LMFDB - Embedded newform 572.2.bg.a.269.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			269.9
Character	$\chi$	$=$	572.269
Dual form			572.2.bg.a.185.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.606615 - 0.270082i) q^{3} +(-0.596743 + 1.83659i) q^{5} +(3.26820 + 1.45509i) q^{7} +(-1.71235 + 1.90176i) q^{9} +O(q^{10})$	\(q+(0.606615 - 0.270082i) q^{3} +(-0.596743 + 1.83659i) q^{5} +(3.26820 + 1.45509i) q^{7} +(-1.71235 + 1.90176i) q^{9} +(-3.00912 + 1.39470i) q^{11} +(-2.76906 + 2.30918i) q^{13} +(0.134036 + 1.27527i) q^{15} +(-1.91815 + 0.407715i) q^{17} +(-0.0461538 + 0.439124i) q^{19} +2.37553 q^{21} +(2.75014 - 4.76339i) q^{23} +(1.02814 + 0.746987i) q^{25} +(-1.14069 + 3.51068i) q^{27} +(-0.552769 - 5.25924i) q^{29} +(0.523420 + 1.61092i) q^{31} +(-1.44869 + 1.65876i) q^{33} +(-4.62268 + 5.13400i) q^{35} +(0.896447 + 8.52912i) q^{37} +(-1.05608 + 2.14866i) q^{39} +(5.80191 - 2.58318i) q^{41} +(4.33947 + 7.51618i) q^{43} +(-2.47091 - 4.27975i) q^{45} +(1.63874 + 1.19061i) q^{47} +(3.87989 + 4.30906i) q^{49} +(-1.05346 + 0.765384i) q^{51} +(-2.00019 - 6.15594i) q^{53} +(-0.765813 - 6.35879i) q^{55} +(0.0906021 + 0.278845i) q^{57} +(5.76932 + 2.56867i) q^{59} +(4.29870 - 0.913717i) q^{61} +(-8.36355 + 3.72369i) q^{63} +(-2.58859 - 6.46360i) q^{65} +(-0.387949 + 0.671947i) q^{67} +(0.381771 - 3.63231i) q^{69} +(0.274065 - 0.0582543i) q^{71} +(11.6845 - 8.48929i) q^{73} +(0.825433 + 0.175451i) q^{75} +(-11.8638 + 0.179595i) q^{77} +(-0.115224 - 0.354622i) q^{79} +(-0.546274 - 5.19745i) q^{81} +(0.852596 - 2.62402i) q^{83} +(0.395838 - 3.76614i) q^{85} +(-1.75575 - 3.04104i) q^{87} +(3.10372 - 5.37580i) q^{89} +(-12.4099 + 3.51760i) q^{91} +(0.752596 + 0.835843i) q^{93} +(-0.778947 - 0.346810i) q^{95} +(3.18872 - 3.54143i) q^{97} +(2.50030 - 8.11085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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
$3$	0.606615	−	0.270082i	0.350229	−	0.155932i	−0.224080	−	0.974571i	$-0.571938\pi$
$3$	0.606615	−	0.270082i	0.350229	−	0.155932i	0.574309	+	0.818639i	$0.305271\pi$
$4$		0			0
$5$	−0.596743	+	1.83659i	−0.266872	+	0.821346i	0.724385	+	0.689396i	$0.242124\pi$
$5$	−0.596743	+	1.83659i	−0.266872	+	0.821346i	−0.991256	+	0.131950i	$0.957876\pi$
$6$		0			0
$7$	3.26820	+	1.45509i	1.23526	+	0.549974i	0.917326	−	0.398138i	$-0.130343\pi$
$7$	3.26820	+	1.45509i	1.23526	+	0.549974i	0.317936	+	0.948112i	$0.397010\pi$
$8$		0			0
$9$	−1.71235	+	1.90176i	−0.570785	+	0.633921i
$10$		0			0
$11$	−3.00912	+	1.39470i	−0.907284	+	0.420518i
$11$	−3.00912	+	1.39470i	−0.907284	+	0.420518i
$12$		0			0
$13$	−2.76906	+	2.30918i	−0.767999	+	0.640451i
$13$	−2.76906	+	2.30918i	−0.767999	+	0.640451i
$14$		0			0
$15$	0.134036	+	1.27527i	0.0346080	+	0.329273i
$16$		0			0
$17$	−1.91815	+	0.407715i	−0.465219	+	0.0988854i	−0.434557	−	0.900644i	$-0.643095\pi$
$17$	−1.91815	+	0.407715i	−0.465219	+	0.0988854i	−0.0306624	+	0.999530i	$0.509762\pi$
$18$		0			0
$19$	−0.0461538	+	0.439124i	−0.0105884	+	0.100742i	−0.998540	−	0.0540233i	$-0.982795\pi$
$19$	−0.0461538	+	0.439124i	−0.0105884	+	0.100742i	0.987951	+	0.154765i	$0.0494621\pi$
$20$		0			0
$21$	2.37553			0.518384
$22$		0			0
$23$	2.75014	−	4.76339i	0.573444	−	0.993235i	−0.422764	−	0.906240i	$-0.638940\pi$
$23$	2.75014	−	4.76339i	0.573444	−	0.993235i	0.996209	−	0.0869952i	$-0.0277265\pi$
$24$		0			0
$25$	1.02814	+	0.746987i	0.205628	+	0.149397i
$26$		0			0
$27$	−1.14069	+	3.51068i	−0.219526	+	0.675631i
$28$		0			0
$29$	−0.552769	−	5.25924i	−0.102647	−	0.976617i	−0.917712	−	0.397247i	$-0.869965\pi$
$29$	−0.552769	−	5.25924i	−0.102647	−	0.976617i	0.815065	−	0.579370i	$-0.196701\pi$
$30$		0			0
$31$	0.523420	+	1.61092i	0.0940090	+	0.289330i	0.986994	−	0.160756i	$-0.0513933\pi$
$31$	0.523420	+	1.61092i	0.0940090	+	0.289330i	−0.892985	+	0.450086i	$0.851393\pi$
$32$		0			0
$33$	−1.44869	+	1.65876i	−0.252185	+	0.288752i
$34$		0			0
$35$	−4.62268	+	5.13400i	−0.781375	+	0.867805i
$36$		0			0
$37$	0.896447	+	8.52912i	0.147375	+	1.40218i	0.779058	+	0.626952i	$0.215698\pi$
$37$	0.896447	+	8.52912i	0.147375	+	1.40218i	−0.631683	+	0.775227i	$0.717636\pi$
$38$		0			0
$39$	−1.05608	+	2.14866i	−0.169109	+	0.344060i
$40$		0			0
$41$	5.80191	−	2.58318i	0.906106	−	0.403424i	0.0998577	−	0.995002i	$-0.468161\pi$
$41$	5.80191	−	2.58318i	0.906106	−	0.403424i	0.806248	+	0.591577i	$0.201495\pi$
$42$		0			0
$43$	4.33947	+	7.51618i	0.661763	+	1.14621i	0.980152	+	0.198247i	$0.0635248\pi$
$43$	4.33947	+	7.51618i	0.661763	+	1.14621i	−0.318389	+	0.947960i	$0.603142\pi$
$44$		0			0
$45$	−2.47091	−	4.27975i	−0.368342	−	0.637987i
$46$		0			0
$47$	1.63874	+	1.19061i	0.239035	+	0.173669i	0.700853	−	0.713306i	$-0.252803\pi$
$47$	1.63874	+	1.19061i	0.239035	+	0.173669i	−0.461818	+	0.886974i	$0.652803\pi$
$48$		0			0
$49$	3.87989	+	4.30906i	0.554270	+	0.615579i
$50$		0			0
$51$	−1.05346	+	0.765384i	−0.147514	+	0.107175i
$52$		0			0
$53$	−2.00019	−	6.15594i	−0.274747	−	0.845584i	−0.989286	−	0.145988i	$-0.953364\pi$
$53$	−2.00019	−	6.15594i	−0.274747	−	0.845584i	0.714540	−	0.699595i	$-0.246636\pi$
$54$		0			0
$55$	−0.765813	−	6.35879i	−0.103262	−	0.857419i
$56$		0			0
$57$	0.0906021	+	0.278845i	0.0120005	+	0.0369339i
$58$		0			0
$59$	5.76932	+	2.56867i	0.751101	+	0.334412i	0.746329	−	0.665577i	$-0.231814\pi$
$59$	5.76932	+	2.56867i	0.751101	+	0.334412i	0.00477202	+	0.999989i	$0.498481\pi$
$60$		0			0
$61$	4.29870	−	0.913717i	0.550392	−	0.116989i	0.0756825	−	0.997132i	$-0.475886\pi$
$61$	4.29870	−	0.913717i	0.550392	−	0.116989i	0.474709	+	0.880143i	$0.342553\pi$
$62$		0			0
$63$	−8.36355	+	3.72369i	−1.05371	+	0.469141i
$64$		0			0
$65$	−2.58859	−	6.46360i	−0.321075	−	0.801711i
$66$		0			0
$67$	−0.387949	+	0.671947i	−0.0473955	+	0.0820914i	−0.888750	−	0.458392i	$-0.848425\pi$
$67$	−0.387949	+	0.671947i	−0.0473955	+	0.0820914i	0.841354	+	0.540484i	$0.181759\pi$
$68$		0			0
$69$	0.381771	−	3.63231i	0.0459598	−	0.437278i
$70$		0			0
$71$	0.274065	−	0.0582543i	0.0325255	−	0.00691352i	−0.191620	−	0.981469i	$-0.561374\pi$
$71$	0.274065	−	0.0582543i	0.0325255	−	0.00691352i	0.224146	+	0.974556i	$0.428041\pi$
$72$		0			0
$73$	11.6845	−	8.48929i	1.36757	−	0.993597i	0.369646	−	0.929173i	$-0.379479\pi$
$73$	11.6845	−	8.48929i	1.36757	−	0.993597i	0.997923	−	0.0644241i	$-0.0205210\pi$
$74$		0			0
$75$	0.825433	+	0.175451i	0.0953128	+	0.0202594i
$76$		0			0
$77$	−11.8638	+	0.179595i	−1.35201	+	0.0204668i
$78$		0			0
$79$	−0.115224	−	0.354622i	−0.0129637	−	0.0398981i	0.944365	−	0.328898i	$-0.106677\pi$
$79$	−0.115224	−	0.354622i	−0.0129637	−	0.0398981i	−0.957329	+	0.289000i	$0.906677\pi$
$80$		0			0
$81$	−0.546274	−	5.19745i	−0.0606971	−	0.577494i
$82$		0			0
