LMFDB - Embedded newform 264.2.q.d.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(25,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,1,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			49.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	264.49
Dual form			264.2.q.d.97.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{3} +(0.190983 - 0.587785i) q^{5} +(1.80902 - 1.31433i) q^{7} +(0.309017 + 0.951057i) q^{9} +(1.69098 - 2.85317i) q^{11} +(1.30902 + 4.02874i) q^{13} +(0.500000 - 0.363271i) q^{15} +(-0.118034 + 0.363271i) q^{17} +(1.11803 + 0.812299i) q^{19} +2.23607 q^{21} -5.47214 q^{23} +(3.73607 + 2.71441i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-1.61803 + 1.17557i) q^{29} +(-2.50000 - 7.69421i) q^{31} +(3.04508 - 1.31433i) q^{33} +(-0.427051 - 1.31433i) q^{35} +(-5.42705 + 3.94298i) q^{37} +(-1.30902 + 4.02874i) q^{39} +(-3.04508 - 2.21238i) q^{41} +5.94427 q^{43} +0.618034 q^{45} +(-7.78115 - 5.65334i) q^{47} +(-0.618034 + 1.90211i) q^{49} +(-0.309017 + 0.224514i) q^{51} +(-2.64590 - 8.14324i) q^{53} +(-1.35410 - 1.53884i) q^{55} +(0.427051 + 1.31433i) q^{57} +(-3.11803 + 2.26538i) q^{59} +(-2.04508 + 6.29412i) q^{61} +(1.80902 + 1.31433i) q^{63} +2.61803 q^{65} -2.90983 q^{67} +(-4.42705 - 3.21644i) q^{69} +(-0.663119 + 2.04087i) q^{71} +(-7.09017 + 5.15131i) q^{73} +(1.42705 + 4.39201i) q^{75} +(-0.690983 - 7.38394i) q^{77} +(-1.92705 - 5.93085i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-4.07295 + 12.5352i) q^{83} +(0.190983 + 0.138757i) q^{85} -2.00000 q^{87} -7.76393 q^{89} +(7.66312 + 5.56758i) q^{91} +(2.50000 - 7.69421i) q^{93} +(0.690983 - 0.502029i) q^{95} +(-5.28115 - 16.2537i) q^{97} +(3.23607 + 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + 3 q^{5} + 5 q^{7} - q^{9} + 9 q^{11} + 3 q^{13} + 2 q^{15} + 4 q^{17} - 4 q^{23} + 6 q^{25} + q^{27} - 2 q^{29} - 10 q^{31} + q^{33} + 5 q^{35} - 15 q^{37} - 3 q^{39} - q^{41} - 12 q^{43}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q + q^3 + 3 * q^5 + 5 * q^7 - q^9 + 9 * q^11 + 3 * q^13 + 2 * q^15 + 4 * q^17 - 4 * q^23 + 6 * q^25 + q^27 - 2 * q^29 - 10 * q^31 + q^33 + 5 * q^35 - 15 * q^37 - 3 * q^39 - q^41 - 12 * q^43 - 2 * q^45 - 11 * q^47 + 2 * q^49 + q^51 - 24 * q^53 + 8 * q^55 - 5 * q^57 - 8 * q^59 + 3 * q^61 + 5 * q^63 + 6 * q^65 - 34 * q^67 - 11 * q^69 + 13 * q^71 - 6 * q^73 - q^75 - 5 * q^77 - q^79 - q^81 - 23 * q^83 + 3 * q^85 - 8 * q^87 - 40 * q^89 + 15 * q^91 + 10 * q^93 + 5 * q^95 - q^97 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$		0			0
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	−0.899226	−	0.437485i	$-0.855869\pi$
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	0.984636	+	0.174619i	$0.0558694\pi$
$6$		0			0
$7$	1.80902	−	1.31433i	0.683744	−	0.496769i	−0.190854	−	0.981619i	$-0.561126\pi$
$7$	1.80902	−	1.31433i	0.683744	−	0.496769i	0.874598	+	0.484849i	$0.161126\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	1.69098	−	2.85317i	0.509851	−	0.860263i
$11$	1.69098	−	2.85317i	0.509851	−	0.860263i
$12$		0			0
$13$	1.30902	+	4.02874i	0.363056	+	1.11737i	0.951189	+	0.308608i	$0.0998630\pi$
$13$	1.30902	+	4.02874i	0.363056	+	1.11737i	−0.588133	+	0.808764i	$0.700137\pi$
$14$		0			0
$15$	0.500000	−	0.363271i	0.129099	−	0.0937962i
$16$		0			0
$17$	−0.118034	+	0.363271i	−0.0286274	+	0.0881062i	−0.964349	−	0.264632i	$-0.914749\pi$
$17$	−0.118034	+	0.363271i	−0.0286274	+	0.0881062i	0.935722	+	0.352738i	$0.114749\pi$
$18$		0			0
$19$	1.11803	+	0.812299i	0.256495	+	0.186354i	0.708600	−	0.705610i	$-0.249327\pi$
$19$	1.11803	+	0.812299i	0.256495	+	0.186354i	−0.452106	+	0.891964i	$0.649327\pi$
$20$		0			0
$21$	2.23607			0.487950
$22$		0			0
$23$	−5.47214			−1.14102			−0.570510	−	0.821291i	$-0.693254\pi$
$23$	−5.47214			−1.14102			−0.570510	+	0.821291i	$0.693254\pi$
$24$		0			0
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	−1.61803	+	1.17557i	−0.300461	+	0.218298i	−0.727793	−	0.685797i	$-0.759454\pi$
$29$	−1.61803	+	1.17557i	−0.300461	+	0.218298i	0.427331	+	0.904095i	$0.359454\pi$
$30$		0			0
$31$	−2.50000	−	7.69421i	−0.449013	−	1.38192i	−0.878022	−	0.478620i	$-0.841137\pi$
$31$	−2.50000	−	7.69421i	−0.449013	−	1.38192i	0.429009	−	0.903300i	$-0.358863\pi$
$32$		0			0
$33$	3.04508	−	1.31433i	0.530081	−	0.228795i
$34$		0			0
$35$	−0.427051	−	1.31433i	−0.0721848	−	0.222162i
$36$		0			0
$37$	−5.42705	+	3.94298i	−0.892202	+	0.648222i	−0.936451	−	0.350798i	$-0.885910\pi$
$37$	−5.42705	+	3.94298i	−0.892202	+	0.648222i	0.0442495	+	0.999021i	$0.485910\pi$
$38$		0			0
$39$	−1.30902	+	4.02874i	−0.209610	+	0.645115i
$40$		0			0
$41$	−3.04508	−	2.21238i	−0.475562	−	0.345516i	0.324043	−	0.946042i	$-0.394958\pi$
$41$	−3.04508	−	2.21238i	−0.475562	−	0.345516i	−0.799605	+	0.600526i	$0.794958\pi$
$42$		0			0
$43$	5.94427			0.906493			0.453246	−	0.891385i	$-0.350266\pi$
$43$	5.94427			0.906493			0.453246	+	0.891385i	$0.350266\pi$
$44$		0			0
$45$	0.618034			0.0921311
$46$		0			0
$47$	−7.78115	−	5.65334i	−1.13500	−	0.824624i	−0.148583	−	0.988900i	$-0.547471\pi$
$47$	−7.78115	−	5.65334i	−1.13500	−	0.824624i	−0.986414	+	0.164276i	$0.947471\pi$
$48$		0			0
$49$	−0.618034	+	1.90211i	−0.0882906	+	0.271730i
$50$		0			0
$51$	−0.309017	+	0.224514i	−0.0432710	+	0.0314382i
$52$		0			0
$53$	−2.64590	−	8.14324i	−0.363442	−	1.11856i	−0.950951	−	0.309342i	$-0.899891\pi$
$53$	−2.64590	−	8.14324i	−0.363442	−	1.11856i	0.587509	−	0.809218i	$-0.300109\pi$
$54$		0			0
$55$	−1.35410	−	1.53884i	−0.182587	−	0.207497i
$56$		0			0
$57$	0.427051	+	1.31433i	0.0565643	+	0.174087i
$58$		0			0
$59$	−3.11803	+	2.26538i	−0.405933	+	0.294928i	−0.771953	−	0.635679i	$-0.780720\pi$
$59$	−3.11803	+	2.26538i	−0.405933	+	0.294928i	0.366020	+	0.930607i	$0.380720\pi$
$60$		0			0
$61$	−2.04508	+	6.29412i	−0.261846	+	0.805880i	0.730557	+	0.682852i	$0.239261\pi$
$61$	−2.04508	+	6.29412i	−0.261846	+	0.805880i	−0.992403	+	0.123028i	$0.960739\pi$
$62$		0			0
$63$	1.80902	+	1.31433i	0.227915	+	0.165590i
$64$		0			0
$65$	2.61803			0.324727
$66$		0			0
$67$	−2.90983			−0.355492			−0.177746	−	0.984076i	$-0.556881\pi$
$67$	−2.90983			−0.355492			−0.177746	+	0.984076i	$0.556881\pi$
$68$		0			0
$69$	−4.42705	−	3.21644i	−0.532954	−	0.387214i
$70$		0			0
$71$	−0.663119	+	2.04087i	−0.0786977	+	0.242207i	−0.982663	−	0.185398i	$-0.940643\pi$
$71$	−0.663119	+	2.04087i	−0.0786977	+	0.242207i	0.903966	+	0.427605i	$0.140643\pi$
$72$		0			0
$73$	−7.09017	+	5.15131i	−0.829842	+	0.602915i	−0.919515	−	0.393056i	$-0.871418\pi$
$73$	−7.09017	+	5.15131i	−0.829842	+	0.602915i	0.0896729	+	0.995971i	$0.471418\pi$
$74$		0			0
$75$	1.42705	+	4.39201i	0.164782	+	0.507146i
$76$		0			0
$77$	−0.690983	−	7.38394i	−0.0787448	−	0.841478i
