LMFDB - Embedded newform 936.2.s.f.529.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(529,936)] 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, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.529"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [40,0,-3,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Character	$\chi$	$=$	936.529
Dual form			936.2.s.f.913.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69053 - 0.376974i) q^{3} +(-0.185033 - 0.320487i) q^{5} +0.220829 q^{7} +(2.71578 + 1.27457i) q^{9} +(-2.10430 - 3.64475i) q^{11} +(-0.829056 + 3.50894i) q^{13} +(0.191989 + 0.611546i) q^{15} +(-1.24758 - 2.16087i) q^{17} +(0.226112 + 0.391637i) q^{19} +(-0.373317 - 0.0832466i) q^{21} -2.05243 q^{23} +(2.43153 - 4.21153i) q^{25} +(-4.11063 - 3.17848i) q^{27} +(1.85085 + 3.20576i) q^{29} +(-0.816082 - 1.41349i) q^{31} +(2.18340 + 6.95482i) q^{33} +(-0.0408606 - 0.0707727i) q^{35} +(-5.00558 + 8.66991i) q^{37} +(2.72432 - 5.61944i) q^{39} -4.07176 q^{41} -11.5147 q^{43} +(-0.0940265 - 1.10621i) q^{45} +(0.918184 - 1.59034i) q^{47} -6.95123 q^{49} +(1.29447 + 4.12331i) q^{51} -7.12781 q^{53} +(-0.778731 + 1.34880i) q^{55} +(-0.234611 - 0.747311i) q^{57} +(2.40843 - 4.17152i) q^{59} -7.82801 q^{61} +(0.599722 + 0.281462i) q^{63} +(1.27797 - 0.383569i) q^{65} -11.6595 q^{67} +(3.46970 + 0.773714i) q^{69} +(-6.89204 - 11.9374i) q^{71} +8.58734 q^{73} +(-5.69820 + 6.20309i) q^{75} +(-0.464689 - 0.804865i) q^{77} +(-6.36242 + 11.0200i) q^{79} +(5.75094 + 6.92291i) q^{81} +(-5.54460 + 9.60353i) q^{83} +(-0.461686 + 0.799664i) q^{85} +(-1.92043 - 6.11716i) q^{87} +(-0.114134 + 0.197686i) q^{89} +(-0.183079 + 0.774874i) q^{91} +(0.846760 + 2.69720i) q^{93} +(0.0836763 - 0.144932i) q^{95} +10.2261 q^{97} +(-1.06932 - 12.5804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Character values

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

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

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
$3$	−1.69053	−	0.376974i	−0.976028	−	0.217646i
$3$	−1.69053	−	0.376974i	−0.976028	−	0.217646i
$4$		0			0
$5$	−0.185033	−	0.320487i	−0.0827494	−	0.143326i	0.821681	−	0.569948i	$-0.193037\pi$
$5$	−0.185033	−	0.320487i	−0.0827494	−	0.143326i	−0.904430	+	0.426622i	$0.859703\pi$
$6$		0			0
$7$	0.220829			0.0834653			0.0417327	−	0.999129i	$-0.486712\pi$
$7$	0.220829			0.0834653			0.0417327	+	0.999129i	$0.486712\pi$
$8$		0			0
$9$	2.71578	+	1.27457i	0.905260	+	0.424857i
$10$		0			0
$11$	−2.10430	−	3.64475i	−0.634470	−	1.09893i	−0.986627	−	0.162993i	$-0.947885\pi$
$11$	−2.10430	−	3.64475i	−0.634470	−	1.09893i	0.352158	−	0.935941i	$-0.385448\pi$
$12$		0			0
$13$	−0.829056	+	3.50894i	−0.229939	+	0.973205i
$13$	−0.829056	+	3.50894i	−0.229939	+	0.973205i
$14$		0			0
$15$	0.191989	+	0.611546i	0.0495714	+	0.157900i
$16$		0			0
$17$	−1.24758	−	2.16087i	−0.302582	−	0.524087i	0.674138	−	0.738605i	$-0.264515\pi$
$17$	−1.24758	−	2.16087i	−0.302582	−	0.524087i	−0.976720	+	0.214518i	$0.931182\pi$
$18$		0			0
$19$	0.226112	+	0.391637i	0.0518735	+	0.0898476i	0.890796	−	0.454403i	$-0.150147\pi$
$19$	0.226112	+	0.391637i	0.0518735	+	0.0898476i	−0.838923	+	0.544251i	$0.816814\pi$
$20$		0			0
$21$	−0.373317	−	0.0832466i	−0.0814645	−	0.0181659i
$22$		0			0
$23$	−2.05243			−0.427962			−0.213981	−	0.976838i	$-0.568643\pi$
$23$	−2.05243			−0.427962			−0.213981	+	0.976838i	$0.568643\pi$
$24$		0			0
$25$	2.43153	−	4.21153i	0.486305	−	0.842305i
$26$		0			0
$27$	−4.11063	−	3.17848i	−0.791091	−	0.611699i
$28$		0			0
$29$	1.85085	+	3.20576i	0.343694	+	0.595295i	0.985116	−	0.171893i	$-0.0549884\pi$
$29$	1.85085	+	3.20576i	0.343694	+	0.595295i	−0.641422	+	0.767189i	$0.721655\pi$
$30$		0			0
$31$	−0.816082	−	1.41349i	−0.146573	−	0.253871i	0.783386	−	0.621536i	$-0.213491\pi$
$31$	−0.816082	−	1.41349i	−0.146573	−	0.253871i	−0.929959	+	0.367664i	$0.880158\pi$
$32$		0			0
$33$	2.18340	+	6.95482i	0.380082	+	1.21068i
$34$		0			0
$35$	−0.0408606	−	0.0707727i	−0.00690671	−	0.0119628i
$36$		0			0
$37$	−5.00558	+	8.66991i	−0.822912	+	1.42533i	0.0805930	+	0.996747i	$0.474319\pi$
$37$	−5.00558	+	8.66991i	−0.822912	+	1.42533i	−0.903505	+	0.428578i	$0.859015\pi$
$38$		0			0
$39$	2.72432	−	5.61944i	0.436241	−	0.899830i
$40$		0			0
$41$	−4.07176			−0.635902			−0.317951	−	0.948107i	$-0.602995\pi$
$41$	−4.07176			−0.635902			−0.317951	+	0.948107i	$0.602995\pi$
$42$		0			0
$43$	−11.5147			−1.75597			−0.877985	−	0.478688i	$-0.841112\pi$
$43$	−11.5147			−1.75597			−0.877985	+	0.478688i	$0.841112\pi$
$44$		0			0
$45$	−0.0940265	−	1.10621i	−0.0140166	−	0.164904i
$46$		0			0
$47$	0.918184	−	1.59034i	0.133931	−	0.231975i	−0.791258	−	0.611483i	$-0.790573\pi$
$47$	0.918184	−	1.59034i	0.133931	−	0.231975i	0.925189	+	0.379508i	$0.123907\pi$
$48$		0			0
$49$	−6.95123			−0.993034
$50$		0			0
$51$	1.29447	+	4.12331i	0.181263	+	0.577379i
$52$		0			0
$53$	−7.12781			−0.979080			−0.489540	−	0.871981i	$-0.662835\pi$
$53$	−7.12781			−0.979080			−0.489540	+	0.871981i	$0.662835\pi$
$54$		0			0
$55$	−0.778731	+	1.34880i	−0.105004	+	0.181872i
$56$		0			0
$57$	−0.234611	−	0.747311i	−0.0310750	−	0.0989838i
$58$		0			0
$59$	2.40843	−	4.17152i	0.313550	−	0.543085i	−0.665578	−	0.746328i	$-0.731815\pi$
$59$	2.40843	−	4.17152i	0.313550	−	0.543085i	0.979128	+	0.203243i	$0.0651482\pi$
$60$		0			0
$61$	−7.82801			−1.00227			−0.501137	−	0.865368i	$-0.667085\pi$
$61$	−7.82801			−1.00227			−0.501137	+	0.865368i	$0.667085\pi$
$62$		0			0
$63$	0.599722	+	0.281462i	0.0755579	+	0.0354608i
$64$		0			0
$65$	1.27797	−	0.383569i	0.158513	−	0.0475759i
$66$		0			0
$67$	−11.6595			−1.42443			−0.712216	−	0.701960i	$-0.752308\pi$
$67$	−11.6595			−1.42443			−0.712216	+	0.701960i	$0.752308\pi$
$68$		0			0
$69$	3.46970	+	0.773714i	0.417703	+	0.0931442i
$70$		0			0
$71$	−6.89204	−	11.9374i	−0.817935	−	1.41670i	−0.907201	−	0.420697i	$-0.861786\pi$
$71$	−6.89204	−	11.9374i	−0.817935	−	1.41670i	0.0892667	−	0.996008i	$-0.471548\pi$
$72$		0			0
$73$	8.58734			1.00507			0.502536	−	0.864556i	$-0.332400\pi$
$73$	8.58734			1.00507			0.502536	+	0.864556i	$0.332400\pi$
$74$		0			0
$75$	−5.69820	+	6.20309i	−0.657972	+	0.716271i
$76$		0			0
$77$	−0.464689	−	0.804865i	−0.0529562	−	0.0917229i
$78$		0			0
$79$	−6.36242	+	11.0200i	−0.715828	+	1.23985i	0.246812	+	0.969063i	$0.420617\pi$
$79$	−6.36242	+	11.0200i	−0.715828	+	1.23985i	−0.962639	+	0.270786i	$0.912716\pi$
$80$		0			0
$81$	5.75094	+	6.92291i	0.638993	+	0.769212i
