LMFDB - Embedded newform 1998.2.k.a.1063.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1998,2,Mod(1063,1998)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1998.1063"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1998, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1998 = 2 \cdot 3^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1998.k (of order $6$, degree $2$, 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:	$15.9541103239$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 666)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1063.32
Character	$\chi$	$=$	1998.1063
Dual form			1998.2.k.a.1639.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000 q^{4} +0.372969i q^{5} +(0.0210491 - 0.0364581i) q^{7} -1.00000i q^{8} -0.372969 q^{10} +(-1.29042 - 2.23507i) q^{11} +2.23210i q^{13} +(0.0364581 + 0.0210491i) q^{14} +1.00000 q^{16} +(2.25134 + 1.29981i) q^{17} +(5.14372 - 2.96973i) q^{19} -0.372969i q^{20} +(2.23507 - 1.29042i) q^{22} +(-3.66709 - 2.11720i) q^{23} +4.86089 q^{25} -2.23210 q^{26} +(-0.0210491 + 0.0364581i) q^{28} +(0.672857 - 0.388474i) q^{29} +(-8.09859 - 4.67573i) q^{31} +1.00000i q^{32} +(-1.29981 + 2.25134i) q^{34} +(0.0135978 + 0.00785067i) q^{35} +(5.51271 - 2.57099i) q^{37} +(2.96973 + 5.14372i) q^{38} +0.372969 q^{40} -7.23366 q^{41} +(9.57847 - 5.53013i) q^{43} +(1.29042 + 2.23507i) q^{44} +(2.11720 - 3.66709i) q^{46} +(5.02395 + 8.70173i) q^{47} +(3.49911 + 6.06064i) q^{49} +4.86089i q^{50} -2.23210i q^{52} +(-3.61144 + 6.25519i) q^{53} +(0.833612 - 0.481286i) q^{55} +(-0.0364581 - 0.0210491i) q^{56} +(0.388474 + 0.672857i) q^{58} +(10.8565 - 6.26801i) q^{59} +(8.09882 + 4.67586i) q^{61} +(4.67573 - 8.09859i) q^{62} -1.00000 q^{64} -0.832506 q^{65} +2.32184 q^{67} +(-2.25134 - 1.29981i) q^{68} +(-0.00785067 + 0.0135978i) q^{70} +(0.342015 + 0.592387i) q^{71} +13.1748 q^{73} +(2.57099 + 5.51271i) q^{74} +(-5.14372 + 2.96973i) q^{76} -0.108649 q^{77} +(-3.39917 - 1.96251i) q^{79} +0.372969i q^{80} -7.23366i q^{82} +8.36842 q^{83} +(-0.484789 + 0.839680i) q^{85} +(5.53013 + 9.57847i) q^{86} +(-2.23507 + 1.29042i) q^{88} +(-5.63029 - 3.25065i) q^{89} +(0.0813784 + 0.0469838i) q^{91} +(3.66709 + 2.11720i) q^{92} +(-8.70173 + 5.02395i) q^{94} +(1.10762 + 1.91845i) q^{95} +(-5.13338 + 2.96376i) q^{97} +(-6.06064 + 3.49911i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} - 2 q^{7} + 4 q^{11} + 76 q^{16} - 12 q^{23} - 100 q^{25} + 24 q^{26} + 2 q^{28} - 18 q^{29} + 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} - 72 q^{41} + 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) $ 76 * q - 76 * q^4 - 2 * q^7 + 4 * q^11 + 76 * q^16 - 12 * q^23 - 100 * q^25 + 24 * q^26 + 2 * q^28 - 18 * q^29 + 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 - 72 * q^41 + 6 * q^43 - 4 * q^44 + 20 * q^47 - 36 * q^49 - 14 * q^53 + 6 * q^59 + 16 * q^62 - 76 * q^64 - 32 * q^65 + 40 * q^67 - 2 * q^71 + 28 * q^73 + 2 * q^74 + 24 * q^77 + 6 * q^79 + 64 * q^83 - 12 * q^85 - 4 * q^86 - 60 * q^89 + 42 * q^91 + 12 * q^92 + 14 * q^95 - 12 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1998\mathbb{Z}\right)^\times$.

$n$	$1297$	$1703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$			0.372969i			0.166797i	0.996516	+	0.0833985i	$0.0265774\pi$
$5$			0.372969i			0.166797i	−0.996516	+	0.0833985i	$0.973423\pi$
$6$		0			0
$7$	0.0210491	−	0.0364581i	0.00795582	−	0.0137799i	−0.862020	−	0.506874i	$-0.830801\pi$
$7$	0.0210491	−	0.0364581i	0.00795582	−	0.0137799i	0.869976	+	0.493094i	$0.164134\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.372969			−0.117943
$11$	−1.29042	−	2.23507i	−0.389076	−	0.673899i	0.603250	−	0.797552i	$-0.293872\pi$
$11$	−1.29042	−	2.23507i	−0.389076	−	0.673899i	−0.992325	+	0.123653i	$0.960539\pi$
$12$		0			0
$13$			2.23210i			0.619074i	0.950887	+	0.309537i	$0.100174\pi$
$13$			2.23210i			0.619074i	−0.950887	+	0.309537i	$0.899826\pi$
$14$	0.0364581	+	0.0210491i	0.00974385	+	0.00562561i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.25134	+	1.29981i	0.546030	+	0.315250i	0.747519	−	0.664240i	$-0.231245\pi$
$17$	2.25134	+	1.29981i	0.546030	+	0.315250i	−0.201489	+	0.979491i	$0.564578\pi$
$18$		0			0
$19$	5.14372	−	2.96973i	1.18005	−	0.681302i	0.224024	−	0.974584i	$-0.428081\pi$
$19$	5.14372	−	2.96973i	1.18005	−	0.681302i	0.956026	+	0.293281i	$0.0947472\pi$
$20$		−	0.372969i		−	0.0833985i
$21$		0			0
$22$	2.23507	−	1.29042i	0.476518	−	0.275118i
$23$	−3.66709	−	2.11720i	−0.764641	−	0.441466i	0.0663185	−	0.997799i	$-0.478875\pi$
$23$	−3.66709	−	2.11720i	−0.764641	−	0.441466i	−0.830960	+	0.556333i	$0.812208\pi$
$24$		0			0
$25$	4.86089			0.972179
$26$	−2.23210			−0.437751
$27$		0			0
$28$	−0.0210491	+	0.0364581i	−0.00397791	+	0.00688994i
$29$	0.672857	−	0.388474i	0.124946	−	0.0721379i	−0.436224	−	0.899838i	$-0.643685\pi$
$29$	0.672857	−	0.388474i	0.124946	−	0.0721379i	0.561171	+	0.827700i	$0.310351\pi$
$30$		0			0
$31$	−8.09859	−	4.67573i	−1.45455	−	0.839785i	−0.455816	−	0.890074i	$-0.650652\pi$
$31$	−8.09859	−	4.67573i	−1.45455	−	0.839785i	−0.998735	+	0.0502891i	$0.983986\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−1.29981	+	2.25134i	−0.222916	+	0.386101i
$35$	0.0135978	+	0.00785067i	0.00229844	+	0.00132701i
$36$		0			0
$37$	5.51271	−	2.57099i	0.906284	−	0.422669i
$37$	5.51271	−	2.57099i	0.906284	−	0.422669i
$38$	2.96973	+	5.14372i	0.481754	+	0.834422i
$39$		0			0
$40$	0.372969			0.0589716
$41$	−7.23366			−1.12971			−0.564854	−	0.825191i	$-0.691068\pi$
$41$	−7.23366			−1.12971			−0.564854	+	0.825191i	$0.691068\pi$
$42$		0			0
$43$	9.57847	−	5.53013i	1.46070	−	0.843337i	0.461659	−	0.887057i	$-0.347254\pi$
$43$	9.57847	−	5.53013i	1.46070	−	0.843337i	0.999044	+	0.0437202i	$0.0139210\pi$
$44$	1.29042	+	2.23507i	0.194538	+	0.336949i
$45$		0			0
$46$	2.11720	−	3.66709i	0.312163	−	0.540683i
$47$	5.02395	+	8.70173i	0.732818	+	1.26928i	0.955674	+	0.294427i	$0.0951287\pi$
$47$	5.02395	+	8.70173i	0.732818	+	1.26928i	−0.222856	+	0.974851i	$0.571538\pi$
$48$		0			0
$49$	3.49911	+	6.06064i	0.499873	+	0.865806i
$50$			4.86089i			0.687434i
$51$		0			0
$52$		−	2.23210i		−	0.309537i
$53$	−3.61144	+	6.25519i	−0.496069	+	0.859217i	−0.999990	−	0.00453324i	$-0.998557\pi$
$53$	−3.61144	+	6.25519i	−0.496069	+	0.859217i	0.503921	+	0.863750i	$0.331890\pi$
$54$		0			0
$55$	0.833612	−	0.481286i	0.112404	−	0.0648966i
$56$	−0.0364581	−	0.0210491i	−0.00487192	−	0.00281281i
$57$		0			0
$58$	0.388474	+	0.672857i	0.0510092	+	0.0883505i
$59$	10.8565	−	6.26801i	1.41340	−	0.816025i	0.417690	−	0.908589i	$-0.362840\pi$
$59$	10.8565	−	6.26801i	1.41340	−	0.816025i	0.995707	+	0.0925642i	$0.0295063\pi$
$60$		0			0
$61$	8.09882	+	4.67586i	1.03695	+	0.598682i	0.918967	−	0.394334i	$-0.129025\pi$
$61$	8.09882	+	4.67586i	1.03695	+	0.598682i	0.117980	+	0.993016i	$0.462358\pi$
$62$	4.67573	−	8.09859i	0.593818	−	1.02852i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.832506			−0.103260
$66$		0			0
$67$	2.32184			0.283658			0.141829	−	0.989891i	$-0.454702\pi$
$67$	2.32184			0.283658			0.141829	+	0.989891i	$0.454702\pi$
$68$	−2.25134	−	1.29981i	−0.273015	−	0.157625i
$69$		0			0
$70$	−0.00785067	+	0.0135978i	−0.000938335	+	0.00162524i
$71$	0.342015	+	0.592387i	0.0405897	+	0.0703034i	0.885607	−	0.464436i	$-0.153743\pi$