$78$		0			0
$79$	−1.92705	−	5.93085i	−0.216810	−	0.667273i	−0.999020	−	0.0442582i	$-0.985908\pi$
$79$	−1.92705	−	5.93085i	−0.216810	−	0.667273i	0.782210	−	0.623015i	$-0.214092\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−4.07295	+	12.5352i	−0.447064	+	1.37592i	0.433140	+	0.901327i	$0.357406\pi$
$83$	−4.07295	+	12.5352i	−0.447064	+	1.37592i	−0.880204	+	0.474595i	$0.842594\pi$
$84$		0			0
$85$	0.190983	+	0.138757i	0.0207150	+	0.0150503i
$86$		0			0
$87$	−2.00000			−0.214423
$88$		0			0
$89$	−7.76393			−0.822975			−0.411488	−	0.911415i	$-0.634991\pi$
$89$	−7.76393			−0.822975			−0.411488	+	0.911415i	$0.634991\pi$
$90$		0			0
$91$	7.66312	+	5.56758i	0.803313	+	0.583641i
$92$		0			0
$93$	2.50000	−	7.69421i	0.259238	−	0.797852i
$94$		0			0
$95$	0.690983	−	0.502029i	0.0708934	−	0.0515070i
$96$		0			0
$97$	−5.28115	−	16.2537i	−0.536220	−	1.65031i	−0.740999	−	0.671507i	$-0.765647\pi$
$97$	−5.28115	−	16.2537i	−0.536220	−	1.65031i	0.204779	−	0.978808i	$-0.434353\pi$
$98$		0			0
$99$	3.23607	+	0.726543i	0.325237	+	0.0730203i
$100$		0			0
$101$	0.218847	+	0.673542i	0.0217761	+	0.0670199i	0.961354	−	0.275315i	$-0.0887822\pi$
$101$	0.218847	+	0.673542i	0.0217761	+	0.0670199i	−0.939578	+	0.342335i	$0.888782\pi$
$102$		0			0
$103$	6.09017	−	4.42477i	0.600082	−	0.435985i	−0.245826	−	0.969314i	$-0.579059\pi$
$103$	6.09017	−	4.42477i	0.600082	−	0.435985i	0.845908	+	0.533329i	$0.179059\pi$
$104$		0			0
$105$	0.427051	−	1.31433i	0.0416759	−	0.128265i
$106$		0			0
$107$	13.8992	+	10.0984i	1.34369	+	0.976244i	0.999300	+	0.0374160i	$0.0119127\pi$
$107$	13.8992	+	10.0984i	1.34369	+	0.976244i	0.344385	+	0.938828i	$0.388087\pi$
$108$		0			0
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$		0			0
$111$	−6.70820			−0.636715
$112$		0			0
$113$	16.1353	+	11.7229i	1.51788	+	1.10280i	0.962527	+	0.271186i	$0.0874157\pi$
$113$	16.1353	+	11.7229i	1.51788	+	1.10280i	0.555350	+	0.831617i	$0.312584\pi$
$114$		0			0
$115$	−1.04508	+	3.21644i	−0.0974547	+	0.299935i
$116$		0			0
$117$	−3.42705	+	2.48990i	−0.316831	+	0.230191i
$118$		0			0
$119$	0.263932	+	0.812299i	0.0241946	+	0.0744633i
$120$		0			0
$121$	−5.28115	−	9.64932i	−0.480105	−	0.877211i
$122$		0			0
$123$	−1.16312	−	3.57971i	−0.104875	−	0.322772i
$124$		0			0
$125$	4.80902	−	3.49396i	0.430132	−	0.312509i
$126$		0			0
$127$	−5.32624	+	16.3925i	−0.472627	+	1.45460i	0.376504	+	0.926415i	$0.377126\pi$
$127$	−5.32624	+	16.3925i	−0.472627	+	1.45460i	−0.849131	+	0.528182i	$0.822874\pi$
$128$		0			0
$129$	4.80902	+	3.49396i	0.423410	+	0.307626i
$130$		0			0
$131$	16.2705			1.42156			0.710781	−	0.703414i	$-0.248342\pi$
$131$	16.2705			1.42156			0.710781	+	0.703414i	$0.248342\pi$
$132$		0			0
$133$	3.09017			0.267952
$134$		0			0
$135$	0.500000	+	0.363271i	0.0430331	+	0.0312654i
$136$		0			0
$137$	4.69098	−	14.4374i	0.400778	−	1.23347i	−0.523592	−	0.851969i	$-0.675408\pi$
$137$	4.69098	−	14.4374i	0.400778	−	1.23347i	0.924370	−	0.381498i	$-0.124592\pi$
$138$		0			0
$139$	10.7812	−	7.83297i	0.914445	−	0.664384i	−0.0276898	−	0.999617i	$-0.508815\pi$
$139$	10.7812	−	7.83297i	0.914445	−	0.664384i	0.942135	+	0.335233i	$0.108815\pi$
$140$		0			0
$141$	−2.97214	−	9.14729i	−0.250299	−	0.770341i
$142$		0			0
$143$	13.7082	+	3.07768i	1.14634	+	0.257369i
$144$		0			0
$145$	0.381966	+	1.17557i	0.0317206	+	0.0976258i
$146$		0			0
$147$	−1.61803	+	1.17557i	−0.133453	+	0.0969594i
$148$		0			0
$149$	0.545085	−	1.67760i	0.0446551	−	0.137434i	−0.926243	−	0.376926i	$-0.876981\pi$
$149$	0.545085	−	1.67760i	0.0446551	−	0.137434i	0.970898	+	0.239492i	$0.0769809\pi$
$150$		0			0
$151$	−14.0902	−	10.2371i	−1.14664	−	0.833084i	−0.158611	−	0.987341i	$-0.550702\pi$
$151$	−14.0902	−	10.2371i	−1.14664	−	0.833084i	−0.988031	+	0.154257i	$0.950702\pi$
$152$		0			0
$153$	−0.381966			−0.0308801
$154$		0			0
$155$	−5.00000			−0.401610
$156$		0			0
$157$	8.70820	+	6.32688i	0.694990	+	0.504940i	0.878297	−	0.478116i	$-0.158680\pi$
$157$	8.70820	+	6.32688i	0.694990	+	0.504940i	−0.183306	+	0.983056i	$0.558680\pi$
$158$		0			0
$159$	2.64590	−	8.14324i	0.209833	−	0.645801i
$160$		0			0
$161$	−9.89919	+	7.19218i	−0.780165	+	0.566823i
$162$		0			0
$163$	1.02786	+	3.16344i	0.0805085	+	0.247780i	0.983207	−	0.182494i	$-0.0584170\pi$
$163$	1.02786	+	3.16344i	0.0805085	+	0.247780i	−0.902698	+	0.430274i	$0.858417\pi$
$164$		0			0
$165$	−0.190983	−	2.04087i	−0.0148680	−	0.158882i
$166$		0			0
$167$	0.336881	+	1.03681i	0.0260686	+	0.0802310i	0.963244	−	0.268626i	$-0.0865697\pi$
$167$	0.336881	+	1.03681i	0.0260686	+	0.0802310i	−0.937176	+	0.348857i	$0.886570\pi$
$168$		0			0
$169$	−4.00000	+	2.90617i	−0.307692	+	0.223552i
$170$		0			0
$171$	−0.427051	+	1.31433i	−0.0326574	+	0.100509i
$172$		0			0
$173$	18.0623	+	13.1230i	1.37325	+	0.997726i	0.997475	+	0.0710154i	$0.0226240\pi$
$173$	18.0623	+	13.1230i	1.37325	+	0.997726i	0.375776	+	0.926710i	$0.377376\pi$
$174$		0			0
$175$	10.3262			0.780590
$176$		0			0
$177$	−3.85410			−0.289692
$178$		0			0
$179$	−0.190983	−	0.138757i	−0.0142747	−	0.0103712i	0.580625	−	0.814171i	$-0.302808\pi$
$179$	−0.190983	−	0.138757i	−0.0142747	−	0.0103712i	−0.594900	+	0.803800i	$0.702808\pi$
$180$		0			0
$181$	−7.10739	+	21.8743i	−0.528288	+	1.62590i	0.229432	+	0.973325i	$0.426313\pi$
$181$	−7.10739	+	21.8743i	−0.528288	+	1.62590i	−0.757720	+	0.652579i	$0.773687\pi$
$182$		0			0
$183$	−5.35410	+	3.88998i	−0.395787	+	0.287556i
$184$		0			0
$185$	1.28115	+	3.94298i	0.0941922	+	0.289894i
$186$		0			0
$187$	0.836881	+	0.951057i	0.0611988	+	0.0695481i
$188$		0			0
$189$	0.690983	+	2.12663i	0.0502616	+	0.154689i
$190$		0			0
$191$	0.0450850	−	0.0327561i	0.00326223	−	0.00237015i	−0.586153	−	0.810200i	$-0.699358\pi$
$191$	0.0450850	−	0.0327561i	0.00326223	−	0.00237015i	0.589415	+	0.807830i	$0.299358\pi$
$192$		0			0
$193$	6.44427	−	19.8334i	0.463869	−	1.42764i	−0.396531	−	0.918021i	$-0.629786\pi$
$193$	6.44427	−	19.8334i	0.463869	−	1.42764i	0.860400	−	0.509620i	$-0.170214\pi$
$194$		0			0
$195$	2.11803	+	1.53884i	0.151676	+	0.110199i
$196$		0			0
$197$	−9.61803			−0.685257			−0.342628	−	0.939471i	$-0.611317\pi$
$197$	−9.61803			−0.685257			−0.342628	+	0.939471i	$0.611317\pi$
$198$		0			0
$199$	−24.4164			−1.73083			−0.865417	−	0.501053i	$-0.832946\pi$
$199$	−24.4164			−1.73083			−0.865417	+	0.501053i	$0.832946\pi$
$200$		0			0
$201$	−2.35410	−	1.71036i	−0.166046	−	0.120639i
$202$		0			0
$203$	−1.38197	+	4.25325i	−0.0969950	+	0.298520i
$204$		0			0
$205$	−1.88197	+	1.36733i	−0.131442	+	0.0954984i
$206$		0			0
$207$	−1.69098	−	5.20431i	−0.117531	−	0.361725i
$208$		0			0
$209$	4.20820	−	1.81636i	0.291088	−	0.125640i
$210$		0			0
$211$	−7.97214	−	24.5357i	−0.548824	−	1.68911i	−0.711719	−	0.702465i	$-0.752083\pi$
