LMFDB - Embedded newform 105.2.p.a.89.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,2,Mod(59,105)] 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("105.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.3
Character	$\chi$	$=$	105.89
Dual form			105.2.p.a.59.3

$q$-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} +(-1.24551 - 1.20362i) q^{3} +(-0.147140 - 0.254854i) q^{4} +(1.42830 + 1.72046i) q^{5} +(2.52214 - 0.722254i) q^{6} +(-0.0753638 + 2.64468i) q^{7} -2.58363 q^{8} +(0.102593 + 2.99825i) q^{9} +(-3.33853 + 0.570605i) q^{10} +(-1.86048 + 1.07415i) q^{11} +(-0.123483 + 0.494525i) q^{12} +3.48097 q^{13} +(-3.41210 - 2.10179i) q^{14} +(0.291817 - 3.86197i) q^{15} +(2.25098 - 3.89881i) q^{16} +(3.09793 - 1.78859i) q^{17} +(-4.01067 - 2.13613i) q^{18} +(-1.05858 - 0.611171i) q^{19} +(0.228305 - 0.617156i) q^{20} +(3.27706 - 3.20326i) q^{21} -3.25401i q^{22} +(0.757344 - 1.31176i) q^{23} +(3.21794 + 3.10972i) q^{24} +(-0.919933 + 4.91464i) q^{25} +(-2.63629 + 4.56619i) q^{26} +(3.48097 - 3.85783i) q^{27} +(0.685096 - 0.369932i) q^{28} -5.95645i q^{29} +(4.84497 + 3.30764i) q^{30} +(2.75098 - 1.58828i) q^{31} +(0.825899 + 1.43050i) q^{32} +(3.61012 + 0.901451i) q^{33} +5.41832i q^{34} +(-4.65769 + 3.64773i) q^{35} +(0.749020 - 0.467309i) q^{36} +(-6.75803 - 3.90175i) q^{37} +(1.60342 - 0.925734i) q^{38} +(-4.33559 - 4.18977i) q^{39} +(-3.69020 - 4.44503i) q^{40} +11.8685 q^{41} +(1.72005 + 6.72468i) q^{42} +2.99294i q^{43} +(0.547504 + 0.316101i) q^{44} +(-5.01181 + 4.45889i) q^{45} +(1.14714 + 1.98691i) q^{46} +(-5.28420 - 3.05084i) q^{47} +(-7.49631 + 2.14668i) q^{48} +(-6.98864 - 0.398626i) q^{49} +(-5.75012 - 4.92881i) q^{50} +(-6.01129 - 1.50103i) q^{51} +(-0.512191 - 0.887140i) q^{52} +(5.61301 + 9.72202i) q^{53} +(2.42425 + 7.48790i) q^{54} +(-4.50535 - 1.66667i) q^{55} +(0.194713 - 6.83288i) q^{56} +(0.582853 + 2.03535i) q^{57} +(7.81342 + 4.51108i) q^{58} +(1.08467 + 1.87871i) q^{59} +(-1.02718 + 0.493881i) q^{60} +(-2.94338 - 1.69936i) q^{61} +4.81149i q^{62} +(-7.93712 + 0.0453652i) q^{63} +6.50196 q^{64} +(4.97186 + 5.98885i) q^{65} +(-3.91659 + 4.05290i) q^{66} +(8.93534 - 5.15882i) q^{67} +(-0.911660 - 0.526347i) q^{68} +(-2.52214 + 0.722254i) q^{69} +(-1.25746 - 8.87235i) q^{70} +10.3968i q^{71} +(-0.265062 - 7.74637i) q^{72} +(3.42779 + 5.93710i) q^{73} +(10.2363 - 5.90993i) q^{74} +(7.06115 - 5.01399i) q^{75} +0.359711i q^{76} +(-2.70057 - 5.00133i) q^{77} +(8.77950 - 2.51414i) q^{78} +(0.941421 - 1.63059i) q^{79} +(9.92280 - 1.69595i) q^{80} +(-8.97895 + 0.615196i) q^{81} +(-8.98853 + 15.5686i) q^{82} -9.10486i q^{83} +(-1.29855 - 0.363843i) q^{84} +(7.50196 + 2.77521i) q^{85} +(-3.92601 - 2.26668i) q^{86} +(-7.16930 + 7.41882i) q^{87} +(4.80681 - 2.77521i) q^{88} +(-0.889962 + 1.54146i) q^{89} +(-2.05332 - 9.95121i) q^{90} +(-0.262339 + 9.20605i) q^{91} -0.445743 q^{92} +(-5.33806 - 1.33292i) q^{93} +(8.00392 - 4.62107i) q^{94} +(-0.460474 - 2.69417i) q^{95} +(0.693113 - 2.77577i) q^{96} -1.32584 q^{97} +(5.81571 - 8.86551i) q^{98} +(-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} - 6 q^{21} + 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^{49} - 12 q^{51} - 36 q^{54} + 12 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) $ 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 6 * q^21 + 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^49 - 12 * q^51 - 36 * q^54 + 12 * q^60 + 36 * q^61 + 24 * q^64 - 72 * q^66 + 108 * q^70 + 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^84 + 48 * q^85 - 96 * q^91 - 72 * q^94 - 90 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.463615	+	0.886037i	$0.346552\pi$
$2$	−0.757344	+	1.31176i	−0.535523	+	0.927553i	−0.999138	+	0.0415164i	$0.986781\pi$
$3$	−1.24551	−	1.20362i	−0.719096	−	0.694911i
$3$	−1.24551	−	1.20362i	−0.719096	−	0.694911i
$4$	−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
$7$	−0.0753638	+	2.64468i	−0.0284849	+	0.999594i
$7$	−0.0753638	+	2.64468i	−0.0284849	+	0.999594i
$8$	−2.58363			−0.913452
$9$	0.102593	+	2.99825i	0.0341975	+	0.999415i
$10$	−3.33853	+	0.570605i	−1.05574	+	0.180441i
$11$	−1.86048	+	1.07415i	−0.560957	+	0.323869i	−0.753529	−	0.657414i	$-0.771650\pi$
$11$	−1.86048	+	1.07415i	−0.560957	+	0.323869i	0.192573	+	0.981283i	$0.438317\pi$
$12$	−0.123483	+	0.494525i	−0.0356466	+	0.142757i
$13$	3.48097			0.965448			0.482724	−	0.875773i	$-0.339647\pi$
$13$	3.48097			0.965448			0.482724	+	0.875773i	$0.339647\pi$
$14$	−3.41210	−	2.10179i	−0.911923	−	0.561727i
$15$	0.291817	−	3.86197i	0.0753468	−	0.997157i
$16$	2.25098	−	3.89881i	0.562745	−	0.974703i
$17$	3.09793	−	1.78859i	0.751359	−	0.433797i	−0.0748259	−	0.997197i	$-0.523840\pi$
$17$	3.09793	−	1.78859i	0.751359	−	0.433797i	0.826185	+	0.563399i	$0.190507\pi$
$18$	−4.01067	−	2.13613i	−0.945324	−	0.503490i
$19$	−1.05858	−	0.611171i	−0.242855	−	0.140212i	0.373633	−	0.927576i	$-0.378112\pi$
$19$	−1.05858	−	0.611171i	−0.242855	−	0.140212i	−0.616488	+	0.787364i	$0.711445\pi$
$20$	0.228305	−	0.617156i	0.0510506	−	0.138000i
$21$	3.27706	−	3.20326i	0.715112	−	0.699010i
$22$		−	3.25401i		−	0.693757i
$23$	0.757344	−	1.31176i	0.157917	−	0.273521i	−0.776200	−	0.630486i	$-0.782855\pi$
$23$	0.757344	−	1.31176i	0.157917	−	0.273521i	0.934117	+	0.356966i	$0.116189\pi$
$24$	3.21794	+	3.10972i	0.656860	+	0.634768i
$25$	−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
$28$	0.685096	−	0.369932i	0.129471	−	0.0699105i
$29$		−	5.95645i		−	1.10608i	−0.833153	−	0.553042i	$-0.813467\pi$
$29$		−	5.95645i		−	1.10608i	0.833153	−	0.553042i	$-0.186533\pi$
$30$	4.84497	+	3.30764i	0.884567	+	0.603889i
$31$	2.75098	−	1.58828i	0.494091	−	0.285263i	−0.232179	−	0.972673i	$-0.574586\pi$
$31$	2.75098	−	1.58828i	0.494091	−	0.285263i	0.726270	+	0.687410i	$0.241252\pi$
$32$	0.825899	+	1.43050i	0.146000	+	0.252879i
$33$	3.61012	+	0.901451i	0.628442	+	0.156923i
$34$			5.41832i			0.929234i
$35$	−4.65769	+	3.64773i	−0.787294	+	0.616578i
$36$	0.749020	−	0.467309i	0.124837	−	0.0778848i
$37$	−6.75803	−	3.90175i	−1.11101	−	0.641444i	−0.171921	−	0.985111i	$-0.554998\pi$
$37$	−6.75803	−	3.90175i	−1.11101	−	0.641444i	−0.939092	+	0.343667i	$0.888331\pi$
$38$	1.60342	−	0.925734i	0.260109	−	0.150174i
$39$	−4.33559	−	4.18977i	−0.694249	−	0.670900i
$40$	−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	$0.122571\pi$
$42$	1.72005	+	6.72468i	0.265409	+	1.03764i
$43$			2.99294i			0.456419i	0.973612	+	0.228209i	$0.0732871\pi$
$43$			2.99294i			0.456419i	−0.973612	+	0.228209i	$0.926713\pi$
$44$	0.547504	+	0.316101i	0.0825393	+	0.0476541i
$45$	−5.01181	+	4.45889i	−0.747117	+	0.664692i
$46$	1.14714	+	1.98691i	0.169137	+	0.292953i
$47$	−5.28420	−	3.05084i	−0.770780	−	0.445010i	0.0623727	−	0.998053i	$-0.480133\pi$
$47$	−5.28420	−	3.05084i	−0.770780	−	0.445010i	−0.833153	+	0.553043i	$0.813467\pi$
$48$	−7.49631	+	2.14668i	−1.08200	+	0.309847i
$49$	−6.98864	−	0.398626i	−0.998377	−	0.0569466i
$50$	−5.75012	−	4.92881i	−0.813190	−	0.697038i
$51$	−6.01129	−	1.50103i	−0.841749	−	0.210186i
$52$	−0.512191	−	0.887140i	−0.0710281	−	0.123024i
$53$	5.61301	+	9.72202i	0.771006	+	1.33542i	0.937012	+	0.349297i	$0.113580\pi$
$53$	5.61301	+	9.72202i	0.771006	+	1.33542i	−0.166006	+	0.986125i	$0.553087\pi$
$54$	2.42425	+	7.48790i	0.329898	+	1.01897i
$55$	−4.50535	−	1.66667i	−0.607502	−	0.224734i
$56$	0.194713	−	6.83288i	0.0260196	−	0.913082i
$57$	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	0.927954	−	0.372696i	$-0.121567\pi$
$59$	1.08467	+	1.87871i	0.141213	+	0.244587i	−0.786741	+	0.617283i	$0.788233\pi$
$60$	−1.02718	+	0.493881i	−0.132608	+	0.0637597i
$61$	−2.94338	−	1.69936i	−0.376861	−	0.217581i	0.299591	−	0.954068i	$-0.403150\pi$
$61$	−2.94338	−	1.69936i	−0.376861	−	0.217581i	−0.676452	+	0.736487i	$0.736483\pi$
$62$			4.81149i			0.611060i
$63$	−7.93712	+	0.0453652i	−0.999984	+	0.00571548i
$64$	6.50196			0.812745
$65$	4.97186	+	5.98885i	0.616684	+	0.742826i
$66$	−3.91659	+	4.05290i	−0.482099	+	0.498877i
$67$	8.93534	−	5.15882i	1.09163	−	0.630250i	0.157617	−	0.987500i	$-0.449619\pi$
$67$	8.93534	−	5.15882i	1.09163	−	0.630250i	0.934009	+	0.357250i	$0.116286\pi$
$68$	−0.911660	−	0.526347i	−0.110555	−	0.0638290i
$69$	−2.52214	+	0.722254i	−0.303630	+	0.0869491i
$70$	−1.25746	−	8.87235i	−0.150295	−	1.06045i
$71$			10.3968i			1.23387i	0.787013	+	0.616936i	$0.211626\pi$
$71$			10.3968i			1.23387i	−0.787013	+	0.616936i	$0.788374\pi$
