LMFDB - Embedded newform 608.2.bf.a.177.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [608,2,Mod(17,608)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("608.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			177.10
Character	$\chi$	$=$	608.177
Dual form			608.2.bf.a.529.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.178255 - 0.489751i) q^{3} +(3.55335 - 0.626551i) q^{5} +(1.81103 - 3.13680i) q^{7} +(2.09005 + 1.75376i) q^{9} +(0.380026 - 0.219408i) q^{11} +(-1.07650 - 2.95765i) q^{13} +(0.326547 - 1.85194i) q^{15} +(-5.14502 + 4.31719i) q^{17} +(-4.34549 - 0.341661i) q^{19} +(-1.21343 - 1.44610i) q^{21} +(-0.958164 + 5.43402i) q^{23} +(7.53526 - 2.74261i) q^{25} +(2.58554 - 1.49276i) q^{27} +(1.67059 - 1.99093i) q^{29} +(-2.59436 + 4.49356i) q^{31} +(-0.0397139 - 0.225229i) q^{33} +(4.46986 - 12.2808i) q^{35} -5.95511i q^{37} -1.64040 q^{39} +(0.621322 + 0.226143i) q^{41} +(0.376394 - 0.0663684i) q^{43} +(8.52551 + 4.92220i) q^{45} +(3.54751 + 2.97672i) q^{47} +(-3.05967 - 5.29950i) q^{49} +(1.19722 + 3.28934i) q^{51} +(-13.0892 - 2.30798i) q^{53} +(1.21289 - 1.01774i) q^{55} +(-0.941933 + 2.06730i) q^{57} +(8.50400 + 10.1347i) q^{59} +(5.02192 + 0.885501i) q^{61} +(9.28635 - 3.37995i) q^{63} +(-5.67829 - 9.83508i) q^{65} +(-0.576990 + 0.687630i) q^{67} +(2.49052 + 1.43790i) q^{69} +(-1.20549 - 6.83668i) q^{71} +(3.14662 + 1.14528i) q^{73} -4.17929i q^{75} -1.58942i q^{77} +(6.23172 + 2.26816i) q^{79} +(1.15113 + 6.52839i) q^{81} +(-5.47269 - 3.15966i) q^{83} +(-15.5771 + 18.5641i) q^{85} +(-0.677270 - 1.17307i) q^{87} +(2.76705 - 1.00712i) q^{89} +(-11.2271 - 1.97964i) q^{91} +(1.73827 + 2.07159i) q^{93} +(-15.6551 + 1.50863i) q^{95} +(-3.66959 + 3.07915i) q^{97} +(1.17906 + 0.207901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 6 q^{7} - 12 q^{9} + 12 q^{15} - 12 q^{17} + 12 q^{23} - 12 q^{25} - 30 q^{31} - 30 q^{33} + 24 q^{39} - 24 q^{41} + 48 q^{47} - 24 q^{49} + 42 q^{55} - 12 q^{57} - 30 q^{63} - 6 q^{65} + 12 q^{71}+ \cdots - 12 q^{97}+O(q^{100}) $ 108 * q + 6 * q^7 - 12 * q^9 + 12 * q^15 - 12 * q^17 + 12 * q^23 - 12 * q^25 - 30 * q^31 - 30 * q^33 + 24 * q^39 - 24 * q^41 + 48 * q^47 - 24 * q^49 + 42 * q^55 - 12 * q^57 - 30 * q^63 - 6 * q^65 + 12 * q^71 + 12 * q^73 + 12 * q^79 - 18 * q^81 + 6 * q^87 - 12 * q^89 + 72 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.178255	−	0.489751i	0.102915	−	0.282758i	−0.877539	−	0.479506i	$-0.840816\pi$
$3$	0.178255	−	0.489751i	0.102915	−	0.282758i	0.980454	+	0.196748i	$0.0630381\pi$
$4$		0			0
$5$	3.55335	−	0.626551i	1.58911	−	0.280202i	0.691960	−	0.721936i	$-0.256747\pi$
$5$	3.55335	−	0.626551i	1.58911	−	0.280202i	0.897146	+	0.441734i	$0.145636\pi$
$6$		0			0
$7$	1.81103	−	3.13680i	0.684506	−	1.18560i	−0.289086	−	0.957303i	$-0.593351\pi$
$7$	1.81103	−	3.13680i	0.684506	−	1.18560i	0.973592	−	0.228295i	$-0.0733152\pi$
$8$		0			0
$9$	2.09005	+	1.75376i	0.696684	+	0.584587i
$10$		0			0
$11$	0.380026	−	0.219408i	0.114582	−	0.0661540i	−0.441614	−	0.897205i	$-0.645594\pi$
$11$	0.380026	−	0.219408i	0.114582	−	0.0661540i	0.556196	+	0.831051i	$0.312260\pi$
$12$		0			0
$13$	−1.07650	−	2.95765i	−0.298566	−	0.820304i	−0.994740	−	0.102431i	$-0.967338\pi$
$13$	−1.07650	−	2.95765i	−0.298566	−	0.820304i	0.696174	−	0.717873i	$-0.254884\pi$
$14$		0			0
$15$	0.326547	−	1.85194i	0.0843142	−	0.478170i
$16$		0			0
$17$	−5.14502	+	4.31719i	−1.24785	+	1.04707i	−0.250984	+	0.967991i	$0.580754\pi$
$17$	−5.14502	+	4.31719i	−1.24785	+	1.04707i	−0.996868	+	0.0790806i	$0.974802\pi$
$18$		0			0
$19$	−4.34549	−	0.341661i	−0.996923	−	0.0783824i
$19$	−4.34549	−	0.341661i	−0.996923	−	0.0783824i
$20$		0			0
$21$	−1.21343	−	1.44610i	−0.264791	−	0.315566i
$22$		0			0
$23$	−0.958164	+	5.43402i	−0.199791	+	1.13307i	0.705638	+	0.708573i	$0.250661\pi$
$23$	−0.958164	+	5.43402i	−0.199791	+	1.13307i	−0.905429	+	0.424498i	$0.860451\pi$
$24$		0			0
$25$	7.53526	−	2.74261i	1.50705	−	0.548522i
$26$		0			0
$27$	2.58554	−	1.49276i	0.497587	−	0.287282i
$28$		0			0
$29$	1.67059	−	1.99093i	0.310221	−	0.369707i	−0.588296	−	0.808646i	$-0.700201\pi$
$29$	1.67059	−	1.99093i	0.310221	−	0.369707i	0.898517	+	0.438939i	$0.144646\pi$
$30$		0			0
$31$	−2.59436	+	4.49356i	−0.465960	+	0.807067i	−0.999244	−	0.0388694i	$-0.987624\pi$
$31$	−2.59436	+	4.49356i	−0.465960	+	0.807067i	0.533284	+	0.845936i	$0.320958\pi$
$32$		0			0
$33$	−0.0397139	−	0.225229i	−0.00691330	−	0.0392073i
$34$		0			0
$35$	4.46986	−	12.2808i	0.755545	−	2.07584i
$36$		0			0
$37$		−	5.95511i		−	0.979014i	−0.871999	−	0.489507i	$-0.837177\pi$
$37$		−	5.95511i		−	0.979014i	0.871999	−	0.489507i	$-0.162823\pi$
$38$		0			0
$39$	−1.64040			−0.262675
$40$		0			0
$41$	0.621322	+	0.226143i	0.0970341	+	0.0353175i	0.390081	−	0.920781i	$-0.372447\pi$
$41$	0.621322	+	0.226143i	0.0970341	+	0.0353175i	−0.293047	+	0.956098i	$0.594669\pi$
$42$		0			0
$43$	0.376394	−	0.0663684i	0.0573995	−	0.0101211i	−0.144875	−	0.989450i	$-0.546278\pi$
$43$	0.376394	−	0.0663684i	0.0573995	−	0.0101211i	0.202274	+	0.979329i	$0.435167\pi$
$44$		0			0
$45$	8.52551	+	4.92220i	1.27091	+	0.733759i
$46$		0			0
$47$	3.54751	+	2.97672i	0.517458	+	0.434199i	0.863744	−	0.503930i	$-0.168113\pi$
$47$	3.54751	+	2.97672i	0.517458	+	0.434199i	−0.346287	+	0.938129i	$0.612558\pi$
$48$		0			0
$49$	−3.05967	−	5.29950i	−0.437096	−	0.757072i
$50$		0			0
$51$	1.19722	+	3.28934i	0.167645	+	0.460600i
$52$		0			0
$53$	−13.0892	−	2.30798i	−1.79794	−	0.317026i	−0.828067	−	0.560629i	$-0.810560\pi$
$53$	−13.0892	−	2.30798i	−1.79794	−	0.317026i	−0.969875	+	0.243603i	$0.921671\pi$
$54$		0			0
$55$	1.21289	−	1.01774i	0.163547	−	0.137232i
$56$		0			0
$57$	−0.941933	+	2.06730i	−0.124762	+	0.273821i
$58$		0			0
$59$	8.50400	+	10.1347i	1.10713	+	1.31942i	0.942929	+	0.332995i	$0.108059\pi$
$59$	8.50400	+	10.1347i	1.10713	+	1.31942i	0.164198	+	0.986427i	$0.447496\pi$
$60$		0			0
$61$	5.02192	+	0.885501i	0.642991	+	0.113377i	0.485630	−	0.874164i	$-0.338590\pi$
$61$	5.02192	+	0.885501i	0.642991	+	0.113377i	0.157361	+	0.987541i	$0.449701\pi$
$62$		0			0
$63$	9.28635	−	3.37995i	1.16997	−	0.425834i
$64$		0			0
$65$	−5.67829	−	9.83508i	−0.704305	−	1.21989i
$66$		0			0
$67$	−0.576990	+	0.687630i	−0.0704905	+	0.0840073i	−0.800137	−	0.599817i	$-0.795240\pi$
$67$	−0.576990	+	0.687630i	−0.0704905	+	0.0840073i	0.729647	+	0.683824i	$0.239685\pi$
$68$		0			0
$69$	2.49052	+	1.43790i	0.299823	+	0.173103i
$70$		0			0
$71$	−1.20549	−	6.83668i	−0.143065	−	0.811365i	−0.968900	−	0.247452i	$-0.920407\pi$
$71$	−1.20549	−	6.83668i	−0.143065	−	0.811365i	0.825835	−	0.563912i	$-0.190704\pi$
$72$		0			0
$73$	3.14662	+	1.14528i	0.368284	+	0.134044i	0.519531	−	0.854452i	$-0.326107\pi$
$73$	3.14662	+	1.14528i	0.368284	+	0.134044i	−0.151247	+	0.988496i	$0.548329\pi$
$74$		0			0
$75$		−	4.17929i		−	0.482582i
