LMFDB - Embedded newform 936.2.cw.b.25.12

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			25.12
Character	$\chi$	$=$	936.25
Dual form			936.2.cw.b.337.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33331 + 1.10556i) q^{3} +(1.12193 - 0.647747i) q^{5} +(1.01499 + 0.586005i) q^{7} +(0.555454 - 2.94813i) q^{9} +(-3.37140 - 1.94648i) q^{11} +(-2.96609 - 2.04996i) q^{13} +(-0.779760 + 2.10402i) q^{15} -6.56850 q^{17} +4.02682i q^{19} +(-2.00117 + 0.340809i) q^{21} +(1.49532 + 2.58997i) q^{23} +(-1.66085 + 2.87667i) q^{25} +(2.51875 + 4.54487i) q^{27} +(4.62537 - 8.01138i) q^{29} +(-6.82747 + 3.94184i) q^{31} +(6.64710 - 1.13203i) q^{33} +1.51833 q^{35} -7.11245i q^{37} +(6.22109 - 0.545961i) q^{39} +(-8.68452 + 5.01401i) q^{41} +(2.21816 - 3.84196i) q^{43} +(-1.28646 - 3.66739i) q^{45} +(-9.72175 - 5.61286i) q^{47} +(-2.81320 - 4.87260i) q^{49} +(8.75787 - 7.26190i) q^{51} +3.94629 q^{53} -5.04331 q^{55} +(-4.45191 - 5.36902i) q^{57} +(-8.74216 + 5.04729i) q^{59} +(-0.267490 + 0.463307i) q^{61} +(2.29140 - 2.66683i) q^{63} +(-4.65560 - 0.378638i) q^{65} +(-0.708619 + 0.409121i) q^{67} +(-4.85712 - 1.80007i) q^{69} -11.3561i q^{71} +9.27918i q^{73} +(-0.965915 - 5.67168i) q^{75} +(-2.28130 - 3.95132i) q^{77} +(-3.92094 + 6.79126i) q^{79} +(-8.38294 - 3.27510i) q^{81} +(6.60302 + 3.81226i) q^{83} +(-7.36940 + 4.25473i) q^{85} +(2.69002 + 15.7953i) q^{87} -18.1154i q^{89} +(-1.80926 - 3.81883i) q^{91} +(4.74520 - 12.8039i) q^{93} +(2.60836 + 4.51782i) q^{95} +(5.94315 + 3.43128i) q^{97} +(-7.61114 + 8.85816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.33331	+	1.10556i	−0.769789	+	0.638298i
$3$	−1.33331	+	1.10556i	−0.769789	+	0.638298i
$4$		0			0
$5$	1.12193	−	0.647747i	0.501743	−	0.289681i	−0.227690	−	0.973734i	$-0.573117\pi$
$5$	1.12193	−	0.647747i	0.501743	−	0.289681i	0.729433	+	0.684052i	$0.239784\pi$
$6$		0			0
$7$	1.01499	+	0.586005i	0.383630	+	0.221489i	0.679397	−	0.733771i	$-0.262242\pi$
$7$	1.01499	+	0.586005i	0.383630	+	0.221489i	−0.295766	+	0.955260i	$0.595575\pi$
$8$		0			0
$9$	0.555454	−	2.94813i	0.185151	−	0.982710i
$10$		0			0
$11$	−3.37140	−	1.94648i	−1.01652	−	0.586886i	−0.103424	−	0.994637i	$-0.532980\pi$
$11$	−3.37140	−	1.94648i	−1.01652	−	0.586886i	−0.913093	+	0.407751i	$0.866313\pi$
$12$		0			0
$13$	−2.96609	−	2.04996i	−0.822644	−	0.568556i
$13$	−2.96609	−	2.04996i	−0.822644	−	0.568556i
$14$		0			0
$15$	−0.779760	+	2.10402i	−0.201333	+	0.543255i
$16$		0			0
$17$	−6.56850			−1.59309			−0.796547	−	0.604576i	$-0.793343\pi$
$17$	−6.56850			−1.59309			−0.796547	+	0.604576i	$0.793343\pi$
$18$		0			0
$19$			4.02682i			0.923817i	0.886928	+	0.461908i	$0.152835\pi$
$19$			4.02682i			0.923817i	−0.886928	+	0.461908i	$0.847165\pi$
$20$		0			0
$21$	−2.00117	+	0.340809i	−0.436691	+	0.0743706i
$22$		0			0
$23$	1.49532	+	2.58997i	0.311796	+	0.540047i	0.978751	−	0.205051i	$-0.0657360\pi$
$23$	1.49532	+	2.58997i	0.311796	+	0.540047i	−0.666955	+	0.745098i	$0.732403\pi$
$24$		0			0
$25$	−1.66085	+	2.87667i	−0.332170	+	0.575335i
$26$		0			0
$27$	2.51875	+	4.54487i	0.484734	+	0.874661i
$28$		0			0
$29$	4.62537	−	8.01138i	0.858910	−	1.48768i	−0.0140595	−	0.999901i	$-0.504475\pi$
$29$	4.62537	−	8.01138i	0.858910	−	1.48768i	0.872970	−	0.487775i	$-0.162191\pi$
$30$		0			0
$31$	−6.82747	+	3.94184i	−1.22625	+	0.707976i	−0.966243	−	0.257631i	$-0.917058\pi$
$31$	−6.82747	+	3.94184i	−1.22625	+	0.707976i	−0.260007	+	0.965607i	$0.583725\pi$
$32$		0			0
$33$	6.64710	−	1.13203i	1.15711	−	0.197062i
$34$		0			0
$35$	1.51833			0.256645
$36$		0			0
$37$		−	7.11245i		−	1.16928i	−0.811293	−	0.584640i	$-0.801236\pi$
$37$		−	7.11245i		−	1.16928i	0.811293	−	0.584640i	$-0.198764\pi$
$38$		0			0
$39$	6.22109	−	0.545961i	0.996171	−	0.0874237i
$40$		0			0
$41$	−8.68452	+	5.01401i	−1.35629	+	0.783056i	−0.989122	−	0.147097i	$-0.953007\pi$
$41$	−8.68452	+	5.01401i	−1.35629	+	0.783056i	−0.367171	+	0.930153i	$0.619674\pi$
$42$		0			0
$43$	2.21816	−	3.84196i	0.338266	−	0.585894i	−0.645841	−	0.763472i	$-0.723493\pi$
$43$	2.21816	−	3.84196i	0.338266	−	0.585894i	0.984107	+	0.177578i	$0.0568263\pi$
$44$		0			0
$45$	−1.28646	−	3.66739i	−0.191774	−	0.546702i
$46$		0			0
$47$	−9.72175	−	5.61286i	−1.41806	−	0.818719i	−0.421935	−	0.906626i	$-0.638649\pi$
$47$	−9.72175	−	5.61286i	−1.41806	−	0.818719i	−0.996129	+	0.0879068i	$0.971982\pi$
$48$		0			0
$49$	−2.81320	−	4.87260i	−0.401885	−	0.696085i
$50$		0			0
$51$	8.75787	−	7.26190i	1.22635	−	1.01687i
$52$		0			0
$53$	3.94629			0.542065			0.271032	−	0.962570i	$-0.412635\pi$
$53$	3.94629			0.542065			0.271032	+	0.962570i	$0.412635\pi$
$54$		0			0
$55$	−5.04331			−0.680040
$56$		0			0
$57$	−4.45191	−	5.36902i	−0.589670	−	0.711144i
$58$		0			0
$59$	−8.74216	+	5.04729i	−1.13813	+	0.657101i	−0.945967	−	0.324262i	$-0.894884\pi$
$59$	−8.74216	+	5.04729i	−1.13813	+	0.657101i	−0.192165	+	0.981363i	$0.561551\pi$
$60$		0			0
$61$	−0.267490	+	0.463307i	−0.0342486	+	0.0593204i	−0.882642	−	0.470046i	$-0.844237\pi$
$61$	−0.267490	+	0.463307i	−0.0342486	+	0.0593204i	0.848393	+	0.529367i	$0.177570\pi$
$62$		0			0
$63$	2.29140	−	2.66683i	0.288689	−	0.335988i
$64$		0			0
$65$	−4.65560	−	0.378638i	−0.577456	−	0.0469643i
$66$		0			0
$67$	−0.708619	+	0.409121i	−0.0865716	+	0.0499821i	−0.542661	−	0.839952i	$-0.682583\pi$
$67$	−0.708619	+	0.409121i	−0.0865716	+	0.0499821i	0.456089	+	0.889934i	$0.349250\pi$
$68$		0			0
$69$	−4.85712	−	1.80007i	−0.584728	−	0.216703i
$70$		0			0
$71$		−	11.3561i		−	1.34773i	−0.738856	−	0.673863i	$-0.764634\pi$
$71$		−	11.3561i		−	1.34773i	0.738856	−	0.673863i	$-0.235366\pi$
$72$		0			0
$73$			9.27918i			1.08605i	0.839718	+	0.543023i	$0.182720\pi$
$73$			9.27918i			1.08605i	−0.839718	+	0.543023i	$0.817280\pi$
$74$		0			0
$75$	−0.965915	−	5.67168i	−0.111534	−	0.654910i
$76$		0			0
$77$	−2.28130	−	3.95132i	−0.259978	−	0.450295i
$78$		0			0
$79$	−3.92094	+	6.79126i	−0.441140	+	0.764076i	−0.997774	−	0.0666810i	$-0.978759\pi$
$79$	−3.92094	+	6.79126i	−0.441140	+	0.764076i	0.556635	+	0.830757i	$0.312092\pi$
$80$		0			0
$81$	−8.38294	−	3.27510i	−0.931438	−	0.363900i
$82$		0			0
$83$	6.60302	+	3.81226i	0.724776	+	0.418449i	0.816508	−	0.577334i	$-0.195907\pi$
$83$	6.60302	+	3.81226i	0.724776	+	0.418449i	−0.0917322	+	0.995784i	$0.529240\pi$
$84$		0			0
$85$	−7.36940	+	4.25473i	−0.799324	+	0.461490i
$86$		0			0
$87$	2.69002	+	15.7953i	0.288401	+	1.69344i
$88$		0			0
$89$		−	18.1154i		−	1.92023i	−0.279606	−	0.960115i	$-0.590204\pi$