$72$	−0.265062	−	7.74637i	−0.0312378	−	0.912918i
$73$	3.42779	+	5.93710i	0.401192	+	0.694885i	0.993870	−	0.110555i	$-0.0352627\pi$
$73$	3.42779	+	5.93710i	0.401192	+	0.694885i	−0.592678	+	0.805439i	$0.701929\pi$
$74$	10.2363	−	5.90993i	1.18995	−	0.687016i
$75$	7.06115	−	5.01399i	0.815352	−	0.578966i
$76$			0.359711i			0.0412617i
$77$	−2.70057	−	5.00133i	−0.307758	−	0.569955i
$78$	8.77950	−	2.51414i	0.994082	−	0.284671i
$79$	0.941421	−	1.63059i	0.105918	−	0.183456i	−0.808195	−	0.588915i	$-0.799555\pi$
$79$	0.941421	−	1.63059i	0.105918	−	0.183456i	0.914113	+	0.405460i	$0.132889\pi$
$80$	9.92280	−	1.69595i	1.10940	−	0.189613i
$81$	−8.97895	+	0.615196i	−0.997661	+	0.0683551i
$82$	−8.98853	+	15.5686i	−0.992617	+	1.71926i
$83$		−	9.10486i		−	0.999388i	−0.866202	−	0.499694i	$-0.833446\pi$
$83$		−	9.10486i		−	0.999388i	0.866202	−	0.499694i	$-0.166554\pi$
$84$	−1.29855	−	0.363843i	−0.141684	−	0.0396985i
$85$	7.50196	+	2.77521i	0.813702	+	0.301014i
$86$	−3.92601	−	2.26668i	−0.423353	−	0.244423i
$87$	−7.16930	+	7.41882i	−0.768630	+	0.795380i
$88$	4.80681	−	2.77521i	0.512407	−	0.295839i
$89$	−0.889962	+	1.54146i	−0.0943358	+	0.163394i	−0.909331	−	0.416073i	$-0.863406\pi$
$89$	−0.889962	+	1.54146i	−0.0943358	+	0.163394i	0.814995	+	0.579467i	$0.196739\pi$
$90$	−2.05332	−	9.95121i	−0.216439	−	1.04895i
$91$	−0.262339	+	9.20605i	−0.0275006	+	0.965056i
$92$	−0.445743			−0.0464719
$93$	−5.33806	−	1.33292i	−0.553531	−	0.138217i
$94$	8.00392	−	4.62107i	0.825541	−	0.476626i
$95$	−0.460474	−	2.69417i	−0.0472436	−	0.276416i
$96$	0.693113	−	2.77577i	0.0707406	−	0.283301i
$97$	−1.32584			−0.134618			−0.0673092	−	0.997732i	$-0.521441\pi$
$97$	−1.32584			−0.134618			−0.0673092	+	0.997732i	$0.521441\pi$
$98$	5.81571	−	8.86551i	0.587475	−	0.895552i
$99$	−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	−0.978553	−	0.205997i	$-0.933956\pi$
$101$	−6.71005	−	11.6221i	−0.667675	−	1.15645i	0.310878	−	0.950450i	$-0.399377\pi$
$102$	6.52160	−	6.74857i	0.645735	−	0.668208i
$103$	2.89342	−	5.01154i	0.285097	−	0.493802i	−0.687536	−	0.726150i	$-0.741308\pi$
$103$	2.89342	−	5.01154i	0.285097	−	0.493802i	0.972633	+	0.232348i	$0.0746409\pi$
$104$	−8.99355			−0.881890
$105$	10.1917	+	1.06281i	0.994607	+	0.103720i
$106$	−17.0039			−1.65157
$107$	1.94323	−	3.36576i	0.187859	−	0.325381i	−0.756677	−	0.653788i	$-0.773179\pi$
$107$	1.94323	−	3.36576i	0.187859	−	0.325381i	0.944536	+	0.328408i	$0.106512\pi$
$108$	−1.49537	−	0.319499i	−0.143893	−	0.0307438i
$109$	−2.60384	−	4.50998i	−0.249403	−	0.431978i	0.713958	−	0.700189i	$-0.246901\pi$
$109$	−2.60384	−	4.50998i	−0.249403	−	0.431978i	−0.963360	+	0.268211i	$0.913568\pi$
$110$	5.59837	−	4.64769i	0.533784	−	0.443140i
$111$	3.72097	+	12.9938i	0.353179	+	1.23331i
$112$	10.1415	+	6.24695i	0.958278	+	0.590281i
$113$	−9.36235			−0.880736			−0.440368	−	0.897817i	$-0.645152\pi$
$113$	−9.36235			−0.880736			−0.440368	+	0.897817i	$0.645152\pi$
$114$	−3.11131	−	0.776896i	−0.291401	−	0.0727630i
$115$	3.33853	−	0.570605i	0.311320	−	0.0532092i
$116$	−1.51803	+	0.876432i	−0.140945	+	0.0813747i
$117$	0.357122	+	10.4368i	0.0330159	+	0.964883i
$118$	−3.28589			−0.302490
$119$	4.49678	+	8.32783i	0.412219	+	0.763411i
$120$	−0.753947	+	9.97793i	−0.0688257	+	0.910856i
$121$	−3.19240	+	5.52940i	−0.290218	+	0.502673i
$122$	4.45830	−	2.57400i	0.403636	−	0.233039i
$123$	−14.7823	−	14.2852i	−1.33288	−	1.28805i
$124$	−0.809559	−	0.467399i	−0.0727006	−	0.0419737i
$125$	−9.76936	+	5.43687i	−0.873798	+	0.486289i
$126$	5.95163	−	10.4459i	0.530213	−	0.930599i
$127$		−	9.57778i		−	0.849891i	−0.905219	−	0.424945i	$-0.860293\pi$
$127$		−	9.57778i		−	0.849891i	0.905219	−	0.424945i	$-0.139707\pi$
$128$	−6.57602	+	11.3900i	−0.581243	+	1.00674i
$129$	3.60236	−	3.72774i	0.317170	−	0.328209i
$130$	−11.6213	+	1.98626i	−1.01926	+	0.174206i
$131$	4.72508	−	8.18408i	0.412832	−	0.715047i	−0.582366	−	0.812927i	$-0.697873\pi$
$131$	4.72508	−	8.18408i	0.412832	−	0.715047i	0.995198	+	0.0978802i	$0.0312062\pi$
$132$	−0.301455	−	1.05269i	−0.0262383	−	0.0916253i
$133$	1.69613	−	2.75354i	0.147073	−	0.238762i
$134$			15.6280i			1.35005i
$135$	11.6091	+	0.478728i	0.999151	+	0.0412023i
$136$	−8.00392	+	4.62107i	−0.686330	+	0.396253i
$137$	5.35276	+	9.27125i	0.457317	+	0.792096i	0.998818	−	0.0486038i	$-0.0154772\pi$
$137$	5.35276	+	9.27125i	0.457317	+	0.792096i	−0.541501	+	0.840700i	$0.682144\pi$
$138$	0.962706	−	3.85543i	0.0819510	−	0.328196i
$139$		−	4.11136i		−	0.348721i	−0.984682	−	0.174360i	$-0.944214\pi$
$139$		−	4.11136i		−	0.348721i	0.984682	−	0.174360i	$-0.0557858\pi$
$140$	1.61497	+	0.650305i	0.136490	+	0.0549608i
$141$	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
$144$	11.9205	+	6.34900i	0.993377	+	0.529083i
$145$	10.2478	−	8.50758i	0.851033	−	0.706516i
$146$	−10.3841			−0.859390
$147$	8.22463	+	8.90817i	0.678356	+	0.734733i
$148$			2.29642i			0.188764i
$149$	2.20294	+	1.27187i	0.180472	+	0.104196i	0.587514	−	0.809214i	$-0.300107\pi$
$149$	2.20294	+	1.27187i	0.180472	+	0.104196i	−0.407042	+	0.913409i	$0.633440\pi$
$150$	1.22942	+	13.0598i	0.100382	+	1.06633i
$151$	2.80956	+	4.86630i	0.228639	+	0.396014i	0.957405	−	0.288749i	$-0.0932392\pi$
$151$	2.80956	+	4.86630i	0.228639	+	0.396014i	−0.728766	+	0.684763i	$0.759906\pi$
$152$	2.73498	+	1.57904i	0.221836	+	0.128077i
$153$	5.68046	+	9.10486i	0.459238	+	0.736084i
$154$	8.60580	+	0.245234i	0.693475	+	0.0197616i
$155$	6.66178	+	2.46440i	0.535087	+	0.197946i
$156$	−0.429842	+	1.72143i	−0.0344149	+	0.137824i
$157$	−6.96194	−	12.0584i	−0.555623	−	0.962368i	−0.997855	−	0.0654670i	$-0.979146\pi$
$157$	−6.96194	−	12.0584i	−0.555623	−	0.962368i	0.442231	−	0.896901i	$-0.354187\pi$
$158$	1.42596	+	2.46983i	0.113443	+	0.196489i
$159$	4.71056	−	18.8648i	0.373572	−	1.49608i
$160$	−1.28148	+	3.46410i	−0.101310	+	0.273861i
$161$	3.41210	+	2.10179i	0.268911	+	0.165644i
$162$	5.99317	−	12.2441i	0.470868	−	0.961990i
$163$	3.52533	+	2.03535i	0.276125	+	0.159421i	0.631668	−	0.775239i	$-0.282371\pi$
$163$	3.52533	+	2.03535i	0.276125	+	0.159421i	−0.355543	+	0.934660i	$0.615704\pi$
$164$	−1.74633	−	3.02473i	−0.136366	−	0.236192i
$165$	3.60542	+	7.49859i	0.280682	+	0.583765i
$166$	11.9434	+	6.89551i	0.926986	+	0.535196i
$167$			13.9722i			1.08120i	0.841279	+	0.540602i	$0.181803\pi$
$167$			13.9722i			1.08120i	−0.841279	+	0.540602i	$0.818197\pi$
$168$	−8.46671	+	8.27606i	−0.653221	+	0.638512i
$169$	−0.882841			−0.0679109
$170$	−9.32197	+	7.73897i	−0.714963	+	0.593552i
$171$	1.72384	−	3.23658i	0.131825	−	0.247508i
$172$	0.762763	−	0.440382i	0.0581602	−	0.0335788i
$173$	−8.66256	−	5.00133i	−0.658602	−	0.380244i	0.133142	−	0.991097i	$-0.457493\pi$
$173$	−8.66256	−	5.00133i	−0.658602	−	0.380244i	−0.791744	+	0.610853i	$0.790827\pi$
$174$	−4.30206	−	15.0230i	−0.326139	−	1.13889i
$175$	−12.9283	−	2.80331i	−0.977289	−	0.211910i
$176$			9.67157i			0.729022i
$177$	0.910283	−	3.64549i	0.0684211	−	0.274012i
$178$	−1.34801	−	2.33483i	−0.101038	−	0.175003i
$179$	−14.0378	+	8.10475i	−1.04924	+	0.605777i	−0.922436	−	0.386151i	$-0.873804\pi$
$179$	−14.0378	+	8.10475i	−1.04924	+	0.605777i	−0.126801	+	0.991928i	$0.540471\pi$
$180$	1.87381	+	0.621200i	0.139665	+	0.0463015i
$181$		−	19.4123i		−	1.44290i	−0.692465	−	0.721451i	$-0.743475\pi$
$181$		−	19.4123i		−	1.44290i	0.692465	−	0.721451i	$-0.256525\pi$
$182$	−11.8774	−	7.31627i	−0.880414	−	0.542318i
$183$	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
$186$	5.79122	−	5.99277i	0.424633	−	0.439411i
$187$	−3.84243	+	6.65529i	−0.280987	+	0.486683i
$188$			1.79560i			0.130958i
$189$	9.94037	+	9.49679i	0.723056	+	0.690790i
$190$	3.88284	+	1.43639i	0.281691	+	0.104206i
$191$	−11.0018	−	6.35188i	−0.796061	−	0.459606i	0.0460309	−	0.998940i	$-0.485343\pi$
$191$	−11.0018	−	6.35188i	−0.796061	−	0.459606i	−0.842092	+	0.539334i	$0.818676\pi$
$192$	−8.09826	−	7.82590i	−0.584441	−	0.564785i
$193$	−18.0302	+	10.4098i	−1.29785	+	0.749311i	−0.980032	−	0.198842i	$-0.936282\pi$
$193$	−18.0302	+	10.4098i	−1.29785	+	0.749311i	−0.317813	+	0.948153i	$0.602949\pi$
$194$	1.00411	−	1.73918i	0.0720912	−	0.124866i
$195$	1.01581	−	13.4434i	0.0727433	−	0.962703i
$196$	0.926718	+	1.83974i	0.0661942	+	0.131410i
$197$	2.23465			0.159212			0.0796062	−	0.996826i	$-0.474634\pi$
$197$	2.23465			0.159212			0.0796062	+	0.996826i	$0.474634\pi$
$198$	9.75631	−	0.333837i	0.693351	−	0.0237248i
