LMFDB - Embedded newform 936.2.cw.b.25.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(25,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.cw (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.23
Character	$\chi$	$=$	936.25
Dual form			936.2.cw.b.337.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.242542 - 1.71498i) q^{3} +(-1.55919 + 0.900198i) q^{5} +(-2.30144 - 1.32873i) q^{7} +(-2.88235 - 0.831913i) q^{9} +(1.01492 + 0.585964i) q^{11} +(-2.35702 - 2.72845i) q^{13} +(1.16566 + 2.89232i) q^{15} +1.33805 q^{17} +7.81675i q^{19} +(-2.83695 + 3.62465i) q^{21} +(2.83598 + 4.91206i) q^{23} +(-0.879286 + 1.52297i) q^{25} +(-2.12581 + 4.74141i) q^{27} +(3.00413 - 5.20331i) q^{29} +(-2.23496 + 1.29036i) q^{31} +(1.25108 - 1.59845i) q^{33} +4.78450 q^{35} +5.90191i q^{37} +(-5.25093 + 3.38049i) q^{39} +(-6.23926 + 3.60224i) q^{41} +(-5.04619 + 8.74025i) q^{43} +(5.24301 - 1.29757i) q^{45} +(-8.20794 - 4.73885i) q^{47} +(0.0310704 + 0.0538156i) q^{49} +(0.324533 - 2.29473i) q^{51} -12.3419 q^{53} -2.10994 q^{55} +(13.4056 + 1.89589i) q^{57} +(10.6080 - 6.12456i) q^{59} +(5.22284 - 9.04622i) q^{61} +(5.52814 + 5.74447i) q^{63} +(6.13119 + 2.13239i) q^{65} +(-5.17129 + 2.98565i) q^{67} +(9.11195 - 3.67228i) q^{69} -1.35532i q^{71} +9.98135i q^{73} +(2.39860 + 1.87735i) q^{75} +(-1.55718 - 2.69712i) q^{77} +(-2.14171 + 3.70956i) q^{79} +(7.61584 + 4.79572i) q^{81} +(-1.70208 - 0.982698i) q^{83} +(-2.08627 + 1.20451i) q^{85} +(-8.19497 - 6.41406i) q^{87} -8.41529i q^{89} +(1.79914 + 9.41121i) q^{91} +(1.67087 + 4.14589i) q^{93} +(-7.03663 - 12.1878i) q^{95} +(-0.765238 - 0.441810i) q^{97} +(-2.43788 - 2.53328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - 6 q^{9} + 6 q^{13} - 4 q^{17} + 10 q^{23} + 44 q^{25} + 6 q^{27} - 52 q^{35} + 40 q^{39} - 26 q^{43} + 48 q^{49} + 36 q^{51} + 60 q^{53} - 16 q^{55} - 10 q^{61} - 26 q^{65} - 38 q^{69}+ \cdots + 8 q^{95}+O(q^{100}) $ 80 * q - 6 * q^3 - 6 * q^9 + 6 * q^13 - 4 * q^17 + 10 * q^23 + 44 * q^25 + 6 * q^27 - 52 * q^35 + 40 * q^39 - 26 * q^43 + 48 * q^49 + 36 * q^51 + 60 * q^53 - 16 * q^55 - 10 * q^61 - 26 * q^65 - 38 * q^69 + 32 * q^75 + 32 * q^77 + 6 * q^79 - 38 * q^81 + 4 * q^87 - 4 * q^91 + 8 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.242542	−	1.71498i	0.140032	−	0.990147i
$3$	0.242542	−	1.71498i	0.140032	−	0.990147i
$4$		0			0
$5$	−1.55919	+	0.900198i	−0.697291	+	0.402581i	−0.806338	−	0.591456i	$-0.798553\pi$
$5$	−1.55919	+	0.900198i	−0.697291	+	0.402581i	0.109047	+	0.994037i	$0.465220\pi$
$6$		0			0
$7$	−2.30144	−	1.32873i	−0.869861	−	0.502214i	−0.00255888	−	0.999997i	$-0.500815\pi$
$7$	−2.30144	−	1.32873i	−0.869861	−	0.502214i	−0.867302	+	0.497782i	$0.834148\pi$
$8$		0			0
$9$	−2.88235	−	0.831913i	−0.960782	−	0.277304i
$10$		0			0
$11$	1.01492	+	0.585964i	0.306010	+	0.176675i	0.645140	−	0.764065i	$-0.276799\pi$
$11$	1.01492	+	0.585964i	0.306010	+	0.176675i	−0.339130	+	0.940740i	$0.610133\pi$
$12$		0			0
$13$	−2.35702	−	2.72845i	−0.653720	−	0.756736i
$13$	−2.35702	−	2.72845i	−0.653720	−	0.756736i
$14$		0			0
$15$	1.16566	+	2.89232i	0.300971	+	0.746794i
$16$		0			0
$17$	1.33805			0.324524			0.162262	−	0.986748i	$-0.448121\pi$
$17$	1.33805			0.324524			0.162262	+	0.986748i	$0.448121\pi$
$18$		0			0
$19$			7.81675i			1.79329i	0.442754	+	0.896643i	$0.354001\pi$
$19$			7.81675i			1.79329i	−0.442754	+	0.896643i	$0.645999\pi$
$20$		0			0
$21$	−2.83695	+	3.62465i	−0.619074	+	0.790964i
$22$		0			0
$23$	2.83598	+	4.91206i	0.591342	+	1.02423i	0.994052	+	0.108907i	$0.0347351\pi$
$23$	2.83598	+	4.91206i	0.591342	+	1.02423i	−0.402710	+	0.915328i	$0.631932\pi$
$24$		0			0
$25$	−0.879286	+	1.52297i	−0.175857	+	0.304594i
$26$		0			0
$27$	−2.12581	+	4.74141i	−0.409112	+	0.912484i
$28$		0			0
$29$	3.00413	−	5.20331i	0.557853	−	0.966230i	−0.439822	−	0.898085i	$-0.644958\pi$
$29$	3.00413	−	5.20331i	0.557853	−	0.966230i	0.997675	−	0.0681455i	$-0.0217082\pi$
$30$		0			0
$31$	−2.23496	+	1.29036i	−0.401411	+	0.231755i	−0.687093	−	0.726570i	$-0.741113\pi$
$31$	−2.23496	+	1.29036i	−0.401411	+	0.231755i	0.285682	+	0.958325i	$0.407780\pi$
$32$		0			0
$33$	1.25108	−	1.59845i	0.217785	−	0.278255i
$34$		0			0
$35$	4.78450			0.808728
$36$		0			0
$37$			5.90191i			0.970268i	0.874440	+	0.485134i	$0.161229\pi$
$37$			5.90191i			0.970268i	−0.874440	+	0.485134i	$0.838771\pi$
$38$		0			0
$39$	−5.25093	+	3.38049i	−0.840822	+	0.541312i
$40$		0			0
$41$	−6.23926	+	3.60224i	−0.974408	+	0.562575i	−0.900577	−	0.434696i	$-0.856856\pi$
$41$	−6.23926	+	3.60224i	−0.974408	+	0.562575i	−0.0738310	+	0.997271i	$0.523523\pi$
$42$		0			0
$43$	−5.04619	+	8.74025i	−0.769536	+	1.33288i	0.168279	+	0.985739i	$0.446179\pi$
$43$	−5.04619	+	8.74025i	−0.769536	+	1.33288i	−0.937815	+	0.347136i	$0.887154\pi$
$44$		0			0
$45$	5.24301	−	1.29757i	0.781582	−	0.193431i
$46$		0			0
$47$	−8.20794	−	4.73885i	−1.19725	−	0.691233i	−0.237309	−	0.971434i	$-0.576265\pi$
$47$	−8.20794	−	4.73885i	−1.19725	−	0.691233i	−0.959941	+	0.280201i	$0.909599\pi$
$48$		0			0
$49$	0.0310704	+	0.0538156i	0.00443864	+	0.00768794i
$50$		0			0
$51$	0.324533	−	2.29473i	0.0454437	−	0.321326i
$52$		0			0
$53$	−12.3419			−1.69529			−0.847645	−	0.530564i	$-0.821980\pi$
$53$	−12.3419			−1.69529			−0.847645	+	0.530564i	$0.821980\pi$
$54$		0			0
$55$	−2.10994			−0.284504
$56$		0			0
$57$	13.4056	+	1.89589i	1.77562	+	0.251117i
$58$		0			0
$59$	10.6080	−	6.12456i	1.38105	−	0.797349i	0.388766	−	0.921337i	$-0.372901\pi$
$59$	10.6080	−	6.12456i	1.38105	−	0.797349i	0.992284	+	0.123987i	$0.0395682\pi$
$60$		0			0
$61$	5.22284	−	9.04622i	0.668716	−	1.15825i	−0.309547	−	0.950884i	$-0.600178\pi$
$61$	5.22284	−	9.04622i	0.668716	−	1.15825i	0.978263	−	0.207366i	$-0.0664891\pi$
$62$		0			0
$63$	5.52814	+	5.74447i	0.696481	+	0.723735i
$64$		0			0
$65$	6.13119	+	2.13239i	0.760481	+	0.264490i
$66$		0			0
$67$	−5.17129	+	2.98565i	−0.631774	+	0.364755i	−0.781439	−	0.623982i	$-0.785514\pi$
$67$	−5.17129	+	2.98565i	−0.631774	+	0.364755i	0.149665	+	0.988737i	$0.452181\pi$
$68$		0			0
$69$	9.11195	−	3.67228i	1.09695	−	0.442090i
$70$		0			0
$71$		−	1.35532i		−	0.160847i	−0.996761	−	0.0804236i	$-0.974373\pi$
$71$		−	1.35532i		−	0.160847i	0.996761	−	0.0804236i	$-0.0256273\pi$
$72$		0			0
$73$			9.98135i			1.16823i	0.811672	+	0.584114i	$0.198558\pi$
$73$			9.98135i			1.16823i	−0.811672	+	0.584114i	$0.801442\pi$
$74$		0			0
$75$	2.39860	+	1.87735i	0.276967	+	0.216777i
$76$		0			0
$77$	−1.55718	−	2.69712i	−0.177457	−	0.307365i
$78$		0			0
$79$	−2.14171	+	3.70956i	−0.240962	+	0.417358i	−0.960988	−	0.276588i	$-0.910796\pi$
