LMFDB - Embedded newform 888.2.br.a.569.27

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)

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")

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);

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			569.27
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.27

$q$-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 $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

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	0.690831	+	0.723016i	$0.257245\pi$
$5$	−0.601400	+	2.24446i	−0.268954	+	1.00375i	−0.959785	+	0.280735i	$0.909422\pi$
$6$		0			0
$7$	−0.786614	−	1.36246i	−0.297312	−	0.514960i	0.678208	−	0.734870i	$-0.262757\pi$
$7$	−0.786614	−	1.36246i	−0.297312	−	0.514960i	−0.975520	+	0.219910i	$0.929424\pi$
$8$		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	−0.554158	−	0.832412i	$-0.686960\pi$
$13$	−5.22905	−	1.40112i	−1.45028	−	0.388601i	−0.896120	+	0.443811i	$0.853626\pi$
$14$		0			0
$15$	−3.77851	+	1.38587i	−0.975608	+	0.357830i
$16$		0			0
$17$	−6.88427	+	1.84463i	−1.66968	+	0.447389i	−0.965024	−	0.262160i	$-0.915565\pi$
$17$	−6.88427	+	1.84463i	−1.66968	+	0.447389i	−0.704656	+	0.709549i	$0.748899\pi$
$18$		0			0
$19$	−2.79810	−	0.749750i	−0.641929	−	0.172004i	−0.0768521	−	0.997043i	$-0.524487\pi$
$19$	−2.79810	−	0.749750i	−0.641929	−	0.172004i	−0.565077	+	0.825038i	$0.691154\pi$
$20$		0			0
$21$	1.14548	−	2.47245i	0.249964	−	0.539533i
$22$		0			0
$23$	5.90122	+	5.90122i	1.23049	+	1.23049i	0.963776	+	0.266713i	$0.0859376\pi$
$23$	5.90122	+	5.90122i	1.23049	+	1.23049i	0.266713	+	0.963776i	$0.414062\pi$
$24$		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	0.0520557	−	0.998644i	$-0.483423\pi$
$29$	5.65819	−	5.65819i	1.05070	−	1.05070i	0.998644	−	0.0520557i	$-0.0165773\pi$
$30$		0			0
$31$	−1.19809	−	1.19809i	−0.215183	−	0.215183i	0.591282	−	0.806465i	$-0.298622\pi$
$31$	−1.19809	−	1.19809i	−0.215183	−	0.215183i	−0.806465	+	0.591282i	$0.798622\pi$
$32$		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	−0.978408	−	0.206682i	$-0.933733\pi$
$41$	−4.27854	−	7.41065i	−0.668196	−	1.15735i	0.310212	−	0.950667i	$-0.399600\pi$
$42$		0			0
$43$	−7.64204	+	7.64204i	−1.16540	+	1.16540i	−0.182125	+	0.983275i	$0.558298\pi$
$43$	−7.64204	+	7.64204i	−1.16540	+	1.16540i	−0.983275	+	0.182125i	$0.941702\pi$
$44$		0			0
$45$	−5.72995	−	3.97002i	−0.854170	−	0.591815i
$46$		0			0
$47$			10.6754i			1.55717i	0.627540	+	0.778584i	$0.284062\pi$
$47$			10.6754i			1.55717i	−0.627540	+	0.778584i	$0.715938\pi$
$48$		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	0.748908	−	0.662674i	$-0.230578\pi$
$53$	4.00020	+	2.30952i	0.549470	+	0.317237i	−0.199438	+	0.979910i	$0.563912\pi$
$54$		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	−0.437532	−	0.899203i	$-0.644147\pi$
$59$	−2.81778	+	0.755023i	−0.366844	+	0.0982956i	0.0706878	+	0.997498i	$0.477481\pi$
$60$		0			0
$61$	−2.69213	+	10.0472i	−0.344692	+	1.28641i	0.548280	+	0.836295i	$0.315283\pi$
$61$	−2.69213	+	10.0472i	−0.344692	+	1.28641i	−0.892972	+	0.450112i	$0.851384\pi$
$62$		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	−0.783348	−	0.621583i	$-0.786490\pi$
$67$	−5.21175	+	3.00900i	−0.636716	+	0.367608i	0.146632	+	0.989191i	$0.453157\pi$
$68$		0			0
$69$	−2.47483	+	14.2415i	−0.297935	+	1.71448i
$70$		0			0
$71$	2.51092	−	1.44968i	0.297991	−	0.172045i	−0.343549	−	0.939135i	$-0.611629\pi$
$71$	2.51092	−	1.44968i	0.297991	−	0.172045i	0.641540	+	0.767089i	$0.278296\pi$
$72$		0			0
$73$		−	14.9577i		−	1.75067i	−0.483517	−	0.875335i	$-0.660641\pi$
$73$		−	14.9577i		−	1.75067i	0.483517	−	0.875335i	$-0.339359\pi$
$74$		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	0.168152	−	0.985761i	$-0.446220\pi$
$79$	−1.59192	−	0.426553i	−0.179105	−	0.0479910i	−0.347257	+	0.937770i	$0.612887\pi$
