LMFDB - Embedded newform 735.2.p.f.374.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(374,735)] 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("735.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.10
Character	$\chi$	$=$	735.374
Dual form			735.2.p.f.509.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.757344 + 1.31176i) q^{2} +(0.419611 - 1.68045i) q^{3} +(-0.147140 + 0.254854i) q^{4} +(1.42830 - 1.72046i) q^{5} +(2.52214 - 0.722254i) q^{6} +2.58363 q^{8} +(-2.64785 - 1.41027i) q^{9} +(3.33853 + 0.570605i) q^{10} +(1.86048 + 1.07415i) q^{11} +(0.366529 + 0.354202i) q^{12} -3.48097 q^{13} +(-2.29182 - 3.12211i) q^{15} +(2.25098 + 3.89881i) q^{16} +(3.09793 + 1.78859i) q^{17} +(-0.155396 - 4.54141i) q^{18} +(1.05858 - 0.611171i) q^{19} +(0.228305 + 0.617156i) q^{20} +3.25401i q^{22} +(-0.757344 - 1.31176i) q^{23} +(1.08412 - 4.34168i) q^{24} +(-0.919933 - 4.91464i) q^{25} +(-2.63629 - 4.56619i) q^{26} +(-3.48097 + 3.85783i) q^{27} -5.95645i q^{29} +(2.35976 - 5.37082i) q^{30} +(-2.75098 - 1.58828i) q^{31} +(-0.825899 + 1.43050i) q^{32} +(2.58574 - 2.67573i) q^{33} +5.41832i q^{34} +(0.749020 - 0.467309i) q^{36} +(-6.75803 + 3.90175i) q^{37} +(1.60342 + 0.925734i) q^{38} +(-1.46065 + 5.84961i) q^{39} +(3.69020 - 4.44503i) q^{40} +11.8685 q^{41} -2.99294i q^{43} +(-0.547504 + 0.316101i) q^{44} +(-6.20824 + 2.54122i) q^{45} +(1.14714 - 1.98691i) q^{46} +(-5.28420 + 3.05084i) q^{47} +(7.49631 - 2.14668i) q^{48} +(5.75012 - 4.92881i) q^{50} +(4.30557 - 4.45542i) q^{51} +(0.512191 - 0.887140i) q^{52} +(-5.61301 + 9.72202i) q^{53} +(-7.69683 - 1.64449i) q^{54} +(4.50535 - 1.66667i) q^{55} +(-0.582853 - 2.03535i) q^{57} +(7.81342 - 4.51108i) q^{58} +(1.08467 - 1.87871i) q^{59} +(1.13290 - 0.124691i) q^{60} +(2.94338 - 1.69936i) q^{61} -4.81149i q^{62} +6.50196 q^{64} +(-4.97186 + 5.98885i) q^{65} +(5.46821 + 1.36542i) q^{66} +(8.93534 + 5.15882i) q^{67} +(-0.911660 + 0.526347i) q^{68} +(-2.52214 + 0.722254i) q^{69} +10.3968i q^{71} +(-6.84108 - 3.64363i) q^{72} +(-3.42779 + 5.93710i) q^{73} +(-10.2363 - 5.90993i) q^{74} +(-8.64485 - 0.516335i) q^{75} +0.359711i q^{76} +(-8.77950 + 2.51414i) q^{78} +(0.941421 + 1.63059i) q^{79} +(9.92280 + 1.69595i) q^{80} +(5.02225 + 7.46840i) q^{81} +(8.98853 + 15.5686i) q^{82} +9.10486i q^{83} +(7.50196 - 2.77521i) q^{85} +(3.92601 - 2.26668i) q^{86} +(-10.0095 - 2.49939i) q^{87} +(4.80681 + 2.77521i) q^{88} +(-0.889962 - 1.54146i) q^{89} +(-8.03524 - 6.21913i) q^{90} +0.445743 q^{92} +(-3.82337 + 3.95644i) q^{93} +(-8.00392 - 4.62107i) q^{94} +(0.460474 - 2.69417i) q^{95} +(2.05733 + 1.98814i) q^{96} +1.32584 q^{97} +(-3.41144 - 5.46799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) $ 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 + 72 * q^40 + 18 * q^45 + 36 * q^46 - 12 * q^51 + 36 * q^54 + 12 * q^60 - 36 * q^61 + 24 * q^64 + 72 * q^66 - 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^85 + 72 * q^94 + 90 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.757344	+	1.31176i	0.535523	+	0.927553i	0.999138	+	0.0415164i	$0.0132189\pi$
$2$	0.757344	+	1.31176i	0.535523	+	0.927553i	−0.463615	+	0.886037i	$0.653448\pi$
$3$	0.419611	−	1.68045i	0.242263	−	0.970211i
$3$	0.419611	−	1.68045i	0.242263	−	0.970211i
$4$	−0.147140	+	0.254854i	−0.0735701	+	0.127427i
$5$	1.42830	−	1.72046i	0.638754	−	0.769411i
$5$	1.42830	−	1.72046i	0.638754	−	0.769411i
$6$	2.52214	−	0.722254i	1.02966	−	0.294859i
$7$		0			0
$7$		0			0
$8$	2.58363			0.913452
$9$	−2.64785	−	1.41027i	−0.882618	−	0.470092i
$10$	3.33853	+	0.570605i	1.05574	+	0.180441i
$11$	1.86048	+	1.07415i	0.560957	+	0.323869i	0.753529	−	0.657414i	$-0.228350\pi$
$11$	1.86048	+	1.07415i	0.560957	+	0.323869i	−0.192573	+	0.981283i	$0.561683\pi$
$12$	0.366529	+	0.354202i	0.105808	+	0.102249i
$13$	−3.48097			−0.965448			−0.482724	−	0.875773i	$-0.660353\pi$
$13$	−3.48097			−0.965448			−0.482724	+	0.875773i	$0.660353\pi$
$14$		0			0
$15$	−2.29182	−	3.12211i	−0.591745	−	0.806126i
$16$	2.25098	+	3.89881i	0.562745	+	0.974703i
$17$	3.09793	+	1.78859i	0.751359	+	0.433797i	0.826185	−	0.563399i	$-0.190507\pi$
$17$	3.09793	+	1.78859i	0.751359	+	0.433797i	−0.0748259	+	0.997197i	$0.523840\pi$
$18$	−0.155396	−	4.54141i	−0.0366272	−	1.07042i
$19$	1.05858	−	0.611171i	0.242855	−	0.140212i	−0.373633	−	0.927576i	$-0.621888\pi$
$19$	1.05858	−	0.611171i	0.242855	−	0.140212i	0.616488	+	0.787364i	$0.288555\pi$
$20$	0.228305	+	0.617156i	0.0510506	+	0.138000i
$21$		0			0
$22$			3.25401i			0.693757i
$23$	−0.757344	−	1.31176i	−0.157917	−	0.273521i	0.776200	−	0.630486i	$-0.217145\pi$
$23$	−0.757344	−	1.31176i	−0.157917	−	0.273521i	−0.934117	+	0.356966i	$0.883811\pi$
$24$	1.08412	−	4.34168i	0.221295	−	0.886241i
$25$	−0.919933	−	4.91464i	−0.183987	−	0.982929i
$26$	−2.63629	−	4.56619i	−0.517020	−	0.895504i
$27$	−3.48097	+	3.85783i	−0.669913	+	0.742439i
$28$		0			0
$29$		−	5.95645i		−	1.10608i	−0.833153	−	0.553042i	$-0.813467\pi$
$29$		−	5.95645i		−	1.10608i	0.833153	−	0.553042i	$-0.186533\pi$
$30$	2.35976	−	5.37082i	0.430832	−	0.980573i
$31$	−2.75098	−	1.58828i	−0.494091	−	0.285263i	0.232179	−	0.972673i	$-0.425414\pi$
$31$	−2.75098	−	1.58828i	−0.494091	−	0.285263i	−0.726270	+	0.687410i	$0.758748\pi$
$32$	−0.825899	+	1.43050i	−0.146000	+	0.252879i
$33$	2.58574	−	2.67573i	0.450120	−	0.465785i
$34$			5.41832i			0.929234i
$35$		0			0
$36$	0.749020	−	0.467309i	0.124837	−	0.0778848i
$37$	−6.75803	+	3.90175i	−1.11101	+	0.641444i	−0.939092	−	0.343667i	$-0.888331\pi$
$37$	−6.75803	+	3.90175i	−1.11101	+	0.641444i	−0.171921	+	0.985111i	$0.554998\pi$
$38$	1.60342	+	0.925734i	0.260109	+	0.150174i
$39$	−1.46065	+	5.84961i	−0.233892	+	0.936688i
$40$	3.69020	−	4.44503i	0.583471	−	0.702820i
$41$	11.8685			1.85355			0.926773	−	0.375622i	$-0.122571\pi$
$41$	11.8685			1.85355			0.926773	+	0.375622i	$0.122571\pi$
$42$		0			0
$43$		−	2.99294i		−	0.456419i	−0.973612	−	0.228209i	$-0.926713\pi$
$43$		−	2.99294i		−	0.456419i	0.973612	−	0.228209i	$-0.0732871\pi$
$44$	−0.547504	+	0.316101i	−0.0825393	+	0.0476541i
$45$	−6.20824	+	2.54122i	−0.925469	+	0.378823i
$46$	1.14714	−	1.98691i	0.169137	−	0.292953i
$47$	−5.28420	+	3.05084i	−0.770780	+	0.445010i	−0.833153	−	0.553043i	$-0.813467\pi$
$47$	−5.28420	+	3.05084i	−0.770780	+	0.445010i	0.0623727	+	0.998053i	$0.480133\pi$
$48$	7.49631	−	2.14668i	1.08200	−	0.309847i
$49$		0			0
$50$	5.75012	−	4.92881i	0.813190	−	0.697038i
$51$	4.30557	−	4.45542i	0.602901	−	0.623883i
$52$	0.512191	−	0.887140i	0.0710281	−	0.123024i
$53$	−5.61301	+	9.72202i	−0.771006	+	1.33542i	0.166006	+	0.986125i	$0.446913\pi$
$53$	−5.61301	+	9.72202i	−0.771006	+	1.33542i	−0.937012	+	0.349297i	$0.886420\pi$
$54$	−7.69683	−	1.64449i	−1.04741	−	0.223787i
$55$	4.50535	−	1.66667i	0.607502	−	0.224734i
$56$		0			0
$57$	−0.582853	−	2.03535i	−0.0772008	−	0.269589i
$58$	7.81342	−	4.51108i	1.02595	−	0.592334i
$59$	1.08467	−	1.87871i	0.141213	−	0.244587i	−0.786741	−	0.617283i	$-0.788233\pi$
$59$	1.08467	−	1.87871i	0.141213	−	0.244587i	0.927954	+	0.372696i	$0.121567\pi$
$60$	1.13290	−	0.124691i	0.146257	−	0.0160976i
$61$	2.94338	−	1.69936i	0.376861	−	0.217581i	−0.299591	−	0.954068i	$-0.596850\pi$
$61$	2.94338	−	1.69936i	0.376861	−	0.217581i	0.676452	+	0.736487i	$0.263517\pi$
$62$		−	4.81149i		−	0.611060i
$63$		0			0
$64$	6.50196			0.812745
$65$	−4.97186	+	5.98885i	−0.616684	+	0.742826i
$66$	5.46821	+	1.36542i	0.673090	+	0.168071i
$67$	8.93534	+	5.15882i	1.09163	+	0.630250i	0.934009	−	0.357250i	$-0.116286\pi$
$67$	8.93534	+	5.15882i	1.09163	+	0.630250i	0.157617	+	0.987500i	$0.449619\pi$
$68$	−0.911660	+	0.526347i	−0.110555	+	0.0638290i
$69$	−2.52214	+	0.722254i	−0.303630	+	0.0869491i
$70$		0			0
$71$			10.3968i			1.23387i	0.787013	+	0.616936i	$0.211626\pi$
$71$			10.3968i			1.23387i	−0.787013	+	0.616936i	$0.788374\pi$
$72$	−6.84108	−	3.64363i	−0.806229	−	0.429406i
$73$	−3.42779	+	5.93710i	−0.401192	+	0.694885i	−0.993870	−	0.110555i	$-0.964737\pi$
$73$	−3.42779	+	5.93710i	−0.401192	+	0.694885i	0.592678	+	0.805439i	$0.298071\pi$
$74$	−10.2363	−	5.90993i	−1.18995	−	0.687016i
$75$	−8.64485	−	0.516335i	−0.998221	−	0.0596212i
$76$			0.359711i			0.0412617i
$77$		0			0
$78$	−8.77950	+	2.51414i	−0.994082	+	0.284671i
$79$	0.941421	+	1.63059i	0.105918	+	0.183456i	0.914113	−	0.405460i	$-0.132889\pi$
$79$	0.941421	+	1.63059i	0.105918	+	0.183456i	−0.808195	+	0.588915i	$0.799555\pi$
$80$	9.92280	+	1.69595i	1.10940	+	0.189613i