$89$		−	18.1154i		−	1.92023i	0.279606	−	0.960115i	$-0.409796\pi$
$90$		0			0
$91$	−1.80926	−	3.81883i	−0.189662	−	0.400322i
$92$		0			0
$93$	4.74520	−	12.8039i	0.492055	−	1.32771i
$94$		0			0
$95$	2.60836	+	4.51782i	0.267612	+	0.463518i
$96$		0			0
$97$	5.94315	+	3.43128i	0.603435	+	0.348393i	0.770392	−	0.637571i	$-0.220061\pi$
$97$	5.94315	+	3.43128i	0.603435	+	0.348393i	−0.166957	+	0.985964i	$0.553394\pi$
$98$		0			0
$99$	−7.61114	+	8.85816i	−0.764948	+	0.890278i
$100$		0			0
$101$	8.12658	−	14.0757i	0.808625	−	1.40058i	−0.105191	−	0.994452i	$-0.533545\pi$
$101$	8.12658	−	14.0757i	0.808625	−	1.40058i	0.913816	−	0.406128i	$-0.133121\pi$
$102$		0			0
$103$	−3.30921	−	5.73172i	−0.326066	−	0.564763i	0.655661	−	0.755055i	$-0.272390\pi$
$103$	−3.30921	−	5.73172i	−0.326066	−	0.564763i	−0.981728	+	0.190292i	$0.939057\pi$
$104$		0			0
$105$	−2.02441	+	1.67861i	−0.197563	+	0.163816i
$106$		0			0
$107$	9.32645			0.901622			0.450811	−	0.892619i	$-0.351135\pi$
$107$	9.32645			0.901622			0.450811	+	0.892619i	$0.351135\pi$
$108$		0			0
$109$			19.9089i			1.90693i	0.301504	+	0.953465i	$0.402511\pi$
$109$			19.9089i			1.90693i	−0.301504	+	0.953465i	$0.597489\pi$
$110$		0			0
$111$	7.86327	+	9.48313i	0.746349	+	0.900099i
$112$		0			0
$113$	−2.78841	−	4.82966i	−0.262311	−	0.454336i	0.704545	−	0.709660i	$-0.251151\pi$
$113$	−2.78841	−	4.82966i	−0.262311	−	0.454336i	−0.966856	+	0.255324i	$0.917818\pi$
$114$		0			0
$115$	3.35530	+	1.93718i	0.312883	+	0.180643i
$116$		0			0
$117$	−7.69107	+	7.60575i	−0.711040	+	0.703152i
$118$		0			0
$119$	−6.66697	−	3.84917i	−0.611160	−	0.352853i
$120$		0			0
$121$	2.07758	+	3.59847i	0.188871	+	0.327134i
$122$		0			0
$123$	6.03588	−	16.2865i	0.544237	−	1.46851i
$124$		0			0
$125$			10.7807i			0.964256i
$126$		0			0
$127$	14.6816			1.30278			0.651391	−	0.758742i	$-0.274186\pi$
$127$	14.6816			1.30278			0.651391	+	0.758742i	$0.274186\pi$
$128$		0			0
$129$	1.29004	+	7.57486i	0.113581	+	0.666929i
$130$		0			0
$131$	−4.50338	−	7.80009i	−0.393462	−	0.681497i	0.599441	−	0.800419i	$-0.295390\pi$
$131$	−4.50338	−	7.80009i	−0.393462	−	0.681497i	−0.992904	+	0.118922i	$0.962056\pi$
$132$		0			0
$133$	−2.35974	+	4.08719i	−0.204615	+	0.354404i
$134$		0			0
$135$	5.76980	+	3.46752i	0.496585	+	0.298437i
$136$		0			0
$137$	1.20317	+	0.694649i	0.102794	+	0.0593479i	0.550515	−	0.834825i	$-0.314431\pi$
$137$	1.20317	+	0.694649i	0.102794	+	0.0593479i	−0.447722	+	0.894173i	$0.647765\pi$
$138$		0			0
$139$	−9.03975	−	15.6573i	−0.766742	−	1.32804i	−0.939321	−	0.343040i	$-0.888543\pi$
$139$	−9.03975	−	15.6573i	−0.766742	−	1.32804i	0.172579	−	0.984996i	$-0.444790\pi$
$140$		0			0
$141$	19.1675	−	3.26432i	1.61420	−	0.274906i
$142$		0			0
$143$	6.00967	+	12.6847i	0.502554	+	1.06075i
$144$		0			0
$145$		−	11.9843i		−	0.995241i
$146$		0			0
$147$	9.13785	+	3.38654i	0.753677	+	0.279317i
$148$		0			0
$149$	7.89426	−	4.55775i	0.646723	−	0.373386i	−0.140477	−	0.990084i	$-0.544864\pi$
$149$	7.89426	−	4.55775i	0.646723	−	0.373386i	0.787200	+	0.616698i	$0.211530\pi$
$150$		0			0
$151$	2.38477	+	1.37685i	0.194070	+	0.112046i	0.593886	−	0.804549i	$-0.297593\pi$
$151$	2.38477	+	1.37685i	0.194070	+	0.112046i	−0.399817	+	0.916595i	$0.630926\pi$
$152$		0			0
$153$	−3.64850	+	19.3648i	−0.294964	+	1.56555i
$154$		0			0
$155$	−5.10663	+	8.84495i	−0.410175	+	0.710443i
$156$		0			0
$157$	10.3386	+	17.9069i	0.825107	+	1.42913i	0.901837	+	0.432076i	$0.142219\pi$
$157$	10.3386	+	17.9069i	0.825107	+	1.42913i	−0.0767297	+	0.997052i	$0.524448\pi$
$158$		0			0
$159$	−5.26165	+	4.36288i	−0.417276	+	0.345999i
$160$		0			0
$161$			3.50507i			0.276238i
$162$		0			0
$163$			10.1790i			0.797284i	0.917107	+	0.398642i	$0.130518\pi$
$163$			10.1790i			0.797284i	−0.917107	+	0.398642i	$0.869482\pi$
$164$		0			0
$165$	6.72432	−	5.57570i	0.523487	−	0.434068i
$166$		0			0
$167$	−1.66878	+	0.963473i	−0.129134	+	0.0745558i	−0.563176	−	0.826337i	$-0.690421\pi$
$167$	−1.66878	+	0.963473i	−0.129134	+	0.0745558i	0.434041	+	0.900893i	$0.357087\pi$
$168$		0			0
$169$	4.59534	+	12.1607i	0.353488	+	0.935439i
$170$		0			0
$171$	11.8716	+	2.23672i	0.907844	+	0.171046i
$172$		0			0
$173$	−0.346784	+	0.600648i	−0.0263655	+	0.0456664i	−0.878907	−	0.476993i	$-0.841727\pi$
$173$	−0.346784	+	0.600648i	−0.0263655	+	0.0456664i	0.852542	+	0.522659i	$0.175060\pi$
$174$		0			0
$175$	−3.37149	+	1.94653i	−0.254861	+	0.147144i
$176$		0			0
$177$	6.07594	−	16.3946i	0.456696	−	1.23230i
$178$		0			0
$179$	−16.1961			−1.21055			−0.605275	−	0.796016i	$-0.706937\pi$
$179$	−16.1961			−1.21055			−0.605275	+	0.796016i	$0.706937\pi$
$180$		0			0
$181$	−7.12194			−0.529370			−0.264685	−	0.964335i	$-0.585268\pi$
$181$	−7.12194			−0.529370			−0.264685	+	0.964335i	$0.585268\pi$
$182$		0			0
$183$	−0.155567	−	0.913462i	−0.0114998	−	0.0675250i
$184$		0			0
$185$	−4.60707	−	7.97967i	−0.338718	−	0.586677i
$186$		0			0
$187$	22.1451	+	12.7855i	1.61941	+	0.934965i
$188$		0			0
$189$	−0.106809	+	6.08901i	−0.00776919	+	0.442910i
$190$		0			0
$191$	−6.63623	+	11.4943i	−0.480181	+	0.831698i	−0.999742	−	0.0227360i	$-0.992762\pi$
$191$	−6.63623	+	11.4943i	−0.480181	+	0.831698i	0.519561	+	0.854434i	$0.326096\pi$
$192$		0			0
$193$	−16.7689	+	9.68153i	−1.20705	+	0.696892i	−0.962114	−	0.272647i	$-0.912101\pi$
$193$	−16.7689	+	9.68153i	−1.20705	+	0.696892i	−0.244938	+	0.969539i	$0.578767\pi$
$194$		0			0
$195$	6.62598	−	4.64222i	0.474497	−	0.332436i
$196$		0			0
$197$		−	2.07336i		−	0.147720i	−0.997269	−	0.0738602i	$-0.976468\pi$
$197$		−	2.07336i		−	0.147720i	0.997269	−	0.0738602i	$-0.0235319\pi$
$198$		0			0
$199$	−9.20616			−0.652607			−0.326304	−	0.945265i	$-0.605803\pi$
$199$	−9.20616			−0.652607			−0.326304	+	0.945265i	$0.605803\pi$
$200$		0			0
$201$	0.492502	−	1.32891i	0.0347384	−	0.0937341i
$202$		0			0
$203$	9.38942	−	5.42098i	0.659008	−	0.380479i
$204$		0			0
$205$	−6.49562	+	11.2507i	−0.453674	+	0.785786i
$206$		0			0
$207$	8.46616	−	2.96979i	0.588439	−	0.206415i
$208$		0			0
$209$	7.83814	−	13.5760i	0.542175	−	0.939075i
$210$		0			0
$211$	8.43931	+	14.6173i	0.580986	+	1.00630i	0.995363	+	0.0961921i	$0.0306663\pi$
$211$	8.43931	+	14.6173i	0.580986	+	1.00630i	−0.414377	+	0.910106i	$0.636000\pi$
$212$		0			0
$213$	12.5550	+	15.1413i	0.860251	+	1.03747i
$214$		0			0
$215$		−	5.74722i		−	0.391957i
$216$		0			0
$217$	−9.23976			−0.627236
$218$		0			0
$219$	−10.2587	−	12.3721i	−0.693221	−	0.836027i
$220$		0			0
