LMFDB - Embedded newform 1824.2.bb.a.31.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1824,2,Mod(31,1824)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1824, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1824.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1824 = 2^{5} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1824.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.5647133287$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.13
Character	$\chi$	$=$	1824.31
Dual form			1824.2.bb.a.1471.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(0.508588 + 0.880900i) q^{5} +1.27458i q^{7} +(-0.500000 + 0.866025i) q^{9} +0.0879656i q^{11} +(-3.47163 - 2.00435i) q^{13} +(0.508588 - 0.880900i) q^{15} +(-2.85692 - 4.94832i) q^{17} +(2.85898 + 3.29032i) q^{19} +(1.10381 - 0.637288i) q^{21} +(3.99307 + 2.30540i) q^{23} +(1.98268 - 3.43410i) q^{25} +1.00000 q^{27} +(2.52234 + 1.45627i) q^{29} +7.52645 q^{31} +(0.0761804 - 0.0439828i) q^{33} +(-1.12277 + 0.648234i) q^{35} -2.94596i q^{37} +4.00869i q^{39} +(2.94846 - 1.70230i) q^{41} +(1.88831 - 1.09022i) q^{43} -1.01718 q^{45} +(2.26213 + 1.30604i) q^{47} +5.37546 q^{49} +(-2.85692 + 4.94832i) q^{51} +(4.74768 + 2.74107i) q^{53} +(-0.0774889 + 0.0447382i) q^{55} +(1.42001 - 4.12111i) q^{57} +(1.68855 + 2.92466i) q^{59} +(-6.37060 + 11.0342i) q^{61} +(-1.10381 - 0.637288i) q^{63} -4.07755i q^{65} +(-2.40354 + 4.16306i) q^{67} -4.61080i q^{69} +(0.644658 + 1.11658i) q^{71} +(3.09225 + 5.35593i) q^{73} -3.96535 q^{75} -0.112119 q^{77} +(7.52313 + 13.0304i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0104i q^{83} +(2.90599 - 5.03332i) q^{85} -2.91255i q^{87} +(3.84299 + 2.21875i) q^{89} +(2.55469 - 4.42485i) q^{91} +(-3.76322 - 6.51809i) q^{93} +(-1.44440 + 4.19190i) q^{95} +(-8.08295 + 4.66669i) q^{97} +(-0.0761804 - 0.0439828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) $ 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1824\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$799$	$1217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	0.508588	+	0.880900i	0.227447	+	0.393951i	0.957051	−	0.289920i	$-0.0936287\pi$
$5$	0.508588	+	0.880900i	0.227447	+	0.393951i	−0.729603	+	0.683870i	$0.760295\pi$
$6$		0			0
$7$			1.27458i			0.481744i	0.970557	+	0.240872i	$0.0774334\pi$
$7$			1.27458i			0.481744i	−0.970557	+	0.240872i	$0.922567\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$			0.0879656i			0.0265226i	0.999912	+	0.0132613i	$0.00422133\pi$
$11$			0.0879656i			0.0265226i	−0.999912	+	0.0132613i	$0.995779\pi$
$12$		0			0
$13$	−3.47163	−	2.00435i	−0.962857	−	0.555906i	−0.0658059	−	0.997832i	$-0.520962\pi$
$13$	−3.47163	−	2.00435i	−0.962857	−	0.555906i	−0.897051	+	0.441927i	$0.854295\pi$
$14$		0			0
$15$	0.508588	−	0.880900i	0.131317	−	0.227447i
$16$		0			0
$17$	−2.85692	−	4.94832i	−0.692904	−	1.20014i	−0.970882	−	0.239557i	$-0.922998\pi$
$17$	−2.85692	−	4.94832i	−0.692904	−	1.20014i	0.277979	−	0.960587i	$-0.410336\pi$
$18$		0			0
$19$	2.85898	+	3.29032i	0.655896	+	0.754852i
$19$	2.85898	+	3.29032i	0.655896	+	0.754852i
$20$		0			0
$21$	1.10381	−	0.637288i	0.240872	−	0.139068i
$22$		0			0
$23$	3.99307	+	2.30540i	0.832612	+	0.480709i	0.854746	−	0.519046i	$-0.173713\pi$
$23$	3.99307	+	2.30540i	0.832612	+	0.480709i	−0.0221340	+	0.999755i	$0.507046\pi$
$24$		0			0
$25$	1.98268	−	3.43410i	0.396535	−	0.686819i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.52234	+	1.45627i	0.468387	+	0.270423i	0.715564	−	0.698547i	$-0.246170\pi$
$29$	2.52234	+	1.45627i	0.468387	+	0.270423i	−0.247177	+	0.968970i	$0.579503\pi$
$30$		0			0
$31$	7.52645			1.35179			0.675895	−	0.736998i	$-0.263757\pi$
$31$	7.52645			1.35179			0.675895	+	0.736998i	$0.263757\pi$
$32$		0			0
$33$	0.0761804	−	0.0439828i	0.0132613	−	0.00765642i
$34$		0			0
$35$	−1.12277	+	0.648234i	−0.189783	+	0.109572i
$36$		0			0
$37$		−	2.94596i		−	0.484313i	−0.970237	−	0.242156i	$-0.922145\pi$
$37$		−	2.94596i		−	0.484313i	0.970237	−	0.242156i	$-0.0778547\pi$
$38$		0			0
$39$			4.00869i			0.641905i
$40$		0			0
$41$	2.94846	−	1.70230i	0.460473	−	0.265854i	−0.251770	−	0.967787i	$-0.581013\pi$
$41$	2.94846	−	1.70230i	0.460473	−	0.265854i	0.712243	+	0.701933i	$0.247679\pi$
$42$		0			0
$43$	1.88831	−	1.09022i	0.287965	−	0.166257i	−0.349059	−	0.937101i	$-0.613499\pi$
$43$	1.88831	−	1.09022i	0.287965	−	0.166257i	0.637024	+	0.770844i	$0.280165\pi$
$44$		0			0
$45$	−1.01718			−0.151632
$46$		0			0
$47$	2.26213	+	1.30604i	0.329966	+	0.190506i	0.655826	−	0.754912i	$-0.272321\pi$
$47$	2.26213	+	1.30604i	0.329966	+	0.190506i	−0.325860	+	0.945418i	$0.605654\pi$
$48$		0			0
$49$	5.37546			0.767923
$50$		0			0
$51$	−2.85692	+	4.94832i	−0.400048	+	0.692904i
$52$		0			0
$53$	4.74768	+	2.74107i	0.652144	+	0.376516i	0.789277	−	0.614037i	$-0.210455\pi$
$53$	4.74768	+	2.74107i	0.652144	+	0.376516i	−0.137133	+	0.990553i	$0.543789\pi$
$54$		0			0
$55$	−0.0774889	+	0.0447382i	−0.0104486	+	0.00603250i
$56$		0			0
$57$	1.42001	−	4.12111i	0.188085	−	0.545855i
$58$		0			0
$59$	1.68855	+	2.92466i	0.219831	+	0.380758i	0.954756	−	0.297390i	$-0.0961161\pi$
$59$	1.68855	+	2.92466i	0.219831	+	0.380758i	−0.734925	+	0.678148i	$0.762783\pi$
$60$		0			0
$61$	−6.37060	+	11.0342i	−0.815671	+	1.41278i	0.0931734	+	0.995650i	$0.470299\pi$
$61$	−6.37060	+	11.0342i	−0.815671	+	1.41278i	−0.908845	+	0.417134i	$0.863034\pi$
$62$		0			0
$63$	−1.10381	−	0.637288i	−0.139068	−	0.0802907i
$64$		0			0
$65$		−	4.07755i		−	0.505758i
$66$		0			0
$67$	−2.40354	+	4.16306i	−0.293640	+	0.508599i	−0.974668	−	0.223659i	$-0.928200\pi$
$67$	−2.40354	+	4.16306i	−0.293640	+	0.508599i	0.681028	+	0.732258i	$0.261533\pi$
$68$		0			0
$69$		−	4.61080i		−	0.555075i
$70$		0			0
$71$	0.644658	+	1.11658i	0.0765068	+	0.132514i	0.901741	−	0.432278i	$-0.142290\pi$
$71$	0.644658	+	1.11658i	0.0765068	+	0.132514i	−0.825234	+	0.564791i	$0.808957\pi$
$72$		0			0
$73$	3.09225	+	5.35593i	0.361920	+	0.626864i	0.988277	−	0.152672i	$-0.0487880\pi$
$73$	3.09225	+	5.35593i	0.361920	+	0.626864i	−0.626357	+	0.779537i	$0.715455\pi$
$74$		0			0
$75$	−3.96535			−0.457879
$76$		0			0
$77$	−0.112119			−0.0127771
$78$		0			0
$79$	7.52313	+	13.0304i	0.846419	+	1.46604i	0.884383	+	0.466761i	$0.154579\pi$