$79$	−2.14171	+	3.70956i	−0.240962	+	0.417358i	0.720027	+	0.693946i	$0.244129\pi$
$80$		0			0
$81$	7.61584	+	4.79572i	0.846205	+	0.532858i
$82$		0			0
$83$	−1.70208	−	0.982698i	−0.186828	−	0.107865i	0.403669	−	0.914905i	$-0.367735\pi$
$83$	−1.70208	−	0.982698i	−0.186828	−	0.107865i	−0.590497	+	0.807040i	$0.701068\pi$
$84$		0			0
$85$	−2.08627	+	1.20451i	−0.226287	+	0.130647i
$86$		0			0
$87$	−8.19497	−	6.41406i	−0.878593	−	0.687660i
$88$		0			0
$89$		−	8.41529i		−	0.892019i	−0.895028	−	0.446009i	$-0.852845\pi$
$89$		−	8.41529i		−	0.892019i	0.895028	−	0.446009i	$-0.147155\pi$
$90$		0			0
$91$	1.79914	+	9.41121i	0.188602	+	0.986563i
$92$		0			0
$93$	1.67087	+	4.14589i	0.173261	+	0.429909i
$94$		0			0
$95$	−7.03663	−	12.1878i	−0.721943	−	1.25044i
$96$		0			0
$97$	−0.765238	−	0.441810i	−0.0776982	−	0.0448591i	0.460648	−	0.887583i	$-0.347617\pi$
$97$	−0.765238	−	0.441810i	−0.0776982	−	0.0448591i	−0.538346	+	0.842724i	$0.680951\pi$
$98$		0			0
$99$	−2.43788	−	2.53328i	−0.245016	−	0.254604i
$100$		0			0
$101$	−0.204568	+	0.354322i	−0.0203553	+	0.0352564i	−0.876024	−	0.482268i	$-0.839813\pi$
$101$	−0.204568	+	0.354322i	−0.0203553	+	0.0352564i	0.855668	+	0.517525i	$0.173146\pi$
$102$		0			0
$103$	5.03049	+	8.71307i	0.495669	+	0.858524i	0.999988	−	0.00499380i	$-0.00158958\pi$
$103$	5.03049	+	8.71307i	0.495669	+	0.858524i	−0.504319	+	0.863518i	$0.668256\pi$
$104$		0			0
$105$	1.16044	−	8.20534i	0.113248	−	0.800759i
$106$		0			0
$107$	−4.44751			−0.429957			−0.214979	−	0.976619i	$-0.568968\pi$
$107$	−4.44751			−0.429957			−0.214979	+	0.976619i	$0.568968\pi$
$108$		0			0
$109$		−	8.51488i		−	0.815578i	−0.913076	−	0.407789i	$-0.866300\pi$
$109$		−	8.51488i		−	0.815578i	0.913076	−	0.407789i	$-0.133700\pi$
$110$		0			0
$111$	10.1217	+	1.43146i	0.960708	+	0.135868i
$112$		0			0
$113$	6.92238	+	11.9899i	0.651203	+	1.12792i	0.982831	+	0.184506i	$0.0590686\pi$
$113$	6.92238	+	11.9899i	0.651203	+	1.12792i	−0.331629	+	0.943410i	$0.607598\pi$
$114$		0			0
$115$	−8.84365	−	5.10588i	−0.824675	−	0.476126i
$116$		0			0
$117$	4.52392	+	9.82518i	0.418236	+	0.908338i
$118$		0			0
$119$	−3.07943	−	1.77791i	−0.282291	−	0.162980i
$120$		0			0
$121$	−4.81329	−	8.33687i	−0.437572	−	0.757897i
$122$		0			0
$123$	4.66450	+	11.5739i	0.420584	+	1.04359i
$124$		0			0
$125$		−	12.1681i		−	1.08835i
$126$		0			0
$127$	−8.12200			−0.720711			−0.360356	−	0.932815i	$-0.617345\pi$
$127$	−8.12200			−0.720711			−0.360356	+	0.932815i	$0.617345\pi$
$128$		0			0
$129$	13.7655	+	10.7740i	1.21198	+	0.948599i
$130$		0			0
$131$	5.89862	+	10.2167i	0.515364	+	0.892637i	0.999841	+	0.0178331i	$0.00567675\pi$
$131$	5.89862	+	10.2167i	0.515364	+	0.892637i	−0.484477	+	0.874804i	$0.660990\pi$
$132$		0			0
$133$	10.3864	−	17.9898i	0.900614	−	1.55991i
$134$		0			0
$135$	−0.953669	−	9.30640i	−0.0820788	−	0.800967i
$136$		0			0
$137$	−17.9997	−	10.3921i	−1.53782	−	0.887861i	−0.998966	−	0.0454612i	$-0.985524\pi$
$137$	−17.9997	−	10.3921i	−1.53782	−	0.887861i	−0.538854	−	0.842399i	$-0.681142\pi$
$138$		0			0
$139$	−2.54165	−	4.40227i	−0.215580	−	0.373396i	0.737872	−	0.674941i	$-0.235831\pi$
$139$	−2.54165	−	4.40227i	−0.215580	−	0.373396i	−0.953452	+	0.301545i	$0.902498\pi$
$140$		0			0
$141$	−10.1178	+	12.9271i	−0.852075	+	1.08866i
$142$		0			0
$143$	−0.793412	−	4.15029i	−0.0663484	−	0.347065i
$144$		0			0
$145$			10.8173i			0.898325i
$146$		0			0
$147$	0.0998288	−	0.0402328i	0.00823374	−	0.00331834i
$148$		0			0
$149$	11.9131	−	6.87805i	0.975962	−	0.563472i	0.0749137	−	0.997190i	$-0.476132\pi$
$149$	11.9131	−	6.87805i	0.975962	−	0.563472i	0.901049	+	0.433718i	$0.142799\pi$
$150$		0			0
$151$	−16.0415	−	9.26157i	−1.30544	−	0.753696i	−0.324108	−	0.946020i	$-0.605064\pi$
$151$	−16.0415	−	9.26157i	−1.30544	−	0.753696i	−0.981331	+	0.192324i	$0.938398\pi$
$152$		0			0
$153$	−3.85671	−	1.11314i	−0.311797	−	0.0899918i
$154$		0			0
$155$	2.32315	−	4.02382i	0.186600	−	0.323201i
$156$		0			0
$157$	−4.00643	−	6.93935i	−0.319748	−	0.553820i	0.660687	−	0.750661i	$-0.270265\pi$
$157$	−4.00643	−	6.93935i	−0.319748	−	0.553820i	−0.980435	+	0.196841i	$0.936932\pi$
$158$		0			0
$159$	−2.99343	+	21.1662i	−0.237395	+	1.67859i
$160$		0			0
$161$		−	15.0730i		−	1.18792i
$162$		0			0
$163$			0.362314i			0.0283786i	0.999899	+	0.0141893i	$0.00451675\pi$
$163$			0.362314i			0.0283786i	−0.999899	+	0.0141893i	$0.995483\pi$
$164$		0			0
$165$	−0.511748	+	3.61851i	−0.0398396	+	0.281700i
$166$		0			0
$167$	−11.3437	+	6.54926i	−0.877798	+	0.506797i	−0.869932	−	0.493172i	$-0.835837\pi$
$167$	−11.3437	+	6.54926i	−0.877798	+	0.506797i	−0.00786643	+	0.999969i	$0.502504\pi$
$168$		0			0
$169$	−1.88890	+	12.8620i	−0.145300	+	0.989388i
$170$		0			0
$171$	6.50285	−	22.5306i	0.497286	−	1.72296i
$172$		0			0
$173$	0.104110	−	0.180324i	0.00791535	−	0.0137098i	−0.862041	−	0.506839i	$-0.830814\pi$
$173$	0.104110	−	0.180324i	0.00791535	−	0.0137098i	0.869956	+	0.493129i	$0.164147\pi$
$174$		0			0
$175$	4.04724	−	2.33668i	0.305943	−	0.176636i
$176$		0			0
$177$	−7.93062	−	19.6781i	−0.596102	−	1.47910i
$178$		0			0
$179$	15.4820			1.15718			0.578589	−	0.815619i	$-0.303603\pi$
$179$	15.4820			1.15718			0.578589	+	0.815619i	$0.303603\pi$
$180$		0			0
$181$	9.66553			0.718433			0.359217	−	0.933254i	$-0.383044\pi$
$181$	9.66553			0.718433			0.359217	+	0.933254i	$0.383044\pi$
$182$		0			0
$183$	−14.2474	−	11.1512i	−1.05320	−	0.824319i
$184$		0			0
$185$	−5.31289	−	9.20219i	−0.390611	−	0.676559i
$186$		0			0
$187$	1.35801	+	0.784047i	0.0993074	+	0.0573352i
$188$		0			0
$189$	11.1925	−	8.08741i	0.814133	−	0.588272i
$190$		0			0
$191$	−2.25148	+	3.89967i	−0.162911	+	0.282171i	−0.935912	−	0.352235i	$-0.885422\pi$
$191$	−2.25148	+	3.89967i	−0.162911	+	0.282171i	0.773000	+	0.634406i	$0.218755\pi$
$192$		0			0
$193$	−13.6732	+	7.89423i	−0.984219	+	0.568239i	−0.903541	−	0.428501i	$-0.859042\pi$
$193$	−13.6732	+	7.89423i	−0.984219	+	0.568239i	−0.0806778	+	0.996740i	$0.525708\pi$
$194$		0			0
$195$	5.14408	−	9.99770i	0.368375	−	0.715950i
$196$		0			0
$197$		−	2.32267i		−	0.165484i	−0.996571	−	0.0827418i	$-0.973632\pi$
$197$		−	2.32267i		−	0.165484i	0.996571	−	0.0827418i	$-0.0263677\pi$
$198$		0			0
$199$	−23.4999			−1.66586			−0.832932	−	0.553375i	$-0.813340\pi$
$199$	−23.4999			−1.66586			−0.832932	+	0.553375i	$0.813340\pi$
$200$		0			0
$201$	3.86608	+	9.59283i	0.272692	+	0.676626i
$202$		0			0
$203$	−13.8276	+	7.98339i	−0.970510	+	0.560324i
$204$		0			0
$205$	6.48546	−	11.2331i	0.452964	−	0.784556i
$206$		0			0
$207$	−4.08787	−	16.5175i	−0.284126	−	1.14805i
$208$		0			0
