LMFDB - Embedded newform 888.2.br.a.785.13

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			785.13
Character	$\chi$	$=$	888.785
Dual form			888.2.br.a.569.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.728108 + 1.57158i) q^{3} +(0.601400 + 2.24446i) q^{5} +(-0.786614 + 1.36246i) q^{7} +(-1.93972 - 2.28856i) q^{9} +0.738125 q^{11} +(-5.22905 + 1.40112i) q^{13} +(-3.96522 - 0.689058i) q^{15} +(6.88427 + 1.84463i) q^{17} +(-2.79810 + 0.749750i) q^{19} +(-1.56847 - 2.22824i) q^{21} +(-5.90122 + 5.90122i) q^{23} +(-0.345771 + 0.199631i) q^{25} +(5.00897 - 1.38210i) q^{27} +(-5.65819 - 5.65819i) q^{29} +(-1.19809 + 1.19809i) q^{31} +(-0.537434 + 1.16002i) q^{33} +(-3.53104 - 0.946139i) q^{35} +(4.55273 - 4.03393i) q^{37} +(1.60534 - 9.23803i) q^{39} +(4.27854 - 7.41065i) q^{41} +(-7.64204 - 7.64204i) q^{43} +(3.97002 - 5.72995i) q^{45} +10.6754i q^{47} +(2.26248 + 3.91872i) q^{49} +(-7.91148 + 9.47607i) q^{51} +(-4.00020 + 2.30952i) q^{53} +(0.443908 + 1.65669i) q^{55} +(0.859031 - 4.94334i) q^{57} +(2.81778 + 0.755023i) q^{59} +(-2.69213 - 10.0472i) q^{61} +(4.64387 - 0.842568i) q^{63} +(-6.28950 - 10.8937i) q^{65} +(-5.21175 - 3.00900i) q^{67} +(-4.97750 - 13.5710i) q^{69} +(-2.51092 - 1.44968i) q^{71} +14.9577i q^{73} +(-0.0619772 - 0.688760i) q^{75} +(-0.580619 + 1.00566i) q^{77} +(-1.59192 + 0.426553i) q^{79} +(-1.47499 + 8.87831i) q^{81} +(-12.2447 + 7.06950i) q^{83} +16.5608i q^{85} +(13.0121 - 4.77252i) q^{87} +(-3.62290 + 13.5208i) q^{89} +(2.20428 - 8.22649i) q^{91} +(-1.01055 - 2.75523i) q^{93} +(-3.36556 - 5.82932i) q^{95} +(0.824155 + 0.824155i) q^{97} +(-1.43175 - 1.68924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.728108	+	1.57158i	−0.420373	+	0.907351i
$3$	−0.728108	+	1.57158i	−0.420373	+	0.907351i
$4$		0			0
$5$	0.601400	+	2.24446i	0.268954	+	1.00375i	0.959785	+	0.280735i	$0.0905781\pi$
$5$	0.601400	+	2.24446i	0.268954	+	1.00375i	−0.690831	+	0.723016i	$0.742755\pi$
$6$		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
$9$	−1.93972	−	2.28856i	−0.646573	−	0.762852i
$10$		0			0
$11$	0.738125			0.222553			0.111276	−	0.993789i	$-0.464506\pi$
$11$	0.738125			0.222553			0.111276	+	0.993789i	$0.464506\pi$
$12$		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
$15$	−3.96522	−	0.689058i	−1.02382	−	0.177914i
$16$		0			0
$17$	6.88427	+	1.84463i	1.66968	+	0.447389i	0.965024	−	0.262160i	$-0.0844348\pi$
$17$	6.88427	+	1.84463i	1.66968	+	0.447389i	0.704656	+	0.709549i	$0.251101\pi$
$18$		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
$21$	−1.56847	−	2.22824i	−0.342267	−	0.486242i
$22$		0			0
$23$	−5.90122	+	5.90122i	−1.23049	+	1.23049i	−0.266713	+	0.963776i	$0.585938\pi$
$23$	−5.90122	+	5.90122i	−1.23049	+	1.23049i	−0.963776	+	0.266713i	$0.914062\pi$
$24$		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	$-0.983423\pi$
$29$	−5.65819	−	5.65819i	−1.05070	−	1.05070i	−0.0520557	−	0.998644i	$-0.516577\pi$
$30$		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
$33$	−0.537434	+	1.16002i	−0.0935553	+	0.201934i
$34$		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
$39$	1.60534	−	9.23803i	0.257061	−	1.47927i
$40$		0			0
$41$	4.27854	−	7.41065i	0.668196	−	1.15735i	−0.310212	−	0.950667i	$-0.600400\pi$
$41$	4.27854	−	7.41065i	0.668196	−	1.15735i	0.978408	−	0.206682i	$-0.0662666\pi$
$42$		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
$45$	3.97002	−	5.72995i	0.591815	−	0.854170i
$46$		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
$51$	−7.91148	+	9.47607i	−1.10783	+	1.32692i
$52$		0			0
$53$	−4.00020	+	2.30952i	−0.549470	+	0.317237i	−0.748908	−	0.662674i	$-0.769422\pi$
$53$	−4.00020	+	2.30952i	−0.549470	+	0.317237i	0.199438	+	0.979910i	$0.436088\pi$
$54$		0			0
$55$	0.443908	+	1.65669i	0.0598566	+	0.223388i
$56$		0			0
$57$	0.859031	−	4.94334i	0.113781	−	0.654761i
$58$		0			0
$59$	2.81778	+	0.755023i	0.366844	+	0.0982956i	0.437532	−	0.899203i	$-0.355853\pi$
$59$	2.81778	+	0.755023i	0.366844	+	0.0982956i	−0.0706878	+	0.997498i	$0.522519\pi$
$60$		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
$69$	−4.97750	−	13.5710i	−0.599221	−	1.63375i
$70$		0			0
$71$	−2.51092	−	1.44968i	−0.297991	−	0.172045i	0.343549	−	0.939135i	$-0.388371\pi$