$76$		0			0
$77$		−	1.58942i		−	0.181131i
$78$		0			0
$79$	6.23172	+	2.26816i	0.701123	+	0.255188i	0.667890	−	0.744260i	$-0.267198\pi$
$79$	6.23172	+	2.26816i	0.701123	+	0.255188i	0.0332326	+	0.999448i	$0.489420\pi$
$80$		0			0
$81$	1.15113	+	6.52839i	0.127904	+	0.725377i
$82$		0			0
$83$	−5.47269	−	3.15966i	−0.600706	−	0.346818i	0.168613	−	0.985682i	$-0.446071\pi$
$83$	−5.47269	−	3.15966i	−0.600706	−	0.346818i	−0.769319	+	0.638865i	$0.779404\pi$
$84$		0			0
$85$	−15.5771	+	18.5641i	−1.68958	+	2.01356i
$86$		0			0
$87$	−0.677270	−	1.17307i	−0.0726110	−	0.125766i
$88$		0			0
$89$	2.76705	−	1.00712i	0.293306	−	0.106755i	−0.191176	−	0.981556i	$-0.561230\pi$
$89$	2.76705	−	1.00712i	0.293306	−	0.106755i	0.484483	+	0.874801i	$0.339008\pi$
$90$		0			0
$91$	−11.2271	−	1.97964i	−1.17692	−	0.207523i
$92$		0			0
$93$	1.73827	+	2.07159i	0.180250	+	0.214814i
$94$		0			0
$95$	−15.6551	+	1.50863i	−1.60618	+	0.154782i
$96$		0			0
$97$	−3.66959	+	3.07915i	−0.372590	+	0.312640i	−0.809785	−	0.586726i	$-0.800416\pi$
$97$	−3.66959	+	3.07915i	−0.372590	+	0.312640i	0.437195	+	0.899367i	$0.355972\pi$
$98$		0			0
$99$	1.17906	+	0.207901i	0.118500	+	0.0208948i
$100$		0			0
$101$	−0.421241	−	1.15735i	−0.0419151	−	0.115161i	0.916969	−	0.398958i	$-0.130628\pi$
$101$	−0.421241	−	1.15735i	−0.0419151	−	0.115161i	−0.958884	+	0.283797i	$0.908406\pi$
$102$		0			0
$103$	−4.23865	−	7.34155i	−0.417646	−	0.723385i	0.578056	−	0.815997i	$-0.303812\pi$
$103$	−4.23865	−	7.34155i	−0.417646	−	0.723385i	−0.995702	+	0.0926126i	$0.970478\pi$
$104$		0			0
$105$	−5.21778	−	4.37824i	−0.509203	−	0.427272i
$106$		0			0
$107$	−3.47844	−	2.00828i	−0.336274	−	0.194148i	0.322349	−	0.946621i	$-0.395527\pi$
$107$	−3.47844	−	2.00828i	−0.336274	−	0.194148i	−0.658623	+	0.752473i	$0.728861\pi$
$108$		0			0
$109$	−3.89574	+	0.686925i	−0.373145	+	0.0657955i	−0.357076	−	0.934075i	$-0.616226\pi$
$109$	−3.89574	+	0.686925i	−0.373145	+	0.0657955i	−0.0160689	+	0.999871i	$0.505115\pi$
$110$		0			0
$111$	−2.91652	−	1.06153i	−0.276824	−	0.100756i
$112$		0			0
$113$	4.12504			0.388051			0.194025	−	0.980996i	$-0.437846\pi$
$113$	4.12504			0.388051			0.194025	+	0.980996i	$0.437846\pi$
$114$		0			0
$115$			19.9093i			1.85655i
$116$		0			0
$117$	2.93708	−	8.06956i	0.271533	−	0.746031i
$118$		0			0
$119$	4.22435	+	23.9575i	0.387245	+	2.19618i
$120$		0			0
$121$	−5.40372	+	9.35952i	−0.491247	+	0.850865i
$122$		0			0
$123$	0.221507	−	0.263982i	0.0199726	−	0.0238025i
$124$		0			0
$125$	9.43322	−	5.44627i	0.843733	−	0.487129i
$126$		0			0
$127$	−6.06982	+	2.20924i	−0.538610	+	0.196038i	−0.596979	−	0.802257i	$-0.703632\pi$
$127$	−6.06982	+	2.20924i	−0.538610	+	0.196038i	0.0583688	+	0.998295i	$0.481410\pi$
$128$		0			0
$129$	0.0345900	−	0.196170i	0.00304548	−	0.0172718i
$130$		0			0
$131$	12.5465	+	14.9523i	1.09619	+	1.30639i	0.948295	+	0.317390i	$0.102806\pi$
$131$	12.5465	+	14.9523i	1.09619	+	1.30639i	0.147898	+	0.989003i	$0.452749\pi$
$132$		0			0
$133$	−8.94154	+	13.0122i	−0.775330	+	1.12830i
$134$		0			0
$135$	8.25203	−	6.92428i	0.710222	−	0.595947i
$136$		0			0
$137$	−0.0298899	+	0.169514i	−0.00255367	+	0.0144826i	−0.986058	−	0.166402i	$-0.946785\pi$
$137$	−0.0298899	+	0.169514i	−0.00255367	+	0.0144826i	0.983504	+	0.180885i	$0.0578961\pi$
$138$		0			0
$139$	−3.32434	−	9.13356i	−0.281967	−	0.774698i	−0.997128	−	0.0757382i	$-0.975869\pi$
$139$	−3.32434	−	9.13356i	−0.281967	−	0.774698i	0.715161	−	0.698960i	$-0.246354\pi$
$140$		0			0
$141$	2.09021	−	1.20678i	0.176028	−	0.101630i
$142$		0			0
$143$	−1.05803	−	0.887791i	−0.0884768	−	0.0742408i
$144$		0			0
$145$	4.68877	−	8.12119i	0.389381	−	0.674428i
$146$		0			0
$147$	−3.14084	+	0.553815i	−0.259052	+	0.0456779i
$148$		0			0
$149$	−3.79804	+	10.4350i	−0.311148	+	0.854871i	0.681278	+	0.732025i	$0.261424\pi$
$149$	−3.79804	+	10.4350i	−0.311148	+	0.854871i	−0.992426	+	0.122846i	$0.960798\pi$
$150$		0			0
$151$	−15.4686			−1.25881			−0.629407	−	0.777076i	$-0.716702\pi$
$151$	−15.4686			−1.25881			−0.629407	+	0.777076i	$0.716702\pi$
$152$		0			0
$153$	−18.3247			−1.48146
$154$		0			0
$155$	−6.40321	+	17.5927i	−0.514318	+	1.41308i
$156$		0			0
$157$	10.4969	−	1.85088i	0.837743	−	0.147717i	0.261713	−	0.965146i	$-0.415713\pi$
$157$	10.4969	−	1.85088i	0.837743	−	0.147717i	0.576029	+	0.817429i	$0.304601\pi$
$158$		0			0
$159$	−3.46355	+	5.99905i	−0.274678	+	0.475756i
$160$		0			0
$161$	15.3101	+	12.8467i	1.20661	+	1.01246i
$162$		0			0
$163$	−12.5659	+	7.25490i	−0.984234	+	0.568248i	−0.903546	−	0.428492i	$-0.859045\pi$
$163$	−12.5659	+	7.25490i	−0.984234	+	0.568248i	−0.0806881	+	0.996739i	$0.525712\pi$
$164$		0			0
$165$	−0.282235	−	0.775433i	−0.0219719	−	0.0603674i
$166$		0			0
$167$	2.62542	−	14.8895i	0.203161	−	1.15218i	−0.697146	−	0.716929i	$-0.745547\pi$
$167$	2.62542	−	14.8895i	0.203161	−	1.15218i	0.900307	−	0.435255i	$-0.143342\pi$
$168$		0			0
$169$	2.36973	−	1.98844i	0.182287	−	0.152957i
$170$		0			0
$171$	−8.48310	−	8.33504i	−0.648719	−	0.637396i
$172$		0			0
$173$	8.86774	+	10.5682i	0.674202	+	0.803482i	0.989349	−	0.145560i	$-0.0464985\pi$
$173$	8.86774	+	10.5682i	0.674202	+	0.803482i	−0.315148	+	0.949043i	$0.602054\pi$
$174$		0			0
$175$	5.04358	−	28.6036i	0.381259	−	2.16223i
$176$		0			0
$177$	6.47935	−	2.35829i	0.487018	−	0.177260i
$178$		0			0
$179$	9.19239	−	5.30723i	0.687072	−	0.396681i	−0.115442	−	0.993314i	$-0.536829\pi$
$179$	9.19239	−	5.30723i	0.687072	−	0.396681i	0.802514	+	0.596633i	$0.203495\pi$
$180$		0			0
$181$	−4.23274	+	5.04438i	−0.314617	+	0.374946i	−0.900059	−	0.435768i	$-0.856477\pi$
$181$	−4.23274	+	5.04438i	−0.314617	+	0.374946i	0.585442	+	0.810714i	$0.300921\pi$
$182$		0			0
$183$	1.32886	−	2.30165i	0.0982319	−	0.170143i
$184$		0			0
$185$	−3.73118	−	21.1606i	−0.274322	−	1.55576i
$186$		0			0
$187$	−1.00802	+	2.76950i	−0.0737135	+	0.202526i
$188$		0			0
$189$		−	10.8138i		−	0.786585i
$190$		0			0
$191$	13.9420			1.00880			0.504402	−	0.863469i	$-0.331713\pi$
$191$	13.9420			1.00880			0.504402	+	0.863469i	$0.331713\pi$
$192$		0			0
$193$	−10.0207	−	3.64723i	−0.721304	−	0.262533i	−0.0448245	−	0.998995i	$-0.514273\pi$
$193$	−10.0207	−	3.64723i	−0.721304	−	0.262533i	−0.676479	+	0.736462i	$0.736495\pi$
$194$		0			0
$195$	−5.82892	+	1.02780i	−0.417418	+	0.0736020i
$196$		0			0
$197$	−16.9554	−	9.78922i	−1.20802	−	0.697453i	−0.245697	−	0.969347i	$-0.579017\pi$
$197$	−16.9554	−	9.78922i	−1.20802	−	0.697453i	−0.962327	+	0.271894i	$0.912350\pi$
$198$		0			0
$199$	−7.65538	−	6.42362i	−0.542675	−	0.455359i	0.329776	−	0.944059i	$-0.393027\pi$
$199$	−7.65538	−	6.42362i	−0.542675	−	0.455359i	−0.872452	+	0.488700i	$0.837471\pi$
$200$		0			0
$201$	0.233916	+	0.405155i	0.0164992	+	0.0285774i
$202$		0			0
$203$	−3.21966	−	8.84594i	−0.225976	−	0.620864i
$204$		0			0
$205$	2.34946	+	0.414274i	0.164094	+	0.0289341i
