LMFDB - Embedded newform 648.2.t.a.613.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			613.31
Character	$\chi$	$=$	648.613
Dual form			648.2.t.a.37.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35161 + 0.416109i) q^{2} +(1.65371 + 1.12483i) q^{4} +(1.34802 - 3.70366i) q^{5} +(0.00177522 - 0.0100678i) q^{7} +(1.76712 + 2.20846i) q^{8} +(3.36313 - 4.44499i) q^{10} +(0.343808 + 0.944604i) q^{11} +(-2.57400 - 3.06757i) q^{13} +(0.00658870 - 0.0128690i) q^{14} +(1.46950 + 3.72029i) q^{16} +(0.948987 + 1.64369i) q^{17} +(3.76245 + 2.17225i) q^{19} +(6.39524 - 4.60847i) q^{20} +(0.0716366 + 1.41980i) q^{22} +(-1.19728 - 6.79010i) q^{23} +(-8.06972 - 6.77130i) q^{25} +(-2.20260 - 5.21723i) q^{26} +(0.0142603 - 0.0146523i) q^{28} +(3.82827 - 4.56236i) q^{29} +(1.38501 + 7.85480i) q^{31} +(0.438140 + 5.63986i) q^{32} +(0.598707 + 2.61652i) q^{34} +(-0.0348946 - 0.0201464i) q^{35} +(-6.65823 + 3.84413i) q^{37} +(4.18148 + 4.50163i) q^{38} +(10.5615 - 3.56775i) q^{40} +(-4.44753 + 3.73192i) q^{41} +(1.42511 + 3.91546i) q^{43} +(-0.493966 + 1.94882i) q^{44} +(1.20716 - 9.67577i) q^{46} +(-1.37530 + 7.79973i) q^{47} +(6.57775 + 2.39411i) q^{49} +(-8.08953 - 12.5100i) q^{50} +(-0.806130 - 7.96819i) q^{52} -2.25567i q^{53} +3.96195 q^{55} +(0.0253713 - 0.0138704i) q^{56} +(7.07277 - 4.57356i) q^{58} +(2.24610 - 6.17111i) q^{59} +(0.106836 + 0.0188381i) q^{61} +(-1.39645 + 11.1930i) q^{62} +(-1.75460 + 7.80522i) q^{64} +(-14.8311 + 5.39806i) q^{65} +(-2.47342 - 2.94771i) q^{67} +(-0.279537 + 3.78564i) q^{68} +(-0.0387808 - 0.0417500i) q^{70} +(-0.442665 - 0.766718i) q^{71} +(-7.26116 + 12.5767i) q^{73} +(-10.5989 + 2.42523i) q^{74} +(3.77857 + 7.82441i) q^{76} +(0.0101204 - 0.00178450i) q^{77} +(2.46319 + 2.06686i) q^{79} +(15.7596 - 0.427473i) q^{80} +(-7.56422 + 3.19345i) q^{82} +(-9.76904 + 11.6423i) q^{83} +(7.36694 - 1.29899i) q^{85} +(0.296940 + 5.88518i) q^{86} +(-1.47857 + 2.42851i) q^{88} +(1.45362 - 2.51775i) q^{89} +(-0.0354530 + 0.0204688i) q^{91} +(5.65779 - 12.5756i) q^{92} +(-5.10441 + 9.96993i) q^{94} +(13.1172 - 11.0066i) q^{95} +(-12.0217 + 4.37554i) q^{97} +(7.89435 + 5.97296i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	1.35161	+	0.416109i	0.955734	+	0.294233i
$2$	1.35161	+	0.416109i	0.955734	+	0.294233i
$3$		0			0
$3$		0			0
$4$	1.65371	+	1.12483i	0.826854	+	0.562417i
$5$	1.34802	−	3.70366i	0.602854	−	1.65633i	−0.142608	−	0.989779i	$-0.545549\pi$
$5$	1.34802	−	3.70366i	0.602854	−	1.65633i	0.745462	−	0.666548i	$-0.232229\pi$
$6$		0			0
$7$	0.00177522	−	0.0100678i	0.000670970	−	0.00380526i	−0.984470	−	0.175550i	$-0.943829\pi$
$7$	0.00177522	−	0.0100678i	0.000670970	−	0.00380526i	0.985141	+	0.171745i	$0.0549406\pi$
$8$	1.76712	+	2.20846i	0.624770	+	0.780809i
$9$		0			0
$10$	3.36313	−	4.44499i	1.06351	−	1.40563i
$11$	0.343808	+	0.944604i	0.103662	+	0.284809i	0.980671	−	0.195666i	$-0.0626867\pi$
$11$	0.343808	+	0.944604i	0.103662	+	0.284809i	−0.877009	+	0.480474i	$0.840465\pi$
$12$		0			0
$13$	−2.57400	−	3.06757i	−0.713899	−	0.850792i	0.280124	−	0.959964i	$-0.409624\pi$
$13$	−2.57400	−	3.06757i	−0.713899	−	0.850792i	−0.994023	+	0.109172i	$0.965180\pi$
$14$	0.00658870	−	0.0128690i	0.00176090	−	0.00343939i
$15$		0			0
$16$	1.46950	+	3.72029i	0.367374	+	0.930073i
$17$	0.948987	+	1.64369i	0.230163	+	0.398654i	0.957856	−	0.287249i	$-0.0927407\pi$
$17$	0.948987	+	1.64369i	0.230163	+	0.398654i	−0.727693	+	0.685903i	$0.759407\pi$
$18$		0			0
$19$	3.76245	+	2.17225i	0.863166	+	0.498349i	0.865071	−	0.501649i	$-0.167273\pi$
$19$	3.76245	+	2.17225i	0.863166	+	0.498349i	−0.00190536	+	0.999998i	$0.500606\pi$
$20$	6.39524	−	4.60847i	1.43002	−	1.03049i
$21$		0			0
$22$	0.0716366	+	1.41980i	0.0152730	+	0.302702i
$23$	−1.19728	−	6.79010i	−0.249650	−	1.41583i	−0.809442	−	0.587200i	$-0.800230\pi$
$23$	−1.19728	−	6.79010i	−0.249650	−	1.41583i	0.559792	−	0.828633i	$-0.310881\pi$
$24$		0			0
$25$	−8.06972	−	6.77130i	−1.61394	−	1.35426i
$26$	−2.20260	−	5.21723i	−0.431966	−	1.02318i
$27$		0			0
$28$	0.0142603	−	0.0146523i	0.00269494	−	0.00276903i
$29$	3.82827	−	4.56236i	0.710892	−	0.847208i	−0.282820	−	0.959173i	$-0.591270\pi$
$29$	3.82827	−	4.56236i	0.710892	−	0.847208i	0.993712	+	0.111965i	$0.0357143\pi$
$30$		0			0
$31$	1.38501	+	7.85480i	0.248756	+	1.41076i	0.811606	+	0.584205i	$0.198594\pi$
$31$	1.38501	+	7.85480i	0.248756	+	1.41076i	−0.562850	+	0.826559i	$0.690295\pi$
$32$	0.438140	+	5.63986i	0.0774530	+	0.996996i
$33$		0			0
$34$	0.598707	+	2.61652i	0.102677	+	0.448729i
$35$	−0.0348946	−	0.0201464i	−0.00589826	−	0.00340536i
$36$		0			0
$37$	−6.65823	+	3.84413i	−1.09461	+	0.631971i	−0.934799	−	0.355177i	$-0.884421\pi$
$37$	−6.65823	+	3.84413i	−1.09461	+	0.631971i	−0.159807	+	0.987148i	$0.551087\pi$
$38$	4.18148	+	4.50163i	0.678326	+	0.730261i
$39$		0			0
$40$	10.5615	−	3.56775i	1.66992	−	0.564110i
$41$	−4.44753	+	3.73192i	−0.694588	+	0.582828i	−0.920228	−	0.391382i	$-0.871997\pi$
$41$	−4.44753	+	3.73192i	−0.694588	+	0.582828i	0.225641	+	0.974211i	$0.427553\pi$
$42$		0			0
$43$	1.42511	+	3.91546i	0.217327	+	0.597102i	0.999668	−	0.0257481i	$-0.00819679\pi$
$43$	1.42511	+	3.91546i	0.217327	+	0.597102i	−0.782341	+	0.622850i	$0.785975\pi$
$44$	−0.493966	+	1.94882i	−0.0744681	+	0.293796i
$45$		0			0
$46$	1.20716	−	9.67577i	0.177987	−	1.42661i
$47$	−1.37530	+	7.79973i	−0.200608	+	1.13771i	0.703594	+	0.710602i	$0.251578\pi$
$47$	−1.37530	+	7.79973i	−0.200608	+	1.13771i	−0.904202	+	0.427105i	$0.859534\pi$
$48$		0			0
$49$	6.57775	+	2.39411i	0.939679	+	0.342015i
$50$	−8.08953	−	12.5100i	−1.14403	−	1.76919i
$51$		0			0
$52$	−0.806130	−	7.96819i	−0.111790	−	1.10499i
$53$		−	2.25567i		−	0.309840i	−0.987927	−	0.154920i	$-0.950488\pi$
$53$		−	2.25567i		−	0.309840i	0.987927	−	0.154920i	$-0.0495120\pi$
$54$		0			0
$55$	3.96195			0.534230
$56$	0.0253713	−	0.0138704i	0.00339038	−	0.00185351i
$57$		0			0
$58$	7.07277	−	4.57356i	0.928701	−	0.600537i
$59$	2.24610	−	6.17111i	0.292417	−	0.803410i	−0.703294	−	0.710899i	$-0.748288\pi$
$59$	2.24610	−	6.17111i	0.292417	−	0.803410i	0.995712	−	0.0925111i	$-0.0294894\pi$
$60$		0			0
$61$	0.106836	+	0.0188381i	0.0136789	+	0.00241197i	0.180483	−	0.983578i	$-0.442234\pi$
$61$	0.106836	+	0.0188381i	0.0136789	+	0.00241197i	−0.166805	+	0.985990i	$0.553345\pi$
$62$	−1.39645	+	11.1930i	−0.177349	+	1.42151i
$63$		0			0
$64$	−1.75460	+	7.80522i	−0.219325	+	0.975652i
$65$	−14.8311	+	5.39806i	−1.83957	+	0.669547i
$66$		0			0
$67$	−2.47342	−	2.94771i	−0.302177	−	0.360120i	0.593494	−	0.804839i	$-0.297748\pi$
$67$	−2.47342	−	2.94771i	−0.302177	−	0.360120i	−0.895670	+	0.444718i	$0.853304\pi$
$68$	−0.279537	+	3.78564i	−0.0338988	+	0.459076i
$69$		0			0
$70$	−0.0387808	−	0.0417500i	−0.00463520	−	0.00499009i
$71$	−0.442665	−	0.766718i	−0.0525346	−	0.0909926i	0.838562	−	0.544806i	$-0.183397\pi$
$71$	−0.442665	−	0.766718i	−0.0525346	−	0.0909926i	−0.891097	+	0.453813i	$0.850063\pi$
$72$		0			0
$73$	−7.26116	+	12.5767i	−0.849854	+	1.47199i	0.0314838	+	0.999504i	$0.489977\pi$
$73$	−7.26116	+	12.5767i	−0.849854	+	1.47199i	−0.881338	+	0.472486i	$0.843357\pi$
$74$	−10.5989	+	2.42523i	−1.23210	+	0.281927i
$75$		0			0
$76$	3.77857	+	7.82441i	0.433432	+	0.897521i
$77$	0.0101204	−	0.00178450i	0.00115333	−	0.000203362i
$78$		0			0
$79$	2.46319	+	2.06686i	0.277131	+	0.232540i	0.770750	−	0.637138i	$-0.219882\pi$
$79$	2.46319	+	2.06686i	0.277131	+	0.232540i	−0.493619	+	0.869678i	$0.664326\pi$
$80$	15.7596	−	0.427473i	1.76198	−	0.0477930i
$81$		0			0
$82$	−7.56422	+	3.19345i	−0.835328	+	0.352658i
$83$	−9.76904	+	11.6423i	−1.07229	+	1.27791i	−0.113579	+	0.993529i	$0.536232\pi$