$71$	−2.51092	−	1.44968i	−0.297991	−	0.172045i	−0.641540	+	0.767089i	$0.721704\pi$
$72$		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
$81$	−1.47499	+	8.87831i	−0.163888	+	0.986479i
$82$		0			0
$83$	−12.2447	+	7.06950i	−1.34403	+	0.775979i	−0.987397	−	0.158264i	$-0.949410\pi$
$83$	−12.2447	+	7.06950i	−1.34403	+	0.775979i	−0.356638	+	0.934243i	$0.616077\pi$
$84$		0			0
$85$			16.5608i			1.79627i
$86$		0			0
$87$	13.0121	−	4.77252i	1.39504	−	0.511668i
$88$		0			0
$89$	−3.62290	+	13.5208i	−0.384027	+	1.43321i	0.455669	+	0.890149i	$0.349400\pi$
$89$	−3.62290	+	13.5208i	−0.384027	+	1.43321i	−0.839695	+	0.543058i	$0.817267\pi$
$90$		0			0
$91$	2.20428	−	8.22649i	0.231072	−	0.862371i
$92$		0			0
$93$	−1.01055	−	2.75523i	−0.104790	−	0.285704i
$94$		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
$99$	−1.43175	−	1.68924i	−0.143897	−	0.169775i
$100$		0			0
$101$	3.91158			0.389217			0.194608	−	0.980881i	$-0.437656\pi$
$101$	3.91158			0.389217			0.194608	+	0.980881i	$0.437656\pi$
$102$		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
$105$	4.05791	−	4.86042i	0.396012	−	0.474328i
$106$		0			0
$107$	9.26572	+	5.34957i	0.895751	+	0.517162i	0.875819	−	0.482639i	$-0.160322\pi$
$107$	9.26572	+	5.34957i	0.895751	+	0.517162i	0.0199320	+	0.999801i	$0.493655\pi$
$108$		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
$111$	3.02476	+	10.0921i	0.287098	+	0.957901i
$112$		0			0
$113$	2.34298	−	8.74411i	0.220409	−	0.822577i	−0.763783	−	0.645473i	$-0.776660\pi$
$113$	2.34298	−	8.74411i	0.220409	−	0.822577i	0.984192	−	0.177104i	$-0.0566729\pi$
$114$		0			0
$115$	−16.7940	−	9.69603i	−1.56605	−	0.904159i
$116$		0			0
$117$	13.3494	+	9.24921i	1.23416	+	0.855090i
$118$		0			0
$119$	−7.92849	+	7.92849i	−0.726804	+	0.726804i
$120$		0			0
$121$	−10.4552			−0.950470
$122$		0			0
$123$	8.53118	+	12.1198i	0.769231	+	1.09281i
$124$		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
$129$	17.5743	−	6.44584i	1.54733	−	0.567525i
$130$		0			0
$131$	−2.66749	+	9.95520i	−0.233060	+	0.869790i	0.745954	+	0.665997i	$0.231994\pi$
$131$	−2.66749	+	9.95520i	−0.233060	+	0.869790i	−0.979014	+	0.203793i	$0.934673\pi$
$132$		0			0
$133$	1.17953	−	4.40206i	0.102278	−	0.381707i
$134$		0			0
$135$	6.11446	+	10.4112i	0.526249	+	0.896055i
$136$		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	0.225491	−	0.974245i	$-0.427601\pi$
$139$	13.9351	−	8.04542i	1.18196	−	0.682404i	0.956467	+	0.291842i	$0.0942680\pi$
$140$		0			0
$141$	−16.7772	−	7.77285i	−1.41290	−	0.654592i
$142$		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	0.932707	−	0.360635i	$-0.117440\pi$
$151$	13.3541	+	7.71000i	1.08674	+	0.627431i	0.154035	+	0.988065i	$0.450773\pi$
$152$		0			0
$153$	−9.13199	−	19.3331i	−0.738277	−	1.56299i
$154$		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
$165$	−2.92683	−	0.508611i	−0.227853	−	0.0395953i
$166$		0			0
$167$	1.49582	+	5.58247i	0.115750	+	0.431984i	0.999342	−	0.0362731i	$-0.0115486\pi$
$167$	1.49582	+	5.58247i	0.115750	+	0.431984i	−0.883592	+	0.468258i	$0.844882\pi$
$168$		0			0
$169$	14.1215	−	8.15306i	1.08627	−	0.627159i
$170$		0			0
$171$	7.14338	+	4.94932i	0.546268	+	0.378484i
$172$		0			0
$173$	3.09539	+	5.36137i	0.235338	+	0.407618i	0.959371	−	0.282148i	$-0.0910469\pi$
$173$	3.09539	+	5.36137i	0.235338	+	0.407618i	−0.724033	+	0.689766i	$0.757714\pi$
$174$		0			0
$175$		−	0.628130i		−	0.0474822i
$176$		0			0
$177$	−3.23823	+	3.87863i	−0.243400	+	0.291536i
$178$		0			0
$179$	7.06290	+	7.06290i	0.527906	+	0.527906i	0.919947	−	0.392042i	$-0.128231\pi$
$179$	7.06290	+	7.06290i	0.527906	+	0.527906i	−0.392042	+	0.919947i	$0.628231\pi$
$180$		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
$183$	17.7501	+	3.08452i	1.31212	+	0.228015i
$184$		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
$189$	−2.05707	+	7.91168i	−0.149630	+	0.575490i
$190$		0			0
$191$	−5.21860	+	5.21860i	−0.377605	+	0.377605i	−0.870237	−	0.492633i	$-0.836035\pi$
$191$	−5.21860	+	5.21860i	−0.377605	+	0.377605i	0.492633	+	0.870237i	$0.336035\pi$
$192$		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	−0.922898	−	0.385045i	$-0.874186\pi$
$197$	−14.7499	+	8.51587i	−1.05089	+	0.606730i	−0.127990	+	0.991775i	$0.540853\pi$