$221$	19.4827	+	13.4652i	1.31055	+	0.905764i
$222$		0			0
$223$	11.6114	+	6.70384i	0.777557	+	0.448923i	0.835564	−	0.549394i	$-0.185141\pi$
$223$	11.6114	+	6.70384i	0.777557	+	0.448923i	−0.0580070	+	0.998316i	$0.518475\pi$
$224$		0			0
$225$	7.55828	+	6.49425i	0.503885	+	0.432950i
$226$		0			0
$227$	−8.22562	−	4.74907i	−0.545954	−	0.315207i	0.201535	−	0.979481i	$-0.435407\pi$
$227$	−8.22562	−	4.74907i	−0.545954	−	0.315207i	−0.747488	+	0.664275i	$0.768740\pi$
$228$		0			0
$229$	−6.81996	+	3.93751i	−0.450676	+	0.260198i	−0.708116	−	0.706097i	$-0.750454\pi$
$229$	−6.81996	+	3.93751i	−0.450676	+	0.260198i	0.257440	+	0.966294i	$0.417121\pi$
$230$		0			0
$231$	7.41013	+	2.74623i	0.487551	+	0.180689i
$232$		0			0
$233$	7.61925			0.499154			0.249577	−	0.968355i	$-0.419708\pi$
$233$	7.61925			0.499154			0.249577	+	0.968355i	$0.419708\pi$
$234$		0			0
$235$	−14.5428			−0.948671
$236$		0			0
$237$	−2.28034	−	13.3897i	−0.148124	−	0.869756i
$238$		0			0
$239$	−15.0862	+	8.70999i	−0.975842	+	0.563403i	−0.901012	−	0.433794i	$-0.857175\pi$
$239$	−15.0862	+	8.70999i	−0.975842	+	0.563403i	−0.0748299	+	0.997196i	$0.523841\pi$
$240$		0			0
$241$	13.7382	+	7.93173i	0.884953	+	0.510928i	0.872288	−	0.488992i	$-0.162635\pi$
$241$	13.7382	+	7.93173i	0.884953	+	0.510928i	0.0126645	+	0.999920i	$0.495969\pi$
$242$		0			0
$243$	14.7979	−	4.90114i	0.949288	−	0.314408i
$244$		0			0
$245$	−6.31242	−	3.64448i	−0.403286	−	0.232837i
$246$		0			0
$247$	8.25482	−	11.9439i	0.525242	−	0.759973i
$248$		0			0
$249$	−13.0186	+	2.21713i	−0.825020	+	0.140505i
$250$		0			0
$251$	9.81440			0.619479			0.309740	−	0.950821i	$-0.399758\pi$
$251$	9.81440			0.619479			0.309740	+	0.950821i	$0.399758\pi$
$252$		0			0
$253$		−	11.6425i		−	0.731956i
$254$		0			0
$255$	5.12185	−	13.8202i	0.320743	−	0.865457i
$256$		0			0
$257$	2.24272	+	3.88451i	0.139897	+	0.242309i	0.927458	−	0.373928i	$-0.121989\pi$
$257$	2.24272	+	3.88451i	0.139897	+	0.242309i	−0.787560	+	0.616238i	$0.788656\pi$
$258$		0			0
$259$	4.16793	−	7.21907i	0.258983	−	0.448571i
$260$		0			0
$261$	−21.0494	−	18.0862i	−1.30293	−	1.11950i
$262$		0			0
$263$	−11.0782	+	19.1881i	−0.683113	+	1.18319i	0.290912	+	0.956750i	$0.406041\pi$
$263$	−11.0782	+	19.1881i	−0.683113	+	1.18319i	−0.974026	+	0.226437i	$0.927292\pi$
$264$		0			0
$265$	4.42747	−	2.55620i	0.271977	−	0.157026i
$266$		0			0
$267$	20.0278	+	24.1535i	1.22568	+	1.47817i
$268$		0			0
$269$	−1.40882			−0.0858975			−0.0429488	−	0.999077i	$-0.513675\pi$
$269$	−1.40882			−0.0858975			−0.0429488	+	0.999077i	$0.513675\pi$
$270$		0			0
$271$		−	13.0804i		−	0.794580i	−0.917693	−	0.397290i	$-0.869951\pi$
$271$		−	13.0804i		−	0.794580i	0.917693	−	0.397290i	$-0.130049\pi$
$272$		0			0
$273$	6.63428	+	3.09144i	0.401525	+	0.187103i
$274$		0			0
$275$	11.1988	−	6.46562i	0.675312	−	0.389891i
$276$		0			0
$277$	9.34430	−	16.1848i	0.561444	−	0.972450i	−0.435926	−	0.899982i	$-0.643579\pi$
$277$	9.34430	−	16.1848i	0.561444	−	0.972450i	0.997371	−	0.0724677i	$-0.0230874\pi$
$278$		0			0
$279$	7.82872	+	22.3178i	0.468693	+	1.33613i
$280$		0			0
$281$	−6.11062	−	3.52797i	−0.364529	−	0.210461i	0.306537	−	0.951859i	$-0.400830\pi$
$281$	−6.11062	−	3.52797i	−0.364529	−	0.210461i	−0.671066	+	0.741398i	$0.734163\pi$
$282$		0			0
$283$	−13.2306	−	22.9160i	−0.786476	−	1.36222i	−0.928113	−	0.372299i	$-0.878570\pi$
$283$	−13.2306	−	22.9160i	−0.786476	−	1.36222i	0.141637	−	0.989919i	$-0.454764\pi$
$284$		0			0
$285$	−8.47250	−	3.13996i	−0.501868	−	0.185995i
$286$		0			0
$287$	−11.7529			−0.693754
$288$		0			0
$289$	26.1452			1.53795
$290$		0			0
$291$	−11.7176	+	1.99556i	−0.686897	+	0.116982i
$292$		0			0
$293$	−6.21621	+	3.58893i	−0.363155	+	0.209668i	−0.670464	−	0.741942i	$-0.733905\pi$
$293$	−6.21621	+	3.58893i	−0.363155	+	0.209668i	0.307309	+	0.951610i	$0.400571\pi$
$294$		0			0
$295$	−6.53873	+	11.3254i	−0.380700	+	0.659391i
$296$		0			0
$297$	0.354777	−	20.2253i	0.0205862	−	1.17359i
$298$		0			0
$299$	0.874084	−	10.7474i	0.0505496	−	0.621540i
$300$		0			0
$301$	4.50282	−	2.59970i	0.259538	−	0.149844i
$302$		0			0
$303$	4.72626	+	27.7517i	0.271516	+	1.59430i
$304$		0			0
$305$			0.693065i			0.0396848i
$306$		0			0
$307$		−	22.7606i		−	1.29901i	−0.760356	−	0.649507i	$-0.774975\pi$
$307$		−	22.7606i		−	1.29901i	0.760356	−	0.649507i	$-0.225025\pi$
$308$		0			0
$309$	10.7490	+	3.98364i	0.611490	+	0.226621i
$310$		0			0
$311$	−0.186725	−	0.323417i	−0.0105882	−	0.0183393i	0.860683	−	0.509142i	$-0.170037\pi$
$311$	−0.186725	−	0.323417i	−0.0105882	−	0.0183393i	−0.871271	+	0.490802i	$0.836704\pi$
$312$		0			0
$313$	0.282788	−	0.489804i	0.0159841	−	0.0276853i	−0.857923	−	0.513779i	$-0.828245\pi$
$313$	0.282788	−	0.489804i	0.0159841	−	0.0276853i	0.873907	+	0.486093i	$0.161579\pi$
$314$		0			0
$315$	0.843364	−	4.47624i	0.0475182	−	0.252208i
$316$		0			0
$317$	2.95778	+	1.70767i	0.166125	+	0.0959124i	0.580757	−	0.814077i	$-0.302756\pi$
$317$	2.95778	+	1.70767i	0.166125	+	0.0959124i	−0.414632	+	0.909989i	$0.636090\pi$
$318$		0			0
$319$	−31.1880	+	18.0064i	−1.74619	+	1.00816i
$320$		0			0
$321$	−12.4351	+	10.3110i	−0.694059	+	0.575504i
$322$		0			0
$323$		−	26.4502i		−	1.47173i
$324$		0			0
$325$	10.8233	−	5.12779i	0.600367	−	0.284439i
$326$		0			0
$327$	−22.0106	−	26.5449i	−1.21719	−	1.46793i
$328$		0			0
$329$	−6.57833	−	11.3940i	−0.362675	−	0.628171i
$330$		0			0
$331$	−2.45863	−	1.41949i	−0.135139	−	0.0780223i	0.430906	−	0.902397i	$-0.358194\pi$
$331$	−2.45863	−	1.41949i	−0.135139	−	0.0780223i	−0.566045	+	0.824374i	$0.691527\pi$
$332$		0			0
$333$	−20.9684	−	3.95064i	−1.14906	−	0.216494i
$334$		0			0
$335$	−0.530014	+	0.918011i	−0.0289578	+	0.0501563i
$336$		0			0
$337$	−3.43582	−	5.95101i	−0.187161	−	0.324172i	0.757142	−	0.653251i	$-0.226595\pi$
$337$	−3.43582	−	5.95101i	−0.187161	−	0.324172i	−0.944303	+	0.329079i	$0.893262\pi$
$338$		0			0
$339$	9.05732	+	3.35669i	0.491926	+	0.182311i
$340$		0			0
$341$	30.6909			1.66200
$342$		0			0
$343$		−	14.7983i		−	0.799031i
$344$		0			0
$345$	−6.61534	+	1.12662i	−0.356158	+	0.0606554i
$346$		0			0
$347$	−5.87270	−	10.1718i	−0.315263	−	0.546051i	0.664231	−	0.747528i	$-0.268759\pi$
$347$	−5.87270	−	10.1718i	−0.315263	−	0.546051i	−0.979493	+	0.201477i	$0.935426\pi$
$348$		0			0
$349$	−21.5356	−	12.4336i	−1.15277	−	0.665555i	−0.203213	−	0.979135i	$-0.565138\pi$
$349$	−21.5356	−	12.4336i	−1.15277	−	0.665555i	−0.949562	+	0.313580i	$0.898472\pi$
$350$		0			0
$351$	1.84596	−	18.6438i	0.0985303	−	0.995134i