$71$	0.342015	+	0.592387i	0.0405897	+	0.0703034i	−0.845017	+	0.534740i	$0.820410\pi$
$72$		0			0
$73$	13.1748			1.54199			0.770995	−	0.636841i	$-0.219759\pi$
$73$	13.1748			1.54199			0.770995	+	0.636841i	$0.219759\pi$
$74$	2.57099	+	5.51271i	0.298872	+	0.640840i
$75$		0			0
$76$	−5.14372	+	2.96973i	−0.590025	+	0.340651i
$77$	−0.108649			−0.0123817
$78$		0			0
$79$	−3.39917	−	1.96251i	−0.382436	−	0.220800i	0.296442	−	0.955051i	$-0.404200\pi$
$79$	−3.39917	−	1.96251i	−0.382436	−	0.220800i	−0.678878	+	0.734251i	$0.737533\pi$
$80$			0.372969i			0.0416992i
$81$		0			0
$82$		−	7.23366i		−	0.798825i
$83$	8.36842			0.918554			0.459277	−	0.888293i	$-0.348109\pi$
$83$	8.36842			0.918554			0.459277	+	0.888293i	$0.348109\pi$
$84$		0			0
$85$	−0.484789	+	0.839680i	−0.0525828	+	0.0910761i
$86$	5.53013	+	9.57847i	0.596329	+	1.03287i
$87$		0			0
$88$	−2.23507	+	1.29042i	−0.238259	+	0.137559i
$89$	−5.63029	−	3.25065i	−0.596809	−	0.344568i	0.170976	−	0.985275i	$-0.445308\pi$
$89$	−5.63029	−	3.25065i	−0.596809	−	0.344568i	−0.767785	+	0.640707i	$0.778641\pi$
$90$		0			0
$91$	0.0813784	+	0.0469838i	0.00853077	+	0.00492524i
$92$	3.66709	+	2.11720i	0.382321	+	0.220733i
$93$		0			0
$94$	−8.70173	+	5.02395i	−0.897515	+	0.518181i
$95$	1.10762	+	1.91845i	0.113639	+	0.196829i
$96$		0			0
$97$	−5.13338	+	2.96376i	−0.521216	+	0.300924i	−0.737432	−	0.675421i	$-0.763962\pi$
$97$	−5.13338	+	2.96376i	−0.521216	+	0.300924i	0.216216	+	0.976346i	$0.430628\pi$
$98$	−6.06064	+	3.49911i	−0.612217	+	0.353464i
$99$		0			0
$100$	−4.86089			−0.486089
$101$	−4.82354	−	8.35461i	−0.479960	−	0.831315i	0.519776	−	0.854303i	$-0.326015\pi$
$101$	−4.82354	−	8.35461i	−0.479960	−	0.831315i	−0.999736	+	0.0229877i	$0.992682\pi$
$102$		0			0
$103$	0.515555	+	0.297656i	0.0507991	+	0.0293289i	0.525184	−	0.850988i	$-0.323996\pi$
$103$	0.515555	+	0.297656i	0.0507991	+	0.0293289i	−0.474385	+	0.880317i	$0.657330\pi$
$104$	2.23210			0.218876
$105$		0			0
$106$	−6.25519	−	3.61144i	−0.607558	−	0.350774i
$107$	−4.79286	−	8.30148i	−0.463343	−	0.802534i	0.535782	−	0.844357i	$-0.320017\pi$
$107$	−4.79286	−	8.30148i	−0.463343	−	0.802534i	−0.999125	+	0.0418223i	$0.986684\pi$
$108$		0			0
$109$	8.01087	+	4.62508i	0.767302	+	0.443002i	0.831911	−	0.554909i	$-0.187247\pi$
$109$	8.01087	+	4.62508i	0.767302	+	0.443002i	−0.0646094	+	0.997911i	$0.520580\pi$
$110$	0.481286	+	0.833612i	0.0458888	+	0.0794818i
$111$		0			0
$112$	0.0210491	−	0.0364581i	0.00198895	−	0.00344497i
$113$	13.3019	−	7.67987i	1.25134	−	0.722462i	0.279965	−	0.960010i	$-0.409677\pi$
$113$	13.3019	−	7.67987i	1.25134	−	0.722462i	0.971376	+	0.237549i	$0.0763439\pi$
$114$		0			0
$115$	0.789649	−	1.36771i	0.0736351	−	0.127540i
$116$	−0.672857	+	0.388474i	−0.0624732	+	0.0360689i
$117$		0			0
$118$	6.26801	+	10.8565i	0.577017	+	0.999423i
$119$	0.0947774	−	0.0547197i	0.00868823	−	0.00501615i
$120$		0			0
$121$	2.16964	−	3.75793i	0.197240	−	0.341630i
$122$	−4.67586	+	8.09882i	−0.423332	+	0.733233i
$123$		0			0
$124$	8.09859	+	4.67573i	0.727275	+	0.419893i
$125$			3.67781i			0.328953i
$126$		0			0
$127$	−1.27625	+	2.21054i	−0.113249	+	0.196153i	−0.917079	−	0.398707i	$-0.869459\pi$
$127$	−1.27625	+	2.21054i	−0.113249	+	0.196153i	0.803829	+	0.594860i	$0.202792\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$		−	0.832506i		−	0.0730156i
$131$	−9.82049	+	5.66986i	−0.858020	+	0.495378i	−0.863349	−	0.504608i	$-0.831637\pi$
$131$	−9.82049	+	5.66986i	−0.858020	+	0.495378i	0.00532877	+	0.999986i	$0.498304\pi$
$132$		0			0
$133$		−	0.250041i		−	0.0216813i
$134$			2.32184i			0.200576i
$135$		0			0
$136$	1.29981	−	2.25134i	0.111458	−	0.193051i
$137$	7.60904	+	13.1792i	0.650084	+	1.12598i	0.983102	+	0.183058i	$0.0585997\pi$
$137$	7.60904	+	13.1792i	0.650084	+	1.12598i	−0.333018	+	0.942921i	$0.608067\pi$
$138$		0			0
$139$	8.10261	+	14.0341i	0.687254	+	1.19036i	0.972723	+	0.231971i	$0.0745175\pi$
$139$	8.10261	+	14.0341i	0.687254	+	1.19036i	−0.285468	+	0.958388i	$0.592149\pi$
$140$	−0.0135978	−	0.00785067i	−0.00114922	−	0.000663503i
$141$		0			0
$142$	−0.592387	+	0.342015i	−0.0497120	+	0.0287013i
$143$	4.98891	−	2.88035i	0.417193	−	0.240867i
$144$		0			0
$145$	0.144889	+	0.250955i	0.0120324	+	0.0208407i
$146$			13.1748i			1.09035i
$147$		0			0
$148$	−5.51271	+	2.57099i	−0.453142	+	0.211334i
$149$	−0.177156	+	0.306844i	−0.0145132	+	0.0251376i	−0.873191	−	0.487379i	$-0.837953\pi$
$149$	−0.177156	+	0.306844i	−0.0145132	+	0.0251376i	0.858678	+	0.512516i	$0.171287\pi$
$150$		0			0
$151$	−3.44680	+	5.97003i	−0.280496	+	0.485834i	−0.971507	−	0.237010i	$-0.923832\pi$
$151$	−3.44680	+	5.97003i	−0.280496	+	0.485834i	0.691011	+	0.722845i	$0.257166\pi$
$152$	−2.96973	−	5.14372i	−0.240877	−	0.417211i
$153$		0			0
$154$		−	0.108649i		−	0.00875516i
$155$	1.74390	−	3.02053i	0.140074	−	0.242615i
$156$		0			0
$157$	−5.77978	−	10.0109i	−0.461276	−	0.798954i	0.537749	−	0.843105i	$-0.319275\pi$
$157$	−5.77978	−	10.0109i	−0.461276	−	0.798954i	−0.999025	+	0.0441513i	$0.985942\pi$
$158$	1.96251	−	3.39917i	0.156129	−	0.270423i
$159$		0			0
$160$	−0.372969			−0.0294858
$161$	−0.154378	+	0.0891302i	−0.0121667	+	0.00702444i
$162$		0			0
$163$	12.6667	+	7.31312i	0.992132	+	0.572808i	0.905911	−	0.423468i	$-0.139187\pi$
$163$	12.6667	+	7.31312i	0.992132	+	0.572808i	0.0862213	+	0.996276i	$0.472521\pi$
$164$	7.23366			0.564854
$165$		0			0
$166$			8.36842i			0.649515i
$167$			11.6626i			0.902478i	0.892403	+	0.451239i	$0.149018\pi$
$167$			11.6626i			0.902478i	−0.892403	+	0.451239i	$0.850982\pi$
$168$		0			0
$169$	8.01771			0.616747
$170$	−0.839680	−	0.484789i	−0.0644005	−	0.0371816i
$171$		0			0
$172$	−9.57847	+	5.53013i	−0.730351	+	0.421669i
$173$	0.0584707			0.00444544			0.00222272	−	0.999998i	$-0.499292\pi$
$173$	0.0584707			0.00444544			0.00222272	+	0.999998i	$0.499292\pi$
$174$		0			0
$175$	0.102318	−	0.177219i	0.00773448	−	0.0133965i
$176$	−1.29042	−	2.23507i	−0.0972689	−	0.168475i
$177$		0			0
$178$	3.25065	−	5.63029i	0.243646	−	0.422008i
$179$		−	8.49336i		−	0.634823i	−0.948288	−	0.317412i	$-0.897186\pi$
$179$		−	8.49336i		−	0.634823i	0.948288	−	0.317412i	$-0.102814\pi$
$180$		0			0
$181$	8.04344	+	13.9316i	0.597864	+	1.03553i	0.993136	+	0.116967i	$0.0373171\pi$
$181$	8.04344	+	13.9316i	0.597864	+	1.03553i	−0.395272	+	0.918564i	$0.629350\pi$
$182$	−0.0469838	+	0.0813784i	−0.00348267	+	0.00603216i
$183$		0			0
$184$	−2.11720	+	3.66709i	−0.156082	+	0.270341i
$185$	0.958902	+	2.05607i	0.0704999	+	0.151165i
$186$		0			0
$187$		−	6.70920i		−	0.490625i
$188$	−5.02395	−	8.70173i	−0.366409	−	0.634639i
$189$		0			0
$190$	−1.91845	+	1.10762i	−0.139179	+	0.0803550i
$191$	7.11315	−	4.10678i	0.514689	−	0.297156i	−0.220070	−	0.975484i	$-0.570628\pi$
$191$	7.11315	−	4.10678i	0.514689	−	0.297156i	0.734759	+	0.678328i	$0.237295\pi$
$192$		0			0
$193$	−16.6788	−	9.62948i	−1.20056	−	0.693145i	−0.239883	−	0.970802i	$-0.577109\pi$
$193$	−16.6788	−	9.62948i	−1.20056	−	0.693145i	−0.960680	+	0.277656i	$0.910442\pi$
$194$	−2.96376	−	5.13338i	−0.212785	−	0.368555i
$195$		0			0
$196$	−3.49911	−	6.06064i	−0.249937	−	0.432903i
$197$	0.245783	−	0.425708i	0.0175113	−	0.0303304i	−0.857137	−	0.515089i	$-0.827759\pi$
$197$	0.245783	−	0.425708i	0.0175113	−	0.0303304i	0.874648	+	0.484758i	$0.161092\pi$
$198$		0			0
