LMFDB - Embedded newform 1332.2.l.b.121.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1332,2,Mod(121,1332)] 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("1332.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1332, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1332 = 2^{2} \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1332.l (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [74] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.6360735492$
Analytic rank:	$0$
Dimension:	$74$
Relative dimension:	$37$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.7
Character	$\chi$	$=$	1332.121
Dual form			1332.2.l.b.1321.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46851 + 0.918407i) q^{3} +0.575944 q^{5} +(1.60251 - 2.77564i) q^{7} +(1.31306 - 2.69738i) q^{9} +(-0.0375596 - 0.0650551i) q^{11} -4.26942 q^{13} +(-0.845780 + 0.528951i) q^{15} +(1.55761 - 2.69786i) q^{17} +(-1.27707 - 2.21194i) q^{19} +(0.195852 + 5.54782i) q^{21} +(-1.32667 + 2.29786i) q^{23} -4.66829 q^{25} +(0.549057 + 5.16706i) q^{27} +(-1.66317 - 2.88070i) q^{29} +(-3.02554 + 5.24038i) q^{31} +(0.114904 + 0.0610392i) q^{33} +(0.922958 - 1.59861i) q^{35} +(-6.07019 - 0.390841i) q^{37} +(6.26969 - 3.92106i) q^{39} -7.83705 q^{41} +(3.04791 + 5.27913i) q^{43} +(0.756247 - 1.55354i) q^{45} +(-1.77361 - 3.07198i) q^{47} +(-1.63611 - 2.83382i) q^{49} +(0.190364 + 5.39237i) q^{51} +(6.49210 - 11.2446i) q^{53} +(-0.0216322 - 0.0374681i) q^{55} +(3.90685 + 2.07540i) q^{57} +(1.01895 + 1.76488i) q^{59} +(-2.27825 + 3.94604i) q^{61} +(-5.38277 - 7.96717i) q^{63} -2.45894 q^{65} -3.27919 q^{67} +(-0.162139 - 4.59285i) q^{69} +(-3.18873 - 5.52304i) q^{71} -2.69979 q^{73} +(6.85544 - 4.28739i) q^{75} -0.240759 q^{77} +(3.13366 - 5.42765i) q^{79} +(-5.55176 - 7.08364i) q^{81} -13.6907 q^{83} +(0.897097 - 1.55382i) q^{85} +(5.08804 + 2.70287i) q^{87} +(8.58321 - 14.8665i) q^{89} +(-6.84180 + 11.8504i) q^{91} +(-0.369767 - 10.4742i) q^{93} +(-0.735518 - 1.27395i) q^{95} +(-8.42871 - 14.5990i) q^{97} +(-0.224796 + 0.0158916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q + 5 q^{3} + 6 q^{5} - q^{7} - q^{9} + q^{11} - 4 q^{13} - 2 q^{15} + 3 q^{17} + q^{19} - 3 q^{21} - 17 q^{23} + 96 q^{25} + 17 q^{27} + 6 q^{29} + 3 q^{31} - 16 q^{33} - 6 q^{35} + 5 q^{37} + 35 q^{39}+ \cdots - 43 q^{99}+O(q^{100}) $ 74 * q + 5 * q^3 + 6 * q^5 - q^7 - q^9 + q^11 - 4 * q^13 - 2 * q^15 + 3 * q^17 + q^19 - 3 * q^21 - 17 * q^23 + 96 * q^25 + 17 * q^27 + 6 * q^29 + 3 * q^31 - 16 * q^33 - 6 * q^35 + 5 * q^37 + 35 * q^39 + 54 * q^41 + 3 * q^43 - 4 * q^45 - 21 * q^47 - 46 * q^49 + 11 * q^51 - 11 * q^53 - 11 * q^55 + 20 * q^57 + 13 * q^59 + 12 * q^61 + 5 * q^63 + 38 * q^65 + 38 * q^67 - 8 * q^69 + 18 * q^73 - 7 * q^75 + 92 * q^77 - q^79 + 31 * q^81 + 40 * q^83 + 9 * q^85 + 6 * q^87 + 13 * q^89 - 11 * q^91 - 3 * q^93 - 13 * q^95 + 17 * q^97 - 43 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1332\mathbb{Z}\right)^\times$.

$n$	$667$	$1037$	$1297$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.46851	+	0.918407i	−0.847846	+	0.530243i
$3$	−1.46851	+	0.918407i	−0.847846	+	0.530243i
$4$		0			0
$5$	0.575944			0.257570			0.128785	−	0.991673i	$-0.458892\pi$
$5$	0.575944			0.257570			0.128785	+	0.991673i	$0.458892\pi$
$6$		0			0
$7$	1.60251	−	2.77564i	0.605694	−	1.04909i	−0.386248	−	0.922395i	$-0.626229\pi$
$7$	1.60251	−	2.77564i	0.605694	−	1.04909i	0.991941	−	0.126697i	$-0.0404376\pi$
$8$		0			0
$9$	1.31306	−	2.69738i	0.437686	−	0.899128i
$10$		0			0
$11$	−0.0375596	−	0.0650551i	−0.0113246	−	0.0196148i	0.860308	−	0.509775i	$-0.170271\pi$
$11$	−0.0375596	−	0.0650551i	−0.0113246	−	0.0196148i	−0.871632	+	0.490161i	$0.836938\pi$
$12$		0			0
$13$	−4.26942			−1.18412			−0.592062	−	0.805893i	$-0.701686\pi$
$13$	−4.26942			−1.18412			−0.592062	+	0.805893i	$0.701686\pi$
$14$		0			0
$15$	−0.845780	+	0.528951i	−0.218380	+	0.136574i
$16$		0			0
$17$	1.55761	−	2.69786i	0.377777	−	0.654328i	−0.612962	−	0.790112i	$-0.710022\pi$
$17$	1.55761	−	2.69786i	0.377777	−	0.654328i	0.990738	+	0.135784i	$0.0433554\pi$
$18$		0			0
$19$	−1.27707	−	2.21194i	−0.292979	−	0.507455i	0.681534	−	0.731787i	$-0.261313\pi$
$19$	−1.27707	−	2.21194i	−0.292979	−	0.507455i	−0.974513	+	0.224332i	$0.927980\pi$
$20$		0			0
$21$	0.195852	+	5.54782i	0.0427385	+	1.21063i
$22$		0			0
$23$	−1.32667	+	2.29786i	−0.276629	+	0.479136i	−0.970545	−	0.240920i	$-0.922551\pi$
$23$	−1.32667	+	2.29786i	−0.276629	+	0.479136i	0.693916	+	0.720056i	$0.255884\pi$
$24$		0			0
$25$	−4.66829			−0.933658
$26$		0			0
$27$	0.549057	+	5.16706i	0.105666	+	0.994402i
$28$		0			0
$29$	−1.66317	−	2.88070i	−0.308843	−	0.534932i	0.669267	−	0.743022i	$-0.266608\pi$
$29$	−1.66317	−	2.88070i	−0.308843	−	0.534932i	−0.978110	+	0.208091i	$0.933275\pi$
$30$		0			0
$31$	−3.02554	+	5.24038i	−0.543402	+	0.941200i	0.455303	+	0.890336i	$0.349531\pi$
$31$	−3.02554	+	5.24038i	−0.543402	+	0.941200i	−0.998706	+	0.0508638i	$0.983803\pi$
$32$		0			0
$33$	0.114904	+	0.0610392i	0.0200022	+	0.0106256i
$34$		0			0
$35$	0.922958	−	1.59861i	0.156008	−	0.270214i
$36$		0			0
$37$	−6.07019	−	0.390841i	−0.997934	−	0.0642538i
$37$	−6.07019	−	0.390841i	−0.997934	−	0.0642538i
$38$		0			0
$39$	6.26969	−	3.92106i	1.00395	−	0.627873i
$40$		0			0
$41$	−7.83705			−1.22394			−0.611971	−	0.790881i	$-0.709623\pi$
$41$	−7.83705			−1.22394			−0.611971	+	0.790881i	$0.709623\pi$
$42$		0			0
$43$	3.04791	+	5.27913i	0.464801	+	0.805059i	0.999193	−	0.0401778i	$-0.0127924\pi$
$43$	3.04791	+	5.27913i	0.464801	+	0.805059i	−0.534391	+	0.845237i	$0.679459\pi$
$44$		0			0
$45$	0.756247	−	1.55354i	0.112735	−	0.231588i
$46$		0			0
$47$	−1.77361	−	3.07198i	−0.258708	−	0.448095i	0.707188	−	0.707025i	$-0.249963\pi$
$47$	−1.77361	−	3.07198i	−0.258708	−	0.448095i	−0.965896	+	0.258931i	$0.916630\pi$
$48$		0			0
$49$	−1.63611	−	2.83382i	−0.233729	−	0.404831i
$50$		0			0
$51$	0.190364	+	5.39237i	0.0266564	+	0.755083i
$52$		0			0
$53$	6.49210	−	11.2446i	0.891758	−	1.54457i	0.0539920	−	0.998541i	$-0.482805\pi$
$53$	6.49210	−	11.2446i	0.891758	−	1.54457i	0.837766	−	0.546029i	$-0.183861\pi$
$54$		0			0
$55$	−0.0216322	−	0.0374681i	−0.00291688	−	0.00505219i
$56$		0			0
$57$	3.90685	+	2.07540i	0.517475	+	0.274893i
$58$		0			0
$59$	1.01895	+	1.76488i	0.132656	+	0.229768i	0.924700	−	0.380697i	$-0.124316\pi$
$59$	1.01895	+	1.76488i	0.132656	+	0.229768i	−0.792043	+	0.610465i	$0.790983\pi$
$60$		0			0
$61$	−2.27825	+	3.94604i	−0.291700	+	0.505239i	−0.974212	−	0.225635i	$-0.927554\pi$
$61$	−2.27825	+	3.94604i	−0.291700	+	0.505239i	0.682512	+	0.730875i	$0.260888\pi$
$62$		0			0
$63$	−5.38277	−	7.96717i	−0.678165	−	1.00377i
$64$		0			0
$65$	−2.45894			−0.304994