$80$		0			0
$81$	−6.95135	−	5.71653i	−0.772372	−	0.635170i
$82$		0			0
$83$	12.2447	+	7.06950i	1.34403	+	0.775979i	0.987397	−	0.158264i	$-0.0505896\pi$
$83$	12.2447	+	7.06950i	1.34403	+	0.775979i	0.356638	+	0.934243i	$0.383923\pi$
$84$		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	0.839695	+	0.543058i	$0.182733\pi$
$89$	3.62290	+	13.5208i	0.384027	+	1.43321i	−0.455669	+	0.890149i	$0.650600\pi$
$90$		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	−0.664028	−	0.747708i	$-0.731154\pi$
$97$	0.824155	−	0.824155i	0.0836803	−	0.0836803i	0.747708	+	0.664028i	$0.231154\pi$
$98$		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	0.841129	−	0.540834i	$-0.181891\pi$
$103$	3.04766	+	3.04766i	0.300295	+	0.300295i	−0.540834	+	0.841129i	$0.681891\pi$
$104$		0			0
$105$	4.86042	+	4.05791i	0.474328	+	0.396012i
$106$		0			0
$107$	−9.26572	+	5.34957i	−0.895751	+	0.517162i	−0.875819	−	0.482639i	$-0.839678\pi$
$107$	−9.26572	+	5.34957i	−0.895751	+	0.517162i	−0.0199320	+	0.999801i	$0.506345\pi$
$108$		0			0
$109$	1.28071	+	4.77966i	0.122669	+	0.457809i	0.999746	−	0.0225422i	$-0.00717600\pi$
$109$	1.28071	+	4.77966i	0.122669	+	0.457809i	−0.877076	+	0.480351i	$0.840509\pi$
$110$		0			0
$111$	−1.17451	+	10.4700i	−0.111479	+	0.993767i
$112$		0			0
$113$	−2.34298	−	8.74411i	−0.220409	−	0.822577i	−0.984192	−	0.177104i	$-0.943327\pi$
$113$	−2.34298	−	8.74411i	−0.220409	−	0.822577i	0.763783	−	0.645473i	$-0.223340\pi$
$114$		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	−0.816529	−	0.577305i	$-0.804104\pi$
$127$	1.03336	−	1.78984i	0.0916963	−	0.158823i	0.908225	+	0.418482i	$0.137438\pi$
$128$		0			0
$129$	−18.4427	−	3.20489i	−1.62379	−	0.282175i
$130$		0			0
$131$	2.66749	+	9.95520i	0.233060	+	0.869790i	0.979014	+	0.203793i	$0.0653270\pi$
$131$	2.66749	+	9.95520i	0.233060	+	0.869790i	−0.745954	+	0.665997i	$0.768006\pi$
$132$		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	$0.0602466\pi$
$137$			4.40430i			0.376285i	−0.982142	+	0.188142i	$0.939753\pi$
$138$		0			0
$139$	13.9351	+	8.04542i	1.18196	+	0.682404i	0.956467	−	0.291842i	$-0.0942680\pi$
$139$	13.9351	+	8.04542i	1.18196	+	0.682404i	0.225491	+	0.974245i	$0.427601\pi$
$140$		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	$0.0780691\pi$
$149$			5.92774i			0.485620i	−0.970074	+	0.242810i	$0.921931\pi$
$150$		0			0
$151$	13.3541	−	7.71000i	1.08674	−	0.627431i	0.154035	−	0.988065i	$-0.450773\pi$
$151$	13.3541	−	7.71000i	1.08674	−	0.627431i	0.932707	+	0.360635i	$0.117440\pi$
$152$		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	−0.821469	−	0.570253i	$-0.806845\pi$
$157$	1.04147	−	1.80388i	0.0831185	−	0.143965i	0.904588	+	0.426287i	$0.140179\pi$
$158$		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	0.262602	−	0.964904i	$-0.415419\pi$
$163$	12.4157	−	3.32678i	0.972475	−	0.260574i	0.709872	+	0.704330i	$0.248753\pi$
$164$		0			0
$165$	2.78901	−	1.02294i	0.217124	−	0.0796361i
$166$		0			0
$167$	−1.49582	+	5.58247i	−0.115750	+	0.431984i	−0.999342	−	0.0362731i	$-0.988451\pi$
$167$	−1.49582	+	5.58247i	−0.115750	+	0.431984i	0.883592	+	0.468258i	$0.155118\pi$
$168$		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	−0.959371	−	0.282148i	$-0.908953\pi$
$173$	−3.09539	+	5.36137i	−0.235338	+	0.407618i	0.724033	+	0.689766i	$0.242286\pi$
$174$		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	−0.919947	−	0.392042i	$-0.871769\pi$
$179$	−7.06290	+	7.06290i	−0.527906	+	0.527906i	0.392042	+	0.919947i	$0.371769\pi$
$180$		0			0
$181$	−7.74084	−	13.4075i	−0.575372	−	0.996574i	−0.996001	−	0.0893411i	$-0.971524\pi$
$181$	−7.74084	−	13.4075i	−0.575372	−	0.996574i	0.420629	−	0.907233i	$-0.361809\pi$
$182$		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	0.870237	−	0.492633i	$-0.163965\pi$
