LMFDB - Embedded newform 700.2.t.d.199.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(199,700)] 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("700.199"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,2,0,0,0,0,16,0,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.12
Character	$\chi$	$=$	700.199
Dual form			700.2.t.d.299.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04701 + 0.950668i) q^{2} +(2.37047 + 1.36859i) q^{3} +(0.192463 + 1.99072i) q^{4} +(1.18083 + 3.68646i) q^{6} +(-2.43939 + 1.02440i) q^{7} +(-1.69100 + 2.26727i) q^{8} +(2.24609 + 3.89033i) q^{9} +(0.0868131 + 0.0501216i) q^{11} +(-2.26825 + 4.98234i) q^{12} +4.11735 q^{13} +(-3.52793 - 1.24649i) q^{14} +(-3.92592 + 0.766277i) q^{16} +(2.69867 - 4.67424i) q^{17} +(-1.34674 + 6.20850i) q^{18} +(-3.72967 - 6.45997i) q^{19} +(-7.18448 - 0.910218i) q^{21} +(0.0432453 + 0.135008i) q^{22} +(0.754151 + 1.30623i) q^{23} +(-7.11143 + 3.06021i) q^{24} +(4.31091 + 3.91424i) q^{26} +4.08434i q^{27} +(-2.50878 - 4.65897i) q^{28} +2.37688 q^{29} +(-2.72129 + 4.71341i) q^{31} +(-4.83895 - 2.92994i) q^{32} +(0.137192 + 0.237623i) q^{33} +(7.26919 - 2.32844i) q^{34} +(-7.31227 + 5.22007i) q^{36} +(-0.899386 + 0.519260i) q^{37} +(2.23629 - 10.3093i) q^{38} +(9.76007 + 5.63498i) q^{39} +7.99125i q^{41} +(-6.65691 - 7.78306i) q^{42} +7.04778 q^{43} +(-0.0830696 + 0.182467i) q^{44} +(-0.452184 + 2.08458i) q^{46} +(3.84841 - 2.22188i) q^{47} +(-10.3550 - 3.55654i) q^{48} +(4.90122 - 4.99781i) q^{49} +(12.7943 - 7.38677i) q^{51} +(0.792437 + 8.19649i) q^{52} +(-5.31966 - 3.07131i) q^{53} +(-3.88285 + 4.27635i) q^{54} +(1.80242 - 7.26301i) q^{56} -20.4176i q^{57} +(2.48862 + 2.25962i) q^{58} +(-4.26148 + 7.38111i) q^{59} +(6.84408 - 3.95143i) q^{61} +(-7.33010 + 2.34795i) q^{62} +(-9.46432 - 7.18914i) q^{63} +(-2.28103 - 7.66791i) q^{64} +(-0.0822594 + 0.379218i) q^{66} +(-0.0549000 + 0.0950895i) q^{67} +(9.82449 + 4.47268i) q^{68} +4.12850i q^{69} +6.73221i q^{71} +(-12.6186 - 1.48607i) q^{72} +(3.07349 - 5.32344i) q^{73} +(-1.43531 - 0.311345i) q^{74} +(12.1422 - 8.66802i) q^{76} +(-0.263115 - 0.0333347i) q^{77} +(4.86190 + 15.1785i) q^{78} +(-3.70178 + 2.13723i) q^{79} +(1.14846 - 1.98919i) q^{81} +(-7.59702 + 8.36692i) q^{82} -6.50159i q^{83} +(0.429245 - 14.4774i) q^{84} +(7.37910 + 6.70009i) q^{86} +(5.63433 + 3.25298i) q^{87} +(-0.260440 + 0.112073i) q^{88} +(2.76417 - 1.59589i) q^{89} +(-10.0438 + 4.21781i) q^{91} +(-2.45519 + 1.75270i) q^{92} +(-12.9015 + 7.44866i) q^{93} +(6.14160 + 1.33223i) q^{94} +(-7.46070 - 13.5679i) q^{96} +11.0691 q^{97} +(9.88288 - 0.573332i) q^{98} +0.450309i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4} + 16 q^{9} + 14 q^{12} + 8 q^{13} - 2 q^{14} - 14 q^{16} - 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} - 32 q^{28} + 40 q^{29} - 60 q^{32} + 24 q^{33} + 60 q^{36} + 60 q^{37} + 46 q^{38}+ \cdots + 124 q^{98}+O(q^{100}) $ 32 * q + 2 * q^4 + 16 * q^9 + 14 * q^12 + 8 * q^13 - 2 * q^14 - 14 * q^16 - 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 - 32 * q^28 + 40 * q^29 - 60 * q^32 + 24 * q^33 + 60 * q^36 + 60 * q^37 + 46 * q^38 - 78 * q^42 + 18 * q^44 + 2 * q^46 + 28 * q^48 + 16 * q^49 + 46 * q^52 + 12 * q^53 - 12 * q^54 - 4 * q^56 - 42 * q^58 + 24 * q^61 - 8 * q^62 - 4 * q^64 + 24 * q^66 + 4 * q^68 - 90 * q^72 + 24 * q^73 - 38 * q^74 - 20 * q^77 - 36 * q^81 - 8 * q^82 + 20 * q^84 + 28 * q^86 + 78 * q^88 + 60 * q^89 - 72 * q^93 - 18 * q^94 - 60 * q^96 + 48 * q^97 + 124 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	1.04701	+	0.950668i	0.740348	+	0.672223i
$2$	1.04701	+	0.950668i	0.740348	+	0.672223i
$3$	2.37047	+	1.36859i	1.36859	+	0.790157i	0.990748	−	0.135713i	$-0.0433325\pi$
$3$	2.37047	+	1.36859i	1.36859	+	0.790157i	0.377843	+	0.925870i	$0.376666\pi$
$4$	0.192463	+	1.99072i	0.0962313	+	0.995359i
$5$		0			0
$5$		0			0
$6$	1.18083	+	3.68646i	0.482073	+	1.50499i
$7$	−2.43939	+	1.02440i	−0.922002	+	0.387186i
$7$	−2.43939	+	1.02440i	−0.922002	+	0.387186i
$8$	−1.69100	+	2.26727i	−0.597859	+	0.801601i
$9$	2.24609	+	3.89033i	0.748695	+	1.29678i
$10$		0			0
$11$	0.0868131	+	0.0501216i	0.0261751	+	0.0151122i	0.513030	−	0.858370i	$-0.328523\pi$
$11$	0.0868131	+	0.0501216i	0.0261751	+	0.0151122i	−0.486855	+	0.873483i	$0.661856\pi$
$12$	−2.26825	+	4.98234i	−0.654788	+	1.43828i
$13$	4.11735			1.14195			0.570974	−	0.820968i	$-0.306566\pi$
$13$	4.11735			1.14195			0.570974	+	0.820968i	$0.306566\pi$
$14$	−3.52793	−	1.24649i	−0.942878	−	0.333138i
$15$		0			0
$16$	−3.92592	+	0.766277i	−0.981479	+	0.191569i
$17$	2.69867	−	4.67424i	0.654525	−	1.13367i	−0.327488	−	0.944855i	$-0.606202\pi$
$17$	2.69867	−	4.67424i	0.654525	−	1.13367i	0.982013	−	0.188815i	$-0.0604646\pi$
$18$	−1.34674	+	6.20850i	−0.317429	+	1.46336i
$19$	−3.72967	−	6.45997i	−0.855645	−	1.48202i	−0.876046	−	0.482228i	$-0.839828\pi$
$19$	−3.72967	−	6.45997i	−0.855645	−	1.48202i	0.0204012	−	0.999792i	$-0.493506\pi$
$20$		0			0
$21$	−7.18448	−	0.910218i	−1.56778	−	0.198626i
$22$	0.0432453	+	0.135008i	0.00921993	+	0.0287838i
$23$	0.754151	+	1.30623i	0.157251	+	0.272367i	0.933877	−	0.357596i	$-0.116403\pi$
$23$	0.754151	+	1.30623i	0.157251	+	0.272367i	−0.776625	+	0.629963i	$0.783070\pi$
$24$	−7.11143	+	3.06021i	−1.45162	+	0.624662i
$25$		0			0
$26$	4.31091	+	3.91424i	0.845440	+	0.767645i
$27$			4.08434i			0.786032i
$28$	−2.50878	−	4.65897i	−0.474115	−	0.880463i
$29$	2.37688			0.441376			0.220688	−	0.975344i	$-0.429170\pi$
$29$	2.37688			0.441376			0.220688	+	0.975344i	$0.429170\pi$
$30$		0			0
$31$	−2.72129	+	4.71341i	−0.488758	+	0.846553i	−0.999916	−	0.0129330i	$-0.995883\pi$
$31$	−2.72129	+	4.71341i	−0.488758	+	0.846553i	0.511159	+	0.859486i	$0.329217\pi$
$32$	−4.83895	−	2.92994i	−0.855414	−	0.517945i
$33$	0.137192	+	0.237623i	0.0238820	+	0.0413649i
$34$	7.26919	−	2.32844i	1.24666	−	0.399324i
$35$		0			0
$36$	−7.31227	+	5.22007i	−1.21871	+	0.870011i
$37$	−0.899386	+	0.519260i	−0.147858	+	0.0853659i	−0.572104	−	0.820181i	$-0.693873\pi$
$37$	−0.899386	+	0.519260i	−0.147858	+	0.0853659i	0.424246	+	0.905547i	$0.360539\pi$
$38$	2.23629	−	10.3093i	0.362773	−	1.67240i
$39$	9.76007	+	5.63498i	1.56286	+	0.902318i
$40$		0			0
$41$			7.99125i			1.24802i	0.781415	+	0.624012i	$0.214498\pi$
$41$			7.99125i			1.24802i	−0.781415	+	0.624012i	$0.785502\pi$
$42$	−6.65691	−	7.78306i	−1.02718	−	1.20095i
$43$	7.04778			1.07478			0.537388	−	0.843335i	$-0.319411\pi$
$43$	7.04778			1.07478			0.537388	+	0.843335i	$0.319411\pi$
$44$	−0.0830696	+	0.182467i	−0.0125232	+	0.0275079i
$45$		0			0
$46$	−0.452184	+	2.08458i	−0.0666710	+	0.307355i
$47$	3.84841	−	2.22188i	0.561348	−	0.324095i	−0.192338	−	0.981329i	$-0.561607\pi$
$47$	3.84841	−	2.22188i	0.561348	−	0.324095i	0.753686	+	0.657234i	$0.228274\pi$
$48$	−10.3550	−	3.55654i	−1.49461	−	0.513342i
$49$	4.90122	−	4.99781i	0.700174	−	0.713973i
$50$		0			0
$51$	12.7943	−	7.38677i	1.79155	−	1.03435i
$52$	0.792437	+	8.19649i	0.109891	+	1.13665i
$53$	−5.31966	−	3.07131i	−0.730711	−	0.421876i	0.0879710	−	0.996123i	$-0.471962\pi$
$53$	−5.31966	−	3.07131i	−0.730711	−	0.421876i	−0.818682	+	0.574247i	$0.805295\pi$
$54$	−3.88285	+	4.27635i	−0.528389	+	0.581938i
$55$		0			0
$56$	1.80242	−	7.26301i	0.240858	−	0.970560i
$57$		−	20.4176i		−	2.70437i
$58$	2.48862	+	2.25962i	0.326772	+	0.296703i
$59$	−4.26148	+	7.38111i	−0.554798	+	0.960938i	0.443121	+	0.896462i	$0.353871\pi$
$59$	−4.26148	+	7.38111i	−0.554798	+	0.960938i	−0.997919	+	0.0644767i	$0.979462\pi$
$60$		0			0
$61$	6.84408	−	3.95143i	0.876295	−	0.505929i	0.00685975	−	0.999976i	$-0.497816\pi$
$61$	6.84408	−	3.95143i	0.876295	−	0.505929i	0.869435	+	0.494048i	$0.164483\pi$
$62$	−7.33010	+	2.34795i	−0.930924	+	0.298190i
$63$	−9.46432	−	7.18914i	−1.19239	−	0.905747i
$64$	−2.28103	−	7.66791i	−0.285129	−	0.958489i
$65$		0			0
$66$	−0.0822594	+	0.379218i	−0.0101254	+	0.0466785i
$67$	−0.0549000	+	0.0950895i	−0.00670710	+	0.0116170i	−0.869359	−	0.494180i	$-0.835468\pi$
$67$	−0.0549000	+	0.0950895i	−0.00670710	+	0.0116170i	0.862652	+	0.505797i	$0.168802\pi$
$68$	9.82449	+	4.47268i	1.19139	+	0.542393i
$69$			4.12850i			0.497013i
$70$		0			0
$71$			6.73221i			0.798967i	0.916740	+	0.399483i	$0.130810\pi$
$71$			6.73221i			0.798967i	−0.916740	+	0.399483i	$0.869190\pi$