$199$			10.8937i			0.772236i	0.922449	+	0.386118i	$0.126184\pi$
$199$			10.8937i			0.772236i	−0.922449	+	0.386118i	$0.873816\pi$
$200$		−	4.86089i		−	0.343717i
$201$		0			0
$202$	8.35461	−	4.82354i	0.587828	−	0.339383i
$203$		−	0.0327082i		−	0.00229566i
$204$		0			0
$205$		−	2.69793i		−	0.188432i
$206$	−0.297656	+	0.515555i	−0.0207387	+	0.0359204i
$207$		0			0
$208$			2.23210i			0.154769i
$209$	−13.2751	−	7.66438i	−0.918258	−	0.530156i
$210$		0			0
$211$	6.38957	−	11.0671i	0.439876	−	0.761888i	−0.557803	−	0.829973i	$-0.688356\pi$
$211$	6.38957	−	11.0671i	0.439876	−	0.761888i	0.997680	+	0.0680853i	$0.0216890\pi$
$212$	3.61144	−	6.25519i	0.248034	−	0.429608i
$213$		0			0
$214$	8.30148	−	4.79286i	0.567477	−	0.327633i
$215$	2.06257	+	3.57247i	0.140666	+	0.243641i
$216$		0			0
$217$	−0.340937	+	0.196840i	−0.0231443	+	0.0133624i
$218$	−4.62508	+	8.01087i	−0.313250	+	0.542564i
$219$		0			0
$220$	−0.833612	+	0.481286i	−0.0562021	+	0.0324483i
$221$	−2.90131	+	5.02522i	−0.195163	+	0.338033i
$222$		0			0
$223$	−14.1726	−	24.5477i	−0.949067	−	1.64383i	−0.747395	−	0.664380i	$-0.768696\pi$
$223$	−14.1726	−	24.5477i	−0.949067	−	1.64383i	−0.201673	−	0.979453i	$-0.564638\pi$
$224$	0.0364581	+	0.0210491i	0.00243596	+	0.00140640i
$225$		0			0
$226$	7.67987	+	13.3019i	0.510858	+	0.884831i
$227$	0.708998	+	0.409340i	0.0470579	+	0.0271689i	0.523344	−	0.852121i	$-0.324684\pi$
$227$	0.708998	+	0.409340i	0.0470579	+	0.0271689i	−0.476286	+	0.879290i	$0.658017\pi$
$228$		0			0
$229$	−17.3120			−1.14401			−0.572004	−	0.820251i	$-0.693834\pi$
$229$	−17.3120			−1.14401			−0.572004	+	0.820251i	$0.693834\pi$
$230$	1.36771	+	0.789649i	0.0901842	+	0.0520679i
$231$		0			0
$232$	−0.388474	−	0.672857i	−0.0255046	−	0.0441752i
$233$	9.20929			0.603320			0.301660	−	0.953416i	$-0.402459\pi$
$233$	9.20929			0.603320			0.301660	+	0.953416i	$0.402459\pi$
$234$		0			0
$235$	−3.24548	+	1.87378i	−0.211712	+	0.122232i
$236$	−10.8565	+	6.26801i	−0.706699	+	0.408013i
$237$		0			0
$238$	0.0547197	+	0.0947774i	0.00354695	+	0.00614350i
$239$	2.00849	−	1.15960i	0.129918	−	0.0750084i	−0.433632	−	0.901090i	$-0.642768\pi$
$239$	2.00849	−	1.15960i	0.129918	−	0.0750084i	0.563551	+	0.826082i	$0.309435\pi$
$240$		0			0
$241$	−5.75406	−	3.32211i	−0.370652	−	0.213996i	0.303091	−	0.952961i	$-0.401981\pi$
$241$	−5.75406	−	3.32211i	−0.370652	−	0.213996i	−0.673743	+	0.738966i	$0.735315\pi$
$242$	3.75793	+	2.16964i	0.241569	+	0.139470i
$243$		0			0
$244$	−8.09882	−	4.67586i	−0.518474	−	0.299341i
$245$	−2.26043	+	1.30506i	−0.144414	+	0.0833773i
$246$		0			0
$247$	6.62874	+	11.4813i	0.421777	+	0.730539i
$248$	−4.67573	+	8.09859i	−0.296909	+	0.514261i
$249$		0			0
$250$	−3.67781			−0.232605
$251$			26.2916i			1.65951i	0.558128	+	0.829755i	$0.311520\pi$
$251$			26.2916i			1.65951i	−0.558128	+	0.829755i	$0.688480\pi$
$252$		0			0
$253$			10.9283i			0.687054i
$254$	−2.21054	−	1.27625i	−0.138701	−	0.0800792i
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.35277	−	3.66777i	0.396275	−	0.228789i	−0.288600	−	0.957450i	$-0.593190\pi$
$257$	6.35277	−	3.66777i	0.396275	−	0.228789i	0.684875	+	0.728660i	$0.259857\pi$
$258$		0			0
$259$	0.0223041	−	0.255100i	0.00138591	−	0.0158512i
$260$	0.832506			0.0516298
$261$		0			0
$262$	−5.66986	−	9.82049i	−0.350285	−	0.606712i
$263$	10.2772	−	17.8006i	0.633719	−	1.09763i	−0.353066	−	0.935598i	$-0.614861\pi$
$263$	10.2772	−	17.8006i	0.633719	−	1.09763i	0.986785	−	0.162035i	$-0.0518057\pi$
$264$		0			0
$265$	−2.33299	−	1.34695i	−0.143315	−	0.0827428i
$266$	0.250041			0.0153310
$267$		0			0
$268$	−2.32184			−0.141829
$269$	−25.4958			−1.55450			−0.777252	−	0.629189i	$-0.783387\pi$
$269$	−25.4958			−1.55450			−0.777252	+	0.629189i	$0.783387\pi$
$270$		0			0
$271$	10.5407	−	18.2571i	0.640303	−	1.10904i	−0.345062	−	0.938580i	$-0.612142\pi$
$271$	10.5407	−	18.2571i	0.640303	−	1.10904i	0.985365	−	0.170457i	$-0.0545245\pi$
$272$	2.25134	+	1.29981i	0.136507	+	0.0788126i
$273$		0			0
$274$	−13.1792	+	7.60904i	−0.796187	+	0.459679i
$275$	−6.27259	−	10.8644i	−0.378251	−	0.655150i
$276$		0			0
$277$	−14.3138	−	8.26407i	−0.860032	−	0.496540i	0.00399116	−	0.999992i	$-0.498730\pi$
$277$	−14.3138	−	8.26407i	−0.860032	−	0.496540i	−0.864023	+	0.503452i	$0.832063\pi$
$278$	−14.0341	+	8.10261i	−0.841711	+	0.485962i
$279$		0			0
$280$	0.00785067	−	0.0135978i	0.000469168	−	0.000812622i
$281$		−	2.09286i		−	0.124849i	−0.998050	−	0.0624247i	$-0.980117\pi$
$281$		−	2.09286i		−	0.124849i	0.998050	−	0.0624247i	$-0.0198833\pi$
$282$		0			0
$283$		−	9.75704i		−	0.579996i	−0.957027	−	0.289998i	$-0.906345\pi$
$283$		−	9.75704i		−	0.579996i	0.957027	−	0.289998i	$-0.0936546\pi$
$284$	−0.342015	−	0.592387i	−0.0202948	−	0.0351517i
$285$		0			0
$286$	2.88035	+	4.98891i	0.170318	+	0.295000i
$287$	−0.152262	+	0.263726i	−0.00898776	+	0.0155673i
$288$		0			0
$289$	−5.12098	−	8.86981i	−0.301234	−	0.521753i
$290$	−0.250955	+	0.144889i	−0.0147366	+	0.00850817i
$291$		0			0
$292$	−13.1748			−0.770995
$293$	1.38135			0.0806992			0.0403496	−	0.999186i	$-0.487153\pi$
$293$	1.38135			0.0806992			0.0403496	+	0.999186i	$0.487153\pi$
$294$		0			0
$295$	2.33777	+	4.04914i	0.136110	+	0.235750i
$296$	−2.57099	−	5.51271i	−0.149436	−	0.320420i
$297$		0			0
$298$	−0.306844	−	0.177156i	−0.0177750	−	0.0102624i
$299$	4.72580	−	8.18532i	0.273300	−	0.473370i
$300$		0			0
$301$		−	0.465618i		−	0.0268378i
$302$	−5.97003	−	3.44680i	−0.343537	−	0.198341i
$303$		0			0
$304$	5.14372	−	2.96973i	0.295013	−	0.170326i
$305$	−1.74395	+	3.02061i	−0.0998583	+	0.172960i
$306$		0			0
$307$	−22.3771			−1.27713			−0.638564	−	0.769569i	$-0.720471\pi$
$307$	−22.3771			−1.27713			−0.638564	+	0.769569i	$0.720471\pi$
$308$	0.108649			0.00619083
$309$		0			0
$310$	3.02053	+	1.74390i	0.171554	+	0.0990470i
$311$	24.5656	−	14.1829i	1.39299	−	0.804241i	0.399342	−	0.916802i	$-0.369239\pi$
$311$	24.5656	−	14.1829i	1.39299	−	0.804241i	0.993645	+	0.112561i	$0.0359054\pi$
$312$		0			0
$313$			13.8093i			0.780548i	0.920699	+	0.390274i	$0.127620\pi$
$313$			13.8093i			0.780548i	−0.920699	+	0.390274i	$0.872380\pi$
$314$	10.0109	−	5.77978i	0.564946	−	0.326172i
$315$		0			0
$316$	3.39917	+	1.96251i	0.191218	+	0.110400i
$317$	−7.32076			−0.411175			−0.205587	−	0.978639i	$-0.565910\pi$
$317$	−7.32076			−0.411175			−0.205587	+	0.978639i	$0.565910\pi$
$318$		0			0
$319$	−1.73653	−	1.00259i	−0.0972273	−	0.0561342i
$320$		−	0.372969i		−	0.0208496i
$321$		0			0
$322$	−0.0891302	−	0.154378i	−0.00496703	−	0.00860315i
$323$	15.4403			0.859123
$324$		0			0
$325$			10.8500i			0.601851i
$326$	−7.31312	+	12.6667i	−0.405036	+	0.701543i
$327$		0			0
$328$			7.23366i			0.399412i
$329$	0.422999			0.0233207
$330$		0			0
$331$			13.2880i			0.730376i	0.930934	+	0.365188i	$0.118995\pi$
$331$			13.2880i			0.730376i	−0.930934	+	0.365188i	$0.881005\pi$
$332$	−8.36842			−0.459277
$333$		0			0
$334$	−11.6626			−0.638148
$335$			0.865975i			0.0473133i
$336$		0			0
$337$	−9.96243			−0.542688			−0.271344	−	0.962482i	$-0.587468\pi$
$337$	−9.96243			−0.542688			−0.271344	+	0.962482i	$0.587468\pi$
$338$			8.01771i			0.436106i
$339$		0			0
$340$	0.484789	−	0.839680i	0.0262914	−	0.0455380i
$341$			24.1346i			1.30696i
$342$		0			0
$343$	0.589301			0.0318193
$344$	−5.53013	−	9.57847i	−0.298165	−	0.516436i