$206$		0			0
$207$	−11.5326	+	9.67699i	−0.801570	+	0.672597i
$208$		0			0
$209$	−1.72636	+	0.823595i	−0.119415	+	0.0569693i
$210$		0			0
$211$	4.97164	+	5.92497i	0.342262	+	0.407892i	0.909528	−	0.415643i	$-0.136443\pi$
$211$	4.97164	+	5.92497i	0.342262	+	0.407892i	−0.567266	+	0.823535i	$0.691999\pi$
$212$		0			0
$213$	−3.56316	−	0.628281i	−0.244143	−	0.0430491i
$214$		0			0
$215$	1.29588	−	0.471660i	0.0883780	−	0.0321670i
$216$		0			0
$217$	9.39692	+	16.2759i	0.637905	+	1.10488i
$218$		0			0
$219$	1.12180	−	1.33691i	0.0758042	−	0.0903399i
$220$		0			0
$221$	18.3073	+	10.5697i	1.23148	+	0.710998i
$222$		0			0
$223$	1.06597	+	6.04540i	0.0713825	+	0.404830i	0.999473	+	0.0324743i	$0.0103387\pi$
$223$	1.06597	+	6.04540i	0.0713825	+	0.404830i	−0.928090	+	0.372356i	$0.878550\pi$
$224$		0			0
$225$	20.5590	+	7.48286i	1.37060	+	0.498857i
$226$		0			0
$227$		−	22.5256i		−	1.49507i	−0.664220	−	0.747537i	$-0.731236\pi$
$227$		−	22.5256i		−	1.49507i	0.664220	−	0.747537i	$-0.268764\pi$
$228$		0			0
$229$		−	2.87289i		−	0.189846i	−0.995485	−	0.0949230i	$-0.969740\pi$
$229$		−	2.87289i		−	0.189846i	0.995485	−	0.0949230i	$-0.0302605\pi$
$230$		0			0
$231$	−0.778420	−	0.283322i	−0.0512163	−	0.0186412i
$232$		0			0
$233$	−0.468956	−	2.65958i	−0.0307223	−	0.174235i	0.965586	−	0.260085i	$-0.0837506\pi$
$233$	−0.468956	−	2.65958i	−0.0307223	−	0.174235i	−0.996308	+	0.0858499i	$0.972639\pi$
$234$		0			0
$235$	14.4706	+	8.35462i	0.943959	+	0.544995i
$236$		0			0
$237$	2.22167	−	2.64768i	0.144313	−	0.171985i
$238$		0			0
$239$	3.74844	+	6.49248i	0.242466	+	0.419964i	0.961416	−	0.275098i	$-0.0887103\pi$
$239$	3.74844	+	6.49248i	0.242466	+	0.419964i	−0.718950	+	0.695062i	$0.755377\pi$
$240$		0			0
$241$	−19.6289	+	7.14435i	−1.26441	+	0.460208i	−0.885247	−	0.465122i	$-0.846011\pi$
$241$	−19.6289	+	7.14435i	−1.26441	+	0.460208i	−0.379164	+	0.925330i	$0.623788\pi$
$242$		0			0
$243$	12.2230	+	2.15524i	0.784105	+	0.138259i
$244$		0			0
$245$	−14.1925	−	16.9139i	−0.906725	−	1.08059i
$246$		0			0
$247$	3.66739	+	13.2202i	0.233350	+	0.841183i
$248$		0			0
$249$	−2.52298	+	2.11703i	−0.159887	+	0.134161i
$250$		0			0
$251$	11.5835	+	2.04249i	0.731146	+	0.128921i	0.526814	−	0.849981i	$-0.323387\pi$
$251$	11.5835	+	2.04249i	0.731146	+	0.128921i	0.204332	+	0.978902i	$0.434498\pi$
$252$		0			0
$253$	0.828140	+	2.27530i	0.0520647	+	0.143047i
$254$		0			0
$255$	6.31509	+	10.9381i	0.395466	+	0.684968i
$256$		0			0
$257$	21.7871	+	18.2816i	1.35904	+	1.14037i	0.976276	+	0.216529i	$0.0694735\pi$
$257$	21.7871	+	18.2816i	1.35904	+	1.14037i	0.382768	+	0.923845i	$0.374971\pi$
$258$		0			0
$259$	−18.6800	−	10.7849i	−1.16072	−	0.670141i
$260$		0			0
$261$	6.98324	−	1.23133i	0.432252	−	0.0762176i
$262$		0			0
$263$	4.40729	+	1.60412i	0.271765	+	0.0989144i	0.474308	−	0.880359i	$-0.342698\pi$
$263$	4.40729	+	1.60412i	0.271765	+	0.0989144i	−0.202543	+	0.979273i	$0.564921\pi$
$264$		0			0
$265$	−47.9566			−2.94595
$266$		0			0
$267$		−	1.53469i		−	0.0939214i
$268$		0			0
$269$	3.37775	−	9.28030i	0.205945	−	0.565830i	−0.793120	−	0.609066i	$-0.791545\pi$
$269$	3.37775	−	9.28030i	0.205945	−	0.565830i	0.999065	+	0.0432360i	$0.0137667\pi$
$270$		0			0
$271$	−2.81763	−	15.9795i	−0.171159	−	0.970688i	−0.942485	−	0.334249i	$-0.891517\pi$
$271$	−2.81763	−	15.9795i	−0.171159	−	0.970688i	0.771326	−	0.636440i	$-0.219594\pi$
$272$		0			0
$273$	−2.97082	+	5.14561i	−0.179802	+	0.311427i
$274$		0			0
$275$	2.26184	−	2.69556i	0.136394	−	0.162548i
$276$		0			0
$277$	8.62292	−	4.97844i	0.518101	−	0.299126i	−0.218056	−	0.975936i	$-0.569972\pi$
$277$	8.62292	−	4.97844i	0.518101	−	0.299126i	0.736157	+	0.676810i	$0.236638\pi$
$278$		0			0
$279$	−13.3030	+	4.84189i	−0.796428	+	0.289876i
$280$		0			0
$281$	2.34289	−	13.2872i	0.139765	−	0.792647i	−0.831657	−	0.555289i	$-0.812608\pi$
$281$	2.34289	−	13.2872i	0.139765	−	0.792647i	0.971422	−	0.237358i	$-0.0762813\pi$
$282$		0			0
$283$	−8.89834	−	10.6046i	−0.528952	−	0.630380i	0.433721	−	0.901047i	$-0.357200\pi$
$283$	−8.89834	−	10.6046i	−0.528952	−	0.630380i	−0.962673	+	0.270667i	$0.912756\pi$
$284$		0			0
$285$	−2.05174	+	7.93603i	−0.121535	+	0.470090i
$286$		0			0
$287$	1.83460	−	1.53941i	0.108293	−	0.0908685i
$288$		0			0
$289$	4.88114	−	27.6823i	0.287126	−	1.62837i
$290$		0			0
$291$	0.853896	+	2.34606i	0.0500562	+	0.137528i
$292$		0			0
$293$	−8.10134	+	4.67731i	−0.473286	+	0.273252i	−0.717614	−	0.696441i	$-0.754766\pi$
$293$	−8.10134	+	4.67731i	−0.473286	+	0.273252i	0.244329	+	0.969693i	$0.421432\pi$
$294$		0			0
$295$	36.5676	+	30.6838i	2.12905	+	1.78648i
$296$		0			0
$297$	0.655048	−	1.13458i	0.0380097	−	0.0658348i
$298$		0			0
$299$	17.1034	−	3.01579i	0.989114	−	0.174407i
$300$		0			0
$301$	0.473477	−	1.30087i	0.0272907	−	0.0749807i
$302$		0			0
$303$	−0.641902			−0.0368763
$304$		0			0
$305$	18.3995			1.05355
$306$		0			0
$307$	4.23577	−	11.6377i	0.241748	−	0.664197i	−0.758178	−	0.652047i	$-0.773910\pi$
$307$	4.23577	−	11.6377i	0.241748	−	0.664197i	0.999926	−	0.0121498i	$-0.00386748\pi$
$308$		0			0
$309$	−4.35109	+	0.767215i	−0.247525	+	0.0436453i
$310$		0			0
$311$	−6.64245	+	11.5051i	−0.376659	+	0.652392i	−0.990574	−	0.136980i	$-0.956260\pi$
$311$	−6.64245	+	11.5051i	−0.376659	+	0.652392i	0.613915	+	0.789372i	$0.289594\pi$
$312$		0			0
$313$	13.6701	+	11.4706i	0.772678	+	0.648354i	0.941393	−	0.337311i	$-0.109517\pi$
$313$	13.6701	+	11.4706i	0.772678	+	0.648354i	−0.168715	+	0.985665i	$0.553962\pi$
$314$		0			0
$315$	30.8799	−	17.8285i	1.73989	−	1.00452i
$316$		0			0
$317$	2.26034	+	6.21023i	0.126953	+	0.348801i	0.986844	−	0.161677i	$-0.0516904\pi$
$317$	2.26034	+	6.21023i	0.126953	+	0.348801i	−0.859890	+	0.510479i	$0.829468\pi$
$318$		0			0
$319$	0.198041	−	1.12315i	0.0110882	−	0.0628841i
$320$		0			0
$321$	−1.60361	+	1.34559i	−0.0895046	+	0.0751032i
$322$		0			0
$323$	23.8327	−	17.0024i	1.32608	−	0.946041i
$324$		0			0
$325$	−16.2234	−	19.3343i	−0.899910	−	1.07247i
$326$		0			0
$327$	−0.358013	+	2.03039i	−0.0197982	+	0.112281i
$328$		0			0
$329$	15.7620	−	5.73691i	0.868988	−	0.316286i
$330$		0			0
$331$	−27.1893	+	15.6977i	−1.49446	+	0.862825i	−0.999980	−	0.00636473i	$-0.997974\pi$
$331$	−27.1893	+	15.6977i	−1.49446	+	0.862825i	−0.494478	+	0.869190i	$0.664641\pi$
$332$		0			0
$333$	10.4438	−	12.4465i	0.572319	−	0.682064i
$334$		0			0
$335$	−1.61941	+	2.80490i	−0.0884779	+	0.153248i
$336$		0			0
$337$	−4.91514	−	27.8751i	−0.267745	−	1.51845i	−0.761104	−	0.648629i	$-0.775343\pi$
$337$	−4.91514	−	27.8751i	−0.267745	−	1.51845i	0.493360	−	0.869825i	$-0.335769\pi$
$338$		0			0
$339$	0.735308	−	2.02024i	0.0399364	−	0.109724i
$340$		0			0
$341$			2.27689i			0.123301i
$342$		0			0
$343$	3.18981			0.172233
$344$		0			0
$345$	9.75060	+	3.54893i	0.524955	+	0.191068i
$346$		0			0
$347$	−9.43422	+	1.66351i	−0.506456	+	0.0893018i	−0.421037	−	0.907043i	$-0.638334\pi$