$72$	−12.6186	−	1.48607i	−1.48711	−	0.175135i
$73$	3.07349	−	5.32344i	0.359725	−	0.623062i	−0.628190	−	0.778060i	$-0.716204\pi$
$73$	3.07349	−	5.32344i	0.359725	−	0.623062i	0.987915	+	0.154998i	$0.0495372\pi$
$74$	−1.43531	−	0.311345i	−0.166851	−	0.0361932i
$75$		0			0
$76$	12.1422	−	8.66802i	1.39280	−	0.994290i
$77$	−0.263115	−	0.0333347i	−0.0299848	−	0.00379884i
$78$	4.86190	+	15.1785i	0.550502	+	1.71862i
$79$	−3.70178	+	2.13723i	−0.416483	+	0.240457i	−0.693572	−	0.720388i	$-0.743964\pi$
$79$	−3.70178	+	2.13723i	−0.416483	+	0.240457i	0.277088	+	0.960844i	$0.410631\pi$
$80$		0			0
$81$	1.14846	−	1.98919i	0.127607	−	0.221021i
$82$	−7.59702	+	8.36692i	−0.838951	+	0.923972i
$83$		−	6.50159i		−	0.713642i	−0.934173	−	0.356821i	$-0.883861\pi$
$83$		−	6.50159i		−	0.713642i	0.934173	−	0.356821i	$-0.116139\pi$
$84$	0.429245	−	14.4774i	0.0468345	−	1.57962i
$85$		0			0
$86$	7.37910	+	6.70009i	0.795709	+	0.722490i
$87$	5.63433	+	3.25298i	0.604063	+	0.348756i
$88$	−0.260440	+	0.112073i	−0.0277630	+	0.0119470i
$89$	2.76417	−	1.59589i	0.293001	−	0.169164i	−0.346293	−	0.938126i	$-0.612560\pi$
$89$	2.76417	−	1.59589i	0.293001	−	0.169164i	0.639294	+	0.768962i	$0.279226\pi$
$90$		0			0
$91$	−10.0438	+	4.21781i	−1.05288	+	0.442147i
$92$	−2.45519	+	1.75270i	−0.255971	+	0.182732i
$93$	−12.9015	+	7.44866i	−1.33782	+	0.772391i
$94$	6.14160	+	1.33223i	0.633457	+	0.137409i
$95$		0			0
$96$	−7.46070	−	13.5679i	−0.761454	−	1.38477i
$97$	11.0691			1.12390			0.561948	−	0.827173i	$-0.310052\pi$
$97$	11.0691			1.12390			0.561948	+	0.827173i	$0.310052\pi$
$98$	9.88288	−	0.573332i	0.998322	−	0.0579152i
$99$			0.450309i			0.0452578i
$100$		0			0
$101$	−6.20412	−	3.58195i	−0.617333	−	0.356418i	0.158497	−	0.987359i	$-0.449335\pi$
$101$	−6.20412	−	3.58195i	−0.617333	−	0.356418i	−0.775830	+	0.630942i	$0.782669\pi$
$102$	20.4181	+	4.42906i	2.02169	+	0.438542i
$103$	−4.23147	+	2.44304i	−0.416939	+	0.240720i	−0.693767	−	0.720200i	$-0.744050\pi$
$103$	−4.23147	+	2.44304i	−0.416939	+	0.240720i	0.276828	+	0.960920i	$0.410717\pi$
$104$	−6.96245	+	9.33516i	−0.682724	+	0.915388i
$105$		0			0
$106$	−2.64995	−	8.27292i	−0.257386	−	0.803537i
$107$	−3.78436	−	6.55470i	−0.365848	−	0.633667i	0.623064	−	0.782171i	$-0.285888\pi$
$107$	−3.78436	−	6.55470i	−0.365848	−	0.633667i	−0.988912	+	0.148504i	$0.952554\pi$
$108$	−8.13077	+	0.786083i	−0.782384	+	0.0756409i
$109$	−9.02662	+	15.6346i	−0.864593	+	1.49752i	0.00285729	+	0.999996i	$0.499090\pi$
$109$	−9.02662	+	15.6346i	−0.864593	+	1.49752i	−0.867451	+	0.497523i	$0.834243\pi$
$110$		0			0
$111$	−2.84262			−0.269810
$112$	8.79185	−	5.89095i	0.830752	−	0.556642i
$113$		−	18.1432i		−	1.70677i	−0.521283	−	0.853384i	$-0.674547\pi$
$113$		−	18.1432i		−	1.70677i	0.521283	−	0.853384i	$-0.325453\pi$
$114$	19.4103	−	21.3774i	1.81794	−	2.00218i
$115$		0			0
$116$	0.457461	+	4.73170i	0.0424742	+	0.439328i
$117$	9.24793	+	16.0179i	0.854971	+	1.48085i
$118$	−11.4788	+	3.67684i	−1.05671	+	0.338481i
$119$	−1.79483	+	14.1668i	−0.164531	+	1.29867i
$120$		0			0
$121$	−5.49498	−	9.51758i	−0.499543	−	0.865234i
$122$	10.9223	+	2.36925i	0.988861	+	0.214502i
$123$	−10.9368	+	18.9430i	−0.986134	+	1.70803i
$124$	−9.90682	−	4.51016i	−0.889658	−	0.405025i
$125$		0			0
$126$	−3.07476	−	16.5245i	−0.273922	−	1.47212i
$127$	−4.37573			−0.388283			−0.194141	−	0.980974i	$-0.562192\pi$
$127$	−4.37573			−0.388283			−0.194141	+	0.980974i	$0.562192\pi$
$128$	4.90137	−	10.1969i	0.433224	−	0.901286i
$129$	16.7065	+	9.64553i	1.47093	+	0.849241i
$130$		0			0
$131$	−1.49073	−	2.58201i	−0.130245	−	0.225592i	0.793526	−	0.608537i	$-0.208243\pi$
$131$	−1.49073	−	2.58201i	−0.130245	−	0.225592i	−0.923771	+	0.382945i	$0.874910\pi$
$132$	−0.446637	+	0.318844i	−0.0388747	+	0.0277518i
$133$	15.7157	+	11.9377i	1.36272	+	1.03513i
$134$	−0.147879	+	0.0473681i	−0.0127748	+	0.00409198i
$135$		0			0
$136$	6.03431	+	14.0228i	0.517438	+	1.20244i
$137$	−1.32048	−	0.762377i	−0.112816	−	0.0651342i	0.442530	−	0.896754i	$-0.354081\pi$
$137$	−1.32048	−	0.762377i	−0.112816	−	0.0651342i	−0.555346	+	0.831619i	$0.687414\pi$
$138$	−3.92483	+	4.32258i	−0.334104	+	0.367963i
$139$	−7.16082			−0.607373			−0.303686	−	0.952772i	$-0.598217\pi$
$139$	−7.16082			−0.607373			−0.303686	+	0.952772i	$0.598217\pi$
$140$		0			0
$141$	12.1634			1.02434
$142$	−6.40010	+	7.04870i	−0.537084	+	0.591514i
$143$	0.357440	+	0.206368i	0.0298907	+	0.0172574i
$144$	−11.7990	−	13.5520i	−0.983251	−	1.12933i
$145$		0			0
$146$	8.27880	−	2.65183i	0.685158	−	0.219467i
$147$	18.4581	−	5.13939i	1.52240	−	0.423890i
$148$	−1.20680	−	1.69048i	−0.0991983	−	0.138957i
$149$	−10.5236	−	18.2275i	−0.862129	−	1.49325i	−0.869870	−	0.493282i	$-0.835797\pi$
$149$	−10.5236	−	18.2275i	−0.862129	−	1.49325i	0.00774027	−	0.999970i	$-0.497536\pi$
$150$		0			0
$151$	−3.31081	−	1.91150i	−0.269430	−	0.155555i	0.359199	−	0.933261i	$-0.383050\pi$
$151$	−3.31081	−	1.91150i	−0.269430	−	0.155555i	−0.628628	+	0.777706i	$0.716383\pi$
$152$	20.9534	+	2.46765i	1.69954	+	0.200153i
$153$	24.2458			1.96016
$154$	−0.243794	−	0.285037i	−0.0196455	−	0.0229689i
$155$		0			0
$156$	−9.33920	+	20.5141i	−0.747735	+	1.64244i
$157$	−0.642065	+	1.11209i	−0.0512423	+	0.0887543i	−0.890509	−	0.454966i	$-0.849651\pi$
$157$	−0.642065	+	1.11209i	−0.0512423	+	0.0887543i	0.839266	+	0.543720i	$0.182985\pi$
$158$	−5.90760	−	1.28147i	−0.469983	−	0.101948i
$159$	−8.40673	−	14.5609i	−0.666697	−	1.15475i
$160$		0			0
$161$	−3.17776	−	2.41384i	−0.250443	−	0.190238i
$162$	3.09351	−	0.990900i	0.243049	−	0.0778525i
$163$	−4.30054	−	7.44875i	−0.336844	−	0.583431i	0.646993	−	0.762496i	$-0.276026\pi$
$163$	−4.30054	−	7.44875i	−0.336844	−	0.583431i	−0.983837	+	0.179064i	$0.942693\pi$
$164$	−15.9083	+	1.53802i	−1.24223	+	0.120099i
$165$		0			0
$166$	6.18085	−	6.80723i	0.479727	−	0.528343i
$167$			8.10448i			0.627144i	0.949565	+	0.313572i	$0.101526\pi$
$167$			8.10448i			0.627144i	−0.949565	+	0.313572i	$0.898474\pi$
$168$	14.2127	−	14.7500i	1.09653	−	1.13799i
$169$	3.95261			0.304047
$170$		0			0
$171$	16.7543	−	29.0193i	1.28123	−	2.21916i
$172$	1.35643	+	14.0301i	0.103427	+	1.06979i
$173$	−4.01688	−	6.95744i	−0.305398	−	0.528964i	0.671952	−	0.740595i	$-0.265456\pi$
$173$	−4.01688	−	6.95744i	−0.305398	−	0.528964i	−0.977350	+	0.211630i	$0.932123\pi$
$174$	2.80670	+	8.76228i	0.212775	+	0.664267i
$175$		0			0
$176$	−0.379228	−	0.130250i	−0.0285854	−	0.00981797i
$177$	−20.2034	+	11.6645i	−1.51858	+	0.876755i
$178$	4.41128	+	0.956887i	0.330639	+	0.0717217i
$179$	7.66309	+	4.42429i	0.572766	+	0.330687i	0.758253	−	0.651960i	$-0.226053\pi$
$179$	7.66309	+	4.42429i	0.572766	+	0.330687i	−0.185487	+	0.982647i	$0.559386\pi$
$180$		0			0
$181$			21.3610i			1.58775i	0.608082	+	0.793874i	$0.291939\pi$
$181$			21.3610i			1.58775i	−0.608082	+	0.793874i	$0.708061\pi$
$182$	−14.5257	−	5.13224i	−1.07672	−	0.380427i
$183$	21.6316			1.59905
$184$	−4.23684	−	0.498968i	−0.312344	−	0.0367844i
$185$		0			0
$186$	−20.5892	−	4.46617i	−1.50967	−	0.327476i
$187$	0.468561	−	0.270524i	0.0342645	−	0.0197826i
$188$	5.16381	+	7.23347i	0.376610	+	0.527555i
$189$	−4.18399	−	9.96329i	−0.304341	−	0.724723i
$190$		0			0
$191$	−21.6710	+	12.5117i	−1.56806	+	0.905317i	−0.571660	+	0.820491i	$0.693700\pi$
$191$	−21.6710	+	12.5117i	−1.56806	+	0.905317i	−0.996396	+	0.0848269i	$0.972966\pi$
$192$	5.08712	−	21.2984i	0.367131	−	1.53708i
$193$	−7.06813	−	4.08078i	−0.508775	−	0.293741i	0.223555	−	0.974691i	$-0.428234\pi$
$193$	−7.06813	−	4.08078i	−0.508775	−	0.293741i	−0.732330	+	0.680950i	$0.761567\pi$
$194$	11.5894	+	10.5230i	0.832074	+	0.755509i
$195$		0			0
$196$	10.8925	+	8.79505i	0.778038	+	0.628218i
$197$			12.4517i			0.887149i	0.896238	+	0.443574i	$0.146290\pi$
$197$			12.4517i			0.887149i	−0.896238	+	0.443574i	$0.853710\pi$
$198$	−0.428094	+	0.471478i	−0.0304233	+	0.0335065i
$199$	11.5867	−	20.0687i	0.821358	−	1.42263i	−0.0833132	−	0.996523i	$-0.526550\pi$
$199$	11.5867	−	20.0687i	0.821358	−	1.42263i	0.904671	−	0.426110i	$-0.140116\pi$
$200$		0			0
$201$	−0.260277	+	0.150271i	−0.0183586	+	0.0105993i
$202$	−3.09054	−	9.64840i	−0.217449	−	0.678859i
$203$	−5.79814	+	2.43487i	−0.406949	+	0.170895i
$204$	17.1674	+	24.0481i	1.20196	+	1.68370i
$205$		0			0
$206$	−6.75291	−	1.46483i	−0.470498	−	0.102060i
$207$	−3.38778	+	5.86780i	−0.235467	+	0.407840i