$82$		0			0
$83$	−5.54460	+	9.60353i	−0.608599	+	1.05412i	0.382873	+	0.923801i	$0.374935\pi$
$83$	−5.54460	+	9.60353i	−0.608599	+	1.05412i	−0.991472	+	0.130323i	$0.958399\pi$
$84$		0			0
$85$	−0.461686	+	0.799664i	−0.0500769	+	0.0867358i
$86$		0			0
$87$	−1.92043	−	6.11716i	−0.205891	−	0.655829i
$88$		0			0
$89$	−0.114134	+	0.197686i	−0.0120982	+	0.0209546i	−0.872011	−	0.489486i	$-0.837184\pi$
$89$	−0.114134	+	0.197686i	−0.0120982	+	0.0209546i	0.859913	+	0.510441i	$0.170518\pi$
$90$		0			0
$91$	−0.183079	+	0.774874i	−0.0191919	+	0.0812289i
$92$		0			0
$93$	0.846760	+	2.69720i	0.0878049	+	0.279686i
$94$		0			0
$95$	0.0836763	−	0.144932i	0.00858501	−	0.0148697i
$96$		0			0
$97$	10.2261			1.03831			0.519153	−	0.854681i	$-0.326247\pi$
$97$	10.2261			1.03831			0.519153	+	0.854681i	$0.326247\pi$
$98$		0			0
$99$	−1.06932	−	12.5804i	−0.107471	−	1.26438i
$100$		0			0
$101$	−3.97569	−	6.88610i	−0.395596	−	0.685193i	0.597581	−	0.801809i	$-0.296129\pi$
$101$	−3.97569	−	6.88610i	−0.395596	−	0.685193i	−0.993177	+	0.116616i	$0.962795\pi$
$102$		0			0
$103$	3.16273	+	5.47801i	0.311633	+	0.539764i	0.978716	−	0.205219i	$-0.0657908\pi$
$103$	3.16273	+	5.47801i	0.311633	+	0.539764i	−0.667083	+	0.744983i	$0.732457\pi$
$104$		0			0
$105$	0.0423967	+	0.135047i	0.00413749	+	0.0131792i
$106$		0			0
$107$	2.59608	−	4.49654i	0.250973	−	0.434697i	−0.712821	−	0.701346i	$-0.752583\pi$
$107$	2.59608	−	4.49654i	0.250973	−	0.434697i	0.963794	+	0.266648i	$0.0859162\pi$
$108$		0			0
$109$	13.6259			1.30513			0.652564	−	0.757733i	$-0.273693\pi$
$109$	13.6259			1.30513			0.652564	+	0.757733i	$0.273693\pi$
$110$		0			0
$111$	11.7304	−	12.7698i	1.11340	−	1.21205i
$112$		0			0
$113$	1.15288	−	1.99685i	0.108454	−	0.187848i	−0.806690	−	0.590975i	$-0.798743\pi$
$113$	1.15288	−	1.99685i	0.108454	−	0.187848i	0.915144	+	0.403127i	$0.132077\pi$
$114$		0			0
$115$	0.379769	+	0.657779i	0.0354136	+	0.0613382i
$116$		0			0
$117$	−6.72393	+	8.47283i	−0.621627	+	0.783313i
$118$		0			0
$119$	−0.275500	−	0.477181i	−0.0252551	−	0.0437431i
$120$		0			0
$121$	−3.35614	+	5.81300i	−0.305103	+	0.528455i
$122$		0			0
$123$	6.88343	+	1.53495i	0.620658	+	0.138401i
$124$		0			0
$125$	−3.64999			−0.326465
$126$		0			0
$127$	5.26106	−	9.11243i	0.466844	−	0.808597i	−0.532439	−	0.846469i	$-0.678724\pi$
$127$	5.26106	−	9.11243i	0.466844	−	0.808597i	0.999283	+	0.0378713i	$0.0120577\pi$
$128$		0			0
$129$	19.4659	+	4.34073i	1.71388	+	0.382180i
$130$		0			0
$131$	−1.94010	−	3.36036i	−0.169508	−	0.293596i	0.768739	−	0.639562i	$-0.220884\pi$
$131$	−1.94010	−	3.36036i	−0.169508	−	0.293596i	−0.938247	+	0.345967i	$0.887551\pi$
$132$		0			0
$133$	0.0499319	+	0.0864845i	0.00432964	+	0.00749916i
$134$		0			0
$135$	−0.258058	+	1.90553i	−0.0222101	+	0.164002i
$136$		0			0
$137$	−11.5781			−0.989188			−0.494594	−	0.869124i	$-0.664683\pi$
$137$	−11.5781			−0.989188			−0.494594	+	0.869124i	$0.664683\pi$
$138$		0			0
$139$	−2.65932	+	4.60607i	−0.225560	+	0.390682i	−0.956487	−	0.291774i	$-0.905755\pi$
$139$	−2.65932	+	4.60607i	−0.225560	+	0.390682i	0.730927	+	0.682456i	$0.239088\pi$
$140$		0			0
$141$	−2.15174	+	2.34239i	−0.181209	+	0.197265i
$142$		0			0
$143$	14.5338	−	4.36215i	1.21538	−	0.364782i
$144$		0			0
$145$	0.684938	−	1.18635i	0.0568810	−	0.0985207i
$146$		0			0
$147$	11.7513	+	2.62043i	0.969228	+	0.216130i
$148$		0			0
$149$	8.88135	−	15.3830i	0.727589	−	1.26022i	−0.230311	−	0.973117i	$-0.573974\pi$
$149$	8.88135	−	15.3830i	0.727589	−	1.26022i	0.957900	−	0.287104i	$-0.0926924\pi$
$150$		0			0
$151$	−8.56540	+	14.8357i	−0.697043	+	1.20731i	0.272445	+	0.962171i	$0.412168\pi$
$151$	−8.56540	+	14.8357i	−0.697043	+	1.20731i	−0.969487	+	0.245142i	$0.921166\pi$
$152$		0			0
$153$	−0.633968	−	7.45856i	−0.0512533	−	0.602989i
$154$		0			0
$155$	−0.302005	+	0.523087i	−0.0242576	+	0.0420154i
$156$		0			0
$157$	−3.23205	−	5.59807i	−0.257946	−	0.446775i	0.707746	−	0.706467i	$-0.249712\pi$
$157$	−3.23205	−	5.59807i	−0.257946	−	0.446775i	−0.965691	+	0.259692i	$0.916379\pi$
$158$		0			0
$159$	12.0498	+	2.68700i	0.955609	+	0.213093i
$160$		0			0
$161$	−0.453236			−0.0357200
$162$		0			0
$163$	0.657316	+	1.13851i	0.0514850	+	0.0891746i	0.890619	−	0.454750i	$-0.150271\pi$
$163$	0.657316	+	1.13851i	0.0514850	+	0.0891746i	−0.839134	+	0.543924i	$0.816938\pi$
$164$		0			0
$165$	1.82493	−	1.98663i	0.142071	−	0.154659i
$166$		0			0
$167$	18.5920			1.43869			0.719346	−	0.694652i	$-0.244442\pi$
$167$	18.5920			1.43869			0.719346	+	0.694652i	$0.244442\pi$
$168$		0			0
$169$	−11.6253	−	5.81822i	−0.894256	−	0.447555i
$170$		0			0
$171$	0.114901	+	1.35179i	0.00878668	+	0.103374i
$172$		0			0
$173$	−2.06795			−0.157223			−0.0786116	−	0.996905i	$-0.525049\pi$
$173$	−2.06795			−0.157223			−0.0786116	+	0.996905i	$0.525049\pi$
$174$		0			0
$175$	0.536950	−	0.930025i	0.0405896	−	0.0703033i
$176$		0			0
$177$	−5.64407	+	6.14416i	−0.424234	+	0.461823i
$178$		0			0
$179$	9.02646	−	15.6343i	0.674669	−	1.16856i	−0.301896	−	0.953341i	$-0.597620\pi$
$179$	9.02646	−	15.6343i	0.674669	−	1.16856i	0.976565	−	0.215221i	$-0.0690471\pi$
$180$		0			0
$181$	12.5383			0.931962			0.465981	−	0.884795i	$-0.345701\pi$
$181$	12.5383			0.931962			0.465981	+	0.884795i	$0.345701\pi$
$182$		0			0
$183$	13.2335	+	2.95096i	0.978248	+	0.218141i
$184$		0			0
$185$	3.70480			0.272382
$186$		0			0
$187$	−5.25054	+	9.09421i	−0.383958	+	0.665034i
$188$		0			0
$189$	−0.907744	−	0.701899i	−0.0660287	−	0.0510556i
$190$		0			0
$191$	−6.39211			−0.462517			−0.231259	−	0.972892i	$-0.574284\pi$
$191$	−6.39211			−0.462517			−0.231259	+	0.972892i	$0.574284\pi$
$192$		0			0
$193$	3.64109			0.262091			0.131046	−	0.991376i	$-0.458167\pi$
$193$	3.64109			0.262091			0.131046	+	0.991376i	$0.458167\pi$
$194$		0			0
$195$	−2.30505	+	0.166673i	−0.165068	+	0.0119357i
$196$		0			0
$197$	−5.16259	+	8.94187i	−0.367820	+	0.637082i	−0.989224	−	0.146408i	$-0.953229\pi$
$197$	−5.16259	+	8.94187i	−0.367820	+	0.637082i	0.621405	+	0.783490i	$0.286562\pi$
$198$		0			0
$199$	4.21204	+	7.29547i	0.298584	+	0.517162i	0.975812	−	0.218611i	$-0.0701524\pi$
$199$	4.21204	+	7.29547i	0.298584	+	0.517162i	−0.677228	+	0.735773i	$0.736819\pi$
$200$		0			0
$201$	19.7107	+	4.39532i	1.39029	+	0.310022i
$202$		0			0
$203$	0.408720	+	0.707924i	0.0286865	+	0.0496865i
$204$		0			0
$205$	0.753411	+	1.30495i	0.0526205	+	0.0911414i
$206$		0			0
$207$	−5.57396	−	2.61597i	−0.387417	−	0.181823i
$208$		0			0
$209$	0.951612	−	1.64824i	0.0658244	−	0.114011i