$191$	5.21860	+	5.21860i	0.377605	+	0.377605i	−0.492633	+	0.870237i	$0.663965\pi$
$192$		0			0
$193$	11.6023	−	11.6023i	0.835153	−	0.835153i	−0.153064	−	0.988216i	$-0.548914\pi$
$193$	11.6023	−	11.6023i	0.835153	−	0.835153i	0.988216	+	0.153064i	$0.0489140\pi$
$194$		0			0
$195$	21.6998	−	1.95263i	1.55396	−	0.139831i
$196$		0			0
$197$	14.7499	+	8.51587i	1.05089	+	0.606730i	0.922898	−	0.385045i	$-0.125814\pi$
$197$	14.7499	+	8.51587i	1.05089	+	0.606730i	0.127990	+	0.991775i	$0.459147\pi$
$198$		0			0
$199$	−16.9980	−	16.9980i	−1.20495	−	1.20495i	−0.972641	−	0.232312i	$-0.925371\pi$
$199$	−16.9980	−	16.9980i	−1.20495	−	1.20495i	−0.232312	−	0.972641i	$-0.574629\pi$
$200$		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	−0.873583	−	0.486675i	$-0.838210\pi$
$227$	1.90289	−	7.10169i	0.126299	−	0.471356i	0.999883	+	0.0153191i	$0.00487640\pi$
$228$		0			0
$229$	−5.67009	−	9.82088i	−0.374690	−	0.648982i	0.615591	−	0.788066i	$-0.288918\pi$
$229$	−5.67009	−	9.82088i	−0.374690	−	0.648982i	−0.990281	+	0.139084i	$0.955584\pi$
$230$		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	0.155465	−	0.987841i	$-0.450312\pi$
$239$	12.1207	−	3.24773i	0.784022	−	0.210078i	0.628557	+	0.777763i	$0.283646\pi$
$240$		0			0
$241$	2.41369	+	0.646746i	0.155479	+	0.0416606i	0.335719	−	0.941962i	$-0.391021\pi$
$241$	2.41369	+	0.646746i	0.155479	+	0.0416606i	−0.180240	+	0.983623i	$0.557687\pi$
$242$		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	−0.961148	−	0.276035i	$-0.910980\pi$
$251$	−10.8542	+	10.8542i	−0.685113	+	0.685113i	0.276035	+	0.961148i	$0.410980\pi$
$252$		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	0.405983	−	0.913881i	$-0.366929\pi$
$257$	19.4702	−	5.21701i	1.21451	−	0.325428i	0.808532	+	0.588452i	$0.200263\pi$
$258$		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	0.999953	−	0.00968732i	$-0.00308362\pi$
$263$	7.97220	+	13.8083i	0.491587	+	0.851454i	−0.508366	+	0.861141i	$0.669750\pi$
$264$		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	$0.0823350\pi$
$269$			8.39048i			0.511577i	−0.966733	+	0.255788i	$0.917665\pi$
$270$		0			0
$271$	−10.4866	+	18.1634i	−0.637017	+	1.10335i	0.349066	+	0.937098i	$0.386499\pi$
$271$	−10.4866	+	18.1634i	−0.637017	+	1.10335i	−0.986084	+	0.166249i	$0.946835\pi$
$272$		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	−0.998513	−	0.0545133i	$-0.982639\pi$
$277$	−1.77283	+	6.61627i	−0.106519	+	0.397533i	0.891994	+	0.452047i	$0.149306\pi$
$278$		0			0
$279$	4.59613	−	2.17098i	0.275163	−	0.129973i
$280$		0			0
$281$	−0.511629	+	0.137091i	−0.0305213	+	0.00817815i	−0.274047	−	0.961716i	$-0.588363\pi$
$281$	−0.511629	+	0.137091i	−0.0305213	+	0.00817815i	0.243526	+	0.969894i	$0.421696\pi$
$282$		0			0
$283$	−4.37955	+	16.3447i	−0.260337	+	0.971593i	0.704705	+	0.709500i	$0.251079\pi$
$283$	−4.37955	+	16.3447i	−0.260337	+	0.971593i	−0.965043	+	0.262092i	$0.915587\pi$
$284$		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	−0.542782	−	0.839873i	$-0.682629\pi$
$293$	−1.48615	+	0.858026i	−0.0868215	+	0.0501264i	0.455961	+	0.890000i	$0.349296\pi$
$294$		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	$0.0100215\pi$
$307$			1.10309i			0.0629568i	−0.999504	+	0.0314784i	$0.989978\pi$
$308$		0			0
$309$	−1.27812	+	7.35499i	−0.0727095	+	0.418411i
$310$		0			0
$311$	−6.46091	−	24.1124i	−0.366364	−	1.36729i	−0.865562	−	0.500802i	$-0.833038\pi$
$311$	−6.46091	−	24.1124i	−0.366364	−	1.36729i	0.499198	−	0.866488i	$-0.333628\pi$
$312$		0			0
$313$	1.74599	+	6.51613i	0.0986892	+	0.368313i	0.997553	−	0.0699151i	$-0.0222728\pi$
$313$	1.74599	+	6.51613i	0.0986892	+	0.368313i	−0.898864	+	0.438228i	$0.855606\pi$
$314$		0			0
$315$	−0.901715	+	10.9297i	−0.0508059	+	0.615817i
$316$		0			0
$317$	1.30334	−	2.25745i	0.0732029	−	0.126791i	−0.827100	−	0.562054i	$-0.810011\pi$