$208$	−16.1644	+	3.15504i	−1.12080	+	0.218762i
$209$		−	0.747747i		−	0.0517228i
$210$		0			0
$211$		−	10.9759i		−	0.755613i	−0.925885	−	0.377807i	$-0.876678\pi$
$211$		−	10.9759i		−	0.755613i	0.925885	−	0.377807i	$-0.123322\pi$
$212$	5.09027	−	11.1811i	0.349601	−	0.767918i
$213$	−9.21365	+	15.9585i	−0.631309	+	1.09346i
$214$	2.26908	−	10.4605i	0.155111	−	0.715066i
$215$		0			0
$216$	−9.26031	−	6.90663i	−0.630084	−	0.469936i
$217$	1.80987	−	14.2855i	0.122862	−	0.969764i
$218$	−24.3142	+	7.78824i	−1.64677	+	0.527486i
$219$	14.5712	−	8.41270i	0.984633	−	0.568478i
$220$		0			0
$221$	11.1114	−	19.2455i	0.747434	−	1.29459i
$222$	−2.97626	−	2.70239i	−0.199753	−	0.181372i
$223$			14.9798i			1.00312i	0.865123	+	0.501559i	$0.167240\pi$
$223$			14.9798i			1.00312i	−0.865123	+	0.501559i	$0.832760\pi$
$224$	14.8055	+	2.19024i	0.989234	+	0.146342i
$225$		0			0
$226$	17.2481	−	18.9961i	1.14733	−	1.26360i
$227$	1.30546	+	0.753708i	0.0866465	+	0.0500254i	0.542697	−	0.839928i	$-0.317403\pi$
$227$	1.30546	+	0.753708i	0.0866465	+	0.0500254i	−0.456051	+	0.889954i	$0.650736\pi$
$228$	40.6456	−	3.92962i	2.69182	−	0.260245i
$229$	−7.38329	+	4.26274i	−0.487901	+	0.281690i	−0.723703	−	0.690111i	$-0.757562\pi$
$229$	−7.38329	+	4.26274i	−0.487901	+	0.281690i	0.235802	+	0.971801i	$0.424228\pi$
$230$		0			0
$231$	−0.578085	−	0.439116i	−0.0380352	−	0.0288917i
$232$	−4.01931	+	5.38904i	−0.263881	+	0.353808i
$233$	−18.3799	+	10.6117i	−1.20411	+	0.695193i	−0.961467	−	0.274922i	$-0.911348\pi$
$233$	−18.3799	+	10.6117i	−1.20411	+	0.695193i	−0.242644	+	0.970115i	$0.578015\pi$
$234$	−5.54500	+	25.5626i	−0.362488	+	1.67108i
$235$		0			0
$236$	−15.5139	−	7.06283i	−1.00987	−	0.459751i
$237$	−11.7000			−0.759994
$238$	−15.3471	+	13.1265i	−0.994806	+	0.850865i
$239$		−	10.1532i		−	0.656754i	−0.944547	−	0.328377i	$-0.893498\pi$
$239$		−	10.1532i		−	0.656754i	0.944547	−	0.328377i	$-0.106502\pi$
$240$		0			0
$241$	16.4985	+	9.52539i	1.06276	+	0.613584i	0.926194	−	0.377047i	$-0.123060\pi$
$241$	16.4985	+	9.52539i	1.06276	+	0.613584i	0.136565	+	0.990631i	$0.456394\pi$
$242$	3.29475	−	15.1889i	0.211795	−	0.976379i
$243$	16.0562	−	9.27006i	1.03001	−	0.594674i
$244$	9.18342	+	12.8641i	0.587908	+	0.823542i
$245$		0			0
$246$	−29.4594	+	9.43632i	−1.87826	+	0.601638i
$247$	−15.3564	−	26.5980i	−0.977102	−	1.69239i
$248$	−6.08488	−	14.1403i	−0.386390	−	0.897909i
$249$	8.89801	−	15.4118i	0.563889	−	0.976684i
$250$		0			0
$251$	−9.46184			−0.597226			−0.298613	−	0.954374i	$-0.596524\pi$
$251$	−9.46184			−0.597226			−0.298613	+	0.954374i	$0.596524\pi$
$252$	12.4900	−	20.2244i	0.786798	−	1.27402i
$253$			0.151197i			0.00950567i
$254$	−4.58143	−	4.15986i	−0.287465	−	0.261013i
$255$		0			0
$256$	14.8256	−	6.01668i	0.926602	−	0.376043i
$257$	−1.37271	−	2.37760i	−0.0856270	−	0.148310i	0.820031	−	0.572319i	$-0.193956\pi$
$257$	−1.37271	−	2.37760i	−0.0856270	−	0.148310i	−0.905658	+	0.424008i	$0.860623\pi$
$258$	8.32224	+	25.9813i	0.518120	+	1.61753i
$259$	1.66202	−	2.18801i	0.103273	−	0.135956i
$260$		0			0
$261$	5.33868	+	9.24686i	0.330456	+	0.572367i
$262$	0.893830	−	4.12058i	0.0552210	−	0.254570i
$263$	12.8384	−	22.2367i	0.791648	−	1.37117i	−0.133298	−	0.991076i	$-0.542557\pi$
$263$	12.8384	−	22.2367i	0.791648	−	1.37117i	0.924946	−	0.380098i	$-0.124110\pi$
$264$	−0.770748	−	0.0907700i	−0.0474363	−	0.00558651i
$265$		0			0
$266$	5.10570	+	27.4393i	0.313051	+	1.68241i
$267$	8.73650			0.534665
$268$	−0.199863	−	0.0909892i	−0.0122086	−	0.00555805i
$269$	−7.10140	−	4.10000i	−0.432980	−	0.249981i	0.267635	−	0.963520i	$-0.413758\pi$
$269$	−7.10140	−	4.10000i	−0.432980	−	0.249981i	−0.700615	+	0.713539i	$0.747091\pi$
$270$		0			0
$271$	3.20364	+	5.54886i	0.194607	+	0.337069i	0.946772	−	0.321906i	$-0.104324\pi$
$271$	3.20364	+	5.54886i	0.194607	+	0.337069i	−0.752165	+	0.658975i	$0.770990\pi$
$272$	−7.01301	+	20.4186i	−0.425226	+	1.23806i
$273$	−29.5810	−	3.74769i	−1.79033	−	0.226821i
$274$	−0.657785	−	2.05355i	−0.0397382	−	0.124059i
$275$		0			0
$276$	−8.21868	+	0.794582i	−0.494706	+	0.0478282i
$277$	13.8297	+	7.98456i	0.830944	+	0.479746i	0.854176	−	0.519984i	$-0.174062\pi$
$277$	13.8297	+	7.98456i	0.830944	+	0.479746i	−0.0232316	+	0.999730i	$0.507396\pi$
$278$	−7.49745	−	6.80756i	−0.449667	−	0.408290i
$279$	−24.4490			−1.46372
$280$		0			0
$281$	−9.68409			−0.577704			−0.288852	−	0.957374i	$-0.593274\pi$
$281$	−9.68409			−0.577704			−0.288852	+	0.957374i	$0.593274\pi$
$282$	12.7352	+	11.5633i	0.758370	+	0.688587i
$283$	22.6264	+	13.0633i	1.34500	+	0.776535i	0.987536	−	0.157393i	$-0.0503088\pi$
$283$	22.6264	+	13.0633i	1.34500	+	0.776535i	0.357462	+	0.933928i	$0.383642\pi$
$284$	−13.4019	+	1.29570i	−0.795259	+	0.0768856i
$285$		0			0
$286$	0.178056	+	0.555877i	0.0105287	+	0.0328697i
$287$	−8.18622	−	19.4937i	−0.483217	−	1.15068i
$288$	0.529749	−	25.4060i	0.0312158	−	1.49706i
$289$	−6.06569	−	10.5061i	−0.356805	−	0.618005i
$290$		0			0
$291$	26.2389	+	15.1491i	1.53815	+	0.888053i
$292$	11.1890	+	5.09389i	0.654787	+	0.298097i
$293$	16.2389			0.948684			0.474342	−	0.880341i	$-0.342686\pi$
$293$	16.2389			0.948684			0.474342	+	0.880341i	$0.342686\pi$
$294$	24.2117	+	12.1666i	1.41206	+	0.709568i
$295$		0			0
$296$	0.343557	−	2.91722i	0.0199689	−	0.169560i
$297$	−0.204714	+	0.354574i	−0.0118787	+	0.0205745i
$298$	6.30990	−	29.0888i	0.365523	−	1.68507i
$299$	3.10511	+	5.37821i	0.179573	+	0.311030i
$300$		0			0
$301$	−17.1923	+	7.21973i	−0.990945	+	0.416138i
$302$	−1.64925	−	5.14883i	−0.0949039	−	0.296282i
$303$	−9.80446	−	16.9818i	−0.563251	−	0.975580i
$304$	19.5925	+	22.5034i	1.12371	+	1.29066i
$305$		0			0
$306$	25.3856	+	23.0497i	1.45120	+	1.31766i
$307$			23.5437i			1.34371i	0.740684	+	0.671854i	$0.234502\pi$
$307$			23.5437i			1.34371i	−0.740684	+	0.671854i	$0.765498\pi$
$308$	0.0157201	−	0.530204i	0.000895737	−	0.0302112i
$309$	−13.3741			−0.760825
$310$		0			0
$311$	−2.69773	+	4.67261i	−0.152974	+	0.264959i	−0.932320	−	0.361635i	$-0.882219\pi$
$311$	−2.69773	+	4.67261i	−0.152974	+	0.264959i	0.779345	+	0.626595i	$0.215552\pi$
$312$	−29.2803	+	12.6000i	−1.65767	+	0.713333i
$313$	16.2807	+	28.1990i	0.920240	+	1.59390i	0.799043	+	0.601274i	$0.205340\pi$
$313$	16.2807	+	28.1990i	0.920240	+	1.59390i	0.121197	+	0.992629i	$0.461327\pi$
$314$	−1.72948	+	0.553979i	−0.0975999	+	0.0312628i
$315$		0			0
$316$	−4.96707	−	6.95787i	−0.279420	−	0.391411i
$317$	−11.8747	+	6.85587i	−0.666951	+	0.385064i	−0.794920	−	0.606714i	$-0.792487\pi$
$317$	−11.8747	+	6.85587i	−0.666951	+	0.385064i	0.127970	+	0.991778i	$0.459154\pi$
$318$	5.04062	−	23.2374i	0.282664	−	1.30309i
$319$	0.206344	+	0.119133i	0.0115531	+	0.00667017i
$320$		0			0
$321$		−	20.7170i		−	1.15631i
$322$	−1.03239	−	5.54832i	−0.0575328	−	0.309196i
$323$	−40.2606			−2.24016
$324$	4.18095	+	1.90341i	0.232275	+	0.105745i
$325$		0			0
$326$	2.57858	−	11.8873i	0.142814	−	0.658377i
$327$	−42.7947	+	24.7075i	−2.36655	+	1.36633i
$328$	−18.1183	−	13.5132i	−1.00042	−	0.746142i
$329$	−7.11167	+	9.36233i	−0.392079	+	0.516162i
$330$		0			0
$331$	−4.92495	+	2.84342i	−0.270700	+	0.156289i	−0.629206	−	0.777239i	$-0.716620\pi$
$331$	−4.92495	+	2.84342i	−0.270700	+	0.156289i	0.358506	+	0.933527i	$0.383286\pi$
$332$	12.9428	−	1.25131i	0.710330	−	0.0686747i
$333$	−4.04019	−	2.33261i	−0.221401	−	0.127826i
$334$	−7.70467	+	8.48548i	−0.421581	+	0.464305i
$335$		0			0
$336$	28.9031	−	1.93186i	1.57680	−	0.105392i
$337$			14.7219i			0.801955i	0.916088	+	0.400978i	$0.131330\pi$
$337$			14.7219i			0.801955i	−0.916088	+	0.400978i	$0.868670\pi$
$338$	4.13843	+	3.75762i	0.225101	+	0.204388i
$339$	24.8306	−	43.0079i	1.34861	−	2.33587i
$340$		0			0
$341$	−0.472487	+	0.272790i	−0.0255866	+	0.0147724i
$342$	45.1296	−	14.4557i	2.44033	−	0.781677i
$343$	−6.83621	+	17.2124i	−0.369121	+	0.929381i
$344$	−11.9178	+	15.9792i	−0.642564	+	0.861542i
$345$		0			0
$346$	2.40850	−	11.1032i	0.129482	−	0.596913i
$347$	7.73454	−	13.3966i	0.415212	−	0.719168i	−0.580239	−	0.814446i	$-0.697041\pi$
$347$	7.73454	−	13.3966i	0.415212	−	0.719168i	0.995451	+	0.0952784i	$0.0303741\pi$
$348$	−5.39137	+	11.8424i	−0.289008	+	0.634821i
$349$		−	11.5290i		−	0.617132i	−0.951203	−	0.308566i	$-0.900151\pi$
$349$		−	11.5290i		−	0.617132i	0.951203	−	0.308566i	$-0.0998491\pi$
$350$		0			0
$351$			16.8167i			0.897608i