$209$	−4.58034	+	7.93337i	−0.316828	+	0.548763i
$210$		0			0
$211$	7.49343	+	12.9790i	0.515869	+	0.893511i	0.999830	+	0.0184218i	$0.00586417\pi$
$211$	7.49343	+	12.9790i	0.515869	+	0.893511i	−0.483961	+	0.875089i	$0.660802\pi$
$212$		0			0
$213$	−2.32436	−	0.328723i	−0.159262	−	0.0225237i
$214$		0			0
$215$		−	18.1703i		−	1.23920i
$216$		0			0
$217$	6.85816			0.465562
$218$		0			0
$219$	17.1179	+	2.42090i	1.15672	+	0.163589i
$220$		0			0
$221$	−3.15380	−	3.65079i	−0.212148	−	0.245579i
$222$		0			0
$223$	−1.22733	−	0.708599i	−0.0821880	−	0.0474513i	0.458343	−	0.888776i	$-0.348443\pi$
$223$	−1.22733	−	0.708599i	−0.0821880	−	0.0474513i	−0.540531	+	0.841324i	$0.681777\pi$
$224$		0			0
$225$	3.80138	−	3.65823i	0.253426	−	0.243882i
$226$		0			0
$227$	−5.77352	−	3.33334i	−0.383202	−	0.221242i	0.296008	−	0.955185i	$-0.404344\pi$
$227$	−5.77352	−	3.33334i	−0.383202	−	0.221242i	−0.679210	+	0.733944i	$0.737678\pi$
$228$		0			0
$229$	−8.33635	+	4.81300i	−0.550882	+	0.318052i	−0.749478	−	0.662030i	$-0.769695\pi$
$229$	−8.33635	+	4.81300i	−0.550882	+	0.318052i	0.198596	+	0.980081i	$0.436362\pi$
$230$		0			0
$231$	−5.00320	+	2.01638i	−0.329186	+	0.132668i
$232$		0			0
$233$	−4.63723			−0.303795			−0.151897	−	0.988396i	$-0.548538\pi$
$233$	−4.63723			−0.303795			−0.151897	+	0.988396i	$0.548538\pi$
$234$		0			0
$235$	17.0636			1.11311
$236$		0			0
$237$	5.84238	+	4.57273i	0.379503	+	0.297031i
$238$		0			0
$239$	20.5980	−	11.8922i	1.33237	−	0.769245i	0.346708	−	0.937973i	$-0.387299\pi$
$239$	20.5980	−	11.8922i	1.33237	−	0.769245i	0.985663	+	0.168728i	$0.0539660\pi$
$240$		0			0
$241$	−19.5297	−	11.2755i	−1.25802	−	0.726318i	−0.285330	−	0.958429i	$-0.592103\pi$
$241$	−19.5297	−	11.2755i	−1.25802	−	0.726318i	−0.972689	+	0.232111i	$0.925437\pi$
$242$		0			0
$243$	10.0718	−	11.8979i	0.646103	−	0.763250i
$244$		0			0
$245$	−0.0968894	−	0.0559391i	−0.00619004	−	0.00357382i
$246$		0			0
$247$	21.3276	−	18.4243i	1.35704	−	1.17231i
$248$		0			0
$249$	−2.09814	+	2.68070i	−0.132964	+	0.169883i
$250$		0			0
$251$	28.2420			1.78262			0.891309	−	0.453396i	$-0.149787\pi$
$251$	28.2420			1.78262			0.891309	+	0.453396i	$0.149787\pi$
$252$		0			0
$253$			6.64712i			0.417901i
$254$		0			0
$255$	1.55970	+	3.87006i	0.0976724	+	0.242352i
$256$		0			0
$257$	3.48493	+	6.03608i	0.217384	+	0.376520i	0.954007	−	0.299783i	$-0.0969143\pi$
$257$	3.48493	+	6.03608i	0.217384	+	0.376520i	−0.736623	+	0.676303i	$0.763581\pi$
$258$		0			0
$259$	7.84207	−	13.5829i	0.487282	−	0.843998i
$260$		0			0
$261$	−12.9877	+	12.4986i	−0.803915	+	0.773642i
$262$		0			0
$263$	−0.777511	+	1.34669i	−0.0479434	+	0.0830404i	−0.889001	−	0.457905i	$-0.848600\pi$
$263$	−0.777511	+	1.34669i	−0.0479434	+	0.0830404i	0.841058	+	0.540945i	$0.181933\pi$
$264$		0			0
$265$	19.2434	−	11.1102i	1.18211	−	0.682491i
$266$		0			0
$267$	−14.4321	−	2.04106i	−0.883230	−	0.124911i
$268$		0			0
$269$	−10.3894			−0.633455			−0.316727	−	0.948517i	$-0.602584\pi$
$269$	−10.3894			−0.633455			−0.316727	+	0.948517i	$0.602584\pi$
$270$		0			0
$271$			23.8498i			1.44877i	0.689394	+	0.724387i	$0.257877\pi$
$271$			23.8498i			1.44877i	−0.689394	+	0.724387i	$0.742123\pi$
$272$		0			0
$273$	16.5765	−	0.802889i	1.00325	−	0.0485930i
$274$		0			0
$275$	−1.78481	+	1.03046i	−0.107628	+	0.0621391i
$276$		0			0
$277$	−10.8536	+	18.7990i	−0.652130	+	1.12952i	0.330475	+	0.943815i	$0.392791\pi$
$277$	−10.8536	+	18.7990i	−0.652130	+	1.12952i	−0.982605	+	0.185707i	$0.940542\pi$
$278$		0			0
$279$	7.51540	−	1.85996i	0.449935	−	0.111353i
$280$		0			0
$281$	−0.843083	−	0.486754i	−0.0502941	−	0.0290373i	0.474642	−	0.880179i	$-0.342577\pi$
$281$	−0.843083	−	0.486754i	−0.0502941	−	0.0290373i	−0.524936	+	0.851142i	$0.675911\pi$
$282$		0			0
$283$	12.2668	+	21.2468i	0.729188	+	1.26299i	0.957227	+	0.289338i	$0.0934352\pi$
$283$	12.2668	+	21.2468i	0.729188	+	1.26299i	−0.228039	+	0.973652i	$0.573231\pi$
$284$		0			0
$285$	−22.6086	+	9.11165i	−1.33922	+	0.539728i
$286$		0			0
$287$	19.1457			1.13013
$288$		0			0
$289$	−15.2096			−0.894684
$290$		0			0
$291$	−0.943301	+	1.20521i	−0.0552973	+	0.0706509i
$292$		0			0
$293$	23.1545	−	13.3682i	1.35270	−	0.780981i	0.364073	−	0.931371i	$-0.381386\pi$
$293$	23.1545	−	13.3682i	1.35270	−	0.780981i	0.988627	+	0.150389i	$0.0480527\pi$
$294$		0			0
$295$	−11.0266	+	19.0987i	−0.641995	+	1.11197i
$296$		0			0
$297$	−4.93582	+	3.56650i	−0.286405	+	0.206949i
$298$		0			0
$299$	6.71785	−	19.3157i	0.388504	−	1.11705i
$300$		0			0
$301$	23.2269	−	13.4101i	1.33878	−	0.772944i
$302$		0			0
$303$	0.558040	+	0.436769i	0.0320586	+	0.0250917i
$304$		0			0
$305$			18.8064i			1.07685i
$306$		0			0
$307$		−	19.0123i		−	1.08509i	−0.840027	−	0.542544i	$-0.817461\pi$
$307$		−	19.0123i		−	1.08509i	0.840027	−	0.542544i	$-0.182539\pi$
$308$		0			0
$309$	16.1629	−	6.51393i	0.919474	−	0.370565i
$310$		0			0
$311$	−4.62413	−	8.00923i	−0.262211	−	0.454162i	0.704618	−	0.709586i	$-0.251118\pi$
$311$	−4.62413	−	8.00923i	−0.262211	−	0.454162i	−0.966829	+	0.255424i	$0.917785\pi$
$312$		0			0
$313$	14.0904	−	24.4053i	0.796436	−	1.37947i	−0.125488	−	0.992095i	$-0.540050\pi$
$313$	14.0904	−	24.4053i	0.796436	−	1.37947i	0.921923	−	0.387372i	$-0.126617\pi$
$314$		0			0
$315$	−13.7906	−	3.98028i	−0.777011	−	0.224264i
$316$		0			0
$317$	4.02813	+	2.32564i	0.226242	+	0.130621i	0.608837	−	0.793295i	$-0.291636\pi$
$317$	4.02813	+	2.32564i	0.226242	+	0.130621i	−0.382595	+	0.923916i	$0.624970\pi$
$318$		0			0
$319$	6.09791	−	3.52063i	0.341417	−	0.197117i
$320$		0			0
$321$	−1.07871	+	7.62741i	−0.0602077	+	0.425721i
$322$		0			0
$323$			10.4592i			0.581964i
$324$		0			0
$325$	6.22784	−	1.19058i	0.345458	−	0.0660414i
$326$		0			0
$327$	−14.6029	−	2.06522i	−0.807542	−	0.114207i
$328$		0			0
$329$	12.5934	+	21.8123i	0.694294	+	1.20255i
$330$		0			0
$331$	−11.1406	−	6.43205i	−0.612345	−	0.353538i	0.161538	−	0.986867i	$-0.448355\pi$
$331$	−11.1406	−	6.43205i	−0.612345	−	0.353538i	−0.773883	+	0.633329i	$0.781688\pi$
$332$		0			0
$333$	4.90987	−	17.0113i	0.269059	−	0.932216i
$334$		0			0
$335$	5.37535	−	9.31038i	0.293687	−	0.508680i
$336$		0			0
$337$	−4.44018	−	7.69061i	−0.241872	−	0.418934i	0.719376	−	0.694621i	$-0.244428\pi$
$337$	−4.44018	−	7.69061i	−0.241872	−	0.418934i	−0.961247	+	0.275687i	$0.911095\pi$
$338$		0			0
$339$	22.2415	−	8.96372i	1.20799	−	0.486842i
$340$		0			0
$341$	−3.02441			−0.163781
$342$		0			0
$343$			18.4371i			0.995512i
$344$		0			0
$345$	−10.9015	+	13.9283i	−0.586916	+	0.749876i
$346$		0			0
$347$	−1.97419	−	3.41939i	−0.105980	−	0.183563i	0.808158	−	0.588965i	$-0.200465\pi$