$199$	−21.5831	+	12.4610i	−1.52998	+	0.883337i	−0.530622	+	0.847608i	$0.678042\pi$
$199$	−21.5831	+	12.4610i	−1.52998	+	0.883337i	−0.999362	+	0.0357284i	$0.988625\pi$
$200$	2.37677	−	12.6976i	0.168063	−	0.897859i
$201$	−17.3383	−	4.32940i	−1.22295	−	0.305372i
$202$	20.3273			1.43022
$203$	15.7529	+	0.448901i	1.10564	+	0.0315066i
$204$	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
$207$	4.01067	+	2.13613i	0.278761	+	0.148471i
$208$	7.83560	−	13.5716i	0.543301	−	0.941025i
$209$	2.62596			0.181641
$210$	−9.11277	+	12.5641i	−0.628841	+	0.867006i
$211$	−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
$213$	12.5138	−	12.9493i	0.857431	−	0.887272i
$214$	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
$217$	3.99316	+	7.39515i	0.271073	+	0.502016i
$218$	7.88801			0.534243
$219$	2.87667	−	11.5205i	0.194388	−	0.778481i
$220$	0.238160	+	1.39344i	0.0160567	+	0.0939459i
$221$	10.7838	−	6.22604i	0.725398	−	0.418808i
$222$	−19.8627	−	4.95975i	−1.33310	−	0.332877i
$223$	4.31027			0.288637			0.144318	−	0.989531i	$-0.453901\pi$
$223$	4.31027			0.288637			0.144318	+	0.989531i	$0.453901\pi$
$224$	−3.84545	+	2.07643i	−0.256935	+	0.138737i
$225$	−14.8297	−	2.25398i	−0.988646	−	0.150265i
$226$	7.09052	−	12.2811i	0.471654	−	0.816929i
$227$	9.62260	−	5.55561i	0.638675	−	0.368739i	−0.145429	−	0.989369i	$-0.546456\pi$
$227$	9.62260	−	5.55561i	0.638675	−	0.368739i	0.784104	+	0.620630i	$0.213123\pi$
$228$	0.432956	−	0.448024i	0.0286732	−	0.0296711i
$229$	8.63774	+	4.98700i	0.570798	+	0.329550i	0.757468	−	0.652872i	$-0.226436\pi$
$229$	8.63774	+	4.98700i	0.570798	+	0.329550i	−0.186670	+	0.982423i	$0.559770\pi$
$230$	−1.77992	+	4.81149i	−0.117365	+	0.317261i
$231$	−2.65612	+	9.47967i	−0.174760	+	0.623717i
$232$			15.3893i			1.01036i
$233$	10.3144	−	17.8650i	0.675716	−	1.17037i	−0.300543	−	0.953768i	$-0.597168\pi$
$233$	10.3144	−	17.8650i	0.675716	−	1.17037i	0.976259	−	0.216606i	$-0.0694988\pi$
$234$	−13.9610	−	7.43579i	−0.912661	−	0.486093i
$235$	−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
$238$	−14.3297	−	0.408345i	−0.928857	−	0.0264691i
$239$		−	2.87353i		−	0.185873i	−0.995672	−	0.0929365i	$-0.970375\pi$
$239$		−	2.87353i		−	0.185873i	0.995672	−	0.0929365i	$-0.0296254\pi$
$240$	−14.4002	−	9.83096i	−0.929531	−	0.634586i
$241$	22.5792	−	13.0361i	1.45445	−	0.839728i	0.455722	−	0.890122i	$-0.349381\pi$
$241$	22.5792	−	13.0361i	1.45445	−	0.839728i	0.998729	+	0.0503940i	$0.0160477\pi$
$242$	−4.83549	−	8.37532i	−0.310837	−	0.538386i
$243$	11.9238	+	10.0410i	0.764915	+	0.644132i
$244$			1.00018i			0.0640298i
$245$	−9.29604	−	12.5930i	−0.593902	−	0.804537i
$246$	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
$249$	−10.9588	+	11.3402i	−0.694486	+	0.718656i
$250$	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	$0.501619\pi$
$252$	1.17943	+	2.01613i	0.0742972	+	0.127005i
$253$			3.25401i			0.204578i
$254$	12.5637	+	7.25368i	0.788319	+	0.455136i
$255$	−6.00347	−	12.4861i	−0.375952	−	0.781908i
$256$	−3.45866	−	5.99057i	−0.216166	−	0.374411i
$257$	−11.3712	−	6.56514i	−0.709314	−	0.409522i	0.101493	−	0.994836i	$-0.467638\pi$
$257$	−11.3712	−	6.56514i	−0.709314	−	0.409522i	−0.810807	+	0.585314i	$0.800971\pi$
$258$	2.16166	+	7.54861i	0.134579	+	0.469956i
$259$	10.8282	−	17.5788i	0.672830	−	1.09229i
$260$	0.794725	−	2.14830i	0.0492867	−	0.133232i
$261$	17.8589	−	0.611087i	1.10544	−	0.0378254i
$262$	7.15703	+	12.3963i	0.442163	+	0.765848i
$263$	8.86526	+	15.3551i	0.546655	+	0.946835i	0.998501	+	0.0547384i	$0.0174325\pi$
$263$	8.86526	+	15.3551i	0.546655	+	0.946835i	−0.451846	+	0.892096i	$0.649234\pi$
$264$	−9.32723	−	2.32902i	−0.574051	−	0.143341i
$265$	−8.70925	+	23.5429i	−0.535005	+	1.44623i
$266$	2.32743	+	4.31029i	0.142704	+	0.264281i
$267$	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	0.791020	−	0.611790i	$-0.209550\pi$
$269$	−2.20294	−	3.81561i	−0.134316	−	0.232642i	−0.925336	+	0.379148i	$0.876217\pi$
$270$	−9.42005	+	14.8658i	−0.573286	+	0.904701i
$271$	20.4287	+	11.7945i	1.24095	+	0.716465i	0.969288	−	0.245927i	$-0.0790923\pi$
$271$	20.4287	+	11.7945i	1.24095	+	0.716465i	0.271665	+	0.962392i	$0.412426\pi$
$272$		−	16.1043i		−	0.976469i
$273$	11.4073	−	11.1505i	0.690403	−	0.674857i
$274$	−16.2155			−0.979615
$275$	−3.56755	−	10.1318i	−0.215131	−	0.610968i
$276$	0.555178	+	0.536506i	0.0334178	+	0.0322938i
$277$	11.1127	−	6.41589i	0.667695	−	0.385494i	−0.127508	−	0.991838i	$-0.540698\pi$
$277$	11.1127	−	6.41589i	0.667695	−	0.385494i	0.795203	+	0.606344i	$0.207364\pi$
$278$	5.39311	+	3.11371i	0.323457	+	0.186748i
$279$	5.04428	+	8.08517i	0.301993	+	0.484046i
$280$	12.0338	−	9.42439i	0.719155	−	0.563215i
$281$		−	21.2397i		−	1.26706i	−0.773719	−	0.633528i	$-0.781606\pi$
$281$		−	21.2397i		−	1.26706i	0.773719	−	0.633528i	$-0.218394\pi$
$282$	−15.5310	−	3.87810i	−0.924856	−	0.230938i
$283$	−3.27706	−	5.67603i	−0.194801	−	0.337405i	0.752034	−	0.659124i	$-0.229073\pi$
$283$	−3.27706	−	5.67603i	−0.194801	−	0.337405i	−0.946835	+	0.321719i	$0.895739\pi$
$284$	2.64967	−	1.52979i	0.157229	−	0.0907761i
$285$	−2.66924	+	3.90986i	−0.158112	+	0.231600i
$286$		−	11.3271i		−	0.669786i
$287$	−0.894454	+	31.3883i	−0.0527980	+	1.85279i
$288$	−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
$291$	1.65134	+	1.59581i	0.0968035	+	0.0935477i
$292$	1.00873	−	1.74717i	0.0590315	−	0.102245i
$293$		−	3.71937i		−	0.217288i	−0.994081	−	0.108644i	$-0.965349\pi$
$293$		−	3.71937i		−	0.217288i	0.994081	−	0.108644i	$-0.0346509\pi$
$294$	−17.9142	+	4.04218i	−1.04478	+	0.235745i
$295$	−1.68300	+	4.54949i	−0.0979881	+	0.264882i
$296$	17.4603	+	10.0807i	1.01486	+	0.585928i
$297$	−2.33240	+	10.9165i	−0.135340	+	0.633440i
$298$	−3.33677	+	1.92648i	−0.193294	+	0.111598i
$299$	2.63629	−	4.56619i	0.152461	−	0.264070i
$300$	−2.31682	−	1.06181i	−0.133761	−	0.0613034i
$301$	−7.91536	−	0.225559i	−0.456234	−	0.0130010i
$302$	−8.51121			−0.489765
$303$	−5.63123	+	22.5519i	−0.323505	+	1.29557i
$304$	−4.76568	+	2.75147i	−0.273331	+	0.157808i
$305$	−1.28035	−	7.49115i	−0.0733125	−	0.428942i
$306$	−16.2454	+	0.555880i	−0.928690	+	0.0317775i
$307$	−11.2102			−0.639800			−0.319900	−	0.947451i	$-0.603649\pi$
$307$	−11.2102			−0.639800			−0.319900	+	0.947451i	$0.603649\pi$
$308$	−0.877248	+	1.42415i	−0.0499859	+	0.0811484i
$309$	−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	0.999091	+	0.0426199i	$0.0135704\pi$
$311$	9.46050	+	16.3861i	0.536456	+	0.929168i	−0.462636	+	0.886548i	$0.653096\pi$
$312$	11.2016	+	10.8248i	0.634164	+	0.612835i
$313$	−8.19024	+	14.1859i	−0.462940	+	0.801835i	−0.999106	−	0.0422775i	$-0.986539\pi$
$313$	−8.19024	+	14.1859i	−0.462940	+	0.801835i	0.536166	+	0.844112i	$0.319872\pi$
$314$	21.0903			1.19020
$315$	−11.4146	−	13.5907i	−0.643141	−	0.765748i
$316$	−0.554083			−0.0311696
$317$	−5.05836	+	8.76134i	−0.284106	+	0.492086i	−0.972392	−	0.233353i	$-0.925030\pi$
$317$	−5.05836	+	8.76134i	−0.284106	+	0.492086i	0.688286	+	0.725439i	$0.258363\pi$
$318$	21.1786	+	20.4663i	1.18763	+	1.14769i
$319$	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
$322$	−5.34118	+	2.88408i	−0.297652	+	0.160723i
$323$	−4.37254			−0.243295
$324$	1.47795	+	2.19780i	0.0821083	+	0.122100i
$325$	−3.20226	+	17.1077i	−0.177629	+	0.948966i
$326$	−5.33977	+	3.08292i	−0.295743	+	0.170747i
$327$	−2.18520	+	8.75127i	−0.120842	+	0.483946i
$328$	−30.6638			−1.69313
$329$	8.46672	−	13.7451i	0.466785	−	0.757791i
$330$	−12.5669	−	0.949574i	−0.691785	−	0.0522723i
$331$	−9.63774	+	16.6931i	−0.529738	+	0.917533i	0.469660	+	0.882847i	$0.344376\pi$
$331$	−9.63774	+	16.6931i	−0.529738	+	0.917533i	−0.999398	+	0.0346861i	$0.988957\pi$
$332$	−2.32041	+	1.33969i	−0.127349	+	0.0735251i
$333$	11.0051	−	20.6625i	0.603075	−	1.13230i
$334$	−18.3282	−	10.5818i	−1.00287	−	0.579009i
$335$	21.6378	+	8.00452i	1.18220	+	0.437334i
$336$	−5.11234	−	19.9871i	−0.278901	−	1.09039i
$337$		−	23.6381i		−	1.28765i	−0.765174	−	0.643824i	$-0.777347\pi$
$337$		−	23.6381i		−	1.28765i	0.765174	−	0.643824i	$-0.222653\pi$
$338$	0.668614	−	1.15807i	0.0363678	−	0.0629909i
$339$	11.6609	+	11.2687i	0.633333	+	0.612033i
$340$	−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
$343$	1.58093	−	18.4527i	0.0853621	−	0.996350i
$344$		−	7.73266i		−	0.416917i
$345$	−4.84497	−	3.30764i	−0.260844	−	0.178077i
$346$	13.1211	−	7.57546i	0.705394	−	0.407259i
$347$	−7.95360	−	13.7760i	−0.426971	−	0.739536i	0.569631	−	0.821901i	$-0.307086\pi$
