LMFDB - Embedded newform 952.2.s.a.421.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(421,952)] 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("952.421"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.s (of order $4$, 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:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$108$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			421.14
Character	$\chi$	$=$	952.421
Dual form			952.2.s.a.701.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29470 - 0.568988i) q^{2} +(-1.37745 + 1.37745i) q^{3} +(1.35251 + 1.47334i) q^{4} +(-1.95944 + 1.95944i) q^{5} +(2.56714 - 0.999634i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.912778 - 2.67709i) q^{8} -0.794737i q^{9} +(3.65179 - 1.42199i) q^{10} +(-1.29313 - 1.29313i) q^{11} +(-3.89246 - 0.166444i) q^{12} -2.48159i q^{13} +(1.31783 - 0.513157i) q^{14} -5.39807i q^{15} +(-0.341460 + 3.98540i) q^{16} +(-4.10033 + 0.432807i) q^{17} +(-0.452196 + 1.02895i) q^{18} -1.95325 q^{19} +(-5.53708 - 0.236768i) q^{20} -1.94801i q^{21} +(0.938445 + 2.41000i) q^{22} +(-3.10969 + 3.10969i) q^{23} +(4.94487 + 2.43026i) q^{24} -2.67882i q^{25} +(-1.41199 + 3.21291i) q^{26} +(-3.03764 - 3.03764i) q^{27} +(-1.99817 - 0.0854429i) q^{28} +(2.19884 - 2.19884i) q^{29} +(-3.07143 + 6.98888i) q^{30} +(1.51572 + 1.51572i) q^{31} +(2.70973 - 4.96562i) q^{32} +3.56246 q^{33} +(5.55496 + 1.77268i) q^{34} -2.77107i q^{35} +(1.17092 - 1.07489i) q^{36} +(0.565767 - 0.565767i) q^{37} +(2.52887 + 1.11137i) q^{38} +(3.41826 + 3.41826i) q^{39} +(7.03415 + 3.45708i) q^{40} +(0.844929 - 0.844929i) q^{41} +(-1.10839 + 2.52209i) q^{42} +5.00303 q^{43} +(0.156255 - 3.65420i) q^{44} +(1.55724 + 1.55724i) q^{45} +(5.79550 - 2.25674i) q^{46} -4.18908 q^{47} +(-5.01934 - 5.96003i) q^{48} -1.00000i q^{49} +(-1.52422 + 3.46827i) q^{50} +(5.05182 - 6.24417i) q^{51} +(3.65622 - 3.35636i) q^{52} +8.35261 q^{53} +(2.20446 + 5.66122i) q^{54} +5.06764 q^{55} +(2.53842 + 1.24756i) q^{56} +(2.69050 - 2.69050i) q^{57} +(-4.09796 + 1.59573i) q^{58} -7.40850 q^{59} +(7.95318 - 7.30091i) q^{60} +(10.8531 + 10.8531i) q^{61} +(-1.09998 - 2.82483i) q^{62} +(0.561964 + 0.561964i) q^{63} +(-6.33367 + 4.88719i) q^{64} +(4.86252 + 4.86252i) q^{65} +(-4.61232 - 2.02699i) q^{66} -9.83400i q^{67} +(-6.18338 - 5.45580i) q^{68} -8.56689i q^{69} +(-1.57670 + 3.58771i) q^{70} +(-1.11377 - 1.11377i) q^{71} +(-2.12759 + 0.725419i) q^{72} +(0.905981 + 0.905981i) q^{73} +(-1.05441 + 0.410585i) q^{74} +(3.68994 + 3.68994i) q^{75} +(-2.64178 - 2.87780i) q^{76} +1.82877 q^{77} +(-2.48068 - 6.37058i) q^{78} +(8.01993 - 8.01993i) q^{79} +(-7.14009 - 8.47823i) q^{80} +10.7526 q^{81} +(-1.57469 + 0.613176i) q^{82} -7.27450 q^{83} +(2.87008 - 2.63469i) q^{84} +(7.18629 - 8.88241i) q^{85} +(-6.47743 - 2.84666i) q^{86} +6.05760i q^{87} +(-2.28150 + 4.64219i) q^{88} +11.1524 q^{89} +(-1.13011 - 2.90221i) q^{90} +(1.75475 + 1.75475i) q^{91} +(-8.78750 - 0.375758i) q^{92} -4.17565 q^{93} +(5.42360 + 2.38353i) q^{94} +(3.82728 - 3.82728i) q^{95} +(3.10737 + 10.5724i) q^{96} +(-3.84098 - 3.84098i) q^{97} +(-0.568988 + 1.29470i) q^{98} +(-1.02770 + 1.02770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{6} - 8 q^{10} - 16 q^{16} + 8 q^{17} + 8 q^{24} - 20 q^{30} + 32 q^{31} - 32 q^{34} - 40 q^{38} + 4 q^{40} + 24 q^{41} - 8 q^{44} - 8 q^{46} + 84 q^{48} + 36 q^{50} + 84 q^{54} - 16 q^{57}+ \cdots + 8 q^{97}+O(q^{100}) $ 216 * q - 8 * q^6 - 8 * q^10 - 16 * q^16 + 8 * q^17 + 8 * q^24 - 20 * q^30 + 32 * q^31 - 32 * q^34 - 40 * q^38 + 4 * q^40 + 24 * q^41 - 8 * q^44 - 8 * q^46 + 84 * q^48 + 36 * q^50 + 84 * q^54 - 16 * q^57 - 60 * q^58 + 16 * q^62 - 48 * q^64 + 48 * q^65 + 52 * q^68 - 84 * q^72 - 40 * q^73 - 16 * q^74 - 76 * q^78 - 32 * q^79 - 128 * q^80 - 184 * q^81 - 16 * q^82 + 56 * q^84 + 20 * q^86 - 52 * q^88 - 36 * q^90 - 168 * q^92 - 80 * q^96 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.29470	−	0.568988i	−0.915492	−	0.402335i
$2$	−1.29470	−	0.568988i	−0.915492	−	0.402335i
$3$	−1.37745	+	1.37745i	−0.795271	+	0.795271i	−0.982346	−	0.187075i	$-0.940099\pi$
$3$	−1.37745	+	1.37745i	−0.795271	+	0.795271i	0.187075	+	0.982346i	$0.440099\pi$
$4$	1.35251	+	1.47334i	0.676253	+	0.736670i
$5$	−1.95944	+	1.95944i	−0.876289	+	0.876289i	−0.993148	−	0.116860i	$-0.962717\pi$
$5$	−1.95944	+	1.95944i	−0.876289	+	0.876289i	0.116860	+	0.993148i	$0.462717\pi$
$6$	2.56714	−	0.999634i	1.04803	−	0.408099i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.912778	−	2.67709i	−0.322716	−	0.946496i
$9$		−	0.794737i		−	0.264912i
$10$	3.65179	−	1.42199i	1.15480	−	0.449674i
$11$	−1.29313	−	1.29313i	−0.389895	−	0.389895i	0.484755	−	0.874650i	$-0.338909\pi$
$11$	−1.29313	−	1.29313i	−0.389895	−	0.389895i	−0.874650	+	0.484755i	$0.838909\pi$
$12$	−3.89246	−	0.166444i	−1.12366	−	0.0480481i
$13$		−	2.48159i		−	0.688268i	−0.938920	−	0.344134i	$-0.888173\pi$
$13$		−	2.48159i		−	0.688268i	0.938920	−	0.344134i	$-0.111827\pi$
$14$	1.31783	−	0.513157i	0.352204	−	0.137147i
$15$		−	5.39807i		−	1.39377i
$16$	−0.341460	+	3.98540i	−0.0853649	+	0.996350i
$17$	−4.10033	+	0.432807i	−0.994475	+	0.104971i
$17$	−4.10033	+	0.432807i	−0.994475	+	0.104971i
$18$	−0.452196	+	1.02895i	−0.106584	+	0.242525i
$19$	−1.95325			−0.448106			−0.224053	−	0.974577i	$-0.571929\pi$
$19$	−1.95325			−0.448106			−0.224053	+	0.974577i	$0.571929\pi$
$20$	−5.53708	−	0.236768i	−1.23813	−	0.0529430i
$21$		−	1.94801i		−	0.425090i
$22$	0.938445	+	2.41000i	0.200077	+	0.513814i
$23$	−3.10969	+	3.10969i	−0.648415	+	0.648415i	−0.952610	−	0.304195i	$-0.901613\pi$
$23$	−3.10969	+	3.10969i	−0.648415	+	0.648415i	0.304195	+	0.952610i	$0.401613\pi$
$24$	4.94487	+	2.43026i	1.00937	+	0.496074i
$25$		−	2.67882i		−	0.535764i
$26$	−1.41199	+	3.21291i	−0.276915	+	0.630104i
$27$	−3.03764	−	3.03764i	−0.584594	−	0.584594i
$28$	−1.99817	−	0.0854429i	−0.377619	−	0.0161472i
$29$	2.19884	−	2.19884i	0.408315	−	0.408315i	−0.472835	−	0.881151i	$-0.656770\pi$
$29$	2.19884	−	2.19884i	0.408315	−	0.408315i	0.881151	+	0.472835i	$0.156770\pi$
$30$	−3.07143	+	6.98888i	−0.560765	+	1.27599i
$31$	1.51572	+	1.51572i	0.272231	+	0.272231i	0.829998	−	0.557767i	$-0.188342\pi$
$31$	1.51572	+	1.51572i	0.272231	+	0.272231i	−0.557767	+	0.829998i	$0.688342\pi$
$32$	2.70973	−	4.96562i	0.479018	−	0.877805i
$33$	3.56246			0.620144
$34$	5.55496	+	1.77268i	0.952668	+	0.304012i
$35$		−	2.77107i		−	0.468396i
$36$	1.17092	−	1.07489i	0.195153	−	0.179148i
$37$	0.565767	−	0.565767i	0.0930115	−	0.0930115i	−0.659070	−	0.752082i	$-0.729050\pi$
$37$	0.565767	−	0.565767i	0.0930115	−	0.0930115i	0.752082	+	0.659070i	$0.229050\pi$
$38$	2.52887	+	1.11137i	0.410238	+	0.180289i
$39$	3.41826	+	3.41826i	0.547360	+	0.547360i
$40$	7.03415	+	3.45708i	1.11220	+	0.546612i
$41$	0.844929	−	0.844929i	0.131956	−	0.131956i	−0.638044	−	0.770000i	$-0.720256\pi$
$41$	0.844929	−	0.844929i	0.131956	−	0.131956i	0.770000	+	0.638044i	$0.220256\pi$
$42$	−1.10839	+	2.52209i	−0.171029	+	0.389167i
$43$	5.00303			0.762954			0.381477	−	0.924378i	$-0.375415\pi$
$43$	5.00303			0.762954			0.381477	+	0.924378i	$0.375415\pi$
$44$	0.156255	−	3.65420i	0.0235564	−	0.550891i
$45$	1.55724	+	1.55724i	0.232140	+	0.232140i
$46$	5.79550	−	2.25674i	0.854500	−	0.332739i
$47$	−4.18908			−0.611040			−0.305520	−	0.952186i	$-0.598830\pi$
$47$	−4.18908			−0.611040			−0.305520	+	0.952186i	$0.598830\pi$
$48$	−5.01934	−	5.96003i	−0.724480	−	0.860256i
$49$		−	1.00000i		−	0.142857i
$50$	−1.52422	+	3.46827i	−0.215557	+	0.490488i
$51$	5.05182	−	6.24417i	0.707397	−	0.874358i
$52$	3.65622	−	3.35636i	0.507026	−	0.465443i
$53$	8.35261			1.14732			0.573660	−	0.819094i	$-0.305523\pi$
$53$	8.35261			1.14732			0.573660	+	0.819094i	$0.305523\pi$
$54$	2.20446	+	5.66122i	0.299988	+	0.770394i
$55$	5.06764			0.683321
$56$	2.53842	+	1.24756i	0.339211	+	0.166712i
$57$	2.69050	−	2.69050i	0.356366	−	0.356366i
$58$	−4.09796	+	1.59573i	−0.538089	+	0.209530i
$59$	−7.40850			−0.964505			−0.482253	−	0.876032i	$-0.660181\pi$
$59$	−7.40850			−0.964505			−0.482253	+	0.876032i	$0.660181\pi$
$60$	7.95318	−	7.30091i	1.02675	−	0.942544i
$61$	10.8531	+	10.8531i	1.38960	+	1.38960i	0.826155	+	0.563443i	$0.190523\pi$
$61$	10.8531	+	10.8531i	1.38960	+	1.38960i	0.563443	+	0.826155i	$0.309477\pi$
$62$	−1.09998	−	2.82483i	−0.139697	−	0.358753i
$63$	0.561964	+	0.561964i	0.0708008	+	0.0708008i
$64$	−6.33367	+	4.88719i	−0.791709	+	0.610898i
$65$	4.86252	+	4.86252i	0.603122	+	0.603122i
$66$	−4.61232	−	2.02699i	−0.567737	−	0.249506i
$67$		−	9.83400i		−	1.20141i	−0.799469	−	0.600707i	$-0.794886\pi$
$67$		−	9.83400i		−	1.20141i	0.799469	−	0.600707i	$-0.205114\pi$
$68$	−6.18338	−	5.45580i	−0.749846	−	0.661613i
$69$		−	8.56689i		−	1.03133i
