LMFDB - Embedded newform 444.2.w.c.125.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [444,2,Mod(29,444)] 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("444.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(444, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.9
Character	$\chi$	$=$	444.125
Dual form			444.2.w.c.341.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.46554 + 0.923136i) q^{3} +(-0.967937 + 3.61239i) q^{5} +(-0.200342 - 0.347003i) q^{7} +(1.29564 + 2.70579i) q^{9} -4.54763 q^{11} +(0.522156 + 0.139911i) q^{13} +(-4.75328 + 4.40058i) q^{15} +(3.45205 - 0.924974i) q^{17} +(-1.44533 - 0.387274i) q^{19} +(0.0267206 - 0.693491i) q^{21} +(0.783440 + 0.783440i) q^{23} +(-7.78232 - 4.49313i) q^{25} +(-0.599000 + 5.16151i) q^{27} +(1.43664 - 1.43664i) q^{29} +(3.22392 + 3.22392i) q^{31} +(-6.66475 - 4.19808i) q^{33} +(1.44743 - 0.387837i) q^{35} +(3.25206 + 5.14044i) q^{37} +(0.636085 + 0.687067i) q^{39} +(2.79545 + 4.84186i) q^{41} +(8.18323 - 8.18323i) q^{43} +(-11.0285 + 2.06132i) q^{45} -3.05293i q^{47} +(3.41973 - 5.92314i) q^{49} +(5.91301 + 1.83112i) q^{51} +(11.2551 + 6.49812i) q^{53} +(4.40182 - 16.4278i) q^{55} +(-1.76068 - 1.90180i) q^{57} +(-11.1916 + 2.99879i) q^{59} +(-2.09095 + 7.80352i) q^{61} +(0.679347 - 0.991675i) q^{63} +(-1.01083 + 1.75080i) q^{65} +(0.299548 - 0.172944i) q^{67} +(0.424944 + 1.87139i) q^{69} +(2.40554 - 1.38884i) q^{71} +6.01987i q^{73} +(-7.25757 - 13.7690i) q^{75} +(0.911082 + 1.57804i) q^{77} +(13.9480 + 3.73737i) q^{79} +(-5.64264 + 7.01146i) q^{81} +(-8.74947 - 5.05151i) q^{83} +13.3655i q^{85} +(3.43168 - 0.779247i) q^{87} +(-4.30651 - 16.0721i) q^{89} +(-0.0560602 - 0.209220i) q^{91} +(1.74868 + 7.70092i) q^{93} +(2.79797 - 4.84622i) q^{95} +(7.51811 - 7.51811i) q^{97} +(-5.89209 - 12.3049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{9} - 24 q^{19} - 18 q^{21} + 32 q^{31} - 44 q^{37} + 62 q^{39} - 4 q^{43} - 54 q^{45} + 24 q^{49} + 14 q^{51} + 20 q^{55} + 34 q^{57} + 36 q^{61} - 36 q^{63} + 12 q^{67} - 50 q^{69} - 20 q^{75}+ \cdots - 12 q^{99}+O(q^{100}) $ 40 * q - 10 * q^9 - 24 * q^19 - 18 * q^21 + 32 * q^31 - 44 * q^37 + 62 * q^39 - 4 * q^43 - 54 * q^45 + 24 * q^49 + 14 * q^51 + 20 * q^55 + 34 * q^57 + 36 * q^61 - 36 * q^63 + 12 * q^67 - 50 * q^69 - 20 * q^75 + 8 * q^79 + 10 * q^81 - 32 * q^87 + 20 * q^91 - 30 * q^93 + 52 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/444\mathbb{Z}\right)^\times$.

$n$	$149$	$223$	$409$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.46554	+	0.923136i	0.846132	+	0.532973i
$3$	1.46554	+	0.923136i	0.846132	+	0.532973i
$4$		0			0
$5$	−0.967937	+	3.61239i	−0.432874	+	1.61551i	0.313228	+	0.949678i	$0.398590\pi$
$5$	−0.967937	+	3.61239i	−0.432874	+	1.61551i	−0.746102	+	0.665831i	$0.768077\pi$
$6$		0			0
$7$	−0.200342	−	0.347003i	−0.0757222	−	0.131155i	0.825678	−	0.564142i	$-0.190793\pi$
$7$	−0.200342	−	0.347003i	−0.0757222	−	0.131155i	−0.901400	+	0.432987i	$0.857460\pi$
$8$		0			0
$9$	1.29564	+	2.70579i	0.431880	+	0.901931i
$10$		0			0
$11$	−4.54763			−1.37116			−0.685581	−	0.727996i	$-0.740452\pi$
$11$	−4.54763			−1.37116			−0.685581	+	0.727996i	$0.740452\pi$
$12$		0			0
$13$	0.522156	+	0.139911i	0.144820	+	0.0388044i	0.330501	−	0.943806i	$-0.392782\pi$
$13$	0.522156	+	0.139911i	0.144820	+	0.0388044i	−0.185681	+	0.982610i	$0.559449\pi$
$14$		0			0
$15$	−4.75328	+	4.40058i	−1.22729	+	1.13622i
$16$		0			0
$17$	3.45205	−	0.924974i	0.837245	−	0.224339i	0.185373	−	0.982668i	$-0.440651\pi$
$17$	3.45205	−	0.924974i	0.837245	−	0.224339i	0.651872	+	0.758329i	$0.273984\pi$
$18$		0			0
$19$	−1.44533	−	0.387274i	−0.331581	−	0.0888467i	0.0891879	−	0.996015i	$-0.471573\pi$
$19$	−1.44533	−	0.387274i	−0.331581	−	0.0888467i	−0.420768	+	0.907168i	$0.638240\pi$
$20$		0			0
$21$	0.0267206	−	0.693491i	0.00583091	−	0.151332i
$22$		0			0
$23$	0.783440	+	0.783440i	0.163358	+	0.163358i	0.784053	−	0.620694i	$-0.213149\pi$
$23$	0.783440	+	0.783440i	0.163358	+	0.163358i	−0.620694	+	0.784053i	$0.713149\pi$
$24$		0			0
$25$	−7.78232	−	4.49313i	−1.55646	−	0.898625i
$26$		0			0
$27$	−0.599000	+	5.16151i	−0.115278	+	0.993333i
$28$		0			0
$29$	1.43664	−	1.43664i	0.266778	−	0.266778i	−0.561023	−	0.827801i	$-0.689592\pi$
$29$	1.43664	−	1.43664i	0.266778	−	0.266778i	0.827801	+	0.561023i	$0.189592\pi$
$30$		0			0
$31$	3.22392	+	3.22392i	0.579034	+	0.579034i	0.934637	−	0.355603i	$-0.115725\pi$
$31$	3.22392	+	3.22392i	0.579034	+	0.579034i	−0.355603	+	0.934637i	$0.615725\pi$
$32$		0			0
$33$	−6.66475	−	4.19808i	−1.16018	−	0.730792i
$34$		0			0
$35$	1.44743	−	0.387837i	0.244660	−	0.0655564i
$36$		0			0
$37$	3.25206	+	5.14044i	0.534635	+	0.845083i
$37$	3.25206	+	5.14044i	0.534635	+	0.845083i
$38$		0			0
$39$	0.636085	+	0.687067i	0.101855	+	0.110019i
$40$		0			0
$41$	2.79545	+	4.84186i	0.436576	+	0.756172i	0.997423	−	0.0717476i	$-0.0228576\pi$
$41$	2.79545	+	4.84186i	0.436576	+	0.756172i	−0.560847	+	0.827920i	$0.689524\pi$
$42$		0			0
$43$	8.18323	−	8.18323i	1.24793	−	1.24793i	0.291298	−	0.956632i	$-0.405913\pi$
$43$	8.18323	−	8.18323i	1.24793	−	1.24793i	0.956632	−	0.291298i	$-0.0940872\pi$
$44$		0			0
$45$	−11.0285	+	2.06132i	−1.64403	+	0.307283i
$46$		0			0
$47$		−	3.05293i		−	0.445316i	−0.974897	−	0.222658i	$-0.928527\pi$
$47$		−	3.05293i		−	0.445316i	0.974897	−	0.222658i	$-0.0714733\pi$
$48$		0			0
$49$	3.41973	−	5.92314i	0.488532	−	0.846163i
$50$		0			0
$51$	5.91301	+	1.83112i	0.827987	+	0.256408i
$52$		0			0
$53$	11.2551	+	6.49812i	1.54600	+	0.892585i	0.998441	+	0.0558207i	$0.0177775\pi$
$53$	11.2551	+	6.49812i	1.54600	+	0.892585i	0.547563	+	0.836765i	$0.315556\pi$
$54$		0			0
$55$	4.40182	−	16.4278i	0.593541	−	2.21512i
$56$		0			0
$57$	−1.76068	−	1.90180i	−0.233208	−	0.251900i
$58$		0			0
$59$	−11.1916	+	2.99879i	−1.45703	+	0.390409i	−0.898462	−	0.439051i	$-0.855315\pi$
$59$	−11.1916	+	2.99879i	−1.45703	+	0.390409i	−0.558566	+	0.829460i	$0.688648\pi$
$60$		0			0
$61$	−2.09095	+	7.80352i	−0.267718	+	0.999139i	0.692847	+	0.721085i	$0.256356\pi$
$61$	−2.09095	+	7.80352i	−0.267718	+	0.999139i	−0.960565	+	0.278054i	$0.910311\pi$
$62$		0			0
$63$	0.679347	−	0.991675i	0.0855896	−	0.124939i
$64$		0			0
$65$	−1.01083	+	1.75080i	−0.125378	+	0.217161i
$66$		0			0
$67$	0.299548	−	0.172944i	0.0365956	−	0.0211285i	−0.481591	−	0.876396i	$-0.659941\pi$
$67$	0.299548	−	0.172944i	0.0365956	−	0.0211285i	0.518186	+	0.855268i	$0.326607\pi$
$68$		0			0
$69$	0.424944	+	1.87139i	0.0511572	+	0.225288i
$70$		0			0
$71$	2.40554	−	1.38884i	0.285485	−	0.164825i	−0.350419	−	0.936593i	$-0.613961\pi$
$71$	2.40554	−	1.38884i	0.285485	−	0.164825i	0.635904	+	0.771768i	$0.280627\pi$
$72$		0			0
$73$			6.01987i			0.704572i	0.935892	+	0.352286i	$0.114596\pi$
$73$			6.01987i			0.704572i	−0.935892	+	0.352286i	$0.885404\pi$
