LMFDB - Embedded newform 888.2.br.a.785.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [888,2,Mod(473,888)] 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("888.473"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(888, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.br (of order $12$, degree $4$, 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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			785.27
Character	$\chi$	$=$	888.785
Dual form			888.2.br.a.569.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.996973 - 1.41635i) q^{3} +(-0.601400 - 2.24446i) q^{5} +(-0.786614 + 1.36246i) q^{7} +(-1.01209 - 2.82412i) q^{9} -0.738125 q^{11} +(-5.22905 + 1.40112i) q^{13} +(-3.77851 - 1.38587i) q^{15} +(-6.88427 - 1.84463i) q^{17} +(-2.79810 + 0.749750i) q^{19} +(1.14548 + 2.47245i) q^{21} +(5.90122 - 5.90122i) q^{23} +(-0.345771 + 0.199631i) q^{25} +(-5.00897 - 1.38210i) q^{27} +(5.65819 + 5.65819i) q^{29} +(-1.19809 + 1.19809i) q^{31} +(-0.735890 + 1.04544i) q^{33} +(3.53104 + 0.946139i) q^{35} +(4.55273 - 4.03393i) q^{37} +(-3.22875 + 8.80304i) q^{39} +(-4.27854 + 7.41065i) q^{41} +(-7.64204 - 7.64204i) q^{43} +(-5.72995 + 3.97002i) q^{45} -10.6754i q^{47} +(2.26248 + 3.91872i) q^{49} +(-9.47607 + 7.91148i) q^{51} +(4.00020 - 2.30952i) q^{53} +(0.443908 + 1.65669i) q^{55} +(-1.72773 + 4.71057i) q^{57} +(-2.81778 - 0.755023i) q^{59} +(-2.69213 - 10.0472i) q^{61} +(4.64387 + 0.842568i) q^{63} +(6.28950 + 10.8937i) q^{65} +(-5.21175 - 3.00900i) q^{67} +(-2.47483 - 14.2415i) q^{69} +(2.51092 + 1.44968i) q^{71} +14.9577i q^{73} +(-0.0619772 + 0.688760i) q^{75} +(0.580619 - 1.00566i) q^{77} +(-1.59192 + 0.426553i) q^{79} +(-6.95135 + 5.71653i) q^{81} +(12.2447 - 7.06950i) q^{83} +16.5608i q^{85} +(13.6550 - 2.37291i) q^{87} +(3.62290 - 13.5208i) q^{89} +(2.20428 - 8.22649i) q^{91} +(0.502450 + 2.89138i) q^{93} +(3.36556 + 5.82932i) q^{95} +(0.824155 + 0.824155i) q^{97} +(0.747049 + 2.08456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) $ 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.996973	−	1.41635i	0.575603	−	0.817730i
$3$	0.996973	−	1.41635i	0.575603	−	0.817730i
$4$		0			0
$5$	−0.601400	−	2.24446i	−0.268954	−	1.00375i	−0.959785	−	0.280735i	$-0.909422\pi$
$5$	−0.601400	−	2.24446i	−0.268954	−	1.00375i	0.690831	−	0.723016i	$-0.257245\pi$
$6$		0			0
$7$	−0.786614	+	1.36246i	−0.297312	+	0.514960i	−0.975520	−	0.219910i	$-0.929424\pi$
$7$	−0.786614	+	1.36246i	−0.297312	+	0.514960i	0.678208	+	0.734870i	$0.262757\pi$
$8$		0			0
$9$	−1.01209	−	2.82412i	−0.337363	−	0.941375i
$10$		0			0
$11$	−0.738125			−0.222553			−0.111276	−	0.993789i	$-0.535494\pi$
$11$	−0.738125			−0.222553			−0.111276	+	0.993789i	$0.535494\pi$
$12$		0			0
$13$	−5.22905	+	1.40112i	−1.45028	+	0.388601i	−0.896120	−	0.443811i	$-0.853626\pi$
$13$	−5.22905	+	1.40112i	−1.45028	+	0.388601i	−0.554158	+	0.832412i	$0.686960\pi$
$14$		0			0
$15$	−3.77851	−	1.38587i	−0.975608	−	0.357830i
$16$		0			0
$17$	−6.88427	−	1.84463i	−1.66968	−	0.447389i	−0.704656	−	0.709549i	$-0.748899\pi$
$17$	−6.88427	−	1.84463i	−1.66968	−	0.447389i	−0.965024	+	0.262160i	$0.915565\pi$
$18$		0			0
$19$	−2.79810	+	0.749750i	−0.641929	+	0.172004i	−0.565077	−	0.825038i	$-0.691154\pi$
$19$	−2.79810	+	0.749750i	−0.641929	+	0.172004i	−0.0768521	+	0.997043i	$0.524487\pi$
$20$		0			0
$21$	1.14548	+	2.47245i	0.249964	+	0.539533i
$22$		0			0
$23$	5.90122	−	5.90122i	1.23049	−	1.23049i	0.266713	−	0.963776i	$-0.414062\pi$
$23$	5.90122	−	5.90122i	1.23049	−	1.23049i	0.963776	−	0.266713i	$-0.0859376\pi$
$24$		0			0
$25$	−0.345771	+	0.199631i	−0.0691542	+	0.0399262i
$26$		0			0
$27$	−5.00897	−	1.38210i	−0.963977	−	0.265986i
$28$		0			0
$29$	5.65819	+	5.65819i	1.05070	+	1.05070i	0.998644	+	0.0520557i	$0.0165773\pi$
$29$	5.65819	+	5.65819i	1.05070	+	1.05070i	0.0520557	+	0.998644i	$0.483423\pi$
$30$		0			0
$31$	−1.19809	+	1.19809i	−0.215183	+	0.215183i	−0.806465	−	0.591282i	$-0.798622\pi$
$31$	−1.19809	+	1.19809i	−0.215183	+	0.215183i	0.591282	+	0.806465i	$0.298622\pi$
$32$		0			0
$33$	−0.735890	+	1.04544i	−0.128102	+	0.181988i
$34$		0			0
$35$	3.53104	+	0.946139i	0.596855	+	0.159927i
$36$		0			0
$37$	4.55273	−	4.03393i	0.748465	−	0.663175i
$37$	4.55273	−	4.03393i	0.748465	−	0.663175i
$38$		0			0
$39$	−3.22875	+	8.80304i	−0.517013	+	1.40962i
$40$		0			0
$41$	−4.27854	+	7.41065i	−0.668196	+	1.15735i	0.310212	+	0.950667i	$0.399600\pi$
$41$	−4.27854	+	7.41065i	−0.668196	+	1.15735i	−0.978408	+	0.206682i	$0.933733\pi$
$42$		0			0
$43$	−7.64204	−	7.64204i	−1.16540	−	1.16540i	−0.983275	−	0.182125i	$-0.941702\pi$
$43$	−7.64204	−	7.64204i	−1.16540	−	1.16540i	−0.182125	−	0.983275i	$-0.558298\pi$
$44$		0			0
$45$	−5.72995	+	3.97002i	−0.854170	+	0.591815i
$46$		0			0
$47$		−	10.6754i		−	1.55717i	−0.627540	−	0.778584i	$-0.715938\pi$
$47$		−	10.6754i		−	1.55717i	0.627540	−	0.778584i	$-0.284062\pi$
$48$		0			0
$49$	2.26248	+	3.91872i	0.323211	+	0.559818i
$50$		0			0
$51$	−9.47607	+	7.91148i	−1.32692	+	1.10783i
$52$		0			0
$53$	4.00020	−	2.30952i	0.549470	−	0.317237i	−0.199438	−	0.979910i	$-0.563912\pi$
$53$	4.00020	−	2.30952i	0.549470	−	0.317237i	0.748908	+	0.662674i	$0.230578\pi$
$54$		0			0
$55$	0.443908	+	1.65669i	0.0598566	+	0.223388i
$56$		0			0
$57$	−1.72773	+	4.71057i	−0.228843	+	0.623931i
$58$		0			0
$59$	−2.81778	−	0.755023i	−0.366844	−	0.0982956i	0.0706878	−	0.997498i	$-0.477481\pi$
$59$	−2.81778	−	0.755023i	−0.366844	−	0.0982956i	−0.437532	+	0.899203i	$0.644147\pi$
$60$		0			0
$61$	−2.69213	−	10.0472i	−0.344692	−	1.28641i	−0.892972	−	0.450112i	$-0.851384\pi$
$61$	−2.69213	−	10.0472i	−0.344692	−	1.28641i	0.548280	−	0.836295i	$-0.315283\pi$
$62$		0			0
$63$	4.64387	+	0.842568i	0.585072	+	0.106154i
$64$		0			0
$65$	6.28950	+	10.8937i	0.780117	+	1.35120i
$66$		0			0
$67$	−5.21175	−	3.00900i	−0.636716	−	0.367608i	0.146632	−	0.989191i	$-0.453157\pi$
$67$	−5.21175	−	3.00900i	−0.636716	−	0.367608i	−0.783348	+	0.621583i	$0.786490\pi$
$68$		0			0
$69$	−2.47483	−	14.2415i	−0.297935	−	1.71448i
$70$		0			0
$71$	2.51092	+	1.44968i	0.297991	+	0.172045i	0.641540	−	0.767089i	$-0.278296\pi$
$71$	2.51092	+	1.44968i	0.297991	+	0.172045i	−0.343549	+	0.939135i	$0.611629\pi$
$72$		0			0
$73$			14.9577i			1.75067i	0.483517	+	0.875335i	$0.339359\pi$
$73$			14.9577i			1.75067i	−0.483517	+	0.875335i	$0.660641\pi$
$74$		0			0
$75$	−0.0619772	+	0.688760i	−0.00715651	+	0.0795311i
$76$		0			0
$77$	0.580619	−	1.00566i	0.0661677	−	0.114606i
$78$		0			0
$79$	−1.59192	+	0.426553i	−0.179105	+	0.0479910i	−0.347257	−	0.937770i	$-0.612887\pi$
$79$	−1.59192	+	0.426553i	−0.179105	+	0.0479910i	0.168152	+	0.985761i	$0.446220\pi$