$83$	−9.76904	+	11.6423i	−1.07229	+	1.27791i	−0.958712	+	0.284378i	$0.908213\pi$
$84$		0			0
$85$	7.36694	−	1.29899i	0.799057	−	0.140895i
$86$	0.296940	+	5.88518i	0.0320198	+	0.634616i
$87$		0			0
$88$	−1.47857	+	2.42851i	−0.157616	+	0.258880i
$89$	1.45362	−	2.51775i	0.154084	−	0.266881i	−0.778641	−	0.627469i	$-0.784091\pi$
$89$	1.45362	−	2.51775i	0.154084	−	0.266881i	0.932725	+	0.360588i	$0.117424\pi$
$90$		0			0
$91$	−0.0354530	+	0.0204688i	−0.00371649	+	0.00214572i
$92$	5.65779	−	12.5756i	0.589865	−	1.31109i
$93$		0			0
$94$	−5.10441	+	9.96993i	−0.526480	+	1.02832i
$95$	13.1172	−	11.0066i	1.34579	−	1.12925i
$96$		0			0
$97$	−12.0217	+	4.37554i	−1.22062	+	0.444269i	−0.870375	−	0.492389i	$-0.836124\pi$
$97$	−12.0217	+	4.37554i	−1.22062	+	0.444269i	−0.350244	+	0.936658i	$0.613901\pi$
$98$	7.89435	+	5.97296i	0.797450	+	0.603360i
$99$		0			0
$100$	−5.72836	−	20.2748i	−0.572836	−	2.02748i
$101$	−8.25225	−	1.45509i	−0.821129	−	0.144787i	−0.252727	−	0.967538i	$-0.581327\pi$
$101$	−8.25225	−	1.45509i	−0.821129	−	0.144787i	−0.568403	+	0.822751i	$0.692438\pi$
$102$		0			0
$103$	6.53199	+	2.37745i	0.643617	+	0.234257i	0.643147	−	0.765743i	$-0.277628\pi$
$103$	6.53199	+	2.37745i	0.643617	+	0.234257i	0.000469418		1.00000i	$0.499851\pi$
$104$	2.22606	−	11.1053i	0.218283	−	1.08897i
$105$		0			0
$106$	0.938605	−	3.04879i	0.0911653	−	0.296125i
$107$		−	14.2756i		−	1.38007i	−0.723776	−	0.690035i	$-0.757595\pi$
$107$		−	14.2756i		−	1.38007i	0.723776	−	0.690035i	$-0.242405\pi$
$108$		0			0
$109$		−	4.88426i		−	0.467827i	−0.972257	−	0.233914i	$-0.924847\pi$
$109$		−	4.88426i		−	0.467827i	0.972257	−	0.233914i	$-0.0751533\pi$
$110$	5.35502	+	1.64860i	0.510581	+	0.157188i
$111$		0			0
$112$	0.0400638	−	0.00819021i	0.00378567	−	0.000773902i
$113$	−4.20463	−	1.53036i	−0.395538	−	0.143964i	0.136591	−	0.990628i	$-0.456386\pi$
$113$	−4.20463	−	1.53036i	−0.395538	−	0.143964i	−0.532129	+	0.846663i	$0.678608\pi$
$114$		0			0
$115$	−26.7622	−	4.71889i	−2.49559	−	0.440039i
$116$	11.4627	−	3.23863i	1.06429	−	0.300699i
$117$		0			0
$118$	5.60371	−	7.40632i	0.515863	−	0.681807i
$119$	0.0182330	−	0.00663627i	0.00167142	−	0.000608346i
$120$		0			0
$121$	7.65242	−	6.42114i	0.695674	−	0.583740i
$122$	0.136562	+	0.0699171i	0.0123638	+	0.00633000i
$123$		0			0
$124$	−6.54495	+	14.5475i	−0.587754	+	1.30640i
$125$	−18.8902	+	10.9063i	−1.68959	+	0.975485i
$126$		0			0
$127$	−0.733337	+	1.27018i	−0.0650731	+	0.112710i	−0.896726	−	0.442585i	$-0.854061\pi$
$127$	−0.733337	+	1.27018i	−0.0650731	+	0.112710i	0.831653	+	0.555295i	$0.187395\pi$
$128$	−5.61935	+	9.81951i	−0.496685	+	0.867931i
$129$		0			0
$130$	−22.2920	+	1.12475i	−1.95514	+	0.0986474i
$131$	−11.2373	+	1.98143i	−0.981805	+	0.173119i	−0.641439	−	0.767174i	$-0.721662\pi$
$131$	−11.2373	+	1.98143i	−0.981805	+	0.173119i	−0.340366	+	0.940293i	$0.610551\pi$
$132$		0			0
$133$	0.0285489	−	0.0340233i	0.00247551	−	0.00295019i
$134$	−2.11654	−	5.01337i	−0.182841	−	0.433089i
$135$		0			0
$136$	−1.95306	+	5.00040i	−0.167474	+	0.428781i
$137$	−3.27137	−	2.74501i	−0.279492	−	0.234522i	0.492255	−	0.870451i	$-0.336173\pi$
$137$	−3.27137	−	2.74501i	−0.279492	−	0.234522i	−0.771748	+	0.635929i	$0.780617\pi$
$138$		0			0
$139$	−1.04893	+	0.184955i	−0.0889693	+	0.0156877i	−0.217956	−	0.975959i	$-0.569939\pi$
$139$	−1.04893	+	0.184955i	−0.0889693	+	0.0156877i	0.128986	+	0.991646i	$0.458828\pi$
$140$	−0.0350441	−	0.0725669i	−0.00296176	−	0.00613302i
$141$		0			0
$142$	−0.279273	−	1.22050i	−0.0234360	−	0.102422i
$143$	2.01268	−	3.48606i	0.168309	−	0.291519i
$144$		0			0
$145$	−11.7368	−	20.3288i	−0.974690	−	1.68821i
$146$	−15.0475	+	13.9774i	−1.24534	+	1.15678i
$147$		0			0
$148$	−15.3348	−	1.13234i	−1.26051	−	0.0930777i
$149$	1.34236	+	1.59976i	0.109970	+	0.131058i	0.818222	−	0.574903i	$-0.194960\pi$
$149$	1.34236	+	1.59976i	0.109970	+	0.131058i	−0.708251	+	0.705960i	$0.750516\pi$
$150$		0			0
$151$	9.89970	−	3.60320i	0.805626	−	0.293224i	0.0938105	−	0.995590i	$-0.470095\pi$
$151$	9.89970	−	3.60320i	0.805626	−	0.293224i	0.711816	+	0.702366i	$0.247873\pi$
$152$	1.85136	+	12.1479i	0.150165	+	0.985321i
$153$		0			0
$154$	0.0144214	+	0.00179923i	0.00116211	+	0.000144986i
$155$	30.9586	+	5.45883i	2.48665	+	0.438464i
$156$		0			0
$157$	7.61747	−	20.9288i	0.607940	−	1.67030i	−0.126779	−	0.991931i	$-0.540464\pi$
$157$	7.61747	−	20.9288i	0.607940	−	1.67030i	0.734720	−	0.678371i	$-0.237314\pi$
$158$	2.46924	+	3.81855i	0.196442	+	0.303788i
$159$		0			0
$160$	21.4788	+	5.97993i	1.69804	+	0.472755i
$161$	−0.0704866			−0.00555512
$162$		0			0
$163$		−	8.64571i		−	0.677184i	−0.940933	−	0.338592i	$-0.890049\pi$
$163$		−	8.64571i		−	0.677184i	0.940933	−	0.338592i	$-0.109951\pi$
$164$	−11.5527	+	1.16877i	−0.902115	+	0.0912656i
$165$		0			0
$166$	−18.0484	+	11.6709i	−1.40083	+	0.905835i
$167$	7.93163	+	2.88688i	0.613768	+	0.223393i	0.630151	−	0.776473i	$-0.282993\pi$
$167$	7.93163	+	2.88688i	0.613768	+	0.223393i	−0.0163833	+	0.999866i	$0.505215\pi$
$168$		0			0
$169$	−0.527105	+	2.98936i	−0.0405465	+	0.229951i
$170$	10.4978	+	1.30972i	0.805142	+	0.100451i
$171$		0			0
$172$	−2.04753	+	8.07804i	−0.156123	+	0.615945i
$173$	4.65008	+	12.7760i	0.353539	+	0.971340i	0.981224	+	0.192872i	$0.0617803\pi$
$173$	4.65008	+	12.7760i	0.353539	+	0.971340i	−0.627685	+	0.778467i	$0.715997\pi$
$174$		0			0
$175$	−0.0824974	+	0.0692236i	−0.00623622	+	0.00523281i
$176$	−3.00898	+	2.66716i	−0.226810	+	0.201044i
$177$		0			0
$178$	3.01239	−	2.79815i	0.225788	−	0.209731i
$179$	−0.257187	+	0.148487i	−0.0192231	+	0.0110985i	−0.509581	−	0.860423i	$-0.670199\pi$
$179$	−0.257187	+	0.148487i	−0.0192231	+	0.0110985i	0.490358	+	0.871521i	$0.336866\pi$
$180$		0			0
$181$	1.63626	+	0.944694i	0.121622	+	0.0702186i	0.559577	−	0.828778i	$-0.310964\pi$
$181$	1.63626	+	0.944694i	0.121622	+	0.0702186i	−0.437955	+	0.898997i	$0.644297\pi$
$182$	−0.0564360	+	0.0129136i	−0.00418332	+	0.000957218i
$183$		0			0
$184$	12.8799	−	14.6430i	0.949521	−	1.07950i
$185$	5.26192	+	29.8418i	0.386864	+	2.19401i
$186$		0			0
$187$	−1.22637	+	1.46153i	−0.0896811	+	0.106878i
$188$	−11.0477	+	11.3515i	−0.805740	+	0.827892i
$189$		0			0
$190$	22.3092	−	9.41849i	1.61848	−	0.683289i
$191$	−10.6897	−	8.96976i	−0.773483	−	0.649029i	0.168116	−	0.985767i	$-0.446232\pi$
$191$	−10.6897	−	8.96976i	−0.773483	−	0.649029i	−0.941598	+	0.336738i	$0.890676\pi$
$192$		0			0
$193$	1.65530	+	9.38768i	0.119151	+	0.675740i	0.984611	+	0.174761i	$0.0559153\pi$
$193$	1.65530	+	9.38768i	0.119151	+	0.675740i	−0.865460	+	0.500979i	$0.832974\pi$
$194$	−18.0694	+	0.911699i	−1.29731	+	0.0654562i
$195$		0			0
$196$	8.18470	+	11.3580i	0.584622	+	0.811288i
$197$	−7.61046	−	4.39390i	−0.542223	−	0.313052i	0.203757	−	0.979022i	$-0.434685\pi$
$197$	−7.61046	−	4.39390i	−0.542223	−	0.313052i	−0.745979	+	0.665969i	$0.768018\pi$
$198$		0			0
$199$	4.70991	+	8.15780i	0.333876	+	0.578291i	0.983268	−	0.182163i	$-0.0583098\pi$
$199$	4.70991	+	8.15780i	0.333876	+	0.578291i	−0.649392	+	0.760454i	$0.724977\pi$
$200$	0.694014	−	29.7873i	0.0490742	−	2.10628i
$201$		0			0
$202$	−10.5484	−	5.40055i	−0.742180	−	0.379982i
$203$	−0.0391368	−	0.0466414i	−0.00274686	−	0.00327358i
$204$		0			0
$205$	7.82640	+	21.5029i	0.546619	+	1.50182i
$206$	7.83944	+	5.93141i	0.546200	+	0.413261i
$207$		0			0
$208$	7.62979	−	14.0838i	0.529031	−	0.976537i
$209$	−0.758358	+	4.30086i	−0.0524567	+	0.297497i
$210$		0			0
$211$	−4.12560	+	11.3350i	−0.284018	+	0.780333i	0.712855	+	0.701311i	$0.247402\pi$
$211$	−4.12560	+	11.3350i	−0.284018	+	0.780333i	−0.996873	+	0.0790214i	$0.974820\pi$
$212$	2.53726	−	3.73022i	0.174260	−	0.256193i
$213$		0			0
$214$	5.94018	−	19.2950i	0.406062	−	1.31898i