$352$		0			0
$353$	28.9770	+	16.7299i	1.54229	+	0.890440i	0.998694	+	0.0510923i	$0.0162703\pi$
$353$	28.9770	+	16.7299i	1.54229	+	0.890440i	0.543594	+	0.839348i	$0.317063\pi$
$354$		0			0
$355$	−7.35591	−	12.7408i	−0.390411	−	0.676212i
$356$		0			0
$357$	13.1447	−	2.23860i	0.695690	−	0.118479i
$358$		0			0
$359$			20.9981i			1.10824i	0.832438	+	0.554118i	$0.186944\pi$
$359$			20.9981i			1.10824i	−0.832438	+	0.554118i	$0.813056\pi$
$360$		0			0
$361$	2.78470			0.146563
$362$		0			0
$363$	−6.74841	−	2.50100i	−0.354200	−	0.131268i
$364$		0			0
$365$	6.01056	+	10.4106i	0.314607	+	0.544916i
$366$		0			0
$367$	−8.49086	+	14.7066i	−0.443219	+	0.767678i	−0.997926	−	0.0643677i	$-0.979497\pi$
$367$	−8.49086	+	14.7066i	−0.443219	+	0.767678i	0.554707	+	0.832046i	$0.312830\pi$
$368$		0			0
$369$	9.95810	+	28.3881i	0.518398	+	1.47783i
$370$		0			0
$371$	4.00545	+	2.31255i	0.207953	+	0.120062i
$372$		0			0
$373$	10.0047	+	17.3286i	0.518023	+	0.897241i	0.999781	+	0.0209372i	$0.00666500\pi$
$373$	10.0047	+	17.3286i	0.518023	+	0.897241i	−0.481758	+	0.876304i	$0.660002\pi$
$374$		0			0
$375$	−11.9188	−	14.3741i	−0.615482	−	0.742274i
$376$		0			0
$377$	−30.1423	+	14.2806i	−1.55240	+	0.735490i
$378$		0			0
$379$		−	17.6142i		−	0.904780i	−0.891820	−	0.452390i	$-0.850571\pi$
$379$		−	17.6142i		−	0.904780i	0.891820	−	0.452390i	$-0.149429\pi$
$380$		0			0
$381$	−19.5752	+	16.2315i	−1.00287	+	0.831564i
$382$		0			0
$383$	−4.07133	+	2.35058i	−0.208035	+	0.120109i	−0.600398	−	0.799701i	$-0.704991\pi$
$383$	−4.07133	+	2.35058i	−0.208035	+	0.120109i	0.392363	+	0.919811i	$0.371658\pi$
$384$		0			0
$385$	−5.11891	−	2.95541i	−0.260884	−	0.150621i
$386$		0			0
$387$	−10.0945	−	8.67345i	−0.513133	−	0.440896i
$388$		0			0
$389$	3.06849	−	5.31479i	0.155579	−	0.269470i	−0.777691	−	0.628647i	$-0.783609\pi$
$389$	3.06849	−	5.31479i	0.155579	−	0.269470i	0.933270	+	0.359177i	$0.116942\pi$
$390$		0			0
$391$	−9.82202	−	17.0122i	−0.496721	−	0.860346i
$392$		0			0
$393$	14.6279	+	5.42119i	0.737881	+	0.273463i
$394$		0			0
$395$			10.1591i			0.511160i
$396$		0			0
$397$			23.3075i			1.16977i	0.811116	+	0.584885i	$0.198860\pi$
$397$			23.3075i			1.16977i	−0.811116	+	0.584885i	$0.801140\pi$
$398$		0			0
$399$	−1.37238	−	8.05835i	−0.0687048	−	0.403422i
$400$		0			0
$401$	12.5604	−	7.25174i	0.627236	−	0.362135i	−0.152445	−	0.988312i	$-0.548715\pi$
$401$	12.5604	−	7.25174i	0.627236	−	0.362135i	0.779681	+	0.626177i	$0.215381\pi$
$402$		0			0
$403$	28.3315	+	2.30419i	1.41129	+	0.114780i
$404$		0			0
$405$	−11.5265	+	1.75559i	−0.572757	+	0.0872359i
$406$		0			0
$407$	−13.8442	+	23.9789i	−0.686234	+	1.18859i
$408$		0			0
$409$	−14.3903	+	8.30824i	−0.711555	+	0.410816i	−0.811636	−	0.584163i	$-0.801423\pi$
$409$	−14.3903	+	8.30824i	−0.711555	+	0.410816i	0.100082	+	0.994979i	$0.468090\pi$
$410$		0			0
$411$	−2.37218	+	0.403994i	−0.117011	+	0.0199276i
$412$		0			0
$413$	−11.8310			−0.582163
$414$		0			0
$415$	9.87751			0.484868
$416$		0			0
$417$	29.3630	+	10.8821i	1.43791	+	0.532898i
$418$		0			0
$419$	3.50413	+	6.06932i	0.171188	+	0.296506i	0.938835	−	0.344366i	$-0.111906\pi$
$419$	3.50413	+	6.06932i	0.171188	+	0.296506i	−0.767648	+	0.640872i	$0.778573\pi$
$420$		0			0
$421$	−3.35071	−	1.93453i	−0.163304	−	0.0942834i	0.416121	−	0.909309i	$-0.363389\pi$
$421$	−3.35071	−	1.93453i	−0.163304	−	0.0942834i	−0.579425	+	0.815026i	$0.696723\pi$
$422$		0			0
$423$	−21.9474	+	25.5433i	−1.06712	+	1.24196i
$424$		0			0
$425$	10.9093	−	18.8954i	0.529178	−	0.916562i
$426$		0			0
$427$	−0.543001	+	0.313502i	−0.0262776	+	0.0151714i
$428$		0			0
$429$	−22.0365	−	10.2686i	−1.06393	−	0.495771i
$430$		0			0
$431$		−	5.94334i		−	0.286281i	−0.989702	−	0.143140i	$-0.954280\pi$
$431$		−	5.94334i		−	0.286281i	0.989702	−	0.143140i	$-0.0457201\pi$
$432$		0			0
$433$	25.3808			1.21973			0.609863	−	0.792507i	$-0.291225\pi$
$433$	25.3808			1.21973			0.609863	+	0.792507i	$0.291225\pi$
$434$		0			0
$435$	13.2494	+	15.9788i	0.635260	+	0.766126i
$436$		0			0
$437$	−10.4294	+	6.02140i	−0.498904	+	0.288042i
$438$		0			0
$439$	3.20445	−	5.55026i	0.152940	−	0.264900i	−0.779367	−	0.626568i	$-0.784459\pi$
$439$	3.20445	−	5.55026i	0.152940	−	0.264900i	0.932307	+	0.361668i	$0.117793\pi$
$440$		0			0
$441$	−15.9277	+	5.58716i	−0.758460	+	0.266055i
$442$		0			0
$443$	−1.08746	+	1.88354i	−0.0516668	+	0.0894895i	−0.890702	−	0.454587i	$-0.849787\pi$
$443$	−1.08746	+	1.88354i	−0.0516668	+	0.0894895i	0.839035	+	0.544077i	$0.183120\pi$
$444$		0			0
$445$	−11.7342	−	20.3242i	−0.556255	−	0.963461i
$446$		0			0
$447$	−5.48664	+	14.8045i	−0.259509	+	0.700230i
$448$		0			0
$449$		−	3.54524i		−	0.167310i	−0.996495	−	0.0836550i	$-0.973341\pi$
$449$		−	3.54524i		−	0.167310i	0.996495	−	0.0836550i	$-0.0266594\pi$
$450$		0			0
$451$	39.0387			1.83826
$452$		0			0
$453$	−4.70184	+	0.800747i	−0.220912	+	0.0376224i
$454$		0			0
$455$	−4.50351	−	3.11252i	−0.211128	−	0.145917i
$456$		0			0
$457$	14.7188	+	8.49788i	0.688514	+	0.397514i	0.803055	−	0.595905i	$-0.203206\pi$
$457$	14.7188	+	8.49788i	0.688514	+	0.397514i	−0.114541	+	0.993419i	$0.536540\pi$
$458$		0			0
$459$	−16.5444	−	29.8530i	−0.772228	−	1.39342i
$460$		0			0
$461$	8.29670	+	4.79010i	0.386416	+	0.223097i	0.680606	−	0.732650i	$-0.261717\pi$
$461$	8.29670	+	4.79010i	0.386416	+	0.223097i	−0.294190	+	0.955747i	$0.595050\pi$
$462$		0			0
$463$	14.5135	−	8.37937i	0.674499	−	0.389422i	−0.123280	−	0.992372i	$-0.539341\pi$
$463$	14.5135	−	8.37937i	0.674499	−	0.389422i	0.797779	+	0.602950i	$0.206008\pi$
$464$		0			0
$465$	−2.96991	−	17.4388i	−0.137726	−	0.808705i
$466$		0			0
$467$	13.8428			0.640567			0.320283	−	0.947322i	$-0.396222\pi$
$467$	13.8428			0.640567			0.320283	+	0.947322i	$0.396222\pi$
$468$		0			0
$469$	−0.958989			−0.0442820
$470$		0			0
$471$	−33.5818	−	12.4456i	−1.54737	−	0.573463i
$472$		0			0
$473$	−14.9566	+	8.63521i	−0.687706	+	0.397047i
$474$		0			0
$475$	−11.5839	−	6.68794i	−0.531504	−	0.306864i
$476$		0			0
$477$	2.19198	−	11.6342i	0.100364	−	0.532693i
$478$		0			0
$479$	−22.5215	−	13.0028i	−1.02903	−	0.594112i	−0.112324	−	0.993672i	$-0.535830\pi$
$479$	−22.5215	−	13.0028i	−1.02903	−	0.594112i	−0.916707	+	0.399560i	$0.869163\pi$
$480$		0			0
$481$	−14.5802	+	21.0961i	−0.664801	+	0.961901i
$482$		0			0
$483$	−3.87508	−	4.67335i	−0.176322	−	0.212645i
$484$		0			0
$485$	8.89040			0.403692
$486$		0			0
$487$		−	27.2672i		−	1.23560i	−0.786337	−	0.617798i	$-0.788025\pi$