$80$		0			0
$81$	−6.95135	+	5.71653i	−0.772372	+	0.635170i
$82$		0			0
$83$	12.2447	−	7.06950i	1.34403	−	0.775979i	0.356638	−	0.934243i	$-0.383923\pi$
$83$	12.2447	−	7.06950i	1.34403	−	0.775979i	0.987397	+	0.158264i	$0.0505896\pi$
$84$		0			0
$85$			16.5608i			1.79627i
$86$		0			0
$87$	13.6550	−	2.37291i	1.46397	−	0.254403i
$88$		0			0
$89$	3.62290	−	13.5208i	0.384027	−	1.43321i	−0.455669	−	0.890149i	$-0.650600\pi$
$89$	3.62290	−	13.5208i	0.384027	−	1.43321i	0.839695	−	0.543058i	$-0.182733\pi$
$90$		0			0
$91$	2.20428	−	8.22649i	0.231072	−	0.862371i
$92$		0			0
$93$	0.502450	+	2.89138i	0.0521017	+	0.299822i
$94$		0			0
$95$	3.36556	+	5.82932i	0.345299	+	0.598076i
$96$		0			0
$97$	0.824155	+	0.824155i	0.0836803	+	0.0836803i	0.747708	−	0.664028i	$-0.231154\pi$
$97$	0.824155	+	0.824155i	0.0836803	+	0.0836803i	−0.664028	+	0.747708i	$0.731154\pi$
$98$		0			0
$99$	0.747049	+	2.08456i	0.0750812	+	0.209506i
$100$		0			0
$101$	−3.91158			−0.389217			−0.194608	−	0.980881i	$-0.562344\pi$
$101$	−3.91158			−0.389217			−0.194608	+	0.980881i	$0.562344\pi$
$102$		0			0
$103$	3.04766	−	3.04766i	0.300295	−	0.300295i	−0.540834	−	0.841129i	$-0.681891\pi$
$103$	3.04766	−	3.04766i	0.300295	−	0.300295i	0.841129	+	0.540834i	$0.181891\pi$
$104$		0			0
$105$	4.86042	−	4.05791i	0.474328	−	0.396012i
$106$		0			0
$107$	−9.26572	−	5.34957i	−0.895751	−	0.517162i	−0.0199320	−	0.999801i	$-0.506345\pi$
$107$	−9.26572	−	5.34957i	−0.895751	−	0.517162i	−0.875819	+	0.482639i	$0.839678\pi$
$108$		0			0
$109$	1.28071	−	4.77966i	0.122669	−	0.457809i	−0.877076	−	0.480351i	$-0.840509\pi$
$109$	1.28071	−	4.77966i	0.122669	−	0.457809i	0.999746	+	0.0225422i	$0.00717600\pi$
$110$		0			0
$111$	−1.17451	−	10.4700i	−0.111479	−	0.993767i
$112$		0			0
$113$	−2.34298	+	8.74411i	−0.220409	+	0.822577i	0.763783	+	0.645473i	$0.223340\pi$
$113$	−2.34298	+	8.74411i	−0.220409	+	0.822577i	−0.984192	+	0.177104i	$0.943327\pi$
$114$		0			0
$115$	−16.7940	−	9.69603i	−1.56605	−	0.904159i
$116$		0			0
$117$	9.24921	+	13.3494i	0.855090	+	1.23416i
$118$		0			0
$119$	7.92849	−	7.92849i	0.726804	−	0.726804i
$120$		0			0
$121$	−10.4552			−0.950470
$122$		0			0
$123$	6.23048	+	13.4481i	0.561783	+	1.21258i
$124$		0			0
$125$	−7.55927	−	7.55927i	−0.676121	−	0.676121i
$126$		0			0
$127$	1.03336	+	1.78984i	0.0916963	+	0.158823i	0.908225	−	0.418482i	$-0.137438\pi$
$127$	1.03336	+	1.78984i	0.0916963	+	0.158823i	−0.816529	+	0.577305i	$0.804104\pi$
$128$		0			0
$129$	−18.4427	+	3.20489i	−1.62379	+	0.282175i
$130$		0			0
$131$	2.66749	−	9.95520i	0.233060	−	0.869790i	−0.745954	−	0.665997i	$-0.768006\pi$
$131$	2.66749	−	9.95520i	0.233060	−	0.869790i	0.979014	−	0.203793i	$-0.0653270\pi$
$132$		0			0
$133$	1.17953	−	4.40206i	0.102278	−	0.381707i
$134$		0			0
$135$	−0.0896718	+	12.0736i	−0.00771772	+	1.03913i
$136$		0			0
$137$		−	4.40430i		−	0.376285i	−0.982142	−	0.188142i	$-0.939753\pi$
$137$		−	4.40430i		−	0.376285i	0.982142	−	0.188142i	$-0.0602466\pi$
$138$		0			0
$139$	13.9351	−	8.04542i	1.18196	−	0.682404i	0.225491	−	0.974245i	$-0.427601\pi$
$139$	13.9351	−	8.04542i	1.18196	−	0.682404i	0.956467	+	0.291842i	$0.0942680\pi$
$140$		0			0
$141$	−15.1201	−	10.6431i	−1.27334	−	0.896310i
$142$		0			0
$143$	3.85969	−	1.03420i	0.322764	−	0.0864843i
$144$		0			0
$145$	9.29672	−	16.1024i	0.772051	−	1.33723i
$146$		0			0
$147$	7.80591	+	0.702406i	0.643821	+	0.0579334i
$148$		0			0
$149$		−	5.92774i		−	0.485620i	−0.970074	−	0.242810i	$-0.921931\pi$
$149$		−	5.92774i		−	0.485620i	0.970074	−	0.242810i	$-0.0780691\pi$
$150$		0			0
$151$	13.3541	+	7.71000i	1.08674	+	0.627431i	0.932707	−	0.360635i	$-0.117440\pi$
$151$	13.3541	+	7.71000i	1.08674	+	0.627431i	0.154035	+	0.988065i	$0.450773\pi$
$152$		0			0
$153$	1.75802	+	21.3090i	0.142128	+	1.72273i
$154$		0			0
$155$	3.40959	+	1.96853i	0.273865	+	0.158116i
$156$		0			0
$157$	1.04147	+	1.80388i	0.0831185	+	0.143965i	0.904588	−	0.426287i	$-0.140179\pi$
$157$	1.04147	+	1.80388i	0.0831185	+	0.143965i	−0.821469	+	0.570253i	$0.806845\pi$
$158$		0			0
$159$	0.717010	−	7.96821i	0.0568626	−	0.631920i
$160$		0			0
$161$	3.39817	+	12.6821i	0.267813	+	0.999492i
$162$		0			0
$163$	12.4157	+	3.32678i	0.972475	+	0.260574i	0.709872	−	0.704330i	$-0.248753\pi$
$163$	12.4157	+	3.32678i	0.972475	+	0.260574i	0.262602	+	0.964904i	$0.415419\pi$
$164$		0			0
$165$	2.78901	+	1.02294i	0.217124	+	0.0796361i
$166$		0			0
$167$	−1.49582	−	5.58247i	−0.115750	−	0.431984i	0.883592	−	0.468258i	$-0.155118\pi$
$167$	−1.49582	−	5.58247i	−0.115750	−	0.431984i	−0.999342	+	0.0362731i	$0.988451\pi$
$168$		0			0
$169$	14.1215	−	8.15306i	1.08627	−	0.627159i
$170$		0			0
$171$	4.94932	+	7.14338i	0.378484	+	0.546268i
$172$		0			0
$173$	−3.09539	−	5.36137i	−0.235338	−	0.407618i	0.724033	−	0.689766i	$-0.242286\pi$
$173$	−3.09539	−	5.36137i	−0.235338	−	0.407618i	−0.959371	+	0.282148i	$0.908953\pi$
$174$		0			0
$175$		−	0.628130i		−	0.0474822i
$176$		0			0
$177$	−3.87863	+	3.23823i	−0.291536	+	0.243400i
$178$		0			0
$179$	−7.06290	−	7.06290i	−0.527906	−	0.527906i	0.392042	−	0.919947i	$-0.371769\pi$
$179$	−7.06290	−	7.06290i	−0.527906	−	0.527906i	−0.919947	+	0.392042i	$0.871769\pi$
$180$		0			0
$181$	−7.74084	+	13.4075i	−0.575372	+	0.996574i	0.420629	+	0.907233i	$0.361809\pi$
$181$	−7.74084	+	13.4075i	−0.575372	+	0.996574i	−0.996001	+	0.0893411i	$0.971524\pi$
$182$		0			0
$183$	−16.9143	−	6.20375i	−1.25034	−	0.458594i
$184$		0			0
$185$	−11.7920	−	7.79240i	−0.866965	−	0.572908i
$186$		0			0
$187$	5.08145	+	1.36157i	0.371592	+	0.0995679i
$188$		0			0
$189$	5.82318	−	5.73732i	0.423574	−	0.417329i
$190$		0			0
$191$	5.21860	−	5.21860i	0.377605	−	0.377605i	−0.492633	−	0.870237i	$-0.663965\pi$
$191$	5.21860	−	5.21860i	0.377605	−	0.377605i	0.870237	+	0.492633i	$0.163965\pi$
$192$		0			0
$193$	11.6023	+	11.6023i	0.835153	+	0.835153i	0.988216	−	0.153064i	$-0.0489140\pi$
$193$	11.6023	+	11.6023i	0.835153	+	0.835153i	−0.153064	+	0.988216i	$0.548914\pi$
$194$		0			0
$195$	21.6998	+	1.95263i	1.55396	+	0.139831i
$196$		0			0
$197$	14.7499	−	8.51587i	1.05089	−	0.606730i	0.127990	−	0.991775i	$-0.459147\pi$
$197$	14.7499	−	8.51587i	1.05089	−	0.606730i	0.922898	+	0.385045i	$0.125814\pi$
$198$		0			0
$199$	−16.9980	+	16.9980i	−1.20495	+	1.20495i	−0.232312	+	0.972641i	$0.574629\pi$
$199$	−16.9980	+	16.9980i	−1.20495	+	1.20495i	−0.972641	+	0.232312i	$0.925371\pi$
$200$		0			0
$201$	−9.45777	+	4.38176i	−0.667100	+	0.309065i
$202$		0			0
$203$	−12.1598	+	3.25822i	−0.853454	+	0.228682i
$204$		0			0
$205$	19.2060	+	5.14623i	1.34140	+	0.359428i
$206$		0			0
$207$	−22.6383	−	10.6932i	−1.57347	−	0.743229i
$208$		0			0