$83$	0.852596	−	2.62402i	0.0935845	−	0.288024i	−0.893298	−	0.449466i	$-0.851614\pi$
$83$	0.852596	−	2.62402i	0.0935845	−	0.288024i	0.986882	+	0.161442i	$0.0516145\pi$
$84$		0			0
$85$	0.395838	−	3.76614i	0.0429346	−	0.408496i
$86$		0			0
$87$	−1.75575	−	3.04104i	−0.188236	−	0.326034i
$88$		0			0
$89$	3.10372	−	5.37580i	0.328993	−	0.569833i	−0.653319	−	0.757083i	$-0.726624\pi$
$89$	3.10372	−	5.37580i	0.328993	−	0.569833i	0.982312	+	0.187249i	$0.0599573\pi$
$90$		0			0
$91$	−12.4099	+	3.51760i	−1.30091	+	0.368745i
$92$		0			0
$93$	0.752596	+	0.835843i	0.0780406	+	0.0866729i
$94$		0			0
$95$	−0.778947	−	0.346810i	−0.0799183	−	0.0355819i
$96$		0			0
$97$	3.18872	−	3.54143i	0.323766	−	0.359578i	−0.559186	−	0.829042i	$-0.688886\pi$
$97$	3.18872	−	3.54143i	0.323766	−	0.359578i	0.882952	+	0.469464i	$0.155553\pi$
$98$		0			0
$99$	2.50030	−	8.11085i	0.251289	−	0.815172i
$100$		0			0
$101$	7.58540	+	1.61233i	0.754775	+	0.160432i	0.569202	−	0.822198i	$-0.307252\pi$
$101$	7.58540	+	1.61233i	0.754775	+	0.160432i	0.185574	+	0.982630i	$0.440586\pi$
$102$		0			0
$103$	−11.2330	+	8.16126i	−1.10682	+	0.804153i	−0.982160	−	0.188046i	$-0.939785\pi$
$103$	−11.2330	+	8.16126i	−1.10682	+	0.804153i	−0.124662	+	0.992199i	$0.539785\pi$
$104$		0			0
$105$	−1.41758	+	4.36287i	−0.138342	+	0.425772i
$106$		0			0
$107$	−6.86385	+	3.05598i	−0.663553	+	0.295433i	−0.710742	−	0.703453i	$-0.751641\pi$
$107$	−6.86385	+	3.05598i	−0.663553	+	0.295433i	0.0471885	+	0.998886i	$0.484974\pi$
$108$		0			0
$109$	−1.99560			−0.191144			−0.0955718	−	0.995423i	$-0.530468\pi$
$109$	−1.99560			−0.191144			−0.0955718	+	0.995423i	$0.530468\pi$
$110$		0			0
$111$	2.84736	+	4.93178i	0.270260	+	0.468104i
$112$		0			0
$113$	0.746676	−	7.10415i	0.0702414	−	0.668302i	−0.901585	−	0.432603i	$-0.857595\pi$
$113$	0.746676	−	7.10415i	0.0702414	−	0.668302i	0.971826	−	0.235699i	$-0.0757381\pi$
$114$		0			0
$115$	7.10724	+	7.89339i	0.662754	+	0.736062i
$116$		0			0
$117$	0.350104	−	9.22023i	0.0323671	−	0.852410i
$118$		0			0
$119$	−6.86215	−	1.45859i	−0.629052	−	0.133709i
$120$		0			0
$121$	7.10963	−	8.39364i	0.646330	−	0.763058i
$122$		0			0
$123$	2.82185	−	3.13399i	0.254438	−	0.282582i
$124$		0			0
$125$	−9.79691	+	7.11787i	−0.876262	+	0.636642i
$126$		0			0
$127$	5.51995	+	6.13053i	0.489817	+	0.543997i	0.936487	−	0.350702i	$-0.114057\pi$
$127$	5.51995	+	6.13053i	0.489817	+	0.543997i	−0.446670	+	0.894699i	$0.647390\pi$
$128$		0			0
$129$	4.66238	+	3.38741i	0.410499	+	0.298245i
$130$		0			0
$131$	6.93275			0.605717			0.302859	−	0.953035i	$-0.402059\pi$
$131$	6.93275			0.605717			0.302859	+	0.953035i	$0.402059\pi$
$132$		0			0
$133$	−0.789807	+	1.36799i	−0.0684849	+	0.118619i
$134$		0			0
$135$	−5.76697	−	4.18995i	−0.496342	−	0.360614i
$136$		0			0
$137$	−13.8232	+	2.93820i	−1.18099	+	0.251028i	−0.756247	−	0.654286i	$-0.772969\pi$
$137$	−13.8232	+	2.93820i	−1.18099	+	0.251028i	−0.424744	+	0.905313i	$0.639636\pi$
$138$		0			0
$139$	−13.5962	−	6.05341i	−1.15321	−	0.513443i	−0.261125	−	0.965305i	$-0.584093\pi$
$139$	−13.5962	−	6.05341i	−1.15321	−	0.513443i	−0.892088	+	0.451862i	$0.850760\pi$
$140$		0			0
$141$	1.31565	+	0.279649i	0.110797	+	0.0235507i
$142$		0			0
$143$	5.11183	−	10.8106i	0.427473	−	0.904028i
$144$		0			0
$145$	9.98891	+	2.12321i	0.829534	+	0.176323i
$146$		0			0
$147$	3.51740	+	1.56605i	0.290110	+	0.129165i
$148$		0			0
$149$	12.2554	−	2.60496i	1.00400	−	0.213406i	0.323556	−	0.946209i	$-0.395121\pi$
$149$	12.2554	−	2.60496i	1.00400	−	0.213406i	0.680441	+	0.732803i	$0.261788\pi$
$150$		0			0
$151$	−8.42520	−	6.12126i	−0.685633	−	0.498141i	0.189589	−	0.981864i	$-0.439284\pi$
$151$	−8.42520	−	6.12126i	−0.685633	−	0.498141i	−0.875222	+	0.483722i	$0.839284\pi$
$152$		0			0
$153$	2.50917	−	4.34601i	0.202855	−	0.351354i
$154$		0			0
$155$	−3.27094			−0.262728
$156$		0			0
$157$	−16.1665	−	11.7457i	−1.29023	−	0.937405i	−0.290418	−	0.956900i	$-0.593794\pi$
$157$	−16.1665	−	11.7457i	−1.29023	−	0.937405i	−0.999810	+	0.0194946i	$0.993794\pi$
$158$		0			0
$159$	−2.87595	−	3.19407i	−0.228078	−	0.253306i
$160$		0			0
$161$	15.9192	−	11.5660i	1.25461	−	0.911526i
$162$		0			0
$163$	12.2762	−	13.6341i	0.961547	−	1.06791i	−0.0360997	−	0.999348i	$-0.511493\pi$
$163$	12.2762	−	13.6341i	0.961547	−	1.06791i	0.997647	−	0.0685583i	$-0.0218399\pi$
$164$		0			0
$165$	−2.18195	−	3.65050i	−0.169865	−	0.284191i
$166$		0			0
$167$	21.0483	+	4.47395i	1.62877	+	0.346205i	0.929547	−	0.368703i	$-0.120198\pi$
$167$	21.0483	+	4.47395i	1.62877	+	0.346205i	0.699219	+	0.714908i	$0.253531\pi$
$168$		0			0
$169$	2.33539	−	12.7885i	0.179645	−	0.983731i
$170$		0			0
$171$	−0.756078	−	0.839710i	−0.0578187	−	0.0642142i
$172$		0			0
$173$	−0.345500	+	3.28721i	−0.0262679	+	0.249922i	0.973506	+	0.228661i	$0.0734348\pi$
$173$	−0.345500	+	3.28721i	−0.0262679	+	0.249922i	−0.999774	+	0.0212611i	$0.993232\pi$
$174$		0			0
$175$	2.27323	+	3.93734i	0.171840	+	0.297635i
$176$		0			0
$177$	4.19351			0.315203
$178$		0			0
$179$	−16.5420	+	7.36499i	−1.23641	+	0.550485i	−0.917665	−	0.397355i	$-0.869928\pi$
$179$	−16.5420	+	7.36499i	−1.23641	+	0.550485i	−0.318745	+	0.947840i	$0.603261\pi$
$180$		0			0
$181$	1.42543	−	4.38703i	0.105952	−	0.326086i	−0.884001	−	0.467485i	$-0.845160\pi$
$181$	1.42543	−	4.38703i	0.105952	−	0.326086i	0.989953	+	0.141399i	$0.0451602\pi$
$182$		0			0
$183$	2.36088	−	1.71528i	0.174521	−	0.126797i
$184$		0			0
$185$	−16.1994	−	3.44329i	−1.19100	−	0.253156i
$186$		0			0
$187$	5.20330	−	3.90210i	0.380503	−	0.285350i
$188$		0			0
$189$	−8.83638	+	9.81379i	−0.642752	+	0.713848i
$190$		0			0
$191$	−14.7670	−	6.57468i	−1.06850	−	0.475727i	−0.204317	−	0.978905i	$-0.565497\pi$
$191$	−14.7670	−	6.57468i	−1.06850	−	0.475727i	−0.864183	+	0.503178i	$0.832164\pi$
$192$		0			0
$193$	7.42653	+	8.24800i	0.534574	+	0.593704i	0.948567	−	0.316576i	$-0.102533\pi$
$193$	7.42653	+	8.24800i	0.534574	+	0.593704i	−0.413994	+	0.910280i	$0.635866\pi$
$194$		0			0
$195$	−3.31598	−	3.22179i	−0.237462	−	0.230717i
$196$		0			0
$197$	2.00057	−	3.46508i	0.142534	−	0.246877i	−0.785916	−	0.618333i	$-0.787808\pi$
$197$	2.00057	−	3.46508i	0.142534	−	0.246877i	0.928450	+	0.371457i	$0.121142\pi$
$198$		0			0
$199$	5.18148	+	8.97458i	0.367305	+	0.636191i	0.989143	−	0.146955i	$-0.0469472\pi$
$199$	5.18148	+	8.97458i	0.367305	+	0.636191i	−0.621838	+	0.783146i	$0.713614\pi$
$200$		0			0
$201$	−0.0538545	+	0.512392i	−0.00379861	+	0.0361413i
$202$		0			0
$203$	5.84614	−	17.9926i	0.410319	−	1.26283i
$204$		0			0
$205$	1.28198	+	12.1972i	0.0895371	+	0.851889i
$206$		0			0
$207$	4.34961	+	13.3867i	0.302319	+	0.930442i
$208$		0			0
$209$	−0.473564	−	1.38575i	−0.0327571	−	0.0958542i
$210$		0			0
$211$	24.7161	+	5.25357i	1.70153	+	0.361670i	0.953359	−	0.301840i	$-0.0976008\pi$