$211$	−7.97214	−	24.5357i	−0.548824	−	1.68911i	0.162894	−	0.986644i	$-0.447917\pi$
$212$		0			0
$213$	−1.73607	+	1.26133i	−0.118953	+	0.0864247i
$214$		0			0
$215$	1.13525	−	3.49396i	0.0774237	−	0.238286i
$216$		0			0
$217$	−14.6353	−	10.6331i	−0.993506	−	0.721824i
$218$		0			0
$219$	−8.76393			−0.592212
$220$		0			0
$221$	−1.61803			−0.108841
$222$		0			0
$223$	10.8992	+	7.91872i	0.729864	+	0.530277i	0.889520	−	0.456896i	$-0.151039\pi$
$223$	10.8992	+	7.91872i	0.729864	+	0.530277i	−0.159657	+	0.987173i	$0.551039\pi$
$224$		0			0
$225$	−1.42705	+	4.39201i	−0.0951367	+	0.292801i
$226$		0			0
$227$	−11.2812	+	8.19624i	−0.748756	+	0.544003i	−0.895441	−	0.445180i	$-0.853140\pi$
$227$	−11.2812	+	8.19624i	−0.748756	+	0.544003i	0.146685	+	0.989183i	$0.453140\pi$
$228$		0			0
$229$	−5.67376	−	17.4620i	−0.374933	−	1.15392i	−0.943524	−	0.331304i	$-0.892511\pi$
$229$	−5.67376	−	17.4620i	−0.374933	−	1.15392i	0.568591	−	0.822620i	$-0.307489\pi$
$230$		0			0
$231$	3.78115	−	6.37988i	0.248782	−	0.419765i
$232$		0			0
$233$	6.98936	+	21.5110i	0.457888	+	1.40923i	0.867711	+	0.497069i	$0.165591\pi$
$233$	6.98936	+	21.5110i	0.457888	+	1.40923i	−0.409823	+	0.912165i	$0.634409\pi$
$234$		0			0
$235$	−4.80902	+	3.49396i	−0.313706	+	0.227921i
$236$		0			0
$237$	1.92705	−	5.93085i	0.125175	−	0.385250i
$238$		0			0
$239$	−9.78115	−	7.10642i	−0.632690	−	0.459676i	0.224641	−	0.974442i	$-0.427879\pi$
$239$	−9.78115	−	7.10642i	−0.632690	−	0.459676i	−0.857331	+	0.514765i	$0.827879\pi$
$240$		0			0
$241$	5.81966			0.374877			0.187439	−	0.982276i	$-0.439981\pi$
$241$	5.81966			0.374877			0.187439	+	0.982276i	$0.439981\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	1.00000	+	0.726543i	0.0638877	+	0.0464171i
$246$		0			0
$247$	−1.80902	+	5.56758i	−0.115105	+	0.354257i
$248$		0			0
$249$	−10.6631	+	7.74721i	−0.675748	+	0.490959i
$250$		0			0
$251$	−3.06231	−	9.42481i	−0.193291	−	0.594889i	−0.999992	−	0.00392916i	$-0.998749\pi$
$251$	−3.06231	−	9.42481i	−0.193291	−	0.594889i	0.806701	−	0.590959i	$-0.201251\pi$
$252$		0			0
$253$	−9.25329	+	15.6129i	−0.581749	+	0.981577i
$254$		0			0
$255$	0.0729490	+	0.224514i	0.00456824	+	0.0140596i
$256$		0			0
$257$	−5.35410	+	3.88998i	−0.333980	+	0.242650i	−0.742117	−	0.670270i	$-0.766178\pi$
$257$	−5.35410	+	3.88998i	−0.333980	+	0.242650i	0.408138	+	0.912920i	$0.366178\pi$
$258$		0			0
$259$	−4.63525	+	14.2658i	−0.288021	+	0.886437i
$260$		0			0
$261$	−1.61803	−	1.17557i	−0.100154	−	0.0727660i
$262$		0			0
$263$	6.50658			0.401213			0.200606	−	0.979672i	$-0.435709\pi$
$263$	6.50658			0.401213			0.200606	+	0.979672i	$0.435709\pi$
$264$		0			0
$265$	−5.29180			−0.325072
$266$		0			0
$267$	−6.28115	−	4.56352i	−0.384400	−	0.279283i
$268$		0			0
$269$	5.67376	−	17.4620i	0.345935	−	1.06468i	−0.615146	−	0.788413i	$-0.710903\pi$
$269$	5.67376	−	17.4620i	0.345935	−	1.06468i	0.961081	−	0.276266i	$-0.0890972\pi$
$270$		0			0
$271$	10.9721	−	7.97172i	0.666510	−	0.484248i	−0.202345	−	0.979314i	$-0.564856\pi$
$271$	10.9721	−	7.97172i	0.666510	−	0.484248i	0.868855	+	0.495067i	$0.164856\pi$
$272$		0			0
$273$	2.92705	+	9.00854i	0.177153	+	0.545221i
$274$		0			0
$275$	14.0623	−	6.06961i	0.847989	−	0.366011i
$276$		0			0
$277$	−3.31966	−	10.2169i	−0.199459	−	0.613872i	−0.999896	−	0.0144542i	$-0.995399\pi$
$277$	−3.31966	−	10.2169i	−0.199459	−	0.613872i	0.800436	−	0.599418i	$-0.204601\pi$
$278$		0			0
$279$	6.54508	−	4.75528i	0.391844	−	0.284691i
$280$		0			0
$281$	−4.70820	+	14.4904i	−0.280868	+	0.864423i	0.706739	+	0.707474i	$0.250166\pi$
$281$	−4.70820	+	14.4904i	−0.280868	+	0.864423i	−0.987607	+	0.156948i	$0.949834\pi$
$282$		0			0
$283$	−5.38197	−	3.91023i	−0.319925	−	0.232439i	0.416219	−	0.909265i	$-0.363355\pi$
$283$	−5.38197	−	3.91023i	−0.319925	−	0.232439i	−0.736143	+	0.676826i	$0.763355\pi$
$284$		0			0
$285$	0.854102			0.0505926
$286$		0			0
$287$	−8.41641			−0.496805
$288$		0			0
$289$	13.6353	+	9.90659i	0.802074	+	0.582741i
$290$		0			0
$291$	5.28115	−	16.2537i	0.309587	−	0.952810i
$292$		0			0
$293$	−19.5172	+	14.1801i	−1.14021	+	0.828410i	−0.987148	−	0.159807i	$-0.948913\pi$
$293$	−19.5172	+	14.1801i	−1.14021	+	0.828410i	−0.153060	+	0.988217i	$0.548913\pi$
$294$		0			0
$295$	0.736068	+	2.26538i	0.0428555	+	0.131896i
$296$		0			0
$297$	2.19098	+	2.48990i	0.127134	+	0.144479i
$298$		0			0
$299$	−7.16312	−	22.0458i	−0.414254	−	1.27494i
$300$		0			0
$301$	10.7533	−	7.81272i	0.619809	−	0.450318i
$302$		0			0
$303$	−0.218847	+	0.673542i	−0.0125724	+	0.0386940i
$304$		0			0
$305$	3.30902	+	2.40414i	0.189474	+	0.137661i
$306$		0			0
$307$	−14.7426			−0.841407			−0.420704	−	0.907198i	$-0.638217\pi$
$307$	−14.7426			−0.841407			−0.420704	+	0.907198i	$0.638217\pi$
$308$		0			0
$309$	7.52786			0.428245
$310$		0			0
$311$	−10.5172	−	7.64121i	−0.596377	−	0.433293i	0.248214	−	0.968705i	$-0.420156\pi$
$311$	−10.5172	−	7.64121i	−0.596377	−	0.433293i	−0.844591	+	0.535412i	$0.820156\pi$
$312$		0			0
$313$	−0.128677	+	0.396027i	−0.00727326	+	0.0223848i	−0.954627	−	0.297803i	$-0.903746\pi$
$313$	−0.128677	+	0.396027i	−0.00727326	+	0.0223848i	0.947354	+	0.320188i	$0.103746\pi$
$314$		0			0
$315$	1.11803	−	0.812299i	0.0629941	−	0.0457679i
$316$		0			0
$317$	−0.836881	−	2.57565i	−0.0470039	−	0.144663i	0.924800	−	0.380454i	$-0.124232\pi$
$317$	−0.836881	−	2.57565i	−0.0470039	−	0.144663i	−0.971804	+	0.235790i	$0.924232\pi$
$318$		0			0
$319$	0.618034	+	6.60440i	0.0346033	+	0.369775i
$320$		0			0
$321$	5.30902	+	16.3395i	0.296320	+	0.911981i
$322$		0			0
$323$	−0.427051	+	0.310271i	−0.0237618	+	0.0172639i
$324$		0			0
$325$	−6.04508	+	18.6049i	−0.335321	+	1.03201i
$326$		0			0
$327$	9.70820	+	7.05342i	0.536865	+	0.390055i
$328$		0			0
$329$	−21.5066			−1.18570
$330$		0			0
$331$	−4.52786			−0.248874			−0.124437	−	0.992228i	$-0.539712\pi$
$331$	−4.52786			−0.248874			−0.124437	+	0.992228i	$0.539712\pi$
$332$		0			0
$333$	−5.42705	−	3.94298i	−0.297401	−	0.216074i
$334$		0			0
$335$	−0.555728	+	1.71036i	−0.0303627	+	0.0934467i
$336$		0			0
$337$	27.1803	−	19.7477i	1.48061	−	1.07572i	0.503247	−	0.864143i	$-0.332139\pi$
$337$	27.1803	−	19.7477i	1.48061	−	1.07572i	0.977360	−	0.211582i	$-0.0678615\pi$
$338$		0			0
$339$	6.16312	+	18.9681i	0.334735	+	1.03021i
$340$		0			0
$341$	−26.1803	−	5.87785i	−1.41774	−	0.318304i
$342$		0			0
$343$	6.21885	+	19.1396i	0.335786	+	1.03344i
$344$		0			0
$345$	−2.73607	+	1.98787i	−0.147305	+	0.107023i
$346$		0			0
$347$	7.52786	−	23.1684i	0.404117	−	1.24374i	−0.517513	−	0.855675i	$-0.673142\pi$
$347$	7.52786	−	23.1684i	0.404117	−	1.24374i	0.921630	−	0.388069i	$-0.126858\pi$
$348$		0			0