$81$	5.02225	+	7.46840i	0.558028	+	0.829822i
$82$	8.98853	+	15.5686i	0.992617	+	1.71926i
$83$			9.10486i			0.999388i	0.866202	+	0.499694i	$0.166554\pi$
$83$			9.10486i			0.999388i	−0.866202	+	0.499694i	$0.833446\pi$
$84$		0			0
$85$	7.50196	−	2.77521i	0.813702	−	0.301014i
$86$	3.92601	−	2.26668i	0.423353	−	0.244423i
$87$	−10.0095	−	2.49939i	−1.07313	−	0.267963i
$88$	4.80681	+	2.77521i	0.512407	+	0.295839i
$89$	−0.889962	−	1.54146i	−0.0943358	−	0.163394i	0.814995	−	0.579467i	$-0.196739\pi$
$89$	−0.889962	−	1.54146i	−0.0943358	−	0.163394i	−0.909331	+	0.416073i	$0.863406\pi$
$90$	−8.03524	−	6.21913i	−0.846989	−	0.655554i
$91$		0			0
$92$	0.445743			0.0464719
$93$	−3.82337	+	3.95644i	−0.396465	+	0.410263i
$94$	−8.00392	−	4.62107i	−0.825541	−	0.476626i
$95$	0.460474	−	2.69417i	0.0472436	−	0.276416i
$96$	2.05733	+	1.98814i	0.209976	+	0.202914i
$97$	1.32584			0.134618			0.0673092	−	0.997732i	$-0.478559\pi$
$97$	1.32584			0.134618			0.0673092	+	0.997732i	$0.478559\pi$
$98$		0			0
$99$	−3.41144	−	5.46799i	−0.342863	−	0.549553i
$100$	1.38788	+	0.488693i	0.138788	+	0.0488693i
$101$	−6.71005	+	11.6221i	−0.667675	+	1.15645i	0.310878	+	0.950450i	$0.399377\pi$
$101$	−6.71005	+	11.6221i	−0.667675	+	1.15645i	−0.978553	+	0.205997i	$0.933956\pi$
$102$	9.10523	+	2.27359i	0.901553	+	0.225119i
$103$	−2.89342	−	5.01154i	−0.285097	−	0.493802i	0.687536	−	0.726150i	$-0.258692\pi$
$103$	−2.89342	−	5.01154i	−0.285097	−	0.493802i	−0.972633	+	0.232348i	$0.925359\pi$
$104$	−8.99355			−0.881890
$105$		0			0
$106$	−17.0039			−1.65157
$107$	−1.94323	−	3.36576i	−0.187859	−	0.325381i	0.756677	−	0.653788i	$-0.226821\pi$
$107$	−1.94323	−	3.36576i	−0.187859	−	0.325381i	−0.944536	+	0.328408i	$0.893488\pi$
$108$	−0.470993	−	1.45478i	−0.0453214	−	0.139986i
$109$	−2.60384	+	4.50998i	−0.249403	+	0.431978i	−0.963360	−	0.268211i	$-0.913568\pi$
$109$	−2.60384	+	4.50998i	−0.249403	+	0.431978i	0.713958	+	0.700189i	$0.246901\pi$
$110$	5.59837	+	4.64769i	0.533784	+	0.443140i
$111$	3.72097	+	12.9938i	0.353179	+	1.23331i
$112$		0			0
$113$	9.36235			0.880736			0.440368	−	0.897817i	$-0.354848\pi$
$113$	9.36235			0.880736			0.440368	+	0.897817i	$0.354848\pi$
$114$	2.22847	−	2.30602i	0.208715	−	0.215979i
$115$	−3.33853	−	0.570605i	−0.311320	−	0.0532092i
$116$	1.51803	+	0.876432i	0.140945	+	0.0813747i
$117$	9.21710	+	4.90913i	0.852121	+	0.453849i
$118$	3.28589			0.302490
$119$		0			0
$120$	−5.92121	−	8.06639i	−0.540530	−	0.736357i
$121$	−3.19240	−	5.52940i	−0.290218	−	0.502673i
$122$	4.45830	+	2.57400i	0.403636	+	0.233039i
$123$	4.98015	−	19.9444i	0.449045	−	1.79833i
$124$	0.809559	−	0.467399i	0.0727006	−	0.0419737i
$125$	−9.76936	−	5.43687i	−0.873798	−	0.486289i
$126$		0			0
$127$			9.57778i			0.849891i	0.905219	+	0.424945i	$0.139707\pi$
$127$			9.57778i			0.849891i	−0.905219	+	0.424945i	$0.860293\pi$
$128$	6.57602	+	11.3900i	0.581243	+	1.00674i
$129$	−5.02950	−	1.25587i	−0.442823	−	0.110573i
$130$	−11.6213	−	1.98626i	−1.01926	−	0.174206i
$131$	4.72508	+	8.18408i	0.412832	+	0.715047i	0.995198	−	0.0978802i	$-0.0312062\pi$
$131$	4.72508	+	8.18408i	0.412832	+	0.715047i	−0.582366	+	0.812927i	$0.697873\pi$
$132$	0.301455	+	1.05269i	0.0262383	+	0.0916253i
$133$		0			0
$134$			15.6280i			1.35005i
$135$	1.66536	+	11.4990i	0.143331	+	0.989675i
$136$	8.00392	+	4.62107i	0.686330	+	0.396253i
$137$	−5.35276	+	9.27125i	−0.457317	+	0.792096i	−0.998818	−	0.0486038i	$-0.984523\pi$
$137$	−5.35276	+	9.27125i	−0.457317	+	0.792096i	0.541501	+	0.840700i	$0.317856\pi$
$138$	−2.85755	−	2.76144i	−0.243251	−	0.235070i
$139$		−	4.11136i		−	0.348721i	−0.984682	−	0.174360i	$-0.944214\pi$
$139$		−	4.11136i		−	0.348721i	0.984682	−	0.174360i	$-0.0557858\pi$
$140$		0			0
$141$	2.90948	+	10.1600i	0.245022	+	0.855629i
$142$	−13.6381	+	7.87395i	−1.14448	+	0.660767i
$143$	−6.47629	−	3.73909i	−0.541575	−	0.312678i
$144$	−0.461868	−	13.4980i	−0.0384890	−	1.12483i
$145$	−10.2478	−	8.50758i	−0.851033	−	0.706516i
$146$	−10.3841			−0.859390
$147$		0			0
$148$		−	2.29642i		−	0.188764i
$149$	−2.20294	+	1.27187i	−0.180472	+	0.104196i	−0.587514	−	0.809214i	$-0.699893\pi$
$149$	−2.20294	+	1.27187i	−0.180472	+	0.104196i	0.407042	+	0.913409i	$0.366560\pi$
$150$	−5.86982	−	11.7310i	−0.479269	−	0.957832i
$151$	2.80956	−	4.86630i	0.228639	−	0.396014i	−0.728766	−	0.684763i	$-0.759906\pi$
$151$	2.80956	−	4.86630i	0.228639	−	0.396014i	0.957405	+	0.288749i	$0.0932392\pi$
$152$	2.73498	−	1.57904i	0.221836	−	0.128077i
$153$	−5.68046	−	9.10486i	−0.459238	−	0.736084i
$154$		0			0
$155$	−6.66178	+	2.46440i	−0.535087	+	0.197946i
$156$	−1.27588	−	1.23297i	−0.102152	−	0.0987164i
$157$	6.96194	−	12.0584i	0.555623	−	0.962368i	−0.442231	−	0.896901i	$-0.645813\pi$
$157$	6.96194	−	12.0584i	0.555623	−	0.962368i	0.997855	−	0.0654670i	$-0.0208537\pi$
$158$	−1.42596	+	2.46983i	−0.113443	+	0.196489i
$159$	13.9821	+	13.5119i	1.10885	+	1.07156i
$160$	1.28148	+	3.46410i	0.101310	+	0.273861i
$161$		0			0
$162$	−5.99317	+	12.2441i	−0.470868	+	0.961990i
$163$	3.52533	−	2.03535i	0.276125	−	0.159421i	−0.355543	−	0.934660i	$-0.615704\pi$
$163$	3.52533	−	2.03535i	0.276125	−	0.159421i	0.631668	+	0.775239i	$0.282371\pi$
$164$	−1.74633	+	3.02473i	−0.136366	+	0.236192i
$165$	−0.910270	−	8.27039i	−0.0708644	−	0.643849i
$166$	−11.9434	+	6.89551i	−0.926986	+	0.535196i
$167$		−	13.9722i		−	1.08120i	−0.841279	−	0.540602i	$-0.818197\pi$
$167$		−	13.9722i		−	1.08120i	0.841279	−	0.540602i	$-0.181803\pi$
$168$		0			0
$169$	−0.882841			−0.0679109
$170$	9.32197	+	7.73897i	0.714963	+	0.593552i
$171$	−3.66488	+	0.125403i	−0.280261	+	0.00958983i
$172$	0.762763	+	0.440382i	0.0581602	+	0.0335788i
$173$	−8.66256	+	5.00133i	−0.658602	+	0.380244i	−0.791744	−	0.610853i	$-0.790827\pi$
$173$	−8.66256	+	5.00133i	−0.658602	+	0.380244i	0.133142	+	0.991097i	$0.457493\pi$
$174$	−4.30206	−	15.0230i	−0.326139	−	1.13889i
$175$		0			0
$176$			9.67157i			0.729022i
$177$	−2.70195	−	2.61107i	−0.203091	−	0.196260i
$178$	1.34801	−	2.33483i	0.101038	−	0.175003i
$179$	14.0378	+	8.10475i	1.04924	+	0.605777i	0.922436	−	0.386151i	$-0.126196\pi$
$179$	14.0378	+	8.10475i	1.04924	+	0.605777i	0.126801	+	0.991928i	$0.459529\pi$
$180$	0.265840	−	1.95611i	0.0198146	−	0.145800i
$181$		−	19.4123i		−	1.44290i	−0.692465	−	0.721451i	$-0.743475\pi$
$181$		−	19.4123i		−	1.44290i	0.692465	−	0.721451i	$-0.256525\pi$
$182$		0			0
$183$	−1.62062	−	5.65929i	−0.119800	−	0.418347i
$184$	−1.95670	−	3.38910i	−0.144250	−	0.249848i
$185$	−2.93969	+	17.1997i	−0.216130	+	1.26455i
$186$	−8.08550	−	2.01896i	−0.592857	−	0.148037i
$187$	3.84243	+	6.65529i	0.280987	+	0.486683i
$188$		−	1.79560i		−	0.130958i
$189$		0			0
$190$	3.88284	−	1.43639i	0.281691	−	0.104206i
$191$	11.0018	−	6.35188i	0.796061	−	0.459606i	−0.0460309	−	0.998940i	$-0.514657\pi$
$191$	11.0018	−	6.35188i	0.796061	−	0.459606i	0.842092	+	0.539334i	$0.181324\pi$
$192$	2.72830	−	10.9262i	0.196898	−	0.788534i
$193$	−18.0302	−	10.4098i	−1.29785	−	0.749311i	−0.317813	−	0.948153i	$-0.602949\pi$
$193$	−18.0302	−	10.4098i	−1.29785	−	0.749311i	−0.980032	+	0.198842i	$0.936282\pi$
$194$	1.00411	+	1.73918i	0.0720912	+	0.124866i
$195$	7.97775	+	10.8680i	0.571298	+	0.778272i
$196$		0			0
$197$	−2.23465			−0.159212			−0.0796062	−	0.996826i	$-0.525366\pi$
$197$	−2.23465			−0.159212			−0.0796062	+	0.996826i	$0.525366\pi$
$198$	4.58904	−	8.61613i	0.326129	−	0.612322i
$199$	21.5831	+	12.4610i	1.52998	+	0.883337i	0.999362	+	0.0357284i	$0.0113751\pi$
$199$	21.5831	+	12.4610i	1.52998	+	0.883337i	0.530622	+	0.847608i	$0.321958\pi$
$200$	−2.37677	−	12.6976i	−0.168063	−	0.897859i
$201$	12.4185	−	12.8507i	0.875936	−	0.906421i
$202$	−20.3273			−1.43022
$203$		0			0
$204$	0.501960	+	1.75286i	0.0351442	+	0.122725i
$205$	16.9517	−	20.4192i	1.18396	−	1.42614i
$206$	4.38262	−	7.59093i	0.305352	−	0.528885i
$207$	0.155396	+	4.54141i	0.0108008	+	0.315650i
$208$	−7.83560	−	13.5716i	−0.543301	−	0.941025i
$209$	2.62596			0.181641
$210$		0			0
$211$	−6.61520			−0.455409			−0.227705	−	0.973730i	$-0.573122\pi$
$211$	−6.61520			−0.455409			−0.227705	+	0.973730i	$0.573122\pi$
$212$	−1.65180	−	2.86100i	−0.113446	−	0.196494i
$213$	17.4713	+	4.36261i	1.19712	+	0.298921i
$214$	2.94338	−	5.09808i	0.201205	−	0.348498i
$215$	−5.14922	−	4.27481i	−0.351174	−	0.291539i
$216$	−8.99355	+	9.96721i	−0.611934	+	0.678183i
$217$		0			0
$218$	−7.88801			−0.534243
$219$	8.53868	+	8.25151i	0.576991	+	0.557585i
