 8.81538i) q^{55} -4.42829i q^{57} +(-5.83826 - 10.1122i) q^{59} +(2.46412 - 4.26799i) q^{61} +(1.22248 - 2.34639i) q^{63} +(-2.94008 - 7.19051i) q^{65} +(9.35985 - 5.40391i) q^{67} +2.02592 q^{69} +10.4314 q^{71} +(-4.41578 + 2.54945i) q^{73} +(-1.33806 + 4.81763i) q^{75} +(-9.14686 - 14.3686i) q^{77} +(-2.72865 + 4.72617i) q^{79} +(-0.500000 - 0.866025i) q^{81} +15.3100i q^{83} +(2.70311 - 3.48971i) q^{85} +(5.41365 - 3.12557i) q^{87} +(5.07049 - 8.78234i) q^{89} +(-0.397768 - 9.18304i) q^{91} +(5.25771 + 3.03554i) q^{93} +(-1.33719 + 9.81125i) q^{95} +9.93481i q^{97} -6.43786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5} + 12 q^{9} - 8 q^{11} + 8 q^{19} + 12 q^{21} + 2 q^{25} - 24 q^{29} + 4 q^{31} + 30 q^{35} + 4 q^{39} + 32 q^{41} - 2 q^{45} - 12 q^{49} - 20 q^{51} + 12 q^{55} - 4 q^{59} + 32 q^{61} + 22 q^{65}+ \cdots - 16 q^{99}+O(q^{100}) \) 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

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Groups

Database

Properties

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