LMFDB - Embedded newform 900.2.z.b.179.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(179,900)] 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("900.179"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [224] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			179.4
Character	$\chi$	$=$	900.179
Dual form			900.2.z.b.719.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37756 - 0.319872i) q^{2} +(1.79536 + 0.881287i) q^{4} +(1.39186 + 1.75006i) q^{5} -0.321783 q^{7} +(-2.19133 - 1.78832i) q^{8} +(-1.35758 - 2.85604i) q^{10} +(-1.41316 + 4.34927i) q^{11} +(3.55729 - 1.15583i) q^{13} +(0.443277 + 0.102929i) q^{14} +(2.44667 + 3.16446i) q^{16} +(-1.30205 + 0.945993i) q^{17} +(-1.03337 - 1.42232i) q^{19} +(0.956590 + 4.36863i) q^{20} +(3.33793 - 5.53936i) q^{22} +(2.13335 + 0.693169i) q^{23} +(-1.12544 + 4.87169i) q^{25} +(-5.27011 + 0.454358i) q^{26} +(-0.577718 - 0.283583i) q^{28} +(-3.06750 + 4.22205i) q^{29} +(2.98367 + 4.10667i) q^{31} +(-2.35822 - 5.14187i) q^{32} +(2.09625 - 0.886678i) q^{34} +(-0.447878 - 0.563141i) q^{35} +(3.74926 - 1.21821i) q^{37} +(0.968580 + 2.28988i) q^{38} +(0.0796366 - 6.32405i) q^{40} +(-5.66966 + 1.84218i) q^{41} -1.04571 q^{43} +(-6.37010 + 6.56312i) q^{44} +(-2.71711 - 1.63728i) q^{46} +(2.08809 - 2.87401i) q^{47} -6.89646 q^{49} +(3.10869 - 6.35107i) q^{50} +(7.40524 + 1.05985i) q^{52} +(-4.57102 - 3.32104i) q^{53} +(-9.57842 + 3.58045i) q^{55} +(0.705133 + 0.575450i) q^{56} +(5.57618 - 4.83493i) q^{58} +(-0.685131 - 2.10862i) q^{59} +(1.00815 - 3.10276i) q^{61} +(-2.79659 - 6.61160i) q^{62} +(1.60386 + 7.83758i) q^{64} +(6.97403 + 4.61672i) q^{65} +(-11.2565 + 8.17833i) q^{67} +(-3.17134 + 0.550924i) q^{68} +(0.436847 + 0.919026i) q^{70} +(8.85844 + 6.43603i) q^{71} +(6.74095 + 2.19027i) q^{73} +(-5.55451 + 0.478878i) q^{74} +(-0.601813 - 3.46428i) q^{76} +(0.454732 - 1.39952i) q^{77} +(-9.11325 + 12.5433i) q^{79} +(-2.13259 + 8.68631i) q^{80} +(8.39958 - 0.724163i) q^{82} +(8.31829 + 11.4491i) q^{83} +(-3.46782 - 0.961975i) q^{85} +(1.44053 + 0.334492i) q^{86} +(10.8746 - 7.00350i) q^{88} +(12.9365 + 4.20332i) q^{89} +(-1.14467 + 0.371927i) q^{91} +(3.21927 + 3.12459i) q^{92} +(-3.79579 + 3.29121i) q^{94} +(1.05083 - 3.78814i) q^{95} +(3.51220 - 4.83412i) q^{97} +(9.50031 + 2.20598i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 8 q^{4} - 12 q^{10} - 8 q^{16} - 8 q^{25} + 92 q^{34} + 40 q^{37} + 36 q^{40} - 40 q^{46} + 368 q^{49} - 100 q^{52} - 120 q^{58} + 48 q^{61} - 16 q^{64} - 40 q^{70} + 24 q^{76} - 120 q^{85} - 120 q^{88}+ \cdots + 200 q^{97}+O(q^{100}) $ 224 * q + 8 * q^4 - 12 * q^10 - 8 * q^16 - 8 * q^25 + 92 * q^34 + 40 * q^37 + 36 * q^40 - 40 * q^46 + 368 * q^49 - 100 * q^52 - 120 * q^58 + 48 * q^61 - 16 * q^64 - 40 * q^70 + 24 * q^76 - 120 * q^85 - 120 * q^88 - 4 * q^94 + 200 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.37756	−	0.319872i	−0.974085	−	0.226183i
$2$	−1.37756	−	0.319872i	−0.974085	−	0.226183i
$3$		0			0
$3$		0			0
$4$	1.79536	+	0.881287i	0.897682	+	0.440644i
$5$	1.39186	+	1.75006i	0.622459	+	0.782652i
$5$	1.39186	+	1.75006i	0.622459	+	0.782652i
$6$		0			0
$7$	−0.321783			−0.121623			−0.0608113	−	0.998149i	$-0.519369\pi$
$7$	−0.321783			−0.121623			−0.0608113	+	0.998149i	$0.519369\pi$
$8$	−2.19133	−	1.78832i	−0.774752	−	0.632265i
$9$		0			0
$10$	−1.35758	−	2.85604i	−0.429305	−	0.903159i
$11$	−1.41316	+	4.34927i	−0.426085	+	1.31135i	0.475867	+	0.879517i	$0.342134\pi$
$11$	−1.41316	+	4.34927i	−0.426085	+	1.31135i	−0.901952	+	0.431837i	$0.857866\pi$
$12$		0			0
$13$	3.55729	−	1.15583i	0.986613	−	0.320570i	0.229109	−	0.973401i	$-0.426419\pi$
$13$	3.55729	−	1.15583i	0.986613	−	0.320570i	0.757504	+	0.652831i	$0.226419\pi$
$14$	0.443277	+	0.102929i	0.118471	+	0.0275090i
$15$		0			0
$16$	2.44667	+	3.16446i	0.611667	+	0.791116i
$17$	−1.30205	+	0.945993i	−0.315793	+	0.229437i	−0.734378	−	0.678740i	$-0.762526\pi$
$17$	−1.30205	+	0.945993i	−0.315793	+	0.229437i	0.418585	+	0.908178i	$0.362526\pi$
$18$		0			0
$19$	−1.03337	−	1.42232i	−0.237072	−	0.326302i	0.673859	−	0.738860i	$-0.264635\pi$
$19$	−1.03337	−	1.42232i	−0.237072	−	0.326302i	−0.910931	+	0.412558i	$0.864635\pi$
$20$	0.956590	+	4.36863i	0.213900	+	0.976856i
$21$		0			0
$22$	3.33793	−	5.53936i	0.711649	−	1.18100i
$23$	2.13335	+	0.693169i	0.444835	+	0.144536i	0.522865	−	0.852415i	$-0.324863\pi$
$23$	2.13335	+	0.693169i	0.444835	+	0.144536i	−0.0780303	+	0.996951i	$0.524863\pi$
$24$		0			0
$25$	−1.12544	+	4.87169i	−0.225089	+	0.974338i
$26$	−5.27011	+	0.454358i	−1.03355	+	0.0891069i
$27$		0			0
$28$	−0.577718	−	0.283583i	−0.109178	−	0.0535922i
$29$	−3.06750	+	4.22205i	−0.569620	+	0.784014i	−0.992510	−	0.122167i	$-0.961016\pi$
$29$	−3.06750	+	4.22205i	−0.569620	+	0.784014i	0.422890	+	0.906181i	$0.361016\pi$
$30$		0			0
$31$	2.98367	+	4.10667i	0.535884	+	0.737580i	0.988013	−	0.154372i	$-0.0493354\pi$
$31$	2.98367	+	4.10667i	0.535884	+	0.737580i	−0.452129	+	0.891952i	$0.649335\pi$
$32$	−2.35822	−	5.14187i	−0.416878	−	0.908963i
$33$		0			0
$34$	2.09625	−	0.886678i	0.359504	−	0.152064i
$35$	−0.447878	−	0.563141i	−0.0757051	−	0.0951882i
$36$		0			0
$37$	3.74926	−	1.21821i	0.616374	−	0.200272i	0.0158442	−	0.999874i	$-0.494956\pi$
$37$	3.74926	−	1.21821i	0.616374	−	0.200272i	0.600530	+	0.799602i	$0.294956\pi$
$38$	0.968580	+	2.28988i	0.157124	+	0.371468i
$39$		0			0
$40$	0.0796366	−	6.32405i	0.0125916	−	0.999921i
$41$	−5.66966	+	1.84218i	−0.885452	+	0.287701i	−0.716219	−	0.697875i	$-0.754129\pi$
$41$	−5.66966	+	1.84218i	−0.885452	+	0.287701i	−0.169233	+	0.985576i	$0.554129\pi$
$42$		0			0
$43$	−1.04571			−0.159469			−0.0797344	−	0.996816i	$-0.525407\pi$
$43$	−1.04571			−0.159469			−0.0797344	+	0.996816i	$0.525407\pi$
$44$	−6.37010	+	6.56312i	−0.960328	+	0.989427i
$45$		0			0
$46$	−2.71711	−	1.63728i	−0.400615	−	0.241404i
$47$	2.08809	−	2.87401i	0.304579	−	0.419217i	−0.629102	−	0.777323i	$-0.716577\pi$
$47$	2.08809	−	2.87401i	0.304579	−	0.419217i	0.933681	+	0.358106i	$0.116577\pi$
$48$		0			0
$49$	−6.89646			−0.985208
$50$	3.10869	−	6.35107i	0.439635	−	0.898177i
$51$		0			0
$52$	7.40524	+	1.05985i	1.02692	+	0.146975i
$53$	−4.57102	−	3.32104i	−0.627878	−	0.456180i	0.227787	−	0.973711i	$-0.426851\pi$
$53$	−4.57102	−	3.32104i	−0.627878	−	0.456180i	−0.855664	+	0.517531i	$0.826851\pi$
$54$		0			0
$55$	−9.57842	+	3.58045i	−1.29155	+	0.482788i
$56$	0.705133	+	0.575450i	0.0942274	+	0.0768977i
$57$		0			0
$58$	5.57618	−	4.83493i	0.732189	−	0.634858i
$59$	−0.685131	−	2.10862i	−0.0891965	−	0.274518i	0.896501	−	0.443041i	$-0.146100\pi$
$59$	−0.685131	−	2.10862i	−0.0891965	−	0.274518i	−0.985698	+	0.168523i	$0.946100\pi$
$60$		0			0
$61$	1.00815	−	3.10276i	0.129080	−	0.397267i	−0.865542	−	0.500836i	$-0.833026\pi$
$61$	1.00815	−	3.10276i	0.129080	−	0.397267i	0.994622	+	0.103568i	$0.0330261\pi$
$62$	−2.79659	−	6.61160i	−0.355168	−	0.839674i
$63$		0			0
$64$	1.60386	+	7.83758i	0.200482	+	0.979697i
$65$	6.97403	+	4.61672i	0.865022	+	0.572633i
$66$		0			0
$67$	−11.2565	+	8.17833i	−1.37520	+	0.999142i	−0.377891	+	0.925850i	$0.623350\pi$
$67$	−11.2565	+	8.17833i	−1.37520	+	0.999142i	−0.997311	+	0.0732920i	$0.976650\pi$
$68$	−3.17134	+	0.550924i	−0.384582	+	0.0668094i
$69$		0			0
$70$	0.436847	+	0.919026i	0.0522132	+	0.109845i
$71$	8.85844	+	6.43603i	1.05130	+	0.763817i	0.972460	−	0.233070i	$-0.0748772\pi$
$71$	8.85844	+	6.43603i	1.05130	+	0.763817i	0.0788437	+	0.996887i	$0.474877\pi$
$72$		0			0
$73$	6.74095	+	2.19027i	0.788968	+	0.256351i	0.675665	−	0.737209i	$-0.263857\pi$
$73$	6.74095	+	2.19027i	0.788968	+	0.256351i	0.113304	+	0.993560i	$0.463857\pi$