$215$	16.4226			1.12001
$216$		0			0
$217$	0.0815391			0.00553524
$218$	2.03238	−	6.60162i	0.137650	−	0.447118i
$219$		0			0
$220$	6.55191	+	4.45654i	0.441730	+	0.300460i
$221$	2.59946	−	7.14195i	0.174858	−	0.480420i
$222$		0			0
$223$	0.616341	−	3.49544i	0.0412732	−	0.234072i	−0.957192	−	0.289454i	$-0.906526\pi$
$223$	0.616341	−	3.49544i	0.0412732	−	0.234072i	0.998465	+	0.0553815i	$0.0176375\pi$
$224$	0.0575587	+	0.00560090i	0.00384580	+	0.000374226i
$225$		0			0
$226$	−5.04623	−	3.81803i	−0.335670	−	0.253972i
$227$	3.72066	+	10.2224i	0.246949	+	0.678486i	0.999794	+	0.0202886i	$0.00645849\pi$
$227$	3.72066	+	10.2224i	0.246949	+	0.678486i	−0.752846	+	0.658197i	$0.771319\pi$
$228$		0			0
$229$	−5.05083	−	6.01935i	−0.333769	−	0.397770i	0.572892	−	0.819631i	$-0.305821\pi$
$229$	−5.05083	−	6.01935i	−0.333769	−	0.397770i	−0.906661	+	0.421861i	$0.861377\pi$
$230$	−34.2085	−	17.5141i	−2.25564	−	1.15484i
$231$		0			0
$232$	16.8408	+	0.392373i	1.10565	+	0.0257606i
$233$	−12.0985	−	20.9553i	−0.792602	−	1.37283i	−0.924351	−	0.381544i	$-0.875392\pi$
$233$	−12.0985	−	20.9553i	−0.792602	−	1.37283i	0.131749	−	0.991283i	$-0.457941\pi$
$234$		0			0
$235$	27.0336	+	15.6079i	1.76348	+	1.01814i
$236$	10.6559	−	7.67872i	0.693638	−	0.499842i
$237$		0			0
$238$	0.0274053	−	0.00138275i	0.00177642	−	8.96303e-5i
$239$	5.23764	+	29.7041i	0.338795	+	1.92140i	0.385963	+	0.922514i	$0.373869\pi$
$239$	5.23764	+	29.7041i	0.338795	+	1.92140i	−0.0471684	+	0.998887i	$0.515020\pi$
$240$		0			0
$241$	−1.91756	−	1.60903i	−0.123521	−	0.103647i	0.578935	−	0.815374i	$-0.303469\pi$
$241$	−1.91756	−	1.60903i	−0.123521	−	0.103647i	−0.702456	+	0.711727i	$0.747913\pi$
$242$	13.0150	−	5.49465i	0.836635	−	0.353209i
$243$		0			0
$244$	0.155486	+	0.151325i	0.00995396	+	0.00968762i
$245$	17.7339	−	21.1344i	1.13298	−	1.35023i
$246$		0			0
$247$	−3.02101	−	17.1330i	−0.192222	−	1.09015i
$248$	−14.8995	+	16.9391i	−0.946122	+	1.07563i
$249$		0			0
$250$	−30.0704	+	6.88065i	−1.90182	+	0.435170i
$251$	14.5027	+	8.37314i	0.915402	+	0.528508i	0.882165	−	0.470940i	$-0.156085\pi$
$251$	14.5027	+	8.37314i	0.915402	+	0.528508i	0.0332368	+	0.999448i	$0.489418\pi$
$252$		0			0
$253$	6.00232	−	3.46544i	0.377363	−	0.217870i
$254$	−1.51972	+	1.41164i	−0.0953556	+	0.0885741i
$255$		0			0
$256$	−11.6812	+	10.9339i	−0.730073	+	0.683369i
$257$	20.4870	−	17.1907i	1.27795	−	1.07232i	0.284423	−	0.958699i	$-0.408198\pi$
$257$	20.4870	−	17.1907i	1.27795	−	1.07232i	0.993524	−	0.113626i	$-0.0362465\pi$
$258$		0			0
$259$	0.0268820	+	0.0738578i	0.00167037	+	0.00458930i
$260$	−30.5982	−	7.75567i	−1.89762	−	0.480986i
$261$		0			0
$262$	−16.0129	−	1.99780i	−0.989281	−	0.123424i
$263$	0.762315	−	4.32330i	0.0470064	−	0.266586i	−0.952242	−	0.305343i	$-0.901229\pi$
$263$	0.762315	−	4.32330i	0.0470064	−	0.266586i	0.999249	+	0.0387571i	$0.0123398\pi$
$264$		0			0
$265$	−8.35424	−	3.04070i	−0.513197	−	0.186788i
$266$	0.0527445	−	0.0341068i	0.00323397	−	0.00209122i
$267$		0			0
$268$	−0.774631	−	7.65684i	−0.0473181	−	0.467716i
$269$			0.741050i			0.0451826i	0.999745	+	0.0225913i	$0.00719165\pi$
$269$			0.741050i			0.0451826i	−0.999745	+	0.0225913i	$0.992808\pi$
$270$		0			0
$271$	−14.1450			−0.859245			−0.429622	−	0.903009i	$-0.641353\pi$
$271$	−14.1450			−0.859245			−0.429622	+	0.903009i	$0.641353\pi$
$272$	−4.72049	+	5.94591i	−0.286222	+	0.360524i
$273$		0			0
$274$	−3.27940	−	5.07143i	−0.198116	−	0.306376i
$275$	3.62176	−	9.95071i	0.218400	−	0.600050i
$276$		0			0
$277$	−8.42697	−	1.48590i	−0.506327	−	0.0892792i	−0.0853514	−	0.996351i	$-0.527201\pi$
$277$	−8.42697	−	1.48590i	−0.506327	−	0.0892792i	−0.420976	+	0.907072i	$0.638312\pi$
$278$	−1.49471	−	0.186482i	−0.0896468	−	0.0111845i
$279$		0			0
$280$	−0.0171703	−	0.112664i	−0.00102612	−	0.00673298i
$281$	17.6483	−	6.42344i	1.05281	−	0.383191i	0.243086	−	0.970005i	$-0.421840\pi$
$281$	17.6483	−	6.42344i	1.05281	−	0.383191i	0.809722	+	0.586814i	$0.199618\pi$
$282$		0			0
$283$	16.5234	+	19.6918i	0.982214	+	1.17056i	0.985347	+	0.170562i	$0.0545582\pi$
$283$	16.5234	+	19.6918i	0.982214	+	1.17056i	−0.00313343	+	0.999995i	$0.500997\pi$
$284$	0.130393	−	1.76585i	0.00773738	−	0.104784i
$285$		0			0
$286$	4.17094	−	3.87431i	0.246633	−	0.229093i
$287$	0.0296768	+	0.0514017i	0.00175177	+	0.00303415i
$288$		0			0
$289$	6.69885	−	11.6027i	0.394050	−	0.682514i
$290$	−7.40465	−	32.3604i	−0.434816	−	1.90027i
$291$		0			0
$292$	−26.1545	+	12.6306i	−1.53058	+	0.739148i
$293$	14.3663	−	2.53317i	0.839288	−	0.147989i	0.262550	−	0.964918i	$-0.415436\pi$
$293$	14.3663	−	2.53317i	0.839288	−	0.147989i	0.576738	+	0.816929i	$0.304325\pi$
$294$		0			0
$295$	−19.8279	−	16.6376i	−1.15442	−	0.968678i
$296$	−20.2555	−	7.91142i	−1.17733	−	0.459842i
$297$		0			0
$298$	1.14868	+	2.72083i	0.0665410	+	0.157613i
$299$	−17.7473	+	21.1504i	−1.02635	+	1.22316i
$300$		0			0
$301$	0.0419499	−	0.00739689i	0.00241795	−	0.000426350i
$302$	14.8799	−	0.750771i	0.856241	−	0.0432020i
$303$		0			0
$304$	−2.55251	+	17.1895i	−0.146397	+	0.985888i
$305$	0.213787	−	0.370290i	0.0122414	−	0.0212028i
$306$		0			0
$307$	8.07578	−	4.66255i	0.460909	−	0.266106i	−0.251517	−	0.967853i	$-0.580930\pi$
$307$	8.07578	−	4.66255i	0.460909	−	0.266106i	0.712426	+	0.701747i	$0.247596\pi$
$308$	0.0187434	+	0.00843273i	0.00106801	+	0.000480499i
$309$		0			0
$310$	39.5725	+	20.2603i	2.24757	+	1.15071i
$311$	6.15253	−	5.16259i	0.348878	−	0.292743i	−0.451461	−	0.892291i	$-0.649097\pi$
$311$	6.15253	−	5.16259i	0.348878	−	0.292743i	0.800339	+	0.599547i	$0.204653\pi$
$312$		0			0
$313$	31.0694	−	11.3083i	1.75615	−	0.639185i	0.756261	−	0.654269i	$-0.227024\pi$
$313$	31.0694	−	11.3083i	1.75615	−	0.639185i	0.999886	+	0.0150840i	$0.00480156\pi$
$314$	19.0045	−	25.1179i	1.07249	−	1.41749i
$315$		0			0
$316$	1.74852	+	6.18867i	0.0983619	+	0.348140i
$317$	−25.6721	−	4.52669i	−1.44189	−	0.254244i	−0.602650	−	0.798006i	$-0.705888\pi$
$317$	−25.6721	−	4.52669i	−1.44189	−	0.254244i	−0.839240	+	0.543762i	$0.817000\pi$
$318$		0			0
$319$	5.62581	+	2.04763i	0.314985	+	0.114645i
$320$	26.5426	+	17.0200i	1.48378	+	0.951449i
$321$		0			0
$322$	−0.0952705	−	0.0293301i	−0.00530922	−	0.00163450i
$323$			8.24576i			0.458806i
$324$		0			0
$325$			42.1838i			2.33993i
$326$	3.59755	−	11.6856i	0.199250	−	0.647207i
$327$		0			0
$328$	−16.1011	−	3.22746i	−0.889035	−	0.178207i
$329$	0.0760844	+	0.0276925i	0.00419467	+	0.00152674i
$330$		0			0
$331$	2.73256	+	0.481823i	0.150195	+	0.0264834i	0.248240	−	0.968699i	$-0.420148\pi$
$331$	2.73256	+	0.481823i	0.150195	+	0.0264834i	−0.0980451	+	0.995182i	$0.531259\pi$
$332$	−29.2508	+	8.26439i	−1.60535	+	0.453567i
$333$		0			0
$334$	9.51922	+	7.20235i	0.520869	+	0.394095i
$335$	−14.2516	+	5.18714i	−0.778645	+	0.283404i
$336$		0			0
$337$	−10.0326	+	8.41837i	−0.546512	+	0.458578i	−0.873758	−	0.486361i	$-0.838324\pi$
$337$	−10.0326	+	8.41837i	−0.546512	+	0.458578i	0.327246	+	0.944939i	$0.393879\pi$
$338$	−1.95634	+	3.82112i	−0.106411	+	0.207841i
$339$		0			0
$340$	13.6439	+	6.13844i	0.739945	+	0.332904i
$341$	−6.94350	+	4.00883i	−0.376012	+	0.217090i
$342$		0			0
$343$	0.0715611	−	0.123947i	0.00386393	−	0.00669253i
$344$	−6.12880	+	10.0664i	−0.330443	+	0.542743i
$345$		0			0
$346$	0.968901	+	19.2031i	0.0520885	+	1.03236i
$347$	−14.2864	+	2.51907i	−0.766932	+	0.135231i	−0.543409	−	0.839468i	$-0.682867\pi$
$347$	−14.2864	+	2.51907i	−0.766932	+	0.135231i	−0.223523	+	0.974699i	$0.571756\pi$
$348$		0			0
$349$	15.0245	−	17.9055i	0.804242	−	0.958459i	−0.195510	−	0.980702i	$-0.562636\pi$
$349$	15.0245	−	17.9055i	0.804242	−	0.958459i	0.999753	+	0.0222430i	$0.00708074\pi$
$350$	−0.140309	+	0.0592355i	−0.00749983	+	0.00316627i