$74$		0			0
$75$	−7.25757	−	13.7690i	−0.838032	−	1.58991i
$76$		0			0
$77$	0.911082	+	1.57804i	0.103827	+	0.179834i
$78$		0			0
$79$	13.9480	+	3.73737i	1.56928	+	0.420486i	0.935586	−	0.353100i	$-0.114872\pi$
$79$	13.9480	+	3.73737i	1.56928	+	0.420486i	0.633691	+	0.773586i	$0.281539\pi$
$80$		0			0
$81$	−5.64264	+	7.01146i	−0.626960	+	0.779052i
$82$		0			0
$83$	−8.74947	−	5.05151i	−0.960379	−	0.554475i	−0.0640894	−	0.997944i	$-0.520414\pi$
$83$	−8.74947	−	5.05151i	−0.960379	−	0.554475i	−0.896290	+	0.443469i	$0.853748\pi$
$84$		0			0
$85$			13.3655i			1.44969i
$86$		0			0
$87$	3.43168	−	0.779247i	0.367915	−	0.0835440i
$88$		0			0
$89$	−4.30651	−	16.0721i	−0.456489	−	1.70364i	−0.683673	−	0.729788i	$-0.739619\pi$
$89$	−4.30651	−	16.0721i	−0.456489	−	1.70364i	0.227184	−	0.973852i	$-0.427048\pi$
$90$		0			0
$91$	−0.0560602	−	0.209220i	−0.00587671	−	0.0219322i
$92$		0			0
$93$	1.74868	+	7.70092i	0.181330	+	0.798548i
$94$		0			0
$95$	2.79797	−	4.84622i	0.287065	−	0.497212i
$96$		0			0
$97$	7.51811	−	7.51811i	0.763348	−	0.763348i	−0.213578	−	0.976926i	$-0.568512\pi$
$97$	7.51811	−	7.51811i	0.763348	−	0.763348i	0.976926	+	0.213578i	$0.0685117\pi$
$98$		0			0
$99$	−5.89209	−	12.3049i	−0.592177	−	1.23669i
$100$		0			0
$101$	−4.51005			−0.448767			−0.224384	−	0.974501i	$-0.572037\pi$
$101$	−4.51005			−0.448767			−0.224384	+	0.974501i	$0.572037\pi$
$102$		0			0
$103$	−8.37368	−	8.37368i	−0.825083	−	0.825083i	0.161749	−	0.986832i	$-0.448287\pi$
$103$	−8.37368	−	8.37368i	−0.825083	−	0.825083i	−0.986832	+	0.161749i	$0.948287\pi$
$104$		0			0
$105$	2.47929	+	0.767780i	0.241954	+	0.0749277i
$106$		0			0
$107$	6.38915	−	3.68878i	0.617662	−	0.356607i	−0.158296	−	0.987392i	$-0.550600\pi$
$107$	6.38915	−	3.68878i	0.617662	−	0.356607i	0.775958	+	0.630784i	$0.217267\pi$
$108$		0			0
$109$	−3.56925	−	13.3206i	−0.341872	−	1.27589i	−0.896224	−	0.443602i	$-0.853700\pi$
$109$	−3.56925	−	13.3206i	−0.341872	−	1.27589i	0.554351	−	0.832283i	$-0.312966\pi$
$110$		0			0
$111$	0.0207083	+	10.5356i	0.00196554	+	0.999998i
$112$		0			0
$113$	0.365862	+	1.36542i	0.0344174	+	0.128448i	0.980997	−	0.194023i	$-0.0621535\pi$
$113$	0.365862	+	1.36542i	0.0344174	+	0.128448i	−0.946580	+	0.322470i	$0.895487\pi$
$114$		0			0
$115$	−3.58841	+	2.07177i	−0.334621	+	0.193193i
$116$		0			0
$117$	0.297955	+	1.59412i	0.0275459	+	0.147376i
$118$		0			0
$119$	−1.01256	−	1.01256i	−0.0928212	−	0.0928212i
$120$		0			0
$121$	9.68094			0.880085
$122$		0			0
$123$	−0.372842	+	9.67655i	−0.0336181	+	0.872505i
$124$		0			0
$125$	10.5414	−	10.5414i	0.942856	−	0.942856i
$126$		0			0
$127$	6.46435	−	11.1966i	0.573618	−	0.993536i	−0.422572	−	0.906329i	$-0.638873\pi$
$127$	6.46435	−	11.1966i	0.573618	−	0.993536i	0.996190	−	0.0872064i	$-0.0277939\pi$
$128$		0			0
$129$	19.5471	−	4.43865i	1.72103	−	0.390801i
$130$		0			0
$131$	−4.82928	−	18.0231i	−0.421936	−	1.57469i	−0.770523	−	0.637412i	$-0.780005\pi$
$131$	−4.82928	−	18.0231i	−0.421936	−	1.57469i	0.348587	−	0.937276i	$-0.386662\pi$
$132$		0			0
$133$	0.155175	+	0.579119i	0.0134553	+	0.0502160i
$134$		0			0
$135$	−18.0656	−	7.15983i	−1.55484	−	0.616220i
$136$		0			0
$137$		−	3.65206i		−	0.312017i	−0.987756	−	0.156008i	$-0.950137\pi$
$137$		−	3.65206i		−	0.312017i	0.987756	−	0.156008i	$-0.0498627\pi$
$138$		0			0
$139$	10.1738	+	5.87386i	0.862932	+	0.498214i	0.864993	−	0.501784i	$-0.167323\pi$
$139$	10.1738	+	5.87386i	0.862932	+	0.498214i	−0.00206117	+	0.999998i	$0.500656\pi$
$140$		0			0
$141$	2.81827	−	4.47420i	0.237341	−	0.376796i
$142$		0			0
$143$	−2.37457	−	0.636265i	−0.198572	−	0.0532071i
$144$		0			0
$145$	3.79913	+	6.58029i	0.315501	+	0.546464i
$146$		0			0
$147$	10.4796	−	5.52375i	0.864345	−	0.455591i
$148$		0			0
$149$			15.0876i			1.23603i	0.786167	+	0.618014i	$0.212062\pi$
$149$			15.0876i			1.23603i	−0.786167	+	0.618014i	$0.787938\pi$
$150$		0			0
$151$	5.44324	−	3.14266i	0.442964	−	0.255746i	−0.261890	−	0.965098i	$-0.584346\pi$
$151$	5.44324	−	3.14266i	0.442964	−	0.255746i	0.704854	+	0.709352i	$0.251012\pi$
$152$		0			0
$153$	6.97540	+	8.14210i	0.563928	+	0.658250i
$154$		0			0
$155$	−14.7666	+	8.52551i	−1.18608	+	0.684785i
$156$		0			0
$157$	−10.0901	+	17.4766i	−0.805279	+	1.39478i	0.110823	+	0.993840i	$0.464651\pi$
$157$	−10.0901	+	17.4766i	−0.805279	+	1.39478i	−0.916102	+	0.400945i	$0.868682\pi$
$158$		0			0
$159$	10.4962	+	19.9132i	0.832399	+	1.57922i
$160$		0			0
$161$	0.114900	−	0.428812i	0.00905537	−	0.0337951i
$162$		0			0
$163$	−16.0844	+	4.30981i	−1.25983	+	0.337570i	−0.826126	−	0.563486i	$-0.809460\pi$
$163$	−16.0844	+	4.30981i	−1.25983	+	0.337570i	−0.433703	+	0.901056i	$0.642793\pi$
$164$		0			0
$165$	21.6162	−	20.0122i	1.68282	−	1.55795i
$166$		0			0
$167$	5.99171	−	22.3614i	0.463652	−	1.73037i	−0.197667	−	0.980269i	$-0.563336\pi$
$167$	5.99171	−	22.3614i	0.463652	−	1.73037i	0.661319	−	0.750105i	$-0.269997\pi$
$168$		0			0
$169$	−11.0053	−	6.35389i	−0.846558	−	0.488761i
$170$		0			0
$171$	−0.824738	−	4.41252i	−0.0630693	−	0.337434i
$172$		0			0
$173$	−8.52545	+	14.7665i	−0.648178	+	1.12268i	0.335379	+	0.942083i	$0.391136\pi$
$173$	−8.52545	+	14.7665i	−0.648178	+	1.12268i	−0.983558	+	0.180595i	$0.942198\pi$
$174$		0			0
$175$			3.60065i			0.272183i
$176$		0			0
$177$	−19.1701	−	5.93655i	−1.44092	−	0.446218i
$178$		0			0
$179$	−3.08154	+	3.08154i	−0.230325	+	0.230325i	−0.812828	−	0.582503i	$-0.802073\pi$
$179$	−3.08154	+	3.08154i	−0.230325	+	0.230325i	0.582503	+	0.812828i	$0.302073\pi$
$180$		0			0
$181$	−4.63252	−	8.02375i	−0.344332	−	0.596401i	0.640900	−	0.767624i	$-0.278561\pi$
$181$	−4.63252	−	8.02375i	−0.344332	−	0.596401i	−0.985232	+	0.171224i	$0.945228\pi$
$182$		0			0
$183$	−10.2681	+	9.50618i	−0.759039	+	0.702717i
$184$		0			0
$185$	−21.7170	+	6.77208i	−1.59667	+	0.497893i
$186$		0			0
$187$	−15.6986	+	4.20644i	−1.14800	+	0.307605i
$188$		0			0
$189$	1.91106	−	0.826214i	0.139009	−	0.0600982i
$190$		0			0
$191$	7.86638	+	7.86638i	0.569191	+	0.569191i	0.931902	−	0.362711i	$-0.118149\pi$
$191$	7.86638	+	7.86638i	0.569191	+	0.569191i	−0.362711	+	0.931902i	$0.618149\pi$
$192$		0			0
$193$	−0.180211	+	0.180211i	−0.0129719	+	0.0129719i	−0.713563	−	0.700591i	$-0.752920\pi$
$193$	−0.180211	+	0.180211i	−0.0129719	+	0.0129719i	0.700591	+	0.713563i	$0.252920\pi$
$194$		0			0
$195$	−3.09764	+	1.63275i	−0.221827	+	0.116924i
$196$		0			0
$197$	9.10042	+	5.25413i	0.648378	+	0.374341i	0.787835	−	0.615887i	$-0.211202\pi$
$197$	9.10042	+	5.25413i	0.648378	+	0.374341i	−0.139456	+	0.990228i	$0.544536\pi$
$198$		0			0
$199$	−4.51838	−	4.51838i	−0.320299	−	0.320299i	0.528583	−	0.848882i	$-0.322724\pi$
$199$	−4.51838	−	4.51838i	−0.320299	−	0.320299i	−0.848882	+	0.528583i	$0.822724\pi$
$200$		0			0
$201$	0.598651	+	0.0230663i	0.0422256	+	0.00162697i