$349$	13.1353	+	9.54332i	0.703114	+	0.510842i	0.880945	−	0.473219i	$-0.156908\pi$
$349$	13.1353	+	9.54332i	0.703114	+	0.510842i	−0.177831	+	0.984061i	$0.556908\pi$
$350$		0			0
$351$	−4.23607			−0.226105
$352$		0			0
$353$	32.9443			1.75345			0.876723	−	0.480995i	$-0.159724\pi$
$353$	32.9443			1.75345			0.876723	+	0.480995i	$0.159724\pi$
$354$		0			0
$355$	1.07295	+	0.779543i	0.0569462	+	0.0413739i
$356$		0			0
$357$	−0.263932	+	0.812299i	−0.0139688	+	0.0429914i
$358$		0			0
$359$	19.0902	−	13.8698i	1.00754	−	0.732021i	0.0438488	−	0.999038i	$-0.486038\pi$
$359$	19.0902	−	13.8698i	1.00754	−	0.732021i	0.963692	+	0.267017i	$0.0860380\pi$
$360$		0			0
$361$	−5.28115	−	16.2537i	−0.277955	−	0.855459i
$362$		0			0
$363$	1.39919	−	10.9106i	0.0734383	−	0.572661i
$364$		0			0
$365$	1.67376	+	5.15131i	0.0876087	+	0.269632i
$366$		0			0
$367$	−3.11803	+	2.26538i	−0.162760	+	0.118252i	−0.666184	−	0.745787i	$-0.732073\pi$
$367$	−3.11803	+	2.26538i	−0.162760	+	0.118252i	0.503424	+	0.864040i	$0.332073\pi$
$368$		0			0
$369$	1.16312	−	3.57971i	0.0605496	−	0.186352i
$370$		0			0
$371$	−15.4894	−	11.2537i	−0.804167	−	0.584262i
$372$		0			0
$373$	14.4164			0.746453			0.373227	−	0.927740i	$-0.378251\pi$
$373$	14.4164			0.746453			0.373227	+	0.927740i	$0.378251\pi$
$374$		0			0
$375$	5.94427			0.306961
$376$		0			0
$377$	−6.85410	−	4.97980i	−0.353004	−	0.256473i
$378$		0			0
$379$	−10.5451	+	32.4544i	−0.541665	+	1.66707i	0.187126	+	0.982336i	$0.440083\pi$
$379$	−10.5451	+	32.4544i	−0.541665	+	1.66707i	−0.728791	+	0.684736i	$0.759917\pi$
$380$		0			0
$381$	−13.9443	+	10.1311i	−0.714387	+	0.519032i
$382$		0			0
$383$	7.83688	+	24.1194i	0.400446	+	1.23245i	0.924638	+	0.380846i	$0.124367\pi$
$383$	7.83688	+	24.1194i	0.400446	+	1.23245i	−0.524193	+	0.851600i	$0.675633\pi$
$384$		0			0
$385$	−4.47214	−	1.00406i	−0.227921	−	0.0511715i
$386$		0			0
$387$	1.83688	+	5.65334i	0.0933739	+	0.287375i
$388$		0			0
$389$	18.1631	−	13.1963i	0.920907	−	0.669078i	−0.0228428	−	0.999739i	$-0.507272\pi$
$389$	18.1631	−	13.1963i	0.920907	−	0.669078i	0.943750	+	0.330661i	$0.107272\pi$
$390$		0			0
$391$	0.645898	−	1.98787i	0.0326645	−	0.100531i
$392$		0			0
$393$	13.1631	+	9.56357i	0.663992	+	0.482418i
$394$		0			0
$395$	−3.85410			−0.193921
$396$		0			0
$397$	35.1803			1.76565			0.882825	−	0.469701i	$-0.155638\pi$
$397$	35.1803			1.76565			0.882825	+	0.469701i	$0.155638\pi$
$398$		0			0
$399$	2.50000	+	1.81636i	0.125157	+	0.0909316i
$400$		0			0
$401$	5.02786	−	15.4742i	0.251080	−	0.772743i	−0.743497	−	0.668739i	$-0.766834\pi$
$401$	5.02786	−	15.4742i	0.251080	−	0.772743i	0.994577	−	0.104004i	$-0.0331656\pi$
$402$		0			0
$403$	27.7254	−	20.1437i	1.38110	−	1.00343i
$404$		0			0
$405$	0.190983	+	0.587785i	0.00949002	+	0.0292073i
$406$		0			0
$407$	2.07295	+	22.1518i	0.102752	+	1.09802i
$408$		0			0
$409$	−1.05573	−	3.24920i	−0.0522024	−	0.160662i	0.921557	−	0.388244i	$-0.126918\pi$
$409$	−1.05573	−	3.24920i	−0.0522024	−	0.160662i	−0.973759	+	0.227581i	$0.926918\pi$
$410$		0			0
$411$	12.2812	−	8.92278i	0.605785	−	0.440128i
$412$		0			0
$413$	−2.66312	+	8.19624i	−0.131044	+	0.403310i
$414$		0			0
$415$	6.59017	+	4.78804i	0.323499	+	0.235036i
$416$		0			0
$417$	13.3262			0.652589
$418$		0			0
$419$	−0.798374			−0.0390031			−0.0195016	−	0.999810i	$-0.506208\pi$
$419$	−0.798374			−0.0390031			−0.0195016	+	0.999810i	$0.506208\pi$
$420$		0			0
$421$	−3.26393	−	2.37139i	−0.159074	−	0.115574i	0.505401	−	0.862885i	$-0.331345\pi$
$421$	−3.26393	−	2.37139i	−0.159074	−	0.115574i	−0.664475	+	0.747311i	$0.731345\pi$
$422$		0			0
$423$	2.97214	−	9.14729i	0.144510	−	0.444757i
$424$		0			0
$425$	−1.42705	+	1.03681i	−0.0692221	+	0.0502928i
$426$		0			0
$427$	4.57295	+	14.0741i	0.221301	+	0.681093i
$428$		0			0
$429$	9.28115	+	10.5474i	0.448098	+	0.509232i
$430$		0			0
$431$	−3.55573	−	10.9434i	−0.171273	−	0.527125i	0.828170	−	0.560477i	$-0.189382\pi$
$431$	−3.55573	−	10.9434i	−0.171273	−	0.527125i	−0.999444	+	0.0333512i	$0.989382\pi$
$432$		0			0
$433$	−9.32624	+	6.77591i	−0.448190	+	0.325629i	−0.788881	−	0.614546i	$-0.789339\pi$
$433$	−9.32624	+	6.77591i	−0.448190	+	0.325629i	0.340690	+	0.940176i	$0.389339\pi$
$434$		0			0
$435$	−0.381966	+	1.17557i	−0.0183139	+	0.0563643i
$436$		0			0
$437$	−6.11803	−	4.44501i	−0.292665	−	0.212634i
$438$		0			0
$439$	10.0557			0.479934			0.239967	−	0.970781i	$-0.422863\pi$
$439$	10.0557			0.479934			0.239967	+	0.970781i	$0.422863\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$		0			0
$443$	−22.0344	−	16.0090i	−1.04689	−	0.760609i	−0.0752697	−	0.997163i	$-0.523982\pi$
$443$	−22.0344	−	16.0090i	−1.04689	−	0.760609i	−0.971618	+	0.236555i	$0.923982\pi$
$444$		0			0
$445$	−1.48278	+	4.56352i	−0.0702905	+	0.216332i
$446$		0			0
$447$	1.42705	−	1.03681i	0.0674972	−	0.0490396i
$448$		0			0
$449$	0.909830	+	2.80017i	0.0429375	+	0.132148i	0.970227	−	0.242196i	$-0.0778678\pi$
$449$	0.909830	+	2.80017i	0.0429375	+	0.132148i	−0.927290	+	0.374344i	$0.877868\pi$
$450$		0			0
$451$	−11.4615	+	4.94704i	−0.539701	+	0.232947i
$452$		0			0
$453$	−5.38197	−	16.5640i	−0.252867	−	0.778244i
$454$		0			0
$455$	4.73607	−	3.44095i	0.222030	−	0.161314i
$456$		0			0
$457$	11.1180	−	34.2178i	0.520080	−	1.60064i	−0.253765	−	0.967266i	$-0.581669\pi$
$457$	11.1180	−	34.2178i	0.520080	−	1.60064i	0.773845	−	0.633375i	$-0.218331\pi$
$458$		0			0
$459$	−0.309017	−	0.224514i	−0.0144237	−	0.0104794i
$460$		0			0
$461$	−9.27051			−0.431771			−0.215885	−	0.976419i	$-0.569264\pi$
$461$	−9.27051			−0.431771			−0.215885	+	0.976419i	$0.569264\pi$
$462$		0			0
$463$	28.4508			1.32222			0.661112	−	0.750288i	$-0.270085\pi$
$463$	28.4508			1.32222			0.661112	+	0.750288i	$0.270085\pi$
$464$		0			0
$465$	−4.04508	−	2.93893i	−0.187586	−	0.136289i
$466$		0			0
$467$	−2.07295	+	6.37988i	−0.0959246	+	0.295226i	−0.987494	−	0.157659i	$-0.949605\pi$
$467$	−2.07295	+	6.37988i	−0.0959246	+	0.295226i	0.891569	+	0.452885i	$0.149605\pi$
$468$		0			0
$469$	−5.26393	+	3.82447i	−0.243066	+	0.176598i
$470$		0			0
$471$	3.32624	+	10.2371i	0.153265	+	0.471701i
$472$		0			0
$473$	10.0517	−	16.9600i	0.462176	−	0.779822i
$474$		0			0
$475$	1.97214	+	6.06961i	0.0904878	+	0.278493i
$476$		0			0
$477$	6.92705	−	5.03280i	0.317168	−	0.230436i
$478$		0			0
$479$	1.97214	−	6.06961i	0.0901092	−	0.277328i	−0.895839	−	0.444379i	$-0.853424\pi$
$479$	1.97214	−	6.06961i	0.0901092	−	0.277328i	0.985948	+	0.167051i	$0.0534245\pi$
$480$		0			0
$481$	−22.9894	−	16.7027i	−1.04822	−	0.761580i
$482$		0			0
$483$	−12.2361			−0.556760
$484$		0			0
$485$	−10.5623			−0.479610
$486$		0			0
$487$	7.28115	+	5.29007i	0.329941	+	0.239716i	0.740405	−	0.672161i	$-0.234634\pi$
$487$	7.28115	+	5.29007i	0.329941	+	0.239716i	−0.410465	+	0.911876i	$0.634634\pi$