$351$		0			0
$352$	−5.17680	+	2.35290i	−0.275924	+	0.125410i
$353$	26.1780	+	21.9660i	1.39332	+	1.16913i	0.963976	+	0.265988i	$0.0856981\pi$
$353$	26.1780	+	21.9660i	1.39332	+	1.16913i	0.429340	+	0.903143i	$0.358746\pi$
$354$		0			0
$355$	−3.43638	+	0.605927i	−0.182384	+	0.0321593i
$356$	5.23592	−	2.52854i	0.277503	−	0.134012i
$357$		0			0
$358$	−0.409404	+	0.0936791i	−0.0216377	+	0.00495110i
$359$	13.5391	−	23.4504i	0.714565	−	1.23766i	−0.248562	−	0.968616i	$-0.579958\pi$
$359$	13.5391	−	23.4504i	0.714565	−	1.23766i	0.963127	−	0.269047i	$-0.0867088\pi$
$360$		0			0
$361$	−0.0626343	−	0.108486i	−0.00329654	−	0.00570978i
$362$	1.81849	+	1.95772i	0.0955777	+	0.102896i
$363$		0			0
$364$	−0.0816530	−	0.00602936i	−0.00427978	−	0.000316024i
$365$	36.7916	+	43.8465i	1.92576	+	2.29503i
$366$		0			0
$367$	4.30354	−	1.56636i	0.224643	−	0.0817633i	−0.227247	−	0.973837i	$-0.572972\pi$
$367$	4.30354	−	1.56636i	0.224643	−	0.0817633i	0.451890	+	0.892074i	$0.350750\pi$
$368$	23.5018	−	14.4322i	1.22511	−	0.752332i
$369$		0			0
$370$	−5.30537	+	42.5241i	−0.275813	+	2.21072i
$371$	−0.0227096	−	0.00400432i	−0.00117902	−	0.000207894i
$372$		0			0
$373$	5.86591	−	16.1165i	0.303725	−	0.834479i	−0.690119	−	0.723696i	$-0.742442\pi$
$373$	5.86591	−	16.1165i	0.303725	−	0.834479i	0.993845	−	0.110783i	$-0.0353359\pi$
$374$	−2.26573	+	1.46512i	−0.117158	+	0.0757595i
$375$		0			0
$376$	−19.6557	+	10.7457i	−1.01367	+	0.554168i
$377$	−23.8493			−1.22830
$378$		0			0
$379$		−	0.380673i		−	0.0195538i	−0.999952	−	0.00977692i	$-0.996888\pi$
$379$		−	0.380673i		−	0.0195538i	0.999952	−	0.00977692i	$-0.00311214\pi$
$380$	34.0725	−	3.44707i	1.74788	−	0.176831i
$381$		0			0
$382$	−10.7160	−	16.5717i	−0.548278	−	0.847883i
$383$	−34.6697	−	12.6187i	−1.77154	−	0.644788i	−0.999963	−	0.00865253i	$-0.997246\pi$
$383$	−34.6697	−	12.6187i	−1.77154	−	0.644788i	−0.771578	−	0.636135i	$-0.780532\pi$
$384$		0			0
$385$	0.00703334	−	0.0398880i	0.000358452	−	0.00203288i
$386$	−1.66897	+	13.3773i	−0.0849483	+	0.680885i
$387$		0			0
$388$	−24.8021	−	6.28656i	−1.25914	−	0.319152i
$389$	−2.44660	−	6.72197i	−0.124047	−	0.340817i	0.862088	−	0.506758i	$-0.169156\pi$
$389$	−2.44660	−	6.72197i	−0.124047	−	0.340817i	−0.986136	+	0.165941i	$0.946934\pi$
$390$		0			0
$391$	10.0246	−	8.41167i	0.506968	−	0.425397i
$392$	6.33636	+	18.7574i	0.320035	+	0.947390i
$393$		0			0
$394$	−8.45804	−	9.10562i	−0.426110	−	0.458735i
$395$	10.9754	−	6.33665i	0.552233	−	0.318832i
$396$		0			0
$397$	−22.6986	−	13.1051i	−1.13921	−	0.657724i	−0.192976	−	0.981203i	$-0.561814\pi$
$397$	−22.6986	−	13.1051i	−1.13921	−	0.657724i	−0.946235	+	0.323479i	$0.895147\pi$
$398$	2.97143	+	12.9860i	0.148945	+	0.650930i
$399$		0			0
$400$	13.3328	−	39.9721i	0.666640	−	1.99861i
$401$	−3.00071	−	17.0179i	−0.149848	−	0.849832i	−0.963346	−	0.268263i	$-0.913550\pi$
$401$	−3.00071	−	17.0179i	−0.149848	−	0.849832i	0.813497	−	0.581569i	$-0.197561\pi$
$402$		0			0
$403$	20.5302	−	24.4669i	1.02268	−	1.21878i
$404$	−12.0101	−	11.6887i	−0.597523	−	0.581535i
$405$		0			0
$406$	−0.0334898	−	0.0793262i	−0.00166207	−	0.00393689i
$407$	−5.92033	−	4.96775i	−0.293460	−	0.246242i
$408$		0			0
$409$	−4.27076	−	24.2207i	−0.211176	−	1.19764i	−0.887421	−	0.460960i	$-0.847505\pi$
$409$	−4.27076	−	24.2207i	−0.211176	−	1.19764i	0.676245	−	0.736677i	$-0.263606\pi$
$410$	1.63073	+	32.3201i	0.0805359	+	1.59618i
$411$		0			0
$412$	8.12777	+	11.2790i	0.400426	+	0.555677i
$413$	−0.0581420	−	0.0335683i	−0.00286098	−	0.00165179i
$414$		0			0
$415$	29.9502	+	51.8753i	1.47020	+	2.54646i
$416$	16.1729	−	15.8610i	0.792942	−	0.777651i
$417$		0			0
$418$	−2.81463	+	5.49754i	−0.137668	+	0.268893i
$419$	−8.86909	−	10.5698i	−0.433283	−	0.516367i	0.504583	−	0.863363i	$-0.331646\pi$
$419$	−8.86909	−	10.5698i	−0.433283	−	0.516367i	−0.937867	+	0.346996i	$0.887202\pi$
$420$		0			0
$421$	12.5029	+	34.3515i	0.609355	+	1.67419i	0.731637	+	0.681695i	$0.238757\pi$
$421$	12.5029	+	34.3515i	0.609355	+	1.67419i	−0.122281	+	0.992496i	$0.539021\pi$
$422$	−10.2928	+	13.6038i	−0.501045	+	0.662223i
$423$		0			0
$424$	4.98156	−	3.98604i	0.241926	−	0.193579i
$425$	3.47188	−	19.6900i	0.168411	−	0.955106i
$426$		0			0
$427$	0.000379315	−	0.00104216i	1.83563e−5	−	5.04336e-5i
$428$	16.0576	−	23.6076i	0.776175	−	1.14112i
$429$		0			0
$430$	22.1970	+	6.83359i	1.07043	+	0.329545i
$431$	−7.44743			−0.358730			−0.179365	−	0.983783i	$-0.557404\pi$
$431$	−7.44743			−0.358730			−0.179365	+	0.983783i	$0.557404\pi$
$432$		0			0
$433$	20.9407			1.00634			0.503172	−	0.864186i	$-0.332166\pi$
$433$	20.9407			1.00634			0.503172	+	0.864186i	$0.332166\pi$
$434$	0.110209	+	0.0339291i	0.00529021	+	0.00162865i
$435$		0			0
$436$	5.49398	−	8.07713i	0.263114	−	0.386824i
$437$	10.2451	−	28.1482i	0.490090	−	1.34651i
$438$		0			0
$439$	4.88555	−	27.7073i	0.233174	−	1.32240i	−0.613250	−	0.789889i	$-0.710138\pi$
$439$	4.88555	−	27.7073i	0.233174	−	1.32240i	0.846424	−	0.532509i	$-0.178751\pi$
$440$	7.00123	+	8.74982i	0.333771	+	0.417131i
$441$		0			0
$442$	6.48529	−	8.57149i	0.308474	−	0.407704i
$443$	−5.98423	−	16.4415i	−0.284319	−	0.781161i	−0.996835	−	0.0795043i	$-0.974666\pi$
$443$	−5.98423	−	16.4415i	−0.284319	−	0.781161i	0.712515	−	0.701657i	$-0.247556\pi$
$444$		0			0
$445$	−7.36537	−	8.77771i	−0.349152	−	0.416103i
$446$	2.28754	−	4.46801i	0.108318	−	0.211567i
$447$		0			0
$448$	0.0754664	+	0.0315209i	0.00356545	+	0.00148922i
$449$	2.99357	+	5.18501i	0.141275	+	0.244696i	0.927977	−	0.372637i	$-0.121546\pi$
$449$	2.99357	+	5.18501i	0.141275	+	0.244696i	−0.786702	+	0.617333i	$0.788213\pi$
$450$		0			0
$451$	−5.05428	−	2.91809i	−0.237997	−	0.137408i
$452$	−5.23182	−	7.26028i	−0.246084	−	0.341495i
$453$		0			0
$454$	0.775245	+	15.3649i	0.0363841	+	0.721112i
$455$	0.0280181	+	0.158899i	0.00131351	+	0.00744928i
$456$		0			0
$457$	18.6279	+	15.6306i	0.871375	+	0.731170i	0.964387	−	0.264495i	$-0.0852052\pi$
$457$	18.6279	+	15.6306i	0.871375	+	0.731170i	−0.0930125	+	0.995665i	$0.529650\pi$
$458$	−4.32206	−	10.2375i	−0.201957	−	0.478368i
$459$		0			0
$460$	−38.9488	−	37.9067i	−1.81600	−	1.76741i
$461$	−10.3010	+	12.2762i	−0.479764	+	0.571761i	−0.950584	−	0.310469i	$-0.899514\pi$
$461$	−10.3010	+	12.2762i	−0.479764	+	0.571761i	0.470819	+	0.882230i	$0.343958\pi$
$462$		0			0
$463$	0.124840	+	0.708003i	0.00580181	+	0.0329037i	0.987571	−	0.157172i	$-0.0502377\pi$
$463$	0.124840	+	0.708003i	0.00580181	+	0.0329037i	−0.981769	+	0.190076i	$0.939127\pi$
$464$	22.5989	+	7.53793i	1.04913	+	0.349940i
$465$		0			0
$466$	−7.63285	−	33.3577i	−0.353585	−	1.54527i
$467$	−16.8793	−	9.74528i	−0.781082	−	0.450958i	0.0557318	−	0.998446i	$-0.482251\pi$
$467$	−16.8793	−	9.74528i	−0.781082	−	0.450958i	−0.836814	+	0.547488i	$0.815584\pi$
$468$		0			0
$469$	−0.0340678	+	0.0196690i	−0.00157310	+	0.000908231i
$470$	30.0444	+	32.3447i	1.38584	+	1.49195i
$471$		0			0
$472$	17.5978	−	5.94464i	0.810003	−	0.273624i
$473$	−3.20859	+	2.69233i	−0.147531	+	0.123794i
$474$		0			0
$475$	−15.6530	−	43.0062i	−0.718207	−	1.97326i
$476$	0.0376168	+	0.00953466i	0.00172416	+	0.000437020i
$477$		0			0
$478$	−5.28089	+	42.3279i	−0.241542	+	1.93603i
$479$	−1.69552	+	9.61575i	−0.0774701	+	0.439355i	0.921259	+	0.388950i	$0.127162\pi$
$479$	−1.69552	+	9.61575i	−0.0774701	+	0.439355i	−0.998729	+	0.0504046i	$0.983949\pi$
$480$		0			0
$481$	28.9304	+	10.5298i	1.31911	+	0.480118i
$482$	−1.92227	−	2.97269i	−0.0875571	−	0.135403i
$483$		0			0
$484$	19.8776	−	2.01098i	0.903526	−	0.0914084i
$485$			50.4227i			2.28958i
$486$		0			0
$487$	−40.7197			−1.84519			−0.922594	−	0.385773i	$-0.873935\pi$
$487$	−40.7197			−1.84519			−0.922594	+	0.385773i	$0.873935\pi$