$66$		0			0
$67$	−3.27919			−0.400617			−0.200308	−	0.979733i	$-0.564194\pi$
$67$	−3.27919			−0.400617			−0.200308	+	0.979733i	$0.564194\pi$
$68$		0			0
$69$	−0.162139	−	4.59285i	−0.0195193	−	0.552914i
$70$		0			0
$71$	−3.18873	−	5.52304i	−0.378433	−	0.655465i	0.612402	−	0.790547i	$-0.290204\pi$
$71$	−3.18873	−	5.52304i	−0.378433	−	0.655465i	−0.990834	+	0.135082i	$0.956870\pi$
$72$		0			0
$73$	−2.69979			−0.315986			−0.157993	−	0.987440i	$-0.550502\pi$
$73$	−2.69979			−0.315986			−0.157993	+	0.987440i	$0.550502\pi$
$74$		0			0
$75$	6.85544	−	4.28739i	0.791598	−	0.495065i
$76$		0			0
$77$	−0.240759			−0.0274370
$78$		0			0
$79$	3.13366	−	5.42765i	0.352564	−	0.610658i	−0.634134	−	0.773223i	$-0.718643\pi$
$79$	3.13366	−	5.42765i	0.352564	−	0.610658i	0.986698	+	0.162565i	$0.0519766\pi$
$80$		0			0
$81$	−5.55176	−	7.08364i	−0.616863	−	0.787071i
$82$		0			0
$83$	−13.6907			−1.50275			−0.751373	−	0.659878i	$-0.770608\pi$
$83$	−13.6907			−1.50275			−0.751373	+	0.659878i	$0.770608\pi$
$84$		0			0
$85$	0.897097	−	1.55382i	0.0973038	−	0.168535i
$86$		0			0
$87$	5.08804	+	2.70287i	0.545495	+	0.289778i
$88$		0			0
$89$	8.58321	−	14.8665i	0.909818	−	1.57585i	0.0955019	−	0.995429i	$-0.469554\pi$
$89$	8.58321	−	14.8665i	0.909818	−	1.57585i	0.814316	−	0.580422i	$-0.197112\pi$
$90$		0			0
$91$	−6.84180	+	11.8504i	−0.717216	+	1.24225i
$92$		0			0
$93$	−0.369767	−	10.4742i	−0.0383431	−	1.08613i
$94$		0			0
$95$	−0.735518	−	1.27395i	−0.0754626	−	0.130705i
$96$		0			0
$97$	−8.42871	−	14.5990i	−0.855806	−	1.48230i	−0.875895	−	0.482501i	$-0.839728\pi$
$97$	−8.42871	−	14.5990i	−0.855806	−	1.48230i	0.0200891	−	0.999798i	$-0.493605\pi$
$98$		0			0
$99$	−0.224796	+	0.0158916i	−0.0225929	+	0.00159716i
$100$		0			0
$101$	−1.35833	−	2.35269i	−0.135159	−	0.234101i	0.790499	−	0.612463i	$-0.209821\pi$
$101$	−1.35833	−	2.35269i	−0.135159	−	0.234101i	−0.925658	+	0.378361i	$0.876488\pi$
$102$		0			0
$103$	6.78392	−	11.7501i	0.668439	−	1.15777i	−0.309901	−	0.950769i	$-0.600296\pi$
$103$	6.78392	−	11.7501i	0.668439	−	1.15777i	0.978341	−	0.207002i	$-0.0663707\pi$
$104$		0			0
$105$	0.112800	+	3.19523i	0.0110081	+	0.311823i
$106$		0			0
$107$	3.64234	+	6.30872i	0.352119	+	0.609887i	0.986620	−	0.163034i	$-0.0521280\pi$
$107$	3.64234	+	6.30872i	0.352119	+	0.609887i	−0.634502	+	0.772921i	$0.718795\pi$
$108$		0			0
$109$	−2.67459	+	4.63253i	−0.256180	+	0.443716i	−0.965215	−	0.261457i	$-0.915797\pi$
$109$	−2.67459	+	4.63253i	−0.256180	+	0.443716i	0.709036	+	0.705173i	$0.249130\pi$
$110$		0			0
$111$	9.27310	−	5.00095i	0.880164	−	0.474670i
$112$		0			0
$113$	−8.79301	−	15.2299i	−0.827176	−	1.43271i	−0.900245	−	0.435385i	$-0.856612\pi$
$113$	−8.79301	−	15.2299i	−0.827176	−	1.43271i	0.0730681	−	0.997327i	$-0.476721\pi$
$114$		0			0
$115$	−0.764086	+	1.32344i	−0.0712514	+	0.123411i
$116$		0			0
$117$	−5.60599	+	11.5163i	−0.518274	+	1.06468i
$118$		0			0
$119$	−4.99219	−	8.64673i	−0.457634	−	0.792645i
$120$		0			0
$121$	5.49718	−	9.52139i	0.499744	−	0.865581i
$122$		0			0
$123$	11.5088	−	7.19760i	1.03771	−	0.648986i
$124$		0			0
$125$	−5.56839			−0.498052
$126$		0			0
$127$	−1.27911	+	2.21549i	−0.113503	+	0.196593i	−0.917180	−	0.398472i	$-0.869540\pi$
$127$	−1.27911	+	2.21549i	−0.113503	+	0.196593i	0.803677	+	0.595065i	$0.202874\pi$
$128$		0			0
$129$	−9.32428	−	4.95325i	−0.820957	−	0.436109i
$130$		0			0
$131$	1.69976	+	2.94408i	0.148509	+	0.257225i	0.930677	−	0.365843i	$-0.119219\pi$
$131$	1.69976	+	2.94408i	0.148509	+	0.257225i	−0.782168	+	0.623068i	$0.785886\pi$
$132$		0			0
$133$	−8.18607			−0.709822
$134$		0			0
$135$	0.316226	+	2.97594i	0.0272164	+	0.256128i
$136$		0			0
$137$	3.19314	+	5.53068i	0.272808	+	0.472518i	0.969580	−	0.244775i	$-0.0787141\pi$
$137$	3.19314	+	5.53068i	0.272808	+	0.472518i	−0.696771	+	0.717293i	$0.745381\pi$
$138$		0			0
$139$	11.6448	+	20.1694i	0.987700	+	1.71075i	0.629262	+	0.777193i	$0.283357\pi$
$139$	11.6448	+	20.1694i	0.987700	+	1.71075i	0.358438	+	0.933554i	$0.383310\pi$
$140$		0			0
$141$	5.42590	+	2.88235i	0.456943	+	0.242737i
$142$		0			0
$143$	0.160357	+	0.277747i	0.0134098	+	0.0232264i
$144$		0			0
$145$	−0.957892	−	1.65912i	−0.0795486	−	0.137782i
$146$		0			0
$147$	5.00524	+	2.65889i	0.412825	+	0.219301i
$148$		0			0
$149$	0.960990	−	1.66448i	0.0787274	−	0.136360i	−0.823974	−	0.566628i	$-0.808248\pi$
$149$	0.960990	−	1.66448i	0.0787274	−	0.136360i	0.902701	+	0.430268i	$0.141581\pi$
$150$		0			0
$151$	−6.00675	+	10.4040i	−0.488823	+	0.846666i	−0.999917	−	0.0128588i	$-0.995907\pi$
$151$	−6.00675	+	10.4040i	−0.488823	+	0.846666i	0.511095	+	0.859524i	$0.329240\pi$
$152$		0			0
$153$	−5.23194	−	7.74393i	−0.422977	−	0.626059i
$154$		0			0
$155$	−1.74254	+	3.01816i	−0.139964	+	0.242425i
$156$		0			0
$157$	7.30144	+	12.6465i	0.582719	+	1.00930i	0.995156	+	0.0983121i	$0.0313444\pi$
$157$	7.30144	+	12.6465i	0.582719	+	1.00930i	−0.412437	+	0.910986i	$0.635322\pi$
$158$		0			0
$159$	0.793435	+	22.4753i	0.0629235	+	1.78241i
$160$		0			0
$161$	4.25201	+	7.36469i	0.335105	+	0.580419i
$162$		0			0
$163$	−2.62629	+	4.54886i	−0.205707	+	0.356294i	−0.950358	−	0.311160i	$-0.899283\pi$
$163$	−2.62629	+	4.54886i	−0.205707	+	0.356294i	0.744651	+	0.667454i	$0.232616\pi$
$164$		0			0
$165$	0.0661781	+	0.0351551i	0.00515196	+	0.00273682i
$166$		0			0
$167$	−0.675121			−0.0522424			−0.0261212	−	0.999659i	$-0.508316\pi$
$167$	−0.675121			−0.0522424			−0.0261212	+	0.999659i	$0.508316\pi$
$168$		0			0
$169$	5.22793			0.402148
$170$		0			0
$171$	−7.64332	+	0.540331i	−0.584499	+	0.0413202i
$172$		0			0
$173$	−16.3910			−1.24618			−0.623092	−	0.782149i	$-0.714124\pi$
$173$	−16.3910			−1.24618			−0.623092	+	0.782149i	$0.714124\pi$
$174$		0			0
$175$	−7.48100	+	12.9575i	−0.565511	+	0.979493i
$176$		0			0
$177$	−3.11722	−	1.65593i	−0.234305	−	0.124467i
$178$		0			0
$179$	14.2606			1.06589			0.532943	−	0.846151i	$-0.321086\pi$
$179$	14.2606			1.06589			0.532943	+	0.846151i	$0.321086\pi$
$180$		0			0
$181$	3.55675	+	6.16047i	0.264371	+	0.457904i	0.967399	−	0.253258i	$-0.0815023\pi$
$181$	3.55675	+	6.16047i	0.264371	+	0.457904i	−0.703028	+	0.711163i	$0.748169\pi$
$182$		0			0
$183$	−0.278438	−	7.88718i	−0.0205827	−	0.583037i
$184$		0			0
$185$	−3.49609	−	0.225102i	−0.257038	−	0.0165498i
$186$		0			0
$187$	−0.234013			−0.0171127
$188$		0			0
$189$	15.2218	+	6.75631i	1.10722	+	0.491449i
$190$		0			0
$191$	6.02429	+	10.4344i	0.435903	+	0.755005i	0.997369	−	0.0724942i	$-0.0230959\pi$
$191$	6.02429	+	10.4344i	0.435903	+	0.755005i	−0.561466	+	0.827500i	$0.689763\pi$
$192$		0			0
$193$	5.67848	−	9.83541i	0.408746	−	0.707968i	−0.586004	−	0.810308i	$-0.699300\pi$
$193$	5.67848	−	9.83541i	0.408746	−	0.707968i	0.994749	+	0.102340i	$0.0326330\pi$