$210$		0			0
$211$	12.3539			0.850475			0.425238	−	0.905082i	$-0.360191\pi$
$211$	12.3539			0.850475			0.425238	+	0.905082i	$0.360191\pi$
$212$		0			0
$213$	7.15112	+	22.7786i	0.489987	+	1.56076i
$214$		0			0
$215$	2.13060	+	3.69030i	0.145306	+	0.251677i
$216$		0			0
$217$	−0.180214	−	0.312140i	−0.0122337	−	0.0211894i
$218$		0			0
$219$	−14.5172	−	3.23720i	−0.980978	−	0.218750i
$220$		0			0
$221$	8.61666	−	2.58619i	0.579619	−	0.173966i
$222$		0			0
$223$	2.78229	+	4.81907i	0.186316	+	0.322709i	0.944019	−	0.329891i	$-0.107012\pi$
$223$	2.78229	+	4.81907i	0.186316	+	0.322709i	−0.757703	+	0.652599i	$0.773679\pi$
$224$		0			0
$225$	11.9714	−	8.33843i	0.798092	−	0.555895i
$226$		0			0
$227$	19.7955			1.31387			0.656937	−	0.753945i	$-0.271852\pi$
$227$	19.7955			1.31387			0.656937	+	0.753945i	$0.271852\pi$
$228$		0			0
$229$	−9.03568	−	15.6502i	−0.597094	−	1.03420i	−0.993248	−	0.116013i	$-0.962988\pi$
$229$	−9.03568	−	15.6502i	−0.597094	−	1.03420i	0.396153	−	0.918184i	$-0.370345\pi$
$230$		0			0
$231$	0.482158	+	1.53582i	0.0317236	+	0.101050i
$232$		0			0
$233$	−18.0216			−1.18063			−0.590317	−	0.807172i	$-0.700997\pi$
$233$	−18.0216			−1.18063			−0.590317	+	0.807172i	$0.700997\pi$
$234$		0			0
$235$	−0.679579			−0.0443308
$236$		0			0
$237$	14.9101	−	16.2312i	0.968516	−	1.05433i
$238$		0			0
$239$	−0.100774	−	0.174546i	−0.00651853	−	0.0112904i	0.862748	−	0.505635i	$-0.168742\pi$
$239$	−0.100774	−	0.174546i	−0.00651853	−	0.0112904i	−0.869266	+	0.494344i	$0.835408\pi$
$240$		0			0
$241$	0.922329			0.0594124			0.0297062	−	0.999559i	$-0.490543\pi$
$241$	0.922329			0.0594124			0.0297062	+	0.999559i	$0.490543\pi$
$242$		0			0
$243$	−7.11237	−	13.8713i	−0.456259	−	0.889847i
$244$		0			0
$245$	1.28621	+	2.22778i	0.0821730	+	0.142328i
$246$		0			0
$247$	−1.56169	+	0.468723i	−0.0993679	+	0.0298241i
$248$		0			0
$249$	12.9936	−	14.1449i	0.823435	−	0.896395i
$250$		0			0
$251$	4.59028	+	7.95060i	0.289736	+	0.501838i	0.973747	−	0.227635i	$-0.0730991\pi$
$251$	4.59028	+	7.95060i	0.289736	+	0.501838i	−0.684011	+	0.729472i	$0.739766\pi$
$252$		0			0
$253$	4.31893	+	7.48061i	0.271529	+	0.470302i
$254$		0			0
$255$	1.08195	−	1.17781i	0.0677542	−	0.0737575i
$256$		0			0
$257$	7.06935			0.440974			0.220487	−	0.975390i	$-0.429235\pi$
$257$	7.06935			0.440974			0.220487	+	0.975390i	$0.429235\pi$
$258$		0			0
$259$	−1.10537	+	1.91456i	−0.0686846	+	0.118965i
$260$		0			0
$261$	0.940527	+	11.0652i	0.0582172	+	0.684918i
$262$		0			0
$263$	0.936478	+	1.62203i	0.0577457	+	0.100019i	0.893453	−	0.449156i	$-0.148275\pi$
$263$	0.936478	+	1.62203i	0.0577457	+	0.100019i	−0.835707	+	0.549175i	$0.814942\pi$
$264$		0			0
$265$	1.31888	+	2.28437i	0.0810183	+	0.140328i
$266$		0			0
$267$	0.267469	−	0.291168i	0.0163688	−	0.0178192i
$268$		0			0
$269$	−13.4883	−	23.3625i	−0.822399	−	1.42444i	−0.903891	−	0.427763i	$-0.859302\pi$
$269$	−13.4883	−	23.3625i	−0.822399	−	1.42444i	0.0814922	−	0.996674i	$-0.474031\pi$
$270$		0			0
$271$	5.17186	−	8.95793i	0.314168	−	0.544155i	−0.665092	−	0.746761i	$-0.731608\pi$
$271$	5.17186	−	8.95793i	0.314168	−	0.544155i	0.979260	+	0.202606i	$0.0649410\pi$
$272$		0			0
$273$	0.601608	−	1.24093i	0.0364110	−	0.0751046i
$274$		0			0
$275$	−20.4666			−1.23418
$276$		0			0
$277$	−9.20237			−0.552917			−0.276458	−	0.961026i	$-0.589161\pi$
$277$	−9.20237			−0.552917			−0.276458	+	0.961026i	$0.589161\pi$
$278$		0			0
$279$	−0.414700	−	4.87890i	−0.0248274	−	0.292092i
$280$		0			0
$281$	−4.27672	+	7.40750i	−0.255128	+	0.441894i	−0.964930	−	0.262507i	$-0.915451\pi$
$281$	−4.27672	+	7.40750i	−0.255128	+	0.441894i	0.709802	+	0.704401i	$0.248784\pi$
$282$		0			0
$283$	−16.8025			−0.998803			−0.499402	−	0.866371i	$-0.666447\pi$
$283$	−16.8025			−0.998803			−0.499402	+	0.866371i	$0.666447\pi$
$284$		0			0
$285$	−0.196093	+	0.213468i	−0.0116155	+	0.0126447i
$286$		0			0
$287$	−0.899160			−0.0530758
$288$		0			0
$289$	5.38711	−	9.33074i	0.316889	−	0.548867i
$290$		0			0
$291$	−17.2876	−	3.85498i	−1.01342	−	0.225983i
$292$		0			0
$293$	8.67333	−	15.0226i	0.506701	−	0.877632i	−0.493269	−	0.869877i	$-0.664198\pi$
$293$	8.67333	−	15.0226i	0.506701	−	0.877632i	0.999970	−	0.00775536i	$-0.00246863\pi$
$294$		0			0
$295$	−1.78256			−0.103784
$296$		0			0
$297$	−2.93477	+	21.6707i	−0.170293	+	1.25746i
$298$		0			0
$299$	1.70158	−	7.20187i	0.0984051	−	0.416495i
$300$		0			0
$301$	−2.54277			−0.146563
$302$		0			0
$303$	4.12515	+	13.1399i	0.236984	+	0.754867i
$304$		0			0
$305$	1.44844	+	2.50878i	0.0829376	+	0.143652i
$306$		0			0
$307$	−4.98311			−0.284401			−0.142201	−	0.989838i	$-0.545418\pi$
$307$	−4.98311			−0.284401			−0.142201	+	0.989838i	$0.545418\pi$
$308$		0			0
$309$	−3.28162	−	10.4530i	−0.186685	−	0.594650i
$310$		0			0
$311$	13.8571	+	24.0011i	0.785762	+	1.36098i	0.928543	+	0.371226i	$0.121062\pi$
$311$	13.8571	+	24.0011i	0.785762	+	1.36098i	−0.142781	+	0.989754i	$0.545604\pi$
$312$		0			0
$313$	−6.97711	+	12.0847i	−0.394369	+	0.683068i	−0.993020	−	0.117942i	$-0.962370\pi$
$313$	−6.97711	+	12.0847i	−0.394369	+	0.683068i	0.598651	+	0.801010i	$0.295704\pi$
$314$		0			0
$315$	−0.0207637	−	0.244283i	−0.00116990	−	0.0137638i
$316$		0			0
$317$	−15.2734	+	26.4544i	−0.857842	+	1.48583i	0.0161410	+	0.999870i	$0.494862\pi$
$317$	−15.2734	+	26.4544i	−0.857842	+	1.48583i	−0.873983	+	0.485956i	$0.838471\pi$
$318$		0			0
$319$	7.78947	−	13.4918i	0.436127	−	0.755394i
$320$		0			0
$321$	−6.08383	+	6.62289i	−0.339566	+	0.369654i
$322$		0			0
$323$	0.564183	−	0.977193i	0.0313920	−	0.0543725i
$324$		0			0
$325$	12.7621	+	12.0237i	0.707915	+	0.666953i
$326$		0			0
$327$	−23.0351	−	5.13663i	−1.27384	−	0.284056i
$328$		0			0
$329$	0.202761	−	0.351193i	0.0111786	−	0.0193619i
$330$		0			0
$331$	−3.85832			−0.212072			−0.106036	−	0.994362i	$-0.533816\pi$
$331$	−3.85832			−0.212072			−0.106036	+	0.994362i	$0.533816\pi$
$332$		0			0
$333$	−24.6445	+	17.1656i	−1.35051	+	0.940671i
$334$		0			0
$335$	2.15739	+	3.73671i	0.117871	+	0.204159i
$336$		0			0
$337$	−4.54153	−	7.86617i	−0.247393	−	0.428497i	0.715409	−	0.698706i	$-0.246241\pi$
$337$	−4.54153	−	7.86617i	−0.247393	−	0.428497i	−0.962802	+	0.270209i	$0.912907\pi$
$338$		0			0
$339$	−2.70174	+	2.94113i	−0.146739	+	0.159740i
$340$		0			0
$341$	−3.43456	+	5.94883i	−0.185992	+	0.322147i
$342$		0			0
$343$	−3.08083			−0.166349
$344$		0			0
$345$	−0.394045	−	1.25516i	−0.0212147	−	0.0675754i
$346$		0			0
$347$	−15.5277	+	26.8948i	−0.833573	+	1.44379i	0.0616141	+	0.998100i	$0.480375\pi$