$198$		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
$201$	8.52360	−	5.99979i	0.601208	−	0.423193i
$202$		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
$207$	24.9520	+	2.05858i	1.73428	+	0.143081i
$208$		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
$213$	4.10651	−	2.89059i	0.281373	−	0.198060i
$214$		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
$219$	−23.5072	−	10.8908i	−1.58847	−	0.735935i
$220$		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
$225$	1.12757	+	0.404089i	0.0751710	+	0.0269393i
$226$		0			0
$227$	−1.90289	−	7.10169i	−0.126299	−	0.471356i	0.873583	−	0.486675i	$-0.161790\pi$
$227$	−1.90289	−	7.10169i	−0.126299	−	0.471356i	−0.999883	+	0.0153191i	$0.995124\pi$
$228$		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
$231$	−1.15772	−	1.64472i	−0.0761726	−	0.108215i
$232$		0			0
$233$	24.3925			1.59801			0.799004	−	0.601325i	$-0.205360\pi$
$233$	24.3925			1.59801			0.799004	+	0.601325i	$0.205360\pi$
$234$		0			0
$235$	−23.9605	+	6.42019i	−1.56301	+	0.418807i
$236$		0			0
$237$	0.488727	−	2.81240i	0.0317462	−	0.182685i
$238$		0			0
$239$	−12.1207	−	3.24773i	−0.784022	−	0.210078i	−0.155465	−	0.987841i	$-0.549688\pi$
$239$	−12.1207	−	3.24773i	−0.784022	−	0.210078i	−0.628557	+	0.777763i	$0.716354\pi$
$240$		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
$243$	−12.8790	−	8.78243i	−0.826189	−	0.563393i
$244$		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	$-0.0890204\pi$
$251$	10.8542	+	10.8542i	0.685113	+	0.685113i	−0.276035	+	0.961148i	$0.589020\pi$
$252$		0			0
$253$	−4.35584	+	4.35584i	−0.273849	+	0.273849i
$254$		0			0
$255$	−26.0266	−	12.0580i	−1.62985	−	0.755104i
$256$		0			0
$257$	−19.4702	−	5.21701i	−1.21451	−	0.325428i	−0.405983	−	0.913881i	$-0.633071\pi$
$257$	−19.4702	−	5.21701i	−1.21451	−	0.325428i	−0.808532	+	0.588452i	$0.799737\pi$
$258$		0			0
$259$	1.91481	+	9.37605i	0.118981	+	0.582599i
$260$		0			0
$261$	−1.97380	+	23.9244i	−0.122175	+	1.48088i
$262$		0			0
$263$	−7.97220	+	13.8083i	−0.491587	+	0.851454i	−0.999953	−	0.00968732i	$-0.996916\pi$
$263$	−7.97220	+	13.8083i	−0.491587	+	0.851454i	0.508366	+	0.861141i	$0.330250\pi$
$264$		0			0
$265$	−7.58933	−	7.58933i	−0.466209	−	0.466209i
$266$		0			0
$267$	−18.6112	−	15.5383i	−1.13899	−	0.950929i
$268$		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	−0.986084	−	0.166249i	$-0.946835\pi$
$271$	−10.4866	−	18.1634i	−0.637017	−	1.10335i	0.349066	−	0.937098i	$-0.386499\pi$
$272$		0			0
$273$	11.3236	+	9.45398i	0.685337	+	0.572181i
$274$		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
$279$	5.06585	+	0.417941i	0.303285	+	0.0250215i
$280$		0			0
$281$	0.511629	+	0.137091i	0.0305213	+	0.00817815i	0.274047	−	0.961716i	$-0.411637\pi$
$281$	0.511629	+	0.137091i	0.0305213	+	0.00817815i	−0.243526	+	0.969894i	$0.578304\pi$
$282$		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
$291$	−1.89530	+	0.695151i	−0.111104	+	0.0407505i
$292$		0			0
$293$	1.48615	+	0.858026i	0.0868215	+	0.0501264i	0.542782	−	0.839873i	$-0.317371\pi$
$293$	1.48615	+	0.858026i	0.0868215	+	0.0501264i	−0.455961	+	0.890000i	$0.650704\pi$
$294$		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
$303$	−2.84805	+	6.14736i	−0.163616	+	0.353156i
$304$		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
$309$	2.57061	+	7.00867i	0.146237	+	0.398709i
$310$		0			0
$311$	6.46091	−	24.1124i	0.366364	−	1.36729i	−0.499198	−	0.866488i	$-0.666372\pi$
$311$	6.46091	−	24.1124i	0.366364	−	1.36729i	0.865562	−	0.500802i	$-0.166962\pi$
$312$		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
$315$	4.68393	+	9.91623i	0.263909	+	0.558716i
$316$		0			0
$317$	−1.30334	−	2.25745i	−0.0732029	−	0.126791i	0.827100	−	0.562054i	$-0.189989\pi$
$317$	−1.30334	−	2.25745i	−0.0732029	−	0.126791i	−0.900303	+	0.435263i	$0.856655\pi$
$318$		0			0
$319$	−4.17645	−	4.17645i	−0.233836	−	0.233836i
$320$		0			0
$321$	−15.1537	+	10.6668i	−0.845798	+	0.595360i
$322$		0			0
$323$	−20.6459			−1.14877
$324$		0			0
$325$	1.52835	−	1.52835i	0.0847775	−	0.0847775i
$326$		0			0
$327$	6.57912	+	5.49284i	0.363826	+	0.303755i
$328$		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
$333$	−18.0629	−	2.59450i	−0.989841	−	0.142177i