$194$		0			0
$195$	3.61099	−	2.25831i	0.258588	−	0.161721i
$196$		0			0
$197$	0.481922	−	0.834714i	0.0343355	−	0.0594709i	−0.848347	−	0.529441i	$-0.822402\pi$
$197$	0.481922	−	0.834714i	0.0343355	−	0.0594709i	0.882683	+	0.469970i	$0.155735\pi$
$198$		0			0
$199$	−6.03947			−0.428126			−0.214063	−	0.976820i	$-0.568670\pi$
$199$	−6.03947			−0.428126			−0.214063	+	0.976820i	$0.568670\pi$
$200$		0			0
$201$	4.81553	−	3.01163i	0.339661	−	0.212424i
$202$		0			0
$203$	−10.6610			−0.748257
$204$		0			0
$205$	−4.51370			−0.315250
$206$		0			0
$207$	4.45621	+	6.59575i	0.309728	+	0.458436i
$208$		0			0
$209$	−0.0959321	+	0.166159i	−0.00663576	+	0.0114935i
$210$		0			0
$211$	2.40332	−	4.16268i	0.165452	−	0.286571i	−0.771364	−	0.636394i	$-0.780425\pi$
$211$	2.40332	−	4.16268i	0.165452	−	0.286571i	0.936816	+	0.349824i	$0.113758\pi$
$212$		0			0
$213$	9.75509	+	5.18210i	0.668408	+	0.355072i
$214$		0			0
$215$	1.75542	+	3.04048i	0.119719	+	0.207359i
$216$		0			0
$217$	9.69693	+	16.7956i	0.658270	+	1.14016i
$218$		0			0
$219$	3.96467	−	2.47950i	0.267908	−	0.167549i
$220$		0			0
$221$	−6.65010	+	11.5183i	−0.447334	+	0.774805i
$222$		0			0
$223$	0.878213	+	1.52111i	0.0588095	+	0.101861i	0.893931	−	0.448204i	$-0.147936\pi$
$223$	0.878213	+	1.52111i	0.0588095	+	0.101861i	−0.835122	+	0.550065i	$0.814603\pi$
$224$		0			0
$225$	−6.12973	+	12.5922i	−0.408649	+	0.839478i
$226$		0			0
$227$	11.5303	−	19.9710i	0.765291	−	1.32552i	−0.174802	−	0.984604i	$-0.555928\pi$
$227$	11.5303	−	19.9710i	0.765291	−	1.32552i	0.940093	−	0.340919i	$-0.110738\pi$
$228$		0			0
$229$	−17.4090			−1.15042			−0.575211	−	0.818005i	$-0.695080\pi$
$229$	−17.4090			−1.15042			−0.575211	+	0.818005i	$0.695080\pi$
$230$		0			0
$231$	0.353558	−	0.221115i	0.0232624	−	0.0145483i
$232$		0			0
$233$	15.2224			0.997250			0.498625	−	0.866818i	$-0.333839\pi$
$233$	15.2224			0.997250			0.498625	+	0.866818i	$0.333839\pi$
$234$		0			0
$235$	−1.02150	−	1.76929i	−0.0666352	−	0.115416i
$236$		0			0
$237$	0.382981	+	10.8485i	0.0248773	+	0.704689i
$238$		0			0
$239$	−12.6683	−	21.9422i	−0.819446	−	1.41932i	−0.906091	−	0.423084i	$-0.860948\pi$
$239$	−12.6683	−	21.9422i	−0.819446	−	1.41932i	0.0866443	−	0.996239i	$-0.472386\pi$
$240$		0			0
$241$	0.331193	−	0.573643i	0.0213340	−	0.0369516i	−0.855161	−	0.518362i	$-0.826542\pi$
$241$	0.331193	−	0.573643i	0.0213340	−	0.0369516i	0.876495	+	0.481410i	$0.159875\pi$
$242$		0			0
$243$	14.6585	+	5.30363i	0.940343	+	0.340228i
$244$		0			0
$245$	−0.942305	−	1.63212i	−0.0602017	−	0.104272i
$246$		0			0
$247$	5.45233	+	9.44371i	0.346923	+	0.600889i
$248$		0			0
$249$	20.1049	−	12.5736i	1.27410	−	0.796820i
$250$		0			0
$251$	22.8429			1.44183			0.720915	−	0.693024i	$-0.243722\pi$
$251$	22.8429			1.44183			0.720915	+	0.693024i	$0.243722\pi$
$252$		0			0
$253$	0.199316			0.0125309
$254$		0			0
$255$	0.109639	+	3.10570i	0.00686587	+	0.194487i
$256$		0			0
$257$	−2.57385	−	4.45804i	−0.160552	−	0.278085i	0.774515	−	0.632556i	$-0.217994\pi$
$257$	−2.57385	−	4.45804i	−0.160552	−	0.278085i	−0.935067	+	0.354471i	$0.884661\pi$
$258$		0			0
$259$	−10.8124	+	16.2223i	−0.671850	+	1.00801i
$260$		0			0
$261$	−9.95418	+	0.703693i	−0.616148	+	0.0435575i
$262$		0			0
$263$	11.0487	−	19.1369i	0.681293	−	1.18003i	−0.293294	−	0.956022i	$-0.594751\pi$
$263$	11.0487	−	19.1369i	0.681293	−	1.18003i	0.974587	−	0.224011i	$-0.0719153\pi$
$264$		0			0
$265$	3.73908	−	6.47628i	0.229690	−	0.397835i
$266$		0			0
$267$	1.04900	+	29.7146i	0.0641978	+	1.81850i
$268$		0			0
$269$	10.1779			0.620556			0.310278	−	0.950646i	$-0.399578\pi$
$269$	10.1779			0.620556			0.310278	+	0.950646i	$0.399578\pi$
$270$		0			0
$271$	−12.9999	+	22.5165i	−0.789688	+	1.36778i	0.136469	+	0.990644i	$0.456424\pi$
$271$	−12.9999	+	22.5165i	−0.789688	+	1.36778i	−0.926158	+	0.377136i	$0.876909\pi$
$272$		0			0
$273$	−0.836175	−	23.6859i	−0.0506076	−	1.43354i
$274$		0			0
$275$	0.175339	+	0.303696i	0.0105733	+	0.0183135i
$276$		0			0
$277$	−1.32468	+	2.29442i	−0.0795925	+	0.137858i	−0.903074	−	0.429485i	$-0.858695\pi$
$277$	−1.32468	+	2.29442i	−0.0795925	+	0.137858i	0.823482	+	0.567343i	$0.192029\pi$
$278$		0			0
$279$	10.1626	+	15.0419i	0.608420	+	0.900538i
$280$		0			0
$281$	21.0180			1.25383			0.626915	−	0.779088i	$-0.284317\pi$
$281$	21.0180			1.25383			0.626915	+	0.779088i	$0.284317\pi$
$282$		0			0
$283$	−21.6906			−1.28937			−0.644686	−	0.764448i	$-0.723012\pi$
$283$	−21.6906			−1.28937			−0.644686	+	0.764448i	$0.723012\pi$
$284$		0			0
$285$	2.25013	+	1.19531i	0.133286	+	0.0708042i
$286$		0			0
$287$	−12.5590	+	21.7528i	−0.741333	+	1.28403i
$288$		0			0
$289$	3.64769	+	6.31798i	0.214570	+	0.371646i
$290$		0			0
$291$	25.7855	+	13.6978i	1.51157	+	0.802977i
$292$		0			0
$293$	14.9436			0.873016			0.436508	−	0.899700i	$-0.356215\pi$
$293$	14.9436			0.873016			0.436508	+	0.899700i	$0.356215\pi$
$294$		0			0
$295$	0.586859	+	1.01647i	0.0341683	+	0.0591812i
$296$		0			0
$297$	0.315521	−	0.229792i	0.0183084	−	0.0133339i
$298$		0			0
$299$	5.66410	−	9.81050i	0.327563	−	0.567356i
$300$		0			0
$301$	19.5373			1.12611
$302$		0			0
$303$	4.15545	+	2.20746i	0.238724	+	0.126815i
$304$		0			0
$305$	−1.31214	+	2.27270i	−0.0751331	+	0.130134i
$306$		0			0
$307$	−19.2086			−1.09629			−0.548145	−	0.836383i	$-0.684666\pi$
$307$	−19.2086			−1.09629			−0.548145	+	0.836383i	$0.684666\pi$
$308$		0			0
$309$	0.829100	+	23.4855i	0.0471659	+	1.33605i
$310$		0			0
$311$	9.55863	+	16.5560i	0.542020	+	0.938806i	0.998788	+	0.0492203i	$0.0156736\pi$
$311$	9.55863	+	16.5560i	0.542020	+	0.938806i	−0.456768	+	0.889586i	$0.650993\pi$
$312$		0			0
$313$	−23.0080			−1.30049			−0.650245	−	0.759724i	$-0.725334\pi$
$313$	−23.0080			−1.30049			−0.650245	+	0.759724i	$0.725334\pi$
$314$		0			0
$315$	−3.10017	−	4.58864i	−0.174675	−	0.258540i
$316$		0			0
$317$	−21.3009			−1.19638			−0.598189	−	0.801355i	$-0.704113\pi$
$317$	−21.3009			−1.19638			−0.598189	+	0.801355i	$0.704113\pi$
$318$		0			0
$319$	−0.124936	+	0.216395i	−0.00699507	+	0.0121158i
$320$		0			0
$321$	−11.1428	−	5.91928i	−0.621931	−	0.330382i
$322$		0			0
$323$	−7.95670			−0.442722
$324$		0			0
$325$	19.9309			1.10557
$326$		0			0
$327$	−0.326877	−	9.25929i	−0.0180763	−	0.512040i
$328$		0			0
$329$	−11.3689			−0.626790
$330$		0			0
$331$	−1.84671			−0.101504			−0.0507521	−	0.998711i	$-0.516162\pi$
$331$	−1.84671			−0.101504			−0.0507521	+	0.998711i	$0.516162\pi$
$332$		0			0
$333$	−9.02476	+	15.8604i	−0.494554	+	0.869147i
$334$		0			0
$335$	−1.88863			−0.103187
$336$		0			0
$337$	−12.3343			−0.671891			−0.335946	−	0.941881i	$-0.609056\pi$
$337$	−12.3343			−0.671891			−0.335946	+	0.941881i	$0.609056\pi$
$338$		0			0
$339$	26.8999	+	14.2898i	1.46100	+	0.776115i