$345$		0			0
$346$			0.0584707i			0.00314340i
$347$	−18.1956	−	10.5053i	−0.976793	−	0.563952i	−0.0754928	−	0.997146i	$-0.524053\pi$
$347$	−18.1956	−	10.5053i	−0.976793	−	0.563952i	−0.901300	+	0.433195i	$0.857386\pi$
$348$		0			0
$349$	−30.7742			−1.64730			−0.823652	−	0.567095i	$-0.808067\pi$
$349$	−30.7742			−1.64730			−0.823652	+	0.567095i	$0.808067\pi$
$350$	0.177219	+	0.102318i	0.00947276	+	0.00546910i
$351$		0			0
$352$	2.23507	−	1.29042i	0.119130	−	0.0687795i
$353$		−	0.288111i		−	0.0153346i	−0.999971	−	0.00766729i	$-0.997559\pi$
$353$		−	0.288111i		−	0.0153346i	0.999971	−	0.00766729i	$-0.00244060\pi$
$354$		0			0
$355$	−0.220942	+	0.127561i	−0.0117264	+	0.00677024i
$356$	5.63029	+	3.25065i	0.298405	+	0.172284i
$357$		0			0
$358$	8.49336			0.448888
$359$	6.45640			0.340756			0.170378	−	0.985379i	$-0.445501\pi$
$359$	6.45640			0.340756			0.170378	+	0.985379i	$0.445501\pi$
$360$		0			0
$361$	8.13857	−	14.0964i	0.428346	−	0.741917i
$362$	−13.9316	+	8.04344i	−0.732231	+	0.422754i
$363$		0			0
$364$	−0.0813784	−	0.0469838i	−0.00426538	−	0.00246262i
$365$			4.91378i			0.257199i
$366$		0			0
$367$	18.2746	−	31.6525i	0.953924	−	1.65225i	0.217113	−	0.976146i	$-0.430336\pi$
$367$	18.2746	−	31.6525i	0.953924	−	1.65225i	0.736811	−	0.676099i	$-0.236331\pi$
$368$	−3.66709	−	2.11720i	−0.191160	−	0.110366i
$369$		0			0
$370$	−2.05607	+	0.958902i	−0.106890	+	0.0498509i
$371$	0.152035	+	0.263333i	0.00789327	+	0.0136715i
$372$		0			0
$373$	2.94276			0.152370			0.0761851	−	0.997094i	$-0.475726\pi$
$373$	2.94276			0.152370			0.0761851	+	0.997094i	$0.475726\pi$
$374$	6.70920			0.346924
$375$		0			0
$376$	8.70173	−	5.02395i	0.448758	−	0.259090i
$377$	0.867115	+	1.50189i	0.0446587	+	0.0773511i
$378$		0			0
$379$	−1.75610	+	3.04166i	−0.0902049	+	0.156239i	−0.907597	−	0.419842i	$-0.862086\pi$
$379$	−1.75610	+	3.04166i	−0.0902049	+	0.156239i	0.817392	+	0.576081i	$0.195419\pi$
$380$	−1.10762	−	1.91845i	−0.0568196	−	0.0984144i
$381$		0			0
$382$	4.10678	+	7.11315i	0.210121	+	0.363940i
$383$		−	17.2557i		−	0.881725i	−0.897575	−	0.440863i	$-0.854673\pi$
$383$		−	17.2557i		−	0.881725i	0.897575	−	0.440863i	$-0.145327\pi$
$384$		0			0
$385$		−	0.0405226i		−	0.00206522i
$386$	9.62948	−	16.6788i	0.490128	−	0.848926i
$387$		0			0
$388$	5.13338	−	2.96376i	0.260608	−	0.150462i
$389$	−16.2892	−	9.40455i	−0.825893	−	0.476830i	0.0265513	−	0.999647i	$-0.491547\pi$
$389$	−16.2892	−	9.40455i	−0.825893	−	0.476830i	−0.852444	+	0.522818i	$0.824881\pi$
$390$		0			0
$391$	−5.50391	−	9.53305i	−0.278345	−	0.482107i
$392$	6.06064	−	3.49911i	0.306109	−	0.176732i
$393$		0			0
$394$	0.425708	+	0.245783i	0.0214469	+	0.0123824i
$395$	0.731956	−	1.26778i	0.0368287	−	0.0637891i
$396$		0			0
$397$	7.41696			0.372246			0.186123	−	0.982526i	$-0.440408\pi$
$397$	7.41696			0.372246			0.186123	+	0.982526i	$0.440408\pi$
$398$	−10.8937			−0.546053
$399$		0			0
$400$	4.86089			0.243045
$401$	17.6319	+	10.1798i	0.880496	+	0.508354i	0.870822	−	0.491599i	$-0.163587\pi$
$401$	17.6319	+	10.1798i	0.880496	+	0.508354i	0.00967393	+	0.999953i	$0.496921\pi$
$402$		0			0
$403$	10.4367	−	18.0769i	0.519889	−	0.900474i
$404$	4.82354	+	8.35461i	0.239980	+	0.415658i
$405$		0			0
$406$	0.0327082			0.00162328
$407$	−12.8601	−	9.00364i	−0.637449	−	0.446294i
$408$		0			0
$409$	−6.60183	+	3.81157i	−0.326439	+	0.188470i	−0.654259	−	0.756270i	$-0.727019\pi$
$409$	−6.60183	+	3.81157i	−0.326439	+	0.188470i	0.327820	+	0.944740i	$0.393686\pi$
$410$	2.69793			0.133241
$411$		0			0
$412$	−0.515555	−	0.297656i	−0.0253996	−	0.0146644i
$413$		−	0.527744i		−	0.0259686i
$414$		0			0
$415$			3.12116i			0.153212i
$416$	−2.23210			−0.109438
$417$		0			0
$418$	7.66438	−	13.2751i	0.374877	−	0.649306i
$419$	−17.2784	−	29.9271i	−0.844106	−	1.46203i	−0.886395	−	0.462929i	$-0.846798\pi$
$419$	−17.2784	−	29.9271i	−0.844106	−	1.46203i	0.0422892	−	0.999105i	$-0.486535\pi$
$420$		0			0
$421$	16.1271	−	9.31096i	0.785985	−	0.453789i	−0.0525623	−	0.998618i	$-0.516739\pi$
$421$	16.1271	−	9.31096i	0.785985	−	0.453789i	0.838547	+	0.544829i	$0.183405\pi$
$422$	11.0671	+	6.38957i	0.538736	+	0.311039i
$423$		0			0
$424$	6.25519	+	3.61144i	0.303779	+	0.175387i
$425$	10.9435	+	6.31824i	0.530838	+	0.306480i
$426$		0			0
$427$	0.340946	−	0.196845i	0.0164995	−	0.00952601i
$428$	4.79286	+	8.30148i	0.231672	+	0.401267i
$429$		0			0
$430$	−3.57247	+	2.06257i	−0.172280	+	0.0994659i
$431$	−18.6073	+	10.7429i	−0.896281	+	0.517468i	−0.875992	−	0.482326i	$-0.839792\pi$
$431$	−18.6073	+	10.7429i	−0.896281	+	0.517468i	−0.0202895	+	0.999794i	$0.506459\pi$
$432$		0			0
$433$	−30.8001			−1.48016			−0.740080	−	0.672519i	$-0.765212\pi$
$433$	−30.8001			−1.48016			−0.740080	+	0.672519i	$0.765212\pi$
$434$	−0.196840	−	0.340937i	−0.00944861	−	0.0163655i
$435$		0			0
$436$	−8.01087	−	4.62508i	−0.383651	−	0.221501i
$437$	−25.1500			−1.20309
$438$		0			0
$439$	−25.6425	−	14.8047i	−1.22385	−	0.706590i	−0.258114	−	0.966115i	$-0.583101\pi$
$439$	−25.6425	−	14.8047i	−1.22385	−	0.706590i	−0.965737	+	0.259524i	$0.916434\pi$
$440$	−0.481286	−	0.833612i	−0.0229444	−	0.0397409i
$441$		0			0
$442$	−5.02522	−	2.90131i	−0.239025	−	0.138001i
$443$	−0.902430	−	1.56305i	−0.0428758	−	0.0742630i	0.843791	−	0.536672i	$-0.180319\pi$
$443$	−0.902430	−	1.56305i	−0.0428758	−	0.0742630i	−0.886667	+	0.462409i	$0.846985\pi$
$444$		0			0
$445$	1.21239	−	2.09992i	0.0574729	−	0.0995459i
$446$	24.5477	−	14.1726i	1.16237	−	0.671092i
$447$		0			0
$448$	−0.0210491	+	0.0364581i	−0.000994477	+	0.00172249i
$449$	32.7760	−	18.9232i	1.54679	−	0.893042i	0.548410	−	0.836210i	$-0.315233\pi$
$449$	32.7760	−	18.9232i	1.54679	−	0.893042i	0.998384	−	0.0568322i	$-0.0181000\pi$
$450$		0			0
$451$	9.33445	+	16.1677i	0.439542	+	0.761309i
$452$	−13.3019	+	7.67987i	−0.625670	+	0.361231i
$453$		0			0
$454$	−0.409340	+	0.708998i	−0.0192113	+	0.0332749i
$455$	−0.0175235	+	0.0303516i	−0.000821515	+	0.00142291i
$456$		0			0
$457$	12.9779	+	7.49278i	0.607079	+	0.350497i	0.771821	−	0.635839i	$-0.219346\pi$
$457$	12.9779	+	7.49278i	0.607079	+	0.350497i	−0.164742	+	0.986337i	$0.552679\pi$
$458$		−	17.3120i		−	0.808936i
$459$		0			0
$460$	−0.789649	+	1.36771i	−0.0368176	+	0.0637699i
$461$		−	17.8177i		−	0.829852i	−0.909855	−	0.414926i	$-0.863807\pi$
$461$		−	17.8177i		−	0.829852i	0.909855	−	0.414926i	$-0.136193\pi$
$462$		0			0
$463$			23.2712i			1.08150i	0.841182	+	0.540752i	$0.181860\pi$
$463$			23.2712i			1.08150i	−0.841182	+	0.540752i	$0.818140\pi$
$464$	0.672857	−	0.388474i	0.0312366	−	0.0180345i
$465$		0			0
$466$			9.20929i			0.426612i
$467$			17.6430i			0.816422i	0.912888	+	0.408211i	$0.133847\pi$
$467$			17.6430i			0.816422i	−0.912888	+	0.408211i	$0.866153\pi$
$468$		0			0
$469$	0.0488727	−	0.0846500i	0.00225673	−	0.00390877i
$470$	−1.87378	−	3.24548i	−0.0864309	−	0.149703i
$471$		0			0
$472$	−6.26801	−	10.8565i	−0.288508	−	0.499711i
$473$	−24.7205	−	14.2724i	−1.13665	−	0.656244i
$474$		0			0
$475$	25.0031	−	14.4355i	1.14722	−	0.662348i
$476$	−0.0947774	+	0.0547197i	−0.00434411	+	0.00250808i
$477$		0			0
$478$	1.15960	+	2.00849i	0.0530389	+	0.0918661i
$479$		−	1.87253i		−	0.0855583i	−0.999085	−	0.0427791i	$-0.986379\pi$
$479$		−	1.87253i		−	0.0855583i	0.999085	−	0.0427791i	$-0.0136212\pi$
$480$		0			0
$481$	5.73872	+	12.3049i	0.261663	+	0.561057i