$220$	−0.238160	+	1.39344i	−0.0160567	+	0.0939459i
$221$	−10.7838	−	6.22604i	−0.725398	−	0.418808i
$222$	−14.2266	+	14.7218i	−0.954830	+	0.988060i
$223$	−4.31027			−0.288637			−0.144318	−	0.989531i	$-0.546099\pi$
$223$	−4.31027			−0.288637			−0.144318	+	0.989531i	$0.546099\pi$
$224$		0			0
$225$	−4.49515	+	14.3106i	−0.299677	+	0.954041i
$226$	7.09052	+	12.2811i	0.471654	+	0.816929i
$227$	9.62260	+	5.55561i	0.638675	+	0.368739i	0.784104	−	0.620630i	$-0.213123\pi$
$227$	9.62260	+	5.55561i	0.638675	+	0.368739i	−0.145429	+	0.989369i	$0.546456\pi$
$228$	0.604478	+	0.150939i	0.0400326	+	0.00999617i
$229$	−8.63774	+	4.98700i	−0.570798	+	0.329550i	−0.757468	−	0.652872i	$-0.773564\pi$
$229$	−8.63774	+	4.98700i	−0.570798	+	0.329550i	0.186670	+	0.982423i	$0.440230\pi$
$230$	−1.77992	−	4.81149i	−0.117365	−	0.317261i
$231$		0			0
$232$		−	15.3893i		−	1.01036i
$233$	−10.3144	−	17.8650i	−0.675716	−	1.17037i	−0.976259	−	0.216606i	$-0.930501\pi$
$233$	−10.3144	−	17.8650i	−0.675716	−	1.17037i	0.300543	−	0.953768i	$-0.402832\pi$
$234$	0.540929	+	15.8085i	0.0353616	+	1.03343i
$235$	−2.29859	+	13.4487i	−0.149943	+	0.877299i
$236$	0.319198	+	0.552868i	0.0207780	+	0.0359886i
$237$	3.13516	−	0.897801i	0.203650	−	0.0583184i
$238$		0			0
$239$		−	2.87353i		−	0.185873i	−0.995672	−	0.0929365i	$-0.970375\pi$
$239$		−	2.87353i		−	0.185873i	0.995672	−	0.0929365i	$-0.0296254\pi$
$240$	7.01369	−	15.9632i	0.452732	−	1.03042i
$241$	−22.5792	−	13.0361i	−1.45445	−	0.839728i	−0.455722	−	0.890122i	$-0.650619\pi$
$241$	−22.5792	−	13.0361i	−1.45445	−	0.839728i	−0.998729	+	0.0503940i	$0.983952\pi$
$242$	4.83549	−	8.37532i	0.310837	−	0.538386i
$243$	14.6577	−	5.30584i	0.940292	−	0.340370i
$244$			1.00018i			0.0640298i
$245$		0			0
$246$	29.9340	−	8.57206i	1.90852	−	0.546534i
$247$	−3.68488	+	2.12747i	−0.234464	+	0.135368i
$248$	−7.10752	−	4.10353i	−0.451328	−	0.260574i
$249$	15.3003	+	3.82050i	0.969617	+	0.242114i
$250$	−0.266908	−	16.9326i	−0.0168807	−	1.07091i
$251$	−0.161120			−0.0101698			−0.00508489	−	0.999987i	$-0.501619\pi$
$251$	−0.161120			−0.0101698			−0.00508489	+	0.999987i	$0.501619\pi$
$252$		0			0
$253$		−	3.25401i		−	0.204578i
$254$	−12.5637	+	7.25368i	−0.788319	+	0.455136i
$255$	−1.51571	−	13.7712i	−0.0949174	−	0.862387i
$256$	−3.45866	+	5.99057i	−0.216166	+	0.374411i
$257$	−11.3712	+	6.56514i	−0.709314	+	0.409522i	−0.810807	−	0.585314i	$-0.800971\pi$
$257$	−11.3712	+	6.56514i	−0.709314	+	0.409522i	0.101493	+	0.994836i	$0.467638\pi$
$258$	−2.16166	−	7.54861i	−0.134579	−	0.469956i
$259$		0			0
$260$	−0.794725	−	2.14830i	−0.0492867	−	0.133232i
$261$	−8.40022	+	15.7718i	−0.519961	+	0.976249i
$262$	−7.15703	+	12.3963i	−0.442163	+	0.765848i
$263$	−8.86526	+	15.3551i	−0.546655	+	0.946835i	0.451846	+	0.892096i	$0.350766\pi$
$263$	−8.86526	+	15.3551i	−0.546655	+	0.946835i	−0.998501	+	0.0547384i	$0.982568\pi$
$264$	6.68061	−	6.91311i	0.411163	−	0.425473i
$265$	8.70925	+	23.5429i	0.535005	+	1.44623i
$266$		0			0
$267$	−2.96379	+	0.848727i	−0.181381	+	0.0519412i
$268$	−2.62950	+	1.51814i	−0.160622	+	0.0927352i
$269$	−2.20294	+	3.81561i	−0.134316	+	0.232642i	−0.925336	−	0.379148i	$-0.876217\pi$
$269$	−2.20294	+	3.81561i	−0.134316	+	0.232642i	0.791020	+	0.611790i	$0.209550\pi$
$270$	−13.8226	+	10.8932i	−0.841219	+	0.662941i
$271$	−20.4287	+	11.7945i	−1.24095	+	0.716465i	−0.969288	−	0.245927i	$-0.920908\pi$
$271$	−20.4287	+	11.7945i	−1.24095	+	0.716465i	−0.271665	+	0.962392i	$0.587574\pi$
$272$			16.1043i			0.976469i
$273$		0			0
$274$	−16.2155			−0.979615
$275$	3.56755	−	10.1318i	0.215131	−	0.610968i
$276$	0.187039	−	0.749051i	0.0112584	−	0.0450876i
$277$	11.1127	+	6.41589i	0.667695	+	0.385494i	0.795203	−	0.606344i	$-0.207364\pi$
$277$	11.1127	+	6.41589i	0.667695	+	0.385494i	−0.127508	+	0.991838i	$0.540698\pi$
$278$	5.39311	−	3.11371i	0.323457	−	0.186748i
$279$	5.04428	+	8.08517i	0.301993	+	0.484046i
$280$		0			0
$281$		−	21.2397i		−	1.26706i	−0.773719	−	0.633528i	$-0.781606\pi$
$281$		−	21.2397i		−	1.26706i	0.773719	−	0.633528i	$-0.218394\pi$
$282$	−11.1240	+	11.5112i	−0.662426	+	0.685480i
$283$	3.27706	−	5.67603i	0.194801	−	0.337405i	−0.752034	−	0.659124i	$-0.770927\pi$
$283$	3.27706	−	5.67603i	0.194801	−	0.337405i	0.946835	+	0.321719i	$0.104261\pi$
$284$	−2.64967	−	1.52979i	−0.157229	−	0.0907761i
$285$	−4.33421	−	1.90431i	−0.256737	−	0.112802i
$286$		−	11.3271i		−	0.669786i
$287$		0			0
$288$	4.20426	−	2.62301i	0.247738	−	0.154562i
$289$	−2.10188	−	3.64056i	−0.123640	−	0.214151i
$290$	3.39878	−	19.8858i	0.199583	−	1.16773i
$291$	0.556336	−	2.22801i	0.0326130	−	0.130608i
$292$	−1.00873	−	1.74717i	−0.0590315	−	0.102245i
$293$			3.71937i			0.217288i	0.994081	+	0.108644i	$0.0346509\pi$
$293$			3.71937i			0.217288i	−0.994081	+	0.108644i	$0.965349\pi$
$294$		0			0
$295$	−1.68300	−	4.54949i	−0.0979881	−	0.264882i
$296$	−17.4603	+	10.0807i	−1.01486	+	0.585928i
$297$	−10.6202	+	3.43834i	−0.616245	+	0.199513i
$298$	−3.33677	−	1.92648i	−0.193294	−	0.111598i
$299$	2.63629	+	4.56619i	0.152461	+	0.264070i
$300$	1.40359	−	2.12720i	0.0810366	−	0.122814i
$301$		0			0
$302$	8.51121			0.489765
$303$	16.7149	+	16.1527i	0.960245	+	0.927949i
$304$	4.76568	+	2.75147i	0.273331	+	0.157808i
$305$	1.28035	−	7.49115i	0.0733125	−	0.428942i
$306$	7.64132	−	14.3469i	0.436825	−	0.820158i
$307$	11.2102			0.639800			0.319900	−	0.947451i	$-0.396351\pi$
$307$	11.2102			0.639800			0.319900	+	0.947451i	$0.396351\pi$
$308$		0			0
$309$	−9.63578	+	2.75935i	−0.548160	+	0.156974i
$310$	−8.27796	−	6.87225i	−0.470157	−	0.390317i
$311$	9.46050	−	16.3861i	0.536456	−	0.929168i	−0.462636	−	0.886548i	$-0.653096\pi$
$311$	9.46050	−	16.3861i	0.536456	−	0.929168i	0.999091	−	0.0426199i	$-0.0135704\pi$
$312$	−3.77380	+	15.1133i	−0.213649	+	0.855620i
$313$	8.19024	+	14.1859i	0.462940	+	0.801835i	0.999106	−	0.0422775i	$-0.0134614\pi$
$313$	8.19024	+	14.1859i	0.462940	+	0.801835i	−0.536166	+	0.844112i	$0.680128\pi$
$314$	21.0903			1.19020
$315$		0			0
$316$	−0.554083			−0.0311696
$317$	5.05836	+	8.76134i	0.284106	+	0.492086i	0.972392	−	0.233353i	$-0.0749699\pi$
$317$	5.05836	+	8.76134i	0.284106	+	0.492086i	−0.688286	+	0.725439i	$0.741637\pi$
$318$	−7.13503	+	28.5743i	−0.400113	+	1.60237i
$319$	6.39812	−	11.0819i	0.358226	−	0.620466i
$320$	9.28673	−	11.1863i	0.519144	−	0.625335i
$321$	−6.47141	+	1.85319i	−0.361199	+	0.103435i
$322$		0			0
$323$	4.37254			0.243295
$324$	−2.64233	+	0.181040i	−0.146796	+	0.0100578i
$325$	3.20226	+	17.1077i	0.177629	+	0.948966i
$326$	5.33977	+	3.08292i	0.295743	+	0.170747i
$327$	6.48622	+	6.26807i	0.358689	+	0.346625i
$328$	30.6638			1.69313
$329$		0			0
$330$	10.1594	−	7.45759i	0.559255	−	0.410527i
$331$	−9.63774	−	16.6931i	−0.529738	−	0.917533i	−0.999398	−	0.0346861i	$-0.988957\pi$
$331$	−9.63774	−	16.6931i	−0.529738	−	0.917533i	0.469660	−	0.882847i	$-0.344376\pi$
$332$	−2.32041	−	1.33969i	−0.127349	−	0.0735251i
$333$	23.3968	−	0.800582i	1.28214	−	0.0438716i
$334$	18.3282	−	10.5818i	1.00287	−	0.579009i
$335$	21.6378	−	8.00452i	1.18220	−	0.437334i
$336$		0			0
$337$			23.6381i			1.28765i	0.765174	+	0.643824i	$0.222653\pi$
$337$			23.6381i			1.28765i	−0.765174	+	0.643824i	$0.777347\pi$
$338$	−0.668614	−	1.15807i	−0.0363678	−	0.0629909i
$339$	3.92855	−	15.7330i	0.213369	−	0.854499i
$340$	−0.396565	+	2.32025i	−0.0215068	+	0.125833i
$341$	−3.41210	−	5.90993i	−0.184776	−	0.320041i
$342$	−2.94008	−	4.71247i	−0.158981	−	0.254821i
$343$		0			0
$344$		−	7.73266i		−	0.416917i
$345$	−2.35976	+	5.37082i	−0.127045	+	0.289155i
$346$	−13.1211	−	7.57546i	−0.705394	−	0.407259i
$347$	7.95360	−	13.7760i	0.426971	−	0.739536i	−0.569631	−	0.821901i	$-0.692914\pi$
$347$	7.95360	−	13.7760i	0.426971	−	0.739536i	0.996602	+	0.0823644i	$0.0262471\pi$
$348$	2.10979	−	2.18321i	0.113096	−	0.117032i
$349$		−	0.0192397i		−	0.00102988i	−1.00000		0.000514938i	$-0.999836\pi$
$349$		−	0.0192397i		−	0.00102988i	1.00000		0.000514938i	$-0.000163910\pi$
$350$		0			0
$351$	12.1172	−	13.4290i	0.646766	−	0.716786i
$352$	−3.07314	+	1.77428i	−0.163799	+	0.0945695i
$353$	−22.0143	−	12.7100i	−1.17170	−	0.676484i	−0.217624	−	0.976033i	$-0.569830\pi$
$353$	−22.0143	−	12.7100i	−1.17170	−	0.676484i	−0.954081	+	0.299549i	$0.903164\pi$
$354$	1.37880	−	5.52178i	0.0732821	−	0.293479i
$355$	17.8872	+	14.8497i	0.949355	+	0.788141i
$356$	0.523797			0.0277612
$357$		0			0
$358$			24.5523i			1.29763i
$359$	20.9396	−	12.0895i	1.10515	−	0.638057i	0.167579	−	0.985859i	$-0.446405\pi$
