LMFDB - Embedded newform 105.2.p.a.89.4

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			89.4
Character	$\chi$	$=$	105.89
Dual form			105.2.p.a.59.4

$q$-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} +(2.20411 + 0.376714i) q^{5} +(-2.52214 - 0.722254i) q^{6} +(0.0753638 - 2.64468i) q^{7} -2.58363 q^{8} +(-2.64785 + 1.41027i) q^{9} +(-2.16343 + 2.60595i) q^{10} +(1.86048 - 1.07415i) q^{11} +(0.366529 - 0.354202i) 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} +(0.155396 - 4.54141i) q^{18} +(-1.05858 - 0.611171i) q^{19} +(-0.228305 - 0.617156i) q^{20} +(4.47588 - 0.983091i) q^{21} +3.25401i q^{22} +(0.757344 - 1.31176i) q^{23} +(-1.08412 - 4.34168i) q^{24} +(4.71617 + 1.66064i) q^{25} +(2.63629 - 4.56619i) q^{26} +(-3.48097 - 3.85783i) q^{27} +(-0.685096 + 0.369932i) q^{28} +5.95645i q^{29} +(-5.28698 - 2.54205i) q^{30} +(2.75098 - 1.58828i) q^{31} +(0.825899 + 1.43050i) q^{32} +(2.58574 + 2.67573i) q^{33} +5.41832i q^{34} +(1.16240 - 5.80076i) q^{35} +(0.749020 + 0.467309i) q^{36} +(6.75803 + 3.90175i) q^{37} +(1.60342 - 0.925734i) q^{38} +(-1.46065 - 5.84961i) q^{39} +(-5.69460 - 0.973292i) q^{40} -11.8685 q^{41} +(-2.10021 + 6.61582i) q^{42} -2.99294i q^{43} +(-0.547504 - 0.316101i) q^{44} +(-6.36742 + 2.11091i) 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} +(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} +(-0.194713 + 6.83288i) q^{56} +(0.582853 - 2.03535i) q^{57} +(-7.81342 - 4.51108i) q^{58} +(-1.08467 - 1.87871i) q^{59} +(0.941303 - 0.642622i) q^{60} +(-2.94338 - 1.69936i) q^{61} +4.81149i q^{62} +(3.53017 + 7.10900i) q^{63} +6.50196 q^{64} +(-7.67243 - 1.31133i) 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} +(6.72886 + 5.91796i) q^{70} -10.3968i q^{71} +(6.84108 - 3.64363i) q^{72} +(-3.42779 - 5.93710i) q^{73} +(-10.2363 + 5.90993i) q^{74} +(-0.811666 + 8.62213i) q^{75} +0.359711i q^{76} +(-2.70057 - 5.00133i) q^{77} +(8.77950 + 2.51414i) q^{78} +(0.941421 - 1.63059i) q^{79} +(6.43014 - 7.74542i) q^{80} +(5.02225 - 7.46840i) q^{81} +(8.98853 - 15.5686i) q^{82} -9.10486i q^{83} +(-0.909127 - 0.996046i) q^{84} +(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} +(2.05332 - 9.95121i) q^{90} +(-0.262339 + 9.20605i) q^{91} -0.445743 q^{92} +(3.82337 + 3.95644i) q^{93} +(8.00392 - 4.62107i) q^{94} +(-2.10299 - 1.74587i) q^{95} +(-2.05733 + 1.98814i) 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	$0.986781\pi$
$3$	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
$5$	2.20411	+	0.376714i	0.985706	+	0.168472i
$5$	2.20411	+	0.376714i	0.985706	+	0.168472i
$6$	−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
$9$	−2.64785	+	1.41027i	−0.882618	+	0.470092i
$10$	−2.16343	+	2.60595i	−0.684135	+	0.824075i
$11$	1.86048	−	1.07415i	0.560957	−	0.323869i	−0.192573	−	0.981283i	$-0.561683\pi$
$11$	1.86048	−	1.07415i	0.560957	−	0.323869i	0.753529	+	0.657414i	$0.228350\pi$
$12$	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	$0.660353\pi$
$14$	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	$0.190507\pi$
$18$	0.155396	−	4.54141i	0.0366272	−	1.07042i
$19$	−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
$21$	4.47588	−	0.983091i	0.976718	−	0.214528i
$22$			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	$0.116189\pi$
$24$	−1.08412	−	4.34168i	−0.221295	−	0.886241i
$25$	4.71617	+	1.66064i	0.943235	+	0.332127i
$26$	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	$0.186533\pi$
$29$			5.95645i			1.10608i	−0.833153	+	0.553042i	$0.813467\pi$
$30$	−5.28698	−	2.54205i	−0.965267	−	0.464113i
$31$	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
$33$	2.58574	+	2.67573i	0.450120	+	0.465785i
$34$			5.41832i			0.929234i
$35$	1.16240	−	5.80076i	0.196481	−	0.980508i
$36$	0.749020	+	0.467309i	0.124837	+	0.0778848i
$37$	6.75803	+	3.90175i	1.11101	+	0.641444i	0.939092	−	0.343667i	$-0.111669\pi$
$37$	6.75803	+	3.90175i	1.11101	+	0.641444i	0.171921	+	0.985111i	$0.445002\pi$
$38$	1.60342	−	0.925734i	0.260109	−	0.150174i
$39$	−1.46065	−	5.84961i	−0.233892	−	0.936688i
$40$	−5.69460	−	0.973292i	−0.900396	−	0.153891i
$41$	−11.8685			−1.85355			−0.926773	−	0.375622i	$-0.877429\pi$
$41$	−11.8685			−1.85355			−0.926773	+	0.375622i	$0.877429\pi$
$42$	−2.10021	+	6.61582i	−0.324069	+	1.02084i
$43$		−	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
$45$	−6.36742	+	2.11091i	−0.949199	+	0.314676i
$46$	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
$51$	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	0.937012	+	0.349297i	$0.113580\pi$
$53$	5.61301	+	9.72202i	0.771006	+	1.33542i	−0.166006	+	0.986125i	$0.553087\pi$
$54$	7.69683	−	1.64449i	1.04741	−	0.223787i
$55$	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	0.786741	−	0.617283i	$-0.211767\pi$
$59$	−1.08467	−	1.87871i	−0.141213	−	0.244587i	−0.927954	+	0.372696i	$0.878433\pi$
$60$	0.941303	−	0.642622i	0.121522	−	0.0829622i
$61$	−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
$63$	3.53017	+	7.10900i	0.444760	+	0.895650i
$64$	6.50196			0.812745
$65$	−7.67243	−	1.31133i	−0.951648	−	0.162651i
$66$	−5.46821	+	1.36542i	−0.673090	+	0.168071i
$67$	−8.93534	+	5.15882i	−1.09163	+	0.630250i	−0.934009	−	0.357250i	$-0.883714\pi$
$67$	−8.93534	+	5.15882i	−1.09163	+	0.630250i	−0.157617	+	0.987500i	$0.550381\pi$
$68$	−0.911660	−	0.526347i	−0.110555	−	0.0638290i
$69$	2.52214	+	0.722254i	0.303630	+	0.0869491i
$70$	6.72886	+	5.91796i	0.804253	+	0.707331i
$71$		−	10.3968i		−	1.23387i	−0.787013	−	0.616936i	$-0.788374\pi$
$71$		−	10.3968i		−	1.23387i	0.787013	−	0.616936i	$-0.211626\pi$
$72$	6.84108	−	3.64363i	0.806229	−	0.429406i
$73$	−3.42779	−	5.93710i	−0.401192	−	0.694885i	0.592678	−	0.805439i	$-0.298071\pi$
$73$	−3.42779	−	5.93710i	−0.401192	−	0.694885i	−0.993870	+	0.110555i	$0.964737\pi$
$74$	−10.2363	+	5.90993i	−1.18995	+	0.687016i
$75$	−0.811666	+	8.62213i	−0.0937231	+	0.995598i