$487$		−	27.2672i		−	1.23560i	0.786337	−	0.617798i	$-0.211975\pi$
$488$		0			0
$489$	−11.2536	−	13.5719i	−0.508905	−	0.613741i
$490$		0			0
$491$	−1.57007	−	2.71945i	−0.0708565	−	0.122727i	0.828420	−	0.560107i	$-0.189240\pi$
$491$	−1.57007	−	2.71945i	−0.0708565	−	0.122727i	−0.899277	+	0.437380i	$0.855907\pi$
$492$		0			0
$493$	−30.3817	+	52.6227i	−1.36833	+	2.37001i
$494$		0			0
$495$	−2.80133	+	14.8683i	−0.125910	+	0.668282i
$496$		0			0
$497$	6.65476	−	11.5264i	0.298507	−	0.517029i
$498$		0			0
$499$	2.63431	−	1.52092i	0.117928	−	0.0680858i	−0.439876	−	0.898059i	$-0.644978\pi$
$499$	2.63431	−	1.52092i	0.117928	−	0.0680858i	0.557804	+	0.829973i	$0.311644\pi$
$500$		0			0
$501$	1.15983	−	3.12956i	0.0518175	−	0.139818i
$502$		0			0
$503$	−10.7638			−0.479933			−0.239967	−	0.970781i	$-0.577136\pi$
$503$	−10.7638			−0.479933			−0.239967	+	0.970781i	$0.577136\pi$
$504$		0			0
$505$		−	21.0559i		−	0.936974i
$506$		0			0
$507$	−19.5715	−	11.1336i	−0.869200	−	0.494461i
$508$		0			0
$509$	−29.0244	+	16.7573i	−1.28649	+	0.742752i	−0.978026	−	0.208485i	$-0.933147\pi$
$509$	−29.0244	+	16.7573i	−1.28649	+	0.742752i	−0.308459	+	0.951237i	$0.599813\pi$
$510$		0			0
$511$	−5.43765	+	9.41828i	−0.240547	+	0.416640i
$512$		0			0
$513$	−18.3014	+	10.1426i	−0.808027	+	0.447806i
$514$		0			0
$515$	−7.42541	−	4.28706i	−0.327203	−	0.188911i
$516$		0			0
$517$	21.8506	+	37.8464i	0.960990	+	1.66448i
$518$		0			0
$519$	−0.201683	−	1.18424i	−0.00885288	−	0.0519825i
$520$		0			0
$521$	−5.80816			−0.254460			−0.127230	−	0.991873i	$-0.540609\pi$
$521$	−5.80816			−0.254460			−0.127230	+	0.991873i	$0.540609\pi$
$522$		0			0
$523$	−39.1530			−1.71204			−0.856020	−	0.516943i	$-0.827070\pi$
$523$	−39.1530			−1.71204			−0.856020	+	0.516943i	$0.827070\pi$
$524$		0			0
$525$	2.34324	−	6.32274i	0.102267	−	0.275947i
$526$		0			0
$527$	44.8462	−	25.8920i	1.95353	−	1.12787i
$528$		0			0
$529$	7.02802	−	12.1729i	0.305566	−	0.529256i
$530$		0			0
$531$	10.0242	+	28.5766i	0.435013	+	1.24012i
$532$		0			0
$533$	36.0375	+	2.93092i	1.56096	+	0.126952i
$534$		0			0
$535$	10.4636	−	6.04118i	0.452382	−	0.261183i
$536$		0			0
$537$	21.5944	−	17.9058i	0.931869	−	0.772692i
$538$		0			0
$539$			21.9033i			0.943443i
$540$		0			0
$541$		−	46.0331i		−	1.97912i	−0.144130	−	0.989559i	$-0.546038\pi$
$541$		−	46.0331i		−	1.97912i	0.144130	−	0.989559i	$-0.453962\pi$
$542$		0			0
$543$	9.49579	−	7.87377i	0.407503	−	0.337896i
$544$		0			0
$545$	12.8960	+	22.3364i	0.552402	+	0.956788i
$546$		0			0
$547$	21.8241	−	37.8005i	0.933131	−	1.61623i	0.155198	−	0.987883i	$-0.450398\pi$
$547$	21.8241	−	37.8005i	0.933131	−	1.61623i	0.777933	−	0.628347i	$-0.216268\pi$
$548$		0			0
$549$	1.21731	+	1.04594i	0.0519536	+	0.0446397i
$550$		0			0
$551$	32.2604	+	18.6256i	1.37434	+	0.793475i
$552$		0			0
$553$	−7.95943	+	4.59538i	−0.338469	+	0.195415i
$554$		0			0
$555$	14.9647	+	5.54600i	0.635217	+	0.235415i
$556$		0			0
$557$		−	25.5959i		−	1.08453i	−0.840206	−	0.542267i	$-0.817566\pi$
$557$		−	25.5959i		−	1.08453i	0.840206	−	0.542267i	$-0.182434\pi$
$558$		0			0
$559$	−14.4551	+	6.84846i	−0.611386	+	0.289659i
$560$		0			0
$561$	−43.6615	+	7.43576i	−1.84339	+	0.313938i
$562$		0			0
$563$	−16.6636	−	28.8622i	−0.702286	−	1.21639i	−0.967662	−	0.252250i	$-0.918829\pi$
$563$	−16.6636	−	28.8622i	−0.702286	−	1.21639i	0.265376	−	0.964145i	$-0.414504\pi$
$564$		0			0
$565$	−6.25680	−	3.61236i	−0.263225	−	0.151973i
$566$		0			0
$567$	−6.58938	−	8.23665i	−0.276728	−	0.345907i
$568$		0			0
$569$	−19.0371	+	32.9733i	−0.798078	+	1.38231i	0.122789	+	0.992433i	$0.460816\pi$
$569$	−19.0371	+	32.9733i	−0.798078	+	1.38231i	−0.920866	+	0.389878i	$0.872517\pi$
$570$		0			0
$571$	0.538092	+	0.932002i	0.0225184	+	0.0390031i	0.877065	−	0.480372i	$-0.159498\pi$
$571$	0.538092	+	0.932002i	0.0225184	+	0.0390031i	−0.854547	+	0.519375i	$0.826165\pi$
$572$		0			0
$573$	−3.85950	−	22.6623i	−0.161233	−	0.946730i
$574$		0			0
$575$	−9.93401			−0.414277
$576$		0			0
$577$		−	1.08287i		−	0.0450804i	−0.999746	−	0.0225402i	$-0.992825\pi$
$577$		−	1.08287i		−	0.0450804i	0.999746	−	0.0225402i	$-0.00717537\pi$
$578$		0			0
$579$	11.6547	−	31.4476i	0.484351	−	1.30692i
$580$		0			0
$581$	4.46800	+	7.73881i	0.185364	+	0.321060i
$582$		0			0
$583$	−13.3045	−	7.68138i	−0.551018	−	0.318130i
$584$		0			0
$585$	−3.70224	+	13.5150i	−0.153069	+	0.558776i
$586$		0			0
$587$	6.75430	+	3.89960i	0.278780	+	0.160954i	0.632871	−	0.774257i	$-0.281876\pi$
$587$	6.75430	+	3.89960i	0.278780	+	0.160954i	−0.354091	+	0.935211i	$0.615210\pi$
$588$		0			0
$589$	−15.8731	−	27.4930i	−0.654040	−	1.13283i
$590$		0			0
$591$	2.29223	+	2.76443i	0.0942897	+	0.113714i
$592$		0			0
$593$		−	27.6766i		−	1.13654i	−0.822841	−	0.568271i	$-0.807612\pi$
$593$		−	27.6766i		−	1.13654i	0.822841	−	0.568271i	$-0.192388\pi$
$594$		0			0
$595$	−9.97316			−0.408860
$596$		0			0
$597$	12.2747	−	10.1780i	0.502370	−	0.416558i
$598$		0			0
$599$	0.164479	+	0.284885i	0.00672041	+	0.0116401i	0.869366	−	0.494169i	$-0.164527\pi$
$599$	0.164479	+	0.284885i	0.00672041	+	0.0116401i	−0.862646	+	0.505809i	$0.831194\pi$
$600$		0			0
$601$	11.4590	−	19.8476i	0.467424	−	0.809602i	−0.531883	−	0.846818i	$-0.678516\pi$
$601$	11.4590	−	19.8476i	0.467424	−	0.809602i	0.999307	+	0.0372156i	$0.0118488\pi$
$602$		0			0
$603$	0.812537	+	2.31635i	0.0330891	+	0.0943290i
$604$		0			0
$605$	4.66180	+	2.69149i	0.189529	+	0.109425i
$606$		0			0
$607$	7.75554	+	13.4330i	0.314788	+	0.545228i	0.979392	−	0.201967i	$-0.0647333\pi$
$607$	7.75554	+	13.4330i	0.314788	+	0.545228i	−0.664605	+	0.747195i	$0.731400\pi$
$608$		0			0
$609$	−6.52580	+	17.6085i	−0.264439	+	0.713532i
$610$		0			0
$611$	17.3294	+	36.5774i	0.701074	+	1.47976i
$612$		0			0
$613$		−	34.7194i		−	1.40230i	−0.713013	−	0.701151i	$-0.752670\pi$
$613$		−	34.7194i		−	1.40230i	0.713013	−	0.701151i	$-0.247330\pi$
$614$		0			0
$615$	−3.77772	−	22.1821i	−0.152332	−	0.894468i
$616$		0			0
$617$	4.04094	−	2.33304i	0.162682	−	0.0939246i	−0.416449	−	0.909159i	$-0.636725\pi$
$617$	4.04094	−	2.33304i	0.162682	−	0.0939246i	0.579131	+	0.815235i	$0.303392\pi$
$618$		0			0
$619$	−30.4860	−	17.6011i	−1.22534	−	0.707448i	−0.259286	−	0.965801i	$-0.583487\pi$
$619$	−30.4860	−	17.6011i	−1.22534	−	0.707448i	−0.966051	+	0.258352i	$0.916820\pi$
$620$		0			0
$621$	−8.00476	+	13.3196i	−0.321220	+	0.534495i
$622$		0			0
$623$	10.6157	−	18.3870i	0.425310	−	0.736659i
$624$		0			0