$359$	20.9396	−	12.0895i	1.10515	−	0.638057i	0.937568	+	0.347801i	$0.113072\pi$
$360$	−16.0398	+	6.56558i	−0.845372	+	0.346037i
$361$	−8.75294	+	15.1605i	−0.460681	+	0.797923i
$362$	25.4642	−	14.7018i	1.33837	−	0.772708i
$363$	−10.6315	+	3.04448i	−0.558007	+	0.159794i
$364$		0			0
$365$	5.31861	+	14.3773i	0.278389	+	0.752542i
$366$	6.19625	−	6.41189i	0.323883	−	0.335155i
$367$	−4.53636	+	7.85721i	−0.236796	+	0.410143i	−0.959793	−	0.280708i	$-0.909431\pi$
$367$	−4.53636	+	7.85721i	−0.236796	+	0.410143i	0.722997	+	0.690851i	$0.242764\pi$
$368$	3.40953	−	5.90548i	0.177734	−	0.307845i
$369$	−31.4260	−	16.7378i	−1.63597	−	0.871336i
$370$	−24.7883	+	9.16996i	−1.28868	+	0.476724i
$371$		0			0
$372$	−0.445743	−	1.55655i	−0.0231107	−	0.0807035i
$373$	−13.4785	+	7.78183i	−0.697891	+	0.402928i	−0.806562	−	0.591150i	$-0.798674\pi$
$373$	−13.4785	+	7.78183i	−0.697891	+	0.402928i	0.108670	+	0.994078i	$0.465341\pi$
$374$	−5.82009	+	10.0807i	−0.300950	+	0.521260i
$375$	−13.2357	+	14.1356i	−0.683491	+	0.729959i
$376$	−13.6524	+	7.88224i	−0.704071	+	0.406496i
$377$			20.7342i			1.06787i
$378$		0			0
$379$	34.0984			1.75152			0.875758	−	0.482751i	$-0.160362\pi$
$379$	34.0984			1.75152			0.875758	+	0.482751i	$0.160362\pi$
$380$	0.618867	+	0.513775i	0.0317472	+	0.0263561i
$381$	16.0950	+	4.01894i	0.824573	+	0.205897i
$382$	16.6643	+	9.62112i	0.852618	+	0.492259i
$383$	−9.15965	+	5.28833i	−0.468036	+	0.270221i	−0.715417	−	0.698697i	$-0.753763\pi$
$383$	−9.15965	+	5.28833i	−0.468036	+	0.270221i	0.247381	+	0.968918i	$0.420430\pi$
$384$	21.8997	−	6.27133i	1.11757	−	0.320032i
$385$		0			0
$386$		−	31.5351i		−	1.60509i
$387$	−4.22087	+	7.92486i	−0.214559	+	0.402843i
$388$	−0.195084	+	0.337895i	−0.00990388	+	0.0171540i
$389$	14.6659	+	8.46736i	0.743590	+	0.429312i	0.823373	−	0.567500i	$-0.192089\pi$
$389$	14.6659	+	8.46736i	0.743590	+	0.429312i	−0.0797828	+	0.996812i	$0.525423\pi$
$390$	−8.21426	+	18.6957i	−0.415945	+	0.946692i
$391$		−	5.41832i		−	0.274016i
$392$		0			0
$393$	15.7357	−	4.50615i	0.793760	−	0.227305i
$394$	−1.69240	−	2.93132i	−0.0852619	−	0.147678i
$395$	4.14998	+	0.709293i	0.208808	+	0.0356884i
$396$	1.89550	−	0.0648594i	0.0952524	−	0.00325931i
$397$	0.203913	+	0.353188i	0.0102341	+	0.0177260i	0.871097	−	0.491111i	$-0.163409\pi$
$397$	0.203913	+	0.353188i	0.0102341	+	0.0177260i	−0.860863	+	0.508837i	$0.830076\pi$
$398$			37.7491i			1.89219i
$399$		0			0
$400$	17.0905	−	14.6494i	0.854526	−	0.732470i
$401$	−24.2302	+	13.9893i	−1.21000	+	0.698593i	−0.962759	−	0.270361i	$-0.912857\pi$
$401$	−24.2302	+	13.9893i	−1.21000	+	0.698593i	−0.247240	+	0.968954i	$0.579524\pi$
$402$	26.2622	+	6.55769i	1.30984	+	0.327068i
$403$	9.57608	+	5.52875i	0.477019	+	0.275407i
$404$	−1.97464	−	3.42017i	−0.0982418	−	0.170160i
$405$	20.0223	+	2.02654i	0.994917	+	0.100700i
$406$		0			0
$407$	−16.7643			−0.830974
$408$	11.1240	−	11.5112i	0.550721	−	0.569888i
$409$	−2.26960	−	1.31036i	−0.112225	−	0.0647929i	0.442837	−	0.896602i	$-0.353972\pi$
$409$	−2.26960	−	1.31036i	−0.112225	−	0.0647929i	−0.555062	+	0.831809i	$0.687305\pi$
$410$	39.6233	+	6.77221i	1.95686	+	0.334456i
$411$	13.3338	+	12.8854i	0.657709	+	0.635589i
$412$	1.70295			0.0838984
$413$		0			0
$414$	−5.83954	+	3.64325i	−0.286998	+	0.179056i
$415$	15.6645	+	13.0045i	0.768940	+	0.638363i
$416$	2.87493	−	4.97953i	0.140955	−	0.244141i
$417$	−6.90895	−	1.72517i	−0.338333	−	0.0844820i
$418$	1.98876	+	3.44462i	0.0972732	+	0.168482i
$419$	8.39649			0.410195			0.205098	−	0.978742i	$-0.434249\pi$
$419$	8.39649			0.410195			0.205098	+	0.978742i	$0.434249\pi$
$420$		0			0
$421$	−7.84952			−0.382562			−0.191281	−	0.981535i	$-0.561264\pi$
$421$	−7.84952			−0.382562			−0.191281	+	0.981535i	$0.561264\pi$
$422$	−5.00998	−	8.67754i	−0.243882	−	0.422416i
$423$	18.2943	−	0.625987i	0.889500	−	0.0304365i
$424$	−14.5020	+	25.1181i	−0.704277	+	1.21984i
$425$	5.94040	−	16.8706i	0.288152	−	0.818345i
$426$	7.50912	+	26.2222i	0.363818	+	1.27047i
$427$		0			0
$428$	1.14371			0.0552831
$429$	−9.00089	+	9.31415i	−0.434567	+	0.449691i
$430$	1.70778	−	9.99203i	0.0823567	−	0.481858i
$431$	−10.6154	−	6.12880i	−0.511326	−	0.295214i	0.222053	−	0.975035i	$-0.428724\pi$
$431$	−10.6154	−	6.12880i	−0.511326	−	0.295214i	−0.733378	+	0.679821i	$0.762058\pi$
$432$	−22.8765	−	4.88776i	−1.10065	−	0.235162i
$433$	−5.13957			−0.246992			−0.123496	−	0.992345i	$-0.539411\pi$
$433$	−5.13957			−0.246992			−0.123496	+	0.992345i	$0.539411\pi$
$434$		0			0
$435$	−18.5967	+	13.6511i	−0.891643	+	0.654519i
$436$	−0.766259	−	1.32720i	−0.0366971	−	0.0635613i
$437$	−1.60342	−	0.925734i	−0.0767019	−	0.0442838i
$438$	−4.35726	+	17.4499i	−0.208198	+	0.833790i
$439$	14.4620	−	8.34964i	0.690234	−	0.398507i	−0.113466	−	0.993542i	$-0.536195\pi$
$439$	14.4620	−	8.34964i	0.690234	−	0.398507i	0.803700	+	0.595035i	$0.202862\pi$
$440$	11.6402	−	4.30607i	0.554924	−	0.205284i
$441$		0			0
$442$		−	18.8610i		−	0.897127i
$443$	0.126110	+	0.218429i	0.00599167	+	0.0103779i	0.869006	−	0.494802i	$-0.164759\pi$
$443$	0.126110	+	0.218429i	0.00599167	+	0.0103779i	−0.863014	+	0.505180i	$0.831426\pi$
$444$	−3.85902	−	0.963602i	−0.183141	−	0.0457305i
$445$	−3.92314	−	0.670523i	−0.185975	−	0.0317858i
$446$	−3.26436	−	5.65403i	−0.154572	−	0.267726i
$447$	1.21294	+	4.23563i	0.0573700	+	0.200339i
$448$		0			0
$449$		−	28.8710i		−	1.36250i	−0.732049	−	0.681252i	$-0.761436\pi$
$449$		−	28.8710i		−	1.36250i	0.732049	−	0.681252i	$-0.238564\pi$
$450$	−22.1764	+	4.94150i	−1.04541	+	0.232945i
$451$	22.0811	+	12.7485i	1.03976	+	0.600305i
$452$	−1.37758	+	2.38603i	−0.0647958	+	0.112230i
$453$	−6.99867	−	6.76329i	−0.328826	−	0.317767i
$454$			16.8300i			0.789873i
$455$		0			0
$456$	−1.50588	−	5.25859i	−0.0705193	−	0.246256i
$457$	20.8483	−	12.0368i	0.975242	−	0.563056i	0.0744117	−	0.997228i	$-0.476292\pi$
$457$	20.8483	−	12.0368i	0.975242	−	0.563056i	0.900830	+	0.434171i	$0.142959\pi$
$458$	−13.0835	−	7.55375i	−0.611351	−	0.352964i
$459$	−17.6839	+	5.72525i	−0.825413	+	0.267232i
$460$	0.636654	−	0.766881i	0.0296841	−	0.0357560i
$461$	−39.8709			−1.85697			−0.928486	−	0.371367i	$-0.878889\pi$
$461$	−39.8709			−1.85697			−0.928486	+	0.371367i	$0.878889\pi$
$462$		0			0
$463$		−	29.8417i		−	1.38686i	−0.720524	−	0.693430i	$-0.756099\pi$
$463$		−	29.8417i		−	1.38686i	0.720524	−	0.693430i	$-0.243901\pi$
$464$	23.2231	−	13.4078i	1.07810	−	0.622443i
$465$	1.34596	+	12.2289i	0.0624173	+	0.567102i
$466$	15.6230	−	27.0599i	0.723723	−	1.25353i
$467$	−3.62140	+	2.09082i	−0.167579	+	0.0967515i	−0.581444	−	0.813587i	$-0.697512\pi$
$467$	−3.62140	+	2.09082i	−0.167579	+	0.0967515i	0.413865	+	0.910338i	$0.364179\pi$
$468$	−2.60732	+	1.62669i	−0.120523	+	0.0751937i
$469$		0			0
$470$	−19.3823	+	7.17013i	−0.894039	+	0.330733i
$471$	−17.3423	−	16.7591i	−0.799093	−	0.772218i
$472$	2.80240	−	4.85390i	0.128991	−	0.223419i
$473$	3.21487	−	5.56831i	0.147820	−	0.256031i
$474$	3.55209	+	3.43263i	0.163153	+	0.157666i
$475$	−3.97751	−	4.64030i	−0.182501	−	0.212912i
$476$		0			0
$477$	28.5731	−	17.8266i	1.30827	−	0.816223i
$478$	3.76937	−	2.17625i	0.172407	−	0.0995393i
$479$	13.9676	−	24.1926i	0.638196	−	1.10539i	−0.347632	−	0.937631i	$-0.613014\pi$
$479$	13.9676	−	24.1926i	0.638196	−	1.10539i	0.985828	−	0.167757i	$-0.0536525\pi$
$480$	6.35899	−	0.699894i	0.290247	−	0.0319456i
$481$	23.5245	−	13.5819i	1.07262	−	0.619280i
$482$		−	39.4912i		−	1.79878i
$483$		0			0
$484$	1.87892			0.0854055
$485$	1.89369	−	2.28104i	0.0859880	−	0.103577i
$486$	18.0609	+	15.2090i	0.819259	+	0.689895i
$487$	−32.2536	−	18.6216i	−1.46155	−	0.843826i	−0.462466	−	0.886637i	$-0.653035\pi$
$487$	−32.2536	−	18.6216i	−1.46155	−	0.843826i	−0.999083	+	0.0428116i	$0.986368\pi$
$488$	7.60462	−	4.39053i	0.344245	−	0.198750i
$489$	−1.94104	−	6.77821i	−0.0877770	−	0.306521i
$490$		0			0
$491$		−	5.90572i		−	0.266522i	−0.991081	−	0.133261i	$-0.957455\pi$
$491$		−	5.90572i		−	0.266522i	0.991081	−	0.133261i	$-0.0425448\pi$
$492$	4.35015	+	4.20384i	0.196120	+	0.189524i
$493$	10.6536	−	18.4527i	0.479816	−	0.831066i
$494$	−5.58145	−	3.22245i	−0.251121	−	0.144985i
$495$	−14.2800	−	1.94068i	−0.641837	−	0.0872272i
$496$		−	14.3007i		−	0.642122i
$497$		0			0
$498$	6.57602	+	22.9637i	0.294678	+	1.02903i
$499$	9.37010	+	16.2295i	0.419463	+	0.726532i	0.995886	−	0.0906204i	$-0.0288850\pi$
$499$	9.37010	+	16.2295i	0.419463	+	0.726532i	−0.576422	+	0.817152i	$0.695552\pi$