$79$	7.52313	+	13.0304i	0.846419	+	1.46604i	−0.0379649	+	0.999279i	$0.512087\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	12.0104i		−	1.31832i	−0.752004	−	0.659159i	$-0.770912\pi$
$83$		−	12.0104i		−	1.31832i	0.752004	−	0.659159i	$-0.229088\pi$
$84$		0			0
$85$	2.90599	−	5.03332i	0.315198	−	0.545940i
$86$		0			0
$87$		−	2.91255i		−	0.312258i
$88$		0			0
$89$	3.84299	+	2.21875i	0.407356	+	0.235187i	0.689653	−	0.724140i	$-0.257763\pi$
$89$	3.84299	+	2.21875i	0.407356	+	0.235187i	−0.282297	+	0.959327i	$0.591096\pi$
$90$		0			0
$91$	2.55469	−	4.42485i	0.267804	−	0.463851i
$92$		0			0
$93$	−3.76322	−	6.51809i	−0.390228	−	0.675895i
$94$		0			0
$95$	−1.44440	+	4.19190i	−0.148192	+	0.430080i
$96$		0			0
$97$	−8.08295	+	4.66669i	−0.820699	+	0.473831i	−0.850657	−	0.525720i	$-0.823796\pi$
$97$	−8.08295	+	4.66669i	−0.820699	+	0.473831i	0.0299584	+	0.999551i	$0.490463\pi$
$98$		0			0
$99$	−0.0761804	−	0.0439828i	−0.00765642	−	0.00442044i
$100$		0			0
$101$	3.80402	−	6.58876i	0.378514	−	0.655606i	−0.612332	−	0.790601i	$-0.709768\pi$
$101$	3.80402	−	6.58876i	0.378514	−	0.655606i	0.990846	+	0.134995i	$0.0431018\pi$
$102$		0			0
$103$	16.9095			1.66614			0.833070	−	0.553167i	$-0.186581\pi$
$103$	16.9095			1.66614			0.833070	+	0.553167i	$0.186581\pi$
$104$		0			0
$105$	1.12277	+	0.648234i	0.109572	+	0.0632611i
$106$		0			0
$107$	1.99749			0.193104			0.0965522	−	0.995328i	$-0.469219\pi$
$107$	1.99749			0.193104			0.0965522	+	0.995328i	$0.469219\pi$
$108$		0			0
$109$	11.1161	−	6.41789i	1.06473	−	0.614723i	0.137994	−	0.990433i	$-0.455935\pi$
$109$	11.1161	−	6.41789i	1.06473	−	0.614723i	0.926737	+	0.375711i	$0.122601\pi$
$110$		0			0
$111$	−2.55128	+	1.47298i	−0.242156	+	0.139809i
$112$		0			0
$113$		−	19.7888i		−	1.86158i	−0.365560	−	0.930788i	$-0.619122\pi$
$113$		−	19.7888i		−	1.86158i	0.365560	−	0.930788i	$-0.380878\pi$
$114$		0			0
$115$			4.68999i			0.437344i
$116$		0			0
$117$	3.47163	−	2.00435i	0.320952	−	0.185302i
$118$		0			0
$119$	6.30701	−	3.64135i	0.578163	−	0.333802i
$120$		0			0
$121$	10.9923			0.999297
$122$		0			0
$123$	−2.94846	−	1.70230i	−0.265854	−	0.153491i
$124$		0			0
$125$	9.11934			0.815659
$126$		0			0
$127$	8.02046	−	13.8918i	0.711700	−	1.23270i	−0.252518	−	0.967592i	$-0.581259\pi$
$127$	8.02046	−	13.8918i	0.711700	−	1.23270i	0.964218	−	0.265109i	$-0.0854080\pi$
$128$		0			0
$129$	−1.88831	−	1.09022i	−0.166257	−	0.0959883i
$130$		0			0
$131$	−17.7628	+	10.2554i	−1.55195	+	0.896016i	−0.553962	+	0.832542i	$0.686885\pi$
$131$	−17.7628	+	10.2554i	−1.55195	+	0.896016i	−0.997983	+	0.0634744i	$0.979782\pi$
$132$		0			0
$133$	−4.19376	+	3.64399i	−0.363645	+	0.315974i
$134$		0			0
$135$	0.508588	+	0.880900i	0.0437723	+	0.0758158i
$136$		0			0
$137$	1.98262	−	3.43400i	0.169387	−	0.293387i	−0.768818	−	0.639468i	$-0.779155\pi$
$137$	1.98262	−	3.43400i	0.169387	−	0.293387i	0.938204	+	0.346082i	$0.112488\pi$
$138$		0			0
$139$	−7.37387	−	4.25731i	−0.625444	−	0.361100i	0.153542	−	0.988142i	$-0.450932\pi$
$139$	−7.37387	−	4.25731i	−0.625444	−	0.361100i	−0.778985	+	0.627042i	$0.784265\pi$
$140$		0			0
$141$		−	2.61208i		−	0.219977i
$142$		0			0
$143$	0.176314	−	0.305384i	0.0147441	−	0.0255375i
$144$		0			0
$145$			2.96257i			0.246028i
$146$		0			0
$147$	−2.68773	−	4.65528i	−0.221680	−	0.383961i
$148$		0			0
$149$	−7.45843	−	12.9184i	−0.611018	−	1.05831i	−0.991069	−	0.133349i	$-0.957427\pi$
$149$	−7.45843	−	12.9184i	−0.611018	−	1.05831i	0.380051	−	0.924966i	$-0.375906\pi$
$150$		0			0
$151$	8.79143			0.715436			0.357718	−	0.933830i	$-0.383555\pi$
$151$	8.79143			0.715436			0.357718	+	0.933830i	$0.383555\pi$
$152$		0			0
$153$	5.71383			0.461936
$154$		0			0
$155$	3.82786	+	6.63005i	0.307461	+	0.532538i
$156$		0			0
$157$	4.42080	+	7.65705i	0.352818	+	0.611099i	0.986742	−	0.162296i	$-0.0518901\pi$
$157$	4.42080	+	7.65705i	0.352818	+	0.611099i	−0.633924	+	0.773395i	$0.718557\pi$
$158$		0			0
$159$		−	5.48215i		−	0.434763i
$160$		0			0
$161$	−2.93840	+	5.08947i	−0.231579	+	0.401106i
$162$		0			0
$163$		−	0.459879i		−	0.0360205i	−0.999838	−	0.0180103i	$-0.994267\pi$
$163$		−	0.459879i		−	0.0360205i	0.999838	−	0.0180103i	$-0.00573315\pi$
$164$		0			0
$165$	0.0774889	+	0.0447382i	0.00603250	+	0.00348287i
$166$		0			0
$167$	−0.827126	+	1.43263i	−0.0640050	+	0.110860i	−0.896252	−	0.443545i	$-0.853721\pi$
$167$	−0.827126	+	1.43263i	−0.0640050	+	0.110860i	0.832247	+	0.554405i	$0.187054\pi$
$168$		0			0
$169$	1.53481	+	2.65838i	0.118063	+	0.204490i
$170$		0			0
$171$	−4.27899	+	0.830790i	−0.327223	+	0.0635321i
$172$		0			0
$173$	8.51406	−	4.91559i	0.647312	−	0.373726i	−0.140114	−	0.990135i	$-0.544747\pi$
$173$	8.51406	−	4.91559i	0.647312	−	0.373726i	0.787426	+	0.616410i	$0.211413\pi$
$174$		0			0
$175$	4.37701	+	2.52707i	0.330871	+	0.191029i
$176$		0			0
$177$	1.68855	−	2.92466i	0.126919	−	0.219831i
$178$		0			0
$179$	−9.42853			−0.704721			−0.352361	−	0.935864i	$-0.614621\pi$
$179$	−9.42853			−0.704721			−0.352361	+	0.935864i	$0.614621\pi$
$180$		0			0
$181$	1.16742	+	0.674010i	0.0867736	+	0.0500987i	0.542759	−	0.839889i	$-0.317380\pi$
$181$	1.16742	+	0.674010i	0.0867736	+	0.0500987i	−0.455985	+	0.889987i	$0.650713\pi$
$182$		0			0
$183$	12.7412			0.941856
$184$		0			0
$185$	2.59510	−	1.49828i	0.190795	−	0.110156i
$186$		0			0
$187$	0.435282	−	0.251310i	0.0318310	−	0.0183776i
$188$		0			0
$189$			1.27458i			0.0927117i
$190$		0			0
$191$		−	8.74988i		−	0.633119i	−0.948573	−	0.316559i	$-0.897472\pi$
$191$		−	8.74988i		−	0.633119i	0.948573	−	0.316559i	$-0.102528\pi$
$192$		0			0
$193$	−12.8551	+	7.42187i	−0.925327	+	0.534238i	−0.885331	−	0.464962i	$-0.846068\pi$
$193$	−12.8551	+	7.42187i	−0.925327	+	0.534238i	−0.0399963	+	0.999200i	$0.512735\pi$
$194$		0			0
$195$	−3.53126	+	2.03877i	−0.252879	+	0.146000i
$196$		0			0
$197$	−21.3626			−1.52203			−0.761013	−	0.648737i	$-0.775297\pi$
$197$	−21.3626			−1.52203			−0.761013	+	0.648737i	$0.775297\pi$
$198$		0			0
$199$	4.58658	+	2.64807i	0.325134	+	0.187716i	0.653679	−	0.756772i	$-0.273225\pi$
$199$	4.58658	+	2.64807i	0.325134	+	0.187716i	−0.328544	+	0.944488i	$0.606558\pi$
$200$		0			0
$201$	4.80709			0.339066
$202$		0			0
$203$	−1.85613	+	3.21491i	−0.130275	+	0.225643i
$204$		0			0
$205$	2.99911	+	1.73154i	0.209467	+	0.120936i
$206$		0			0
$207$	−3.99307	+	2.30540i	−0.277537	+	0.160236i
$208$		0			0