$340$		0			0
$341$	0.454551			0.0246153
$342$		0			0
$343$	11.9477			0.645113
$344$		0			0
$345$	−0.0933832	−	2.64522i	−0.00502758	−	0.142414i
$346$		0			0
$347$	12.1631	−	21.0671i	0.652948	−	1.13094i	−0.329456	−	0.944171i	$-0.606865\pi$
$347$	12.1631	−	21.0671i	0.652948	−	1.13094i	0.982404	−	0.186768i	$-0.0598014\pi$
$348$		0			0
$349$	3.47535			0.186031			0.0930157	−	0.995665i	$-0.470349\pi$
$349$	3.47535			0.186031			0.0930157	+	0.995665i	$0.470349\pi$
$350$		0			0
$351$	−2.34415	−	22.0603i	−0.125122	−	1.17749i
$352$		0			0
$353$	7.54888			0.401786			0.200893	−	0.979613i	$-0.435616\pi$
$353$	7.54888			0.401786			0.200893	+	0.979613i	$0.435616\pi$
$354$		0			0
$355$	−1.83653	−	3.18096i	−0.0974728	−	0.168828i
$356$		0			0
$357$	15.2723	+	8.11297i	0.808297	+	0.429384i
$358$		0			0
$359$	−8.54145			−0.450801			−0.225400	−	0.974266i	$-0.572369\pi$
$359$	−8.54145			−0.450801			−0.225400	+	0.974266i	$0.572369\pi$
$360$		0			0
$361$	6.23820	−	10.8049i	0.328327	−	0.568678i
$362$		0			0
$363$	0.671841	+	19.0309i	0.0352625	+	0.998865i
$364$		0			0
$365$	−1.55493			−0.0813885
$366$		0			0
$367$	12.8464	−	22.2507i	0.670579	−	1.16148i	−0.307162	−	0.951657i	$-0.599379\pi$
$367$	12.8464	−	22.2507i	0.670579	−	1.16148i	0.977740	−	0.209819i	$-0.0672874\pi$
$368$		0			0
$369$	−10.2905	+	21.1395i	−0.535701	+	1.10048i
$370$		0			0
$371$	−20.8074	−	36.0394i	−1.08026	−	1.87107i
$372$		0			0
$373$	1.03390			0.0535333			0.0267667	−	0.999642i	$-0.491479\pi$
$373$	1.03390			0.0535333			0.0267667	+	0.999642i	$0.491479\pi$
$374$		0			0
$375$	8.17725	−	5.11405i	0.422271	−	0.264088i
$376$		0			0
$377$	7.10077	+	12.2989i	0.365708	+	0.633425i
$378$		0			0
$379$	1.50666	−	2.60962i	0.0773921	−	0.134047i	−0.824732	−	0.565524i	$-0.808674\pi$
$379$	1.50666	−	2.60962i	0.0773921	−	0.134047i	0.902124	+	0.431477i	$0.142007\pi$
$380$		0			0
$381$	−0.156327	−	4.42822i	−0.00800890	−	0.226864i
$382$		0			0
$383$	3.33042			0.170176			0.0850882	−	0.996373i	$-0.472883\pi$
$383$	3.33042			0.170176			0.0850882	+	0.996373i	$0.472883\pi$
$384$		0			0
$385$	−0.138664			−0.00706695
$386$		0			0
$387$	18.2419	−	1.28958i	0.927288	−	0.0655530i
$388$		0			0
$389$	−5.00374	+	8.66672i	−0.253699	+	0.439420i	−0.964541	−	0.263931i	$-0.914981\pi$
$389$	−5.00374	+	8.66672i	−0.253699	+	0.439420i	0.710842	+	0.703352i	$0.248314\pi$
$390$		0			0
$391$	4.13287	+	7.15834i	0.209008	+	0.362013i
$392$		0			0
$393$	−5.19999	−	2.76234i	−0.262305	−	0.139342i
$394$		0			0
$395$	1.80481	−	3.12602i	0.0908098	−	0.157287i
$396$		0			0
$397$	−17.2761			−0.867062			−0.433531	−	0.901139i	$-0.642733\pi$
$397$	−17.2761			−0.867062			−0.433531	+	0.901139i	$0.642733\pi$
$398$		0			0
$399$	12.0213	−	7.51814i	0.601820	−	0.376378i
$400$		0			0
$401$	−13.0022	+	22.5204i	−0.649298	+	1.12462i	0.333993	+	0.942575i	$0.391604\pi$
$401$	−13.0022	+	22.5204i	−0.649298	+	1.12462i	−0.983291	+	0.182041i	$0.941730\pi$
$402$		0			0
$403$	12.9173	−	22.3734i	0.643455	−	1.11450i
$404$		0			0
$405$	−3.19750	−	4.07978i	−0.158885	−	0.202726i
$406$		0			0
$407$	0.202568	+	0.409577i	0.0100409	+	0.0203020i
$408$		0			0
$409$	−5.70891	−	9.88812i	−0.282287	−	0.488936i	0.689660	−	0.724133i	$-0.257760\pi$
$409$	−5.70891	−	9.88812i	−0.282287	−	0.488936i	−0.971948	+	0.235197i	$0.924426\pi$
$410$		0			0
$411$	−9.76858	−	5.18927i	−0.481849	−	0.255968i
$412$		0			0
$413$	6.53155			0.321396
$414$		0			0
$415$	−7.88505			−0.387062
$416$		0			0
$417$	−35.6243	−	18.9243i	−1.74453	−	0.926729i
$418$		0			0
$419$	−11.4175	−	19.7757i	−0.557781	−	0.966105i	−0.997681	−	0.0680583i	$-0.978320\pi$
$419$	−11.4175	−	19.7757i	−0.557781	−	0.966105i	0.439900	−	0.898047i	$-0.355014\pi$
$420$		0			0
$421$	−0.00308737	−	0.00534748i	−0.000150469	−	0.000260620i	0.865950	−	0.500130i	$-0.166715\pi$
$421$	−0.00308737	−	0.00534748i	−0.000150469	−	0.000260620i	−0.866101	+	0.499870i	$0.833381\pi$
$422$		0			0
$423$	−10.6152	+	0.750420i	−0.516127	+	0.0364867i
$424$		0			0
$425$	−7.27139	+	12.5944i	−0.352714	+	0.610919i
$426$		0			0
$427$	7.30186	+	12.6472i	0.353362	+	0.612040i
$428$		0			0
$429$	−0.490572	−	0.260602i	−0.0236850	−	0.0125820i
$430$		0			0
$431$	−14.5496	−	25.2007i	−0.700831	−	1.21387i	−0.968175	−	0.250273i	$-0.919480\pi$
$431$	−14.5496	−	25.2007i	−0.700831	−	1.21387i	0.267345	−	0.963601i	$-0.413854\pi$
$432$		0			0
$433$	9.61908			0.462263			0.231132	−	0.972922i	$-0.425757\pi$
$433$	9.61908			0.462263			0.231132	+	0.972922i	$0.425757\pi$
$434$		0			0
$435$	2.93042	+	1.55670i	0.140503	+	0.0746381i
$436$		0			0
$437$	6.77697			0.324186
$438$		0			0
$439$	−3.98904	+	6.90921i	−0.190386	+	0.329759i	−0.945378	−	0.325975i	$-0.894307\pi$
$439$	−3.98904	+	6.90921i	−0.190386	+	0.329759i	0.754992	+	0.655734i	$0.227641\pi$
$440$		0			0
$441$	−9.79220	+	0.692242i	−0.466295	+	0.0329639i
$442$		0			0
$443$	14.8906	+	25.7913i	0.707475	+	1.22538i	0.965791	+	0.259323i	$0.0834993\pi$
$443$	14.8906	+	25.7913i	0.707475	+	1.22538i	−0.258315	+	0.966061i	$0.583167\pi$
$444$		0			0
$445$	4.94344	−	8.56229i	0.234342	−	0.405892i
$446$		0			0
$447$	0.117448	+	3.32689i	0.00555510	+	0.157357i
$448$		0			0
$449$	14.7508	+	25.5491i	0.696132	+	1.20574i	0.969798	+	0.243911i	$0.0784306\pi$
$449$	14.7508	+	25.5491i	0.696132	+	1.20574i	−0.273665	+	0.961825i	$0.588236\pi$
$450$		0			0
$451$	0.294356	+	0.509840i	0.0138607	+	0.0240074i
$452$		0			0
$453$	−0.734119	−	20.7950i	−0.0344919	−	0.977037i
$454$		0			0
$455$	−3.94049	+	6.82513i	−0.184733	+	0.319967i
$456$		0			0
$457$	2.37707	−	4.11720i	0.111194	−	0.192594i	−0.805058	−	0.593197i	$-0.797866\pi$
$457$	2.37707	−	4.11720i	0.111194	−	0.192594i	0.916252	+	0.400602i	$0.131199\pi$
$458$		0			0
$459$	14.7953	+	6.56700i	0.690583	+	0.306521i
$460$		0			0
$461$	−21.5090			−1.00177			−0.500887	−	0.865513i	$-0.666993\pi$
$461$	−21.5090			−1.00177			−0.500887	+	0.865513i	$0.666993\pi$
$462$		0			0
$463$	18.1858			0.845164			0.422582	−	0.906325i	$-0.361124\pi$
$463$	18.1858			0.845164			0.422582	+	0.906325i	$0.361124\pi$
$464$		0			0
$465$	−0.212965	−	6.03257i	−0.00987603	−	0.279754i
$466$		0			0
$467$	22.3309			1.03335			0.516676	−	0.856181i	$-0.327169\pi$
$467$	22.3309			1.03335			0.516676	+	0.856181i	$0.327169\pi$
$468$		0			0
$469$	−5.25495	+	9.10184i	−0.242651	+	0.420284i
$470$		0			0
$471$	−22.3369	−	11.8658i	−1.02923	−	0.546747i
$472$		0			0
$473$	0.228956	−	0.396563i	0.0105274	−	0.0182340i
$474$		0			0
$475$	5.96171	+	10.3260i	0.273542	+	0.473789i
$476$		0			0
$477$	−21.8066	−	32.2765i	−0.998457	−	1.47784i
$478$		0			0
$479$	−4.83208			−0.220783			−0.110392	−	0.993888i	$-0.535211\pi$
$479$	−4.83208			−0.220783			−0.110392	+	0.993888i	$0.535211\pi$
$480$		0			0
$481$	25.9162	+	1.66866i	1.18168	+	0.0760845i