$202$		0			0
$203$	−0.786340	−	0.210699i	−0.0551902	−	0.0147882i
$204$		0			0
$205$	−20.1965	+	5.41164i	−1.41059	+	0.377965i
$206$		0			0
$207$	−1.10477	+	3.13488i	−0.0767869	+	0.217889i
$208$		0			0
$209$	6.57281	+	1.76118i	0.454651	+	0.121823i
$210$		0			0
$211$	11.1919			0.770483			0.385241	−	0.922816i	$-0.374118\pi$
$211$	11.1919			0.770483			0.385241	+	0.922816i	$0.374118\pi$
$212$		0			0
$213$	4.80751	+	0.185236i	0.329405	+	0.0126922i
$214$		0			0
$215$	21.6402	+	37.4818i	1.47585	+	2.55624i
$216$		0			0
$217$	0.472823	−	1.76460i	0.0320973	−	0.119789i
$218$		0			0
$219$	−5.55716	+	8.82238i	−0.375518	+	0.596161i
$220$		0			0
$221$	1.93192			0.129955
$222$		0			0
$223$	−21.3837			−1.43196			−0.715978	−	0.698122i	$-0.754019\pi$
$223$	−21.3837			−1.43196			−0.715978	+	0.698122i	$0.754019\pi$
$224$		0			0
$225$	2.07439	−	26.8788i	0.138293	−	1.79192i
$226$		0			0
$227$	−1.33005	+	4.96382i	−0.0882786	+	0.329460i	−0.995915	−	0.0902974i	$-0.971218\pi$
$227$	−1.33005	+	4.96382i	−0.0882786	+	0.329460i	0.907636	+	0.419758i	$0.137885\pi$
$228$		0			0
$229$	12.0578	+	20.8848i	0.796804	+	1.38011i	0.921687	+	0.387934i	$0.126811\pi$
$229$	12.0578	+	20.8848i	0.796804	+	1.38011i	−0.124883	+	0.992172i	$0.539855\pi$
$230$		0			0
$231$	−0.121515	+	3.15374i	−0.00799512	+	0.207501i
$232$		0			0
$233$	−14.1974			−0.930101			−0.465051	−	0.885284i	$-0.653964\pi$
$233$	−14.1974			−0.930101			−0.465051	+	0.885284i	$0.653964\pi$
$234$		0			0
$235$	11.0284	+	2.95504i	0.719412	+	0.192766i
$236$		0			0
$237$	16.9914	+	18.3532i	1.10371	+	1.19217i
$238$		0			0
$239$	3.06518	−	0.821313i	0.198270	−	0.0531263i	−0.158317	−	0.987388i	$-0.550607\pi$
$239$	3.06518	−	0.821313i	0.198270	−	0.0531263i	0.356587	+	0.934262i	$0.383940\pi$
$240$		0			0
$241$	21.0011	+	5.62724i	1.35280	+	0.362482i	0.861169	−	0.508319i	$-0.169733\pi$
$241$	21.0011	+	5.62724i	1.35280	+	0.362482i	0.491634	+	0.870802i	$0.336400\pi$
$242$		0			0
$243$	−14.7421	+	5.06669i	−0.945704	+	0.325028i
$244$		0			0
$245$	18.0866	+	18.0866i	1.15551	+	1.15551i
$246$		0			0
$247$	−0.700502	−	0.404435i	−0.0445718	−	0.0257336i
$248$		0			0
$249$	−8.15950	−	15.4802i	−0.517088	−	0.981015i
$250$		0			0
$251$	6.95415	−	6.95415i	0.438942	−	0.438942i	−0.452714	−	0.891656i	$-0.649544\pi$
$251$	6.95415	−	6.95415i	0.438942	−	0.438942i	0.891656	+	0.452714i	$0.149544\pi$
$252$		0			0
$253$	−3.56279	−	3.56279i	−0.223991	−	0.223991i
$254$		0			0
$255$	−12.3381	+	19.5877i	−0.772645	+	1.22663i
$256$		0			0
$257$	−5.76497	+	1.54472i	−0.359609	+	0.0963569i	−0.434100	−	0.900865i	$-0.642933\pi$
$257$	−5.76497	+	1.54472i	−0.359609	+	0.0963569i	0.0744909	+	0.997222i	$0.476267\pi$
$258$		0			0
$259$	1.13222	−	2.15832i	0.0703529	−	0.134111i
$260$		0			0
$261$	5.74863	+	2.02589i	0.355831	+	0.125399i
$262$		0			0
$263$	12.3637	+	21.4146i	0.762381	+	1.32048i	0.941620	+	0.336677i	$0.109303\pi$
$263$	12.3637	+	21.4146i	0.762381	+	1.32048i	−0.179239	+	0.983806i	$0.557364\pi$
$264$		0			0
$265$	−34.3679	+	34.3679i	−2.11121	+	2.11121i
$266$		0			0
$267$	8.52537	−	27.5299i	0.521744	−	1.68480i
$268$		0			0
$269$		−	14.4779i		−	0.882733i	−0.897327	−	0.441367i	$-0.854494\pi$
$269$		−	14.4779i		−	0.882733i	0.897327	−	0.441367i	$-0.145506\pi$
$270$		0			0
$271$	−11.3828	+	19.7157i	−0.691458	+	1.19764i	0.279902	+	0.960029i	$0.409698\pi$
$271$	−11.3828	+	19.7157i	−0.691458	+	1.19764i	−0.971360	+	0.237612i	$0.923635\pi$
$272$		0			0
$273$	0.110979	−	0.358372i	0.00671678	−	0.0216897i
$274$		0			0
$275$	35.3911	+	20.4331i	2.13416	+	1.23216i
$276$		0			0
$277$	7.46348	−	27.8541i	0.448437	−	1.67359i	−0.258260	−	0.966075i	$-0.583149\pi$
$277$	7.46348	−	27.8541i	0.448437	−	1.67359i	0.706698	−	0.707516i	$-0.250184\pi$
$278$		0			0
$279$	−4.54623	+	12.9003i	−0.272176	+	0.772321i
$280$		0			0
$281$	−14.7557	+	3.95378i	−0.880251	+	0.235863i	−0.670515	−	0.741896i	$-0.733927\pi$
$281$	−14.7557	+	3.95378i	−0.880251	+	0.235863i	−0.209735	+	0.977758i	$0.567260\pi$
$282$		0			0
$283$	−3.08377	+	11.5088i	−0.183311	+	0.684127i	0.811674	+	0.584110i	$0.198556\pi$
$283$	−3.08377	+	11.5088i	−0.183311	+	0.684127i	−0.994986	+	0.100017i	$0.968110\pi$
$284$		0			0
$285$	8.57427	−	4.51945i	0.507896	−	0.267709i
$286$		0			0
$287$	1.12009	−	1.94006i	0.0661170	−	0.114518i
$288$		0			0
$289$	−3.66135	+	2.11388i	−0.215374	+	0.124346i
$290$		0			0
$291$	17.9584	−	4.07788i	1.05274	−	0.239050i
$292$		0			0
$293$	3.48667	−	2.01303i	0.203693	−	0.117602i	−0.394684	−	0.918817i	$-0.629146\pi$
$293$	3.48667	−	2.01303i	0.203693	−	0.117602i	0.598377	+	0.801215i	$0.295813\pi$
$294$		0			0
$295$		−	43.3312i		−	2.52284i
$296$		0			0
$297$	2.72403	−	23.4726i	0.158064	−	1.36202i
$298$		0			0
$299$	0.299466	+	0.518690i	0.0173185	+	0.0299966i
$300$		0			0
$301$	−4.47905	−	1.20016i	−0.258168	−	0.0691759i
$302$		0			0
$303$	−6.60968	−	4.16339i	−0.379716	−	0.239181i
$304$		0			0
$305$	−26.1654	−	15.1066i	−1.49823	−	0.865003i
$306$		0			0
$307$		−	20.2996i		−	1.15856i	−0.815128	−	0.579281i	$-0.803333\pi$
$307$		−	20.2996i		−	1.15856i	0.815128	−	0.579281i	$-0.196667\pi$
$308$		0			0
$309$	−4.54195	−	20.0020i	−0.258382	−	1.13788i
$310$		0			0
$311$	−3.26840	−	12.1978i	−0.185334	−	0.691676i	−0.994559	−	0.104177i	$-0.966779\pi$
$311$	−3.26840	−	12.1978i	−0.185334	−	0.691676i	0.809225	−	0.587499i	$-0.199887\pi$
$312$		0			0
$313$	1.75350	+	6.54416i	0.0991139	+	0.369898i	0.997611	−	0.0690814i	$-0.0220068\pi$
$313$	1.75350	+	6.54416i	0.0991139	+	0.369898i	−0.898497	+	0.438979i	$0.855340\pi$
$314$		0			0
$315$	2.92475	+	3.41394i	0.164791	+	0.192354i
$316$		0			0
$317$	15.8266	−	27.4124i	0.888908	−	1.53963i	0.0477410	−	0.998860i	$-0.484798\pi$
$317$	15.8266	−	27.4124i	0.888908	−	1.53963i	0.841167	−	0.540775i	$-0.181869\pi$
$318$		0			0
$319$	−6.53332	+	6.53332i	−0.365796	+	0.365796i
$320$		0			0
$321$	12.7688	+	0.491989i	0.712686	+	0.0274602i
$322$		0			0
$323$	−5.34756			−0.297546
$324$		0			0
$325$	−3.43495	−	3.43495i	−0.190537	−	0.190537i
$326$		0			0
$327$	7.06586	−	22.8169i	0.390743	−	1.26178i
$328$		0			0
$329$	−1.05938	+	0.611631i	−0.0584053	+	0.0337203i
$330$		0			0
$331$	5.32520	+	19.8739i	0.292700	+	1.09237i	0.943027	+	0.332716i	$0.107965\pi$
$331$	5.32520	+	19.8739i	0.292700	+	1.09237i	−0.650327	+	0.759654i	$0.725368\pi$
$332$		0			0
$333$	−9.69548	+	15.4596i	−0.531309	+	0.847178i
$334$		0			0
$335$	0.334797	+	1.24948i	0.0182919	+	0.0682664i
$336$		0			0
$337$	−20.8342	+	12.0286i	−1.13491	+	0.655241i	−0.945165	−	0.326593i	$-0.894099\pi$
$337$	−20.8342	+	12.0286i	−1.13491	+	0.655241i	−0.189745	+	0.981833i	$0.560766\pi$
$338$		0			0
$339$	−0.724278	+	2.33882i	−0.0393374	+	0.127027i
$340$		0			0
$341$	−14.6612	−	14.6612i	−0.793949	−	0.793949i
$342$		0			0
$343$	−5.54525			−0.299415
$344$		0			0