$347$	−9.43422	+	1.66351i	−0.506456	+	0.0893018i	−0.0854184	+	0.996345i	$0.527223\pi$
$348$		0			0
$349$	−24.8657	−	14.3562i	−1.33103	−	0.768470i	−0.345571	−	0.938392i	$-0.612315\pi$
$349$	−24.8657	−	14.3562i	−1.33103	−	0.768470i	−0.985457	+	0.169923i	$0.945648\pi$
$350$		0			0
$351$	−7.19839	−	6.04017i	−0.384222	−	0.322400i
$352$		0			0
$353$	−9.10896	−	15.7772i	−0.484821	−	0.839735i	0.515027	−	0.857174i	$-0.327782\pi$
$353$	−9.10896	−	15.7772i	−0.484821	−	0.839735i	−0.999848	+	0.0174391i	$0.994449\pi$
$354$		0			0
$355$	−8.56706	−	23.5378i	−0.454692	−	1.24926i
$356$		0			0
$357$	12.4862	+	2.20166i	0.660840	+	0.116524i
$358$		0			0
$359$	17.5349	−	14.7135i	0.925455	−	0.776549i	−0.0495409	−	0.998772i	$-0.515776\pi$
$359$	17.5349	−	14.7135i	0.925455	−	0.776549i	0.974996	+	0.222223i	$0.0713314\pi$
$360$		0			0
$361$	18.7665	+	2.96937i	0.987712	+	0.156282i
$362$		0			0
$363$	3.62059	+	4.31486i	0.190032	+	0.226471i
$364$		0			0
$365$	11.8986	+	2.09805i	0.622801	+	0.109817i
$366$		0			0
$367$	8.79345	−	3.20055i	0.459014	−	0.167068i	−0.102155	−	0.994768i	$-0.532574\pi$
$367$	8.79345	−	3.20055i	0.459014	−	0.167068i	0.561170	+	0.827701i	$0.310352\pi$
$368$		0			0
$369$	0.901994	+	1.56230i	0.0469560	+	0.0813301i
$370$		0			0
$371$	−30.9447	+	36.8784i	−1.60657	+	1.91463i
$372$		0			0
$373$	−9.42605	−	5.44213i	−0.488062	−	0.281783i	0.235708	−	0.971824i	$-0.424259\pi$
$373$	−9.42605	−	5.44213i	−0.488062	−	0.281783i	−0.723770	+	0.690041i	$0.757592\pi$
$374$		0			0
$375$	−0.985801	−	5.59075i	−0.0509065	−	0.288705i
$376$		0			0
$377$	−7.68686	−	2.79779i	−0.395894	−	0.144093i
$378$		0			0
$379$			10.4146i			0.534963i	0.963563	+	0.267482i	$0.0861915\pi$
$379$			10.4146i			0.534963i	−0.963563	+	0.267482i	$0.913809\pi$
$380$		0			0
$381$			3.36651i			0.172472i
$382$		0			0
$383$	20.1708	+	7.34157i	1.03068	+	0.375137i	0.801340	−	0.598210i	$-0.204121\pi$
$383$	20.1708	+	7.34157i	1.03068	+	0.375137i	0.229340	+	0.973346i	$0.426343\pi$
$384$		0			0
$385$	−0.995853	−	5.64776i	−0.0507534	−	0.287837i
$386$		0			0
$387$	0.903077	+	0.521392i	0.0459060	+	0.0265038i
$388$		0			0
$389$	12.0248	−	14.3306i	0.609684	−	0.726593i	−0.369576	−	0.929200i	$-0.620497\pi$
$389$	12.0248	−	14.3306i	0.609684	−	0.726593i	0.979260	+	0.202608i	$0.0649416\pi$
$390$		0			0
$391$	−18.5299	−	32.0947i	−0.937097	−	1.62310i
$392$		0			0
$393$	9.55940	−	3.47934i	0.482208	−	0.175509i
$394$		0			0
$395$	23.5646	+	4.15507i	1.18566	+	0.209064i
$396$		0			0
$397$	−0.0151058	−	0.0180024i	−0.000758139	−	0.000903515i	0.765665	−	0.643239i	$-0.222410\pi$
$397$	−0.0151058	−	0.0180024i	−0.000758139	−	0.000903515i	−0.766423	+	0.642336i	$0.777965\pi$
$398$		0			0
$399$	4.77885	+	6.69861i	0.239242	+	0.335350i
$400$		0			0
$401$	−9.71472	+	8.15162i	−0.485130	+	0.407072i	−0.852277	−	0.523091i	$-0.824779\pi$
$401$	−9.71472	+	8.15162i	−0.485130	+	0.407072i	0.367147	+	0.930163i	$0.380335\pi$
$402$		0			0
$403$	16.0832	+	2.83590i	0.801161	+	0.141266i
$404$		0			0
$405$	8.18075	+	22.4764i	0.406505	+	1.11686i
$406$		0			0
$407$	−1.30660	−	2.26310i	−0.0647657	−	0.112178i
$408$		0			0
$409$	8.05259	+	6.75693i	0.398175	+	0.334109i	0.819788	−	0.572667i	$-0.194091\pi$
$409$	8.05259	+	6.75693i	0.398175	+	0.334109i	−0.421613	+	0.906776i	$0.638536\pi$
$410$		0			0
$411$	0.0776917	+	0.0448553i	0.00383225	+	0.00221255i
$412$		0			0
$413$	47.1914	−	8.32113i	2.32214	−	0.409456i
$414$		0			0
$415$	−21.4261	−	7.79845i	−1.05176	−	0.382811i
$416$		0			0
$417$	−5.06575			−0.248071
$418$		0			0
$419$		−	30.4034i		−	1.48531i	−0.669677	−	0.742653i	$-0.733567\pi$
$419$		−	30.4034i		−	1.48531i	0.669677	−	0.742653i	$-0.266433\pi$
$420$		0			0
$421$	−11.1442	+	30.6184i	−0.543134	+	1.49225i	0.299677	+	0.954041i	$0.403121\pi$
$421$	−11.1442	+	30.6184i	−0.543134	+	1.49225i	−0.842812	+	0.538209i	$0.819101\pi$
$422$		0			0
$423$	2.19403	+	12.4430i	0.106678	+	0.604999i
$424$		0			0
$425$	−26.9287	+	46.6420i	−1.30624	+	2.26247i
$426$		0			0
$427$	11.8725	−	14.1491i	0.574551	−	0.684723i
$428$		0			0
$429$	−0.623395	+	0.359918i	−0.0300978	+	0.0173770i
$430$		0			0
$431$	−29.1465	+	10.6084i	−1.40394	+	0.510991i	−0.929344	−	0.369215i	$-0.879627\pi$
$431$	−29.1465	+	10.6084i	−1.40394	+	0.510991i	−0.474592	+	0.880206i	$0.657404\pi$
$432$		0			0
$433$	−4.85572	+	27.5382i	−0.233351	+	1.32340i	0.612707	+	0.790310i	$0.290080\pi$
$433$	−4.85572	+	27.5382i	−0.233351	+	1.32340i	−0.846058	+	0.533090i	$0.821031\pi$
$434$		0			0
$435$	−3.14156	−	3.74397i	−0.150626	−	0.179510i
$436$		0			0
$437$	6.02028	−	23.2861i	0.287989	−	1.11392i
$438$		0			0
$439$	18.9839	−	15.9294i	0.906054	−	0.760269i	−0.0653103	−	0.997865i	$-0.520804\pi$
$439$	18.9839	−	15.9294i	0.906054	−	0.760269i	0.971364	+	0.237596i	$0.0763593\pi$
$440$		0			0
$441$	2.89920	−	16.4422i	0.138057	−	0.782960i
$442$		0			0
$443$	−1.79167	−	4.92257i	−0.0851248	−	0.233879i	0.889826	−	0.456301i	$-0.150826\pi$
$443$	−1.79167	−	4.92257i	−0.0851248	−	0.233879i	−0.974950	+	0.222422i	$0.928604\pi$
$444$		0			0
$445$	9.20127	−	5.31236i	0.436182	−	0.251830i
$446$		0			0
$447$	4.43355	+	3.72019i	0.209700	+	0.175959i
$448$		0			0
$449$	−12.7259	+	22.0418i	−0.600570	+	1.04022i	0.392165	+	0.919895i	$0.371726\pi$
$449$	−12.7259	+	22.0418i	−0.600570	+	1.04022i	−0.992735	+	0.120323i	$0.961607\pi$
$450$		0			0
$451$	0.285736	−	0.0503829i	0.0134548	−	0.00237244i
$452$		0			0
$453$	−2.75735	+	7.57575i	−0.129551	+	0.355940i
$454$		0			0
$455$	−41.1342			−1.92840
$456$		0			0
$457$	36.2633			1.69633			0.848163	−	0.529736i	$-0.177709\pi$
$457$	36.2633			1.69633			0.848163	+	0.529736i	$0.177709\pi$
$458$		0			0
$459$	−6.85813	+	18.8426i	−0.320110	+	0.879495i
$460$		0			0
$461$	−2.09253	+	0.368969i	−0.0974588	+	0.0171846i	−0.222165	−	0.975009i	$-0.571312\pi$
$461$	−2.09253	+	0.368969i	−0.0974588	+	0.0171846i	0.124706	+	0.992194i	$0.460201\pi$
$462$		0			0
$463$	−5.19412	+	8.99648i	−0.241391	+	0.418102i	−0.961111	−	0.276163i	$-0.910937\pi$
$463$	−5.19412	+	8.99648i	−0.241391	+	0.418102i	0.719720	+	0.694265i	$0.244270\pi$
$464$		0			0
$465$	7.47463	+	6.27196i	0.346628	+	0.290855i
$466$		0			0
$467$	−23.6707	+	13.6663i	−1.09535	+	0.632400i	−0.934995	−	0.354660i	$-0.884597\pi$
$467$	−23.6707	+	13.6663i	−1.09535	+	0.632400i	−0.160353	+	0.987060i	$0.551263\pi$
$468$		0			0
$469$	1.11201	+	3.05522i	0.0513478	+	0.141077i
$470$		0			0
$471$	0.964648	−	5.47079i	0.0444486	−	0.252081i
$472$		0			0
$473$	0.128478	−	0.107806i	0.00590741	−	0.00495690i
$474$		0			0
$475$	−33.6814	+	9.34348i	−1.54541	+	0.428708i
$476$		0			0
$477$	−23.3095	−	27.7792i	−1.06727	−	1.27192i
$478$		0			0
$479$	7.02555	−	39.8439i	0.321006	−	1.82051i	−0.215368	−	0.976533i	$-0.569095\pi$
$479$	7.02555	−	39.8439i	0.321006	−	1.82051i	0.536374	−	0.843980i	$-0.319794\pi$
$480$		0			0