$74$	−5.55451	+	0.478878i	−0.645699	+	0.0556684i
$75$		0			0
$76$	−0.601813	−	3.46428i	−0.0690327	−	0.397380i
$77$	0.454732	−	1.39952i	0.0518215	−	0.159490i
$78$		0			0
$79$	−9.11325	+	12.5433i	−1.02532	+	1.41123i	−0.116915	+	0.993142i	$0.537301\pi$
$79$	−9.11325	+	12.5433i	−1.02532	+	1.41123i	−0.908405	+	0.418091i	$0.862699\pi$
$80$	−2.13259	+	8.68631i	−0.238431	+	0.971159i
$81$		0			0
$82$	8.39958	−	0.724163i	0.927578	−	0.0799704i
$83$	8.31829	+	11.4491i	0.913051	+	1.25671i	0.966114	+	0.258115i	$0.0831015\pi$
$83$	8.31829	+	11.4491i	0.913051	+	1.25671i	−0.0530634	+	0.998591i	$0.516899\pi$
$84$		0			0
$85$	−3.46782	−	0.961975i	−0.376138	−	0.104341i
$86$	1.44053	+	0.334492i	0.155336	+	0.0360692i
$87$		0			0
$88$	10.8746	−	7.00350i	1.15923	−	0.746576i
$89$	12.9365	+	4.20332i	1.37126	+	0.445551i	0.899788	−	0.436328i	$-0.143721\pi$
$89$	12.9365	+	4.20332i	1.37126	+	0.445551i	0.471477	+	0.881878i	$0.343721\pi$
$90$		0			0
$91$	−1.14467	+	0.371927i	−0.119995	+	0.0389886i
$92$	3.21927	+	3.12459i	0.335632	+	0.325761i
$93$		0			0
$94$	−3.79579	+	3.29121i	−0.391506	+	0.339462i
$95$	1.05083	−	3.78814i	0.107813	−	0.388655i
$96$		0			0
$97$	3.51220	−	4.83412i	0.356610	−	0.490831i	−0.592591	−	0.805504i	$-0.701895\pi$
$97$	3.51220	−	4.83412i	0.356610	−	0.490831i	0.949200	+	0.314673i	$0.101895\pi$
$98$	9.50031	+	2.20598i	0.959676	+	0.222838i
$99$		0			0
$100$	−6.31394	+	7.75462i	−0.631394	+	0.775462i
$101$			3.92996i			0.391046i	0.980699	+	0.195523i	$0.0626404\pi$
$101$			3.92996i			0.391046i	−0.980699	+	0.195523i	$0.937360\pi$
$102$		0			0
$103$	12.4116	+	9.01755i	1.22295	+	0.888526i	0.996342	−	0.0854600i	$-0.0272360\pi$
$103$	12.4116	+	9.01755i	1.22295	+	0.888526i	0.226609	+	0.973986i	$0.427236\pi$
$104$	−9.86218	−	3.82874i	−0.967066	−	0.375439i
$105$		0			0
$106$	5.23456	+	6.03708i	0.508426	+	0.586373i
$107$		−	13.3699i		−	1.29252i	−0.763118	−	0.646259i	$-0.776332\pi$
$107$		−	13.3699i		−	1.29252i	0.763118	−	0.646259i	$-0.223668\pi$
$108$		0			0
$109$	4.08361	+	12.5681i	0.391139	+	1.20380i	0.931928	+	0.362643i	$0.118126\pi$
$109$	4.08361	+	12.5681i	0.391139	+	1.20380i	−0.540789	+	0.841158i	$0.681874\pi$
$110$	14.3402	−	1.86844i	1.36728	−	0.178149i
$111$		0			0
$112$	−0.787296	−	1.01827i	−0.0743925	−	0.0962176i
$113$	0.587814	+	1.80911i	0.0552969	+	0.170186i	0.974891	−	0.222684i	$-0.0714820\pi$
$113$	0.587814	+	1.80911i	0.0552969	+	0.170186i	−0.919594	+	0.392871i	$0.871482\pi$
$114$		0			0
$115$	1.75624	+	4.69830i	0.163771	+	0.438119i
$116$	−9.22811	+	4.87677i	−0.856808	+	0.452796i
$117$		0			0
$118$	0.269325	+	3.12391i	0.0247934	+	0.287579i
$119$	0.418977	−	0.304405i	0.0384076	−	0.0279047i
$120$		0			0
$121$	−8.01992	−	5.82681i	−0.729083	−	0.529710i
$122$	−2.38127	+	3.95177i	−0.215590	+	0.357776i
$123$		0			0
$124$	1.73762	+	10.0024i	0.156043	+	0.898246i
$125$	−10.0922	+	4.81112i	−0.902676	+	0.430320i
$126$		0			0
$127$	−3.75369	+	11.5527i	−0.333086	+	1.02513i	0.634571	+	0.772864i	$0.281177\pi$
$127$	−3.75369	+	11.5527i	−0.333086	+	1.02513i	−0.967657	+	0.252269i	$0.918823\pi$
$128$	0.297603	−	11.3098i	0.0263046	−	0.999654i
$129$		0			0
$130$	−8.13041	−	8.59061i	−0.713084	−	0.753447i
$131$	5.60911	−	4.07525i	0.490070	−	0.356057i	−0.315141	−	0.949045i	$-0.602052\pi$
$131$	5.60911	−	4.07525i	0.490070	−	0.356057i	0.805211	+	0.592988i	$0.202052\pi$
$132$		0			0
$133$	0.332523	+	0.457678i	0.0288334	+	0.0396857i
$134$	18.1226	−	7.66554i	1.56555	−	0.662202i
$135$		0			0
$136$	4.54495	+	0.255489i	0.389726	+	0.0219080i
$137$	−2.17721	−	6.70075i	−0.186011	−	0.572484i	0.813953	−	0.580931i	$-0.197311\pi$
$137$	−2.17721	−	6.70075i	−0.186011	−	0.572484i	−0.999964	+	0.00844669i	$0.997311\pi$
$138$		0			0
$139$	−1.14396	−	0.371695i	−0.0970295	−	0.0315268i	0.260100	−	0.965582i	$-0.416244\pi$
$139$	−1.14396	−	0.371695i	−0.0970295	−	0.0315268i	−0.357129	+	0.934055i	$0.616244\pi$
$140$	−0.307815	−	1.40575i	−0.0260151	−	0.118808i
$141$		0			0
$142$	−10.1444	−	11.6996i	−0.851296	−	0.981810i
$143$			17.1050i			1.43039i
$144$		0			0
$145$	−11.6584	+	0.508191i	−0.968175	+	0.0422030i
$146$	−8.58548	−	5.17347i	−0.710540	−	0.428159i
$147$		0			0
$148$	7.80487	+	1.11705i	0.641557	+	0.0918206i
$149$		−	22.9799i		−	1.88259i	−0.337588	−	0.941294i	$-0.609611\pi$
$149$		−	22.9799i		−	1.88259i	0.337588	−	0.941294i	$-0.390389\pi$
$150$		0			0
$151$		−	16.1758i		−	1.31637i	−0.752858	−	0.658183i	$-0.771325\pi$
$151$		−	16.1758i		−	1.31637i	0.752858	−	0.658183i	$-0.228675\pi$
$152$	−0.279088	+	4.96477i	−0.0226370	+	0.402696i
$153$		0			0
$154$	−1.07409	+	1.78247i	−0.0865526	+	0.143636i
$155$	−3.03408	+	10.9375i	−0.243703	+	0.878524i
$156$		0			0
$157$		−	18.9989i		−	1.51628i	−0.652093	−	0.758139i	$-0.726109\pi$
$157$		−	18.9989i		−	1.51628i	0.652093	−	0.758139i	$-0.273891\pi$
$158$	16.5663	−	14.3641i	1.31795	−	1.14275i
$159$		0			0
$160$	5.71628	−	11.2838i	0.451912	−	0.892063i
$161$	−0.686477	−	0.223050i	−0.0541020	−	0.0175788i
$162$		0			0
$163$	−1.19334	−	3.67271i	−0.0934693	−	0.287669i	0.893382	−	0.449297i	$-0.148326\pi$
$163$	−1.19334	−	3.67271i	−0.0934693	−	0.287669i	−0.986852	+	0.161628i	$0.948326\pi$
$164$	−11.8026	−	1.68921i	−0.921628	−	0.131905i
$165$		0			0
$166$	−7.79672	−	18.4327i	−0.605143	−	1.43066i
$167$	−10.0626	−	13.8500i	−0.778670	−	1.07175i	−0.995427	−	0.0955213i	$-0.969548\pi$
$167$	−10.0626	−	13.8500i	−0.778670	−	1.07175i	0.216758	−	0.976225i	$-0.430452\pi$
$168$		0			0
$169$	0.801109	−	0.582039i	0.0616237	−	0.0447723i
$170$	4.46943	+	2.43444i	0.342790	+	0.186713i
$171$		0			0
$172$	−1.87742	−	0.921568i	−0.143152	−	0.0702689i
$173$	1.16544	−	3.58687i	0.0886071	−	0.272705i	−0.896928	−	0.442177i	$-0.854206\pi$
$173$	1.16544	−	3.58687i	0.0886071	−	0.272705i	0.985535	+	0.169472i	$0.0542063\pi$
$174$		0			0
$175$	0.362149	−	1.56763i	0.0273759	−	0.118502i
$176$	−17.2206	+	6.16931i	−1.29805	+	0.465029i
$177$		0			0
$178$	−16.4763	−	9.92835i	−1.23495	−	0.744162i
$179$	12.3848	+	8.99807i	0.925682	+	0.672547i	0.944932	−	0.327267i	$-0.106128\pi$
$179$	12.3848	+	8.99807i	0.925682	+	0.672547i	−0.0192499	+	0.999815i	$0.506128\pi$
$180$		0			0
$181$	−11.2051	+	8.14098i	−0.832868	+	0.605114i	−0.920369	−	0.391050i	$-0.872112\pi$
$181$	−11.2051	+	8.14098i	−0.832868	+	0.605114i	0.0875013	+	0.996164i	$0.472112\pi$
$182$	1.69583	−	0.146205i	0.125703	−	0.0108374i
$183$		0			0
$184$	−3.43528	−	5.33407i	−0.253252	−	0.393233i
$185$	7.35039	+	4.86586i	0.540411	+	0.357745i
$186$		0			0
$187$	−2.27437	−	6.99980i	−0.166319	−	0.511876i
$188$	6.28171	−	3.31969i	0.458141	−	0.242113i
$189$		0			0
$190$	−2.65931	+	4.88227i	−0.192926	+	0.354197i
$191$	7.10664	+	21.8720i	0.514218	+	1.58260i	0.784700	+	0.619876i	$0.212817\pi$
$191$	7.10664	+	21.8720i	0.514218	+	1.58260i	−0.270482	+	0.962725i	$0.587183\pi$
$192$		0			0
$193$			9.24193i			0.665249i	0.943059	+	0.332624i	$0.107934\pi$
$193$			9.24193i			0.665249i	−0.943059	+	0.332624i	$0.892066\pi$
$194$	−6.38458	+	5.53586i	−0.458386	+	0.397452i
$195$		0			0
$196$	−12.3817	−	6.07776i	−0.884404	−	0.434125i
$197$	−20.5793	−	14.9518i	−1.46622	−	1.06527i	−0.981689	−	0.190492i	$-0.938992\pi$
$197$	−20.5793	−	14.9518i	−1.46622	−	1.06527i	−0.484528	−	0.874776i	$-0.661008\pi$
$198$		0			0
$199$		−	20.3886i		−	1.44531i	−0.691208	−	0.722656i	$-0.742921\pi$
$199$		−	20.3886i		−	1.44531i	0.691208	−	0.722656i	$-0.257079\pi$
$200$	11.1783	−	8.66284i	0.790428	−	0.612555i
$201$		0			0
$202$	1.25708	−	5.41377i	0.0884480	−	0.380912i
$203$	0.987069	−	1.35858i	0.0692786	−	0.0953539i
$204$		0			0
$205$	−11.1153	−	7.35820i	−0.776327	−	0.513919i
$206$	−14.2133	−	16.3924i	−0.990288	−	1.14211i
$207$		0			0
$208$	12.3611	+	8.42896i	0.857086	+	0.584443i