$347$	−15.5277	+	26.8948i	−0.833573	+	1.44379i	−0.895187	+	0.445691i	$0.852958\pi$
$348$		0			0
$349$	7.16311	+	12.4069i	0.383432	+	0.664124i	0.991550	−	0.129722i	$-0.0414086\pi$
$349$	7.16311	+	12.4069i	0.383432	+	0.664124i	−0.608118	+	0.793847i	$0.708075\pi$
$350$		0			0
$351$	14.5610	−	11.7888i	0.777211	−	0.629241i
$352$		0			0
$353$	−12.6460	−	21.9035i	−0.673079	−	1.16581i	−0.977026	−	0.213118i	$-0.931638\pi$
$353$	−12.6460	−	21.9035i	−0.673079	−	1.16581i	0.303948	−	0.952689i	$-0.401695\pi$
$354$		0			0
$355$	−2.55051	+	4.41762i	−0.135367	+	0.234463i
$356$		0			0
$357$	0.285857	+	0.910545i	0.0151292	+	0.0481911i
$358$		0			0
$359$	7.28756			0.384623			0.192311	−	0.981334i	$-0.438402\pi$
$359$	7.28756			0.384623			0.192311	+	0.981334i	$0.438402\pi$
$360$		0			0
$361$	9.39775	−	16.2774i	0.494618	−	0.856704i
$362$		0			0
$363$	7.86500	−	8.56188i	0.412806	−	0.449382i
$364$		0			0
$365$	−1.58894	−	2.75213i	−0.0831692	−	0.144053i
$366$		0			0
$367$	11.9161	+	20.6393i	0.622017	+	1.07736i	0.989110	+	0.147180i	$0.0470198\pi$
$367$	11.9161	+	20.6393i	0.622017	+	1.07736i	−0.367093	+	0.930184i	$0.619647\pi$
$368$		0			0
$369$	−11.0580	−	5.18974i	−0.575657	−	0.270167i
$370$		0			0
$371$	−1.57402			−0.0817193
$372$		0			0
$373$	6.15807	−	10.6661i	0.318853	−	0.552269i	−0.661396	−	0.750037i	$-0.730036\pi$
$373$	6.15807	−	10.6661i	0.318853	−	0.552269i	0.980249	+	0.197767i	$0.0633691\pi$
$374$		0			0
$375$	6.17041	+	1.37595i	0.318639	+	0.0710537i
$376$		0			0
$377$	−12.7833	+	3.83676i	−0.658373	+	0.197603i
$378$		0			0
$379$	−7.07147	+	12.2481i	−0.363237	+	0.629145i	−0.988492	−	0.151276i	$-0.951662\pi$
$379$	−7.07147	+	12.2481i	−0.363237	+	0.629145i	0.625255	+	0.780421i	$0.284995\pi$
$380$		0			0
$381$	−12.3291	+	13.4215i	−0.631640	+	0.687607i
$382$		0			0
$383$	4.08658	−	7.07816i	0.208814	−	0.361677i	−0.742527	−	0.669816i	$-0.766373\pi$
$383$	4.08658	−	7.07816i	0.208814	−	0.361677i	0.951341	+	0.308139i	$0.0997062\pi$
$384$		0			0
$385$	−0.171966	+	0.297854i	−0.00876420	+	0.0151800i
$386$		0			0
$387$	−31.2713	−	14.6763i	−1.58961	−	0.746036i
$388$		0			0
$389$	18.8420	−	32.6353i	0.955326	−	1.65467i	0.221706	−	0.975114i	$-0.428838\pi$
$389$	18.8420	−	32.6353i	0.955326	−	1.65467i	0.733620	−	0.679559i	$-0.237829\pi$
$390$		0			0
$391$	2.56057	+	4.43503i	0.129493	+	0.224289i
$392$		0			0
$393$	2.01304	+	6.41215i	0.101544	+	0.323450i
$394$		0			0
$395$	4.70904			0.236937
$396$		0			0
$397$	8.81974	+	15.2762i	0.442650	+	0.766692i	0.997885	−	0.0650010i	$-0.0207051\pi$
$397$	8.81974	+	15.2762i	0.442650	+	0.766692i	−0.555235	+	0.831693i	$0.687372\pi$
$398$		0			0
$399$	−0.0518089	−	0.165028i	−0.00259369	−	0.00826172i
$400$		0			0
$401$	−31.4806			−1.57207			−0.786034	−	0.618183i	$-0.787869\pi$
$401$	−31.4806			−1.57207			−0.786034	+	0.618183i	$0.787869\pi$
$402$		0			0
$403$	5.63645	−	1.69172i	0.280771	−	0.0842704i
$404$		0			0
$405$	1.15459	−	3.12407i	0.0573720	−	0.155236i
$406$		0			0
$407$	42.1329			2.08845
$408$		0			0
$409$	17.9819	−	31.1455i	0.889147	−	1.54005i	0.0482615	−	0.998835i	$-0.484632\pi$
$409$	17.9819	−	31.1455i	0.889147	−	1.54005i	0.840885	−	0.541213i	$-0.182035\pi$
$410$		0			0
$411$	19.5732	+	4.36466i	0.965475	+	0.215293i
$412$		0			0
$413$	0.531849	−	0.921190i	0.0261706	−	0.0453288i
$414$		0			0
$415$	4.10374			0.201445
$416$		0			0
$417$	6.23202	−	6.78421i	0.305183	−	0.332224i
$418$		0			0
$419$	−27.3743			−1.33732			−0.668661	−	0.743567i	$-0.733132\pi$
$419$	−27.3743			−1.33732			−0.668661	+	0.743567i	$0.733132\pi$
$420$		0			0
$421$	8.31205	−	14.3969i	0.405104	−	0.701661i	−0.589229	−	0.807966i	$-0.700568\pi$
$421$	8.31205	−	14.3969i	0.405104	−	0.701661i	0.994334	+	0.106304i	$0.0339018\pi$
$422$		0			0
$423$	4.52059	−	3.14873i	0.219799	−	0.153096i
$424$		0			0
$425$	−12.1341			−0.588588
$426$		0			0
$427$	−1.72865			−0.0836552
$428$		0			0
$429$	−26.2142	+	1.89549i	−1.26564	+	0.0915151i
$430$		0			0
$431$	6.96462	−	12.0631i	0.335474	−	0.581058i	−0.648102	−	0.761554i	$-0.724437\pi$
$431$	6.96462	−	12.0631i	0.335474	−	0.581058i	0.983576	+	0.180496i	$0.0577703\pi$
$432$		0			0
$433$	−19.6355	−	34.0097i	−0.943621	−	1.63440i	−0.758489	−	0.651686i	$-0.774062\pi$
$433$	−19.6355	−	34.0097i	−0.943621	−	1.63440i	−0.185133	−	0.982714i	$-0.559271\pi$
$434$		0			0
$435$	−1.60513	+	1.74735i	−0.0769600	+	0.0837791i
$436$		0			0
$437$	−0.464079	−	0.803808i	−0.0221999	−	0.0384514i
$438$		0			0
$439$	−17.9844	−	31.1498i	−0.858347	−	1.48670i	−0.873505	−	0.486815i	$-0.838159\pi$
$439$	−17.9844	−	31.1498i	−0.858347	−	1.48670i	0.0151587	−	0.999885i	$-0.495175\pi$
$440$		0			0
$441$	−18.8780	−	8.85984i	−0.898954	−	0.421897i
$442$		0			0
$443$	−7.79412	+	13.4998i	−0.370310	+	0.641395i	−0.989613	−	0.143757i	$-0.954082\pi$
$443$	−7.79412	+	13.4998i	−0.370310	+	0.641395i	0.619303	+	0.785152i	$0.287415\pi$
$444$		0			0
$445$	0.0844743			0.00400446
$446$		0			0
$447$	−20.8132	+	22.6573i	−0.984429	+	1.07165i
$448$		0			0
$449$	18.9254	+	32.7797i	0.893143	+	1.54697i	0.836086	+	0.548598i	$0.184838\pi$
$449$	18.9254	+	32.7797i	0.893143	+	1.54697i	0.0570564	+	0.998371i	$0.481829\pi$
$450$		0			0
$451$	8.56819	+	14.8405i	0.403460	+	0.698814i
$452$		0			0
$453$	20.0727	−	21.8513i	0.943100	−	1.02666i
$454$		0			0
$455$	0.282213	−	0.0847030i	0.0132304	−	0.00397094i
$456$		0			0
$457$	3.37506	+	5.84577i	0.157878	+	0.273453i	0.934103	−	0.357003i	$-0.116201\pi$
$457$	3.37506	+	5.84577i	0.157878	+	0.273453i	−0.776225	+	0.630456i	$0.782868\pi$
$458$		0			0
$459$	−1.73994	+	12.8479i	−0.0812135	+	0.599689i
$460$		0			0
$461$	22.3590			1.04136			0.520681	−	0.853752i	$-0.325678\pi$
$461$	22.3590			1.04136			0.520681	+	0.853752i	$0.325678\pi$
$462$		0			0
$463$	−1.62174	−	2.80893i	−0.0753686	−	0.130542i	0.825878	−	0.563849i	$-0.190680\pi$
$463$	−1.62174	−	2.80893i	−0.0753686	−	0.130542i	−0.901246	+	0.433307i	$0.857347\pi$
$464$		0			0
$465$	0.707738	−	0.770447i	0.0328206	−	0.0357286i
$466$		0			0
$467$	15.5291			0.718603			0.359302	−	0.933221i	$-0.383015\pi$
$467$	15.5291			0.718603			0.359302	+	0.933221i	$0.383015\pi$
$468$		0			0
$469$	−2.57475			−0.118891
$470$		0			0
$471$	3.35355	+	10.6821i	0.154523	+	0.492205i
$472$		0			0
$473$	24.2303	+	41.9681i	1.11411	+	1.92969i
$474$		0			0
$475$	2.19918			0.100905
$476$		0			0
$477$	−19.3576	−	9.08490i	−0.886322	−	0.415969i
$478$		0			0
$479$	−1.82016	−	3.15262i	−0.0831654	−	0.144047i	0.821443	−	0.570291i	$-0.193170\pi$