$70$	−1.57670	+	3.58771i	−0.188452	+	0.428813i
$71$	−1.11377	−	1.11377i	−0.132180	−	0.132180i	0.637921	−	0.770101i	$-0.279794\pi$
$71$	−1.11377	−	1.11377i	−0.132180	−	0.132180i	−0.770101	+	0.637921i	$0.779794\pi$
$72$	−2.12759	+	0.725419i	−0.250739	+	0.0854914i
$73$	0.905981	+	0.905981i	0.106037	+	0.106037i	0.758135	−	0.652098i	$-0.226111\pi$
$73$	0.905981	+	0.905981i	0.106037	+	0.106037i	−0.652098	+	0.758135i	$0.726111\pi$
$74$	−1.05441	+	0.410585i	−0.122573	+	0.0477295i
$75$	3.68994	+	3.68994i	0.426078	+	0.426078i
$76$	−2.64178	−	2.87780i	−0.303033	−	0.330106i
$77$	1.82877			0.208407
$78$	−2.48068	−	6.37058i	−0.280882	−	0.721326i
$79$	8.01993	−	8.01993i	0.902312	−	0.902312i	−0.0933236	−	0.995636i	$-0.529749\pi$
$79$	8.01993	−	8.01993i	0.902312	−	0.902312i	0.995636	+	0.0933236i	$0.0297491\pi$
$80$	−7.14009	−	8.47823i	−0.798286	−	0.947894i
$81$	10.7526			1.19473
$82$	−1.57469	+	0.613176i	−0.173895	+	0.0677140i
$83$	−7.27450			−0.798480			−0.399240	−	0.916846i	$-0.630726\pi$
$83$	−7.27450			−0.798480			−0.399240	+	0.916846i	$0.630726\pi$
$84$	2.87008	−	2.63469i	0.313151	−	0.287468i
$85$	7.18629	−	8.88241i	0.779463	−	0.963433i
$86$	−6.47743	−	2.84666i	−0.698479	−	0.306964i
$87$			6.05760i			0.649443i
$88$	−2.28150	+	4.64219i	−0.243209	+	0.494859i
$89$	11.1524			1.18215			0.591074	−	0.806618i	$-0.298704\pi$
$89$	11.1524			1.18215			0.591074	+	0.806618i	$0.298704\pi$
$90$	−1.13011	−	2.90221i	−0.119124	−	0.305920i
$91$	1.75475	+	1.75475i	0.183947	+	0.183947i
$92$	−8.78750	−	0.375758i	−0.916161	−	0.0391755i
$93$	−4.17565			−0.432995
$94$	5.42360	+	2.38353i	0.559402	+	0.245843i
$95$	3.82728	−	3.82728i	0.392670	−	0.392670i
$96$	3.10737	+	10.5724i	0.317144	+	1.07904i
$97$	−3.84098	−	3.84098i	−0.389992	−	0.389992i	0.484693	−	0.874685i	$-0.338931\pi$
$97$	−3.84098	−	3.84098i	−0.389992	−	0.389992i	−0.874685	+	0.484693i	$0.838931\pi$
$98$	−0.568988	+	1.29470i	−0.0574765	+	0.130785i
$99$	−1.02770	+	1.02770i	−0.103288	+	0.103288i
$100$	3.94681	−	3.62312i	0.394681	−	0.362312i
$101$		−	13.2503i		−	1.31845i	−0.751946	−	0.659225i	$-0.770885\pi$
$101$		−	13.2503i		−	1.31845i	0.751946	−	0.659225i	$-0.229115\pi$
$102$	−10.0935	+	5.20990i	−0.999402	+	0.515857i
$103$	−3.09260			−0.304723			−0.152361	−	0.988325i	$-0.548688\pi$
$103$	−3.09260			−0.304723			−0.152361	+	0.988325i	$0.548688\pi$
$104$	−6.64344	+	2.26514i	−0.651443	+	0.222115i
$105$	3.81701	+	3.81701i	0.372502	+	0.372502i
$106$	−10.8141	−	4.75254i	−1.05036	−	0.461607i
$107$	−5.25704	+	5.25704i	−0.508217	+	0.508217i	−0.913979	−	0.405762i	$-0.867006\pi$
$107$	−5.25704	+	5.25704i	−0.508217	+	0.508217i	0.405762	+	0.913979i	$0.367006\pi$
$108$	0.367052	−	8.58390i	0.0353196	−	0.825986i
$109$	12.6379	+	12.6379i	1.21049	+	1.21049i	0.970866	+	0.239623i	$0.0770240\pi$
$109$	12.6379	+	12.6379i	1.21049	+	1.21049i	0.239623	+	0.970866i	$0.422976\pi$
$110$	−6.56108	−	2.88343i	−0.625575	−	0.274924i
$111$			1.55863i			0.147939i
$112$	−2.57665	−	3.05955i	−0.243471	−	0.289100i
$113$	4.74411	−	4.74411i	0.446289	−	0.446289i	−0.447830	−	0.894119i	$-0.647803\pi$
$113$	4.74411	−	4.74411i	0.446289	−	0.446289i	0.894119	+	0.447830i	$0.147803\pi$
$114$	−5.01426	+	1.95253i	−0.469629	+	0.182872i
$115$		−	12.1865i		−	1.13640i
$116$	6.21359	+	0.265696i	0.576918	+	0.0246693i
$117$	−1.97221			−0.182331
$118$	9.59180	+	4.21535i	0.882997	+	0.388054i
$119$	2.59333	−	3.20541i	0.237730	−	0.293839i
$120$	−14.4511	+	4.92724i	−1.31920	+	0.449793i
$121$		−	7.65561i		−	0.695964i
$122$	−7.87625	−	20.2268i	−0.713082	−	1.83125i
$123$			2.32769i			0.209881i
$124$	−0.183151	+	4.28318i	−0.0164474	+	0.384641i
$125$	−4.54821	−	4.54821i	−0.406805	−	0.406805i
$126$	−0.407825	−	1.04733i	−0.0363319	−	0.0933033i
$127$		−	21.0825i		−	1.87077i	−0.353633	−	0.935384i	$-0.615054\pi$
$127$		−	21.0825i		−	1.87077i	0.353633	−	0.935384i	$-0.384946\pi$
$128$	10.9810	−	2.72366i	0.970590	−	0.240740i
$129$	−6.89142	+	6.89142i	−0.606756	+	0.606756i
$130$	−3.52880	−	9.06224i	−0.309496	−	0.794811i
$131$	−9.94743	+	9.94743i	−0.869111	+	0.869111i	−0.992374	−	0.123263i	$-0.960664\pi$
$131$	−9.94743	+	9.94743i	−0.869111	+	0.869111i	0.123263	+	0.992374i	$0.460664\pi$
$132$	4.81824	+	5.24871i	0.419374	+	0.456841i
$133$	1.38116	−	1.38116i	0.119761	−	0.119761i
$134$	−5.59543	+	12.7321i	−0.483372	+	1.09989i
$135$	11.9042			1.02455
$136$	4.90135	+	10.5819i	0.420288	+	0.907391i
$137$	−13.5137			−1.15456			−0.577279	−	0.816547i	$-0.695885\pi$
$137$	−13.5137			−1.15456			−0.577279	+	0.816547i	$0.695885\pi$
$138$	−4.87446	+	11.0916i	−0.414941	+	0.944177i
$139$	−6.91475	+	6.91475i	−0.586501	+	0.586501i	−0.936682	−	0.350181i	$-0.886120\pi$
$139$	−6.91475	+	6.91475i	−0.586501	+	0.586501i	0.350181	+	0.936682i	$0.386120\pi$
$140$	4.08273	−	3.74788i	0.345053	−	0.316754i
$141$	5.77024	−	5.77024i	0.485942	−	0.485942i
$142$	0.808277	+	2.07572i	0.0678291	+	0.174190i
$143$	−3.20902	+	3.20902i	−0.268352	+	0.268352i
$144$	3.16735	+	0.271371i	0.263945	+	0.0226142i
$145$			8.61702i			0.715604i
$146$	−0.657483	−	1.68847i	−0.0544137	−	0.139739i
$147$	1.37745	+	1.37745i	0.113610	+	0.113610i
$148$	1.59877	+	0.0683642i	0.131418	+	0.00561950i
$149$		−	8.05855i		−	0.660182i	−0.943949	−	0.330091i	$-0.892920\pi$
$149$		−	8.05855i		−	0.660182i	0.943949	−	0.330091i	$-0.107080\pi$
$150$	−2.67784	−	6.87691i	−0.218645	−	0.561497i
$151$		−	3.19258i		−	0.259809i	−0.991527	−	0.129904i	$-0.958533\pi$
$151$		−	3.19258i		−	0.259809i	0.991527	−	0.129904i	$-0.0414670\pi$
$152$	1.78288	+	5.22903i	0.144611	+	0.424130i
$153$	0.343968	+	3.25868i	0.0278082	+	0.263449i
$154$	−2.36771	−	1.04055i	−0.190795	−	0.0838497i
$155$	−5.93992			−0.477106
$156$	−0.413044	+	9.65948i	−0.0330700	+	0.773377i
$157$			3.08474i			0.246189i	0.992395	+	0.123095i	$0.0392818\pi$
$157$			3.08474i			0.246189i	−0.992395	+	0.123095i	$0.960718\pi$
$158$	−14.9467	+	5.82017i	−1.18909	+	0.463028i
$159$	−11.5053	+	11.5053i	−0.912430	+	0.912430i
$160$	4.42027	+	15.0394i	0.349453	+	1.18897i
$161$		−	4.39777i		−	0.346593i
$162$	−13.9214	−	6.11810i	−1.09377	−	0.480684i
$163$	−13.2885	−	13.2885i	−1.04084	−	1.04084i	−0.999130	−	0.0417073i	$-0.986720\pi$
$163$	−13.2885	−	13.2885i	−1.04084	−	1.04084i	−0.0417073	−	0.999130i	$-0.513280\pi$
$164$	2.38764	+	0.102097i	0.186443	+	0.00797241i
$165$	−6.98042	+	6.98042i	−0.543425	+	0.543425i
$166$	9.41831	+	4.13910i	0.731003	+	0.321257i
$167$	15.2822	+	15.2822i	1.18257	+	1.18257i	0.979076	+	0.203496i	$0.0652305\pi$
$167$	15.2822	+	15.2822i	1.18257	+	1.18257i	0.203496	+	0.979076i	$0.434770\pi$
$168$	−5.21500	+	1.77810i	−0.402346	+	0.137183i
$169$	6.84173			0.526287
$170$	−14.3581	+	7.41116i	−1.10121	+	0.568410i
$171$			1.55232i			0.118709i
$172$	6.76662	+	7.37116i	0.515950	+	0.562046i
$173$	8.36893	−	8.36893i	0.636278	−	0.636278i	−0.313357	−	0.949635i	$-0.601454\pi$
$173$	8.36893	−	8.36893i	0.636278	−	0.636278i	0.949635	+	0.313357i	$0.101454\pi$
$174$	3.44670	−	7.84278i	0.261294	−	0.594560i
$175$	1.89421	+	1.89421i	0.143189	+	0.143189i
$176$	5.59521	−	4.71210i	0.421755	−	0.355188i
$177$	10.2048	−	10.2048i	0.767043	−	0.767043i
$178$	−14.4390	−	6.34556i	−1.08225	−	0.475620i
$179$	11.4016			0.852198			0.426099	−	0.904676i	$-0.359887\pi$
$179$	11.4016			0.852198			0.426099	+	0.904676i	$0.359887\pi$
$180$	−0.188169	+	4.40052i	−0.0140253	+	0.327996i
$181$	4.14161	+	4.14161i	0.307844	+	0.307844i	0.844073	−	0.536229i	$-0.180152\pi$
$181$	4.14161	+	4.14161i	0.307844	+	0.307844i	−0.536229	+	0.844073i	$0.680152\pi$
$182$	−1.27344	−	3.27030i	−0.0943939	−	0.242411i
$183$	−29.8992			−2.21021
$184$	11.1634	+	5.48648i	0.822976	+	0.404469i
$185$			2.21717i			0.163010i
$186$	5.40622	+	2.37589i	0.396403	+	0.174209i
$187$	5.86195	+	4.74259i	0.428668	+	0.346813i
$188$	−5.66575	−	6.17193i	−0.413217	−	0.450134i
$189$	4.29587			0.312479
$190$	−7.13285	+	2.77751i	−0.517472	+	0.201501i
$191$	−13.2158			−0.956260			−0.478130	−	0.878289i	$-0.658685\pi$
$191$	−13.2158			−0.956260			−0.478130	+	0.878289i	$0.658685\pi$
$192$	1.99246	−	15.4562i	0.143794	−	1.11545i
$193$	−9.76473	+	9.76473i	−0.702881	+	0.702881i	−0.965028	−	0.262147i	$-0.915569\pi$
$193$	−9.76473	+	9.76473i	−0.702881	+	0.702881i	0.262147	+	0.965028i	$0.415569\pi$
$194$	2.78745	+	7.15839i	0.200127	+	0.513942i
$195$	−13.3958			−0.959291
$196$	1.47334	−	1.35251i	0.105239	−	0.0966075i
$197$	9.58566	+	9.58566i	0.682950	+	0.682950i	0.960664	−	0.277714i	$-0.0895768\pi$
$197$	9.58566	+	9.58566i	0.682950	+	0.682950i	−0.277714	+	0.960664i	$0.589577\pi$
$198$	1.91532	−	0.745817i	0.136116	−	0.0530029i
$199$	13.5242	+	13.5242i	0.958708	+	0.958708i	0.999181	−	0.0404731i	$-0.0128865\pi$
$199$	13.5242	+	13.5242i	0.958708	+	0.958708i	−0.0404731	+	0.999181i	$0.512887\pi$
$200$	−7.17146	+	2.44517i	−0.507099	+	0.172900i