$211$	24.7161	+	5.25357i	1.70153	+	0.361670i	0.748167	+	0.663510i	$0.230934\pi$
$212$		0			0
$213$	0.150519	−	0.109358i	0.0103134	−	0.00749309i
$214$		0			0
$215$	−16.3937	+	3.48458i	−1.11804	+	0.237646i
$216$		0			0
$217$	−0.633404	+	6.02643i	−0.0429982	+	0.409101i
$218$		0			0
$219$	4.79519	−	8.30551i	0.324029	−	0.561235i
$220$		0			0
$221$	4.36998	−	5.55833i	0.293957	−	0.373894i
$222$		0			0
$223$	−10.9575	+	4.87859i	−0.733767	+	0.326694i	−0.739378	−	0.673290i	$-0.764881\pi$
$223$	−10.9575	+	4.87859i	−0.733767	+	0.326694i	0.00561123	+	0.999984i	$0.498214\pi$
$224$		0			0
$225$	−3.18113	+	0.676171i	−0.212076	+	0.0450780i
$226$		0			0
$227$	8.16255	+	3.63420i	0.541767	+	0.241210i	0.659328	−	0.751855i	$-0.270841\pi$
$227$	8.16255	+	3.63420i	0.541767	+	0.241210i	−0.117561	+	0.993066i	$0.537508\pi$
$228$		0			0
$229$	6.36729	+	19.5965i	0.420763	+	1.29497i	0.906994	+	0.421144i	$0.138371\pi$
$229$	6.36729	+	19.5965i	0.420763	+	1.29497i	−0.486231	+	0.873830i	$0.661629\pi$
$230$		0			0
$231$	−7.14827	+	3.31315i	−0.470321	+	0.217990i
$232$		0			0
$233$	4.65279	+	14.3198i	0.304814	+	0.938122i	0.979746	+	0.200242i	$0.0641728\pi$
$233$	4.65279	+	14.3198i	0.304814	+	0.938122i	−0.674932	+	0.737880i	$0.735827\pi$
$234$		0			0
$235$	−3.16457	+	2.29919i	−0.206434	+	0.149983i
$236$		0			0
$237$	−0.165674	−	0.183999i	−0.0107617	−	0.0119520i
$238$		0			0
$239$	10.6335	+	7.72570i	0.687825	+	0.499734i	0.875944	−	0.482412i	$-0.160239\pi$
$239$	10.6335	+	7.72570i	0.687825	+	0.499734i	−0.188119	+	0.982146i	$0.560239\pi$
$240$		0			0
$241$	−12.6539	−	21.9172i	−0.815110	−	1.41181i	−0.909249	−	0.416253i	$-0.863343\pi$
$241$	−12.6539	−	21.9172i	−0.815110	−	1.41181i	0.0941386	−	0.995559i	$-0.469990\pi$
$242$		0			0
$243$	−7.27215	−	12.5957i	−0.466508	−	0.808016i
$244$		0			0
$245$	−10.2292	+	4.55435i	−0.653523	+	0.290967i
$246$		0			0
$247$	−0.886213	−	1.32254i	−0.0563884	−	0.0841511i
$248$		0			0
$249$	−0.191504	−	1.82204i	−0.0121361	−	0.115467i
$250$		0			0
$251$	−7.33510	+	8.14645i	−0.462987	+	0.514200i	−0.928748	−	0.370711i	$-0.879114\pi$
$251$	−7.33510	+	8.14645i	−0.462987	+	0.514200i	0.465761	+	0.884911i	$0.345781\pi$
$252$		0			0
$253$	−1.63202	+	18.1692i	−0.102604	+	1.14229i
$254$		0			0
$255$	−0.777048	−	2.39151i	−0.0486606	−	0.149762i
$256$		0			0
$257$	2.97535	+	28.3085i	0.185597	+	1.76584i	0.550540	+	0.834809i	$0.314422\pi$
$257$	2.97535	+	28.3085i	0.185597	+	1.76584i	−0.364943	+	0.931030i	$0.618912\pi$
$258$		0			0
$259$	−9.48091	+	29.1793i	−0.589115	+	1.81311i
$260$		0			0
$261$	10.9484	+	7.95445i	0.677687	+	0.492368i
$262$		0			0
$263$	−11.6538	+	20.1850i	−0.718604	+	1.24466i	0.242949	+	0.970039i	$0.421885\pi$
$263$	−11.6538	+	20.1850i	−0.718604	+	1.24466i	−0.961553	+	0.274620i	$0.911448\pi$
$264$		0			0
$265$	12.4995			0.767839
$266$		0			0
$267$	0.430854	−	4.09930i	0.0263678	−	0.250873i
$268$		0			0
$269$	−29.1939	+	6.20536i	−1.77998	+	0.378347i	−0.976251	−	0.216642i	$-0.930490\pi$
$269$	−29.1939	+	6.20536i	−1.77998	+	0.378347i	−0.803733	+	0.594989i	$0.797156\pi$
$270$		0			0
$271$	1.04629	+	9.95481i	0.0635578	+	0.604712i	0.979225	+	0.202775i	$0.0649961\pi$
$271$	1.04629	+	9.95481i	0.0635578	+	0.604712i	−0.915668	+	0.401937i	$0.868337\pi$
$272$		0			0
$273$	−6.57799	+	5.48553i	−0.398118	+	0.331999i
$274$		0			0
$275$	−4.13562	−	0.813830i	−0.249387	−	0.0490758i
$276$		0			0
$277$	11.4954	−	12.7669i	0.690690	−	0.767089i	−0.291175	−	0.956670i	$-0.594046\pi$
$277$	11.4954	−	12.7669i	0.690690	−	0.767089i	0.981865	+	0.189581i	$0.0607129\pi$
$278$		0			0
$279$	−3.95987	−	1.76305i	−0.237071	−	0.105551i
$280$		0			0
$281$	9.48935	−	29.2052i	0.566087	−	1.74224i	−0.0986108	−	0.995126i	$-0.531440\pi$
$281$	9.48935	−	29.2052i	0.566087	−	1.74224i	0.664698	−	0.747112i	$-0.268560\pi$
$282$		0			0
$283$	8.61839	−	3.83715i	0.512310	−	0.228095i	−0.134265	−	0.990945i	$-0.542867\pi$
$283$	8.61839	−	3.83715i	0.512310	−	0.228095i	0.646575	+	0.762850i	$0.276201\pi$
$284$		0			0
$285$	−0.566188			−0.0335381
$286$		0			0
$287$	22.7205			1.34115
$288$		0			0
$289$	−12.0172	+	5.35041i	−0.706895	+	0.314730i
$290$		0			0
$291$	0.977847	−	3.00950i	0.0573224	−	0.176420i
$292$		0			0
$293$	−12.3616	−	5.50372i	−0.722170	−	0.321531i	0.0125313	−	0.999921i	$-0.496011\pi$
$293$	−12.3616	−	5.50372i	−0.722170	−	0.321531i	−0.734701	+	0.678391i	$0.762678\pi$
$294$		0			0
$295$	−8.16038	+	9.06302i	−0.475116	+	0.527669i
$296$		0			0
$297$	−1.46387	−	12.1550i	−0.0849426	−	0.705304i
$298$		0			0
$299$	3.38420	+	19.5407i	0.195713	+	1.13007i
$300$		0			0
$301$	3.24548	+	30.8787i	0.187066	+	1.77982i
$302$		0			0
$303$	5.03688	−	1.07062i	0.289361	−	0.0615056i
$304$		0			0
$305$	−0.887099	+	8.44018i	−0.0507951	+	0.483283i
$306$		0			0
$307$	33.4366			1.90833			0.954163	−	0.299287i	$-0.0967490\pi$
$307$	33.4366			1.90833			0.954163	+	0.299287i	$0.0967490\pi$
$308$		0			0
$309$	−4.60990	+	7.98458i	−0.262248	+	0.454227i
$310$		0			0
$311$	0.832146	+	0.604589i	0.0471867	+	0.0342831i	0.611129	−	0.791531i	$-0.290716\pi$
$311$	0.832146	+	0.604589i	0.0471867	+	0.0342831i	−0.563942	+	0.825814i	$0.690716\pi$
$312$		0			0
$313$	5.36875	−	16.5233i	0.303460	−	0.933953i	−0.676788	−	0.736178i	$-0.736629\pi$
$313$	5.36875	−	16.5233i	0.303460	−	0.933953i	0.980248	−	0.197775i	$-0.0633714\pi$
$314$		0			0
$315$	−1.84799	−	17.5825i	−0.104123	−	0.990660i
$316$		0			0
$317$	−5.26704	−	16.2103i	−0.295827	−	0.910460i	−0.982943	−	0.183913i	$-0.941124\pi$
$317$	−5.26704	−	16.2103i	−0.295827	−	0.910460i	0.687116	−	0.726548i	$-0.258876\pi$
$318$		0			0
$319$	8.99841	+	15.0548i	0.503814	+	0.842905i
$320$		0			0
$321$	−3.33835	+	3.70761i	−0.186328	+	0.206939i
$322$		0			0
$323$	−0.0905076	−	0.861123i	−0.00503598	−	0.0479141i
$324$		0			0
$325$	−4.57191	+	0.305706i	−0.253604	+	0.0169575i
$326$		0			0
$327$	−1.21056	+	0.538976i	−0.0669441	+	0.0298054i
$328$		0			0
$329$	3.62326	+	6.27568i	0.199757	+	0.345989i
$330$		0			0
$331$	8.81428	+	15.2668i	0.484477	+	0.839138i	0.999841	−	0.0178331i	$-0.00567676\pi$
$331$	8.81428	+	15.2668i	0.484477	+	0.839138i	−0.515364	+	0.856971i	$0.672343\pi$
$332$		0			0
$333$	−17.7554	−	12.9000i	−0.972990	−	0.706918i
$334$		0			0
$335$	−1.00258	−	1.11348i	−0.0547770	−	0.0608360i
$336$		0			0
$337$	19.0115	−	13.8127i	1.03562	−	0.752425i	0.0661974	−	0.997807i	$-0.478913\pi$
$337$	19.0115	−	13.8127i	1.03562	−	0.752425i	0.969427	+	0.245382i	$0.0789133\pi$
$338$		0			0
$339$	−1.46576	−	4.51115i	−0.0796092	−	0.245012i
$340$		0			0
$341$	−3.82179	−	4.11745i	−0.206961	−	0.222972i
$342$		0			0
$343$	−1.32837	−	4.08829i	−0.0717251	−	0.220747i
$344$		0			0
$345$	6.44322	+	2.86871i	0.346892	+	0.154446i
$346$		0			0
$347$	−29.5551	+	6.28212i	−1.58660	+	0.337242i	−0.914931	−	0.403610i	$-0.867755\pi$