$317$	1.30334	−	2.25745i	0.0732029	−	0.126791i	0.900303	+	0.435263i	$0.143345\pi$
$318$		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	0.886591	−	0.462555i	$-0.153067\pi$
$331$	−2.04670	−	7.63839i	−0.112497	−	0.419844i	−0.999087	+	0.0427110i	$0.986401\pi$
$332$		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	−0.455697	−	0.890135i	$-0.650610\pi$
$337$	1.60325	−	0.925638i	0.0873347	−	0.0504227i	0.543031	+	0.839712i	$0.317276\pi$
$338$		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	−0.887211	−	0.461364i	$-0.847360\pi$
$347$	−7.93266	+	7.93266i	−0.425848	+	0.425848i	0.461364	+	0.887211i	$0.347360\pi$
$348$		0			0
$349$	10.9449	−	18.9571i	0.585866	−	1.01475i	−0.408901	−	0.912579i	$-0.634088\pi$
$349$	10.9449	−	18.9571i	0.585866	−	1.01475i	0.994767	−	0.102171i	$-0.0325787\pi$
$350$		0			0
$351$	28.1287	−	0.208914i	1.50140	−	0.0111510i
$352$		0			0
$353$	3.38668	+	12.6392i	0.180255	+	0.672719i	0.995597	+	0.0937398i	$0.0298822\pi$
$353$	3.38668	+	12.6392i	0.180255	+	0.672719i	−0.815342	+	0.578979i	$0.803451\pi$
$354$		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	$-0.901078\pi$
$359$		−	11.5880i		−	0.611590i	0.952097	−	0.305795i	$-0.0989222\pi$
$360$		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	0.972052	−	0.234767i	$-0.0754328\pi$
$367$	5.41597	+	9.38074i	0.282711	+	0.489671i	−0.689340	+	0.724438i	$0.742099\pi$
$368$		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	0.117401	−	0.993085i	$-0.462544\pi$
$373$	20.0111	−	11.5534i	1.03614	−	0.598214i	0.918737	+	0.394870i	$0.129211\pi$
$374$		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	−0.999998	−	0.00194516i	$-0.999381\pi$
$379$	−9.70115	+	16.8029i	−0.498314	+	0.863106i	0.501684	+	0.865051i	$0.332714\pi$
$380$		0			0
$381$	3.56527	−	0.320817i	0.182655	−	0.0164359i
$382$		0			0
$383$	3.55621	−	13.2720i	0.181714	−	0.678166i	−0.813596	−	0.581430i	$-0.802493\pi$
$383$	3.55621	−	13.2720i	0.181714	−	0.678166i	0.995310	−	0.0967353i	$-0.0308400\pi$
$384$		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	−0.984691	−	0.174308i	$-0.944231\pi$
$389$	−0.882991	+	3.29537i	−0.0447694	+	0.167082i	0.939922	+	0.341390i	$0.110898\pi$
$390$		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	$-0.853291\pi$
$397$		−	17.7233i		−	0.889506i	0.895653	−	0.444753i	$-0.146709\pi$
$398$		0			0
$399$	−5.05889	+	6.05935i	−0.253261	+	0.303347i
$400$		0			0
$401$	−3.96835	+	3.96835i	−0.198170	+	0.198170i	−0.799215	−	0.601045i	$-0.794751\pi$
$401$	−3.96835	+	3.96835i	−0.198170	+	0.198170i	0.601045	+	0.799215i	$0.294751\pi$
$402$		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	−0.773877	−	0.633336i	$-0.781685\pi$
$409$	−22.8004	+	6.10934i	−1.12741	+	0.302087i	−0.353529	+	0.935424i	$0.615018\pi$
$410$		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	0.259972	−	0.965616i	$-0.416287\pi$
$419$	−9.13532	−	5.27428i	−0.446289	−	0.257665i	−0.706262	+	0.707951i	$0.749620\pi$
$420$		0			0
$421$	−1.74417	−	1.74417i	−0.0850059	−	0.0850059i	0.663325	−	0.748331i	$-0.269145\pi$
$421$	−1.74417	−	1.74417i	−0.0850059	−	0.0850059i	−0.748331	+	0.663325i	$0.769145\pi$
$422$		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	−0.301577	−	0.953442i	$-0.597513\pi$
$431$	−21.5800	−	5.78234i	−1.03947	−	0.278525i	−0.737894	+	0.674916i	$0.764180\pi$
$432$		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	0.309621	+	0.950860i	$0.399798\pi$
$439$	−9.09223	+	33.9327i	−0.433949	+	1.61952i	−0.743570	+	0.668658i	$0.766869\pi$
$440$		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	−0.981111	−	0.193448i	$-0.938033\pi$
$449$	−0.735701	+	2.74567i	−0.0347199	+	0.129576i	0.946391	+	0.323024i	$0.104700\pi$
$450$		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	−0.606821	−	0.794839i	$-0.707555\pi$
$457$	−32.7026	−	8.76263i	−1.52976	−	0.409899i	−0.922941	+	0.384940i	$0.874222\pi$