$209$	−0.289435	+	0.251492i	−0.0200206	+	0.0173961i
$210$		0			0
$211$	2.10211	+	3.64097i	0.144715	+	0.250655i	0.929267	−	0.369409i	$-0.120440\pi$
$211$	2.10211	+	3.64097i	0.144715	+	0.250655i	−0.784551	+	0.620064i	$0.787107\pi$
$212$		0			0
$213$	0.644658	−	1.11658i	0.0441712	−	0.0765068i
$214$		0			0
$215$	1.92075	+	1.10894i	0.130994	+	0.0756293i
$216$		0			0
$217$			9.59302i			0.651217i
$218$		0			0
$219$	3.09225	−	5.35593i	0.208955	−	0.361920i
$220$		0			0
$221$			22.9050i			1.54076i
$222$		0			0
$223$	3.66065	+	6.34043i	0.245135	+	0.424586i	0.962170	−	0.272451i	$-0.0878343\pi$
$223$	3.66065	+	6.34043i	0.245135	+	0.424586i	−0.717034	+	0.697038i	$0.754501\pi$
$224$		0			0
$225$	1.98268	+	3.43410i	0.132178	+	0.228940i
$226$		0			0
$227$	−11.7450			−0.779544			−0.389772	−	0.920911i	$-0.627446\pi$
$227$	−11.7450			−0.779544			−0.389772	+	0.920911i	$0.627446\pi$
$228$		0			0
$229$	−8.43141			−0.557163			−0.278581	−	0.960413i	$-0.589864\pi$
$229$	−8.43141			−0.557163			−0.278581	+	0.960413i	$0.589864\pi$
$230$		0			0
$231$	0.0560594	+	0.0970977i	0.00368844	+	0.00638856i
$232$		0			0
$233$	−12.8114	−	22.1900i	−0.839301	−	1.45371i	−0.890480	−	0.455023i	$-0.849631\pi$
$233$	−12.8114	−	22.1900i	−0.839301	−	1.45371i	0.0511785	−	0.998690i	$-0.483702\pi$
$234$		0			0
$235$			2.65695i			0.173320i
$236$		0			0
$237$	7.52313	−	13.0304i	0.488680	−	0.846419i
$238$		0			0
$239$			4.18663i			0.270811i	0.990790	+	0.135405i	$0.0432337\pi$
$239$			4.18663i			0.270811i	−0.990790	+	0.135405i	$0.956766\pi$
$240$		0			0
$241$	6.94509	+	4.00975i	0.447373	+	0.258291i	0.706720	−	0.707493i	$-0.250174\pi$
$241$	6.94509	+	4.00975i	0.447373	+	0.258291i	−0.259347	+	0.965784i	$0.583507\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	2.73389	+	4.73524i	0.174662	+	0.302524i
$246$		0			0
$247$	−3.33038	−	17.1532i	−0.211907	−	1.09143i
$248$		0			0
$249$	−10.4014	+	6.00522i	−0.659159	+	0.380566i
$250$		0			0
$251$	−5.43141	−	3.13582i	−0.342827	−	0.197931i	0.318694	−	0.947858i	$-0.396756\pi$
$251$	−5.43141	−	3.13582i	−0.342827	−	0.197931i	−0.661522	+	0.749926i	$0.730089\pi$
$252$		0			0
$253$	−0.202796	+	0.351252i	−0.0127497	+	0.0220831i
$254$		0			0
$255$	−5.81197			−0.363960
$256$		0			0
$257$	−10.9231	−	6.30645i	−0.681363	−	0.393385i	0.119005	−	0.992894i	$-0.462029\pi$
$257$	−10.9231	−	6.30645i	−0.681363	−	0.393385i	−0.800368	+	0.599508i	$0.795363\pi$
$258$		0			0
$259$	3.75485			0.233315
$260$		0			0
$261$	−2.52234	+	1.45627i	−0.156129	+	0.0901411i
$262$		0			0
$263$	14.7368	−	8.50828i	0.908708	−	0.524643i	0.0286929	−	0.999588i	$-0.490866\pi$
$263$	14.7368	−	8.50828i	0.908708	−	0.524643i	0.880015	+	0.474945i	$0.157532\pi$
$264$		0			0
$265$			5.57631i			0.342550i
$266$		0			0
$267$		−	4.43751i		−	0.271571i
$268$		0			0
$269$	5.52202	−	3.18814i	0.336684	−	0.194384i	−0.322121	−	0.946699i	$-0.604396\pi$
$269$	5.52202	−	3.18814i	0.336684	−	0.194384i	0.658805	+	0.752314i	$0.271062\pi$
$270$		0			0
$271$	−10.3400	+	5.96983i	−0.628113	+	0.362641i	−0.780021	−	0.625753i	$-0.784792\pi$
$271$	−10.3400	+	5.96983i	−0.628113	+	0.362641i	0.151908	+	0.988395i	$0.451458\pi$
$272$		0			0
$273$	−5.10938			−0.309234
$274$		0			0
$275$	0.302082	+	0.174407i	0.0182162	+	0.0105172i
$276$		0			0
$277$	−8.54848			−0.513628			−0.256814	−	0.966461i	$-0.582673\pi$
$277$	−8.54848			−0.513628			−0.256814	+	0.966461i	$0.582673\pi$
$278$		0			0
$279$	−3.76322	+	6.51809i	−0.225298	+	0.390228i
$280$		0			0
$281$	7.53614	+	4.35099i	0.449568	+	0.259558i	0.707648	−	0.706565i	$-0.249756\pi$
$281$	7.53614	+	4.35099i	0.449568	+	0.259558i	−0.258080	+	0.966124i	$0.583090\pi$
$282$		0			0
$283$	0.457715	−	0.264262i	0.0272083	−	0.0157087i	−0.486334	−	0.873773i	$-0.661666\pi$
$283$	0.457715	−	0.264262i	0.0272083	−	0.0157087i	0.513542	+	0.858064i	$0.328333\pi$
$284$		0			0
$285$	4.35249	−	0.845060i	0.257819	−	0.0500570i
$286$		0			0
$287$	2.16971	+	3.75804i	0.128074	+	0.221830i
$288$		0			0
$289$	−7.82393	+	13.5514i	−0.460231	+	0.797144i
$290$		0			0
$291$	8.08295	+	4.66669i	0.473831	+	0.273566i
$292$		0			0
$293$			14.0740i			0.822215i	0.911587	+	0.411107i	$0.134858\pi$
$293$			14.0740i			0.822215i	−0.911587	+	0.411107i	$0.865142\pi$
$294$		0			0
$295$	−1.71756	+	2.97489i	−0.100000	+	0.173205i
$296$		0			0
$297$			0.0879656i			0.00510428i
$298$		0			0
$299$	−9.24164	−	16.0070i	−0.534458	−	0.925708i
$300$		0			0
$301$	1.38956	+	2.40680i	0.0800932	+	0.138725i
$302$		0			0
$303$	−7.60804			−0.437070
$304$		0			0
$305$	−12.9600			−0.742090
$306$		0			0
$307$	−4.03566	−	6.98997i	−0.230327	−	0.398938i	0.727577	−	0.686026i	$-0.240646\pi$
$307$	−4.03566	−	6.98997i	−0.230327	−	0.398938i	−0.957904	+	0.287087i	$0.907313\pi$
$308$		0			0
$309$	−8.45474	−	14.6440i	−0.480973	−	0.833070i
$310$		0			0
$311$			4.11163i			0.233149i	0.993182	+	0.116574i	$0.0371914\pi$
$311$			4.11163i			0.233149i	−0.993182	+	0.116574i	$0.962809\pi$
$312$		0			0
$313$	−16.3926	+	28.3929i	−0.926566	+	1.60486i	−0.137542	+	0.990496i	$0.543920\pi$
$313$	−16.3926	+	28.3929i	−0.926566	+	1.60486i	−0.789023	+	0.614363i	$0.789413\pi$
$314$		0			0
$315$		−	1.29647i		−	0.0730477i
$316$		0			0
$317$	17.7896	+	10.2708i	0.999165	+	0.576868i	0.908001	−	0.418968i	$-0.137608\pi$
$317$	17.7896	+	10.2708i	0.999165	+	0.576868i	0.0911637	+	0.995836i	$0.470941\pi$
$318$		0			0
$319$	−0.128102	+	0.221879i	−0.00717233	+	0.0124228i
$320$		0			0
$321$	−0.998744	−	1.72987i	−0.0557444	−	0.0965522i
$322$		0			0
$323$	8.11370	−	23.5473i	0.451459	−	1.31021i
$324$		0			0
$325$	−13.7662	+	7.94794i	−0.763614	+	0.440873i
$326$		0			0
$327$	−11.1161	−	6.41789i	−0.614723	−	0.354910i
$328$		0			0
$329$	−1.66465	+	2.88326i	−0.0917751	+	0.158959i
$330$		0			0
$331$	25.9353			1.42553			0.712766	−	0.701402i	$-0.247442\pi$
$331$	25.9353			1.42553			0.712766	+	0.701402i	$0.247442\pi$
$332$		0			0
$333$	2.55128	+	1.47298i	0.139809	+	0.0807188i
$334$		0			0
$335$	−4.88966			−0.267150
$336$		0			0
$337$	9.37369	−	5.41190i	0.510617	−	0.294805i	−0.222470	−	0.974940i	$-0.571412\pi$
$337$	9.37369	−	5.41190i	0.510617	−	0.294805i	0.733087	+	0.680135i	$0.238079\pi$
$338$		0			0
$339$	−17.1376	+	9.89441i	−0.930788	+	0.537391i
$340$		0			0
$341$			0.662068i			0.0358530i
$342$		0			0
$343$			15.7735i			0.851686i
$344$		0			0