$347$	−1.97419	−	3.41939i	−0.105980	−	0.183563i	−0.914138	+	0.405403i	$0.867131\pi$
$348$		0			0
$349$	−26.8533	−	15.5037i	−1.43742	−	0.829896i	−0.439752	−	0.898119i	$-0.644933\pi$
$349$	−26.8533	−	15.5037i	−1.43742	−	0.829896i	−0.997670	+	0.0682238i	$0.978267\pi$
$350$		0			0
$351$	17.9473	−	5.37543i	0.957955	−	0.286919i
$352$		0			0
$353$	−4.29737	−	2.48109i	−0.228726	−	0.132055i	0.381258	−	0.924469i	$-0.375491\pi$
$353$	−4.29737	−	2.48109i	−0.228726	−	0.132055i	−0.609984	+	0.792414i	$0.708824\pi$
$354$		0			0
$355$	1.22006	+	2.11320i	0.0647540	+	0.112157i
$356$		0			0
$357$	−3.79598	+	4.84995i	−0.200904	+	0.256687i
$358$		0			0
$359$			23.5827i			1.24465i	0.782760	+	0.622324i	$0.213811\pi$
$359$			23.5827i			1.24465i	−0.782760	+	0.622324i	$0.786189\pi$
$360$		0			0
$361$	−42.1016			−2.21587
$362$		0			0
$363$	−15.4650	+	6.23268i	−0.811703	+	0.327131i
$364$		0			0
$365$	−8.98519	−	15.5628i	−0.470306	−	0.814595i
$366$		0			0
$367$	−1.98759	+	3.44261i	−0.103752	+	0.179703i	−0.913227	−	0.407450i	$-0.866418\pi$
$367$	−1.98759	+	3.44261i	−0.103752	+	0.179703i	0.809476	+	0.587153i	$0.199751\pi$
$368$		0			0
$369$	20.9804	−	5.19238i	1.09220	−	0.270304i
$370$		0			0
$371$	28.4041	+	16.3991i	1.47467	+	0.851399i
$372$		0			0
$373$	11.4714	+	19.8691i	0.593969	+	1.02878i	0.993692	+	0.112148i	$0.0357730\pi$
$373$	11.4714	+	19.8691i	0.593969	+	1.02878i	−0.399723	+	0.916636i	$0.630894\pi$
$374$		0			0
$375$	−20.8681	−	2.95128i	−1.07763	−	0.152403i
$376$		0			0
$377$	−21.2778	+	4.06768i	−1.09586	+	0.209496i
$378$		0			0
$379$			14.0412i			0.721246i	0.932712	+	0.360623i	$0.117436\pi$
$379$			14.0412i			0.721246i	−0.932712	+	0.360623i	$0.882564\pi$
$380$		0			0
$381$	−1.96993	+	13.9291i	−0.100923	+	0.713610i
$382$		0			0
$383$	1.22496	−	0.707232i	0.0625926	−	0.0361379i	−0.468377	−	0.883529i	$-0.655161\pi$
$383$	1.22496	−	0.707232i	0.0625926	−	0.0361379i	0.530970	+	0.847391i	$0.321828\pi$
$384$		0			0
$385$	4.85588	+	2.80354i	0.247479	+	0.142882i
$386$		0			0
$387$	21.8160	−	20.9944i	1.10897	−	1.06721i
$388$		0			0
$389$	−12.7767	+	22.1299i	−0.647805	+	1.12203i	0.335841	+	0.941919i	$0.390980\pi$
$389$	−12.7767	+	22.1299i	−0.647805	+	1.12203i	−0.983646	+	0.180113i	$0.942354\pi$
$390$		0			0
$391$	3.79467	+	6.57256i	0.191905	+	0.332389i
$392$		0			0
$393$	18.9522	−	7.63805i	0.956010	−	0.385289i
$394$		0			0
$395$		−	7.71187i		−	0.388026i
$396$		0			0
$397$		−	0.254531i		−	0.0127746i	−0.999980	−	0.00638728i	$-0.997967\pi$
$397$		−	0.254531i		−	0.0127746i	0.999980	−	0.00638728i	$-0.00203315\pi$
$398$		0			0
$399$	−28.3330	−	22.1758i	−1.41842	−	1.11018i
$400$		0			0
$401$	−0.372180	+	0.214878i	−0.0185858	+	0.0107305i	−0.509264	−	0.860610i	$-0.670082\pi$
$401$	−0.372180	+	0.214878i	−0.0185858	+	0.0107305i	0.490678	+	0.871341i	$0.336749\pi$
$402$		0			0
$403$	8.78853	+	3.05659i	0.437788	+	0.152260i
$404$		0			0
$405$	−16.1916	−	0.621667i	−0.804569	−	0.0308909i
$406$		0			0
$407$	−3.45831	+	5.98996i	−0.171422	+	0.296911i
$408$		0			0
$409$	4.51984	−	2.60953i	0.223492	−	0.129033i	−0.384074	−	0.923302i	$-0.625479\pi$
$409$	4.51984	−	2.60953i	0.223492	−	0.129033i	0.607566	+	0.794269i	$0.292146\pi$
$410$		0			0
$411$	−22.1881	+	28.3487i	−1.09446	+	1.39834i
$412$		0			0
$413$	−32.5516			−1.60176
$414$		0			0
$415$	3.53849			0.173698
$416$		0			0
$417$	−8.16629	+	3.29116i	−0.399905	+	0.161169i
$418$		0			0
$419$	−11.5418	−	19.9910i	−0.563853	−	0.976622i	−0.997155	−	0.0753735i	$-0.975985\pi$
$419$	−11.5418	−	19.9910i	−0.563853	−	0.976622i	0.433302	−	0.901249i	$-0.357348\pi$
$420$		0			0
$421$	13.6048	+	7.85475i	0.663059	+	0.382817i	0.793441	−	0.608647i	$-0.208287\pi$
$421$	13.6048	+	7.85475i	0.663059	+	0.382817i	−0.130383	+	0.991464i	$0.541621\pi$
$422$		0			0
$423$	19.7158	+	20.4873i	0.958615	+	0.996127i
$424$		0			0
$425$	−1.17652	+	2.03780i	−0.0570698	+	0.0988479i
$426$		0			0
$427$	−24.0401	+	13.8795i	−1.16338	+	0.671678i
$428$		0			0
$429$	−7.31012	+	0.354069i	−0.352936	+	0.0170946i
$430$		0			0
$431$			28.2548i			1.36098i	0.732756	+	0.680492i	$0.238234\pi$
$431$			28.2548i			1.36098i	−0.732756	+	0.680492i	$0.761766\pi$
$432$		0			0
$433$	1.00582			0.0483366			0.0241683	−	0.999708i	$-0.492306\pi$
$433$	1.00582			0.0483366			0.0241683	+	0.999708i	$0.492306\pi$
$434$		0			0
$435$	18.5514	+	2.62364i	0.889473	+	0.125794i
$436$		0			0
$437$	−38.3963	+	22.1681i	−1.83675	+	1.06045i
$438$		0			0
$439$	1.05111	−	1.82057i	0.0501667	−	0.0868912i	−0.839852	−	0.542816i	$-0.817358\pi$
$439$	1.05111	−	1.82057i	0.0501667	−	0.0868912i	0.890018	+	0.455925i	$0.150691\pi$
$440$		0			0
$441$	−0.0447859	−	0.180963i	−0.00213266	−	0.00861729i
$442$		0			0
$443$	−11.5606	+	20.0236i	−0.549262	+	0.951350i	0.449063	+	0.893500i	$0.351758\pi$
$443$	−11.5606	+	20.0236i	−0.549262	+	0.951350i	−0.998325	+	0.0578496i	$0.981576\pi$
$444$		0			0
$445$	7.57543	+	13.1210i	0.359110	+	0.621996i
$446$		0			0
$447$	−8.90632	−	22.0991i	−0.421254	−	1.04525i
$448$		0			0
$449$			0.677149i			0.0319566i	0.999872	+	0.0159783i	$0.00508627\pi$
$449$			0.677149i			0.0319566i	−0.999872	+	0.0159783i	$0.994914\pi$
$450$		0			0
$451$	−8.44313			−0.397571
$452$		0			0
$453$	−19.7742	+	25.2646i	−0.929073	+	1.18704i
$454$		0			0
$455$	−11.2772	−	13.0543i	−0.528682	−	0.611994i
$456$		0			0
$457$	10.1204	+	5.84300i	0.473411	+	0.273324i	0.717667	−	0.696387i	$-0.245210\pi$
$457$	10.1204	+	5.84300i	0.473411	+	0.273324i	−0.244255	+	0.969711i	$0.578543\pi$
$458$		0			0
$459$	−2.84443	+	6.34422i	−0.132767	+	0.296123i
$460$		0			0
$461$	7.11644	+	4.10868i	0.331446	+	0.191360i	0.656483	−	0.754341i	$-0.272043\pi$
$461$	7.11644	+	4.10868i	0.331446	+	0.191360i	−0.325037	+	0.945701i	$0.605377\pi$
$462$		0			0
$463$	3.75857	−	2.17001i	0.174676	−	0.100849i	−0.410113	−	0.912035i	$-0.634511\pi$
$463$	3.75857	−	2.17001i	0.174676	−	0.100849i	0.584789	+	0.811186i	$0.301177\pi$
$464$		0			0
$465$	−6.33732	−	4.96012i	−0.293886	−	0.230020i
$466$		0			0
$467$	31.2648			1.44676			0.723382	−	0.690448i	$-0.242587\pi$
$467$	31.2648			1.44676			0.723382	+	0.690448i	$0.242587\pi$
$468$		0			0
$469$	15.8685			0.732740
$470$		0			0
$471$	−12.8726	+	5.18789i	−0.593138	+	0.239045i
$472$		0			0
$473$	−10.2429	+	5.91377i	−0.470971	+	0.271915i
$474$		0			0
$475$	−11.9047	−	6.87316i	−0.546223	−	0.315362i
$476$		0			0
$477$	35.5736	+	10.2674i	1.62880	+	0.470111i
$478$		0			0
$479$	−4.58937	−	2.64967i	−0.209694	−	0.121067i	0.391475	−	0.920189i	$-0.371965\pi$
$479$	−4.58937	−	2.64967i	−0.209694	−	0.121067i	−0.601169	+	0.799122i	$0.705298\pi$
$480$		0			0