$488$	0.147189	+	0.269232i	0.00666291	+	0.0121876i
$489$		0			0
$490$	32.7636	−	21.1863i	1.48011	−	0.957101i
$491$	4.27622	−	11.7488i	0.192983	−	0.530217i	−0.805029	−	0.593235i	$-0.797850\pi$
$491$	4.27622	−	11.7488i	0.192983	−	0.530217i	0.998012	+	0.0630180i	$0.0200726\pi$
$492$		0			0
$493$	11.1321	+	1.96289i	0.501365	+	0.0884041i
$494$	3.04595	−	24.4142i	0.137044	−	1.09845i
$495$		0			0
$496$	−27.1869	+	16.6953i	−1.22073	+	0.749639i
$497$	−0.00850497	+	0.00309555i	−0.000381500	+	0.000138855i
$498$		0			0
$499$	−2.94192	−	3.50604i	−0.131698	−	0.156952i	0.696165	−	0.717882i	$-0.254888\pi$
$499$	−2.94192	−	3.50604i	−0.131698	−	0.156952i	−0.827863	+	0.560930i	$0.810444\pi$
$500$	−43.5066	−	3.21258i	−1.94567	−	0.143671i
$501$		0			0
$502$	16.1179	+	17.3519i	0.719376	+	0.774454i
$503$	9.68900	+	16.7818i	0.432011	+	0.748265i	0.997046	−	0.0768015i	$-0.0244708\pi$
$503$	9.68900	+	16.7818i	0.432011	+	0.748265i	−0.565035	+	0.825067i	$0.691137\pi$
$504$		0			0
$505$	−16.5134	+	28.6020i	−0.734836	+	1.27277i
$506$	9.55480	−	2.18631i	0.424763	−	0.0971934i
$507$		0			0
$508$	−2.64146	+	1.27562i	−0.117196	+	0.0565964i
$509$	2.30682	−	0.406755i	0.102248	−	0.0180291i	−0.122290	−	0.992494i	$-0.539024\pi$
$509$	2.30682	−	0.406755i	0.102248	−	0.0180291i	0.224538	+	0.974465i	$0.427913\pi$
$510$		0			0
$511$	0.113729	+	0.0954301i	0.00503108	+	0.00422158i
$512$	−20.3381	+	9.91776i	−0.898825	+	0.438307i
$513$		0			0
$514$	34.8437	−	14.7103i	1.53689	−	0.648842i
$515$	17.6105	−	20.9874i	0.776014	−	0.924817i
$516$		0			0
$517$	−7.84049	+	1.38249i	−0.344824	+	0.0608018i
$518$	0.00560121	+	0.111013i	0.000246103	+	0.00487762i
$519$		0			0
$520$	−38.1296	−	23.2148i	−1.67209	−	1.01804i
$521$	3.33988	−	5.78485i	0.146323	−	0.253439i	−0.783543	−	0.621338i	$-0.786589\pi$
$521$	3.33988	−	5.78485i	0.146323	−	0.253439i	0.929866	+	0.367899i	$0.119923\pi$
$522$		0			0
$523$	25.4719	−	14.7062i	1.11381	−	0.643057i	0.173994	−	0.984747i	$-0.444333\pi$
$523$	25.4719	−	14.7062i	1.11381	−	0.643057i	0.939813	+	0.341690i	$0.110999\pi$
$524$	−20.8119	−	9.36336i	−0.909174	−	0.409040i
$525$		0			0
$526$	2.82932	−	5.52622i	0.123364	−	0.240955i
$527$	−11.5965	+	9.73065i	−0.505153	+	0.423874i
$528$		0			0
$529$	−23.0590	+	8.39280i	−1.00257	+	0.364904i
$530$	−10.0264	−	7.58611i	−0.435520	−	0.329520i
$531$		0			0
$532$	0.0854822	−	0.0241517i	0.00370612	−	0.00104711i
$533$	22.8959	+	4.03716i	0.991731	+	0.174869i
$534$		0			0
$535$	−52.8718	−	19.2438i	−2.28585	−	0.831980i
$536$	2.13908	−	10.6714i	0.0923941	−	0.460935i
$537$		0			0
$538$	−0.308357	+	1.00161i	−0.0132942	+	0.0431826i
$539$			7.03648i			0.303083i
$540$		0			0
$541$			1.09392i			0.0470312i	0.999723	+	0.0235156i	$0.00748594\pi$
$541$			1.09392i			0.0470312i	−0.999723	+	0.0235156i	$0.992514\pi$
$542$	−19.1185	−	5.88584i	−0.821209	−	0.252818i
$543$		0			0
$544$	−8.85442	+	6.07232i	−0.379630	+	0.260349i
$545$	−18.0896	−	6.58409i	−0.774875	−	0.282031i
$546$		0			0
$547$	−11.4033	−	2.01070i	−0.487568	−	0.0859714i	−0.0755403	−	0.997143i	$-0.524068\pi$
$547$	−11.4033	−	2.01070i	−0.487568	−	0.0859714i	−0.412028	+	0.911171i	$0.635179\pi$
$548$	−2.32221	−	8.21919i	−0.0992001	−	0.351107i
$549$		0			0
$550$	9.03579	−	11.9424i	0.385287	−	0.509228i
$551$	24.3143	−	8.84968i	1.03582	−	0.377009i
$552$		0			0
$553$	0.0251814	−	0.0211297i	0.00107082	−	0.000898528i
$554$	−10.7717	−	5.51490i	−0.457645	−	0.234305i
$555$		0			0
$556$	−1.94267	−	0.874014i	−0.0823876	−	0.0370665i
$557$	11.9979	−	6.92697i	0.508366	−	0.293505i	−0.223796	−	0.974636i	$-0.571845\pi$
$557$	11.9979	−	6.92697i	0.508366	−	0.293505i	0.732162	+	0.681131i	$0.238512\pi$
$558$		0			0
$559$	8.34273	−	14.4500i	0.352860	−	0.611171i
$560$	0.0236731	−	0.159423i	0.00100037	−	0.00673686i
$561$		0			0
$562$	26.5264	−	1.33840i	1.11895	−	0.0564572i
$563$	−29.5384	+	5.20841i	−1.24489	+	0.219508i	−0.757012	−	0.653401i	$-0.773341\pi$
$563$	−29.5384	+	5.20841i	−1.24489	+	0.219508i	−0.487882	+	0.872910i	$0.662230\pi$
$564$		0			0
$565$	−11.3359	+	13.5096i	−0.476903	+	0.568351i
$566$	14.1393	+	33.4912i	0.594318	+	1.40774i
$567$		0			0
$568$	0.911026	−	2.33249i	0.0382258	−	0.0978690i
$569$	13.1491	+	11.0334i	0.551241	+	0.462546i	0.875361	−	0.483470i	$-0.160624\pi$
$569$	13.1491	+	11.0334i	0.551241	+	0.462546i	−0.324120	+	0.946016i	$0.605068\pi$
$570$		0			0
$571$	−16.7116	+	2.94670i	−0.699357	+	0.123316i	−0.512012	−	0.858978i	$-0.671100\pi$
$571$	−16.7116	+	2.94670i	−0.699357	+	0.123316i	−0.187346	+	0.982294i	$0.559988\pi$
$572$	7.24963	−	3.50100i	0.303122	−	0.146384i
$573$		0			0
$574$	0.0187228	+	0.0818239i	0.000781475	+	0.00341526i
$575$	−36.3161	+	62.9013i	−1.51449	+	2.62317i
$576$		0			0
$577$	−4.49809	−	7.79092i	−0.187258	−	0.324340i	0.757077	−	0.653326i	$-0.226627\pi$
$577$	−4.49809	−	7.79092i	−0.187258	−	0.324340i	−0.944335	+	0.328985i	$0.893293\pi$
$578$	13.8822	−	12.8950i	0.577425	−	0.536359i
$579$		0			0
$580$	3.45724	−	46.8198i	0.143554	−	1.94409i
$581$	0.0998698	+	0.119020i	0.00414330	+	0.00493779i
$582$		0			0
$583$	2.13072	−	0.775517i	0.0882453	−	0.0321186i
$584$	−40.6064	+	6.18850i	−1.68031	+	0.256082i
$585$		0			0
$586$	20.4717	+	2.55408i	0.845679	+	0.105508i
$587$	−29.2734	−	5.16169i	−1.20824	−	0.213046i	−0.466984	−	0.884266i	$-0.654660\pi$
$587$	−29.2734	−	5.16169i	−1.20824	−	0.213046i	−0.741258	+	0.671220i	$0.765771\pi$
$588$		0			0
$589$	−11.8516	+	32.5619i	−0.488336	+	1.34169i
$590$	−19.8766	−	30.7381i	−0.818306	−	1.26547i
$591$		0			0
$592$	−24.0855	−	19.1216i	−0.989909	−	0.785895i
$593$	21.5451			0.884750			0.442375	−	0.896830i	$-0.354136\pi$
$593$	21.5451			0.884750			0.442375	+	0.896830i	$0.354136\pi$
$594$		0			0
$595$		−	0.0764747i		−	0.00313516i
$596$	0.420403	+	4.15547i	0.0172204	+	0.170215i
$597$		0			0
$598$	−32.7884	+	21.2024i	−1.34082	+	0.867029i
$599$	10.2586	+	3.73384i	0.419156	+	0.152560i	0.542983	−	0.839743i	$-0.317295\pi$
$599$	10.2586	+	3.73384i	0.419156	+	0.152560i	−0.123827	+	0.992304i	$0.539517\pi$
$600$		0			0
$601$	−2.62710	+	14.8990i	−0.107162	+	0.607744i	0.883173	+	0.469047i	$0.155403\pi$
$601$	−2.62710	+	14.8990i	−0.107162	+	0.607744i	−0.990335	+	0.138697i	$0.955709\pi$
$602$	0.0597778	+	0.00745798i	0.00243636	+	0.000303964i
$603$		0			0
$604$	20.4242	+	5.17689i	0.831049	+	0.210645i
$605$	−13.4661	−	36.9978i	−0.547475	−	1.50417i
$606$		0			0
$607$	−18.8283	+	15.7988i	−0.764216	+	0.641253i	−0.939221	−	0.343314i	$-0.888450\pi$
$607$	−18.8283	+	15.7988i	−0.764216	+	0.641253i	0.175005	+	0.984568i	$0.444006\pi$
$608$	−10.6027	+	22.1715i	−0.429997	+	0.899171i
$609$		0			0
$610$	0.443038	−	0.411530i	0.0179381	−	0.0166624i
$611$	27.4663	−	15.8577i	1.11117	−	0.641532i
$612$		0			0
$613$	−15.6018	−	9.00768i	−0.630149	−	0.363817i	0.150661	−	0.988586i	$-0.451860\pi$
$613$	−15.6018	−	9.00768i	−0.630149	−	0.363817i	−0.780810	+	0.624769i	$0.785193\pi$
$614$	12.8554	−	2.94156i	0.518804	−	0.118712i
$615$		0			0
$616$	0.0218249	+	0.0191971i	0.000879351	+	0.000773472i
$617$	4.06887	+	23.0757i	0.163807	+	0.928994i	0.950286	+	0.311378i	$0.100790\pi$
$617$	4.06887	+	23.0757i	0.163807	+	0.928994i	−0.786480	+	0.617616i	$0.788098\pi$
$618$		0			0
$619$	−21.6871	+	25.8457i	−0.871679	+	1.03883i	0.127219	+	0.991875i	$0.459395\pi$
$619$	−21.6871	+	25.8457i	−0.871679	+	1.03883i	−0.998897	+	0.0469514i	$0.985049\pi$
$620$	45.0561	+	43.8506i	1.80950	+	1.76108i
$621$		0			0
$622$	10.4640	−	4.41769i	0.419569	−	0.177133i
$623$	−0.0227676	−	0.0191043i	−0.000912166	−	0.000765398i
$624$		0			0
$625$	5.78239	+	32.7936i	0.231296	+	1.31174i
$626$	46.6993	−	2.35623i	1.86648	−	0.0941741i
$627$		0			0
$628$	36.1385	−	26.0418i	1.44208	−	1.03918i