$345$	4.06165	−	2.34500i	0.218672	−	0.126250i
$346$		0			0
$347$	−31.2427	+	18.0380i	−1.67720	+	0.968331i	−0.713764	+	0.700387i	$0.753011\pi$
$347$	−31.2427	+	18.0380i	−1.67720	+	0.968331i	−0.963434	+	0.267944i	$0.913656\pi$
$348$		0			0
$349$	−18.1481			−0.971447			−0.485724	−	0.874112i	$-0.661444\pi$
$349$	−18.1481			−0.971447			−0.485724	+	0.874112i	$0.661444\pi$
$350$		0			0
$351$	−3.47163	−	2.00435i	−0.185302	−	0.106984i
$352$		0			0
$353$	8.07939			0.430023			0.215011	−	0.976612i	$-0.431021\pi$
$353$	8.07939			0.430023			0.215011	+	0.976612i	$0.431021\pi$
$354$		0			0
$355$	−0.655731	+	1.13576i	−0.0348026	+	0.0602798i
$356$		0			0
$357$	−6.30701	−	3.64135i	−0.333802	−	0.192721i
$358$		0			0
$359$	−31.1089	+	17.9607i	−1.64186	+	0.947931i	−0.661695	+	0.749773i	$0.730162\pi$
$359$	−31.1089	+	17.9607i	−1.64186	+	0.947931i	−0.980170	+	0.198158i	$0.936504\pi$
$360$		0			0
$361$	−2.65244	+	18.8139i	−0.139602	+	0.990208i
$362$		0			0
$363$	−5.49613	−	9.51958i	−0.288472	−	0.499648i
$364$		0			0
$365$	−3.14536	+	5.44792i	−0.164636	+	0.285157i
$366$		0			0
$367$	8.67237	+	5.00700i	0.452694	+	0.261363i	0.708967	−	0.705241i	$-0.249161\pi$
$367$	8.67237	+	5.00700i	0.452694	+	0.261363i	−0.256273	+	0.966604i	$0.582495\pi$
$368$		0			0
$369$			3.40459i			0.177236i
$370$		0			0
$371$	−3.49371	+	6.05128i	−0.181384	+	0.314167i
$372$		0			0
$373$			6.58299i			0.340854i	0.985370	+	0.170427i	$0.0545147\pi$
$373$			6.58299i			0.340854i	−0.985370	+	0.170427i	$0.945485\pi$
$374$		0			0
$375$	−4.55967	−	7.89758i	−0.235460	−	0.407829i
$376$		0			0
$377$	−5.83776	−	10.1113i	−0.300660	−	0.520758i
$378$		0			0
$379$	18.6606			0.958531			0.479266	−	0.877670i	$-0.340903\pi$
$379$	18.6606			0.958531			0.479266	+	0.877670i	$0.340903\pi$
$380$		0			0
$381$	−16.0409			−0.821801
$382$		0			0
$383$	0.0551431	+	0.0955106i	0.00281768	+	0.00488036i	0.867431	−	0.497558i	$-0.165770\pi$
$383$	0.0551431	+	0.0955106i	0.00281768	+	0.00488036i	−0.864613	+	0.502438i	$0.832436\pi$
$384$		0			0
$385$	−0.0570223	−	0.0987654i	−0.00290612	−	0.00503355i
$386$		0			0
$387$			2.18044i			0.110838i
$388$		0			0
$389$	5.89866	−	10.2168i	0.299074	−	0.518011i	−0.676851	−	0.736120i	$-0.736656\pi$
$389$	5.89866	−	10.2168i	0.299074	−	0.518011i	0.975924	+	0.218110i	$0.0699890\pi$
$390$		0			0
$391$		−	26.3453i		−	1.33234i
$392$		0			0
$393$	17.7628	+	10.2554i	0.896016	+	0.517315i
$394$		0			0
$395$	−7.65235	+	13.2543i	−0.385032	+	0.666894i
$396$		0			0
$397$	7.45758	+	12.9169i	0.374285	+	0.648281i	0.990220	−	0.139516i	$-0.0445548\pi$
$397$	7.45758	+	12.9169i	0.374285	+	0.648281i	−0.615935	+	0.787797i	$0.711221\pi$
$398$		0			0
$399$	5.25267	+	1.80991i	0.262962	+	0.0906089i
$400$		0			0
$401$	−23.2566	+	13.4272i	−1.16138	+	0.670522i	−0.951634	−	0.307234i	$-0.900597\pi$
$401$	−23.2566	+	13.4272i	−1.16138	+	0.670522i	−0.209745	+	0.977756i	$0.567263\pi$
$402$		0			0
$403$	−26.1290	−	15.0856i	−1.30158	−	0.751468i
$404$		0			0
$405$	0.508588	−	0.880900i	0.0252719	−	0.0437723i
$406$		0			0
$407$	0.259143			0.0128452
$408$		0			0
$409$	15.1020	+	8.71915i	0.746746	+	0.431134i	0.824517	−	0.565837i	$-0.191447\pi$
$409$	15.1020	+	8.71915i	0.746746	+	0.431134i	−0.0777709	+	0.996971i	$0.524780\pi$
$410$		0			0
$411$	−3.96524			−0.195591
$412$		0			0
$413$	−3.72770	+	2.15219i	−0.183428	+	0.105902i
$414$		0			0
$415$	10.5800	−	6.10837i	0.519352	−	0.299848i
$416$		0			0
$417$			8.51461i			0.416962i
$418$		0			0
$419$		−	38.7316i		−	1.89216i	−0.323927	−	0.946082i	$-0.605003\pi$
$419$		−	38.7316i		−	1.89216i	0.323927	−	0.946082i	$-0.394997\pi$
$420$		0			0
$421$	3.07427	−	1.77493i	0.149831	−	0.0865049i	−0.423210	−	0.906031i	$-0.639097\pi$
$421$	3.07427	−	1.77493i	0.149831	−	0.0865049i	0.573041	+	0.819527i	$0.305764\pi$
$422$		0			0
$423$	−2.26213	+	1.30604i	−0.109989	+	0.0635020i
$424$		0			0
$425$	−22.6574			−1.09904
$426$		0			0
$427$	−14.0639	−	8.11981i	−0.680601	−	0.392945i
$428$		0			0
$429$	−0.352627			−0.0170250
$430$		0			0
$431$	7.88744	−	13.6615i	0.379925	−	0.658049i	−0.611126	−	0.791533i	$-0.709283\pi$
$431$	7.88744	−	13.6615i	0.379925	−	0.658049i	0.991051	+	0.133484i	$0.0426165\pi$
$432$		0			0
$433$	−23.5792	−	13.6135i	−1.13314	−	0.654221i	−0.188420	−	0.982089i	$-0.560337\pi$
$433$	−23.5792	−	13.6135i	−1.13314	−	0.654221i	−0.944724	+	0.327868i	$0.893670\pi$
$434$		0			0
$435$	2.56567	−	1.48129i	0.123014	−	0.0710223i
$436$		0			0
$437$	3.83061	+	19.7296i	0.183243	+	0.943794i
$438$		0			0
$439$	−6.38314	−	11.0559i	−0.304651	−	0.527670i	0.672533	−	0.740067i	$-0.265206\pi$
$439$	−6.38314	−	11.0559i	−0.304651	−	0.527670i	−0.977183	+	0.212397i	$0.931873\pi$
$440$		0			0
$441$	−2.68773	+	4.65528i	−0.127987	+	0.221680i
$442$		0			0
$443$	−1.77150	−	1.02277i	−0.0841664	−	0.0485935i	0.457326	−	0.889299i	$-0.348807\pi$
$443$	−1.77150	−	1.02277i	−0.0841664	−	0.0485935i	−0.541493	+	0.840706i	$0.682141\pi$
$444$		0			0
$445$			4.51373i			0.213971i
$446$		0			0
$447$	−7.45843	+	12.9184i	−0.352771	+	0.611018i
$448$		0			0
$449$		−	33.7617i		−	1.59331i	−0.604433	−	0.796656i	$-0.706600\pi$
$449$		−	33.7617i		−	1.59331i	0.604433	−	0.796656i	$-0.293400\pi$
$450$		0			0
$451$	0.149744	+	0.259363i	0.00705115	+	0.0122129i
$452$		0			0
$453$	−4.39572	−	7.61360i	−0.206529	−	0.357718i
$454$		0			0
$455$	5.19714			0.243646
$456$		0			0
$457$	40.2004			1.88049			0.940247	−	0.340494i	$-0.110594\pi$
$457$	40.2004			1.88049			0.940247	+	0.340494i	$0.110594\pi$
$458$		0			0
$459$	−2.85692	−	4.94832i	−0.133349	−	0.230968i
$460$		0			0
$461$	15.2260	+	26.3721i	0.709144	+	1.22827i	0.965175	+	0.261605i	$0.0842517\pi$
$461$	15.2260	+	26.3721i	0.709144	+	1.22827i	−0.256031	+	0.966669i	$0.582415\pi$
$462$		0			0
$463$			16.4408i			0.764067i	0.924148	+	0.382034i	$0.124776\pi$
$463$			16.4408i			0.764067i	−0.924148	+	0.382034i	$0.875224\pi$
$464$		0			0
$465$	3.82786	−	6.63005i	0.177513	−	0.307461i
$466$		0			0
$467$			20.3955i			0.943790i	0.881655	+	0.471895i	$0.156430\pi$
$467$			20.3955i			0.943790i	−0.881655	+	0.471895i	$0.843570\pi$
$468$		0			0
$469$	−5.30614	−	3.06350i	−0.245015	−	0.141459i
$470$		0			0
$471$	4.42080	−	7.65705i	0.203700	−	0.352818i
$472$		0			0
$473$	0.0959016	+	0.166107i	0.00440956	+	0.00763759i
$474$		0			0
$475$	16.9677	−	3.29438i	0.778532	−	0.151156i
$476$		0			0