$481$	16.1031	−	13.9109i	0.734237	−	0.634283i
$482$		0			0
$483$	−25.8500	−	3.65585i	−1.17622	−	0.166347i
$484$		0			0
$485$	1.59087			0.0722376
$486$		0			0
$487$			13.6948i			0.620571i	0.950643	+	0.310285i	$0.100425\pi$
$487$			13.6948i			0.620571i	−0.950643	+	0.310285i	$0.899575\pi$
$488$		0			0
$489$	0.621362	+	0.0878764i	0.0280990	+	0.00397391i
$490$		0			0
$491$	−0.206712	−	0.358035i	−0.00932876	−	0.0161579i	0.861323	−	0.508057i	$-0.169636\pi$
$491$	−0.206712	−	0.358035i	−0.00932876	−	0.0161579i	−0.870652	+	0.491899i	$0.836303\pi$
$492$		0			0
$493$	4.01967	−	6.96227i	0.181037	−	0.313565i
$494$		0			0
$495$	6.08156	+	1.75528i	0.273346	+	0.0788940i
$496$		0			0
$497$	−1.80086	+	3.11919i	−0.0807798	+	0.139915i
$498$		0			0
$499$	34.2594	−	19.7796i	1.53366	−	0.885459i	0.534471	−	0.845187i	$-0.320511\pi$
$499$	34.2594	−	19.7796i	1.53366	−	0.885459i	0.999189	−	0.0402716i	$-0.0128223\pi$
$500$		0			0
$501$	8.48057	+	21.0427i	0.378884	+	0.940117i
$502$		0			0
$503$	−5.35395			−0.238721			−0.119360	−	0.992851i	$-0.538084\pi$
$503$	−5.35395			−0.238721			−0.119360	+	0.992851i	$0.538084\pi$
$504$		0			0
$505$		−	0.736607i		−	0.0327786i
$506$		0			0
$507$	21.6001	+	6.35903i	0.959293	+	0.282414i
$508$		0			0
$509$	−29.8564	+	17.2376i	−1.32336	+	0.764044i	−0.984264	−	0.176706i	$-0.943456\pi$
$509$	−29.8564	+	17.2376i	−1.32336	+	0.764044i	−0.339100	+	0.940750i	$0.610122\pi$
$510$		0			0
$511$	13.2626	−	22.9714i	0.586701	−	1.01620i
$512$		0			0
$513$	−37.0624	−	16.6169i	−1.63635	−	0.733655i
$514$		0			0
$515$	−15.6870	−	9.05688i	−0.691251	−	0.399094i
$516$		0			0
$517$	−5.55360	−	9.61911i	−0.244247	−	0.423048i
$518$		0			0
$519$	−0.284002	−	0.222284i	−0.0124663	−	0.00975716i
$520$		0			0
$521$	0.293147			0.0128430			0.00642149	−	0.999979i	$-0.497956\pi$
$521$	0.293147			0.0128430			0.00642149	+	0.999979i	$0.497956\pi$
$522$		0			0
$523$	−8.15975			−0.356801			−0.178401	−	0.983958i	$-0.557092\pi$
$523$	−8.15975			−0.356801			−0.178401	+	0.983958i	$0.557092\pi$
$524$		0			0
$525$	−3.02574	−	7.50770i	−0.132054	−	0.327663i
$526$		0			0
$527$	−2.99048	+	1.72655i	−0.130267	+	0.0752099i
$528$		0			0
$529$	−4.58554	+	7.94239i	−0.199371	+	0.345321i
$530$		0			0
$531$	−35.6712	+	8.82813i	−1.54800	+	0.383108i
$532$		0			0
$533$	24.5346	+	8.53297i	1.06271	+	0.369604i
$534$		0			0
$535$	6.93451	−	4.00364i	0.299805	−	0.173093i
$536$		0			0
$537$	3.75504	−	26.5514i	0.162042	−	1.14578i
$538$		0			0
$539$			0.0728247i			0.00313678i
$540$		0			0
$541$			24.8891i			1.07007i	0.844831	+	0.535034i	$0.179701\pi$
$541$			24.8891i			1.07007i	−0.844831	+	0.535034i	$0.820299\pi$
$542$		0			0
$543$	2.34430	−	16.5762i	0.100604	−	0.711354i
$544$		0			0
$545$	7.66508	+	13.2763i	0.328336	+	0.568695i
$546$		0			0
$547$	−4.99309	+	8.64829i	−0.213489	+	0.369774i	−0.952804	−	0.303586i	$-0.901816\pi$
$547$	−4.99309	+	8.64829i	−0.213489	+	0.369774i	0.739315	+	0.673360i	$0.235150\pi$
$548$		0			0
$549$	−22.5797	+	21.7294i	−0.963678	+	0.927388i
$550$		0			0
$551$	40.6730	+	23.4826i	1.73273	+	1.00039i
$552$		0			0
$553$	9.85803	−	5.69154i	0.419206	−	0.242029i
$554$		0			0
$555$	−17.0702	+	6.87960i	−0.724590	+	0.292023i
$556$		0			0
$557$			10.3622i			0.439059i	0.975606	+	0.219530i	$0.0704522\pi$
$557$			10.3622i			0.439059i	−0.975606	+	0.219530i	$0.929548\pi$
$558$		0			0
$559$	35.7413	−	6.83268i	1.51170	−	0.288992i
$560$		0			0
$561$	1.67400	−	2.13880i	0.0706764	−	0.0903002i
$562$		0			0
$563$	0.0915592	+	0.158585i	0.00385876	+	0.00668357i	0.867948	−	0.496654i	$-0.165438\pi$
$563$	0.0915592	+	0.158585i	0.00385876	+	0.00668357i	−0.864090	+	0.503338i	$0.832105\pi$
$564$		0			0
$565$	−21.5866	−	12.4630i	−0.908155	−	0.524324i
$566$		0			0
$567$	−11.1551	−	21.1565i	−0.468472	−	0.888488i
$568$		0			0
$569$	5.73133	−	9.92696i	0.240270	−	0.416160i	−0.720521	−	0.693433i	$-0.756097\pi$
$569$	5.73133	−	9.92696i	0.240270	−	0.416160i	0.960791	+	0.277273i	$0.0894307\pi$
$570$		0			0
$571$	−17.1416	−	29.6902i	−0.717356	−	1.24250i	−0.962044	−	0.272894i	$-0.912019\pi$
$571$	−17.1416	−	29.6902i	−0.717356	−	1.24250i	0.244688	−	0.969602i	$-0.421314\pi$
$572$		0			0
$573$	6.14180	+	4.80709i	0.256578	+	0.200819i
$574$		0			0
$575$	−9.97454			−0.415967
$576$		0			0
$577$			0.249728i			0.0103963i	0.999986	+	0.00519815i	$0.00165463\pi$
$577$			0.249728i			0.0103963i	−0.999986	+	0.00519815i	$0.998345\pi$
$578$		0			0
$579$	10.2222	+	25.3640i	0.424818	+	1.05409i
$580$		0			0
$581$	2.61149	+	4.52323i	0.108343	+	0.187655i
$582$		0			0
$583$	−12.5260	−	7.23191i	−0.518775	−	0.299515i
$584$		0			0
$585$	−15.8983	−	11.2469i	−0.657312	−	0.465002i
$586$		0			0
$587$	8.57593	+	4.95132i	0.353967	+	0.204363i	0.666431	−	0.745567i	$-0.267821\pi$
$587$	8.57593	+	4.95132i	0.353967	+	0.204363i	−0.312464	+	0.949929i	$0.601154\pi$
$588$		0			0
$589$	−10.0864	−	17.4701i	−0.415603	−	0.719845i
$590$		0			0
$591$	−3.98335	−	0.563346i	−0.163853	−	0.0231730i
$592$		0			0
$593$			40.4008i			1.65906i	0.558461	+	0.829531i	$0.311392\pi$
$593$			40.4008i			1.65906i	−0.558461	+	0.829531i	$0.688608\pi$
$594$		0			0
$595$	6.40188			0.262451
$596$		0			0
$597$	−5.69972	+	40.3020i	−0.233274	+	1.64945i
$598$		0			0
$599$	2.83916	+	4.91757i	0.116005	+	0.200926i	0.918181	−	0.396161i	$-0.129658\pi$
$599$	2.83916	+	4.91757i	0.116005	+	0.200926i	−0.802176	+	0.597087i	$0.796325\pi$
$600$		0			0
$601$	3.12330	−	5.40971i	0.127402	−	0.220667i	−0.795267	−	0.606259i	$-0.792670\pi$
$601$	3.12330	−	5.40971i	0.127402	−	0.220667i	0.922669	+	0.385592i	$0.126003\pi$
$602$		0			0
$603$	17.3893	−	4.30361i	0.708145	−	0.175256i
$604$		0			0
$605$	15.0097	+	8.66584i	0.610230	+	0.352316i
$606$		0			0
$607$	−20.8317	−	36.0816i	−0.845532	−	1.46451i	−0.885158	−	0.465291i	$-0.845950\pi$
$607$	−20.8317	−	36.0816i	−0.845532	−	1.46451i	0.0396256	−	0.999215i	$-0.487383\pi$
$608$		0			0
$609$	10.3376	+	25.6505i	0.418901	+	1.03941i
$610$		0			0
$611$	6.41654	+	33.5645i	0.259586	+	1.35788i
$612$		0			0
$613$			5.54519i			0.223968i	0.993710	+	0.111984i	$0.0357205\pi$
$613$			5.54519i			0.223968i	−0.993710	+	0.111984i	$0.964279\pi$
$614$		0			0
$615$	−17.6917	−	13.8470i	−0.713397	−	0.558364i
$616$		0			0
$617$	28.6171	−	16.5221i	1.15208	−	0.665154i	0.202688	−	0.979243i	$-0.435032\pi$
$617$	28.6171	−	16.5221i	1.15208	−	0.665154i	0.949393	+	0.314089i	$0.101699\pi$
$618$		0			0
$619$	41.7437	+	24.1007i	1.67782	+	0.968689i	0.963047	+	0.269332i	$0.0868028\pi$
$619$	41.7437	+	24.1007i	1.67782	+	0.968689i	0.714772	+	0.699358i	$0.246530\pi$
$620$		0			0
$621$	−29.3188	+	3.00443i	−1.17652	+	0.120564i
$622$		0			0