$334$		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
$339$	12.0361	+	10.0488i	0.653712	+	0.545777i
$340$		0			0
$341$	−0.884340	+	0.884340i	−0.0478897	+	0.0478897i
$342$		0			0
$343$	−18.1314			−0.979003
$344$		0			0
$345$	27.4659	−	19.3334i	1.47872	−	1.04087i
$346$		0			0
$347$	7.93266	+	7.93266i	0.425848	+	0.425848i	0.887211	−	0.461364i	$-0.152640\pi$
$347$	7.93266	+	7.93266i	0.425848	+	0.425848i	−0.461364	+	0.887211i	$0.652640\pi$
$348$		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
$351$	−24.2557	+	14.2453i	−1.29467	+	0.760356i
$352$		0			0
$353$	−3.38668	+	12.6392i	−0.180255	+	0.672719i	0.815342	+	0.578979i	$0.196549\pi$
$353$	−3.38668	+	12.6392i	−0.180255	+	0.672719i	−0.995597	+	0.0937398i	$0.970118\pi$
$354$		0			0
$355$	1.74368	−	6.50749i	0.0925447	−	0.345382i
$356$		0			0
$357$	−6.68745	−	18.2330i	−0.353937	−	0.964995i
$358$		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
$363$	7.61249	−	16.4311i	0.399552	−	0.862410i
$364$		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
$375$	−17.3839	+	6.37602i	−0.897703	+	0.329256i
$376$		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	$-0.969160\pi$
$383$	−3.55621	−	13.2720i	−0.181714	−	0.678166i	0.813596	−	0.581430i	$-0.197507\pi$
$384$		0			0
$385$	−2.60635	−	0.698369i	−0.132832	−	0.0355922i
$386$		0			0
$387$	−2.66585	+	32.3127i	−0.135513	+	1.64254i
$388$		0			0
$389$	0.882991	+	3.29537i	0.0447694	+	0.167082i	0.984691	−	0.174308i	$-0.0557689\pi$
$389$	0.882991	+	3.29537i	0.0447694	+	0.167082i	−0.939922	+	0.341390i	$0.889102\pi$
$390$		0			0
$391$	−51.5112	+	29.7400i	−2.60503	+	1.50402i
$392$		0			0
$393$	−13.7032	−	11.4406i	−0.691233	−	0.577103i
$394$		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
$399$	6.05935	+	5.05889i	0.303347	+	0.253261i
$400$		0			0
$401$	3.96835	+	3.96835i	0.198170	+	0.198170i	0.799215	−	0.601045i	$-0.205249\pi$
$401$	3.96835	+	3.96835i	0.198170	+	0.198170i	−0.601045	+	0.799215i	$0.705249\pi$
$402$		0			0
$403$	4.58621	−	7.94354i	0.228455	−	0.395696i
$404$		0			0
$405$	−20.8140	+	2.02887i	−1.03426	+	0.100815i
$406$		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
$411$	−6.92170	−	3.20680i	−0.341422	−	0.158180i
$412$		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	$-0.583713\pi$
$419$	9.13532	−	5.27428i	0.446289	−	0.257665i	0.706262	+	0.707951i	$0.250380\pi$
$420$		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
$423$	24.4313	−	20.7073i	1.18789	−	1.00682i
$424$		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
$429$	1.18494	−	6.81882i	0.0572096	−	0.329216i
$430$		0			0
$431$	21.5800	−	5.78234i	1.03947	−	0.278525i	0.301577	−	0.953442i	$-0.402487\pi$
$431$	21.5800	−	5.78234i	1.03947	−	0.278525i	0.737894	+	0.674916i	$0.235820\pi$
$432$		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
$435$	18.5372	+	26.3348i	0.888789	+	1.26266i
$436$		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
$441$	4.57966	−	12.7790i	0.218079	−	0.608525i
$442$		0			0
$443$	−22.8962			−1.08783			−0.543916	−	0.839139i	$-0.683059\pi$
$443$	−22.8962			−1.08783			−0.543916	+	0.839139i	$0.683059\pi$
$444$		0			0
$445$	−32.5258			−1.54187
$446$		0			0
$447$	−9.31592	−	4.31604i	−0.440628	−	0.204142i
$448$		0			0
$449$	0.735701	+	2.74567i	0.0347199	+	0.129576i	0.981111	−	0.193448i	$-0.0619671\pi$
$449$	0.735701	+	2.74567i	0.0347199	+	0.129576i	−0.946391	+	0.323024i	$0.895300\pi$
$450$		0			0
$451$	3.15810	−	5.46999i	0.148709	−	0.257572i
$452$		0			0
$453$	−21.8401	+	15.3733i	−1.02614	+	0.722302i
$454$		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
$459$	37.0326	−	0.275044i	1.72853	−	0.0128380i
$460$		0			0
$461$	34.9168	+	9.35594i	1.62624	+	0.435749i	0.952826	−	0.303517i	$-0.0981610\pi$
$461$	34.9168	+	9.35594i	1.62624	+	0.435749i	0.673413	+	0.739267i	$0.264828\pi$
$462$		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
$465$	5.57625	−	3.92514i	0.258592	−	0.182024i
$466$		0			0
$467$	−4.40877	+	4.40877i	−0.204013	+	0.204013i	−0.801717	−	0.597704i	$-0.796080\pi$
$467$	−4.40877	+	4.40877i	−0.204013	+	0.204013i	0.597704	+	0.801717i	$0.296080\pi$
$468$		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
$477$	13.0447	+	4.67488i	0.597277	+	0.214048i
$478$		0			0