$482$	3.32211	−	5.75406i	0.151318	−	0.262090i
$483$		0			0
$484$	−2.16964	+	3.75793i	−0.0986201	+	0.170815i
$485$	−1.10539	−	1.91459i	−0.0501932	−	0.0869372i
$486$		0			0
$487$		−	5.36851i		−	0.243270i	−0.992575	−	0.121635i	$-0.961186\pi$
$487$		−	5.36851i		−	0.243270i	0.992575	−	0.121635i	$-0.0388138\pi$
$488$	4.67586	−	8.09882i	0.211666	−	0.366616i
$489$		0			0
$490$	−1.30506	−	2.26043i	−0.0589567	−	0.102116i
$491$	−19.2176	+	33.2859i	−0.867279	+	1.50217i	−0.00251360	+	0.999997i	$0.500800\pi$
$491$	−19.2176	+	33.2859i	−0.867279	+	1.50217i	−0.864766	+	0.502175i	$0.832533\pi$
$492$		0			0
$493$	2.01977			0.0909660
$494$	−11.4813	+	6.62874i	−0.516569	+	0.298241i
$495$		0			0
$496$	−8.09859	−	4.67573i	−0.363638	−	0.209946i
$497$	0.0287964			0.00129170
$498$		0			0
$499$			3.32725i			0.148948i	0.997223	+	0.0744740i	$0.0237278\pi$
$499$			3.32725i			0.148948i	−0.997223	+	0.0744740i	$0.976272\pi$
$500$		−	3.67781i		−	0.164477i
$501$		0			0
$502$	−26.2916			−1.17345
$503$	−10.6045	−	6.12250i	−0.472830	−	0.272989i	0.244594	−	0.969626i	$-0.421345\pi$
$503$	−10.6045	−	6.12250i	−0.472830	−	0.272989i	−0.717424	+	0.696637i	$0.754679\pi$
$504$		0			0
$505$	3.11601	−	1.79903i	0.138661	−	0.0800558i
$506$	−10.9283			−0.485821
$507$		0			0
$508$	1.27625	−	2.21054i	0.0566246	−	0.0980766i
$509$	−0.866989	−	1.50167i	−0.0384286	−	0.0665603i	0.846171	−	0.532911i	$-0.178902\pi$
$509$	−0.866989	−	1.50167i	−0.0384286	−	0.0665603i	−0.884600	+	0.466351i	$0.845569\pi$
$510$		0			0
$511$	0.277317	−	0.480328i	0.0122678	−	0.0212484i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.66777	+	6.35277i	0.161779	+	0.280209i
$515$	−0.111016	+	0.192286i	−0.00489197	+	0.00847313i
$516$		0			0
$517$	12.9660	−	22.4577i	0.570243	−	0.987691i
$518$	0.255100	+	0.0223041i	0.0112085	+	0.000979984i
$519$		0			0
$520$			0.832506i			0.0365078i
$521$	−3.37632	−	5.84796i	−0.147919	−	0.256204i	0.782539	−	0.622602i	$-0.213924\pi$
$521$	−3.37632	−	5.84796i	−0.147919	−	0.256204i	−0.930458	+	0.366398i	$0.880591\pi$
$522$		0			0
$523$	−24.4520	+	14.1174i	−1.06921	+	0.617309i	−0.927966	−	0.372666i	$-0.878444\pi$
$523$	−24.4520	+	14.1174i	−1.06921	+	0.617309i	−0.141245	+	0.989975i	$0.545110\pi$
$524$	9.82049	−	5.66986i	0.429010	−	0.247689i
$525$		0			0
$526$	17.8006	+	10.2772i	0.776144	+	0.448107i
$527$	−12.1551	−	21.0533i	−0.529485	−	0.917095i
$528$		0			0
$529$	−2.53497	−	4.39069i	−0.110216	−	0.190900i
$530$	1.34695	−	2.33299i	0.0585080	−	0.101339i
$531$		0			0
$532$			0.250041i			0.0108406i
$533$		−	16.1463i		−	0.699373i
$534$		0			0
$535$	3.09620	−	1.78759i	0.133860	−	0.0772842i
$536$		−	2.32184i		−	0.100288i
$537$		0			0
$538$		−	25.4958i		−	1.09920i
$539$	9.03064	−	15.6415i	0.388977	−	0.673728i
$540$		0			0
$541$			13.9031i			0.597741i	0.954294	+	0.298870i	$0.0966098\pi$
$541$			13.9031i			0.597741i	−0.954294	+	0.298870i	$0.903390\pi$
$542$	18.2571	+	10.5407i	0.784208	+	0.452763i
$543$		0			0
$544$	−1.29981	+	2.25134i	−0.0557289	+	0.0965253i
$545$	−1.72501	+	2.98781i	−0.0738913	+	0.127984i
$546$		0			0
$547$	−6.72089	+	3.88031i	−0.287365	+	0.165910i	−0.636753	−	0.771068i	$-0.719723\pi$
$547$	−6.72089	+	3.88031i	−0.287365	+	0.165910i	0.349388	+	0.936978i	$0.386389\pi$
$548$	−7.60904	−	13.1792i	−0.325042	−	0.562989i
$549$		0			0
$550$	10.8644	−	6.27259i	0.463261	−	0.267464i
$551$	2.30733	−	3.99641i	0.0982954	−	0.170253i
$552$		0			0
$553$	−0.143099	+	0.0826182i	−0.00608518	+	0.00351328i
$554$	8.26407	−	14.3138i	0.351106	−	0.608134i
$555$		0			0
$556$	−8.10261	−	14.0341i	−0.343627	−	0.595180i
$557$	19.0159	+	10.9788i	0.805730	+	0.465189i	0.845471	−	0.534021i	$-0.179320\pi$
$557$	19.0159	+	10.9788i	0.805730	+	0.465189i	−0.0397407	+	0.999210i	$0.512653\pi$
$558$		0			0
$559$	12.3438	+	21.3801i	0.522088	+	0.904283i
$560$	0.0135978	+	0.00785067i	0.000574611	+	0.000331752i
$561$		0			0
$562$	2.09286			0.0882819
$563$	9.39056	+	5.42164i	0.395765	+	0.228495i	0.684655	−	0.728867i	$-0.259953\pi$
$563$	9.39056	+	5.42164i	0.395765	+	0.228495i	−0.288890	+	0.957362i	$0.593286\pi$
$564$		0			0
$565$	2.86436	+	4.96121i	0.120504	+	0.208720i
$566$	9.75704			0.410119
$567$		0			0
$568$	0.592387	−	0.342015i	0.0248560	−	0.0143506i
$569$	−7.21399	+	4.16500i	−0.302426	+	0.174606i	−0.643532	−	0.765419i	$-0.722532\pi$
$569$	−7.21399	+	4.16500i	−0.302426	+	0.174606i	0.341106	+	0.940025i	$0.389198\pi$
$570$		0			0
$571$	6.63685	+	11.4954i	0.277744	+	0.481066i	0.970824	−	0.239795i	$-0.0770801\pi$
$571$	6.63685	+	11.4954i	0.277744	+	0.481066i	−0.693080	+	0.720861i	$0.743747\pi$
$572$	−4.98891	+	2.88035i	−0.208597	+	0.120433i
$573$		0			0
$574$	−0.263726	−	0.152262i	−0.0110077	−	0.00635530i
$575$	−17.8253	−	10.2915i	−0.743368	−	0.429184i
$576$		0			0
$577$	24.9225	+	14.3890i	1.03754	+	0.599022i	0.919134	−	0.393944i	$-0.128890\pi$
$577$	24.9225	+	14.3890i	1.03754	+	0.599022i	0.118402	+	0.992966i	$0.462223\pi$
$578$	8.86981	−	5.12098i	0.368935	−	0.213005i
$579$		0			0
$580$	−0.144889	−	0.250955i	−0.00601619	−	0.0104203i
$581$	0.176148	−	0.305097i	0.00730785	−	0.0126576i
$582$		0			0
$583$	18.6411			0.772033
$584$		−	13.1748i		−	0.545176i
$585$		0			0
$586$			1.38135i			0.0570630i
$587$	21.2120	+	12.2468i	0.875514	+	0.505478i	0.869177	−	0.494502i	$-0.164649\pi$
$587$	21.2120	+	12.2468i	0.875514	+	0.505478i	0.00633710	+	0.999980i	$0.497983\pi$
$588$		0			0
$589$	−55.5425			−2.28859
$590$	−4.04914	+	2.33777i	−0.166701	+	0.0962446i
$591$		0			0
$592$	5.51271	−	2.57099i	0.226571	−	0.105667i
$593$	33.7386			1.38548			0.692740	−	0.721188i	$-0.256403\pi$
$593$	33.7386			1.38548			0.692740	+	0.721188i	$0.256403\pi$
$594$		0			0
$595$	0.0204088	+	0.0353490i	0.000836678	+	0.00144917i
$596$	0.177156	−	0.306844i	0.00725660	−	0.0125688i
$597$		0			0
$598$	8.18532	+	4.72580i	0.334723	+	0.193252i
$599$	19.7504			0.806979			0.403489	−	0.914984i	$-0.367797\pi$
$599$	19.7504			0.806979			0.403489	+	0.914984i	$0.367797\pi$
$600$		0			0
$601$	−13.7029			−0.558952			−0.279476	−	0.960153i	$-0.590161\pi$
$601$	−13.7029			−0.558952			−0.279476	+	0.960153i	$0.590161\pi$
$602$	0.465618			0.0189772
$603$		0			0
$604$	3.44680	−	5.97003i	0.140248	−	0.242917i
$605$	1.40159	+	0.809210i	0.0569828	+	0.0328991i
$606$		0			0
$607$	−9.37497	+	5.41264i	−0.380518	+	0.219692i	−0.678044	−	0.735021i	$-0.737172\pi$
$607$	−9.37497	+	5.41264i	−0.380518	+	0.219692i	0.297525	+	0.954714i	$0.403839\pi$
$608$	2.96973	+	5.14372i	0.120438	+	0.208605i
$609$		0			0
$610$	−3.02061	−	1.74395i	−0.122301	−	0.0706105i
$611$	−19.4232	+	11.2140i	−0.785777	+	0.453669i
$612$		0			0
$613$	10.2622	−	17.7747i	0.414487	−	0.717913i	−0.580887	−	0.813984i	$-0.697294\pi$
$613$	10.2622	−	17.7747i	0.414487	−	0.717913i	0.995375	+	0.0960708i	$0.0306275\pi$
$614$		−	22.3771i		−	0.903065i
$615$		0			0
$616$			0.108649i			0.00437758i
$617$	−7.71528	−	13.3633i	−0.310605	−	0.537984i	0.667888	−	0.744262i	$-0.267198\pi$
$617$	−7.71528	−	13.3633i	−0.310605	−	0.537984i	−0.978494	+	0.206277i	$0.933865\pi$
$618$		0			0
$619$	−6.19852	−	10.7361i	−0.249139	−	0.431522i	0.714148	−	0.699995i	$-0.246814\pi$
$619$	−6.19852	−	10.7361i	−0.249139	−	0.431522i	−0.963287	+	0.268473i	$0.913481\pi$
$620$	−1.74390	+	3.02053i	−0.0700368	+	0.121307i
$621$		0			0
$622$	14.1829	+	24.5656i	0.568684	+	0.984990i