$201$	13.5458	+	13.5458i	0.955451	+	0.955451i
$202$	−7.53924	+	17.1551i	−0.530459	+	1.20703i
$203$			3.10964i			0.218254i
$204$	16.0324	−	1.00221i	1.12249	−	0.0701689i
$205$			3.31118i			0.231263i
$206$	4.00399	+	1.75965i	0.278971	+	0.122601i
$207$	2.47139	+	2.47139i	0.171773	+	0.171773i
$208$	9.89011	+	0.847362i	0.685756	+	0.0587540i
$209$	2.52581	+	2.52581i	0.174714	+	0.174714i
$210$	−2.77006	−	7.11372i	−0.191152	−	0.490893i
$211$	−4.42950	−	4.42950i	−0.304939	−	0.304939i	0.538003	−	0.842943i	$-0.319179\pi$
$211$	−4.42950	−	4.42950i	−0.304939	−	0.304939i	−0.842943	+	0.538003i	$0.819179\pi$
$212$	11.2970	+	12.3062i	0.775878	+	0.845196i
$213$	3.06832			0.210238
$214$	9.79749	−	3.81510i	0.669742	−	0.260795i
$215$	−9.80314	+	9.80314i	−0.668568	+	0.668568i
$216$	−5.35936	+	10.9047i	−0.364658	+	0.741973i
$217$	−2.14355			−0.145513
$218$	−9.17148	−	23.5531i	−0.621171	−	1.59522i
$219$	−2.49589			−0.168656
$220$	6.85401	+	7.46636i	0.462097	+	0.503382i
$221$	1.07405	+	10.1753i	0.0722483	+	0.684466i
$222$	0.886843	−	2.01796i	0.0595210	−	0.135437i
$223$			8.89964i			0.595964i	0.954571	+	0.297982i	$0.0963136\pi$
$223$			8.89964i			0.595964i	−0.954571	+	0.297982i	$0.903686\pi$
$224$	1.59515	+	5.42729i	0.106580	+	0.362626i
$225$	−2.12896			−0.141931
$226$	−8.84155	+	3.44287i	−0.588131	+	0.229016i
$227$	−12.6448	−	12.6448i	−0.839264	−	0.839264i	0.149498	−	0.988762i	$-0.452234\pi$
$227$	−12.6448	−	12.6448i	−0.839264	−	0.839264i	−0.988762	+	0.149498i	$0.952234\pi$
$228$	7.60294	+	0.325106i	0.503517	+	0.0215306i
$229$	−9.88995			−0.653547			−0.326773	−	0.945103i	$-0.605961\pi$
$229$	−9.88995			−0.653547			−0.326773	+	0.945103i	$0.605961\pi$
$230$	−6.93398	+	15.7779i	−0.457213	+	1.04036i
$231$	−2.51904	+	2.51904i	−0.165740	+	0.165740i
$232$	−7.89357	−	3.87946i	−0.518238	−	0.254699i
$233$	−2.58090	−	2.58090i	−0.169081	−	0.169081i	0.617495	−	0.786575i	$-0.288148\pi$
$233$	−2.58090	−	2.58090i	−0.169081	−	0.169081i	−0.786575	+	0.617495i	$0.788148\pi$
$234$	2.55342	+	1.12216i	0.166922	+	0.0733581i
$235$	8.20825	−	8.20825i	0.535447	−	0.535447i
$236$	−10.0200	−	10.9152i	−0.652249	−	0.710522i
$237$			22.0941i			1.43517i
$238$	−5.18143	+	2.67448i	−0.335862	+	0.173361i
$239$	−4.84136			−0.313162			−0.156581	−	0.987665i	$-0.550047\pi$
$239$	−4.84136			−0.313162			−0.156581	+	0.987665i	$0.550047\pi$
$240$	21.5134	+	1.84322i	1.38869	+	0.118979i
$241$	−16.9930	−	16.9930i	−1.09462	−	1.09462i	−0.995029	−	0.0995875i	$-0.968248\pi$
$241$	−16.9930	−	16.9930i	−1.09462	−	1.09462i	−0.0995875	−	0.995029i	$-0.531752\pi$
$242$	−4.35595	+	9.91173i	−0.280011	+	0.637150i
$243$	−5.69826	+	5.69826i	−0.365543	+	0.365543i
$244$	−1.31143	+	30.6692i	−0.0839557	+	1.96339i
$245$	1.95944	+	1.95944i	0.125184	+	0.125184i
$246$	1.32443	−	3.01367i	0.0844426	−	0.192145i
$247$			4.84715i			0.308417i
$248$	2.67420	−	5.44123i	0.169812	−	0.345518i
$249$	10.0203	−	10.0203i	0.635008	−	0.635008i
$250$	3.30070	+	8.47646i	0.208755	+	0.536098i
$251$		−	22.9644i		−	1.44950i	−0.689013	−	0.724749i	$-0.741956\pi$
$251$		−	22.9644i		−	1.44950i	0.689013	−	0.724749i	$-0.258044\pi$
$252$	−0.0679047	+	1.58802i	−0.00427759	+	0.100036i
$253$	8.04249			0.505627
$254$	−11.9957	+	27.2955i	−0.752676	+	1.71267i
$255$	2.33632	+	22.1338i	0.146306	+	1.38607i
$256$	−15.7668	−	2.72171i	−0.985426	−	0.170107i
$257$			6.07171i			0.378743i	0.981906	+	0.189371i	$0.0606450\pi$
$257$			6.07171i			0.378743i	−0.981906	+	0.189371i	$0.939355\pi$
$258$	12.8435	−	5.00120i	0.799599	−	0.311361i
$259$			0.800115i			0.0497168i
$260$	−0.587561	+	13.7407i	−0.0364390	+	0.852164i
$261$	−1.74750	−	1.74750i	−0.108168	−	0.108168i
$262$	18.5389	−	7.21898i	1.14534	−	0.445990i
$263$			0.279797i			0.0172530i	0.999963	+	0.00862650i	$0.00274593\pi$
$263$			0.279797i			0.0172530i	−0.999963	+	0.00862650i	$0.997254\pi$
$264$	−3.25173	−	9.53703i	−0.200130	−	0.586964i
$265$	−16.3665	+	16.3665i	−1.00538	+	1.00538i
$266$	−2.57404	+	1.00232i	−0.157825	+	0.0614564i
$267$	−15.3618	+	15.3618i	−0.940128	+	0.940128i
$268$	14.4888	−	13.3005i	0.885046	−	0.812460i
$269$	−6.45930	+	6.45930i	−0.393831	+	0.393831i	−0.876050	−	0.482220i	$-0.839831\pi$
$269$	−6.45930	+	6.45930i	−0.393831	+	0.393831i	0.482220	+	0.876050i	$0.339831\pi$
$270$	−15.4123	−	6.77332i	−0.937964	−	0.412211i
$271$	6.38216			0.387688			0.193844	−	0.981032i	$-0.437904\pi$
$271$	6.38216			0.387688			0.193844	+	0.981032i	$0.437904\pi$
$272$	−0.324813	−	16.4892i	−0.0196947	−	0.999806i
$273$	−4.83415			−0.292576
$274$	17.4963	+	7.68916i	1.05699	+	0.464519i
$275$	−3.46408	+	3.46408i	−0.208892	+	0.208892i
$276$	12.6219	−	11.5868i	0.759751	−	0.697441i
$277$	−14.8589	+	14.8589i	−0.892786	+	0.892786i	−0.994785	−	0.101999i	$-0.967476\pi$
$277$	−14.8589	+	14.8589i	−0.892786	+	0.892786i	0.101999	+	0.994785i	$0.467476\pi$
$278$	12.8869	−	5.01813i	0.772907	−	0.300967i
$279$	1.20460	−	1.20460i	0.0721173	−	0.0721173i
$280$	−7.41841	+	2.52937i	−0.443335	+	0.151159i
$281$		−	25.5039i		−	1.52144i	−0.649082	−	0.760718i	$-0.724847\pi$
$281$		−	25.5039i		−	1.52144i	0.649082	−	0.760718i	$-0.275153\pi$
$282$	−10.7539	+	4.18754i	−0.640388	+	0.249365i
$283$	−7.84780	−	7.84780i	−0.466504	−	0.466504i	0.434276	−	0.900780i	$-0.357004\pi$
$283$	−7.84780	−	7.84780i	−0.466504	−	0.466504i	−0.900780	+	0.434276i	$0.857004\pi$
$284$	0.134582	−	3.14734i	0.00798595	−	0.186760i
$285$			10.5438i			0.624559i
$286$	5.98063	−	2.32883i	0.353642	−	0.137707i
$287$			1.19491i			0.0705333i
$288$	−3.94636	−	2.15353i	−0.232542	−	0.126898i
$289$	16.6254	−	3.54930i	0.977962	−	0.208782i
$290$	4.90298	−	11.1565i	0.287913	−	0.655130i
$291$	10.5815			0.620299
$292$	−0.109474	+	2.56016i	−0.00640647	+	0.149822i
$293$		−	18.5859i		−	1.08580i	−0.839798	−	0.542899i	$-0.817326\pi$
$293$		−	18.5859i		−	1.08580i	0.839798	−	0.542899i	$-0.182674\pi$
$294$	−0.999634	−	2.56714i	−0.0582999	−	0.149719i
$295$	14.5165	−	14.5165i	0.845185	−	0.845185i
$296$	−2.03103	−	0.998192i	−0.118051	−	0.0580187i
$297$			7.85615i			0.455860i
$298$	−4.58522	+	10.4334i	−0.265615	+	0.604392i
$299$	7.71697	+	7.71697i	0.446284	+	0.446284i
$300$	−0.445873	+	10.4272i	−0.0257425	+	0.602015i
$301$	−3.53767	+	3.53767i	−0.203908	+	0.203908i
$302$	−1.81654	+	4.13344i	−0.104530	+	0.237853i
$303$	18.2516	+	18.2516i	1.04852	+	1.04852i
$304$	0.666956	−	7.78447i	0.0382525	−	0.446470i
$305$	−42.5321			−2.43538
$306$	1.40882	−	4.41474i	0.0805366	−	0.252374i
$307$		−	14.0179i		−	0.800046i	−0.916505	−	0.400023i	$-0.869002\pi$
$307$		−	14.0179i		−	0.800046i	0.916505	−	0.400023i	$-0.130998\pi$
$308$	2.47342	+	2.69440i	0.140936	+	0.153527i
$309$	4.25990	−	4.25990i	0.242337	−	0.242337i
$310$	7.69042	+	3.37974i	0.436786	+	0.191956i
$311$	−14.3313	−	14.3313i	−0.812651	−	0.812651i	0.172380	−	0.985031i	$-0.444854\pi$
$311$	−14.3313	−	14.3313i	−0.812651	−	0.812651i	−0.985031	+	0.172380i	$0.944854\pi$
$312$	6.03090	−	12.2711i	0.341432	−	0.694716i
$313$	14.2837	−	14.2837i	0.807363	−	0.807363i	−0.176871	−	0.984234i	$-0.556598\pi$
$313$	14.2837	−	14.2837i	0.807363	−	0.807363i	0.984234	+	0.176871i	$0.0565975\pi$
$314$	1.75518	−	3.99382i	0.0990506	−	0.225384i
$315$	−2.20227			−0.124084
$316$	22.6631	+	0.969084i	1.27490	+	0.0545152i
$317$	−5.54164	−	5.54164i	−0.311250	−	0.311250i	0.534144	−	0.845394i	$-0.320634\pi$
$317$	−5.54164	−	5.54164i	−0.311250	−	0.311250i	−0.845394	+	0.534144i	$0.820634\pi$
$318$	21.4423	−	8.34956i	1.20243	−	0.468220i
$319$	−5.68680			−0.318400
$320$	2.83430	−	21.9866i	0.158442	−	1.22909i
$321$		−	14.4826i		−	0.808341i
$322$	−2.50228	+	5.69380i	−0.139446	+	0.317303i
$323$	8.00896	−	0.845380i	0.445630	−	0.0470382i
$324$	14.5430	+	15.8422i	0.807942	+	0.880124i
$325$	−6.64773			−0.368750
$326$	9.64366	+	24.7657i	0.534113	+	1.37164i
$327$	−34.8161			−1.92533
$328$	−3.03319	−	1.49072i	−0.167480	−	0.0823114i
$329$	2.96212	−	2.96212i	0.163307	−	0.163307i
$330$	13.0093	−	5.06579i	0.716141	−	0.278862i
$331$	−2.07642			−0.114131			−0.0570653	−	0.998370i	$-0.518174\pi$
$331$	−2.07642			−0.114131			−0.0570653	+	0.998370i	$0.518174\pi$
$332$	−9.83880	−	10.7178i	−0.539974	−	0.588216i
$333$	−0.449636	−	0.449636i	−0.0246399	−	0.0246399i
$334$	−11.0905	−	28.4813i	−0.606845	−	1.55843i
$335$	19.2692	+	19.2692i	1.05279	+	1.05279i
$336$	7.76359	+	0.665166i	0.423539	+	0.0362878i
$337$	−12.4425	−	12.4425i	−0.677785	−	0.677785i	0.281713	−	0.959499i	$-0.409097\pi$
$337$	−12.4425	−	12.4425i	−0.677785	−	0.677785i	−0.959499	+	0.281713i	$0.909097\pi$
$338$	−8.85800	−	3.89286i	−0.481812	−	0.211744i
$339$			13.0696i			0.709841i
$340$	22.8063	−	1.42566i	1.23685	−	0.0773173i
$341$		−	3.92005i		−	0.212283i
$342$	0.883251	−	2.00979i	0.0477608	−	0.108677i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−4.56665	−	13.3936i	−0.246217	−	0.722133i