$458$		0			0
$459$	31.9336	−	18.7545i	1.49053	−	0.875384i
$460$		0			0
$461$	−34.9168	+	9.35594i	−1.62624	+	0.435749i	−0.952826	−	0.303517i	$-0.901839\pi$
$461$	−34.9168	+	9.35594i	−1.62624	+	0.435749i	−0.673413	+	0.739267i	$0.735172\pi$
$462$		0			0
$463$	10.7494	+	2.88030i	0.499568	+	0.133859i	0.499799	−	0.866141i	$-0.333407\pi$
$463$	10.7494	+	2.88030i	0.499568	+	0.133859i	−0.000231714		1.00000i	$0.500074\pi$
$464$		0			0
$465$	6.18739	+	2.86660i	0.286933	+	0.132935i
$466$		0			0
$467$	4.40877	+	4.40877i	0.204013	+	0.204013i	0.801717	−	0.597704i	$-0.203920\pi$
$467$	4.40877	+	4.40877i	0.204013	+	0.204013i	−0.597704	+	0.801717i	$0.703920\pi$
$468$		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	0.439941	−	0.898027i	$-0.354999\pi$
$479$	27.7943	−	7.44746i	1.26995	−	0.340283i	0.830014	+	0.557743i	$0.188333\pi$
$480$		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	−0.124724	−	0.992191i	$-0.539805\pi$
$487$	19.1433	−	19.1433i	0.867467	−	0.867467i	0.992191	+	0.124724i	$0.0398046\pi$
$488$		0			0
$489$	17.0900	+	14.2683i	0.772838	+	0.645234i
$490$		0			0
$491$			26.1251i			1.17901i	0.807766	+	0.589504i	$0.200677\pi$
$491$			26.1251i			1.17901i	−0.807766	+	0.589504i	$0.799323\pi$
$492$		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	−0.964031	−	0.265790i	$-0.914367\pi$
$499$	0.0835255	−	0.311722i	0.00373912	−	0.0139546i	0.967770	+	0.251835i	$0.0810340\pi$
$500$		0			0
$501$	−9.39802	+	3.44697i	−0.419872	+	0.153999i
$502$		0			0
$503$	3.07410	−	0.823702i	0.137067	−	0.0367271i	−0.189633	−	0.981855i	$-0.560730\pi$
$503$	3.07410	−	0.823702i	0.137067	−	0.0367271i	0.326700	+	0.945128i	$0.394063\pi$
$504$		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	−0.884644	−	0.466267i	$-0.845598\pi$
$509$	−0.869109	+	1.50534i	−0.0385226	+	0.0667231i	0.846121	+	0.532990i	$0.178932\pi$
$510$		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	−0.963043	−	0.269347i	$-0.913192\pi$
$521$	−16.3152	−	28.2588i	−0.714783	−	1.23804i	0.248260	−	0.968693i	$-0.420141\pi$
$522$		0			0
$523$	8.61180	+	2.30753i	0.376568	+	0.100901i	0.442138	−	0.896947i	$-0.354220\pi$
$523$	8.61180	+	2.30753i	0.376568	+	0.100901i	−0.0655704	+	0.997848i	$0.520887\pi$
$524$		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	−0.0804666	+	0.996757i	$0.525641\pi$
$541$	−25.0556	+	25.0556i	−1.07722	+	1.07722i	−0.996757	+	0.0804666i	$0.974359\pi$
$542$		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	0.309943	−	0.950755i	$-0.399690\pi$
$547$	−14.9873	−	14.9873i	−0.640813	−	0.640813i	−0.950755	+	0.309943i	$0.899690\pi$
$548$		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	0.947574	−	0.319535i	$-0.103527\pi$
$557$	−0.774505	−	2.89049i	−0.0328168	−	0.122474i	−0.980391	+	0.197061i	$0.936860\pi$
$558$		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	0.448467	−	0.893799i	$-0.351970\pi$
$563$	−10.5667	−	10.5667i	−0.445333	−	0.445333i	−0.893799	+	0.448467i	$0.851970\pi$
$564$		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	−0.137375	−	0.990519i	$-0.543867\pi$
$569$	20.3507	−	20.3507i	0.853144	−	0.853144i	0.990519	+	0.137375i	$0.0438666\pi$
$570$		0			0
$571$	−4.11144	+	7.12122i	−0.172058	+	0.298014i	−0.939139	−	0.343537i	$-0.888375\pi$
$571$	−4.11144	+	7.12122i	−0.172058	+	0.298014i	0.767081	+	0.641550i	$0.221708\pi$
$572$		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	0.910300	+	0.413949i	$0.135851\pi$
$577$	7.90121	+	29.4877i	0.328932	+	1.22759i	−0.581368	+	0.813640i	$0.697482\pi$
$578$		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	0.0875968	−	0.996156i	$-0.472081\pi$
$587$	−8.10721	−	2.17232i	−0.334620	−	0.0896612i	−0.422217	+	0.906495i	$0.638748\pi$
$588$		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	$-0.868636\pi$
$593$		−	19.5338i		−	0.802155i	0.916044	−	0.401078i	$-0.131364\pi$