$347$	−7.95360	−	13.7760i	−0.426971	−	0.739536i	−0.996602	+	0.0823644i	$0.973753\pi$
$348$	2.94561	+	0.735522i	0.157901	+	0.0394281i
$349$		−	0.0192397i		−	0.00102988i	−1.00000		0.000514938i	$-0.999836\pi$
$349$		−	0.0192397i		−	0.00102988i	1.00000		0.000514938i	$-0.000163910\pi$
$350$	13.4685	−	14.8358i	0.719919	−	0.793005i
$351$	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	−0.954081	−	0.299549i	$-0.903164\pi$
$353$	−22.0143	+	12.7100i	−1.17170	+	0.676484i	−0.217624	+	0.976033i	$0.569830\pi$
$354$	4.09261	+	3.95496i	0.217520	+	0.210204i
$355$	−17.8872	+	14.8497i	−0.949355	+	0.788141i
$356$	0.523797			0.0277612
$357$	4.42276	−	15.7848i	0.234078	−	0.835421i
$358$		−	24.5523i		−	1.29763i
$359$	−20.9396	−	12.0895i	−1.10515	−	0.638057i	−0.167579	−	0.985859i	$-0.553595\pi$
$359$	−20.9396	−	12.0895i	−1.10515	−	0.638057i	−0.937568	+	0.347801i	$0.886928\pi$
$360$	12.9487	−	11.5201i	0.682456	−	0.607165i
$361$	−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
$364$	2.38480	−	1.28772i	0.124998	−	0.0674949i
$365$	−5.31861	+	14.3773i	−0.278389	+	0.752542i
$366$	−8.65099	−	2.16016i	−0.452194	−	0.112913i
$367$	4.53636	+	7.85721i	0.236796	+	0.410143i	0.959793	−	0.280708i	$-0.0905693\pi$
$367$	4.53636	+	7.85721i	0.236796	+	0.410143i	−0.722997	+	0.690851i	$0.757236\pi$
$368$	−3.40953	−	5.90548i	−0.177734	−	0.307845i
$369$	1.21762	+	35.5846i	0.0633867	+	1.85246i
$370$	24.7883	+	9.16996i	1.28868	+	0.476724i
$371$	−26.1346	+	14.1119i	−1.35684	+	0.732654i
$372$	0.445743	+	1.55655i	0.0231107	+	0.0807035i
$373$	−13.4785	−	7.78183i	−0.697891	−	0.402928i	0.108670	−	0.994078i	$-0.465341\pi$
$373$	−13.4785	−	7.78183i	−0.697891	−	0.402928i	−0.806562	+	0.591150i	$0.798674\pi$
$374$	−5.82009	−	10.0807i	−0.300950	−	0.521260i
$375$	18.7118	+	4.98693i	0.966272	+	0.257524i
$376$	13.6524	+	7.88224i	0.704071	+	0.406496i
$377$		−	20.7342i		−	1.06787i
$378$	−19.9858	+	5.84703i	−1.02796	+	0.300739i
$379$	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
$381$	−11.5280	+	11.9292i	−0.590598	+	0.611153i
$382$	16.6643	−	9.62112i	0.852618	−	0.492259i
$383$	−9.15965	−	5.28833i	−0.468036	−	0.270221i	0.247381	−	0.968918i	$-0.420430\pi$
$383$	−9.15965	−	5.28833i	−0.468036	−	0.270221i	−0.715417	+	0.698697i	$0.753763\pi$
$384$	21.8997	−	6.27133i	1.11757	−	0.320032i
$385$	4.74735	−	11.7896i	0.241947	−	0.600854i
$386$		−	31.5351i		−	1.60509i
$387$	−8.97356	+	0.307054i	−0.456152	+	0.0156084i
$388$	0.195084	+	0.337895i	0.00990388	+	0.0171540i
$389$	−14.6659	+	8.46736i	−0.743590	+	0.429312i	−0.823373	−	0.567500i	$-0.807911\pi$
$389$	−14.6659	+	8.46736i	−0.743590	+	0.429312i	0.0797828	+	0.996812i	$0.474577\pi$
$390$	16.8652	+	11.5138i	0.854003	+	0.583023i
$391$		−	5.41832i		−	0.274016i
$392$	18.0561	+	1.02990i	0.911970	+	0.0520180i
$393$	−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
$396$	−0.891580	+	1.67398i	−0.0448036	+	0.0841207i
$397$	−0.203913	+	0.353188i	−0.0102341	+	0.0177260i	−0.871097	−	0.491111i	$-0.836591\pi$
$397$	−0.203913	+	0.353188i	−0.0102341	+	0.0177260i	0.860863	+	0.508837i	$0.169924\pi$
$398$		−	37.7491i		−	1.89219i
$399$	−5.42677	+	1.38807i	−0.271678	+	0.0694903i
$400$	17.0905	+	14.6494i	0.854526	+	0.732470i
$401$	24.2302	+	13.9893i	1.21000	+	0.698593i	0.962759	−	0.270361i	$-0.0871430\pi$
$401$	24.2302	+	13.9893i	1.21000	+	0.698593i	0.247240	+	0.968954i	$0.420476\pi$
$402$	18.8102	−	19.4649i	0.938168	−	0.970819i
$403$	9.57608	−	5.52875i	0.477019	−	0.275407i
$404$	−1.97464	+	3.42017i	−0.0982418	+	0.170160i
$405$	−13.8830	−	14.5692i	−0.689853	−	0.723949i
$406$	−12.5192	+	20.3240i	−0.621317	+	1.00866i
$407$	16.7643			0.830974
$408$	15.5310	+	3.87810i	0.768898	+	0.191995i
$409$	2.26960	−	1.31036i	0.112225	−	0.0647929i	−0.442837	−	0.896602i	$-0.646028\pi$
$409$	2.26960	−	1.31036i	0.112225	−	0.0647929i	0.555062	+	0.831809i	$0.312695\pi$
$410$	−39.6233	+	6.77221i	−1.95686	+	0.334456i
$411$	4.49215	−	17.9901i	0.221582	−	0.887388i
$412$	−1.70295			−0.0838984
$413$	−5.05033	+	2.72703i	−0.248511	+	0.134188i
$414$	−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
$417$	−4.94852	+	5.12074i	−0.242330	+	0.250764i
$418$	−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	$0.434249\pi$
$420$	−1.22874	−	2.75378i	−0.0599565	−	0.134371i
$421$	−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
$423$	8.60503	−	16.1563i	0.418391	−	0.785548i
$424$	−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
$427$	4.71609	−	7.65622i	0.228227	−	0.370511i
$428$	−1.14371			−0.0552831
$429$	12.5667	+	3.13793i	0.606727	+	0.151500i
$430$	−1.70778	−	9.99203i	−0.0823567	−	0.481858i
$431$	10.6154	−	6.12880i	0.511326	−	0.295214i	−0.222053	−	0.975035i	$-0.571276\pi$
$431$	10.6154	−	6.12880i	0.511326	−	0.295214i	0.733378	+	0.679821i	$0.237942\pi$
$432$	−7.20535	−	22.2555i	−0.346668	−	1.07077i
$433$	5.13957			0.246992			0.123496	−	0.992345i	$-0.460589\pi$
$433$	5.13957			0.246992			0.123496	+	0.992345i	$0.460589\pi$
$434$	−12.7249	−	0.362613i	−0.610813	−	0.0174060i
$435$	−23.0036	−	1.73819i	−1.10294	−	0.0833398i
$436$	−0.766259	+	1.32720i	−0.0366971	+	0.0635613i
$437$	−1.60342	+	0.925734i	−0.0767019	+	0.0442838i
$438$	12.9334	+	12.4985i	0.617984	+	0.597200i
$439$	−14.4620	−	8.34964i	−0.690234	−	0.398507i	0.113466	−	0.993542i	$-0.463805\pi$
$439$	−14.4620	−	8.34964i	−0.690234	−	0.398507i	−0.803700	+	0.595035i	$0.797138\pi$
$440$	11.6402	+	4.30607i	0.554924	+	0.205284i
$441$	0.478196	−	20.9946i	0.0227712	−	0.999741i
$442$			18.8610i			0.897127i
$443$	−0.126110	+	0.218429i	−0.00599167	+	0.0103779i	−0.869006	−	0.494802i	$-0.835241\pi$
$443$	−0.126110	+	0.218429i	−0.00599167	+	0.0103779i	0.863014	+	0.505180i	$0.168574\pi$
$444$	2.76402	−	2.86021i	0.131174	−	0.135740i
$445$	−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
$448$	−0.490013	+	17.1956i	−0.0231509	+	0.812415i
$449$		−	28.8710i		−	1.36250i	−0.732049	−	0.681252i	$-0.761436\pi$
$449$		−	28.8710i		−	1.36250i	0.732049	−	0.681252i	$-0.238564\pi$
$450$	14.1878	−	17.7459i	0.668822	−	0.836551i
$451$	−22.0811	+	12.7485i	−1.03976	+	0.600305i
$452$	1.37758	+	2.38603i	0.0647958	+	0.112230i
$453$	2.35785	−	9.44267i	0.110781	−	0.443655i
$454$			16.8300i			0.789873i
$455$	−16.2133	+	12.6976i	−0.760091	+	0.595274i
$456$	−1.50588	−	5.25859i	−0.0705193	−	0.246256i
$457$	20.8483	+	12.0368i	0.975242	+	0.563056i	0.900830	−	0.434171i	$-0.142959\pi$
$457$	20.8483	+	12.0368i	0.975242	+	0.563056i	0.0744117	+	0.997228i	$0.476292\pi$
$458$	−13.0835	+	7.55375i	−0.611351	+	0.352964i
$459$	3.88373	−	18.1773i	0.181277	−	0.848445i
$460$	−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	$0.878889\pi$
$462$	−10.4234	−	10.6636i	−0.484943	−	0.496114i
$463$			29.8417i			1.38686i	0.720524	+	0.693430i	$0.243901\pi$
$463$			29.8417i			1.38686i	−0.720524	+	0.693430i	$0.756099\pi$
$464$	−23.2231	−	13.4078i	−1.07810	−	0.622443i
$465$	−5.33111	−	11.0877i	−0.247224	−	0.514180i
$466$	15.6230	+	27.0599i	0.723723	+	1.25353i
$467$	−3.62140	−	2.09082i	−0.167579	−	0.0967515i	0.413865	−	0.910338i	$-0.364179\pi$
$467$	−3.62140	−	2.09082i	−0.167579	−	0.0967515i	−0.581444	+	0.813587i	$0.697512\pi$
$468$	2.60732	−	1.62669i	0.120523	−	0.0751937i
$469$	12.9700	+	24.0199i	0.598900	+	1.10914i
$470$	19.3823	+	7.17013i	0.894039	+	0.330733i
$471$	−5.84262	+	23.3984i	−0.269214	+	1.07814i
$472$	−2.80240	−	4.85390i	−0.128991	−	0.223419i
$473$	−3.21487	−	5.56831i	−0.147820	−	0.256031i
$474$	1.19670	−	4.79252i	0.0549661	−	0.220128i
$475$	3.97751	−	4.64030i	0.182501	−	0.212912i
$476$	1.46073	−	2.37138i	0.0669522	−	0.108692i
$477$	−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	0.985828	+	0.167757i	$0.0536525\pi$
$479$	13.9676	+	24.1926i	0.638196	+	1.10539i	−0.347632	+	0.937631i	$0.613014\pi$
$480$	5.76556	−	2.77216i	0.263161	−	0.126531i
$481$	−23.5245	−	13.5819i	−1.07262	−	0.619280i
$482$			39.4912i			1.79878i
$483$	−1.72005	−	6.72468i	−0.0782650	−	0.305984i
$484$	1.87892			0.0854055
$485$	−1.89369	−	2.28104i	−0.0859880	−	0.103577i
$486$	−22.2018	+	8.03669i	−1.00710	+	0.364552i
$487$	−32.2536	+	18.6216i	−1.46155	+	0.843826i	−0.999083	−	0.0428116i	$-0.986368\pi$
$487$	−32.2536	+	18.6216i	−1.46155	+	0.843826i	−0.462466	+	0.886637i	$0.653035\pi$
$488$	7.60462	+	4.39053i	0.344245	+	0.198750i
$489$	−1.94104	−	6.77821i	−0.0877770	−	0.306521i
$490$	23.5593	−	2.65692i	1.06430	−	0.120028i
$491$		−	5.90572i		−	0.266522i	−0.991081	−	0.133261i	$-0.957455\pi$
$491$		−	5.90572i		−	0.266522i	0.991081	−	0.133261i	$-0.0425448\pi$