$482$		0			0
$483$	−13.0079	−	6.91007i	−0.591881	−	0.314419i
$484$		0			0
$485$	−4.85446	−	8.40818i	−0.220430	−	0.381796i
$486$		0			0
$487$	7.15512			0.324229			0.162115	−	0.986772i	$-0.448169\pi$
$487$	7.15512			0.324229			0.162115	+	0.986772i	$0.448169\pi$
$488$		0			0
$489$	−0.320973	−	9.09206i	−0.0145149	−	0.411157i
$490$		0			0
$491$	−6.69512	+	11.5963i	−0.302146	+	0.523333i	−0.976622	−	0.214964i	$-0.931036\pi$
$491$	−6.69512	+	11.5963i	−0.302146	+	0.523333i	0.674475	+	0.738297i	$0.264370\pi$
$492$		0			0
$493$	−10.3623			−0.466694
$494$		0			0
$495$	−0.129470	+	0.00915266i	−0.00581925	+	0.000411381i
$496$		0			0
$497$	−20.4399			−0.916857
$498$		0			0
$499$	−8.13628			−0.364230			−0.182115	−	0.983277i	$-0.558294\pi$
$499$	−8.13628			−0.364230			−0.182115	+	0.983277i	$0.558294\pi$
$500$		0			0
$501$	0.991423	−	0.620036i	0.0442935	−	0.0277011i
$502$		0			0
$503$	2.06641	−	3.57912i	0.0921365	−	0.159585i	−0.816273	−	0.577666i	$-0.803964\pi$
$503$	2.06641	−	3.57912i	0.0921365	−	0.159585i	0.908410	+	0.418081i	$0.137297\pi$
$504$		0			0
$505$	−0.782320	−	1.35502i	−0.0348128	−	0.0602975i
$506$		0			0
$507$	−7.67727	+	4.80136i	−0.340960	+	0.213236i
$508$		0			0
$509$	5.69720	+	9.86784i	0.252524	+	0.437384i	0.964220	−	0.265103i	$-0.0854060\pi$
$509$	5.69720	+	9.86784i	0.252524	+	0.437384i	−0.711696	+	0.702487i	$0.752073\pi$
$510$		0			0
$511$	−4.32645	+	7.49363i	−0.191391	+	0.331499i
$512$		0			0
$513$	10.7281	−	7.81316i	0.473656	−	0.344960i
$514$		0			0
$515$	3.90715	−	6.76739i	0.172170	−	0.298207i
$516$		0			0
$517$	−0.133232	+	0.230765i	−0.00585954	+	0.0101490i
$518$		0			0
$519$	24.0704	−	15.0536i	1.05657	−	0.660780i
$520$		0			0
$521$	14.7499	+	25.5475i	0.646204	+	1.11926i	0.984022	+	0.178046i	$0.0569777\pi$
$521$	14.7499	+	25.5475i	0.646204	+	1.11926i	−0.337818	+	0.941211i	$0.609689\pi$
$522$		0			0
$523$	−14.8523	−	25.7250i	−0.649446	−	1.12487i	−0.983255	−	0.182233i	$-0.941668\pi$
$523$	−14.8523	−	25.7250i	−0.649446	−	1.12487i	0.333809	−	0.942641i	$-0.391666\pi$
$524$		0			0
$525$	−0.914295	−	25.8988i	−0.0399031	−	1.13032i
$526$		0			0
$527$	9.42522	+	16.3250i	0.410569	+	0.711127i
$528$		0			0
$529$	7.97991	+	13.8216i	0.346952	+	0.600939i
$530$		0			0
$531$	6.09850	−	0.431122i	0.264652	−	0.0187091i
$532$		0			0
$533$	33.4596			1.44930
$534$		0			0
$535$	2.09778	+	3.63347i	0.0906951	+	0.157089i
$536$		0			0
$537$	−20.9419	+	13.0970i	−0.903708	+	0.565179i
$538$		0			0
$539$	−0.122903	+	0.212874i	−0.00529380	+	0.00916913i
$540$		0			0
$541$	30.6614			1.31824			0.659118	−	0.752039i	$-0.270930\pi$
$541$	30.6614			1.31824			0.659118	+	0.752039i	$0.270930\pi$
$542$		0			0
$543$	−10.8810	−	5.78018i	−0.466946	−	0.248051i
$544$		0			0
$545$	−1.54041	+	2.66808i	−0.0659841	+	0.114288i
$546$		0			0
$547$	−11.9148	−	20.6370i	−0.509439	−	0.882374i	−0.999940	−	0.0109338i	$-0.996520\pi$
$547$	−11.9148	−	20.6370i	−0.509439	−	0.882374i	0.490501	−	0.871441i	$-0.336814\pi$
$548$		0			0
$549$	7.65253	+	11.3267i	0.326602	+	0.483412i
$550$		0			0
$551$	−4.24796	+	7.35768i	−0.180969	+	0.313448i
$552$		0			0
$553$	−10.0435	−	17.3958i	−0.427091	−	0.739744i
$554$		0			0
$555$	5.34079	−	2.88027i	0.226704	−	0.122261i
$556$		0			0
$557$	14.6164	−	25.3163i	0.619316	−	1.07269i	−0.370294	−	0.928914i	$-0.620743\pi$
$557$	14.6164	−	25.3163i	0.619316	−	1.07269i	0.989611	−	0.143773i	$-0.0459235\pi$
$558$		0			0
$559$	−13.0128	−	22.5388i	−0.550382	−	0.953290i
$560$		0			0
$561$	0.343651	−	0.214919i	0.0145090	−	0.00907390i
$562$		0			0
$563$	−13.0251	+	22.5601i	−0.548941	+	0.950794i	0.449406	+	0.893327i	$0.351636\pi$
$563$	−13.0251	+	22.5601i	−0.548941	+	0.950794i	−0.998347	+	0.0574663i	$0.981698\pi$
$564$		0			0
$565$	−5.06428	−	8.77158i	−0.213056	−	0.369023i
$566$		0			0
$567$	−28.5584	+	4.05805i	−1.19934	+	0.170422i
$568$		0			0
$569$	−10.5598	−	18.2901i	−0.442690	−	0.766761i	0.555198	−	0.831718i	$-0.312642\pi$
$569$	−10.5598	−	18.2901i	−0.442690	−	0.766761i	−0.997888	+	0.0649569i	$0.979309\pi$
$570$		0			0
$571$	−0.810298	−	1.40348i	−0.0339099	−	0.0587337i	0.848572	−	0.529079i	$-0.177463\pi$
$571$	−0.810298	−	1.40348i	−0.0339099	−	0.0587337i	−0.882482	+	0.470346i	$0.844129\pi$
$572$		0			0
$573$	−18.4298	−	9.79027i	−0.769914	−	0.408994i
$574$		0			0
$575$	6.19327	−	10.7271i	0.258277	−	0.447349i
$576$		0			0
$577$	12.2714	−	21.2547i	0.510865	−	0.884844i	−0.489056	−	0.872252i	$-0.662659\pi$
$577$	12.2714	−	21.2547i	0.510865	−	0.884844i	0.999921	−	0.0125915i	$-0.00400810\pi$
$578$		0			0
$579$	0.693998	+	19.6586i	0.0288416	+	0.816982i
$580$		0			0
$581$	−21.9395	+	38.0003i	−0.910203	+	1.57652i
$582$		0			0
$583$	−0.975361			−0.0403953
$584$		0			0
$585$	−3.22873	+	6.63272i	−0.133492	+	0.274229i
$586$		0			0
$587$	−3.15252	+	5.46033i	−0.130119	+	0.225372i	−0.923722	−	0.383063i	$-0.874869\pi$
$587$	−3.15252	+	5.46033i	−0.130119	+	0.225372i	0.793604	+	0.608435i	$0.208202\pi$
$588$		0			0
$589$	15.4552			0.636822
$590$		0			0
$591$	0.0588984	+	1.66839i	0.00242276	+	0.0686283i
$592$		0			0
$593$	−16.6321			−0.682999			−0.341499	−	0.939882i	$-0.610935\pi$
$593$	−16.6321			−0.682999			−0.341499	+	0.939882i	$0.610935\pi$
$594$		0			0
$595$	−2.87522	−	4.98003i	−0.117873	−	0.204161i
$596$		0			0
$597$	8.86903	−	5.54669i	0.362985	−	0.227011i
$598$		0			0
$599$	−10.8048			−0.441472			−0.220736	−	0.975334i	$-0.570846\pi$
$599$	−10.8048			−0.441472			−0.220736	+	0.975334i	$0.570846\pi$
$600$		0			0
$601$	34.9467			1.42550			0.712752	−	0.701416i	$-0.247448\pi$
$601$	34.9467			1.42550			0.712752	+	0.701416i	$0.247448\pi$
$602$		0			0
$603$	−4.30576	+	8.84524i	−0.175344	+	0.360206i
$604$		0			0
$605$	3.16606	−	5.48379i	0.128719	−	0.222948i
$606$		0			0
$607$	−7.85839	−	13.6111i	−0.318962	−	0.552459i	0.661310	−	0.750113i	$-0.270001\pi$
$607$	−7.85839	−	13.6111i	−0.318962	−	0.552459i	−0.980272	+	0.197654i	$0.936668\pi$
$608$		0			0
$609$	15.6558	−	9.79116i	0.634406	−	0.396758i
$610$		0			0
$611$	7.57228	+	13.1156i	0.306342	+	0.530599i
$612$		0			0
$613$	−5.82048	+	10.0814i	−0.235087	+	0.407183i	−0.959298	−	0.282396i	$-0.908871\pi$
$613$	−5.82048	+	10.0814i	−0.235087	+	0.407183i	0.724211	+	0.689578i	$0.242204\pi$
$614$		0			0
$615$	6.62842	−	4.14541i	0.267284	−	0.167159i
$616$		0			0
$617$	−2.28757	−	3.96219i	−0.0920942	−	0.159512i	0.816298	−	0.577631i	$-0.196023\pi$
$617$	−2.28757	−	3.96219i	−0.0920942	−	0.159512i	−0.908392	+	0.418119i	$0.862689\pi$
$618$		0			0
$619$	13.4894	+	23.3643i	0.542185	+	0.939092i	0.998778	+	0.0494163i	$0.0157361\pi$
$619$	13.4894	+	23.3643i	0.542185	+	0.939092i	−0.456593	+	0.889676i	$0.650931\pi$
$620$		0			0
$621$	−12.6016	−	5.59332i	−0.505684	−	0.224452i
$622$		0			0
$623$	−27.5094	−	47.6477i	−1.10214	−	1.90897i