$76$			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	$0.132889\pi$
$80$	6.43014	−	7.74542i	0.718911	−	0.865964i
$81$	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	$-0.833446\pi$
$83$		−	9.10486i		−	0.999388i	0.866202	−	0.499694i	$-0.166554\pi$
$84$	−0.909127	−	0.996046i	−0.0991939	−	0.108678i
$85$	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	$-0.803261\pi$
$89$	0.889962	−	1.54146i	0.0943358	−	0.163394i	0.909331	+	0.416073i	$0.136594\pi$
$90$	2.05332	−	9.95121i	0.216439	−	1.04895i
$91$	−0.262339	+	9.20605i	−0.0275006	+	0.965056i
$92$	−0.445743			−0.0464719
$93$	3.82337	+	3.95644i	0.396465	+	0.410263i
$94$	8.00392	−	4.62107i	0.825541	−	0.476626i
$95$	−2.10299	−	1.74587i	−0.215762	−	0.179122i
$96$	−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	$0.478559\pi$
$98$	5.81571	−	8.86551i	0.587475	−	0.895552i
$99$	−3.41144	+	5.46799i	−0.342863	+	0.549553i
$100$	−0.270718	−	1.44628i	−0.0270718	−	0.144628i
$101$	6.71005	+	11.6221i	0.667675	+	1.15645i	0.978553	+	0.205997i	$0.0660438\pi$
$101$	6.71005	+	11.6221i	0.667675	+	1.15645i	−0.310878	+	0.950450i	$0.600623\pi$
$102$	−9.10523	+	2.27359i	−0.901553	+	0.225119i
$103$	−2.89342	+	5.01154i	−0.285097	+	0.493802i	−0.972633	−	0.232348i	$-0.925359\pi$
$103$	−2.89342	+	5.01154i	−0.285097	+	0.493802i	0.687536	+	0.726150i	$0.258692\pi$
$104$	8.99355			0.881890
$105$	10.2357	−	0.480708i	0.998899	−	0.0469123i
$106$	−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	$0.106512\pi$
$108$	−0.470993	+	1.45478i	−0.0453214	+	0.139986i
$109$	−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	$0.913568\pi$
$110$	−1.22583	+	7.17218i	−0.116878	+	0.683840i
$111$	−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	$0.645152\pi$
$114$	2.22847	+	2.30602i	0.208715	+	0.215979i
$115$	2.16343	−	2.60595i	0.201740	−	0.243006i
$116$	1.51803	−	0.876432i	0.140945	−	0.0813747i
$117$	9.21710	−	4.90913i	0.852121	−	0.453849i
$118$	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
$123$	−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
$126$	−11.9988	−	0.753230i	−1.06894	−	0.0671030i
$127$			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
$130$	7.53082	−	9.07125i	0.660497	−	0.795601i
$131$	−4.72508	+	8.18408i	−0.412832	+	0.715047i	−0.995198	−	0.0978802i	$-0.968794\pi$
$131$	−4.72508	+	8.18408i	−0.412832	+	0.715047i	0.582366	+	0.812927i	$0.302127\pi$
$132$	0.301455	−	1.05269i	0.0262383	−	0.0916253i
$133$	−1.69613	+	2.75354i	−0.147073	+	0.238762i
$134$		−	15.6280i		−	1.35005i
$135$	−6.21913	−	9.81440i	−0.535258	−	0.844689i
$136$	−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	$0.682144\pi$
$138$	−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	$-0.0557858\pi$
$140$	−1.64938	+	0.557283i	−0.139398	+	0.0470990i
$141$	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
$145$	−2.24388	+	13.1286i	−0.186344	+	1.09027i
$146$	10.3841			0.859390
$147$	−2.26264	−	11.9114i	−0.186619	−	0.982432i
$148$		−	2.29642i		−	0.188764i
$149$	−2.20294	−	1.27187i	−0.180472	−	0.104196i	0.407042	−	0.913409i	$-0.366560\pi$
$149$	−2.20294	−	1.27187i	−0.180472	−	0.104196i	−0.587514	+	0.809214i	$0.699893\pi$
$150$	−10.6954	−	7.59463i	−0.873280	−	0.620099i
$151$	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
$156$	−1.27588	+	1.23297i	−0.102152	+	0.0987164i
$157$	6.96194	+	12.0584i	0.555623	+	0.962368i	0.997855	+	0.0654670i	$0.0208537\pi$
$157$	6.96194	+	12.0584i	0.555623	+	0.962368i	−0.442231	+	0.896901i	$0.645813\pi$
$158$	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
$161$	−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	0.355543	−	0.934660i	$-0.384296\pi$
$163$	−3.52533	−	2.03535i	−0.276125	−	0.159421i	−0.631668	+	0.775239i	$0.717629\pi$
$164$	1.74633	+	3.02473i	0.136366	+	0.236192i
$165$	4.69126	+	6.87168i	0.365214	+	0.534960i
$166$	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	$0.818197\pi$
$168$	−11.5640	+	2.53995i	−0.892185	+	0.195961i
$169$	−0.882841			−0.0679109
$170$	−2.04116	+	11.9425i	−0.156550	+	0.915952i
$171$	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	0.133142	−	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
$175$	4.74728	−	12.3476i	0.358861	−	0.933391i
$176$		−	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	0.126801	−	0.991928i	$-0.459529\pi$
$179$	14.0378	−	8.10475i	1.04924	−	0.605777i	0.922436	+	0.386151i	$0.126196\pi$
$180$	1.47488	+	1.31216i	0.109931	+	0.0978030i
$181$		−	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
$185$	13.4256	+	11.1457i	0.987068	+	0.819450i
$186$	−8.08550	+	2.01896i	−0.592857	+	0.148037i
$187$	3.84243	−	6.65529i	0.280987	−	0.486683i
$188$			1.79560i			0.130958i
$189$	−10.4651	+	8.91531i	−0.761221	+	0.648493i
$190$	3.88284	−	1.43639i	0.281691	−	0.104206i
$191$	11.0018	+	6.35188i	0.796061	+	0.459606i	0.842092	−	0.539334i	$-0.181324\pi$
$191$	11.0018	+	6.35188i	0.796061	+	0.459606i	−0.0460309	+	0.998940i	$0.514657\pi$
$192$	2.72830	+	10.9262i	0.196898	+	0.788534i
$193$	18.0302	−	10.4098i	1.29785	−	0.749311i	0.317813	−	0.948153i	$-0.397051\pi$
$193$	18.0302	−	10.4098i	1.29785	−	0.749311i	0.980032	+	0.198842i	$0.0637181\pi$
$194$	−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	$0.474634\pi$
$198$	−4.58904	−	8.61613i	−0.326129	−	0.612322i
$199$	−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	$0.988625\pi$
$200$	−12.1849	−	4.29048i	−0.861600	−	0.303383i
$201$	−12.4185	−	12.8507i	−0.875936	−	0.906421i
$202$	−20.3273			−1.43022
$203$	15.7529	+	0.448901i	1.10564	+	0.0315066i
$204$	0.501960	−	1.75286i	0.0351442	−	0.122725i
$205$	−26.1594	−	4.47103i	−1.82705	−	0.312270i
$206$	−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
$210$	−7.12135	+	13.7908i	−0.491420	+	0.951655i
$211$	−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
$215$	1.12748	−	6.59676i	0.0768937	−	0.449895i
$216$	8.99355	+	9.96721i	0.611934	+	0.678183i
$217$	−3.99316	−	7.39515i	−0.271073	−	0.502016i