$479$	−1.82016	−	3.15262i	−0.0831654	−	0.144047i	−0.904608	+	0.426245i	$0.859836\pi$
$480$		0			0
$481$	−26.2723	−	24.7521i	−1.19791	−	1.12860i
$482$		0			0
$483$	0.766209	+	0.170858i	0.0348637	+	0.00777431i
$484$		0			0
$485$	−1.89217	−	3.27734i	−0.0859192	−	0.148816i
$486$		0			0
$487$	10.2651	+	17.7797i	0.465157	+	0.805676i	0.999209	−	0.0397759i	$-0.0126644\pi$
$487$	10.2651	+	17.7797i	0.465157	+	0.805676i	−0.534051	+	0.845452i	$0.679331\pi$
$488$		0			0
$489$	−0.682026	−	2.17247i	−0.0308423	−	0.0982424i
$490$		0			0
$491$	−43.3226			−1.95512			−0.977561	−	0.210651i	$-0.932442\pi$
$491$	−43.3226			−1.95512			−0.977561	+	0.210651i	$0.932442\pi$
$492$		0			0
$493$	4.61815	−	7.99887i	0.207991	−	0.360251i
$494$		0			0
$495$	−3.83400	+	2.67050i	−0.172326	+	0.120030i
$496$		0			0
$497$	−1.52196	−	2.63611i	−0.0682692	−	0.118246i
$498$		0			0
$499$	−7.22040	−	12.5061i	−0.323229	−	0.559850i	0.657923	−	0.753085i	$-0.271435\pi$
$499$	−7.22040	−	12.5061i	−0.323229	−	0.559850i	−0.981152	+	0.193235i	$0.938102\pi$
$500$		0			0
$501$	−31.4303	−	7.00869i	−1.40420	−	0.313125i
$502$		0			0
$503$	10.9732	+	19.0061i	0.489269	+	0.847439i	0.999924	−	0.0123470i	$-0.00393026\pi$
$503$	10.9732	+	19.0061i	0.489269	+	0.847439i	−0.510655	+	0.859786i	$0.670597\pi$
$504$		0			0
$505$	−1.47127	+	2.54832i	−0.0654708	+	0.113399i
$506$		0			0
$507$	17.4597	+	14.2183i	0.775410	+	0.631458i
$508$		0			0
$509$	−5.53986			−0.245550			−0.122775	−	0.992435i	$-0.539179\pi$
$509$	−5.53986			−0.245550			−0.122775	+	0.992435i	$0.539179\pi$
$510$		0			0
$511$	1.89633			0.0838887
$512$		0			0
$513$	0.315348	−	2.32856i	0.0139230	−	0.102809i
$514$		0			0
$515$	1.17042	−	2.02723i	0.0515749	−	0.0893303i
$516$		0			0
$517$	−7.72853			−0.339900
$518$		0			0
$519$	3.49593	+	0.779562i	0.153454	+	0.0342190i
$520$		0			0
$521$	−22.2041			−0.972779			−0.486390	−	0.873742i	$-0.661686\pi$
$521$	−22.2041			−0.972779			−0.486390	+	0.873742i	$0.661686\pi$
$522$		0			0
$523$	−10.1092	+	17.5096i	−0.442043	+	0.765641i	−0.997841	−	0.0656764i	$-0.979080\pi$
$523$	−10.1092	+	17.5096i	−0.442043	+	0.765641i	0.555798	+	0.831317i	$0.312413\pi$
$524$		0			0
$525$	−1.25833	+	1.36982i	−0.0549178	+	0.0597838i
$526$		0			0
$527$	−2.03625	+	3.52689i	−0.0887004	+	0.153634i
$528$		0			0
$529$	−18.7875			−0.816848
$530$		0			0
$531$	11.8577	−	8.25922i	0.514578	−	0.358420i
$532$		0			0
$533$	3.37572	−	14.2876i	0.146218	−	0.618863i
$534$		0			0
$535$	−1.92145			−0.0830714
$536$		0			0
$537$	−21.1532	+	23.0275i	−0.912829	+	0.993709i
$538$		0			0
$539$	14.6275	+	25.3355i	0.630050	+	1.09128i
$540$		0			0
$541$	27.3228			1.17470			0.587349	−	0.809334i	$-0.300172\pi$
$541$	27.3228			1.17470			0.587349	+	0.809334i	$0.300172\pi$
$542$		0			0
$543$	−21.1963	−	4.72660i	−0.909621	−	0.202838i
$544$		0			0
$545$	−2.52125	−	4.36694i	−0.107999	−	0.187059i
$546$		0			0
$547$	−17.0211	+	29.4815i	−0.727771	+	1.26054i	0.230052	+	0.973178i	$0.426110\pi$
$547$	−17.0211	+	29.4815i	−0.727771	+	1.26054i	−0.957823	+	0.287358i	$0.907223\pi$
$548$		0			0
$549$	−21.2592	−	9.97736i	−0.907319	−	0.425823i
$550$		0			0
$551$	−0.836996	+	1.44972i	−0.0356572	+	0.0617602i
$552$		0			0
$553$	−1.40500	+	2.43354i	−0.0597468	+	0.103485i
$554$		0			0
$555$	−6.26307	−	1.39661i	−0.265852	−	0.0592828i
$556$		0			0
$557$	−15.8408	+	27.4371i	−0.671196	+	1.16255i	0.306369	+	0.951913i	$0.400886\pi$
$557$	−15.8408	+	27.4371i	−0.671196	+	1.16255i	−0.977565	+	0.210633i	$0.932447\pi$
$558$		0			0
$559$	9.54630	−	40.4043i	0.403766	−	1.70892i
$560$		0			0
$561$	12.3045	−	13.3947i	0.519496	−	0.565525i
$562$		0			0
$563$	18.9329	−	32.7927i	0.797925	−	1.38205i	−0.123041	−	0.992402i	$-0.539265\pi$
$563$	18.9329	−	32.7927i	0.797925	−	1.38205i	0.920965	−	0.389644i	$-0.127402\pi$
$564$		0			0
$565$	−0.853287			−0.0358981
$566$		0			0
$567$	1.26997	+	1.52878i	0.0533338	+	0.0642026i
$568$		0			0
$569$	6.13065	+	10.6186i	0.257010	+	0.445155i	0.965440	−	0.260627i	$-0.0839293\pi$
$569$	6.13065	+	10.6186i	0.257010	+	0.445155i	−0.708429	+	0.705782i	$0.750596\pi$
$570$		0			0
$571$	−9.51424	−	16.4791i	−0.398158	−	0.689631i	0.595340	−	0.803474i	$-0.297017\pi$
$571$	−9.51424	−	16.4791i	−0.398158	−	0.689631i	−0.993499	+	0.113843i	$0.963684\pi$
$572$		0			0
$573$	10.8061	+	2.40966i	0.451430	+	0.100665i
$574$		0			0
$575$	−4.99055	+	8.64388i	−0.208120	+	0.360475i
$576$		0			0
$577$	−14.0939			−0.586735			−0.293368	−	0.956000i	$-0.594776\pi$
$577$	−14.0939			−0.586735			−0.293368	+	0.956000i	$0.594776\pi$
$578$		0			0
$579$	−6.15537	−	1.37260i	−0.255809	−	0.0570432i
$580$		0			0
$581$	−1.22441	+	2.12073i	−0.0507969	+	0.0879828i
$582$		0			0
$583$	14.9990	+	25.9791i	0.621197	+	1.07594i
$584$		0			0
$585$	3.95958	+	0.587178i	0.163709	+	0.0242768i
$586$		0			0
$587$	11.9125	+	20.6330i	0.491681	+	0.851616i	0.999954	−	0.00957978i	$-0.00304938\pi$
$587$	11.9125	+	20.6330i	0.491681	+	0.851616i	−0.508273	+	0.861196i	$0.669716\pi$
$588$		0			0
$589$	0.369051	−	0.639215i	0.0152065	−	0.0263384i
$590$		0			0
$591$	12.0984	−	13.1703i	0.497660	−	0.541755i
$592$		0			0
$593$	0.951141			0.0390587			0.0195293	−	0.999809i	$-0.493783\pi$
$593$	0.951141			0.0390587			0.0195293	+	0.999809i	$0.493783\pi$
$594$		0			0
$595$	−0.101954	+	0.176589i	−0.00417969	+	0.00723943i
$596$		0			0
$597$	−4.37038	−	13.9210i	−0.178868	−	0.569750i
$598$		0			0
$599$	3.59422	+	6.22538i	0.146856	+	0.254362i	0.930064	−	0.367398i	$-0.119751\pi$
$599$	3.59422	+	6.22538i	0.146856	+	0.254362i	−0.783208	+	0.621760i	$0.786418\pi$
$600$		0			0
$601$	14.5771	+	25.2483i	0.594613	+	1.02990i	0.993601	+	0.112945i	$0.0360282\pi$
$601$	14.5771	+	25.2483i	0.594613	+	1.02990i	−0.398988	+	0.916956i	$0.630638\pi$
$602$		0			0
$603$	−31.6646	−	14.8608i	−1.28948	−	0.605180i
$604$		0			0
$605$	2.48399			0.100989
$606$		0			0
$607$	12.8603	−	22.2747i	0.521984	−	0.904102i	−0.477689	−	0.878529i	$-0.658526\pi$
$607$	12.8603	−	22.2747i	0.521984	−	0.904102i	0.999673	−	0.0255732i	$-0.00814109\pi$
$608$		0			0
$609$	−0.424085	−	1.35084i	−0.0171848	−	0.0547390i
$610$		0			0
$611$	4.81919	+	4.54034i	0.194964	+	0.183682i
$612$		0			0
$613$	10.8372	−	18.7706i	0.437711	−	0.758138i	−0.559802	−	0.828627i	$-0.689123\pi$
$613$	10.8372	−	18.7706i	0.437711	−	0.758138i	0.997513	+	0.0704890i	$0.0224560\pi$
$614$		0			0
$615$	−0.781733	−	2.49007i	−0.0315225	−	0.100409i
$616$		0			0
$617$	−11.9349	+	20.6718i	−0.480480	+	0.832216i	−0.999749	−	0.0223946i	$-0.992871\pi$
$617$	−11.9349	+	20.6718i	−0.480480	+	0.832216i	0.519269	+	0.854611i	$0.326204\pi$