$492$	−1.46556	+	5.86926i	−0.0660725	+	0.264607i
$493$	−10.6536	−	18.4527i	−0.479816	−	0.831066i
$494$	5.58145	−	3.22245i	0.251121	−	0.144985i
$495$	4.53488	−	13.6791i	0.203827	−	0.614832i
$496$		−	14.3007i		−	0.642122i
$497$	−27.4962	−	0.783542i	−1.23337	−	0.0351467i
$498$	−6.57602	−	22.9637i	−0.294678	−	1.02903i
$499$	9.37010	−	16.2295i	0.419463	−	0.726532i	−0.576422	−	0.817152i	$-0.695552\pi$
$499$	9.37010	−	16.2295i	0.419463	−	0.726532i	0.995886	+	0.0906204i	$0.0288850\pi$
$500$	2.82308	+	1.68978i	0.126252	+	0.0755693i
$501$	16.8173	−	17.4025i	0.751340	−	0.777489i
$502$	0.122023	−	0.211350i	0.00544615	−	0.00943301i
$503$			32.0398i			1.42858i	0.699849	+	0.714291i	$0.253251\pi$
$503$			32.0398i			1.42858i	−0.699849	+	0.714291i	$0.746749\pi$
$504$	20.5066	−	0.117207i	0.913437	−	0.00522082i
$505$	10.4114	−	28.1442i	0.463303	−	1.25240i
$506$	−4.26847	−	2.46440i	−0.189757	−	0.109556i
$507$	1.09959	+	1.06261i	0.0488344	+	0.0471920i
$508$	−2.44094	+	1.40928i	−0.108299	+	0.0625265i
$509$	−9.57465	+	16.5838i	−0.424389	+	0.735063i	−0.996363	−	0.0852085i	$-0.972844\pi$
$509$	−9.57465	+	16.5838i	−0.424389	+	0.735063i	0.571974	+	0.820272i	$0.306178\pi$
$510$	20.9254	+	1.58116i	0.926592	+	0.0700147i
$511$	−15.9600	+	8.61794i	−0.706031	+	0.381235i
$512$	−15.8265			−0.699439
$513$	−6.04268	+	1.95635i	−0.266791	+	0.0863749i
$514$	17.2238	−	9.94415i	0.759708	−	0.438617i
$515$	12.7548	−	2.17998i	0.562044	−	0.0960615i
$516$	−1.48008	−	0.369578i	−0.0651570	−	0.0162698i
$517$	13.1082			0.576499
$518$	14.8584	+	27.5171i	0.652842	+	1.20903i
$519$	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	0.820369	−	0.571834i	$-0.193768\pi$
$521$	−1.94104	−	3.36199i	−0.0850387	−	0.147291i	−0.905408	+	0.424543i	$0.860435\pi$
$522$	−12.7237	+	23.8893i	−0.556902	+	1.04561i
$523$	1.06192	−	1.83929i	0.0464343	−	0.0804266i	−0.841874	−	0.539674i	$-0.818548\pi$
$523$	1.06192	−	1.83929i	0.0464343	−	0.0804266i	0.888308	+	0.459247i	$0.151881\pi$
$524$	−2.78100			−0.121488
$525$	12.7282	+	19.0524i	0.555506	+	0.831513i
$526$	−26.8562			−1.17099
$527$	5.68157	−	9.84076i	0.247493	−	0.428670i
$528$	11.6409	−	12.0460i	0.506605	−	0.524236i
$529$	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
$532$	−0.951321	−	0.0271092i	−0.0412450	−	0.00117533i
$533$	41.3138			1.78950
$534$	−1.13128	+	4.53055i	−0.0489555	+	0.196056i
$535$	8.56615	−	1.46408i	0.370347	−	0.0632978i
$536$	−23.0856	+	13.3285i	−0.997148	+	0.575704i
$537$	27.2393	+	6.80168i	1.17546	+	0.293514i
$538$	6.67354			0.287717
$539$	13.4304	−	6.76522i	0.578490	−	0.291398i
$540$	−1.58616	−	3.02906i	−0.0682573	−	0.130350i
$541$	7.59052	−	13.1472i	0.326342	−	0.565241i	−0.655441	−	0.755246i	$-0.727517\pi$
$541$	7.59052	−	13.1472i	0.326342	−	0.565241i	0.981783	+	0.190005i	$0.0608506\pi$
$542$	−30.9431	+	17.8650i	−1.32912	+	0.767367i
$543$	−23.3650	+	24.1782i	−1.00269	+	1.03759i
$544$	5.11716	+	2.95439i	0.219396	+	0.126669i
$545$	4.04017	−	10.9214i	0.173062	−	0.467821i
$546$	5.98744	+	23.4084i	0.256239	+	1.00179i
$547$		−	11.7540i		−	0.502566i	−0.967914	−	0.251283i	$-0.919148\pi$
$547$		−	11.7540i		−	0.502566i	0.967914	−	0.251283i	$-0.0808525\pi$
$548$	1.57521	−	2.72835i	0.0672897	−	0.116549i
$549$	4.79313	−	8.99932i	0.204566	−	0.384082i
$550$	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
$553$	4.24143	+	2.61264i	0.180364	+	0.111101i
$554$			19.4362i			0.825763i
$555$	−17.0406	+	24.9607i	−0.723332	+	1.05952i
$556$	−1.04780	+	0.604946i	−0.0444365	+	0.0256554i
$557$	−4.70135	−	8.14298i	−0.199203	−	0.345029i	0.749068	−	0.662494i	$-0.230502\pi$
$557$	−4.70135	−	8.14298i	−0.199203	−	0.345029i	−0.948270	+	0.317465i	$0.897169\pi$
$558$	−14.4260	+	0.493624i	−0.610703	+	0.0208968i
$559$			10.4183i			0.440649i
$560$	3.73743	+	26.3704i	0.157935	+	1.11435i
$561$	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	−0.0993632	−	0.995051i	$-0.531681\pi$
$563$	16.9106	−	9.76331i	0.712695	−	0.411475i	0.812058	+	0.583577i	$0.198347\pi$
$564$	2.16122	−	2.23644i	0.0910040	−	0.0941712i
$565$	−13.3722	−	16.1075i	−0.562574	−	0.677648i
$566$	9.92744			0.417281
$567$	−0.950307	−	23.7928i	−0.0399091	−	0.999203i
$568$		−	26.8615i		−	1.12708i
$569$	11.1702	+	6.44911i	0.468279	+	0.270361i	0.715519	−	0.698593i	$-0.246190\pi$
$569$	11.1702	+	6.44911i	0.468279	+	0.270361i	−0.247240	+	0.968954i	$0.579524\pi$
$570$	−3.10726	−	6.46250i	−0.130149	−	0.270684i
$571$	20.8321	+	36.0823i	0.871796	+	1.51000i	0.860137	+	0.510063i	$0.170378\pi$
$571$	20.8321	+	36.0823i	0.871796	+	1.51000i	0.0116595	+	0.999932i	$0.496289\pi$
$572$	1.90584	+	1.10034i	0.0796874	+	0.0460075i
$573$	6.05758	+	21.1533i	0.253059	+	0.883692i
$574$	−40.4965	−	24.9451i	−1.69029	−	1.04119i
$575$	5.75012	+	4.92881i	0.239797	+	0.205545i
$576$	0.667053	+	19.4945i	0.0277939	+	0.812270i
$577$	−3.74489	−	6.48634i	−0.155902	−	0.270030i	0.777485	−	0.628901i	$-0.216495\pi$
$577$	−3.74489	−	6.48634i	−0.155902	−	0.270030i	−0.933387	+	0.358871i	$0.883162\pi$
$578$	−3.18369	−	5.51432i	−0.132424	−	0.229365i
$579$	34.9863	+	8.73611i	1.45398	+	0.363060i
$580$	−3.67605	−	1.35989i	−0.152640	−	0.0564663i
$581$	24.0794	+	0.686177i	0.998983	+	0.0284674i
$582$	−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
$585$	−17.4460	+	15.5213i	−0.721302	+	0.641726i
$586$	4.87892	+	2.81685i	0.201546	+	0.116363i
$587$		−	22.1920i		−	0.915961i	−0.888962	−	0.457981i	$-0.848573\pi$
$587$		−	22.1920i		−	0.915961i	0.888962	−	0.457981i	$-0.151427\pi$
$588$	1.06011	−	3.40683i	0.0437182	−	0.140495i
$589$	−3.88284			−0.159990
$590$	−4.69322	−	5.65322i	−0.193217	−	0.232739i
$591$	−2.78328	−	2.68967i	−0.114489	−	0.110638i
$592$	−30.4244	+	17.5655i	−1.25043	+	0.721938i
$593$	5.46787	+	3.15687i	0.224538	+	0.129637i	0.608050	−	0.793899i	$-0.291952\pi$
$593$	5.46787	+	3.15687i	0.224538	+	0.129637i	−0.383512	+	0.923536i	$0.625285\pi$
$594$	−12.5534	−	11.3271i	−0.515072	−	0.464757i
$595$	−7.90492	+	19.6311i	−0.324070	+	0.804797i
$596$		−	0.748572i		−	0.0306627i
$597$	41.8803	+	10.4575i	1.71405	+	0.427999i
$598$	3.99316	+	6.91636i	0.163293	+	0.282831i
$599$	17.8962	−	10.3324i	0.731219	−	0.422170i	−0.0876487	−	0.996151i	$-0.527935\pi$
$599$	17.8962	−	10.3324i	0.731219	−	0.422170i	0.818868	+	0.573982i	$0.194602\pi$
$600$	−18.2434	+	12.9543i	−0.744785	+	0.528858i
$601$		−	12.5956i		−	0.513785i	−0.966440	−	0.256892i	$-0.917301\pi$
$601$		−	12.5956i		−	0.513785i	0.966440	−	0.256892i	$-0.0826986\pi$
$602$	6.29053	−	10.2122i	0.256383	−	0.416219i
$603$	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
$606$	−25.3178	−	24.4663i	−1.02847	−	0.993877i
$607$	21.3383	−	36.9590i	0.866095	−	1.50012i	0.000139312	−	1.00000i	$-0.499956\pi$
$607$	21.3383	−	36.9590i	0.866095	−	1.50012i	0.865956	−	0.500121i	$-0.166711\pi$
$608$		−	2.01906i		−	0.0818838i
$609$	−19.0801	−	19.5196i	−0.773163	−	0.790974i
$610$	10.7962	+	3.99387i	0.437127	+	0.161707i
$611$	−18.3942	−	10.6199i	−0.744148	−	0.429634i
$612$	1.48459	−	2.78738i	0.0600110	−	0.112673i
$613$	−4.60972	+	2.66142i	−0.186185	+	0.107494i	−0.590195	−	0.807261i	$-0.700949\pi$
$613$	−4.60972	+	2.66142i	−0.186185	+	0.107494i	0.404011	+	0.914754i	$0.367616\pi$
$614$	8.48998	−	14.7051i	0.342628	−	0.593448i
$615$	3.46342	−	45.8358i	0.139659	−	1.84828i
$616$	6.97728	+	12.9216i	0.281123	+	0.520626i
$617$	30.1002			1.21179			0.605895	−	0.795545i	$-0.292815\pi$
$617$	30.1002			1.21179			0.605895	+	0.795545i	$0.292815\pi$
$618$	3.67800	−	14.7296i	0.147951	−	0.592511i
$619$	11.0265	−	6.36613i	0.443191	−	0.255876i	−0.261759	−	0.965133i	$-0.584303\pi$
$619$	11.0265	−	6.36613i	0.443191	−	0.255876i	0.704950	+	0.709257i	$0.250969\pi$
$620$	−0.352152	−	2.06040i	−0.0141428	−	0.0827475i
$621$	−2.42425	−	7.48790i	−0.0972817	−	0.300479i
$622$	−28.6594			−1.14914
$623$	−4.00959	−	2.46983i	−0.160641	−	0.0989518i
$624$	−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
$627$	−3.27066	−	3.16066i	−0.130618	−	0.126225i
$628$	−2.04876	+	3.54856i	−0.0817545	+	0.141603i
$629$	−27.9145			−1.11303
$630$	26.4725	−	4.68041i	1.05469	−	0.186472i
$631$	−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
$633$	8.23930	+	7.96219i	0.327483	+	0.316469i
$634$	−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
$637$	−24.3273	−	1.38761i	−0.963881	−	0.0549789i
$638$	−19.3823			−0.767353
$639$	−31.1721	+	1.06663i	−1.23315	+	0.0421954i
$640$	−28.9885	+	4.95456i	−1.14587	+	0.195846i