$347$	−29.5551	+	6.28212i	−1.58660	+	0.337242i	−0.671668	+	0.740852i	$0.734422\pi$
$348$		0			0
$349$	−7.00387	+	3.11832i	−0.374908	+	0.166920i	−0.585536	−	0.810646i	$-0.699116\pi$
$349$	−7.00387	+	3.11832i	−0.374908	+	0.166920i	0.210628	+	0.977566i	$0.432449\pi$
$350$		0			0
$351$	−4.94816	−	12.3554i	−0.264113	−	0.659480i
$352$		0			0
$353$	3.13896	−	5.43683i	0.167070	−	0.289373i	−0.770319	−	0.637659i	$-0.779903\pi$
$353$	3.13896	−	5.43683i	0.167070	−	0.289373i	0.937388	+	0.348286i	$0.113236\pi$
$354$		0			0
$355$	−0.0565573	+	0.538107i	−0.00300175	+	0.0285597i
$356$		0			0
$357$	−4.55662	+	0.968540i	−0.241162	+	0.0512606i
$358$		0			0
$359$	−1.71570	+	1.24653i	−0.0905510	+	0.0657892i	−0.632140	−	0.774855i	$-0.717823\pi$
$359$	−1.71570	+	1.24653i	−0.0905510	+	0.0657892i	0.541589	+	0.840644i	$0.317823\pi$
$360$		0			0
$361$	18.3941	+	3.90979i	0.968111	+	0.205778i
$362$		0			0
$363$	2.04583	−	7.01189i	0.107378	−	0.368029i
$364$		0			0
$365$	8.61867	+	26.5255i	0.451122	+	1.38841i
$366$		0			0
$367$	−0.826959	−	7.86799i	−0.0431669	−	0.410706i	−0.994673	−	0.103077i	$-0.967131\pi$
$367$	−0.826959	−	7.86799i	−0.0431669	−	0.410706i	0.951506	−	0.307629i	$-0.0995355\pi$
$368$		0			0
$369$	−5.02234	+	15.4572i	−0.261452	+	0.804668i
$370$		0			0
$371$	2.42048	−	23.0293i	0.125665	−	1.19562i
$372$		0			0
$373$	9.00016	+	15.5887i	0.466011	+	0.807154i	0.999247	−	0.0388124i	$-0.0123575\pi$
$373$	9.00016	+	15.5887i	0.466011	+	0.807154i	−0.533236	+	0.845967i	$0.679024\pi$
$374$		0			0
$375$	−4.02054	+	6.96378i	−0.207620	+	0.359608i
$376$		0			0
$377$	13.6752	+	13.2867i	0.704308	+	0.684301i
$378$		0			0
$379$	17.8859	+	19.8643i	0.918736	+	1.02036i	0.999720	+	0.0236448i	$0.00752708\pi$
$379$	17.8859	+	19.8643i	0.918736	+	1.02036i	−0.0809839	+	0.996715i	$0.525806\pi$
$380$		0			0
$381$	5.00424	+	2.22803i	0.256375	+	0.114145i
$382$		0			0
$383$	24.2206	−	26.8997i	1.23761	−	1.37451i	0.336063	−	0.941840i	$-0.390905\pi$
$383$	24.2206	−	26.8997i	1.23761	−	1.37451i	0.901552	−	0.432671i	$-0.142429\pi$
$384$		0			0
$385$	6.74981	−	21.8961i	0.344002	−	1.11593i
$386$		0			0
$387$	−21.7247	−	4.61773i	−1.10433	−	0.234732i
$388$		0			0
$389$	−31.8478	+	23.1388i	−1.61475	+	1.17318i	−0.769939	+	0.638117i	$0.779713\pi$
$389$	−31.8478	+	23.1388i	−1.61475	+	1.17318i	−0.844810	+	0.535067i	$0.820287\pi$
$390$		0			0
$391$	−3.33308	+	10.2582i	−0.168561	+	0.518777i
$392$		0			0
$393$	4.20551	−	1.87241i	0.212140	−	0.0944508i
$394$		0			0
$395$	0.720053			0.0362298
$396$		0			0
$397$	−3.88486	−	6.72877i	−0.194975	−	0.337707i	0.751917	−	0.659258i	$-0.229129\pi$
$397$	−3.88486	−	6.72877i	−0.194975	−	0.337707i	−0.946892	+	0.321551i	$0.895796\pi$
$398$		0			0
$399$	−0.109640	+	1.04315i	−0.00548886	+	0.0522230i
$400$		0			0
$401$	16.1773	+	17.9667i	0.807855	+	0.897214i	0.996394	−	0.0848515i	$-0.0270416\pi$
$401$	16.1773	+	17.9667i	0.807855	+	0.897214i	−0.188538	+	0.982066i	$0.560375\pi$
$402$		0			0
$403$	−5.16929	−	3.25207i	−0.257501	−	0.161997i
$404$		0			0
$405$	9.87155	+	2.09826i	0.490521	+	0.104263i
$406$		0			0
$407$	−14.5931	−	24.4149i	−0.723352	−	1.21020i
$408$		0			0
$409$	−19.1896	+	21.3123i	−0.948867	+	1.05382i	0.0496166	+	0.998768i	$0.484200\pi$
$409$	−19.1896	+	21.3123i	−0.948867	+	1.05382i	−0.998483	+	0.0550550i	$0.982467\pi$
$410$		0			0
$411$	−7.59178	+	5.51575i	−0.374475	+	0.272072i
$412$		0			0
$413$	15.1176	+	16.7898i	0.743889	+	0.826173i
$414$		0			0
$415$	4.31046	+	3.13173i	0.211592	+	0.153731i
$416$		0			0
$417$	−9.88257			−0.483951
$418$		0			0
$419$	16.9379	−	29.3373i	0.827469	−	1.43322i	−0.0725480	−	0.997365i	$-0.523113\pi$
$419$	16.9379	−	29.3373i	0.827469	−	1.43322i	0.900017	−	0.435854i	$-0.143554\pi$
$420$		0			0
$421$	−13.4515	−	9.77312i	−0.655588	−	0.476312i	0.209582	−	0.977791i	$-0.432790\pi$
$421$	−13.4515	−	9.77312i	−0.655588	−	0.476312i	−0.865170	+	0.501479i	$0.832790\pi$
$422$		0			0
$423$	−5.07037	+	1.07774i	−0.246530	+	0.0524015i
$424$		0			0
$425$	−2.27668	−	1.01364i	−0.110435	−	0.0491690i
$426$		0			0
$427$	15.3785	+	3.26881i	0.744219	+	0.158189i
$428$		0			0
$429$	0.181157	−	7.93849i	0.00874635	−	0.383274i
$430$		0			0
$431$	−13.5491	−	2.87995i	−0.652636	−	0.138722i	−0.130317	−	0.991472i	$-0.541600\pi$
$431$	−13.5491	−	2.87995i	−0.652636	−	0.138722i	−0.522319	+	0.852750i	$0.674933\pi$
$432$		0			0
$433$	12.4844	+	5.55841i	0.599962	+	0.267120i	0.684164	−	0.729329i	$-0.260167\pi$
$433$	12.4844	+	5.55841i	0.599962	+	0.267120i	−0.0842019	+	0.996449i	$0.526834\pi$
$434$		0			0
$435$	6.63287	−	1.40986i	0.318022	−	0.0675976i
$436$		0			0
$437$	1.96479	+	1.42750i	0.0939886	+	0.0682867i
$438$		0			0
$439$	0.946165	−	1.63881i	0.0451580	−	0.0782159i	−0.842563	−	0.538598i	$-0.818954\pi$
$439$	0.946165	−	1.63881i	0.0451580	−	0.0782159i	0.887721	+	0.460382i	$0.152288\pi$
$440$		0			0
$441$	−14.8385			−0.706598
$442$		0			0
$443$	−13.5793	−	9.86595i	−0.645173	−	0.468746i	0.216451	−	0.976294i	$-0.430552\pi$
$443$	−13.5793	−	9.86595i	−0.645173	−	0.468746i	−0.861623	+	0.507548i	$0.830552\pi$
$444$		0			0
$445$	8.02099	+	8.90821i	0.380231	+	0.422290i
$446$		0			0
$447$	6.73073	−	4.89016i	0.318353	−	0.231297i
$448$		0			0
$449$	−5.42857	+	6.02904i	−0.256190	+	0.284528i	−0.857496	−	0.514491i	$-0.827981\pi$
$449$	−5.42857	+	6.02904i	−0.256190	+	0.284528i	0.601306	+	0.799019i	$0.294647\pi$
$450$		0			0
$451$	−13.8559	+	15.8650i	−0.652449	+	0.747054i
$452$		0			0
$453$	−6.76410	−	1.43775i	−0.317805	−	0.0675515i
$454$		0			0
$455$	0.945141	−	24.8910i	0.0443089	−	1.16691i
$456$		0			0
$457$	−22.3276	−	24.7973i	−1.04444	−	1.15997i	−0.986852	−	0.161628i	$-0.948326\pi$
$457$	−22.3276	−	24.7973i	−1.04444	−	1.15997i	−0.0575881	−	0.998340i	$-0.518341\pi$
$458$		0			0
$459$	0.756655	−	7.19909i	0.0353176	−	0.336025i
$460$		0			0
$461$	3.32818	+	5.76458i	0.155009	+	0.268483i	0.933062	−	0.359715i	$-0.117126\pi$
$461$	3.32818	+	5.76458i	0.155009	+	0.268483i	−0.778053	+	0.628198i	$0.783793\pi$
$462$		0			0
$463$	25.1883			1.17060			0.585299	−	0.810818i	$-0.300977\pi$
$463$	25.1883			1.17060			0.585299	+	0.810818i	$0.300977\pi$
$464$		0			0
$465$	−1.98420	+	0.883424i	−0.0920152	+	0.0409678i
$466$		0			0
$467$	8.72820	−	26.8626i	0.403893	−	1.24305i	−0.517923	−	0.855427i	$-0.673295\pi$
$467$	8.72820	−	26.8626i	0.403893	−	1.24305i	0.921816	−	0.387628i	$-0.126705\pi$
$468$		0			0
$469$	−2.24564	+	1.63155i	−0.103694	+	0.0753381i
$470$		0			0
$471$	−12.9791	−	2.75880i	−0.598047	−	0.127119i
$472$		0			0
$473$	−23.5408	−	16.5648i	−1.08241	−	0.761653i
$474$		0			0
$475$	−0.375473	+	0.417005i	−0.0172279	+	0.0191335i
$476$		0			0
$477$	15.1322	+	6.73727i	0.692854	+	0.308479i
$478$		0			0
$479$	7.67545	+	8.52446i	0.350700	+	0.389492i	0.892524	−	0.451000i	$-0.148933\pi$