$345$	16.7863	+	16.7863i	0.903745	+	0.903745i
$346$	−15.5971	+	6.07345i	−0.838505	+	0.326511i
$347$	17.7698	+	17.7698i	0.953932	+	0.953932i	0.998985	−	0.0450529i	$-0.0143456\pi$
$347$	17.7698	+	17.7698i	0.953932	+	0.953932i	−0.0450529	+	0.998985i	$0.514346\pi$
$348$	−8.92490	+	8.19293i	−0.478425	+	0.439187i
$349$	14.5407			0.778346			0.389173	−	0.921165i	$-0.372761\pi$
$349$	14.5407			0.778346			0.389173	+	0.921165i	$0.372761\pi$
$350$	−1.37466	−	3.53022i	−0.0734785	−	0.188698i
$351$	−7.53816	+	7.53816i	−0.402357	+	0.402357i
$352$	−9.92526	+	2.91716i	−0.529018	+	0.155485i
$353$	−31.0408			−1.65214			−0.826068	−	0.563570i	$-0.809428\pi$
$353$	−31.0408			−1.65214			−0.826068	+	0.563570i	$0.809428\pi$
$354$	−19.0187	+	7.40579i	−1.01083	+	0.393614i
$355$	4.36473			0.231656
$356$	15.0836	+	16.4312i	0.799430	+	0.870852i
$357$	0.843112	+	7.98747i	0.0446222	+	0.422742i
$358$	−14.7617	−	6.48739i	−0.780181	−	0.342869i
$359$			8.80951i			0.464948i	0.972603	+	0.232474i	$0.0746821\pi$
$359$			8.80951i			0.464948i	−0.972603	+	0.232474i	$0.925318\pi$
$360$	2.74747	−	5.59030i	0.144804	−	0.294635i
$361$	−15.1848			−0.799201
$362$	−3.00563	−	7.71869i	−0.157972	−	0.405685i
$363$	10.5452	+	10.5452i	0.553480	+	0.553480i
$364$	−0.212034	+	4.95864i	−0.0111136	+	0.259903i
$365$	−3.55043			−0.185838
$366$	38.7106	+	17.0123i	2.02343	+	0.889247i
$367$	−2.34232	+	2.34232i	−0.122268	+	0.122268i	−0.765593	−	0.643325i	$-0.777554\pi$
$367$	−2.34232	+	2.34232i	−0.122268	+	0.122268i	0.643325	+	0.765593i	$0.277554\pi$
$368$	−11.3315	−	13.4552i	−0.590697	−	0.701400i
$369$	−0.671497	−	0.671497i	−0.0349567	−	0.0349567i
$370$	1.26155	−	2.87058i	0.0655847	−	0.149234i
$371$	−5.90619	+	5.90619i	−0.306634	+	0.306634i
$372$	−5.64759	−	6.15215i	−0.292814	−	0.318974i
$373$		−	15.0995i		−	0.781820i	−0.920429	−	0.390910i	$-0.872160\pi$
$373$		−	15.0995i		−	0.781820i	0.920429	−	0.390910i	$-0.127840\pi$
$374$	−4.89100	−	9.47563i	−0.252907	−	0.489973i
$375$	12.5299			0.647040
$376$	3.82370	+	11.2146i	0.197192	+	0.578346i
$377$	−5.45662	−	5.45662i	−0.281030	−	0.281030i
$378$	−5.56187	−	2.44430i	−0.286072	−	0.125721i
$379$	−3.20446	+	3.20446i	−0.164602	+	0.164602i	−0.784602	−	0.620000i	$-0.787133\pi$
$379$	−3.20446	+	3.20446i	−0.164602	+	0.164602i	0.620000	+	0.784602i	$0.287133\pi$
$380$	10.8153	+	0.462467i	0.554813	+	0.0237241i
$381$	29.0401	+	29.0401i	1.48777	+	1.48777i
$382$	17.1105	+	7.51962i	0.875449	+	0.384737i
$383$		−	15.8443i		−	0.809607i	−0.914404	−	0.404804i	$-0.867340\pi$
$383$		−	15.8443i		−	0.809607i	0.914404	−	0.404804i	$-0.132660\pi$
$384$	−11.3740	+	18.8774i	−0.580428	+	0.963336i
$385$	−3.58336	+	3.58336i	−0.182625	+	0.182625i
$386$	18.1984	−	7.08640i	0.926276	−	0.360688i
$387$		−	3.97609i		−	0.202116i
$388$	0.464123	−	10.8540i	0.0235623	−	0.551028i
$389$	3.14431			0.159423			0.0797113	−	0.996818i	$-0.474600\pi$
$389$	3.14431			0.159423			0.0797113	+	0.996818i	$0.474600\pi$
$390$	17.3435	+	7.62203i	0.878223	+	0.385957i
$391$	11.4049	−	14.0966i	0.576768	−	0.712898i
$392$	−2.67709	+	0.912778i	−0.135214	+	0.0461023i
$393$		−	27.4042i		−	1.38236i
$394$	−6.95644	−	17.8647i	−0.350461	−	0.900010i
$395$			31.4292i			1.58137i
$396$	−2.90413	−	0.124182i	−0.145938	−	0.00624038i
$397$	−25.0662	−	25.0662i	−1.25804	−	1.25804i	−0.952029	−	0.306007i	$-0.901007\pi$
$397$	−25.0662	−	25.0662i	−1.25804	−	1.25804i	−0.306007	−	0.952029i	$-0.598993\pi$
$398$	−9.81472	−	25.2050i	−0.491968	−	1.26341i
$399$			3.80494i			0.190485i
$400$	10.6762	+	0.914709i	0.533809	+	0.0457355i
$401$	−20.4093	+	20.4093i	−1.01919	+	1.01919i	−0.0193807	+	0.999812i	$0.506169\pi$
$401$	−20.4093	+	20.4093i	−1.01919	+	1.01919i	−0.999812	+	0.0193807i	$0.993831\pi$
$402$	−9.83041	−	25.2453i	−0.490296	−	1.25912i
$403$	3.76138	−	3.76138i	0.187368	−	0.187368i
$404$	19.5221	−	17.9210i	0.971262	−	0.891605i
$405$	−21.0691	+	21.0691i	−1.04693	+	1.04693i
$406$	1.76935	−	4.02605i	0.0878112	−	0.199810i
$407$	−1.46323			−0.0725294
$408$	−21.3274	−	7.82468i	−1.05586	−	0.387379i
$409$	−11.6825			−0.577665			−0.288832	−	0.957380i	$-0.593267\pi$
$409$	−11.6825			−0.577665			−0.288832	+	0.957380i	$0.593267\pi$
$410$	1.88402	−	4.28699i	0.0930451	−	0.211719i
$411$	18.6145	−	18.6145i	0.918186	−	0.918186i
$412$	−4.18275	−	4.55645i	−0.206069	−	0.224480i
$413$	5.23860	−	5.23860i	0.257775	−	0.257775i
$414$	−1.79352	−	4.60590i	−0.0881467	−	0.226368i
$415$	14.2540	−	14.2540i	0.699699	−	0.699699i
$416$	−12.3226	−	6.72444i	−0.604166	−	0.329693i
$417$		−	19.0494i		−	0.932855i
$418$	−1.83302	−	4.70733i	−0.0896558	−	0.230243i
$419$	−4.16020	−	4.16020i	−0.203239	−	0.203239i	0.598147	−	0.801386i	$-0.295904\pi$
$419$	−4.16020	−	4.16020i	−0.203239	−	0.203239i	−0.801386	+	0.598147i	$0.795904\pi$
$420$	−0.461226	+	10.7863i	−0.0225055	+	0.526316i
$421$		−	18.4431i		−	0.898861i	−0.893315	−	0.449430i	$-0.851627\pi$
$421$		−	18.4431i		−	0.898861i	0.893315	−	0.449430i	$-0.148373\pi$
$422$	3.21455	+	8.25521i	0.156482	+	0.401858i
$423$			3.32922i			0.161872i
$424$	−7.62408	−	22.3607i	−0.370258	−	1.08593i
$425$	1.15941	+	10.9840i	0.0562398	+	0.532804i
$426$	−3.97256	−	1.74584i	−0.192471	−	0.0845861i
$427$	−15.3486			−0.742771
$428$	−14.8556	−	0.635232i	−0.718071	−	0.0307051i
$429$		−	8.84054i		−	0.426825i
$430$	18.2700	−	7.11427i	0.881058	−	0.343081i
$431$	−3.00697	+	3.00697i	−0.144841	+	0.144841i	−0.775809	−	0.630968i	$-0.782658\pi$
$431$	−3.00697	+	3.00697i	−0.144841	+	0.144841i	0.630968	+	0.775809i	$0.282658\pi$
$432$	13.1434	−	11.0690i	0.632364	−	0.532556i
$433$		−	31.6878i		−	1.52282i	−0.648271	−	0.761410i	$-0.724508\pi$
$433$		−	31.6878i		−	1.52282i	0.648271	−	0.761410i	$-0.275492\pi$
$434$	2.77525	+	1.21965i	0.133216	+	0.0585452i
$435$	−11.8695	−	11.8695i	−0.569099	−	0.569099i
$436$	−1.52709	+	35.7127i	−0.0731345	+	1.71033i
$437$	6.07400	−	6.07400i	0.290559	−	0.290559i
$438$	3.23143	+	1.42013i	0.154404	+	0.0678565i
$439$	−1.13129	−	1.13129i	−0.0539934	−	0.0539934i	0.679595	−	0.733588i	$-0.262156\pi$
$439$	−1.13129	−	1.13129i	−0.0539934	−	0.0539934i	−0.733588	+	0.679595i	$0.762156\pi$
$440$	−4.62563	−	13.5666i	−0.220518	−	0.646760i
$441$	−0.794737			−0.0378446
$442$	4.39906	−	13.7851i	0.209242	−	0.655691i
$443$		−	16.1970i		−	0.769544i	−0.923012	−	0.384772i	$-0.874280\pi$
$443$		−	16.1970i		−	0.769544i	0.923012	−	0.384772i	$-0.125720\pi$
$444$	−2.29639	+	2.10806i	−0.108982	+	0.100044i
$445$	−21.8524	+	21.8524i	−1.03590	+	1.03590i
$446$	5.06379	−	11.5224i	0.239777	−	0.545601i
$447$	11.1003	+	11.1003i	0.525024	+	0.525024i
$448$	1.02282	−	7.93435i	0.0483237	−	0.374863i
$449$	17.6213	−	17.6213i	0.831600	−	0.831600i	−0.156135	−	0.987736i	$-0.549904\pi$
$449$	17.6213	−	17.6213i	0.831600	−	0.831600i	0.987736	+	0.156135i	$0.0499036\pi$
$450$	2.75637	+	1.21135i	0.129936	+	0.0571037i
$451$	−2.18521			−0.102898
$452$	13.4061	+	0.573253i	0.630571	+	0.0269635i
$453$	4.39762	+	4.39762i	0.206618	+	0.206618i
$454$	9.17649	+	23.5660i	0.430674	+	1.10601i
$455$	−6.87665			−0.322382
$456$	−9.65856	−	4.74690i	−0.452304	−	0.222294i
$457$			4.54198i			0.212465i	0.994341	+	0.106232i	$0.0338788\pi$
$457$			4.54198i			0.212465i	−0.994341	+	0.106232i	$0.966121\pi$
$458$	12.8045	+	5.62727i	0.598317	+	0.262945i
$459$	13.7700	+	11.1406i	0.642730	+	0.519999i
$460$	17.9549	−	16.4823i	0.837150	−	0.768492i
$461$	14.8331			0.690844			0.345422	−	0.938447i	$-0.387736\pi$
$461$	14.8331			0.690844			0.345422	+	0.938447i	$0.387736\pi$
$462$	4.69470	−	1.82810i	0.218417	−	0.0850509i
$463$	−26.4817			−1.23071			−0.615354	−	0.788251i	$-0.710987\pi$
$463$	−26.4817			−1.23071			−0.615354	+	0.788251i	$0.710987\pi$
$464$	8.01246	+	9.51409i	0.371969	+	0.441681i
$465$	8.18194	−	8.18194i	0.379428	−	0.379428i
$466$	1.87300	+	4.81000i	0.0867649	+	0.222819i
$467$	−19.0557			−0.881792			−0.440896	−	0.897558i	$-0.645339\pi$
$467$	−19.0557			−0.881792			−0.440896	+	0.897558i	$0.645339\pi$
$468$	−2.66742	−	2.90573i	−0.123302	−	0.134318i
$469$	6.95369	+	6.95369i	0.321092	+	0.321092i
$470$	−15.2976	+	5.95684i	−0.705627	+	0.274768i
$471$	−4.24908	−	4.24908i	−0.195787	−	0.195787i
$472$	6.76232	+	19.8333i	0.311261	+	0.912900i
$473$	−6.46958	−	6.46958i	−0.297472	−	0.297472i
$474$	12.5713	−	28.6053i	0.577418	−	1.31388i
$475$			5.23240i			0.240079i
$476$	8.23015	−	0.514480i	0.377228	−	0.0235812i
$477$		−	6.63813i		−	0.303939i
$478$	6.26812	+	2.75468i	0.286697	+	0.125996i
$479$	−25.9729	−	25.9729i	−1.18673	−	1.18673i	−0.977966	−	0.208766i	$-0.933055\pi$
$479$	−25.9729	−	25.9729i	−1.18673	−	1.18673i	−0.208766	−	0.977966i	$-0.566945\pi$
$480$	−26.8047	−	14.6273i	−1.22346	−	0.667643i
$481$	−1.40400	−	1.40400i	−0.0640169	−	0.0640169i
$482$	12.3321	+	31.6697i	0.561710	+	1.44252i
$483$	6.05770	+	6.05770i	0.275635	+	0.275635i