$623$	−0.237025	+	0.136847i	−0.00949621	+	0.00548264i
$624$		0			0
$625$	22.9328			0.917310
$626$	−13.8093			−0.551931
$627$		0			0
$628$	5.77978	+	10.0109i	0.230638	+	0.399477i
$629$	15.7528	+	1.37730i	0.628105	+	0.0549167i
$630$		0			0
$631$	−31.5489	−	18.2148i	−1.25594	−	0.725118i	−0.283658	−	0.958925i	$-0.591548\pi$
$631$	−31.5489	−	18.2148i	−1.25594	−	0.725118i	−0.972283	+	0.233808i	$0.924881\pi$
$632$	−1.96251	+	3.39917i	−0.0780644	+	0.135212i
$633$		0			0
$634$		−	7.32076i		−	0.290744i
$635$	−0.824462	−	0.476003i	−0.0327178	−	0.0188896i
$636$		0			0
$637$	−13.5280	+	7.81038i	−0.535998	+	0.309459i
$638$	1.00259	−	1.73653i	0.0396929	−	0.0687501i
$639$		0			0
$640$	0.372969			0.0147429
$641$	−48.4888			−1.91519			−0.957596	−	0.288115i	$-0.906972\pi$
$641$	−48.4888			−1.91519			−0.957596	+	0.288115i	$0.906972\pi$
$642$		0			0
$643$	18.1536	+	10.4810i	0.715907	+	0.413329i	0.813244	−	0.581922i	$-0.197699\pi$
$643$	18.1536	+	10.4810i	0.715907	+	0.413329i	−0.0973375	+	0.995251i	$0.531033\pi$
$644$	0.154378	−	0.0891302i	0.00608335	−	0.00351222i
$645$		0			0
$646$			15.4403i			0.607492i
$647$	33.9152	−	19.5810i	1.33334	−	0.769807i	0.347534	−	0.937667i	$-0.387019\pi$
$647$	33.9152	−	19.5810i	1.33334	−	0.769807i	0.985811	+	0.167861i	$0.0536859\pi$
$648$		0			0
$649$	−28.0189	−	16.1767i	−1.09984	−	0.634991i
$650$	−10.8500			−0.425573
$651$		0			0
$652$	−12.6667	−	7.31312i	−0.496066	−	0.286404i
$653$			39.0374i			1.52765i	0.645423	+	0.763825i	$0.276681\pi$
$653$			39.0374i			1.52765i	−0.645423	+	0.763825i	$0.723319\pi$
$654$		0			0
$655$	−2.11468	−	3.66274i	−0.0826275	−	0.143115i
$656$	−7.23366			−0.282427
$657$		0			0
$658$			0.422999i			0.0164902i
$659$	23.2367	−	40.2472i	0.905174	−	1.56781i	0.0844908	−	0.996424i	$-0.473074\pi$
$659$	23.2367	−	40.2472i	0.905174	−	1.56781i	0.820683	−	0.571383i	$-0.193593\pi$
$660$		0			0
$661$			40.3144i			1.56805i	0.620730	+	0.784024i	$0.286836\pi$
$661$			40.3144i			1.56805i	−0.620730	+	0.784024i	$0.713164\pi$
$662$	−13.2880			−0.516454
$663$		0			0
$664$		−	8.36842i		−	0.324758i
$665$	0.0932575			0.00361637
$666$		0			0
$667$	−3.28990			−0.127386
$668$		−	11.6626i		−	0.451239i
$669$		0			0
$670$	−0.865975			−0.0334555
$671$		−	24.1352i		−	0.931730i
$672$		0			0
$673$	−23.0883	+	39.9902i	−0.889990	+	1.54151i	−0.0501056	+	0.998744i	$0.515956\pi$
$673$	−23.0883	+	39.9902i	−0.889990	+	1.54151i	−0.839885	+	0.542765i	$0.817378\pi$
$674$		−	9.96243i		−	0.383738i
$675$		0			0
$676$	−8.01771			−0.308374
$677$	−21.2133	−	36.7426i	−0.815294	−	1.41213i	−0.909116	−	0.416542i	$-0.863242\pi$
$677$	−21.2133	−	36.7426i	−0.815294	−	1.41213i	0.0938220	−	0.995589i	$-0.470092\pi$
$678$		0			0
$679$			0.249538i			0.00957639i
$680$	0.839680	+	0.484789i	0.0322003	+	0.0185908i
$681$		0			0
$682$	−24.1346			−0.924160
$683$	−44.0035	−	25.4054i	−1.68375	−	0.972112i	−0.959132	−	0.282960i	$-0.908684\pi$
$683$	−44.0035	−	25.4054i	−1.68375	−	0.972112i	−0.724616	−	0.689153i	$-0.757983\pi$
$684$		0			0
$685$	−4.91545	+	2.83794i	−0.187810	+	0.108432i
$686$			0.589301i			0.0224996i
$687$		0			0
$688$	9.57847	−	5.53013i	0.365176	−	0.210834i
$689$	−13.9622	−	8.06110i	−0.531919	−	0.307103i
$690$		0			0
$691$	−4.33821			−0.165033			−0.0825166	−	0.996590i	$-0.526296\pi$
$691$	−4.33821			−0.165033			−0.0825166	+	0.996590i	$0.526296\pi$
$692$	−0.0584707			−0.00222272
$693$		0			0
$694$	10.5053	−	18.1956i	0.398774	−	0.690697i
$695$	−5.23430	+	3.02202i	−0.198548	+	0.114632i
$696$		0			0
$697$	−16.2854	−	9.40239i	−0.616854	−	0.356141i
$698$		−	30.7742i		−	1.16482i
$699$		0			0
$700$	−0.102318	+	0.177219i	−0.00386724	+	0.00669826i
$701$	39.9218	+	23.0488i	1.50782	+	0.870542i	0.999959	+	0.00910594i	$0.00289855\pi$
$701$	39.9218	+	23.0488i	1.50782	+	0.870542i	0.507865	+	0.861437i	$0.330435\pi$
$702$		0			0
$703$	20.7207	−	29.5957i	0.781496	−	1.11622i
$704$	1.29042	+	2.23507i	0.0486345	+	0.0842374i
$705$		0			0
$706$	0.288111			0.0108432
$707$	−0.406125			−0.0152739
$708$		0			0
$709$	−39.1822	+	22.6218i	−1.47152	+	0.849581i	−0.999488	−	0.0320017i	$-0.989812\pi$
$709$	−39.1822	+	22.6218i	−1.47152	+	0.849581i	−0.472030	+	0.881583i	$0.656478\pi$
$710$	−0.127561	−	0.220942i	−0.00478728	−	0.00829181i
$711$		0			0
$712$	−3.25065	+	5.63029i	−0.121823	+	0.211004i
$713$	19.7989	+	34.2926i	0.741473	+	1.28427i
$714$		0			0
$715$	1.07428	+	1.86071i	0.0401758	+	0.0695866i
$716$			8.49336i			0.317412i
$717$		0			0
$718$			6.45640i			0.240951i
$719$	1.96437	−	3.40238i	0.0732585	−	0.126887i	−0.827069	−	0.562100i	$-0.809994\pi$
$719$	1.96437	−	3.40238i	0.0732585	−	0.126887i	0.900328	+	0.435213i	$0.143327\pi$
$720$		0			0
$721$	0.0217039	−	0.0125308i	0.000808297	−	0.000466671i
$722$	14.0964	+	8.13857i	0.524614	+	0.302886i
$723$		0			0
$724$	−8.04344	−	13.9316i	−0.298932	−	0.517765i
$725$	3.27069	−	1.88833i	0.121470	−	0.0701309i
$726$		0			0
$727$	36.6043	+	21.1335i	1.35758	+	0.783798i	0.989297	−	0.145916i	$-0.0466129\pi$
$727$	36.6043	+	21.1335i	1.35758	+	0.783798i	0.368282	+	0.929714i	$0.379946\pi$
$728$	0.0469838	−	0.0813784i	0.00174134	−	0.00301608i
$729$		0			0
$730$	−4.91378			−0.181867
$731$	28.7525			1.06345
$732$		0			0
$733$	−4.09527			−0.151262			−0.0756312	−	0.997136i	$-0.524097\pi$
$733$	−4.09527			−0.151262			−0.0756312	+	0.997136i	$0.524097\pi$
$734$	31.6525	+	18.2746i	1.16831	+	0.674526i
$735$		0			0
$736$	2.11720	−	3.66709i	0.0780409	−	0.135171i
$737$	−2.99615	−	5.18948i	−0.110364	−	0.191157i
$738$		0			0
$739$	43.9364			1.61623			0.808114	−	0.589027i	$-0.200489\pi$
$739$	43.9364			1.61623			0.808114	+	0.589027i	$0.200489\pi$
$740$	−0.958902	−	2.05607i	−0.0352499	−	0.0755827i
$741$		0			0
$742$	−0.263333	+	0.152035i	−0.00966724	+	0.00558139i
$743$	17.8855			0.656156			0.328078	−	0.944651i	$-0.393599\pi$
$743$	17.8855			0.656156			0.328078	+	0.944651i	$0.393599\pi$
$744$		0			0
$745$	−0.114443	−	0.0660738i	−0.00419288	−	0.00242076i
$746$			2.94276i			0.107742i
$747$		0			0
$748$			6.70920i			0.245313i
$749$	−0.403542			−0.0147451
$750$		0			0
$751$	8.35475	−	14.4709i	0.304869	−	0.528049i	−0.672363	−	0.740222i	$-0.734721\pi$
$751$	8.35475	−	14.4709i	0.304869	−	0.528049i	0.977232	+	0.212173i	$0.0680539\pi$
$752$	5.02395	+	8.70173i	0.183205	+	0.317320i
$753$		0			0
$754$	−1.50189	+	0.867115i	−0.0546955	+	0.0315785i
$755$	−2.22664	−	1.28555i	−0.0810356	−	0.0467859i
$756$		0			0
$757$	7.69103	+	4.44042i	0.279535	+	0.161390i	0.633213	−	0.773978i	$-0.281736\pi$
$757$	7.69103	+	4.44042i	0.279535	+	0.161390i	−0.353678	+	0.935367i	$0.615069\pi$
$758$	−3.04166	−	1.75610i	−0.110478	−	0.0637845i
$759$		0			0
$760$	1.91845	−	1.10762i	0.0695895	−	0.0401775i
$761$	14.0530	+	24.3406i	0.509423	+	0.882346i	0.999940	+	0.0109147i	$0.00347433\pi$
$761$	14.0530	+	24.3406i	0.509423	+	0.882346i	−0.490518	+	0.871431i	$0.663192\pi$
$762$		0			0
$763$	0.337243	−	0.194708i	0.0122090	−	0.00704889i
$764$	−7.11315	+	4.10678i	−0.257345	+	0.148578i
$765$		0			0
$766$	17.2557			0.623474
$767$	13.9908	+	24.2329i	0.505180	+	0.874998i
$768$		0			0
$769$	8.59532	+	4.96251i	0.309955	+	0.178953i	0.646906	−	0.762569i	$-0.276062\pi$
$769$	8.59532	+	4.96251i	0.309955	+	0.178953i	−0.336951	+	0.941522i	$0.609396\pi$
$770$	0.0405226			0.00146033
$771$		0			0
$772$	16.6788	+	9.62948i	0.600282	+	0.346573i