$479$	7.67545	+	8.52446i	0.350700	+	0.389492i	−0.541824	+	0.840492i	$0.682266\pi$
$480$		0			0
$481$	−22.1776	−	21.5476i	−1.01121	−	0.982486i
$482$		0			0
$483$	6.53305	−	11.3156i	0.297264	−	0.514877i
$484$		0			0
$485$	4.60130	+	7.96968i	0.208934	+	0.361885i
$486$		0			0
$487$	4.07170	−	38.7396i	0.184506	−	1.75546i	−0.375363	−	0.926878i	$-0.622482\pi$
$487$	4.07170	−	38.7396i	0.184506	−	1.75546i	0.559870	−	0.828581i	$-0.310851\pi$
$488$		0			0
$489$	3.76460	−	11.5863i	0.170241	−	0.523948i
$490$		0			0
$491$	−1.69896	−	16.1645i	−0.0766730	−	0.729495i	−0.963557	−	0.267503i	$-0.913802\pi$
$491$	−1.69896	−	16.1645i	−0.0766730	−	0.729495i	0.886884	−	0.461992i	$-0.152865\pi$
$492$		0			0
$493$	3.20456	+	9.86263i	0.144326	+	0.444191i
$494$		0			0
$495$	13.4042	+	9.43210i	0.602476	+	0.423941i
$496$		0			0
$497$	0.980464	+	0.208404i	0.0439798	+	0.00934820i
$498$		0			0
$499$	−30.7128	+	22.3142i	−1.37489	+	0.998919i	−0.377557	+	0.925986i	$0.623236\pi$
$499$	−30.7128	+	22.3142i	−1.37489	+	0.998919i	−0.997337	+	0.0729326i	$0.976764\pi$
$500$		0			0
$501$	13.9765	−	2.97081i	0.624426	−	0.132726i
$502$		0			0
$503$	2.58678	−	24.6115i	0.115339	−	1.09737i	−0.771798	−	0.635867i	$-0.780642\pi$
$503$	2.58678	−	24.6115i	0.115339	−	1.09737i	0.887137	−	0.461506i	$-0.152691\pi$
$504$		0			0
$505$	−7.48771	+	12.9691i	−0.333199	+	0.577117i
$506$		0			0
$507$	−2.03727	−	8.38845i	−0.0904783	−	0.372544i
$508$		0			0
$509$	−3.93589	+	1.75237i	−0.174455	+	0.0776725i	−0.492106	−	0.870535i	$-0.663773\pi$
$509$	−3.93589	+	1.75237i	−0.174455	+	0.0776725i	0.317651	+	0.948208i	$0.397106\pi$
$510$		0			0
$511$	50.5400	−	10.7426i	2.23576	−	0.475225i
$512$		0			0
$513$	−1.48898	−	0.662936i	−0.0657400	−	0.0292693i
$514$		0			0
$515$	−8.28564	−	25.5006i	−0.365109	−	1.12369i
$516$		0			0
$517$	−6.59171	−	1.29715i	−0.289903	−	0.0570487i
$518$		0			0
$519$	0.678233	+	2.08739i	0.0297711	+	0.0916261i
$520$		0			0
$521$	15.7477	−	11.4413i	0.689917	−	0.501254i	−0.186716	−	0.982414i	$-0.559784\pi$
$521$	15.7477	−	11.4413i	0.689917	−	0.501254i	0.876633	+	0.481160i	$0.159784\pi$
$522$		0			0
$523$	18.2261	+	20.2422i	0.796974	+	0.885129i	0.995480	−	0.0949708i	$-0.0302758\pi$
$523$	18.2261	+	20.2422i	0.796974	+	0.885129i	−0.198507	+	0.980100i	$0.563609\pi$
$524$		0			0
$525$	2.44238	+	1.77449i	0.106594	+	0.0774452i
$526$		0			0
$527$	−1.66079	−	2.87658i	−0.0723453	−	0.125306i
$528$		0			0
$529$	−3.62657	−	6.28140i	−0.157677	−	0.273105i
$530$		0			0
$531$	−14.7641	+	6.57341i	−0.640708	+	0.285262i
$532$		0			0
$533$	−10.1008	+	20.5506i	−0.437515	+	0.890146i
$534$		0			0
$535$	−1.51662	−	14.4297i	−0.0655692	−	0.623849i
$536$		0			0
$537$	−8.04549	+	8.93543i	−0.347189	+	0.385592i
$538$		0			0
$539$	−17.6849	−	7.55519i	−0.761743	−	0.325425i
$540$		0			0
$541$	−6.15806	−	18.9525i	−0.264755	−	0.814834i	−0.991750	−	0.128190i	$-0.959083\pi$
$541$	−6.15806	−	18.9525i	−0.264755	−	0.814834i	0.726994	−	0.686644i	$-0.240917\pi$
$542$		0			0
$543$	−0.320171	−	3.04623i	−0.0137399	−	0.130726i
$544$		0			0
$545$	1.19086	−	3.66508i	0.0510108	−	0.156995i
$546$		0			0
$547$	−20.1427	−	14.6345i	−0.861238	−	0.625726i	0.0669834	−	0.997754i	$-0.478663\pi$
$547$	−20.1427	−	14.6345i	−0.861238	−	0.625726i	−0.928222	+	0.372028i	$0.878663\pi$
$548$		0			0
$549$	−5.62322	+	9.73971i	−0.239993	+	0.415681i
$550$		0			0
$551$	2.33497			0.0994732
$552$		0			0
$553$	0.139435	−	1.32664i	0.00592939	−	0.0564143i
$554$		0			0
$555$	−10.7568	+	2.28642i	−0.456600	+	0.0970533i
$556$		0			0
$557$	3.25955	+	31.0126i	0.138112	+	1.31405i	0.815645	+	0.578553i	$0.196382\pi$
$557$	3.25955	+	31.0126i	0.138112	+	1.31405i	−0.677533	+	0.735492i	$0.736951\pi$
$558$		0			0
$559$	−29.3725	−	10.7921i	−1.24232	−	0.456459i
$560$		0			0
$561$	2.10251	−	3.77240i	0.0887681	−	0.159271i
$562$		0			0
$563$	22.8902	−	25.4222i	0.964707	−	1.07142i	−0.0327008	−	0.999465i	$-0.510411\pi$
$563$	22.8902	−	25.4222i	0.964707	−	1.07142i	0.997408	−	0.0719509i	$-0.0229225\pi$
$564$		0			0
$565$	12.6018	+	5.61069i	0.530162	+	0.236043i
$566$		0			0
$567$	5.77745	−	17.7812i	0.242630	−	0.746739i
$568$		0			0
$569$	17.3914	−	7.74314i	0.729084	−	0.324609i	−0.00840827	−	0.999965i	$-0.502676\pi$
$569$	17.3914	−	7.74314i	0.729084	−	0.324609i	0.737492	+	0.675356i	$0.236010\pi$
$570$		0			0
$571$	−19.7614			−0.826987			−0.413493	−	0.910507i	$-0.635692\pi$
$571$	−19.7614			−0.826987			−0.413493	+	0.910507i	$0.635692\pi$
$572$		0			0
$573$	−10.7336			−0.448401
$574$		0			0
$575$	6.38572	−	2.84311i	0.266303	−	0.118566i
$576$		0			0
$577$	6.16748	−	18.9815i	0.256755	−	0.790212i	−0.736723	−	0.676194i	$-0.763628\pi$
$577$	6.16748	−	18.9815i	0.256755	−	0.790212i	0.993479	−	0.114018i	$-0.0363720\pi$
$578$		0			0
$579$	6.73269	+	2.99758i	0.279801	+	0.124575i
$580$		0			0
$581$	6.60465	−	7.33520i	0.274007	−	0.304316i
$582$		0			0
$583$	14.6045	+	15.7343i	0.604856	+	0.651649i
$584$		0			0
$585$	16.7248	+	6.14510i	0.691486	+	0.254069i
$586$		0			0
$587$	3.98413	+	37.9065i	0.164443	+	1.56457i	0.696311	+	0.717740i	$0.254824\pi$
$587$	3.98413	+	37.9065i	0.164443	+	1.56457i	−0.531868	+	0.846827i	$0.678510\pi$
$588$		0			0
$589$	−0.731552	+	0.155496i	−0.0301431	+	0.00640711i
$590$		0			0
$591$	0.277716	−	2.64229i	0.0114237	−	0.108689i
$592$		0			0
$593$	25.9203			1.06442			0.532210	−	0.846613i	$-0.321362\pi$
$593$	25.9203			1.06442			0.532210	+	0.846613i	$0.321362\pi$
$594$		0			0
$595$	6.77377	−	11.7325i	0.277698	−	0.480986i
$596$		0			0
$597$	5.56704	+	4.04469i	0.227844	+	0.165538i
$598$		0			0
$599$	−14.2025	+	43.7107i	−0.580297	+	1.78597i	0.0370921	+	0.999312i	$0.488191\pi$
$599$	−14.2025	+	43.7107i	−0.580297	+	1.78597i	−0.617389	+	0.786658i	$0.711809\pi$
$600$		0			0
$601$	−2.92849	−	27.8628i	−0.119456	−	1.13655i	−0.875902	−	0.482490i	$-0.839733\pi$
$601$	−2.92849	−	27.8628i	−0.119456	−	1.13655i	0.756446	−	0.654056i	$-0.226934\pi$
$602$		0			0
$603$	−0.613578	−	1.88840i	−0.0249868	−	0.0769016i
$604$		0			0
$605$	11.1730	+	18.0663i	0.454248	+	0.734499i
$606$		0			0
$607$	8.00257	−	8.88776i	0.324814	−	0.360743i	−0.558516	−	0.829494i	$-0.688629\pi$
$607$	8.00257	−	8.88776i	0.324814	−	0.360743i	0.883330	+	0.468751i	$0.155296\pi$
$608$		0			0
$609$	−1.31312	−	12.4935i	−0.0532103	−	0.506262i
$610$		0			0
$611$	−7.28710	+	0.487260i	−0.294805	+	0.0197124i
$612$		0			0
$613$	−8.38106	+	3.73149i	−0.338508	+	0.150713i	−0.568949	−	0.822373i	$-0.692650\pi$
$613$	−8.38106	+	3.73149i	−0.338508	+	0.150713i	0.230441	+	0.973086i	$0.425983\pi$
$614$		0			0
$615$	4.07191	+	7.05276i	0.164195	+	0.284395i
$616$		0			0
$617$	−4.41413	−	7.64550i	−0.177706	−	0.307796i	0.763388	−	0.645940i	$-0.223534\pi$
$617$	−4.41413	−	7.64550i	−0.177706	−	0.307796i	−0.941095	+	0.338144i	$0.890201\pi$
$618$		0			0