$209$	2.06535	−	0.553409i	0.142863	−	0.0382801i
$210$		0			0
$211$	−0.208227			−0.0143350			−0.00716748	−	0.999974i	$-0.502281\pi$
$211$	−0.208227			−0.0143350			−0.00716748	+	0.999974i	$0.502281\pi$
$212$		0			0
$213$	4.55657	−	2.11105i	0.312211	−	0.144647i
$214$		0			0
$215$	−12.5563	+	21.7482i	−0.856333	+	1.48321i
$216$		0			0
$217$	−0.689910	−	2.57478i	−0.0468341	−	0.174787i
$218$		0			0
$219$	21.1854	+	14.9125i	1.43157	+	1.00769i
$220$		0			0
$221$	38.5828			2.59536
$222$		0			0
$223$	26.8429			1.79753			0.898767	−	0.438428i	$-0.144464\pi$
$223$	26.8429			1.79753			0.898767	+	0.438428i	$0.144464\pi$
$224$		0			0
$225$	0.913734	+	0.774456i	0.0609156	+	0.0516304i
$226$		0			0
$227$	1.90289	+	7.10169i	0.126299	+	0.471356i	0.999883	−	0.0153191i	$-0.00487640\pi$
$227$	1.90289	+	7.10169i	0.126299	+	0.471356i	−0.873583	+	0.486675i	$0.838210\pi$
$228$		0			0
$229$	−5.67009	+	9.82088i	−0.374690	+	0.648982i	−0.990281	−	0.139084i	$-0.955584\pi$
$229$	−5.67009	+	9.82088i	−0.374690	+	0.648982i	0.615591	+	0.788066i	$0.288918\pi$
$230$		0			0
$231$	−0.845507	−	1.82498i	−0.0556303	−	0.120075i
$232$		0			0
$233$	−24.3925			−1.59801			−0.799004	−	0.601325i	$-0.794640\pi$
$233$	−24.3925			−1.59801			−0.799004	+	0.601325i	$0.794640\pi$
$234$		0			0
$235$	−23.9605	+	6.42019i	−1.56301	+	0.418807i
$236$		0			0
$237$	−0.982952	+	2.67998i	−0.0638496	+	0.174083i
$238$		0			0
$239$	12.1207	+	3.24773i	0.784022	+	0.210078i	0.628557	−	0.777763i	$-0.283646\pi$
$239$	12.1207	+	3.24773i	0.784022	+	0.210078i	0.155465	+	0.987841i	$0.450312\pi$
$240$		0			0
$241$	2.41369	−	0.646746i	0.155479	−	0.0416606i	−0.180240	−	0.983623i	$-0.557687\pi$
$241$	2.41369	−	0.646746i	0.155479	−	0.0416606i	0.335719	+	0.941962i	$0.391021\pi$
$242$		0			0
$243$	1.16630	+	15.5448i	0.0748182	+	0.997197i
$244$		0			0
$245$	7.43475	−	7.43475i	0.474989	−	0.474989i
$246$		0			0
$247$	13.5809	−	7.84096i	0.864135	−	0.498908i
$248$		0			0
$249$	2.19479	−	24.3909i	0.139089	−	1.54571i
$250$		0			0
$251$	−10.8542	−	10.8542i	−0.685113	−	0.685113i	0.276035	−	0.961148i	$-0.410980\pi$
$251$	−10.8542	−	10.8542i	−0.685113	−	0.685113i	−0.961148	+	0.276035i	$0.910980\pi$
$252$		0			0
$253$	−4.35584	+	4.35584i	−0.273849	+	0.273849i
$254$		0			0
$255$	23.4559	+	16.5107i	1.46886	+	1.03394i
$256$		0			0
$257$	19.4702	+	5.21701i	1.21451	+	0.325428i	0.808532	−	0.588452i	$-0.200263\pi$
$257$	19.4702	+	5.21701i	1.21451	+	0.325428i	0.405983	+	0.913881i	$0.366929\pi$
$258$		0			0
$259$	1.91481	+	9.37605i	0.118981	+	0.582599i
$260$		0			0
$261$	10.2528	−	21.7060i	0.634635	−	1.34357i
$262$		0			0
$263$	7.97220	−	13.8083i	0.491587	−	0.851454i	−0.508366	−	0.861141i	$-0.669750\pi$
$263$	7.97220	−	13.8083i	0.491587	−	0.851454i	0.999953	+	0.00968732i	$0.00308362\pi$
$264$		0			0
$265$	−7.58933	−	7.58933i	−0.466209	−	0.466209i
$266$		0			0
$267$	−15.5383	−	18.6112i	−0.950929	−	1.13899i
$268$		0			0
$269$		−	8.39048i		−	0.511577i	−0.966733	−	0.255788i	$-0.917665\pi$
$269$		−	8.39048i		−	0.511577i	0.966733	−	0.255788i	$-0.0823350\pi$
$270$		0			0
$271$	−10.4866	−	18.1634i	−0.637017	−	1.10335i	−0.986084	−	0.166249i	$-0.946835\pi$
$271$	−10.4866	−	18.1634i	−0.637017	−	1.10335i	0.349066	−	0.937098i	$-0.386499\pi$
$272$		0			0
$273$	−9.45398	−	11.3236i	−0.572181	−	0.685337i
$274$		0			0
$275$	0.255222	−	0.147353i	0.0153905	−	0.00888570i
$276$		0			0
$277$	−1.77283	−	6.61627i	−0.106519	−	0.397533i	0.891994	−	0.452047i	$-0.149306\pi$
$277$	−1.77283	−	6.61627i	−0.106519	−	0.397533i	−0.998513	+	0.0545133i	$0.982639\pi$
$278$		0			0
$279$	4.59613	+	2.17098i	0.275163	+	0.129973i
$280$		0			0
$281$	−0.511629	−	0.137091i	−0.0305213	−	0.00817815i	0.243526	−	0.969894i	$-0.421696\pi$
$281$	−0.511629	−	0.137091i	−0.0305213	−	0.00817815i	−0.274047	+	0.961716i	$0.588363\pi$
$282$		0			0
$283$	−4.37955	−	16.3447i	−0.260337	−	0.971593i	−0.965043	−	0.262092i	$-0.915587\pi$
$283$	−4.37955	−	16.3447i	−0.260337	−	0.971593i	0.704705	−	0.709500i	$-0.251079\pi$
$284$		0			0
$285$	11.6117	+	1.04487i	0.687819	+	0.0618926i
$286$		0			0
$287$	−6.73112	−	11.6586i	−0.397326	−	0.688188i
$288$		0			0
$289$	29.2680	+	16.8979i	1.72165	+	0.993995i
$290$		0			0
$291$	1.98895	−	0.345631i	0.116594	−	0.0202613i
$292$		0			0
$293$	−1.48615	−	0.858026i	−0.0868215	−	0.0501264i	0.455961	−	0.890000i	$-0.349296\pi$
$293$	−1.48615	−	0.858026i	−0.0868215	−	0.0501264i	−0.542782	+	0.839873i	$0.682629\pi$
$294$		0			0
$295$			6.77846i			0.394657i
$296$		0			0
$297$	3.69725	+	1.02016i	0.214536	+	0.0591959i
$298$		0			0
$299$	−22.5895	+	39.1261i	−1.30638	+	2.26272i
$300$		0			0
$301$	16.4233	−	4.40061i	0.946622	−	0.253647i
$302$		0			0
$303$	−3.89974	+	5.54016i	−0.224034	+	0.318274i
$304$		0			0
$305$	−20.9313	+	12.0847i	−1.19853	+	0.691969i
$306$		0			0
$307$		−	1.10309i		−	0.0629568i	−0.999504	−	0.0314784i	$-0.989978\pi$
$307$		−	1.10309i		−	0.0629568i	0.999504	−	0.0314784i	$-0.0100215\pi$
$308$		0			0
$309$	−1.27812	−	7.35499i	−0.0727095	−	0.418411i
$310$		0			0
$311$	−6.46091	+	24.1124i	−0.366364	+	1.36729i	0.499198	+	0.866488i	$0.333628\pi$
$311$	−6.46091	+	24.1124i	−0.366364	+	1.36729i	−0.865562	+	0.500802i	$0.833038\pi$
$312$		0			0
$313$	1.74599	−	6.51613i	0.0986892	−	0.368313i	−0.898864	−	0.438228i	$-0.855606\pi$
$313$	1.74599	−	6.51613i	0.0986892	−	0.368313i	0.997553	+	0.0699151i	$0.0222728\pi$
$314$		0			0
$315$	−0.901715	−	10.9297i	−0.0508059	−	0.615817i
$316$		0			0
$317$	1.30334	+	2.25745i	0.0732029	+	0.126791i	0.900303	−	0.435263i	$-0.143345\pi$
$317$	1.30334	+	2.25745i	0.0732029	+	0.126791i	−0.827100	+	0.562054i	$0.810011\pi$
$318$		0			0
$319$	−4.17645	−	4.17645i	−0.233836	−	0.233836i
$320$		0			0
$321$	−16.8145	+	7.79013i	−0.938496	+	0.434802i
$322$		0			0
$323$	20.6459			1.14877
$324$		0			0
$325$	1.52835	−	1.52835i	0.0847775	−	0.0847775i
$326$		0			0
$327$	−5.49284	−	6.57912i	−0.303755	−	0.363826i
$328$		0			0
$329$	14.5448	+	8.39742i	0.801879	+	0.462965i
$330$		0			0
$331$	−2.04670	+	7.63839i	−0.112497	+	0.419844i	−0.999087	−	0.0427110i	$-0.986401\pi$
$331$	−2.04670	+	7.63839i	−0.112497	+	0.419844i	0.886591	+	0.462555i	$0.153067\pi$
$332$		0			0
$333$	−16.0001	−	8.77478i	−0.876800	−	0.480855i
$334$		0			0
$335$	−3.61923	+	13.5071i	−0.197740	+	0.737974i
$336$		0			0
$337$	1.60325	+	0.925638i	0.0873347	+	0.0504227i	0.543031	−	0.839712i	$-0.317276\pi$
$337$	1.60325	+	0.925638i	0.0873347	+	0.0504227i	−0.455697	+	0.890135i	$0.650610\pi$
$338$		0			0
$339$	10.0488	+	12.0361i	0.545777	+	0.653712i
$340$		0			0
$341$	0.884340	−	0.884340i	0.0478897	−	0.0478897i
$342$		0			0
$343$	−18.1314			−0.979003
$344$		0			0
$345$	−30.4761	+	14.1195i	−1.64078	+	0.760169i