$477$	−4.74768	+	2.74107i	−0.217381	+	0.125505i
$478$		0			0
$479$	−23.8711	−	13.7820i	−1.09070	−	0.629714i	−0.156935	−	0.987609i	$-0.550161\pi$
$479$	−23.8711	−	13.7820i	−1.09070	−	0.629714i	−0.933762	+	0.357895i	$0.883495\pi$
$480$		0			0
$481$	−5.90473	+	10.2273i	−0.269232	+	0.466324i
$482$		0			0
$483$	5.87681			0.267404
$484$		0			0
$485$	−8.22178	−	4.74685i	−0.373332	−	0.215543i
$486$		0			0
$487$	15.1073			0.684577			0.342288	−	0.939595i	$-0.388798\pi$
$487$	15.1073			0.684577			0.342288	+	0.939595i	$0.388798\pi$
$488$		0			0
$489$	−0.398267	+	0.229940i	−0.0180103	+	0.0103982i
$490$		0			0
$491$	−9.57915	+	5.53052i	−0.432301	+	0.249589i	−0.700326	−	0.713823i	$-0.746962\pi$
$491$	−9.57915	+	5.53052i	−0.432301	+	0.249589i	0.268026	+	0.963412i	$0.413629\pi$
$492$		0			0
$493$		−	16.6418i		−	0.749509i
$494$		0			0
$495$		−	0.0894765i		−	0.00402167i
$496$		0			0
$497$	−1.42317	+	0.821665i	−0.0638377	+	0.0368567i
$498$		0			0
$499$	1.24304	−	0.717669i	0.0556461	−	0.0321273i	−0.471919	−	0.881642i	$-0.656438\pi$
$499$	1.24304	−	0.717669i	0.0556461	−	0.0321273i	0.527565	+	0.849515i	$0.323105\pi$
$500$		0			0
$501$	1.65425			0.0739066
$502$		0			0
$503$	−24.2013	−	13.9727i	−1.07908	−	0.623010i	−0.148435	−	0.988922i	$-0.547424\pi$
$503$	−24.2013	−	13.9727i	−1.07908	−	0.623010i	−0.930649	+	0.365912i	$0.880757\pi$
$504$		0			0
$505$	7.73872			0.344368
$506$		0			0
$507$	1.53481	−	2.65838i	0.0681635	−	0.118063i
$508$		0			0
$509$	−7.55707	−	4.36308i	−0.334961	−	0.193390i	0.323080	−	0.946372i	$-0.395282\pi$
$509$	−7.55707	−	4.36308i	−0.334961	−	0.193390i	−0.658042	+	0.752982i	$0.728615\pi$
$510$		0			0
$511$	−6.82654	+	3.94130i	−0.301988	+	0.174353i
$512$		0			0
$513$	2.85898	+	3.29032i	0.126227	+	0.145271i
$514$		0			0
$515$	8.59996	+	14.8956i	0.378960	+	0.656377i
$516$		0			0
$517$	−0.114887	+	0.198990i	−0.00505271	+	0.00875156i
$518$		0			0
$519$	−8.51406	−	4.91559i	−0.373726	−	0.215771i
$520$		0			0
$521$		−	3.59660i		−	0.157570i	−0.996892	−	0.0787849i	$-0.974896\pi$
$521$		−	3.59660i		−	0.157570i	0.996892	−	0.0787849i	$-0.0251040\pi$
$522$		0			0
$523$	−11.4155	+	19.7722i	−0.499164	+	0.864578i	−1.00000		0.000964547i	$-0.999693\pi$
$523$	−11.4155	+	19.7722i	−0.499164	+	0.864578i	0.500835	+	0.865543i	$0.333026\pi$
$524$		0			0
$525$		−	5.05414i		−	0.220581i
$526$		0			0
$527$	−21.5024	−	37.2433i	−0.936660	−	1.62234i
$528$		0			0
$529$	−0.870273	−	1.50736i	−0.0378380	−	0.0655373i
$530$		0			0
$531$	−3.37711			−0.146554
$532$		0			0
$533$	−13.6480			−0.591159
$534$		0			0
$535$	1.01590	+	1.75959i	0.0439211	+	0.0760736i
$536$		0			0
$537$	4.71426	+	8.16534i	0.203435	+	0.352361i
$538$		0			0
$539$			0.472855i			0.0203673i
$540$		0			0
$541$	4.57120	−	7.91755i	0.196531	−	0.340402i	−0.750870	−	0.660450i	$-0.770366\pi$
$541$	4.57120	−	7.91755i	0.196531	−	0.340402i	0.947401	+	0.320048i	$0.103699\pi$
$542$		0			0
$543$		−	1.34802i		−	0.0578490i
$544$		0			0
$545$	11.3070	+	6.52813i	0.484341	+	0.279634i
$546$		0			0
$547$	3.91037	−	6.77297i	0.167195	−	0.289591i	−0.770237	−	0.637757i	$-0.779862\pi$
$547$	3.91037	−	6.77297i	0.167195	−	0.289591i	0.937433	+	0.348166i	$0.113196\pi$
$548$		0			0
$549$	−6.37060	−	11.0342i	−0.271890	−	0.470928i
$550$		0			0
$551$	2.41972	+	12.4628i	0.103083	+	0.530932i
$552$		0			0
$553$	−16.6083	+	9.58880i	−0.706256	+	0.407757i
$554$		0			0
$555$	−2.59510	−	1.49828i	−0.110156	−	0.0635984i
$556$		0			0
$557$	−12.0609	+	20.8901i	−0.511037	+	0.885143i	0.488881	+	0.872351i	$0.337405\pi$
$557$	−12.0609	+	20.8901i	−0.511037	+	0.885143i	−0.999918	+	0.0127920i	$0.995928\pi$
$558$		0			0
$559$	−8.74070			−0.369692
$560$		0			0
$561$	−0.435282	−	0.251310i	−0.0183776	−	0.0106103i
$562$		0			0
$563$	45.2764			1.90817			0.954087	−	0.299531i	$-0.0968301\pi$
$563$	45.2764			1.90817			0.954087	+	0.299531i	$0.0968301\pi$
$564$		0			0
$565$	17.4320	−	10.0644i	0.733369	−	0.423411i
$566$		0			0
$567$	1.10381	−	0.637288i	0.0463559	−	0.0267636i
$568$		0			0
$569$			11.0826i			0.464605i	0.972644	+	0.232303i	$0.0746259\pi$
$569$			11.0826i			0.464605i	−0.972644	+	0.232303i	$0.925374\pi$
$570$		0			0
$571$			2.23402i			0.0934909i	0.998907	+	0.0467454i	$0.0148850\pi$
$571$			2.23402i			0.0934909i	−0.998907	+	0.0467454i	$0.985115\pi$
$572$		0			0
$573$	−7.57762	+	4.37494i	−0.316559	+	0.182766i
$574$		0			0
$575$	15.8339	−	9.14172i	0.660320	−	0.381236i
$576$		0			0
$577$	−26.1791			−1.08985			−0.544926	−	0.838484i	$-0.683442\pi$
$577$	−26.1791			−1.08985			−0.544926	+	0.838484i	$0.683442\pi$
$578$		0			0
$579$	12.8551	+	7.42187i	0.534238	+	0.308442i
$580$		0			0
$581$	15.3082			0.635092
$582$		0			0
$583$	−0.241120	+	0.417632i	−0.00998618	+	0.0172966i
$584$		0			0
$585$	3.53126	+	2.03877i	0.146000	+	0.0842929i
$586$		0			0
$587$	35.7635	−	20.6481i	1.47612	−	0.852237i	0.476482	−	0.879184i	$-0.341912\pi$
$587$	35.7635	−	20.6481i	1.47612	−	0.852237i	0.999637	+	0.0269471i	$0.00857857\pi$
$588$		0			0
$589$	21.5180	+	24.7644i	0.886633	+	1.02040i
$590$		0			0
$591$	10.6813	+	18.5006i	0.439371	+	0.761013i
$592$		0			0
$593$	16.1529	−	27.9776i	0.663319	−	1.14890i	−0.316419	−	0.948619i	$-0.602481\pi$
$593$	16.1529	−	27.9776i	0.663319	−	1.14890i	0.979738	−	0.200283i	$-0.0641861\pi$
$594$		0			0
$595$	6.41534	+	3.70390i	0.263003	+	0.151845i
$596$		0			0
$597$		−	5.29613i		−	0.216756i
$598$		0			0
$599$	−3.36941	+	5.83598i	−0.137670	+	0.238452i	−0.926614	−	0.376013i	$-0.877295\pi$
$599$	−3.36941	+	5.83598i	−0.137670	+	0.238452i	0.788944	+	0.614465i	$0.210628\pi$
$600$		0			0
$601$			22.8234i			0.930987i	0.885051	+	0.465493i	$0.154123\pi$
$601$			22.8234i			0.930987i	−0.885051	+	0.465493i	$0.845877\pi$
$602$		0			0
$603$	−2.40354	−	4.16306i	−0.0978799	−	0.169533i
$604$		0			0
$605$	5.59053	+	9.68309i	0.227287	+	0.393673i
$606$		0			0
$607$	−41.9125			−1.70117			−0.850587	−	0.525834i	$-0.823753\pi$
$607$	−41.9125			−1.70117			−0.850587	+	0.525834i	$0.823753\pi$
$608$		0			0
$609$	3.71226			0.150428
$610$		0			0
$611$	−5.23552	−	9.06819i	−0.211807	−	0.366860i
$612$		0			0
$613$	−17.0403	−	29.5147i	−0.688252	−	1.19209i	−0.972403	−	0.233308i	$-0.925045\pi$
$613$	−17.0403	−	29.5147i	−0.688252	−	1.19209i	0.284150	−	0.958780i	$-0.408289\pi$
$614$		0			0
$615$		−	3.46307i		−	0.139645i
$616$		0			0