$629$	−12.6372	−	7.29606i	−0.503876	−	0.290913i
$630$		0			0
$631$	−3.55095	−	6.15043i	−0.141361	−	0.244845i	0.786648	−	0.617401i	$-0.211815\pi$
$631$	−3.55095	−	6.15043i	−0.141361	−	0.244845i	−0.928009	+	0.372557i	$0.878481\pi$
$632$	−0.211840	+	9.09226i	−0.00842655	+	0.361671i
$633$		0			0
$634$	−32.8151	−	16.8007i	−1.30326	−	0.667241i
$635$	3.71575	+	4.42826i	0.147455	+	0.175730i
$636$		0			0
$637$	−9.58703	−	26.3402i	−0.379852	−	1.04363i
$638$	6.75187	+	5.10854i	0.267309	+	0.202249i
$639$		0			0
$640$	28.7931	+	34.0491i	1.13815	+	1.34591i
$641$	0.826096	−	4.68502i	0.0326288	−	0.185047i	−0.964137	−	0.265404i	$-0.914495\pi$
$641$	0.826096	−	4.68502i	0.0326288	−	0.185047i	0.996766	+	0.0803565i	$0.0256059\pi$
$642$		0			0
$643$	−5.88956	+	16.1814i	−0.232262	+	0.638134i	−0.999997	−	0.00263392i	$-0.999162\pi$
$643$	−5.88956	+	16.1814i	−0.232262	+	0.638134i	0.767735	+	0.640768i	$0.221384\pi$
$644$	−0.116564	−	0.0792858i	−0.00459327	−	0.00312430i
$645$		0			0
$646$	−3.43113	+	11.1451i	−0.134996	+	0.438497i
$647$	−38.9704			−1.53208			−0.766042	−	0.642791i	$-0.777776\pi$
$647$	−38.9704			−1.53208			−0.766042	+	0.642791i	$0.777776\pi$
$648$		0			0
$649$	6.60148			0.259131
$650$	−17.5530	+	57.0161i	−0.688486	+	2.23635i
$651$		0			0
$652$	9.72499	−	14.2975i	0.380860	−	0.559932i
$653$	−7.50821	+	20.6286i	−0.293819	+	0.807261i	0.701680	+	0.712492i	$0.252434\pi$
$653$	−7.50821	+	20.6286i	−0.293819	+	0.807261i	−0.995499	+	0.0947692i	$0.969789\pi$
$654$		0			0
$655$	−7.80953	+	44.2901i	−0.305144	+	1.73056i
$656$	−20.4195	−	11.0621i	−0.797246	−	0.431902i
$657$		0			0
$658$	0.0913135	+	0.0690889i	0.00355977	+	0.00269336i
$659$	10.8064	+	29.6905i	0.420960	+	1.15658i	0.951158	+	0.308703i	$0.0998950\pi$
$659$	10.8064	+	29.6905i	0.420960	+	1.15658i	−0.530199	+	0.847873i	$0.677883\pi$
$660$		0			0
$661$	−0.564964	−	0.673298i	−0.0219746	−	0.0261883i	0.754945	−	0.655788i	$-0.227663\pi$
$661$	−0.564964	−	0.673298i	−0.0219746	−	0.0261883i	−0.776920	+	0.629600i	$0.783219\pi$
$662$	3.49286	+	1.78828i	0.135754	+	0.0695034i
$663$		0			0
$664$	−42.9746	−	1.00126i	−1.66774	−	0.0388566i
$665$	−0.0875262	−	0.151600i	−0.00339412	−	0.00587879i
$666$		0			0
$667$	−35.5624	−	20.5319i	−1.37698	−	0.795000i
$668$	9.86933	+	13.6958i	0.381856	+	0.529907i
$669$		0			0
$670$	−21.4210	+	1.08081i	−0.827564	+	0.0417552i
$671$	0.0189365	+	0.107394i	0.000731036	+	0.00414591i
$672$		0			0
$673$	2.60760	+	2.18804i	0.100516	+	0.0843426i	0.691661	−	0.722223i	$-0.256879\pi$
$673$	2.60760	+	2.18804i	0.100516	+	0.0843426i	−0.591145	+	0.806565i	$0.701324\pi$
$674$	−17.0632	+	7.20371i	−0.657249	+	0.277477i
$675$		0			0
$676$	−4.23421	+	4.35062i	−0.162854	+	0.167331i
$677$	12.0910	−	14.4095i	0.464695	−	0.553802i	−0.481900	−	0.876226i	$-0.660053\pi$
$677$	12.0910	−	14.4095i	0.464695	−	0.553802i	0.946595	+	0.322424i	$0.104498\pi$
$678$		0			0
$679$	0.0227108	+	0.128799i	0.000871561	+	0.00494287i
$680$	15.8870	+	13.9741i	0.609239	+	0.535884i
$681$		0			0
$682$	−11.0530	+	2.52913i	−0.423242	+	0.0968455i
$683$	−19.4488	−	11.2288i	−0.744188	−	0.429657i	0.0794021	−	0.996843i	$-0.474699\pi$
$683$	−19.4488	−	11.2288i	−0.744188	−	0.429657i	−0.823590	+	0.567186i	$0.808032\pi$
$684$		0			0
$685$	−14.5765	+	8.41573i	−0.556938	+	0.321548i
$686$	0.148298	−	0.137752i	0.00566206	−	0.00525938i
$687$		0			0
$688$	−12.4725	+	11.0556i	−0.475508	+	0.421490i
$689$	−6.91944	+	5.80610i	−0.263610	+	0.221195i
$690$		0			0
$691$	14.6665	+	40.2960i	0.557941	+	1.53293i	0.822618	+	0.568594i	$0.192512\pi$
$691$	14.6665	+	40.2960i	0.557941	+	1.53293i	−0.264677	+	0.964337i	$0.585265\pi$
$692$	−6.68100	+	26.3583i	−0.253973	+	1.00199i
$693$		0			0
$694$	−20.3578	−	2.53987i	−0.772773	−	0.0964123i
$695$	−0.728974	+	4.13422i	−0.0276515	+	0.156820i
$696$		0			0
$697$	−10.3548	−	3.76883i	−0.392215	−	0.142755i
$698$	27.7579	−	17.9494i	1.05065	−	0.679396i
$699$		0			0
$700$	−0.214292	+	0.0216796i	−0.00809946	+	0.000819410i
$701$		−	30.9274i		−	1.16811i	−0.811714	−	0.584055i	$-0.801465\pi$
$701$		−	30.9274i		−	1.16811i	0.811714	−	0.584055i	$-0.198535\pi$
$702$		0			0
$703$	−33.4017			−1.25977
$704$	−7.97608	+	1.02609i	−0.300610	+	0.0386723i
$705$		0			0
$706$	26.2423	+	40.5824i	0.987642	+	1.52734i
$707$	−0.0292991	+	0.0804987i	−0.00110191	+	0.00302746i
$708$		0			0
$709$	−10.5402	−	1.85852i	−0.395845	−	0.0697982i	−0.0278175	−	0.999613i	$-0.508856\pi$
$709$	−10.5402	−	1.85852i	−0.395845	−	0.0697982i	−0.368028	+	0.929815i	$0.619967\pi$
$710$	−4.89679	−	0.610931i	−0.183773	−	0.0229278i
$711$		0			0
$712$	8.12907	−	1.23889i	0.304650	−	0.0464292i
$713$	51.6766	−	18.8088i	1.93531	−	0.704394i
$714$		0			0
$715$	−10.1981	−	12.1536i	−0.381386	−	0.454518i
$716$	−0.592336	−	0.0437388i	−0.0221366	−	0.00163460i
$717$		0			0
$718$	28.0575	−	26.0621i	1.04710	−	0.972628i
$719$	−7.98318	−	13.8273i	−0.297723	−	0.515671i	0.677892	−	0.735161i	$-0.262894\pi$
$719$	−7.98318	−	13.8273i	−0.297723	−	0.515671i	−0.975615	+	0.219491i	$0.929560\pi$
$720$		0			0
$721$	0.0355314	−	0.0615422i	0.00132326	−	0.00229195i
$722$	−0.0395154	−	0.172693i	−0.00147061	−	0.00642698i
$723$		0			0
$724$	1.64327	+	3.40277i	0.0610716	+	0.126463i
$725$	−61.7861	+	10.8946i	−2.29468	+	0.404614i
$726$		0			0
$727$	18.0652	+	15.1585i	0.670002	+	0.562198i	0.913066	−	0.407812i	$-0.133708\pi$
$727$	18.0652	+	15.1585i	0.670002	+	0.562198i	−0.243064	+	0.970010i	$0.578153\pi$
$728$	−0.107854	−	0.0421259i	−0.00399735	−	0.00156129i
$729$		0			0
$730$	31.4830	+	74.5728i	1.16524	+	2.76006i
$731$	−5.08341	+	6.05817i	−0.188017	+	0.224069i
$732$		0			0
$733$	−5.12011	+	0.902813i	−0.189115	+	0.0333462i	−0.267404	−	0.963585i	$-0.586166\pi$
$733$	−5.12011	+	0.902813i	−0.189115	+	0.0333462i	0.0782882	+	0.996931i	$0.475055\pi$
$734$	6.46849	−	0.326371i	0.238756	−	0.0120466i
$735$		0			0
$736$	37.7706	−	9.72749i	1.39224	−	0.358560i
$737$	1.93404	−	3.34985i	0.0712412	−	0.123393i
$738$		0			0
$739$	−10.5638	+	6.09903i	−0.388596	+	0.224356i	−0.681552	−	0.731770i	$-0.738695\pi$
$739$	−10.5638	+	6.09903i	−0.388596	+	0.224356i	0.292955	+	0.956126i	$0.405361\pi$
$740$	−24.8654	+	55.2684i	−0.914071	+	2.03171i
$741$		0			0
$742$	−0.0290283	−	0.0148619i	−0.00106566	−	0.000545599i
$743$	11.5486	−	9.69040i	0.423676	−	0.355506i	−0.405883	−	0.913925i	$-0.633036\pi$
$743$	11.5486	−	9.69040i	0.423676	−	0.355506i	0.829559	+	0.558419i	$0.188592\pi$
$744$		0			0
$745$	7.73451	−	2.81513i	0.283371	−	0.103138i
$746$	14.6346	−	19.3423i	0.535812	−	0.708173i
$747$		0			0
$748$	−3.67204	+	1.03748i	−0.134263	+	0.0379341i
$749$	−0.143723	−	0.0253422i	−0.00525153	−	0.000925986i
$750$		0			0
$751$	−1.35242	−	0.492239i	−0.0493504	−	0.0179621i	0.317227	−	0.948350i	$-0.397248\pi$
$751$	−1.35242	−	0.492239i	−0.0493504	−	0.0179621i	−0.366577	+	0.930388i	$0.619471\pi$
$752$	−31.0383	+	6.34513i	−1.13185	+	0.231383i
$753$		0			0
$754$	−32.2350	−	9.92391i	−1.17393	−	0.361408i
$755$		−	41.5223i		−	1.51115i
$756$		0			0
$757$		−	15.3476i		−	0.557818i	−0.960318	−	0.278909i	$-0.910027\pi$
$757$		−	15.3476i		−	0.557818i	0.960318	−	0.278909i	$-0.0899727\pi$
$758$	0.158401	−	0.514521i	0.00575339	−	0.0186883i
$759$		0			0
$760$	47.4872	+	9.51878i	1.72254	+	0.345283i
$761$	3.86991	+	1.40853i	0.140284	+	0.0510593i	0.411208	−	0.911541i	$-0.365107\pi$
$761$	3.86991	+	1.40853i	0.140284	+	0.0510593i	−0.270924	+	0.962601i	$0.587329\pi$
$762$		0			0
$763$	−0.0491736	−	0.00867063i	−0.00178020	−	0.000313898i
$764$	−7.58821	−	26.8576i	−0.274532	−	0.971672i
$765$		0			0
$766$	−41.6092	−	31.4820i	−1.50340	−	1.13749i
$767$	−24.7118	+	8.99435i	−0.892291	+	0.324767i
$768$		0			0