$345$	−7.17149	−	0.276321i	−0.386100	−	0.0148766i
$346$		0			0
$347$	−10.4757	+	10.4757i	−0.562364	+	0.562364i	−0.929978	−	0.367615i	$-0.880175\pi$
$347$	−10.4757	+	10.4757i	−0.562364	+	0.562364i	0.367615	+	0.929978i	$0.380175\pi$
$348$		0			0
$349$	−11.2485	+	19.4830i	−0.602120	+	1.04290i	0.390379	+	0.920654i	$0.372344\pi$
$349$	−11.2485	+	19.4830i	−0.602120	+	1.04290i	−0.992499	+	0.122249i	$0.960989\pi$
$350$		0			0
$351$	−1.03492	+	2.61131i	−0.0552402	+	0.139381i
$352$		0			0
$353$	−2.87775	−	10.7399i	−0.153167	−	0.571627i	−0.999255	−	0.0385845i	$-0.987715\pi$
$353$	−2.87775	−	10.7399i	−0.153167	−	0.571627i	0.846088	−	0.533043i	$-0.178952\pi$
$354$		0			0
$355$	2.68862	+	10.0340i	0.142697	+	0.532552i
$356$		0			0
$357$	−0.549221	−	2.41868i	−0.0290678	−	0.128010i
$358$		0			0
$359$		−	14.9484i		−	0.788945i	−0.918908	−	0.394472i	$-0.870927\pi$
$359$		−	14.9484i		−	0.788945i	0.918908	−	0.394472i	$-0.129073\pi$
$360$		0			0
$361$	−14.5155	−	8.38053i	−0.763973	−	0.441080i
$362$		0			0
$363$	14.1878	+	8.93682i	0.744668	+	0.469061i
$364$		0			0
$365$	−21.7461	−	5.82685i	−1.13824	−	0.304991i
$366$		0			0
$367$	10.8304	+	18.7587i	0.565340	+	0.979198i	0.997018	+	0.0771701i	$0.0245885\pi$
$367$	10.8304	+	18.7587i	0.565340	+	0.979198i	−0.431678	+	0.902028i	$0.642078\pi$
$368$		0			0
$369$	−9.47919	+	13.8372i	−0.493467	+	0.720337i
$370$		0			0
$371$		−	5.20739i		−	0.270354i
$372$		0			0
$373$	−1.62360	+	0.937384i	−0.0840667	+	0.0485359i	−0.541444	−	0.840737i	$-0.682122\pi$
$373$	−1.62360	+	0.937384i	−0.0840667	+	0.0485359i	0.457377	+	0.889273i	$0.348789\pi$
$374$		0			0
$375$	25.1801	−	5.71776i	1.30030	−	0.295264i
$376$		0			0
$377$	0.951155	−	0.549149i	0.0489869	−	0.0282826i
$378$		0			0
$379$	4.20204	−	7.27814i	0.215844	−	0.373853i	−0.737689	−	0.675140i	$-0.764083\pi$
$379$	4.20204	−	7.27814i	0.215844	−	0.373853i	0.953533	+	0.301287i	$0.0974164\pi$
$380$		0			0
$381$	19.8098	−	10.4416i	1.01488	−	0.534940i
$382$		0			0
$383$	2.51359	−	9.38085i	0.128439	−	0.479339i	−0.871500	−	0.490395i	$-0.836853\pi$
$383$	2.51359	−	9.38085i	0.128439	−	0.479339i	0.999939	+	0.0110557i	$0.00351921\pi$
$384$		0			0
$385$	−6.58236	+	1.76374i	−0.335468	+	0.0898885i
$386$		0			0
$387$	32.7446	+	11.5396i	1.66450	+	0.586592i
$388$		0			0
$389$	6.51259	−	24.3053i	0.330201	−	1.23233i	−0.578777	−	0.815486i	$-0.696470\pi$
$389$	6.51259	−	24.3053i	0.330201	−	1.23233i	0.908979	−	0.416843i	$-0.136863\pi$
$390$		0			0
$391$	3.42913	+	1.97981i	0.173419	+	0.100123i
$392$		0			0
$393$	9.56028	−	30.8718i	0.482252	−	1.55728i
$394$		0			0
$395$	−27.0016	+	46.7682i	−1.35860	+	2.35316i
$396$		0			0
$397$			4.93446i			0.247654i	0.992304	+	0.123827i	$0.0395167\pi$
$397$			4.93446i			0.247654i	−0.992304	+	0.123827i	$0.960483\pi$
$398$		0			0
$399$	−0.307191	+	0.991972i	−0.0153788	+	0.0496607i
$400$		0			0
$401$	18.8678	−	18.8678i	0.942212	−	0.942212i	−0.0562068	−	0.998419i	$-0.517901\pi$
$401$	18.8678	−	18.8678i	0.942212	−	0.942212i	0.998419	+	0.0562068i	$0.0179006\pi$
$402$		0			0
$403$	1.23233	+	2.13445i	0.0613866	+	0.106325i
$404$		0			0
$405$	−19.8664	−	27.1701i	−0.987170	−	1.35009i
$406$		0			0
$407$	−14.7892	−	23.3768i	−0.733071	−	1.15875i
$408$		0			0
$409$	35.8678	−	9.61075i	1.77355	−	0.475221i	0.784165	−	0.620552i	$-0.213091\pi$
$409$	35.8678	−	9.61075i	1.77355	−	0.475221i	0.989383	+	0.145331i	$0.0464247\pi$
$410$		0			0
$411$	3.37135	−	5.35226i	0.166296	−	0.264007i
$412$		0			0
$413$	3.28275	+	3.28275i	0.161533	+	0.161533i
$414$		0			0
$415$	26.7169	−	26.7169i	1.31148	−	1.31148i
$416$		0			0
$417$	9.48781	+	18.0002i	0.464620	+	0.881474i
$418$		0			0
$419$	12.9550	+	7.47958i	0.632894	+	0.365401i	0.781872	−	0.623439i	$-0.214265\pi$
$419$	12.9550	+	7.47958i	0.632894	+	0.365401i	−0.148978	+	0.988840i	$0.547598\pi$
$420$		0			0
$421$	−2.47407	−	2.47407i	−0.120579	−	0.120579i	0.644242	−	0.764821i	$-0.277173\pi$
$421$	−2.47407	−	2.47407i	−0.120579	−	0.120579i	−0.764821	+	0.644242i	$0.777173\pi$
$422$		0			0
$423$	8.26060	−	3.95550i	0.401644	−	0.192323i
$424$		0			0
$425$	−31.0210	−	8.31205i	−1.50474	−	0.403194i
$426$		0			0
$427$	3.12675	−	0.837810i	0.151314	−	0.0405445i
$428$		0			0
$429$	−2.89268	−	3.12453i	−0.139660	−	0.150854i
$430$		0			0
$431$	−6.06848	−	1.62604i	−0.292308	−	0.0783237i	0.109685	−	0.993966i	$-0.465016\pi$
$431$	−6.06848	−	1.62604i	−0.292308	−	0.0783237i	−0.401993	+	0.915643i	$0.631682\pi$
$432$		0			0
$433$	2.55564			0.122816			0.0614081	−	0.998113i	$-0.480441\pi$
$433$	2.55564			0.122816			0.0614081	+	0.998113i	$0.480441\pi$
$434$		0			0
$435$	−0.506708	+	13.1508i	−0.0242948	+	0.630534i
$436$		0			0
$437$	−0.828920	−	1.43573i	−0.0396526	−	0.0686804i
$438$		0			0
$439$	0.849250	−	3.16944i	0.0405325	−	0.151269i	−0.942694	−	0.333659i	$-0.891717\pi$
$439$	0.849250	−	3.16944i	0.0405325	−	0.151269i	0.983226	+	0.182390i	$0.0583833\pi$
$440$		0			0
$441$	20.4575	+	1.57882i	0.974168	+	0.0751820i
$442$		0			0
$443$	25.6668			1.21947			0.609733	−	0.792607i	$-0.291276\pi$
$443$	25.6668			1.21947			0.609733	+	0.792607i	$0.291276\pi$
$444$		0			0
$445$	62.2271			2.94985
$446$		0			0
$447$	−13.9279	+	22.1116i	−0.658769	+	1.04584i
$448$		0			0
$449$	3.31277	−	12.3634i	0.156339	−	0.583467i	−0.842648	−	0.538466i	$-0.819004\pi$
$449$	3.31277	−	12.3634i	0.156339	−	0.583467i	0.998987	−	0.0450011i	$-0.0143291\pi$
$450$		0			0
$451$	−12.7127	−	22.0190i	−0.598617	−	1.03683i
$452$		0			0
$453$	10.8784	+	0.419151i	0.511112	+	0.0196934i
$454$		0			0
$455$	0.810045			0.0379755
$456$		0			0
$457$	10.0331	+	2.68835i	0.469327	+	0.125756i	0.485729	−	0.874110i	$-0.338554\pi$
$457$	10.0331	+	2.68835i	0.469327	+	0.125756i	−0.0164016	+	0.999865i	$0.505221\pi$
$458$		0			0
$459$	2.70649	+	18.3719i	0.126328	+	0.857525i
$460$		0			0
$461$	28.5898	−	7.66060i	1.33156	−	0.356790i	0.478262	−	0.878217i	$-0.341267\pi$
$461$	28.5898	−	7.66060i	1.33156	−	0.356790i	0.853296	+	0.521427i	$0.174600\pi$
$462$		0			0
$463$	−32.6190	−	8.74023i	−1.51593	−	0.406193i	−0.597532	−	0.801845i	$-0.703852\pi$
$463$	−32.6190	−	8.74023i	−1.51593	−	0.406193i	−0.918401	+	0.395652i	$0.870519\pi$
$464$		0			0
$465$	−29.5113	−	1.13709i	−1.36856	−	0.0527311i
$466$		0			0
$467$	−14.9204	−	14.9204i	−0.690434	−	0.690434i	0.271894	−	0.962327i	$-0.412350\pi$
$467$	−14.9204	−	14.9204i	−0.690434	−	0.690434i	−0.962327	+	0.271894i	$0.912350\pi$
$468$		0			0
$469$	−0.120024	−	0.0692959i	−0.00554219	−	0.00319979i
$470$		0			0
$471$	−30.9208	+	16.2982i	−1.42476	+	0.750980i
$472$		0			0
$473$	−37.2143	+	37.2143i	−1.71111	+	1.71111i
$474$		0			0
$475$	9.50792	+	9.50792i	0.436253	+	0.436253i
$476$		0			0
$477$	−3.00006	+	38.8731i	−0.137363	+	1.77988i
$478$		0			0
$479$	−8.29683	+	2.22313i	−0.379092	+	0.101577i	−0.443333	−	0.896357i	$-0.646204\pi$