$500$	2.82308	−	1.68978i	0.126252	−	0.0755693i
$501$	−23.4797	−	5.86290i	−1.04899	−	0.261935i
$502$	−0.122023	−	0.211350i	−0.00544615	−	0.00943301i
$503$		−	32.0398i		−	1.42858i	−0.699849	−	0.714291i	$-0.746749\pi$
$503$		−	32.0398i		−	1.42858i	0.699849	−	0.714291i	$-0.253251\pi$
$504$		0			0
$505$	10.4114	+	28.1442i	0.463303	+	1.25240i
$506$	4.26847	−	2.46440i	0.189757	−	0.109556i
$507$	−0.370450	+	1.48357i	−0.0164523	+	0.0658878i
$508$	−2.44094	−	1.40928i	−0.108299	−	0.0625265i
$509$	−9.57465	−	16.5838i	−0.424389	−	0.735063i	0.571974	−	0.820272i	$-0.306178\pi$
$509$	−9.57465	−	16.5838i	−0.424389	−	0.735063i	−0.996363	+	0.0852085i	$0.972844\pi$
$510$	16.9166	−	12.4178i	0.749079	−	0.549869i
$511$		0			0
$512$	15.8265			0.699439
$513$	−1.32709	+	6.21129i	−0.0585925	+	0.274235i
$514$	−17.2238	−	9.94415i	−0.759708	−	0.438617i
$515$	−12.7548	−	2.17998i	−0.562044	−	0.0960615i
$516$	1.06011	−	1.09700i	0.0466685	−	0.0482927i
$517$	−13.1082			−0.576499
$518$		0			0
$519$	4.76960	+	16.6557i	0.209362	+	0.731102i
$520$	−12.8455	+	15.4730i	−0.563311	+	0.678536i
$521$	−1.94104	+	3.36199i	−0.0850387	+	0.147291i	−0.905408	−	0.424543i	$-0.860435\pi$
$521$	−1.94104	+	3.36199i	−0.0850387	+	0.147291i	0.820369	+	0.571834i	$0.193768\pi$
$522$	−27.0506	+	0.925607i	−1.18397	+	0.0405127i
$523$	−1.06192	−	1.83929i	−0.0464343	−	0.0804266i	0.841874	−	0.539674i	$-0.181452\pi$
$523$	−1.06192	−	1.83929i	−0.0464343	−	0.0804266i	−0.888308	+	0.459247i	$0.848119\pi$
$524$	−2.78100			−0.121488
$525$		0			0
$526$	−26.8562			−1.17099
$527$	−5.68157	−	9.84076i	−0.247493	−	0.428670i
$528$	16.2526	+	4.05830i	0.707305	+	0.176615i
$529$	10.3529	−	17.9317i	0.450124	−	0.779638i
$530$	−24.2867	+	29.2545i	−1.05494	+	1.27073i
$531$	−5.52156	+	3.44486i	−0.239615	+	0.149494i
$532$		0			0
$533$	−41.3138			−1.78950
$534$	−3.35793	−	3.24500i	−0.145312	−	0.140425i
$535$	−8.56615	−	1.46408i	−0.370347	−	0.0632978i
$536$	23.0856	+	13.3285i	0.997148	+	0.575704i
$537$	19.5101	−	20.1891i	0.841922	−	0.871224i
$538$	−6.67354			−0.287717
$539$		0			0
$540$	−3.17561	−	1.26754i	−0.136656	−	0.0545462i
$541$	7.59052	+	13.1472i	0.326342	+	0.565241i	0.981783	−	0.190005i	$-0.0608506\pi$
$541$	7.59052	+	13.1472i	0.326342	+	0.565241i	−0.655441	+	0.755246i	$0.727517\pi$
$542$	−30.9431	−	17.8650i	−1.32912	−	0.767367i
$543$	−32.6214	−	8.14561i	−1.39992	−	0.349561i
$544$	−5.11716	+	2.95439i	−0.219396	+	0.126669i
$545$	4.04017	+	10.9214i	0.173062	+	0.467821i
$546$		0			0
$547$			11.7540i			0.502566i	0.967914	+	0.251283i	$0.0808525\pi$
$547$			11.7540i			0.502566i	−0.967914	+	0.251283i	$0.919148\pi$
$548$	−1.57521	−	2.72835i	−0.0672897	−	0.116549i
$549$	−10.1902	+	0.348684i	−0.434907	+	0.0148815i
$550$	15.9923	−	2.99347i	0.681913	−	0.127642i
$551$	−3.64041	−	6.30537i	−0.155087	−	0.268618i
$552$	−6.51629	+	1.86604i	−0.277352	+	0.0794239i
$553$		0			0
$554$			19.4362i			0.825763i
$555$	27.6699	+	12.1572i	1.17452	+	0.516045i
$556$	1.04780	+	0.604946i	0.0444365	+	0.0256554i
$557$	4.70135	−	8.14298i	0.199203	−	0.345029i	−0.749068	−	0.662494i	$-0.769498\pi$
$557$	4.70135	−	8.14298i	0.199203	−	0.345029i	0.948270	+	0.317465i	$0.102831\pi$
$558$	−6.78553	+	12.7401i	−0.287254	+	0.539333i
$559$			10.4183i			0.440649i
$560$		0			0
$561$	12.7962	−	3.66440i	0.540258	−	0.154711i
$562$	27.8614	−	16.0858i	1.17526	−	0.678538i
$563$	16.9106	+	9.76331i	0.712695	+	0.411475i	0.812058	−	0.583577i	$-0.198347\pi$
$563$	16.9106	+	9.76331i	0.712695	+	0.411475i	−0.0993632	+	0.995051i	$0.531681\pi$
$564$	−3.01743	−	0.753455i	−0.127057	−	0.0317262i
$565$	13.3722	−	16.1075i	0.562574	−	0.677648i
$566$	9.92744			0.417281
$567$		0			0
$568$			26.8615i			1.12708i
$569$	−11.1702	+	6.44911i	−0.468279	+	0.270361i	−0.715519	−	0.698593i	$-0.753810\pi$
$569$	−11.1702	+	6.44911i	−0.468279	+	0.270361i	0.247240	+	0.968954i	$0.420476\pi$
$570$	−0.784496	−	7.12766i	−0.0328589	−	0.298545i
$571$	20.8321	−	36.0823i	0.871796	−	1.51000i	0.0116595	−	0.999932i	$-0.496289\pi$
$571$	20.8321	−	36.0823i	0.871796	−	1.51000i	0.860137	−	0.510063i	$-0.170378\pi$
$572$	1.90584	−	1.10034i	0.0796874	−	0.0460075i
$573$	−6.05758	−	21.1533i	−0.253059	−	0.883692i
$574$		0			0
$575$	−5.75012	+	4.92881i	−0.239797	+	0.205545i
$576$	−17.2162	−	9.16955i	−0.717343	−	0.382065i
$577$	3.74489	−	6.48634i	0.155902	−	0.270030i	−0.777485	−	0.628901i	$-0.783505\pi$
$577$	3.74489	−	6.48634i	0.155902	−	0.270030i	0.933387	+	0.358871i	$0.116838\pi$
$578$	3.18369	−	5.51432i	0.132424	−	0.229365i
$579$	−25.0588	+	25.9309i	−1.04141	+	1.07765i
$580$	3.67605	−	1.35989i	0.152640	−	0.0564663i
$581$		0			0
$582$	3.34395	−	0.957590i	0.138611	−	0.0396934i
$583$	−20.8858	+	12.0584i	−0.865003	+	0.499409i
$584$	−8.85614	+	15.3393i	−0.366470	+	0.634744i
$585$	21.6107	−	8.84591i	0.893492	−	0.365734i
$586$	−4.87892	+	2.81685i	−0.201546	+	0.116363i
$587$			22.1920i			0.915961i	0.888962	+	0.457981i	$0.151427\pi$
$587$			22.1920i			0.915961i	−0.888962	+	0.457981i	$0.848573\pi$
$588$		0			0
$589$	−3.88284			−0.159990
$590$	4.69322	−	5.65322i	0.193217	−	0.232739i
$591$	−0.937685	+	3.75523i	−0.0385712	+	0.154470i
$592$	−30.4244	−	17.5655i	−1.25043	−	0.721938i
$593$	5.46787	−	3.15687i	0.224538	−	0.129637i	−0.383512	−	0.923536i	$-0.625285\pi$
$593$	5.46787	−	3.15687i	0.224538	−	0.129637i	0.608050	+	0.793899i	$0.291952\pi$
$594$	−12.5534	−	11.3271i	−0.515072	−	0.464757i
$595$		0			0
$596$		−	0.748572i		−	0.0306627i
$597$	29.9966	−	31.0406i	1.22768	−	1.27041i
$598$	−3.99316	+	6.91636i	−0.163293	+	0.282831i
$599$	−17.8962	−	10.3324i	−0.731219	−	0.422170i	0.0876487	−	0.996151i	$-0.472065\pi$
$599$	−17.8962	−	10.3324i	−0.731219	−	0.422170i	−0.818868	+	0.573982i	$0.805398\pi$
$600$	−22.3351	−	1.33402i	−0.911827	−	0.0544612i
$601$		−	12.5956i		−	0.513785i	−0.966440	−	0.256892i	$-0.917301\pi$
$601$		−	12.5956i		−	0.513785i	0.966440	−	0.256892i	$-0.0826986\pi$
$602$		0			0
$603$	−16.3841	−	26.2611i	−0.667213	−	1.06943i
$604$	0.826798	+	1.43206i	0.0336419	+	0.0582695i
$605$	−14.0728	−	2.40525i	−0.572140	−	0.0977871i
$606$	−8.52955	+	34.1590i	−0.346489	+	1.38762i
$607$	−21.3383	−	36.9590i	−0.866095	−	1.50012i	−0.865956	−	0.500121i	$-0.833289\pi$
$607$	−21.3383	−	36.9590i	−0.866095	−	1.50012i	−0.000139312	−	1.00000i	$-0.500044\pi$
$608$			2.01906i			0.0818838i
$609$		0			0
$610$	10.7962	−	3.99387i	0.437127	−	0.161707i
$611$	18.3942	−	10.6199i	0.744148	−	0.429634i
$612$	3.15624	−	0.107999i	0.127583	−	0.00436559i
$613$	−4.60972	−	2.66142i	−0.186185	−	0.107494i	0.404011	−	0.914754i	$-0.367616\pi$
$613$	−4.60972	−	2.66142i	−0.186185	−	0.107494i	−0.590195	+	0.807261i	$0.700949\pi$
$614$	8.48998	+	14.7051i	0.342628	+	0.593448i
$615$	−27.2004	−	37.0547i	−1.09683	−	1.49419i
$616$		0			0
$617$	−30.1002			−1.21179			−0.605895	−	0.795545i	$-0.707185\pi$
$617$	−30.1002			−1.21179			−0.605895	+	0.795545i	$0.707185\pi$
$618$	−10.9172	−	10.5500i	−0.439154	−	0.424385i
$619$	−11.0265	−	6.36613i	−0.443191	−	0.255876i	0.261759	−	0.965133i	$-0.415697\pi$
$619$	−11.0265	−	6.36613i	−0.443191	−	0.255876i	−0.704950	+	0.709257i	$0.749031\pi$
$620$	0.352152	−	2.06040i	0.0141428	−	0.0827475i
$621$	7.69683	+	1.64449i	0.308863	+	0.0659911i
$622$	28.6594			1.14914
$623$		0			0
$624$	−26.0944	+	7.47254i	−1.04461	+	0.299141i
$625$	−23.3074	+	9.04228i	−0.932298	+	0.361691i
$626$	−12.4057	+	21.4872i	−0.495830	+	0.858802i
$627$	1.10188	−	4.41281i	0.0440049	−	0.176230i
$628$	2.04876	+	3.54856i	0.0817545	+	0.141603i
$629$	−27.9145			−1.11303
$630$		0			0
$631$	−17.4114			−0.693138			−0.346569	−	0.938024i	$-0.612653\pi$
$631$	−17.4114			−0.693138			−0.346569	+	0.938024i	$0.612653\pi$
$632$	2.43229	+	4.21284i	0.0967511	+	0.167578i
$633$	−2.77581	+	11.1165i	−0.110329	+	0.441843i
$634$	−7.66184	+	13.2707i	−0.304291	+	0.527047i
$635$	16.4781	+	13.6799i	0.653915	+	0.542871i
$636$	−5.50089	+	1.57526i	−0.218125	+	0.0624633i
$637$		0			0
$638$	19.3823			0.767353
$639$	14.6623	−	27.5292i	0.580033	−	1.08904i
$640$	28.9885	+	4.95456i	1.14587	+	0.195846i
$641$	−1.13893	−	0.657564i	−0.0449852	−	0.0259722i	0.477339	−	0.878719i	$-0.341601\pi$
$641$	−1.13893	−	0.657564i	−0.0449852	−	0.0259722i	−0.522324	+	0.852747i	$0.674935\pi$
$642$	−7.33202	−	7.08543i	−0.289372	−	0.279640i
$643$	−39.2223			−1.54678			−0.773389	−	0.633932i	$-0.781440\pi$
$643$	−39.2223			−1.54678			−0.773389	+	0.633932i	$0.781440\pi$
$644$		0			0
$645$	−9.34429	+	6.85927i	−0.367931	+	0.270083i