$218$	7.88801			0.534243
$219$	8.53868	−	8.25151i	0.576991	−	0.557585i
$220$	−1.08768	−	0.902974i	−0.0733312	−	0.0608785i
$221$	−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	$0.546099\pi$
$224$	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	$0.213123\pi$
$228$	−0.604478	+	0.150939i	−0.0400326	+	0.00999617i
$229$	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
$231$	7.27132	−	6.63680i	0.478418	−	0.436669i
$232$		−	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	$-0.0694988\pi$
$234$	−0.540929	+	15.8085i	−0.0353616	+	1.03343i
$235$	−10.4977	−	8.71500i	−0.684791	−	0.568504i
$236$	−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	$0.0296254\pi$
$239$			2.87353i			0.185873i	−0.995672	+	0.0929365i	$0.970375\pi$
$240$	15.7140	+	7.55549i	1.01433	+	0.487705i
$241$	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
$243$	14.6577	+	5.30584i	0.940292	+	0.340370i
$244$			1.00018i			0.0640298i
$245$	−15.2535	−	3.51134i	−0.974513	−	0.224331i
$246$	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
$250$	−14.5306	+	8.69746i	−0.918998	+	0.550076i
$251$	0.161120			0.0101698			0.00508489	−	0.999987i	$-0.498381\pi$
$251$	0.161120			0.0101698			0.00508489	+	0.999987i	$0.498381\pi$
$252$	1.29233	−	1.94570i	0.0814091	−	0.122567i
$253$		−	3.25401i		−	0.204578i
$254$	−12.5637	−	7.25368i	−0.788319	−	0.455136i
$255$	7.81152	+	11.4422i	0.489177	+	0.716538i
$256$	−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
$261$	−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	0.998501	+	0.0547384i	$0.0174325\pi$
$263$	8.86526	+	15.3551i	0.546655	+	0.946835i	−0.451846	+	0.892096i	$0.649234\pi$
$264$	−6.68061	−	6.91311i	−0.411163	−	0.425473i
$265$	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	0.925336	−	0.379148i	$-0.123783\pi$
$269$	2.20294	+	3.81561i	0.134316	+	0.232642i	−0.791020	+	0.611790i	$0.790450\pi$
$270$	17.5841	−	0.725124i	1.07014	−	0.0441296i
$271$	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
$273$	−15.5804	+	3.42211i	−0.942970	+	0.207116i
$274$	−16.2155			−0.979615
$275$	10.5581	−	1.97629i	0.636680	−	0.119175i
$276$	−0.187039	−	0.749051i	−0.0112584	−	0.0450876i
$277$	−11.1127	+	6.41589i	−0.667695	+	0.385494i	−0.795203	−	0.606344i	$-0.792636\pi$
$277$	−11.1127	+	6.41589i	−0.667695	+	0.385494i	0.127508	+	0.991838i	$0.459302\pi$
$278$	5.39311	+	3.11371i	0.323457	+	0.186748i
$279$	−5.04428	+	8.08517i	−0.301993	+	0.484046i
$280$	−3.00321	+	14.9870i	−0.179476	+	0.895647i
$281$			21.2397i			1.26706i	0.773719	+	0.633528i	$0.218394\pi$
$281$			21.2397i			1.26706i	−0.773719	+	0.633528i	$0.781606\pi$
$282$	11.1240	+	11.5112i	0.662426	+	0.685480i
$283$	3.27706	+	5.67603i	0.194801	+	0.337405i	0.946835	−	0.321719i	$-0.104261\pi$
$283$	3.27706	+	5.67603i	0.194801	+	0.337405i	−0.752034	+	0.659124i	$0.770927\pi$
$284$	−2.64967	+	1.52979i	−0.157229	+	0.0907761i
$285$	2.05142	−	4.26656i	0.121515	−	0.252729i
$286$		−	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
$290$	−15.5222	−	12.8863i	−0.911496	−	0.756711i
$291$	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	$-0.965349\pi$
$293$		−	3.71937i		−	0.217288i	0.994081	−	0.108644i	$-0.0346509\pi$
$294$	17.3384	+	6.05296i	1.01120	+	0.353016i
$295$	−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
$300$	2.31682	−	1.06181i	0.133761	−	0.0613034i
$301$	−7.91536	−	0.225559i	−0.456234	−	0.0130010i
$302$	−8.51121			−0.489765
$303$	−16.7149	+	16.1527i	−0.960245	+	0.927949i
$304$	−4.76568	+	2.75147i	−0.273331	+	0.157808i
$305$	−5.84735	−	4.85439i	−0.334818	−	0.277961i
$306$	−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	$0.396351\pi$
$308$	−0.877248	+	1.42415i	−0.0499859	+	0.0811484i
$309$	−9.63578	−	2.75935i	−0.548160	−	0.156974i
$310$	−1.81256	+	10.6050i	−0.102946	+	0.602326i
$311$	−9.46050	−	16.3861i	−0.536456	−	0.929168i	−0.999091	−	0.0426199i	$-0.986430\pi$
$311$	−9.46050	−	16.3861i	−0.536456	−	0.929168i	0.462636	−	0.886548i	$-0.346904\pi$
$312$	3.77380	+	15.1133i	0.213649	+	0.855620i
$313$	8.19024	−	14.1859i	0.462940	−	0.801835i	−0.536166	−	0.844112i	$-0.680128\pi$
$313$	8.19024	−	14.1859i	0.462940	−	0.801835i	0.999106	+	0.0422775i	$0.0134614\pi$
$314$	−21.0903			−1.19020
$315$	5.10281	+	16.9989i	0.287511	+	0.957777i
$316$	−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	$0.258363\pi$
$318$	−7.13503	−	28.5743i	−0.400113	−	1.60237i
$319$	6.39812	+	11.0819i	0.358226	+	0.620466i
$320$	14.3310	+	2.44938i	0.801128	+	0.136925i
$321$	6.47141	+	1.85319i	0.361199	+	0.103435i
$322$	5.34118	−	2.88408i	0.297652	−	0.160723i
$323$	−4.37254			−0.243295
$324$	−2.64233	−	0.181040i	−0.146796	−	0.0100578i
$325$	−16.4169	−	5.78063i	−0.910644	−	0.320652i
$326$	5.33977	−	3.08292i	0.295743	−	0.170747i
$327$	6.48622	−	6.26807i	0.358689	−	0.346625i
$328$	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
$333$	−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
$336$	6.24224	−	19.6635i	0.340542	−	1.07273i
$337$			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
$340$	−1.81111	−	1.50356i	−0.0982215	−	0.0815421i
$341$	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
$345$	5.28698	+	2.54205i	0.284642	+	0.136859i
$346$	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	$0.973753\pi$
$348$	2.10979	+	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	$-0.000163910\pi$
$350$	12.6018	+	15.5787i	0.673592	+	0.832715i
$351$	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	$0.569830\pi$
$354$	1.37880	+	5.52178i	0.0732821	+	0.293479i
$355$	3.91662	−	22.9156i	0.207873	−	1.21624i
$356$	−0.523797			−0.0277612
$357$	12.1076	−	11.0511i	0.640804	−	0.584885i
$358$			24.5523i			1.29763i
$359$	20.9396	+	12.0895i	1.10515	+	0.638057i	0.937568	−	0.347801i	$-0.113072\pi$
$359$	20.9396	+	12.0895i	1.10515	+	0.638057i	0.167579	+	0.985859i	$0.446405\pi$
$360$	16.4511	−	5.45382i	0.867048	−	0.287442i
$361$	−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