$346$		0			0
$347$	−7.93266	−	7.93266i	−0.425848	−	0.425848i	0.461364	−	0.887211i	$-0.347360\pi$
$347$	−7.93266	−	7.93266i	−0.425848	−	0.425848i	−0.887211	+	0.461364i	$0.847360\pi$
$348$		0			0
$349$	10.9449	+	18.9571i	0.585866	+	1.01475i	0.994767	+	0.102171i	$0.0325787\pi$
$349$	10.9449	+	18.9571i	0.585866	+	1.01475i	−0.408901	+	0.912579i	$0.634088\pi$
$350$		0			0
$351$	28.1287	+	0.208914i	1.50140	+	0.0111510i
$352$		0			0
$353$	3.38668	−	12.6392i	0.180255	−	0.672719i	−0.815342	−	0.578979i	$-0.803451\pi$
$353$	3.38668	−	12.6392i	0.180255	−	0.672719i	0.995597	−	0.0937398i	$-0.0298822\pi$
$354$		0			0
$355$	1.74368	−	6.50749i	0.0925447	−	0.345382i
$356$		0			0
$357$	−3.32502	−	19.1340i	−0.175979	−	1.01268i
$358$		0			0
$359$			11.5880i			0.611590i	0.952097	+	0.305795i	$0.0989222\pi$
$359$			11.5880i			0.611590i	−0.952097	+	0.305795i	$0.901078\pi$
$360$		0			0
$361$	−9.18722	+	5.30424i	−0.483538	+	0.279171i
$362$		0			0
$363$	−10.4235	+	14.8082i	−0.547093	+	0.777228i
$364$		0			0
$365$	33.5720	−	8.99558i	1.75724	−	0.470850i
$366$		0			0
$367$	5.41597	−	9.38074i	0.282711	−	0.489671i	−0.689340	−	0.724438i	$-0.742099\pi$
$367$	5.41597	−	9.38074i	0.282711	−	0.489671i	0.972052	+	0.234767i	$0.0754328\pi$
$368$		0			0
$369$	25.2589	+	4.58289i	1.31492	+	0.238576i
$370$		0			0
$371$			7.26680i			0.377273i
$372$		0			0
$373$	20.0111	+	11.5534i	1.03614	+	0.598214i	0.918737	−	0.394870i	$-0.129211\pi$
$373$	20.0111	+	11.5534i	1.03614	+	0.598214i	0.117401	+	0.993085i	$0.462544\pi$
$374$		0			0
$375$	−18.2429	+	3.17018i	−0.942062	+	0.163707i
$376$		0			0
$377$	−37.5148	−	21.6592i	−1.93211	−	1.11550i
$378$		0			0
$379$	−9.70115	−	16.8029i	−0.498314	−	0.863106i	0.501684	−	0.865051i	$-0.332714\pi$
$379$	−9.70115	−	16.8029i	−0.498314	−	0.863106i	−0.999998	+	0.00194516i	$0.999381\pi$
$380$		0			0
$381$	3.56527	+	0.320817i	0.182655	+	0.0164359i
$382$		0			0
$383$	3.55621	+	13.2720i	0.181714	+	0.678166i	0.995310	+	0.0967353i	$0.0308400\pi$
$383$	3.55621	+	13.2720i	0.181714	+	0.678166i	−0.813596	+	0.581430i	$0.802493\pi$
$384$		0			0
$385$	−2.60635	−	0.698369i	−0.132832	−	0.0355922i
$386$		0			0
$387$	−13.8476	+	29.3165i	−0.703915	+	1.49024i
$388$		0			0
$389$	−0.882991	−	3.29537i	−0.0447694	−	0.167082i	0.939922	−	0.341390i	$-0.110898\pi$
$389$	−0.882991	−	3.29537i	−0.0447694	−	0.167082i	−0.984691	+	0.174308i	$0.944231\pi$
$390$		0			0
$391$	−51.5112	+	29.7400i	−2.60503	+	1.50402i
$392$		0			0
$393$	−11.4406	−	13.7032i	−0.577103	−	0.691233i
$394$		0			0
$395$	1.91476	+	3.31646i	0.0963421	+	0.166869i
$396$		0			0
$397$			17.7233i			0.889506i	0.895653	+	0.444753i	$0.146709\pi$
$397$			17.7233i			0.889506i	−0.895653	+	0.444753i	$0.853291\pi$
$398$		0			0
$399$	−5.05889	−	6.05935i	−0.253261	−	0.303347i
$400$		0			0
$401$	−3.96835	−	3.96835i	−0.198170	−	0.198170i	0.601045	−	0.799215i	$-0.294751\pi$
$401$	−3.96835	−	3.96835i	−0.198170	−	0.198170i	−0.799215	+	0.601045i	$0.794751\pi$
$402$		0			0
$403$	4.58621	−	7.94354i	0.228455	−	0.395696i
$404$		0			0
$405$	17.0110	+	12.1641i	0.845286	+	0.604437i
$406$		0			0
$407$	−3.36048	+	2.97755i	−0.166573	+	0.147592i
$408$		0			0
$409$	−22.8004	−	6.10934i	−1.12741	−	0.302087i	−0.353529	−	0.935424i	$-0.615018\pi$
$409$	−22.8004	−	6.10934i	−1.12741	−	0.302087i	−0.773877	+	0.633336i	$0.781685\pi$
$410$		0			0
$411$	−6.23803	−	4.39097i	−0.307699	−	0.216590i
$412$		0			0
$413$	3.24519	−	3.24519i	0.159685	−	0.159685i
$414$		0			0
$415$	−23.2312	−	23.2312i	−1.14037	−	1.14037i
$416$		0			0
$417$	2.49777	−	27.7580i	0.122316	−	1.35932i
$418$		0			0
$419$	−9.13532	+	5.27428i	−0.446289	+	0.257665i	−0.706262	−	0.707951i	$-0.749620\pi$
$419$	−9.13532	+	5.27428i	−0.446289	+	0.257665i	0.259972	+	0.965616i	$0.416287\pi$
$420$		0			0
$421$	−1.74417	+	1.74417i	−0.0850059	+	0.0850059i	−0.748331	−	0.663325i	$-0.769145\pi$
$421$	−1.74417	+	1.74417i	−0.0850059	+	0.0850059i	0.663325	+	0.748331i	$0.269145\pi$
$422$		0			0
$423$	−30.1487	+	10.8045i	−1.46588	+	0.525331i
$424$		0			0
$425$	2.74863	−	0.736493i	0.133328	−	0.0357251i
$426$		0			0
$427$	15.8065	+	4.23533i	0.764929	+	0.204962i
$428$		0			0
$429$	2.38322	−	6.49774i	0.115063	−	0.313714i
$430$		0			0
$431$	−21.5800	+	5.78234i	−1.03947	+	0.278525i	−0.737894	−	0.674916i	$-0.764180\pi$
$431$	−21.5800	+	5.78234i	−1.03947	+	0.278525i	−0.301577	+	0.953442i	$0.597513\pi$
$432$		0			0
$433$	−12.1314			−0.582996			−0.291498	−	0.956571i	$-0.594154\pi$
$433$	−12.1314			−0.582996			−0.291498	+	0.956571i	$0.594154\pi$
$434$		0			0
$435$	−13.5380	−	29.2211i	−0.649099	−	1.40104i
$436$		0			0
$437$	−12.0878	+	20.9367i	−0.578237	+	1.00154i
$438$		0			0
$439$	−9.09223	−	33.9327i	−0.433949	−	1.61952i	−0.743570	−	0.668658i	$-0.766869\pi$
$439$	−9.09223	−	33.9327i	−0.433949	−	1.61952i	0.309621	−	0.950860i	$-0.399798\pi$
$440$		0			0
$441$	8.77713	−	10.3556i	0.417959	−	0.493125i
$442$		0			0
$443$	22.8962			1.08783			0.543916	−	0.839139i	$-0.316941\pi$
$443$	22.8962			1.08783			0.543916	+	0.839139i	$0.316941\pi$
$444$		0			0
$445$	−32.5258			−1.54187
$446$		0			0
$447$	−8.39576	−	5.90980i	−0.397106	−	0.279524i
$448$		0			0
$449$	−0.735701	−	2.74567i	−0.0347199	−	0.129576i	0.946391	−	0.323024i	$-0.104700\pi$
$449$	−0.735701	−	2.74567i	−0.0347199	−	0.129576i	−0.981111	+	0.193448i	$0.938033\pi$
$450$		0			0
$451$	3.15810	−	5.46999i	0.148709	−	0.257572i
$452$		0			0
$453$	24.2337	−	11.2274i	1.13860	−	0.527510i
$454$		0			0
$455$	−19.7896			−0.927753
$456$		0			0
$457$	−32.7026	+	8.76263i	−1.52976	+	0.409899i	−0.922941	−	0.384940i	$-0.874222\pi$
$457$	−32.7026	+	8.76263i	−1.52976	+	0.409899i	−0.606821	+	0.794839i	$0.707555\pi$
$458$		0			0
$459$	31.9336	+	18.7545i	1.49053	+	0.875384i
$460$		0			0
$461$	−34.9168	−	9.35594i	−1.62624	−	0.435749i	−0.673413	−	0.739267i	$-0.735172\pi$
$461$	−34.9168	−	9.35594i	−1.62624	−	0.435749i	−0.952826	+	0.303517i	$0.901839\pi$
$462$		0			0
$463$	10.7494	−	2.88030i	0.499568	−	0.133859i	−0.000231714	−	1.00000i	$-0.500074\pi$
$463$	10.7494	−	2.88030i	0.499568	−	0.133859i	0.499799	+	0.866141i	$0.333407\pi$
$464$		0			0
$465$	6.18739	−	2.86660i	0.286933	−	0.132935i
$466$		0			0
$467$	4.40877	−	4.40877i	0.204013	−	0.204013i	−0.597704	−	0.801717i	$-0.703920\pi$
$467$	4.40877	−	4.40877i	0.204013	−	0.204013i	0.801717	+	0.597704i	$0.203920\pi$
$468$		0			0
$469$	8.19927	−	4.73385i	0.378607	−	0.218589i
$470$		0			0
$471$	3.59325	+	0.323334i	0.165568	+	0.0148984i
$472$		0			0
$473$	5.64078	+	5.64078i	0.259363	+	0.259363i
$474$		0			0
$475$	0.817830	−	0.817830i	0.0375246	−	0.0375246i
$476$		0			0
$477$	−10.5709	−	8.95963i	−0.484010	−	0.410233i
$478$		0			0