$594$		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	−0.503451	−	0.864024i	$-0.667936\pi$
$599$	−0.169109	+	0.0976351i	−0.00690960	+	0.00398926i	0.496541	+	0.868013i	$0.334603\pi$
$600$		0			0
$601$	17.8418	−	30.9029i	0.727782	−	1.26055i	−0.230037	−	0.973182i	$-0.573885\pi$
$601$	17.8418	−	30.9029i	0.727782	−	1.26055i	0.957819	−	0.287373i	$-0.0927818\pi$
$602$		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	−0.0470466	−	0.998893i	$-0.514981\pi$
$607$	10.1421	−	2.71757i	0.411656	−	0.110303i	0.458703	+	0.888590i	$0.348314\pi$
$608$		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	0.315847	−	0.948810i	$-0.397711\pi$
$613$	−8.61416	−	4.97339i	−0.347923	−	0.200873i	−0.663770	+	0.747937i	$0.731045\pi$
$614$		0			0
$615$	26.4367	+	22.0717i	1.06603	+	0.890018i
$616$		0			0
$617$	−5.84248	+	10.1195i	−0.235210	+	0.407395i	−0.959334	−	0.282275i	$-0.908911\pi$
$617$	−5.84248	+	10.1195i	−0.235210	+	0.407395i	0.724124	+	0.689670i	$0.242244\pi$
$618$		0			0
$619$		−	1.66106i		−	0.0667635i	−0.999443	−	0.0333818i	$-0.989372\pi$
$619$		−	1.66106i		−	0.0667635i	0.999443	−	0.0333818i	$-0.0106277\pi$
$620$		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	0.0989317	−	0.995094i	$-0.468457\pi$
$631$	17.1356	−	4.59146i	0.682156	−	0.182783i	0.583224	+	0.812311i	$0.301791\pi$
$632$		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	0.324816	−	0.945777i	$-0.394698\pi$
$641$	−8.40159	−	4.85066i	−0.331843	−	0.191590i	−0.656659	+	0.754188i	$0.728031\pi$
$642$		0			0
$643$	20.6922	+	20.6922i	0.816021	+	0.816021i	0.985529	−	0.169508i	$-0.0542178\pi$
$643$	20.6922	+	20.6922i	0.816021	+	0.816021i	−0.169508	+	0.985529i	$0.554218\pi$
$644$		0			0
$645$	18.2847	−	39.4664i	0.719959	−	1.55399i
$646$		0			0
$647$	−45.9218	−	12.3047i	−1.80537	−	0.483748i	−0.810576	−	0.585633i	$-0.800846\pi$
$647$	−45.9218	−	12.3047i	−1.80537	−	0.483748i	−0.994796	+	0.101885i	$0.967513\pi$
$648$		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	0.560438	−	0.828196i	$-0.310633\pi$
$653$	16.1422	+	4.32530i	0.631694	+	0.169262i	0.0712560	+	0.997458i	$0.477299\pi$
$654$		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	0.557430	−	0.830224i	$-0.311787\pi$
$659$	−11.3024	−	19.5764i	−0.440280	−	0.762587i	−0.997710	+	0.0676367i	$0.978454\pi$
$660$		0			0
$661$	−0.890448	+	3.32320i	−0.0346344	+	0.129257i	−0.981079	−	0.193610i	$-0.937980\pi$
$661$	−0.890448	+	3.32320i	−0.0346344	+	0.129257i	0.946444	+	0.322868i	$0.104647\pi$
$662$		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	−0.993307	−	0.115508i	$-0.963150\pi$
$673$	−15.4794	−	26.8111i	−0.596686	−	1.03349i	0.396621	−	0.917983i	$-0.370183\pi$
$674$		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	−0.656301	−	0.754499i	$-0.727880\pi$
$683$	−22.1468	+	5.93422i	−0.847424	+	0.227067i	−0.191123	+	0.981566i	$0.561213\pi$
$684$		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	0.165657	−	0.986184i	$-0.447026\pi$
$691$	−15.9187	−	9.19065i	−0.605575	−	0.349629i	−0.771232	+	0.636555i	$0.780359\pi$
$692$		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	0.0168851	−	0.999857i	$-0.494625\pi$
$701$	14.0705	−	3.77019i	0.531437	−	0.142398i	0.514552	+	0.857459i	$0.327958\pi$
$702$		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	0.00358773	−	0.999994i	$-0.498858\pi$
$709$	26.7224	−	26.7224i	1.00358	−	1.00358i	0.999994	−	0.00358773i	$-0.00114201\pi$
$710$		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	0.993629	−	0.112704i	$-0.0359512\pi$
$719$	37.3478	+	21.5628i	1.39284	+	0.804156i	0.399210	+	0.916860i	$0.369285\pi$
$720$		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	−0.858046	−	0.513573i	$-0.828321\pi$
$727$	3.82417	−	14.2720i	0.141830	−	0.529318i	0.999876	−	0.0157449i	$-0.00501196\pi$