$624$		0			0
$625$	20.1344			0.805375
$626$		0			0
$627$	−0.0117244	−	0.332112i	−0.000468227	−	0.0132633i
$628$		0			0
$629$	−10.5094	+	15.7678i	−0.419039	+	0.628702i
$630$		0			0
$631$	0.810368	−	1.40360i	0.0322602	−	0.0558764i	−0.849445	−	0.527678i	$-0.823063\pi$
$631$	0.810368	−	1.40360i	0.0322602	−	0.0558764i	0.881705	+	0.471802i	$0.156396\pi$
$632$		0			0
$633$	0.293724	+	8.32018i	0.0116745	+	0.330697i
$634$		0			0
$635$	−0.736697	+	1.27600i	−0.0292349	+	0.0506364i
$636$		0			0
$637$	6.98522	+	12.0988i	0.276765	+	0.479370i
$638$		0			0
$639$	−19.0848	+	1.34916i	−0.754981	+	0.0533721i
$640$		0			0
$641$	−30.3511			−1.19880			−0.599399	−	0.800450i	$-0.704594\pi$
$641$	−30.3511			−1.19880			−0.599399	+	0.800450i	$0.704594\pi$
$642$		0			0
$643$	−17.3876	+	30.1161i	−0.685698	+	1.18766i	0.287518	+	0.957775i	$0.407170\pi$
$643$	−17.3876	+	30.1161i	−0.685698	+	1.18766i	−0.973217	+	0.229889i	$0.926164\pi$
$644$		0			0
$645$	−5.37026	−	2.85279i	−0.211454	−	0.112329i
$646$		0			0
$647$	6.21251	+	10.7604i	0.244239	+	0.423034i	0.961917	−	0.273340i	$-0.0881285\pi$
$647$	6.21251	+	10.7604i	0.244239	+	0.423034i	−0.717678	+	0.696375i	$0.754795\pi$
$648$		0			0
$649$	0.0765428	−	0.132576i	0.00300457	−	0.00520407i
$650$		0			0
$651$	−29.6652	−	15.7588i	−1.16267	−	0.617635i
$652$		0			0
$653$	−5.59924			−0.219115			−0.109558	−	0.993980i	$-0.534943\pi$
$653$	−5.59924			−0.219115			−0.109558	+	0.993980i	$0.534943\pi$
$654$		0			0
$655$	0.978969	+	1.69562i	0.0382515	+	0.0662535i
$656$		0			0
$657$	−3.54497	+	7.28236i	−0.138303	+	0.284112i
$658$		0			0
$659$	20.7215	−	35.8907i	0.807195	−	1.39810i	−0.107604	−	0.994194i	$-0.534318\pi$
$659$	20.7215	−	35.8907i	0.807195	−	1.39810i	0.914799	−	0.403909i	$-0.132349\pi$
$660$		0			0
$661$	−37.6678			−1.46511			−0.732554	−	0.680709i	$-0.761672\pi$
$661$	−37.6678			−1.46511			−0.732554	+	0.680709i	$0.761672\pi$
$662$		0			0
$663$	−0.812745	−	23.0223i	−0.0315644	−	0.894111i
$664$		0			0
$665$	−4.71471			−0.182829
$666$		0			0
$667$	8.82589			0.341740
$668$		0			0
$669$	−2.68667	−	1.42721i	−0.103872	−	0.0551792i
$670$		0			0
$671$	0.342280			0.0132136
$672$		0			0
$673$	23.7584	−	41.1508i	0.915819	−	1.58625i	0.110122	−	0.993918i	$-0.464876\pi$
$673$	23.7584	−	41.1508i	0.915819	−	1.58625i	0.805697	−	0.592327i	$-0.201791\pi$
$674$		0			0
$675$	−2.56316	−	24.1213i	−0.0986560	−	0.928431i
$676$		0			0
$677$	12.5005	+	21.6515i	0.480433	+	0.832135i	0.999748	−	0.0224484i	$-0.00714614\pi$
$677$	12.5005	+	21.6515i	0.480433	+	0.832135i	−0.519315	+	0.854583i	$0.673813\pi$
$678$		0			0
$679$	−54.0285			−2.07343
$680$		0			0
$681$	1.40918	+	39.9172i	0.0539998	+	1.52963i
$682$		0			0
$683$	8.99830	−	15.5855i	0.344310	−	0.596363i	−0.640918	−	0.767610i	$-0.721446\pi$
$683$	8.99830	−	15.5855i	0.344310	−	0.596363i	0.985228	+	0.171246i	$0.0547794\pi$
$684$		0			0
$685$	1.83907	+	3.18536i	0.0702672	+	0.121706i
$686$		0			0
$687$	25.5654	−	15.9886i	0.975380	−	0.610003i
$688$		0			0
$689$	−27.7175	+	48.0081i	−1.05595	+	1.82896i
$690$		0			0
$691$	−2.63293			−0.100162			−0.0500808	−	0.998745i	$-0.515948\pi$
$691$	−2.63293			−0.100162			−0.0500808	+	0.998745i	$0.515948\pi$
$692$		0			0
$693$	−0.316130	+	0.649420i	−0.0120088	+	0.0246694i
$694$		0			0
$695$	6.70675	+	11.6164i	0.254402	+	0.440637i
$696$		0			0
$697$	−12.2071	+	21.1433i	−0.462376	+	0.800859i
$698$		0			0
$699$	−22.3542	+	13.9803i	−0.845514	+	0.528784i
$700$		0			0
$701$	21.6823	−	37.5548i	0.818928	−	1.41842i	−0.0875454	−	0.996161i	$-0.527902\pi$
$701$	21.6823	−	37.5548i	0.818928	−	1.41842i	0.906473	−	0.422264i	$-0.138764\pi$
$702$		0			0
$703$	6.88752	+	13.9261i	0.259768	+	0.525231i
$704$		0			0
$705$	3.12501	+	1.66007i	0.117695	+	0.0625218i
$706$		0			0
$707$	−8.70695			−0.327459
$708$		0			0
$709$	10.2027	+	17.6716i	0.383171	+	0.663671i	0.991514	−	0.130003i	$-0.0414988\pi$
$709$	10.2027	+	17.6716i	0.383171	+	0.663671i	−0.608343	+	0.793674i	$0.708165\pi$
$710$		0			0
$711$	−10.5258	−	15.5795i	−0.394748	−	0.584276i
$712$		0			0
$713$	−8.02776	−	13.9045i	−0.300642	−	0.520727i
$714$		0			0
$715$	0.0923569	+	0.159967i	0.00345395	+	0.00598242i
$716$		0			0
$717$	38.7555	+	20.5877i	1.44735	+	0.768862i
$718$		0			0
$719$	1.75639	−	3.04216i	0.0655023	−	0.113453i	−0.831414	−	0.555653i	$-0.812468\pi$
$719$	1.75639	−	3.04216i	0.0655023	−	0.113453i	0.896917	+	0.442200i	$0.145802\pi$
$720$		0			0
$721$	−21.7427	−	37.6594i	−0.809739	−	1.40251i
$722$		0			0
$723$	0.0404769	+	1.14657i	0.00150535	+	0.0426414i
$724$		0			0
$725$	7.76416	+	13.4479i	0.288354	+	0.499443i
$726$		0			0
$727$	−16.1622	+	27.9938i	−0.599424	+	1.03823i	0.393482	+	0.919332i	$0.371270\pi$
$727$	−16.1622	+	27.9938i	−0.599424	+	1.03823i	−0.992906	+	0.118901i	$0.962063\pi$
$728$		0			0
$729$	−26.3971	+	5.67403i	−0.977669	+	0.210149i
$730$		0			0
$731$	18.9898			0.702364
$732$		0			0
$733$	−6.56180			−0.242366			−0.121183	−	0.992630i	$-0.538669\pi$
$733$	−6.56180			−0.242366			−0.121183	+	0.992630i	$0.538669\pi$
$734$		0			0
$735$	2.88274	+	1.53137i	0.106331	+	0.0564854i
$736$		0			0
$737$	0.123165	+	0.213328i	0.00453684	+	0.00785804i
$738$		0			0
$739$	46.6524			1.71613			0.858067	−	0.513537i	$-0.171665\pi$
$739$	46.6524			1.71613			0.858067	+	0.513537i	$0.171665\pi$
$740$		0			0
$741$	−16.6800	−	8.86075i	−0.612754	−	0.325508i
$742$		0			0
$743$	3.36618			0.123493			0.0617467	−	0.998092i	$-0.480333\pi$
$743$	3.36618			0.123493			0.0617467	+	0.998092i	$0.480333\pi$
$744$		0			0
$745$	0.553476	−	0.958649i	0.0202778	−	0.0351222i
$746$		0			0
$747$	−17.9766	+	36.9290i	−0.657730	+	1.35116i
$748$		0			0
$749$	23.3476			0.853104
$750$		0			0
$751$	4.99696	−	8.65498i	0.182342	−	0.315825i	−0.760336	−	0.649530i	$-0.774966\pi$
$751$	4.99696	−	8.65498i	0.182342	−	0.315825i	0.942677	+	0.333705i	$0.108299\pi$
$752$		0			0
$753$	−33.5450	+	20.9791i	−1.22245	+	0.764520i
$754$		0			0
$755$	−3.45955	+	5.99212i	−0.125906	+	0.218075i
$756$		0			0
$757$	18.4865	−	32.0195i	0.671902	−	1.16377i	−0.305461	−	0.952204i	$-0.598811\pi$
$757$	18.4865	−	32.0195i	0.671902	−	1.16377i	0.977364	−	0.211565i	$-0.0678559\pi$
$758$		0			0
$759$	−0.292698	+	0.183053i	−0.0106243	+	0.00664442i
$760$		0			0
$761$	23.0405	+	39.9074i	0.835219	+	1.44664i	0.893852	+	0.448362i	$0.147992\pi$
$761$	23.0405	+	39.9074i	0.835219	+	1.44664i	−0.0586331	+	0.998280i	$0.518674\pi$
$762$		0			0
$763$	8.57215	+	14.8474i	0.310333	+	0.537512i
$764$		0			0
$765$	−3.01330	−	4.46007i	−0.108946	−	0.161254i
$766$		0			0
$767$	−4.35033	−	7.53500i	−0.157081	−	0.272073i
$768$		0			0
$769$	16.0434	−	27.7879i	0.578539	−	1.00206i	−0.417108	−	0.908857i	$-0.636956\pi$
$769$	16.0434	−	27.7879i	0.578539	−	1.00206i	0.995647	−	0.0932018i	$-0.0297102\pi$