$366$	6.19625	+	6.41189i	0.323883	+	0.335155i
$367$	−4.53636	−	7.85721i	−0.236796	−	0.410143i	0.722997	−	0.690851i	$-0.242764\pi$
$367$	−4.53636	−	7.85721i	−0.236796	−	0.410143i	−0.959793	+	0.280708i	$0.909431\pi$
$368$	−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
$371$	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	0.806562	−	0.591150i	$-0.201326\pi$
$373$	13.4785	+	7.78183i	0.697891	+	0.402928i	−0.108670	+	0.994078i	$0.534659\pi$
$374$	5.82009	+	10.0807i	0.300950	+	0.521260i
$375$	−5.03708	+	18.6983i	−0.260114	+	0.965578i
$376$	13.6524	+	7.88224i	0.704071	+	0.406496i
$377$		−	20.7342i		−	1.06787i
$378$	−3.76908	−	20.4796i	−0.193861	−	1.05336i
$379$	34.0984			1.75152			0.875758	−	0.482751i	$-0.160362\pi$
$379$	34.0984			1.75152			0.875758	+	0.482751i	$0.160362\pi$
$380$	−0.135508	+	0.792842i	−0.00695143	+	0.0406719i
$381$	−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	0.247381	−	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
$385$	−4.06827	−	12.0408i	−0.207338	−	0.613657i
$386$			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	−0.0797828	−	0.996812i	$-0.525423\pi$
$389$	14.6659	−	8.46736i	0.743590	−	0.429312i	0.823373	+	0.567500i	$0.192089\pi$
$390$	18.4038	+	8.84880i	0.931914	+	0.448077i
$391$		−	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
$395$	2.68926	−	3.23934i	0.135311	−	0.162989i
$396$	1.89550	+	0.0648594i	0.0952524	+	0.00325931i
$397$	0.203913	−	0.353188i	0.0102341	−	0.0177260i	−0.860863	−	0.508837i	$-0.830076\pi$
$397$	0.203913	−	0.353188i	0.0102341	−	0.0177260i	0.871097	+	0.491111i	$0.163409\pi$
$398$		−	37.7491i		−	1.89219i
$399$	−5.33892	−	1.69485i	−0.267280	−	0.0848487i
$400$	17.0905	−	14.6494i	0.854526	−	0.732470i
$401$	−24.2302	−	13.9893i	−1.21000	−	0.698593i	−0.247240	−	0.968954i	$-0.579524\pi$
$401$	−24.2302	−	13.9893i	−1.21000	−	0.698593i	−0.962759	+	0.270361i	$0.912857\pi$
$402$	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
$405$	13.8830	−	14.5692i	0.689853	−	0.723949i
$406$	−12.5192	+	20.3240i	−0.621317	+	1.00866i
$407$	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	$-0.646028\pi$
$409$	2.26960	−	1.31036i	0.112225	−	0.0647929i	0.555062	+	0.831809i	$0.312695\pi$
$410$	25.6766	−	30.9287i	1.26808	−	1.52746i
$411$	−13.3338	+	12.8854i	−0.657709	+	0.635589i
$412$	1.70295			0.0838984
$413$	−5.05033	+	2.72703i	−0.248511	+	0.134188i
$414$	−5.83954	−	3.64325i	−0.286998	−	0.179056i
$415$	3.42993	−	20.0681i	0.168369	−	0.985104i
$416$	−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	$-0.565751\pi$
$419$	−8.39649			−0.410195			−0.205098	+	0.978742i	$0.565751\pi$
$420$	−1.62859	−	2.53787i	−0.0794670	−	0.123835i
$421$	−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
$425$	17.5806	−	3.29077i	0.852783	−	0.159626i
$426$	−7.50912	+	26.2222i	−0.363818	+	1.27047i
$427$	−4.71609	+	7.65622i	−0.228227	+	0.370511i
$428$	−1.14371			−0.0552831
$429$	−9.00089	−	9.31415i	−0.434567	−	0.449691i
$430$	7.79946	+	6.47500i	0.376123	+	0.312252i
$431$	−10.6154	+	6.12880i	−0.511326	+	0.295214i	−0.733378	−	0.679821i	$-0.762058\pi$
$431$	−10.6154	+	6.12880i	−0.511326	+	0.295214i	0.222053	+	0.975035i	$0.428724\pi$
$432$	−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	$0.539411\pi$
$434$	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
$438$	4.35726	+	17.4499i	0.208198	+	0.833790i
$439$	−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
$441$	19.0671	−	8.80040i	0.907955	−	0.419067i
$442$		−	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	$0.168574\pi$
$444$	3.85902	−	0.963602i	0.183141	−	0.0457305i
$445$	2.54226	−	3.06228i	0.120515	−	0.145166i
$446$	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	$0.238564\pi$
$449$			28.8710i			1.36250i	−0.732049	+	0.681252i	$0.761436\pi$
$450$	8.27450	−	21.1600i	0.390064	−	0.997492i
$451$	−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
$455$	−4.04627	+	20.1923i	−0.189692	+	0.946629i
$456$	−1.50588	+	5.25859i	−0.0705193	+	0.246256i
$457$	−20.8483	−	12.0368i	−0.975242	−	0.563056i	−0.0744117	−	0.997228i	$-0.523708\pi$
$457$	−20.8483	−	12.0368i	−0.975242	−	0.563056i	−0.900830	+	0.434171i	$0.857041\pi$
$458$	−13.0835	+	7.55375i	−0.611351	+	0.352964i
$459$	−17.6839	−	5.72525i	−0.825413	−	0.267232i
$460$	−0.982465	−	0.167918i	−0.0458077	−	0.00782921i
$461$	39.8709			1.85697			0.928486	−	0.371367i	$-0.121111\pi$
$461$	39.8709			1.85697			0.928486	+	0.371367i	$0.121111\pi$
$462$	3.19898	+	14.5646i	0.148830	+	0.677604i
$463$		−	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
$465$	6.93667	+	10.1607i	0.321681	+	0.471192i
$466$	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
$471$	−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
$476$	−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	$-0.946348\pi$
$479$	−13.9676	−	24.1926i	−0.638196	−	1.10539i	0.347632	−	0.937631i	$-0.386986\pi$
$480$	−5.28354	+	3.60705i	−0.241160	+	0.164638i
$481$	−23.5245	−	13.5819i	−1.07262	−	0.619280i
$482$			39.4912i			1.79878i
$483$	2.10021	−	6.61582i	0.0955627	−	0.301030i
$484$	1.87892			0.0854055
$485$	2.92229	+	0.499462i	0.132694	+	0.0226794i
$486$	−18.0609	+	15.2090i	−0.819259	+	0.689895i
$487$	32.2536	−	18.6216i	1.46155	−	0.843826i	0.462466	−	0.886637i	$-0.346965\pi$
$487$	32.2536	−	18.6216i	1.46155	−	0.843826i	0.999083	+	0.0428116i	$0.0136315\pi$
$488$	7.60462	+	4.39053i	0.344245	+	0.198750i
$489$	1.94104	−	6.77821i	0.0877770	−	0.306521i
$490$	16.1582	−	17.3497i	0.729953	−	0.783778i
$491$			5.90572i			0.266522i	0.991081	+	0.133261i	$0.0425448\pi$
$491$			5.90572i			0.266522i	−0.991081	+	0.133261i	$0.957455\pi$
$492$	−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
$495$	−9.57904	+	10.7669i	−0.430546	+	0.483936i
$496$		−	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	$0.0288850\pi$
$500$	−0.0518560	−	3.28975i	−0.00231907	−	0.147122i