$728$		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	−0.661530	−	0.749918i	$-0.730093\pi$
$733$	−9.28224	+	5.35911i	−0.342847	+	0.197943i	0.318683	+	0.947861i	$0.396759\pi$
$734$		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	$0.0599026\pi$
$739$			10.1714i			0.374162i	−0.982345	+	0.187081i	$0.940097\pi$
$740$		0			0
$741$	2.43429	+	27.0526i	0.0894261	+	0.993802i
$742$		0			0
$743$	6.19620	+	10.7321i	0.227317	+	0.393724i	0.957012	−	0.290049i	$-0.0936714\pi$
$743$	6.19620	+	10.7321i	0.227317	+	0.393724i	−0.729695	+	0.683772i	$0.760338\pi$
$744$		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	$-0.934986\pi$
$751$		−	11.1169i		−	0.405660i	0.979214	−	0.202830i	$-0.0650138\pi$
$752$		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	0.971266	+	0.237995i	$0.0764902\pi$
$757$	6.85426	+	25.5805i	0.249122	+	0.929738i	−0.722144	+	0.691743i	$0.756843\pi$
$758$		0			0
$759$	1.82673	−	10.5120i	0.0663062	−	0.381563i
$760$		0			0
$761$	11.2680	−	19.5167i	0.408463	−	0.707479i	−0.586255	−	0.810127i	$-0.699398\pi$
$761$	11.2680	−	19.5167i	0.408463	−	0.707479i	0.994718	+	0.102648i	$0.0327315\pi$
$762$		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	0.982899	+	0.184145i	$0.0589516\pi$
$769$	32.3631	+	32.3631i	1.16704	+	1.16704i	0.184145	+	0.982899i	$0.441048\pi$
$770$		0			0
$771$	26.8003	+	22.3753i	0.965190	+	0.805827i
$772$		0			0
$773$	−17.1782	+	9.91786i	−0.617858	+	0.356721i	−0.776035	−	0.630690i	$-0.782772\pi$
$773$	−17.1782	+	9.91786i	−0.617858	+	0.356721i	0.158177	+	0.987411i	$0.449438\pi$
$774$		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	−0.927049	−	0.374940i	$-0.877663\pi$
$797$	−8.79885	−	32.8377i	−0.311671	−	1.16317i	0.615378	−	0.788232i	$-0.289003\pi$
$798$		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	−0.148708	−	0.988881i	$-0.547512\pi$
$809$	−21.9561	−	5.88311i	−0.771934	−	0.206839i	−0.623226	+	0.782042i	$0.714178\pi$
$810$		0			0
$811$	−14.5931	−	25.2761i	−0.512434	−	0.887562i	−0.999896	−	0.0144181i	$-0.995410\pi$
$811$	−14.5931	−	25.2761i	−0.512434	−	0.887562i	0.487462	−	0.873144i	$-0.337923\pi$
$812$		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	−0.0417829	−	0.999127i	$-0.513304\pi$
$821$	22.9968	−	13.2772i	0.802595	−	0.463378i	0.844378	+	0.535748i	$0.179970\pi$
$822$		0			0
$823$	−14.1533	+	24.5143i	−0.493354	+	0.854514i	−0.999971	−	0.00765756i	$-0.997562\pi$
$823$	−14.1533	+	24.5143i	−0.493354	+	0.854514i	0.506617	+	0.862171i	$0.330896\pi$
$824$		0			0
$825$	0.0457469	+	0.508390i	0.00159270	+	0.0176999i
$826$		0			0
$827$	−6.54668	+	24.4325i	−0.227650	+	0.849602i	0.753675	+	0.657247i	$0.228279\pi$
$827$	−6.54668	+	24.4325i	−0.227650	+	0.849602i	−0.981325	+	0.192355i	$0.938387\pi$
$828$		0			0
$829$	40.4430	−	10.8367i	1.40464	−	0.376373i	0.524633	−	0.851328i	$-0.324203\pi$
$829$	40.4430	−	10.8367i	1.40464	−	0.376373i	0.880010	+	0.474956i	$0.157536\pi$
$830$		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	−0.766732	−	0.641967i	$-0.778119\pi$
$839$	4.99925	−	8.65896i	0.172593	−	0.298941i	0.939326	+	0.343026i	$0.111452\pi$
$840$		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	−0.310963	−	0.950422i	$-0.600652\pi$
$853$	−3.06823	+	0.822129i	−0.105054	+	0.0281492i	0.205909	+	0.978571i	$0.433985\pi$
$854$		0			0
$855$	13.0565	+	15.4046i	0.446522	+	0.526825i
$856$		0			0
$857$	−1.38018	−	1.38018i	−0.0471460	−	0.0471460i	0.683141	−	0.730287i	$-0.260614\pi$
$857$	−1.38018	−	1.38018i	−0.0471460	−	0.0471460i	−0.730287	+	0.683141i	$0.760614\pi$
$858$		0			0
$859$	−37.4233	+	37.4233i	−1.27687	+	1.27687i	−0.334453	+	0.942412i	$0.608552\pi$
$859$	−37.4233	+	37.4233i	−1.27687	+	1.27687i	−0.942412	+	0.334453i	$0.891448\pi$
$860$		0			0
$861$	−23.2235	+	2.08974i	−0.791453	+	0.0712180i
$862$		0			0
$863$	−31.6227	−	18.2574i	−1.07645	−	0.621489i	−0.146513	−	0.989209i	$-0.546805\pi$