$484$	11.2793	−	10.3542i	0.512696	−	0.470648i
$485$	15.0523			0.683491
$486$	10.6198	−	4.13530i	0.481723	−	0.187581i
$487$	29.1847	−	29.1847i	1.32249	−	1.32249i	0.410727	−	0.911758i	$-0.365275\pi$
$487$	29.1847	−	29.1847i	1.32249	−	1.32249i	0.911758	−	0.410727i	$-0.134725\pi$
$488$	19.1483	−	38.9613i	0.866804	−	1.76369i
$489$	36.6085			1.65550
$490$	−1.42199	−	3.65179i	−0.0642391	−	0.164971i
$491$	35.4162			1.59831			0.799155	−	0.601126i	$-0.205281\pi$
$491$	35.4162			1.59831			0.799155	+	0.601126i	$0.205281\pi$
$492$	−3.42949	+	3.14822i	−0.154613	+	0.141933i
$493$	−8.06431	+	9.96766i	−0.363198	+	0.448921i
$494$	2.75797	−	6.27562i	0.124087	−	0.282353i
$495$		−	4.02744i		−	0.181020i
$496$	−6.55829	+	5.52318i	−0.294476	+	0.247998i
$497$	1.57511			0.0706532
$498$	−18.6747	+	7.27184i	−0.836831	+	0.325859i
$499$	−13.9109	−	13.9109i	−0.622737	−	0.622737i	0.323494	−	0.946230i	$-0.395143\pi$
$499$	−13.9109	−	13.9109i	−0.622737	−	0.622737i	−0.946230	+	0.323494i	$0.895143\pi$
$500$	0.549581	−	12.8525i	0.0245780	−	0.574783i
$501$	−42.1009			−1.88093
$502$	−13.0664	+	29.7320i	−0.583184	+	1.32700i
$503$	16.4162	−	16.4162i	0.731963	−	0.731963i	−0.239046	−	0.971008i	$-0.576835\pi$
$503$	16.4162	−	16.4162i	0.731963	−	0.731963i	0.971008	+	0.239046i	$0.0768345\pi$
$504$	0.991483	−	2.01738i	0.0441642	−	0.0898612i
$505$	25.9631	+	25.9631i	1.15534	+	1.15534i
$506$	−10.4126	−	4.57608i	−0.462898	−	0.203432i
$507$	−9.42414	+	9.42414i	−0.418541	+	0.418541i
$508$	31.0617	−	28.5142i	1.37814	−	1.26511i
$509$			8.76166i			0.388354i	0.980967	+	0.194177i	$0.0622036\pi$
$509$			8.76166i			0.388354i	−0.980967	+	0.194177i	$0.937796\pi$
$510$	9.56905	−	29.9860i	0.423724	−	1.32780i
$511$	−1.28125			−0.0566792
$512$	18.8647	+	12.4949i	0.833710	+	0.552203i
$513$	5.93326	+	5.93326i	0.261960	+	0.261960i
$514$	3.45473	−	7.86105i	0.152382	−	0.346736i
$515$	6.05976	−	6.05976i	0.267025	−	0.267025i
$516$	−19.4741	−	0.832722i	−0.857299	−	0.0366585i
$517$	5.41704	+	5.41704i	0.238241	+	0.238241i
$518$	0.455256	−	1.03591i	0.0200028	−	0.0455153i
$519$			23.0556i			1.01203i
$520$	8.57903	−	17.4558i	0.376215	−	0.765489i
$521$	10.6286	−	10.6286i	0.465646	−	0.465646i	−0.434855	−	0.900501i	$-0.643200\pi$
$521$	10.6286	−	10.6286i	0.465646	−	0.465646i	0.900501	+	0.434855i	$0.143200\pi$
$522$	1.26819	+	3.25681i	0.0555071	+	0.142547i
$523$			24.5672i			1.07425i	0.843504	+	0.537123i	$0.180489\pi$
$523$			24.5672i			1.07425i	−0.843504	+	0.537123i	$0.819511\pi$
$524$	−28.1099	−	1.20199i	−1.22799	−	0.0525093i
$525$	−5.21837			−0.227748
$526$	0.159201	−	0.362253i	0.00694149	−	0.0157950i
$527$	−6.87095	−	5.55892i	−0.299303	−	0.242150i
$528$	−1.21643	+	14.1978i	−0.0529385	+	0.617880i
$529$			3.65965i			0.159115i
$530$	30.5020	−	11.8774i	1.32492	−	0.515920i
$531$			5.88781i			0.255509i
$532$	3.90293	+	0.166891i	0.169213	+	0.00723565i
$533$	−2.09676	−	2.09676i	−0.0908209	−	0.0908209i
$534$	28.6297	−	11.1483i	1.23893	−	0.482433i
$535$		−	20.6017i		−	0.890690i
$536$	−26.3266	+	8.97626i	−1.13713	+	0.387715i
$537$	−15.7052	+	15.7052i	−0.677729	+	0.677729i
$538$	12.0381	−	4.68760i	0.519001	−	0.202097i
$539$	−1.29313	+	1.29313i	−0.0556992	+	0.0556992i
$540$	16.1004	+	17.5389i	0.692852	+	0.754752i
$541$	−16.1731	+	16.1731i	−0.695334	+	0.695334i	−0.963400	−	0.268066i	$-0.913615\pi$
$541$	−16.1731	+	16.1731i	−0.695334	+	0.695334i	0.268066	+	0.963400i	$0.413615\pi$
$542$	−8.26299	−	3.63137i	−0.354926	−	0.155981i
$543$	−11.4097			−0.489639
$544$	−8.96164	+	21.5334i	−0.384227	+	0.923239i
$545$	−49.5264			−2.12148
$546$	6.25878	+	2.75057i	0.267851	+	0.117714i
$547$	−5.36962	+	5.36962i	−0.229588	+	0.229588i	−0.812521	−	0.582932i	$-0.801905\pi$
$547$	−5.36962	+	5.36962i	−0.229588	+	0.229588i	0.582932	+	0.812521i	$0.301905\pi$
$548$	−18.2774	−	19.9103i	−0.780772	−	0.850528i
$549$	8.62537	−	8.62537i	0.368122	−	0.368122i
$550$	6.45596	−	2.51393i	0.275283	−	0.107194i
$551$	−4.29489	+	4.29489i	−0.182968	+	0.182968i
$552$	−22.9344	+	7.81967i	−0.976152	+	0.332827i
$553$			11.3419i			0.482306i
$554$	27.6924	−	10.7833i	1.17654	−	0.458139i
$555$	−3.05405	−	3.05405i	−0.129637	−	0.129637i
$556$	−19.5400	−	0.835540i	−0.828681	−	0.0354348i
$557$		−	0.727301i		−	0.0308167i	−0.999881	−	0.0154084i	$-0.995095\pi$
$557$		−	0.727301i		−	0.0308167i	0.999881	−	0.0154084i	$-0.00490483\pi$
$558$	−2.24499	+	0.874192i	−0.0950382	+	0.0370075i
$559$		−	12.4154i		−	0.525117i
$560$	11.0438	+	0.946208i	0.466686	+	0.0399846i
$561$	−14.6072	+	1.54186i	−0.616718	+	0.0650972i
$562$	−14.5114	+	33.0200i	−0.612128	+	1.39286i
$563$	19.4476			0.819620			0.409810	−	0.912171i	$-0.365595\pi$
$563$	19.4476			0.819620			0.409810	+	0.912171i	$0.365595\pi$
$564$	16.3058	+	0.697245i	0.686599	+	0.0293593i
$565$			18.5916i			0.782155i
$566$	5.69526	+	14.6259i	0.239390	+	0.614771i
$567$	−7.60324	+	7.60324i	−0.319306	+	0.319306i
$568$	−1.96504	+	3.99829i	−0.0824512	+	0.167764i
$569$		−	2.05010i		−	0.0859448i	−0.999076	−	0.0429724i	$-0.986317\pi$
$569$		−	2.05010i		−	0.0859448i	0.999076	−	0.0429724i	$-0.0136828\pi$
$570$	5.99927	−	13.6510i	0.251282	−	0.571779i
$571$	−5.69492	−	5.69492i	−0.238325	−	0.238325i	0.577831	−	0.816156i	$-0.303899\pi$
$571$	−5.69492	−	5.69492i	−0.238325	−	0.238325i	−0.816156	+	0.577831i	$0.803899\pi$
$572$	−9.06821	−	0.387761i	−0.379161	−	0.0162131i
$573$	18.2041	−	18.2041i	0.760486	−	0.760486i
$574$	0.679890	−	1.54705i	0.0283780	−	0.0645727i
$575$	8.33031	+	8.33031i	0.347398	+	0.347398i
$576$	3.88403	+	5.03361i	0.161835	+	0.209734i
$577$	−24.8801			−1.03577			−0.517885	−	0.855450i	$-0.673281\pi$
$577$	−24.8801			−1.03577			−0.517885	+	0.855450i	$0.673281\pi$
$578$	−23.5444	−	4.86434i	−0.979317	−	0.202330i
$579$		−	26.9009i		−	1.11796i
$580$	−12.6958	+	11.6546i	−0.527164	+	0.483929i
$581$	5.14385	−	5.14385i	0.213403	−	0.213403i
$582$	−13.6999	−	6.02075i	−0.567879	−	0.249568i
$583$	−10.8010	−	10.8010i	−0.447334	−	0.447334i
$584$	1.59844	−	3.25236i	0.0661438	−	0.134584i
$585$	3.86443	−	3.86443i	0.159774	−	0.159774i
$586$	−10.5751	+	24.0632i	−0.436855	+	0.994041i
$587$	−9.90520			−0.408831			−0.204416	−	0.978884i	$-0.565529\pi$
$587$	−9.90520			−0.408831			−0.204416	+	0.978884i	$0.565529\pi$
$588$	−0.166444	+	3.89246i	−0.00686402	+	0.160522i
$589$	−2.96057	−	2.96057i	−0.121988	−	0.121988i
$590$	−27.0543	+	10.5348i	−1.11381	+	0.433713i
$591$	−26.4075			−1.08626
$592$	2.06162	+	2.44799i	0.0847321	+	0.100612i
$593$			35.7081i			1.46636i	0.680037	+	0.733178i	$0.261964\pi$
$593$			35.7081i			1.46636i	−0.680037	+	0.733178i	$0.738036\pi$
$594$	4.47006	−	10.1714i	0.183409	−	0.417336i
$595$	1.19934	+	11.3623i	0.0491681	+	0.465808i
$596$	11.8730	−	10.8992i	0.486337	−	0.446450i
$597$	−37.2579			−1.52486
$598$	−5.60031	−	14.3820i	−0.229014	−	0.588125i
$599$	−30.6988			−1.25432			−0.627160	−	0.778890i	$-0.715783\pi$
$599$	−30.6988			−1.25432			−0.627160	+	0.778890i	$0.715783\pi$
$600$	6.51023	−	13.2464i	0.265779	−	0.540783i
$601$	15.1587	−	15.1587i	0.618336	−	0.618336i	−0.326768	−	0.945104i	$-0.605960\pi$
$601$	15.1587	−	15.1587i	0.618336	−	0.618336i	0.945104	+	0.326768i	$0.105960\pi$
$602$	6.59313	−	2.56734i	0.268716	−	0.104637i
$603$	−7.81545			−0.318270
$604$	4.70376	−	4.31798i	0.191393	−	0.175696i
$605$	15.0007	+	15.0007i	0.609866	+	0.609866i
$606$	−13.2454	−	34.0153i	−0.538058	−	1.38178i
$607$	3.82490	+	3.82490i	0.155248	+	0.155248i	0.780457	−	0.625209i	$-0.214986\pi$
$607$	3.82490	+	3.82490i	0.155248	+	0.155248i	−0.625209	+	0.780457i	$0.714986\pi$
$608$	−5.29278	+	9.69908i	−0.214651	+	0.393350i
$609$	−4.28337	−	4.28337i	−0.173571	−	0.173571i
$610$	55.0663	+	24.2002i	2.22957	+	0.979839i
$611$			10.3956i			0.420559i
$612$	−4.33593	+	4.91417i	−0.175269	+	0.198643i
$613$			17.7119i			0.715378i	0.933841	+	0.357689i	$0.116435\pi$
$613$			17.7119i			0.715378i	−0.933841	+	0.357689i	$0.883565\pi$
$614$	−7.97604	+	18.1491i	−0.321887	+	0.732436i
$615$	−4.56098	−	4.56098i	−0.183917	−	0.183917i
$616$	−1.66926	−	4.89578i	−0.0672564	−	0.197257i
$617$	25.9067	+	25.9067i	1.04296	+	1.04296i	0.999035	+	0.0439279i	$0.0139872\pi$
$617$	25.9067	+	25.9067i	1.04296	+	1.04296i	0.0439279	+	0.999035i	$0.486013\pi$
$618$	−7.93913	+	3.09147i	−0.319359	+	0.124357i
$619$	32.9110	+	32.9110i	1.32281	+	1.32281i	0.911496	+	0.411309i	$0.134928\pi$
$619$	32.9110	+	32.9110i	1.32281	+	1.32281i	0.411309	+	0.911496i	$0.365072\pi$
$620$	−8.03377	−	8.75151i	−0.322644	−	0.351469i
$621$	18.8922			0.758119
$622$	10.4004	+	26.7090i	0.417018	+	1.07093i
$623$	−7.88591	+	7.88591i	−0.315942	+	0.315942i
$624$	−14.7903	+	12.4559i	−0.592087	+	0.498637i
$625$	31.2180			1.24872
$626$	−26.6204	+	10.3659i	−1.06397	+	0.414304i
$627$	−6.95836			−0.277890
$628$	−4.54487	+	4.17213i	−0.181360	+	0.166486i