$501$	−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	$0.253251\pi$
$503$			32.0398i			1.42858i	−0.699849	+	0.714291i	$0.746749\pi$
$504$	−9.12067	−	18.3671i	−0.406267	−	0.818134i
$505$	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	$-0.693822\pi$
$509$	9.57465	−	16.5838i	0.424389	−	0.735063i	0.996363	+	0.0852085i	$0.0271556\pi$
$510$	−20.9254	+	1.58116i	−0.926592	+	0.0700147i
$511$	−15.9600	+	8.61794i	−0.706031	+	0.381235i
$512$	−15.8265			−0.699439
$513$	1.32709	+	6.21129i	0.0585925	+	0.274235i
$514$	17.2238	−	9.94415i	0.759708	−	0.438617i
$515$	−8.26532	+	9.95599i	−0.364213	+	0.438713i
$516$	−1.06011	−	1.09700i	−0.0466685	−	0.0482927i
$517$	−13.1082			−0.576499
$518$	14.8584	+	27.5171i	0.652842	+	1.20903i
$519$	4.76960	−	16.6557i	0.209362	−	0.731102i
$520$	19.8228	+	3.38800i	0.869285	+	0.148574i
$521$	1.94104	+	3.36199i	0.0850387	+	0.147291i	0.905408	−	0.424543i	$-0.139565\pi$
$521$	1.94104	+	3.36199i	0.0850387	+	0.147291i	−0.820369	+	0.571834i	$0.806232\pi$
$522$	27.0506	+	0.925607i	1.18397	+	0.0405127i
$523$	−1.06192	+	1.83929i	−0.0464343	+	0.0804266i	−0.888308	−	0.459247i	$-0.848119\pi$
$523$	−1.06192	+	1.83929i	−0.0464343	+	0.0804266i	0.841874	+	0.539674i	$0.181452\pi$
$524$	2.78100			0.121488
$525$	22.7416	+	2.79639i	0.992525	+	0.122045i
$526$	−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
$530$	−37.4785	−	6.40562i	−1.62796	−	0.278242i
$531$	5.52156	+	3.44486i	0.239615	+	0.149494i
$532$	0.951321	+	0.0271092i	0.0412450	+	0.00117533i
$533$	41.3138			1.78950
$534$	−3.35793	+	3.24500i	−0.145312	+	0.140425i
$535$	5.55101	−	6.68646i	0.239991	−	0.289081i
$536$	23.0856	−	13.3285i	0.997148	−	0.575704i
$537$	19.5101	+	20.1891i	0.841922	+	0.871224i
$538$	−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
$543$	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
$546$	7.31076	−	23.0295i	0.312871	−	0.985570i
$547$			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
$550$	−5.40372	+	15.3465i	−0.230416	+	0.654375i
$551$	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
$555$	−13.0963	+	27.2379i	−0.555909	+	1.15619i
$556$	−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	$0.897169\pi$
$558$	−6.78553	−	12.7401i	−0.287254	−	0.539333i
$559$			10.4183i			0.440649i
$560$	−19.9995	−	17.5894i	−0.845135	−	0.743286i
$561$	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	$0.198347\pi$
$564$	−3.01743	+	0.753455i	−0.127057	+	0.0317262i
$565$	−20.6356	−	3.52693i	−0.868147	−	0.148379i
$566$	−9.92744			−0.417281
$567$	−19.3730	−	13.8451i	−0.813590	−	0.581439i
$568$			26.8615i			1.12708i
$569$	−11.1702	−	6.44911i	−0.468279	−	0.270361i	0.247240	−	0.968954i	$-0.420476\pi$
$569$	−11.1702	−	6.44911i	−0.468279	−	0.270361i	−0.715519	+	0.698593i	$0.753810\pi$
$570$	4.04306	+	5.92221i	0.169345	+	0.248054i
$571$	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
$576$	−17.2162	+	9.16955i	−0.717343	+	0.382065i
$577$	3.74489	+	6.48634i	0.155902	+	0.270030i	0.933387	−	0.358871i	$-0.116838\pi$
$577$	3.74489	+	6.48634i	0.155902	+	0.270030i	−0.777485	+	0.628901i	$0.783505\pi$
$578$	−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
$581$	−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
$585$	22.1648	−	7.34802i	0.916402	−	0.303803i
$586$	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	$-0.151427\pi$
$588$	−2.70274	+	2.32928i	−0.111459	+	0.0960580i
$589$	−3.88284			−0.159990
$590$	7.24245	+	1.23784i	0.298167	+	0.0509611i
$591$	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	0.608050	−	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
$595$	−6.77416	−	20.0494i	−0.277714	−	0.821946i
$596$			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	−0.818868	−	0.573982i	$-0.805398\pi$
$599$	−17.8962	+	10.3324i	−0.731219	+	0.422170i	0.0876487	+	0.996151i	$0.472065\pi$
$600$	2.09705	−	22.2764i	0.0856116	−	0.909432i
$601$		−	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
$605$	−9.11940	+	10.9848i	−0.370756	+	0.446594i
$606$	−8.52955	−	34.1590i	−0.346489	−	1.38762i
$607$	−21.3383	+	36.9590i	−0.866095	+	1.50012i	−0.000139312		1.00000i	$0.500044\pi$
$607$	−21.3383	+	36.9590i	−0.866095	+	1.50012i	−0.865956	+	0.500121i	$0.833289\pi$
$608$		−	2.01906i		−	0.0818838i
$609$	5.85573	+	26.6604i	0.237286	+	1.08033i
$610$	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	$-0.632384\pi$
$613$	4.60972	−	2.66142i	0.186185	−	0.107494i	0.590195	+	0.807261i	$0.299051\pi$
$614$	−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	$0.292815\pi$
$618$	10.9172	−	10.5500i	0.439154	−	0.424385i
$619$	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	$0.250969\pi$
$620$	−1.60828	−	1.33517i	−0.0645900	−	0.0536217i
$621$	−7.69683	+	1.64449i	−0.308863	+	0.0659911i
$622$	28.6594			1.14914
$623$	−4.00959	−	2.46983i	−0.160641	−	0.0989518i
$624$	−26.0944	−	7.47254i	−1.04461	−	0.299141i
$625$	19.4846	+	15.6637i	0.779383	+	0.626548i
$626$	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
$630$	−26.1630	−	6.18034i	−1.04236	−	0.246230i
$631$	−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
$635$	−3.60809	+	21.1104i	−0.143183	+	0.837743i
$636$	5.50089	+	1.57526i	0.218125	+	0.0624633i
$637$	24.3273	+	1.38761i	0.963881	+	0.0549789i
$638$	−19.3823			−0.767353
$639$	14.6623	+	27.5292i	0.580033	+	1.08904i
$640$	−18.7850	+	22.6275i	−0.742543	+	0.894430i
$641$	−1.13893	+	0.657564i	−0.0449852	+	0.0259722i	−0.522324	−	0.852747i	$-0.674935\pi$
$641$	−1.13893	+	0.657564i	−0.0449852	+	0.0259722i	0.477339	+	0.878719i	$0.341601\pi$
$642$	−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	$0.781440\pi$
$644$	−0.0335929	+	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	$0.294247\pi$
$648$	−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
$651$	10.7516	−	9.81341i	0.421390	−	0.384618i
$652$			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	$0.0463464\pi$
$654$	3.30990	+	13.2554i	0.129427	+	0.518329i