$479$	−27.7943	−	7.44746i	−1.26995	−	0.340283i	−0.439941	−	0.898027i	$-0.645001\pi$
$479$	−27.7943	−	7.44746i	−1.26995	−	0.340283i	−0.830014	+	0.557743i	$0.811667\pi$
$480$		0			0
$481$	−18.1545	+	27.4726i	−0.827772	+	1.25264i
$482$		0			0
$483$	22.4052	+	3.89347i	1.01947	+	0.177159i
$484$		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
$489$	−14.2683	+	17.0900i	−0.645234	+	0.772838i
$490$		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
$495$	2.93037	−	4.22942i	0.131710	−	0.190098i
$496$		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
$501$	−9.86241	−	1.71384i	−0.440620	−	0.0765689i
$502$		0			0
$503$	−3.07410	−	0.823702i	−0.137067	−	0.0367271i	0.189633	−	0.981855i	$-0.439270\pi$
$503$	−3.07410	−	0.823702i	−0.137067	−	0.0367271i	−0.326700	+	0.945128i	$0.605937\pi$
$504$		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	$-0.154402\pi$
$509$	0.869109	+	1.50534i	0.0385226	+	0.0667231i	−0.846121	+	0.532990i	$0.821068\pi$
$510$		0			0
$511$	−20.3792	−	11.7660i	−0.901525	−	0.520495i
$512$		0			0
$513$	−12.9794	+	7.62274i	−0.573054	+	0.336552i
$514$		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	$-0.579859\pi$
$521$	16.3152	−	28.2588i	0.714783	−	1.23804i	0.963043	−	0.269347i	$-0.0868080\pi$
$522$		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
$525$	0.987156	+	0.457347i	0.0430830	+	0.0199602i
$526$		0			0
$527$	−10.4580	+	6.03793i	−0.455558	+	0.263017i
$528$		0			0
$529$		−	46.6488i		−	2.02821i
$530$		0			0
$531$	−3.73779	−	7.91319i	−0.162206	−	0.343403i
$532$		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
$537$	−16.2425	+	5.95735i	−0.700913	+	0.257079i
$538$		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
$543$	−15.4348	−	21.9275i	−0.662371	−	0.940998i
$544$		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
$549$	−17.7715	+	25.6497i	−0.758470	+	1.09470i
$550$		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
$555$	−20.8322	+	12.8583i	−0.884278	+	0.545806i
$556$		0			0
$557$	0.774505	−	2.89049i	0.0328168	−	0.122474i	−0.947574	−	0.319535i	$-0.896473\pi$
$557$	0.774505	−	2.89049i	0.0328168	−	0.122474i	0.980391	+	0.197061i	$0.0631398\pi$
$558$		0			0
$559$	50.6681	+	29.2532i	2.14303	+	1.23728i
$560$		0			0
$561$	−5.83966	+	6.99453i	−0.246550	+	0.295309i
$562$		0			0
$563$	10.5667	−	10.5667i	0.445333	−	0.445333i	−0.448467	−	0.893799i	$-0.648030\pi$
$563$	10.5667	−	10.5667i	0.445333	−	0.445333i	0.893799	+	0.448467i	$0.148030\pi$
$564$		0			0
$565$	21.0348			0.884942
$566$		0			0
$567$	−10.9361	−	8.99341i	−0.459271	−	0.377688i
$568$		0			0
$569$	−20.3507	−	20.3507i	−0.853144	−	0.853144i	0.137375	−	0.990519i	$-0.456133\pi$
$569$	−20.3507	−	20.3507i	−0.853144	−	0.853144i	−0.990519	+	0.137375i	$0.956133\pi$
$570$		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
$573$	−4.40174	−	12.0011i	−0.183885	−	0.501355i
$574$		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
$579$	−26.6817	+	9.78621i	−1.10885	+	0.406701i
$580$		0			0
$581$		−	22.2439i		−	0.922832i
$582$		0			0
$583$	−2.95265	+	1.70471i	−0.122286	+	0.0706020i
$584$		0			0
$585$	−12.7311	+	35.5247i	−0.526366	+	1.46876i
$586$		0			0
$587$	8.10721	−	2.17232i	0.334620	−	0.0896612i	−0.0875968	−	0.996156i	$-0.527919\pi$
$587$	8.10721	−	2.17232i	0.334620	−	0.0896612i	0.422217	+	0.906495i	$0.361252\pi$
$588$		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
$597$	−14.3373	−	39.0900i	−0.586786	−	1.59985i
$598$		0			0
$599$	0.169109	+	0.0976351i	0.00690960	+	0.00398926i	0.503451	−	0.864024i	$-0.332064\pi$
$599$	0.169109	+	0.0976351i	0.00690960	+	0.00398926i	−0.496541	+	0.868013i	$0.665397\pi$
$600$		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
$609$	−3.73313	+	21.4825i	−0.151274	+	0.870515i
$610$		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
$615$	−22.0717	+	26.4367i	−0.890018	+	1.06603i
$616$		0			0
$617$	5.84248	+	10.1195i	0.235210	+	0.407395i	0.959334	−	0.282275i	$-0.0910890\pi$
$617$	5.84248	+	10.1195i	0.235210	+	0.407395i	−0.724124	+	0.689670i	$0.757756\pi$
$618$		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
$621$	−21.4029	+	37.7151i	−0.858871	+	1.51346i
$622$		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
$627$	0.634072	−	3.64880i	0.0253224	−	0.145719i