$479$	−8.29683	+	2.22313i	−0.379092	+	0.101577i	0.0642411	+	0.997934i	$0.479537\pi$
$480$		0			0
$481$	0.978876	+	3.13911i	0.0446329	+	0.143131i
$482$		0			0
$483$	0.564242	−	0.522374i	0.0256739	−	0.0237689i
$484$		0			0
$485$	19.8813	+	34.4354i	0.902762	+	1.56363i
$486$		0			0
$487$	−7.28706	+	7.28706i	−0.330208	+	0.330208i	−0.852665	−	0.522457i	$-0.825015\pi$
$487$	−7.28706	+	7.28706i	−0.330208	+	0.330208i	0.522457	+	0.852665i	$0.325015\pi$
$488$		0			0
$489$	−27.5510	−	8.53190i	−1.24590	−	0.385826i
$490$		0			0
$491$		−	36.0804i		−	1.62829i	−0.580664	−	0.814143i	$-0.697207\pi$
$491$		−	36.0804i		−	1.62829i	0.580664	−	0.814143i	$-0.302793\pi$
$492$		0			0
$493$	3.63051	−	6.28823i	0.163510	−	0.283207i
$494$		0			0
$495$	50.1534	−	9.37410i	2.25423	−	0.421334i
$496$		0			0
$497$	−0.963862	−	0.556486i	−0.0432351	−	0.0249618i
$498$		0			0
$499$	−4.42552	+	16.5163i	−0.198114	+	0.739370i	0.793325	+	0.608798i	$0.208348\pi$
$499$	−4.42552	+	16.5163i	−0.198114	+	0.739370i	−0.991439	+	0.130572i	$0.958319\pi$
$500$		0			0
$501$	29.4237	−	27.2404i	1.31455	−	1.21701i
$502$		0			0
$503$	−29.7452	+	7.97019i	−1.32627	+	0.355373i	−0.851324	−	0.524641i	$-0.824200\pi$
$503$	−29.7452	+	7.97019i	−1.32627	+	0.355373i	−0.474947	+	0.880014i	$0.657533\pi$
$504$		0			0
$505$	4.36544	−	16.2921i	0.194260	−	0.724987i
$506$		0			0
$507$	−10.2632	−	19.4713i	−0.455804	−	0.864749i
$508$		0			0
$509$	4.38414	−	7.59354i	0.194323	−	0.336578i	−0.752355	−	0.658758i	$-0.771082\pi$
$509$	4.38414	−	7.59354i	0.194323	−	0.336578i	0.946679	+	0.322180i	$0.104416\pi$
$510$		0			0
$511$	2.08891	−	1.20603i	0.0924079	−	0.0533517i
$512$		0			0
$513$	2.86467	−	7.22809i	0.126478	−	0.319128i
$514$		0			0
$515$	38.3542	−	22.1438i	1.69009	−	0.975772i
$516$		0			0
$517$			13.8836i			0.610600i
$518$		0			0
$519$	−26.1259	+	13.7708i	−1.14680	+	0.604472i
$520$		0			0
$521$	−5.71195	−	9.89338i	−0.250245	−	0.433437i	0.713348	−	0.700810i	$-0.247178\pi$
$521$	−5.71195	−	9.89338i	−0.250245	−	0.433437i	−0.963593	+	0.267373i	$0.913844\pi$
$522$		0			0
$523$	−7.19523	−	1.92796i	−0.314626	−	0.0843037i	0.0980507	−	0.995181i	$-0.468739\pi$
$523$	−7.19523	−	1.92796i	−0.314626	−	0.0843037i	−0.412676	+	0.910878i	$0.635406\pi$
$524$		0			0
$525$	−3.32389	+	5.27691i	−0.145066	+	0.230303i
$526$		0			0
$527$	14.1112	+	8.14710i	0.614693	+	0.354893i
$528$		0			0
$529$		−	21.7724i		−	0.946628i
$530$		0			0
$531$	−22.6144	−	26.3969i	−0.981383	−	1.14553i
$532$		0			0
$533$	0.782230	+	2.91932i	0.0338822	+	0.126450i
$534$		0			0
$535$	7.14100	+	26.6506i	0.308732	+	1.15221i
$536$		0			0
$537$	−7.36082	+	1.67145i	−0.317643	+	0.0721285i
$538$		0			0
$539$	−15.5516	+	26.9362i	−0.669857	+	1.16023i
$540$		0			0
$541$	−12.5374	+	12.5374i	−0.539023	+	0.539023i	−0.923242	−	0.384219i	$-0.874471\pi$
$541$	−12.5374	+	12.5374i	−0.539023	+	0.539023i	0.384219	+	0.923242i	$0.374471\pi$
$542$		0			0
$543$	0.617860	−	16.0356i	0.0265149	−	0.688154i
$544$		0			0
$545$	51.5741			2.20919
$546$		0			0
$547$	7.81206	+	7.81206i	0.334019	+	0.334019i	0.854111	−	0.520091i	$-0.174102\pi$
$547$	7.81206	+	7.81206i	0.334019	+	0.334019i	−0.520091	+	0.854111i	$0.674102\pi$
$548$		0			0
$549$	−23.8238	+	4.45288i	−1.01678	+	0.190044i
$550$		0			0
$551$	−2.63279	+	1.52004i	−0.112161	+	0.0647560i
$552$		0			0
$553$	−1.49750	−	5.58876i	−0.0636803	−	0.237658i
$554$		0			0
$555$	−38.0788	−	10.1230i	−1.61636	−	0.429698i
$556$		0			0
$557$	−2.74596	−	10.2481i	−0.116350	−	0.434224i	0.883034	−	0.469308i	$-0.155497\pi$
$557$	−2.74596	−	10.2481i	−0.116350	−	0.434224i	−0.999384	+	0.0350842i	$0.988830\pi$
$558$		0			0
$559$	5.41785	−	3.12799i	0.229150	−	0.132300i
$560$		0			0
$561$	−26.8902	−	8.32727i	−1.13530	−	0.351577i
$562$		0			0
$563$	2.80007	+	2.80007i	0.118009	+	0.118009i	0.763645	−	0.645636i	$-0.223408\pi$
$563$	2.80007	+	2.80007i	0.118009	+	0.118009i	−0.645636	+	0.763645i	$0.723408\pi$
$564$		0			0
$565$	−5.28654			−0.222407
$566$		0			0
$567$	3.56346	+	0.553319i	0.149651	+	0.0232372i
$568$		0			0
$569$	30.7198	−	30.7198i	1.28784	−	1.28784i	0.351743	−	0.936097i	$-0.385589\pi$
$569$	30.7198	−	30.7198i	1.28784	−	1.28784i	0.936097	−	0.351743i	$-0.114411\pi$
$570$		0			0
$571$	−14.4323	+	24.9975i	−0.603974	+	1.04611i	0.388238	+	0.921559i	$0.373084\pi$
$571$	−14.4323	+	24.9975i	−0.603974	+	1.04611i	−0.992213	+	0.124555i	$0.960250\pi$
$572$		0			0
$573$	4.26679	+	18.7903i	0.178248	+	0.784975i
$574$		0			0
$575$	−2.57689	−	9.61707i	−0.107464	−	0.401060i
$576$		0			0
$577$	−5.63570	−	21.0327i	−0.234617	−	0.875604i	−0.978321	−	0.207095i	$-0.933599\pi$
$577$	−5.63570	−	21.0327i	−0.234617	−	0.875604i	0.743703	−	0.668510i	$-0.233067\pi$
$578$		0			0
$579$	−0.430466	+	0.0977478i	−0.0178896	+	0.00406226i
$580$		0			0
$581$			4.04812i			0.167944i
$582$		0			0
$583$	−51.1839	−	29.5510i	−2.11982	−	1.22388i
$584$		0			0
$585$	−6.04698	−	0.466680i	−0.250012	−	0.0192948i
$586$		0			0
$587$	−14.4941	−	3.88367i	−0.598234	−	0.160296i	−0.0530202	−	0.998593i	$-0.516885\pi$
$587$	−14.4941	−	3.88367i	−0.598234	−	0.160296i	−0.545214	+	0.838297i	$0.683551\pi$
$588$		0			0
$589$	−3.41108	−	5.90816i	−0.140551	−	0.243442i
$590$		0			0
$591$	8.48679	+	16.1011i	0.349100	+	0.662310i
$592$		0			0
$593$			38.7388i			1.59081i	0.606076	+	0.795407i	$0.292743\pi$
$593$			38.7388i			1.59081i	−0.606076	+	0.795407i	$0.707257\pi$
$594$		0			0
$595$	4.63785	−	2.67767i	0.190133	−	0.109774i
$596$		0			0
$597$	−2.45080	−	10.7930i	−0.100305	−	0.441726i
$598$		0			0
$599$	−11.4197	+	6.59315i	−0.466595	+	0.269389i	−0.714813	−	0.699315i	$-0.753488\pi$
$599$	−11.4197	+	6.59315i	−0.466595	+	0.269389i	0.248218	+	0.968704i	$0.420155\pi$
$600$		0			0
$601$	17.7850	−	30.8045i	0.725465	−	1.25654i	−0.233317	−	0.972401i	$-0.574958\pi$
$601$	17.7850	−	30.8045i	0.725465	−	1.25654i	0.958782	−	0.284142i	$-0.0917086\pi$
$602$		0			0
$603$	0.856056	+	0.586441i	0.0348613	+	0.0238817i
$604$		0			0
$605$	−9.37053	+	34.9713i	−0.380966	+	1.42179i
$606$		0			0
$607$	−19.2009	+	5.14486i	−0.779340	+	0.208824i	−0.626494	−	0.779426i	$-0.715511\pi$
$607$	−19.2009	+	5.14486i	−0.779340	+	0.208824i	−0.152846	+	0.988250i	$0.548844\pi$
$608$		0			0
$609$	−0.957911	−	1.03469i	−0.0388165	−	0.0419276i
$610$		0			0
$611$	0.427139	−	1.59411i	0.0172802	−	0.0644906i
$612$		0			0
$613$	−24.4792	−	14.1331i	−0.988707	−	0.570830i	−0.0838193	−	0.996481i	$-0.526712\pi$
$613$	−24.4792	−	14.1331i	−0.988707	−	0.570830i	−0.904887	+	0.425651i	$0.860045\pi$
$614$		0			0
$615$	−34.5946	−	10.7131i	−1.39499	−	0.431995i
$616$		0			0
$617$	−14.1785	+	24.5579i	−0.570806	+	0.988664i	0.425678	+	0.904875i	$0.360036\pi$
$617$	−14.1785	+	24.5579i	−0.570806	+	0.988664i	−0.996483	+	0.0837895i	$0.973298\pi$
$618$		0			0
$619$		−	17.0435i		−	0.685037i	−0.939511	−	0.342519i	$-0.888720\pi$