$769$	36.4911	−	30.6197i	1.31590	−	1.10417i	0.328748	−	0.944418i	$-0.393373\pi$
$769$	36.4911	−	30.6197i	1.31590	−	1.10417i	0.987156	−	0.159757i	$-0.0510710\pi$
$770$	0.0261041	−	0.0509865i	0.000940727	−	0.00183743i
$771$		0			0
$772$	−7.82220	+	17.3864i	−0.281527	+	0.625751i
$773$	4.04314	−	2.33431i	0.145422	−	0.0839592i	−0.425524	−	0.904947i	$-0.639910\pi$
$773$	4.04314	−	2.33431i	0.145422	−	0.0839592i	0.570945	+	0.820988i	$0.306577\pi$
$774$		0			0
$775$	42.0105	−	72.7644i	1.50906	−	2.61377i
$776$	−30.9070	−	18.8174i	−1.10950	−	0.675504i
$777$		0			0
$778$	−0.509779	−	10.1035i	−0.0182765	−	0.362229i
$779$	−24.8403	+	4.38001i	−0.889996	+	0.156930i
$780$		0			0
$781$	0.572053	−	0.681746i	0.0204697	−	0.0243948i
$782$	17.0496	−	7.19797i	0.609692	−	0.257399i
$783$		0			0
$784$	0.759198	+	27.9893i	0.0271142	+	0.999617i
$785$	−67.2447	−	56.4250i	−2.40007	−	2.01390i
$786$		0			0
$787$	16.1106	−	2.84073i	0.574279	−	0.101261i	0.121037	−	0.992648i	$-0.461378\pi$
$787$	16.1106	−	2.84073i	0.574279	−	0.101261i	0.453243	+	0.891387i	$0.350267\pi$
$788$	−7.64306	−	15.8267i	−0.272273	−	0.563804i
$789$		0			0
$790$	17.4712	−	3.99773i	0.621598	−	0.142233i
$791$	−0.0228715	+	0.0396145i	−0.000813215	+	0.00140853i
$792$		0			0
$793$	−0.217209	−	0.376216i	−0.00771330	−	0.0133598i
$794$	−25.2266	−	27.1580i	−0.895258	−	0.963803i
$795$		0			0
$796$	−1.38736	+	18.7885i	−0.0491738	+	0.665940i
$797$	−6.71611	−	8.00395i	−0.237897	−	0.283514i	0.633866	−	0.773443i	$-0.281467\pi$
$797$	−6.71611	−	8.00395i	−0.237897	−	0.283514i	−0.871762	+	0.489929i	$0.837023\pi$
$798$		0			0
$799$	−14.1255	+	5.14126i	−0.499725	+	0.181885i
$800$	34.6535	−	48.4789i	1.22519	−	1.71399i
$801$		0			0
$802$	3.02549	−	24.2502i	0.106834	−	0.856303i
$803$	−14.3764	−	2.53495i	−0.507333	−	0.0894566i
$804$		0			0
$805$	−0.0950175	+	0.261058i	−0.00334893	+	0.00920110i
$806$	37.9297	−	24.5270i	1.33602	−	0.863925i
$807$		0			0
$808$	−11.3692	−	20.7961i	−0.399966	−	0.731604i
$809$	−5.87774			−0.206650			−0.103325	−	0.994648i	$-0.532948\pi$
$809$	−5.87774			−0.206650			−0.103325	+	0.994648i	$0.532948\pi$
$810$		0			0
$811$		−	40.3341i		−	1.41632i	−0.706052	−	0.708160i	$-0.749525\pi$
$811$		−	40.3341i		−	1.41632i	0.706052	−	0.708160i	$-0.250475\pi$
$812$	−0.0122569	−	0.121154i	−0.000430134	−	0.00425166i
$813$		0			0
$814$	−5.93487	−	9.17797i	−0.208017	−	0.321688i
$815$	−32.0208	−	11.6546i	−1.12164	−	0.408243i
$816$		0			0
$817$	−3.14346	+	17.8274i	−0.109976	+	0.623703i
$818$	4.30603	−	34.5141i	0.150557	−	1.20676i
$819$		0			0
$820$	−11.2446	+	44.3628i	−0.392678	+	1.54922i
$821$	−8.31903	−	22.8563i	−0.290336	−	0.797692i	−0.996017	−	0.0891622i	$-0.971581\pi$
$821$	−8.31903	−	22.8563i	−0.290336	−	0.797692i	0.705681	−	0.708530i	$-0.250641\pi$
$822$		0			0
$823$	−22.0384	+	18.4924i	−0.768211	+	0.644605i	−0.940250	−	0.340485i	$-0.889409\pi$
$823$	−22.0384	+	18.4924i	−0.768211	+	0.644605i	0.172039	+	0.985090i	$0.444964\pi$
$824$	6.29229	+	18.6269i	0.219202	+	0.648898i
$825$		0			0
$826$	−0.0646173	−	0.0695647i	−0.00224833	−	0.00242047i
$827$	12.6598	−	7.30915i	0.440225	−	0.254164i	−0.263468	−	0.964668i	$-0.584866\pi$
$827$	12.6598	−	7.30915i	0.440225	−	0.254164i	0.703693	+	0.710504i	$0.251533\pi$
$828$		0			0
$829$	−38.2098	−	22.0604i	−1.32708	−	0.766191i	−0.342234	−	0.939615i	$-0.611184\pi$
$829$	−38.2098	−	22.0604i	−1.32708	−	0.766191i	−0.984847	+	0.173424i	$0.944517\pi$
$830$	18.8953	+	82.5778i	0.655865	+	2.86632i
$831$		0			0
$832$	28.4594	−	14.7083i	0.986652	−	0.509917i
$833$	2.30702	+	13.0838i	0.0799336	+	0.453326i
$834$		0			0
$835$	21.3840	−	25.4845i	0.740025	−	0.881927i
$836$	−6.09186	+	6.25934i	−0.210691	+	0.216484i
$837$		0			0
$838$	−7.58939	−	17.9767i	−0.262171	−	0.620995i
$839$	28.2388	+	23.6951i	0.974911	+	0.818047i	0.983314	−	0.181917i	$-0.0582303\pi$
$839$	28.2388	+	23.6951i	0.974911	+	0.818047i	−0.00840301	+	0.999965i	$0.502675\pi$
$840$		0			0
$841$	−1.12364	−	6.37246i	−0.0387461	−	0.219740i
$842$	2.60514	+	51.6325i	0.0897791	+	1.77937i
$843$		0			0
$844$	−19.5725	+	14.1041i	−0.673714	+	0.485484i
$845$	10.3610	+	5.98194i	0.356430	+	0.205785i
$846$		0			0
$847$	−0.0510619	−	0.0884417i	−0.00175451	−	0.00303889i
$848$	8.39176	−	3.31470i	0.288174	−	0.113827i
$849$		0			0
$850$	12.8858	−	25.1686i	0.441980	−	0.863275i
$851$	34.0738	+	40.6075i	1.16803	+	1.39201i
$852$		0			0
$853$	−12.7574	−	35.0506i	−0.436804	−	1.20011i	−0.941560	−	0.336846i	$-0.890640\pi$
$853$	−12.7574	−	35.0506i	−0.436804	−	1.20011i	0.504756	−	0.863262i	$-0.331583\pi$
$854$	0.000946338	−	0.00125076i	3.23830e−5	−	4.28001e-5i
$855$		0			0
$856$	31.5270	−	25.2266i	1.07757	−	0.862226i
$857$	2.38265	−	13.5127i	0.0813899	−	0.461585i	−0.916687	−	0.399605i	$-0.869147\pi$
$857$	2.38265	−	13.5127i	0.0813899	−	0.461585i	0.998077	−	0.0619803i	$-0.0197416\pi$
$858$		0			0
$859$	−10.4655	+	28.7538i	−0.357079	+	0.981067i	0.622958	+	0.782255i	$0.285931\pi$
$859$	−10.4655	+	28.7538i	−0.357079	+	0.981067i	−0.980038	+	0.198812i	$0.936292\pi$
$860$	27.1582	+	18.4727i	0.926087	+	0.629915i
$861$		0			0
$862$	−10.0660	−	3.09894i	−0.342850	−	0.105550i
$863$	7.80840			0.265801			0.132900	−	0.991129i	$-0.457571\pi$
$863$	7.80840			0.265801			0.132900	+	0.991129i	$0.457571\pi$
$864$		0			0
$865$	53.5863			1.82199
$866$	28.3037	+	8.71360i	0.961797	+	0.296100i
$867$		0			0
$868$	0.134842	+	0.0917180i	0.00457683	+	0.00311311i
$869$	−1.10550	+	3.03735i	−0.0375016	+	0.103035i
$870$		0			0
$871$	−2.67573	+	15.1748i	−0.0906636	+	0.514179i
$872$	10.7867	−	8.63105i	0.365283	−	0.292284i
$873$		0			0
$874$	25.5601	−	33.7824i	0.864584	−	1.14271i
$875$	0.0762675	+	0.209543i	0.00257831	+	0.00708385i
$876$		0			0
$877$	22.5373	+	26.8589i	0.761029	+	0.906959i	0.997913	−	0.0645787i	$-0.0205703\pi$
$877$	22.5373	+	26.8589i	0.761029	+	0.906959i	−0.236883	+	0.971538i	$0.576126\pi$
$878$	18.1326	−	35.4166i	0.611946	−	1.19525i
$879$		0			0
$880$	5.82207	+	14.7396i	0.196262	+	0.496873i
$881$	17.3596	+	30.0677i	0.584859	+	1.01301i	0.994893	+	0.100936i	$0.0321836\pi$
$881$	17.3596	+	30.0677i	0.584859	+	1.01301i	−0.410034	+	0.912070i	$0.634483\pi$
$882$		0			0
$883$	48.4749	+	27.9870i	1.63131	+	0.941837i	0.983690	+	0.179874i	$0.0575690\pi$
$883$	48.4749	+	27.9870i	1.63131	+	0.941837i	0.647620	+	0.761963i	$0.275764\pi$
$884$	12.3323	−	8.88674i	0.414779	−	0.298893i
$885$		0			0
$886$	−1.24689	−	24.7127i	−0.0418901	−	0.830238i
$887$	−5.13500	−	29.1221i	−0.172417	−	0.977823i	−0.941084	−	0.338174i	$-0.890191\pi$
$887$	−5.13500	−	29.1221i	−0.172417	−	0.977823i	0.768667	−	0.639649i	$-0.220920\pi$
$888$		0			0
$889$	0.0114860	+	0.00963792i	0.000385229	+	0.000323245i
$890$	−6.30264	−	14.9289i	−0.211265	−	0.500416i
$891$		0			0
$892$	4.95104	−	5.08716i	0.165773	−	0.170331i
$893$	−22.1175	+	26.3586i	−0.740134	+	0.882057i
$894$		0			0
$895$	0.203252	+	1.15270i	0.00679396	+	0.0385305i
$896$	0.0888851	+	0.0740062i	0.00296944	+	0.00247237i
$897$		0			0
$898$	1.88861	+	8.25377i	0.0630239	+	0.275432i
$899$	41.1386	+	23.7514i	1.37205	+	0.792154i
$900$		0			0
$901$	3.70763	−	2.14060i	0.123519	−	0.0713138i
$902$	−5.61718	−	6.04726i	−0.187032	−	0.201352i
$903$		0			0
$904$	−4.05033	−	11.9901i	−0.134712	−	0.398784i
$905$	5.70454	−	4.78668i	0.189625	−	0.159115i
$906$		0			0
$907$	−11.8324	−	32.5093i	−0.392889	−	1.07945i	−0.965676	−	0.259749i	$-0.916360\pi$
$907$	−11.8324	−	32.5093i	−0.392889	−	1.07945i	0.572787	−	0.819704i	$-0.305862\pi$
$908$	−5.34565	+	21.0900i	−0.177402	+	0.699897i
$909$		0			0
$910$	−0.0282495	+	0.226428i	−0.000936461	+	0.00750600i
$911$	2.10465	−	11.9361i	0.0697303	−	0.395460i	−0.929888	−	0.367842i	$-0.880097\pi$
$911$	2.10465	−	11.9361i	0.0697303	−	0.395460i	0.999619	−	0.0276180i	$-0.00879219\pi$