$625$	−1.32107	−	2.28816i	−0.0528427	−	0.0915263i
$626$		0			0
$627$	4.55850	+	26.7667i	0.182049	+	1.06896i
$628$		0			0
$629$			46.7181i			1.86277i
$630$		0			0
$631$			14.5335i			0.578569i	0.957243	+	0.289284i	$0.0934174\pi$
$631$			14.5335i			0.578569i	−0.957243	+	0.289284i	$0.906583\pi$
$632$		0			0
$633$	−27.4126	−	10.1593i	−1.08955	−	0.403795i
$634$		0			0
$635$	16.4718	−	9.50997i	0.653662	−	0.377392i
$636$		0			0
$637$	−1.64444	+	20.2195i	−0.0651552	+	0.801125i
$638$		0			0
$639$	−33.4794	−	6.30782i	−1.32442	−	0.249533i
$640$		0			0
$641$	−8.17292	+	14.1559i	−0.322811	+	0.559125i	−0.981067	−	0.193669i	$-0.937961\pi$
$641$	−8.17292	+	14.1559i	−0.322811	+	0.559125i	0.658256	+	0.752794i	$0.271294\pi$
$642$		0			0
$643$	−25.7847	+	14.8868i	−1.01685	+	0.587079i	−0.913190	−	0.407534i	$-0.866389\pi$
$643$	−25.7847	+	14.8868i	−1.01685	+	0.587079i	−0.103661	+	0.994613i	$0.533056\pi$
$644$		0			0
$645$	6.35392	+	7.66285i	0.250185	+	0.301724i
$646$		0			0
$647$	6.87304			0.270207			0.135103	−	0.990831i	$-0.456863\pi$
$647$	6.87304			0.270207			0.135103	+	0.990831i	$0.456863\pi$
$648$		0			0
$649$	39.2978			1.54257
$650$		0			0
$651$	12.3195	−	10.2152i	0.482839	−	0.400363i
$652$		0			0
$653$	−1.01601	−	1.75979i	−0.0397597	−	0.0688658i	0.845461	−	0.534038i	$-0.179326\pi$
$653$	−1.01601	−	1.75979i	−0.0397597	−	0.0688658i	−0.885220	+	0.465172i	$0.845993\pi$
$654$		0			0
$655$	−10.1050	−	5.83411i	−0.394834	−	0.227957i
$656$		0			0
$657$	27.3562	+	5.15416i	1.06727	+	0.201083i
$658$		0			0
$659$	−21.1157	+	36.5735i	−0.822551	+	1.42470i	0.0812254	+	0.996696i	$0.474117\pi$
$659$	−21.1157	+	36.5735i	−0.822551	+	1.42470i	−0.903777	+	0.428005i	$0.859217\pi$
$660$		0			0
$661$	−24.5947	+	14.1998i	−0.956625	+	0.552308i	−0.895133	−	0.445800i	$-0.852919\pi$
$661$	−24.5947	+	14.1998i	−0.956625	+	0.552308i	−0.0614922	+	0.998108i	$0.519586\pi$
$662$		0			0
$663$	−40.8632	+	3.58614i	−1.58700	+	0.139274i
$664$		0			0
$665$			6.11406i			0.237093i
$666$		0			0
$667$	27.6657			1.07122
$668$		0			0
$669$	−22.8932	+	3.89882i	−0.885101	+	0.150737i
$670$		0			0
$671$	1.80364	−	1.04133i	0.0696286	−	0.0402001i
$672$		0			0
$673$	18.9395	−	32.8042i	0.730065	−	1.26451i	−0.226789	−	0.973944i	$-0.572823\pi$
$673$	18.9395	−	32.8042i	0.730065	−	1.26451i	0.956855	−	0.290567i	$-0.0938438\pi$
$674$		0			0
$675$	−17.2574	−	0.302716i	−0.664237	−	0.0116515i
$676$		0			0
$677$	−1.86904	+	3.23726i	−0.0718329	+	0.124418i	−0.899705	−	0.436499i	$-0.856218\pi$
$677$	−1.86904	+	3.23726i	−0.0718329	+	0.124418i	0.827872	+	0.560917i	$0.189551\pi$
$678$		0			0
$679$	4.02149	+	6.96543i	0.154331	+	0.267309i
$680$		0			0
$681$	16.2177	−	2.76196i	0.621465	−	0.105839i
$682$		0			0
$683$		−	17.5633i		−	0.672042i	−0.941854	−	0.336021i	$-0.890919\pi$
$683$		−	17.5633i		−	0.672042i	0.941854	−	0.336021i	$-0.109081\pi$
$684$		0			0
$685$	1.79983			0.0687679
$686$		0			0
$687$	4.73998	−	12.7898i	0.180842	−	0.487963i
$688$		0			0
$689$	−11.7050	−	8.08974i	−0.445927	−	0.308194i
$690$		0			0
$691$	−17.5312	−	10.1216i	−0.666918	−	0.385045i	0.127990	−	0.991776i	$-0.459148\pi$
$691$	−17.5312	−	10.1216i	−0.666918	−	0.385045i	−0.794908	+	0.606730i	$0.792481\pi$
$692$		0			0
$693$	−12.9162	+	4.53078i	−0.490645	+	0.172110i
$694$		0			0
$695$	−20.2839	−	11.7109i	−0.769414	−	0.444221i
$696$		0			0
$697$	57.0442	−	32.9345i	2.16070	−	1.24748i
$698$		0			0
$699$	−10.1589	+	8.42357i	−0.384243	+	0.318609i
$700$		0			0
$701$	−21.7160			−0.820202			−0.410101	−	0.912040i	$-0.634507\pi$
$701$	−21.7160			−0.820202			−0.410101	+	0.912040i	$0.634507\pi$
$702$		0			0
$703$	28.6406			1.08020
$704$		0			0
$705$	19.3902	−	16.0781i	0.730277	−	0.605535i
$706$		0			0
$707$	16.4968	−	9.52444i	0.620427	−	0.358203i
$708$		0			0
$709$	−12.5657	−	7.25481i	−0.471915	−	0.272460i	0.245126	−	0.969491i	$-0.421171\pi$
$709$	−12.5657	−	7.25481i	−0.471915	−	0.272460i	−0.717041	+	0.697031i	$0.754504\pi$
$710$		0			0
$711$	17.8436	+	15.3317i	0.669188	+	0.574982i
$712$		0			0
$713$	−20.4185	−	11.7886i	−0.764680	−	0.441488i
$714$		0			0
$715$	14.9589	+	10.3386i	0.559431	+	0.386641i
$716$		0			0
$717$	10.4851	−	28.2919i	0.391574	−	1.05658i
$718$		0			0
$719$	20.4539			0.762801			0.381400	−	0.924410i	$-0.375442\pi$
$719$	20.4539			0.762801			0.381400	+	0.924410i	$0.375442\pi$
$720$		0			0
$721$		−	7.75686i		−	0.288881i
$722$		0			0
$723$	−27.0863	+	4.61293i	−1.00735	+	0.171557i
$724$		0			0
$725$	15.3641	+	26.6114i	0.570607	+	0.988321i
$726$		0			0
$727$	4.66361	−	8.07761i	0.172964	−	0.299582i	−0.766491	−	0.642255i	$-0.777999\pi$
$727$	4.66361	−	8.07761i	0.172964	−	0.299582i	0.939455	+	0.342673i	$0.111332\pi$
$728$		0			0
$729$	−14.3118	+	22.8948i	−0.530065	+	0.847957i
$730$		0			0
$731$	−14.5700	+	25.2359i	−0.538890	+	0.933384i
$732$		0			0
$733$	8.45225	−	4.87991i	0.312191	−	0.180243i	−0.335716	−	0.941963i	$-0.608978\pi$
$733$	8.45225	−	4.87991i	0.312191	−	0.180243i	0.647906	+	0.761720i	$0.275645\pi$
$734$		0			0
$735$	12.4456	−	2.11955i	0.459065	−	0.0781809i
$736$		0			0
$737$	3.18539			0.117335
$738$		0			0
$739$		−	14.3579i		−	0.528164i	−0.964500	−	0.264082i	$-0.914931\pi$
$739$		−	14.3579i		−	0.528164i	0.964500	−	0.264082i	$-0.0850690\pi$
$740$		0			0
$741$	2.19849	+	25.0512i	0.0807635	+	0.920279i
$742$		0			0
$743$	−17.0494	+	9.84349i	−0.625483	+	0.361123i	−0.779001	−	0.627023i	$-0.784273\pi$
$743$	−17.0494	+	9.84349i	−0.625483	+	0.361123i	0.153518	+	0.988146i	$0.450940\pi$
$744$		0			0
$745$	5.90454	−	10.2270i	0.216326	−	0.374687i
$746$		0			0
$747$	14.9067	−	17.3490i	0.545408	−	0.634768i
$748$		0			0
$749$	9.46626	+	5.46535i	0.345890	+	0.199700i
$750$		0			0
$751$	−2.92800	−	5.07145i	−0.106844	−	0.185060i	0.807646	−	0.589668i	$-0.200741\pi$
$751$	−2.92800	−	5.07145i	−0.106844	−	0.185060i	−0.914490	+	0.404608i	$0.867408\pi$
$752$		0			0
$753$	−13.0857	+	10.8505i	−0.476869	+	0.395413i
$754$		0			0
$755$	3.56740			0.129831
$756$		0			0
$757$	−10.4064			−0.378228			−0.189114	−	0.981955i	$-0.560562\pi$
$757$	−10.4064			−0.378228			−0.189114	+	0.981955i	$0.560562\pi$
$758$		0			0
$759$	12.8715	+	15.5231i	0.467206	+	0.563452i
$760$		0			0
$761$	40.2552	−	23.2414i	1.45925	−	0.842499i	0.460276	−	0.887776i	$-0.347750\pi$
$761$	40.2552	−	23.2414i	1.45925	−	0.842499i	0.998974	+	0.0452769i	$0.0144170\pi$
$762$		0			0
$763$	−11.6667	+	20.2074i	−0.422364	+	0.731556i
$764$		0			0
$765$	8.45012	+	24.0893i	0.305515	+	0.870949i
$766$		0			0
$767$	36.2767	+	2.95037i	1.30988	+	0.106532i