$773$	18.3764	+	31.8289i	0.660954	+	1.14481i	0.980365	+	0.197190i	$0.0631815\pi$
$773$	18.3764	+	31.8289i	0.660954	+	1.14481i	−0.319411	+	0.947616i	$0.603485\pi$
$774$		0			0
$775$	−39.3664	−	22.7282i	−1.41408	−	0.816421i
$776$	2.96376	+	5.13338i	0.106393	+	0.184278i
$777$		0			0
$778$	9.40455	−	16.2892i	0.337169	−	0.583995i
$779$	−37.2079	+	21.4820i	−1.33311	+	0.769673i
$780$		0			0
$781$	0.882684	−	1.52885i	0.0315849	−	0.0547067i
$782$	9.53305	−	5.50391i	0.340901	−	0.196819i
$783$		0			0
$784$	3.49911	+	6.06064i	0.124968	+	0.216452i
$785$	3.73374	−	2.15568i	0.133263	−	0.0769395i
$786$		0			0
$787$	−1.31315	+	2.27445i	−0.0468088	+	0.0810752i	−0.888481	−	0.458914i	$-0.848238\pi$
$787$	−1.31315	+	2.27445i	−0.0468088	+	0.0810752i	0.841672	+	0.539990i	$0.181572\pi$
$788$	−0.245783	+	0.425708i	−0.00875565	+	0.0151652i
$789$		0			0
$790$	1.26778	+	0.731956i	0.0451057	+	0.0260418i
$791$		−	0.646618i		−	0.0229911i
$792$		0			0
$793$	−10.4370	+	18.0774i	−0.370628	+	0.641947i
$794$			7.41696i			0.263218i
$795$		0			0
$796$		−	10.8937i		−	0.386118i
$797$	−25.5748	+	14.7656i	−0.905905	+	0.523024i	−0.879111	−	0.476617i	$-0.841863\pi$
$797$	−25.5748	+	14.7656i	−0.905905	+	0.523024i	−0.0267936	+	0.999641i	$0.508530\pi$
$798$		0			0
$799$			26.1207i			0.924085i
$800$			4.86089i			0.171859i
$801$		0			0
$802$	−10.1798	+	17.6319i	−0.359461	+	0.622605i
$803$	−17.0010	−	29.4465i	−0.599951	−	1.03915i
$804$		0			0
$805$	−0.0332428	−	0.0575783i	−0.00117166	−	0.00202937i
$806$	18.0769	+	10.4367i	0.636732	+	0.367617i
$807$		0			0
$808$	−8.35461	+	4.82354i	−0.293914	+	0.169691i
$809$	−10.2145	+	5.89735i	−0.359123	+	0.207340i	−0.668696	−	0.743536i	$-0.733147\pi$
$809$	−10.2145	+	5.89735i	−0.359123	+	0.207340i	0.309573	+	0.950876i	$0.399814\pi$
$810$		0			0
$811$	11.7556	+	20.3614i	0.412797	+	0.714985i	0.995194	−	0.0979192i	$-0.0312187\pi$
$811$	11.7556	+	20.3614i	0.412797	+	0.714985i	−0.582398	+	0.812904i	$0.697885\pi$
$812$			0.0327082i			0.00114783i
$813$		0			0
$814$	9.00364	−	12.8601i	0.315577	−	0.450745i
$815$	−2.72757	+	4.72429i	−0.0955426	+	0.165485i
$816$		0			0
$817$	32.8460	−	56.8909i	1.14914	−	1.99036i
$818$	−3.81157	−	6.60183i	−0.133268	−	0.230828i
$819$		0			0
$820$			2.69793i			0.0942159i
$821$	−16.9663	+	29.3865i	−0.592127	+	1.02559i	0.401818	+	0.915719i	$0.368378\pi$
$821$	−16.9663	+	29.3865i	−0.592127	+	1.02559i	−0.993945	+	0.109875i	$0.964955\pi$
$822$		0			0
$823$	−9.93334	−	17.2051i	−0.346255	−	0.599731i	0.639326	−	0.768936i	$-0.279213\pi$
$823$	−9.93334	−	17.2051i	−0.346255	−	0.599731i	−0.985581	+	0.169205i	$0.945880\pi$
$824$	0.297656	−	0.515555i	0.0103693	−	0.0179602i
$825$		0			0
$826$	0.527744			0.0183626
$827$	15.8162	−	9.13148i	0.549982	−	0.317533i	−0.199132	−	0.979973i	$-0.563812\pi$
$827$	15.8162	−	9.13148i	0.549982	−	0.317533i	0.749115	+	0.662440i	$0.230479\pi$
$828$		0			0
$829$	−39.8474	−	23.0059i	−1.38396	−	0.799028i	−0.391331	−	0.920250i	$-0.627985\pi$
$829$	−39.8474	−	23.0059i	−1.38396	−	0.799028i	−0.992625	+	0.121223i	$0.961319\pi$
$830$	−3.12116			−0.108337
$831$		0			0
$832$		−	2.23210i		−	0.0773843i
$833$			18.1927i			0.630341i
$834$		0			0
$835$	−4.34979			−0.150531
$836$	13.2751	+	7.66438i	0.459129	+	0.265078i
$837$		0			0
$838$	29.9271	−	17.2784i	1.03381	−	0.596873i
$839$	12.2387			0.422525			0.211263	−	0.977429i	$-0.432242\pi$
$839$	12.2387			0.422525			0.211263	+	0.977429i	$0.432242\pi$
$840$		0			0
$841$	−14.1982	+	24.5920i	−0.489592	+	0.847999i
$842$	9.31096	+	16.1271i	0.320877	+	0.555775i
$843$		0			0
$844$	−6.38957	+	11.0671i	−0.219938	+	0.380944i
$845$			2.99036i			0.102872i
$846$		0			0
$847$	−0.0913381	−	0.158202i	−0.00313842	−	0.00543589i
$848$	−3.61144	+	6.25519i	−0.124017	+	0.214804i
$849$		0			0
$850$	−6.31824	+	10.9435i	−0.216714	+	0.375359i
$851$	−25.6589	−	2.24342i	−0.879576	−	0.0769035i
$852$		0			0
$853$		−	17.9609i		−	0.614970i	−0.951553	−	0.307485i	$-0.900513\pi$
$853$		−	17.9609i		−	0.614970i	0.951553	−	0.307485i	$-0.0994874\pi$
$854$	0.196845	+	0.340946i	0.00673591	+	0.0116669i
$855$		0			0
$856$	−8.30148	+	4.79286i	−0.283739	+	0.163817i
$857$	−44.5684	+	25.7316i	−1.52243	+	0.878975i	−0.522780	+	0.852468i	$0.675105\pi$
$857$	−44.5684	+	25.7316i	−1.52243	+	0.878975i	−0.999649	+	0.0265070i	$0.991562\pi$
$858$		0			0
$859$	−6.87771	−	3.97085i	−0.234664	−	0.135484i	0.378058	−	0.925782i	$-0.376592\pi$
$859$	−6.87771	−	3.97085i	−0.234664	−	0.135484i	−0.612722	+	0.790299i	$0.709925\pi$
$860$	−2.06257	−	3.57247i	−0.0703330	−	0.121820i
$861$		0			0
$862$	−10.7429	−	18.6073i	−0.365905	−	0.633767i
$863$	−12.2981	+	21.3010i	−0.418634	+	0.725095i	−0.995802	−	0.0915301i	$-0.970824\pi$
$863$	−12.2981	+	21.3010i	−0.418634	+	0.725095i	0.577169	+	0.816625i	$0.304158\pi$
$864$		0			0
$865$			0.0218078i			0.000741486i
$866$		−	30.8001i		−	1.04663i
$867$		0			0
$868$	0.340937	−	0.196840i	0.0115721	−	0.00668118i
$869$			10.1298i			0.343631i
$870$		0			0
$871$			5.18259i			0.175605i
$872$	4.62508	−	8.01087i	0.156625	−	0.271282i
$873$		0			0
$874$		−	25.1500i		−	0.850711i
$875$	0.134086	+	0.0774147i	0.00453294	+	0.00261709i
$876$		0			0
$877$	−6.30917	+	10.9278i	−0.213046	+	0.369006i	−0.952666	−	0.304018i	$-0.901672\pi$
$877$	−6.30917	+	10.9278i	−0.213046	+	0.369006i	0.739621	+	0.673024i	$0.235005\pi$
$878$	14.8047	−	25.6425i	0.499635	−	0.865393i
$879$		0			0
$880$	0.833612	−	0.481286i	0.0281011	−	0.0162242i
$881$	6.02320	+	10.4325i	0.202927	+	0.351480i	0.949470	−	0.313857i	$-0.101621\pi$
$881$	6.02320	+	10.4325i	0.202927	+	0.351480i	−0.746543	+	0.665337i	$0.768288\pi$
$882$		0			0
$883$	−10.3476	+	5.97418i	−0.348224	+	0.201047i	−0.663903	−	0.747819i	$-0.731101\pi$
$883$	−10.3476	+	5.97418i	−0.348224	+	0.201047i	0.315679	+	0.948866i	$0.397768\pi$
$884$	2.90131	−	5.02522i	0.0975817	−	0.169016i
$885$		0			0
$886$	1.56305	−	0.902430i	0.0525119	−	0.0303177i
$887$	−20.6333	+	35.7380i	−0.692800	+	1.19996i	0.278117	+	0.960547i	$0.410290\pi$
$887$	−20.6333	+	35.7380i	−0.692800	+	1.19996i	−0.970917	+	0.239417i	$0.923044\pi$
$888$		0			0
$889$	0.0537280	+	0.0930596i	0.00180198	+	0.00312112i
$890$	2.09992	+	1.21239i	0.0703896	+	0.0406394i
$891$		0			0
$892$	14.1726	+	24.5477i	0.474534	+	0.821917i
$893$	51.6836	+	29.8395i	1.72952	+	0.998542i
$894$		0			0
$895$	3.16776			0.105887
$896$	−0.0364581	−	0.0210491i	−0.00121798	−	0.000703202i
$897$		0			0
$898$	18.9232	+	32.7760i	0.631476	+	1.09375i
$899$	−7.26560			−0.242321
$900$		0			0
$901$	−16.2611	+	9.38837i	−0.541737	+	0.312772i
$902$	−16.1677	+	9.33445i	−0.538327	+	0.310803i
$903$		0			0
$904$	−7.67987	−	13.3019i	−0.255429	−	0.442416i
$905$	−5.19607	+	2.99995i	−0.172723	+	0.0997219i
$906$		0			0
$907$	−19.3749	−	11.1861i	−0.643332	−	0.371428i	0.142565	−	0.989785i	$-0.454465\pi$
$907$	−19.3749	−	11.1861i	−0.643332	−	0.371428i	−0.785897	+	0.618358i	$0.787798\pi$
$908$	−0.708998	−	0.409340i	−0.0235289	−	0.0135844i
$909$		0			0
$910$	−0.0303516	−	0.0175235i	−0.00100615	−	0.000580899i
$911$	42.7829	−	24.7007i	1.41746	−	0.818371i	0.421384	−	0.906882i	$-0.361544\pi$
$911$	42.7829	−	24.7007i	1.41746	−	0.818371i	0.996075	+	0.0885116i	$0.0282110\pi$
$912$		0			0
$913$	−10.7988	−	18.7040i	−0.357387	−	0.619012i
$914$	−7.49278	+	12.9779i	−0.247839	+	0.429270i
$915$		0			0
$916$	17.3120			0.572004