$488$		0			0
$489$	−1.02786	+	3.16344i	−0.0464816	+	0.143056i
$490$		0			0
$491$	−19.6353	+	14.2658i	−0.886127	+	0.643809i	−0.934865	−	0.355003i	$-0.884480\pi$
$491$	−19.6353	+	14.2658i	−0.886127	+	0.643809i	0.0487386	+	0.998812i	$0.484480\pi$
$492$		0			0
$493$	−0.236068	−	0.726543i	−0.0106320	−	0.0327218i
$494$		0			0
$495$	1.04508	−	1.76336i	0.0469731	−	0.0792569i
$496$		0			0
$497$	1.48278	+	4.56352i	0.0665117	+	0.204702i
$498$		0			0
$499$	−9.35410	+	6.79615i	−0.418747	+	0.304238i	−0.777134	−	0.629336i	$-0.783327\pi$
$499$	−9.35410	+	6.79615i	−0.418747	+	0.304238i	0.358386	+	0.933573i	$0.383327\pi$
$500$		0			0
$501$	−0.336881	+	1.03681i	−0.0150507	+	0.0463214i
$502$		0			0
$503$	27.1803	+	19.7477i	1.21191	+	0.880505i	0.995403	−	0.0957755i	$-0.0305331\pi$
$503$	27.1803	+	19.7477i	1.21191	+	0.880505i	0.216508	+	0.976281i	$0.430533\pi$
$504$		0			0
$505$	0.437694			0.0194771
$506$		0			0
$507$	−4.94427			−0.219583
$508$		0			0
$509$	−30.2533	−	21.9803i	−1.34095	−	0.974260i	−0.999408	−	0.0343943i	$-0.989050\pi$
$509$	−30.2533	−	21.9803i	−1.34095	−	0.974260i	−0.341545	−	0.939865i	$-0.610950\pi$
$510$		0			0
$511$	−6.05573	+	18.6376i	−0.267890	+	0.824480i
$512$		0			0
$513$	−1.11803	+	0.812299i	−0.0493624	+	0.0358639i
$514$		0			0
$515$	−1.43769	−	4.42477i	−0.0633524	−	0.194979i
$516$		0			0
$517$	−29.2877	+	12.6412i	−1.28807	+	0.555962i
$518$		0			0
$519$	6.89919	+	21.2335i	0.302841	+	0.932048i
$520$		0			0
$521$	−30.6525	+	22.2703i	−1.34291	+	0.975681i	−0.343578	+	0.939124i	$0.611639\pi$
$521$	−30.6525	+	22.2703i	−1.34291	+	0.975681i	−0.999332	+	0.0365565i	$0.988361\pi$
$522$		0			0
$523$	2.26393	−	6.96767i	0.0989948	−	0.304675i	−0.889279	−	0.457364i	$-0.848793\pi$
$523$	2.26393	−	6.96767i	0.0989948	−	0.304675i	0.988274	+	0.152690i	$0.0487935\pi$
$524$		0			0
$525$	8.35410	+	6.06961i	0.364603	+	0.264900i
$526$		0			0
$527$	3.09017			0.134610
$528$		0			0
$529$	6.94427			0.301925
$530$		0			0
$531$	−3.11803	−	2.26538i	−0.135311	−	0.0983093i
$532$		0			0
$533$	4.92705	−	15.1639i	0.213414	−	0.656822i
$534$		0			0
$535$	8.59017	−	6.24112i	0.371385	−	0.269827i
$536$		0			0
$537$	−0.0729490	−	0.224514i	−0.00314798	−	0.00968849i
$538$		0			0
$539$	4.38197	+	4.97980i	0.188745	+	0.214495i
$540$		0			0
$541$	−1.19098	−	3.66547i	−0.0512044	−	0.157591i	0.922185	−	0.386750i	$-0.126402\pi$
$541$	−1.19098	−	3.66547i	−0.0512044	−	0.157591i	−0.973389	+	0.229159i	$0.926402\pi$
$542$		0			0
$543$	−18.6074	+	13.5191i	−0.798520	+	0.580158i
$544$		0			0
$545$	2.29180	−	7.05342i	0.0981698	−	0.302135i
$546$		0			0
$547$	−25.8713	−	18.7966i	−1.10618	−	0.803685i	−0.124120	−	0.992267i	$-0.539611\pi$
$547$	−25.8713	−	18.7966i	−1.10618	−	0.803685i	−0.982057	+	0.188582i	$0.939611\pi$
$548$		0			0
$549$	−6.61803			−0.282451
$550$		0			0
$551$	−2.76393			−0.117747
$552$		0			0
$553$	−11.2812	−	8.19624i	−0.479723	−	0.348539i
$554$		0			0
$555$	−1.28115	+	3.94298i	−0.0543819	+	0.167370i
$556$		0			0
$557$	31.8607	−	23.1481i	1.34998	−	0.980818i	0.350968	−	0.936388i	$-0.385853\pi$
$557$	31.8607	−	23.1481i	1.34998	−	0.980818i	0.999012	−	0.0444306i	$-0.0141474\pi$
$558$		0			0
$559$	7.78115	+	23.9479i	0.329108	+	1.01289i
$560$		0			0
$561$	0.118034	+	1.26133i	0.00498340	+	0.0532533i
$562$		0			0
$563$	8.48936	+	26.1276i	0.357784	+	1.10115i	0.954378	+	0.298602i	$0.0965203\pi$
$563$	8.48936	+	26.1276i	0.357784	+	1.10115i	−0.596594	+	0.802543i	$0.703480\pi$
$564$		0			0
$565$	9.97214	−	7.24518i	0.419531	−	0.304807i
$566$		0			0
$567$	−0.690983	+	2.12663i	−0.0290186	+	0.0893099i
$568$		0			0
$569$	−25.1803	−	18.2946i	−1.05561	−	0.766949i	−0.0823427	−	0.996604i	$-0.526240\pi$
$569$	−25.1803	−	18.2946i	−1.05561	−	0.766949i	−0.973272	+	0.229655i	$0.926240\pi$
$570$		0			0
$571$	−25.8541			−1.08196			−0.540980	−	0.841035i	$-0.681947\pi$
$571$	−25.8541			−1.08196			−0.540980	+	0.841035i	$0.681947\pi$
$572$		0			0
$573$	0.0557281			0.00232807
$574$		0			0
$575$	−20.4443	−	14.8536i	−0.852585	−	0.619439i
$576$		0			0
$577$	−6.96556	+	21.4378i	−0.289980	+	0.892467i	0.694882	+	0.719124i	$0.255457\pi$
$577$	−6.96556	+	21.4378i	−0.289980	+	0.892467i	−0.984862	+	0.173342i	$0.944543\pi$
$578$		0			0
$579$	16.8713	−	12.2577i	0.701148	−	0.509414i
$580$		0			0
$581$	9.10739	+	28.0297i	0.377838	+	1.16287i
$582$		0			0
$583$	−27.7082	−	6.22088i	−1.14756	−	0.257642i
$584$		0			0
$585$	0.809017	+	2.48990i	0.0334487	+	0.102945i
$586$		0			0
$587$	−18.6074	+	13.5191i	−0.768009	+	0.557991i	−0.901356	−	0.433078i	$-0.857427\pi$
$587$	−18.6074	+	13.5191i	−0.768009	+	0.557991i	0.133347	+	0.991069i	$0.457427\pi$
$588$		0			0
$589$	3.45492	−	10.6331i	0.142357	−	0.438131i
$590$		0			0
$591$	−7.78115	−	5.65334i	−0.320074	−	0.232547i
$592$		0			0
$593$	−40.7984			−1.67539			−0.837694	−	0.546140i	$-0.816097\pi$
$593$	−40.7984			−1.67539			−0.837694	+	0.546140i	$0.816097\pi$
$594$		0			0
$595$	0.527864			0.0216403
$596$		0			0
$597$	−19.7533	−	14.3516i	−0.808448	−	0.587372i
$598$		0			0
$599$	2.27051	−	6.98791i	0.0927705	−	0.285518i	−0.893896	−	0.448275i	$-0.852039\pi$
$599$	2.27051	−	6.98791i	0.0927705	−	0.285518i	0.986666	+	0.162757i	$0.0520386\pi$
$600$		0			0
$601$	−9.66312	+	7.02067i	−0.394167	+	0.286379i	−0.767161	−	0.641455i	$-0.778331\pi$
$601$	−9.66312	+	7.02067i	−0.394167	+	0.286379i	0.372994	+	0.927834i	$0.378331\pi$
$602$		0			0
$603$	−0.899187	−	2.76741i	−0.0366177	−	0.112698i
$604$		0			0
$605$	−6.68034	+	1.26133i	−0.271594	+	0.0512802i
$606$		0			0
$607$	−1.26393	−	3.88998i	−0.0513014	−	0.157890i	0.922124	−	0.386895i	$-0.126453\pi$
$607$	−1.26393	−	3.88998i	−0.0513014	−	0.157890i	−0.973425	+	0.229006i	$0.926453\pi$
$608$		0			0
$609$	−3.61803	+	2.62866i	−0.146610	+	0.106518i
$610$		0			0
$611$	12.5902	−	38.7486i	0.509344	−	1.56760i
$612$		0			0
$613$	−13.0902	−	9.51057i	−0.528707	−	0.384128i	0.291167	−	0.956672i	$-0.405957\pi$
$613$	−13.0902	−	9.51057i	−0.528707	−	0.384128i	−0.819874	+	0.572544i	$0.805957\pi$
$614$		0			0
$615$	−2.32624			−0.0938030
$616$		0			0
$617$	11.6525			0.469111			0.234556	−	0.972103i	$-0.424637\pi$
$617$	11.6525			0.469111			0.234556	+	0.972103i	$0.424637\pi$
$618$		0			0
$619$	13.6631	+	9.92684i	0.549167	+	0.398993i	0.827478	−	0.561498i	$-0.189775\pi$
$619$	13.6631	+	9.92684i	0.549167	+	0.398993i	−0.278311	+	0.960491i	$0.589775\pi$
$620$		0			0
$621$	1.69098	−	5.20431i	0.0678568	−	0.208842i
$622$		0			0
$623$	−14.0451	+	10.2044i	−0.562704	+	0.408829i
$624$		0			0
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$		0			0
$627$	4.47214	+	1.00406i	0.178600	+	0.0400982i
$628$		0			0
$629$	−0.791796	−	2.43690i	−0.0315710	−	0.0971655i
$630$		0			0