$628$		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
$633$	0.151612	−	0.327245i	0.00602603	−	0.0130068i
$634$		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	$-0.605302\pi$
$641$	8.40159	−	4.85066i	0.331843	−	0.191590i	0.656659	+	0.754188i	$0.271969\pi$
$642$		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
$645$	25.0366	+	35.5682i	0.985815	+	1.40050i
$646$		0			0
$647$	45.9218	−	12.3047i	1.80537	−	0.483748i	0.810576	−	0.585633i	$-0.199154\pi$
$647$	45.9218	−	12.3047i	1.80537	−	0.483748i	0.994796	+	0.101885i	$0.0324873\pi$
$648$		0			0
$649$	2.07988	+	0.557301i	0.0816422	+	0.0218760i
$650$		0			0
$651$	4.54879	+	0.790469i	0.178281	+	0.0309809i
$652$		0			0
$653$	−16.1422	+	4.32530i	−0.631694	+	0.169262i	−0.560438	−	0.828196i	$-0.689367\pi$
$653$	−16.1422	+	4.32530i	−0.631694	+	0.169262i	−0.0712560	+	0.997458i	$0.522701\pi$
$654$		0			0
$655$	−23.9482			−0.935735
$656$		0			0
$657$	34.2316	−	29.0138i	1.33550	−	1.13194i
$658$		0			0
$659$	11.3024	−	19.5764i	0.440280	−	0.762587i	−0.557430	−	0.830224i	$-0.688213\pi$
$659$	11.3024	−	19.5764i	0.440280	−	0.762587i	0.997710	+	0.0676367i	$0.0215459\pi$
$660$		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
$663$	28.0924	−	60.6358i	1.09102	−	2.35490i
$664$		0			0
$665$	10.5896			0.410647
$666$		0			0
$667$	66.7805			2.58575
$668$		0			0
$669$	−19.5445	+	42.1857i	−0.755635	+	1.63099i
$670$		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
$675$	−1.45605	+	1.47784i	−0.0560433	+	0.0568820i
$676$		0			0
$677$	0.490033			0.0188335			0.00941674	−	0.999956i	$-0.497003\pi$
$677$	0.490033			0.0188335			0.00941674	+	0.999956i	$0.497003\pi$
$678$		0			0
$679$	−1.77117	+	0.474583i	−0.0679712	+	0.0182128i
$680$		0			0
$681$	12.5464	+	2.18025i	0.480778	+	0.0835474i
$682$		0			0
$683$	22.1468	+	5.93422i	0.847424	+	0.227067i	0.656301	−	0.754499i	$-0.272120\pi$
$683$	22.1468	+	5.93422i	0.847424	+	0.227067i	0.191123	+	0.981566i	$0.438787\pi$
$684$		0			0
$685$	−9.88525	+	2.64875i	−0.377696	+	0.101203i
$686$		0			0
$687$	−11.3059	−	16.0617i	−0.431345	−	0.612790i
$688$		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
$699$	−17.7604	+	38.3348i	−0.671760	+	1.44996i
$700$		0			0
$701$	−14.0705	−	3.77019i	−0.531437	−	0.142398i	−0.0168851	−	0.999857i	$-0.505375\pi$
$701$	−14.0705	−	3.77019i	−0.531437	−	0.142398i	−0.514552	+	0.857459i	$0.672042\pi$
$702$		0			0
$703$	−9.71458	+	14.7008i	−0.366392	+	0.554450i
$704$		0			0
$705$	7.35598	−	42.3304i	0.277042	−	1.59425i
$706$		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
$711$	4.06407	+	2.81581i	0.152414	+	0.105601i
$712$		0			0
$713$		−	14.1404i		−	0.529561i
$714$		0			0
$715$	−4.64244	−	8.04094i	−0.173617	−	0.300714i
$716$		0			0
$717$	13.9292	−	16.6839i	0.520197	−	0.623072i
$718$		0			0
$719$	−37.3478	+	21.5628i	−1.39284	+	0.804156i	−0.993629	−	0.112704i	$-0.964049\pi$
$719$	−37.3478	+	21.5628i	−1.39284	+	0.804156i	−0.399210	+	0.916860i	$0.630715\pi$
$720$		0			0
$721$	1.75497	+	6.54964i	0.0653585	+	0.243921i
$722$		0			0
$723$	−0.741014	+	4.26420i	−0.0275586	+	0.158587i
$724$		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
$735$	−6.27099	−	17.0976i	−0.231309	−	0.630654i
$736$		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	−0.957012	−	0.290049i	$-0.906329\pi$
$743$	−6.19620	+	10.7321i	−0.227317	+	0.393724i	0.729695	+	0.683772i	$0.239662\pi$
$744$		0			0
$745$	−13.3046	+	3.56495i	−0.487441	+	0.130609i
$746$		0			0
$747$	39.9303	+	14.3099i	1.46097	+	0.523574i
$748$		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
$753$	−24.9613	+	9.15523i	−0.909641	+	0.333635i
$754$		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
$759$	−3.67402	−	10.0171i	−0.133358	−	0.363596i
$760$		0			0
$761$	−11.2680	−	19.5167i	−0.408463	−	0.707479i	0.586255	−	0.810127i	$-0.300602\pi$
$761$	−11.2680	−	19.5167i	−0.408463	−	0.707479i	−0.994718	+	0.102648i	$0.967268\pi$
$762$		0			0
$763$	5.50466	+	5.50466i	0.199282	+	0.199282i
$764$		0			0
$765$	37.9003	−	32.1233i	1.37029	−	1.16142i
$766$		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
$771$	22.3753	−	26.8003i	0.805827	−	0.965190i
$772$		0			0
$773$	17.1782	+	9.91786i	0.617858	+	0.356721i	0.776035	−	0.630690i	$-0.217228\pi$