$619$		−	17.0435i		−	0.685037i	0.939511	−	0.342519i	$-0.111280\pi$
$620$		0			0
$621$	−4.51301	+	3.57445i	−0.181101	+	0.143438i
$622$		0			0
$623$	−4.71429	+	4.71429i	−0.188874	+	0.188874i
$624$		0			0
$625$	5.41072	+	9.37164i	0.216429	+	0.374866i
$626$		0			0
$627$	8.00693	+	8.64868i	0.319766	+	0.345395i
$628$		0			0
$629$	15.9810	+	14.7370i	0.637206	+	0.587602i
$630$		0			0
$631$	26.8138	−	7.18473i	1.06744	−	0.286019i	0.317999	−	0.948091i	$-0.396989\pi$
$631$	26.8138	−	7.18473i	1.06744	−	0.286019i	0.749440	+	0.662072i	$0.230323\pi$
$632$		0			0
$633$	16.4022	+	10.3317i	0.651930	+	0.410647i
$634$		0			0
$635$	34.1893	+	34.1893i	1.35676	+	1.35676i
$636$		0			0
$637$	2.61434	−	2.61434i	0.103584	−	0.103584i
$638$		0			0
$639$	6.87462	+	4.70946i	0.271956	+	0.186303i
$640$		0			0
$641$	34.1211	+	19.6998i	1.34770	+	0.778096i	0.987924	−	0.154942i	$-0.0495191\pi$
$641$	34.1211	+	19.6998i	1.34770	+	0.778096i	0.359778	+	0.933038i	$0.382852\pi$
$642$		0			0
$643$	17.1426	+	17.1426i	0.676039	+	0.676039i	0.959102	−	0.283062i	$-0.0913503\pi$
$643$	17.1426	+	17.1426i	0.676039	+	0.676039i	−0.283062	+	0.959102i	$0.591350\pi$
$644$		0			0
$645$	−2.88625	+	74.9081i	−0.113646	+	2.94950i
$646$		0			0
$647$	−14.5312	−	3.89362i	−0.571280	−	0.153074i	−0.0383963	−	0.999263i	$-0.512225\pi$
$647$	−14.5312	−	3.89362i	−0.571280	−	0.153074i	−0.532883	+	0.846189i	$0.678892\pi$
$648$		0			0
$649$	50.8954	−	13.6374i	1.99782	−	0.535315i
$650$		0			0
$651$	2.32191	−	2.14962i	0.0910027	−	0.0842501i
$652$		0			0
$653$	−1.65353	−	0.443061i	−0.0647075	−	0.0173383i	0.226320	−	0.974053i	$-0.427330\pi$
$653$	−1.65353	−	0.443061i	−0.0647075	−	0.0173383i	−0.291028	+	0.956715i	$0.593997\pi$
$654$		0			0
$655$	69.7810			2.72657
$656$		0			0
$657$	−16.2885	+	7.79957i	−0.635475	+	0.304290i
$658$		0			0
$659$	1.95850	+	3.39222i	0.0762922	+	0.132142i	0.901647	−	0.432472i	$-0.142358\pi$
$659$	1.95850	+	3.39222i	0.0762922	+	0.132142i	−0.825355	+	0.564614i	$0.809025\pi$
$660$		0			0
$661$	−6.79931	+	25.3754i	−0.264463	+	0.986988i	0.698116	+	0.715985i	$0.254022\pi$
$661$	−6.79931	+	25.3754i	−0.264463	+	0.986988i	−0.962578	+	0.271003i	$0.912645\pi$
$662$		0			0
$663$	2.83132	+	1.78343i	0.109959	+	0.0692626i
$664$		0			0
$665$	−2.24220			−0.0869489
$666$		0			0
$667$	2.25105			0.0871609
$668$		0			0
$669$	−31.3387	−	19.7400i	−1.21163	−	0.763194i
$670$		0			0
$671$	9.50885	−	35.4875i	0.367085	−	1.36998i
$672$		0			0
$673$	−12.3036	−	21.3105i	−0.474270	−	0.821460i	0.525296	−	0.850920i	$-0.323955\pi$
$673$	−12.3036	−	21.3105i	−0.474270	−	0.821460i	−0.999566	+	0.0294596i	$0.990621\pi$
$674$		0			0
$675$	27.8529	−	37.4772i	1.07206	−	1.44250i
$676$		0			0
$677$	11.1846			0.429857			0.214929	−	0.976630i	$-0.431048\pi$
$677$	11.1846			0.429857			0.214929	+	0.976630i	$0.431048\pi$
$678$		0			0
$679$	−4.11500	−	1.10261i	−0.157919	−	0.0423143i
$680$		0			0
$681$	−6.53153	+	6.04688i	−0.250289	+	0.231717i
$682$		0			0
$683$	−43.9177	+	11.7677i	−1.68047	+	0.450279i	−0.967902	−	0.251328i	$-0.919133\pi$
$683$	−43.9177	+	11.7677i	−1.68047	+	0.450279i	−0.712563	+	0.701608i	$0.752466\pi$
$684$		0			0
$685$	13.1927	+	3.53496i	0.504066	+	0.135064i
$686$		0			0
$687$	−1.60821	+	41.7386i	−0.0613570	+	1.59243i
$688$		0			0
$689$	4.96774	+	4.96774i	0.189256	+	0.189256i
$690$		0			0
$691$	−25.7644	−	14.8751i	−0.980125	−	0.565876i	−0.0778173	−	0.996968i	$-0.524795\pi$
$691$	−25.7644	−	14.8751i	−0.980125	−	0.565876i	−0.902308	+	0.431092i	$0.858128\pi$
$692$		0			0
$693$	−3.08942	+	4.50977i	−0.117357	+	0.171312i
$694$		0			0
$695$	−31.0663	+	31.0663i	−1.17841	+	1.17841i
$696$		0			0
$697$	14.1286	+	14.1286i	0.535160	+	0.535160i
$698$		0			0
$699$	−20.8069	−	13.1061i	−0.786989	−	0.495719i
$700$		0			0
$701$	−14.5329	+	3.89409i	−0.548902	+	0.147078i	−0.522603	−	0.852576i	$-0.675039\pi$
$701$	−14.5329	+	3.89409i	−0.548902	+	0.147078i	−0.0262989	+	0.999654i	$0.508372\pi$
$702$		0			0
$703$	−2.70953	−	8.68905i	−0.102192	−	0.327714i
$704$		0			0
$705$	13.4347	+	14.5114i	0.505978	+	0.546532i
$706$		0			0
$707$	0.903554	+	1.56500i	0.0339816	+	0.0588579i
$708$		0			0
$709$	23.3288	−	23.3288i	0.876132	−	0.876132i	−0.117000	−	0.993132i	$-0.537328\pi$
$709$	23.3288	−	23.3288i	0.876132	−	0.876132i	0.993132	+	0.117000i	$0.0373278\pi$
$710$		0			0
$711$	7.95908	+	42.5828i	0.298489	+	1.59698i
$712$		0			0
$713$			5.05150i			0.189180i
$714$		0			0
$715$	4.59687	−	7.96201i	0.171913	−	0.297762i
$716$		0			0
$717$	5.25034	+	1.62591i	0.196078	+	0.0607207i
$718$		0			0
$719$	27.8606	+	16.0853i	1.03903	+	0.599882i	0.919557	−	0.392956i	$-0.128547\pi$
$719$	27.8606	+	16.0853i	1.03903	+	0.599882i	0.119469	+	0.992838i	$0.461881\pi$
$720$		0			0
$721$	−1.22809	+	4.58329i	−0.0457364	+	0.170691i
$722$		0			0
$723$	25.5834	+	27.6339i	0.951457	+	1.02772i
$724$		0			0
$725$	−17.6354	+	4.72540i	−0.654964	+	0.175497i
$726$		0			0
$727$	−8.54781	+	31.9009i	−0.317021	+	1.18314i	0.605072	+	0.796170i	$0.293144\pi$
$727$	−8.54781	+	31.9009i	−0.317021	+	1.18314i	−0.922093	+	0.386968i	$0.873523\pi$
$728$		0			0
$729$	−26.2824	−	6.18349i	−0.973422	−	0.229018i
$730$		0			0
$731$	20.6796	−	35.8182i	0.764864	−	1.32478i
$732$		0			0
$733$	−23.0689	+	13.3188i	−0.852070	+	0.491943i	−0.861349	−	0.508014i	$-0.830380\pi$
$733$	−23.0689	+	13.3188i	−0.852070	+	0.491943i	0.00927885	+	0.999957i	$0.497046\pi$
$734$		0			0
$735$	9.81032	+	43.2031i	0.361859	+	1.59357i
$736$		0			0
$737$	−1.36223	+	0.786485i	−0.0501785	+	0.0289705i
$738$		0			0
$739$			14.2028i			0.522457i	0.965277	+	0.261229i	$0.0841276\pi$
$739$			14.2028i			0.522457i	−0.965277	+	0.261229i	$0.915872\pi$
$740$		0			0
$741$	−0.653268	−	1.23938i	−0.0239984	−	0.0455296i
$742$		0			0
$743$	5.82579	+	10.0906i	0.213727	+	0.370187i	0.952878	−	0.303353i	$-0.0981062\pi$
$743$	5.82579	+	10.0906i	0.213727	+	0.370187i	−0.739151	+	0.673540i	$0.764773\pi$
$744$		0			0
$745$	−54.5024	−	14.6039i	−1.99681	−	0.535045i
$746$		0			0
$747$	2.33218	−	30.2192i	0.0853302	−	1.10566i
$748$		0			0
$749$	−2.56003	−	1.47803i	−0.0935415	−	0.0540062i
$750$		0			0
$751$		−	29.7920i		−	1.08713i	−0.839368	−	0.543563i	$-0.817075\pi$
$751$		−	29.7920i		−	1.08713i	0.839368	−	0.543563i	$-0.182925\pi$
$752$		0			0
$753$	16.6112	−	3.77198i	0.605347	−	0.137459i
$754$		0			0
$755$	6.08378	+	22.7050i	0.221411	+	0.826319i
$756$		0			0
$757$	6.37067	+	23.7757i	0.231546	+	0.864142i	0.979676	+	0.200589i	$0.0642855\pi$
$757$	6.37067	+	23.7757i	0.231546	+	0.864142i	−0.748129	+	0.663553i	$0.769048\pi$
$758$		0			0
$759$	−1.93249	−	8.51037i	−0.0701448	−	0.308907i
$760$		0			0
$761$	−2.21508	+	3.83664i	−0.0802967	+	0.139078i	−0.903377	−	0.428846i	$-0.858920\pi$
$761$	−2.21508	+	3.83664i	−0.0802967	+	0.139078i	0.823081	+	0.567925i	$0.192253\pi$
$762$		0			0
$763$	−3.90722	+	3.90722i	−0.141451	+	0.141451i