$631$	1.78115	−	1.29408i	0.0709066	−	0.0515166i	−0.551767	−	0.833998i	$-0.686046\pi$
$631$	1.78115	−	1.29408i	0.0709066	−	0.0515166i	0.622674	+	0.782481i	$0.286046\pi$
$632$		0			0
$633$	7.97214	−	24.5357i	0.316864	−	0.975207i
$634$		0			0
$635$	8.61803	+	6.26137i	0.341996	+	0.248475i
$636$		0			0
$637$	−8.47214			−0.335678
$638$		0			0
$639$	−2.14590			−0.0848904
$640$		0			0
$641$	34.5344	+	25.0907i	1.36403	+	0.991025i	0.998177	+	0.0603513i	$0.0192221\pi$
$641$	34.5344	+	25.0907i	1.36403	+	0.991025i	0.365851	+	0.930673i	$0.380778\pi$
$642$		0			0
$643$	7.64590	−	23.5317i	0.301525	−	0.927998i	−0.679426	−	0.733744i	$-0.737771\pi$
$643$	7.64590	−	23.5317i	0.301525	−	0.927998i	0.980951	−	0.194254i	$-0.0622287\pi$
$644$		0			0
$645$	2.97214	−	2.15938i	0.117028	−	0.0850256i
$646$		0			0
$647$	9.64590	+	29.6870i	0.379219	+	1.16712i	0.940588	+	0.339551i	$0.110275\pi$
$647$	9.64590	+	29.6870i	0.379219	+	1.16712i	−0.561368	+	0.827566i	$0.689725\pi$
$648$		0			0
$649$	1.19098	+	12.7270i	0.0467502	+	0.499579i
$650$		0			0
$651$	−5.59017	−	17.2048i	−0.219096	−	0.674308i
$652$		0			0
$653$	22.8713	−	16.6170i	0.895024	−	0.650273i	−0.0421591	−	0.999111i	$-0.513424\pi$
$653$	22.8713	−	16.6170i	0.895024	−	0.650273i	0.937183	+	0.348838i	$0.113424\pi$
$654$		0			0
$655$	3.10739	−	9.56357i	0.121416	−	0.373679i
$656$		0			0
$657$	−7.09017	−	5.15131i	−0.276614	−	0.200972i
$658$		0			0
$659$	−13.1246			−0.511262			−0.255631	−	0.966774i	$-0.582283\pi$
$659$	−13.1246			−0.511262			−0.255631	+	0.966774i	$0.582283\pi$
$660$		0			0
$661$	23.6180			0.918635			0.459318	−	0.888272i	$-0.348094\pi$
$661$	23.6180			0.918635			0.459318	+	0.888272i	$0.348094\pi$
$662$		0			0
$663$	−1.30902	−	0.951057i	−0.0508380	−	0.0369360i
$664$		0			0
$665$	0.590170	−	1.81636i	0.0228858	−	0.0704353i
$666$		0			0
$667$	8.85410	−	6.43288i	0.342832	−	0.249082i
$668$		0			0
$669$	4.16312	+	12.8128i	0.160955	+	0.495370i
$670$		0			0
$671$	14.5000	+	16.4782i	0.559766	+	0.636135i
$672$		0			0
$673$	5.83688	+	17.9641i	0.224995	+	0.692464i	0.998292	+	0.0584200i	$0.0186063\pi$
$673$	5.83688	+	17.9641i	0.224995	+	0.692464i	−0.773297	+	0.634044i	$0.781394\pi$
$674$		0			0
$675$	−3.73607	+	2.71441i	−0.143801	+	0.104478i
$676$		0			0
$677$	−7.81966	+	24.0664i	−0.300534	+	0.924948i	0.680772	+	0.732495i	$0.261644\pi$
$677$	−7.81966	+	24.0664i	−0.300534	+	0.924948i	−0.981306	+	0.192453i	$0.938356\pi$
$678$		0			0
$679$	−30.9164	−	22.4621i	−1.18646	−	0.862016i
$680$		0			0
$681$	−13.9443			−0.534346
$682$		0			0
$683$	25.4721			0.974664			0.487332	−	0.873217i	$-0.337970\pi$
$683$	25.4721			0.974664			0.487332	+	0.873217i	$0.337970\pi$
$684$		0			0
$685$	−7.59017	−	5.51458i	−0.290005	−	0.210701i
$686$		0			0
$687$	5.67376	−	17.4620i	0.216468	−	0.666219i
$688$		0			0
$689$	29.3435	−	21.3193i	1.11790	−	0.812200i
$690$		0			0
$691$	−10.2361	−	31.5034i	−0.389398	−	1.19844i	−0.933239	−	0.359256i	$-0.883030\pi$
$691$	−10.2361	−	31.5034i	−0.389398	−	1.19844i	0.543841	−	0.839189i	$-0.316970\pi$
$692$		0			0
$693$	6.80902	−	2.93893i	0.258653	−	0.111641i
$694$		0			0
$695$	−2.54508	−	7.83297i	−0.0965406	−	0.297121i
$696$		0			0
$697$	1.16312	−	0.845055i	0.0440563	−	0.0320088i
$698$		0			0
$699$	−6.98936	+	21.5110i	−0.264362	+	0.813622i
$700$		0			0
$701$	34.0967	+	24.7727i	1.28782	+	0.935653i	0.999759	−	0.0219597i	$-0.00699056\pi$
$701$	34.0967	+	24.7727i	1.28782	+	0.935653i	0.288058	+	0.957613i	$0.406991\pi$
$702$		0			0
$703$	−9.27051			−0.349644
$704$		0			0
$705$	−5.94427			−0.223874
$706$		0			0
$707$	1.28115	+	0.930812i	0.0481827	+	0.0350068i
$708$		0			0
$709$	−7.11803	+	21.9071i	−0.267323	+	0.822737i	0.723826	+	0.689983i	$0.242382\pi$
$709$	−7.11803	+	21.9071i	−0.267323	+	0.822737i	−0.991149	+	0.132754i	$0.957618\pi$
$710$		0			0
$711$	5.04508	−	3.66547i	0.189205	−	0.137466i
$712$		0			0
$713$	13.6803	+	42.1038i	0.512333	+	1.57680i
$714$		0			0
$715$	4.42705	−	7.46969i	0.165562	−	0.279351i
$716$		0			0
$717$	−3.73607	−	11.4984i	−0.139526	−	0.429417i
$718$		0			0
$719$	6.33688	−	4.60401i	0.236326	−	0.171701i	−0.463319	−	0.886192i	$-0.653342\pi$
$719$	6.33688	−	4.60401i	0.236326	−	0.171701i	0.699645	+	0.714491i	$0.253342\pi$
$720$		0			0
$721$	5.20163	−	16.0090i	0.193719	−	0.596205i
$722$		0			0
$723$	4.70820	+	3.42071i	0.175100	+	0.127218i
$724$		0			0
$725$	−9.23607			−0.343019
$726$		0			0
$727$	17.4377			0.646728			0.323364	−	0.946275i	$-0.395186\pi$
$727$	17.4377			0.646728			0.323364	+	0.946275i	$0.395186\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−0.701626	+	2.15938i	−0.0259506	+	0.0798677i
$732$		0			0
$733$	−16.3262	+	11.8617i	−0.603023	+	0.438122i	−0.846951	−	0.531671i	$-0.821564\pi$
$733$	−16.3262	+	11.8617i	−0.603023	+	0.438122i	0.243927	+	0.969794i	$0.421564\pi$
$734$		0			0
$735$	0.381966	+	1.17557i	0.0140890	+	0.0433616i
$736$		0			0
$737$	−4.92047	+	8.30224i	−0.181248	+	0.305817i
$738$		0			0
$739$	−2.98278	−	9.18005i	−0.109723	−	0.337694i	0.881087	−	0.472955i	$-0.156813\pi$
$739$	−2.98278	−	9.18005i	−0.109723	−	0.337694i	−0.990810	+	0.135261i	$0.956813\pi$
$740$		0			0
$741$	−4.73607	+	3.44095i	−0.173984	+	0.126407i
$742$		0			0
$743$	0.871323	−	2.68166i	0.0319657	−	0.0983804i	−0.933801	−	0.357794i	$-0.883529\pi$
$743$	0.871323	−	2.68166i	0.0319657	−	0.0983804i	0.965766	+	0.259413i	$0.0835291\pi$
$744$		0			0
$745$	−0.881966	−	0.640786i	−0.0323127	−	0.0234766i
$746$		0			0
$747$	−13.1803			−0.482243
$748$		0			0
$749$	38.4164			1.40370
$750$		0			0
$751$	13.9164	+	10.1109i	0.507817	+	0.368951i	0.811995	−	0.583665i	$-0.198382\pi$
$751$	13.9164	+	10.1109i	0.507817	+	0.368951i	−0.304178	+	0.952615i	$0.598382\pi$
$752$		0			0
$753$	3.06231	−	9.42481i	0.111597	−	0.343459i
$754$		0			0
$755$	−8.70820	+	6.32688i	−0.316924	+	0.230259i
$756$		0			0
$757$	1.65654	+	5.09831i	0.0602080	+	0.185301i	0.976637	−	0.214897i	$-0.0689414\pi$
$757$	1.65654	+	5.09831i	0.0602080	+	0.185301i	−0.916429	+	0.400198i	$0.868941\pi$
$758$		0			0
$759$	−16.6631	+	7.19218i	−0.604833	+	0.261060i
$760$		0			0
$761$	3.30902	+	10.1841i	0.119952	+	0.369174i	0.992948	−	0.118554i	$-0.0378259\pi$
$761$	3.30902	+	10.1841i	0.119952	+	0.369174i	−0.872996	+	0.487728i	$0.837826\pi$
$762$		0			0
$763$	21.7082	−	15.7719i	0.785890	−	0.570982i
$764$		0			0
$765$	−0.0729490	+	0.224514i	−0.00263748	+	0.00811732i
$766$		0			0
$767$	−13.2082	−	9.59632i	−0.476921	−	0.346503i
$768$		0			0
$769$	12.9098			0.465540			0.232770	−	0.972532i	$-0.425221\pi$
$769$	12.9098			0.465540			0.232770	+	0.972532i	$0.425221\pi$
$770$		0			0
$771$	−6.61803			−0.238343
$772$		0			0
$773$	8.57295	+	6.22861i	0.308348	+	0.224028i	0.731187	−	0.682177i	$-0.238967\pi$
$773$	8.57295	+	6.22861i	0.308348	+	0.224028i	−0.422840	+	0.906205i	$0.638967\pi$