$209$	7.64637	−	2.48446i	0.528910	−	0.171853i
$210$		0			0
$211$	16.7601	+	5.44567i	1.15381	+	0.374895i	0.822577	−	0.568654i	$-0.192536\pi$
$211$	16.7601	+	5.44567i	1.15381	+	0.374895i	0.331232	+	0.943549i	$0.392536\pi$
$212$	−5.27985	−	9.99086i	−0.362622	−	0.686175i
$213$		0			0
$214$	−4.27666	+	18.4179i	−0.292346	+	1.25902i
$215$	−1.45548	−	1.83005i	−0.0992628	−	0.124809i
$216$		0			0
$217$	−0.960096	−	1.32146i	−0.0651756	−	0.0897065i
$218$	−1.60527	−	18.6195i	−0.108722	−	1.26107i
$219$		0			0
$220$	−20.3522	−	2.01312i	−1.37214	−	0.135724i
$221$	−3.53835	+	4.87012i	−0.238015	+	0.327599i
$222$		0			0
$223$	−1.14475	+	3.52318i	−0.0766581	+	0.235929i	−0.982041	−	0.188666i	$-0.939584\pi$
$223$	−1.14475	+	3.52318i	−0.0766581	+	0.235929i	0.905383	+	0.424595i	$0.139584\pi$
$224$	0.758835	+	1.65457i	0.0507018	+	0.110550i
$225$		0			0
$226$	−0.231070	−	2.68018i	−0.0153705	−	0.178283i
$227$	−10.4013	−	3.37958i	−0.690358	−	0.224311i	−0.0572334	−	0.998361i	$-0.518228\pi$
$227$	−10.4013	−	3.37958i	−0.690358	−	0.224311i	−0.633125	+	0.774050i	$0.718228\pi$
$228$		0			0
$229$	16.2754	+	11.8248i	1.07551	+	0.781402i	0.976894	−	0.213724i	$-0.0685592\pi$
$229$	16.2754	+	11.8248i	1.07551	+	0.781402i	0.0986137	+	0.995126i	$0.468559\pi$
$230$	−0.916486	−	7.03398i	−0.0604313	−	0.463807i
$231$		0			0
$232$	14.2722	−	3.76625i	0.937019	−	0.247266i
$233$	22.9156	−	16.6491i	1.50125	−	1.09072i	0.531368	−	0.847141i	$-0.321678\pi$
$233$	22.9156	−	16.6491i	1.50125	−	1.09072i	0.969881	−	0.243580i	$-0.0783218\pi$
$234$		0			0
$235$	7.93603	−	0.345933i	0.517689	−	0.0225662i
$236$	0.628237	−	4.38953i	0.0408947	−	0.285734i
$237$		0			0
$238$	−0.674538	+	0.285318i	−0.0437238	+	0.0184944i
$239$	7.69394	−	23.6795i	0.497680	−	1.53170i	−0.315059	−	0.949072i	$-0.602024\pi$
$239$	7.69394	−	23.6795i	0.497680	−	1.53170i	0.812738	−	0.582629i	$-0.197976\pi$
$240$		0			0
$241$	−5.87427	−	18.0791i	−0.378395	−	1.16458i	−0.941160	−	0.337962i	$-0.890262\pi$
$241$	−5.87427	−	18.0791i	−0.378395	−	1.16458i	0.562765	−	0.826617i	$-0.309738\pi$
$242$	9.18412	+	10.5921i	0.590377	+	0.680889i
$243$		0			0
$244$	4.54441	−	4.68211i	0.290926	−	0.299742i
$245$	−9.59891	−	12.0692i	−0.613252	−	0.771075i
$246$		0			0
$247$	−5.31997	−	3.86518i	−0.338501	−	0.245936i
$248$	0.805814	−	14.3348i	0.0511692	−	0.910262i
$249$		0			0
$250$	15.4416	−	3.39941i	0.976615	−	0.214998i
$251$	−4.12240			−0.260204			−0.130102	−	0.991501i	$-0.541530\pi$
$251$	−4.12240			−0.260204			−0.130102	+	0.991501i	$0.541530\pi$
$252$		0			0
$253$	−6.02955	+	8.29897i	−0.379075	+	0.521752i
$254$	8.86631	−	14.7138i	0.556322	−	0.923228i
$255$		0			0
$256$	−4.02765	+	15.4848i	−0.251728	+	0.967798i
$257$	30.1419			1.88020			0.940099	−	0.340901i	$-0.110732\pi$
$257$	30.1419			1.88020			0.940099	+	0.340901i	$0.110732\pi$
$258$		0			0
$259$	−1.20645	+	0.391999i	−0.0749650	+	0.0243576i
$260$	8.45227	+	14.4348i	0.524187	+	0.895209i
$261$		0			0
$262$	−9.03046	+	3.81973i	−0.557904	+	0.235984i
$263$	−26.8221	+	8.71502i	−1.65392	+	0.537391i	−0.979584	−	0.201035i	$-0.935570\pi$
$263$	−26.8221	+	8.71502i	−1.65392	+	0.537391i	−0.674335	+	0.738426i	$0.735570\pi$
$264$		0			0
$265$	−0.550196	−	12.6220i	−0.0337982	−	0.775363i
$266$	−0.311673	−	0.736845i	−0.0191099	−	0.0451789i
$267$		0			0
$268$	−27.4170	+	4.76287i	−1.67476	+	0.290939i
$269$	10.5303	+	14.4937i	0.642043	+	0.883697i	0.998723	−	0.0505300i	$-0.0160910\pi$
$269$	10.5303	+	14.4937i	0.642043	+	0.883697i	−0.356679	+	0.934227i	$0.616091\pi$
$270$		0			0
$271$	14.5782	−	20.0652i	0.885563	−	1.21887i	−0.0892856	−	0.996006i	$-0.528458\pi$
$271$	14.5782	−	20.0652i	0.885563	−	1.21887i	0.974849	−	0.222867i	$-0.0715416\pi$
$272$	−6.17924	−	1.80575i	−0.374671	−	0.109490i
$273$		0			0
$274$	0.855861	+	9.92714i	0.0517044	+	0.599721i
$275$	−19.5979	−	11.7793i	−1.18180	−	0.710321i
$276$		0			0
$277$	6.43663	+	2.09139i	0.386739	+	0.125659i	0.495932	−	0.868361i	$-0.334827\pi$
$277$	6.43663	+	2.09139i	0.386739	+	0.125659i	−0.109193	+	0.994021i	$0.534827\pi$
$278$	1.45698	+	0.877955i	0.0873841	+	0.0526562i
$279$		0			0
$280$	−0.0256257	+	2.03497i	−0.00153143	+	0.121613i
$281$	−3.81009	−	5.24413i	−0.227291	−	0.312839i	0.680106	−	0.733114i	$-0.261934\pi$
$281$	−3.81009	−	5.24413i	−0.227291	−	0.312839i	−0.907397	+	0.420275i	$0.861934\pi$
$282$		0			0
$283$	13.3462	−	9.69660i	0.793351	−	0.576403i	−0.115605	−	0.993295i	$-0.536881\pi$
$283$	13.3462	−	9.69660i	0.793351	−	0.576403i	0.908956	+	0.416892i	$0.136881\pi$
$284$	10.2321	+	19.3619i	0.607166	+	1.14891i
$285$		0			0
$286$	5.47139	−	23.5632i	0.323530	−	1.39332i
$287$	1.82440	−	0.592784i	0.107691	−	0.0349909i
$288$		0			0
$289$	−4.45286	+	13.7045i	−0.261933	+	0.806147i
$290$	16.2227	+	3.02912i	0.952630	+	0.177876i
$291$		0			0
$292$	10.1722	+	9.87304i	0.595283	+	0.577776i
$293$	−11.6562			−0.680965			−0.340482	−	0.940251i	$-0.610590\pi$
$293$	−11.6562			−0.680965			−0.340482	+	0.940251i	$0.610590\pi$
$294$		0			0
$295$	2.73660	−	4.13392i	0.159331	−	0.240686i
$296$	−10.3944	−	4.03536i	−0.604162	−	0.234550i
$297$		0			0
$298$	−7.35062	+	31.6563i	−0.425810	+	1.83380i
$299$	8.39013			0.485214
$300$		0			0
$301$	0.336491			0.0193950
$302$	−5.17417	+	22.2832i	−0.297740	+	1.28225i
$303$		0			0
$304$	1.97255	−	6.75001i	0.113133	−	0.387140i
$305$	6.83322	−	2.55429i	0.391269	−	0.146258i
$306$		0			0
$307$	−16.6045			−0.947672			−0.473836	−	0.880613i	$-0.657131\pi$
$307$	−16.6045			−0.947672			−0.473836	+	0.880613i	$0.657131\pi$
$308$	2.04979	−	2.11190i	0.116798	−	0.120337i
$309$		0			0
$310$	7.67825	−	14.0966i	0.436095	−	0.800635i
$311$	3.61093	−	11.1133i	0.204757	−	0.630178i	−0.794966	−	0.606654i	$-0.792511\pi$
$311$	3.61093	−	11.1133i	0.204757	−	0.630178i	0.999723	−	0.0235239i	$-0.00748859\pi$
$312$		0			0
$313$	23.7012	−	7.70100i	1.33967	−	0.435286i	0.450467	−	0.892793i	$-0.351258\pi$
$313$	23.7012	−	7.70100i	1.33967	−	0.435286i	0.889206	+	0.457507i	$0.151258\pi$
$314$	−6.07721	+	26.1722i	−0.342957	+	1.47698i
$315$		0			0
$316$	−27.4159	+	14.4884i	−1.54226	+	0.815037i
$317$	−13.2670	+	9.63904i	−0.745149	+	0.541382i	−0.894319	−	0.447429i	$-0.852340\pi$
$317$	−13.2670	+	9.63904i	−0.745149	+	0.541382i	0.149171	+	0.988811i	$0.452340\pi$
$318$		0			0
$319$	−14.0279	−	19.3078i	−0.785414	−	1.08103i
$320$	−11.4839	+	13.7157i	−0.641970	+	0.766730i
$321$		0			0
$322$	0.874319	+	0.526850i	0.0487239	+	0.0293602i
$323$	2.69101	+	0.874361i	0.149732	+	0.0486507i
$324$		0			0
$325$	1.62733	+	18.6308i	0.0902683	+	1.03345i
$326$	0.469101	+	5.44111i	0.0259811	+	0.301355i
$327$		0			0
$328$	15.7185	+	6.10230i	0.867909	+	0.336943i
$329$	−0.671912	+	0.924807i	−0.0370437	+	0.0509863i
$330$		0			0
$331$	−2.76411	−	3.80447i	−0.151929	−	0.209112i	0.726268	−	0.687412i	$-0.241253\pi$
$331$	−2.76411	−	3.80447i	−0.151929	−	0.209112i	−0.878197	+	0.478300i	$0.841253\pi$
$332$	4.84438	+	27.8862i	0.265870	+	1.53045i
$333$		0			0
$334$	9.43168	+	22.2980i	0.516079	+	1.22009i
$335$	−29.9801	−	8.31650i	−1.63799	−	0.454379i
$336$		0			0
$337$	−0.648413	+	0.210682i	−0.0353213	+	0.0114766i	−0.326624	−	0.945154i	$-0.605911\pi$
$337$	−0.648413	+	0.210682i	−0.0353213	+	0.0114766i	0.291303	+	0.956631i	$0.405911\pi$
$338$	−1.28976	+	0.545545i	−0.0701535	+	0.0296737i
$339$		0			0
$340$	−5.37822	−	4.78324i	−0.291675	−	0.259408i
$341$	−22.0774	+	7.17340i	−1.19556	+	0.388461i
$342$		0			0
$343$	4.47165			0.241446
$344$	2.29149	+	1.87005i	0.123549	+	0.100827i
$345$		0			0
$346$	−2.75281	+	4.56835i	−0.147992	+	0.245596i
$347$	13.8203	−	19.0220i	0.741913	−	1.02116i	−0.256594	−	0.966519i	$-0.582600\pi$