$646$	3.31152	+	5.73572i	0.130290	+	0.225669i
$647$	5.39634	+	3.11558i	0.212152	+	0.122486i	0.602311	−	0.798261i	$-0.294247\pi$
$647$	5.39634	+	3.11558i	0.212152	+	0.122486i	−0.390159	+	0.920747i	$0.627580\pi$
$648$	12.9757	+	19.2956i	0.509732	+	0.758003i
$649$	4.03604	−	2.33021i	0.158428	−	0.0914687i
$650$	−20.0160	+	17.1570i	−0.785092	+	0.672954i
$651$		0			0
$652$			1.19793i			0.0469144i
$653$	−9.43091	−	16.3348i	−0.369060	−	0.639230i	0.620359	−	0.784318i	$-0.286987\pi$
$653$	−9.43091	−	16.3348i	−0.369060	−	0.639230i	−0.989419	+	0.145088i	$0.953654\pi$
$654$	−3.30990	+	13.2554i	−0.129427	+	0.518329i
$655$	20.8292	+	3.56001i	0.813863	+	0.139101i
$656$	26.7157	+	46.2730i	1.04307	+	1.80666i
$657$	17.4492	−	10.8864i	0.680759	−	0.424721i
$658$		0			0
$659$			41.6170i			1.62117i	0.585622	+	0.810584i	$0.300850\pi$
$659$			41.6170i			1.62117i	−0.585622	+	0.810584i	$0.699150\pi$
$660$	2.24168	+	0.984921i	0.0872574	+	0.0383380i
$661$	−3.27232	−	1.88927i	−0.127278	−	0.0734842i	0.435009	−	0.900426i	$-0.356745\pi$
$661$	−3.27232	−	1.88927i	−0.127278	−	0.0734842i	−0.562287	+	0.826942i	$0.690079\pi$
$662$	14.5982	−	25.2848i	0.567374	−	0.982721i
$663$	−14.9876	+	15.5092i	−0.582069	+	0.602327i
$664$			23.5236i			0.912894i
$665$		0			0
$666$	18.7696	+	30.0846i	0.727307	+	1.16576i
$667$	−7.81342	+	4.51108i	−0.302537	+	0.174670i
$668$	3.56088	+	2.05588i	0.137775	+	0.0795442i
$669$	−1.80864	+	7.24321i	−0.0699259	+	0.280039i
$670$	26.8873	+	22.3215i	1.03875	+	0.862353i
$671$	7.30148			0.281871
$672$		0			0
$673$		−	31.2573i		−	1.20488i	−0.798163	−	0.602441i	$-0.794195\pi$
$673$		−	31.2573i		−	1.20488i	0.798163	−	0.602441i	$-0.205805\pi$
$674$	−31.0075	+	17.9022i	−1.19436	+	0.689565i
$675$	22.1621	+	13.5588i	0.853020	+	0.521878i
$676$	0.129901	−	0.224996i	0.00499621	−	0.00865369i
$677$	7.56724	−	4.36895i	0.290832	−	0.167912i	−0.347485	−	0.937686i	$-0.612964\pi$
$677$	7.56724	−	4.36895i	0.290832	−	0.167912i	0.638317	+	0.769773i	$0.279631\pi$
$678$	23.6132	−	6.76199i	0.906858	−	0.259693i
$679$		0			0
$680$	19.3823	−	7.17013i	0.743278	−	0.274962i
$681$	13.3737	−	13.8391i	0.512481	−	0.530317i
$682$	5.16827	−	8.95171i	0.197903	−	0.342779i
$683$	10.9346	−	18.9393i	0.418401	−	0.724691i	−0.577378	−	0.816477i	$-0.695924\pi$
$683$	10.9346	−	18.9393i	0.418401	−	0.724691i	0.995779	+	0.0917858i	$0.0292575\pi$
$684$	0.507292	−	0.952463i	0.0193968	−	0.0364183i
$685$	8.30544	+	22.4513i	0.317334	+	0.857819i
$686$		0			0
$687$	4.75594	+	16.6079i	0.181450	+	0.633632i
$688$	11.6689	−	6.73705i	0.444873	−	0.256847i
$689$	19.5387	−	33.8421i	0.744366	−	1.28928i
$690$	−8.83237	+	0.972123i	−0.336243	+	0.0370081i
$691$	−19.5167	+	11.2680i	−0.742449	+	0.428653i	−0.822959	−	0.568101i	$-0.807678\pi$
$691$	−19.5167	+	11.2680i	−0.742449	+	0.428653i	0.0805102	+	0.996754i	$0.474345\pi$
$692$		−	2.94359i		−	0.111898i
$693$		0			0
$694$	24.0944			0.914612
$695$	−7.07341	−	5.87224i	−0.268310	−	0.222747i
$696$	−25.8610	−	6.45751i	−0.980257	−	0.244771i
$697$	36.7678	+	21.2279i	1.39268	+	0.804063i
$698$	0.0252378	−	0.0145711i	0.000955266	−	0.000551523i
$699$	−34.3493	+	9.83646i	−1.29921	+	0.372049i
$700$		0			0
$701$			35.5019i			1.34089i	0.741960	+	0.670444i	$0.233896\pi$
$701$			35.5019i			1.34089i	−0.741960	+	0.670444i	$0.766104\pi$
$702$	26.7924	+	5.72442i	1.01122	+	0.216054i
$703$	−4.76927	+	8.26062i	−0.179877	+	0.311555i
$704$	12.0968	+	6.98408i	0.455915	+	0.263223i
$705$	21.6355	+	9.50591i	0.814839	+	0.358013i
$706$		−	38.5033i		−	1.44909i
$707$		0			0
$708$	1.06301	−	0.304409i	0.0399503	−	0.0114404i
$709$	−2.03390	−	3.52282i	−0.0763847	−	0.132302i	0.825303	−	0.564690i	$-0.191004\pi$
$709$	−2.03390	−	3.52282i	−0.0763847	−	0.132302i	−0.901688	+	0.432388i	$0.857671\pi$
$710$	−5.93246	+	34.7100i	−0.222641	+	1.30264i
$711$	−0.193166	−	5.64522i	−0.00724428	−	0.211712i
$712$	−2.29934	−	3.98257i	−0.0861712	−	0.149253i
$713$			4.81149i			0.180192i
$714$		0			0
$715$	−15.6830	+	5.80164i	−0.586511	+	0.216969i
$716$	−4.13106	+	2.38507i	−0.154385	+	0.0891342i
$717$	−4.82883	−	1.20576i	−0.180336	−	0.0450301i
$718$	31.7169	+	18.3118i	1.18366	+	0.683389i
$719$	15.2703	+	26.4489i	0.569484	+	0.986376i	0.996617	+	0.0821868i	$0.0261904\pi$
$719$	15.2703	+	26.4489i	0.569484	+	0.986376i	−0.427133	+	0.904189i	$0.640476\pi$
$720$	−23.8824	−	18.4845i	−0.890043	−	0.688877i
$721$		0			0
$722$	−26.5159			−0.986821
$723$	−31.3810	+	32.4732i	−1.16707	+	1.20769i
$724$	4.94730	+	2.85632i	0.183865	+	0.106154i
$725$	−29.2738	+	5.47953i	−1.08720	+	0.203505i
$726$	−12.0453	−	11.6402i	−0.447043	−	0.432008i
$727$	23.4181			0.868528			0.434264	−	0.900786i	$-0.357008\pi$
$727$	23.4181			0.868528			0.434264	+	0.900786i	$0.357008\pi$
$728$		0			0
$729$	−2.76568	−	26.8580i	−0.102433	−	0.994740i
$730$	−14.8315	+	17.8653i	−0.548939	+	0.661224i
$731$	5.35315	−	9.27192i	0.197993	−	0.342934i
$732$	1.68075	+	0.419686i	0.0621224	+	0.0155120i
$733$	8.44533	+	14.6277i	0.311935	+	0.540288i	0.978781	−	0.204908i	$-0.0656894\pi$
$733$	8.44533	+	14.6277i	0.311935	+	0.540288i	−0.666846	+	0.745196i	$0.732356\pi$
$734$	−13.7423			−0.507239
$735$		0			0
$736$	2.50196			0.0922235
$737$	11.0827	+	19.1958i	0.408237	+	0.707087i
$738$	−1.84431	−	53.8996i	−0.0678901	−	1.98407i
$739$	−13.8321	+	23.9579i	−0.508822	+	0.881306i	0.491126	+	0.871089i	$0.336586\pi$
$739$	−13.8321	+	23.9579i	−0.508822	+	0.881306i	−0.999948	+	0.0102170i	$0.996748\pi$
$740$	−3.95088	−	3.27997i	−0.145237	−	0.120574i
$741$	2.02890	+	7.08499i	0.0745333	+	0.260274i
$742$		0			0
$743$	40.1701			1.47370			0.736850	−	0.676056i	$-0.236312\pi$
$743$	40.1701			1.47370			0.736850	+	0.676056i	$0.236312\pi$
$744$	−9.87819	+	10.2220i	−0.362152	+	0.374756i
$745$	−0.958262	+	5.60667i	−0.0351080	+	0.205412i
$746$	−20.4158	−	11.7870i	−0.747474	−	0.431554i
$747$	12.8404	−	24.1083i	0.469804	−	0.882078i
$748$	−2.26151			−0.0826888
$749$		0			0
$750$	−28.5665	−	6.65659i	−1.04310	−	0.243064i
$751$	24.8188	+	42.9874i	0.905650	+	1.56863i	0.820042	+	0.572303i	$0.193950\pi$
$751$	24.8188	+	42.9874i	0.905650	+	1.56863i	0.0856082	+	0.996329i	$0.472717\pi$
$752$	−23.7893	−	13.7347i	−0.867505	−	0.500854i
$753$	−0.0676076	+	0.270754i	−0.00246376	+	0.00986683i
$754$	−27.1983	+	15.7029i	−0.990503	+	0.571867i
$755$	−4.35936	−	11.7842i	−0.158654	−	0.428873i
$756$		0			0
$757$		−	47.7116i		−	1.73411i	−0.498214	−	0.867054i	$-0.666011\pi$
$757$		−	47.7116i		−	1.73411i	0.498214	−	0.867054i	$-0.333989\pi$
$758$	25.8242	+	44.7288i	0.937977	+	1.62462i
$759$	−5.46821	−	1.36542i	−0.198483	−	0.0495615i
$760$	1.18970	−	6.96075i	0.0431548	−	0.252493i
$761$	−9.91711	−	17.1769i	−0.359495	−	0.622663i	0.628382	−	0.777905i	$-0.283718\pi$
$761$	−9.91711	−	17.1769i	−0.359495	−	0.622663i	−0.987876	+	0.155242i	$0.950384\pi$
$762$	6.91759	+	24.1565i	0.250598	+	0.875098i
$763$		0			0
$764$			3.73847i			0.135253i
$765$	−23.7779	−	3.23147i	−0.859692	−	0.116834i
$766$	−13.8740	−	8.01017i	−0.501289	−	0.289419i
$767$	−3.77572	+	6.53974i	−0.136333	+	0.236136i
$768$	8.61559	+	8.32583i	0.310888	+	0.300433i
$769$		−	10.6337i		−	0.383461i	−0.981448	−	0.191731i	$-0.938590\pi$
$769$		−	10.6337i		−	0.383461i	0.981448	−	0.191731i	$-0.0614100\pi$
$770$		0			0
$771$	6.26096	+	21.8635i	0.225483	+	0.787396i
$772$	5.30595	−	3.06339i	0.190965	−	0.110254i
$773$	−12.4039	−	7.16138i	−0.446136	−	0.257577i	0.260061	−	0.965592i	$-0.416257\pi$
$773$	−12.4039	−	7.16138i	−0.446136	−	0.257577i	−0.706197	+	0.708015i	$0.749591\pi$
$774$	−13.5922	+	0.465090i	−0.488560	+	0.0167173i
$775$	−5.27511	+	14.9812i	−0.189488	+	0.538140i
$776$	3.42548			0.122967
$777$		0			0
$778$			25.6508i			0.919626i
$779$	12.5637	−	7.25368i	0.450142	−	0.259890i
$780$	−3.94360	+	0.434047i	−0.141203	+	0.0155414i
$781$	−11.1677	+	19.3431i	−0.399613	+	0.692149i
$782$	7.10752	−	4.10353i	0.254165	−	0.146742i
$783$	22.9789	+	20.7342i	0.821200	+	0.740980i
$784$		0			0
$785$	−10.8023	−	29.2007i	−0.385550	−	1.04222i
$786$	17.8283	+	17.2287i	0.635914	+	0.614527i
$787$	−18.4671	+	31.9859i	−0.658280	+	1.14017i	0.322781	+	0.946474i	$0.395382\pi$
$787$	−18.4671	+	31.9859i	−0.658280	+	1.14017i	−0.981061	+	0.193700i	$0.937951\pi$
$788$	0.328807	−	0.569511i	0.0117133	−	0.0202880i
$789$	22.0835	+	21.3408i	0.786195	+	0.759753i
$790$	2.21254	+	5.98095i	0.0787188	+	0.212793i
$791$		0			0
$792$	−8.81391	−	14.1273i	−0.313189	−	0.501991i
$793$	−10.2458	+	5.91543i	−0.363840	+	0.210063i