$629$	−2.07496	+	2.56470i	−0.0827341	+	0.102261i
$630$	2.85128	+	1.25307i	0.113598	+	0.0499234i
$631$		−	11.2105i		−	0.446282i	−0.974786	−	0.223141i	$-0.928369\pi$
$631$		−	11.2105i		−	0.446282i	0.974786	−	0.223141i	$-0.0716310\pi$
$632$	−28.7905	−	14.1497i	−1.14523	−	0.562844i
$633$	12.2028			0.485019
$634$	4.02165	+	10.3279i	0.159720	+	0.410173i
$635$	41.3099	+	41.3099i	1.63933	+	1.63933i
$636$	−32.5122	−	1.39024i	−1.28919	−	0.0551265i
$637$	−2.48159			−0.0983240
$638$	7.36271	+	3.23572i	0.291493	+	0.128104i
$639$	−0.885153	+	0.885153i	−0.0350161	+	0.0350161i
$640$	−16.1797	+	26.8534i	−0.639559	+	1.06147i
$641$	17.2894	+	17.2894i	0.682889	+	0.682889i	0.960650	−	0.277761i	$-0.0895924\pi$
$641$	17.2894	+	17.2894i	0.682889	+	0.682889i	−0.277761	+	0.960650i	$0.589592\pi$
$642$	−8.24043	+	18.7507i	−0.325224	+	0.740030i
$643$	9.73490	−	9.73490i	0.383907	−	0.383907i	−0.488601	−	0.872508i	$-0.662492\pi$
$643$	9.73490	−	9.73490i	0.383907	−	0.383907i	0.872508	+	0.488601i	$0.162492\pi$
$644$	6.47940	−	5.94800i	0.255324	−	0.234384i
$645$		−	27.0067i		−	1.06339i
$646$	−10.8502	−	3.46249i	−0.426896	−	0.136230i
$647$	37.2439			1.46421			0.732104	−	0.681193i	$-0.238539\pi$
$647$	37.2439			1.46421			0.732104	+	0.681193i	$0.238539\pi$
$648$	−9.81474	−	28.7857i	−0.385559	−	1.13081i
$649$	9.58019	+	9.58019i	0.376055	+	0.376055i
$650$	8.60682	+	3.78248i	0.337587	+	0.148361i
$651$	2.95263	−	2.95263i	0.115723	−	0.115723i
$652$	1.60571	−	37.5513i	0.0628845	−	1.47062i
$653$	−28.0425	−	28.0425i	−1.09739	−	1.09739i	−0.994715	−	0.102672i	$-0.967261\pi$
$653$	−28.0425	−	28.0425i	−1.09739	−	1.09739i	−0.102672	−	0.994715i	$-0.532739\pi$
$654$	45.0765	+	19.8099i	1.76263	+	0.774630i
$655$		−	38.9828i		−	1.52318i
$656$	3.07887	+	3.65589i	0.120210	+	0.142738i
$657$	0.720017	−	0.720017i	0.0280905	−	0.0280905i
$658$	−5.52048	+	2.14965i	−0.215211	+	0.0838022i
$659$			25.7355i			1.00251i	0.865299	+	0.501256i	$0.167129\pi$
$659$			25.7355i			1.00251i	−0.865299	+	0.501256i	$0.832871\pi$
$660$	−19.7256	−	0.843476i	−0.767818	−	0.0328323i
$661$	23.0881			0.898024			0.449012	−	0.893526i	$-0.351776\pi$
$661$	23.0881			0.898024			0.449012	+	0.893526i	$0.351776\pi$
$662$	2.68835	+	1.18146i	0.104486	+	0.0459188i
$663$	−15.4954	−	12.5365i	−0.601793	−	0.486879i
$664$	6.64000	+	19.4745i	0.257682	+	0.755758i
$665$			5.41259i			0.209891i
$666$	0.326307	+	0.837982i	0.0126441	+	0.0324712i
$667$			13.6755i			0.529516i
$668$	−1.84662	+	43.1851i	−0.0714478	+	1.67088i
$669$	−12.2588	−	12.2588i	−0.473953	−	0.473953i
$670$	−13.9839	−	35.9117i	−0.540245	−	1.38739i
$671$		−	28.0690i		−	1.08359i
$672$	−9.67306	−	5.27858i	−0.373147	−	0.203626i
$673$	−18.4436	+	18.4436i	−0.710950	+	0.710950i	−0.966734	−	0.255784i	$-0.917666\pi$
$673$	−18.4436	+	18.4436i	−0.710950	+	0.710950i	0.255784	+	0.966734i	$0.417666\pi$
$674$	9.02968	+	23.1889i	0.347810	+	0.893204i
$675$	−8.13729	+	8.13729i	−0.313205	+	0.313205i
$676$	9.25347	+	10.0802i	0.355903	+	0.387700i
$677$	2.31339	−	2.31339i	0.0889110	−	0.0889110i	−0.661252	−	0.750163i	$-0.729975\pi$
$677$	2.31339	−	2.31339i	0.0889110	−	0.0889110i	0.750163	+	0.661252i	$0.229975\pi$
$678$	7.43642	−	16.9212i	0.285594	−	0.649854i
$679$	5.43196			0.208459
$680$	−30.3385	−	11.1307i	−1.16343	−	0.426843i
$681$	34.8351			1.33488
$682$	−2.23046	+	5.07530i	−0.0854088	+	0.194343i
$683$	26.0339	−	26.0339i	0.996161	−	0.996161i	−0.00383207	−	0.999993i	$-0.501220\pi$
$683$	26.0339	−	26.0339i	0.996161	−	0.996161i	0.999993	+	0.00383207i	$0.00121979\pi$
$684$	−2.28709	+	2.09952i	−0.0874492	+	0.0802772i
$685$	26.4794	−	26.4794i	1.01173	−	1.01173i
$686$	−0.513157	−	1.31783i	−0.0195924	−	0.0503149i
$687$	13.6229	−	13.6229i	0.519747	−	0.519747i
$688$	−1.70833	+	19.9391i	−0.0651295	+	0.760169i
$689$		−	20.7277i		−	0.789664i
$690$	−12.1821	−	31.2845i	−0.463763	−	1.19098i
$691$	−27.1068	−	27.1068i	−1.03119	−	1.03119i	−0.999498	−	0.0316927i	$-0.989910\pi$
$691$	−27.1068	−	27.1068i	−1.03119	−	1.03119i	−0.0316927	−	0.999498i	$-0.510090\pi$
$692$	23.6493	+	1.01126i	0.899012	+	0.0384422i
$693$		−	1.45339i		−	0.0552097i
$694$	−12.8958	−	33.1174i	−0.489517	−	1.25712i
$695$		−	27.0981i		−	1.02789i
$696$	16.2168	−	5.52924i	0.614695	−	0.209585i
$697$	−3.09879	+	3.83018i	−0.117375	+	0.145078i
$698$	−18.8259	−	8.27348i	−0.712570	−	0.313156i
$699$	7.11013			0.268930
$700$	−0.228886	+	5.35275i	−0.00865109	+	0.202315i
$701$			9.05539i			0.342017i	0.985270	+	0.171009i	$0.0547026\pi$
$701$			9.05539i			0.342017i	−0.985270	+	0.171009i	$0.945297\pi$
$702$	14.0488	−	5.47055i	0.530238	−	0.206473i
$703$	−1.10508	+	1.10508i	−0.0416790	+	0.0416790i
$704$	14.5101	+	1.87050i	0.546869	+	0.0704971i
$705$			22.6129i			0.851651i
$706$	40.1886	+	17.6619i	1.51252	+	0.664713i
$707$	9.36935	+	9.36935i	0.352370	+	0.352370i
$708$	28.8373	+	1.23310i	1.08377	+	0.0463426i
$709$	−25.0383	+	25.0383i	−0.940334	+	0.940334i	−0.998318	−	0.0579832i	$-0.981533\pi$
$709$	−25.0383	+	25.0383i	−0.940334	+	0.940334i	0.0579832	+	0.998318i	$0.481533\pi$
$710$	−5.65102	−	2.48348i	−0.212079	−	0.0932032i
$711$	−6.37374	−	6.37374i	−0.239034	−	0.239034i
$712$	−10.1796	−	29.8559i	−0.381498	−	1.11890i
$713$	−9.42682			−0.353037
$714$	3.45320	−	10.8211i	0.129233	−	0.404970i
$715$		−	12.5758i		−	0.470308i
$716$	15.4208	+	16.7985i	0.576301	+	0.627789i
$717$	6.66874	−	6.66874i	0.249049	−	0.249049i
$718$	5.01251	−	11.4057i	0.187065	−	0.425657i
$719$	21.8126	+	21.8126i	0.813474	+	0.813474i	0.985153	−	0.171679i	$-0.0549192\pi$
$719$	21.8126	+	21.8126i	0.813474	+	0.813474i	−0.171679	+	0.985153i	$0.554919\pi$
$720$	−6.73796	+	5.67449i	−0.251109	+	0.211476i
$721$	2.18680	−	2.18680i	0.0814406	−	0.0814406i
$722$	19.6598	+	8.63998i	0.731663	+	0.321547i
$723$	46.8141			1.74103
$724$	−0.500450	+	11.7036i	−0.0185991	+	0.434959i
$725$	−5.89031	−	5.89031i	−0.218761	−	0.218761i
$726$	−7.65281	−	19.6530i	−0.284022	−	0.729392i
$727$	49.8023			1.84706			0.923532	−	0.383521i	$-0.125289\pi$
$727$	49.8023			1.84706			0.923532	+	0.383521i	$0.125289\pi$
$728$	3.09593	−	6.29932i	0.114743	−	0.233468i
$729$			16.5597i			0.613322i
$730$	4.59675	+	2.02015i	0.170133	+	0.0747693i
$731$	−20.5140	+	2.16535i	−0.758739	+	0.0800882i
$732$	−40.4389	−	44.0517i	−1.49466	−	1.62820i
$733$	−26.9902			−0.996905			−0.498452	−	0.866917i	$-0.666098\pi$
$733$	−26.9902			−0.996905			−0.498452	+	0.866917i	$0.666098\pi$
$734$	4.36536	−	1.69986i	0.161129	−	0.0627428i
$735$	−5.39807			−0.199111
$736$	7.01510	+	23.8680i	0.258580	+	0.879785i
$737$	−12.7167	+	12.7167i	−0.468425	+	0.468425i
$738$	0.487314	+	1.25146i	0.0179383	+	0.0460669i
$739$	42.4284			1.56075			0.780377	−	0.625310i	$-0.215027\pi$
$739$	42.4284			1.56075			0.780377	+	0.625310i	$0.215027\pi$
$740$	−3.26665	+	2.99874i	−0.120084	+	0.110236i
$741$	−6.67671	−	6.67671i	−0.245275	−	0.245275i
$742$	11.0073	−	4.28620i	0.404091	−	0.157351i
$743$	0.560463	+	0.560463i	0.0205614	+	0.0205614i	0.717313	−	0.696751i	$-0.245372\pi$
$743$	0.560463	+	0.560463i	0.0205614	+	0.0205614i	−0.696751	+	0.717313i	$0.745372\pi$
$744$	3.81144	+	11.1786i	0.139734	+	0.409828i
$745$	15.7903	+	15.7903i	0.578511	+	0.578511i
$746$	−8.59141	+	19.5493i	−0.314554	+	0.715751i
$747$			5.78132i			0.211527i
$748$	0.940865	+	15.0510i	0.0344014	+	0.550320i
$749$		−	7.43457i		−	0.271653i
$750$	−16.2225	−	7.12935i	−0.592360	−	0.260327i
$751$	−31.4120	−	31.4120i	−1.14624	−	1.14624i	−0.987286	−	0.158955i	$-0.949188\pi$
$751$	−31.4120	−	31.4120i	−1.14624	−	1.14624i	−0.158955	−	0.987286i	$-0.550812\pi$
$752$	1.43040	−	16.6951i	0.0521613	−	0.608809i
$753$	31.6323	+	31.6323i	1.15274	+	1.15274i
$754$	3.95995	+	10.1695i	0.144213	+	0.370350i
$755$	6.25568	+	6.25568i	0.227667	+	0.227667i
$756$	5.81019	+	6.32928i	0.211314	+	0.230194i
$757$	−6.63593			−0.241187			−0.120594	−	0.992702i	$-0.538480\pi$
$757$	−6.63593			−0.241187			−0.120594	+	0.992702i	$0.538480\pi$
$758$	5.97212	−	2.32552i	0.216917	−	0.0844667i
$759$	−11.0781	+	11.0781i	−0.402111	+	0.402111i
$760$	−13.7394	−	6.75253i	−0.498382	−	0.244940i
$761$	2.13456			0.0773778			0.0386889	−	0.999251i	$-0.487682\pi$
$761$	2.13456			0.0773778			0.0386889	+	0.999251i	$0.487682\pi$
$762$	−21.0748	−	54.1217i	−0.763459	−	1.96062i
$763$	−17.8727			−0.647034
$764$	−17.8744	−	19.4713i	−0.646674	−	0.704448i
$765$	−7.05918	−	5.71121i	−0.255225	−	0.206489i
$766$	−9.01523	+	20.5137i	−0.325734	+	0.741189i
$767$			18.3848i			0.663838i
$768$	25.4670	−	17.9690i	0.918962	−	0.648400i
$769$	−3.64245			−0.131350			−0.0656751	−	0.997841i	$-0.520920\pi$
$769$	−3.64245			−0.131350			−0.0656751	+	0.997841i	$0.520920\pi$
$770$	6.67828	−	2.60050i	0.240668	−	0.0937154i
$771$	−8.36347	−	8.36347i	−0.301203	−	0.301203i
$772$	−27.5936	−	1.17992i	−0.993116	−	0.0424661i