$641$	1.13893	−	0.657564i	0.0449852	−	0.0259722i	−0.477339	−	0.878719i	$-0.658399\pi$
$641$	1.13893	−	0.657564i	0.0449852	−	0.0259722i	0.522324	+	0.852747i	$0.325065\pi$
$642$	2.47015	−	9.89243i	0.0974891	−	0.390423i
$643$	39.2223			1.54678			0.773389	−	0.633932i	$-0.218560\pi$
$643$	39.2223			1.54678			0.773389	+	0.633932i	$0.218560\pi$
$644$	0.0335929	−	1.17885i	0.00132375	−	0.0464531i
$645$	11.5587	+	0.873390i	0.455121	+	0.0343897i
$646$	3.31152	−	5.73572i	0.130290	−	0.225669i
$647$	5.39634	−	3.11558i	0.212152	−	0.122486i	−0.390159	−	0.920747i	$-0.627580\pi$
$647$	5.39634	−	3.11558i	0.212152	−	0.122486i	0.602311	+	0.798261i	$0.294247\pi$
$648$	23.1983	−	1.58944i	0.911316	−	0.0624391i
$649$	−4.03604	−	2.33021i	−0.158428	−	0.0914687i
$650$	−20.0160	−	17.1570i	−0.785092	−	0.672954i
$651$	3.92744	−	14.0170i	0.153928	−	0.549369i
$652$		−	1.19793i		−	0.0469144i
$653$	9.43091	−	16.3348i	0.369060	−	0.639230i	−0.620359	−	0.784318i	$-0.713013\pi$
$653$	9.43091	−	16.3348i	0.369060	−	0.639230i	0.989419	+	0.145088i	$0.0463464\pi$
$654$	−9.82460	−	9.49418i	−0.384172	−	0.371252i
$655$	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
$658$	11.6180	+	21.5160i	0.452918	+	0.838783i
$659$			41.6170i			1.62117i	0.585622	+	0.810584i	$0.300850\pi$
$659$			41.6170i			1.62117i	−0.585622	+	0.810584i	$0.699150\pi$
$660$	1.38055	−	2.02220i	0.0537377	−	0.0787141i
$661$	3.27232	−	1.88927i	0.127278	−	0.0734842i	−0.435009	−	0.900426i	$-0.643255\pi$
$661$	3.27232	−	1.88927i	0.127278	−	0.0734842i	0.562287	+	0.826942i	$0.309921\pi$
$662$	−14.5982	−	25.2848i	−0.567374	−	0.982721i
$663$	−20.9251	−	5.22503i	−0.812665	−	0.202923i
$664$			23.5236i			0.912894i
$665$	7.15992	−	1.01476i	0.277650	−	0.0393508i
$666$	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
$669$	−5.36848	−	5.18793i	−0.207558	−	0.200577i
$670$	−26.8873	+	22.3215i	−1.03875	+	0.862353i
$671$	7.30148			0.281871
$672$	7.28879	+	2.04225i	0.281171	+	0.0787816i
$673$			31.2573i			1.20488i	0.798163	+	0.602441i	$0.205805\pi$
$673$			31.2573i			1.20488i	−0.798163	+	0.602441i	$0.794195\pi$
$674$	31.0075	+	17.9022i	1.19436	+	0.689565i
$675$	15.7576	+	20.6567i	0.606510	+	0.795076i
$676$	0.129901	+	0.224996i	0.00499621	+	0.00865369i
$677$	7.56724	+	4.36895i	0.290832	+	0.167912i	0.638317	−	0.769773i	$-0.279631\pi$
$677$	7.56724	+	4.36895i	0.290832	+	0.167912i	−0.347485	+	0.937686i	$0.612964\pi$
$678$	−23.6132	+	6.76199i	−0.906858	+	0.259693i
$679$	0.0999201	−	3.50641i	0.00383458	−	0.134564i
$680$	−19.3823	−	7.17013i	−0.743278	−	0.274962i
$681$	−18.6719	−	4.66239i	−0.715509	−	0.178663i
$682$	−5.16827	−	8.95171i	−0.197903	−	0.342779i
$683$	−10.9346	−	18.9393i	−0.418401	−	0.724691i	0.577378	−	0.816477i	$-0.304076\pi$
$683$	−10.9346	−	18.9393i	−0.418401	−	0.724691i	−0.995779	+	0.0917858i	$0.970743\pi$
$684$	−1.07850	+	0.0369037i	−0.0412376	+	0.00141105i
$685$	−8.30544	+	22.4513i	−0.317334	+	0.857819i
$686$	23.0081	+	16.0488i	0.878454	+	0.612746i
$687$	−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
$690$	8.00813	−	3.85041i	0.304864	−	0.146583i
$691$	19.5167	+	11.2680i	0.742449	+	0.428653i	0.822959	−	0.568101i	$-0.192322\pi$
$691$	19.5167	+	11.2680i	0.742449	+	0.428653i	−0.0805102	+	0.996754i	$0.525655\pi$
$692$			2.94359i			0.111898i
$693$	14.7182	−	8.61007i	0.559097	−	0.327069i
$694$	24.0944			0.914612
$695$	7.07341	−	5.87224i	0.268310	−	0.222747i
$696$	18.5229	−	19.1675i	0.702107	−	0.726542i
$697$	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
$700$	1.18784	+	3.70732i	0.0448961	+	0.140123i
$701$			35.5019i			1.34089i	0.741960	+	0.670444i	$0.233896\pi$
$701$			35.5019i			1.34089i	−0.741960	+	0.670444i	$0.766104\pi$
$702$	8.43873	+	26.0652i	0.318499	+	0.983766i
$703$	4.76927	+	8.26062i	0.179877	+	0.311555i
$704$	−12.0968	+	6.98408i	−0.455915	+	0.263223i
$705$	−13.3243	+	19.5172i	−0.501821	+	0.735059i
$706$		−	38.5033i		−	1.44909i
$707$	31.2425	−	16.8700i	1.17500	−	0.634463i
$708$	−1.06301	+	0.304409i	−0.0399503	+	0.0114404i
$709$	−2.03390	+	3.52282i	−0.0763847	+	0.132302i	−0.901688	−	0.432388i	$-0.857671\pi$
$709$	−2.03390	+	3.52282i	−0.0763847	+	0.132302i	0.825303	+	0.564690i	$0.191004\pi$
$710$	−5.93246	−	34.7100i	−0.222641	−	1.30264i
$711$	4.98549	+	2.65532i	0.186970	+	0.0995824i
$712$	2.29934	−	3.98257i	0.0861712	−	0.149253i
$713$		−	4.81149i		−	0.180192i
$714$	17.3563	+	17.7561i	0.649543	+	0.664506i
$715$	−15.6830	−	5.80164i	−0.586511	−	0.216969i
$716$	4.13106	+	2.38507i	0.154385	+	0.0891342i
$717$	−3.45864	+	3.57901i	−0.129165	+	0.133660i
$718$	31.7169	−	18.3118i	1.18366	−	0.683389i
$719$	15.2703	−	26.4489i	0.569484	−	0.986376i	−0.427133	−	0.904189i	$-0.640476\pi$
$719$	15.2703	−	26.4489i	0.569484	−	0.986376i	0.996617	−	0.0821868i	$-0.0261904\pi$
$720$	6.10289	+	29.5770i	0.227441	+	1.10227i
$721$	13.0359	+	8.02984i	0.485481	+	0.299047i
$722$	26.5159			0.986821
$723$	−43.8131	−	10.9402i	−1.62943	−	0.406869i
$724$	−4.94730	+	2.85632i	−0.183865	+	0.106154i
$725$	29.2738	+	5.47953i	1.08720	+	0.203505i
$726$	−4.05805	+	16.2516i	−0.150608	+	0.603155i
$727$	−23.4181			−0.868528			−0.434264	−	0.900786i	$-0.642992\pi$
$727$	−23.4181			−0.868528			−0.434264	+	0.900786i	$0.642992\pi$
$728$	0.677789	−	23.7850i	0.0251205	−	0.881533i
$729$	−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
$732$	1.20383	−	1.24573i	0.0444950	−	0.0460436i
$733$	−8.44533	+	14.6277i	−0.311935	+	0.540288i	−0.978781	−	0.204908i	$-0.934311\pi$
$733$	−8.44533	+	14.6277i	−0.311935	+	0.540288i	0.666846	+	0.745196i	$0.267644\pi$
$734$	−13.7423			−0.507239
$735$	−3.57889	+	26.8736i	−0.132009	+	0.991248i
$736$	2.50196			0.0922235
$737$	−11.0827	+	19.1958i	−0.408237	+	0.707087i
$738$	−47.6006	−	25.3526i	−1.75220	−	0.933242i
$739$	−13.8321	−	23.9579i	−0.508822	−	0.881306i	−0.999948	−	0.0102170i	$-0.996748\pi$
$739$	−13.8321	−	23.9579i	−0.508822	−	0.881306i	0.491126	−	0.871089i	$-0.336586\pi$
$740$	−3.95088	+	3.27997i	−0.145237	+	0.120574i
$741$	2.02890	+	7.08499i	0.0745333	+	0.260274i
$742$	1.28148	−	44.9699i	0.0470446	−	1.65090i
$743$	−40.1701			−1.47370			−0.736850	−	0.676056i	$-0.763688\pi$
$743$	−40.1701			−1.47370			−0.736850	+	0.676056i	$0.763688\pi$
$744$	13.7916	+	3.44377i	0.505624	+	0.126255i
$745$	0.958262	+	5.60667i	0.0351080	+	0.205412i
$746$	20.4158	−	11.7870i	0.747474	−	0.431554i
$747$	27.2986	−	0.934092i	0.998804	−	0.0341766i
$748$	2.26151			0.0826888
$749$	8.75491	+	5.39286i	0.319898	+	0.197051i
$750$	−20.7129	+	20.7685i	−0.756328	+	0.758359i
$751$	24.8188	−	42.9874i	0.905650	−	1.56863i	0.0856082	−	0.996329i	$-0.472717\pi$
$751$	24.8188	−	42.9874i	0.905650	−	1.56863i	0.820042	−	0.572303i	$-0.193950\pi$
$752$	−23.7893	+	13.7347i	−0.867505	+	0.500854i
$753$	0.200676	+	0.193927i	0.00731305	+	0.00706709i
$754$	27.1983	+	15.7029i	0.990503	+	0.571867i
$755$	−4.35936	+	11.7842i	−0.158654	+	0.428873i
$756$	0.957668	−	3.93071i	0.0348301	−	0.142958i
$757$			47.7116i			1.73411i	0.498214	+	0.867054i	$0.333989\pi$
$757$			47.7116i			1.73411i	−0.498214	+	0.867054i	$0.666011\pi$
$758$	−25.8242	+	44.7288i	−0.937977	+	1.62462i
$759$	3.91659	−	4.05290i	0.142163	−	0.147111i
$760$	1.18970	+	6.96075i	0.0431548	+	0.252493i
$761$	−9.91711	+	17.1769i	−0.359495	+	0.622663i	−0.987876	−	0.155242i	$-0.950384\pi$
$761$	−9.91711	+	17.1769i	−0.359495	+	0.622663i	0.628382	+	0.777905i	$0.283718\pi$
$762$	−6.91759	−	24.1565i	−0.250598	−	0.875098i
$763$	12.1237	−	6.54643i	0.438907	−	0.236997i
$764$			3.73847i			0.135253i
$765$	−7.55112	+	22.7774i	−0.273011	+	0.823520i
$766$	13.8740	−	8.01017i	0.501289	−	0.289419i
$767$	3.77572	+	6.53974i	0.136333	+	0.236136i
$768$	−2.90258	+	11.6242i	−0.104738	+	0.419454i
$769$		−	10.6337i		−	0.383461i	−0.981448	−	0.191731i	$-0.938590\pi$
$769$		−	10.6337i		−	0.383461i	0.981448	−	0.191731i	$-0.0614100\pi$
$770$	11.8697	+	15.1562i	0.427755	+	0.546190i
$771$	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	−0.706197	−	0.708015i	$-0.749591\pi$
$773$	−12.4039	+	7.16138i	−0.446136	+	0.257577i	0.260061	+	0.965592i	$0.416257\pi$
$774$	6.39330	−	12.0037i	0.229802	−	0.431464i
$775$	5.27511	+	14.9812i	0.189488	+	0.538140i
$776$	3.42548			0.122967
$777$	−34.6448	+	8.86150i	−1.24287	+	0.317904i
$778$		−	25.6508i		−	0.919626i
$779$	−12.5637	−	7.25368i	−0.450142	−	0.259890i
$780$	−3.57558	+	1.71918i	−0.128026	+	0.0615567i
$781$	−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
$784$	−17.2855	+	26.3501i	−0.617338	+	0.941075i