$347$	13.8203	−	19.0220i	0.741913	−	1.02116i	0.998506	−	0.0546358i	$-0.0173998\pi$
$348$		0			0
$349$	−1.19111			−0.0637585			−0.0318792	−	0.999492i	$-0.510149\pi$
$349$	−1.19111			−0.0637585			−0.0318792	+	0.999492i	$0.510149\pi$
$350$	−1.00032	+	2.04367i	−0.0534695	+	0.109239i
$351$		0			0
$352$	25.6959	−	2.99022i	1.36960	−	0.159379i
$353$	−2.38763	−	1.73471i	−0.127081	−	0.0923294i	0.522429	−	0.852683i	$-0.325026\pi$
$353$	−2.38763	−	1.73471i	−0.127081	−	0.0923294i	−0.649510	+	0.760353i	$0.725026\pi$
$354$		0			0
$355$	1.06626	+	24.4609i	0.0565910	+	1.29825i
$356$	19.5214	+	18.9472i	1.03463	+	1.00420i
$357$		0			0
$358$	−14.1826	−	16.3570i	−0.749574	−	0.864492i
$359$	−3.33796	−	10.2732i	−0.176171	−	0.542197i	0.823514	−	0.567295i	$-0.192010\pi$
$359$	−3.33796	−	10.2732i	−0.176171	−	0.542197i	−0.999685	+	0.0250979i	$0.992010\pi$
$360$		0			0
$361$	4.91620	−	15.1305i	0.258747	−	0.796342i
$362$	18.0398	−	7.63052i	0.948151	−	0.401051i
$363$		0			0
$364$	−2.38288	−	0.341042i	−0.124897	−	0.0178755i
$365$	5.54936	+	14.8456i	0.290467	+	0.777056i
$366$		0			0
$367$	25.9350	−	18.8429i	1.35380	−	0.983591i	0.354985	−	0.934872i	$-0.384486\pi$
$367$	25.9350	−	18.8429i	1.35380	−	0.983591i	0.998813	−	0.0487194i	$-0.0155140\pi$
$368$	3.02610	+	8.44687i	0.157746	+	0.440324i
$369$		0			0
$370$	−8.56918	−	9.05421i	−0.445490	−	0.470706i
$371$	1.47088	+	1.06865i	0.0763641	+	0.0554818i
$372$		0			0
$373$	6.46069	+	2.09920i	0.334522	+	0.108693i	0.471461	−	0.881887i	$-0.343727\pi$
$373$	6.46069	+	2.09920i	0.334522	+	0.108693i	−0.136940	+	0.990579i	$0.543727\pi$
$374$	0.894057	+	10.3702i	0.0462306	+	0.536229i
$375$		0			0
$376$	−9.71532	+	2.56374i	−0.501030	+	0.132215i
$377$	−6.03198	+	18.5645i	−0.310663	+	0.956122i
$378$		0			0
$379$	3.07997	−	4.23921i	0.158207	−	0.217754i	−0.722554	−	0.691315i	$-0.757032\pi$
$379$	3.07997	−	4.23921i	0.158207	−	0.217754i	0.880761	+	0.473561i	$0.157032\pi$
$380$	5.22507	−	5.87501i	0.268040	−	0.301381i
$381$		0			0
$382$	−2.79362	−	32.4033i	−0.142934	−	1.65789i
$383$	−3.72210	−	5.12302i	−0.190190	−	0.261774i	0.703264	−	0.710929i	$-0.251725\pi$
$383$	−3.72210	−	5.12302i	−0.190190	−	0.261774i	−0.893454	+	0.449155i	$0.851725\pi$
$384$		0			0
$385$	3.08218	−	1.15213i	0.157082	−	0.0587180i
$386$	2.95623	−	12.7314i	0.150468	−	0.648009i
$387$		0			0
$388$	10.5659	−	5.58376i	0.536404	−	0.283473i
$389$	−7.91708	−	2.57242i	−0.401412	−	0.130427i	0.101351	−	0.994851i	$-0.467683\pi$
$389$	−7.91708	−	2.57242i	−0.401412	−	0.130427i	−0.502763	+	0.864424i	$0.667683\pi$
$390$		0			0
$391$	−3.43346	+	1.11560i	−0.173638	+	0.0564183i
$392$	15.1124	+	12.3330i	0.763292	+	0.622912i
$393$		0			0
$394$	23.5667	+	27.1797i	1.18727	+	1.36930i
$395$	−34.6360	+	1.50979i	−1.74272	+	0.0759657i
$396$		0			0
$397$	−10.5904	+	14.5764i	−0.531515	+	0.731568i	−0.987360	−	0.158491i	$-0.949337\pi$
$397$	−10.5904	+	14.5764i	−0.531515	+	0.731568i	0.455845	+	0.890059i	$0.349337\pi$
$398$	−6.52174	+	28.0866i	−0.326906	+	1.40786i
$399$		0			0
$400$	−18.1699	+	8.35798i	−0.908493	+	0.417899i
$401$			13.7548i			0.686881i	0.939174	+	0.343441i	$0.111592\pi$
$401$			13.7548i			0.686881i	−0.939174	+	0.343441i	$0.888408\pi$
$402$		0			0
$403$	15.3604	+	11.1600i	0.765156	+	0.555918i
$404$	−3.46342	+	7.05571i	−0.172312	+	0.351035i
$405$		0			0
$406$	−1.79432	+	1.55580i	−0.0890507	+	0.0772131i
$407$			18.0280i			0.893617i
$408$		0			0
$409$	−4.55283	−	14.0122i	−0.225123	−	0.692857i	−0.998279	−	0.0586416i	$-0.981323\pi$
$409$	−4.55283	−	14.0122i	−0.225123	−	0.692857i	0.773156	−	0.634216i	$-0.218677\pi$
$410$	12.9584	+	13.6919i	0.639969	+	0.676193i
$411$		0			0
$412$	14.3363	+	27.1280i	0.706298	+	1.33650i
$413$	0.220464	+	0.678517i	0.0108483	+	0.0333877i
$414$		0			0
$415$	−8.45882	+	30.4931i	−0.415227	+	1.49685i
$416$	−14.3320	−	15.5654i	−0.702683	−	0.763156i
$417$		0			0
$418$	−11.3281	+	0.976640i	−0.554074	+	0.0477690i
$419$	21.3657	−	15.5231i	1.04378	−	0.758353i	0.0727632	−	0.997349i	$-0.476818\pi$
$419$	21.3657	−	15.5231i	1.04378	−	0.758353i	0.971021	+	0.238996i	$0.0768183\pi$
$420$		0			0
$421$	−6.59412	−	4.79091i	−0.321378	−	0.233495i	0.415385	−	0.909646i	$-0.363647\pi$
$421$	−6.59412	−	4.79091i	−0.321378	−	0.233495i	−0.736763	+	0.676151i	$0.763647\pi$
$422$	−21.3461	−	12.8628i	−1.03911	−	0.626152i
$423$		0			0
$424$	4.07755	+	15.4519i	0.198023	+	0.750411i
$425$	−3.14321	−	7.40784i	−0.152468	−	0.359333i
$426$		0			0
$427$	−0.324405	+	0.998415i	−0.0156990	+	0.0483167i
$428$	11.7827	−	24.0039i	0.569540	−	1.16027i
$429$		0			0
$430$	1.41963	+	2.98658i	0.0684608	+	0.144026i
$431$	21.8253	−	15.8570i	1.05129	−	0.763806i	0.0788322	−	0.996888i	$-0.474881\pi$
$431$	21.8253	−	15.8570i	1.05129	−	0.763806i	0.972457	+	0.233081i	$0.0748809\pi$
$432$		0			0
$433$	4.82024	+	6.63449i	0.231646	+	0.318833i	0.908978	−	0.416844i	$-0.136864\pi$
$433$	4.82024	+	6.63449i	0.231646	+	0.318833i	−0.677332	+	0.735677i	$0.736864\pi$
$434$	0.899896	+	2.12750i	0.0431964	+	0.102123i
$435$		0			0
$436$	−3.74450	+	26.1631i	−0.179329	+	1.25298i
$437$	−1.21865	−	3.75061i	−0.0582958	−	0.179416i
$438$		0			0
$439$	1.92506	+	0.625490i	0.0918781	+	0.0298530i	0.354595	−	0.935020i	$-0.384619\pi$
$439$	1.92506	+	0.625490i	0.0918781	+	0.0298530i	−0.262717	+	0.964873i	$0.584619\pi$
$440$	27.3925	+	9.28328i	1.30588	+	0.442563i
$441$		0			0
$442$	6.43211	−	5.57708i	0.305944	−	0.265275i
$443$			11.5023i			0.546489i	0.961945	+	0.273244i	$0.0880967\pi$
$443$			11.5023i			0.546489i	−0.961945	+	0.273244i	$0.911903\pi$
$444$		0			0
$445$	10.6497	+	28.4901i	0.504845	+	1.35056i
$446$	2.70393	−	4.48723i	0.128035	−	0.212476i
$447$		0			0
$448$	−0.516094	−	2.52200i	−0.0243832	−	0.119153i
$449$			22.4572i			1.05982i	0.848054	+	0.529910i	$0.177774\pi$
$449$			22.4572i			1.05982i	−0.848054	+	0.529910i	$0.822226\pi$
$450$		0			0
$451$		−	27.2622i		−	1.28373i
$452$	−0.539001	+	3.76604i	−0.0253525	+	0.177140i
$453$		0			0
$454$	13.2474	+	7.98267i	0.621732	+	0.374645i
$455$	−2.24412	−	1.48558i	−0.105206	−	0.0696451i
$456$		0			0
$457$		−	19.8864i		−	0.930249i	−0.885245	−	0.465124i	$-0.846010\pi$
$457$		−	19.8864i		−	0.930249i	0.885245	−	0.465124i	$-0.153990\pi$
$458$	−18.6380	−	21.4954i	−0.870896	−	1.00441i
$459$		0			0
$460$	−0.987452	+	9.98291i	−0.0460402	+	0.465456i
$461$	15.1145	+	4.91101i	0.703955	+	0.228729i	0.639053	−	0.769163i	$-0.279327\pi$
$461$	15.1145	+	4.91101i	0.703955	+	0.228729i	0.0649020	+	0.997892i	$0.479327\pi$
$462$		0			0
$463$	3.31165	+	10.1922i	0.153906	+	0.473673i	0.998048	−	0.0624458i	$-0.0198900\pi$
$463$	3.31165	+	10.1922i	0.153906	+	0.473673i	−0.844143	+	0.536118i	$0.819890\pi$
$464$	−20.8656	+	0.622961i	−0.968663	+	0.0289202i
$465$		0			0
$466$	−36.8932	+	15.6052i	−1.70905	+	0.722897i
$467$	−16.6028	−	22.8517i	−0.768284	−	1.05745i	−0.996479	−	0.0838372i	$-0.973282\pi$
$467$	−16.6028	−	22.8517i	−0.768284	−	1.05745i	0.228195	−	0.973615i	$-0.426718\pi$
$468$		0			0
$469$	3.62216	−	2.63165i	0.167256	−	0.121518i
$470$	−11.0430	−	2.06196i	−0.509377	−	0.0951113i
$471$		0			0
$472$	−2.26952	+	5.84591i	−0.104463	+	0.269080i
$473$	1.47775	−	4.54806i	0.0679472	−	0.209120i
$474$		0			0
$475$	8.09210	−	3.43354i	0.371291	−	0.157542i
$476$	1.02048	−	0.177278i	0.0467738	−	0.00812553i
$477$		0			0
$478$	−18.1733	+	30.1590i	−0.831228	+	1.37944i
$479$	5.92005	+	4.30117i	0.270494	+	0.196525i	0.714761	−	0.699369i	$-0.246536\pi$
$479$	5.92005	+	4.30117i	0.270494	+	0.196525i	−0.444266	+	0.895895i	$0.646536\pi$
$480$		0			0
$481$	11.9291	−	8.66702i	0.543922	−	0.395182i
$482$	2.30918	+	26.7842i	0.105180	+	1.21999i
$483$		0			0
$484$	−9.26358	−	17.5291i	−0.421072	−	0.796777i
$485$	13.3485	−	0.581865i	0.606125	−	0.0264211i