$773$	17.1782	+	9.91786i	0.617858	+	0.356721i	−0.158177	+	0.987411i	$0.550562\pi$
$774$		0			0
$775$	0.175089	−	0.653441i	0.00628938	−	0.0234723i
$776$		0			0
$777$	−16.1294	−	3.81749i	−0.578638	−	0.136952i
$778$		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
$783$	−36.1619	−	20.5215i	−1.29232	−	0.733379i
$784$		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
$789$	−15.8961	−	22.5828i	−0.565918	−	0.803971i
$790$		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
$795$	17.4531	−	6.40138i	0.618997	−	0.227034i
$796$		0			0
$797$	8.79885	−	32.8377i	0.311671	−	1.16317i	−0.615378	−	0.788232i	$-0.710997\pi$
$797$	8.79885	−	32.8377i	0.311671	−	1.16317i	0.927049	−	0.374940i	$-0.122337\pi$
$798$		0			0
$799$	−19.6922	+	73.4924i	−0.696661	+	2.59997i
$800$		0			0
$801$	37.9706	−	17.9354i	1.34163	−	0.633717i
$802$		0			0
$803$			11.0407i			0.389617i
$804$		0			0
$805$	26.4208	−	15.2541i	0.931211	−	0.537635i
$806$		0			0
$807$	−13.1863	−	6.10918i	−0.464180	−	0.215053i
$808$		0			0
$809$	21.9561	−	5.88311i	0.771934	−	0.206839i	0.148708	−	0.988881i	$-0.452488\pi$
$809$	21.9561	−	5.88311i	0.771934	−	0.206839i	0.623226	+	0.782042i	$0.285822\pi$
$810$		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
$819$	−23.1025	+	10.9124i	−0.807266	+	0.381312i
$820$		0			0
$821$	−22.9968	−	13.2772i	−0.802595	−	0.463378i	0.0417829	−	0.999127i	$-0.486696\pi$
$821$	−22.9968	−	13.2772i	−0.802595	−	0.463378i	−0.844378	+	0.535748i	$0.820030\pi$
$822$		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	$0.0616125\pi$
$827$	6.54668	+	24.4325i	0.227650	+	0.849602i	−0.753675	+	0.657247i	$0.771721\pi$
$828$		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
$831$	11.6888	+	2.03123i	0.405480	+	0.0704625i
$832$		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
$837$	−4.34531	+	7.65708i	−0.150196	+	0.264667i
$838$		0			0
$839$	−4.99925	−	8.65896i	−0.172593	−	0.298941i	0.766732	−	0.641967i	$-0.221881\pi$
$839$	−4.99925	−	8.65896i	−0.172593	−	0.298941i	−0.939326	+	0.343026i	$0.888548\pi$
$840$		0			0
$841$			35.0303i			1.20794i
$842$		0			0
$843$	−0.587970	+	0.704249i	−0.0202508	+	0.0242556i
$844$		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
$849$	28.8758	+	5.01790i	0.991015	+	0.172214i
$850$		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
$855$	−6.81250	+	19.0095i	−0.232983	+	0.650112i
$856$		0			0
$857$	1.38018	−	1.38018i	0.0471460	−	0.0471460i	−0.683141	−	0.730287i	$-0.739386\pi$
$857$	1.38018	−	1.38018i	0.0471460	−	0.0471460i	0.730287	+	0.683141i	$0.239386\pi$
$858$		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	0.146513	−	0.989209i	$-0.453195\pi$
$863$	31.6227	−	18.2574i	1.07645	−	0.621489i	0.929937	+	0.367720i	$0.119861\pi$
$864$		0			0
$865$	−10.1718	+	10.1718i	−0.345851	+	0.345851i
$866$		0			0
$867$	−47.8667	+	33.6935i	−1.62564	+	1.14429i
$868$		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
$873$	0.287498	−	3.48476i	0.00973033	−	0.117941i
$874$		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
$879$	−2.43053	+	1.71086i	−0.0819797	+	0.0577058i
$880$		0			0
$881$	−18.3911	+	31.8543i	−0.619611	+	1.07320i	0.369945	+	0.929054i	$0.379376\pi$
$881$	−18.3911	+	31.8543i	−0.619611	+	1.07320i	−0.989557	+	0.144145i	$0.953957\pi$
$882$		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
$885$	−10.6529	−	4.93545i	−0.358093	−	0.165903i
$886$		0			0
$887$	−1.05111			−0.0352928			−0.0176464	−	0.999844i	$-0.505617\pi$
$887$	−1.05111			−0.0352928			−0.0176464	+	0.999844i	$0.505617\pi$
$888$		0			0
$889$	−3.25144			−0.109050
$890$		0			0
$891$	−1.08873	+	6.55330i	−0.0364737	+	0.219544i
$892$		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
$897$	45.0422	+	63.9891i	1.50391	+	2.13653i
$898$		0			0
$899$	13.5580			0.452186
$900$		0			0
$901$	−31.7987	+	8.52043i	−1.05937	+	0.283857i
$902$		0			0
$903$	−5.04202	+	29.0146i	−0.167788	+	0.965545i
$904$		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
$909$	−7.58736	−	8.95188i	−0.251657	−	0.296915i
$910$		0			0
$911$	−33.4058	+	33.4058i	−1.10678	+	1.10678i	−0.113214	+	0.993571i	$0.536115\pi$
$911$	−33.4058	+	33.4058i	−1.10678	+	1.10678i	−0.993571	+	0.113214i	$0.963885\pi$
$912$		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