$794$	−0.308865	+	0.534970i	−0.0109612	+	0.0189854i
$795$	43.2172	−	4.75664i	1.53276	−	0.168701i
$796$	−6.35148	+	3.66703i	−0.225122	+	0.129974i
$797$		−	37.4862i		−	1.32783i	−0.747809	−	0.663914i	$-0.768894\pi$
$797$		−	37.4862i		−	1.32783i	0.747809	−	0.663914i	$-0.231106\pi$
$798$		0			0
$799$	−21.8268			−0.772177
$800$	7.79017	+	2.74304i	0.275424	+	0.0969810i
$801$	0.182607	+	5.33665i	0.00645210	+	0.188561i
$802$	−36.7012	−	21.1895i	−1.29597	−	0.748226i
$803$	−12.7547	+	7.36392i	−0.450103	+	0.259867i
$804$	1.44780	+	5.05578i	0.0510599	+	0.178303i
$805$		0			0
$806$			16.7487i			0.589947i
$807$	5.48757	+	5.30301i	0.193172	+	0.186675i
$808$	−17.3363	+	30.0274i	−0.609889	+	1.05636i
$809$	−22.1518	−	12.7893i	−0.778814	−	0.449649i	0.0571956	−	0.998363i	$-0.481784\pi$
$809$	−22.1518	−	12.7893i	−0.778814	−	0.449649i	−0.836010	+	0.548714i	$0.815117\pi$
$810$	12.5055	+	27.7992i	0.439397	+	0.976765i
$811$			7.28791i			0.255913i	0.991780	+	0.127957i	$0.0408418\pi$
$811$			7.28791i			0.255913i	−0.991780	+	0.127957i	$0.959158\pi$
$812$		0			0
$813$	11.2480	+	39.2786i	0.394485	+	1.37756i
$814$	−12.6963	−	21.9907i	−0.445006	−	0.770773i
$815$	1.53349	−	8.97225i	0.0537158	−	0.314284i
$816$	27.0626	+	6.75756i	0.947380	+	0.236562i
$817$	−1.82920	−	3.16826i	−0.0639955	−	0.110844i
$818$		−	3.96956i		−	0.138792i
$819$		0			0
$820$	2.70964	+	7.32470i	0.0946247	+	0.255790i
$821$	−0.00729231	+	0.00421022i	−0.000254504	+	0.000146938i	−0.500127	−	0.865952i	$-0.666713\pi$
$821$	−0.00729231	+	0.00421022i	−0.000254504	+	0.000146938i	0.499873	+	0.866099i	$0.333380\pi$
$822$	−6.80421	+	27.2494i	−0.237324	+	0.950433i
$823$	27.0406	+	15.6119i	0.942578	+	0.544198i	0.890767	−	0.454459i	$-0.150168\pi$
$823$	27.0406	+	15.6119i	0.942578	+	0.544198i	0.0518103	+	0.998657i	$0.483501\pi$
$824$	−7.47553	−	12.9480i	−0.260422	−	0.451065i
$825$	−15.5290	−	10.2465i	−0.540650	−	0.356737i
$826$		0			0
$827$	38.3189			1.33248			0.666239	−	0.745738i	$-0.267903\pi$
$827$	38.3189			1.33248			0.666239	+	0.745738i	$0.267903\pi$
$828$	−1.18026	−	0.628620i	−0.0410169	−	0.0218461i
$829$	1.94142	+	1.12088i	0.0674283	+	0.0389298i	0.533335	−	0.845904i	$-0.320938\pi$
$829$	1.94142	+	1.12088i	0.0674283	+	0.0389298i	−0.465907	+	0.884834i	$0.654272\pi$
$830$	−5.19528	+	30.3969i	−0.180331	+	1.05509i
$831$	15.4446	−	15.9821i	0.535768	−	0.554414i
$832$	−22.6331			−0.784663
$833$		0			0
$834$	−2.96944	−	10.3694i	−0.102823	−	0.359064i
$835$	−24.0386	−	19.9565i	−0.831889	−	0.690623i
$836$	−0.386384	+	0.669237i	−0.0133634	+	0.0231460i
$837$	15.7034	−	5.08406i	0.542789	−	0.175731i
$838$	6.35903	+	11.0142i	0.219669	+	0.380478i
$839$	−20.6544			−0.713069			−0.356535	−	0.934282i	$-0.616042\pi$
$839$	−20.6544			−0.713069			−0.356535	+	0.934282i	$0.616042\pi$
$840$		0			0
$841$	−6.47924			−0.223422
$842$	−5.94479	−	10.2967i	−0.204871	−	0.354847i
$843$	−35.6924	−	8.91243i	−1.22931	−	0.306961i
$844$	0.973362	−	1.68591i	0.0335045	−	0.0580315i
$845$	−1.26096	+	1.51889i	−0.0433783	+	0.0522514i
$846$	14.6762	+	23.5236i	0.504579	+	0.808759i
$847$		0			0
$848$	−50.5391			−1.73552
$849$	−8.16322	−	7.88867i	−0.280161	−	0.270738i
$850$	26.6291	−	4.98449i	0.913371	−	0.170966i
$851$	10.2363	+	5.90993i	0.350896	+	0.202590i
$852$	−3.68257	+	3.81073i	−0.126163	+	0.130553i
$853$	7.06831			0.242014			0.121007	−	0.992652i	$-0.461388\pi$
$853$	7.06831			0.242014			0.121007	+	0.992652i	$0.461388\pi$
$854$		0			0
$855$	−5.01879	+	6.48438i	−0.171639	+	0.221761i
$856$	−5.02058	−	8.69590i	−0.171600	−	0.297220i
$857$	14.5780	+	8.41661i	0.497975	+	0.287506i	0.727877	−	0.685708i	$-0.240507\pi$
$857$	14.5780	+	8.41661i	0.497975	+	0.287506i	−0.229902	+	0.973214i	$0.573841\pi$
$858$	−19.0347	−	4.75298i	−0.649833	−	0.162264i
$859$	30.4698	−	17.5918i	1.03962	−	0.600223i	0.119893	−	0.992787i	$-0.461745\pi$
$859$	30.4698	−	17.5918i	1.03962	−	0.600223i	0.919725	+	0.392563i	$0.128412\pi$
$860$	1.84711	−	0.683304i	0.0629859	−	0.0233005i
$861$		0			0
$862$		−	18.5665i		−	0.632376i
$863$	−18.9879	−	32.8880i	−0.646356	−	1.11952i	−0.983986	−	0.178243i	$-0.942959\pi$
$863$	−18.9879	−	32.8880i	−0.646356	−	1.11952i	0.337630	−	0.941279i	$-0.390375\pi$
$864$	−2.64369	−	8.16571i	−0.0899402	−	0.277803i
$865$	−3.76815	+	22.0469i	−0.128121	+	0.749618i
$866$	−3.89242	−	6.74187i	−0.132270	−	0.229098i
$867$	−6.99977	+	2.00449i	−0.237725	+	0.0680761i
$868$		0			0
$869$			4.04491i			0.137214i
$870$	−31.9910	−	14.0558i	−1.08460	−	0.476536i
$871$	−31.1037	−	17.9577i	−1.05391	−	0.608474i
$872$	−6.72737	+	11.6521i	−0.227817	+	0.394591i
$873$	−3.51062	−	1.86979i	−0.118817	−	0.0632829i
$874$		−	2.80440i		−	0.0948601i
$875$		0			0
$876$	−3.35932	+	0.961992i	−0.113501	+	0.0325027i
$877$	9.91566	−	5.72481i	0.334828	−	0.193313i	−0.323155	−	0.946346i	$-0.604743\pi$
$877$	9.91566	−	5.72481i	0.334828	−	0.193313i	0.657983	+	0.753033i	$0.271410\pi$
$878$	21.9054	+	12.6471i	0.739272	+	0.426819i
$879$	6.25024	+	1.56069i	0.210815	+	0.0526408i
$880$	16.6395	+	13.8139i	0.560917	+	0.465666i
$881$	23.6698			0.797455			0.398728	−	0.917069i	$-0.369452\pi$
$881$	23.6698			0.797455			0.398728	+	0.917069i	$0.369452\pi$
$882$		0			0
$883$			16.8355i			0.566560i	0.959037	+	0.283280i	$0.0914226\pi$
$883$			16.8355i			0.566560i	−0.959037	+	0.283280i	$0.908577\pi$
$884$	3.17346	−	1.83220i	0.106735	−	0.0616236i
$885$	−8.35142	+	0.919188i	−0.280730	+	0.0308982i
$886$	−0.191017	+	0.330852i	−0.00641735	+	0.0111152i
$887$	−45.5385	+	26.2917i	−1.52903	+	0.882789i	−0.529632	+	0.848227i	$0.677670\pi$
$887$	−45.5385	+	26.2917i	−1.52903	+	0.882789i	−0.999403	+	0.0345613i	$0.988997\pi$
$888$	9.61362	+	33.5712i	0.322612	+	1.12657i
$889$		0			0
$890$	−2.09160	−	5.65403i	−0.0701107	−	0.189524i
$891$	1.32163	+	19.2895i	0.0442761	+	0.646222i
$892$	0.634214	−	1.09849i	0.0212350	−	0.0367802i
$893$	−3.72917	+	6.45910i	−0.124792	+	0.216146i
$894$	−4.63752	+	4.79891i	−0.155102	+	0.160500i
$895$	33.9941	−	12.5755i	1.13630	−	0.420352i
$896$		0			0
$897$	8.77950	−	2.51414i	0.293139	−	0.0839448i
$898$	37.8717	−	21.8652i	1.26380	−	0.729653i
$899$	−9.46050	+	16.3861i	−0.315525	+	0.546506i
$900$	−2.98570	−	3.25127i	−0.0995234	−	0.108376i
$901$	−34.7774	+	20.0788i	−1.15860	+	0.668921i
$902$			38.6201i			1.28591i
$903$		0			0
$904$	24.1889			0.804510
$905$	−33.3979	−	27.7265i	−1.11019	−	0.921660i
$906$	3.57140	−	14.3027i	0.118652	−	0.475176i
$907$	−43.9694	−	25.3858i	−1.45998	−	0.842920i	−0.460971	−	0.887415i	$-0.652499\pi$
$907$	−43.9694	−	25.3858i	−1.45998	−	0.842920i	−0.999010	+	0.0444946i	$0.985832\pi$
$908$	−2.83174	+	1.63491i	−0.0939747	+	0.0542563i
$909$	34.1577	−	21.3107i	1.13294	−	0.706832i
$910$		0			0
$911$			16.1165i			0.533963i	0.963702	+	0.266981i	$0.0860262\pi$
$911$			16.1165i			0.533963i	−0.963702	+	0.266981i	$0.913974\pi$
$912$	6.62345	−	6.85396i	0.219324	−	0.226957i
$913$	−9.77999	+	16.9394i	−0.323671	+	0.560614i
$914$	31.5787	+	18.2319i	1.04453	+	0.603059i
$915$	−12.0513	−	5.29493i	−0.398403	−	0.175045i
$916$		−	2.93515i		−	0.0969802i
$917$		0			0
$918$	−20.9029	−	18.8610i	−0.689900	−	0.622506i
$919$	−19.8721	−	34.4194i	−0.655519	−	1.13539i	−0.981763	−	0.190106i	$-0.939117\pi$
$919$	−19.8721	−	34.4194i	−0.655519	−	1.13539i	0.326245	−	0.945285i	$-0.394217\pi$
$920$	−8.62555	−	1.47423i	−0.284376	−	0.0486040i
$921$	4.70392	−	18.8382i	0.155000	−	0.620740i
$922$	−30.1960	−	52.3010i	−0.994452	−	1.72244i
$923$		−	36.1909i		−	1.19124i
$924$		0			0
$925$	25.3926	+	29.6240i	0.834905	+	0.974030i
$926$	39.1451	−	22.6004i	1.28639	−	0.742696i
$927$	0.593686	+	17.3503i	0.0194992	+	0.569860i
$928$	8.52069	+	4.91942i	0.279705	+	0.161488i
$929$	−18.2593	−	31.6261i	−0.599069	−	1.03762i	−0.992959	−	0.118461i	$-0.962204\pi$
$929$	−18.2593	−	31.6261i	−0.599069	−	1.03762i	0.393889	−	0.919158i	$-0.371129\pi$
$930$	−15.0220	+	11.0271i	−0.492591	+	0.361592i
$931$		0			0
$932$	6.07063			0.198850
$933$	−23.5663	−	22.7737i	−0.771526	−	0.745578i
$934$	−5.48530	−	3.16694i	−0.179484	−	0.103625i
$935$	16.9383	+	2.89500i	0.553941	+	0.0946766i
$936$	23.8136	+	12.6834i	0.778372	+	0.414569i
$937$	7.60980			0.248601			0.124301	−	0.992245i	$-0.460331\pi$
$937$	7.60980			0.248601			0.124301	+	0.992245i	$0.460331\pi$
$938$		0			0
$939$	27.2755	−	7.81075i	0.890102	−	0.254894i
$940$	−3.08925	−	2.56465i	−0.100760	−	0.0836498i
$941$	−11.0121	+	19.0735i	−0.358985	+	0.621780i	−0.987791	−	0.155782i	$-0.950210\pi$
$941$	−11.0121	+	19.0735i	−0.358985	+	0.621780i	0.628807	+	0.777562i	$0.283544\pi$