$619$	30.2540	+	21.9809i	1.21601	+	0.883485i	0.995763	−	0.0919585i	$-0.0293127\pi$
$619$	30.2540	+	21.9809i	1.21601	+	0.883485i	0.220250	+	0.975443i	$0.429313\pi$
$620$		0			0
$621$	13.5857	+	15.0884i	0.545175	+	0.605478i
$622$		0			0
$623$	17.9659	−	13.0530i	0.719787	−	0.522956i
$624$		0			0
$625$	−5.26277	−	16.1971i	−0.210511	−	0.647886i
$626$		0			0
$627$	−0.661537	−	0.712715i	−0.0264193	−	0.0284631i
$628$		0			0
$629$	−5.19697	−	15.9946i	−0.207217	−	0.637747i
$630$		0			0
$631$	−23.7704	−	10.5833i	−0.946285	−	0.421313i	−0.125208	−	0.992131i	$-0.539960\pi$
$631$	−23.7704	−	10.5833i	−0.946285	−	0.421313i	−0.821077	+	0.570817i	$0.806626\pi$
$632$		0			0
$633$	16.4120	−	3.48849i	0.652320	−	0.138655i
$634$		0			0
$635$	−14.5532	+	6.47952i	−0.577528	+	0.257132i
$636$		0			0
$637$	−20.6940	−	2.97267i	−0.819927	−	0.117782i
$638$		0			0
$639$	−0.358511	+	0.620959i	−0.0141825	+	0.0245647i
$640$		0			0
$641$	−2.92470	+	27.8266i	−0.115519	+	1.09909i	0.771141	+	0.636664i	$0.219686\pi$
$641$	−2.92470	+	27.8266i	−0.115519	+	1.09909i	−0.886660	+	0.462422i	$0.846981\pi$
$642$		0			0
$643$	1.41376	−	0.300504i	0.0557532	−	0.0118507i	−0.179951	−	0.983676i	$-0.557594\pi$
$643$	1.41376	−	0.300504i	0.0557532	−	0.0118507i	0.235704	+	0.971825i	$0.424260\pi$
$644$		0			0
$645$	−9.00352	+	6.54144i	−0.354513	+	0.257569i
$646$		0			0
$647$	3.41510	+	0.725901i	0.134261	+	0.0285381i	0.274552	−	0.961572i	$-0.411470\pi$
$647$	3.41510	+	0.725901i	0.134261	+	0.0285381i	−0.140291	+	0.990110i	$0.544804\pi$
$648$		0			0
$649$	−20.9431	+	0.317038i	−0.822089	+	0.0124448i
$650$		0			0
$651$	1.24340	+	3.82680i	0.0487328	+	0.149984i
$652$		0			0
$653$	−5.22803	−	49.7414i	−0.204589	−	1.94653i	−0.306812	−	0.951770i	$-0.599262\pi$
$653$	−5.22803	−	49.7414i	−0.204589	−	1.94653i	0.102223	−	0.994762i	$-0.467405\pi$
$654$		0			0
$655$	−4.13707	+	12.7326i	−0.161649	+	0.497504i
$656$		0			0
$657$	−3.86341	+	36.7578i	−0.150726	+	1.43406i
$658$		0			0
$659$	1.21638	+	2.10683i	0.0473833	+	0.0820703i	0.888744	−	0.458403i	$-0.151578\pi$
$659$	1.21638	+	2.10683i	0.0473833	+	0.0820703i	−0.841361	+	0.540474i	$0.818245\pi$
$660$		0			0
$661$	1.68250	−	2.91417i	0.0654416	−	0.113348i	−0.831448	−	0.555602i	$-0.812488\pi$
$661$	1.68250	−	2.91417i	0.0654416	−	0.113348i	0.896890	+	0.442254i	$0.145821\pi$
$662$		0			0
$663$	1.14969	−	4.55202i	0.0446502	−	0.176786i
$664$		0			0
$665$	−2.04111	−	2.26688i	−0.0791509	−	0.0879060i
$666$		0			0
$667$	−26.5720	−	11.8306i	−1.02887	−	0.458083i
$668$		0			0
$669$	−5.32935	+	5.91885i	−0.206045	+	0.228836i
$670$		0			0
$671$	−11.6609	+	8.74488i	−0.450166	+	0.337592i
$672$		0			0
$673$	−17.8771	−	3.79989i	−0.689111	−	0.146475i	−0.149970	−	0.988691i	$-0.547918\pi$
$673$	−17.8771	−	3.79989i	−0.689111	−	0.146475i	−0.539141	+	0.842215i	$0.681251\pi$
$674$		0			0
$675$	−3.79523	+	2.75739i	−0.146078	+	0.106132i
$676$		0			0
$677$	3.73109	−	11.4831i	0.143397	−	0.441332i	−0.853404	−	0.521250i	$-0.825466\pi$
$677$	3.73109	−	11.4831i	0.143397	−	0.441332i	0.996801	+	0.0799182i	$0.0254659\pi$
$678$		0			0
$679$	15.5745	−	6.93421i	0.597694	−	0.266110i
$680$		0			0
$681$	5.93306			0.227355
$682$		0			0
$683$	8.91959	+	15.4492i	0.341299	+	0.591147i	0.984674	−	0.174404i	$-0.0557999\pi$
$683$	8.91959	+	15.4492i	0.341299	+	0.591147i	−0.643375	+	0.765551i	$0.722467\pi$
$684$		0			0
$685$	2.85261	−	27.1408i	0.108993	−	1.03700i
$686$		0			0
$687$	9.15517	+	10.1678i	0.349292	+	0.387928i
$688$		0			0
$689$	19.7538	+	12.4274i	0.752560	+	0.473446i
$690$		0			0
$691$	−8.60256	−	1.82853i	−0.327257	−	0.0695606i	0.0413536	−	0.999145i	$-0.486833\pi$
$691$	−8.60256	−	1.82853i	−0.327257	−	0.0695606i	−0.368610	+	0.929584i	$0.620166\pi$
$692$		0			0
$693$	19.9735	−	22.8697i	0.758731	−	0.868748i
$694$		0			0
$695$	19.2310	−	21.3582i	0.729474	−	0.810163i
$696$		0			0
$697$	−10.0757	+	7.32044i	−0.381645	+	0.277281i
$698$		0			0
$699$	6.68998	+	7.42997i	0.253038	+	0.281027i
$700$		0			0
$701$	−16.4694	−	11.9657i	−0.622039	−	0.451938i	0.231594	−	0.972813i	$-0.425606\pi$
$701$	−16.4694	−	11.9657i	−0.622039	−	0.451938i	−0.853633	+	0.520875i	$0.825606\pi$
$702$		0			0
$703$	−3.78672			−0.142819
$704$		0			0
$705$	−1.29870	+	2.24942i	−0.0489120	+	0.0847181i
$706$		0			0
$707$	22.4445	+	16.3069i	0.844112	+	0.613283i
$708$		0			0
$709$	−27.9200	+	5.93458i	−1.04856	+	0.222878i	−0.699803	−	0.714336i	$-0.746729\pi$
$709$	−27.9200	+	5.93458i	−1.04856	+	0.222878i	−0.348755	+	0.937214i	$0.613395\pi$
$710$		0			0
$711$	0.871711	+	0.388111i	0.0326917	+	0.0145553i
$712$		0			0
$713$	9.11292	+	1.93701i	0.341282	+	0.0725417i
$714$		0			0
$715$	16.8042	+	15.8395i	0.628440	+	0.592362i
$716$		0			0
$717$	8.53703	+	1.81460i	0.318821	+	0.0677675i
$718$		0			0
$719$	−3.62070	−	1.61204i	−0.135029	−	0.0601189i	0.338110	−	0.941107i	$-0.390212\pi$
$719$	−3.62070	−	1.61204i	−0.135029	−	0.0601189i	−0.473139	+	0.880988i	$0.656879\pi$
$720$		0			0
$721$	−48.5871	+	10.3275i	−1.80948	+	0.384616i
$722$		0			0
$723$	−13.5955	−	9.87772i	−0.505622	−	0.367356i
$724$		0			0
$725$	3.36026	−	5.82015i	0.124797	−	0.216155i
$726$		0			0
$727$	−1.08990			−0.0404220			−0.0202110	−	0.999796i	$-0.506434\pi$
$727$	−1.08990			−0.0404220			−0.0202110	+	0.999796i	$0.506434\pi$
$728$		0			0
$729$	4.87068	+	3.53876i	0.180396	+	0.131065i
$730$		0			0
$731$	−11.3882	−	12.6479i	−0.421208	−	0.467799i
$732$		0			0
$733$	10.4754	−	7.61084i	0.386918	−	0.281113i	−0.377273	−	0.926102i	$-0.623138\pi$
$733$	10.4754	−	7.61084i	0.386918	−	0.281113i	0.764192	+	0.644989i	$0.223138\pi$
$734$		0			0
$735$	−4.97516	+	5.52548i	−0.183512	+	0.203810i
$736$		0			0
$737$	0.230221	−	2.56304i	0.00848030	−	0.0944109i
$738$		0			0
$739$	4.58115	+	0.973753i	0.168520	+	0.0358201i	0.291399	−	0.956602i	$-0.405879\pi$
$739$	4.58115	+	0.973753i	0.168520	+	0.0358201i	−0.122879	+	0.992422i	$0.539213\pi$
$740$		0			0
$741$	−0.894785	−	0.562921i	−0.0328707	−	0.0206794i
$742$		0			0
$743$	−25.5143	−	28.3365i	−0.936029	−	1.03957i	−0.999136	−	0.0415583i	$-0.986768\pi$
$743$	−25.5143	−	28.3365i	−0.936029	−	1.03957i	0.0631075	−	0.998007i	$-0.479899\pi$
$744$		0			0
$745$	−2.52907	+	24.0625i	−0.0926580	+	0.881582i
$746$		0			0
$747$	3.53032	+	6.11469i	0.129168	+	0.223725i
$748$		0			0
$749$	−26.8791			−0.982142
$750$		0			0
$751$	4.26927	−	1.90080i	0.155788	−	0.0693612i	−0.327361	−	0.944899i	$-0.606159\pi$
$751$	4.26927	−	1.90080i	0.155788	−	0.0693612i	0.483149	+	0.875538i	$0.339493\pi$
$752$		0			0
$753$	−2.24937	+	6.92284i	−0.0819715	+	0.252282i
$754$		0			0
$755$	16.2699	−	11.8208i	0.592122	−	0.430202i
$756$		0			0
$757$	−26.4164	−	5.61498i	−0.960120	−	0.204080i	−0.298910	−	0.954281i	$-0.596623\pi$
$757$	−26.4164	−	5.61498i	−0.960120	−	0.204080i	−0.661209	+	0.750201i	$0.729957\pi$