$481$	−17.6131	+	6.41066i	−0.803090	+	0.292301i
$482$		0			0
$483$	9.02081	−	5.20817i	0.410461	−	0.236980i
$484$		0			0
$485$	−11.1101	+	13.2405i	−0.504483	+	0.601219i
$486$		0			0
$487$	−12.3436	+	21.3797i	−0.559341	+	0.968807i	0.438210	+	0.898872i	$0.355613\pi$
$487$	−12.3436	+	21.3797i	−0.559341	+	0.968807i	−0.997552	+	0.0699350i	$0.977721\pi$
$488$		0			0
$489$	1.31317	+	7.44736i	0.0593836	+	0.336781i
$490$		0			0
$491$	−13.0447	+	35.8400i	−0.588698	+	1.61744i	0.184188	+	0.982891i	$0.441034\pi$
$491$	−13.0447	+	35.8400i	−0.588698	+	1.61744i	−0.772887	+	0.634544i	$0.781188\pi$
$492$		0			0
$493$			17.4556i			0.786163i
$494$		0			0
$495$	4.31988			0.194164
$496$		0			0
$497$	−23.6285	−	8.60006i	−1.05988	−	0.385765i
$498$		0			0
$499$	−34.4027	+	6.06613i	−1.54008	+	0.271557i	−0.878288	−	0.478132i	$-0.841314\pi$
$499$	−34.4027	+	6.06613i	−1.54008	+	0.271557i	−0.661790	+	0.749689i	$0.730203\pi$
$500$		0			0
$501$	−6.82415	−	3.93993i	−0.304881	−	0.176023i
$502$		0			0
$503$	18.2787	+	15.3377i	0.815008	+	0.683873i	0.951797	−	0.306727i	$-0.0992339\pi$
$503$	18.2787	+	15.3377i	0.815008	+	0.683873i	−0.136789	+	0.990600i	$0.543678\pi$
$504$		0			0
$505$	−2.22196	−	3.84854i	−0.0988758	−	0.171258i
$506$		0			0
$507$	−0.551425	−	1.51503i	−0.0244896	−	0.0672847i
$508$		0			0
$509$	5.87494	+	1.03591i	0.260402	+	0.0459159i	0.302325	−	0.953205i	$-0.402237\pi$
$509$	5.87494	+	1.03591i	0.260402	+	0.0459159i	−0.0419228	+	0.999121i	$0.513348\pi$
$510$		0			0
$511$	9.29112	−	7.79618i	0.411015	−	0.344883i
$512$		0			0
$513$	−11.7455	+	5.60340i	−0.518574	+	0.247396i
$514$		0			0
$515$	−19.6613	−	23.4314i	−0.866378	−	1.03251i
$516$		0			0
$517$	2.00126	+	0.352877i	0.0880154	+	0.0155195i
$518$		0			0
$519$	6.75648	−	2.45916i	0.296577	−	0.107945i
$520$		0			0
$521$	−5.49276	−	9.51375i	−0.240642	−	0.416805i	0.720255	−	0.693709i	$-0.244025\pi$
$521$	−5.49276	−	9.51375i	−0.240642	−	0.416805i	−0.960897	+	0.276904i	$0.910691\pi$
$522$		0			0
$523$	17.0985	−	20.3773i	0.747667	−	0.891035i	−0.249334	−	0.968418i	$-0.580212\pi$
$523$	17.0985	−	20.3773i	0.747667	−	0.891035i	0.997001	+	0.0773823i	$0.0246562\pi$
$524$		0			0
$525$	−13.1096	−	7.56882i	−0.572149	−	0.330330i
$526$		0			0
$527$	−6.05151	−	34.3198i	−0.263608	−	1.49499i
$528$		0			0
$529$	−6.99752	−	2.54689i	−0.304240	−	0.110734i
$530$		0			0
$531$			36.0960i			1.56643i
$532$		0			0
$533$		−	2.08109i		−	0.0901422i
$534$		0			0
$535$	−13.6184	−	4.95670i	−0.588775	−	0.214297i
$536$		0			0
$537$	−0.960634	−	5.44802i	−0.0414544	−	0.235100i
$538$		0			0
$539$	−2.32551	−	1.34263i	−0.100167	−	0.0578313i
$540$		0			0
$541$	−27.5103	+	32.7855i	−1.18276	+	1.40956i	−0.291200	+	0.956662i	$0.594054\pi$
$541$	−27.5103	+	32.7855i	−1.18276	+	1.40956i	−0.891562	+	0.452898i	$0.850390\pi$
$542$		0			0
$543$	1.71599	+	2.97217i	0.0736400	+	0.127548i
$544$		0			0
$545$	−13.4125	+	4.88177i	−0.574530	+	0.209112i
$546$		0			0
$547$	20.2198	+	3.56530i	0.864536	+	0.152441i	0.588294	−	0.808647i	$-0.299800\pi$
$547$	20.2198	+	3.56530i	0.864536	+	0.152441i	0.276242	+	0.961088i	$0.410911\pi$
$548$		0			0
$549$	8.94313	+	10.6580i	0.381683	+	0.454872i
$550$		0			0
$551$	−7.93975	+	8.08079i	−0.338245	+	0.344253i
$552$		0			0
$553$	18.4006	−	15.4399i	0.782473	−	0.656573i
$554$		0			0
$555$	−11.0285	−	1.94463i	−0.468135	−	0.0825448i
$556$		0			0
$557$	3.60818	+	9.91340i	0.152884	+	0.420044i	0.992364	−	0.123346i	$-0.0393626\pi$
$557$	3.60818	+	9.91340i	0.152884	+	0.420044i	−0.839480	+	0.543390i	$0.817140\pi$
$558$		0			0
$559$	−0.601481	−	1.04180i	−0.0254399	−	0.0440633i
$560$		0			0
$561$	1.17668	+	0.987354i	0.0496796	+	0.0416861i
$562$		0			0
$563$	36.5165	+	21.0828i	1.53899	+	0.888534i	0.998898	+	0.0469245i	$0.0149420\pi$
$563$	36.5165	+	21.0828i	1.53899	+	0.888534i	0.540087	+	0.841609i	$0.318391\pi$
$564$		0			0
$565$	14.6577	−	2.58455i	0.616654	−	0.108733i
$566$		0			0
$567$	22.5630	+	8.21226i	0.947557	+	0.344882i
$568$		0			0
$569$	8.23726			0.345324			0.172662	−	0.984981i	$-0.444763\pi$
$569$	8.23726			0.345324			0.172662	+	0.984981i	$0.444763\pi$
$570$		0			0
$571$			13.0718i			0.547038i	0.961867	+	0.273519i	$0.0881877\pi$
$571$			13.0718i			0.547038i	−0.961867	+	0.273519i	$0.911812\pi$
$572$		0			0
$573$	2.48522	−	6.82809i	0.103822	−	0.285248i
$574$		0			0
$575$	7.68338	+	43.5746i	0.320419	+	1.81719i
$576$		0			0
$577$	14.4695	−	25.0619i	0.602374	−	1.04334i	−0.390087	−	0.920778i	$-0.627555\pi$
$577$	14.4695	−	25.0619i	0.602374	−	1.04334i	0.992461	−	0.122564i	$-0.0391116\pi$
$578$		0			0
$579$	−3.57247	+	4.25750i	−0.148467	+	0.176936i
$580$		0			0
$581$	−19.8224	+	11.4445i	−0.822373	+	0.474797i
$582$		0			0
$583$	−5.48063	+	1.99479i	−0.226985	+	0.0826156i
$584$		0			0
$585$	5.38048	−	30.5142i	0.222455	−	1.26161i
$586$		0			0
$587$	−27.2123	−	32.4304i	−1.12317	−	1.33855i	−0.934277	−	0.356548i	$-0.883954\pi$
$587$	−27.2123	−	32.4304i	−1.12317	−	1.33855i	−0.188896	−	0.981997i	$-0.560491\pi$
$588$		0			0
$589$	12.8090	−	18.6403i	0.527786	−	0.768061i
$590$		0			0
$591$	−7.81667	+	6.55896i	−0.321535	+	0.269800i
$592$		0			0
$593$	4.67524	−	26.5146i	0.191989	−	1.08882i	−0.724653	−	0.689114i	$-0.758000\pi$
$593$	4.67524	−	26.5146i	0.191989	−	1.08882i	0.916642	−	0.399710i	$-0.130889\pi$
$594$		0			0
$595$	30.0212	+	82.4825i	1.23075	+	3.38145i
$596$		0			0
$597$	−4.51058	+	2.60419i	−0.184606	+	0.106582i
$598$		0			0
$599$	−21.1301	−	17.7303i	−0.863354	−	0.724440i	0.0993337	−	0.995054i	$-0.468329\pi$
$599$	−21.1301	−	17.7303i	−0.863354	−	0.724440i	−0.962688	+	0.270614i	$0.912773\pi$
$600$		0			0
$601$	16.5323	−	28.6348i	0.674367	−	1.16804i	−0.302287	−	0.953217i	$-0.597750\pi$
$601$	16.5323	−	28.6348i	0.674367	−	1.16804i	0.976654	−	0.214821i	$-0.0689167\pi$
$602$		0			0
$603$	−2.41188	+	0.425279i	−0.0982192	+	0.0173187i
$604$		0			0
$605$	−13.3371	+	36.6433i	−0.542230	+	1.48976i
$606$		0			0
$607$	−40.8887			−1.65962			−0.829811	−	0.558045i	$-0.811552\pi$
$607$	−40.8887			−1.65962			−0.829811	+	0.558045i	$0.811552\pi$
$608$		0			0
$609$	−4.90623			−0.198810
$610$		0			0
$611$	4.98520	−	13.6967i	0.201680	−	0.554110i
$612$		0			0
$613$	−35.2118	+	6.20880i	−1.42219	+	0.250771i	−0.831230	−	0.555928i	$-0.812363\pi$
$613$	−35.2118	+	6.20880i	−1.42219	+	0.250771i	−0.590962	+	0.806699i	$0.701252\pi$
$614$		0			0
$615$	0.621694	−	1.07681i	0.0250691	−	0.0434210i
$616$		0			0
$617$	3.08965	+	2.59252i	0.124384	+	0.104371i	0.702858	−	0.711330i	$-0.251907\pi$
$617$	3.08965	+	2.59252i	0.124384	+	0.104371i	−0.578474	+	0.815701i	$0.696351\pi$
$618$		0			0
$619$	31.7781	−	18.3471i	1.27727	−	0.737432i	0.300924	−	0.953648i	$-0.402705\pi$
$619$	31.7781	−	18.3471i	1.27727	−	0.737432i	0.976346	+	0.216216i	$0.0693716\pi$
$620$		0			0
$621$	5.63432	+	15.4802i	0.226098	+	0.621198i
$622$		0			0
$623$	1.85207	−	10.5036i	0.0742016	−	0.420818i