$618$		0			0
$619$	14.1119	−	24.4426i	0.567206	−	0.982430i	−0.429634	−	0.903003i	$-0.641358\pi$
$619$	14.1119	−	24.4426i	0.567206	−	0.982430i	0.996841	−	0.0794271i	$-0.0253091\pi$
$620$		0			0
$621$	8.43680	+	6.52362i	0.338557	+	0.261784i
$622$		0			0
$623$	−0.0252040	+	0.0436546i	−0.00100978	+	0.00174899i
$624$		0			0
$625$	−11.4823	−	19.8879i	−0.459290	−	0.795514i
$626$		0			0
$627$	−2.23007	+	2.42767i	−0.0890605	+	0.0969516i
$628$		0			0
$629$	24.9794			0.995992
$630$		0			0
$631$	1.90270	+	3.29557i	0.0757453	+	0.131195i	0.901410	−	0.432966i	$-0.142533\pi$
$631$	1.90270	+	3.29557i	0.0757453	+	0.131195i	−0.825665	+	0.564161i	$0.809200\pi$
$632$		0			0
$633$	−20.8846	−	4.65708i	−0.830087	−	0.185102i
$634$		0			0
$635$	−3.89389			−0.154524
$636$		0			0
$637$	5.76296	−	24.3915i	0.228337	−	0.966425i
$638$		0			0
$639$	−3.50226	−	41.2037i	−0.138547	−	1.62999i
$640$		0			0
$641$	−36.3468			−1.43561			−0.717806	−	0.696243i	$-0.754854\pi$
$641$	−36.3468			−1.43561			−0.717806	+	0.696243i	$0.754854\pi$
$642$		0			0
$643$	4.94485	−	8.56473i	0.195006	−	0.337760i	−0.751897	−	0.659281i	$-0.770861\pi$
$643$	4.94485	−	8.56473i	0.195006	−	0.337760i	0.946902	+	0.321521i	$0.104194\pi$
$644$		0			0
$645$	−2.21069	−	7.04174i	−0.0870458	−	0.277268i
$646$		0			0
$647$	−5.31723	+	9.20972i	−0.209042	+	0.362071i	−0.951413	−	0.307918i	$-0.900368\pi$
$647$	−5.31723	+	9.20972i	−0.209042	+	0.362071i	0.742371	+	0.669989i	$0.233701\pi$
$648$		0			0
$649$	−20.2722			−0.795753
$650$		0			0
$651$	0.186989	+	0.595618i	0.00732867	+	0.0233441i
$652$		0			0
$653$	−0.759157			−0.0297081			−0.0148541	−	0.999890i	$-0.504728\pi$
$653$	−0.759157			−0.0297081			−0.0148541	+	0.999890i	$0.504728\pi$
$654$		0			0
$655$	−0.717968	+	1.24356i	−0.0280533	+	0.0485898i
$656$		0			0
$657$	23.3213	+	10.9452i	0.909852	+	0.427012i
$658$		0			0
$659$	−26.7401			−1.04165			−0.520824	−	0.853664i	$-0.674375\pi$
$659$	−26.7401			−1.04165			−0.520824	+	0.853664i	$0.674375\pi$
$660$		0			0
$661$	−8.93479			−0.347523			−0.173761	−	0.984788i	$-0.555592\pi$
$661$	−8.93479			−0.347523			−0.173761	+	0.984788i	$0.555592\pi$
$662$		0			0
$663$	−15.5416	+	1.12378i	−0.603588	+	0.0436440i
$664$		0			0
$665$	0.0184781	−	0.0320051i	0.000716551	−	0.00124110i
$666$		0			0
$667$	−3.79875	−	6.57962i	−0.147088	−	0.254764i
$668$		0			0
$669$	−2.88688	−	9.19562i	−0.111613	−	0.355523i
$670$		0			0
$671$	16.4725	+	28.5312i	0.635913	+	1.10143i
$672$		0			0
$673$	−3.02784	−	5.24438i	−0.116715	−	0.202156i	0.801749	−	0.597661i	$-0.203903\pi$
$673$	−3.02784	−	5.24438i	−0.116715	−	0.202156i	−0.918464	+	0.395505i	$0.870570\pi$
$674$		0			0
$675$	−23.3813	+	9.58347i	−0.899948	+	0.368868i
$676$		0			0
$677$	5.52459	−	9.56887i	0.212327	−	0.367761i	−0.740115	−	0.672480i	$-0.765229\pi$
$677$	5.52459	−	9.56887i	0.212327	−	0.367761i	0.952442	+	0.304719i	$0.0985624\pi$
$678$		0			0
$679$	2.25822			0.0866626
$680$		0			0
$681$	−33.4649	−	7.46239i	−1.28238	−	0.285960i
$682$		0			0
$683$	6.80171	+	11.7809i	0.260260	+	0.450784i	0.966311	−	0.257377i	$-0.0828584\pi$
$683$	6.80171	+	11.7809i	0.260260	+	0.450784i	−0.706051	+	0.708161i	$0.749525\pi$
$684$		0			0
$685$	2.14234	+	3.71065i	0.0818547	+	0.141777i
$686$		0			0
$687$	9.37534	+	29.8634i	0.357692	+	1.13936i
$688$		0			0
$689$	5.90935	−	25.0111i	0.225128	−	0.952846i
$690$		0			0
$691$	22.7560	+	39.4146i	0.865679	+	1.49940i	0.866371	+	0.499401i	$0.166447\pi$
$691$	22.7560	+	39.4146i	0.865679	+	1.49940i	−0.000691486		1.00000i	$0.500220\pi$
$692$		0			0
$693$	−0.236136	−	2.77812i	−0.00897007	−	0.105532i
$694$		0			0
$695$	1.96825			0.0746600
$696$		0			0
$697$	5.07983	+	8.79852i	0.192412	+	0.333268i
$698$		0			0
$699$	30.4660	+	6.79367i	1.15233	+	0.256960i
$700$		0			0
$701$	−2.09001			−0.0789388			−0.0394694	−	0.999221i	$-0.512567\pi$
$701$	−2.09001			−0.0789388			−0.0394694	+	0.999221i	$0.512567\pi$
$702$		0			0
$703$	−4.52727			−0.170749
$704$		0			0
$705$	1.14885	+	0.256183i	0.0432681	+	0.00964843i
$706$		0			0
$707$	−0.877947	−	1.52065i	−0.0330186	−	0.0571899i
$708$		0			0
$709$	30.9501			1.16236			0.581178	−	0.813776i	$-0.302592\pi$
$709$	30.9501			1.16236			0.581178	+	0.813776i	$0.302592\pi$
$710$		0			0
$711$	−31.3247	+	21.8186i	−1.17477	+	0.818263i
$712$		0			0
$713$	1.67495	+	2.90111i	0.0627275	+	0.108647i
$714$		0			0
$715$	−4.08725	−	3.85075i	−0.152855	−	0.144010i
$716$		0			0
$717$	0.104562	+	0.333064i	0.00390495	+	0.0124385i
$718$		0			0
$719$	−24.5017	−	42.4382i	−0.913759	−	1.58268i	−0.808708	−	0.588210i	$-0.799833\pi$
$719$	−24.5017	−	42.4382i	−0.913759	−	1.58268i	−0.105051	−	0.994467i	$-0.533501\pi$
$720$		0			0
$721$	0.698421	+	1.20970i	0.0260105	+	0.0450516i
$722$		0			0
$723$	−1.55922	−	0.347694i	−0.0579882	−	0.0129309i
$724$		0			0
$725$	18.0015			0.668561
$726$		0			0
$727$	−4.70130	+	8.14289i	−0.174361	+	0.302003i	−0.939940	−	0.341339i	$-0.889119\pi$
$727$	−4.70130	+	8.14289i	−0.174361	+	0.302003i	0.765579	+	0.643342i	$0.222453\pi$
$728$		0			0
$729$	6.79455	+	26.1311i	0.251650	+	0.967818i
$730$		0			0
$731$	14.3654	+	24.8816i	0.531324	+	0.920281i
$732$		0			0
$733$	11.3717	+	19.6963i	0.420022	+	0.727499i	0.995941	−	0.0900077i	$-0.0286892\pi$
$733$	11.3717	+	19.6963i	0.420022	+	0.727499i	−0.575919	+	0.817506i	$0.695356\pi$
$734$		0			0
$735$	−1.33456	−	4.25100i	−0.0492260	−	0.156800i
$736$		0			0
$737$	24.5350	+	42.4959i	0.903759	+	1.56536i
$738$		0			0
$739$	24.6444	−	42.6853i	0.906558	−	1.57021i	0.0877471	−	0.996143i	$-0.472033\pi$
$739$	24.6444	−	42.6853i	0.906558	−	1.57021i	0.818811	−	0.574063i	$-0.194633\pi$
$740$		0			0
$741$	2.81678	−	0.203675i	0.103477	−	0.00748217i
$742$		0			0
$743$	−32.6289			−1.19704			−0.598519	−	0.801109i	$-0.704244\pi$
$743$	−32.6289			−1.19704			−0.598519	+	0.801109i	$0.704244\pi$
$744$		0			0
$745$	−6.57339			−0.240830
$746$		0			0
$747$	−27.2983	+	19.0141i	−0.998793	+	0.695690i
$748$		0			0
$749$	0.573289	−	0.992965i	0.0209475	−	0.0362822i
$750$		0			0
$751$	6.73072			0.245607			0.122804	−	0.992431i	$-0.460811\pi$
$751$	6.73072			0.245607			0.122804	+	0.992431i	$0.460811\pi$
$752$		0			0
$753$	−4.76284	−	15.1711i	−0.173568	−	0.552867i
$754$		0			0
$755$	6.33954			0.230720
$756$		0			0
$757$	−17.1722	+	29.7432i	−0.624135	+	1.08103i	0.364572	+	0.931175i	$0.381215\pi$
$757$	−17.1722	+	29.7432i	−0.624135	+	1.08103i	−0.988707	+	0.149859i	$0.952118\pi$
$758$		0			0
$759$	−4.48129	−	14.2743i	−0.162661	−	0.518125i
$760$		0			0