$758$		0			0
$759$	3.91718	+	11.4625i	0.142185	+	0.416063i
$760$		0			0
$761$	−8.91265	+	9.89850i	−0.323083	+	0.358820i	−0.882705	−	0.469928i	$-0.844280\pi$
$761$	−8.91265	+	9.89850i	−0.323083	+	0.358820i	0.559622	+	0.828748i	$0.310947\pi$
$762$		0			0
$763$	−6.52200	−	2.90378i	−0.236112	−	0.105124i
$764$		0			0
$765$	6.48450	+	7.20176i	0.234447	+	0.260380i
$766$		0			0
$767$	−21.9071	+	6.20960i	−0.791020	+	0.224216i
$768$		0			0
$769$	25.3860	−	43.9699i	0.915443	−	1.58559i	0.109192	−	0.994021i	$-0.465174\pi$
$769$	25.3860	−	43.9699i	0.915443	−	1.58559i	0.806251	−	0.591574i	$-0.201493\pi$
$770$		0			0
$771$	9.45053	+	16.3688i	0.340353	+	0.589508i
$772$		0			0
$773$	1.86290	−	17.7243i	0.0670039	−	0.637500i	−0.908556	−	0.417764i	$-0.862814\pi$
$773$	1.86290	−	17.7243i	0.0670039	−	0.637500i	0.975559	−	0.219736i	$-0.0705195\pi$
$774$		0			0
$775$	−0.665189	+	2.04724i	−0.0238943	+	0.0735391i
$776$		0			0
$777$	2.12954	+	20.2612i	0.0763968	+	0.726867i
$778$		0			0
$779$	0.866555	+	2.66698i	0.0310476	+	0.0955545i
$780$		0			0
$781$	−0.743448	+	0.557533i	−0.0266027	+	0.0199501i
$782$		0			0
$783$	19.0941	+	4.05857i	0.682367	+	0.145042i
$784$		0			0
$785$	31.2192	−	22.6820i	1.11426	−	0.809557i
$786$		0			0
$787$	5.11175	−	1.08654i	0.182214	−	0.0387308i	−0.115901	−	0.993261i	$-0.536975\pi$
$787$	5.11175	−	1.08654i	0.182214	−	0.0387308i	0.298115	+	0.954530i	$0.403642\pi$
$788$		0			0
$789$	−1.61776	+	15.3920i	−0.0575939	+	0.547969i
$790$		0			0
$791$	12.7775	−	22.1313i	0.454315	−	0.786897i
$792$		0			0
$793$	−9.79342	+	12.4566i	−0.347775	+	0.442347i
$794$		0			0
$795$	7.58239	−	3.37590i	0.268920	−	0.119731i
$796$		0			0
$797$	−26.3744	+	5.60606i	−0.934230	+	0.198577i	−0.649787	−	0.760116i	$-0.725142\pi$
$797$	−26.3744	+	5.60606i	−0.934230	+	0.198577i	−0.284443	+	0.958693i	$0.591809\pi$
$798$		0			0
$799$	−3.62877	−	1.61563i	−0.128377	−	0.0571570i
$800$		0			0
$801$	4.90882	+	15.1078i	0.173445	+	0.533808i
$802$		0			0
$803$	−23.3201	+	41.8417i	−0.822948	+	1.47656i
$804$		0			0
$805$	11.7422	+	36.1389i	0.413859	+	1.27373i
$806$		0			0
$807$	−16.0335	+	11.6490i	−0.564406	+	0.410065i
$808$		0			0
$809$	28.8419	+	32.0321i	1.01403	+	1.12619i	0.991975	+	0.126433i	$0.0403528\pi$
$809$	28.8419	+	32.0321i	1.01403	+	1.12619i	0.0220505	+	0.999757i	$0.492981\pi$
$810$		0			0
$811$	28.5848	+	20.7680i	1.00375	+	0.729265i	0.962888	−	0.269900i	$-0.0869907\pi$
$811$	28.5848	+	20.7680i	1.00375	+	0.729265i	0.0408585	+	0.999165i	$0.486991\pi$
$812$		0			0
$813$	3.32332	+	5.75615i	0.116554	+	0.201877i
$814$		0			0
$815$	17.7145	+	30.6824i	0.620511	+	1.07476i
$816$		0			0
$817$	−3.50082	+	1.55867i	−0.122478	+	0.0545308i
$818$		0			0
$819$	14.5605	−	29.6241i	0.508785	−	1.03515i
$820$		0			0
$821$	4.09513	+	38.9626i	0.142921	+	1.35980i	0.797275	+	0.603616i	$0.206274\pi$
$821$	4.09513	+	38.9626i	0.142921	+	1.35980i	−0.654354	+	0.756188i	$0.727059\pi$
$822$		0			0
$823$	−20.4356	+	22.6960i	−0.712339	+	0.791132i	−0.985289	−	0.170896i	$-0.945334\pi$
$823$	−20.4356	+	22.6960i	−0.712339	+	0.791132i	0.272950	+	0.962028i	$0.412001\pi$
$824$		0			0
$825$	−2.72853	+	0.623277i	−0.0949953	+	0.0216997i
$826$		0			0
$827$	3.07140	+	9.45280i	0.106803	+	0.328706i	0.990149	−	0.140015i	$-0.0447150\pi$
$827$	3.07140	+	9.45280i	0.106803	+	0.328706i	−0.883346	+	0.468721i	$0.844715\pi$
$828$		0			0
$829$	−3.86525	−	36.7754i	−0.134246	−	1.27726i	−0.829504	−	0.558501i	$-0.811377\pi$
$829$	−3.86525	−	36.7754i	−0.134246	−	1.27726i	0.695258	−	0.718760i	$-0.255290\pi$
$830$		0			0
$831$	3.52515	−	10.8493i	0.122286	−	0.376358i
$832$		0			0
$833$	−9.19907	−	6.68352i	−0.318729	−	0.231570i
$834$		0			0
$835$	−20.7772	+	35.9872i	−0.719025	+	1.24539i
$836$		0			0
$837$	−6.25250			−0.216118
$838$		0			0
$839$	−3.92094	+	37.3052i	−0.135366	+	1.28792i	0.690202	+	0.723617i	$0.257522\pi$
$839$	−3.92094	+	37.3052i	−0.135366	+	1.28792i	−0.825568	+	0.564303i	$0.809145\pi$
$840$		0			0
$841$	1.01220	−	0.215149i	0.0349033	−	0.00741893i
$842$		0			0
$843$	−2.13143	−	20.2792i	−0.0734105	−	0.698454i
$844$		0			0
$845$	22.0936	+	11.9206i	0.760042	+	0.410081i
$846$		0			0
$847$	35.4492	−	17.0869i	1.21805	−	0.587112i
$848$		0			0
$849$	4.19170	−	4.65535i	0.143859	−	0.159771i
$850$		0			0
$851$	43.0929	+	19.1862i	1.47720	+	0.657694i
$852$		0			0
$853$	10.4669	−	32.2137i	0.358379	−	1.10298i	−0.595646	−	0.803247i	$-0.703104\pi$
$853$	10.4669	−	32.2137i	0.358379	−	1.10298i	0.954024	−	0.299729i	$-0.0968962\pi$
$854$		0			0
$855$	1.99338	−	0.887511i	0.0681723	−	0.0303522i
$856$		0			0
$857$	−1.12486			−0.0384244			−0.0192122	−	0.999815i	$-0.506116\pi$
$857$	−1.12486			−0.0384244			−0.0192122	+	0.999815i	$0.506116\pi$
$858$		0			0
$859$	−15.2919			−0.521752			−0.260876	−	0.965372i	$-0.584011\pi$
$859$	−15.2919			−0.521752			−0.260876	+	0.965372i	$0.584011\pi$
$860$		0			0
$861$	13.7826	−	6.13642i	0.469711	−	0.209129i
$862$		0			0
$863$	−3.68927	+	11.3544i	−0.125584	+	0.386509i	−0.994007	−	0.109316i	$-0.965134\pi$
$863$	−3.68927	+	11.3544i	−0.125584	+	0.386509i	0.868423	+	0.495824i	$0.165134\pi$
$864$		0			0
$865$	−5.83107	−	2.59616i	−0.198262	−	0.0882721i
$866$		0			0
$867$	−5.84477	+	6.49128i	−0.198499	+	0.220455i
$868$		0			0
$869$	0.841314	+	0.906399i	0.0285396	+	0.0307475i
$870$		0			0
$871$	−0.477392	−	2.75651i	−0.0161758	−	0.0934007i
$872$		0			0
$873$	1.27474	+	12.1284i	0.0431435	+	0.410483i
$874$		0			0
$875$	−42.3754	+	9.00717i	−1.43255	+	0.304498i
$876$		0			0
$877$	−5.06768	+	48.2158i	−0.171124	+	1.62813i	0.485727	+	0.874111i	$0.338555\pi$
$877$	−5.06768	+	48.2158i	−0.171124	+	1.62813i	−0.656850	+	0.754021i	$0.728112\pi$
$878$		0			0
$879$	−8.98517			−0.303062
$880$		0			0
$881$	24.0372	−	41.6337i	0.809834	−	1.40267i	−0.103144	−	0.994666i	$-0.532890\pi$
$881$	24.0372	−	41.6337i	0.809834	−	1.40267i	0.912978	−	0.408008i	$-0.133776\pi$
$882$		0			0
$883$	6.91318	+	5.02272i	0.232647	+	0.169028i	0.698001	−	0.716097i	$-0.254073\pi$
$883$	6.91318	+	5.02272i	0.232647	+	0.169028i	−0.465354	+	0.885125i	$0.654073\pi$
$884$		0			0
$885$	−2.50245	+	7.70174i	−0.0841188	+	0.258891i
$886$		0			0
$887$	3.00267	+	28.5685i	0.100820	+	0.959237i	0.921639	+	0.388049i	$0.126851\pi$
$887$	3.00267	+	28.5685i	0.100820	+	0.959237i	−0.820819	+	0.571189i	$0.806483\pi$
$888$		0			0
$889$	9.11979	+	28.0678i	0.305868	+	0.941365i
$890$		0			0
$891$	8.89269	+	14.8779i	0.297916	+	0.498427i
$892$		0			0
$893$	−0.598461	+	0.664658i	−0.0200267	+	0.0222419i
$894$		0			0
$895$	−3.65509	−	34.7759i	−0.122176	−	1.16243i
$896$		0			0
$897$	7.33050	+	10.9397i	0.244758	+	0.365264i
$898$		0			0
$899$	8.18290	−	3.64326i	0.272915	−	0.121510i
$900$		0			0
$901$	6.34652	+	10.9925i	0.211433	+	0.366213i
$902$		0			0