$863$	−31.6227	−	18.2574i	−1.07645	−	0.621489i	−0.929937	+	0.367720i	$0.880139\pi$
$864$		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	0.989557	+	0.144145i	$0.0460431\pi$
$881$	18.3911	+	31.8543i	0.619611	+	1.07320i	−0.369945	+	0.929054i	$0.620624\pi$
$882$		0			0
$883$	−10.8500	+	40.4928i	−0.365132	+	1.36269i	0.502110	+	0.864804i	$0.332557\pi$
$883$	−10.8500	+	40.4928i	−0.365132	+	1.36269i	−0.867242	+	0.497887i	$0.834109\pi$
$884$		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	0.848143	−	0.529767i	$-0.177720\pi$
$907$	39.6867	+	10.6340i	1.31777	+	0.353096i	0.469631	+	0.882863i	$0.344387\pi$
$908$		0			0
$909$	3.95887	−	11.0468i	0.131307	−	0.366399i
$910$		0			0
$911$	33.4058	+	33.4058i	1.10678	+	1.10678i	0.993571	+	0.113214i	$0.0361146\pi$
$911$	33.4058	+	33.4058i	1.10678	+	1.10678i	0.113214	+	0.993571i	$0.463885\pi$
$912$		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	0.999067	−	0.0431807i	$-0.0137491\pi$
$919$	28.9777	+	28.9777i	0.955887	+	0.955887i	−0.0431807	+	0.999067i	$0.513749\pi$
$920$		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	0.953081	−	0.302716i	$-0.0978933\pi$
$929$	6.53422	+	11.3176i	0.214381	+	0.371319i	−0.738700	+	0.674034i	$0.764560\pi$
$930$		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	−0.890505	−	0.454974i	$-0.849649\pi$
$937$	−1.56828	+	2.71634i	−0.0512334	+	0.0887388i	0.839271	+	0.543713i	$0.182982\pi$
$938$		0			0
$939$	−7.48840	+	8.96933i	−0.244375	+	0.292703i
$940$		0			0
$941$	0.104995	+	0.0606190i	0.00342275	+	0.00197612i	0.501710	−	0.865036i	$-0.332704\pi$
$941$	0.104995	+	0.0606190i	0.00342275	+	0.00197612i	−0.498288	+	0.867012i	$0.666038\pi$
$942$		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	0.320574	−	0.947224i	$-0.396124\pi$
$947$	32.9832	−	8.83783i	1.07181	−	0.287191i	0.751237	+	0.660033i	$0.229458\pi$
$948$		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	−0.694626	−	0.719371i	$-0.744430\pi$
$953$	8.51043	−	14.7405i	0.275680	−	0.477492i	0.970306	+	0.241879i	$0.0777637\pi$
$954$		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	0.641035	−	0.767512i	$-0.278505\pi$
$967$	25.2639	+	6.76943i	0.812431	+	0.217690i	0.171396	+	0.985202i	$0.445172\pi$
$968$		0			0
$969$	20.5834	+	29.2418i	0.661235	+	0.939383i
$970$		0			0
$971$	−38.6025	−	22.2872i	−1.23881	−	0.715229i	−0.269961	−	0.962871i	$-0.587011\pi$
$971$	−38.6025	−	22.2872i	−1.23881	−	0.715229i	−0.968851	+	0.247642i	$0.920344\pi$
$972$		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	0.992254	−	0.124225i	$-0.0396444\pi$
$977$	2.21376	+	8.26186i	0.0708244	+	0.264320i	−0.921430	+	0.388545i	$0.872978\pi$
$978$		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	0.367282	+	0.930110i	$0.380288\pi$
$983$	−19.4970	+	33.7698i	−0.621858	+	1.07709i	−0.989140	+	0.146979i	$0.953045\pi$
$984$		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	0.853746	−	0.520690i	$-0.174325\pi$
$991$	10.4846	+	10.4846i	0.333056	+	0.333056i	−0.520690	+	0.853746i	$0.674325\pi$
$992$		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	0.985776	+	0.168062i	$0.0537508\pi$
$997$	6.82342	+	25.4654i	0.216100	+	0.806496i	−0.769677	+	0.638434i	$0.779583\pi$
$998$		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.569.27	yes	152
3.2	odd	2	inner	888.2.br.a.569.13	✓	152
37.8	odd	12	inner	888.2.br.a.785.13	yes	152
111.8	even	12	inner	888.2.br.a.785.27	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.13	✓	152	3.2	odd	2	inner
888.2.br.a.569.27	yes	152	1.1	even	1	trivial
888.2.br.a.785.13	yes	152	37.8	odd	12	inner
888.2.br.a.785.27	yes	152	111.8	even	12	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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
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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