$479$	27.7943	+	7.44746i	1.26995	+	0.340283i	0.830014	−	0.557743i	$-0.188333\pi$
$479$	27.7943	+	7.44746i	1.26995	+	0.340283i	0.439941	+	0.898027i	$0.354999\pi$
$480$		0			0
$481$	−18.1545	+	27.4726i	−0.827772	+	1.25264i
$482$		0			0
$483$	21.3502	+	7.83075i	0.971468	+	0.356311i
$484$		0			0
$485$	1.35413	−	2.34543i	0.0614880	−	0.106500i
$486$		0			0
$487$	19.1433	+	19.1433i	0.867467	+	0.867467i	0.992191	−	0.124724i	$-0.0398046\pi$
$487$	19.1433	+	19.1433i	0.867467	+	0.867467i	−0.124724	+	0.992191i	$0.539805\pi$
$488$		0			0
$489$	17.0900	−	14.2683i	0.772838	−	0.645234i
$490$		0			0
$491$		−	26.1251i		−	1.17901i	−0.807766	−	0.589504i	$-0.799323\pi$
$491$		−	26.1251i		−	1.17901i	0.807766	−	0.589504i	$-0.200677\pi$
$492$		0			0
$493$	−28.5152	−	49.3898i	−1.28426	−	2.22440i
$494$		0			0
$495$	4.22942	−	2.93037i	0.190098	−	0.131710i
$496$		0			0
$497$	−3.95025	+	2.28068i	−0.177193	+	0.102302i
$498$		0			0
$499$	0.0835255	+	0.311722i	0.00373912	+	0.0139546i	0.967770	−	0.251835i	$-0.0810340\pi$
$499$	0.0835255	+	0.311722i	0.00373912	+	0.0139546i	−0.964031	+	0.265790i	$0.914367\pi$
$500$		0			0
$501$	−9.39802	−	3.44697i	−0.419872	−	0.153999i
$502$		0			0
$503$	3.07410	+	0.823702i	0.137067	+	0.0367271i	0.326700	−	0.945128i	$-0.394063\pi$
$503$	3.07410	+	0.823702i	0.137067	+	0.0367271i	−0.189633	+	0.981855i	$0.560730\pi$
$504$		0			0
$505$	2.35242	+	8.77937i	0.104682	+	0.390677i
$506$		0			0
$507$	2.53119	−	28.1294i	0.112414	−	1.24927i
$508$		0			0
$509$	−0.869109	−	1.50534i	−0.0385226	−	0.0667231i	0.846121	−	0.532990i	$-0.178932\pi$
$509$	−0.869109	−	1.50534i	−0.0385226	−	0.0667231i	−0.884644	+	0.466267i	$0.845598\pi$
$510$		0			0
$511$	−20.3792	−	11.7660i	−0.901525	−	0.520495i
$512$		0			0
$513$	15.0519	+	0.111792i	0.664556	+	0.00493572i
$514$		0			0
$515$	−8.67321	−	5.00748i	−0.382187	−	0.220656i
$516$		0			0
$517$			7.87978i			0.346552i
$518$		0			0
$519$	−10.6796	−	0.960991i	−0.468782	−	0.0421828i
$520$		0			0
$521$	−16.3152	+	28.2588i	−0.714783	+	1.23804i	0.248260	+	0.968693i	$0.420141\pi$
$521$	−16.3152	+	28.2588i	−0.714783	+	1.23804i	−0.963043	+	0.269347i	$0.913192\pi$
$522$		0			0
$523$	8.61180	−	2.30753i	0.376568	−	0.100901i	−0.0655704	−	0.997848i	$-0.520887\pi$
$523$	8.61180	−	2.30753i	0.376568	−	0.100901i	0.442138	+	0.896947i	$0.354220\pi$
$524$		0			0
$525$	−0.889652	−	0.626229i	−0.0388276	−	0.0273309i
$526$		0			0
$527$	10.4580	−	6.03793i	0.455558	−	0.263017i
$528$		0			0
$529$		−	46.6488i		−	2.02821i
$530$		0			0
$531$	0.719572	+	8.72192i	0.0312268	+	0.378499i
$532$		0			0
$533$	11.9895	−	44.7454i	0.519323	−	1.93814i
$534$		0			0
$535$	−6.43446	+	24.0137i	−0.278186	+	1.03820i
$536$		0			0
$537$	−17.0450	+	2.96201i	−0.735548	+	0.127820i
$538$		0			0
$539$	−1.66999	−	2.89251i	−0.0719316	−	0.124589i
$540$		0			0
$541$	−25.0556	−	25.0556i	−1.07722	−	1.07722i	−0.996757	−	0.0804666i	$-0.974359\pi$
$541$	−25.0556	−	25.0556i	−1.07722	−	1.07722i	−0.0804666	−	0.996757i	$-0.525641\pi$
$542$		0			0
$543$	11.2723	+	24.3307i	0.483742	+	1.04413i
$544$		0			0
$545$	−11.4980			−0.492518
$546$		0			0
$547$	−14.9873	+	14.9873i	−0.640813	+	0.640813i	−0.950755	−	0.309943i	$-0.899690\pi$
$547$	−14.9873	+	14.9873i	−0.640813	+	0.640813i	0.309943	+	0.950755i	$0.399690\pi$
$548$		0			0
$549$	−25.6497	+	17.7715i	−1.09470	+	0.758470i
$550$		0			0
$551$	−20.0744	−	11.5900i	−0.855200	−	0.493750i
$552$		0			0
$553$	0.671066	−	2.50445i	0.0285366	−	0.106500i
$554$		0			0
$555$	−22.7931	+	8.93278i	−0.967512	+	0.379175i
$556$		0			0
$557$	−0.774505	+	2.89049i	−0.0328168	+	0.122474i	−0.980391	−	0.197061i	$-0.936860\pi$
$557$	−0.774505	+	2.89049i	−0.0328168	+	0.122474i	0.947574	+	0.319535i	$0.103527\pi$
$558$		0			0
$559$	50.6681	+	29.2532i	2.14303	+	1.23728i
$560$		0			0
$561$	6.99453	−	5.83966i	0.295309	−	0.246550i
$562$		0			0
$563$	−10.5667	+	10.5667i	−0.445333	+	0.445333i	−0.893799	−	0.448467i	$-0.851970\pi$
$563$	−10.5667	+	10.5667i	−0.445333	+	0.445333i	0.448467	+	0.893799i	$0.351970\pi$
$564$		0			0
$565$	21.0348			0.884942
$566$		0			0
$567$	−2.32049	−	13.9676i	−0.0974516	−	0.586584i
$568$		0			0
$569$	20.3507	+	20.3507i	0.853144	+	0.853144i	0.990519	−	0.137375i	$-0.0438666\pi$
$569$	20.3507	+	20.3507i	0.853144	+	0.853144i	−0.137375	+	0.990519i	$0.543867\pi$
$570$		0			0
$571$	−4.11144	−	7.12122i	−0.172058	−	0.298014i	0.767081	−	0.641550i	$-0.221708\pi$
$571$	−4.11144	−	7.12122i	−0.172058	−	0.298014i	−0.939139	+	0.343537i	$0.888375\pi$
$572$		0			0
$573$	−2.18856	−	12.5942i	−0.0914283	−	0.526129i
$574$		0			0
$575$	−0.862405	+	3.21854i	−0.0359648	+	0.134222i
$576$		0			0
$577$	7.90121	−	29.4877i	0.328932	−	1.22759i	−0.581368	−	0.813640i	$-0.697482\pi$
$577$	7.90121	−	29.4877i	0.328932	−	1.22759i	0.910300	−	0.413949i	$-0.135851\pi$
$578$		0			0
$579$	28.0001	−	4.86573i	1.16364	−	0.202213i
$580$		0			0
$581$			22.2439i			0.922832i
$582$		0			0
$583$	−2.95265	+	1.70471i	−0.122286	+	0.0706020i
$584$		0			0
$585$	24.3997	−	28.7878i	1.00880	−	1.19023i
$586$		0			0
$587$	−8.10721	+	2.17232i	−0.334620	+	0.0896612i	−0.422217	−	0.906495i	$-0.638748\pi$
$587$	−8.10721	+	2.17232i	−0.334620	+	0.0896612i	0.0875968	+	0.996156i	$0.472081\pi$
$588$		0			0
$589$	2.45411	−	4.25065i	0.101120	−	0.175145i
$590$		0			0
$591$	2.64382	−	29.3811i	0.108752	−	1.20858i
$592$		0			0
$593$			19.5338i			0.802155i	0.916044	+	0.401078i	$0.131364\pi$
$593$			19.5338i			0.802155i	−0.916044	+	0.401078i	$0.868636\pi$
$594$		0			0
$595$	−22.5633	−	13.0270i	−0.925007	−	0.534053i
$596$		0			0
$597$	7.12854	+	41.0215i	0.291752	+	1.67890i
$598$		0			0
$599$	−0.169109	−	0.0976351i	−0.00690960	−	0.00398926i	0.496541	−	0.868013i	$-0.334603\pi$
$599$	−0.169109	−	0.0976351i	−0.00690960	−	0.00398926i	−0.503451	+	0.864024i	$0.667936\pi$
$600$		0			0
$601$	17.8418	+	30.9029i	0.727782	+	1.26055i	0.957819	+	0.287373i	$0.0927818\pi$
$601$	17.8418	+	30.9029i	0.727782	+	1.26055i	−0.230037	+	0.973182i	$0.573885\pi$
$602$		0			0
$603$	−3.22304	+	17.7640i	−0.131252	+	0.723406i
$604$		0			0
$605$	6.28774	+	23.4662i	0.255633	+	0.954035i
$606$		0			0
$607$	10.1421	+	2.71757i	0.411656	+	0.110303i	0.458703	−	0.888590i	$-0.348314\pi$
$607$	10.1421	+	2.71757i	0.411656	+	0.110303i	−0.0470466	+	0.998893i	$0.514981\pi$
$608$		0			0
$609$	−7.50826	+	20.4709i	−0.304250	+	0.829525i
$610$		0			0
$611$	14.9575	+	55.8223i	0.605117	+	2.25833i
$612$		0			0
$613$	−8.61416	+	4.97339i	−0.347923	+	0.200873i	−0.663770	−	0.747937i	$-0.731045\pi$
$613$	−8.61416	+	4.97339i	−0.347923	+	0.200873i	0.315847	+	0.948810i	$0.397711\pi$
$614$		0			0
$615$	26.4367	−	22.0717i	1.06603	−	0.890018i
$616$		0			0