$942$	8.84974	−	35.4414i	0.288340	−	1.15474i
$943$	−8.98853	−	15.5686i	−0.292707	−	0.506983i
$944$	9.76632			0.317867
$945$		0			0
$946$	9.73904			0.316644
$947$	24.6291	+	42.6589i	0.800339	+	1.38623i	0.919393	+	0.393341i	$0.128681\pi$
$947$	24.6291	+	42.6589i	0.800339	+	1.38623i	−0.119053	+	0.992888i	$0.537986\pi$
$948$	−0.232499	+	0.931111i	−0.00755123	+	0.0302411i
$949$	11.9320	−	20.6669i	0.387330	−	0.670875i
$950$	3.07462	−	8.73184i	0.0997537	−	0.283298i
$951$	16.8456	−	4.82399i	0.546255	−	0.156429i
$952$		0			0
$953$	−10.2538			−0.332154			−0.166077	−	0.986113i	$-0.553110\pi$
$953$	−10.2538			−0.332154			−0.166077	+	0.986113i	$0.553110\pi$
$954$	45.0239	+	23.9802i	1.45770	+	0.776388i
$955$	4.78569	−	28.0005i	0.154861	−	0.906073i
$956$	0.732331	+	0.422811i	0.0236853	+	0.0136747i
$957$	−15.9379	−	15.4018i	−0.515198	−	0.497870i
$958$	42.3131			1.36708
$959$		0			0
$960$	−14.9013	−	20.2998i	−0.480937	−	0.655174i
$961$	−10.4547	−	18.1081i	−0.337250	−	0.584134i
$962$	35.6323	+	20.5723i	1.14883	+	0.663278i
$963$	0.398721	+	11.6525i	0.0128486	+	0.375498i
$964$	6.64460	−	3.83626i	0.214008	−	0.123558i
$965$	−43.6621	+	16.1520i	−1.40553	+	0.519951i
$966$		0			0
$967$		−	4.62632i		−	0.148772i	−0.997230	−	0.0743862i	$-0.976300\pi$
$967$		−	4.62632i		−	0.148772i	0.997230	−	0.0743862i	$-0.0236998\pi$
$968$	−8.24799	−	14.2859i	−0.265101	−	0.459168i
$969$	1.83477	−	7.34786i	0.0589412	−	0.236047i
$970$	4.42635	+	0.756529i	0.142122	+	0.0242907i
$971$	−12.6443	−	21.9006i	−0.405775	−	0.702822i	0.588637	−	0.808398i	$-0.299665\pi$
$971$	−12.6443	−	21.9006i	−0.405775	−	0.702822i	−0.994411	+	0.105575i	$0.966332\pi$
$972$	−0.804521	+	4.51628i	−0.0258050	+	0.144860i
$973$		0			0
$974$		−	56.4119i		−	1.80755i
$975$	30.0925	+	1.79735i	0.963730	+	0.0575612i
$976$	13.2510	+	7.65046i	0.424154	+	0.244885i
$977$	−12.0549	+	20.8797i	−0.385670	+	0.668000i	−0.991862	−	0.127318i	$-0.959363\pi$
$977$	−12.0549	+	20.8797i	−0.385670	+	0.668000i	0.606192	+	0.795318i	$0.292696\pi$
$978$	7.42133	−	7.67961i	0.237308	−	0.245567i
$979$		−	3.82381i		−	0.122210i
$980$		0			0
$981$	13.2549	−	8.26964i	0.423196	−	0.264029i
$982$	7.74688	−	4.47267i	0.247213	−	0.142728i
$983$	41.6456	+	24.0441i	1.32829	+	0.766888i	0.985035	−	0.172354i	$-0.0551374\pi$
$983$	41.6456	+	24.0441i	1.32829	+	0.766888i	0.343254	+	0.939243i	$0.388471\pi$
$984$	12.8669	−	51.5291i	0.410181	−	1.64269i
$985$	−3.19175	+	3.84462i	−0.101698	+	0.122500i
$986$	32.2739			1.02781
$987$		0			0
$988$		−	1.25214i		−	0.0398360i
$989$	−3.92601	+	2.26668i	−0.124840	+	0.0720764i
$990$	−8.26915	−	20.2016i	−0.262811	−	0.642050i
$991$	−14.8587	+	25.7361i	−0.472003	+	0.817534i	−0.999487	−	0.0320314i	$-0.989802\pi$
$991$	−14.8587	+	25.7361i	−0.472003	+	0.817534i	0.527483	+	0.849565i	$0.323136\pi$
$992$	4.54406	−	2.62352i	0.144274	−	0.0832967i
$993$	−32.0960	+	9.19119i	−1.01854	+	0.291674i
$994$		0			0
$995$	52.2656	−	19.3347i	1.65693	−	0.612952i
$996$	−3.22496	+	3.33720i	−0.102187	+	0.105743i
$997$	13.3742	−	23.1647i	0.423564	−	0.733634i	−0.572721	−	0.819750i	$-0.694112\pi$
$997$	13.3742	−	23.1647i	0.423564	−	0.733634i	0.996285	+	0.0861161i	$0.0274456\pi$
$998$	−14.1928	+	24.5826i	−0.449265	+	0.778149i
$999$	8.47222	−	39.6532i	0.268049	−	1.25457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.f.374.10		24
3.2	odd	2	inner	735.2.p.f.374.4		24
5.4	even	2	inner	735.2.p.f.374.3		24
7.2	even	3		105.2.p.a.89.10	yes	24
7.3	odd	6		735.2.g.b.734.7		24
7.4	even	3		735.2.g.b.734.6		24
7.5	odd	6	inner	735.2.p.f.509.9		24
7.6	odd	2		105.2.p.a.59.9	yes	24
15.14	odd	2	inner	735.2.p.f.374.9		24
21.2	odd	6		105.2.p.a.89.4	yes	24
21.5	even	6	inner	735.2.p.f.509.3		24
21.11	odd	6		735.2.g.b.734.17		24
21.17	even	6		735.2.g.b.734.20		24
21.20	even	2		105.2.p.a.59.3	✓	24
35.2	odd	12		525.2.t.j.26.10		24
35.4	even	6		735.2.g.b.734.19		24
35.9	even	6		105.2.p.a.89.3	yes	24
35.13	even	4		525.2.t.j.101.9		24
35.19	odd	6	inner	735.2.p.f.509.4		24
35.23	odd	12		525.2.t.j.26.3		24
35.24	odd	6		735.2.g.b.734.18		24
35.27	even	4		525.2.t.j.101.4		24
35.34	odd	2		105.2.p.a.59.4	yes	24
105.2	even	12		525.2.t.j.26.4		24
105.23	even	12		525.2.t.j.26.9		24
105.44	odd	6		105.2.p.a.89.9	yes	24
105.59	even	6		735.2.g.b.734.5		24
105.62	odd	4		525.2.t.j.101.10		24
105.74	odd	6		735.2.g.b.734.8		24
105.83	odd	4		525.2.t.j.101.3		24
105.89	even	6	inner	735.2.p.f.509.10		24
105.104	even	2		105.2.p.a.59.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.3	✓	24	21.20	even	2
105.2.p.a.59.4	yes	24	35.34	odd	2
105.2.p.a.59.9	yes	24	7.6	odd	2
105.2.p.a.59.10	yes	24	105.104	even	2
105.2.p.a.89.3	yes	24	35.9	even	6
105.2.p.a.89.4	yes	24	21.2	odd	6
105.2.p.a.89.9	yes	24	105.44	odd	6
105.2.p.a.89.10	yes	24	7.2	even	3
525.2.t.j.26.3		24	35.23	odd	12
525.2.t.j.26.4		24	105.2	even	12
525.2.t.j.26.9		24	105.23	even	12
525.2.t.j.26.10		24	35.2	odd	12
525.2.t.j.101.3		24	105.83	odd	4
525.2.t.j.101.4		24	35.27	even	4
525.2.t.j.101.9		24	35.13	even	4
525.2.t.j.101.10		24	105.62	odd	4
735.2.g.b.734.5		24	105.59	even	6
735.2.g.b.734.6		24	7.4	even	3
735.2.g.b.734.7		24	7.3	odd	6
735.2.g.b.734.8		24	105.74	odd	6
735.2.g.b.734.17		24	21.11	odd	6
735.2.g.b.734.18		24	35.24	odd	6
735.2.g.b.734.19		24	35.4	even	6
735.2.g.b.734.20		24	21.17	even	6
735.2.p.f.374.3		24	5.4	even	2	inner
735.2.p.f.374.4		24	3.2	odd	2	inner
735.2.p.f.374.9		24	15.14	odd	2	inner
735.2.p.f.374.10		24	1.1	even	1	trivial
735.2.p.f.509.3		24	21.5	even	6	inner
735.2.p.f.509.4		24	35.19	odd	6	inner
735.2.p.f.509.9		24	7.5	odd	6	inner
735.2.p.f.509.10		24	105.89	even	6	inner

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.757344 + 1.31176i) q^{2} +(0.419611 - 1.68045i) q^{3} +(-0.147140 + 0.254854i) q^{4} +(1.42830 - 1.72046i) q^{5} +(2.52214 - 0.722254i) q^{6} +2.58363 q^{8} +(-2.64785 - 1.41027i) q^{9} +(3.33853 + 0.570605i) q^{10} +(1.86048 + 1.07415i) q^{11} +(0.366529 + 0.354202i) q^{12} -3.48097 q^{13} +(-2.29182 - 3.12211i) q^{15} +(2.25098 + 3.89881i) q^{16} +(3.09793 + 1.78859i) q^{17} +(-0.155396 - 4.54141i) q^{18} +(1.05858 - 0.611171i) q^{19} +(0.228305 + 0.617156i) q^{20} +3.25401i q^{22} +(-0.757344 - 1.31176i) q^{23} +(1.08412 - 4.34168i) q^{24} +(-0.919933 - 4.91464i) q^{25} +(-2.63629 - 4.56619i) q^{26} +(-3.48097 + 3.85783i) q^{27} -5.95645i q^{29} +(2.35976 - 5.37082i) q^{30} +(-2.75098 - 1.58828i) q^{31} +(-0.825899 + 1.43050i) q^{32} +(2.58574 - 2.67573i) q^{33} +5.41832i q^{34} +(0.749020 - 0.467309i) q^{36} +(-6.75803 + 3.90175i) q^{37} +(1.60342 + 0.925734i) q^{38} +(-1.46065 + 5.84961i) q^{39} +(3.69020 - 4.44503i) q^{40} +11.8685 q^{41} -2.99294i q^{43} +(-0.547504 + 0.316101i) q^{44} +(-6.20824 + 2.54122i) q^{45} +(1.14714 - 1.98691i) q^{46} +(-5.28420 + 3.05084i) q^{47} +(7.49631 - 2.14668i) q^{48} +(5.75012 - 4.92881i) q^{50} +(4.30557 - 4.45542i) q^{51} +(0.512191 - 0.887140i) q^{52} +(-5.61301 + 9.72202i) q^{53} +(-7.69683 - 1.64449i) q^{54} +(4.50535 - 1.66667i) q^{55} +(-0.582853 - 2.03535i) q^{57} +(7.81342 - 4.51108i) q^{58} +(1.08467 - 1.87871i) q^{59} +(1.13290 - 0.124691i) q^{60} +(2.94338 - 1.69936i) q^{61} -4.81149i q^{62} +6.50196 q^{64} +(-4.97186 + 5.98885i) q^{65} +(5.46821 + 1.36542i) q^{66} +(8.93534 + 5.15882i) q^{67} +(-0.911660 + 0.526347i) q^{68} +(-2.52214 + 0.722254i) q^{69} +10.3968i q^{71} +(-6.84108 - 3.64363i) q^{72} +(-3.42779 + 5.93710i) q^{73} +(-10.2363 - 5.90993i) q^{74} +(-8.64485 - 0.516335i) q^{75} +0.359711i q^{76} +(-8.77950 + 2.51414i) q^{78} +(0.941421 + 1.63059i) q^{79} +(9.92280 + 1.69595i) q^{80} +(5.02225 + 7.46840i) q^{81} +(8.98853 + 15.5686i) q^{82} +9.10486i q^{83} +(7.50196 - 2.77521i) q^{85} +(3.92601 - 2.26668i) q^{86} +(-10.0095 - 2.49939i) q^{87} +(4.80681 + 2.77521i) q^{88} +(-0.889962 - 1.54146i) q^{89} +(-8.03524 - 6.21913i) q^{90} +0.445743 q^{92} +(-3.82337 + 3.95644i) q^{93} +(-8.00392 - 4.62107i) q^{94} +(0.460474 - 2.69417i) q^{95} +(2.05733 + 1.98814i) q^{96} +1.32584 q^{97} +(-3.41144 - 5.46799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) \) 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 + 72 * q^40 + 18 * q^45 + 36 * q^46 - 12 * q^51 + 36 * q^54 + 12 * q^60 - 36 * q^61 + 24 * q^64 + 72 * q^66 - 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^85 + 72 * q^94 + 90 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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