$352$	−0.273231	−	0.496893i	−0.0145633	−	0.0264845i
$353$	−10.2181	+	17.6983i	−0.543855	+	0.941985i	0.454823	+	0.890582i	$0.349703\pi$
$353$	−10.2181	+	17.6983i	−0.543855	+	0.941985i	−0.998678	+	0.0514030i	$0.983631\pi$
$354$	−32.2422	−	6.99394i	−1.71366	−	0.371724i
$355$		0			0
$356$	3.70897	+	5.19553i	0.196575	+	0.275362i
$357$	−23.6431	+	31.1256i	−1.25133	+	1.64734i
$358$	3.81731	+	11.9173i	0.201751	+	0.629850i
$359$	−18.3761	+	10.6095i	−0.969856	+	0.559946i	−0.899192	−	0.437554i	$-0.855845\pi$
$359$	−18.3761	+	10.6095i	−0.969856	+	0.559946i	−0.0706634	+	0.997500i	$0.522512\pi$
$360$		0			0
$361$	−18.3208	+	31.7326i	−0.964255	+	1.67014i
$362$	−20.3072	+	22.3652i	−1.06732	+	1.17549i
$363$		−	30.0815i		−	1.57887i
$364$	−10.3295	−	19.1826i	−0.541415	−	1.00544i
$365$		0			0
$366$	22.6485	+	20.5644i	1.18386	+	1.07492i
$367$	−6.62637	−	3.82574i	−0.345894	−	0.199702i	0.316982	−	0.948432i	$-0.397331\pi$
$367$	−6.62637	−	3.82574i	−0.345894	−	0.199702i	−0.662875	+	0.748730i	$0.730664\pi$
$368$	−3.96167	−	4.55025i	−0.206516	−	0.237198i
$369$	−31.0886	+	17.9490i	−1.61841	+	0.934389i
$370$		0			0
$371$	16.1229	+	2.04265i	0.837062	+	0.106049i
$372$	−17.3112	−	24.2496i	−0.897546	−	1.25728i
$373$	22.2000	−	12.8172i	1.14947	−	0.663647i	0.200713	−	0.979650i	$-0.435674\pi$
$373$	22.2000	−	12.8172i	1.14947	−	0.663647i	0.948758	+	0.316003i	$0.102341\pi$
$374$	0.747766	+	0.162204i	0.0386661	+	0.00838738i
$375$		0			0
$376$	−1.47006	+	12.4826i	−0.0758125	+	0.643740i
$377$	9.78647			0.504029
$378$	5.09109	−	14.4093i	0.261857	−	0.741132i
$379$			29.1039i			1.49497i	0.664279	+	0.747485i	$0.268739\pi$
$379$			29.1039i			1.49497i	−0.664279	+	0.747485i	$0.731261\pi$
$380$		0			0
$381$	−10.3725	−	5.98858i	−0.531401	−	0.306804i
$382$	−34.5842	−	7.50196i	−1.76948	−	0.383834i
$383$	−7.48525	+	4.32161i	−0.382478	+	0.220824i	−0.678896	−	0.734234i	$-0.737541\pi$
$383$	−7.48525	+	4.32161i	−0.382478	+	0.220824i	0.296418	+	0.955058i	$0.404208\pi$
$384$	25.5739	−	17.4635i	1.30506	−	0.891178i
$385$		0			0
$386$	−3.52093	−	10.9921i	−0.179211	−	0.559481i
$387$	15.8299	+	27.4182i	0.804679	+	1.39375i
$388$	2.13038	+	22.0354i	0.108154	+	1.11868i
$389$	−7.08846	+	12.2776i	−0.359399	+	0.622498i	−0.987861	−	0.155343i	$-0.950352\pi$
$389$	−7.08846	+	12.2776i	−0.359399	+	0.622498i	0.628461	+	0.777841i	$0.283685\pi$
$390$		0			0
$391$	8.14084			0.411700
$392$	3.04343	+	19.5637i	0.153716	+	0.988115i
$393$		−	8.16078i		−	0.411657i
$394$	−11.8375	+	13.0371i	−0.596362	+	0.656799i
$395$		0			0
$396$	−0.896438	+	0.0866677i	−0.0450477	+	0.00435521i
$397$	−0.0875029	−	0.151559i	−0.00439164	−	0.00760655i	0.863821	−	0.503798i	$-0.168065\pi$
$397$	−0.0875029	−	0.151559i	−0.00439164	−	0.00760655i	−0.868213	+	0.496192i	$0.834731\pi$
$398$	31.2101	−	9.99708i	1.56442	−	0.501108i
$399$	20.9157	+	49.8063i	1.04710	+	2.49344i
$400$		0			0
$401$	−12.0285	−	20.8339i	−0.600674	−	1.04040i	−0.992719	−	0.120452i	$-0.961566\pi$
$401$	−12.0285	−	20.8339i	−0.600674	−	1.04040i	0.392046	−	0.919946i	$-0.371768\pi$
$402$	−0.415371	−	0.0901017i	−0.0207168	−	0.00449386i
$403$	−11.2045	+	19.4068i	−0.558136	+	0.966721i
$404$	5.93659	−	13.0401i	0.295357	−	0.648767i
$405$		0			0
$406$	−8.38547	−	2.96276i	−0.416164	−	0.147039i
$407$	−0.104105			−0.00516027
$408$	−4.88729	+	41.4991i	−0.241957	+	2.05451i
$409$	10.3372	+	5.96818i	0.511141	+	0.295108i	0.733303	−	0.679902i	$-0.237978\pi$
$409$	10.3372	+	5.96818i	0.511141	+	0.295108i	−0.222161	+	0.975010i	$0.571311\pi$
$410$		0			0
$411$	−2.08676	−	3.61438i	−0.102932	−	0.178284i
$412$	−5.67780	−	7.95347i	−0.279725	−	0.391839i
$413$	2.83421	−	22.3708i	0.139463	−	1.10080i
$414$	−9.12536	+	2.92300i	−0.448487	+	0.143658i
$415$		0			0
$416$	−19.9237	−	12.0636i	−0.976839	−	0.591467i
$417$	−16.9745	−	9.80023i	−0.831245	−	0.479919i
$418$	0.710859	−	0.782899i	0.0347692	−	0.0382929i
$419$	−30.1003			−1.47050			−0.735249	−	0.677798i	$-0.762935\pi$
$419$	−30.1003			−1.47050			−0.735249	+	0.677798i	$0.762935\pi$
$420$		0			0
$421$	6.78256			0.330562			0.165281	−	0.986247i	$-0.447147\pi$
$421$	6.78256			0.330562			0.165281	+	0.986247i	$0.447147\pi$
$422$	10.4344	−	11.4919i	0.507941	−	0.559417i
$423$	17.2877	+	9.98107i	0.840557	+	0.485296i
$424$	15.9590	−	6.86753i	0.775039	−	0.333517i
$425$		0			0
$426$	−24.8180	+	7.94961i	−1.20244	+	0.385160i
$427$	−12.6475	+	16.6501i	−0.612056	+	0.805756i
$428$	12.3202	−	8.79513i	0.595520	−	0.425128i
$429$	0.564868	+	0.978379i	0.0272721	+	0.0472366i
$430$		0			0
$431$	13.8010	+	7.96802i	0.664772	+	0.383806i	0.794093	−	0.607797i	$-0.207946\pi$
$431$	13.8010	+	7.96802i	0.664772	+	0.383806i	−0.129321	+	0.991603i	$0.541280\pi$
$432$	−3.12974	−	16.0348i	−0.150580	−	0.771474i
$433$	−15.1291			−0.727057			−0.363529	−	0.931583i	$-0.618428\pi$
$433$	−15.1291			−0.727057			−0.363529	+	0.931583i	$0.618428\pi$
$434$	15.4757	−	13.2365i	0.742858	−	0.635373i
$435$		0			0
$436$	−32.8613	−	14.9604i	−1.57377	−	0.716472i
$437$	5.62547	−	9.74360i	0.269103	−	0.466099i
$438$	23.2539	+	5.04421i	1.11112	+	0.241021i
$439$	2.18337	+	3.78171i	0.104207	+	0.180491i	0.913414	−	0.407032i	$-0.133436\pi$
$439$	2.18337	+	3.78171i	0.104207	+	0.180491i	−0.809207	+	0.587523i	$0.800103\pi$
$440$		0			0
$441$	30.4517	+	7.84186i	1.45008	+	0.373422i
$442$	29.9298	−	9.58701i	1.42362	−	0.456007i
$443$	−7.04909	−	12.2094i	−0.334913	−	0.580086i	0.648555	−	0.761167i	$-0.275373\pi$
$443$	−7.04909	−	12.2094i	−0.334913	−	0.580086i	−0.983468	+	0.181082i	$0.942040\pi$
$444$	−0.547098	−	5.65886i	−0.0259641	−	0.268558i
$445$		0			0
$446$	−14.2408	+	15.6840i	−0.674320	+	0.742657i
$447$		−	57.6102i		−	2.72487i
$448$	13.4193	+	16.3683i	0.634003	+	0.773330i
$449$	−17.0120			−0.802848			−0.401424	−	0.915892i	$-0.631485\pi$
$449$	−17.0120			−0.802848			−0.401424	+	0.915892i	$0.631485\pi$
$450$		0			0
$451$	−0.400534	+	0.693745i	−0.0188604	+	0.0326672i
$452$	36.1180	−	3.49188i	1.69885	−	0.164244i
$453$	−5.23211	−	9.06228i	−0.245826	−	0.425783i
$454$	0.650306	+	2.03020i	0.0305204	+	0.0952820i
$455$		0			0
$456$	46.2922	+	34.5261i	2.16783	+	1.61683i
$457$	−10.1019	+	5.83234i	−0.472548	+	0.272825i	−0.717306	−	0.696759i	$-0.754625\pi$
$457$	−10.1019	+	5.83234i	−0.472548	+	0.272825i	0.244758	+	0.969584i	$0.421291\pi$
$458$	−11.7828	−	2.55591i	−0.550575	−	0.119430i
$459$	19.0912	+	11.0223i	0.891101	+	0.514477i
$460$		0			0
$461$		−	26.4488i		−	1.23184i	−0.787808	−	0.615921i	$-0.788784\pi$
$461$		−	26.4488i		−	1.23184i	0.787808	−	0.615921i	$-0.211216\pi$
$462$	−0.187808	−	1.00933i	−0.00873761	−	0.0469581i
$463$	3.13685			0.145782			0.0728909	−	0.997340i	$-0.476778\pi$
$463$	3.13685			0.145782			0.0728909	+	0.997340i	$0.476778\pi$
$464$	−9.33144	+	1.82135i	−0.433201	+	0.0845541i
$465$		0			0
$466$	−29.3322	−	6.36269i	−1.35879	−	0.294746i
$467$	−7.05043	+	4.07057i	−0.326255	+	0.188363i	−0.654177	−	0.756341i	$-0.726985\pi$
$467$	−7.05043	+	4.07057i	−0.326255	+	0.188363i	0.327922	+	0.944705i	$0.393652\pi$
$468$	−30.1072	+	21.4929i	−1.39171	+	0.993508i
$469$	0.0365127	−	0.288200i	0.00168600	−	0.0133078i
$470$		0			0
$471$	−3.04399	+	1.75745i	−0.140260	+	0.0809789i
$472$	−9.52880	−	22.1434i	−0.438599	−	1.01923i
$473$	0.611839	+	0.353246i	0.0281324	+	0.0162422i
$474$	−12.2500	−	11.1228i	−0.562660	−	0.510886i
$475$		0			0
$476$	−28.5475	−	0.846412i	−1.30847	−	0.0387952i
$477$		−	27.5937i		−	1.26343i
$478$	9.65229	−	10.6305i	0.441485	−	0.486227i
$479$	−12.3904	+	21.4608i	−0.566131	+	0.980567i	0.430813	+	0.902441i	$0.358227\pi$
$479$	−12.3904	+	21.4608i	−0.566131	+	0.980567i	−0.996944	+	0.0781258i	$0.975106\pi$
$480$		0			0
$481$	−3.70309	+	2.13798i	−0.168846	+	0.0974835i
$482$	8.21858	+	25.6577i	0.374346	+	1.16868i
$483$	−4.22923	−	10.0710i	−0.192437	−	0.458247i
$484$	17.8892	−	12.7707i	0.813147	−	0.580487i
$485$		0			0
$486$	25.6238	+	5.55827i	1.16232	+	0.252128i
$487$	6.34726	−	10.9938i	0.287622	−	0.498175i	−0.685620	−	0.727960i	$-0.740469\pi$
$487$	6.34726	−	10.9938i	0.287622	−	0.498175i	0.973242	+	0.229784i	$0.0738021\pi$
$488$	−2.61438	+	22.1993i	−0.118347	+	1.00491i
$489$		−	23.5427i		−	1.06464i
$490$		0			0
$491$		−	9.51192i		−	0.429267i	−0.976695	−	0.214633i	$-0.931144\pi$
$491$		−	9.51192i		−	0.429267i	0.976695	−	0.214633i	$-0.0688557\pi$
$492$	−39.8151	−	18.1262i	−1.79500	−	0.817191i