$774$		0			0
$775$	11.5451	−	35.5321i	0.414712	−	1.27635i
$776$		0			0
$777$	−12.1353	+	8.81678i	−0.435350	+	0.316300i
$778$		0			0
$779$	−1.60739	−	4.94704i	−0.0575908	−	0.177246i
$780$		0			0
$781$	4.70163	+	5.34307i	0.168237	+	0.191190i
$782$		0			0
$783$	−0.618034	−	1.90211i	−0.0220867	−	0.0679760i
$784$		0			0
$785$	5.38197	−	3.91023i	0.192091	−	0.139562i
$786$		0			0
$787$	−2.23607	+	6.88191i	−0.0797072	+	0.245314i	−0.982967	−	0.183779i	$-0.941167\pi$
$787$	−2.23607	+	6.88191i	−0.0797072	+	0.245314i	0.903260	+	0.429093i	$0.141167\pi$
$788$		0			0
$789$	5.26393	+	3.82447i	0.187401	+	0.136155i
$790$		0			0
$791$	44.5967			1.58568
$792$		0			0
$793$	−28.0344			−0.995532
$794$		0			0
$795$	−4.28115	−	3.11044i	−0.151837	−	0.110316i
$796$		0			0
$797$	−9.90983	+	30.4993i	−0.351024	+	1.08034i	0.607255	+	0.794507i	$0.292271\pi$
$797$	−9.90983	+	30.4993i	−0.351024	+	1.08034i	−0.958279	+	0.285834i	$0.907729\pi$
$798$		0			0
$799$	2.97214	−	2.15938i	0.105147	−	0.0763935i
$800$		0			0
$801$	−2.39919	−	7.38394i	−0.0847711	−	0.260899i
$802$		0			0
$803$	2.70820	+	28.9402i	0.0955704	+	1.02128i
$804$		0			0
$805$	2.33688	+	7.19218i	0.0823642	+	0.253491i
$806$		0			0
$807$	14.8541	−	10.7921i	0.522889	−	0.379901i
$808$		0			0
$809$	10.7533	−	33.0952i	0.378066	−	1.16357i	−0.563322	−	0.826238i	$-0.690477\pi$
$809$	10.7533	−	33.0952i	0.378066	−	1.16357i	0.941387	−	0.337328i	$-0.109523\pi$
$810$		0			0
$811$	17.3435	+	12.6008i	0.609011	+	0.442473i	0.849066	−	0.528287i	$-0.177165\pi$
$811$	17.3435	+	12.6008i	0.609011	+	0.442473i	−0.240055	+	0.970759i	$0.577165\pi$
$812$		0			0
$813$	13.5623			0.475651
$814$		0			0
$815$	2.05573			0.0720090
$816$		0			0
$817$	6.64590	+	4.82853i	0.232511	+	0.168929i
$818$		0			0
$819$	−2.92705	+	9.00854i	−0.102279	+	0.314784i
$820$		0			0
$821$	26.8435	−	19.5029i	0.936843	−	0.680656i	−0.0108155	−	0.999942i	$-0.503443\pi$
$821$	26.8435	−	19.5029i	0.936843	−	0.680656i	0.947659	+	0.319285i	$0.103443\pi$
$822$		0			0
$823$	−7.16312	−	22.0458i	−0.249691	−	0.768469i	−0.994829	−	0.101559i	$-0.967617\pi$
$823$	−7.16312	−	22.0458i	−0.249691	−	0.768469i	0.745139	−	0.666909i	$-0.232383\pi$
$824$		0			0
$825$	14.9443	+	3.35520i	0.520293	+	0.116813i
$826$		0			0
$827$	6.88854	+	21.2008i	0.239538	+	0.737223i	0.996487	+	0.0837484i	$0.0266892\pi$
$827$	6.88854	+	21.2008i	0.239538	+	0.737223i	−0.756949	+	0.653474i	$0.773311\pi$
$828$		0			0
$829$	−8.78115	+	6.37988i	−0.304982	+	0.221582i	−0.729740	−	0.683724i	$-0.760359\pi$
$829$	−8.78115	+	6.37988i	−0.304982	+	0.221582i	0.424758	+	0.905307i	$0.360359\pi$
$830$		0			0
$831$	3.31966	−	10.2169i	0.115158	−	0.354419i
$832$		0			0
$833$	−0.618034	−	0.449028i	−0.0214136	−	0.0155579i
$834$		0			0
$835$	0.673762			0.0233165
$836$		0			0
$837$	8.09017			0.279637
$838$		0			0
$839$	−13.1353	−	9.54332i	−0.453479	−	0.329472i	0.337489	−	0.941330i	$-0.390423\pi$
$839$	−13.1353	−	9.54332i	−0.453479	−	0.329472i	−0.790968	+	0.611858i	$0.790423\pi$
$840$		0			0
$841$	−7.72542	+	23.7764i	−0.266394	+	0.819876i
$842$		0			0
$843$	−12.3262	+	8.95554i	−0.424538	+	0.308445i
$844$		0			0
$845$	0.944272	+	2.90617i	0.0324839	+	0.0999753i
$846$		0			0
$847$	−22.2361	−	10.5146i	−0.764040	−	0.361287i
$848$		0			0
$849$	−2.05573	−	6.32688i	−0.0705524	−	0.217138i
$850$		0			0
$851$	29.6976	−	21.5765i	1.01802	−	0.739634i
$852$		0			0
$853$	−3.54508	+	10.9106i	−0.121381	+	0.373574i	−0.993224	−	0.116212i	$-0.962925\pi$
$853$	−3.54508	+	10.9106i	−0.121381	+	0.373574i	0.871843	+	0.489785i	$0.162925\pi$
$854$		0			0
$855$	0.690983	+	0.502029i	0.0236311	+	0.0171690i
$856$		0			0
$857$	14.3475			0.490102			0.245051	−	0.969510i	$-0.421195\pi$
$857$	14.3475			0.490102			0.245051	+	0.969510i	$0.421195\pi$
$858$		0			0
$859$	45.0689			1.53773			0.768865	−	0.639411i	$-0.220822\pi$
$859$	45.0689			1.53773			0.768865	+	0.639411i	$0.220822\pi$
$860$		0			0
$861$	−6.80902	−	4.94704i	−0.232051	−	0.168595i
$862$		0			0
$863$	−10.0344	+	30.8828i	−0.341576	+	1.05126i	0.621815	+	0.783164i	$0.286396\pi$
$863$	−10.0344	+	30.8828i	−0.341576	+	1.05126i	−0.963391	+	0.268100i	$0.913604\pi$
$864$		0			0
$865$	11.1631	−	8.11048i	0.379557	−	0.275765i
$866$		0			0
$867$	5.20820	+	16.0292i	0.176880	+	0.544380i
$868$		0			0
$869$	−20.1803	−	4.53077i	−0.684571	−	0.153696i
$870$		0			0
$871$	−3.80902	−	11.7229i	−0.129064	−	0.397217i
$872$		0			0
$873$	13.8262	−	10.0453i	0.467947	−	0.339984i
$874$		0			0
$875$	4.10739	−	12.6412i	0.138855	−	0.427352i
$876$		0			0
$877$	13.2812	+	9.64932i	0.448473	+	0.325834i	0.788992	−	0.614403i	$-0.210603\pi$
$877$	13.2812	+	9.64932i	0.448473	+	0.325834i	−0.340520	+	0.940237i	$0.610603\pi$
$878$		0			0
$879$	−24.1246			−0.813703
$880$		0			0
$881$	−57.0344			−1.92154			−0.960770	−	0.277348i	$-0.910545\pi$
$881$	−57.0344			−1.92154			−0.960770	+	0.277348i	$0.910545\pi$
$882$		0			0
$883$	−31.0344	−	22.5478i	−1.04439	−	0.758795i	−0.0732541	−	0.997313i	$-0.523338\pi$
$883$	−31.0344	−	22.5478i	−1.04439	−	0.758795i	−0.971138	+	0.238518i	$0.923338\pi$
$884$		0			0
$885$	−0.736068	+	2.26538i	−0.0247427	+	0.0761501i
$886$		0			0
$887$	−12.8992	+	9.37181i	−0.433112	+	0.314675i	−0.782892	−	0.622157i	$-0.786256\pi$
$887$	−12.8992	+	9.37181i	−0.433112	+	0.314675i	0.349780	+	0.936832i	$0.386256\pi$
$888$		0			0
$889$	11.9098	+	36.6547i	0.399443	+	1.22936i
$890$		0			0
$891$	0.309017	+	3.30220i	0.0103525	+	0.110628i
$892$		0			0
$893$	−4.10739	−	12.6412i	−0.137449	−	0.423023i
$894$		0			0
$895$	−0.118034	+	0.0857567i	−0.00394544	+	0.00286653i
$896$		0			0
$897$	7.16312	−	22.0458i	0.239170	−	0.736088i
$898$		0			0
$899$	13.0902	+	9.51057i	0.436582	+	0.317195i
$900$		0			0
$901$	3.27051			0.108956
$902$		0			0
$903$	13.2918			0.442323
$904$		0			0
$905$	11.5000	+	8.35524i	0.382273	+	0.277738i
$906$		0			0
$907$	0.371323	−	1.14281i	0.0123296	−	0.0379465i	−0.944702	−	0.327929i	$-0.893649\pi$
$907$	0.371323	−	1.14281i	0.0123296	−	0.0379465i	0.957032	+	0.289982i	$0.0936494\pi$
$908$		0			0
$909$	−0.572949	+	0.416272i	−0.0190035	+	0.0138069i
$910$		0			0
$911$	−8.78115	−	27.0256i	−0.290933	−	0.895398i	−0.984557	−	0.175062i	$-0.943987\pi$
$911$	−8.78115	−	27.0256i	−0.290933	−	0.895398i	0.693625	−	0.720336i	$-0.256013\pi$
$912$		0			0
$913$	28.8779	+	32.8177i	0.955719	+	1.08611i
$914$		0			0
$915$	1.26393	+	3.88998i	0.0417843	+	0.128599i
$916$		0			0
$917$	29.4336	−	21.3848i	0.971984	−	0.706188i
$918$		0			0
$919$	9.83688	−	30.2748i	0.324489	−	0.998674i	−0.647182	−	0.762335i	$-0.724053\pi$
$919$	9.83688	−	30.2748i	0.324489	−	0.998674i	0.971671	−	0.236338i	$-0.0759473\pi$
$920$		0			0
$921$	−11.9271	−	8.66551i	−0.393010	−	0.285538i
$922$		0			0
$923$	−9.09017			−0.299207