$768$		0			0
$769$	19.1017	−	11.0283i	0.688823	−	0.397692i	−0.114348	−	0.993441i	$-0.536478\pi$
$769$	19.1017	−	11.0283i	0.688823	−	0.397692i	0.803171	+	0.595748i	$0.203144\pi$
$770$		0			0
$771$	−7.28484	−	2.69980i	−0.262357	−	0.0972309i
$772$		0			0
$773$		−	3.52236i		−	0.126690i	−0.997992	−	0.0633452i	$-0.979823\pi$
$773$		−	3.52236i		−	0.126690i	0.997992	−	0.0633452i	$-0.0201769\pi$
$774$		0			0
$775$		−	26.1872i		−	0.940672i
$776$		0			0
$777$	2.42398	+	14.2332i	0.0869600	+	0.510613i
$778$		0			0
$779$	−20.1905	−	34.9710i	−0.723400	−	1.25297i
$780$		0			0
$781$	−22.1045	+	38.2862i	−0.790962	+	1.36999i
$782$		0			0
$783$	48.0609	+	0.843047i	1.71756	+	0.0301280i
$784$		0			0
$785$	23.1983	+	13.3936i	0.827983	+	0.478036i
$786$		0			0
$787$	20.3257	−	11.7350i	0.724531	−	0.418308i	−0.0918869	−	0.995769i	$-0.529290\pi$
$787$	20.3257	−	11.7350i	0.724531	−	0.418308i	0.816418	+	0.577461i	$0.195956\pi$
$788$		0			0
$789$	−6.44288	−	37.8314i	−0.229372	−	1.34683i
$790$		0			0
$791$		−	6.53608i		−	0.232396i
$792$		0			0
$793$	1.74316	−	0.825864i	0.0619014	−	0.0293273i
$794$		0			0
$795$	−3.07716	+	8.30307i	−0.109136	+	0.294479i
$796$		0			0
$797$	0.665795	+	1.15319i	0.0235837	+	0.0408481i	0.877576	−	0.479437i	$-0.159159\pi$
$797$	0.665795	+	1.15319i	0.0235837	+	0.0408481i	−0.853993	+	0.520285i	$0.825826\pi$
$798$		0			0
$799$	63.8573	+	36.8680i	2.25911	+	1.30430i
$800$		0			0
$801$	−53.4066	−	10.0623i	−1.88703	−	0.355533i
$802$		0			0
$803$	18.0618	−	31.2839i	0.637385	−	1.10398i
$804$		0			0
$805$	2.27040	+	3.93244i	0.0800209	+	0.138600i
$806$		0			0
$807$	1.87841	−	1.55755i	0.0661230	−	0.0548282i
$808$		0			0
$809$	−51.9672			−1.82707			−0.913535	−	0.406760i	$-0.866658\pi$
$809$	−51.9672			−1.82707			−0.913535	+	0.406760i	$0.866658\pi$
$810$		0			0
$811$			35.6357i			1.25134i	0.780088	+	0.625670i	$0.215174\pi$
$811$			35.6357i			1.25134i	−0.780088	+	0.625670i	$0.784826\pi$
$812$		0			0
$813$	14.4613	+	17.4403i	0.507179	+	0.611659i
$814$		0			0
$815$	6.59344	+	11.4202i	0.230958	+	0.400031i
$816$		0			0
$817$	15.4709	+	8.93213i	0.541258	+	0.312496i
$818$		0			0
$819$	−12.2634	+	3.21276i	−0.428517	+	0.112263i
$820$		0			0
$821$	8.92925	+	5.15531i	0.311633	+	0.179921i	0.647657	−	0.761932i	$-0.275749\pi$
$821$	8.92925	+	5.15531i	0.311633	+	0.179921i	−0.336024	+	0.941853i	$0.609082\pi$
$822$		0			0
$823$	20.9553	+	36.2957i	0.730456	+	1.26519i	0.956688	+	0.291114i	$0.0940259\pi$
$823$	20.9553	+	36.2957i	0.730456	+	1.26519i	−0.226232	+	0.974073i	$0.572641\pi$
$824$		0			0
$825$	−7.78333	+	21.0017i	−0.270981	+	0.731184i
$826$		0			0
$827$		−	14.6304i		−	0.508748i	−0.967106	−	0.254374i	$-0.918131\pi$
$827$		−	14.6304i		−	0.508748i	0.967106	−	0.254374i	$-0.0818694\pi$
$828$		0			0
$829$	−5.45165			−0.189344			−0.0946719	−	0.995509i	$-0.530180\pi$
$829$	−5.45165			−0.189344			−0.0946719	+	0.995509i	$0.530180\pi$
$830$		0			0
$831$	5.43445	+	31.9101i	0.188519	+	1.10695i
$832$		0			0
$833$	18.4785	+	32.0057i	0.640241	+	1.10893i
$834$		0			0
$835$	−1.24817	+	2.16190i	−0.0431948	+	0.0748156i
$836$		0			0
$837$	−35.1119	−	21.1015i	−1.21364	−	0.729374i
$838$		0			0
$839$	−5.64378	−	3.25844i	−0.194845	−	0.112494i	0.399404	−	0.916775i	$-0.369217\pi$
$839$	−5.64378	−	3.25844i	−0.194845	−	0.112494i	−0.594249	+	0.804281i	$0.702551\pi$
$840$		0			0
$841$	−28.2881	−	48.9965i	−0.975453	−	1.68953i
$842$		0			0
$843$	12.0478	−	2.05179i	0.414947	−	0.0706676i
$844$		0			0
$845$	13.0327	+	10.6669i	0.448339	+	0.366951i
$846$		0			0
$847$			4.86989i			0.167331i
$848$		0			0
$849$	42.9757	+	15.9270i	1.47492	+	0.546614i
$850$		0			0
$851$	18.4211	−	10.6354i	0.631466	−	0.364577i
$852$		0			0
$853$	27.5422	+	15.9015i	0.943029	+	0.544458i	0.890908	−	0.454183i	$-0.150069\pi$
$853$	27.5422	+	15.9015i	0.943029	+	0.544458i	0.0521202	+	0.998641i	$0.483402\pi$
$854$		0			0
$855$	14.7679	−	5.18035i	0.505053	−	0.177164i
$856$		0			0
$857$	−1.82625	+	3.16316i	−0.0623836	+	0.108052i	−0.895530	−	0.445000i	$-0.853204\pi$
$857$	−1.82625	+	3.16316i	−0.0623836	+	0.108052i	0.833147	+	0.553052i	$0.186537\pi$
$858$		0			0
$859$	0.814178	+	1.41020i	0.0277794	+	0.0481153i	0.879581	−	0.475749i	$-0.157823\pi$
$859$	0.814178	+	1.41020i	0.0277794	+	0.0481153i	−0.851801	+	0.523865i	$0.824490\pi$
$860$		0			0
$861$	15.6704	−	12.9936i	0.534044	−	0.442822i
$862$		0			0
$863$			1.90203i			0.0647458i	0.999476	+	0.0323729i	$0.0103064\pi$
$863$			1.90203i			0.0647458i	−0.999476	+	0.0323729i	$0.989694\pi$
$864$		0			0
$865$			0.898513i			0.0305504i
$866$		0			0
$867$	−34.8597	+	28.9052i	−1.18390	+	0.981671i
$868$		0			0
$869$	26.4381	−	15.2641i	0.896852	−	0.517798i
$870$		0			0
$871$	2.94051	+	0.239150i	0.0996352	+	0.00810329i
$872$		0			0
$873$	13.4170	−	15.6153i	0.454097	−	0.528496i
$874$		0			0
$875$	−6.31755	+	10.9423i	−0.213572	+	0.369918i
$876$		0			0
$877$	−12.4613	+	7.19456i	−0.420790	+	0.242943i	−0.695415	−	0.718608i	$-0.744779\pi$
$877$	−12.4613	+	7.19456i	−0.420790	+	0.242943i	0.274625	+	0.961551i	$0.411446\pi$
$878$		0			0
$879$	4.32037	−	11.6576i	0.145722	−	0.393201i
$880$		0			0
$881$	−47.2375			−1.59147			−0.795736	−	0.605644i	$-0.792915\pi$
$881$	−47.2375			−1.59147			−0.795736	+	0.605644i	$0.792915\pi$
$882$		0			0
$883$	10.5214			0.354073			0.177036	−	0.984204i	$-0.443349\pi$
$883$	10.5214			0.354073			0.177036	+	0.984204i	$0.443349\pi$
$884$		0			0
$885$	−3.80279	−	22.3293i	−0.127830	−	0.750592i
$886$		0			0
$887$	18.5854	+	32.1908i	0.624036	+	1.08086i	0.988726	+	0.149733i	$0.0478413\pi$
$887$	18.5854	+	32.1908i	0.624036	+	1.08086i	−0.364691	+	0.931129i	$0.618825\pi$
$888$		0			0
$889$	14.9017	+	8.60350i	0.499787	+	0.288552i
$890$		0			0
$891$	21.8874	+	27.3589i	0.733254	+	0.916559i
$892$		0			0
$893$	22.6020	−	39.1478i	0.756347	−	1.31003i
$894$		0			0
$895$	−18.1709	+	10.4909i	−0.607385	+	0.350674i
$896$		0			0
$897$	10.7166	+	15.2961i	0.357815	+	0.510721i
$898$		0			0
$899$			72.9300i			2.43235i
$900$		0			0
$901$	−25.9212			−0.863561
$902$		0			0
$903$	−3.12953	+	8.44438i	−0.104144	+	0.281011i
$904$		0			0
$905$	−7.99033	+	4.61322i	−0.265607	+	0.153349i
$906$		0			0
$907$	−4.73223	+	8.19647i	−0.157131	+	0.272159i	−0.933833	−	0.357709i	$-0.883558\pi$
$907$	−4.73223	+	8.19647i	−0.157131	+	0.272159i	0.776702	+	0.629868i	$0.216891\pi$
$908$		0			0
$909$	−36.9829	−	31.7766i	−1.22665	−	1.05396i
$910$		0			0
$911$	−14.3065	+	24.7795i	−0.473995	+	0.820983i	−0.999557	−	0.0297724i	$-0.990522\pi$