$617$	12.8555	−	22.2664i	0.517543	−	0.896411i	−0.482249	−	0.876034i	$-0.660180\pi$
$617$	12.8555	−	22.2664i	0.517543	−	0.896411i	0.999792	−	0.0203773i	$-0.00648673\pi$
$618$		0			0
$619$		−	24.6868i		−	0.992245i	−0.868253	−	0.496122i	$-0.834757\pi$
$619$		−	24.6868i		−	0.992245i	0.868253	−	0.496122i	$-0.165243\pi$
$620$		0			0
$621$	3.99307	+	2.30540i	0.160236	+	0.0925125i
$622$		0			0
$623$	−2.82797	+	4.89818i	−0.113300	+	0.196242i
$624$		0			0
$625$	−5.27539	−	9.13725i	−0.211016	−	0.365490i
$626$		0			0
$627$	0.362516	+	0.124912i	0.0144775	+	0.00498851i
$628$		0			0
$629$	−14.5776	+	8.41636i	−0.581245	+	0.335582i
$630$		0			0
$631$	−13.9123	−	8.03226i	−0.553839	−	0.319759i	0.196830	−	0.980438i	$-0.436935\pi$
$631$	−13.9123	−	8.03226i	−0.553839	−	0.319759i	−0.750669	+	0.660678i	$0.770269\pi$
$632$		0			0
$633$	2.10211	−	3.64097i	0.0835515	−	0.144715i
$634$		0			0
$635$	16.3164			0.647498
$636$		0			0
$637$	−18.6616	−	10.7743i	−0.739400	−	0.426893i
$638$		0			0
$639$	−1.28932			−0.0510046
$640$		0			0
$641$	3.72801	−	2.15237i	0.147248	−	0.0850135i	−0.424566	−	0.905397i	$-0.639573\pi$
$641$	3.72801	−	2.15237i	0.147248	−	0.0850135i	0.571814	+	0.820383i	$0.306240\pi$
$642$		0			0
$643$	16.8712	−	9.74061i	0.665336	−	0.384132i	−0.128971	−	0.991648i	$-0.541167\pi$
$643$	16.8712	−	9.74061i	0.665336	−	0.384132i	0.794307	+	0.607516i	$0.207834\pi$
$644$		0			0
$645$		−	2.21789i		−	0.0873292i
$646$		0			0
$647$			26.1058i			1.02632i	0.858292	+	0.513162i	$0.171526\pi$
$647$			26.1058i			1.02632i	−0.858292	+	0.513162i	$0.828474\pi$
$648$		0			0
$649$	−0.257269	+	0.148535i	−0.0100987	+	0.00583049i
$650$		0			0
$651$	8.30780	−	4.79651i	0.325608	−	0.187990i
$652$		0			0
$653$	39.4702			1.54459			0.772294	−	0.635265i	$-0.219109\pi$
$653$	39.4702			1.54459			0.772294	+	0.635265i	$0.219109\pi$
$654$		0			0
$655$	−18.0679	−	10.4315i	−0.705972	−	0.407593i
$656$		0			0
$657$	−6.18449			−0.241280
$658$		0			0
$659$	6.30387	−	10.9186i	0.245564	−	0.425329i	−0.716726	−	0.697355i	$-0.754360\pi$
$659$	6.30387	−	10.9186i	0.245564	−	0.425329i	0.962290	+	0.272026i	$0.0876936\pi$
$660$		0			0
$661$	−20.7860	−	12.0008i	−0.808481	−	0.466777i	0.0379472	−	0.999280i	$-0.487918\pi$
$661$	−20.7860	−	12.0008i	−0.808481	−	0.466777i	−0.846428	+	0.532503i	$0.821251\pi$
$662$		0			0
$663$	19.8363	−	11.4525i	0.770378	−	0.444778i
$664$		0			0
$665$	−5.34289	−	1.84100i	−0.207188	−	0.0713909i
$666$		0			0
$667$	6.71459	+	11.6300i	0.259990	+	0.450316i
$668$		0			0
$669$	3.66065	−	6.34043i	0.141529	−	0.245135i
$670$		0			0
$671$	−0.970630	−	0.560393i	−0.0374707	−	0.0216337i
$672$		0			0
$673$		−	42.8304i		−	1.65099i	−0.564409	−	0.825495i	$-0.690896\pi$
$673$		−	42.8304i		−	1.65099i	0.564409	−	0.825495i	$-0.309104\pi$
$674$		0			0
$675$	1.98268	−	3.43410i	0.0763132	−	0.132178i
$676$		0			0
$677$			35.7250i			1.37302i	0.727119	+	0.686512i	$0.240859\pi$
$677$			35.7250i			1.37302i	−0.727119	+	0.686512i	$0.759141\pi$
$678$		0			0
$679$	−5.94805	−	10.3023i	−0.228265	−	0.395367i
$680$		0			0
$681$	5.87251	+	10.1715i	0.225035	+	0.389772i
$682$		0			0
$683$	6.35337			0.243105			0.121552	−	0.992585i	$-0.461213\pi$
$683$	6.35337			0.243105			0.121552	+	0.992585i	$0.461213\pi$
$684$		0			0
$685$	4.03335			0.154106
$686$		0			0
$687$	4.21570	+	7.30181i	0.160839	+	0.278581i
$688$		0			0
$689$	−10.9881	−	19.0320i	−0.418614	−	0.725061i
$690$		0			0
$691$			16.4169i			0.624529i	0.949995	+	0.312264i	$0.101087\pi$
$691$			16.4169i			0.624529i	−0.949995	+	0.312264i	$0.898913\pi$
$692$		0			0
$693$	0.0560594	−	0.0970977i	0.00212952	−	0.00368844i
$694$		0			0
$695$		−	8.66086i		−	0.328525i
$696$		0			0
$697$	−16.8470	−	9.72664i	−0.638127	−	0.368423i
$698$		0			0
$699$	−12.8114	+	22.1900i	−0.484571	+	0.839301i
$700$		0			0
$701$	−0.917013	−	1.58831i	−0.0346351	−	0.0599898i	0.848188	−	0.529695i	$-0.177694\pi$
$701$	−0.917013	−	1.58831i	−0.0346351	−	0.0599898i	−0.882823	+	0.469705i	$0.844360\pi$
$702$		0			0
$703$	9.69316	−	8.42245i	0.365584	−	0.317659i
$704$		0			0
$705$	2.30099	−	1.32848i	0.0866602	−	0.0500333i
$706$		0			0
$707$	8.39786	+	4.84851i	0.315834	+	0.182347i
$708$		0			0
$709$	−7.34878	+	12.7285i	−0.275989	+	0.478027i	−0.970384	−	0.241567i	$-0.922339\pi$
$709$	−7.34878	+	12.7285i	−0.275989	+	0.478027i	0.694395	+	0.719594i	$0.255672\pi$
$710$		0			0
$711$	−15.0463			−0.564279
$712$		0			0
$713$	30.0536	+	17.3515i	1.12552	+	0.649817i
$714$		0			0
$715$	0.358684			0.0134140
$716$		0			0
$717$	3.62573	−	2.09332i	0.135405	−	0.0781764i
$718$		0			0
$719$	−9.39866	+	5.42632i	−0.350511	+	0.202368i	−0.664910	−	0.746923i	$-0.731530\pi$
$719$	−9.39866	+	5.42632i	−0.350511	+	0.202368i	0.314399	+	0.949291i	$0.398197\pi$
$720$		0			0
$721$			21.5524i			0.802654i
$722$		0			0
$723$		−	8.01950i		−	0.298248i
$724$		0			0
$725$	10.0020	−	5.77464i	0.371464	−	0.214465i
$726$		0			0
$727$	−44.7498	+	25.8363i	−1.65968	+	0.958215i	−0.686813	+	0.726834i	$0.740991\pi$
$727$	−44.7498	+	25.8363i	−1.65968	+	0.958215i	−0.972863	+	0.231381i	$0.925676\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−10.7895	−	6.22932i	−0.399064	−	0.230400i
$732$		0			0
$733$	31.6478			1.16894			0.584469	−	0.811416i	$-0.301303\pi$
$733$	31.6478			1.16894			0.584469	+	0.811416i	$0.301303\pi$
$734$		0			0
$735$	2.73389	−	4.73524i	0.100841	−	0.174662i
$736$		0			0
$737$	−0.366206	−	0.211429i	−0.0134894	−	0.00778809i
$738$		0			0
$739$	−39.7982	+	22.9775i	−1.46400	+	0.845242i	−0.999193	−	0.0401696i	$-0.987210\pi$
$739$	−39.7982	+	22.9775i	−1.46400	+	0.845242i	−0.464809	+	0.885411i	$0.653877\pi$
$740$		0			0
$741$	−13.1899	+	11.4608i	−0.484543	+	0.421022i
$742$		0			0
$743$	7.04194	+	12.1970i	0.258344	+	0.447464i	0.965798	−	0.259294i	$-0.0834900\pi$
$743$	7.04194	+	12.1970i	0.258344	+	0.447464i	−0.707455	+	0.706759i	$0.750157\pi$
$744$		0			0
$745$	7.58653	−	13.1403i	0.277949	−	0.481422i
$746$		0			0
$747$	10.4014	+	6.00522i	0.380566	+	0.219720i
$748$		0			0
$749$			2.54595i			0.0930269i
$750$		0			0
$751$	−11.5173	+	19.9485i	−0.420271	+	0.727931i	−0.995966	−	0.0897339i	$-0.971398\pi$
$751$	−11.5173	+	19.9485i	−0.420271	+	0.727931i	0.575695	+	0.817665i	$0.304732\pi$
$752$		0			0
$753$			6.27165i			0.228552i
$754$		0			0
$755$	4.47122	+	7.74437i	0.162724	+	0.281847i
$756$		0			0
$757$	1.67333	+	2.89830i	0.0608183	+	0.105340i	0.894831	−	0.446404i	$-0.147296\pi$