$486$		0			0
$487$	2.03880	+	6.27477i	0.0923868	+	0.284337i	0.986564	−	0.163376i	$-0.0522385\pi$
$487$	2.03880	+	6.27477i	0.0923868	+	0.284337i	−0.894177	+	0.447713i	$0.852238\pi$
$488$	−7.75789	+	4.99628i	−0.351183	+	0.226171i
$489$		0			0
$490$	9.36251	+	19.6966i	0.422955	+	0.889800i
$491$	5.97797	+	18.3983i	0.269782	+	0.830304i	0.990553	+	0.137131i	$0.0437880\pi$
$491$	5.97797	+	18.3983i	0.269782	+	0.830304i	−0.720771	+	0.693173i	$0.756212\pi$
$492$		0			0
$493$		−	8.39913i		−	0.378278i
$494$	6.09223	+	7.02624i	0.274103	+	0.316126i
$495$		0			0
$496$	−5.69536	+	19.4894i	−0.255729	+	0.875099i
$497$	−2.85050	−	2.07101i	−0.127862	−	0.0928974i
$498$		0			0
$499$		−	37.2376i		−	1.66698i	−0.552533	−	0.833491i	$-0.686339\pi$
$499$		−	37.2376i		−	1.66698i	0.552533	−	0.833491i	$-0.313661\pi$
$500$	−22.3592	−	0.256433i	−0.999934	−	0.0114680i
$501$		0			0
$502$	5.67887	+	1.31864i	0.253460	+	0.0588537i
$503$	−8.59268	+	11.8268i	−0.383129	+	0.527331i	−0.956410	−	0.292027i	$-0.905670\pi$
$503$	−8.59268	+	11.8268i	−0.383129	+	0.527331i	0.573281	+	0.819359i	$0.305670\pi$
$504$		0			0
$505$	−6.87768	+	5.46996i	−0.306053	+	0.243410i
$506$	10.9607	−	9.50367i	0.487262	−	0.422490i
$507$		0			0
$508$	−16.9204	+	17.4332i	−0.750723	+	0.773471i
$509$	−8.42153	+	2.73632i	−0.373278	+	0.121285i	−0.489647	−	0.871921i	$-0.662874\pi$
$509$	−8.42153	+	2.73632i	−0.373278	+	0.121285i	0.116369	+	0.993206i	$0.462874\pi$
$510$		0			0
$511$	−2.16912	−	0.704791i	−0.0959564	−	0.0311781i
$512$	10.5015	−	20.0429i	0.464104	−	0.885781i
$513$		0			0
$514$	−41.5224	−	9.64153i	−1.83147	−	0.425270i
$515$	1.49393	+	34.2723i	0.0658306	+	1.51022i
$516$		0			0
$517$	9.54902	+	13.1431i	0.419965	+	0.578033i
$518$	1.78735	−	0.154095i	0.0785316	−	0.00677054i
$519$		0			0
$520$	−7.02625	−	22.5885i	−0.308122	−	0.990572i
$521$	14.1825	−	19.5206i	0.621349	−	0.855213i	−0.376102	−	0.926578i	$-0.622736\pi$
$521$	14.1825	−	19.5206i	0.621349	−	0.855213i	0.997450	+	0.0713654i	$0.0227357\pi$
$522$		0			0
$523$	−3.36413	+	10.3537i	−0.147103	+	0.452737i	−0.997275	−	0.0737676i	$-0.976498\pi$
$523$	−3.36413	+	10.3537i	−0.147103	+	0.452737i	0.850172	+	0.526505i	$0.176498\pi$
$524$	13.6619	−	2.37333i	0.596821	−	0.103680i
$525$		0			0
$526$	39.7368	−	3.42588i	1.73261	−	0.149375i
$527$	−7.76977	−	2.52455i	−0.338457	−	0.109971i
$528$		0			0
$529$	−14.5367	−	10.5615i	−0.632029	−	0.459196i
$530$	−3.27949	+	17.5636i	−0.142452	+	0.762914i
$531$		0			0
$532$	0.193653	+	1.11475i	0.00839594	+	0.0483304i
$533$	−18.0393	+	13.1063i	−0.781370	+	0.567699i
$534$		0			0
$535$	23.3982	−	18.6091i	1.01159	−	0.804540i
$536$	39.2922	+	2.20876i	1.69716	+	0.0954038i
$537$		0			0
$538$	−9.87003	−	23.3344i	−0.425527	−	1.00602i
$539$	9.74581	−	29.9945i	0.419782	−	1.29196i
$540$		0			0
$541$	13.6200	+	41.9181i	0.585571	+	1.80220i	0.596967	+	0.802266i	$0.296372\pi$
$541$	13.6200	+	41.9181i	0.585571	+	1.80220i	−0.0113966	+	0.999935i	$0.503628\pi$
$542$	−26.5007	+	22.9779i	−1.13830	+	0.986986i
$543$		0			0
$544$	7.93468	+	4.46410i	0.340197	+	0.191397i
$545$	−16.3111	+	24.6396i	−0.698689	+	1.05544i
$546$		0			0
$547$	19.6030	+	14.2424i	0.838164	+	0.608961i	0.921857	−	0.387530i	$-0.126672\pi$
$547$	19.6030	+	14.2424i	0.838164	+	0.608961i	−0.0836935	+	0.996492i	$0.526672\pi$
$548$	1.99641	−	13.9490i	0.0852823	−	0.595873i
$549$		0			0
$550$	23.2294	+	22.4956i	0.990506	+	0.959216i
$551$	9.17496			0.390866
$552$		0			0
$553$	2.93249	−	4.03623i	0.124702	−	0.171638i
$554$	−8.19789	−	4.93991i	−0.348295	−	0.209877i
$555$		0			0
$556$	−1.72626	−	1.67549i	−0.0732096	−	0.0710565i
$557$	0.256453			0.0108663			0.00543314	−	0.999985i	$-0.498271\pi$
$557$	0.256453			0.0108663			0.00543314	+	0.999985i	$0.498271\pi$
$558$		0			0
$559$	−3.71988	+	1.20866i	−0.157334	+	0.0511209i
$560$	0.686232	−	2.79511i	0.0289986	−	0.118115i
$561$		0			0
$562$	3.57119	+	8.44287i	0.150641	+	0.356141i
$563$	−18.3999	+	5.97851i	−0.775465	+	0.251964i	−0.669903	−	0.742449i	$-0.733664\pi$
$563$	−18.3999	+	5.97851i	−0.775465	+	0.251964i	−0.105562	+	0.994413i	$0.533664\pi$
$564$		0			0
$565$	−2.34789	+	3.54674i	−0.0987767	+	0.149212i
$566$	−21.4870	+	9.08861i	−0.903164	+	0.382023i
$567$		0			0
$568$	−7.90211	−	29.9452i	−0.331565	−	1.25647i
$569$	6.62973	+	9.12504i	0.277933	+	0.382542i	0.925048	−	0.379851i	$-0.124025\pi$
$569$	6.62973	+	9.12504i	0.277933	+	0.382542i	−0.647115	+	0.762392i	$0.724025\pi$
$570$		0			0
$571$	12.9073	−	17.7654i	0.540154	−	0.743458i	−0.448481	−	0.893792i	$-0.648035\pi$
$571$	12.9073	−	17.7654i	0.540154	−	0.743458i	0.988635	+	0.150334i	$0.0480349\pi$
$572$	−15.0744	+	30.7096i	−0.630292	+	1.28403i
$573$		0			0
$574$	−2.70284	+	0.233023i	−0.112814	+	0.00972621i
$575$	−5.77787	+	9.61292i	−0.240954	+	0.400886i
$576$		0			0
$577$	27.8575	+	9.05144i	1.15972	+	0.376816i	0.824797	−	0.565429i	$-0.191289\pi$
$577$	27.8575	+	9.05144i	1.15972	+	0.376816i	0.334924	+	0.942245i	$0.391289\pi$
$578$	10.5178	−	17.4545i	0.437482	−	0.726011i
$579$		0			0
$580$	−21.3789	−	9.36199i	−0.887710	−	0.388735i
$581$	−2.67669	−	3.68414i	−0.111048	−	0.152844i
$582$		0			0
$583$	20.9037	−	15.1874i	0.865742	−	0.628999i
$584$	−10.8548	−	16.8545i	−0.449173	−	0.697446i
$585$		0			0
$586$	16.0572	+	3.72850i	0.663317	+	0.154023i
$587$	−20.2924	+	6.59341i	−0.837558	+	0.272139i	−0.696225	−	0.717823i	$-0.745139\pi$
$587$	−20.2924	+	6.59341i	−0.837558	+	0.272139i	−0.141332	+	0.989962i	$0.545139\pi$
$588$		0			0
$589$	2.75774	−	8.48746i	0.113631	−	0.349720i
$590$	−5.09217	+	4.81938i	−0.209641	+	0.198411i
$591$		0			0
$592$	13.0282	+	8.88384i	0.535454	+	0.365123i
$593$	−0.0961650			−0.00394902			−0.00197451	−	0.999998i	$-0.500629\pi$
$593$	−0.0961650			−0.00394902			−0.00197451	+	0.999998i	$0.500629\pi$
$594$		0			0
$595$	1.11589	+	0.309547i	0.0457469	+	0.0126902i
$596$	20.2519	−	41.2573i	0.829550	−	1.68997i
$597$		0			0
$598$	−11.5579	−	2.68377i	−0.472640	−	0.109747i
$599$	15.2194			0.621846			0.310923	−	0.950435i	$-0.399362\pi$
$599$	15.2194			0.621846			0.310923	+	0.950435i	$0.399362\pi$
$600$		0			0
$601$	38.1539			1.55633			0.778165	−	0.628060i	$-0.216151\pi$
$601$	38.1539			1.55633			0.778165	+	0.628060i	$0.216151\pi$
$602$	−0.463538	−	0.107634i	−0.0188924	−	0.00438683i
$603$		0			0
$604$	14.2555	−	29.0414i	0.580048	−	1.18168i
$605$	−0.965326	−	22.1455i	−0.0392461	−	0.900342i
$606$		0			0
$607$	−36.5306			−1.48273			−0.741365	−	0.671102i	$-0.765821\pi$
$607$	−36.5306			−1.48273			−0.741365	+	0.671102i	$0.765821\pi$
$608$	−4.87645	+	8.66761i	−0.197766	+	0.351518i
$609$		0			0
$610$	−10.2302	+	1.33294i	−0.414210	+	0.0539692i
$611$	4.10606	−	12.6371i	0.166113	−	0.511244i
$612$		0			0
$613$	−9.84314	+	3.19823i	−0.397561	+	0.129175i	−0.500972	−	0.865463i	$-0.667024\pi$
$613$	−9.84314	+	3.19823i	−0.397561	+	0.129175i	0.103411	+	0.994639i	$0.467024\pi$
$614$	22.8738	+	5.31132i	0.923112	+	0.214348i
$615$		0			0
$616$	−3.49925	+	2.25361i	−0.140989	+	0.0908005i
$617$	23.9803	−	17.4227i	0.965411	−	0.701412i	0.0110096	−	0.999939i	$-0.496495\pi$
$617$	23.9803	−	17.4227i	0.965411	−	0.701412i	0.954401	+	0.298527i	$0.0964955\pi$
$618$		0			0
$619$	−15.5116	−	21.3499i	−0.623464	−	0.858124i	0.374136	−	0.927374i	$-0.377939\pi$
$619$	−15.5116	−	21.3499i	−0.623464	−	0.858124i	−0.997599	+	0.0692499i	$0.977939\pi$
$620$	−15.0864	+	16.9630i	−0.605884	+	0.681249i
$621$		0			0
$622$	−8.52912	+	14.1543i	−0.341987	+	0.567534i
$623$	−4.16274	−	1.35256i	−0.166777	−	0.0541891i
$624$		0			0
$625$	−22.4668	−	10.9656i	−0.898670	−	0.438625i
$626$	−35.1133	+	3.02726i	−1.40341	+	0.120994i
$627$		0			0
$628$	16.7435	−	34.1100i	0.668138	−	1.36114i