$655$	−13.4976	+	16.2586i	−0.527397	+	0.635275i
$656$	−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	$-0.699150\pi$
$659$		−	41.6170i		−	1.62117i	0.585622	−	0.810584i	$-0.300850\pi$
$660$	1.06100	−	2.20669i	0.0412996	−	0.0858953i
$661$	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
$663$	−14.9876	−	15.5092i	−0.582069	−	0.602327i
$664$			23.5236i			0.912894i
$665$	−4.77575	+	5.43014i	−0.185196	+	0.210572i
$666$	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
$670$	5.88730	−	34.4458i	0.227446	−	1.33076i
$671$	−7.30148			−0.281871
$672$	5.10294	+	5.59081i	0.196850	+	0.215670i
$673$		−	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
$675$	−10.0104	−	23.9748i	−0.385301	−	0.922791i
$676$	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
$681$	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	$-0.304076\pi$
$683$	−10.9346	−	18.9393i	−0.418401	−	0.724691i	−0.995779	+	0.0917858i	$0.970743\pi$
$684$	−0.507292	−	0.952463i	−0.0193968	−	0.0364183i
$685$	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
$690$	−7.33862	+	5.01004i	−0.279377	+	0.190729i
$691$	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
$693$	14.2040	+	9.43425i	0.539564	+	0.358377i
$694$	24.0944			0.914612
$695$	1.54881	−	9.06187i	0.0587496	−	0.343736i
$696$	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
$700$	−3.84536	+	0.606965i	−0.145341	+	0.0229411i
$701$		−	35.5019i		−	1.34089i	−0.741960	−	0.670444i	$-0.766104\pi$
$701$		−	35.5019i		−	1.34089i	0.741960	−	0.670444i	$-0.233896\pi$
$702$	−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
$705$	10.2402	−	21.2977i	0.385669	−	0.802119i
$706$		−	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	$0.191004\pi$
$710$	27.0936	+	22.4927i	1.01680	+	0.844135i
$711$	−0.193166	+	5.64522i	−0.00724428	+	0.211712i
$712$	−2.29934	+	3.98257i	−0.0861712	+	0.149253i
$713$		−	4.81149i		−	0.180192i
$714$	5.32670	+	24.2518i	0.199347	+	0.907599i
$715$	−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	0.427133	+	0.904189i	$0.359524\pi$
$719$	−15.2703	+	26.4489i	−0.569484	+	0.986376i	−0.996617	+	0.0821868i	$0.973810\pi$
$720$	−6.10289	+	29.5770i	−0.227441	+	1.10227i
$721$	13.0359	+	8.02984i	0.485481	+	0.299047i
$722$	26.5159			0.986821
$723$	31.3810	+	32.4732i	1.16707	+	1.20769i
$724$	−4.94730	+	2.85632i	−0.183865	+	0.106154i
$725$	−9.89149	+	28.0916i	−0.367361	+	1.04330i
$726$	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	$0.357008\pi$
$728$	0.677789	−	23.7850i	0.0251205	−	0.881533i
$729$	−2.76568	+	26.8580i	−0.102433	+	0.994740i
$730$	22.8876	+	3.91182i	0.847107	+	0.144783i
$731$	−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	−0.666846	−	0.745196i	$-0.732356\pi$
$733$	8.44533	−	14.6277i	0.311935	−	0.540288i	0.978781	+	0.204908i	$0.0656894\pi$
$734$	13.7423			0.507239
$735$	−0.499919	−	27.1063i	−0.0184398	−	0.999830i
$736$	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	−0.999948	−	0.0102170i	$-0.996748\pi$
$739$	−13.8321	−	23.9579i	−0.508822	−	0.881306i	0.491126	−	0.871089i	$-0.336586\pi$
$740$	0.865093	−	5.06155i	0.0318014	−	0.186066i
$741$	−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	$0.763688\pi$
$744$	−9.87819	−	10.2220i	−0.362152	−	0.374756i
$745$	−4.37639	−	3.63321i	−0.160338	−	0.133111i
$746$	−20.4158	+	11.7870i	−0.747474	+	0.431554i
$747$	12.8404	+	24.1083i	0.469804	+	0.882078i
$748$	−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
$753$	0.0676076	+	0.270754i	0.00246376	+	0.00986683i
$754$	27.1983	+	15.7029i	0.990503	+	0.571867i
$755$	4.35936	+	11.7842i	0.158654	+	0.428873i
$756$	3.81193	+	1.35526i	0.138639	+	0.0492905i
$757$		−	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
$760$	5.43334	+	4.51068i	0.197088	+	0.163620i
$761$	9.91711	−	17.1769i	0.359495	−	0.622663i	−0.628382	−	0.777905i	$-0.716282\pi$
$761$	9.91711	−	17.1769i	0.359495	−	0.622663i	0.987876	+	0.155242i	$0.0496157\pi$
$762$	6.91759	−	24.1565i	0.250598	−	0.875098i
$763$	−12.1237	+	6.54643i	−0.438907	+	0.236997i
$764$		−	3.73847i		−	0.135253i
$765$	−15.9503	+	17.9282i	−0.576683	+	0.648195i
$766$	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	$-0.0614100\pi$
$770$	18.8757	+	3.78245i	0.680234	+	0.136310i
$771$	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	$0.416257\pi$
$774$	−13.5922	−	0.465090i	−0.488560	−	0.0167173i
$775$	15.6117	−	2.92222i	0.560787	−	0.104969i
$776$	−3.42548			−0.122967
$777$	34.0839	+	10.8200i	1.22275	+	0.388166i
$778$			25.6508i			0.919626i
$779$	12.5637	+	7.25368i	0.450142	+	0.259890i
$780$	−3.27665	+	2.23695i	−0.117323	+	0.0800956i
$781$	−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
$786$	17.8283	−	17.2287i	0.635914	−	0.614527i
$787$	−18.4671	−	31.9859i	−0.658280	−	1.14017i	−0.981061	−	0.193700i	$-0.937951\pi$
$787$	−18.4671	−	31.9859i	−0.658280	−	1.14017i	0.322781	−	0.946474i	$-0.395382\pi$
$788$	−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
$791$	−0.705583	+	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
$795$	−35.9082	+	24.5143i	−1.27353	+	0.869434i
$796$	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	$0.768894\pi$
$798$	6.26663	−	5.71978i	0.221836	−	0.202478i
$799$	−21.8268			−0.772177
$800$	1.51954	+	8.11800i	0.0537240	+	0.287015i
$801$	−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
$805$	−6.72886	−	5.91796i	−0.237161	−	0.208581i
$806$		−	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	−0.836010	−	0.548714i	$-0.815117\pi$
$809$	−22.1518	+	12.7893i	−0.778814	+	0.449649i	0.0571956	+	0.998363i	$0.481784\pi$
$810$	8.59704	+	29.2451i	0.302069	+	1.02757i
$811$			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
$815$	−7.00345	−	5.81417i	−0.245320	−	0.203661i
$816$	27.0626	−	6.75756i	0.947380	−	0.236562i
$817$	−1.82920	+	3.16826i	−0.0639955	+	0.110844i
$818$			3.96956i			0.138792i
$819$	−12.2884	−	24.7462i	−0.429392	−	0.864703i
$820$	2.70964	+	7.32470i	0.0946247	+	0.255790i