$757$	1.67333	+	2.89830i	0.0608183	+	0.105340i	−0.834013	+	0.551745i	$0.813962\pi$
$758$		0			0
$759$	0.405591			0.0147220
$760$		0			0
$761$	28.2813			1.02520			0.512598	−	0.858628i	$-0.328683\pi$
$761$	28.2813			1.02520			0.512598	+	0.858628i	$0.328683\pi$
$762$		0			0
$763$	8.18009	+	14.1683i	0.296139	+	0.512928i
$764$		0			0
$765$	2.90599	+	5.03332i	0.105066	+	0.181980i
$766$		0			0
$767$		−	13.5378i		−	0.488821i
$768$		0			0
$769$	6.57596	−	11.3899i	0.237135	−	0.410730i	−0.722756	−	0.691103i	$-0.757125\pi$
$769$	6.57596	−	11.3899i	0.237135	−	0.410730i	0.959891	+	0.280373i	$0.0904583\pi$
$770$		0			0
$771$			12.6129i			0.454242i
$772$		0			0
$773$	−13.9449	−	8.05110i	−0.501564	−	0.289578i	0.227795	−	0.973709i	$-0.426848\pi$
$773$	−13.9449	−	8.05110i	−0.501564	−	0.289578i	−0.729359	+	0.684131i	$0.760182\pi$
$774$		0			0
$775$	14.9225	−	25.8465i	0.536032	−	0.928435i
$776$		0			0
$777$	−1.87742	−	3.25179i	−0.0673522	−	0.116657i
$778$		0			0
$779$	14.0307	+	4.83456i	0.502703	+	0.173216i
$780$		0			0
$781$	−0.0982207	+	0.0567077i	−0.00351461	+	0.00202916i
$782$		0			0
$783$	2.52234	+	1.45627i	0.0901411	+	0.0520430i
$784$		0			0
$785$	−4.49673	+	7.78857i	−0.160495	+	0.277986i
$786$		0			0
$787$	17.2063			0.613338			0.306669	−	0.951816i	$-0.400786\pi$
$787$	17.2063			0.613338			0.306669	+	0.951816i	$0.400786\pi$
$788$		0			0
$789$	−14.7368	−	8.50828i	−0.524643	−	0.302903i
$790$		0			0
$791$	25.2223			0.896803
$792$		0			0
$793$	44.2327	−	25.5378i	1.57075	−	0.906873i
$794$		0			0
$795$	4.82923	−	2.78816i	0.171275	−	0.0988857i
$796$		0			0
$797$		−	28.9665i		−	1.02605i	−0.858375	−	0.513023i	$-0.828526\pi$
$797$		−	28.9665i		−	1.02605i	0.858375	−	0.513023i	$-0.171474\pi$
$798$		0			0
$799$		−	14.9250i		−	0.528009i
$800$		0			0
$801$	−3.84299	+	2.21875i	−0.135785	+	0.0783958i
$802$		0			0
$803$	−0.471137	+	0.272011i	−0.0166261	+	0.00959907i
$804$		0			0
$805$	−5.97775			−0.210688
$806$		0			0
$807$	−5.52202	−	3.18814i	−0.194384	−	0.112228i
$808$		0			0
$809$	30.5568			1.07432			0.537161	−	0.843480i	$-0.319497\pi$
$809$	30.5568			1.07432			0.537161	+	0.843480i	$0.319497\pi$
$810$		0			0
$811$	−3.77885	+	6.54516i	−0.132693	+	0.229832i	−0.924714	−	0.380663i	$-0.875696\pi$
$811$	−3.77885	+	6.54516i	−0.132693	+	0.229832i	0.792021	+	0.610494i	$0.209029\pi$
$812$		0			0
$813$	10.3400	+	5.96983i	0.362641	+	0.209371i
$814$		0			0
$815$	0.405108	−	0.233889i	0.0141903	−	0.00819278i
$816$		0			0
$817$	8.98582	+	3.09624i	0.314374	+	0.108324i
$818$		0			0
$819$	2.55469	+	4.42485i	0.0892681	+	0.154617i
$820$		0			0
$821$	−8.43577	+	14.6112i	−0.294411	+	0.509934i	−0.974848	−	0.222873i	$-0.928457\pi$
$821$	−8.43577	+	14.6112i	−0.294411	+	0.509934i	0.680437	+	0.732807i	$0.261790\pi$
$822$		0			0
$823$	13.6013	+	7.85273i	0.474113	+	0.273729i	0.717960	−	0.696085i	$-0.245076\pi$
$823$	13.6013	+	7.85273i	0.474113	+	0.273729i	−0.243847	+	0.969814i	$0.578409\pi$
$824$		0			0
$825$		−	0.348815i		−	0.0121442i
$826$		0			0
$827$	−17.7366	+	30.7207i	−0.616762	+	1.06826i	0.373311	+	0.927706i	$0.378223\pi$
$827$	−17.7366	+	30.7207i	−0.616762	+	1.06826i	−0.990073	+	0.140557i	$0.955111\pi$
$828$		0			0
$829$			37.9948i			1.31961i	0.751436	+	0.659807i	$0.229362\pi$
$829$			37.9948i			1.31961i	−0.751436	+	0.659807i	$0.770638\pi$
$830$		0			0
$831$	4.27424	+	7.40320i	0.148272	+	0.256814i
$832$		0			0
$833$	−15.3572	−	26.5995i	−0.532096	−	0.921618i
$834$		0			0
$835$	−1.68267			−0.0582311
$836$		0			0
$837$	7.52645			0.260152
$838$		0			0
$839$	10.0098	+	17.3374i	0.345576	+	0.598555i	0.985458	−	0.169918i	$-0.0543503\pi$
$839$	10.0098	+	17.3374i	0.345576	+	0.598555i	−0.639883	+	0.768473i	$0.721017\pi$
$840$		0			0
$841$	−10.2585	−	17.7683i	−0.353742	−	0.612700i
$842$		0			0
$843$		−	8.70198i		−	0.299712i
$844$		0			0
$845$	−1.56118	+	2.70404i	−0.0537061	+	0.0930217i
$846$		0			0
$847$			14.0105i			0.481405i
$848$		0			0
$849$	−0.457715	−	0.264262i	−0.0157087	−	0.00906944i
$850$		0			0
$851$	6.79161	−	11.7634i	0.232813	−	0.403245i
$852$		0			0
$853$	−12.2806	−	21.2707i	−0.420481	−	0.728295i	0.575505	−	0.817798i	$-0.304805\pi$
$853$	−12.2806	−	21.2707i	−0.420481	−	0.728295i	−0.995987	+	0.0895031i	$0.971472\pi$
$854$		0			0
$855$	−2.90809	−	3.34684i	−0.0994545	−	0.114459i
$856$		0			0
$857$	−2.73112	+	1.57682i	−0.0932934	+	0.0538630i	−0.545921	−	0.837837i	$-0.683820\pi$
$857$	−2.73112	+	1.57682i	−0.0932934	+	0.0538630i	0.452627	+	0.891700i	$0.350487\pi$
$858$		0			0
$859$	21.5085	+	12.4179i	0.733860	+	0.423694i	0.819833	−	0.572603i	$-0.194066\pi$
$859$	21.5085	+	12.4179i	0.733860	+	0.423694i	−0.0859727	+	0.996297i	$0.527400\pi$
$860$		0			0
$861$	2.16971	−	3.75804i	0.0739434	−	0.128074i
$862$		0			0
$863$	5.64262			0.192077			0.0960386	−	0.995378i	$-0.469383\pi$
$863$	5.64262			0.192077			0.0960386	+	0.995378i	$0.469383\pi$
$864$		0			0
$865$	8.66030	+	5.00003i	0.294459	+	0.170006i
$866$		0			0
$867$	15.6479			0.531429
$868$		0			0
$869$	−1.14623	+	0.661777i	−0.0388832	+	0.0224492i
$870$		0			0
$871$	16.6884	−	9.63508i	0.565466	−	0.326472i
$872$		0			0
$873$		−	9.33339i		−	0.315887i
$874$		0			0
$875$			11.6233i			0.392939i
$876$		0			0
$877$	50.1106	−	28.9314i	1.69211	−	0.976943i	0.739307	−	0.673369i	$-0.235153\pi$
$877$	50.1106	−	28.9314i	1.69211	−	0.976943i	0.952808	−	0.303574i	$-0.0981801\pi$
$878$		0			0
$879$	12.1885	−	7.03702i	0.411107	−	0.237353i
$880$		0			0
$881$	−37.5637			−1.26555			−0.632776	−	0.774335i	$-0.718085\pi$
$881$	−37.5637			−1.26555			−0.632776	+	0.774335i	$0.718085\pi$
$882$		0			0
$883$	23.8307	+	13.7587i	0.801967	+	0.463016i	0.844159	−	0.536093i	$-0.180101\pi$
$883$	23.8307	+	13.7587i	0.801967	+	0.463016i	−0.0421913	+	0.999110i	$0.513434\pi$
$884$		0			0
$885$	3.43511			0.115470
$886$		0			0
$887$	−22.3871	+	38.7757i	−0.751686	+	1.30196i	0.195318	+	0.980740i	$0.437426\pi$
$887$	−22.3871	+	38.7757i	−0.751686	+	1.30196i	−0.947005	+	0.321219i	$0.895907\pi$
$888$		0			0
$889$	17.7062	+	10.2227i	0.593847	+	0.342858i
$890$		0			0
$891$	0.0761804	−	0.0439828i	0.00255214	−	0.00147348i
$892$		0			0
$893$	2.17009	+	11.1771i	0.0726194	+	0.374027i
$894$		0			0
$895$	−4.79524	−	8.30559i	−0.160287	−	0.277625i
$896$		0			0
$897$	−9.24164	+	16.0070i	−0.308569	+	0.534458i
$898$		0			0