$903$	10.3085	+	17.8549i	0.343047	+	0.594175i
$904$		0			0
$905$	7.20655	+	5.23586i	0.239554	+	0.174046i
$906$		0			0
$907$	−11.9935	−	13.3201i	−0.398238	−	0.442288i	0.510359	−	0.859961i	$-0.329512\pi$
$907$	−11.9935	−	13.3201i	−0.398238	−	0.442288i	−0.908597	+	0.417673i	$0.862846\pi$
$908$		0			0
$909$	−16.0552	+	11.6648i	−0.532516	+	0.386895i
$910$		0			0
$911$	−2.87260	−	8.84095i	−0.0951734	−	0.292914i	0.892125	−	0.451788i	$-0.149214\pi$
$911$	−2.87260	−	8.84095i	−0.0951734	−	0.292914i	−0.987299	+	0.158874i	$0.949214\pi$
$912$		0			0
$913$	1.09416	+	9.08511i	0.0362113	+	0.300673i
$914$		0			0
$915$	1.74142	+	5.35953i	0.0575695	+	0.177181i
$916$		0			0
$917$	22.6576	+	10.0878i	0.748220	+	0.333129i
$918$		0			0
$919$	−11.1699	+	2.37423i	−0.368460	+	0.0783185i	−0.388420	−	0.921482i	$-0.626979\pi$
$919$	−11.1699	+	2.37423i	−0.368460	+	0.0783185i	0.0199608	+	0.999801i	$0.493646\pi$
$920$		0			0
$921$	20.2831	−	9.03063i	0.668352	−	0.297569i
$922$		0			0
$923$	−0.624383	+	0.794175i	−0.0205518	+	0.0261406i
$924$		0			0
$925$	−5.44947	+	9.43876i	−0.179178	+	0.310345i
$926$		0			0
$927$	3.71412	−	35.3375i	0.121988	−	1.16064i
$928$		0			0
$929$	−36.5348	+	7.76572i	−1.19867	+	0.254785i	−0.763646	−	0.645635i	$-0.776593\pi$
$929$	−36.5348	+	7.76572i	−1.19867	+	0.254785i	−0.435022	+	0.900420i	$0.643260\pi$
$930$		0			0
$931$	−2.07128	+	1.50487i	−0.0678835	+	0.0493203i
$932$		0			0
$933$	0.668081	+	0.142005i	0.0218720	+	0.00464904i
$934$		0			0
$935$	4.06152	+	11.8849i	0.132826	+	0.388677i
$936$		0			0
$937$	−6.17911	−	19.0173i	−0.201863	−	0.621269i	−0.999828	−	0.0185655i	$-0.994090\pi$
$937$	−6.17911	−	19.0173i	−0.201863	−	0.621269i	0.797965	−	0.602704i	$-0.205910\pi$
$938$		0			0
$939$	−1.20589	−	11.4733i	−0.0393528	−	0.374417i
$940$		0			0
$941$	6.92548	−	21.3144i	0.225764	−	0.694830i	−0.772449	−	0.635077i	$-0.780968\pi$
$941$	6.92548	−	21.3144i	0.225764	−	0.694830i	0.998213	−	0.0597536i	$-0.0190315\pi$
$942$		0			0
$943$	3.65141	−	34.7408i	0.118906	−	1.13132i
$944$		0			0
$945$	−12.7508	−	22.0851i	−0.414784	−	0.718428i
$946$		0			0
$947$	−12.1433	+	21.0329i	−0.394605	+	0.683477i	−0.993051	−	0.117687i	$-0.962452\pi$
$947$	−12.1433	+	21.0329i	−0.394605	+	0.683477i	0.598445	+	0.801164i	$0.295785\pi$
$948$		0			0
$949$	−12.7518	+	50.4890i	−0.413941	+	1.63894i
$950$		0			0
$951$	−7.57318	−	8.41087i	−0.245577	−	0.272741i
$952$		0			0
$953$	14.7352	+	6.56052i	0.477319	+	0.212516i	0.631271	−	0.775562i	$-0.282533\pi$
$953$	14.7352	+	6.56052i	0.477319	+	0.212516i	−0.153952	+	0.988078i	$0.549200\pi$
$954$		0			0
$955$	20.8870	−	23.1974i	0.675889	−	0.750650i
$956$		0			0
$957$	9.52460	+	6.70213i	0.307886	+	0.216649i
$958$		0			0
$959$	−49.4521	−	10.5114i	−1.59689	−	0.339430i
$960$		0			0
$961$	22.7584	−	16.5350i	0.734143	−	0.533386i
$962$		0			0
$963$	5.94159	−	18.2863i	0.191465	−	0.589269i
$964$		0			0
$965$	−19.5799	+	8.71753i	−0.630299	+	0.280627i
$966$		0			0
$967$	−9.01198			−0.289806			−0.144903	−	0.989446i	$-0.546287\pi$
$967$	−9.01198			−0.289806			−0.144903	+	0.989446i	$0.546287\pi$
$968$		0			0
$969$	−0.287477	−	0.497925i	−0.00923510	−	0.0159957i
$970$		0			0
$971$	−0.843342	+	8.02387i	−0.0270641	+	0.257498i	0.972621	+	0.232398i	$0.0746572\pi$
$971$	−0.843342	+	8.02387i	−0.0270641	+	0.257498i	−0.999685	+	0.0251002i	$0.992010\pi$
$972$		0			0
$973$	−35.6267	−	39.5675i	−1.14214	−	1.26847i
$974$		0			0
$975$	−2.69082	+	1.42024i	−0.0861753	+	0.0454840i
$976$		0			0
$977$	17.6869	+	3.75946i	0.565853	+	0.120276i	0.481951	−	0.876198i	$-0.339928\pi$
$977$	17.6869	+	3.75946i	0.565853	+	0.120276i	0.0839022	+	0.996474i	$0.473262\pi$
$978$		0			0
$979$	−1.84184	+	20.5052i	−0.0588655	+	0.655348i
$980$		0			0
$981$	3.41717	−	3.79515i	0.109102	−	0.121170i
$982$		0			0
$983$	−34.6162	+	25.1501i	−1.10409	+	0.802165i	−0.981722	−	0.190320i	$-0.939047\pi$
$983$	−34.6162	+	25.1501i	−1.10409	+	0.802165i	−0.122364	+	0.992485i	$0.539047\pi$
$984$		0			0
$985$	5.17010	+	5.74197i	0.164733	+	0.182954i
$986$		0			0
$987$	3.89288	+	2.82834i	0.123912	+	0.0900271i
$988$		0			0
$989$	47.7366			1.51794
$990$		0			0
$991$	−24.5823	+	42.5778i	−0.780883	+	1.35253i	0.150546	+	0.988603i	$0.451897\pi$
$991$	−24.5823	+	42.5778i	−0.780883	+	1.35253i	−0.931428	+	0.363925i	$0.881436\pi$
$992$		0			0
$993$	9.47016	+	6.88048i	0.300526	+	0.218345i
$994$		0			0
$995$	−19.5746	+	4.16071i	−0.620556	+	0.131903i
$996$		0			0
$997$	−53.4724	−	23.8075i	−1.69349	−	0.753990i	−0.999419	−	0.0340815i	$-0.989149\pi$
$997$	−53.4724	−	23.8075i	−1.69349	−	0.753990i	−0.694069	−	0.719908i	$-0.744184\pi$
$998$		0			0
$999$	−30.9656	−	6.58195i	−0.979709	−	0.208244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.269.9	yes	112
11.9	even	5	inner	572.2.bg.a.9.6	✓	112
13.3	even	3	inner	572.2.bg.a.445.6	yes	112
143.42	even	15	inner	572.2.bg.a.185.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.9.6	✓	112	11.9	even	5	inner
572.2.bg.a.185.9	yes	112	143.42	even	15	inner
572.2.bg.a.269.9	yes	112	1.1	even	1	trivial
572.2.bg.a.445.6	yes	112	13.3	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.606615 - 0.270082i) q^{3} +(-0.596743 + 1.83659i) q^{5} +(3.26820 + 1.45509i) q^{7} +(-1.71235 + 1.90176i) q^{9} +O(q^{10})\)	\(q+(0.606615 - 0.270082i) q^{3} +(-0.596743 + 1.83659i) q^{5} +(3.26820 + 1.45509i) q^{7} +(-1.71235 + 1.90176i) q^{9} +(-3.00912 + 1.39470i) q^{11} +(-2.76906 + 2.30918i) q^{13} +(0.134036 + 1.27527i) q^{15} +(-1.91815 + 0.407715i) q^{17} +(-0.0461538 + 0.439124i) q^{19} +2.37553 q^{21} +(2.75014 - 4.76339i) q^{23} +(1.02814 + 0.746987i) q^{25} +(-1.14069 + 3.51068i) q^{27} +(-0.552769 - 5.25924i) q^{29} +(0.523420 + 1.61092i) q^{31} +(-1.44869 + 1.65876i) q^{33} +(-4.62268 + 5.13400i) q^{35} +(0.896447 + 8.52912i) q^{37} +(-1.05608 + 2.14866i) q^{39} +(5.80191 - 2.58318i) q^{41} +(4.33947 + 7.51618i) q^{43} +(-2.47091 - 4.27975i) q^{45} +(1.63874 + 1.19061i) q^{47} +(3.87989 + 4.30906i) q^{49} +(-1.05346 + 0.765384i) q^{51} +(-2.00019 - 6.15594i) q^{53} +(-0.765813 - 6.35879i) q^{55} +(0.0906021 + 0.278845i) q^{57} +(5.76932 + 2.56867i) q^{59} +(4.29870 - 0.913717i) q^{61} +(-8.36355 + 3.72369i) q^{63} +(-2.58859 - 6.46360i) q^{65} +(-0.387949 + 0.671947i) q^{67} +(0.381771 - 3.63231i) q^{69} +(0.274065 - 0.0582543i) q^{71} +(11.6845 - 8.48929i) q^{73} +(0.825433 + 0.175451i) q^{75} +(-11.8638 + 0.179595i) q^{77} +(-0.115224 - 0.354622i) q^{79} +(-0.546274 - 5.19745i) q^{81} +(0.852596 - 2.62402i) q^{83} +(0.395838 - 3.76614i) q^{85} +(-1.75575 - 3.04104i) q^{87} +(3.10372 - 5.37580i) q^{89} +(-12.4099 + 3.51760i) q^{91} +(0.752596 + 0.835843i) q^{93} +(-0.778947 - 0.346810i) q^{95} +(3.18872 - 3.54143i) q^{97} +(2.50030 - 8.11085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more