$773$	22.6015			0.812921			0.406460	−	0.913668i	$-0.366763\pi$
$773$	22.6015			0.812921			0.406460	+	0.913668i	$0.366763\pi$
$774$	−2.26235	+	5.14785i	−0.0813185	+	0.185036i
$775$	4.06033	−	4.06033i	0.145852	−	0.145852i
$776$	−6.77670	+	13.7886i	−0.243269	+	0.494982i
$777$	−1.10212	−	1.10212i	−0.0395383	−	0.0395383i
$778$	−4.07094	−	1.78907i	−0.145950	−	0.0641414i
$779$	−1.65036	+	1.65036i	−0.0591301	+	0.0591301i
$780$	−18.1178	−	19.7365i	−0.648723	−	0.706681i
$781$			2.88050i			0.103073i
$782$	−22.7867	+	11.7617i	−0.814851	+	0.420598i
$783$	−13.3586			−0.477397
$784$	3.98540	+	0.341460i	0.142336	+	0.0121950i
$785$	−6.04437	−	6.04437i	−0.215733	−	0.215733i
$786$	−15.5926	+	35.4802i	−0.556171	+	1.26554i
$787$	−18.3051	+	18.3051i	−0.652505	+	0.652505i	−0.953596	−	0.301091i	$-0.902649\pi$
$787$	−18.3051	+	18.3051i	−0.652505	+	0.652505i	0.301091	+	0.953596i	$0.402649\pi$
$788$	−1.15828	+	27.0876i	−0.0412620	+	0.964955i
$789$	−0.385406	−	0.385406i	−0.0137208	−	0.0137208i
$790$	17.8828	−	40.6914i	0.636242	−	1.44773i
$791$			6.70919i			0.238551i
$792$	3.68932	+	1.81319i	0.131094	+	0.0644290i
$793$	26.9329	−	26.9329i	0.956416	−	0.956416i
$794$	18.1909	+	46.7156i	0.645570	+	1.65788i
$795$		−	45.0879i		−	1.59910i
$796$	−1.63419	+	38.2174i	−0.0579225	+	1.35458i
$797$	29.6499			1.05025			0.525127	−	0.851024i	$-0.324018\pi$
$797$	29.6499			1.05025			0.525127	+	0.851024i	$0.324018\pi$
$798$	2.16497	−	4.92627i	0.0766390	−	0.174388i
$799$	17.1766	−	1.81306i	0.607664	−	0.0641415i
$800$	−13.3020	−	7.25889i	−0.470297	−	0.256641i
$801$		−	8.86319i		−	0.313166i
$802$	38.0366	−	14.8113i	1.34312	−	0.523006i
$803$		−	2.34311i		−	0.0826866i
$804$	−1.63681	+	38.2785i	−0.0577257	+	1.34998i
$805$	8.61717	+	8.61717i	0.303715	+	0.303715i
$806$	−7.01005	+	2.72969i	−0.246918	+	0.0961491i
$807$		−	17.7947i		−	0.626404i
$808$	−35.4722	+	12.0945i	−1.24791	+	0.425484i
$809$	−9.99178	+	9.99178i	−0.351292	+	0.351292i	−0.860590	−	0.509298i	$-0.829905\pi$
$809$	−9.99178	+	9.99178i	−0.351292	+	0.351292i	0.509298	+	0.860590i	$0.329905\pi$
$810$	39.2663	−	15.2901i	1.37968	−	0.537240i
$811$	−21.8392	+	21.8392i	−0.766878	+	0.766878i	−0.977556	−	0.210678i	$-0.932433\pi$
$811$	−21.8392	+	21.8392i	−0.766878	+	0.766878i	0.210678	+	0.977556i	$0.432433\pi$
$812$	−4.58155	+	4.20580i	−0.160781	+	0.147595i
$813$	−8.79110	+	8.79110i	−0.308317	+	0.308317i
$814$	1.89444	+	0.832558i	0.0664001	+	0.0291811i
$815$	52.0762			1.82415
$816$	23.1605	+	22.2657i	0.810780	+	0.779454i
$817$	−9.77215			−0.341884
$818$	15.1254	+	6.64723i	0.528847	+	0.232415i
$819$	1.39456	−	1.39456i	0.0487300	−	0.0487300i
$820$	−4.87849	+	4.47838i	−0.170364	+	0.156392i
$821$	19.4339	−	19.4339i	0.678247	−	0.678247i	−0.281356	−	0.959603i	$-0.590784\pi$
$821$	19.4339	−	19.4339i	0.678247	−	0.678247i	0.959603	+	0.281356i	$0.0907843\pi$
$822$	−34.6917	+	13.5088i	−1.21001	+	0.471174i
$823$	−32.5153	+	32.5153i	−1.13341	+	1.13341i	−0.143806	+	0.989606i	$0.545934\pi$
$823$	−32.5153	+	32.5153i	−1.13341	+	1.13341i	−0.989606	+	0.143806i	$0.954066\pi$
$824$	2.82285	+	8.27918i	0.0983388	+	0.288419i
$825$		−	9.54318i		−	0.332251i
$826$	−9.76313	+	3.80173i	−0.339703	+	0.132279i
$827$	−17.2544	−	17.2544i	−0.599995	−	0.599995i	0.340316	−	0.940311i	$-0.389466\pi$
$827$	−17.2544	−	17.2544i	−0.599995	−	0.599995i	−0.940311	+	0.340316i	$0.889466\pi$
$828$	−0.298629	+	6.98376i	−0.0103781	+	0.242702i
$829$		−	26.0820i		−	0.905865i	−0.891545	−	0.452933i	$-0.850378\pi$
$829$		−	26.0820i		−	0.905865i	0.891545	−	0.452933i	$-0.149622\pi$
$830$	−26.5650	+	10.3443i	−0.922083	+	0.359056i
$831$		−	40.9348i		−	1.42001i
$832$	12.1280	+	15.7176i	0.420462	+	0.544908i
$833$	0.432807	+	4.10033i	0.0149959	+	0.142068i
$834$	−10.8389	+	24.6633i	−0.375320	+	0.854021i
$835$	−59.8891			−2.07255
$836$	−0.305205	+	7.13755i	−0.0105557	+	0.246857i
$837$		−	9.20840i		−	0.318289i
$838$	3.01911	+	7.75332i	0.104293	+	0.267834i
$839$	13.8404	−	13.8404i	0.477824	−	0.477824i	−0.426611	−	0.904435i	$-0.640293\pi$
$839$	13.8404	−	13.8404i	0.477824	−	0.477824i	0.904435	+	0.426611i	$0.140293\pi$
$840$	6.73441	−	13.7026i	0.232359	−	0.472784i
$841$			19.3302i			0.666557i
$842$	−10.4939	+	23.8783i	−0.361643	+	0.822900i
$843$	35.1304	+	35.1304i	1.20995	+	1.20995i
$844$	0.535237	−	12.5171i	0.0184236	−	0.430856i
$845$	−13.4060	+	13.4060i	−0.461179	+	0.461179i
$846$	1.89428	−	4.31034i	0.0651268	−	0.148193i
$847$	5.41333	+	5.41333i	0.186004	+	0.186004i
$848$	−2.85208	+	33.2885i	−0.0979408	+	1.14313i
$849$	21.6199			0.741994
$850$	4.74869	−	14.8808i	0.162879	−	0.510406i
$851$			3.51872i			0.120620i
$852$	4.14992	+	4.52068i	0.142174	+	0.154876i
$853$	−30.5993	+	30.5993i	−1.04770	+	1.04770i	−0.0488957	+	0.998804i	$0.515570\pi$
$853$	−30.5993	+	30.5993i	−1.04770	+	1.04770i	−0.998804	+	0.0488957i	$0.984430\pi$
$854$	19.8719	+	8.73318i	0.680001	+	0.298843i
$855$	−3.04168	−	3.04168i	−0.104023	−	0.104023i
$856$	18.8721	+	9.27508i	0.645035	+	0.317016i
$857$	−17.6890	+	17.6890i	−0.604246	+	0.604246i	−0.941436	−	0.337191i	$-0.890523\pi$
$857$	−17.6890	+	17.6890i	−0.604246	+	0.604246i	0.337191	+	0.941436i	$0.390523\pi$
$858$	−5.03016	+	11.4459i	−0.171727	+	0.390755i
$859$	−1.55812			−0.0531625			−0.0265813	−	0.999647i	$-0.508462\pi$
$859$	−1.55812			−0.0531625			−0.0265813	+	0.999647i	$0.508462\pi$
$860$	−27.7021	−	1.18456i	−0.944635	−	0.0403931i
$861$	−1.64593	−	1.64593i	−0.0560931	−	0.0560931i
$862$	5.60406	−	2.18220i	0.190875	−	0.0743260i
$863$	12.7873			0.435286			0.217643	−	0.976028i	$-0.430163\pi$
$863$	12.7873			0.435286			0.217643	+	0.976028i	$0.430163\pi$
$864$	−23.3149	+	6.85256i	−0.793190	+	0.233129i
$865$			32.7969i			1.11513i
$866$	−18.0300	+	41.0263i	−0.612684	+	1.39413i
$867$	−18.0116	+	27.7896i	−0.611706	+	0.943784i
$868$	−2.89916	−	3.15817i	−0.0984039	−	0.107195i
$869$	−20.7417			−0.703613
$870$	8.61386	+	22.1211i	0.292037	+	0.749975i
$871$	−24.4039			−0.826896
$872$	22.2972	−	45.3684i	0.755079	−	1.53637i
$873$	−3.05257	+	3.05257i	−0.103314	+	0.103314i
$874$	−11.3200	+	4.40798i	−0.382906	+	0.149102i
$875$	6.43215			0.217446
$876$	−3.37570	−	3.67729i	−0.114054	−	0.124244i
$877$	−24.0701	−	24.0701i	−0.812791	−	0.812791i	0.172260	−	0.985051i	$-0.444893\pi$
$877$	−24.0701	−	24.0701i	−0.812791	−	0.812791i	−0.985051	+	0.172260i	$0.944893\pi$
$878$	0.820991	+	2.10837i	0.0277071	+	0.0711540i
$879$	25.6011	+	25.6011i	0.863505	+	0.863505i
$880$	−1.73040	+	20.1966i	−0.0583316	+	0.680826i
$881$	−16.6693	−	16.6693i	−0.561604	−	0.561604i	0.368159	−	0.929763i	$-0.379988\pi$
$881$	−16.6693	−	16.6693i	−0.561604	−	0.561604i	−0.929763	+	0.368159i	$0.879988\pi$
$882$	1.02895	+	0.452196i	0.0346465	+	0.0152262i
$883$		−	5.20868i		−	0.175286i	−0.996152	−	0.0876430i	$-0.972067\pi$
$883$		−	5.20868i		−	0.175286i	0.996152	−	0.0876430i	$-0.0279335\pi$
$884$	−13.5390	+	15.3446i	−0.455367	+	0.516095i
$885$			39.9916i			1.34430i
$886$	−9.21592	+	20.9703i	−0.309615	+	0.704512i
$887$	16.1992	+	16.1992i	0.543916	+	0.543916i	0.924674	−	0.380759i	$-0.124337\pi$
$887$	16.1992	+	16.1992i	0.543916	+	0.543916i	−0.380759	+	0.924674i	$0.624337\pi$
$888$	4.17260	−	1.42268i	0.140023	−	0.0477422i
$889$	14.9076	+	14.9076i	0.499984	+	0.499984i
$890$	40.7261	−	15.8586i	1.36514	−	0.531581i
$891$	−13.9046	−	13.9046i	−0.465820	−	0.465820i
$892$	−13.1122	+	12.0368i	−0.439029	+	0.403022i
$893$	8.18231			0.273810
$894$	−8.05561	−	20.6874i	−0.269420	−	0.691891i
$895$	−22.3408	+	22.3408i	−0.746772	+	0.746772i
$896$	−5.83879	+	9.69064i	−0.195060	+	0.323742i
$897$	−21.2595			−0.709833
$898$	−32.8406	+	12.7880i	−1.09591	+	0.426742i
$899$	6.66565			0.222312
$900$	−2.87943	−	3.13668i	−0.0959809	−	0.104556i
$901$	−34.2484	+	3.61507i	−1.14098	+	0.120435i
$902$	2.82920	+	1.24336i	0.0942020	+	0.0413994i
$903$		−	9.74594i		−	0.324325i
$904$	−17.0308	−	8.37012i	−0.566435	−	0.278386i
$905$	−16.2305			−0.539520
$906$	−3.19141	−	8.19580i	−0.106028	−	0.272287i
$907$	−31.0098	−	31.0098i	−1.02966	−	1.02966i	−0.999546	−	0.0301156i	$-0.990412\pi$
$907$	−31.0098	−	31.0098i	−1.02966	−	1.02966i	−0.0301156	−	0.999546i	$-0.509588\pi$
$908$	1.52793	−	35.7322i	0.0507060	−	1.18581i
$909$	−10.5305			−0.349274
$910$	8.90321	+	3.91273i	0.295138	+	0.129706i
$911$	−18.5613	+	18.5613i	−0.614965	+	0.614965i	−0.944236	−	0.329271i	$-0.893197\pi$
$911$	−18.5613	+	18.5613i	−0.614965	+	0.614965i	0.329271	+	0.944236i	$0.393197\pi$
$912$	9.80403	+	11.6414i	0.324644	+	0.385486i
$913$	9.40691	+	9.40691i	0.311323	+	0.311323i
$914$	2.58433	−	5.88051i	0.0854822	−	0.194510i
$915$	58.5858	−	58.5858i	1.93679	−	1.93679i
$916$	−13.3762	−	14.5713i	−0.441963	−	0.481448i
$917$		−	14.0678i		−	0.464559i
$918$	−11.4892	−	22.2587i	−0.379200	−	0.734648i
$919$	−11.0382			−0.364118			−0.182059	−	0.983288i	$-0.558276\pi$