$764$		0			0
$765$	−36.1642	+	17.3168i	−1.30752	+	0.626091i
$766$		0			0
$767$	−6.26335			−0.226156
$768$		0			0
$769$	13.5540	+	13.5540i	0.488769	+	0.488769i	0.907918	−	0.419149i	$-0.137671\pi$
$769$	13.5540	+	13.5540i	0.488769	+	0.488769i	−0.419149	+	0.907918i	$0.637671\pi$
$770$		0			0
$771$	−9.87480	−	3.05800i	−0.355632	−	0.110131i
$772$		0			0
$773$	−12.6701	+	7.31511i	−0.455713	+	0.263106i	−0.710240	−	0.703960i	$-0.751414\pi$
$773$	−12.6701	+	7.31511i	−0.455713	+	0.263106i	0.254527	+	0.967066i	$0.418080\pi$
$774$		0			0
$775$	−10.6041	−	39.5751i	−0.380911	−	1.42158i
$776$		0			0
$777$	3.65175	−	2.11792i	0.131006	−	0.0759799i
$778$		0			0
$779$	−2.16521	−	8.08068i	−0.0775767	−	0.289520i
$780$		0			0
$781$	−10.9395	+	6.31592i	−0.391446	+	0.226002i
$782$		0			0
$783$	6.55470	+	8.27580i	0.234246	+	0.295753i
$784$		0			0
$785$	−53.3657	−	53.3657i	−1.90470	−	1.90470i
$786$		0			0
$787$	55.0389			1.96192			0.980962	−	0.194199i	$-0.0622109\pi$
$787$	55.0389			1.96192			0.980962	+	0.194199i	$0.0622109\pi$
$788$		0			0
$789$	−1.64901	+	42.7975i	−0.0587063	+	1.52363i
$790$		0			0
$791$	0.400506	−	0.400506i	0.0142403	−	0.0142403i
$792$		0			0
$793$	−2.18360	+	3.78211i	−0.0775419	+	0.134307i
$794$		0			0
$795$	−82.0940	+	18.6414i	−2.91157	+	0.661144i
$796$		0			0
$797$	2.75041	+	10.2647i	0.0974247	+	0.363594i	0.997376	−	0.0723968i	$-0.0230648\pi$
$797$	2.75041	+	10.2647i	0.0974247	+	0.363594i	−0.899951	+	0.435991i	$0.856398\pi$
$798$		0			0
$799$	−2.82388	−	10.5389i	−0.0999018	−	0.372839i
$800$		0			0
$801$	37.9081	−	32.4762i	1.33942	−	1.14749i
$802$		0			0
$803$		−	27.3761i		−	0.966082i
$804$		0			0
$805$	1.43782	+	0.830125i	0.0506764	+	0.0292581i
$806$		0			0
$807$	13.3651	−	21.2180i	0.470473	−	0.746909i
$808$		0			0
$809$	−0.0547801	−	0.0146783i	−0.00192597	−	0.000516061i	0.257856	−	0.966183i	$-0.416984\pi$
$809$	−0.0547801	−	0.0146783i	−0.00192597	−	0.000516061i	−0.259782	+	0.965667i	$0.583651\pi$
$810$		0			0
$811$	−20.3327	−	35.2173i	−0.713978	−	1.23665i	−0.963353	−	0.268238i	$-0.913558\pi$
$811$	−20.3327	−	35.2173i	−0.713978	−	1.23665i	0.249375	−	0.968407i	$-0.419775\pi$
$812$		0			0
$813$	−34.8823	+	18.3863i	−1.22338	+	0.644834i
$814$		0			0
$815$		−	62.2748i		−	2.18139i
$816$		0			0
$817$	−14.9966	+	8.65828i	−0.524664	+	0.302915i
$818$		0			0
$819$	0.493471	−	0.422761i	0.0172433	−	0.0147725i
$820$		0			0
$821$	−7.62925	+	4.40475i	−0.266263	+	0.153727i	−0.627188	−	0.778868i	$-0.715794\pi$
$821$	−7.62925	+	4.40475i	−0.266263	+	0.153727i	0.360925	+	0.932595i	$0.382461\pi$
$822$		0			0
$823$	5.26829	−	9.12495i	0.183641	−	0.318076i	−0.759477	−	0.650535i	$-0.774545\pi$
$823$	5.26829	−	9.12495i	0.183641	−	0.318076i	0.943118	+	0.332459i	$0.107878\pi$
$824$		0			0
$825$	33.0047	+	62.6164i	1.14908	+	2.18002i
$826$		0			0
$827$	8.37001	−	31.2373i	0.291054	−	1.08623i	−0.653247	−	0.757144i	$-0.726594\pi$
$827$	8.37001	−	31.2373i	0.291054	−	1.08623i	0.944301	−	0.329083i	$-0.106739\pi$
$828$		0			0
$829$	−10.5225	+	2.81949i	−0.365461	+	0.0979249i	−0.436876	−	0.899522i	$-0.643915\pi$
$829$	−10.5225	+	2.81949i	−0.365461	+	0.0979249i	0.0714151	+	0.997447i	$0.477248\pi$
$830$		0			0
$831$	36.6512	−	33.9316i	1.27142	−	1.17707i
$832$		0			0
$833$	6.32632	−	23.6101i	0.219194	−	0.818043i
$834$		0			0
$835$	74.9783	+	43.2888i	2.59473	+	1.49807i
$836$		0			0
$837$	−18.5714	+	14.7092i	−0.641923	+	0.508424i
$838$		0			0
$839$	−22.9664	+	39.7790i	−0.792889	+	1.37332i	0.131282	+	0.991345i	$0.458091\pi$
$839$	−22.9664	+	39.7790i	−0.792889	+	1.37332i	−0.924171	+	0.381979i	$0.875243\pi$
$840$		0			0
$841$			24.8721i			0.857659i
$842$		0			0
$843$	−25.2750	−	7.82708i	−0.870517	−	0.269579i
$844$		0			0
$845$	33.6051	−	33.6051i	1.15605	−	1.15605i
$846$		0			0
$847$	−1.93950	−	3.35931i	−0.0666420	−	0.115427i
$848$		0			0
$849$	−15.1436	+	14.0199i	−0.519727	+	0.481162i
$850$		0			0
$851$	−1.47943	+	6.57501i	−0.0507143	+	0.225389i
$852$		0			0
$853$	−18.1100	+	4.85256i	−0.620075	+	0.166149i	−0.555162	−	0.831742i	$-0.687344\pi$
$853$	−18.1100	+	4.85256i	−0.620075	+	0.166149i	−0.0649132	+	0.997891i	$0.520677\pi$
$854$		0			0
$855$	16.7380	+	1.29177i	0.572429	+	0.0441775i
$856$		0			0
$857$	38.2384	+	38.2384i	1.30620	+	1.30620i	0.924138	+	0.382060i	$0.124785\pi$
$857$	38.2384	+	38.2384i	1.30620	+	1.30620i	0.382060	+	0.924138i	$0.375215\pi$
$858$		0			0
$859$	31.9246	−	31.9246i	1.08925	−	1.08925i	0.0936494	−	0.995605i	$-0.470147\pi$
$859$	31.9246	−	31.9246i	1.08925	−	1.08925i	0.995605	−	0.0936494i	$-0.0298533\pi$
$860$		0			0
$861$	3.43249	−	1.80924i	0.116979	−	0.0616588i
$862$		0			0
$863$	5.39825	+	3.11668i	0.183759	+	0.106093i	0.589057	−	0.808091i	$-0.299499\pi$
$863$	5.39825	+	3.11668i	0.183759	+	0.106093i	−0.405299	+	0.914184i	$0.632833\pi$
$864$		0			0
$865$	−45.0903	−	45.0903i	−1.53312	−	1.53312i
$866$		0			0
$867$	−7.31728	−	0.281939i	−0.248508	−	0.00957514i
$868$		0			0
$869$	−63.4305	−	16.9962i	−2.15173	−	0.576555i
$870$		0			0
$871$	0.180607	−	0.0483936i	0.00611965	−	0.00163975i
$872$		0			0
$873$	30.0832	+	10.6017i	1.01816	+	0.358813i
$874$		0			0
$875$	−5.76981	−	1.54602i	−0.195055	−	0.0522648i
$876$		0			0
$877$	13.4153			0.453001			0.226501	−	0.974011i	$-0.427271\pi$
$877$	13.4153			0.453001			0.226501	+	0.974011i	$0.427271\pi$
$878$		0			0
$879$	6.96816	+	0.268487i	0.235030	+	0.00905584i
$880$		0			0
$881$	−0.791101	−	1.37023i	−0.0266529	−	0.0461641i	0.852391	−	0.522904i	$-0.175152\pi$
$881$	−0.791101	−	1.37023i	−0.0266529	−	0.0461641i	−0.879044	+	0.476740i	$0.841818\pi$
$882$		0			0
$883$	−6.84824	+	25.5580i	−0.230462	+	0.860094i	0.749681	+	0.661799i	$0.230207\pi$
$883$	−6.84824	+	25.5580i	−0.230462	+	0.860094i	−0.980142	+	0.198295i	$0.936460\pi$
$884$		0			0
$885$	40.0006	−	63.5038i	1.34461	−	2.13466i
$886$		0			0
$887$	−34.8765			−1.17104			−0.585518	−	0.810659i	$-0.699109\pi$
$887$	−34.8765			−1.17104			−0.585518	+	0.810659i	$0.699109\pi$
$888$		0			0
$889$	−5.18032			−0.173743
$890$		0			0
$891$	25.6606	−	31.8855i	0.859663	−	1.06821i
$892$		0			0
$893$	−1.18232	+	4.41248i	−0.0395649	+	0.147658i
$894$		0			0
$895$	−8.14899	−	14.1145i	−0.272391	−	0.471794i
$896$		0			0
$897$	−0.0399411	+	1.03661i	−0.00133360	+	0.0346114i
$898$		0			0
$899$	9.26326			0.308947
$900$		0			0
$901$	44.8637	+	12.0212i	1.49463	+	0.400484i
$902$		0			0
$903$	−5.45633	−	5.89365i	−0.181575	−	0.196129i
$904$		0			0
$905$	33.4689	−	8.96796i	1.11254	−	0.298105i
$906$		0			0
$907$	2.28696	+	0.612788i	0.0759371	+	0.0203473i	0.296588	−	0.955006i	$-0.404151\pi$
$907$	2.28696	+	0.612788i	0.0759371	+	0.0203473i	−0.220650	+	0.975353i	$0.570818\pi$
$908$		0			0
$909$	−5.84340	−	12.2033i	−0.193813	−	0.404757i
$910$		0			0
$911$	1.06913	+	1.06913i	0.0354218	+	0.0354218i	0.724596	−	0.689174i	$-0.242026\pi$