$770$		0			0
$771$	7.87403	+	4.18284i	0.283576	+	0.150641i
$772$		0			0
$773$	−26.4288	−	45.7760i	−0.950577	−	1.64645i	−0.744179	−	0.667980i	$-0.767159\pi$
$773$	−26.4288	−	45.7760i	−0.950577	−	1.64645i	−0.206399	−	0.978468i	$-0.566174\pi$
$774$		0			0
$775$	14.1241	−	24.4636i	0.507352	−	0.878759i
$776$		0			0
$777$	0.979453	−	33.7529i	0.0351377	−	1.21088i
$778$		0			0
$779$	10.0084	+	17.3351i	0.358589	+	0.621094i
$780$		0			0
$781$	−0.239535	+	0.414886i	−0.00857122	+	0.0148458i
$782$		0			0
$783$	13.9716	−	10.1754i	0.499303	−	0.363638i
$784$		0			0
$785$	4.20522	+	7.28365i	0.150091	+	0.259965i
$786$		0			0
$787$	12.8330	−	22.2275i	0.457449	−	0.792324i	−0.541377	−	0.840780i	$-0.682097\pi$
$787$	12.8330	−	22.2275i	0.457449	−	0.792324i	0.998825	+	0.0484558i	$0.0154300\pi$
$788$		0			0
$789$	1.35032	+	38.2500i	0.0480728	+	1.36174i
$790$		0			0
$791$	−56.3637			−2.00406
$792$		0			0
$793$	9.72680	−	16.8473i	0.345409	−	0.598266i
$794$		0			0
$795$	0.456974	+	12.9445i	0.0162072	+	0.459094i
$796$		0			0
$797$	−0.0648977	−	0.112406i	−0.00229880	−	0.00398163i	0.864874	−	0.501989i	$-0.167398\pi$
$797$	−0.0648977	−	0.112406i	−0.00229880	−	0.00398163i	−0.867173	+	0.498008i	$0.834065\pi$
$798$		0			0
$799$	−11.0504			−0.390934
$800$		0			0
$801$	−28.8306	−	42.6728i	−1.01868	−	1.50777i
$802$		0			0
$803$	0.101403	+	0.175635i	0.00357843	+	0.00619802i
$804$		0			0
$805$	2.44892	+	4.24165i	0.0863130	+	0.149498i
$806$		0			0
$807$	−14.9463	+	9.34744i	−0.526136	+	0.329045i
$808$		0			0
$809$	6.53220	+	11.3141i	0.229660	+	0.397783i	0.957707	−	0.287744i	$-0.0929052\pi$
$809$	6.53220	+	11.3141i	0.229660	+	0.397783i	−0.728047	+	0.685527i	$0.759572\pi$
$810$		0			0
$811$	−7.84361	−	13.5855i	−0.275426	−	0.477053i	0.694816	−	0.719187i	$-0.255486\pi$
$811$	−7.84361	−	13.5855i	−0.275426	−	0.477053i	−0.970243	+	0.242135i	$0.922152\pi$
$812$		0			0
$813$	−1.58879	−	45.0050i	−0.0557214	−	1.57839i
$814$		0			0
$815$	−1.51259	+	2.61989i	−0.0529838	+	0.0917707i
$816$		0			0
$817$	7.78475	−	13.4836i	0.272354	−	0.471731i
$818$		0			0
$819$	22.9813	+	34.0152i	0.803031	+	1.18859i
$820$		0			0
$821$	12.5848	−	21.7975i	0.439212	−	0.760738i	−0.558417	−	0.829561i	$-0.688591\pi$
$821$	12.5848	−	21.7975i	0.439212	−	0.760738i	0.997629	+	0.0688226i	$0.0219243\pi$
$822$		0			0
$823$	−7.76521	−	13.4497i	−0.270678	−	0.468829i	0.698357	−	0.715749i	$-0.253915\pi$
$823$	−7.76521	−	13.4497i	−0.270678	−	0.468829i	−0.969036	+	0.246921i	$0.920581\pi$
$824$		0			0
$825$	−0.536404	−	0.284949i	−0.0186752	−	0.00992064i
$826$		0			0
$827$	23.4020	+	40.5334i	0.813766	+	1.40948i	0.910210	+	0.414146i	$0.135920\pi$
$827$	23.4020	+	40.5334i	0.813766	+	1.40948i	−0.0964438	+	0.995338i	$0.530747\pi$
$828$		0			0
$829$	−4.30975	+	7.46471i	−0.149684	+	0.259260i	−0.931111	−	0.364737i	$-0.881159\pi$
$829$	−4.30975	+	7.46471i	−0.149684	+	0.259260i	0.781427	+	0.623997i	$0.214492\pi$
$830$		0			0
$831$	−0.161897	−	4.58598i	−0.00561614	−	0.159086i
$832$		0			0
$833$	−10.1937			−0.353190
$834$		0			0
$835$	−0.388831			−0.0134561
$836$		0			0
$837$	−28.7386	−	12.7559i	−0.993350	−	0.440907i
$838$		0			0
$839$	37.9863			1.31143			0.655716	−	0.755008i	$-0.272367\pi$
$839$	37.9863			1.31143			0.655716	+	0.755008i	$0.272367\pi$
$840$		0			0
$841$	8.96773	−	15.5326i	0.309232	−	0.535606i
$842$		0			0
$843$	−30.8652	+	19.3031i	−1.06305	+	0.664834i
$844$		0			0
$845$	3.01099			0.103581
$846$		0			0
$847$	−17.6186	−	30.5163i	−0.605383	−	1.04855i
$848$		0			0
$849$	31.8529	−	19.9208i	1.09319	−	0.683680i
$850$		0			0
$851$	8.95122	−	13.4299i	0.306844	−	0.460371i
$852$		0			0
$853$	−49.9965			−1.71185			−0.855923	−	0.517103i	$-0.827010\pi$
$853$	−49.9965			−1.71185			−0.855923	+	0.517103i	$0.827010\pi$
$854$		0			0
$855$	−4.40212	+	0.311200i	−0.150549	+	0.0106428i
$856$		0			0
$857$	7.71792	+	13.3678i	0.263639	+	0.456636i	0.967206	−	0.253992i	$-0.0817439\pi$
$857$	7.71792	+	13.3678i	0.263639	+	0.456636i	−0.703567	+	0.710629i	$0.748411\pi$
$858$		0			0
$859$	−27.5880	+	47.7839i	−0.941292	+	1.63036i	−0.178280	+	0.983980i	$0.557053\pi$
$859$	−27.5880	+	47.7839i	−0.941292	+	1.63036i	−0.763011	+	0.646385i	$0.776280\pi$
$860$		0			0
$861$	−1.53490	−	43.4785i	−0.0523094	−	1.48174i
$862$		0			0
$863$	−19.3322	+	33.4843i	−0.658075	+	1.13982i	0.323038	+	0.946386i	$0.395296\pi$
$863$	−19.3322	+	33.4843i	−0.658075	+	1.13982i	−0.981113	+	0.193434i	$0.938037\pi$
$864$		0			0
$865$	−9.44028			−0.320979
$866$		0			0
$867$	−11.1591	−	5.92797i	−0.378985	−	0.201324i
$868$		0			0
$869$	−0.470795			−0.0159706
$870$		0			0
$871$	14.0002			0.474380
$872$		0			0
$873$	−50.4464	+	3.56622i	−1.70735	+	0.120698i
$874$		0			0
$875$	−8.92343	+	15.4558i	−0.301667	+	0.522502i
$876$		0			0
$877$	9.72814	−	16.8496i	0.328496	−	0.568972i	−0.653718	−	0.756739i	$-0.726792\pi$
$877$	9.72814	−	16.8496i	0.328496	−	0.568972i	0.982214	+	0.187767i	$0.0601249\pi$
$878$		0			0
$879$	−21.9449	+	13.7243i	−0.740183	+	0.462910i
$880$		0			0
$881$	6.24031	+	10.8085i	0.210241	+	0.364149i	0.951790	−	0.306750i	$-0.0992416\pi$
$881$	6.24031	+	10.8085i	0.210241	+	0.364149i	−0.741549	+	0.670899i	$0.765908\pi$
$882$		0			0
$883$	−6.88419	−	11.9238i	−0.231672	−	0.401267i	0.726629	−	0.687031i	$-0.241086\pi$
$883$	−6.88419	−	11.9238i	−0.231672	−	0.401267i	−0.958300	+	0.285764i	$0.907753\pi$
$884$		0			0
$885$	−1.79534	−	0.953723i	−0.0603498	−	0.0320590i
$886$		0			0
$887$	23.6980	−	41.0461i	0.795699	−	1.37819i	−0.126695	−	0.991942i	$-0.540437\pi$
$887$	23.6980	−	41.0461i	0.795699	−	1.37819i	0.922394	−	0.386250i	$-0.126230\pi$
$888$		0			0
$889$	4.09959	+	7.10070i	0.137496	+	0.238150i
$890$		0			0
$891$	−0.252305	+	0.627229i	−0.00845252	+	0.0210130i
$892$		0			0
$893$	−4.53003	+	7.84625i	−0.151592	+	0.262565i
$894$		0			0
$895$	8.21330			0.274540
$896$		0			0
$897$	0.692241	+	19.6088i	0.0231132	+	0.654719i
$898$		0			0
$899$	20.1279			0.671304
$900$		0			0
$901$	−20.2243	−	35.0296i	−0.673771	−	1.16700i
$902$		0			0
$903$	−28.6907	+	17.9432i	−0.954767	+	0.597111i
$904$		0			0
$905$	2.04849	+	3.54808i	0.0680940	+	0.117942i
$906$		0			0
$907$	12.6877	−	21.9757i	0.421288	−	0.729692i	−0.574778	−	0.818309i	$-0.694912\pi$
$907$	12.6877	−	21.9757i	0.421288	−	0.729692i	0.996066	+	0.0886175i	$0.0282449\pi$
$908$		0			0
$909$	−8.12967	+	0.574713i	−0.269644	+	0.0190620i
$910$		0			0
$911$	−24.7883	−	42.9347i	−0.821274	−	1.42249i	−0.904734	−	0.425977i	$-0.859930\pi$
$911$	−24.7883	−	42.9347i	−0.821274	−	1.42249i	0.0834596	−	0.996511i	$-0.473403\pi$
$912$		0			0
$913$	0.514215	+	0.890647i	0.0170180	+	0.0294761i
$914$		0			0
$915$	−0.160364	−	4.54257i	−0.00530148	−	0.150173i
$916$		0			0
$917$	10.8956			0.359804
$918$		0			0