$821$	−0.00729231	−	0.00421022i	−0.000254504	−	0.000146938i	0.499873	−	0.866099i	$-0.333380\pi$
$821$	−0.00729231	−	0.00421022i	−0.000254504	−	0.000146938i	−0.500127	+	0.865952i	$0.666713\pi$
$822$	−6.80421	−	27.2494i	−0.237324	−	0.950433i
$823$	−27.0406	+	15.6119i	−0.942578	+	0.544198i	−0.890767	−	0.454459i	$-0.849832\pi$
$823$	−27.0406	+	15.6119i	−0.942578	+	0.544198i	−0.0518103	+	0.998657i	$0.516499\pi$
$824$	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	$0.732097\pi$
$828$	1.18026	−	0.628620i	0.0410169	−	0.0218461i
$829$	−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	$0.345728\pi$
$830$	23.7268	+	19.6977i	0.823571	+	0.683717i
$831$	−15.4446	−	15.9821i	−0.535768	−	0.554414i
$832$	−22.6331			−0.784663
$833$	−22.3633	+	11.2649i	−0.774843	+	0.390306i
$834$	−2.96944	+	10.3694i	−0.102823	+	0.359064i
$835$	−5.26354	+	30.7963i	−0.182152	+	1.06575i
$836$	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	$-0.383958\pi$
$839$	20.6544			0.713069			0.356535	+	0.934282i	$0.383958\pi$
$840$	−26.4452	+	1.24197i	−0.912447	+	0.0428521i
$841$	−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
$845$	−1.94588	−	0.332579i	−0.0669402	−	0.0114411i
$846$	−14.6762	+	23.5236i	−0.504579	+	0.808759i
$847$	14.3829	+	8.85959i	0.494202	+	0.304419i
$848$	50.5391			1.73552
$849$	−8.16322	+	7.88867i	−0.280161	+	0.270738i
$850$	−8.99786	+	25.5537i	−0.308624	+	0.876485i
$851$	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	$0.461388\pi$
$854$	−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	$0.240507\pi$
$858$	19.0347	−	4.75298i	0.649833	−	0.162264i
$859$	−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
$861$	−53.1220	+	11.6678i	−1.81039	+	0.397638i
$862$		−	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	$-0.0570414\pi$
$864$	2.64369	−	8.16571i	0.0899402	−	0.277803i
$865$	−17.2091	−	14.2868i	−0.585128	−	0.485765i
$866$	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
$870$	15.1416	−	31.4916i	0.513348	−	1.06767i
$871$	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
$875$	15.1150	−	25.4271i	0.510981	−	0.859592i
$876$	−3.35932	−	0.961992i	−0.113501	−	0.0325027i
$877$	−9.91566	−	5.72481i	−0.334828	−	0.193313i	0.323155	−	0.946346i	$-0.395257\pi$
$877$	−9.91566	−	5.72481i	−0.334828	−	0.193313i	−0.657983	+	0.753033i	$0.728590\pi$
$878$	21.9054	−	12.6471i	0.739272	−	0.426819i
$879$	6.25024	−	1.56069i	0.210815	−	0.0526408i
$880$	3.64342	−	21.3172i	0.122820	−	0.718601i
$881$	−23.6698			−0.797455			−0.398728	−	0.917069i	$-0.630548\pi$
$881$	−23.6698			−0.797455			−0.398728	+	0.917069i	$0.630548\pi$
$882$	−2.89633	+	31.6763i	−0.0975245	+	1.06660i
$883$			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
$885$	6.93901	−	4.73722i	0.233252	−	0.159240i
$886$	−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
$891$	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
$896$	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
$900$	2.75648	+	3.44776i	0.0918826	+	0.114925i
$901$	34.7774	+	20.0788i	1.15860	+	0.668921i
$902$		−	38.6201i		−	1.28591i
$903$	−2.94233	−	13.3960i	−0.0979146	−	0.445792i
$904$	24.1889			0.804510
$905$	7.31288	−	42.7867i	0.243088	−	1.42228i
$906$	−3.57140	−	14.3027i	−0.118652	−	0.475176i
$907$	43.9694	−	25.3858i	1.45998	−	0.842920i	0.460971	−	0.887415i	$-0.347501\pi$
$907$	43.9694	−	25.3858i	1.45998	−	0.842920i	0.999010	+	0.0444946i	$0.0141678\pi$
$908$	−2.83174	−	1.63491i	−0.0939747	−	0.0542563i
$909$	−34.1577	−	21.3107i	−1.13294	−	0.706832i
$910$	−23.4230	−	20.6002i	−0.776464	−	0.682891i
$911$		−	16.1165i		−	0.533963i	−0.963702	−	0.266981i	$-0.913974\pi$
$911$		−	16.1165i		−	0.533963i	0.963702	−	0.266981i	$-0.0860262\pi$
$912$	−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
$915$	5.70396	−	11.8632i	0.188567	−	0.392184i
$916$		−	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	$0.939117\pi$
$920$	−5.58950	+	6.73283i	−0.184280	+	0.221975i
$921$	4.70392	+	18.8382i	0.155000	+	0.620740i
$922$	−30.1960	+	52.3010i	−0.994452	+	1.72244i
$923$			36.1909i			1.19124i
$924$	−2.76132	−	0.876587i	−0.0908407	−	0.0288376i
$925$	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	−0.393889	−	0.919158i	$-0.628871\pi$
$929$	18.2593	−	31.6261i	0.599069	−	1.03762i	0.992959	−	0.118461i	$-0.0377960\pi$
$930$	−18.5819	+	1.40407i	−0.609323	+	0.0460414i
$931$	7.15440	+	4.69323i	0.234476	+	0.153814i
$932$	−6.07063			−0.198850
$933$	23.5663	−	22.7737i	0.771526	−	0.745578i
$934$	5.48530	−	3.16694i	0.179484	−	0.103625i
$935$	10.9763	−	13.2215i	0.358963	−	0.432388i
$936$	−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	$0.460331\pi$
$938$	−41.3311	−	1.17779i	−1.34951	−	0.0384561i
$939$	27.2755	+	7.81075i	0.890102	+	0.254894i
$940$	−0.676429	+	3.95770i	−0.0220627	+	0.129086i
$941$	11.0121	+	19.0735i	0.358985	+	0.621780i	0.987791	−	0.155782i	$-0.0497897\pi$
$941$	11.0121	+	19.0735i	0.358985	+	0.621780i	−0.628807	+	0.777562i	$0.716456\pi$
$942$	−8.84974	−	35.4414i	−0.288340	−	1.15474i
$943$	−8.98853	+	15.5686i	−0.292707	+	0.506983i
$944$	−9.76632			−0.317867
$945$	−26.4246	+	15.7080i	−0.859593	+	0.510980i
$946$	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	$0.871319\pi$
$948$	−0.232499	−	0.931111i	−0.00755123	−	0.0302411i
$949$	11.9320	+	20.6669i	0.387330	+	0.670875i
$950$	9.09930	−	1.70323i	0.295220	−	0.0552599i
$951$	−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	$0.446890\pi$
$954$	45.0239	−	23.9802i	1.45770	−	0.776388i
$955$	21.8563	+	18.1448i	0.707252	+	0.587150i
$956$	0.732331	−	0.422811i	0.0236853	−	0.0136747i
$957$	−15.9379	+	15.4018i	−0.515198	+	0.497870i
$958$	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
$963$	−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
$966$	7.08777	+	7.76541i	0.228045	+	0.249848i
$967$		−	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
$970$	−2.86835	+	3.45507i	−0.0920971	+	0.110936i