$623$	−11.1817	+	19.3672i	−0.447985	+	0.775932i
$624$		0			0
$625$	6.55728	+	11.3575i	0.262291	+	0.454302i
$626$		0			0
$627$	12.4947	+	9.77938i	0.498990	+	0.390551i
$628$		0			0
$629$			7.89702i			0.314875i
$630$		0			0
$631$		−	47.4191i		−	1.88773i	−0.330337	−	0.943863i	$-0.607162\pi$
$631$		−	47.4191i		−	1.88773i	0.330337	−	0.943863i	$-0.392838\pi$
$632$		0			0
$633$	24.0763	−	9.70316i	0.956945	−	0.385666i
$634$		0			0
$635$	12.6637	−	7.31141i	0.502545	−	0.290145i
$636$		0			0
$637$	0.0735996	−	0.211619i	0.00291612	−	0.00838464i
$638$		0			0
$639$	−1.12751	+	3.90651i	−0.0446036	+	0.154539i
$640$		0			0
$641$	7.76535	−	13.4500i	0.306713	−	0.531242i	−0.670928	−	0.741522i	$-0.734104\pi$
$641$	7.76535	−	13.4500i	0.306713	−	0.531242i	0.977641	+	0.210280i	$0.0674375\pi$
$642$		0			0
$643$	25.4196	−	14.6760i	1.00245	−	0.578766i	0.0934792	−	0.995621i	$-0.470201\pi$
$643$	25.4196	−	14.6760i	1.00245	−	0.578766i	0.908973	+	0.416855i	$0.136868\pi$
$644$		0			0
$645$	−31.1617	−	4.40706i	−1.22699	−	0.173528i
$646$		0			0
$647$	−2.49961			−0.0982699			−0.0491350	−	0.998792i	$-0.515646\pi$
$647$	−2.49961			−0.0982699			−0.0491350	+	0.998792i	$0.515646\pi$
$648$		0			0
$649$	14.3551			0.563486
$650$		0			0
$651$	1.66339	−	11.7616i	0.0651935	−	0.460975i
$652$		0			0
$653$	−0.184801	−	0.320085i	−0.00723182	−	0.0125259i	0.862387	−	0.506250i	$-0.168969\pi$
$653$	−0.184801	−	0.320085i	−0.00723182	−	0.0125259i	−0.869619	+	0.493724i	$0.835635\pi$
$654$		0			0
$655$	−18.3941	−	10.6198i	−0.718718	−	0.414952i
$656$		0			0
$657$	8.30361	−	28.7697i	0.323955	−	1.12241i
$658$		0			0
$659$	−7.51113	+	13.0097i	−0.292592	+	0.506784i	−0.974422	−	0.224727i	$-0.927851\pi$
$659$	−7.51113	+	13.0097i	−0.292592	+	0.506784i	0.681830	+	0.731511i	$0.261184\pi$
$660$		0			0
$661$	29.4593	−	17.0084i	1.14584	−	0.661548i	0.197967	−	0.980209i	$-0.436566\pi$
$661$	29.4593	−	17.0084i	1.14584	−	0.661548i	0.947869	+	0.318660i	$0.103233\pi$
$662$		0			0
$663$	−7.02599	+	4.52325i	−0.272867	+	0.175669i
$664$		0			0
$665$			37.3992i			1.45028i
$666$		0			0
$667$	34.0786			1.31953
$668$		0			0
$669$	−1.51292	+	1.93299i	−0.0584927	+	0.0747336i
$670$		0			0
$671$	10.6015	−	6.12079i	0.409267	−	0.236291i
$672$		0			0
$673$	−14.0001	+	24.2489i	−0.539664	+	0.934726i	0.459258	+	0.888303i	$0.348116\pi$
$673$	−14.0001	+	24.2489i	−0.539664	+	0.934726i	−0.998922	+	0.0464229i	$0.985218\pi$
$674$		0			0
$675$	−5.35182	−	7.40659i	−0.205992	−	0.285080i
$676$		0			0
$677$	12.4662	−	21.5921i	0.479115	−	0.829852i	−0.520598	−	0.853802i	$-0.674291\pi$
$677$	12.4662	−	21.5921i	0.479115	−	0.829852i	0.999713	+	0.0239498i	$0.00762420\pi$
$678$		0			0
$679$	1.17410	+	2.03360i	0.0450577	+	0.0780423i
$680$		0			0
$681$	−7.11696	+	9.09302i	−0.272722	+	0.348445i
$682$		0			0
$683$		−	33.7051i		−	1.28969i	−0.764313	−	0.644845i	$-0.776922\pi$
$683$		−	33.7051i		−	1.28969i	0.764313	−	0.644845i	$-0.223078\pi$
$684$		0			0
$685$	37.4200			1.42974
$686$		0			0
$687$	6.23230	+	15.4641i	0.237777	+	0.589991i
$688$		0			0
$689$	29.0901	+	33.6743i	1.10825	+	1.28289i
$690$		0			0
$691$	4.02127	+	2.32168i	0.152976	+	0.0883209i	0.574534	−	0.818481i	$-0.305183\pi$
$691$	4.02127	+	2.32168i	0.152976	+	0.0883209i	−0.421558	+	0.906802i	$0.638517\pi$
$692$		0			0
$693$	2.24457	+	9.06946i	0.0852642	+	0.344520i
$694$		0			0
$695$	7.92583	+	4.57598i	0.300644	+	0.173577i
$696$		0			0
$697$	−8.34841	+	4.81996i	−0.316219	+	0.182569i
$698$		0			0
$699$	−1.12472	+	7.95278i	−0.0425410	+	0.300802i
$700$		0			0
$701$	−27.8138			−1.05051			−0.525257	−	0.850944i	$-0.676031\pi$
$701$	−27.8138			−1.05051			−0.525257	+	0.850944i	$0.676031\pi$
$702$		0			0
$703$	−46.1338			−1.73997
$704$		0			0
$705$	4.13865	−	29.2639i	0.155871	−	1.10214i
$706$		0			0
$707$	0.941600	−	0.543633i	0.0354125	−	0.0204454i
$708$		0			0
$709$	34.1616	+	19.7232i	1.28297	+	0.740721i	0.977390	−	0.211447i	$-0.0678175\pi$
$709$	34.1616	+	19.7232i	1.28297	+	0.740721i	0.305576	+	0.952168i	$0.401151\pi$
$710$		0			0
$711$	9.25919	−	8.91051i	0.347247	−	0.334170i
$712$		0			0
$713$	−12.6766	−	7.31884i	−0.474743	−	0.274093i
$714$		0			0
$715$	4.97316	+	5.75686i	0.185986	+	0.215294i
$716$		0			0
$717$	−15.3991	−	38.2096i	−0.575091	−	1.42696i
$718$		0			0
$719$	−31.1306			−1.16097			−0.580487	−	0.814269i	$-0.697138\pi$
$719$	−31.1306			−1.16097			−0.580487	+	0.814269i	$0.697138\pi$
$720$		0			0
$721$		−	26.7367i		−	0.995728i
$722$		0			0
$723$	−24.0741	+	30.7584i	−0.895324	+	1.14392i
$724$		0			0
$725$	5.28298	+	9.15040i	0.196205	+	0.339837i
$726$		0			0
$727$	−13.2138	+	22.8869i	−0.490071	+	0.848829i	−0.999935	−	0.0114268i	$-0.996363\pi$
$727$	−13.2138	+	22.8869i	−0.490071	+	0.848829i	0.509863	+	0.860255i	$0.329696\pi$
$728$		0			0
$729$	−17.9619	−	20.1586i	−0.665255	−	0.746616i
$730$		0			0
$731$	−6.75203	+	11.6949i	−0.249733	+	0.432550i
$732$		0			0
$733$	9.72200	−	5.61300i	0.359090	−	0.207321i	−0.309591	−	0.950870i	$-0.600192\pi$
$733$	9.72200	−	5.61300i	0.359090	−	0.207321i	0.668682	+	0.743549i	$0.266859\pi$
$734$		0			0
$735$	−0.119435	+	0.152596i	−0.00440541	+	0.00562860i
$736$		0			0
$737$	−6.99793			−0.257772
$738$		0			0
$739$		−	13.7910i		−	0.507310i	−0.967295	−	0.253655i	$-0.918367\pi$
$739$		−	13.7910i		−	0.507310i	0.967295	−	0.253655i	$-0.0816327\pi$
$740$		0			0
$741$	−26.4245	−	41.0452i	−0.970727	−	1.50783i
$742$		0			0
$743$	−30.7527	+	17.7551i	−1.12821	+	0.651371i	−0.943483	−	0.331420i	$-0.892472\pi$
$743$	−30.7527	+	17.7551i	−1.12821	+	0.651371i	−0.184724	+	0.982791i	$0.559139\pi$
$744$		0			0
$745$	−12.3832	+	21.4484i	−0.453686	+	0.785808i
$746$		0			0
$747$	4.08848	+	4.24846i	0.149589	+	0.155443i
$748$		0			0
$749$	10.2357	+	5.90956i	0.374003	+	0.215931i
$750$		0			0
$751$	6.23222	+	10.7945i	0.227417	+	0.393898i	0.957042	−	0.289950i	$-0.0936387\pi$
$751$	6.23222	+	10.7945i	0.227417	+	0.393898i	−0.729625	+	0.683848i	$0.760305\pi$
$752$		0			0
$753$	6.84988	−	48.4346i	0.249623	−	1.76505i
$754$		0			0
$755$	33.3490			1.21369
$756$		0			0
$757$	27.3303			0.993336			0.496668	−	0.867941i	$-0.334557\pi$
$757$	27.3303			0.993336			0.496668	+	0.867941i	$0.334557\pi$
$758$		0			0
$759$	11.3997	+	1.61221i	0.413784	+	0.0585195i
$760$		0			0
$761$	36.2143	−	20.9083i	1.31277	−	0.757926i	0.330213	−	0.943906i	$-0.392879\pi$
$761$	36.2143	−	20.9083i	1.31277	−	0.757926i	0.982553	+	0.185981i	$0.0595461\pi$
$762$		0			0
$763$	−11.3140	+	19.5965i	−0.409595	+	0.709439i
$764$		0			0
$765$	7.01539	−	1.73621i	0.253642	−	0.0627729i
$766$		0			0
$767$	−41.7139	−	14.5078i	−1.50620	−	0.523847i
$768$		0			0