$785$	10.8023	−	29.2007i	0.385550	−	1.04222i
$786$	6.00634	−	24.0541i	0.214239	−	0.857982i
$787$	18.4671	+	31.9859i	0.658280	+	1.14017i	0.981061	+	0.193700i	$0.0620490\pi$
$787$	18.4671	+	31.9859i	0.658280	+	1.14017i	−0.322781	+	0.946474i	$0.604618\pi$
$788$	−0.328807	−	0.569511i	−0.0117133	−	0.0202880i
$789$	7.43992	−	29.7953i	0.264868	−	1.06074i
$790$	−2.21254	+	5.98095i	−0.0787188	+	0.212793i
$791$	0.705583	−	24.7604i	0.0250876	−	0.880378i
$792$	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
$795$	39.1842	−	18.8403i	1.38972	−	0.668195i
$796$	6.35148	+	3.66703i	0.225122	+	0.129974i
$797$			37.4862i			1.32783i	0.747809	+	0.663914i	$0.231106\pi$
$797$			37.4862i			1.32783i	−0.747809	+	0.663914i	$0.768894\pi$
$798$	2.28912	−	8.16985i	0.0810340	−	0.289210i
$799$	−21.8268			−0.772177
$800$	−7.79017	+	2.74304i	−0.275424	+	0.0969810i
$801$	−4.71298	−	2.51018i	−0.166525	−	0.0886929i
$802$	−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
$805$	1.25746	+	8.87235i	0.0443197	+	0.312709i
$806$			16.7487i			0.589947i
$807$	−1.84876	+	7.40389i	−0.0650794	+	0.260629i
$808$	17.3363	+	30.0274i	0.609889	+	1.05636i
$809$	22.1518	−	12.7893i	0.778814	−	0.449649i	−0.0571956	−	0.998363i	$-0.518216\pi$
$809$	22.1518	−	12.7893i	0.778814	−	0.449649i	0.836010	+	0.548714i	$0.184883\pi$
$810$	29.6255	−	7.17728i	1.04093	−	0.252184i
$811$			7.28791i			0.255913i	0.991780	+	0.127957i	$0.0408418\pi$
$811$			7.28791i			0.255913i	−0.991780	+	0.127957i	$0.959158\pi$
$812$	−2.20348	−	4.08074i	−0.0773269	−	0.143206i
$813$	−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
$816$	−19.3835	+	20.0581i	−0.678559	+	0.702175i
$817$	1.82920	−	3.16826i	0.0639955	−	0.110844i
$818$			3.96956i			0.138792i
$819$	−27.6289	+	0.157915i	−0.965432	+	0.00551800i
$820$	2.70964	−	7.32470i	0.0946247	−	0.255790i
$821$	0.00729231	+	0.00421022i	0.000254504	+	0.000146938i	0.500127	−	0.865952i	$-0.333287\pi$
$821$	0.00729231	+	0.00421022i	0.000254504	+	0.000146938i	−0.499873	+	0.866099i	$0.666620\pi$
$822$	20.1966	+	19.5173i	0.704437	+	0.680745i
$823$	27.0406	−	15.6119i	0.942578	−	0.544198i	0.0518103	−	0.998657i	$-0.483501\pi$
$823$	27.0406	−	15.6119i	0.942578	−	0.544198i	0.890767	+	0.454459i	$0.150168\pi$
$824$	−7.47553	+	12.9480i	−0.260422	+	0.451065i
$825$	−7.75138	+	16.9132i	−0.269868	+	0.588842i
$826$	0.247637	−	8.69011i	0.00861639	−	0.302368i
$827$	−38.3189			−1.33248			−0.666239	−	0.745738i	$-0.732097\pi$
$827$	−38.3189			−1.33248			−0.666239	+	0.745738i	$0.732097\pi$
$828$	−0.0457300	−	1.33645i	−0.00158923	−	0.0464447i
$829$	−1.94142	+	1.12088i	−0.0674283	+	0.0389298i	−0.533335	−	0.845904i	$-0.679062\pi$
$829$	−1.94142	+	1.12088i	−0.0674283	+	0.0389298i	0.465907	+	0.884834i	$0.345728\pi$
$830$	5.19528	+	30.3969i	0.180331	+	1.05509i
$831$	−21.5632	−	5.38436i	−0.748020	−	0.186781i
$832$	22.6331			0.784663
$833$	−22.3633	+	11.2649i	−0.774843	+	0.390306i
$834$	−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
$837$	3.44877	−	16.1416i	0.119207	−	0.557934i
$838$	−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	$0.616042\pi$
$840$	−26.3316	−	2.74592i	−0.908526	−	0.0947433i
$841$	−6.47924			−0.223422
$842$	5.94479	−	10.2967i	0.204871	−	0.354847i
$843$	−25.5646	+	26.4543i	−0.880492	+	0.911135i
$844$	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
$847$	−14.3829	−	8.85959i	−0.494202	−	0.304419i
$848$	50.5391			1.73552
$849$	−2.75018	+	11.0139i	−0.0943859	+	0.377996i
$850$	−26.6291	−	4.98449i	−0.913371	−	0.170966i
$851$	−10.2363	+	5.90993i	−0.350896	+	0.202590i
$852$	−5.14147	−	1.28383i	−0.176144	−	0.0439833i
$853$	−7.06831			−0.242014			−0.121007	−	0.992652i	$-0.538612\pi$
$853$	−7.06831			−0.242014			−0.121007	+	0.992652i	$0.538612\pi$
$854$	6.47141	+	11.9848i	0.221447	+	0.410110i
$855$	8.03055	−	1.65702i	0.274639	−	0.0566687i
$856$	−5.02058	+	8.69590i	−0.171600	+	0.297220i
$857$	14.5780	−	8.41661i	0.497975	−	0.287506i	−0.229902	−	0.973214i	$-0.573841\pi$
$857$	14.5780	−	8.41661i	0.497975	−	0.287506i	0.727877	+	0.685708i	$0.240507\pi$
$858$	−13.6335	+	14.1080i	−0.465441	+	0.481640i
$859$	−30.4698	−	17.5918i	−1.03962	−	0.600223i	−0.119893	−	0.992787i	$-0.538255\pi$
$859$	−30.4698	−	17.5918i	−1.03962	−	0.600223i	−0.919725	+	0.392563i	$0.871588\pi$
$860$	1.84711	+	0.683304i	0.0629859	+	0.0233005i
$861$	38.8937	−	38.0179i	1.32549	−	1.29565i
$862$			18.5665i			0.632376i
$863$	18.9879	−	32.8880i	0.646356	−	1.11952i	−0.337630	−	0.941279i	$-0.609625\pi$
$863$	18.9879	−	32.8880i	0.646356	−	1.11952i	0.983986	−	0.178243i	$-0.0570414\pi$
$864$	8.39355	+	1.79335i	0.285554	+	0.0610110i
$865$	−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
$868$	1.29713	−	2.10580i	0.0440275	−	0.0714755i
$869$			4.04491i			0.137214i
$870$	19.7018	−	28.8588i	0.667952	−	0.978405i
$871$	31.1037	−	17.9577i	1.05391	−	0.608474i
$872$	6.72737	+	11.6521i	0.227817	+	0.394591i
$873$	−0.136021	−	3.97518i	−0.00460362	−	0.134540i
$874$		−	2.80440i		−	0.0948601i
$875$	−13.6425	−	26.2466i	−0.461201	−	0.887296i
$876$	−3.35932	+	0.961992i	−0.113501	+	0.0325027i
$877$	9.91566	+	5.72481i	0.334828	+	0.193313i	0.657983	−	0.753033i	$-0.271410\pi$
$877$	9.91566	+	5.72481i	0.334828	+	0.193313i	−0.323155	+	0.946346i	$0.604743\pi$
$878$	21.9054	−	12.6471i	0.739272	−	0.426819i
$879$	−4.47672	+	4.63252i	−0.150996	+	0.156251i
$880$	−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	$0.369452\pi$
$882$	27.1776	+	16.5274i	0.915118	+	0.556506i
$883$		−	16.8355i		−	0.566560i	−0.959037	−	0.283280i	$-0.908577\pi$
$883$		−	16.8355i		−	0.566560i	0.959037	−	0.283280i	$-0.0914226\pi$
$884$	−3.17346	−	1.83220i	−0.106735	−	0.0616236i
$885$	7.57206	−	3.64075i	0.254532	−	0.122382i
$886$	−0.191017	−	0.330852i	−0.00641735	−	0.0111152i
$887$	−45.5385	−	26.2917i	−1.52903	−	0.882789i	−0.999403	−	0.0345613i	$-0.988997\pi$
$887$	−45.5385	−	26.2917i	−1.52903	−	0.882789i	−0.529632	−	0.848227i	$-0.677670\pi$
$888$	−9.61362	−	33.5712i	−0.322612	−	1.12657i
$889$	25.3301	+	0.721818i	0.849546	+	0.0242090i
$890$	2.09160	−	5.65403i	0.0701107	−	0.189524i
$891$	16.0444	−	10.7893i	0.537507	−	0.361455i
$892$	−0.634214	−	1.09849i	−0.0212350	−	0.0367802i
$893$	3.72917	+	6.45910i	0.124792	+	0.216146i
$894$	6.47474	+	1.61675i	0.216548	+	0.0540722i
$895$	−33.9941	−	12.5755i	−1.13630	−	0.420352i
$896$	−29.6273	−	18.2498i	−0.989778	−	0.609685i
$897$	−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
$900$	1.60761	+	4.11106i	0.0535869	+	0.137035i
$901$	34.7774	+	20.0788i	1.15860	+	0.668921i
$902$		−	38.6201i		−	1.28591i
$903$	9.58717	+	9.80803i	0.319041	+	0.326391i
$904$	24.1889			0.804510
$905$	33.3979	−	27.7265i	1.11019	−	0.921660i
$906$	10.6008	+	10.2443i	0.352188	+	0.340343i
$907$	−43.9694	+	25.3858i	−1.45998	+	0.842920i	−0.999010	−	0.0444946i	$-0.985832\pi$
$907$	−43.9694	+	25.3858i	−1.45998	+	0.842920i	−0.460971	+	0.887415i	$0.652499\pi$
$908$	−2.83174	−	1.63491i	−0.0939747	−	0.0542563i
$909$	34.1577	−	21.3107i	1.13294	−	0.706832i
$910$	−4.37718	−	30.8844i	−0.145102	−	1.02381i
$911$			16.1165i			0.533963i	0.963702	+	0.266981i	$0.0860262\pi$
$911$			16.1165i			0.533963i	−0.963702	+	0.266981i	$0.913974\pi$
$912$	9.24743	+	2.30909i	0.306213	+	0.0764617i
$913$	9.77999	+	16.9394i	0.323671	+	0.560614i
$914$	−31.5787	+	18.2319i	−1.04453	+	0.603059i
$915$	−7.42182	+	10.8714i	−0.245358	+	0.359396i
$916$		−	2.93515i		−	0.0969802i
$917$	21.2882	+	13.1131i	0.702997	+	0.433033i
$918$	20.9029	+	18.8610i	0.689900	+	0.622506i
$919$	−19.8721	+	34.4194i	−0.655519	+	1.13539i	0.326245	+	0.945285i	$0.394217\pi$
$919$	−19.8721	+	34.4194i	−0.655519	+	1.13539i	−0.981763	+	0.190106i	$0.939117\pi$
$920$	−8.62555	+	1.47423i	−0.284376	+	0.0486040i
$921$	13.9624	+	13.4928i	0.460077	+	0.444604i
$922$	30.1960	−	52.3010i	0.994452	−	1.72244i
$923$			36.1909i			1.19124i
$924$	2.80676	−	0.717917i	0.0923355	−	0.0236177i
$925$	25.3926	−	29.6240i	0.834905	−	0.974030i
$926$	−39.1451	−	22.6004i	−1.28639	−	0.742696i
$927$	15.3227	+	8.16102i	0.503263	+	0.268043i
$928$	8.52069	−	4.91942i	0.279705	−	0.161488i
$929$	−18.2593	+	31.6261i	−0.599069	+	1.03762i	0.393889	+	0.919158i	$0.371129\pi$
$929$	−18.2593	+	31.6261i	−0.599069	+	1.03762i	−0.992959	+	0.118461i	$0.962204\pi$
$930$	18.5819	+	1.40407i	0.609323	+	0.0460414i
$931$	7.15440	+	4.69323i	0.234476	+	0.153814i
$932$	−6.07063			−0.198850
$933$	7.93946	−	31.7959i	0.259926	−	1.04095i
$934$	5.48530	−	3.16694i	0.179484	−	0.103625i