$971$	12.6443	−	21.9006i	0.405775	−	0.702822i	−0.588637	−	0.808398i	$-0.700335\pi$
$971$	12.6443	−	21.9006i	0.405775	−	0.702822i	0.994411	+	0.105575i	$0.0336684\pi$
$972$	−0.804521	−	4.51628i	−0.0258050	−	0.144860i
$973$	−10.8732	−	0.309848i	−0.348579	−	0.00993326i
$974$			56.4119i			1.80755i
$975$	2.82538	−	30.0134i	0.0904847	−	0.961198i
$976$	−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	$0.707304\pi$
$978$	7.42133	+	7.67961i	0.237308	+	0.245567i
$979$		−	3.82381i		−	0.122210i
$980$	1.34953	+	4.40409i	0.0431092	+	0.140683i
$981$	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	$0.0551374\pi$
$984$	12.8669	+	51.5291i	0.410181	+	1.64269i
$985$	4.92541	+	0.841825i	0.156937	+	0.0268228i
$986$	−32.2739			−1.02781
$987$	−26.6507	−	8.46033i	−0.848302	−	0.269295i
$988$		−	1.25214i		−	0.0398360i
$989$	−3.92601	−	2.26668i	−0.124840	−	0.0720764i
$990$	−6.86892	−	20.7196i	−0.218309	−	0.658513i
$991$	−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
$996$	−3.22496	−	3.33720i	−0.102187	−	0.105743i
$997$	13.3742	+	23.1647i	0.423564	+	0.733634i	0.996285	−	0.0861161i	$-0.0274456\pi$
$997$	13.3742	+	23.1647i	0.423564	+	0.733634i	−0.572721	+	0.819750i	$0.694112\pi$
$998$	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	105.2.p.a.89.4	yes	24
3.2	odd	2	inner	105.2.p.a.89.10	yes	24
5.2	odd	4		525.2.t.j.26.4		24
5.3	odd	4		525.2.t.j.26.9		24
5.4	even	2	inner	105.2.p.a.89.9	yes	24
7.2	even	3		735.2.g.b.734.17		24
7.3	odd	6	inner	105.2.p.a.59.3	✓	24
7.4	even	3		735.2.p.f.374.4		24
7.5	odd	6		735.2.g.b.734.20		24
7.6	odd	2		735.2.p.f.509.3		24
15.2	even	4		525.2.t.j.26.10		24
15.8	even	4		525.2.t.j.26.3		24
15.14	odd	2	inner	105.2.p.a.89.3	yes	24
21.2	odd	6		735.2.g.b.734.6		24
21.5	even	6		735.2.g.b.734.7		24
21.11	odd	6		735.2.p.f.374.10		24
21.17	even	6	inner	105.2.p.a.59.9	yes	24
21.20	even	2		735.2.p.f.509.9		24
35.3	even	12		525.2.t.j.101.3		24
35.4	even	6		735.2.p.f.374.9		24
35.9	even	6		735.2.g.b.734.8		24
35.17	even	12		525.2.t.j.101.10		24
35.19	odd	6		735.2.g.b.734.5		24
35.24	odd	6	inner	105.2.p.a.59.10	yes	24
35.34	odd	2		735.2.p.f.509.10		24
105.17	odd	12		525.2.t.j.101.4		24
105.38	odd	12		525.2.t.j.101.9		24
105.44	odd	6		735.2.g.b.734.19		24
105.59	even	6	inner	105.2.p.a.59.4	yes	24
105.74	odd	6		735.2.p.f.374.3		24
105.89	even	6		735.2.g.b.734.18		24
105.104	even	2		735.2.p.f.509.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.3	✓	24	7.3	odd	6	inner
105.2.p.a.59.4	yes	24	105.59	even	6	inner
105.2.p.a.59.9	yes	24	21.17	even	6	inner
105.2.p.a.59.10	yes	24	35.24	odd	6	inner
105.2.p.a.89.3	yes	24	15.14	odd	2	inner
105.2.p.a.89.4	yes	24	1.1	even	1	trivial
105.2.p.a.89.9	yes	24	5.4	even	2	inner
105.2.p.a.89.10	yes	24	3.2	odd	2	inner
525.2.t.j.26.3		24	15.8	even	4
525.2.t.j.26.4		24	5.2	odd	4
525.2.t.j.26.9		24	5.3	odd	4
525.2.t.j.26.10		24	15.2	even	4
525.2.t.j.101.3		24	35.3	even	12
525.2.t.j.101.4		24	105.17	odd	12
525.2.t.j.101.9		24	105.38	odd	12
525.2.t.j.101.10		24	35.17	even	12
735.2.g.b.734.5		24	35.19	odd	6
735.2.g.b.734.6		24	21.2	odd	6
735.2.g.b.734.7		24	21.5	even	6
735.2.g.b.734.8		24	35.9	even	6
735.2.g.b.734.17		24	7.2	even	3
735.2.g.b.734.18		24	105.89	even	6
735.2.g.b.734.19		24	105.44	odd	6
735.2.g.b.734.20		24	7.5	odd	6
735.2.p.f.374.3		24	105.74	odd	6
735.2.p.f.374.4		24	7.4	even	3
735.2.p.f.374.9		24	35.4	even	6
735.2.p.f.374.10		24	21.11	odd	6
735.2.p.f.509.3		24	7.6	odd	2
735.2.p.f.509.4		24	105.104	even	2
735.2.p.f.509.9		24	21.20	even	2
735.2.p.f.509.10		24	35.34	odd	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} +(0.419611 + 1.68045i) q^{3} +(-0.147140 - 0.254854i) q^{4} +(2.20411 + 0.376714i) q^{5} +(-2.52214 - 0.722254i) q^{6} +(0.0753638 - 2.64468i) q^{7} -2.58363 q^{8} +(-2.64785 + 1.41027i) q^{9} +(-2.16343 + 2.60595i) q^{10} +(1.86048 - 1.07415i) q^{11} +(0.366529 - 0.354202i) 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} +(0.155396 - 4.54141i) q^{18} +(-1.05858 - 0.611171i) q^{19} +(-0.228305 - 0.617156i) q^{20} +(4.47588 - 0.983091i) q^{21} +3.25401i q^{22} +(0.757344 - 1.31176i) q^{23} +(-1.08412 - 4.34168i) q^{24} +(4.71617 + 1.66064i) q^{25} +(2.63629 - 4.56619i) q^{26} +(-3.48097 - 3.85783i) q^{27} +(-0.685096 + 0.369932i) q^{28} +5.95645i q^{29} +(-5.28698 - 2.54205i) q^{30} +(2.75098 - 1.58828i) q^{31} +(0.825899 + 1.43050i) q^{32} +(2.58574 + 2.67573i) q^{33} +5.41832i q^{34} +(1.16240 - 5.80076i) q^{35} +(0.749020 + 0.467309i) q^{36} +(6.75803 + 3.90175i) q^{37} +(1.60342 - 0.925734i) q^{38} +(-1.46065 - 5.84961i) q^{39} +(-5.69460 - 0.973292i) q^{40} -11.8685 q^{41} +(-2.10021 + 6.61582i) q^{42} -2.99294i q^{43} +(-0.547504 - 0.316101i) q^{44} +(-6.36742 + 2.11091i) 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} +(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} +(-0.194713 + 6.83288i) q^{56} +(0.582853 - 2.03535i) q^{57} +(-7.81342 - 4.51108i) q^{58} +(-1.08467 - 1.87871i) q^{59} +(0.941303 - 0.642622i) q^{60} +(-2.94338 - 1.69936i) q^{61} +4.81149i q^{62} +(3.53017 + 7.10900i) q^{63} +6.50196 q^{64} +(-7.67243 - 1.31133i) 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} +(6.72886 + 5.91796i) q^{70} -10.3968i q^{71} +(6.84108 - 3.64363i) q^{72} +(-3.42779 - 5.93710i) q^{73} +(-10.2363 + 5.90993i) q^{74} +(-0.811666 + 8.62213i) q^{75} +0.359711i q^{76} +(-2.70057 - 5.00133i) q^{77} +(8.77950 + 2.51414i) q^{78} +(0.941421 - 1.63059i) q^{79} +(6.43014 - 7.74542i) q^{80} +(5.02225 - 7.46840i) q^{81} +(8.98853 - 15.5686i) q^{82} -9.10486i q^{83} +(-0.909127 - 0.996046i) q^{84} +(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} +(2.05332 - 9.95121i) q^{90} +(-0.262339 + 9.20605i) q^{91} -0.445743 q^{92} +(3.82337 + 3.95644i) q^{93} +(8.00392 - 4.62107i) q^{94} +(-2.10299 - 1.74587i) q^{95} +(-2.05733 + 1.98814i) 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

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