$911$	1.06913	+	1.06913i	0.0354218	+	0.0354218i	−0.689174	+	0.724596i	$0.742026\pi$
$912$		0			0
$913$	39.7894	+	22.9724i	1.31684	+	0.760275i
$914$		0			0
$915$	−24.4011	−	46.2937i	−0.806677	−	1.53042i
$916$		0			0
$917$	−5.28657	+	5.28657i	−0.174578	+	0.174578i
$918$		0			0
$919$	−0.102572	−	0.102572i	−0.00338353	−	0.00338353i	0.705413	−	0.708797i	$-0.250762\pi$
$919$	−0.102572	−	0.102572i	−0.00338353	−	0.00338353i	−0.708797	+	0.705413i	$0.750762\pi$
$920$		0			0
$921$	18.7393	−	29.7500i	0.617482	−	0.980296i
$922$		0			0
$923$	1.45038	−	0.388628i	0.0477399	−	0.0127919i
$924$		0			0
$925$	−2.21192	−	54.6165i	−0.0727274	−	1.79578i
$926$		0			0
$927$	11.8082	−	33.5067i	0.387832	−	1.10050i
$928$		0			0
$929$	−2.08718	−	3.61510i	−0.0684781	−	0.118608i	0.829753	−	0.558130i	$-0.188481\pi$
$929$	−2.08718	−	3.61510i	−0.0684781	−	0.118608i	−0.898232	+	0.439522i	$0.855148\pi$
$930$		0			0
$931$	−7.23650	+	7.23650i	−0.237167	+	0.237167i
$932$		0			0
$933$	6.47028	−	20.8936i	0.211827	−	0.684027i
$934$		0			0
$935$		−	60.7812i		−	1.98776i
$936$		0			0
$937$	27.0778	−	46.9001i	0.884593	−	1.53216i	0.0384128	−	0.999262i	$-0.487770\pi$
$937$	27.0778	−	46.9001i	0.884593	−	1.53216i	0.846180	−	0.532897i	$-0.178897\pi$
$938$		0			0
$939$	−3.47132	+	11.2095i	−0.113282	+	0.365808i
$940$		0			0
$941$	−22.9494	−	13.2499i	−0.748131	−	0.431933i	0.0768875	−	0.997040i	$-0.475502\pi$
$941$	−22.9494	−	13.2499i	−0.748131	−	0.431933i	−0.825018	+	0.565106i	$0.808835\pi$
$942$		0			0
$943$	−1.60324	+	5.98338i	−0.0522087	+	0.194846i
$944$		0			0
$945$	1.13482	+	7.70323i	0.0369156	+	0.250586i
$946$		0			0
$947$	28.7227	−	7.69622i	0.933362	−	0.250094i	0.240074	−	0.970754i	$-0.422828\pi$
$947$	28.7227	−	7.69622i	0.933362	−	0.250094i	0.693288	+	0.720661i	$0.256162\pi$
$948$		0			0
$949$	−0.842247	+	3.14331i	−0.0273405	+	0.102036i
$950$		0			0
$951$	48.4999	−	25.5640i	1.57272	−	0.828970i
$952$		0			0
$953$	−3.52226	+	6.10073i	−0.114097	+	0.197622i	−0.917418	−	0.397924i	$-0.869731\pi$
$953$	−3.52226	+	6.10073i	−0.114097	+	0.197622i	0.803321	+	0.595546i	$0.203064\pi$
$954$		0			0
$955$	−36.0306	+	20.8023i	−1.16592	+	0.673145i
$956$		0			0
$957$	−15.6060	+	3.54373i	−0.504471	+	0.114552i
$958$		0			0
$959$	−1.26727	+	0.731662i	−0.0409224	+	0.0236266i
$960$		0			0
$961$		−	10.2126i		−	0.329440i
$962$		0			0
$963$	18.2591	+	12.5084i	0.588391	+	0.403077i
$964$		0			0
$965$	−0.476559	−	0.825424i	−0.0153410	−	0.0265714i
$966$		0			0
$967$	8.85398	+	2.37242i	0.284725	+	0.0762918i	0.398355	−	0.917231i	$-0.369581\pi$
$967$	8.85398	+	2.37242i	0.284725	+	0.0762918i	−0.113630	+	0.993523i	$0.536248\pi$
$968$		0			0
$969$	−7.83708	−	4.93652i	−0.251763	−	0.158584i
$970$		0			0
$971$	27.5167	+	15.8868i	0.883053	+	0.509831i	0.871664	−	0.490104i	$-0.163041\pi$
$971$	27.5167	+	15.8868i	0.883053	+	0.509831i	0.0113894	+	0.999935i	$0.496375\pi$
$972$		0			0
$973$		−	4.70712i		−	0.150903i
$974$		0			0
$975$	−1.86314	−	8.20499i	−0.0596683	−	0.262770i
$976$		0			0
$977$	8.56426	+	31.9622i	0.273995	+	1.02256i	0.956512	+	0.291693i	$0.0942186\pi$
$977$	8.56426	+	31.9622i	0.273995	+	1.02256i	−0.682517	+	0.730870i	$0.739115\pi$
$978$		0			0
$979$	19.5844	+	73.0900i	0.625920	+	2.33597i
$980$		0			0
$981$	31.4184	−	26.9164i	1.00311	−	0.859374i
$982$		0			0
$983$	−2.63711	+	4.56762i	−0.0841109	+	0.145684i	−0.905012	−	0.425386i	$-0.860138\pi$
$983$	−2.63711	+	4.56762i	−0.0841109	+	0.145684i	0.820901	+	0.571070i	$0.193472\pi$
$984$		0			0
$985$	−27.7886	+	27.7886i	−0.885418	+	0.885418i
$986$		0			0
$987$	−2.11718	−	0.0815760i	−0.0673906	−	0.00259659i
$988$		0			0
$989$	12.8221			0.407720
$990$		0			0
$991$	−1.54450	−	1.54450i	−0.0490626	−	0.0490626i	0.682150	−	0.731212i	$-0.261045\pi$
$991$	−1.54450	−	1.54450i	−0.0490626	−	0.0490626i	−0.731212	+	0.682150i	$0.761045\pi$
$992$		0			0
$993$	−10.5420	+	34.0420i	−0.334541	+	1.08029i
$994$		0			0
$995$	20.6956	−	11.9486i	0.656096	−	0.378797i
$996$		0			0
$997$	−11.1481	−	41.6053i	−0.353064	−	1.31765i	−0.882903	−	0.469555i	$-0.844414\pi$
$997$	−11.1481	−	41.6053i	−0.353064	−	1.31765i	0.529839	−	0.848098i	$-0.322252\pi$
$998$		0			0
$999$	−28.4804	+	13.7064i	−0.901081	+	0.433652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	444.2.w.c.125.9	yes	40
3.2	odd	2	inner	444.2.w.c.125.5	✓	40
37.8	odd	12	inner	444.2.w.c.341.5	yes	40
111.8	even	12	inner	444.2.w.c.341.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.w.c.125.5	✓	40	3.2	odd	2	inner
444.2.w.c.125.9	yes	40	1.1	even	1	trivial
444.2.w.c.341.5	yes	40	37.8	odd	12	inner
444.2.w.c.341.9	yes	40	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:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46554 + 0.923136i) q^{3} +(-0.967937 + 3.61239i) q^{5} +(-0.200342 - 0.347003i) q^{7} +(1.29564 + 2.70579i) q^{9} -4.54763 q^{11} +(0.522156 + 0.139911i) q^{13} +(-4.75328 + 4.40058i) q^{15} +(3.45205 - 0.924974i) q^{17} +(-1.44533 - 0.387274i) q^{19} +(0.0267206 - 0.693491i) q^{21} +(0.783440 + 0.783440i) q^{23} +(-7.78232 - 4.49313i) q^{25} +(-0.599000 + 5.16151i) q^{27} +(1.43664 - 1.43664i) q^{29} +(3.22392 + 3.22392i) q^{31} +(-6.66475 - 4.19808i) q^{33} +(1.44743 - 0.387837i) q^{35} +(3.25206 + 5.14044i) q^{37} +(0.636085 + 0.687067i) q^{39} +(2.79545 + 4.84186i) q^{41} +(8.18323 - 8.18323i) q^{43} +(-11.0285 + 2.06132i) q^{45} -3.05293i q^{47} +(3.41973 - 5.92314i) q^{49} +(5.91301 + 1.83112i) q^{51} +(11.2551 + 6.49812i) q^{53} +(4.40182 - 16.4278i) q^{55} +(-1.76068 - 1.90180i) q^{57} +(-11.1916 + 2.99879i) q^{59} +(-2.09095 + 7.80352i) q^{61} +(0.679347 - 0.991675i) q^{63} +(-1.01083 + 1.75080i) q^{65} +(0.299548 - 0.172944i) q^{67} +(0.424944 + 1.87139i) q^{69} +(2.40554 - 1.38884i) q^{71} +6.01987i q^{73} +(-7.25757 - 13.7690i) q^{75} +(0.911082 + 1.57804i) q^{77} +(13.9480 + 3.73737i) q^{79} +(-5.64264 + 7.01146i) q^{81} +(-8.74947 - 5.05151i) q^{83} +13.3655i q^{85} +(3.43168 - 0.779247i) q^{87} +(-4.30651 - 16.0721i) q^{89} +(-0.0560602 - 0.209220i) q^{91} +(1.74868 + 7.70092i) q^{93} +(2.79797 - 4.84622i) q^{95} +(7.51811 - 7.51811i) q^{97} +(-5.89209 - 12.3049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{9} - 24 q^{19} - 18 q^{21} + 32 q^{31} - 44 q^{37} + 62 q^{39} - 4 q^{43} - 54 q^{45} + 24 q^{49} + 14 q^{51} + 20 q^{55} + 34 q^{57} + 36 q^{61} - 36 q^{63} + 12 q^{67} - 50 q^{69} - 20 q^{75}+ \cdots - 12 q^{99}+O(q^{100}) \) 40 * q - 10 * q^9 - 24 * q^19 - 18 * q^21 + 32 * q^31 - 44 * q^37 + 62 * q^39 - 4 * q^43 - 54 * q^45 + 24 * q^49 + 14 * q^51 + 20 * q^55 + 34 * q^57 + 36 * q^61 - 36 * q^63 + 12 * q^67 - 50 * q^69 - 20 * q^75 + 8 * q^79 + 10 * q^81 - 32 * q^87 + 20 * q^91 - 30 * q^93 + 52 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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