$493$	6.41443	−	11.1101i	0.288892	−	0.500375i
$494$	9.20758	−	42.4472i	0.414269	−	1.90979i
$495$		0			0
$496$	7.07177	−	20.5897i	0.317532	−	0.924506i
$497$	−6.89647	−	16.4225i	−0.309349	−	0.736649i
$498$	23.9678	−	7.67728i	1.07402	−	0.344027i
$499$	7.35497	−	4.24639i	0.329254	−	0.190095i	−0.326256	−	0.945281i	$-0.605787\pi$
$499$	7.35497	−	4.24639i	0.329254	−	0.190095i	0.655510	+	0.755187i	$0.272454\pi$
$500$		0			0
$501$	−11.0917	+	19.2114i	−0.495542	+	0.858303i
$502$	−9.90665	−	8.99507i	−0.442155	−	0.401469i
$503$		−	10.4796i		−	0.467261i	−0.972325	−	0.233630i	$-0.924939\pi$
$503$		−	10.4796i		−	0.467261i	0.972325	−	0.233630i	$-0.0750606\pi$
$504$	32.3039	−	9.30134i	1.43893	−	0.414315i
$505$		0			0
$506$	−0.143738	+	0.158305i	−0.00638993	+	0.00703751i
$507$	9.36955	+	5.40951i	0.416116	+	0.240245i
$508$	−0.842164	−	8.71084i	−0.0373650	−	0.386481i
$509$	19.7483	−	11.4017i	0.875329	−	0.505371i	0.00621337	−	0.999981i	$-0.498022\pi$
$509$	19.7483	−	11.4017i	0.875329	−	0.505371i	0.869115	+	0.494609i	$0.164689\pi$
$510$		0			0
$511$	−2.04411	+	16.1344i	−0.0904259	+	0.713744i
$512$	21.2425	+	7.79472i	0.938793	+	0.344481i
$513$	26.3847	−	15.2332i	1.16492	−	0.672564i
$514$	0.823066	−	3.79435i	0.0363039	−	0.167362i
$515$		0			0
$516$	−15.9861	+	35.1144i	−0.703751	+	1.54583i
$517$	0.445456			0.0195912
$518$	3.82022	−	0.710838i	0.167851	−	0.0312324i
$519$		−	21.9899i		−	0.965248i
$520$		0			0
$521$	−7.88048	−	4.54980i	−0.345250	−	0.199330i	0.317341	−	0.948311i	$-0.397210\pi$
$521$	−7.88048	−	4.54980i	−0.345250	−	0.199330i	−0.662591	+	0.748981i	$0.730543\pi$
$522$	−3.20104	+	14.7569i	−0.140106	+	0.645891i
$523$	−4.12311	+	2.38048i	−0.180291	+	0.104091i	−0.587429	−	0.809275i	$-0.699860\pi$
$523$	−4.12311	+	2.38048i	−0.180291	+	0.104091i	0.407138	+	0.913366i	$0.366527\pi$
$524$	4.85315	−	3.46456i	0.212011	−	0.151350i
$525$		0			0
$526$	34.5816	−	11.0771i	1.50783	−	0.482982i
$527$	14.6877	+	25.4399i	0.639808	+	1.10818i
$528$	−0.720689	−	0.827762i	−0.0313640	−	0.0360237i
$529$	10.3625	−	17.9484i	0.450544	−	0.780365i
$530$		0			0
$531$	−38.2866			−1.66150
$532$	−20.7399	+	33.5831i	−0.899190	+	1.45601i
$533$			32.9028i			1.42518i
$534$	9.14721	+	8.30551i	0.395838	+	0.359414i
$535$		0			0
$536$	−0.122758	−	0.285270i	−0.00530233	−	0.0123218i
$537$	12.1101	+	20.9753i	0.522588	+	0.905150i
$538$	−3.53751	−	11.0438i	−0.152513	−	0.476133i
$539$	0.675988	−	0.188219i	0.0291168	−	0.00810715i
$540$		0			0
$541$	11.2312	+	19.4530i	0.482867	+	0.836350i	0.999806	−	0.0196717i	$-0.00626211\pi$
$541$	11.2312	+	19.4530i	0.482867	+	0.836350i	−0.516939	+	0.856022i	$0.672929\pi$
$542$	−1.92088	+	8.85531i	−0.0825089	+	0.380368i
$543$	−29.2344	+	50.6355i	−1.25457	+	2.17298i
$544$	−26.7540	+	14.7115i	−1.14707	+	0.630749i
$545$		0			0
$546$	−27.4089	−	32.0456i	−1.17299	−	1.37143i
$547$	24.4644			1.04602			0.523012	−	0.852326i	$-0.324808\pi$
$547$	24.4644			1.04602			0.523012	+	0.852326i	$0.324808\pi$
$548$	1.26353	−	2.77542i	0.0539755	−	0.118560i
$549$	30.7448	+	17.7505i	1.31215	+	0.757573i
$550$		0			0
$551$	−8.86498	−	15.3546i	−0.377661	−	0.654128i
$552$	−9.36043	−	6.98130i	−0.398406	−	0.297144i
$553$	6.84071	−	9.00562i	0.290897	−	0.382958i
$554$	6.88915	+	21.5073i	0.292692	+	0.913759i
$555$		0			0
$556$	−1.37819	−	14.2552i	−0.0584483	−	0.604554i
$557$	−7.30280	−	4.21627i	−0.309430	−	0.178649i	0.337242	−	0.941418i	$-0.390506\pi$
$557$	−7.30280	−	4.21627i	−0.309430	−	0.178649i	−0.646671	+	0.762769i	$0.723839\pi$
$558$	−25.5983	−	23.2429i	−1.08366	−	0.983948i
$559$	29.0182			1.22734
$560$		0			0
$561$	1.48095			0.0625255
$562$	−10.1393	−	9.20635i	−0.427702	−	0.388346i
$563$	23.5269	+	13.5833i	0.991541	+	0.572467i	0.905735	−	0.423845i	$-0.139320\pi$
$563$	23.5269	+	13.5833i	0.991541	+	0.572467i	0.0858067	+	0.996312i	$0.472653\pi$
$564$	2.34100	+	24.2139i	0.0985738	+	1.01959i
$565$		0			0
$566$	11.2712	+	35.1876i	0.473762	+	1.47905i
$567$	−0.763813	+	6.02888i	−0.0320771	+	0.253189i
$568$	−15.2638	−	11.3842i	−0.640453	−	0.477669i
$569$	7.11643	+	12.3260i	0.298336	+	0.516733i	0.975755	−	0.218864i	$-0.0702350\pi$
$569$	7.11643	+	12.3260i	0.298336	+	0.516733i	−0.677419	+	0.735597i	$0.736902\pi$
$570$		0			0
$571$	−14.5870	−	8.42181i	−0.610447	−	0.352442i	0.162693	−	0.986677i	$-0.447982\pi$
$571$	−14.5870	−	8.42181i	−0.610447	−	0.352442i	−0.773140	+	0.634235i	$0.781315\pi$
$572$	−0.342027	+	0.751281i	−0.0143009	+	0.0314126i
$573$	−68.4938			−2.86137
$574$	9.96101	−	28.1925i	0.415764	−	1.17673i
$575$		0			0
$576$	24.7073	−	26.0968i	1.02947	−	1.08737i
$577$	1.07668	−	1.86487i	0.0448230	−	0.0776356i	−0.842744	−	0.538315i	$-0.819061\pi$
$577$	1.07668	−	1.86487i	0.0448230	−	0.0776356i	0.887566	+	0.460680i	$0.152394\pi$
$578$	3.63695	−	16.7664i	0.151277	−	0.697392i
$579$	−11.1699	−	19.3468i	−0.464203	−	0.804024i
$580$		0			0
$581$	6.66021	+	15.8599i	0.276312	+	0.657979i
$582$	13.0707	+	40.8057i	0.541799	+	1.69145i
$583$	−0.307877	−	0.533259i	−0.0127510	−	0.0220853i
$584$	6.87241	+	15.9704i	0.284382	+	0.660859i
$585$		0			0
$586$	17.0023	+	15.4378i	0.702357	+	0.637728i
$587$			11.3061i			0.466652i	0.972399	+	0.233326i	$0.0749609\pi$
$587$			11.3061i			0.466652i	−0.972399	+	0.233326i	$0.925039\pi$
$588$	13.7836	+	35.7558i	0.568425	+	1.47454i
$589$	40.5980			1.67281
$590$		0			0
$591$	−17.0413	+	29.5164i	−0.700986	+	1.21414i
$592$	3.13301	−	2.72775i	0.128766	−	0.112110i
$593$	8.51993	+	14.7570i	0.349872	+	0.605996i	0.986226	−	0.165401i	$-0.0528918\pi$
$593$	8.51993	+	14.7570i	0.349872	+	0.605996i	−0.636355	+	0.771397i	$0.719558\pi$
$594$	−0.551420	+	0.176629i	−0.0226250	+	0.00724716i
$595$		0			0
$596$	34.2603	−	24.4577i	1.40336	−	1.00183i
$597$	54.9318	−	31.7149i	2.24821	−	1.29800i
$598$	−1.86180	+	8.58296i	−0.0761348	+	0.350984i
$599$	−3.39864	−	1.96221i	−0.138865	−	0.0801736i	0.428958	−	0.903324i	$-0.358881\pi$
$599$	−3.39864	−	1.96221i	−0.138865	−	0.0801736i	−0.567823	+	0.823151i	$0.692214\pi$
$600$		0			0
$601$			8.98026i			0.366312i	0.983084	+	0.183156i	$0.0586314\pi$
$601$			8.98026i			0.366312i	−0.983084	+	0.183156i	$0.941369\pi$
$602$	−24.8640	−	8.78498i	−1.01338	−	0.358049i
$603$	−0.493240			−0.0200863
$604$	3.16804	−	6.95877i	0.128906	−	0.283149i
$605$		0			0
$606$	5.87869	−	27.1009i	0.238806	−	1.10090i
$607$	32.5444	−	18.7895i	1.32094	−	0.762644i	0.337059	−	0.941483i	$-0.390568\pi$
$607$	32.5444	−	18.7895i	1.32094	−	0.762644i	0.983878	+	0.178840i	$0.0572344\pi$
$608$	−0.879659	+	42.1872i	−0.0356749	+	1.71092i
$609$	−17.0767	−	2.16348i	−0.691981	−	0.0876687i
$610$		0			0
$611$	15.8453	−	9.14827i	0.641031	−	0.370099i
$612$	4.66641	+	48.2666i	0.188629	+	1.95106i
$613$	40.0621	+	23.1299i	1.61809	+	0.934207i	0.987413	+	0.158165i	$0.0505578\pi$
$613$	40.0621	+	23.1299i	1.61809	+	0.934207i	0.630681	+	0.776042i	$0.282776\pi$
$614$	−22.3822	+	24.6505i	−0.903272	+	0.994812i
$615$		0			0
$616$	0.520507	−	0.540184i	0.0209718	−	0.0217646i
$617$			42.8844i			1.72646i	0.504809	+	0.863231i	$0.331563\pi$
$617$			42.8844i			1.72646i	−0.504809	+	0.863231i	$0.668437\pi$
$618$	−14.0028	−	12.7143i	−0.563276	−	0.511445i
$619$	14.7503	−	25.5483i	0.592865	−	1.02687i	−0.400980	−	0.916087i	$-0.631330\pi$
$619$	14.7503	−	25.5483i	0.592865	−	1.02687i	0.993844	−	0.110785i	$-0.0353364\pi$
$620$		0			0
$621$	−5.33508	+	3.08021i	−0.214090	+	0.123605i
$622$	−7.26665	+	2.32762i	−0.291366	+	0.0933293i
$623$	−5.10804	+	6.72461i	−0.204649	+	0.269416i
$624$	−42.6352	−	14.6435i	−1.70677	−	0.586210i
$625$		0			0
$626$	−9.76181	+	45.0022i	−0.390160	+	1.79865i
$627$	1.02336	−	1.77251i	0.0408691	−	0.0707873i
$628$	−2.33743	−	1.06413i	−0.0932735	−	0.0424636i
$629$			5.60526i			0.223496i
$630$		0			0
$631$		−	20.5872i		−	0.819563i	−0.912184	−	0.409781i	$-0.865605\pi$
$631$		−	20.5872i		−	0.819563i	0.912184	−	0.409781i	$-0.134395\pi$
$632$	1.41405	−	12.0070i	0.0562478	−	0.477613i
$633$	15.0215	−	26.0181i	0.597053	−	1.03413i
$634$	−18.9506	−	4.11074i	−0.752625	−	0.163258i
$635$		0			0
$636$	27.3686	−	19.5378i	1.08524	−	0.774726i
$637$	20.1800	−	20.5777i	0.799562	−	0.815320i
$638$	0.102789	+	0.320899i	0.00406945	+	0.0127045i
$639$	−26.1906	+	15.1211i	−1.03608	+	0.598182i
$640$		0			0
$641$	18.4263	−	31.9153i	0.727795	−	1.26058i	−0.230018	−	0.973186i	$-0.573878\pi$