$629$	−3.72930	+	5.13294i	−0.148697	+	0.204664i
$630$		0			0
$631$	7.90252	+	10.8769i	0.314594	+	0.433002i	0.936807	−	0.349846i	$-0.113766\pi$
$631$	7.90252	+	10.8769i	0.314594	+	0.433002i	−0.622213	+	0.782848i	$0.713766\pi$
$632$	42.4015	−	11.1892i	1.68664	−	0.445081i
$633$		0			0
$634$	21.3594	−	9.03465i	0.848290	−	0.358812i
$635$	−25.4425	+	9.51051i	−1.00965	+	0.377413i
$636$		0			0
$637$	−24.5327	+	7.97114i	−0.972019	+	0.315828i
$638$	13.1484	+	31.0849i	0.520549	+	1.23066i
$639$		0			0
$640$	20.2071	−	15.2208i	0.798755	−	0.601657i
$641$	1.18980	−	0.386591i	0.0469945	−	0.0152694i	−0.285425	−	0.958401i	$-0.592135\pi$
$641$	1.18980	−	0.386591i	0.0469945	−	0.0152694i	0.332420	+	0.943131i	$0.392135\pi$
$642$		0			0
$643$	0.561823			0.0221562			0.0110781	−	0.999939i	$-0.496474\pi$
$643$	0.561823			0.0221562			0.0110781	+	0.999939i	$0.496474\pi$
$644$	−1.03591	−	1.00544i	−0.0408204	−	0.0396199i
$645$		0			0
$646$	−3.42735	−	2.06526i	−0.134847	−	0.0812567i
$647$	10.1975	−	14.0356i	0.400904	−	0.551797i	−0.560066	−	0.828448i	$-0.689224\pi$
$647$	10.1975	−	14.0356i	0.400904	−	0.551797i	0.960971	+	0.276650i	$0.0892244\pi$
$648$		0			0
$649$	10.1391			0.397996
$650$	3.71771	−	26.1857i	0.145821	−	1.02709i
$651$		0			0
$652$	1.09424	−	7.64553i	0.0428537	−	0.299422i
$653$	−7.18264	−	5.21849i	−0.281078	−	0.204215i	0.438309	−	0.898824i	$-0.355577\pi$
$653$	−7.18264	−	5.21849i	−0.281078	−	0.204215i	−0.719388	+	0.694609i	$0.755577\pi$
$654$		0			0
$655$	14.9390	+	4.14410i	0.583717	+	0.161923i
$656$	−19.7013	−	13.4342i	−0.769206	−	0.524518i
$657$		0			0
$658$	1.22142	−	1.05906i	0.0476160	−	0.0412863i
$659$	9.04824	+	27.8476i	0.352469	+	1.08479i	0.957462	+	0.288558i	$0.0931760\pi$
$659$	9.04824	+	27.8476i	0.352469	+	1.08479i	−0.604993	+	0.796231i	$0.706824\pi$
$660$		0			0
$661$	−4.56399	+	14.0465i	−0.177519	+	0.546347i	−0.999740	−	0.0228220i	$-0.992735\pi$
$661$	−4.56399	+	14.0465i	−0.177519	+	0.546347i	0.822221	+	0.569169i	$0.192735\pi$
$662$	2.59079	+	6.12506i	0.100694	+	0.238057i
$663$		0			0
$664$	2.24656	−	39.9646i	0.0871833	−	1.55093i
$665$	−0.338140	+	1.21896i	−0.0131125	+	0.0472692i
$666$		0			0
$667$	−9.47064	+	6.88082i	−0.366705	+	0.266427i
$668$	−5.86024	−	33.7339i	−0.226740	−	1.30520i
$669$		0			0
$670$	38.6393	+	21.0463i	1.49277	+	0.813089i
$671$	12.0700	+	8.76940i	0.465959	+	0.338539i
$672$		0			0
$673$	−39.6055	−	12.8686i	−1.52668	−	0.496048i	−0.579016	−	0.815316i	$-0.696563\pi$
$673$	−39.6055	−	12.8686i	−1.52668	−	0.496048i	−0.947664	+	0.319268i	$0.896563\pi$
$674$	0.960622	−	0.0828193i	0.0370018	−	0.00319008i
$675$		0			0
$676$	1.95123	−	0.338966i	0.0750471	−	0.0130372i
$677$	−12.6393	+	38.8997i	−0.485767	+	1.49504i	0.345100	+	0.938566i	$0.387845\pi$
$677$	−12.6393	+	38.8997i	−0.485767	+	1.49504i	−0.830867	+	0.556471i	$0.812155\pi$
$678$		0			0
$679$	−1.13017	+	1.55554i	−0.0433718	+	0.0596962i
$680$	5.87882	+	8.30956i	0.225443	+	0.318657i
$681$		0			0
$682$	32.7077	−	2.81986i	1.25244	−	0.107978i
$683$	−18.0803	−	24.8853i	−0.691822	−	0.952211i	−1.00000		0.000882444i	$-0.999719\pi$
$683$	−18.0803	−	24.8853i	−0.691822	−	0.952211i	0.308178	−	0.951329i	$-0.400281\pi$
$684$		0			0
$685$	8.69637	−	13.1368i	0.332271	−	0.501930i
$686$	−6.15998	−	1.43035i	−0.235189	−	0.0546111i
$687$		0			0
$688$	−2.55850	−	3.30910i	−0.0975417	−	0.126158i
$689$	−20.0990	−	6.53055i	−0.765710	−	0.248794i
$690$		0			0
$691$	−48.6761	+	15.8158i	−1.85173	+	0.601662i	−0.855207	+	0.518287i	$0.826570\pi$
$691$	−48.6761	+	15.8158i	−1.85173	+	0.601662i	−0.996518	+	0.0833754i	$0.973430\pi$
$692$	5.25346	−	5.41265i	0.199707	−	0.205758i
$693$		0			0
$694$	−25.1230	+	21.7833i	−0.953654	+	0.826883i
$695$	−0.941744	−	2.51935i	−0.0357224	−	0.0955645i
$696$		0			0
$697$	5.63947	−	7.76207i	0.213610	−	0.294009i
$698$	1.64082	+	0.381001i	0.0621061	+	0.0144211i
$699$		0			0
$700$	2.03172	−	2.49531i	0.0767918	−	0.0943138i
$701$			8.28321i			0.312853i	0.987690	+	0.156426i	$0.0499974\pi$
$701$			8.28321i			0.312853i	−0.987690	+	0.156426i	$0.950003\pi$
$702$		0			0
$703$	−5.60706	−	4.07377i	−0.211474	−	0.153645i
$704$	−36.3542	−	4.10017i	−1.37015	−	0.154531i
$705$		0			0
$706$	2.73422	+	3.15341i	0.102904	+	0.118680i
$707$		−	1.26460i		−	0.0475600i
$708$		0			0
$709$	−1.35797	−	4.17941i	−0.0509997	−	0.156961i	0.922313	−	0.386444i	$-0.126297\pi$
$709$	−1.35797	−	4.17941i	−0.0509997	−	0.156961i	−0.973313	+	0.229483i	$0.926297\pi$
$710$	6.35551	−	34.0375i	0.238518	−	1.27741i
$711$		0			0
$712$	−20.8313	−	32.3454i	−0.780684	−	1.21219i
$713$	3.51861	+	10.8292i	0.131773	+	0.405556i
$714$		0			0
$715$	−29.9348	+	23.8077i	−1.11950	+	0.890359i
$716$	14.3053	+	27.0694i	0.534615	+	1.01163i
$717$		0			0
$718$	1.31215	+	15.2197i	0.0489691	+	0.567993i
$719$	−3.19616	+	2.32215i	−0.119197	+	0.0866014i	−0.645786	−	0.763518i	$-0.723470\pi$
$719$	−3.19616	+	2.32215i	−0.119197	+	0.0866014i	0.526590	+	0.850119i	$0.323470\pi$
$720$		0			0
$721$	−3.99384	−	2.90170i	−0.148738	−	0.108065i
$722$	−11.6122	+	19.2707i	−0.432161	+	0.717180i
$723$		0			0
$724$	−27.2918	+	4.74112i	−1.01429	+	0.176202i
$725$	−17.1162	−	19.6956i	−0.635680	−	0.731475i
$726$		0			0
$727$	−11.7451	+	36.1477i	−0.435601	+	1.34064i	0.456868	+	0.889534i	$0.348971\pi$
$727$	−11.7451	+	36.1477i	−0.435601	+	1.34064i	−0.892469	+	0.451108i	$0.851029\pi$
$728$	3.17348	+	1.23202i	0.117617	+	0.0456618i
$729$		0			0
$730$	−2.89590	−	22.2259i	−0.107182	−	0.822617i
$731$	1.36156	−	0.989231i	0.0503591	−	0.0365880i
$732$		0			0
$733$	−14.6602	−	20.1780i	−0.541487	−	0.745293i	0.447340	−	0.894364i	$-0.352372\pi$
$733$	−14.6602	−	20.1780i	−0.541487	−	0.745293i	−0.988826	+	0.149071i	$0.952372\pi$
$734$	−41.7545	+	17.6614i	−1.54119	+	0.651895i
$735$		0			0
$736$	−1.46673	−	12.6041i	−0.0540644	−	0.464592i
$737$	−19.6625	−	60.5149i	−0.724277	−	2.22909i
$738$		0			0
$739$	40.1828	+	13.0562i	1.47815	+	0.480279i	0.933559	−	0.358424i	$-0.116686\pi$
$739$	40.1828	+	13.0562i	1.47815	+	0.480279i	0.544589	+	0.838703i	$0.316686\pi$
$740$	8.90840	+	15.2138i	0.327479	+	0.559270i
$741$		0			0
$742$	−1.68439	−	1.94263i	−0.0618361	−	0.0713163i
$743$			15.9381i			0.584712i	0.956310	+	0.292356i	$0.0944392\pi$
$743$			15.9381i			0.584712i	−0.956310	+	0.292356i	$0.905561\pi$
$744$		0			0
$745$	40.2163	−	31.9849i	1.47341	−	1.17183i
$746$	−8.22853	−	4.95838i	−0.301268	−	0.181539i
$747$		0			0
$748$	2.08550	−	14.5716i	0.0762536	−	0.532789i
$749$			4.30222i			0.157200i
$750$		0			0
$751$		−	31.1098i		−	1.13521i	−0.823300	−	0.567606i	$-0.807870\pi$
$751$		−	31.1098i		−	1.13521i	0.823300	−	0.567606i	$-0.192130\pi$
$752$	14.2035	−	0.424059i	0.517950	−	0.0154638i
$753$		0			0
$754$	14.2477	−	23.6444i	0.518871	−	0.861077i
$755$	28.3086	−	22.5144i	1.03026	−	0.819384i
$756$		0			0
$757$			0.498169i			0.0181063i	0.999959	+	0.00905314i	$0.00288174\pi$
$757$			0.498169i			0.0181063i	−0.999959	+	0.00905314i	$0.997118\pi$
$758$	−5.59886	+	4.85459i	−0.203360	+	0.176327i
$759$		0			0
$760$	−9.07711	+	6.42185i	−0.329261	+	0.232945i
$761$	39.6388	+	12.8794i	1.43690	+	0.466878i	0.920931	−	0.389726i	$-0.127430\pi$
$761$	39.6388	+	12.8794i	1.43690	+	0.466878i	0.515973	+	0.856605i	$0.327430\pi$
$762$		0			0
$763$	−1.31404	−	4.04419i	−0.0475713	−	0.146409i
$764$	−6.51649	+	45.5312i	−0.235758	+	1.64726i
$765$		0			0
$766$	3.48871	+	8.24789i	0.126052	+	0.298008i
$767$	−4.87441	−	6.70905i	−0.176005	−	0.242250i
$768$		0			0
$769$	0.816236	−	0.593030i	0.0294342	−	0.0213852i	−0.572971	−	0.819576i	$-0.694209\pi$
$769$	0.816236	−	0.593030i	0.0294342	−	0.0213852i	0.602405	+	0.798191i	$0.294209\pi$
$770$	−4.61443	+	0.601232i	−0.166292	+	0.0216669i
$771$		0			0