$761$	−13.6369	+	23.6198i	−0.494337	+	0.856217i	−0.999979	−	0.00652664i	$-0.997922\pi$
$761$	−13.6369	+	23.6198i	−0.494337	+	0.856217i	0.505642	+	0.862744i	$0.331256\pi$
$762$		0			0
$763$	3.00900			0.108933
$764$		0			0
$765$	−2.27307	+	1.58326i	−0.0821830	+	0.0572429i
$766$		0			0
$767$	12.6409	+	11.9094i	0.456436	+	0.430025i
$768$		0			0
$769$	39.8446			1.43683			0.718417	−	0.695612i	$-0.244867\pi$
$769$	39.8446			1.43683			0.718417	+	0.695612i	$0.244867\pi$
$770$		0			0
$771$	−11.9509	−	2.66496i	−0.430403	−	0.0959762i
$772$		0			0
$773$	7.98669	+	13.8334i	0.287261	+	0.497551i	0.973155	−	0.230151i	$-0.0739219\pi$
$773$	7.98669	+	13.8334i	0.287261	+	0.497551i	−0.685894	+	0.727702i	$0.740589\pi$
$774$		0			0
$775$	−7.93729			−0.285116
$776$		0			0
$777$	2.59041	−	2.81993i	0.0929304	−	0.101164i
$778$		0			0
$779$	−0.920671	−	1.59465i	−0.0329865	−	0.0571342i
$780$		0			0
$781$	−29.0058	+	50.2395i	−1.03791	+	1.79771i
$782$		0			0
$783$	2.58130	−	19.0606i	0.0922481	−	0.681170i
$784$		0			0
$785$	−1.19607	+	2.07166i	−0.0426897	+	0.0739407i
$786$		0			0
$787$	27.1931	−	47.0999i	0.969331	−	1.67893i	0.271832	−	0.962345i	$-0.412371\pi$
$787$	27.1931	−	47.0999i	0.969331	−	1.67893i	0.697499	−	0.716586i	$-0.254296\pi$
$788$		0			0
$789$	−0.971682	−	3.09511i	−0.0345928	−	0.110189i
$790$		0			0
$791$	0.254589	−	0.440962i	0.00905216	−	0.0156788i
$792$		0			0
$793$	6.48986	−	27.4680i	0.230462	−	0.975418i
$794$		0			0
$795$	−1.36846	−	4.35898i	−0.0485343	−	0.154597i
$796$		0			0
$797$	22.9718	−	39.7884i	0.813704	−	1.40938i	−0.0965501	−	0.995328i	$-0.530781\pi$
$797$	22.9718	−	39.7884i	0.813704	−	1.40938i	0.910255	−	0.414049i	$-0.135886\pi$
$798$		0			0
$799$	−4.58202			−0.162100
$800$		0			0
$801$	−0.561927	+	0.391399i	−0.0198547	+	0.0138294i
$802$		0			0
$803$	−18.0703	−	31.2987i	−0.637688	−	1.10451i
$804$		0			0
$805$	0.0838638	+	0.145256i	0.00295581	+	0.00511961i
$806$		0			0
$807$	13.9954	+	44.5798i	0.492661	+	1.56928i
$808$		0			0
$809$	0.753915	−	1.30582i	0.0265062	−	0.0459101i	−0.852468	−	0.522779i	$-0.824895\pi$
$809$	0.753915	−	1.30582i	0.0265062	−	0.0459101i	0.878974	+	0.476869i	$0.158228\pi$
$810$		0			0
$811$	34.4445			1.20951			0.604755	−	0.796411i	$-0.293271\pi$
$811$	34.4445			1.20951			0.604755	+	0.796411i	$0.293271\pi$
$812$		0			0
$813$	−12.1201	+	13.1940i	−0.425070	+	0.462733i
$814$		0			0
$815$	0.243251	−	0.421323i	0.00852071	−	0.0147583i
$816$		0			0
$817$	−2.60360	−	4.50956i	−0.0910884	−	0.157770i
$818$		0			0
$819$	−1.48484	+	1.87104i	−0.0518844	+	0.0653795i
$820$		0			0
$821$	−9.36575	−	16.2220i	−0.326867	−	0.566150i	0.655021	−	0.755610i	$-0.272660\pi$
$821$	−9.36575	−	16.2220i	−0.326867	−	0.566150i	−0.981888	+	0.189460i	$0.939326\pi$
$822$		0			0
$823$	8.17238	−	14.1550i	0.284871	−	0.493411i	−0.687707	−	0.725989i	$-0.741383\pi$
$823$	8.17238	−	14.1550i	0.284871	−	0.493411i	0.972578	+	0.232577i	$0.0747159\pi$
$824$		0			0
$825$	34.5994	+	7.71538i	1.20460	+	0.268615i
$826$		0			0
$827$	3.88733			0.135176			0.0675878	−	0.997713i	$-0.478470\pi$
$827$	3.88733			0.135176			0.0675878	+	0.997713i	$0.478470\pi$
$828$		0			0
$829$	−4.20485	+	7.28302i	−0.146041	+	0.252950i	−0.929761	−	0.368164i	$-0.879986\pi$
$829$	−4.20485	+	7.28302i	−0.146041	+	0.252950i	0.783720	+	0.621114i	$0.213320\pi$
$830$		0			0
$831$	15.5569	+	3.46905i	0.539662	+	0.120340i
$832$		0			0
$833$	8.67220	+	15.0207i	0.300474	+	0.520436i
$834$		0			0
$835$	−3.44014	−	5.95849i	−0.119051	−	0.206202i
$836$		0			0
$837$	−1.13815	+	8.40425i	−0.0393404	+	0.290493i
$838$		0			0
$839$	3.36871			0.116301			0.0581504	−	0.998308i	$-0.481480\pi$
$839$	3.36871			0.116301			0.0581504	+	0.998308i	$0.481480\pi$
$840$		0			0
$841$	7.64872	−	13.2480i	0.263749	−	0.456826i
$842$		0			0
$843$	10.0224	−	10.9104i	0.345188	−	0.375773i
$844$		0			0
$845$	0.286410	+	4.80233i	0.00985280	+	0.165205i
$846$		0			0
$847$	−0.741131	+	1.28368i	−0.0254656	+	0.0441077i
$848$		0			0
$849$	28.4051	+	6.33409i	0.974860	+	0.217386i
$850$		0			0
$851$	10.2736	−	17.7944i	0.352175	−	0.609985i
$852$		0			0
$853$	6.68642	−	11.5812i	0.228939	−	0.396533i	−0.728555	−	0.684987i	$-0.759808\pi$
$853$	6.68642	−	11.5812i	0.228939	−	0.396533i	0.957494	+	0.288454i	$0.0931411\pi$
$854$		0			0
$855$	0.411972	−	0.286951i	0.0140892	−	0.00981353i
$856$		0			0
$857$	8.35202	−	14.4661i	0.285300	−	0.494153i	−0.687382	−	0.726296i	$-0.741240\pi$
$857$	8.35202	−	14.4661i	0.285300	−	0.494153i	0.972682	+	0.232143i	$0.0745736\pi$
$858$		0			0
$859$	10.2946	+	17.8308i	0.351247	+	0.608378i	0.986468	−	0.163952i	$-0.0524244\pi$
$859$	10.2946	+	17.8308i	0.351247	+	0.608378i	−0.635221	+	0.772330i	$0.719091\pi$
$860$		0			0
$861$	1.52006	+	0.338960i	0.0518034	+	0.0115517i
$862$		0			0
$863$	6.86690			0.233752			0.116876	−	0.993147i	$-0.462712\pi$
$863$	6.86690			0.233752			0.116876	+	0.993147i	$0.462712\pi$
$864$		0			0
$865$	0.382639	+	0.662751i	0.0130101	+	0.0225342i
$866$		0			0
$867$	−12.6245	+	13.7431i	−0.428751	+	0.466740i
$868$		0			0
$869$	53.5537			1.81668
$870$		0			0
$871$	9.66636	−	40.9124i	0.327532	−	1.38626i
$872$		0			0
$873$	27.7719	+	13.0339i	0.939937	+	0.441132i
$874$		0			0
$875$	−0.806021			−0.0272485
$876$		0			0
$877$	1.51694	−	2.62741i	0.0512233	−	0.0887213i	−0.839277	−	0.543704i	$-0.817021\pi$
$877$	1.51694	−	2.62741i	0.0512233	−	0.0887213i	0.890500	+	0.454983i	$0.150355\pi$
$878$		0			0
$879$	−20.3257	+	22.1266i	−0.685568	+	0.746312i
$880$		0			0
$881$	22.4166	−	38.8267i	0.755234	−	1.30810i	−0.190024	−	0.981780i	$-0.560856\pi$
$881$	22.4166	−	38.8267i	0.755234	−	1.30810i	0.945258	−	0.326325i	$-0.105810\pi$
$882$		0			0
$883$	−4.01343			−0.135063			−0.0675314	−	0.997717i	$-0.521512\pi$
$883$	−4.01343			−0.135063			−0.0675314	+	0.997717i	$0.521512\pi$
$884$		0			0
$885$	3.01347	+	0.671977i	0.101297	+	0.0225883i
$886$		0			0
$887$	−39.9321			−1.34079			−0.670394	−	0.742006i	$-0.733875\pi$
$887$	−39.9321			−1.34079			−0.670394	+	0.742006i	$0.733875\pi$
$888$		0			0
$889$	1.16179	−	2.01228i	0.0389653	−	0.0674898i
$890$		0			0
$891$	13.1306	−	35.5286i	0.439892	−	1.19025i
$892$		0			0
$893$	0.830448			0.0277899
$894$		0			0
$895$	−6.68078			−0.223314
$896$		0			0
$897$	−5.59149	+	11.5335i	−0.186695	+	0.385093i
$898$		0			0
$899$	3.02089	−	5.23233i	0.100752	−	0.174508i
$900$		0			0
$901$	8.89249	+	15.4022i	0.296252	+	0.513123i
$902$		0			0
$903$	4.29862	+	0.958556i	0.143049	+	0.0318988i
$904$		0			0
$905$	−2.32000	−	4.01836i	−0.0771194	−	0.133575i
$906$		0			0