$912$		0			0
$913$	−14.3560	−	5.22516i	−0.475115	−	0.172928i
$914$	18.6736	+	28.8778i	0.617668	+	0.955191i
$915$		0			0
$916$	−1.58183	−	15.6356i	−0.0522651	−	0.516615i
$917$			0.116652i			0.00385218i
$918$		0			0
$919$	11.2018			0.369514			0.184757	−	0.982784i	$-0.440850\pi$
$919$	11.2018			0.369514			0.184757	+	0.982784i	$0.440850\pi$
$920$	−36.8704	−	67.4421i	−1.21558	−	2.22350i
$921$		0			0
$922$	−19.0312	+	12.3064i	−0.626758	+	0.405288i
$923$	−1.21254	+	3.33144i	−0.0399114	+	0.109656i
$924$		0			0
$925$	79.7598	+	14.0638i	2.62249	+	0.462415i
$926$	−0.125871	+	1.00889i	−0.00413637	+	0.0331542i
$927$		0			0
$928$	27.4084	+	19.5920i	0.899724	+	0.643138i
$929$	−33.5582	+	12.2142i	−1.10101	+	0.400734i	−0.827687	−	0.561189i	$-0.810344\pi$
$929$	−33.5582	+	12.2142i	−1.10101	+	0.400734i	−0.273320	+	0.961923i	$0.588122\pi$
$930$		0			0
$931$	19.5479	+	23.2962i	0.640656	+	0.763504i
$932$	3.56378	−	48.2628i	0.116736	−	1.58090i
$933$		0			0
$934$	−18.7592	−	20.1955i	−0.613819	−	0.660816i
$935$	3.75984	+	6.51224i	0.122960	+	0.212973i
$936$		0			0
$937$	−13.9023	+	24.0795i	−0.454169	+	0.786643i	−0.998640	−	0.0521363i	$-0.983397\pi$
$937$	−13.9023	+	24.0795i	−0.454169	+	0.786643i	0.544471	+	0.838779i	$0.316730\pi$
$938$	−0.0542308	+	0.0124090i	−0.00177070	+	0.000405168i
$939$		0			0
$940$	27.1494	+	56.2192i	0.885516	+	1.83367i
$941$	17.4040	−	3.06880i	0.567355	−	0.100040i	0.117390	−	0.993086i	$-0.462547\pi$
$941$	17.4040	−	3.06880i	0.567355	−	0.100040i	0.449965	+	0.893046i	$0.351436\pi$
$942$		0			0
$943$	30.6650	+	25.7310i	0.998591	+	0.837917i
$944$	26.2590	−	0.712264i	0.854657	−	0.0231822i
$945$		0			0
$946$	−5.45708	+	2.30386i	−0.177425	+	0.0749050i
$947$	31.1472	−	37.1197i	1.01215	−	1.20623i	0.0337637	−	0.999430i	$-0.489251\pi$
$947$	31.1472	−	37.1197i	1.01215	−	1.20623i	0.978383	−	0.206800i	$-0.0663049\pi$
$948$		0			0
$949$	57.2701	−	10.0983i	1.85907	−	0.327804i
$950$	−3.26149	−	64.6409i	−0.105817	−	2.09723i
$951$		0			0
$952$	0.0468758	+	0.0285398i	0.00151925	+	0.000924981i
$953$	−6.84000	+	11.8472i	−0.221569	+	0.383770i	−0.955285	−	0.295688i	$-0.904451\pi$
$953$	−6.84000	+	11.8472i	−0.221569	+	0.383770i	0.733715	+	0.679457i	$0.237785\pi$
$954$		0			0
$955$	−47.6310	+	27.4998i	−1.54130	+	0.889871i
$956$	−24.7507	+	55.0134i	−0.800495	+	1.77926i
$957$		0			0
$958$	−6.29288	+	12.2912i	−0.203314	+	0.397112i
$959$	−0.0334435	+	0.0280625i	−0.00107995	+	0.000906184i
$960$		0			0
$961$	−30.6492	+	11.1554i	−0.988684	+	0.359852i
$962$	34.7212	+	26.2704i	1.11946	+	0.846993i
$963$		0			0
$964$	−1.36120	−	4.81780i	−0.0438413	−	0.155171i
$965$	37.0002	+	6.52413i	1.19108	+	0.210019i
$966$		0			0
$967$	28.0120	+	10.1955i	0.900806	+	0.327867i	0.750576	−	0.660785i	$-0.229776\pi$
$967$	28.0120	+	10.1955i	0.900806	+	0.327867i	0.150230	+	0.988651i	$0.451999\pi$
$968$	27.7035	+	5.55316i	0.890426	+	0.178485i
$969$		0			0
$970$	−20.9813	+	68.1518i	−0.673669	+	2.18822i
$971$			31.5563i			1.01269i	0.862331	+	0.506345i	$0.169004\pi$
$971$			31.5563i			1.01269i	−0.862331	+	0.506345i	$0.830996\pi$
$972$		0			0
$973$			0.0108888i			0.000349078i
$974$	−55.0373	−	16.9438i	−1.76351	−	0.542916i
$975$		0			0
$976$	0.0869119	+	0.425144i	0.00278198	+	0.0136085i
$977$	−26.2819	−	9.56585i	−0.840834	−	0.306039i	−0.114536	−	0.993419i	$-0.536538\pi$
$977$	−26.2819	−	9.56585i	−0.840834	−	0.306039i	−0.726297	+	0.687381i	$0.758760\pi$
$978$		0			0
$979$	2.87804	+	0.507477i	0.0919827	+	0.0162190i
$980$	53.0994	−	15.0025i	1.69620	−	0.479237i
$981$		0			0
$982$	10.6686	−	14.1005i	0.340448	−	0.449964i
$983$	−23.5384	+	8.56727i	−0.750758	+	0.273253i	−0.688925	−	0.724833i	$-0.741917\pi$
$983$	−23.5384	+	8.56727i	−0.750758	+	0.273253i	−0.0618331	+	0.998087i	$0.519695\pi$
$984$		0			0
$985$	−26.5326	+	22.2635i	−0.845398	+	0.709373i
$986$	14.2295	+	7.28523i	0.453160	+	0.232009i
$987$		0			0
$988$	14.2759	−	31.7311i	0.454177	−	1.00950i
$989$	24.8801	−	14.3645i	0.791141	−	0.456766i
$990$		0			0
$991$	11.3147	−	19.5976i	0.359422	−	0.622537i	−0.628442	−	0.777856i	$-0.716307\pi$
$991$	11.3147	−	19.5976i	0.359422	−	0.622537i	0.987864	+	0.155319i	$0.0496405\pi$
$992$	−43.6932	+	11.2528i	−1.38726	+	0.357277i
$993$		0			0
$994$	−0.0127835		0.000644997i	−0.000405468		2.04581e-5i
$995$	36.5628	−	6.44700i	1.15912	−	0.204384i
$996$		0			0
$997$	6.16806	−	7.35081i	0.195344	−	0.232802i	−0.659477	−	0.751725i	$-0.729222\pi$
$997$	6.16806	−	7.35081i	0.195344	−	0.232802i	0.854821	+	0.518922i	$0.173667\pi$
$998$	−2.51744	−	5.96297i	−0.0796881	−	0.188754i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.613.31		204
3.2	odd	2		216.2.t.a.205.4	yes	204
8.5	even	2	inner	648.2.t.a.613.22		204
12.11	even	2		864.2.bf.a.529.19		204
24.5	odd	2		216.2.t.a.205.13	yes	204
24.11	even	2		864.2.bf.a.529.16		204
27.5	odd	18		216.2.t.a.157.13	yes	204
27.22	even	9	inner	648.2.t.a.37.22		204
108.59	even	18		864.2.bf.a.49.16		204
216.5	odd	18		216.2.t.a.157.4	✓	204
216.59	even	18		864.2.bf.a.49.19		204
216.157	even	18	inner	648.2.t.a.37.31		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.4	✓	204	216.5	odd	18
216.2.t.a.157.13	yes	204	27.5	odd	18
216.2.t.a.205.4	yes	204	3.2	odd	2
216.2.t.a.205.13	yes	204	24.5	odd	2
648.2.t.a.37.22		204	27.22	even	9	inner
648.2.t.a.37.31		204	216.157	even	18	inner
648.2.t.a.613.22		204	8.5	even	2	inner
648.2.t.a.613.31		204	1.1	even	1	trivial
864.2.bf.a.49.16		204	108.59	even	18
864.2.bf.a.49.19		204	216.59	even	18
864.2.bf.a.529.16		204	24.11	even	2
864.2.bf.a.529.19		204	12.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35161 + 0.416109i) q^{2} +(1.65371 + 1.12483i) q^{4} +(1.34802 - 3.70366i) q^{5} +(0.00177522 - 0.0100678i) q^{7} +(1.76712 + 2.20846i) q^{8} +(3.36313 - 4.44499i) q^{10} +(0.343808 + 0.944604i) q^{11} +(-2.57400 - 3.06757i) q^{13} +(0.00658870 - 0.0128690i) q^{14} +(1.46950 + 3.72029i) q^{16} +(0.948987 + 1.64369i) q^{17} +(3.76245 + 2.17225i) q^{19} +(6.39524 - 4.60847i) q^{20} +(0.0716366 + 1.41980i) q^{22} +(-1.19728 - 6.79010i) q^{23} +(-8.06972 - 6.77130i) q^{25} +(-2.20260 - 5.21723i) q^{26} +(0.0142603 - 0.0146523i) q^{28} +(3.82827 - 4.56236i) q^{29} +(1.38501 + 7.85480i) q^{31} +(0.438140 + 5.63986i) q^{32} +(0.598707 + 2.61652i) q^{34} +(-0.0348946 - 0.0201464i) q^{35} +(-6.65823 + 3.84413i) q^{37} +(4.18148 + 4.50163i) q^{38} +(10.5615 - 3.56775i) q^{40} +(-4.44753 + 3.73192i) q^{41} +(1.42511 + 3.91546i) q^{43} +(-0.493966 + 1.94882i) q^{44} +(1.20716 - 9.67577i) q^{46} +(-1.37530 + 7.79973i) q^{47} +(6.57775 + 2.39411i) q^{49} +(-8.08953 - 12.5100i) q^{50} +(-0.806130 - 7.96819i) q^{52} -2.25567i q^{53} +3.96195 q^{55} +(0.0253713 - 0.0138704i) q^{56} +(7.07277 - 4.57356i) q^{58} +(2.24610 - 6.17111i) q^{59} +(0.106836 + 0.0188381i) q^{61} +(-1.39645 + 11.1930i) q^{62} +(-1.75460 + 7.80522i) q^{64} +(-14.8311 + 5.39806i) q^{65} +(-2.47342 - 2.94771i) q^{67} +(-0.279537 + 3.78564i) q^{68} +(-0.0387808 - 0.0417500i) q^{70} +(-0.442665 - 0.766718i) q^{71} +(-7.26116 + 12.5767i) q^{73} +(-10.5989 + 2.42523i) q^{74} +(3.77857 + 7.82441i) q^{76} +(0.0101204 - 0.00178450i) q^{77} +(2.46319 + 2.06686i) q^{79} +(15.7596 - 0.427473i) q^{80} +(-7.56422 + 3.19345i) q^{82} +(-9.76904 + 11.6423i) q^{83} +(7.36694 - 1.29899i) q^{85} +(0.296940 + 5.88518i) q^{86} +(-1.47857 + 2.42851i) q^{88} +(1.45362 - 2.51775i) q^{89} +(-0.0354530 + 0.0204688i) q^{91} +(5.65779 - 12.5756i) q^{92} +(-5.10441 + 9.96993i) q^{94} +(13.1172 - 11.0066i) q^{95} +(-12.0217 + 4.37554i) q^{97} +(7.89435 + 5.97296i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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