$924$		0			0
$925$	−30.9787			−1.01857
$926$		0			0
$927$	6.09017	+	4.42477i	0.200027	+	0.145328i
$928$		0			0
$929$	11.3435	−	34.9116i	0.372167	−	1.14541i	−0.573203	−	0.819413i	$-0.694300\pi$
$929$	11.3435	−	34.9116i	0.372167	−	1.14541i	0.945370	−	0.325999i	$-0.105700\pi$
$930$		0			0
$931$	−2.23607	+	1.62460i	−0.0732842	+	0.0532441i
$932$		0			0
$933$	−4.01722	−	12.3637i	−0.131518	−	0.404771i
$934$		0			0
$935$	0.718847	−	0.310271i	0.0235088	−	0.0101469i
$936$		0			0
$937$	−3.89261	−	11.9802i	−0.127166	−	0.391377i	0.867123	−	0.498093i	$-0.165966\pi$
$937$	−3.89261	−	11.9802i	−0.127166	−	0.391377i	−0.994289	+	0.106717i	$0.965966\pi$
$938$		0			0
$939$	−0.336881	+	0.244758i	−0.0109937	+	0.00798739i
$940$		0			0
$941$	−16.2984	+	50.1612i	−0.531312	+	1.63521i	0.220174	+	0.975461i	$0.429337\pi$
$941$	−16.2984	+	50.1612i	−0.531312	+	1.63521i	−0.751486	+	0.659749i	$0.770663\pi$
$942$		0			0
$943$	16.6631	+	12.1065i	0.542626	+	0.394241i
$944$		0			0
$945$	1.38197			0.0449554
$946$		0			0
$947$	41.7426			1.35645			0.678227	−	0.734853i	$-0.262749\pi$
$947$	41.7426			1.35645			0.678227	+	0.734853i	$0.262749\pi$
$948$		0			0
$949$	−30.0344	−	21.8213i	−0.974959	−	0.708349i
$950$		0			0
$951$	0.836881	−	2.57565i	0.0271377	−	0.0835213i
$952$		0			0
$953$	−15.6525	+	11.3722i	−0.507033	+	0.368381i	−0.811697	−	0.584079i	$-0.801456\pi$
$953$	−15.6525	+	11.3722i	−0.507033	+	0.368381i	0.304664	+	0.952460i	$0.401456\pi$
$954$		0			0
$955$	−0.0106431	−	0.0327561i	−0.000344403	−	0.00105996i
$956$		0			0
$957$	−3.38197	+	5.70634i	−0.109323	+	0.184460i
$958$		0			0
$959$	−10.4894	−	32.2829i	−0.338719	−	1.04247i
$960$		0			0
$961$	−27.8713	+	20.2497i	−0.899075	+	0.653216i
$962$		0			0
$963$	−5.30902	+	16.3395i	−0.171081	+	0.526532i
$964$		0			0
$965$	−10.4271	−	7.57570i	−0.335659	−	0.243870i
$966$		0			0
$967$	−52.3951			−1.68491			−0.842457	−	0.538764i	$-0.818891\pi$
$967$	−52.3951			−1.68491			−0.842457	+	0.538764i	$0.818891\pi$
$968$		0			0
$969$	−0.527864			−0.0169574
$970$		0			0
$971$	8.56231	+	6.22088i	0.274777	+	0.199638i	0.716636	−	0.697447i	$-0.245681\pi$
$971$	8.56231	+	6.22088i	0.274777	+	0.199638i	−0.441859	+	0.897085i	$0.645681\pi$
$972$		0			0
$973$	9.20820	−	28.3399i	0.295201	−	0.908537i
$974$		0			0
$975$	−15.8262	+	11.4984i	−0.506845	+	0.368245i
$976$		0			0
$977$	−0.690983	−	2.12663i	−0.0221065	−	0.0680368i	0.939395	−	0.342838i	$-0.111388\pi$
$977$	−0.690983	−	2.12663i	−0.0221065	−	0.0680368i	−0.961501	+	0.274801i	$0.911388\pi$
$978$		0			0
$979$	−13.1287	+	22.1518i	−0.419594	+	0.707975i
$980$		0			0
$981$	3.70820	+	11.4127i	0.118394	+	0.364379i
$982$		0			0
$983$	−35.7984	+	26.0090i	−1.14179	+	0.829560i	−0.987368	−	0.158445i	$-0.949352\pi$
$983$	−35.7984	+	26.0090i	−1.14179	+	0.829560i	−0.154423	+	0.988005i	$0.549352\pi$
$984$		0			0
$985$	−1.83688	+	5.65334i	−0.0585279	+	0.180130i
$986$		0			0
$987$	−17.3992	−	12.6412i	−0.553822	−	0.402375i
$988$		0			0
$989$	−32.5279			−1.03433
$990$		0			0
$991$	15.9230			0.505810			0.252905	−	0.967491i	$-0.418614\pi$
$991$	15.9230			0.505810			0.252905	+	0.967491i	$0.418614\pi$
$992$		0			0
$993$	−3.66312	−	2.66141i	−0.116246	−	0.0844573i
$994$		0			0
$995$	−4.66312	+	14.3516i	−0.147831	+	0.454976i
$996$		0			0
$997$	15.4443	−	11.2209i	0.489125	−	0.355370i	−0.315723	−	0.948851i	$-0.602247\pi$
$997$	15.4443	−	11.2209i	0.489125	−	0.355370i	0.804848	+	0.593481i	$0.202247\pi$
$998$		0			0
$999$	−2.07295	−	6.37988i	−0.0655852	−	0.201851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.q.d.49.1	✓	4
3.2	odd	2		792.2.r.c.577.1		4
4.3	odd	2		528.2.y.c.49.1		4
11.3	even	5		2904.2.a.q.1.2		2
11.8	odd	10		2904.2.a.p.1.2		2
11.9	even	5	inner	264.2.q.d.97.1	yes	4
33.8	even	10		8712.2.a.bn.1.1		2
33.14	odd	10		8712.2.a.bo.1.1		2
33.20	odd	10		792.2.r.c.361.1		4
44.3	odd	10		5808.2.a.ce.1.2		2
44.19	even	10		5808.2.a.cd.1.2		2
44.31	odd	10		528.2.y.c.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.q.d.49.1	✓	4	1.1	even	1	trivial
264.2.q.d.97.1	yes	4	11.9	even	5	inner
528.2.y.c.49.1		4	4.3	odd	2
528.2.y.c.97.1		4	44.31	odd	10
792.2.r.c.361.1		4	33.20	odd	10
792.2.r.c.577.1		4	3.2	odd	2
2904.2.a.p.1.2		2	11.8	odd	10
2904.2.a.q.1.2		2	11.3	even	5
5808.2.a.cd.1.2		2	44.19	even	10
5808.2.a.ce.1.2		2	44.3	odd	10
8712.2.a.bn.1.1		2	33.8	even	10
8712.2.a.bo.1.1		2	33.14	odd	10

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:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +(0.190983 - 0.587785i) q^{5} +(1.80902 - 1.31433i) q^{7} +(0.309017 + 0.951057i) q^{9} +(1.69098 - 2.85317i) q^{11} +(1.30902 + 4.02874i) q^{13} +(0.500000 - 0.363271i) q^{15} +(-0.118034 + 0.363271i) q^{17} +(1.11803 + 0.812299i) q^{19} +2.23607 q^{21} -5.47214 q^{23} +(3.73607 + 2.71441i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-1.61803 + 1.17557i) q^{29} +(-2.50000 - 7.69421i) q^{31} +(3.04508 - 1.31433i) q^{33} +(-0.427051 - 1.31433i) q^{35} +(-5.42705 + 3.94298i) q^{37} +(-1.30902 + 4.02874i) q^{39} +(-3.04508 - 2.21238i) q^{41} +5.94427 q^{43} +0.618034 q^{45} +(-7.78115 - 5.65334i) q^{47} +(-0.618034 + 1.90211i) q^{49} +(-0.309017 + 0.224514i) q^{51} +(-2.64590 - 8.14324i) q^{53} +(-1.35410 - 1.53884i) q^{55} +(0.427051 + 1.31433i) q^{57} +(-3.11803 + 2.26538i) q^{59} +(-2.04508 + 6.29412i) q^{61} +(1.80902 + 1.31433i) q^{63} +2.61803 q^{65} -2.90983 q^{67} +(-4.42705 - 3.21644i) q^{69} +(-0.663119 + 2.04087i) q^{71} +(-7.09017 + 5.15131i) q^{73} +(1.42705 + 4.39201i) q^{75} +(-0.690983 - 7.38394i) q^{77} +(-1.92705 - 5.93085i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-4.07295 + 12.5352i) q^{83} +(0.190983 + 0.138757i) q^{85} -2.00000 q^{87} -7.76393 q^{89} +(7.66312 + 5.56758i) q^{91} +(2.50000 - 7.69421i) q^{93} +(0.690983 - 0.502029i) q^{95} +(-5.28115 - 16.2537i) q^{97} +(3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + 3 q^{5} + 5 q^{7} - q^{9} + 9 q^{11} + 3 q^{13} + 2 q^{15} + 4 q^{17} - 4 q^{23} + 6 q^{25} + q^{27} - 2 q^{29} - 10 q^{31} + q^{33} + 5 q^{35} - 15 q^{37} - 3 q^{39} - q^{41} - 12 q^{43}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q + q^3 + 3 * q^5 + 5 * q^7 - q^9 + 9 * q^11 + 3 * q^13 + 2 * q^15 + 4 * q^17 - 4 * q^23 + 6 * q^25 + q^27 - 2 * q^29 - 10 * q^31 + q^33 + 5 * q^35 - 15 * q^37 - 3 * q^39 - q^41 - 12 * q^43 - 2 * q^45 - 11 * q^47 + 2 * q^49 + q^51 - 24 * q^53 + 8 * q^55 - 5 * q^57 - 8 * q^59 + 3 * q^61 + 5 * q^63 + 6 * q^65 - 34 * q^67 - 11 * q^69 + 13 * q^71 - 6 * q^73 - q^75 - 5 * q^77 - q^79 - q^81 - 23 * q^83 + 3 * q^85 - 8 * q^87 - 40 * q^89 + 15 * q^91 + 10 * q^93 + 5 * q^95 - q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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