$617$	−5.84248	−	10.1195i	−0.235210	−	0.407395i	0.724124	−	0.689670i	$-0.242244\pi$
$617$	−5.84248	−	10.1195i	−0.235210	−	0.407395i	−0.959334	+	0.282275i	$0.908911\pi$
$618$		0			0
$619$			1.66106i			0.0667635i	0.999443	+	0.0333818i	$0.0106277\pi$
$619$			1.66106i			0.0667635i	−0.999443	+	0.0333818i	$0.989372\pi$
$620$		0			0
$621$	−37.7151	+	21.4029i	−1.51346	+	0.858871i
$622$		0			0
$623$	15.5717	+	15.5717i	0.623868	+	0.623868i
$624$		0			0
$625$	−13.4185	+	23.2414i	−0.536738	+	0.929658i
$626$		0			0
$627$	1.27528	−	3.47699i	0.0509297	−	0.138858i
$628$		0			0
$629$	−38.7834	+	19.3726i	−1.54639	+	0.772434i
$630$		0			0
$631$	17.1356	+	4.59146i	0.682156	+	0.182783i	0.583224	−	0.812311i	$-0.301791\pi$
$631$	17.1356	+	4.59146i	0.682156	+	0.182783i	0.0989317	+	0.995094i	$0.468457\pi$
$632$		0			0
$633$	−0.207597	+	0.294922i	−0.00825124	+	0.0117221i
$634$		0			0
$635$	3.39575	−	3.39575i	0.134756	−	0.134756i
$636$		0			0
$637$	−17.3212	−	17.3212i	−0.686291	−	0.686291i
$638$		0			0
$639$	1.55280	−	8.55836i	0.0614278	−	0.338563i
$640$		0			0
$641$	−8.40159	+	4.85066i	−0.331843	+	0.191590i	−0.656659	−	0.754188i	$-0.728031\pi$
$641$	−8.40159	+	4.85066i	−0.331843	+	0.191590i	0.324816	+	0.945777i	$0.394698\pi$
$642$		0			0
$643$	20.6922	−	20.6922i	0.816021	−	0.816021i	−0.169508	−	0.985529i	$-0.554218\pi$
$643$	20.6922	−	20.6922i	0.816021	−	0.816021i	0.985529	+	0.169508i	$0.0542178\pi$
$644$		0			0
$645$	18.2847	+	39.4664i	0.719959	+	1.55399i
$646$		0			0
$647$	−45.9218	+	12.3047i	−1.80537	+	0.483748i	−0.994796	−	0.101885i	$-0.967513\pi$
$647$	−45.9218	+	12.3047i	−1.80537	+	0.483748i	−0.810576	+	0.585633i	$0.800846\pi$
$648$		0			0
$649$	2.07988	+	0.557301i	0.0816422	+	0.0218760i
$650$		0			0
$651$	−4.33461	−	1.58983i	−0.169887	−	0.0623104i
$652$		0			0
$653$	16.1422	−	4.32530i	0.631694	−	0.169262i	0.0712560	−	0.997458i	$-0.477299\pi$
$653$	16.1422	−	4.32530i	0.631694	−	0.169262i	0.560438	+	0.828196i	$0.310633\pi$
$654$		0			0
$655$	−23.9482			−0.935735
$656$		0			0
$657$	42.2425	−	15.1386i	1.64804	−	0.590612i
$658$		0			0
$659$	−11.3024	+	19.5764i	−0.440280	+	0.762587i	−0.997710	−	0.0676367i	$-0.978454\pi$
$659$	−11.3024	+	19.5764i	−0.440280	+	0.762587i	0.557430	+	0.830224i	$0.311787\pi$
$660$		0			0
$661$	−0.890448	−	3.32320i	−0.0346344	−	0.129257i	0.946444	−	0.322868i	$-0.104647\pi$
$661$	−0.890448	−	3.32320i	−0.0346344	−	0.129257i	−0.981079	+	0.193610i	$0.937980\pi$
$662$		0			0
$663$	38.4660	−	54.6466i	1.49389	−	2.12230i
$664$		0			0
$665$	−10.5896			−0.410647
$666$		0			0
$667$	66.7805			2.58575
$668$		0			0
$669$	26.7616	−	38.0189i	1.03466	−	1.46990i
$670$		0			0
$671$	1.98713	+	7.41605i	0.0767121	+	0.286294i
$672$		0			0
$673$	−15.4794	+	26.8111i	−0.596686	+	1.03349i	0.396621	+	0.917983i	$0.370183\pi$
$673$	−15.4794	+	26.8111i	−0.596686	+	1.03349i	−0.993307	+	0.115508i	$0.963150\pi$
$674$		0			0
$675$	2.00787	−	0.522055i	0.0772829	−	0.0200939i
$676$		0			0
$677$	−0.490033			−0.0188335			−0.00941674	−	0.999956i	$-0.502997\pi$
$677$	−0.490033			−0.0188335			−0.00941674	+	0.999956i	$0.502997\pi$
$678$		0			0
$679$	−1.77117	+	0.474583i	−0.0679712	+	0.0182128i
$680$		0			0
$681$	11.9556	+	4.38503i	0.458140	+	0.168035i
$682$		0			0
$683$	−22.1468	−	5.93422i	−0.847424	−	0.227067i	−0.191123	−	0.981566i	$-0.561213\pi$
$683$	−22.1468	−	5.93422i	−0.847424	−	0.227067i	−0.656301	+	0.754499i	$0.727880\pi$
$684$		0			0
$685$	−9.88525	+	2.64875i	−0.377696	+	0.101203i
$686$		0			0
$687$	8.25687	+	17.8220i	0.315019	+	0.679951i
$688$		0			0
$689$	−17.6814	+	17.6814i	−0.673606	+	0.673606i
$690$		0			0
$691$	−15.9187	+	9.19065i	−0.605575	+	0.349629i	−0.771232	−	0.636555i	$-0.780359\pi$
$691$	−15.9187	+	9.19065i	−0.605575	+	0.349629i	0.165657	+	0.986184i	$0.447026\pi$
$692$		0			0
$693$	−3.42775	−	0.621920i	−0.130210	−	0.0236248i
$694$		0			0
$695$	−26.4381	−	26.4381i	−1.00286	−	1.00286i
$696$		0			0
$697$	43.1246	−	43.1246i	1.63346	−	1.63346i
$698$		0			0
$699$	−24.3187	+	34.5484i	−0.919818	+	1.30674i
$700$		0			0
$701$	14.0705	+	3.77019i	0.531437	+	0.142398i	0.514552	−	0.857459i	$-0.327958\pi$
$701$	14.0705	+	3.77019i	0.531437	+	0.142398i	0.0168851	+	0.999857i	$0.494625\pi$
$702$		0			0
$703$	−9.71458	+	14.7008i	−0.366392	+	0.554450i
$704$		0			0
$705$	−14.7947	+	40.3372i	−0.557201	+	1.51918i
$706$		0			0
$707$	3.07690	−	5.32935i	0.115719	−	0.200431i
$708$		0			0
$709$	26.7224	+	26.7224i	1.00358	+	1.00358i	0.999994	+	0.00358773i	$0.00114201\pi$
$709$	26.7224	+	26.7224i	1.00358	+	1.00358i	0.00358773	+	0.999994i	$0.498858\pi$
$710$		0			0
$711$	2.81581	+	4.06407i	0.105601	+	0.152414i
$712$		0			0
$713$			14.1404i			0.529561i
$714$		0			0
$715$	−4.64244	−	8.04094i	−0.173617	−	0.300714i
$716$		0			0
$717$	16.6839	−	13.9292i	0.623072	−	0.520197i
$718$		0			0
$719$	37.3478	−	21.5628i	1.39284	−	0.804156i	0.399210	−	0.916860i	$-0.369285\pi$
$719$	37.3478	−	21.5628i	1.39284	−	0.804156i	0.993629	+	0.112704i	$0.0359512\pi$
$720$		0			0
$721$	1.75497	+	6.54964i	0.0653585	+	0.243921i
$722$		0			0
$723$	1.49037	−	4.06342i	0.0554273	−	0.151120i
$724$		0			0
$725$	−3.08599	−	0.826889i	−0.114611	−	0.0307099i
$726$		0			0
$727$	3.82417	+	14.2720i	0.141830	+	0.529318i	0.999876	+	0.0157449i	$0.00501196\pi$
$727$	3.82417	+	14.2720i	0.141830	+	0.529318i	−0.858046	+	0.513573i	$0.828321\pi$
$728$		0			0
$729$	23.1796	+	13.8458i	0.858503	+	0.512808i
$730$		0			0
$731$	38.5131	+	66.7066i	1.42446	+	2.46723i
$732$		0			0
$733$	−9.28224	−	5.35911i	−0.342847	−	0.197943i	0.318683	−	0.947861i	$-0.396759\pi$
$733$	−9.28224	−	5.35911i	−0.342847	−	0.197943i	−0.661530	+	0.749918i	$0.730093\pi$
$734$		0			0
$735$	−3.11796	−	17.9424i	−0.115008	−	0.661817i
$736$		0			0
$737$	3.84692	+	2.22102i	0.141703	+	0.0818123i
$738$		0			0
$739$		−	10.1714i		−	0.374162i	−0.982345	−	0.187081i	$-0.940097\pi$
$739$		−	10.1714i		−	0.374162i	0.982345	−	0.187081i	$-0.0599026\pi$
$740$		0			0
$741$	2.43429	−	27.0526i	0.0894261	−	0.993802i
$742$		0			0
$743$	6.19620	−	10.7321i	0.227317	−	0.393724i	−0.729695	−	0.683772i	$-0.760338\pi$
$743$	6.19620	−	10.7321i	0.227317	−	0.393724i	0.957012	+	0.290049i	$0.0936714\pi$
$744$		0			0
$745$	−13.3046	+	3.56495i	−0.487441	+	0.130609i
$746$		0			0
$747$	−32.3579	−	27.4257i	−1.18391	−	1.00345i
$748$		0			0
$749$	14.5771	−	8.41609i	0.532636	−	0.307517i
$750$		0			0
$751$			11.1169i			0.405660i	0.979214	+	0.202830i	$0.0650138\pi$
$751$			11.1169i			0.405660i	−0.979214	+	0.202830i	$0.934986\pi$
$752$		0			0
$753$	−26.1948	+	4.55201i	−0.954590	+	0.165884i
$754$		0			0
$755$	9.27359	−	34.6095i	0.337500	−	1.25957i
$756$		0			0
$757$	6.85426	−	25.5805i	0.249122	−	0.929738i	−0.722144	−	0.691743i	$-0.756843\pi$