$899$	18.9843	+	10.9606i	0.633161	+	0.365555i
$900$		0			0
$901$		−	31.3241i		−	1.04356i
$902$		0			0
$903$	1.38956	−	2.40680i	0.0462418	−	0.0800932i
$904$		0			0
$905$			1.37117i			0.0455793i
$906$		0			0
$907$	−2.63038	−	4.55595i	−0.0873403	−	0.151278i	0.819046	−	0.573728i	$-0.194503\pi$
$907$	−2.63038	−	4.55595i	−0.0873403	−	0.151278i	−0.906386	+	0.422450i	$0.861170\pi$
$908$		0			0
$909$	3.80402	+	6.58876i	0.126171	+	0.218535i
$910$		0			0
$911$	15.4245			0.511035			0.255517	−	0.966804i	$-0.417754\pi$
$911$	15.4245			0.511035			0.255517	+	0.966804i	$0.417754\pi$
$912$		0			0
$913$	1.05651			0.0349652
$914$		0			0
$915$	6.48002	+	11.2237i	0.214223	+	0.371045i
$916$		0			0
$917$	−13.0712	−	22.6401i	−0.431651	−	0.747641i
$918$		0			0
$919$			5.93620i			0.195817i	0.995195	+	0.0979087i	$0.0312153\pi$
$919$			5.93620i			0.195817i	−0.995195	+	0.0979087i	$0.968785\pi$
$920$		0			0
$921$	−4.03566	+	6.98997i	−0.132979	+	0.230327i
$922$		0			0
$923$		−	5.16847i		−	0.170122i
$924$		0			0
$925$	−10.1167	−	5.84088i	−0.332635	−	0.192047i
$926$		0			0
$927$	−8.45474	+	14.6440i	−0.277690	+	0.480973i
$928$		0			0
$929$	−21.2461	−	36.7994i	−0.697063	−	1.20735i	−0.969480	−	0.245170i	$-0.921156\pi$
$929$	−21.2461	−	36.7994i	−0.697063	−	1.20735i	0.272417	−	0.962179i	$-0.412177\pi$
$930$		0			0
$931$	15.3683	+	17.6870i	0.503677	+	0.579668i
$932$		0			0
$933$	3.56077	−	2.05581i	0.116574	−	0.0673043i
$934$		0			0
$935$	0.442758	+	0.255627i	0.0144797	+	0.00835989i
$936$		0			0
$937$	7.75363	−	13.4297i	0.253300	−	0.438729i	−0.711132	−	0.703058i	$-0.751817\pi$
$937$	7.75363	−	13.4297i	0.253300	−	0.438729i	0.964432	+	0.264329i	$0.0851506\pi$
$938$		0			0
$939$	32.7852			1.06991
$940$		0			0
$941$	−10.6746	−	6.16300i	−0.347983	−	0.200908i	0.315813	−	0.948821i	$-0.397723\pi$
$941$	−10.6746	−	6.16300i	−0.347983	−	0.200908i	−0.663797	+	0.747913i	$0.731056\pi$
$942$		0			0
$943$	15.6979			0.511194
$944$		0			0
$945$	−1.12277	+	0.648234i	−0.0365238	+	0.0210870i
$946$		0			0
$947$	21.4030	−	12.3570i	0.695503	−	0.401549i	−0.110168	−	0.993913i	$-0.535139\pi$
$947$	21.4030	−	12.3570i	0.695503	−	0.401549i	0.805670	+	0.592364i	$0.201805\pi$
$948$		0			0
$949$		−	24.7917i		−	0.804774i
$950$		0			0
$951$		−	20.5417i		−	0.666110i
$952$		0			0
$953$	−52.5164	+	30.3204i	−1.70117	+	0.982173i	−0.756598	+	0.653880i	$0.773140\pi$
$953$	−52.5164	+	30.3204i	−1.70117	+	0.982173i	−0.944576	+	0.328293i	$0.893527\pi$
$954$		0			0
$955$	7.70777	−	4.45008i	0.249418	−	0.144001i
$956$		0			0
$957$	0.256204			0.00828190
$958$		0			0
$959$	4.37689	+	2.52700i	0.141337	+	0.0816011i
$960$		0			0
$961$	25.6474			0.827335
$962$		0			0
$963$	−0.998744	+	1.72987i	−0.0321841	+	0.0557444i
$964$		0			0
$965$	−13.0759	−	7.54935i	−0.420927	−	0.243022i
$966$		0			0
$967$	−38.4465	+	22.1971i	−1.23636	+	0.713810i	−0.968347	−	0.249606i	$-0.919699\pi$
$967$	−38.4465	+	22.1971i	−1.23636	+	0.713810i	−0.268008	+	0.963417i	$0.586365\pi$
$968$		0			0
$969$	−24.4494	+	4.74699i	−0.785429	+	0.152495i
$970$		0			0
$971$	23.0117	+	39.8575i	0.738482	+	1.27909i	0.953179	+	0.302407i	$0.0977902\pi$
$971$	23.0117	+	39.8575i	0.738482	+	1.27909i	−0.214697	+	0.976681i	$0.568876\pi$
$972$		0			0
$973$	5.42626	−	9.39855i	0.173958	−	0.301304i
$974$		0			0
$975$	13.7662	+	7.94794i	0.440873	+	0.254538i
$976$		0			0
$977$			21.5927i			0.690811i	0.938454	+	0.345405i	$0.112259\pi$
$977$			21.5927i			0.690811i	−0.938454	+	0.345405i	$0.887741\pi$
$978$		0			0
$979$	−0.195174	+	0.338051i	−0.00623778	+	0.0108042i
$980$		0			0
$981$			12.8358i			0.409815i
$982$		0			0
$983$	−17.1749	−	29.7477i	−0.547793	−	0.948805i	−0.998425	−	0.0560956i	$-0.982135\pi$
$983$	−17.1749	−	29.7477i	−0.547793	−	0.948805i	0.450632	−	0.892710i	$-0.351198\pi$
$984$		0			0
$985$	−10.8648	−	18.8184i	−0.346181	−	0.599603i
$986$		0			0
$987$	3.32930			0.105973
$988$		0			0
$989$	10.0535			0.319684
$990$		0			0
$991$	13.3954	+	23.2015i	0.425519	+	0.737020i	0.996469	−	0.0839649i	$-0.0267584\pi$
$991$	13.3954	+	23.2015i	0.425519	+	0.737020i	−0.570950	+	0.820985i	$0.693425\pi$
$992$		0			0
$993$	−12.9676	−	22.4606i	−0.411515	−	0.712766i
$994$		0			0
$995$			5.38710i			0.170782i
$996$		0			0
$997$	−2.36286	+	4.09260i	−0.0748326	+	0.129614i	−0.901013	−	0.433791i	$-0.857176\pi$
$997$	−2.36286	+	4.09260i	−0.0748326	+	0.129614i	0.826181	+	0.563405i	$0.190509\pi$
$998$		0			0
$999$		−	2.94596i		−	0.0932060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1824.2.bb.a.31.13	✓	40
4.3	odd	2		1824.2.bb.b.31.13	yes	40
19.8	odd	6		1824.2.bb.b.1471.13	yes	40
76.27	even	6	inner	1824.2.bb.a.1471.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1824.2.bb.a.31.13	✓	40	1.1	even	1	trivial
1824.2.bb.a.1471.13	yes	40	76.27	even	6	inner
1824.2.bb.b.31.13	yes	40	4.3	odd	2
1824.2.bb.b.1471.13	yes	40	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(0.508588 + 0.880900i) q^{5} +1.27458i q^{7} +(-0.500000 + 0.866025i) q^{9} +0.0879656i q^{11} +(-3.47163 - 2.00435i) q^{13} +(0.508588 - 0.880900i) q^{15} +(-2.85692 - 4.94832i) q^{17} +(2.85898 + 3.29032i) q^{19} +(1.10381 - 0.637288i) q^{21} +(3.99307 + 2.30540i) q^{23} +(1.98268 - 3.43410i) q^{25} +1.00000 q^{27} +(2.52234 + 1.45627i) q^{29} +7.52645 q^{31} +(0.0761804 - 0.0439828i) q^{33} +(-1.12277 + 0.648234i) q^{35} -2.94596i q^{37} +4.00869i q^{39} +(2.94846 - 1.70230i) q^{41} +(1.88831 - 1.09022i) q^{43} -1.01718 q^{45} +(2.26213 + 1.30604i) q^{47} +5.37546 q^{49} +(-2.85692 + 4.94832i) q^{51} +(4.74768 + 2.74107i) q^{53} +(-0.0774889 + 0.0447382i) q^{55} +(1.42001 - 4.12111i) q^{57} +(1.68855 + 2.92466i) q^{59} +(-6.37060 + 11.0342i) q^{61} +(-1.10381 - 0.637288i) q^{63} -4.07755i q^{65} +(-2.40354 + 4.16306i) q^{67} -4.61080i q^{69} +(0.644658 + 1.11658i) q^{71} +(3.09225 + 5.35593i) q^{73} -3.96535 q^{75} -0.112119 q^{77} +(7.52313 + 13.0304i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0104i q^{83} +(2.90599 - 5.03332i) q^{85} -2.91255i q^{87} +(3.84299 + 2.21875i) q^{89} +(2.55469 - 4.42485i) q^{91} +(-3.76322 - 6.51809i) q^{93} +(-1.44440 + 4.19190i) q^{95} +(-8.08295 + 4.66669i) q^{97} +(-0.0761804 - 0.0439828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) \) 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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