$772$	−8.14479	+	16.5926i	−0.293138	+	0.597182i
$773$	−7.66092	+	23.5779i	−0.275544	+	0.848038i	0.713531	+	0.700624i	$0.247095\pi$
$773$	−7.66092	+	23.5779i	−0.275544	+	0.848038i	−0.989075	+	0.147414i	$0.952905\pi$
$774$		0			0
$775$	−23.3644	+	9.91371i	−0.839274	+	0.356111i
$776$	−16.3413	+	4.31225i	−0.586619	+	0.154801i
$777$		0			0
$778$	10.0834	+	6.07612i	0.361509	+	0.217839i
$779$	8.47905	+	6.16039i	0.303793	+	0.220719i
$780$		0			0
$781$	−40.5105	+	29.4326i	−1.44958	+	1.05318i
$782$	5.08666	−	0.438542i	0.181899	−	0.0156822i
$783$		0			0
$784$	−16.8733	−	21.8236i	−0.602619	−	0.779413i
$785$	33.2493	−	26.4438i	1.18672	−	0.943821i
$786$		0			0
$787$	−16.1972	−	49.8499i	−0.577368	−	1.77696i	−0.627970	−	0.778237i	$-0.716114\pi$
$787$	−16.1972	−	49.8499i	−0.577368	−	1.77696i	0.0506023	−	0.998719i	$-0.483886\pi$
$788$	−23.7706	−	44.9801i	−0.846793	−	1.60235i
$789$		0			0
$790$	48.1962	+	8.99923i	1.71474	+	0.320178i
$791$	−0.189149	−	0.582140i	−0.00672535	−	0.0206985i
$792$		0			0
$793$		−	12.2026i		−	0.433328i
$794$	19.2515	−	16.6923i	0.683209	−	0.592389i
$795$		0			0
$796$	17.9682	−	36.6050i	0.636867	−	1.29743i
$797$	21.1459	+	15.3634i	0.749026	+	0.544199i	0.895525	−	0.445012i	$-0.146800\pi$
$797$	21.1459	+	15.3634i	0.749026	+	0.544199i	−0.146499	+	0.989211i	$0.546800\pi$
$798$		0			0
$799$			5.71741i			0.202268i
$800$	27.7036	−	5.70163i	0.979471	−	0.201583i
$801$		0			0
$802$	4.39976	−	18.9481i	0.155361	−	0.669080i
$803$	−19.0521	+	26.2230i	−0.672335	+	0.925389i
$804$		0			0
$805$	−0.565130	−	1.51183i	−0.0199182	−	0.0532851i
$806$	−17.5902	−	20.2869i	−0.619587	−	0.714577i
$807$		0			0
$808$	7.02801	−	8.61184i	0.247244	−	0.302963i
$809$	25.4877	−	8.28146i	0.896100	−	0.291161i	0.175474	−	0.984484i	$-0.443854\pi$
$809$	25.4877	−	8.28146i	0.896100	−	0.291161i	0.720626	+	0.693324i	$0.243854\pi$
$810$		0			0
$811$	27.7483	+	9.01598i	0.974375	+	0.316594i	0.752581	−	0.658500i	$-0.228809\pi$
$811$	27.7483	+	9.01598i	0.974375	+	0.316594i	0.221794	+	0.975093i	$0.428809\pi$
$812$	2.96945	−	1.56926i	0.104207	−	0.0550703i
$813$		0			0
$814$	5.76666	−	24.8348i	0.202121	−	0.870459i
$815$	4.76652	−	7.20032i	0.166964	−	0.252216i
$816$		0			0
$817$	1.08061	+	1.48733i	0.0378056	+	0.0520350i
$818$	1.78972	+	20.7590i	0.0625761	+	0.725821i
$819$		0			0
$820$	−13.4714	−	23.0064i	−0.470440	−	0.803419i
$821$	19.7994	−	27.2516i	0.691006	−	0.951088i	−0.308994	−	0.951064i	$-0.599992\pi$
$821$	19.7994	−	27.2516i	0.691006	−	0.951088i	1.00000		2.36846e-5i	$-7.53904e-6\pi$
$822$		0			0
$823$	−13.1730	+	40.5424i	−0.459183	+	1.41322i	0.406971	+	0.913441i	$0.366585\pi$
$823$	−13.1730	+	40.5424i	−0.459183	+	1.41322i	−0.866154	+	0.499778i	$0.833415\pi$
$824$	−11.0717	−	41.9563i	−0.385700	−	1.46162i
$825$		0			0
$826$	−0.0866643	−	1.00522i	−0.00301544	−	0.0349761i
$827$	39.4784	+	12.8273i	1.37280	+	0.446049i	0.900295	−	0.435280i	$-0.143351\pi$
$827$	39.4784	+	12.8273i	1.37280	+	0.446049i	0.472503	+	0.881329i	$0.343351\pi$
$828$		0			0
$829$	−11.5730	−	8.40831i	−0.401948	−	0.292033i	0.368386	−	0.929673i	$-0.379911\pi$
$829$	−11.5730	−	8.40831i	−0.401948	−	0.292033i	−0.770334	+	0.637640i	$0.779911\pi$
$830$	21.4065	−	39.3005i	0.743029	−	1.36414i
$831$		0			0
$832$	14.7643	+	26.0267i	0.511860	+	0.902314i
$833$	8.97952	−	6.52400i	0.311122	−	0.226043i
$834$		0			0
$835$	10.2326	−	36.8875i	0.354115	−	1.27655i
$836$	15.9175	+	2.27814i	0.550519	+	0.0787912i
$837$		0			0
$838$	−34.3980	+	14.5498i	−1.18826	+	0.502614i
$839$	7.36602	−	22.6703i	0.254303	−	0.782665i	−0.739663	−	0.672977i	$-0.765015\pi$
$839$	7.36602	−	22.6703i	0.254303	−	0.782665i	0.993966	−	0.109687i	$-0.0349849\pi$
$840$		0			0
$841$	0.545355	+	1.67843i	0.0188053	+	0.0578769i
$842$	7.55135	+	8.70905i	0.260237	+	0.300134i
$843$		0			0
$844$	25.2912	+	24.5474i	0.870559	+	0.844956i
$845$	2.13364	+	0.591872i	0.0733994	+	0.0203610i
$846$		0			0
$847$	2.58067	+	1.87497i	0.0886730	+	0.0644247i
$848$	−0.674452	−	22.5903i	−0.0231608	−	0.775754i
$849$		0			0
$850$	1.96041	+	11.2102i	0.0672415	+	0.384506i
$851$	8.84291			0.303131
$852$		0			0
$853$	−6.16691	+	8.48802i	−0.211151	+	0.290624i	−0.901435	−	0.432914i	$-0.857485\pi$
$853$	−6.16691	+	8.48802i	−0.211151	+	0.290624i	0.690284	+	0.723538i	$0.257485\pi$
$854$	0.766253	−	1.27161i	0.0262206	−	0.0435137i
$855$		0			0
$856$	−23.9096	+	29.2979i	−0.817214	+	1.00138i
$857$	30.3385			1.03634			0.518172	−	0.855277i	$-0.326613\pi$
$857$	30.3385			1.03634			0.518172	+	0.855277i	$0.326613\pi$
$858$		0			0
$859$	−37.0855	+	12.0498i	−1.26534	+	0.411134i	−0.863395	−	0.504529i	$-0.831666\pi$
$859$	−37.0855	+	12.0498i	−1.26534	+	0.411134i	−0.401946	+	0.915663i	$0.631666\pi$
$860$	−1.00031	−	4.56831i	−0.0341104	−	0.155778i
$861$		0			0
$862$	−35.1380	+	14.8628i	−1.19681	+	0.506228i
$863$	31.8477	−	10.3479i	1.08411	−	0.352248i	0.288141	−	0.957588i	$-0.406963\pi$
$863$	31.8477	−	10.3479i	1.08411	−	0.352248i	0.795967	+	0.605340i	$0.206963\pi$
$864$		0			0
$865$	7.89939	−	2.95282i	0.268587	−	0.100399i
$866$	−4.51800	−	10.6813i	−0.153528	−	0.362965i
$867$		0			0
$868$	−0.559138	−	3.21862i	−0.0189784	−	0.109247i
$869$	−41.6757	−	57.3617i	−1.41375	−	1.94586i
$870$		0			0
$871$	−30.5898	+	42.1033i	−1.03650	+	1.42662i
$872$	13.5271	−	34.8435i	0.458086	−	1.17995i
$873$		0			0
$874$	0.479051	+	5.55651i	0.0162041	+	0.187952i
$875$	3.24751	−	1.54814i	0.109786	−	0.0523366i
$876$		0			0
$877$	−13.5129	−	4.39061i	−0.456299	−	0.148260i	0.0718442	−	0.997416i	$-0.477112\pi$
$877$	−13.5129	−	4.39061i	−0.456299	−	0.148260i	−0.528143	+	0.849155i	$0.677112\pi$
$878$	−2.45182	−	1.47742i	−0.0827448	−	0.0498607i
$879$		0			0
$880$	−34.7654	−	21.5504i	−1.17194	−	0.726463i
$881$	−19.5222	−	26.8700i	−0.657720	−	0.905274i	0.341683	−	0.939815i	$-0.389003\pi$
$881$	−19.5222	−	26.8700i	−0.657720	−	0.905274i	−0.999403	+	0.0345412i	$0.989003\pi$
$882$		0			0
$883$	5.42102	−	3.93860i	0.182432	−	0.132544i	−0.492821	−	0.870131i	$-0.664034\pi$
$883$	5.42102	−	3.93860i	0.182432	−	0.132544i	0.675253	+	0.737586i	$0.264034\pi$
$884$	−10.6446	+	5.62533i	−0.358016	+	0.189200i
$885$		0			0
$886$	3.67924	−	15.8451i	0.123607	−	0.532326i
$887$	2.06908	−	0.672284i	0.0694728	−	0.0225731i	−0.274074	−	0.961708i	$-0.588371\pi$
$887$	2.06908	−	0.672284i	0.0694728	−	0.0225731i	0.343547	+	0.939135i	$0.388371\pi$
$888$		0			0
$889$	1.20787	−	3.71745i	0.0405108	−	0.124679i
$890$	−5.55750	−	42.6535i	−0.186288	−	1.42975i
$891$		0			0
$892$	−5.16017	+	5.31653i	−0.172775	+	0.178011i
$893$	−6.24553			−0.208999
$894$		0			0
$895$	1.49071	+	34.1982i	0.0498288	+	1.14312i
$896$	−0.0957636	+	3.63930i	−0.00319924	+	0.121581i
$897$		0			0
$898$	7.18341	−	30.9362i	0.239714	−	1.03235i
$899$	−26.4910			−0.883523
$900$		0			0
$901$	9.09337			0.302944
$902$	−8.72039	+	37.5554i	−0.290357	+	1.25046i
$903$		0			0
$904$	1.94716	−	5.01555i	0.0647615	−	0.166815i
$905$	−29.8432	−	8.27851i	−0.992020	−	0.275187i
$906$		0			0
$907$	0.618420			0.0205343			0.0102672	−	0.999947i	$-0.496732\pi$
$907$	0.618420			0.0205343			0.0102672	+	0.999947i	$0.496732\pi$
$908$	−15.6957	−	15.2341i	−0.520881	−	0.505562i
$909$		0			0
$910$	2.61623	+	2.76432i	0.0867272	+	0.0916362i
$911$	−13.7397	+	42.2864i	−0.455216	+	1.40101i	0.415666	+	0.909517i	$0.363548\pi$
$911$	−13.7397	+	42.2864i	−0.455216	+	1.40101i	−0.870882	+	0.491492i	$0.836452\pi$
$912$		0			0
$913$	−61.5505	+	19.9990i	−2.03702	+	0.661869i
$914$	−6.36111	+	27.3948i	−0.210407	+	0.906141i
$915$		0			0
$916$	18.7992	+	35.5730i	0.621144	+	1.17537i
$917$	−1.80492	+	1.31135i	−0.0596036	+	0.0433045i
$918$		0			0
$919$	0.873532	+	1.20231i	0.0288152	+	0.0396607i	0.823182	−	0.567778i	$-0.192197\pi$