$757$	6.85426	−	25.5805i	0.249122	−	0.929738i	0.971266	−	0.237995i	$-0.0764902\pi$
$758$		0			0
$759$	1.82673	+	10.5120i	0.0663062	+	0.381563i
$760$		0			0
$761$	11.2680	+	19.5167i	0.408463	+	0.707479i	0.994718	−	0.102648i	$-0.0327315\pi$
$761$	11.2680	+	19.5167i	0.408463	+	0.707479i	−0.586255	+	0.810127i	$0.699398\pi$
$762$		0			0
$763$	5.50466	+	5.50466i	0.199282	+	0.199282i
$764$		0			0
$765$	46.7697	−	16.7610i	1.69096	−	0.605996i
$766$		0			0
$767$	15.7922			0.570224
$768$		0			0
$769$	32.3631	−	32.3631i	1.16704	−	1.16704i	0.184145	−	0.982899i	$-0.441048\pi$
$769$	32.3631	−	32.3631i	1.16704	−	1.16704i	0.982899	−	0.184145i	$-0.0589516\pi$
$770$		0			0
$771$	26.8003	−	22.3753i	0.965190	−	0.805827i
$772$		0			0
$773$	−17.1782	−	9.91786i	−0.617858	−	0.356721i	0.158177	−	0.987411i	$-0.449438\pi$
$773$	−17.1782	−	9.91786i	−0.617858	−	0.356721i	−0.776035	+	0.630690i	$0.782772\pi$
$774$		0			0
$775$	0.175089	−	0.653441i	0.00628938	−	0.0234723i
$776$		0			0
$777$	15.1888	+	6.63562i	0.544894	+	0.238052i
$778$		0			0
$779$	6.41567	−	23.9436i	0.229865	−	0.857869i
$780$		0			0
$781$	−1.85337	−	1.07005i	−0.0663189	−	0.0382892i
$782$		0			0
$783$	−20.5215	−	36.1619i	−0.733379	−	1.29232i
$784$		0			0
$785$	3.42239	−	3.42239i	0.122150	−	0.122150i
$786$		0			0
$787$	43.0619			1.53499			0.767495	−	0.641055i	$-0.221503\pi$
$787$	43.0619			1.53499			0.767495	+	0.641055i	$0.221503\pi$
$788$		0			0
$789$	−11.6092	−	25.0579i	−0.413300	−	0.892084i
$790$		0			0
$791$	−10.0704	−	10.0704i	−0.358064	−	0.358064i
$792$		0			0
$793$	28.1546	+	48.7651i	0.999797	+	1.73170i
$794$		0			0
$795$	−18.3155	+	3.18279i	−0.649584	+	0.112882i
$796$		0			0
$797$	−8.79885	+	32.8377i	−0.311671	+	1.16317i	0.615378	+	0.788232i	$0.289003\pi$
$797$	−8.79885	+	32.8377i	−0.311671	+	1.16317i	−0.927049	+	0.374940i	$0.877663\pi$
$798$		0			0
$799$	−19.6922	+	73.4924i	−0.696661	+	2.59997i
$800$		0			0
$801$	−41.8512	+	3.45279i	−1.47874	+	0.121998i
$802$		0			0
$803$		−	11.0407i		−	0.389617i
$804$		0			0
$805$	26.4208	−	15.2541i	0.931211	−	0.537635i
$806$		0			0
$807$	−11.8839	−	8.36508i	−0.418331	−	0.294465i
$808$		0			0
$809$	−21.9561	+	5.88311i	−0.771934	+	0.206839i	−0.623226	−	0.782042i	$-0.714178\pi$
$809$	−21.9561	+	5.88311i	−0.771934	+	0.206839i	−0.148708	+	0.988881i	$0.547512\pi$
$810$		0			0
$811$	−14.5931	+	25.2761i	−0.512434	+	0.887562i	0.487462	+	0.873144i	$0.337923\pi$
$811$	−14.5931	+	25.2761i	−0.512434	+	0.887562i	−0.999896	+	0.0144181i	$0.995410\pi$
$812$		0			0
$813$	−36.1806	−	3.25567i	−1.26891	−	0.114181i
$814$		0			0
$815$		−	29.8673i		−	1.04621i
$816$		0			0
$817$	27.1129	+	15.6536i	0.948559	+	0.547651i
$818$		0			0
$819$	−25.4636	+	2.10078i	−0.889769	+	0.0734073i
$820$		0			0
$821$	22.9968	+	13.2772i	0.802595	+	0.463378i	0.844378	−	0.535748i	$-0.179970\pi$
$821$	22.9968	+	13.2772i	0.802595	+	0.463378i	−0.0417829	+	0.999127i	$0.513304\pi$
$822$		0			0
$823$	−14.1533	−	24.5143i	−0.493354	−	0.854514i	0.506617	−	0.862171i	$-0.330896\pi$
$823$	−14.1533	−	24.5143i	−0.493354	−	0.854514i	−0.999971	+	0.00765756i	$0.997562\pi$
$824$		0			0
$825$	0.0457469	−	0.508390i	0.00159270	−	0.0176999i
$826$		0			0
$827$	−6.54668	−	24.4325i	−0.227650	−	0.849602i	−0.981325	−	0.192355i	$-0.938387\pi$
$827$	−6.54668	−	24.4325i	−0.227650	−	0.849602i	0.753675	−	0.657247i	$-0.228279\pi$
$828$		0			0
$829$	40.4430	+	10.8367i	1.40464	+	0.376373i	0.880010	−	0.474956i	$-0.157536\pi$
$829$	40.4430	+	10.8367i	1.40464	+	0.376373i	0.524633	+	0.851328i	$0.324203\pi$
$830$		0			0
$831$	−11.1384	−	4.08531i	−0.386387	−	0.141718i
$832$		0			0
$833$	−8.34688	−	31.1510i	−0.289202	−	1.07932i
$834$		0			0
$835$	−11.6300	+	6.71459i	−0.402473	+	0.232368i
$836$		0			0
$837$	7.65708	−	4.34531i	0.264667	−	0.150196i
$838$		0			0
$839$	4.99925	+	8.65896i	0.172593	+	0.298941i	0.939326	−	0.343026i	$-0.111452\pi$
$839$	4.99925	+	8.65896i	0.172593	+	0.298941i	−0.766732	+	0.641967i	$0.778119\pi$
$840$		0			0
$841$			35.0303i			1.20794i
$842$		0			0
$843$	−0.704249	+	0.587970i	−0.0242556	+	0.0202508i
$844$		0			0
$845$	−26.7919	−	26.7919i	−0.921668	−	0.921668i
$846$		0			0
$847$	8.22419	−	14.2447i	0.282586	−	0.489454i
$848$		0			0
$849$	−27.5161	−	10.0923i	−0.944351	−	0.346366i
$850$		0			0
$851$	3.06154	−	50.6718i	0.104948	−	1.73701i
$852$		0			0
$853$	−3.06823	−	0.822129i	−0.105054	−	0.0281492i	0.205909	−	0.978571i	$-0.433985\pi$
$853$	−3.06823	−	0.822129i	−0.105054	−	0.0281492i	−0.310963	+	0.950422i	$0.600652\pi$
$854$		0			0
$855$	13.0565	−	15.4046i	0.446522	−	0.526825i
$856$		0			0
$857$	−1.38018	+	1.38018i	−0.0471460	+	0.0471460i	−0.730287	−	0.683141i	$-0.760614\pi$
$857$	−1.38018	+	1.38018i	−0.0471460	+	0.0471460i	0.683141	+	0.730287i	$0.260614\pi$
$858$		0			0
$859$	−37.4233	−	37.4233i	−1.27687	−	1.27687i	−0.942412	−	0.334453i	$-0.891448\pi$
$859$	−37.4233	−	37.4233i	−1.27687	−	1.27687i	−0.334453	−	0.942412i	$-0.608552\pi$
$860$		0			0
$861$	−23.2235	−	2.08974i	−0.791453	−	0.0712180i
$862$		0			0
$863$	−31.6227	+	18.2574i	−1.07645	+	0.621489i	−0.929937	−	0.367720i	$-0.880139\pi$
$863$	−31.6227	+	18.2574i	−1.07645	+	0.621489i	−0.146513	+	0.989209i	$0.546805\pi$
$864$		0			0
$865$	−10.1718	+	10.1718i	−0.345851	+	0.345851i
$866$		0			0
$867$	53.1128	−	24.6070i	1.80380	−	0.835698i
$868$		0			0
$869$	1.17504	−	0.314850i	0.0398603	−	0.0106805i
$870$		0			0
$871$	31.4685	+	8.43195i	1.06627	+	0.285706i
$872$		0			0
$873$	1.49340	−	3.16164i	0.0505438	−	0.107005i
$874$		0			0
$875$	16.2454	−	4.35294i	0.549194	−	0.147156i
$876$		0			0
$877$	53.5958			1.80980			0.904900	−	0.425623i	$-0.139945\pi$
$877$	53.5958			1.80980			0.904900	+	0.425623i	$0.139945\pi$
$878$		0			0
$879$	−2.69691	+	1.24947i	−0.0909646	+	0.0421436i
$880$		0			0
$881$	18.3911	−	31.8543i	0.619611	−	1.07320i	−0.369945	−	0.929054i	$-0.620624\pi$
$881$	18.3911	−	31.8543i	0.619611	−	1.07320i	0.989557	−	0.144145i	$-0.0460431\pi$
$882$		0			0
$883$	−10.8500	−	40.4928i	−0.365132	−	1.36269i	−0.867242	−	0.497887i	$-0.834109\pi$
$883$	−10.8500	−	40.4928i	−0.365132	−	1.36269i	0.502110	−	0.864804i	$-0.332557\pi$
$884$		0			0
$885$	9.60066	+	6.75794i	0.322723	+	0.227166i
$886$		0			0
$887$	1.05111			0.0352928			0.0176464	−	0.999844i	$-0.494383\pi$
$887$	1.05111			0.0352928			0.0176464	+	0.999844i	$0.494383\pi$
$888$		0			0
$889$	−3.25144			−0.109050
$890$		0			0
$891$	5.13096	−	4.21951i	0.171894	−	0.141359i
$892$		0			0
$893$	8.00388	+	29.8709i	0.267840	+	0.999592i
$894$		0			0
$895$	−11.6047	+	20.1000i	−0.387903	+	0.671868i
$896$		0			0
$897$	32.8951	+	71.0022i	1.09834	+	2.37070i
$898$		0			0
$899$	−13.5580			−0.452186
$900$		0			0