$641$	18.4263	−	31.9153i	0.727795	−	1.26058i	0.957813	−	0.287392i	$-0.0927883\pi$
$642$	19.6949	−	21.6909i	0.777297	−	0.856071i
$643$		−	48.4719i		−	1.91154i	−0.294108	−	0.955772i	$-0.595023\pi$
$643$		−	48.4719i		−	1.91154i	0.294108	−	0.955772i	$-0.404977\pi$
$644$	4.19368	−	6.79061i	0.165254	−	0.267587i
$645$		0			0
$646$	−42.1533	−	38.2745i	−1.65850	−	1.50589i
$647$	−33.9366	−	19.5933i	−1.33418	−	0.770292i	−0.348247	−	0.937403i	$-0.613223\pi$
$647$	−33.9366	−	19.5933i	−1.33418	−	0.770292i	−0.985938	+	0.167111i	$0.946556\pi$
$648$	2.56799	+	5.96759i	0.100880	+	0.234429i
$649$	−0.739905	+	0.427185i	−0.0290438	+	0.0167685i
$650$		0			0
$651$	23.8413	−	31.3864i	0.934413	−	1.23013i
$652$	14.0007	−	9.99477i	0.548309	−	0.391425i
$653$	5.96105	−	3.44161i	0.233274	−	0.134681i	−0.378808	−	0.925475i	$-0.623666\pi$
$653$	5.96105	−	3.44161i	0.233274	−	0.134681i	0.612082	+	0.790795i	$0.290332\pi$
$654$	−68.2951	−	14.8145i	−2.67055	−	0.579291i
$655$		0			0
$656$	−6.12351	−	31.3730i	−0.239083	−	1.22491i
$657$	27.6133			1.07730
$658$	−16.3465	+	3.04163i	−0.637251	+	0.118575i
$659$		−	40.9792i		−	1.59632i	−0.602444	−	0.798161i	$-0.705806\pi$
$659$		−	40.9792i		−	1.59632i	0.602444	−	0.798161i	$-0.294194\pi$
$660$		0			0
$661$	10.4696	+	6.04460i	0.407219	+	0.235108i	0.689594	−	0.724196i	$-0.257789\pi$
$661$	10.4696	+	6.04460i	0.407219	+	0.235108i	−0.282375	+	0.959304i	$0.591122\pi$
$662$	−7.85962	−	1.70490i	−0.305473	−	0.0662627i
$663$	52.6785	−	30.4139i	2.04586	−	1.18118i
$664$	14.7409	+	10.9942i	0.572056	+	0.426657i
$665$		0			0
$666$	−2.01259	−	6.28314i	−0.0779863	−	0.243467i
$667$	1.79253	+	3.10475i	0.0694070	+	0.120216i
$668$	−16.1337	+	1.55981i	−0.624233	+	0.0603508i
$669$	−20.5012	+	35.5091i	−0.792621	+	1.37286i
$670$		0			0
$671$	0.792208			0.0305828
$672$	32.0984	+	25.4546i	1.23822	+	0.981932i
$673$			29.0006i			1.11789i	0.829205	+	0.558945i	$0.188794\pi$
$673$			29.0006i			1.11789i	−0.829205	+	0.558945i	$0.811206\pi$
$674$	−13.9957	+	15.4140i	−0.539093	+	0.593726i
$675$		0			0
$676$	0.760730	+	7.86853i	0.0292588	+	0.302636i
$677$	−24.1541	−	41.8361i	−0.928317	−	1.60789i	−0.786138	−	0.618051i	$-0.787923\pi$
$677$	−24.1541	−	41.8361i	−0.928317	−	1.60789i	−0.142178	−	0.989841i	$-0.545411\pi$
$678$	66.8841	−	21.4240i	2.56867	−	0.822786i
$679$	−27.0018	+	11.3392i	−1.03623	+	0.435157i
$680$		0			0
$681$	2.06304	+	3.57329i	0.0790558	+	0.136929i
$682$	−0.754032	−	0.163563i	−0.0288734	−	0.00626317i
$683$	−6.61231	+	11.4528i	−0.253013	+	0.438231i	−0.964354	−	0.264616i	$-0.914755\pi$
$683$	−6.61231	+	11.4528i	−0.253013	+	0.438231i	0.711341	+	0.702847i	$0.248088\pi$
$684$	60.9938	+	27.7680i	2.33216	+	1.06173i
$685$		0			0
$686$	−23.5208	+	11.5226i	−0.898030	+	0.439934i
$687$	−23.3358			−0.890317
$688$	−27.6690	+	5.40055i	−1.05487	+	0.205894i
$689$	−21.9029	−	12.6457i	−0.834435	−	0.481761i
$690$		0			0
$691$	−19.9447	−	34.5453i	−0.758733	−	1.31416i	−0.943497	−	0.331382i	$-0.892485\pi$
$691$	−19.9447	−	34.5453i	−0.758733	−	1.31416i	0.184763	−	0.982783i	$-0.440848\pi$
$692$	13.0772	−	9.33552i	0.497121	−	0.354883i
$693$	−0.461296	−	1.09848i	−0.0175232	−	0.0417277i
$694$	20.8339	−	6.67342i	0.790843	−	0.253320i
$695$		0			0
$696$	−16.9030	+	7.27376i	−0.640708	+	0.275711i
$697$	37.3530	+	21.5658i	1.41485	+	0.816862i
$698$	10.9602	−	12.0710i	0.414851	−	0.456893i
$699$	−58.0921			−2.19725
$700$		0			0
$701$	−5.82647			−0.220063			−0.110031	−	0.993928i	$-0.535095\pi$
$701$	−5.82647			−0.220063			−0.110031	+	0.993928i	$0.535095\pi$
$702$	−15.9871	+	17.6072i	−0.603393	+	0.664543i
$703$	6.70882	+	3.87334i	0.253028	+	0.146086i
$704$	0.186304	−	0.780004i	0.00702160	−	0.0293975i
$705$		0			0
$706$	−27.5237	+	8.81627i	−1.03587	+	0.331805i
$707$	18.8036	+	2.38227i	0.707182	+	0.0895946i
$708$	−27.1091	−	37.9744i	−1.01882	−	1.42716i
$709$	−8.29615	−	14.3694i	−0.311569	−	0.539653i	0.667134	−	0.744938i	$-0.267521\pi$
$709$	−8.29615	−	14.3694i	−0.311569	−	0.539653i	−0.978702	+	0.205286i	$0.934188\pi$
$710$		0			0
$711$	−16.6290	−	9.60078i	−0.623638	−	0.360058i
$712$	−1.05589	+	8.96577i	−0.0395710	+	0.336006i
$713$	−8.20905			−0.307431
$714$	−54.3447	+	10.1121i	−2.03380	+	0.378434i
$715$		0			0
$716$	−7.33265	+	16.1066i	−0.274034	+	0.601930i
$717$	13.8955	−	24.0678i	0.518938	−	0.898828i
$718$	−29.3261	−	6.36137i	−1.09444	−	0.237404i
$719$	−1.69923	−	2.94314i	−0.0633704	−	0.109761i	0.832600	−	0.553875i	$-0.186852\pi$
$719$	−1.69923	−	2.94314i	−0.0633704	−	0.109761i	−0.895970	+	0.444115i	$0.853518\pi$
$720$		0			0
$721$	7.81954	−	10.2942i	0.291215	−	0.383377i
$722$	−49.3493	+	15.8074i	−1.83659	+	0.588290i
$723$	26.0727	+	45.1593i	0.969655	+	1.67949i
$724$	−42.5237	+	4.11119i	−1.58038	+	0.152791i
$725$		0			0
$726$	28.5975	−	31.4957i	1.06135	−	1.16891i
$727$			14.3045i			0.530526i	0.964176	+	0.265263i	$0.0854588\pi$
$727$			14.3045i			0.530526i	−0.964176	+	0.265263i	$0.914541\pi$
$728$	7.42118	−	29.9044i	0.275047	−	1.10833i
$729$	43.8569			1.62433
$730$		0			0
$731$	19.0197	−	32.9430i	0.703468	−	1.21844i
$732$	4.16327	+	43.0624i	0.153879	+	1.59163i
$733$	−24.7457	−	42.8607i	−0.914001	−	1.58310i	−0.808357	−	0.588693i	$-0.799643\pi$
$733$	−24.7457	−	42.8607i	−0.914001	−	1.58310i	−0.105645	−	0.994404i	$-0.533691\pi$
$734$	−3.30088	−	10.3051i	−0.121838	−	0.380367i
$735$		0			0
$736$	0.177870	−	8.53039i	0.00655637	−	0.314434i
$737$	−0.00953207	+	0.00550334i	−0.000351118	+	0.000202718i
$738$	−49.6137	−	10.7621i	−1.82630	−	0.396159i
$739$	23.2184	+	13.4052i	0.854104	+	0.493117i	0.862033	−	0.506852i	$-0.169191\pi$
$739$	23.2184	+	13.4052i	0.854104	+	0.493117i	−0.00792968	+	0.999969i	$0.502524\pi$
$740$		0			0
$741$		−	84.0664i		−	3.08826i
$742$	14.9390	+	17.4662i	0.548428	+	0.641206i
$743$	22.2896			0.817727			0.408863	−	0.912596i	$-0.365925\pi$
$743$	22.2896			0.817727			0.408863	+	0.912596i	$0.365925\pi$
$744$	4.92824	−	41.8468i	0.180678	−	1.53418i
$745$		0			0
$746$	35.4285	+	7.68509i	1.29713	+	0.281371i
$747$	25.2933	−	14.6031i	0.925435	−	0.534300i
$748$	0.628717	+	0.880706i	0.0229882	+	0.0322018i
$749$	15.9461	+	12.1128i	0.582659	+	0.442591i
$750$		0			0
$751$	−11.1427	+	6.43324i	−0.406603	+	0.234752i	−0.689329	−	0.724448i	$-0.742095\pi$
$751$	−11.1427	+	6.43324i	−0.406603	+	0.234752i	0.282726	+	0.959201i	$0.408761\pi$
$752$	−13.4060	+	11.6719i	−0.488865	+	0.425629i
$753$	−22.4290	−	12.9494i	−0.817359	−	0.471902i
$754$	10.2465	+	9.30368i	0.373157	+	0.338820i
$755$		0			0
$756$	19.0288	−	10.2467i	0.692072	−	0.372669i
$757$			3.66830i			0.133327i	0.997776	+	0.0666633i	$0.0212354\pi$
$757$			3.66830i			0.133327i	−0.997776	+	0.0666633i	$0.978765\pi$
$758$	−27.6682	+	30.4721i	−1.00495	+	1.10680i
$759$	−0.206927	+	0.358408i	−0.00751097	+	0.0130094i
$760$		0			0
$761$	−2.56137	+	1.47880i	−0.0928494	+	0.0536066i	−0.545706	−	0.837977i	$-0.683738\pi$
$761$	−2.56137	+	1.47880i	−0.0928494	+	0.0536066i	0.452856	+	0.891583i	$0.350405\pi$
$762$	−5.16700	−	16.1309i	−0.187181	−	0.584362i
$763$	6.00339	−	47.3856i	0.217337	−	1.71547i
$764$	−29.0782	−	40.7327i	−1.05201	−	1.47366i
$765$		0			0
$766$	−11.9456	−	2.59121i	−0.431610	−	0.0936243i
$767$	−17.5460	+	30.3906i	−0.633551	+	1.09734i
$768$	43.3781	+	6.02788i	1.56527	+	0.217512i
$769$			32.6324i			1.17676i	0.808586	+	0.588378i	$0.200233\pi$
$769$			32.6324i			1.17676i	−0.808586	+	0.588378i	$0.799767\pi$
$770$		0			0
$771$		−	7.51469i		−	0.270635i
$772$	6.76334	−	14.8560i	0.243418	−	0.534681i
$773$	2.74844	−	4.76043i	0.0988544	−	0.171221i	−0.812356	−	0.583161i	$-0.801816\pi$
$773$	2.74844	−	4.76043i	0.0988544	−	0.171221i	0.911211	+	0.411941i	$0.135149\pi$
$774$	−9.49151	+	43.7561i	−0.341165	+	1.57278i
$775$		0			0
$776$	−18.7178	+	25.0966i	−0.671931	+	0.900916i
$777$	6.93425	−	2.91198i	0.248765	−	0.104467i
$778$	−19.0936	+	6.11598i	−0.684538	+	0.219269i
$779$	51.6233	−	29.8047i	1.84960	−	1.06786i
$780$		0			0
$781$	−0.337429	+	0.584444i	−0.0120742	+	0.0209131i
$782$	8.52354	+	7.73923i	0.304801	+	0.276754i
$783$			9.70800i			0.346936i
$784$	−15.4121	+	23.3767i	−0.550431	+	0.834881i
$785$		0			0
$786$	7.75819	−	8.54443i	0.276725	−	0.304770i
$787$	27.2677	+	15.7430i	0.971987	+	0.561177i	0.899841	−	0.436217i	$-0.143682\pi$
$787$	27.2677	+	15.7430i	0.971987	+	0.561177i	0.0721455	+	0.997394i	$0.477015\pi$
$788$	−24.7879	+	2.39649i	−0.883031	+	0.0853715i