$624$		0			0
$625$	−0.606854	+	0.509211i	−0.0242742	+	0.0203684i
$626$		0			0
$627$	0.0956244	+	0.992297i	0.00381887	+	0.0396285i
$628$		0			0
$629$	25.7093	+	30.6392i	1.02510	+	1.22166i
$630$		0			0
$631$	−0.183226	+	1.03913i	−0.00729412	+	0.0413670i	−0.988238	−	0.152926i	$-0.951130\pi$
$631$	−0.183226	+	1.03913i	−0.00729412	+	0.0413670i	0.980943	+	0.194293i	$0.0622414\pi$
$632$		0			0
$633$	3.78798	−	1.37871i	0.150559	−	0.0547989i
$634$		0			0
$635$	−20.1840	+	11.6532i	−0.800978	+	0.462445i
$636$		0			0
$637$	−12.3804	+	14.7543i	−0.490527	+	0.584588i
$638$		0			0
$639$	9.47037	−	16.4032i	0.374642	−	0.648899i
$640$		0			0
$641$	−0.252757	−	1.43346i	−0.00998330	−	0.0566181i	0.979409	−	0.201885i	$-0.0647069\pi$
$641$	−0.252757	−	1.43346i	−0.00998330	−	0.0566181i	−0.989392	+	0.145267i	$0.953596\pi$
$642$		0			0
$643$	4.69667	−	12.9040i	0.185218	−	0.508884i	−0.811980	−	0.583685i	$-0.801610\pi$
$643$	4.69667	−	12.9040i	0.185218	−	0.508884i	0.997198	+	0.0748018i	$0.0238324\pi$
$644$		0			0
$645$		−	0.718732i		−	0.0283001i
$646$		0			0
$647$	18.7166			0.735825			0.367913	−	0.929860i	$-0.380073\pi$
$647$	18.7166			0.735825			0.367913	+	0.929860i	$0.380073\pi$
$648$		0			0
$649$	5.45537	+	1.98559i	0.214142	+	0.0779413i
$650$		0			0
$651$	9.64621	−	1.70089i	0.378065	−	0.0666630i
$652$		0			0
$653$	−16.6282	−	9.60032i	−0.650714	−	0.375690i	0.138016	−	0.990430i	$-0.455927\pi$
$653$	−16.6282	−	9.60032i	−0.650714	−	0.375690i	−0.788730	+	0.614740i	$0.789261\pi$
$654$		0			0
$655$	53.9505	+	45.2699i	2.10802	+	1.76884i
$656$		0			0
$657$	4.56805	+	7.91210i	0.178217	+	0.308681i
$658$		0			0
$659$	0.514540	+	1.41369i	0.0200436	+	0.0550694i	0.949311	−	0.314339i	$-0.101783\pi$
$659$	0.514540	+	1.41369i	0.0200436	+	0.0550694i	−0.929267	+	0.369408i	$0.879560\pi$
$660$		0			0
$661$	29.4696	+	5.19629i	1.14624	+	0.202112i	0.714332	−	0.699807i	$-0.246731\pi$
$661$	29.4696	+	5.19629i	1.14624	+	0.202112i	0.431904	+	0.901920i	$0.357842\pi$
$662$		0			0
$663$	8.43991	−	7.08193i	0.327779	−	0.275039i
$664$		0			0
$665$	−23.6196	+	51.8391i	−0.915930	+	2.01023i
$666$		0			0
$667$	9.21806	+	10.9857i	0.356925	+	0.425366i
$668$		0			0
$669$	3.15076	+	0.555563i	0.121815	+	0.0214793i
$670$		0			0
$671$	2.10275	−	0.765337i	0.0811756	−	0.0295455i
$672$		0			0
$673$	−24.4237	−	42.3031i	−0.941464	−	1.63066i	−0.762681	−	0.646775i	$-0.776117\pi$
$673$	−24.4237	−	42.3031i	−0.941464	−	1.63066i	−0.178783	−	0.983889i	$-0.557216\pi$
$674$		0			0
$675$	15.3887	−	18.3395i	0.592310	−	0.705887i
$676$		0			0
$677$	−16.9015	−	9.75807i	−0.649576	−	0.375033i	0.138718	−	0.990332i	$-0.455702\pi$
$677$	−16.9015	−	9.75807i	−0.649576	−	0.375033i	−0.788294	+	0.615299i	$0.789035\pi$
$678$		0			0
$679$	3.01293	+	17.0872i	0.115626	+	0.655747i
$680$		0			0
$681$	−11.0319	−	4.01529i	−0.422744	−	0.153866i
$682$		0			0
$683$		−	28.6592i		−	1.09662i	−0.836277	−	0.548308i	$-0.815272\pi$
$683$		−	28.6592i		−	1.09662i	0.836277	−	0.548308i	$-0.184728\pi$
$684$		0			0
$685$			0.621071i			0.0237299i
$686$		0			0
$687$	−1.40700	−	0.512107i	−0.0536804	−	0.0195381i
$688$		0			0
$689$	7.26429	+	41.1979i	0.276748	+	1.56951i
$690$		0			0
$691$	−12.0352	−	6.94855i	−0.457842	−	0.264335i	0.253295	−	0.967389i	$-0.418486\pi$
$691$	−12.0352	−	6.94855i	−0.457842	−	0.264335i	−0.711136	+	0.703054i	$0.751819\pi$
$692$		0			0
$693$	2.78746	−	3.32197i	0.105887	−	0.126191i
$694$		0			0
$695$	−17.5352	−	30.3719i	−0.665148	−	1.15207i
$696$		0			0
$697$	−4.17302	+	1.51885i	−0.158064	+	0.0575307i
$698$		0			0
$699$	−1.38613	−	0.244412i	−0.0524282	−	0.00924450i
$700$		0			0
$701$	−2.84915	−	3.39548i	−0.107611	−	0.128246i	0.709551	−	0.704655i	$-0.248898\pi$
$701$	−2.84915	−	3.39548i	−0.107611	−	0.128246i	−0.817161	+	0.576409i	$0.804454\pi$
$702$		0			0
$703$	−2.03463	+	25.8779i	−0.0767375	+	0.976002i
$704$		0			0
$705$	6.67114	−	5.59775i	0.251250	−	0.210824i
$706$		0			0
$707$	−4.39326	−	0.774650i	−0.165225	−	0.0291337i
$708$		0			0
$709$	−9.17608	−	25.2111i	−0.344615	−	0.946822i	−0.984037	−	0.177966i	$-0.943048\pi$
$709$	−9.17608	−	25.2111i	−0.344615	−	0.946822i	0.639422	−	0.768856i	$-0.279174\pi$
$710$		0			0
$711$	9.04680	+	15.6695i	0.339281	+	0.587653i
$712$		0			0
$713$	−21.9322	−	18.4033i	−0.821369	−	0.689211i
$714$		0			0
$715$	−4.31579	−	2.49172i	−0.161401	−	0.0931852i
$716$		0			0
$717$	3.84788	−	0.678484i	0.143702	−	0.0253385i
$718$		0			0
$719$	2.76943	+	1.00799i	0.103282	+	0.0375916i	0.393144	−	0.919477i	$-0.371387\pi$
$719$	2.76943	+	1.00799i	0.103282	+	0.0375916i	−0.289862	+	0.957068i	$0.593609\pi$
$720$		0			0
$721$	−30.7053			−1.14352
$722$		0			0
$723$			10.8868i			0.404885i
$724$		0			0
$725$	7.12798	−	19.5840i	0.264727	−	0.727330i
$726$		0			0
$727$	−6.04291	−	34.2710i	−0.224119	−	1.27104i	−0.864362	−	0.502870i	$-0.832278\pi$
$727$	−6.04291	−	34.2710i	−0.224119	−	1.27104i	0.640243	−	0.768172i	$-0.278834\pi$
$728$		0			0
$729$	−6.70932	+	11.6209i	−0.248493	+	0.430403i
$730$		0			0
$731$	−1.65003	+	1.96643i	−0.0610286	+	0.0727310i
$732$		0			0
$733$	1.42948	−	0.825308i	0.0527989	−	0.0304835i	−0.473368	−	0.880865i	$-0.656962\pi$
$733$	1.42948	−	0.825308i	0.0527989	−	0.0304835i	0.526167	+	0.850381i	$0.323629\pi$
$734$		0			0
$735$	−10.8135	+	3.93579i	−0.398862	+	0.145174i
$736$		0			0
$737$	−0.0683996	+	0.387913i	−0.00251953	+	0.0142890i
$738$		0			0
$739$	3.40363	+	4.05629i	0.125204	+	0.149213i	0.825005	−	0.565125i	$-0.191172\pi$
$739$	3.40363	+	4.05629i	0.125204	+	0.149213i	−0.699801	+	0.714338i	$0.746728\pi$
$740$		0			0
$741$	7.12835	+	0.560461i	0.261867	+	0.0205891i
$742$		0			0
$743$	−19.8541	+	16.6596i	−0.728376	+	0.611180i	−0.929688	−	0.368347i	$-0.879924\pi$
$743$	−19.8541	+	16.6596i	−0.728376	+	0.611180i	0.201313	+	0.979527i	$0.435479\pi$
$744$		0			0
$745$	−6.95768	+	39.4590i	−0.254910	+	1.44567i
$746$		0			0
$747$	−5.89692	−	16.2016i	−0.215757	−	0.592787i
$748$		0			0
$749$	−12.5991	+	7.27411i	−0.460362	+	0.265790i
$750$		0			0
$751$	−9.20184	−	7.72126i	−0.335780	−	0.281753i	0.459270	−	0.888297i	$-0.348111\pi$
$751$	−9.20184	−	7.72126i	−0.335780	−	0.281753i	−0.795050	+	0.606544i	$0.792555\pi$
$752$		0			0
$753$	3.06513	−	5.30896i	0.111700	−	0.193469i
$754$		0			0
$755$	−54.9652	+	9.69185i	−2.00039	+	0.352723i
$756$		0			0
$757$	18.1225	−	49.7911i	0.658673	−	1.80969i	0.0758026	−	0.997123i	$-0.475848\pi$
$757$	18.1225	−	49.7911i	0.658673	−	1.80969i	0.582870	−	0.812565i	$-0.301930\pi$
$758$		0			0
$759$	1.26195			0.0458058
$760$		0			0
$761$	−5.98803			−0.217066			−0.108533	−	0.994093i	$-0.534615\pi$
$761$	−5.98803			−0.217066			−0.108533	+	0.994093i	$0.534615\pi$
$762$		0			0
$763$	−4.90057	+	13.4642i	−0.177413	+	0.487437i
$764$		0			0
$765$	−65.1140	+	11.4814i	−2.35420	+	0.415109i
$766$		0			0
$767$	20.8203	−	36.0618i	0.751777	−	1.30212i
$768$		0			0