$901$	−31.7987	+	8.52043i	−1.05937	+	0.283857i
$902$		0			0
$903$	10.1408	−	27.6484i	0.337464	−	0.920081i
$904$		0			0
$905$	34.7479	+	9.31068i	1.15506	+	0.309498i
$906$		0			0
$907$	39.6867	−	10.6340i	1.31777	−	0.353096i	0.469631	−	0.882863i	$-0.344387\pi$
$907$	39.6867	−	10.6340i	1.31777	−	0.353096i	0.848143	+	0.529767i	$0.177720\pi$
$908$		0			0
$909$	3.95887	+	11.0468i	0.131307	+	0.366399i
$910$		0			0
$911$	33.4058	−	33.4058i	1.10678	−	1.10678i	0.113214	−	0.993571i	$-0.463885\pi$
$911$	33.4058	−	33.4058i	1.10678	−	1.10678i	0.993571	−	0.113214i	$-0.0361146\pi$
$912$		0			0
$913$	−9.03815	+	5.21818i	−0.299119	+	0.172696i
$914$		0			0
$915$	−3.75181	+	41.6942i	−0.124031	+	1.37837i
$916$		0			0
$917$	11.4652	+	11.4652i	0.378616	+	0.378616i
$918$		0			0
$919$	28.9777	−	28.9777i	0.955887	−	0.955887i	−0.0431807	−	0.999067i	$-0.513749\pi$
$919$	28.9777	−	28.9777i	0.955887	−	0.955887i	0.999067	+	0.0431807i	$0.0137491\pi$
$920$		0			0
$921$	−1.56236	−	1.09975i	−0.0514816	−	0.0362381i
$922$		0			0
$923$	−15.1609	−	4.06235i	−0.499028	−	0.133714i
$924$		0			0
$925$	−0.768905	+	2.30369i	−0.0252814	+	0.0757447i
$926$		0			0
$927$	−11.6915	−	5.52247i	−0.383999	−	0.181382i
$928$		0			0
$929$	6.53422	−	11.3176i	0.214381	−	0.371319i	−0.738700	−	0.674034i	$-0.764560\pi$
$929$	6.53422	−	11.3176i	0.214381	−	0.371319i	0.953081	+	0.302716i	$0.0978933\pi$
$930$		0			0
$931$	−9.26871	−	9.26871i	−0.303770	−	0.303770i
$932$		0			0
$933$	27.7103	+	33.1903i	0.907193	+	1.08660i
$934$		0			0
$935$		−	12.2239i		−	0.399765i
$936$		0			0
$937$	−1.56828	−	2.71634i	−0.0512334	−	0.0887388i	0.839271	−	0.543713i	$-0.182982\pi$
$937$	−1.56828	−	2.71634i	−0.0512334	−	0.0887388i	−0.890505	+	0.454974i	$0.849649\pi$
$938$		0			0
$939$	−7.48840	−	8.96933i	−0.244375	−	0.292703i
$940$		0			0
$941$	0.104995	−	0.0606190i	0.00342275	−	0.00197612i	−0.498288	−	0.867012i	$-0.666038\pi$
$941$	0.104995	−	0.0606190i	0.00342275	−	0.00197612i	0.501710	+	0.865036i	$0.332704\pi$
$942$		0			0
$943$	18.4833	+	68.9805i	0.601898	+	2.24631i
$944$		0			0
$945$	−16.3792	−	9.61944i	−0.532816	−	0.312921i
$946$		0			0
$947$	32.9832	+	8.83783i	1.07181	+	0.287191i	0.751237	−	0.660033i	$-0.229458\pi$
$947$	32.9832	+	8.83783i	1.07181	+	0.287191i	0.320574	+	0.947224i	$0.396124\pi$
$948$		0			0
$949$	−20.9576	−	78.2148i	−0.680312	−	2.53896i
$950$		0			0
$951$	4.49673	+	0.404633i	0.145817	+	0.0131211i
$952$		0			0
$953$	8.51043	+	14.7405i	0.275680	+	0.477492i	0.970306	−	0.241879i	$-0.0777637\pi$
$953$	8.51043	+	14.7405i	0.275680	+	0.477492i	−0.694626	+	0.719371i	$0.744430\pi$
$954$		0			0
$955$	−14.8514	−	8.57445i	−0.480580	−	0.277463i
$956$		0			0
$957$	−10.0791	+	1.75150i	−0.325812	+	0.0566181i
$958$		0			0
$959$	6.00066	+	3.46448i	0.193771	+	0.111874i
$960$		0			0
$961$			28.1292i			0.907392i
$962$		0			0
$963$	−5.73010	+	31.5818i	−0.184650	+	1.01771i
$964$		0			0
$965$	19.0632	−	33.0185i	0.613667	−	1.06290i
$966$		0			0
$967$	25.2639	−	6.76943i	0.812431	−	0.217690i	0.171396	−	0.985202i	$-0.445172\pi$
$967$	25.2639	−	6.76943i	0.812431	−	0.217690i	0.641035	+	0.767512i	$0.278505\pi$
$968$		0			0
$969$	20.5834	−	29.2418i	0.661235	−	0.939383i
$970$		0			0
$971$	−38.6025	+	22.2872i	−1.23881	+	0.715229i	−0.968851	−	0.247642i	$-0.920344\pi$
$971$	−38.6025	+	22.2872i	−1.23881	+	0.715229i	−0.269961	+	0.962871i	$0.587011\pi$
$972$		0			0
$973$			25.3146i			0.811548i
$974$		0			0
$975$	−0.640953	−	3.68840i	−0.0205269	−	0.118123i
$976$		0			0
$977$	2.21376	−	8.26186i	0.0708244	−	0.264320i	−0.921430	−	0.388545i	$-0.872978\pi$
$977$	2.21376	−	8.26186i	0.0708244	−	0.264320i	0.992254	+	0.124225i	$0.0396444\pi$
$978$		0			0
$979$	−2.67415	+	9.98007i	−0.0854663	+	0.318964i
$980$		0			0
$981$	−14.7946	+	1.22057i	−0.472354	+	0.0389699i
$982$		0			0
$983$	−19.4970	−	33.7698i	−0.621858	−	1.07709i	−0.989140	−	0.146979i	$-0.953045\pi$
$983$	−19.4970	−	33.7698i	−0.621858	−	1.07709i	0.367282	−	0.930110i	$-0.380288\pi$
$984$		0			0
$985$	−27.9841	−	27.9841i	−0.891647	−	0.891647i
$986$		0			0
$987$	26.3944	−	12.2285i	0.840144	−	0.389236i
$988$		0			0
$989$	−90.1947			−2.86803
$990$		0			0
$991$	10.4846	−	10.4846i	0.333056	−	0.333056i	−0.520690	−	0.853746i	$-0.674325\pi$
$991$	10.4846	−	10.4846i	0.333056	−	0.333056i	0.853746	+	0.520690i	$0.174325\pi$
$992$		0			0
$993$	8.77812	+	10.5141i	0.278565	+	0.333655i
$994$		0			0
$995$	48.3737	+	27.9286i	1.53355	+	0.885395i
$996$		0			0
$997$	6.82342	−	25.4654i	0.216100	−	0.806496i	−0.769677	−	0.638434i	$-0.779583\pi$
$997$	6.82342	−	25.4654i	0.216100	−	0.806496i	0.985776	−	0.168062i	$-0.0537508\pi$
$998$		0			0
$999$	−28.3798	+	13.9135i	−0.897898	+	0.440204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.785.27	yes	152
3.2	odd	2	inner	888.2.br.a.785.13	yes	152
37.14	odd	12	inner	888.2.br.a.569.13	✓	152
111.14	even	12	inner	888.2.br.a.569.27	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.13	✓	152	37.14	odd	12	inner
888.2.br.a.569.27	yes	152	111.14	even	12	inner
888.2.br.a.785.13	yes	152	3.2	odd	2	inner
888.2.br.a.785.27	yes	152	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.996973 - 1.41635i) q^{3} +(-0.601400 - 2.24446i) q^{5} +(-0.786614 + 1.36246i) q^{7} +(-1.01209 - 2.82412i) q^{9} -0.738125 q^{11} +(-5.22905 + 1.40112i) q^{13} +(-3.77851 - 1.38587i) q^{15} +(-6.88427 - 1.84463i) q^{17} +(-2.79810 + 0.749750i) q^{19} +(1.14548 + 2.47245i) q^{21} +(5.90122 - 5.90122i) q^{23} +(-0.345771 + 0.199631i) q^{25} +(-5.00897 - 1.38210i) q^{27} +(5.65819 + 5.65819i) q^{29} +(-1.19809 + 1.19809i) q^{31} +(-0.735890 + 1.04544i) q^{33} +(3.53104 + 0.946139i) q^{35} +(4.55273 - 4.03393i) q^{37} +(-3.22875 + 8.80304i) q^{39} +(-4.27854 + 7.41065i) q^{41} +(-7.64204 - 7.64204i) q^{43} +(-5.72995 + 3.97002i) q^{45} -10.6754i q^{47} +(2.26248 + 3.91872i) q^{49} +(-9.47607 + 7.91148i) q^{51} +(4.00020 - 2.30952i) q^{53} +(0.443908 + 1.65669i) q^{55} +(-1.72773 + 4.71057i) q^{57} +(-2.81778 - 0.755023i) q^{59} +(-2.69213 - 10.0472i) q^{61} +(4.64387 + 0.842568i) q^{63} +(6.28950 + 10.8937i) q^{65} +(-5.21175 - 3.00900i) q^{67} +(-2.47483 - 14.2415i) q^{69} +(2.51092 + 1.44968i) q^{71} +14.9577i q^{73} +(-0.0619772 + 0.688760i) q^{75} +(0.580619 - 1.00566i) q^{77} +(-1.59192 + 0.426553i) q^{79} +(-6.95135 + 5.71653i) q^{81} +(12.2447 - 7.06950i) q^{83} +16.5608i q^{85} +(13.6550 - 2.37291i) q^{87} +(3.62290 - 13.5208i) q^{89} +(2.20428 - 8.22649i) q^{91} +(0.502450 + 2.89138i) q^{93} +(3.36556 + 5.82932i) q^{95} +(0.824155 + 0.824155i) q^{97} +(0.747049 + 2.08456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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