$919$	−11.0382			−0.364118			−0.182059	+	0.983288i	$0.558276\pi$
$920$	−32.6245	+	11.1236i	−1.07560	+	0.366734i
$921$	19.3090	+	19.3090i	0.636254	+	0.636254i
$922$	−19.2044	−	8.43983i	−0.632463	−	0.277951i
$923$	−2.76391	+	2.76391i	−0.0909753	+	0.0909753i
$924$	−7.11841	−	0.304387i	−0.234178	−	0.0100136i
$925$	−1.51559	−	1.51559i	−0.0498323	−	0.0498323i
$926$	34.2859	+	15.0678i	1.12670	+	0.495157i
$927$			2.45780i			0.0807248i
$928$	−4.96034	−	16.8769i	−0.162831	−	0.554011i
$929$	31.4556	−	31.4556i	1.03202	−	1.03202i	0.0325543	−	0.999470i	$-0.489636\pi$
$929$	31.4556	−	31.4556i	1.03202	−	1.03202i	0.999470	−	0.0325543i	$-0.0103642\pi$
$930$	−15.2486	+	5.93774i	−0.500021	+	0.194706i
$931$			1.95325i			0.0640151i
$932$	0.311862	−	7.29323i	0.0102154	−	0.238898i
$933$	39.4812			1.29256
$934$	24.6714	+	10.8425i	0.807274	+	0.354776i
$935$	−20.7790	+	2.19331i	−0.679545	+	0.0717290i
$936$	1.80019	+	5.27979i	0.0588410	+	0.172575i
$937$			51.1366i			1.67056i	0.549824	+	0.835280i	$0.314695\pi$
$937$			51.1366i			1.67056i	−0.549824	+	0.835280i	$0.685305\pi$
$938$	−5.04639	−	12.9595i	−0.164770	−	0.423143i
$939$			39.3502i			1.28415i
$940$	23.1952	+	0.991840i	0.756545	+	0.0323503i
$941$	−9.03170	−	9.03170i	−0.294425	−	0.294425i	0.544400	−	0.838826i	$-0.316757\pi$
$941$	−9.03170	−	9.03170i	−0.294425	−	0.294425i	−0.838826	+	0.544400i	$0.816757\pi$
$942$	3.08361	+	7.91896i	0.100470	+	0.258014i
$943$			5.25494i			0.171124i
$944$	2.52971	−	29.5258i	0.0823349	−	0.960984i
$945$	−8.41751	+	8.41751i	−0.273822	+	0.273822i
$946$	4.69507	+	12.0573i	0.152650	+	0.392017i
$947$	19.5141	−	19.5141i	0.634124	−	0.634124i	−0.314976	−	0.949100i	$-0.601996\pi$
$947$	19.5141	−	19.5141i	0.634124	−	0.634124i	0.949100	+	0.314976i	$0.101996\pi$
$948$	−32.5521	+	29.8824i	−1.05724	+	0.970535i
$949$	2.24827	−	2.24827i	0.0729820	−	0.0729820i
$950$	2.97717	−	6.77440i	0.0965923	−	0.219791i
$951$	15.2667			0.495056
$952$	−10.9483	−	4.01676i	−0.354837	−	0.130184i
$953$	−38.0056			−1.23112			−0.615562	−	0.788089i	$-0.711071\pi$
$953$	−38.0056			−1.23112			−0.615562	+	0.788089i	$0.711071\pi$
$954$	−3.77702	+	8.59440i	−0.122285	+	0.278254i
$955$	25.8955	−	25.8955i	0.837960	−	0.837960i
$956$	−6.54797	−	7.13297i	−0.211776	−	0.230697i
$957$	7.83329	−	7.83329i	0.253214	−	0.253214i
$958$	18.8489	+	48.4054i	0.608980	+	1.56391i
$959$	9.55566	−	9.55566i	0.308568	−	0.308568i
$960$	26.3814	+	34.1896i	0.851454	+	1.10346i
$961$		−	26.4052i		−	0.851781i
$962$	1.01890	+	2.61662i	0.0328507	+	0.0843632i
$963$	4.17796	+	4.17796i	0.134633	+	0.134633i
$964$	2.05334	−	48.0196i	0.0661337	−	1.54661i
$965$		−	38.2668i		−	1.23185i
$966$	−4.39616	−	11.2897i	−0.141444	−	0.363240i
$967$			26.1879i			0.842145i	0.907027	+	0.421073i	$0.138346\pi$
$967$			26.1879i			0.842145i	−0.907027	+	0.421073i	$0.861654\pi$
$968$	−20.4948	+	6.98787i	−0.658727	+	0.224599i
$969$	−9.86747	+	12.1964i	−0.316989	+	0.391805i
$970$	−19.4883	−	8.56460i	−0.625731	−	0.274993i
$971$	52.0924			1.67172			0.835862	−	0.548940i	$-0.184968\pi$
$971$	52.0924			1.67172			0.835862	+	0.548940i	$0.184968\pi$
$972$	−16.1024	−	0.688546i	−0.516485	−	0.0220851i
$973$		−	9.77893i		−	0.313498i
$974$	−54.3912	+	21.1797i	−1.74281	+	0.678643i
$975$	9.15691	−	9.15691i	0.293256	−	0.293256i
$976$	−46.9599	+	39.5481i	−1.50315	+	1.26590i
$977$			46.0086i			1.47195i	0.677011	+	0.735973i	$0.263275\pi$
$977$			46.0086i			1.47195i	−0.677011	+	0.735973i	$0.736725\pi$
$978$	−47.3971	−	20.8298i	−1.51559	−	0.666064i
$979$	−14.4215	−	14.4215i	−0.460913	−	0.460913i
$980$	−0.236768	+	5.53708i	−0.00756328	+	0.176875i
$981$	10.0438	−	10.0438i	0.320674	−	0.320674i
$982$	−45.8534	−	20.1514i	−1.46324	−	0.643056i
$983$	16.8265	+	16.8265i	0.536683	+	0.536683i	0.922553	−	0.385870i	$-0.126099\pi$
$983$	16.8265	+	16.8265i	0.536683	+	0.536683i	−0.385870	+	0.922553i	$0.626099\pi$
$984$	6.23146	−	2.12467i	0.198652	−	0.0677320i
$985$	−37.5651			−1.19692
$986$	16.1123	−	8.31665i	0.513122	−	0.264856i
$987$			8.16036i			0.259747i
$988$	−7.14151	+	6.55580i	−0.227202	+	0.208568i
$989$	−15.5579	+	15.5579i	−0.494711	+	0.494711i
$990$	−2.29157	+	5.21434i	−0.0728308	+	0.165723i
$991$	−20.1483	−	20.1483i	−0.640032	−	0.640032i	0.310531	−	0.950563i	$-0.399493\pi$
$991$	−20.1483	−	20.1483i	−0.640032	−	0.640032i	−0.950563	+	0.310531i	$0.899493\pi$
$992$	11.6337	−	3.41928i	0.369369	−	0.108562i
$993$	2.86017	−	2.86017i	0.0907648	−	0.0907648i
$994$	−2.03929	−	0.896216i	−0.0646824	−	0.0284263i
$995$	−52.9999			−1.68021
$996$	28.3157	+	1.21079i	0.897217	+	0.0383655i
$997$	−6.59075	−	6.59075i	−0.208731	−	0.208731i	0.594997	−	0.803728i	$-0.297153\pi$
$997$	−6.59075	−	6.59075i	−0.208731	−	0.208731i	−0.803728	+	0.594997i	$0.797153\pi$
$998$	10.0953	+	25.9256i	0.319562	+	0.820660i
$999$	−3.43719			−0.108748

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.s.a.421.14	✓	216
8.5	even	2	inner	952.2.s.a.421.95	yes	216
17.4	even	4	inner	952.2.s.a.701.95	yes	216
136.21	even	4	inner	952.2.s.a.701.14	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.s.a.421.14	✓	216	1.1	even	1	trivial
952.2.s.a.421.95	yes	216	8.5	even	2	inner
952.2.s.a.701.14	yes	216	136.21	even	4	inner
952.2.s.a.701.95	yes	216	17.4	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29470 - 0.568988i) q^{2} +(-1.37745 + 1.37745i) q^{3} +(1.35251 + 1.47334i) q^{4} +(-1.95944 + 1.95944i) q^{5} +(2.56714 - 0.999634i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.912778 - 2.67709i) q^{8} -0.794737i q^{9} +(3.65179 - 1.42199i) q^{10} +(-1.29313 - 1.29313i) q^{11} +(-3.89246 - 0.166444i) q^{12} -2.48159i q^{13} +(1.31783 - 0.513157i) q^{14} -5.39807i q^{15} +(-0.341460 + 3.98540i) q^{16} +(-4.10033 + 0.432807i) q^{17} +(-0.452196 + 1.02895i) q^{18} -1.95325 q^{19} +(-5.53708 - 0.236768i) q^{20} -1.94801i q^{21} +(0.938445 + 2.41000i) q^{22} +(-3.10969 + 3.10969i) q^{23} +(4.94487 + 2.43026i) q^{24} -2.67882i q^{25} +(-1.41199 + 3.21291i) q^{26} +(-3.03764 - 3.03764i) q^{27} +(-1.99817 - 0.0854429i) q^{28} +(2.19884 - 2.19884i) q^{29} +(-3.07143 + 6.98888i) q^{30} +(1.51572 + 1.51572i) q^{31} +(2.70973 - 4.96562i) q^{32} +3.56246 q^{33} +(5.55496 + 1.77268i) q^{34} -2.77107i q^{35} +(1.17092 - 1.07489i) q^{36} +(0.565767 - 0.565767i) q^{37} +(2.52887 + 1.11137i) q^{38} +(3.41826 + 3.41826i) q^{39} +(7.03415 + 3.45708i) q^{40} +(0.844929 - 0.844929i) q^{41} +(-1.10839 + 2.52209i) q^{42} +5.00303 q^{43} +(0.156255 - 3.65420i) q^{44} +(1.55724 + 1.55724i) q^{45} +(5.79550 - 2.25674i) q^{46} -4.18908 q^{47} +(-5.01934 - 5.96003i) q^{48} -1.00000i q^{49} +(-1.52422 + 3.46827i) q^{50} +(5.05182 - 6.24417i) q^{51} +(3.65622 - 3.35636i) q^{52} +8.35261 q^{53} +(2.20446 + 5.66122i) q^{54} +5.06764 q^{55} +(2.53842 + 1.24756i) q^{56} +(2.69050 - 2.69050i) q^{57} +(-4.09796 + 1.59573i) q^{58} -7.40850 q^{59} +(7.95318 - 7.30091i) q^{60} +(10.8531 + 10.8531i) q^{61} +(-1.09998 - 2.82483i) q^{62} +(0.561964 + 0.561964i) q^{63} +(-6.33367 + 4.88719i) q^{64} +(4.86252 + 4.86252i) q^{65} +(-4.61232 - 2.02699i) q^{66} -9.83400i q^{67} +(-6.18338 - 5.45580i) q^{68} -8.56689i q^{69} +(-1.57670 + 3.58771i) q^{70} +(-1.11377 - 1.11377i) q^{71} +(-2.12759 + 0.725419i) q^{72} +(0.905981 + 0.905981i) q^{73} +(-1.05441 + 0.410585i) q^{74} +(3.68994 + 3.68994i) q^{75} +(-2.64178 - 2.87780i) q^{76} +1.82877 q^{77} +(-2.48068 - 6.37058i) q^{78} +(8.01993 - 8.01993i) q^{79} +(-7.14009 - 8.47823i) q^{80} +10.7526 q^{81} +(-1.57469 + 0.613176i) q^{82} -7.27450 q^{83} +(2.87008 - 2.63469i) q^{84} +(7.18629 - 8.88241i) q^{85} +(-6.47743 - 2.84666i) q^{86} +6.05760i q^{87} +(-2.28150 + 4.64219i) q^{88} +11.1524 q^{89} +(-1.13011 - 2.90221i) q^{90} +(1.75475 + 1.75475i) q^{91} +(-8.78750 - 0.375758i) q^{92} -4.17565 q^{93} +(5.42360 + 2.38353i) q^{94} +(3.82728 - 3.82728i) q^{95} +(3.10737 + 10.5724i) q^{96} +(-3.84098 - 3.84098i) q^{97} +(-0.568988 + 1.29470i) q^{98} +(-1.02770 + 1.02770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{6} - 8 q^{10} - 16 q^{16} + 8 q^{17} + 8 q^{24} - 20 q^{30} + 32 q^{31} - 32 q^{34} - 40 q^{38} + 4 q^{40} + 24 q^{41} - 8 q^{44} - 8 q^{46} + 84 q^{48} + 36 q^{50} + 84 q^{54} - 16 q^{57}+ \cdots + 8 q^{97}+O(q^{100}) \) 216 * q - 8 * q^6 - 8 * q^10 - 16 * q^16 + 8 * q^17 + 8 * q^24 - 20 * q^30 + 32 * q^31 - 32 * q^34 - 40 * q^38 + 4 * q^40 + 24 * q^41 - 8 * q^44 - 8 * q^46 + 84 * q^48 + 36 * q^50 + 84 * q^54 - 16 * q^57 - 60 * q^58 + 16 * q^62 - 48 * q^64 + 48 * q^65 + 52 * q^68 - 84 * q^72 - 40 * q^73 - 16 * q^74 - 76 * q^78 - 32 * q^79 - 128 * q^80 - 184 * q^81 - 16 * q^82 + 56 * q^84 + 20 * q^86 - 52 * q^88 - 36 * q^90 - 168 * q^92 - 80 * q^96 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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