$911$	−14.3065	+	24.7795i	−0.473995	+	0.820983i	0.525562	+	0.850755i	$0.323855\pi$
$912$		0			0
$913$	−14.8410	−	25.7053i	−0.491164	−	0.850722i
$914$		0			0
$915$	−0.766228	−	0.924073i	−0.0253307	−	0.0305489i
$916$		0			0
$917$		−	10.5560i		−	0.348591i
$918$		0			0
$919$	−12.3995			−0.409021			−0.204510	−	0.978864i	$-0.565560\pi$
$919$	−12.3995			−0.409021			−0.204510	+	0.978864i	$0.565560\pi$
$920$		0			0
$921$	25.1633	+	30.3470i	0.829158	+	0.999967i
$922$		0			0
$923$	−23.2796	+	33.6833i	−0.766259	+	1.10870i
$924$		0			0
$925$	20.4602	+	11.8127i	0.672727	+	0.388399i
$926$		0			0
$927$	−18.7360	+	6.57228i	−0.615370	+	0.215862i
$928$		0			0
$929$	17.0132	+	9.82260i	0.558186	+	0.322269i	0.752417	−	0.658687i	$-0.228888\pi$
$929$	17.0132	+	9.82260i	0.558186	+	0.322269i	−0.194231	+	0.980956i	$0.562221\pi$
$930$		0			0
$931$	19.6211	−	11.3282i	0.643055	−	0.371268i
$932$		0			0
$933$	0.606521	+	0.224780i	0.0198566	+	0.00735897i
$934$		0			0
$935$	33.1270			1.08337
$936$		0			0
$937$	−45.1494			−1.47497			−0.737483	−	0.675366i	$-0.763986\pi$
$937$	−45.1494			−1.47497			−0.737483	+	0.675366i	$0.763986\pi$
$938$		0			0
$939$	0.164464	+	0.965703i	0.00536708	+	0.0315145i
$940$		0			0
$941$	10.1924	−	5.88460i	0.332263	−	0.191832i	−0.324582	−	0.945857i	$-0.605224\pi$
$941$	10.1924	−	5.88460i	0.332263	−	0.191832i	0.656846	+	0.754025i	$0.271890\pi$
$942$		0			0
$943$	−25.9723	−	14.9951i	−0.845774	−	0.488308i
$944$		0			0
$945$	3.82430	+	6.90063i	0.124405	+	0.224478i
$946$		0			0
$947$	13.4450	+	7.76245i	0.436902	+	0.252246i	0.702283	−	0.711898i	$-0.252164\pi$
$947$	13.4450	+	7.76245i	0.436902	+	0.252246i	−0.265380	+	0.964144i	$0.585498\pi$
$948$		0			0
$949$	19.0219	−	27.5229i	0.617478	−	0.893430i
$950$		0			0
$951$	−5.83159	+	0.993147i	−0.189102	+	0.0322050i
$952$		0			0
$953$	−40.6782			−1.31770			−0.658848	−	0.752276i	$-0.728956\pi$
$953$	−40.6782			−1.31770			−0.658848	+	0.752276i	$0.728956\pi$
$954$		0			0
$955$			17.1944i			0.556398i
$956$		0			0
$957$	21.6762	−	58.4885i	0.700691	−	1.89067i
$958$		0			0
$959$	0.814136	+	1.41013i	0.0262898	+	0.0455353i
$960$		0			0
$961$	15.5762	−	26.9788i	0.502459	−	0.870285i
$962$		0			0
$963$	5.18042	−	27.4956i	0.166937	−	0.886033i
$964$		0			0
$965$	−12.5424	+	21.7240i	−0.403753	+	0.699320i
$966$		0			0
$967$	−16.3248	+	9.42513i	−0.524970	+	0.303092i	−0.738966	−	0.673743i	$-0.764686\pi$
$967$	−16.3248	+	9.42513i	−0.524970	+	0.303092i	0.213996	+	0.976835i	$0.431352\pi$
$968$		0			0
$969$	29.2424	+	35.2664i	0.939401	+	1.13292i
$970$		0			0
$971$	25.4536			0.816845			0.408423	−	0.912793i	$-0.366079\pi$
$971$	25.4536			0.816845			0.408423	+	0.912793i	$0.366079\pi$
$972$		0			0
$973$		−	21.1894i		−	0.679300i
$974$		0			0
$975$	−8.76173	+	18.8028i	−0.280600	+	0.602171i
$976$		0			0
$977$	−3.81800	+	2.20432i	−0.122149	+	0.0705225i	−0.559829	−	0.828608i	$-0.689133\pi$
$977$	−3.81800	+	2.20432i	−0.122149	+	0.0705225i	0.437681	+	0.899130i	$0.355800\pi$
$978$		0			0
$979$	−35.2613	+	61.0744i	−1.12696	+	1.95195i
$980$		0			0
$981$	58.6941	+	11.0585i	1.87396	+	0.353071i
$982$		0			0
$983$	31.7489	+	18.3303i	1.01263	+	0.584644i	0.911962	−	0.410275i	$-0.134567\pi$
$983$	31.7489	+	18.3303i	1.01263	+	0.584644i	0.100672	+	0.994920i	$0.467901\pi$
$984$		0			0
$985$	−1.34301	−	2.32616i	−0.0427918	−	0.0741176i
$986$		0			0
$987$	21.3678	+	7.91901i	0.680144	+	0.252065i
$988$		0			0
$989$	13.2674			0.421880
$990$		0			0
$991$	21.7867			0.692078			0.346039	−	0.938220i	$-0.387526\pi$
$991$	21.7867			0.692078			0.346039	+	0.938220i	$0.387526\pi$
$992$		0			0
$993$	4.84747	−	0.825548i	0.153830	−	0.0261980i
$994$		0			0
$995$	−10.3287	+	5.96326i	−0.327441	+	0.189048i
$996$		0			0
$997$	−0.925027	+	1.60219i	−0.0292959	+	0.0507420i	−0.880302	−	0.474414i	$-0.842660\pi$
$997$	−0.925027	+	1.60219i	−0.0292959	+	0.0507420i	0.851006	+	0.525156i	$0.175993\pi$
$998$		0			0
$999$	32.3252	−	17.9145i	1.02272	−	0.566790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.cw.b.25.12	yes	80
3.2	odd	2		2808.2.cw.b.1585.13		80
9.4	even	3	inner	936.2.cw.b.337.11	yes	80
9.5	odd	6		2808.2.cw.b.2521.28		80
13.12	even	2	inner	936.2.cw.b.25.11	✓	80
39.38	odd	2		2808.2.cw.b.1585.28		80
117.77	odd	6		2808.2.cw.b.2521.13		80
117.103	even	6	inner	936.2.cw.b.337.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cw.b.25.11	✓	80	13.12	even	2	inner
936.2.cw.b.25.12	yes	80	1.1	even	1	trivial
936.2.cw.b.337.11	yes	80	9.4	even	3	inner
936.2.cw.b.337.12	yes	80	117.103	even	6	inner
2808.2.cw.b.1585.13		80	3.2	odd	2
2808.2.cw.b.1585.28		80	39.38	odd	2
2808.2.cw.b.2521.13		80	117.77	odd	6
2808.2.cw.b.2521.28		80	9.5	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)

\(f(q)\)	\(=\)	\(q+(-1.33331 + 1.10556i) q^{3} +(1.12193 - 0.647747i) q^{5} +(1.01499 + 0.586005i) q^{7} +(0.555454 - 2.94813i) q^{9} +(-3.37140 - 1.94648i) q^{11} +(-2.96609 - 2.04996i) q^{13} +(-0.779760 + 2.10402i) q^{15} -6.56850 q^{17} +4.02682i q^{19} +(-2.00117 + 0.340809i) q^{21} +(1.49532 + 2.58997i) q^{23} +(-1.66085 + 2.87667i) q^{25} +(2.51875 + 4.54487i) q^{27} +(4.62537 - 8.01138i) q^{29} +(-6.82747 + 3.94184i) q^{31} +(6.64710 - 1.13203i) q^{33} +1.51833 q^{35} -7.11245i q^{37} +(6.22109 - 0.545961i) q^{39} +(-8.68452 + 5.01401i) q^{41} +(2.21816 - 3.84196i) q^{43} +(-1.28646 - 3.66739i) q^{45} +(-9.72175 - 5.61286i) q^{47} +(-2.81320 - 4.87260i) q^{49} +(8.75787 - 7.26190i) q^{51} +3.94629 q^{53} -5.04331 q^{55} +(-4.45191 - 5.36902i) q^{57} +(-8.74216 + 5.04729i) q^{59} +(-0.267490 + 0.463307i) q^{61} +(2.29140 - 2.66683i) q^{63} +(-4.65560 - 0.378638i) q^{65} +(-0.708619 + 0.409121i) q^{67} +(-4.85712 - 1.80007i) q^{69} -11.3561i q^{71} +9.27918i q^{73} +(-0.965915 - 5.67168i) q^{75} +(-2.28130 - 3.95132i) q^{77} +(-3.92094 + 6.79126i) q^{79} +(-8.38294 - 3.27510i) q^{81} +(6.60302 + 3.81226i) q^{83} +(-7.36940 + 4.25473i) q^{85} +(2.69002 + 15.7953i) q^{87} -18.1154i q^{89} +(-1.80926 - 3.81883i) q^{91} +(4.74520 - 12.8039i) q^{93} +(2.60836 + 4.51782i) q^{95} +(5.94315 + 3.43128i) q^{97} +(-7.61114 + 8.85816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - 6 q^{9} + 6 q^{13} - 4 q^{17} + 10 q^{23} + 44 q^{25} + 6 q^{27} - 52 q^{35} + 40 q^{39} - 26 q^{43} + 48 q^{49} + 36 q^{51} + 60 q^{53} - 16 q^{55} - 10 q^{61} - 26 q^{65} - 38 q^{69}+ \cdots + 8 q^{95}+O(q^{100}) \) 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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