$769$	38.4184	−	22.1809i	1.38540	−	0.799864i	0.392611	−	0.919704i	$-0.371572\pi$
$769$	38.4184	−	22.1809i	1.38540	−	0.799864i	0.992793	+	0.119841i	$0.0382384\pi$
$770$		0			0
$771$	11.1970	−	4.51260i	0.403251	−	0.162517i
$772$		0			0
$773$		−	29.3084i		−	1.05415i	−0.849818	−	0.527076i	$-0.823288\pi$
$773$		−	29.3084i		−	1.05415i	0.849818	−	0.527076i	$-0.176712\pi$
$774$		0			0
$775$		−	4.53837i		−	0.163023i
$776$		0			0
$777$	−21.3924	−	16.7434i	−0.767447	−	0.600668i
$778$		0			0
$779$	−28.1578	−	48.7707i	−1.00886	−	1.74739i
$780$		0			0
$781$	0.794170	−	1.37554i	0.0284176	−	0.0492208i
$782$		0			0
$783$	18.2848	+	25.3051i	0.653445	+	0.904329i
$784$		0			0
$785$	12.4936	+	7.21317i	0.445915	+	0.257449i
$786$		0			0
$787$	−17.9606	+	10.3696i	−0.640228	+	0.369636i	−0.784702	−	0.619873i	$-0.787184\pi$
$787$	−17.9606	+	10.3696i	−0.640228	+	0.369636i	0.144475	+	0.989509i	$0.453851\pi$
$788$		0			0
$789$	2.12097	+	1.66005i	0.0755086	+	0.0590993i
$790$		0			0
$791$		−	36.7920i		−	1.30817i
$792$		0			0
$793$	−36.9925	+	7.07187i	−1.31364	+	0.251130i
$794$		0			0
$795$	−14.3864	−	35.6967i	−0.510234	−	1.26603i
$796$		0			0
$797$	1.07189	+	1.85657i	0.0379683	+	0.0657630i	0.884385	−	0.466758i	$-0.154578\pi$
$797$	1.07189	+	1.85657i	0.0379683	+	0.0657630i	−0.846417	+	0.532521i	$0.821245\pi$
$798$		0			0
$799$	−10.9826	−	6.34080i	−0.388536	−	0.224322i
$800$		0			0
$801$	−7.00078	+	24.2558i	−0.247361	+	0.857036i
$802$		0			0
$803$	−5.84871	+	10.1303i	−0.206396	+	0.357489i
$804$		0			0
$805$	13.5687	+	23.5017i	0.478235	+	0.828327i
$806$		0			0
$807$	−2.51988	+	17.8177i	−0.0887039	+	0.627214i
$808$		0			0
$809$	35.4976			1.24803			0.624014	−	0.781413i	$-0.285501\pi$
$809$	35.4976			1.24803			0.624014	+	0.781413i	$0.285501\pi$
$810$		0			0
$811$		−	47.1960i		−	1.65728i	−0.559785	−	0.828638i	$-0.689116\pi$
$811$		−	47.1960i		−	1.65728i	0.559785	−	0.828638i	$-0.310884\pi$
$812$		0			0
$813$	40.9021	+	5.78459i	1.43450	+	0.202874i
$814$		0			0
$815$	−0.326154	−	0.564916i	−0.0114247	−	0.0197881i
$816$		0			0
$817$	−68.3204	−	39.4448i	−2.39023	−	1.38000i
$818$		0			0
$819$	2.64355	−	28.6231i	0.0923731	−	1.00017i
$820$		0			0
$821$	−31.4493	−	18.1573i	−1.09759	−	0.633693i	−0.162002	−	0.986790i	$-0.551795\pi$
$821$	−31.4493	−	18.1573i	−1.09759	−	0.633693i	−0.935586	+	0.353098i	$0.885128\pi$
$822$		0			0
$823$	8.48337	+	14.6936i	0.295712	+	0.512188i	0.975150	−	0.221545i	$-0.0711099\pi$
$823$	8.48337	+	14.6936i	0.295712	+	0.512188i	−0.679438	+	0.733732i	$0.737777\pi$
$824$		0			0
$825$	1.33433	+	3.31085i	0.0464555	+	0.115269i
$826$		0			0
$827$			24.9508i			0.867626i	0.901003	+	0.433813i	$0.142832\pi$
$827$			24.9508i			0.867626i	−0.901003	+	0.433813i	$0.857168\pi$
$828$		0			0
$829$	8.49384			0.295003			0.147502	−	0.989062i	$-0.452877\pi$
$829$	8.49384			0.295003			0.147502	+	0.989062i	$0.452877\pi$
$830$		0			0
$831$	29.6075	+	23.1733i	1.02707	+	0.803873i
$832$		0			0
$833$	0.0415737	+	0.0720077i	0.00144044	+	0.00249492i
$834$		0			0
$835$	11.7913	−	20.4231i	0.408054	−	0.706770i
$836$		0			0
$837$	−1.36700	−	13.3399i	−0.0472505	−	0.461095i
$838$		0			0
$839$	33.7446	+	19.4825i	1.16499	+	0.672610i	0.952496	−	0.304551i	$-0.0985065\pi$
$839$	33.7446	+	19.4825i	1.16499	+	0.672610i	0.212499	+	0.977161i	$0.431840\pi$
$840$		0			0
$841$	−3.54962	−	6.14813i	−0.122401	−	0.212004i
$842$		0			0
$843$	−1.03926	+	1.32782i	−0.0357940	+	0.0457324i
$844$		0			0
$845$	−8.63323	−	21.7547i	−0.296992	−	0.748386i
$846$		0			0
$847$			25.5823i			0.879020i
$848$		0			0
$849$	39.4131	−	15.8842i	1.35266	−	0.545144i
$850$		0			0
$851$	−28.9905	+	16.7377i	−0.993782	+	0.573760i
$852$		0			0
$853$	13.4418	+	7.76062i	0.460238	+	0.265719i	0.712144	−	0.702033i	$-0.247724\pi$
$853$	13.4418	+	7.76062i	0.460238	+	0.265719i	−0.251906	+	0.967752i	$0.581057\pi$
$854$		0			0
$855$	10.1428	+	40.9833i	0.346877	+	1.40160i
$856$		0			0
$857$	20.9017	−	36.2027i	0.713987	−	1.23666i	−0.249362	−	0.968410i	$-0.580221\pi$
$857$	20.9017	−	36.2027i	0.713987	−	1.23666i	0.963349	−	0.268252i	$-0.0864459\pi$
$858$		0			0
$859$	23.7115	+	41.0695i	0.809025	+	1.40127i	0.913540	+	0.406749i	$0.133338\pi$
$859$	23.7115	+	41.0695i	0.809025	+	1.40127i	−0.104515	+	0.994523i	$0.533329\pi$
$860$		0			0
$861$	4.64363	−	32.8345i	0.158255	−	1.11900i
$862$		0			0
$863$			49.1903i			1.67446i	0.546853	+	0.837229i	$0.315826\pi$
$863$			49.1903i			1.67446i	−0.546853	+	0.837229i	$0.684174\pi$
$864$		0			0
$865$			0.374879i			0.0127463i
$866$		0			0
$867$	−3.68898	+	26.0843i	−0.125284	+	0.885869i
$868$		0			0
$869$	−4.34733	+	2.50993i	−0.147473	+	0.0851437i
$870$		0			0
$871$	20.3350	+	7.07239i	0.689026	+	0.239639i
$872$		0			0
$873$	1.83813	+	1.91006i	0.0622114	+	0.0646458i
$874$		0			0
$875$	−16.1682	+	28.0041i	−0.546584	+	0.946712i
$876$		0			0
$877$	−8.93127	+	5.15647i	−0.301587	+	0.174122i	−0.643156	−	0.765735i	$-0.722375\pi$
$877$	−8.93127	+	5.15647i	−0.301587	+	0.174122i	0.341568	+	0.939857i	$0.389042\pi$
$878$		0			0
$879$	−17.3104	−	42.9520i	−0.583865	−	1.44873i
$880$		0			0
$881$	−10.1849			−0.343139			−0.171570	−	0.985172i	$-0.554884\pi$
$881$	−10.1849			−0.343139			−0.171570	+	0.985172i	$0.554884\pi$
$882$		0			0
$883$	−12.2488			−0.412206			−0.206103	−	0.978530i	$-0.566078\pi$
$883$	−12.2488			−0.412206			−0.206103	+	0.978530i	$0.566078\pi$
$884$		0			0
$885$	30.0795	+	23.5427i	1.01111	+	0.791381i
$886$		0			0
$887$	5.18061	+	8.97309i	0.173948	+	0.301287i	0.939797	−	0.341734i	$-0.111014\pi$
$887$	5.18061	+	8.97309i	0.173948	+	0.301287i	−0.765849	+	0.643021i	$0.777681\pi$
$888$		0			0
$889$	18.6923	+	10.7920i	0.626918	+	0.361952i
$890$		0			0
$891$	4.91935	+	9.32988i	0.164804	+	0.312563i
$892$		0			0
$893$	37.0425	−	64.1594i	1.23958	−	2.14701i
$894$		0			0
$895$	−24.1394	+	13.9369i	−0.806890	+	0.465858i
$896$		0			0
$897$	−31.4967	−	16.2059i	−1.05164	−	0.541099i
$898$		0			0
$899$			15.5056i			0.517141i
$900$		0			0
$901$	−16.5140			−0.550162
$902$		0			0
$903$	−17.3646	−	43.0864i	−0.577857	−	1.43382i
$904$		0			0
$905$	−15.0704	+	8.70089i	−0.500957	+	0.289227i
$906$		0			0
$907$	11.2973	−	19.5674i	0.375119	−	0.649726i	−0.615226	−	0.788351i	$-0.710935\pi$
$907$	11.2973	−	19.5674i	0.375119	−	0.649726i	0.990345	+	0.138625i	$0.0442684\pi$
$908$		0			0
$909$	0.884400	−	0.851096i	0.0293337	−	0.0282291i
$910$		0			0
$911$	10.9088	−	18.8945i	0.361423	−	0.626003i	−0.626772	−	0.779203i	$-0.715624\pi$
$911$	10.9088	−	18.8945i	0.361423	−	0.626003i	0.988195	+	0.153199i	$0.0489576\pi$
$912$		0			0
$913$	−1.15165	−	1.99472i	−0.0381141	−	0.0660156i
$914$		0			0