$769$	26.6631	+	22.3730i	0.961495	+	0.806790i	0.981196	−	0.193016i	$-0.0618269\pi$
$769$	26.6631	+	22.3730i	0.961495	+	0.806790i	−0.0197007	+	0.999806i	$0.506271\pi$
$770$		0			0
$771$	12.8371	−	7.41149i	0.462316	−	0.266918i
$772$		0			0
$773$	−3.40354	−	9.35115i	−0.122417	−	0.336337i	0.863314	−	0.504667i	$-0.168385\pi$
$773$	−3.40354	−	9.35115i	−0.122417	−	0.336337i	−0.985731	+	0.168330i	$0.946163\pi$
$774$		0			0
$775$	−7.22508	+	40.9755i	−0.259532	+	1.47188i
$776$		0			0
$777$	−8.61171	+	7.22608i	−0.308943	+	0.259234i
$778$		0			0
$779$	−2.62268	−	1.19498i	−0.0939673	−	0.0428146i
$780$		0			0
$781$	−1.95814	−	2.33362i	−0.0700678	−	0.0835035i
$782$		0			0
$783$	1.34739	−	7.64143i	0.0481518	−	0.273082i
$784$		0			0
$785$	36.1394	−	13.1537i	1.28987	−	0.469475i
$786$		0			0
$787$	32.6750	−	18.8649i	1.16474	−	0.672461i	0.212302	−	0.977204i	$-0.431904\pi$
$787$	32.6750	−	18.8649i	1.16474	−	0.672461i	0.952435	+	0.304743i	$0.0985707\pi$
$788$		0			0
$789$	1.57124	−	1.87253i	0.0559377	−	0.0666639i
$790$		0			0
$791$	7.47057	−	12.9394i	0.265623	−	0.460072i
$792$		0			0
$793$	−2.78708	−	15.8063i	−0.0989722	−	0.561299i
$794$		0			0
$795$	−8.54850	+	23.4868i	−0.303184	+	0.832991i
$796$		0			0
$797$		−	18.2325i		−	0.645830i	−0.946428	−	0.322915i	$-0.895337\pi$
$797$		−	18.2325i		−	0.645830i	0.946428	−	0.322915i	$-0.104663\pi$
$798$		0			0
$799$	−31.1031			−1.10035
$800$		0			0
$801$	7.54953	+	2.74780i	0.266749	+	0.0970889i
$802$		0			0
$803$	1.44708	−	0.255159i	0.0510663	−	0.00900437i
$804$		0			0
$805$	62.4515	+	36.0564i	2.20112	+	1.27082i
$806$		0			0
$807$	−3.94294	−	3.30852i	−0.138798	−	0.116465i
$808$		0			0
$809$	−18.6895	−	32.3711i	−0.657086	−	1.13811i	−0.981366	−	0.192146i	$-0.938455\pi$
$809$	−18.6895	−	32.3711i	−0.657086	−	1.13811i	0.324280	−	0.945961i	$-0.394878\pi$
$810$		0			0
$811$	2.07199	+	5.69274i	0.0727574	+	0.199899i	0.970741	−	0.240130i	$-0.0771902\pi$
$811$	2.07199	+	5.69274i	0.0727574	+	0.199899i	−0.897983	+	0.440030i	$0.854968\pi$
$812$		0			0
$813$	−8.32826	−	1.46850i	−0.292085	−	0.0515024i
$814$		0			0
$815$	−40.1053	+	33.6523i	−1.40483	+	1.17879i
$816$		0			0
$817$	−1.65829	+	0.159804i	−0.0580162	+	0.00559083i
$818$		0			0
$819$	−19.9934	−	23.8273i	−0.698627	−	0.832592i
$820$		0			0
$821$	3.02314	+	0.533062i	0.105508	+	0.0186040i	0.226153	−	0.974092i	$-0.427385\pi$
$821$	3.02314	+	0.533062i	0.105508	+	0.0186040i	−0.120645	+	0.992696i	$0.538496\pi$
$822$		0			0
$823$	43.8007	−	15.9421i	1.52680	−	0.555708i	0.563961	−	0.825801i	$-0.309277\pi$
$823$	43.8007	−	15.9421i	1.52680	−	0.555708i	0.962834	+	0.270093i	$0.0870545\pi$
$824$		0			0
$825$	−0.916969	−	1.58824i	−0.0319248	−	0.0552953i
$826$		0			0
$827$	−2.44449	+	2.91324i	−0.0850034	+	0.101303i	−0.806870	−	0.590729i	$-0.798840\pi$
$827$	−2.44449	+	2.91324i	−0.0850034	+	0.101303i	0.721866	+	0.692033i	$0.243285\pi$
$828$		0			0
$829$	0.877638	+	0.506704i	0.0304816	+	0.0175986i	0.515163	−	0.857092i	$-0.327731\pi$
$829$	0.877638	+	0.506704i	0.0304816	+	0.0175986i	−0.484682	+	0.874691i	$0.661065\pi$
$830$		0			0
$831$	−0.901122	−	5.11051i	−0.0312596	−	0.177282i
$832$		0			0
$833$	38.6210	+	14.0569i	1.33814	+	0.487043i
$834$		0			0
$835$		−	54.5526i		−	1.88787i
$836$		0			0
$837$			15.4910i			0.535448i
$838$		0			0
$839$	13.3269	+	4.85058i	0.460095	+	0.167461i	0.561660	−	0.827368i	$-0.310163\pi$
$839$	13.3269	+	4.85058i	0.460095	+	0.167461i	−0.101565	+	0.994829i	$0.532385\pi$
$840$		0			0
$841$	3.86286	+	21.9074i	0.133202	+	0.755426i
$842$		0			0
$843$	−6.08978	−	3.51594i	−0.209743	−	0.121095i
$844$		0			0
$845$	7.17462	−	8.55038i	0.246815	−	0.294142i
$846$		0			0
$847$	19.5726	+	33.9008i	0.672523	+	1.16484i
$848$		0			0
$849$	−6.77980	+	2.46765i	−0.232682	+	0.0846894i
$850$		0			0
$851$	32.3602	+	5.70597i	1.10929	+	0.195598i
$852$		0			0
$853$	10.9246	+	13.0194i	0.374050	+	0.445775i	0.919927	−	0.392090i	$-0.128248\pi$
$853$	10.9246	+	13.0194i	0.374050	+	0.445775i	−0.545877	+	0.837865i	$0.683803\pi$
$854$		0			0
$855$	−35.3658	−	24.3022i	−1.20948	−	0.831118i
$856$		0			0
$857$	7.76836	−	6.51843i	0.265362	−	0.222665i	−0.500392	−	0.865799i	$-0.666811\pi$
$857$	7.76836	−	6.51843i	0.265362	−	0.222665i	0.765754	+	0.643134i	$0.222366\pi$
$858$		0			0
$859$	16.0564	+	2.83118i	0.547839	+	0.0965988i	0.440715	−	0.897647i	$-0.354725\pi$
$859$	16.0564	+	2.83118i	0.547839	+	0.0965988i	0.107124	+	0.994246i	$0.465836\pi$
$860$		0			0
$861$	−0.426902	−	1.17290i	−0.0145488	−	0.0399724i
$862$		0			0
$863$	−19.8160	−	34.3223i	−0.674545	−	1.16835i	−0.976602	−	0.215056i	$-0.931007\pi$
$863$	−19.8160	−	34.3223i	−0.674545	−	1.16835i	0.302057	−	0.953290i	$-0.402327\pi$
$864$		0			0
$865$	38.1317	+	31.9963i	1.29652	+	1.08791i
$866$		0			0
$867$	−12.6874	−	7.32506i	−0.430886	−	0.248772i
$868$		0			0
$869$	2.86587	−	0.505329i	0.0972178	−	0.0171421i
$870$		0			0
$871$	2.65489	+	0.966303i	0.0899577	+	0.0327419i
$872$		0			0
$873$	−13.0697			−0.442343
$874$		0			0
$875$		−	39.4535i		−	1.33377i
$876$		0			0
$877$	2.92760	−	8.04352i	0.0988581	−	0.271610i	−0.880398	−	0.474235i	$-0.842725\pi$
$877$	2.92760	−	8.04352i	0.0988581	−	0.271610i	0.979257	+	0.202624i	$0.0649470\pi$
$878$		0			0
$879$	0.846616	+	4.80140i	0.0285556	+	0.161947i
$880$		0			0
$881$	10.6857	−	18.5082i	0.360010	−	0.623556i	−0.627952	−	0.778252i	$-0.716107\pi$
$881$	10.6857	−	18.5082i	0.360010	−	0.623556i	0.987962	+	0.154696i	$0.0494399\pi$
$882$		0			0
$883$	−18.3568	+	21.8768i	−0.617755	+	0.736212i	−0.980683	−	0.195605i	$-0.937333\pi$
$883$	−18.3568	+	21.8768i	−0.617755	+	0.736212i	0.362927	+	0.931817i	$0.381777\pi$
$884$		0			0
$885$	21.5458	−	12.4395i	0.724254	−	0.418148i
$886$		0			0
$887$	43.5438	−	15.8486i	1.46206	−	0.532146i	0.516127	−	0.856512i	$-0.327373\pi$
$887$	43.5438	−	15.8486i	1.46206	−	0.532146i	0.945931	+	0.324367i	$0.105151\pi$
$888$		0			0
$889$	−4.06272	+	23.0408i	−0.136259	+	0.772764i
$890$		0			0
$891$	1.86984	+	2.22839i	0.0626421	+	0.0746539i
$892$		0			0
$893$	−14.3986	−	14.1473i	−0.481832	−	0.473422i
$894$		0			0
$895$	29.3385	−	24.6180i	0.980679	−	0.822887i
$896$		0			0
$897$	1.57177	−	8.91397i	0.0524800	−	0.297629i
$898$		0			0
$899$	4.61226	+	12.6721i	0.153827	+	0.422638i
$900$		0			0
$901$	77.3083	−	44.6340i	2.57551	−	1.48697i
$902$		0			0
$903$	−0.552701	−	0.463772i	−0.0183928	−	0.0154334i
$904$		0			0
$905$	−11.8798	+	20.5765i	−0.394899	+	0.683985i
$906$		0			0
$907$	49.7852	−	8.77847i	1.65309	−	0.291484i	0.732137	−	0.681158i	$-0.238523\pi$
$907$	49.7852	−	8.77847i	1.65309	−	0.291484i	0.920953	+	0.389674i	$0.127412\pi$
$908$		0			0
$909$	1.14930	−	3.15768i	0.0381199	−	0.104734i
$910$		0			0
$911$	35.4145			1.17333			0.586667	−	0.809828i	$-0.300440\pi$
$911$	35.4145			1.17333			0.586667	+	0.809828i	$0.300440\pi$
$912$		0			0
$913$	−2.77302			−0.0917735
$914$		0			0