$935$	−16.9383	+	2.89500i	−0.553941	+	0.0946766i
$936$	−0.922672	−	26.9649i	−0.0301585	−	0.881375i
$937$	−7.60980			−0.248601			−0.124301	−	0.992245i	$-0.539669\pi$
$937$	−7.60980			−0.248601			−0.124301	+	0.992245i	$0.539669\pi$
$938$	−41.3311	−	1.17779i	−1.34951	−	0.0384561i
$939$	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	0.628807	−	0.777562i	$-0.283544\pi$
$941$	−11.0121	−	19.0735i	−0.358985	−	0.621780i	−0.987791	+	0.155782i	$0.950210\pi$
$942$	−26.2682	−	25.3848i	−0.855866	−	0.827081i
$943$	8.98853	−	15.5686i	0.292707	−	0.506983i
$944$	9.76632			0.317867
$945$	−2.14099	+	30.6662i	−0.0696463	+	0.997572i
$946$	9.73904			0.316644
$947$	−24.6291	+	42.6589i	−0.800339	+	1.38623i	0.119053	+	0.992888i	$0.462014\pi$
$947$	−24.6291	+	42.6589i	−0.800339	+	1.38623i	−0.919393	+	0.393341i	$0.871319\pi$
$948$	0.690116	+	0.666906i	0.0224139	+	0.0216601i
$949$	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
$952$	−11.6180	−	21.5160i	−0.376542	−	0.697339i
$953$	10.2538			0.332154			0.166077	−	0.986113i	$-0.446890\pi$
$953$	10.2538			0.332154			0.166077	+	0.986113i	$0.446890\pi$
$954$	−1.74448	−	50.9819i	−0.0564795	−	1.65060i
$955$	−4.78569	−	28.0005i	−0.154861	−	0.906073i
$956$	−0.732331	+	0.422811i	−0.0236853	+	0.0136747i
$957$	5.36945	−	21.5035i	0.173570	−	0.695109i
$958$	−42.3131			−1.36708
$959$	−24.9229	+	13.4576i	−0.804801	+	0.434569i
$960$	1.89738	−	25.1104i	0.0612377	−	0.810435i
$961$	−10.4547	+	18.1081i	−0.337250	+	0.584134i
$962$	35.6323	−	20.5723i	1.14883	−	0.663278i
$963$	10.2907	+	5.48096i	0.331615	+	0.176622i
$964$	−6.64460	−	3.83626i	−0.214008	−	0.123558i
$965$	−43.6621	−	16.1520i	−1.40553	−	0.519951i
$966$	10.1238	+	2.83661i	0.325729	+	0.0912663i
$967$			4.62632i			0.148772i	0.997230	+	0.0743862i	$0.0236998\pi$
$967$			4.62632i			0.148772i	−0.997230	+	0.0743862i	$0.976300\pi$
$968$	8.24799	−	14.2859i	0.265101	−	0.459168i
$969$	5.44605	+	5.26288i	0.174952	+	0.169068i
$970$	4.42635	−	0.756529i	0.142122	−	0.0242907i
$971$	−12.6443	+	21.9006i	−0.405775	+	0.702822i	−0.994411	−	0.105575i	$-0.966332\pi$
$971$	−12.6443	+	21.9006i	−0.405775	+	0.702822i	0.588637	+	0.808398i	$0.299665\pi$
$972$	0.804521	−	4.51628i	0.0258050	−	0.144860i
$973$	10.8732	+	0.309848i	0.348579	+	0.00993326i
$974$		−	56.4119i		−	1.80755i
$975$	24.5797	−	17.4536i	0.787180	−	0.558961i
$976$	−13.2510	+	7.65046i	−0.424154	+	0.244885i
$977$	12.0549	+	20.8797i	0.385670	+	0.668000i	0.991862	−	0.127318i	$-0.0406370\pi$
$977$	12.0549	+	20.8797i	0.385670	+	0.668000i	−0.606192	+	0.795318i	$0.707304\pi$
$978$	10.3614	+	2.58725i	0.331321	+	0.0827313i
$979$		−	3.82381i		−	0.122210i
$980$	−1.84156	+	4.22207i	−0.0588264	+	0.134869i
$981$	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	0.343254	−	0.939243i	$-0.388471\pi$
$983$	41.6456	−	24.0441i	1.32829	−	0.766888i	0.985035	+	0.172354i	$0.0551374\pi$
$984$	38.1921	+	36.9076i	1.21752	+	1.17657i
$985$	3.19175	+	3.84462i	0.101698	+	0.122500i
$986$	32.2739			1.02781
$987$	−27.0893	+	6.92894i	−0.862261	+	0.220550i
$988$			1.25214i			0.0398360i
$989$	3.92601	+	2.26668i	0.124840	+	0.0720764i
$990$	14.5093	+	16.3085i	0.461135	+	0.518317i
$991$	−14.8587	−	25.7361i	−0.472003	−	0.817534i	0.527483	−	0.849565i	$-0.323136\pi$
$991$	−14.8587	−	25.7361i	−0.472003	−	0.817534i	−0.999487	+	0.0320314i	$0.989802\pi$
$992$	4.54406	+	2.62352i	0.144274	+	0.0832967i
$993$	32.0960	−	9.19119i	1.01854	−	0.291674i
$994$	21.8519	−	35.4749i	0.693099	−	1.12520i
$995$	−52.2656	−	19.3347i	−1.65693	−	0.612952i
$996$	4.50258	+	1.12430i	0.142670	+	0.0356248i
$997$	−13.3742	−	23.1647i	−0.423564	−	0.733634i	0.572721	−	0.819750i	$-0.305888\pi$
$997$	−13.3742	−	23.1647i	−0.423564	−	0.733634i	−0.996285	+	0.0861161i	$0.972554\pi$
$998$	14.1928	+	24.5826i	0.449265	+	0.778149i
$999$	−38.5768	+	12.4894i	−1.22052	+	0.395148i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.3	✓	24	105.59	even	6	inner
105.2.p.a.59.4	yes	24	7.3	odd	6	inner
105.2.p.a.59.9	yes	24	35.24	odd	6	inner
105.2.p.a.59.10	yes	24	21.17	even	6	inner
105.2.p.a.89.3	yes	24	1.1	even	1	trivial
105.2.p.a.89.4	yes	24	15.14	odd	2	inner
105.2.p.a.89.9	yes	24	3.2	odd	2	inner
105.2.p.a.89.10	yes	24	5.4	even	2	inner
525.2.t.j.26.3		24	5.2	odd	4
525.2.t.j.26.4		24	15.8	even	4
525.2.t.j.26.9		24	15.2	even	4
525.2.t.j.26.10		24	5.3	odd	4
525.2.t.j.101.3		24	105.17	odd	12
525.2.t.j.101.4		24	35.3	even	12
525.2.t.j.101.9		24	35.17	even	12
525.2.t.j.101.10		24	105.38	odd	12
735.2.g.b.734.5		24	21.5	even	6
735.2.g.b.734.6		24	35.9	even	6
735.2.g.b.734.7		24	35.19	odd	6
735.2.g.b.734.8		24	21.2	odd	6
735.2.g.b.734.17		24	105.44	odd	6
735.2.g.b.734.18		24	7.5	odd	6
735.2.g.b.734.19		24	7.2	even	3
735.2.g.b.734.20		24	105.89	even	6
735.2.p.f.374.3		24	7.4	even	3
735.2.p.f.374.4		24	105.74	odd	6
735.2.p.f.374.9		24	21.11	odd	6
735.2.p.f.374.10		24	35.4	even	6
735.2.p.f.509.3		24	105.104	even	2
735.2.p.f.509.4		24	7.6	odd	2
735.2.p.f.509.9		24	35.34	odd	2
735.2.p.f.509.10		24	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.757344 + 1.31176i) q^{2} +(-1.24551 - 1.20362i) q^{3} +(-0.147140 - 0.254854i) q^{4} +(1.42830 + 1.72046i) q^{5} +(2.52214 - 0.722254i) q^{6} +(-0.0753638 + 2.64468i) q^{7} -2.58363 q^{8} +(0.102593 + 2.99825i) q^{9} +(-3.33853 + 0.570605i) q^{10} +(-1.86048 + 1.07415i) q^{11} +(-0.123483 + 0.494525i) q^{12} +3.48097 q^{13} +(-3.41210 - 2.10179i) q^{14} +(0.291817 - 3.86197i) q^{15} +(2.25098 - 3.89881i) q^{16} +(3.09793 - 1.78859i) q^{17} +(-4.01067 - 2.13613i) q^{18} +(-1.05858 - 0.611171i) q^{19} +(0.228305 - 0.617156i) q^{20} +(3.27706 - 3.20326i) q^{21} -3.25401i q^{22} +(0.757344 - 1.31176i) q^{23} +(3.21794 + 3.10972i) q^{24} +(-0.919933 + 4.91464i) q^{25} +(-2.63629 + 4.56619i) q^{26} +(3.48097 - 3.85783i) q^{27} +(0.685096 - 0.369932i) q^{28} -5.95645i q^{29} +(4.84497 + 3.30764i) q^{30} +(2.75098 - 1.58828i) q^{31} +(0.825899 + 1.43050i) q^{32} +(3.61012 + 0.901451i) q^{33} +5.41832i q^{34} +(-4.65769 + 3.64773i) q^{35} +(0.749020 - 0.467309i) q^{36} +(-6.75803 - 3.90175i) q^{37} +(1.60342 - 0.925734i) q^{38} +(-4.33559 - 4.18977i) q^{39} +(-3.69020 - 4.44503i) q^{40} +11.8685 q^{41} +(1.72005 + 6.72468i) q^{42} +2.99294i q^{43} +(0.547504 + 0.316101i) q^{44} +(-5.01181 + 4.45889i) q^{45} +(1.14714 + 1.98691i) q^{46} +(-5.28420 - 3.05084i) q^{47} +(-7.49631 + 2.14668i) q^{48} +(-6.98864 - 0.398626i) q^{49} +(-5.75012 - 4.92881i) q^{50} +(-6.01129 - 1.50103i) q^{51} +(-0.512191 - 0.887140i) q^{52} +(5.61301 + 9.72202i) q^{53} +(2.42425 + 7.48790i) q^{54} +(-4.50535 - 1.66667i) q^{55} +(0.194713 - 6.83288i) q^{56} +(0.582853 + 2.03535i) q^{57} +(7.81342 + 4.51108i) q^{58} +(1.08467 + 1.87871i) q^{59} +(-1.02718 + 0.493881i) q^{60} +(-2.94338 - 1.69936i) q^{61} +4.81149i q^{62} +(-7.93712 + 0.0453652i) q^{63} +6.50196 q^{64} +(4.97186 + 5.98885i) q^{65} +(-3.91659 + 4.05290i) q^{66} +(8.93534 - 5.15882i) q^{67} +(-0.911660 - 0.526347i) q^{68} +(-2.52214 + 0.722254i) q^{69} +(-1.25746 - 8.87235i) q^{70} +10.3968i q^{71} +(-0.265062 - 7.74637i) q^{72} +(3.42779 + 5.93710i) q^{73} +(10.2363 - 5.90993i) q^{74} +(7.06115 - 5.01399i) q^{75} +0.359711i q^{76} +(-2.70057 - 5.00133i) q^{77} +(8.77950 - 2.51414i) q^{78} +(0.941421 - 1.63059i) q^{79} +(9.92280 - 1.69595i) q^{80} +(-8.97895 + 0.615196i) q^{81} +(-8.98853 + 15.5686i) q^{82} -9.10486i q^{83} +(-1.29855 - 0.363843i) q^{84} +(7.50196 + 2.77521i) q^{85} +(-3.92601 - 2.26668i) q^{86} +(-7.16930 + 7.41882i) q^{87} +(4.80681 - 2.77521i) q^{88} +(-0.889962 + 1.54146i) q^{89} +(-2.05332 - 9.95121i) q^{90} +(-0.262339 + 9.20605i) q^{91} -0.445743 q^{92} +(-5.33806 - 1.33292i) q^{93} +(8.00392 - 4.62107i) q^{94} +(-0.460474 - 2.69417i) q^{95} +(0.693113 - 2.77577i) q^{96} -1.32584 q^{97} +(5.81571 - 8.86551i) q^{98} +(-3.41144 - 5.46799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 6 q^{21} + 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} - 72 q^{40} - 18 q^{45} + 36 q^{46} - 12 q^{49} - 12 q^{51} - 36 q^{54} + 12 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) \) 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 6 * q^21 + 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^49 - 12 * q^51 - 36 * q^54 + 12 * q^60 + 36 * q^61 + 24 * q^64 - 72 * q^66 + 108 * q^70 + 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^84 + 48 * q^85 - 96 * q^91 - 72 * q^94 - 90 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more