$915$	32.2526	+	4.56134i	1.06624	+	0.150793i
$916$		0			0
$917$		−	31.3508i		−	1.03529i
$918$		0			0
$919$	−13.4021			−0.442094			−0.221047	−	0.975263i	$-0.570947\pi$
$919$	−13.4021			−0.442094			−0.221047	+	0.975263i	$0.570947\pi$
$920$		0			0
$921$	−32.6058	−	4.61128i	−1.07440	−	0.151947i
$922$		0			0
$923$	−3.69793	+	3.19452i	−0.121719	+	0.105149i
$924$		0			0
$925$	−8.98842	−	5.18947i	−0.295537	−	0.170629i
$926$		0			0
$927$	−7.25111	−	29.2990i	−0.238158	−	0.962306i
$928$		0			0
$929$	8.30493	+	4.79485i	0.272476	+	0.157314i	0.630012	−	0.776585i	$-0.283050\pi$
$929$	8.30493	+	4.79485i	0.272476	+	0.157314i	−0.357536	+	0.933899i	$0.616383\pi$
$930$		0			0
$931$	−0.420663	+	0.242870i	−0.0137867	+	0.00795974i
$932$		0			0
$933$	−14.8573	+	5.98774i	−0.486405	+	0.196030i
$934$		0			0
$935$	−2.82319			−0.0923282
$936$		0			0
$937$	−48.2050			−1.57479			−0.787394	−	0.616450i	$-0.788570\pi$
$937$	−48.2050			−1.57479			−0.787394	+	0.616450i	$0.788570\pi$
$938$		0			0
$939$	−38.4372	−	30.0841i	−1.25435	−	0.981758i
$940$		0			0
$941$	35.4422	−	20.4625i	1.15538	−	0.667060i	0.205189	−	0.978722i	$-0.434219\pi$
$941$	35.4422	−	20.4625i	1.15538	−	0.667060i	0.950193	+	0.311663i	$0.100886\pi$
$942$		0			0
$943$	−35.3888	−	20.4317i	−1.15242	−	0.665349i
$944$		0			0
$945$	−10.1709	+	22.6853i	−0.330860	+	0.737951i
$946$		0			0
$947$	−16.5907	−	9.57865i	−0.539125	−	0.311264i	0.205599	−	0.978636i	$-0.434086\pi$
$947$	−16.5907	−	9.57865i	−0.539125	−	0.311264i	−0.744724	+	0.667372i	$0.767419\pi$
$948$		0			0
$949$	27.2336	−	23.5262i	0.884041	−	0.763694i
$950$		0			0
$951$	4.96544	−	6.34412i	0.161015	−	0.205722i
$952$		0			0
$953$	58.5490			1.89659			0.948294	−	0.317393i	$-0.102807\pi$
$953$	58.5490			1.89659			0.948294	+	0.317393i	$0.102807\pi$
$954$		0			0
$955$		−	8.10711i		−	0.262340i
$956$		0			0
$957$	−4.55882	−	11.3117i	−0.147366	−	0.365656i
$958$		0			0
$959$	27.6168	+	47.8337i	0.891793	+	1.54463i
$960$		0			0
$961$	−12.1700	+	21.0790i	−0.392579	+	0.679968i
$962$		0			0
$963$	12.8193	+	3.69994i	0.413095	+	0.119229i
$964$		0			0
$965$	14.2127	−	24.6172i	0.457524	−	0.792456i
$966$		0			0
$967$	12.5783	−	7.26210i	0.404491	−	0.233533i	−0.283929	−	0.958845i	$-0.591638\pi$
$967$	12.5783	−	7.26210i	0.404491	−	0.233533i	0.688420	+	0.725312i	$0.258305\pi$
$968$		0			0
$969$	17.9373	+	2.53679i	0.576230	+	0.0814935i
$970$		0			0
$971$	−4.10205			−0.131641			−0.0658206	−	0.997831i	$-0.520967\pi$
$971$	−4.10205			−0.131641			−0.0658206	+	0.997831i	$0.520967\pi$
$972$		0			0
$973$			13.5087i			0.433070i
$974$		0			0
$975$	−0.531309	−	10.9694i	−0.0170155	−	0.351303i
$976$		0			0
$977$	−33.7487	+	19.4848i	−1.07972	+	0.623374i	−0.930820	−	0.365479i	$-0.880905\pi$
$977$	−33.7487	+	19.4848i	−1.07972	+	0.623374i	−0.148896	+	0.988853i	$0.547572\pi$
$978$		0			0
$979$	4.93106	−	8.54084i	0.157597	−	0.272966i
$980$		0			0
$981$	−7.08364	+	24.5428i	−0.226163	+	0.783593i
$982$		0			0
$983$	17.1004	+	9.87292i	0.545418	+	0.314897i	0.747272	−	0.664518i	$-0.231363\pi$
$983$	17.1004	+	9.87292i	0.545418	+	0.314897i	−0.201854	+	0.979416i	$0.564697\pi$
$984$		0			0
$985$	2.09087	+	3.62149i	0.0666205	+	0.115390i
$986$		0			0
$987$	40.4622	−	16.3070i	1.28793	−	0.519058i
$988$		0			0
$989$	−57.2435			−1.82024
$990$		0			0
$991$	−15.2644			−0.484890			−0.242445	−	0.970165i	$-0.577949\pi$
$991$	−15.2644			−0.484890			−0.242445	+	0.970165i	$0.577949\pi$
$992$		0			0
$993$	−13.7329	+	17.5460i	−0.435802	+	0.556805i
$994$		0			0
$995$	36.6408	−	21.1546i	1.16159	−	0.670645i
$996$		0			0
$997$	26.5012	−	45.9014i	0.839301	−	1.45371i	−0.0511787	−	0.998690i	$-0.516298\pi$
$997$	26.5012	−	45.9014i	0.839301	−	1.45371i	0.890480	−	0.455023i	$-0.150369\pi$
$998$		0			0
$999$	−27.9833	−	12.5463i	−0.885354	−	0.396948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.cw.b.25.23	✓	80
3.2	odd	2		2808.2.cw.b.1585.30		80
9.4	even	3	inner	936.2.cw.b.337.24	yes	80
9.5	odd	6		2808.2.cw.b.2521.11		80
13.12	even	2	inner	936.2.cw.b.25.24	yes	80
39.38	odd	2		2808.2.cw.b.1585.11		80
117.77	odd	6		2808.2.cw.b.2521.30		80
117.103	even	6	inner	936.2.cw.b.337.23	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cw.b.25.23	✓	80	1.1	even	1	trivial
936.2.cw.b.25.24	yes	80	13.12	even	2	inner
936.2.cw.b.337.23	yes	80	117.103	even	6	inner
936.2.cw.b.337.24	yes	80	9.4	even	3	inner
2808.2.cw.b.1585.11		80	39.38	odd	2
2808.2.cw.b.1585.30		80	3.2	odd	2
2808.2.cw.b.2521.11		80	9.5	odd	6
2808.2.cw.b.2521.30		80	117.77	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.cw (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.242542 - 1.71498i) q^{3} +(-1.55919 + 0.900198i) q^{5} +(-2.30144 - 1.32873i) q^{7} +(-2.88235 - 0.831913i) q^{9} +(1.01492 + 0.585964i) q^{11} +(-2.35702 - 2.72845i) q^{13} +(1.16566 + 2.89232i) q^{15} +1.33805 q^{17} +7.81675i q^{19} +(-2.83695 + 3.62465i) q^{21} +(2.83598 + 4.91206i) q^{23} +(-0.879286 + 1.52297i) q^{25} +(-2.12581 + 4.74141i) q^{27} +(3.00413 - 5.20331i) q^{29} +(-2.23496 + 1.29036i) q^{31} +(1.25108 - 1.59845i) q^{33} +4.78450 q^{35} +5.90191i q^{37} +(-5.25093 + 3.38049i) q^{39} +(-6.23926 + 3.60224i) q^{41} +(-5.04619 + 8.74025i) q^{43} +(5.24301 - 1.29757i) q^{45} +(-8.20794 - 4.73885i) q^{47} +(0.0310704 + 0.0538156i) q^{49} +(0.324533 - 2.29473i) q^{51} -12.3419 q^{53} -2.10994 q^{55} +(13.4056 + 1.89589i) q^{57} +(10.6080 - 6.12456i) q^{59} +(5.22284 - 9.04622i) q^{61} +(5.52814 + 5.74447i) q^{63} +(6.13119 + 2.13239i) q^{65} +(-5.17129 + 2.98565i) q^{67} +(9.11195 - 3.67228i) q^{69} -1.35532i q^{71} +9.98135i q^{73} +(2.39860 + 1.87735i) q^{75} +(-1.55718 - 2.69712i) q^{77} +(-2.14171 + 3.70956i) q^{79} +(7.61584 + 4.79572i) q^{81} +(-1.70208 - 0.982698i) q^{83} +(-2.08627 + 1.20451i) q^{85} +(-8.19497 - 6.41406i) q^{87} -8.41529i q^{89} +(1.79914 + 9.41121i) q^{91} +(1.67087 + 4.14589i) q^{93} +(-7.03663 - 12.1878i) q^{95} +(-0.765238 - 0.441810i) q^{97} +(-2.43788 - 2.53328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - 6 q^{9} + 6 q^{13} - 4 q^{17} + 10 q^{23} + 44 q^{25} + 6 q^{27} - 52 q^{35} + 40 q^{39} - 26 q^{43} + 48 q^{49} + 36 q^{51} + 60 q^{53} - 16 q^{55} - 10 q^{61} - 26 q^{65} - 38 q^{69}+ \cdots + 8 q^{95}+O(q^{100}) \) 80 * q - 6 * q^3 - 6 * q^9 + 6 * q^13 - 4 * q^17 + 10 * q^23 + 44 * q^25 + 6 * q^27 - 52 * q^35 + 40 * q^39 - 26 * q^43 + 48 * q^49 + 36 * q^51 + 60 * q^53 - 16 * q^55 - 10 * q^61 - 26 * q^65 - 38 * q^69 + 32 * q^75 + 32 * q^77 + 6 * q^79 - 38 * q^81 + 4 * q^87 - 4 * q^91 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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