$919$	0.873532	+	1.20231i	0.0288152	+	0.0396607i	−0.794366	+	0.607439i	$0.792197\pi$
$920$	4.55353	−	13.4362i	0.150125	−	0.442980i
$921$		0			0
$922$	−19.2504	−	11.6000i	−0.633977	−	0.382024i
$923$	38.9510	+	12.6559i	1.28209	+	0.416575i
$924$		0			0
$925$	1.71515	+	19.6362i	0.0563939	+	0.645636i
$926$	−1.30181	−	15.0997i	−0.0427802	−	0.496208i
$927$		0			0
$928$	28.9430	+	5.81616i	0.950101	+	0.190925i
$929$	16.2714	−	22.3957i	0.533847	−	0.734777i	−0.453864	−	0.891071i	$-0.649955\pi$
$929$	16.2714	−	22.3957i	0.533847	−	0.734777i	0.987711	+	0.156294i	$0.0499546\pi$
$930$		0			0
$931$	7.12662	+	9.80895i	0.233566	+	0.321475i
$932$	55.8145	−	9.69607i	1.82826	−	0.317605i
$933$		0			0
$934$	15.5617	+	36.7905i	0.509196	+	1.20382i
$935$	9.08448	−	13.7230i	0.297094	−	0.448792i
$936$		0			0
$937$	−29.2129	+	9.49185i	−0.954344	+	0.310085i	−0.744480	−	0.667645i	$-0.767302\pi$
$937$	−29.2129	+	9.49185i	−0.954344	+	0.310085i	−0.209865	+	0.977730i	$0.567302\pi$
$938$	−5.83154	+	2.46664i	−0.190407	+	0.0805387i
$939$		0			0
$940$	14.5529	+	6.37284i	0.474664	+	0.207859i
$941$	−6.93022	+	2.25176i	−0.225919	+	0.0734054i	−0.419789	−	0.907622i	$-0.637896\pi$
$941$	−6.93022	+	2.25176i	−0.225919	+	0.0734054i	0.193870	+	0.981027i	$0.437896\pi$
$942$		0			0
$943$	−13.3723			−0.435463
$944$	4.99635	−	7.32715i	0.162617	−	0.238478i
$945$		0			0
$946$	−3.49050	+	5.79255i	−0.113486	+	0.188332i
$947$	4.45747	−	6.13518i	0.144848	−	0.199367i	−0.730428	−	0.682990i	$-0.760679\pi$
$947$	4.45747	−	6.13518i	0.144848	−	0.199367i	0.875276	+	0.483623i	$0.160679\pi$
$948$		0			0
$949$	26.5111			0.860585
$950$	−12.2457	+	2.14149i	−0.397302	+	0.0694792i
$951$		0			0
$952$	−1.46249	−	0.0822119i	−0.0473995	−	0.00266450i
$953$	38.6087	+	28.0508i	1.25066	+	0.908656i	0.998260	−	0.0589678i	$-0.0187809\pi$
$953$	38.6087	+	28.0508i	1.25066	+	0.908656i	0.252398	+	0.967624i	$0.418781\pi$
$954$		0			0
$955$	−28.3859	+	42.8798i	−0.918546	+	1.38756i
$956$	34.6819	−	35.7328i	1.12169	−	1.15568i
$957$		0			0
$958$	−6.77943	−	7.81879i	−0.219033	−	0.252614i
$959$	0.700589	+	2.15619i	0.0226232	+	0.0696270i
$960$		0			0
$961$	1.61706	−	4.97680i	0.0521633	−	0.160542i
$962$	−19.2055	+	8.12359i	−0.619209	+	0.261915i
$963$		0			0
$964$	5.38646	−	37.6355i	0.173486	−	1.21216i
$965$	−16.1740	+	12.8635i	−0.520658	+	0.414090i
$966$		0			0
$967$	10.5626	−	7.67421i	0.339672	−	0.246786i	−0.404852	−	0.914382i	$-0.632677\pi$
$967$	10.5626	−	7.67421i	0.339672	−	0.246786i	0.744523	+	0.667597i	$0.232677\pi$
$968$	7.15411	+	27.1106i	0.229942	+	0.871368i
$969$		0			0
$970$	−18.5746	−	3.46826i	−0.596393	−	0.111359i
$971$	25.1655	+	18.2838i	0.807598	+	0.586755i	0.913133	−	0.407661i	$-0.133656\pi$
$971$	25.1655	+	18.2838i	0.807598	+	0.586755i	−0.105535	+	0.994416i	$0.533656\pi$
$972$		0			0
$973$	0.368107	+	0.119605i	0.0118010	+	0.00383437i
$974$	−0.801452	−	9.29606i	−0.0256802	−	0.297865i
$975$		0			0
$976$	12.2852	−	4.40117i	0.393238	−	0.140878i
$977$	−13.2325	+	40.7253i	−0.423344	+	1.30292i	0.481227	+	0.876596i	$0.340191\pi$
$977$	−13.2325	+	40.7253i	−0.423344	+	1.30292i	−0.904571	+	0.426323i	$0.859809\pi$
$978$		0			0
$979$	−36.5627	+	50.3243i	−1.16855	+	1.60837i
$980$	−6.59708	−	30.1281i	−0.210736	−	0.962406i
$981$		0			0
$982$	−2.34994	−	27.2570i	−0.0749897	−	0.869807i
$983$	19.6002	+	26.9774i	0.625150	+	0.860445i	0.997715	−	0.0675608i	$-0.0215217\pi$
$983$	19.6002	+	26.9774i	0.625150	+	0.860445i	−0.372565	+	0.928006i	$0.621522\pi$
$984$		0			0
$985$	−2.47705	−	56.8259i	−0.0789254	−	1.81062i
$986$	−2.68664	+	11.5703i	−0.0855602	+	0.368475i
$987$		0			0
$988$	−6.14494	−	11.6278i	−0.195497	−	0.369931i
$989$	−2.23086	−	0.724851i	−0.0709373	−	0.0230489i
$990$		0			0
$991$	22.1874	−	7.20911i	0.704805	−	0.229005i	0.0653819	−	0.997860i	$-0.479173\pi$
$991$	22.1874	−	7.20911i	0.704805	−	0.229005i	0.639423	+	0.768855i	$0.279173\pi$
$992$	14.0798	−	25.0261i	0.447035	−	0.794579i
$993$		0			0
$994$	3.26429	+	3.76474i	0.103537	+	0.119410i
$995$	35.6814	−	28.3782i	1.13118	−	0.899648i
$996$		0			0
$997$	−34.8864	+	48.0170i	−1.10486	+	1.52071i	−0.276085	+	0.961133i	$0.589037\pi$
$997$	−34.8864	+	48.0170i	−1.10486	+	1.52071i	−0.828777	+	0.559579i	$0.810963\pi$
$998$	−11.9112	+	51.2971i	−0.377044	+	1.62378i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.z.b.179.4	✓	224
3.2	odd	2	inner	900.2.z.b.179.53	yes	224
4.3	odd	2	inner	900.2.z.b.179.48	yes	224
12.11	even	2	inner	900.2.z.b.179.9	yes	224
25.19	even	10	inner	900.2.z.b.719.9	yes	224
75.44	odd	10	inner	900.2.z.b.719.48	yes	224
100.19	odd	10	inner	900.2.z.b.719.53	yes	224
300.119	even	10	inner	900.2.z.b.719.4	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.z.b.179.4	✓	224	1.1	even	1	trivial
900.2.z.b.179.9	yes	224	12.11	even	2	inner
900.2.z.b.179.48	yes	224	4.3	odd	2	inner
900.2.z.b.179.53	yes	224	3.2	odd	2	inner
900.2.z.b.719.4	yes	224	300.119	even	10	inner
900.2.z.b.719.9	yes	224	25.19	even	10	inner
900.2.z.b.719.48	yes	224	75.44	odd	10	inner
900.2.z.b.719.53	yes	224	100.19	odd	10	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37756 - 0.319872i) q^{2} +(1.79536 + 0.881287i) q^{4} +(1.39186 + 1.75006i) q^{5} -0.321783 q^{7} +(-2.19133 - 1.78832i) q^{8} +(-1.35758 - 2.85604i) q^{10} +(-1.41316 + 4.34927i) q^{11} +(3.55729 - 1.15583i) q^{13} +(0.443277 + 0.102929i) q^{14} +(2.44667 + 3.16446i) q^{16} +(-1.30205 + 0.945993i) q^{17} +(-1.03337 - 1.42232i) q^{19} +(0.956590 + 4.36863i) q^{20} +(3.33793 - 5.53936i) q^{22} +(2.13335 + 0.693169i) q^{23} +(-1.12544 + 4.87169i) q^{25} +(-5.27011 + 0.454358i) q^{26} +(-0.577718 - 0.283583i) q^{28} +(-3.06750 + 4.22205i) q^{29} +(2.98367 + 4.10667i) q^{31} +(-2.35822 - 5.14187i) q^{32} +(2.09625 - 0.886678i) q^{34} +(-0.447878 - 0.563141i) q^{35} +(3.74926 - 1.21821i) q^{37} +(0.968580 + 2.28988i) q^{38} +(0.0796366 - 6.32405i) q^{40} +(-5.66966 + 1.84218i) q^{41} -1.04571 q^{43} +(-6.37010 + 6.56312i) q^{44} +(-2.71711 - 1.63728i) q^{46} +(2.08809 - 2.87401i) q^{47} -6.89646 q^{49} +(3.10869 - 6.35107i) q^{50} +(7.40524 + 1.05985i) q^{52} +(-4.57102 - 3.32104i) q^{53} +(-9.57842 + 3.58045i) q^{55} +(0.705133 + 0.575450i) q^{56} +(5.57618 - 4.83493i) q^{58} +(-0.685131 - 2.10862i) q^{59} +(1.00815 - 3.10276i) q^{61} +(-2.79659 - 6.61160i) q^{62} +(1.60386 + 7.83758i) q^{64} +(6.97403 + 4.61672i) q^{65} +(-11.2565 + 8.17833i) q^{67} +(-3.17134 + 0.550924i) q^{68} +(0.436847 + 0.919026i) q^{70} +(8.85844 + 6.43603i) q^{71} +(6.74095 + 2.19027i) q^{73} +(-5.55451 + 0.478878i) q^{74} +(-0.601813 - 3.46428i) q^{76} +(0.454732 - 1.39952i) q^{77} +(-9.11325 + 12.5433i) q^{79} +(-2.13259 + 8.68631i) q^{80} +(8.39958 - 0.724163i) q^{82} +(8.31829 + 11.4491i) q^{83} +(-3.46782 - 0.961975i) q^{85} +(1.44053 + 0.334492i) q^{86} +(10.8746 - 7.00350i) q^{88} +(12.9365 + 4.20332i) q^{89} +(-1.14467 + 0.371927i) q^{91} +(3.21927 + 3.12459i) q^{92} +(-3.79579 + 3.29121i) q^{94} +(1.05083 - 3.78814i) q^{95} +(3.51220 - 4.83412i) q^{97} +(9.50031 + 2.20598i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 8 q^{4} - 12 q^{10} - 8 q^{16} - 8 q^{25} + 92 q^{34} + 40 q^{37} + 36 q^{40} - 40 q^{46} + 368 q^{49} - 100 q^{52} - 120 q^{58} + 48 q^{61} - 16 q^{64} - 40 q^{70} + 24 q^{76} - 120 q^{85} - 120 q^{88}+ \cdots + 200 q^{97}+O(q^{100}) \) 224 * q + 8 * q^4 - 12 * q^10 - 8 * q^16 - 8 * q^25 + 92 * q^34 + 40 * q^37 + 36 * q^40 - 40 * q^46 + 368 * q^49 - 100 * q^52 - 120 * q^58 + 48 * q^61 - 16 * q^64 - 40 * q^70 + 24 * q^76 - 120 * q^85 - 120 * q^88 - 4 * q^94 + 200 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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