$921$	1.73360	+	0.803170i	0.0571239	+	0.0264654i
$922$		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
$927$	−12.8864	−	1.06314i	−0.423243	−	0.0349182i
$928$		0			0
$929$	−6.53422	+	11.3176i	−0.214381	+	0.371319i	−0.953081	−	0.302716i	$-0.902107\pi$
$929$	−6.53422	+	11.3176i	−0.214381	+	0.371319i	0.738700	+	0.674034i	$0.235440\pi$
$930$		0			0
$931$	−9.26871	−	9.26871i	−0.303770	−	0.303770i
$932$		0			0
$933$	33.1903	+	27.7103i	1.08660	+	0.907193i
$934$		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
$939$	8.96933	+	7.48840i	0.292703	+	0.244375i
$940$		0			0
$941$	−0.104995	+	0.0606190i	−0.00342275	+	0.00197612i	−0.501710	−	0.865036i	$-0.667296\pi$
$941$	−0.104995	+	0.0606190i	−0.00342275	+	0.00197612i	0.498288	+	0.867012i	$0.333962\pi$
$942$		0			0
$943$	18.4833	+	68.9805i	0.601898	+	2.24631i
$944$		0			0
$945$	−18.9945	+	0.141074i	−0.617892	+	0.00458915i
$946$		0			0
$947$	−32.9832	−	8.83783i	−1.07181	−	0.287191i	−0.320574	−	0.947224i	$-0.603876\pi$
$947$	−32.9832	−	8.83783i	−1.07181	−	0.287191i	−0.751237	+	0.660033i	$0.770542\pi$
$948$		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	$-0.255570\pi$
$953$	−8.51043	−	14.7405i	−0.275680	−	0.477492i	−0.970306	+	0.241879i	$0.922236\pi$
$954$		0			0
$955$	−14.8514	−	8.57445i	−0.480580	−	0.277463i
$956$		0			0
$957$	9.60453	−	3.52271i	0.310470	−	0.113873i
$958$		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
$969$	15.0325	−	32.4467i	0.482912	−	1.04234i
$970$		0			0
$971$	38.6025	−	22.2872i	1.23881	−	0.715229i	0.269961	−	0.962871i	$-0.412989\pi$
$971$	38.6025	−	22.2872i	1.23881	−	0.715229i	0.968851	+	0.247642i	$0.0796558\pi$
$972$		0			0
$973$			25.3146i			0.811548i
$974$		0			0
$975$	1.28912	+	3.51472i	0.0412848	+	0.112561i
$976$		0			0
$977$	−2.21376	+	8.26186i	−0.0708244	+	0.264320i	−0.992254	−	0.124225i	$-0.960356\pi$
$977$	−2.21376	+	8.26186i	−0.0708244	+	0.264320i	0.921430	+	0.388545i	$0.127022\pi$
$978$		0			0
$979$	−2.67415	+	9.98007i	−0.0854663	+	0.318964i
$980$		0			0
$981$	−13.4227	+	6.34023i	−0.428555	+	0.202428i
$982$		0			0
$983$	19.4970	+	33.7698i	0.621858	+	1.07709i	0.989140	+	0.146979i	$0.0469551\pi$
$983$	19.4970	+	33.7698i	0.621858	+	1.07709i	−0.367282	+	0.930110i	$0.619712\pi$
$984$		0			0
$985$	−27.9841	−	27.9841i	−0.891647	−	0.891647i
$986$		0			0
$987$	23.7874	−	16.7440i	0.757160	−	0.532968i
$988$		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
$993$	−10.5141	−	8.77812i	−0.333655	−	0.278565i
$994$		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
$999$	17.2292	−	26.4982i	0.545108	−	0.838366i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.728108 + 1.57158i) q^{3} +(0.601400 + 2.24446i) q^{5} +(-0.786614 + 1.36246i) q^{7} +(-1.93972 - 2.28856i) q^{9} +0.738125 q^{11} +(-5.22905 + 1.40112i) q^{13} +(-3.96522 - 0.689058i) q^{15} +(6.88427 + 1.84463i) q^{17} +(-2.79810 + 0.749750i) q^{19} +(-1.56847 - 2.22824i) q^{21} +(-5.90122 + 5.90122i) q^{23} +(-0.345771 + 0.199631i) q^{25} +(5.00897 - 1.38210i) q^{27} +(-5.65819 - 5.65819i) q^{29} +(-1.19809 + 1.19809i) q^{31} +(-0.537434 + 1.16002i) q^{33} +(-3.53104 - 0.946139i) q^{35} +(4.55273 - 4.03393i) q^{37} +(1.60534 - 9.23803i) q^{39} +(4.27854 - 7.41065i) q^{41} +(-7.64204 - 7.64204i) q^{43} +(3.97002 - 5.72995i) q^{45} +10.6754i q^{47} +(2.26248 + 3.91872i) q^{49} +(-7.91148 + 9.47607i) q^{51} +(-4.00020 + 2.30952i) q^{53} +(0.443908 + 1.65669i) q^{55} +(0.859031 - 4.94334i) q^{57} +(2.81778 + 0.755023i) q^{59} +(-2.69213 - 10.0472i) q^{61} +(4.64387 - 0.842568i) q^{63} +(-6.28950 - 10.8937i) q^{65} +(-5.21175 - 3.00900i) q^{67} +(-4.97750 - 13.5710i) q^{69} +(-2.51092 - 1.44968i) q^{71} +14.9577i q^{73} +(-0.0619772 - 0.688760i) q^{75} +(-0.580619 + 1.00566i) q^{77} +(-1.59192 + 0.426553i) q^{79} +(-1.47499 + 8.87831i) q^{81} +(-12.2447 + 7.06950i) q^{83} +16.5608i q^{85} +(13.0121 - 4.77252i) q^{87} +(-3.62290 + 13.5208i) q^{89} +(2.20428 - 8.22649i) q^{91} +(-1.01055 - 2.75523i) q^{93} +(-3.36556 - 5.82932i) q^{95} +(0.824155 + 0.824155i) q^{97} +(-1.43175 - 1.68924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 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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