$915$	3.27979	−	9.01116i	0.108427	−	0.297900i
$916$		0			0
$917$	69.6246	−	12.2767i	2.29921	−	0.405412i
$918$		0			0
$919$	−10.2605	+	17.7717i	−0.338462	+	0.586233i	−0.984144	−	0.177374i	$-0.943240\pi$
$919$	−10.2605	+	17.7717i	−0.338462	+	0.586233i	0.645682	+	0.763607i	$0.276573\pi$
$920$		0			0
$921$	−4.94452	−	4.14894i	−0.162927	−	0.136712i
$922$		0			0
$923$	−18.9228	+	10.9251i	−0.622851	+	0.359603i
$924$		0			0
$925$	−16.3326	−	44.8733i	−0.537011	−	1.47543i
$926$		0			0
$927$	4.01634	−	22.7778i	0.131914	−	0.748121i
$928$		0			0
$929$	15.6951	−	13.1697i	0.514938	−	0.432085i	−0.347925	−	0.937523i	$-0.613113\pi$
$929$	15.6951	−	13.1697i	0.514938	−	0.432085i	0.862863	+	0.505438i	$0.168669\pi$
$930$		0			0
$931$	11.4851	+	24.0743i	0.376410	+	0.789003i
$932$		0			0
$933$	4.45057	+	5.30398i	0.145705	+	0.173645i
$934$		0			0
$935$	−1.84660	+	10.4726i	−0.0603903	+	0.342490i
$936$		0			0
$937$	48.0662	−	17.4947i	1.57025	−	0.571526i	0.597198	−	0.802094i	$-0.296281\pi$
$937$	48.0662	−	17.4947i	1.57025	−	0.571526i	0.973056	+	0.230569i	$0.0740586\pi$
$938$		0			0
$939$	8.05447	−	4.65025i	0.262848	−	0.151755i
$940$		0			0
$941$	−5.29132	+	6.30595i	−0.172492	+	0.205568i	−0.845364	−	0.534191i	$-0.820616\pi$
$941$	−5.29132	+	6.30595i	−0.172492	+	0.205568i	0.672872	+	0.739759i	$0.265061\pi$
$942$		0			0
$943$	−1.82419	+	3.15959i	−0.0594038	+	0.102890i
$944$		0			0
$945$	−6.77537	−	38.4251i	−0.220403	−	1.24997i
$946$		0			0
$947$	5.52282	−	15.1738i	0.179467	−	0.493083i	−0.817041	−	0.576580i	$-0.804387\pi$
$947$	5.52282	−	15.1738i	0.179467	−	0.493083i	0.996508	+	0.0834975i	$0.0266090\pi$
$948$		0			0
$949$		−	10.5395i		−	0.342126i
$950$		0			0
$951$	3.44438			0.111692
$952$		0			0
$953$	27.6668	+	10.0699i	0.896214	+	0.326195i	0.748735	−	0.662870i	$-0.230662\pi$
$953$	27.6668	+	10.0699i	0.896214	+	0.326195i	0.147479	+	0.989065i	$0.452884\pi$
$954$		0			0
$955$	49.5407	−	8.73535i	1.60310	−	0.282669i
$956$		0			0
$957$	−0.514760	−	0.297197i	−0.0166398	−	0.00960702i
$958$		0			0
$959$	0.477600	+	0.400754i	0.0154225	+	0.0129410i
$960$		0			0
$961$	2.03863	+	3.53100i	0.0657621	+	0.113903i
$962$		0			0
$963$	−3.74808	−	10.2978i	−0.120780	−	0.331841i
$964$		0			0
$965$	−37.8921	−	6.68140i	−1.21979	−	0.215082i
$966$		0			0
$967$	−26.9862	+	22.6441i	−0.867818	+	0.728186i	−0.963637	−	0.267213i	$-0.913897\pi$
$967$	−26.9862	+	22.6441i	−0.867818	+	0.728186i	0.0958196	+	0.995399i	$0.469453\pi$
$968$		0			0
$969$	−4.07868	−	14.7028i	−0.131026	−	0.472323i
$970$		0			0
$971$	22.9117	+	27.3051i	0.735272	+	0.876263i	0.996019	−	0.0891439i	$-0.0284131\pi$
$971$	22.9117	+	27.3051i	0.735272	+	0.876263i	−0.260746	+	0.965407i	$0.583969\pi$
$972$		0			0
$973$	−34.6706	−	6.11337i	−1.11149	−	0.195986i
$974$		0			0
$975$	−12.3609	+	4.49899i	−0.395865	+	0.144083i
$976$		0			0
$977$	23.8606	+	41.3278i	0.763369	+	1.32219i	0.941105	+	0.338115i	$0.109789\pi$
$977$	23.8606	+	41.3278i	0.763369	+	1.32219i	−0.177736	+	0.984078i	$0.556877\pi$
$978$		0			0
$979$	0.830579	−	0.989845i	0.0265454	−	0.0316356i
$980$		0			0
$981$	−9.34701	−	5.39650i	−0.298427	−	0.172297i
$982$		0			0
$983$	−0.872531	−	4.94837i	−0.0278294	−	0.157829i	0.967726	−	0.252004i	$-0.0810896\pi$
$983$	−0.872531	−	4.94837i	−0.0278294	−	0.157829i	−0.995556	+	0.0941755i	$0.969979\pi$
$984$		0			0
$985$	−66.3820	−	24.1611i	−2.11511	−	0.769836i
$986$		0			0
$987$		−	8.74210i		−	0.278264i
$988$		0			0
$989$			2.10892i			0.0670598i
$990$		0			0
$991$	9.63806	+	3.50797i	0.306163	+	0.111434i	0.490533	−	0.871423i	$-0.336802\pi$
$991$	9.63806	+	3.50797i	0.306163	+	0.111434i	−0.184370	+	0.982857i	$0.559024\pi$
$992$		0			0
$993$	2.84136	+	16.1142i	0.0901679	+	0.511368i
$994$		0			0
$995$	−31.2270	−	18.0289i	−0.989961	−	0.571554i
$996$		0			0
$997$	10.2645	−	12.2327i	0.325079	−	0.387414i	−0.578610	−	0.815605i	$-0.696404\pi$
$997$	10.2645	−	12.2327i	0.325079	−	0.387414i	0.903688	+	0.428191i	$0.140849\pi$
$998$		0			0
$999$	−8.88957	−	15.3972i	−0.281253	−	0.487145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.bf.a.177.10		108
4.3	odd	2		152.2.t.a.101.8	yes	108
8.3	odd	2		152.2.t.a.101.1	✓	108
8.5	even	2	inner	608.2.bf.a.177.9		108
19.16	even	9	inner	608.2.bf.a.529.9		108
76.35	odd	18		152.2.t.a.149.1	yes	108
152.35	odd	18		152.2.t.a.149.8	yes	108
152.149	even	18	inner	608.2.bf.a.529.10		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.t.a.101.1	✓	108	8.3	odd	2
152.2.t.a.101.8	yes	108	4.3	odd	2
152.2.t.a.149.1	yes	108	76.35	odd	18
152.2.t.a.149.8	yes	108	152.35	odd	18
608.2.bf.a.177.9		108	8.5	even	2	inner
608.2.bf.a.177.10		108	1.1	even	1	trivial
608.2.bf.a.529.9		108	19.16	even	9	inner
608.2.bf.a.529.10		108	152.149	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.178255 - 0.489751i) q^{3} +(3.55335 - 0.626551i) q^{5} +(1.81103 - 3.13680i) q^{7} +(2.09005 + 1.75376i) q^{9} +(0.380026 - 0.219408i) q^{11} +(-1.07650 - 2.95765i) q^{13} +(0.326547 - 1.85194i) q^{15} +(-5.14502 + 4.31719i) q^{17} +(-4.34549 - 0.341661i) q^{19} +(-1.21343 - 1.44610i) q^{21} +(-0.958164 + 5.43402i) q^{23} +(7.53526 - 2.74261i) q^{25} +(2.58554 - 1.49276i) q^{27} +(1.67059 - 1.99093i) q^{29} +(-2.59436 + 4.49356i) q^{31} +(-0.0397139 - 0.225229i) q^{33} +(4.46986 - 12.2808i) q^{35} -5.95511i q^{37} -1.64040 q^{39} +(0.621322 + 0.226143i) q^{41} +(0.376394 - 0.0663684i) q^{43} +(8.52551 + 4.92220i) q^{45} +(3.54751 + 2.97672i) q^{47} +(-3.05967 - 5.29950i) q^{49} +(1.19722 + 3.28934i) q^{51} +(-13.0892 - 2.30798i) q^{53} +(1.21289 - 1.01774i) q^{55} +(-0.941933 + 2.06730i) q^{57} +(8.50400 + 10.1347i) q^{59} +(5.02192 + 0.885501i) q^{61} +(9.28635 - 3.37995i) q^{63} +(-5.67829 - 9.83508i) q^{65} +(-0.576990 + 0.687630i) q^{67} +(2.49052 + 1.43790i) q^{69} +(-1.20549 - 6.83668i) q^{71} +(3.14662 + 1.14528i) q^{73} -4.17929i q^{75} -1.58942i q^{77} +(6.23172 + 2.26816i) q^{79} +(1.15113 + 6.52839i) q^{81} +(-5.47269 - 3.15966i) q^{83} +(-15.5771 + 18.5641i) q^{85} +(-0.677270 - 1.17307i) q^{87} +(2.76705 - 1.00712i) q^{89} +(-11.2271 - 1.97964i) q^{91} +(1.73827 + 2.07159i) q^{93} +(-15.6551 + 1.50863i) q^{95} +(-3.66959 + 3.07915i) q^{97} +(1.17906 + 0.207901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 6 q^{7} - 12 q^{9} + 12 q^{15} - 12 q^{17} + 12 q^{23} - 12 q^{25} - 30 q^{31} - 30 q^{33} + 24 q^{39} - 24 q^{41} + 48 q^{47} - 24 q^{49} + 42 q^{55} - 12 q^{57} - 30 q^{63} - 6 q^{65} + 12 q^{71}+ \cdots - 12 q^{97}+O(q^{100}) \) 108 * q + 6 * q^7 - 12 * q^9 + 12 * q^15 - 12 * q^17 + 12 * q^23 - 12 * q^25 - 30 * q^31 - 30 * q^33 + 24 * q^39 - 24 * q^41 + 48 * q^47 - 24 * q^49 + 42 * q^55 - 12 * q^57 - 30 * q^63 - 6 * q^65 + 12 * q^71 + 12 * q^73 + 12 * q^79 - 18 * q^81 + 6 * q^87 - 12 * q^89 + 72 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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