$789$	60.8659	−	35.1410i	2.16689	−	1.25105i
$790$		0			0
$791$	18.5858	+	44.2582i	0.660837	+	1.57364i
$792$	−1.02097	−	0.761473i	−0.0362787	−	0.0270578i
$793$	28.1795	−	16.2694i	1.00068	−	0.577745i
$794$	0.0524662	−	0.241870i	0.00186195	−	0.00858366i
$795$		0			0
$796$	42.1812	+	19.2033i	1.49507	+	0.680644i
$797$	−20.2691			−0.717968			−0.358984	−	0.933344i	$-0.616877\pi$
$797$	−20.2691			−0.717968			−0.358984	+	0.933344i	$0.616877\pi$
$798$	−25.4503	+	72.0317i	−0.900930	+	2.54989i
$799$		−	23.9845i		−	0.848512i
$800$		0			0
$801$	12.4171	+	7.16902i	0.438737	+	0.253305i
$802$	7.21220	−	33.2484i	0.254672	−	1.17404i
$803$	0.533638	−	0.308096i	0.0188317	−	0.0108725i
$804$	−0.349241	−	0.489217i	−0.0123168	−	0.0172534i
$805$		0			0
$806$	−30.1806	+	9.66734i	−1.06307	+	0.340518i
$807$	−11.2224	−	19.4378i	−0.395049	−	0.684244i
$808$	18.6124	−	8.00934i	0.654783	−	0.281768i
$809$	−15.6376	+	27.0851i	−0.549789	+	0.952262i	0.448500	+	0.893783i	$0.351958\pi$
$809$	−15.6376	+	27.0851i	−0.549789	+	0.952262i	−0.998289	+	0.0584790i	$0.981375\pi$
$810$		0			0
$811$	51.4855			1.80790			0.903950	−	0.427638i	$-0.140654\pi$
$811$	51.4855			1.80790			0.903950	+	0.427638i	$0.140654\pi$
$812$	−5.96307	−	11.0738i	−0.209263	−	0.388615i
$813$			17.5379i			0.615080i
$814$	−0.108999	−	0.0989688i	−0.00382040	−	0.00346886i
$815$		0			0
$816$	−44.5689	+	38.8038i	−1.56022	+	1.35840i
$817$	−26.2859	−	45.5285i	−0.919626	−	1.59284i
$818$	5.14940	+	16.0760i	0.180044	+	0.562084i
$819$	−38.9680	−	29.6002i	−1.36165	−	1.03432i
$820$		0			0
$821$	24.0601	+	41.6733i	0.839702	+	1.45441i	0.890144	+	0.455680i	$0.150604\pi$
$821$	24.0601	+	41.6733i	0.839702	+	1.45441i	−0.0504413	+	0.998727i	$0.516063\pi$
$822$	1.25121	−	5.76812i	0.0436410	−	0.201186i
$823$	−12.3490	+	21.3892i	−0.430461	+	0.745580i	−0.996913	−	0.0785148i	$-0.974982\pi$
$823$	−12.3490	+	21.3892i	−0.430461	+	0.745580i	0.566452	+	0.824095i	$0.308316\pi$
$824$	1.61638	−	13.7251i	0.0563094	−	0.478135i
$825$		0			0
$826$	24.2347	−	20.7281i	0.843232	−	0.721223i
$827$	19.9120			0.692408			0.346204	−	0.938159i	$-0.387470\pi$
$827$	19.9120			0.692408			0.346204	+	0.938159i	$0.387470\pi$
$828$	−12.3332	−	5.61477i	−0.428607	−	0.195127i
$829$	13.8257	+	7.98225i	0.480185	+	0.277235i	0.720494	−	0.693461i	$-0.243915\pi$
$829$	13.8257	+	7.98225i	0.480185	+	0.277235i	−0.240308	+	0.970697i	$0.577249\pi$
$830$		0			0
$831$	21.8552	+	37.8543i	0.758149	+	1.31315i
$832$	−9.39183	−	31.5715i	−0.325603	−	1.09455i
$833$	−10.1342	−	36.3969i	−0.351128	−	1.26108i
$834$	−8.45572	−	26.3981i	−0.292798	−	0.914090i
$835$		0			0
$836$	1.48855	−	0.143913i	0.0514827	−	0.00497735i
$837$	−19.2512	−	11.1147i	−0.665418	−	0.384179i
$838$	−31.5154	−	28.6154i	−1.08868	−	0.988503i
$839$	14.5375			0.501889			0.250944	−	0.968002i	$-0.419259\pi$
$839$	14.5375			0.501889			0.250944	+	0.968002i	$0.419259\pi$
$840$		0			0
$841$	−23.3504			−0.805187
$842$	7.10141	+	6.44796i	0.244731	+	0.222211i
$843$	−22.9558	−	13.2536i	−0.790641	−	0.456477i
$844$	21.8500	−	2.11245i	0.752106	−	0.0727136i
$845$		0			0
$846$	8.61174	+	26.8851i	0.296078	+	0.924330i
$847$	23.1542	+	17.5880i	0.795586	+	0.604331i
$848$	23.2380	+	7.98136i	0.797996	+	0.274081i
$849$	35.7568	+	61.9325i	1.22717	+	2.12552i
$850$		0			0
$851$	−1.35655	−	0.783202i	−0.0465018	−	0.0268478i
$852$	−33.5422	−	15.2704i	−1.14914	−	0.523154i
$853$	36.2299			1.24049			0.620245	−	0.784408i	$-0.287033\pi$
$853$	36.2299			1.24049			0.620245	+	0.784408i	$0.287033\pi$
$854$	−29.0708	+	5.40928i	−0.994783	+	0.185102i
$855$		0			0
$856$	21.2606	+	2.50384i	0.726674	+	0.0855794i
$857$	−19.0281	+	32.9576i	−0.649986	+	1.12581i	0.333139	+	0.942878i	$0.391892\pi$
$857$	−19.0281	+	32.9576i	−0.649986	+	1.12581i	−0.983126	+	0.182932i	$0.941441\pi$
$858$	−0.338691	+	1.56137i	−0.0115627	+	0.0533045i
$859$	13.3104	+	23.0543i	0.454145	+	0.786602i	0.998639	−	0.0521630i	$-0.0166115\pi$
$859$	13.3104	+	23.0543i	0.454145	+	0.786602i	−0.544494	+	0.838765i	$0.683278\pi$
$860$		0			0
$861$	7.27378	−	57.4129i	0.247890	−	1.95663i
$862$	6.87487	+	21.4628i	0.234159	+	0.731025i
$863$	−11.6160	−	20.1195i	−0.395413	−	0.684876i	0.597741	−	0.801690i	$-0.296065\pi$
$863$	−11.6160	−	20.1195i	−0.395413	−	0.684876i	−0.993154	+	0.116814i	$0.962732\pi$
$864$	11.9669	−	19.7639i	0.407122	−	0.672383i
$865$		0			0
$866$	−15.8403	−	14.3827i	−0.538276	−	0.488745i
$867$		−	33.2058i		−	1.12773i
$868$	28.7868	+	0.853505i	0.977086	+	0.0289698i
$869$	−0.428484			−0.0145353
$870$		0			0
$871$	−0.226043	+	0.391517i	−0.00765916	+	0.0132661i
$872$	−20.1838	−	46.9038i	−0.683509	−	1.58836i
$873$	24.8621	+	43.0624i	0.841455	+	1.45744i
$874$	15.1528	−	4.85370i	0.512553	−	0.164179i
$875$		0			0
$876$	19.5517	+	27.3881i	0.660592	+	0.925358i
$877$	2.22052	−	1.28202i	0.0749817	−	0.0432907i	−0.462040	−	0.886859i	$-0.652882\pi$
$877$	2.22052	−	1.28202i	0.0749817	−	0.0432907i	0.537022	+	0.843568i	$0.319549\pi$
$878$	−1.30914	+	6.03515i	−0.0441812	+	0.203676i
$879$	38.4937	+	22.2244i	1.29836	+	0.749609i
$880$		0			0
$881$			11.4074i			0.384324i	0.981363	+	0.192162i	$0.0615498\pi$
$881$			11.4074i			0.384324i	−0.981363	+	0.192162i	$0.938450\pi$
$882$	24.4282	+	37.1599i	0.822542	+	1.25124i
$883$	15.8634			0.533845			0.266922	−	0.963718i	$-0.413993\pi$
$883$	15.8634			0.533845			0.266922	+	0.963718i	$0.413993\pi$
$884$	40.4509	+	18.4156i	1.36051	+	0.619385i
$885$		0			0
$886$	4.22659	−	19.4847i	0.141995	−	0.654601i
$887$	23.4277	−	13.5260i	0.786626	−	0.454159i	−0.0521471	−	0.998639i	$-0.516606\pi$
$887$	23.4277	−	13.5260i	0.786626	−	0.454159i	0.838774	+	0.544480i	$0.183273\pi$
$888$	4.80687	−	6.44499i	0.161308	−	0.216280i
$889$	10.6741	−	4.48249i	0.357997	−	0.150338i
$890$		0			0
$891$	0.199403	−	0.115125i	0.00668024	−	0.00385684i
$892$	−29.8205	+	2.88304i	−0.998463	+	0.0965314i
$893$	−28.7066	−	16.5738i	−0.960629	−	0.554620i
$894$	54.7681	−	60.3185i	1.83172	−	2.01735i
$895$		0			0
$896$	−1.51065	+	29.8951i	−0.0504674	+	0.998726i
$897$			16.9985i			0.567563i
$898$	−17.8118	−	16.1728i	−0.594387	−	0.539693i
$899$	−6.46818	+	11.2032i	−0.215726	+	0.373648i
$900$		0			0
$901$	−28.7121	+	16.5769i	−0.956537	+	0.552257i
$902$	−1.07888	+	0.345584i	−0.0359229	+	0.0115067i
$903$	−50.6346	−	6.41502i	−1.68501	−	0.213478i
$904$	41.1355	+	30.6801i	1.36815	+	1.02041i
$905$		0			0
$906$	3.13714	−	14.4623i	0.104225	−	0.480478i
$907$	−5.21256	+	9.02842i	−0.173080	+	0.299784i	−0.939495	−	0.342562i	$-0.888705\pi$
$907$	−5.21256	+	9.02842i	−0.173080	+	0.299784i	0.766415	+	0.642346i	$0.222039\pi$
$908$	−1.24917	+	2.74387i	−0.0414551	+	0.0910584i
$909$		−	32.1815i		−	1.06739i
$910$		0			0
$911$		−	43.7727i		−	1.45026i	−0.688614	−	0.725128i	$-0.741781\pi$
$911$		−	43.7727i		−	1.45026i	0.688614	−	0.725128i	$-0.258219\pi$
$912$	15.6455	+	80.1577i	0.518075	+	2.65429i
$913$	0.325870	−	0.564423i	0.0107847	−	0.0186797i
$914$	−16.1214	−	3.49704i	−0.533250	−	0.115672i
$915$		0			0
$916$	−9.90692	−	13.8776i	−0.327334	−	0.458529i
$917$	6.28147	+	4.77143i	0.207432	+	0.157567i
$918$	9.51014	+	29.6899i	0.313881	+	0.979912i
$919$	−43.5772	+	25.1593i	−1.43748	+	0.829929i	−0.997674	−	0.0681637i	$-0.978286\pi$
$919$	−43.5772	+	25.1593i	−1.43748	+	0.829929i	−0.439806	+	0.898093i	$0.644953\pi$
$920$		0			0
$921$	−32.2216	+	55.8095i	−1.06174	+	1.83899i
$922$	25.1440	−	27.6922i	0.828073	−	0.911993i
$923$			27.7189i			0.912379i
$924$	0.762896	−	1.23532i	0.0250974	−	0.0406390i
$925$		0			0
$926$	3.28432	+	2.98210i	0.107929	+	0.0979980i
$927$	−19.0085	−	10.9745i	−0.624320	−	0.360451i
$928$	−11.5016	−	6.96412i	−0.377559	−	0.228609i
$929$	16.4494	−	9.49704i	0.539686	−	0.311588i	−0.205266	−	0.978706i	$-0.565806\pi$
$929$	16.4494	−	9.49704i	0.539686	−	0.311588i	0.744952	+	0.667118i	$0.232473\pi$
$930$		0			0
$931$	−50.5656	−	13.0216i	−1.65722	−	0.426765i
$932$	−24.6623	−	34.5469i	−0.807840	−	1.13162i
$933$	−12.7898	+	7.38419i	−0.418719	+	0.241747i
$934$	−11.2516	−	2.44069i	−0.368164	−	0.0798617i
$935$		0			0
$936$	−51.9551	−	6.11869i	−1.69821	−	0.199996i
$937$	−44.7192			−1.46091			−0.730457	−	0.682959i	$-0.760693\pi$
$937$	−44.7192			−1.46091			−0.730457	+	0.682959i	$0.760693\pi$
$938$	0.312211	−	0.267037i	0.0101941	−	0.00871905i
$939$			89.1265i			2.90853i
$940$		0			0
$941$	8.88040	+	5.12710i	0.289493	+	0.167139i	0.637713	−	0.770274i	$-0.279881\pi$