$917$			0.477382i			0.0157646i
$918$		0			0
$919$		−	23.9475i		−	0.789956i	−0.918691	−	0.394978i	$-0.870752\pi$
$919$		−	23.9475i		−	0.789956i	0.918691	−	0.394978i	$-0.129248\pi$
$920$	−1.36771	−	0.789649i	−0.0450921	−	0.0260339i
$921$		0			0
$922$	17.8177			0.586794
$923$	−1.32227	+	0.763413i	−0.0435230	+	0.0251280i
$924$		0			0
$925$	26.7967	−	12.4973i	0.881070	−	0.410910i
$926$	−23.2712			−0.764739
$927$		0			0
$928$	0.388474	+	0.672857i	0.0127523	+	0.0220876i
$929$	−5.88326	+	10.1901i	−0.193024	+	0.334327i	−0.946251	−	0.323434i	$-0.895163\pi$
$929$	−5.88326	+	10.1901i	−0.193024	+	0.334327i	0.753227	+	0.657760i	$0.228496\pi$
$930$		0			0
$931$	35.9969	+	20.7828i	1.17975	+	0.681130i
$932$	−9.20929			−0.301660
$933$		0			0
$934$	−17.6430			−0.577297
$935$	2.50232			0.0818347
$936$		0			0
$937$	−3.04601	+	5.27585i	−0.0995090	+	0.172355i	−0.911482	−	0.411341i	$-0.865061\pi$
$937$	−3.04601	+	5.27585i	−0.0995090	+	0.172355i	0.811973	+	0.583696i	$0.198394\pi$
$938$	0.0846500	+	0.0488727i	0.00276392	+	0.00159575i
$939$		0			0
$940$	3.24548	−	1.87378i	0.105856	−	0.0611159i
$941$	−4.01840	−	6.96008i	−0.130996	−	0.226892i	0.793065	−	0.609137i	$-0.208484\pi$
$941$	−4.01840	−	6.96008i	−0.130996	−	0.226892i	−0.924061	+	0.382245i	$0.875151\pi$
$942$		0			0
$943$	26.5265	+	15.3151i	0.863822	+	0.498728i
$944$	10.8565	−	6.26801i	0.353349	−	0.204006i
$945$		0			0
$946$	14.2724	−	24.7205i	0.464035	−	0.803731i
$947$			20.8482i			0.677476i	0.940881	+	0.338738i	$0.110000\pi$
$947$			20.8482i			0.677476i	−0.940881	+	0.338738i	$0.890000\pi$
$948$		0			0
$949$			29.4074i			0.954606i
$950$	14.4355	+	25.0031i	0.468351	+	0.811207i
$951$		0			0
$952$	−0.0547197	−	0.0947774i	−0.00177348	−	0.00307175i
$953$	−20.3122	+	35.1818i	−0.657978	+	1.13965i	0.323161	+	0.946344i	$0.395255\pi$
$953$	−20.3122	+	35.1818i	−0.657978	+	1.13965i	−0.981138	+	0.193307i	$0.938079\pi$
$954$		0			0
$955$	1.53170	+	2.65299i	0.0495647	+	0.0858486i
$956$	−2.00849	+	1.15960i	−0.0649591	+	0.0375042i
$957$		0			0
$958$	1.87253			0.0604988
$959$	0.640655			0.0206878
$960$		0			0
$961$	28.2248	+	48.8868i	0.910478	+	1.57699i
$962$	−12.3049	+	5.73872i	−0.396727	+	0.185024i
$963$		0			0
$964$	5.75406	+	3.32211i	0.185326	+	0.106998i
$965$	3.59150	−	6.22066i	0.115615	−	0.200250i
$966$		0			0
$967$			0.593848i			0.0190969i	0.999954	+	0.00954843i	$0.00303941\pi$
$967$			0.593848i			0.0190969i	−0.999954	+	0.00954843i	$0.996961\pi$
$968$	−3.75793	−	2.16964i	−0.120784	−	0.0697349i
$969$		0			0
$970$	1.91459	−	1.10539i	0.0614739	−	0.0354920i
$971$	−3.85800	+	6.68226i	−0.123809	+	0.214444i	−0.921267	−	0.388931i	$-0.872844\pi$
$971$	−3.85800	+	6.68226i	−0.123809	+	0.214444i	0.797458	+	0.603375i	$0.206178\pi$
$972$		0			0
$973$	0.682211			0.0218707
$974$	5.36851			0.172018
$975$		0			0
$976$	8.09882	+	4.67586i	0.259237	+	0.149670i
$977$	−26.0268	+	15.0266i	−0.832671	+	0.480743i	−0.854766	−	0.519013i	$-0.826300\pi$
$977$	−26.0268	+	15.0266i	−0.832671	+	0.480743i	0.0220950	+	0.999756i	$0.492966\pi$
$978$		0			0
$979$			16.7788i			0.536252i
$980$	2.26043	−	1.30506i	0.0722069	−	0.0416887i
$981$		0			0
$982$	−33.2859	−	19.2176i	−1.06220	−	0.613259i
$983$	−13.5572			−0.432408			−0.216204	−	0.976348i	$-0.569368\pi$
$983$	−13.5572			−0.432408			−0.216204	+	0.976348i	$0.569368\pi$
$984$		0			0
$985$	0.158776	+	0.0916694i	0.00505902	+	0.00292083i
$986$			2.01977i			0.0643226i
$987$		0			0
$988$	−6.62874	−	11.4813i	−0.210888	−	0.365269i
$989$	−46.8335			−1.48922
$990$		0			0
$991$		−	16.5362i		−	0.525288i	−0.964893	−	0.262644i	$-0.915405\pi$
$991$		−	16.5362i		−	0.525288i	0.964893	−	0.262644i	$-0.0845945\pi$
$992$	4.67573	−	8.09859i	0.148454	−	0.257131i
$993$		0			0
$994$			0.0287964i			0.000913368i
$995$	−4.06302			−0.128806
$996$		0			0
$997$		−	20.2725i		−	0.642037i	−0.947073	−	0.321019i	$-0.895975\pi$
$997$		−	20.2725i		−	0.642037i	0.947073	−	0.321019i	$-0.104025\pi$
$998$	−3.32725			−0.105322
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1998.2.k.a.1063.32		76
3.2	odd	2		666.2.k.a.175.1	✓	76
9.2	odd	6		666.2.t.a.619.13	yes	76
9.7	even	3		1998.2.t.a.397.33		76
37.11	even	6		1998.2.t.a.307.33		76
111.11	odd	6		666.2.t.a.85.13	yes	76
333.11	odd	6		666.2.k.a.529.20	yes	76
333.196	even	6	inner	1998.2.k.a.1639.7		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.1	✓	76	3.2	odd	2
666.2.k.a.529.20	yes	76	333.11	odd	6
666.2.t.a.85.13	yes	76	111.11	odd	6
666.2.t.a.619.13	yes	76	9.2	odd	6
1998.2.k.a.1063.32		76	1.1	even	1	trivial
1998.2.k.a.1639.7		76	333.196	even	6	inner
1998.2.t.a.307.33		76	37.11	even	6
1998.2.t.a.397.33		76	9.7	even	3

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:	\( N \)	\(=\)	\( 1998 = 2 \cdot 3^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1998.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +0.372969i q^{5} +(0.0210491 - 0.0364581i) q^{7} -1.00000i q^{8} -0.372969 q^{10} +(-1.29042 - 2.23507i) q^{11} +2.23210i q^{13} +(0.0364581 + 0.0210491i) q^{14} +1.00000 q^{16} +(2.25134 + 1.29981i) q^{17} +(5.14372 - 2.96973i) q^{19} -0.372969i q^{20} +(2.23507 - 1.29042i) q^{22} +(-3.66709 - 2.11720i) q^{23} +4.86089 q^{25} -2.23210 q^{26} +(-0.0210491 + 0.0364581i) q^{28} +(0.672857 - 0.388474i) q^{29} +(-8.09859 - 4.67573i) q^{31} +1.00000i q^{32} +(-1.29981 + 2.25134i) q^{34} +(0.0135978 + 0.00785067i) q^{35} +(5.51271 - 2.57099i) q^{37} +(2.96973 + 5.14372i) q^{38} +0.372969 q^{40} -7.23366 q^{41} +(9.57847 - 5.53013i) q^{43} +(1.29042 + 2.23507i) q^{44} +(2.11720 - 3.66709i) q^{46} +(5.02395 + 8.70173i) q^{47} +(3.49911 + 6.06064i) q^{49} +4.86089i q^{50} -2.23210i q^{52} +(-3.61144 + 6.25519i) q^{53} +(0.833612 - 0.481286i) q^{55} +(-0.0364581 - 0.0210491i) q^{56} +(0.388474 + 0.672857i) q^{58} +(10.8565 - 6.26801i) q^{59} +(8.09882 + 4.67586i) q^{61} +(4.67573 - 8.09859i) q^{62} -1.00000 q^{64} -0.832506 q^{65} +2.32184 q^{67} +(-2.25134 - 1.29981i) q^{68} +(-0.00785067 + 0.0135978i) q^{70} +(0.342015 + 0.592387i) q^{71} +13.1748 q^{73} +(2.57099 + 5.51271i) q^{74} +(-5.14372 + 2.96973i) q^{76} -0.108649 q^{77} +(-3.39917 - 1.96251i) q^{79} +0.372969i q^{80} -7.23366i q^{82} +8.36842 q^{83} +(-0.484789 + 0.839680i) q^{85} +(5.53013 + 9.57847i) q^{86} +(-2.23507 + 1.29042i) q^{88} +(-5.63029 - 3.25065i) q^{89} +(0.0813784 + 0.0469838i) q^{91} +(3.66709 + 2.11720i) q^{92} +(-8.70173 + 5.02395i) q^{94} +(1.10762 + 1.91845i) q^{95} +(-5.13338 + 2.96376i) q^{97} +(-6.06064 + 3.49911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} - 2 q^{7} + 4 q^{11} + 76 q^{16} - 12 q^{23} - 100 q^{25} + 24 q^{26} + 2 q^{28} - 18 q^{29} + 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} - 72 q^{41} + 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) \) 76 * q - 76 * q^4 - 2 * q^7 + 4 * q^11 + 76 * q^16 - 12 * q^23 - 100 * q^25 + 24 * q^26 + 2 * q^28 - 18 * q^29 + 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 - 72 * q^41 + 6 * q^43 - 4 * q^44 + 20 * q^47 - 36 * q^49 - 14 * q^53 + 6 * q^59 + 16 * q^62 - 76 * q^64 - 32 * q^65 + 40 * q^67 - 2 * q^71 + 28 * q^73 + 2 * q^74 + 24 * q^77 + 6 * q^79 + 64 * q^83 - 12 * q^85 - 4 * q^86 - 60 * q^89 + 42 * q^91 + 12 * q^92 + 14 * q^95 - 12 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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