$907$	−28.9682	−	50.1744i	−0.961874	−	1.66601i	−0.717789	−	0.696260i	$-0.754846\pi$
$907$	−28.9682	−	50.1744i	−0.961874	−	1.66601i	−0.244084	−	0.969754i	$-0.578487\pi$
$908$		0			0
$909$	−2.02029	−	23.7685i	−0.0670087	−	0.788350i
$910$		0			0
$911$	16.7679	−	29.0429i	0.555546	−	0.962234i	−0.442315	−	0.896860i	$-0.645843\pi$
$911$	16.7679	−	29.0429i	0.555546	−	0.962234i	0.997861	−	0.0653740i	$-0.0208240\pi$
$912$		0			0
$913$	46.6700			1.54455
$914$		0			0
$915$	−1.50289	−	4.78719i	−0.0496841	−	0.158260i
$916$		0			0
$917$	−0.428430	−	0.742063i	−0.0141480	−	0.0245051i
$918$		0			0
$919$	6.42095	+	11.1214i	0.211807	+	0.366861i	0.952280	−	0.305225i	$-0.0987317\pi$
$919$	6.42095	+	11.1214i	0.211807	+	0.366861i	−0.740473	+	0.672086i	$0.765398\pi$
$920$		0			0
$921$	8.42410	+	1.87850i	0.277583	+	0.0618988i
$922$		0			0
$923$	47.6014	−	14.2870i	1.56682	−	0.470263i
$924$		0			0
$925$	24.3424	+	42.1622i	0.800372	+	1.38629i
$926$		0			0
$927$	1.60717	+	18.9082i	0.0527864	+	0.621026i
$928$		0			0
$929$	38.2646			1.25542			0.627711	−	0.778447i	$-0.283992\pi$
$929$	38.2646			1.25542			0.627711	+	0.778447i	$0.283992\pi$
$930$		0			0
$931$	−1.57175	−	2.72236i	−0.0515122	−	0.0892217i
$932$		0			0
$933$	−14.3780	−	45.7984i	−0.470714	−	1.49937i
$934$		0			0
$935$	3.88610			0.127089
$936$		0			0
$937$	−24.2557			−0.792398			−0.396199	−	0.918165i	$-0.629671\pi$
$937$	−24.2557			−0.792398			−0.396199	+	0.918165i	$0.629671\pi$
$938$		0			0
$939$	16.3506	−	17.7994i	0.533583	−	0.580860i
$940$		0			0
$941$	29.6711	+	51.3919i	0.967250	+	1.67533i	0.703444	+	0.710751i	$0.251645\pi$
$941$	29.6711	+	51.3919i	0.967250	+	1.67533i	0.263807	+	0.964576i	$0.415022\pi$
$942$		0			0
$943$	8.35701			0.272142
$944$		0			0
$945$	−0.0569866	+	0.420795i	−0.00185377	+	0.0136885i
$946$		0			0
$947$	13.5820	+	23.5248i	0.441357	+	0.764453i	0.997790	−	0.0664391i	$-0.0211638\pi$
$947$	13.5820	+	23.5248i	0.441357	+	0.764453i	−0.556433	+	0.830892i	$0.687830\pi$
$948$		0			0
$949$	−7.11939	+	30.1325i	−0.231105	+	0.978141i
$950$		0			0
$951$	35.7928	−	38.9642i	1.16066	−	1.26350i
$952$		0			0
$953$	22.4206	+	38.8335i	0.726273	+	1.25794i	0.958448	+	0.285267i	$0.0920824\pi$
$953$	22.4206	+	38.8335i	0.726273	+	1.25794i	−0.232175	+	0.972674i	$0.574584\pi$
$954$		0			0
$955$	1.18275	+	2.04859i	0.0382730	+	0.0662908i
$956$		0			0
$957$	−18.2544	+	19.8718i	−0.590080	+	0.642364i
$958$		0			0
$959$	−2.55679			−0.0825629
$960$		0			0
$961$	14.1680	−	24.5397i	0.457033	−	0.791604i
$962$		0			0
$963$	12.7816	−	8.90274i	0.411880	−	0.286887i
$964$		0			0
$965$	−0.673723	−	1.16692i	−0.0216879	−	0.0375646i
$966$		0			0
$967$	−11.8394	−	20.5064i	−0.380729	−	0.659443i	0.610437	−	0.792065i	$-0.290994\pi$
$967$	−11.8394	−	20.5064i	−0.380729	−	0.659443i	−0.991167	+	0.132622i	$0.957660\pi$
$968$		0			0
$969$	−1.32214	+	1.43929i	−0.0424734	+	0.0462367i
$970$		0			0
$971$	−24.3425	−	42.1624i	−0.781187	−	1.35306i	−0.931251	−	0.364379i	$-0.881281\pi$
$971$	−24.3425	−	42.1624i	−0.781187	−	1.35306i	0.150063	−	0.988676i	$-0.452052\pi$
$972$		0			0
$973$	−0.587253	+	1.01715i	−0.0188265	+	0.0326084i
$974$		0			0
$975$	−17.0421	−	25.1374i	−0.545785	−	0.805040i
$976$		0			0
$977$	−7.78019			−0.248910			−0.124455	−	0.992225i	$-0.539718\pi$
$977$	−7.78019			−0.248910			−0.124455	+	0.992225i	$0.539718\pi$
$978$		0			0
$979$	0.960686			0.0307037
$980$		0			0
$981$	37.0051	+	17.3672i	1.18148	+	0.554493i
$982$		0			0
$983$	−27.3156	+	47.3121i	−0.871234	+	1.50902i	−0.0105121	+	0.999945i	$0.503346\pi$
$983$	−27.3156	+	47.3121i	−0.871234	+	1.50902i	−0.860722	+	0.509076i	$0.829987\pi$
$984$		0			0
$985$	3.82101			0.121747
$986$		0			0
$987$	−0.475165	+	0.517266i	−0.0151247	+	0.0164648i
$988$		0			0
$989$	23.6331			0.751489
$990$		0			0
$991$	−11.7645	+	20.3767i	−0.373712	+	0.647288i	−0.990133	−	0.140128i	$-0.955248\pi$
$991$	−11.7645	+	20.3767i	−0.373712	+	0.647288i	0.616421	+	0.787416i	$0.288582\pi$
$992$		0			0
$993$	6.52260	+	1.45449i	0.206989	+	0.0461567i
$994$		0			0
$995$	1.55874	−	2.69981i	0.0494153	−	0.0855898i
$996$		0			0
$997$	27.3208			0.865257			0.432629	−	0.901572i	$-0.357586\pi$
$997$	27.3208			0.865257			0.432629	+	0.901572i	$0.357586\pi$
$998$		0			0
$999$	48.1332	−	19.7287i	1.52287	−	0.624188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.s.f.529.3	yes	40
3.2	odd	2		2808.2.s.f.1153.12		40
9.4	even	3		936.2.r.f.841.15	yes	40
9.5	odd	6		2808.2.r.f.2089.12		40
13.3	even	3		936.2.r.f.601.15	✓	40
39.29	odd	6		2808.2.r.f.289.12		40
117.68	odd	6		2808.2.s.f.1225.12		40
117.94	even	3	inner	936.2.s.f.913.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.15	✓	40	13.3	even	3
936.2.r.f.841.15	yes	40	9.4	even	3
936.2.s.f.529.3	yes	40	1.1	even	1	trivial
936.2.s.f.913.3	yes	40	117.94	even	3	inner
2808.2.r.f.289.12		40	39.29	odd	6
2808.2.r.f.2089.12		40	9.5	odd	6
2808.2.s.f.1153.12		40	3.2	odd	2
2808.2.s.f.1225.12		40	117.68	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.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69053 - 0.376974i) q^{3} +(-0.185033 - 0.320487i) q^{5} +0.220829 q^{7} +(2.71578 + 1.27457i) q^{9} +(-2.10430 - 3.64475i) q^{11} +(-0.829056 + 3.50894i) q^{13} +(0.191989 + 0.611546i) q^{15} +(-1.24758 - 2.16087i) q^{17} +(0.226112 + 0.391637i) q^{19} +(-0.373317 - 0.0832466i) q^{21} -2.05243 q^{23} +(2.43153 - 4.21153i) q^{25} +(-4.11063 - 3.17848i) q^{27} +(1.85085 + 3.20576i) q^{29} +(-0.816082 - 1.41349i) q^{31} +(2.18340 + 6.95482i) q^{33} +(-0.0408606 - 0.0707727i) q^{35} +(-5.00558 + 8.66991i) q^{37} +(2.72432 - 5.61944i) q^{39} -4.07176 q^{41} -11.5147 q^{43} +(-0.0940265 - 1.10621i) q^{45} +(0.918184 - 1.59034i) q^{47} -6.95123 q^{49} +(1.29447 + 4.12331i) q^{51} -7.12781 q^{53} +(-0.778731 + 1.34880i) q^{55} +(-0.234611 - 0.747311i) q^{57} +(2.40843 - 4.17152i) q^{59} -7.82801 q^{61} +(0.599722 + 0.281462i) q^{63} +(1.27797 - 0.383569i) q^{65} -11.6595 q^{67} +(3.46970 + 0.773714i) q^{69} +(-6.89204 - 11.9374i) q^{71} +8.58734 q^{73} +(-5.69820 + 6.20309i) q^{75} +(-0.464689 - 0.804865i) q^{77} +(-6.36242 + 11.0200i) q^{79} +(5.75094 + 6.92291i) q^{81} +(-5.54460 + 9.60353i) q^{83} +(-0.461686 + 0.799664i) q^{85} +(-1.92043 - 6.11716i) q^{87} +(-0.114134 + 0.197686i) q^{89} +(-0.183079 + 0.774874i) q^{91} +(0.846760 + 2.69720i) q^{93} +(0.0836763 - 0.144932i) q^{95} +10.2261 q^{97} +(-1.06932 - 12.5804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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