$941$	8.88040	+	5.12710i	0.289493	+	0.167139i	−0.348220	+	0.937413i	$0.613214\pi$
$942$	−4.85784	−	1.05376i	−0.158277	−	0.0343332i
$943$	−10.4384	+	6.02661i	−0.339921	+	0.196253i
$944$	11.0743	−	32.2431i	0.360436	−	1.04942i
$945$		0			0
$946$	0.304783	+	0.951508i	0.00990936	+	0.0309362i
$947$	−12.4847	−	21.6242i	−0.405699	−	0.702691i	0.588704	−	0.808349i	$-0.299638\pi$
$947$	−12.4847	−	21.6242i	−0.405699	−	0.702691i	−0.994403	+	0.105658i	$0.966305\pi$
$948$	−2.25180	−	23.2913i	−0.0731352	−	0.756467i
$949$	12.6546	−	21.9185i	0.410787	−	0.711504i
$950$		0			0
$951$	−37.5316			−1.21704
$952$	−29.0849	−	28.0254i	−0.942648	−	0.908309i
$953$			26.3831i			0.854633i	0.904102	+	0.427317i	$0.140541\pi$
$953$			26.3831i			0.854633i	−0.904102	+	0.427317i	$0.859459\pi$
$954$	26.2324	−	28.8909i	0.849305	−	0.935376i
$955$		0			0
$956$	20.2121	−	1.95410i	0.653706	−	0.0632003i
$957$	0.326089	+	0.564803i	0.0105410	+	0.0182575i
$958$	−33.3749	+	10.6905i	−1.07829	+	0.345395i
$959$	4.00213	+	0.507039i	0.129235	+	0.0163731i
$960$		0			0
$961$	0.689177	+	1.19369i	0.0222315	+	0.0385061i
$962$	−5.90968	−	1.28192i	−0.190536	−	0.0413307i
$963$	17.0000	−	29.4448i	0.547817	−	0.948846i
$964$	−15.7870	+	34.6771i	−0.508466	+	1.11687i
$965$		0			0
$966$	5.14613	−	14.5650i	0.165574	−	0.468623i
$967$	−47.1287			−1.51556			−0.757778	−	0.652512i	$-0.773715\pi$
$967$	−47.1287			−1.51556			−0.757778	+	0.652512i	$0.773715\pi$
$968$	30.8709	+	3.63563i	0.992229	+	0.116854i
$969$	−95.4367	−	55.1004i	−3.06587	−	1.77008i
$970$		0			0
$971$	27.6416	+	47.8767i	0.887062	+	1.53644i	0.843332	+	0.537394i	$0.180591\pi$
$971$	27.6416	+	47.8767i	0.887062	+	1.53644i	0.0437306	+	0.999043i	$0.486076\pi$
$972$	21.5443	+	30.1792i	0.691033	+	0.968000i
$973$	17.4680	−	7.33553i	0.559998	−	0.235166i
$974$	17.0971	−	5.47647i	0.547826	−	0.175477i
$975$		0			0
$976$	−23.8414	+	20.7575i	−0.763144	+	0.664430i
$977$	7.32085	+	4.22669i	0.234215	+	0.135224i	0.612515	−	0.790459i	$-0.290158\pi$
$977$	7.32085	+	4.22669i	0.234215	+	0.135224i	−0.378300	+	0.925683i	$0.623491\pi$
$978$	22.3813	−	24.6495i	0.715675	−	0.788204i
$979$	0.319954			0.0102258
$980$		0			0
$981$	−81.0982			−2.58927
$982$	9.04267	−	9.95908i	0.288563	−	0.317807i
$983$	−28.4854	−	16.4461i	−0.908543	−	0.524548i	−0.0285811	−	0.999591i	$-0.509099\pi$
$983$	−28.4854	−	16.4461i	−0.908543	−	0.524548i	−0.879962	+	0.475044i	$0.842432\pi$
$984$	−24.4549	−	56.8292i	−0.779593	−	1.81165i
$985$		0			0
$986$	17.2780	−	5.53442i	0.550244	−	0.176252i
$987$	−29.6712	+	12.4602i	−0.944445	+	0.396611i
$988$	49.9936	−	35.6893i	1.59051	−	1.13543i
$989$	5.31509	+	9.20601i	0.169010	+	0.292734i
$990$		0			0
$991$	26.5344	+	15.3196i	0.842893	+	0.486645i	0.858247	−	0.513238i	$-0.171554\pi$
$991$	26.5344	+	15.3196i	0.842893	+	0.486645i	−0.0153535	+	0.999882i	$0.504887\pi$
$992$	26.9782	−	14.8347i	0.856559	−	0.471004i
$993$	−15.5659			−0.493970
$994$	8.39163	−	23.7508i	0.266166	−	0.753328i
$995$		0			0
$996$	32.3931	+	14.7472i	1.02641	+	0.467284i
$997$	21.2349	−	36.7799i	0.672516	−	1.16483i	−0.304673	−	0.952457i	$-0.598547\pi$
$997$	21.2349	−	36.7799i	0.672516	−	1.16483i	0.977188	−	0.212374i	$-0.0681196\pi$
$998$	11.7376	+	2.54611i	0.371548	+	0.0805957i
$999$	−2.12084	−	3.67340i	−0.0671003	−	0.116221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.d.199.12		32
4.3	odd	2	inner	700.2.t.d.199.8		32
5.2	odd	4		140.2.o.a.31.4	✓	32
5.3	odd	4		700.2.p.c.451.13		32
5.4	even	2		700.2.t.c.199.5		32
7.5	odd	6		700.2.t.c.299.9		32
20.3	even	4		700.2.p.c.451.1		32
20.7	even	4		140.2.o.a.31.16	yes	32
20.19	odd	2		700.2.t.c.199.9		32
28.19	even	6		700.2.t.c.299.5		32
35.2	odd	12		980.2.o.f.411.16		32
35.12	even	12		140.2.o.a.131.16	yes	32
35.17	even	12		980.2.g.a.391.14		32
35.19	odd	6	inner	700.2.t.d.299.8		32
35.27	even	4		980.2.o.f.31.4		32
35.32	odd	12		980.2.g.a.391.13		32
35.33	even	12		700.2.p.c.551.1		32
140.19	even	6	inner	700.2.t.d.299.12		32
140.27	odd	4		980.2.o.f.31.16		32
140.47	odd	12		140.2.o.a.131.4	yes	32
140.67	even	12		980.2.g.a.391.16		32
140.87	odd	12		980.2.g.a.391.15		32
140.103	odd	12		700.2.p.c.551.13		32
140.107	even	12		980.2.o.f.411.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.4	✓	32	5.2	odd	4
140.2.o.a.31.16	yes	32	20.7	even	4
140.2.o.a.131.4	yes	32	140.47	odd	12
140.2.o.a.131.16	yes	32	35.12	even	12
700.2.p.c.451.1		32	20.3	even	4
700.2.p.c.451.13		32	5.3	odd	4
700.2.p.c.551.1		32	35.33	even	12
700.2.p.c.551.13		32	140.103	odd	12
700.2.t.c.199.5		32	5.4	even	2
700.2.t.c.199.9		32	20.19	odd	2
700.2.t.c.299.5		32	28.19	even	6
700.2.t.c.299.9		32	7.5	odd	6
700.2.t.d.199.8		32	4.3	odd	2	inner
700.2.t.d.199.12		32	1.1	even	1	trivial
700.2.t.d.299.8		32	35.19	odd	6	inner
700.2.t.d.299.12		32	140.19	even	6	inner
980.2.g.a.391.13		32	35.32	odd	12
980.2.g.a.391.14		32	35.17	even	12
980.2.g.a.391.15		32	140.87	odd	12
980.2.g.a.391.16		32	140.67	even	12
980.2.o.f.31.4		32	35.27	even	4
980.2.o.f.31.16		32	140.27	odd	4
980.2.o.f.411.4		32	140.107	even	12
980.2.o.f.411.16		32	35.2	odd	12

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.04701 + 0.950668i) q^{2} +(2.37047 + 1.36859i) q^{3} +(0.192463 + 1.99072i) q^{4} +(1.18083 + 3.68646i) q^{6} +(-2.43939 + 1.02440i) q^{7} +(-1.69100 + 2.26727i) q^{8} +(2.24609 + 3.89033i) q^{9} +(0.0868131 + 0.0501216i) q^{11} +(-2.26825 + 4.98234i) q^{12} +4.11735 q^{13} +(-3.52793 - 1.24649i) q^{14} +(-3.92592 + 0.766277i) q^{16} +(2.69867 - 4.67424i) q^{17} +(-1.34674 + 6.20850i) q^{18} +(-3.72967 - 6.45997i) q^{19} +(-7.18448 - 0.910218i) q^{21} +(0.0432453 + 0.135008i) q^{22} +(0.754151 + 1.30623i) q^{23} +(-7.11143 + 3.06021i) q^{24} +(4.31091 + 3.91424i) q^{26} +4.08434i q^{27} +(-2.50878 - 4.65897i) q^{28} +2.37688 q^{29} +(-2.72129 + 4.71341i) q^{31} +(-4.83895 - 2.92994i) q^{32} +(0.137192 + 0.237623i) q^{33} +(7.26919 - 2.32844i) q^{34} +(-7.31227 + 5.22007i) q^{36} +(-0.899386 + 0.519260i) q^{37} +(2.23629 - 10.3093i) q^{38} +(9.76007 + 5.63498i) q^{39} +7.99125i q^{41} +(-6.65691 - 7.78306i) q^{42} +7.04778 q^{43} +(-0.0830696 + 0.182467i) q^{44} +(-0.452184 + 2.08458i) q^{46} +(3.84841 - 2.22188i) q^{47} +(-10.3550 - 3.55654i) q^{48} +(4.90122 - 4.99781i) q^{49} +(12.7943 - 7.38677i) q^{51} +(0.792437 + 8.19649i) q^{52} +(-5.31966 - 3.07131i) q^{53} +(-3.88285 + 4.27635i) q^{54} +(1.80242 - 7.26301i) q^{56} -20.4176i q^{57} +(2.48862 + 2.25962i) q^{58} +(-4.26148 + 7.38111i) q^{59} +(6.84408 - 3.95143i) q^{61} +(-7.33010 + 2.34795i) q^{62} +(-9.46432 - 7.18914i) q^{63} +(-2.28103 - 7.66791i) q^{64} +(-0.0822594 + 0.379218i) q^{66} +(-0.0549000 + 0.0950895i) q^{67} +(9.82449 + 4.47268i) q^{68} +4.12850i q^{69} +6.73221i q^{71} +(-12.6186 - 1.48607i) q^{72} +(3.07349 - 5.32344i) q^{73} +(-1.43531 - 0.311345i) q^{74} +(12.1422 - 8.66802i) q^{76} +(-0.263115 - 0.0333347i) q^{77} +(4.86190 + 15.1785i) q^{78} +(-3.70178 + 2.13723i) q^{79} +(1.14846 - 1.98919i) q^{81} +(-7.59702 + 8.36692i) q^{82} -6.50159i q^{83} +(0.429245 - 14.4774i) q^{84} +(7.37910 + 6.70009i) q^{86} +(5.63433 + 3.25298i) q^{87} +(-0.260440 + 0.112073i) q^{88} +(2.76417 - 1.59589i) q^{89} +(-10.0438 + 4.21781i) q^{91} +(-2.45519 + 1.75270i) q^{92} +(-12.9015 + 7.44866i) q^{93} +(6.14160 + 1.33223i) q^{94} +(-7.46070 - 13.5679i) q^{96} +11.0691 q^{97} +(9.88288 - 0.573332i) q^{98} +0.450309i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4} + 16 q^{9} + 14 q^{12} + 8 q^{13} - 2 q^{14} - 14 q^{16} - 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} - 32 q^{28} + 40 q^{29} - 60 q^{32} + 24 q^{33} + 60 q^{36} + 60 q^{37} + 46 q^{38}+ \cdots + 124 q^{98}+O(q^{100}) \) 32 * q + 2 * q^4 + 16 * q^9 + 14 * q^12 + 8 * q^13 - 2 * q^14 - 14 * q^16 - 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 - 32 * q^28 + 40 * q^29 - 60 * q^32 + 24 * q^33 + 60 * q^36 + 60 * q^37 + 46 * q^38 - 78 * q^42 + 18 * q^44 + 2 * q^46 + 28 * q^48 + 16 * q^49 + 46 * q^52 + 12 * q^53 - 12 * q^54 - 4 * q^56 - 42 * q^58 + 24 * q^61 - 8 * q^62 - 4 * q^64 + 24 * q^66 + 4 * q^68 - 90 * q^72 + 24 * q^73 - 38 * q^74 - 20 * q^77 - 36 * q^81 - 8 * q^82 + 20 * q^84 + 28 * q^86 + 78 * q^88 + 60 * q^89 - 72 * q^93 - 18 * q^94 - 60 * q^96 + 48 * q^97 + 124 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more