$919$	−41.9316			−1.38320			−0.691598	−	0.722282i	$-0.743093\pi$
$919$	−41.9316			−1.38320			−0.691598	+	0.722282i	$0.743093\pi$
$920$		0			0
$921$	28.2080	−	17.6413i	0.929486	−	0.581300i
$922$		0			0
$923$	13.6140	+	23.5802i	0.448111	+	0.776151i
$924$		0			0
$925$	28.3374	+	1.82456i	0.931728	+	0.0599911i
$926$		0			0
$927$	−22.7868	−	33.7274i	−0.748418	−	1.10775i
$928$		0			0
$929$	15.7399	−	27.2623i	0.516410	−	0.894448i	−0.483409	−	0.875395i	$-0.660601\pi$
$929$	15.7399	−	27.2623i	0.516410	−	0.894448i	0.999818	−	0.0190532i	$-0.00606518\pi$
$930$		0			0
$931$	−4.17883	+	7.23795i	−0.136956	+	0.237214i
$932$		0			0
$933$	−29.2421	−	15.5340i	−0.957345	−	0.508561i
$934$		0			0
$935$	−0.134778			−0.00440772
$936$		0			0
$937$	−24.2043	+	41.9230i	−0.790719	+	1.36957i	0.134803	+	0.990872i	$0.456960\pi$
$937$	−24.2043	+	41.9230i	−0.790719	+	1.36957i	−0.925522	+	0.378693i	$0.876373\pi$
$938$		0			0
$939$	33.7876	−	21.1307i	1.10262	−	0.689576i
$940$		0			0
$941$	17.1944	+	29.7815i	0.560520	+	0.970850i	0.997451	+	0.0713547i	$0.0227322\pi$
$941$	17.1944	+	29.7815i	0.560520	+	0.970850i	−0.436931	+	0.899495i	$0.643934\pi$
$942$		0			0
$943$	10.3972	−	18.0084i	0.338578	−	0.586434i
$944$		0			0
$945$	8.76688	+	3.89125i	0.285187	+	0.126582i
$946$		0			0
$947$	−21.5407			−0.699977			−0.349989	−	0.936754i	$-0.613815\pi$
$947$	−21.5407			−0.699977			−0.349989	+	0.936754i	$0.613815\pi$
$948$		0			0
$949$	11.5265			0.374167
$950$		0			0
$951$	31.2807	−	19.5629i	1.01434	−	0.634371i
$952$		0			0
$953$	−1.99864	+	3.46174i	−0.0647423	+	0.112137i	−0.896580	−	0.442883i	$-0.853956\pi$
$953$	−1.99864	+	3.46174i	−0.0647423	+	0.112137i	0.831837	+	0.555019i	$0.187289\pi$
$954$		0			0
$955$	3.46965	+	6.00962i	0.112275	+	0.194467i
$956$		0			0
$957$	−0.0152691	−	0.432521i	−0.000493580	−	0.0139814i
$958$		0			0
$959$	20.4682			0.660953
$960$		0			0
$961$	−2.80773	−	4.86312i	−0.0905718	−	0.156875i
$962$		0			0
$963$	21.7997	−	1.54109i	0.702484	−	0.0496609i
$964$		0			0
$965$	3.27048	−	5.66464i	0.105281	−	0.182351i
$966$		0			0
$967$	6.10100			0.196195			0.0980975	−	0.995177i	$-0.468724\pi$
$967$	6.10100			0.196195			0.0980975	+	0.995177i	$0.468724\pi$
$968$		0			0
$969$	11.6845	−	7.30749i	0.375360	−	0.234750i
$970$		0			0
$971$	−11.7811	+	20.4054i	−0.378073	+	0.654842i	−0.990782	−	0.135467i	$-0.956747\pi$
$971$	−11.7811	+	20.4054i	−0.378073	+	0.654842i	0.612709	+	0.790309i	$0.290080\pi$
$972$		0			0
$973$	74.6439			2.39297
$974$		0			0
$975$	−29.2687	+	18.3047i	−0.937350	+	0.586218i
$976$		0			0
$977$	21.6544	+	37.5065i	0.692785	+	1.19994i	0.970922	+	0.239397i	$0.0769497\pi$
$977$	21.6544	+	37.5065i	0.692785	+	1.19994i	−0.278137	+	0.960541i	$0.589717\pi$
$978$		0			0
$979$	−1.28953			−0.0412134
$980$		0			0
$981$	8.98382	+	13.2972i	0.286831	+	0.424546i
$982$		0			0
$983$	−60.7058			−1.93622			−0.968108	−	0.250534i	$-0.919394\pi$
$983$	−60.7058			−1.93622			−0.968108	+	0.250534i	$0.919394\pi$
$984$		0			0
$985$	0.277560	−	0.480748i	0.00884380	−	0.0153179i
$986$		0			0
$987$	16.6954	−	10.4413i	0.531421	−	0.332351i
$988$		0			0
$989$	−16.1742			−0.514311
$990$		0			0
$991$	34.6483			1.10064			0.550320	−	0.834954i	$-0.314506\pi$
$991$	34.6483			1.10064			0.550320	+	0.834954i	$0.314506\pi$
$992$		0			0
$993$	2.71191	−	1.69603i	0.0860600	−	0.0538219i
$994$		0			0
$995$	−3.47839			−0.110272
$996$		0			0
$997$	34.6459			1.09725			0.548623	−	0.836070i	$-0.315152\pi$
$997$	34.6459			1.09725			0.548623	+	0.836070i	$0.315152\pi$
$998$		0			0
$999$	−1.31338	−	31.5797i	−0.0415537	−	0.999136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1332.2.l.b.121.7	yes	74
3.2	odd	2		3996.2.l.b.1009.19		74
9.2	odd	6		3996.2.k.b.2341.19		74
9.7	even	3		1332.2.k.b.565.31	✓	74
37.26	even	3		1332.2.k.b.877.31	yes	74
111.26	odd	6		3996.2.k.b.1765.19		74
333.137	odd	6		3996.2.l.b.3097.19		74
333.322	even	3	inner	1332.2.l.b.1321.7	yes	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1332.2.k.b.565.31	✓	74	9.7	even	3
1332.2.k.b.877.31	yes	74	37.26	even	3
1332.2.l.b.121.7	yes	74	1.1	even	1	trivial
1332.2.l.b.1321.7	yes	74	333.322	even	3	inner
3996.2.k.b.1765.19		74	111.26	odd	6
3996.2.k.b.2341.19		74	9.2	odd	6
3996.2.l.b.1009.19		74	3.2	odd	2
3996.2.l.b.3097.19		74	333.137	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:	\( N \)	\(=\)	\( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1332.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46851 + 0.918407i) q^{3} +0.575944 q^{5} +(1.60251 - 2.77564i) q^{7} +(1.31306 - 2.69738i) q^{9} +(-0.0375596 - 0.0650551i) q^{11} -4.26942 q^{13} +(-0.845780 + 0.528951i) q^{15} +(1.55761 - 2.69786i) q^{17} +(-1.27707 - 2.21194i) q^{19} +(0.195852 + 5.54782i) q^{21} +(-1.32667 + 2.29786i) q^{23} -4.66829 q^{25} +(0.549057 + 5.16706i) q^{27} +(-1.66317 - 2.88070i) q^{29} +(-3.02554 + 5.24038i) q^{31} +(0.114904 + 0.0610392i) q^{33} +(0.922958 - 1.59861i) q^{35} +(-6.07019 - 0.390841i) q^{37} +(6.26969 - 3.92106i) q^{39} -7.83705 q^{41} +(3.04791 + 5.27913i) q^{43} +(0.756247 - 1.55354i) q^{45} +(-1.77361 - 3.07198i) q^{47} +(-1.63611 - 2.83382i) q^{49} +(0.190364 + 5.39237i) q^{51} +(6.49210 - 11.2446i) q^{53} +(-0.0216322 - 0.0374681i) q^{55} +(3.90685 + 2.07540i) q^{57} +(1.01895 + 1.76488i) q^{59} +(-2.27825 + 3.94604i) q^{61} +(-5.38277 - 7.96717i) q^{63} -2.45894 q^{65} -3.27919 q^{67} +(-0.162139 - 4.59285i) q^{69} +(-3.18873 - 5.52304i) q^{71} -2.69979 q^{73} +(6.85544 - 4.28739i) q^{75} -0.240759 q^{77} +(3.13366 - 5.42765i) q^{79} +(-5.55176 - 7.08364i) q^{81} -13.6907 q^{83} +(0.897097 - 1.55382i) q^{85} +(5.08804 + 2.70287i) q^{87} +(8.58321 - 14.8665i) q^{89} +(-6.84180 + 11.8504i) q^{91} +(-0.369767 - 10.4742i) q^{93} +(-0.735518 - 1.27395i) q^{95} +(-8.42871 - 14.5990i) q^{97} +(-0.224796 + 0.0158916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q + 5 q^{3} + 6 q^{5} - q^{7} - q^{9} + q^{11} - 4 q^{13} - 2 q^{15} + 3 q^{17} + q^{19} - 3 q^{21} - 17 q^{23} + 96 q^{25} + 17 q^{27} + 6 q^{29} + 3 q^{31} - 16 q^{33} - 6 q^{35} + 5 q^{37} + 35 q^{39}+ \cdots - 43 q^{99}+O(q^{100}) \) 74 * q + 5 * q^3 + 6 * q^5 - q^7 - q^9 + q^11 - 4 * q^13 - 2 * q^15 + 3 * q^17 + q^19 - 3 * q^21 - 17 * q^23 + 96 * q^25 + 17 * q^27 + 6 * q^29 + 3 * q^31 - 16 * q^33 - 6 * q^35 + 5 * q^37 + 35 * q^39 + 54 * q^41 + 3 * q^43 - 4 * q^45 - 21 * q^47 - 46 * q^49 + 11 * q^51 - 11 * q^53 - 11 * q^55 + 20 * q^57 + 13 * q^59 + 12 * q^61 + 5 * q^63 + 38 * q^65 + 38 * q^67 - 8 * q^69 + 18 * q^73 - 7 * q^75 + 92 * q^77 - q^79 + 31 * q^81 + 40 * q^83 + 9 * q^85 + 6 * q^87 + 13 * q^89 - 11 * q^91 - 3 * q^93 - 13 * q^95 + 17 * q^97 - 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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