LMFDB - Embedded newform 972.2.l.d.107.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,3,0,3,6,0,0,-9,0,-3,0,0,6,33] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			107.10
Character	$\chi$	$=$	972.107
Dual form			972.2.l.d.863.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.419187 - 1.35066i) q^{2} +(-1.64856 - 1.13236i) q^{4} +(-0.776998 + 2.13478i) q^{5} +(-1.29035 - 0.227523i) q^{7} +(-2.22049 + 1.75198i) q^{8} +(2.55766 + 1.94434i) q^{10} +(2.54138 - 0.924988i) q^{11} +(3.48118 - 2.92106i) q^{13} +(-0.848202 + 1.64744i) q^{14} +(1.43553 + 3.73353i) q^{16} +(4.20783 - 2.42939i) q^{17} +(-5.44971 - 3.14639i) q^{19} +(3.69827 - 2.63949i) q^{20} +(-0.184028 - 3.82029i) q^{22} +(-0.440555 - 2.49851i) q^{23} +(-0.123358 - 0.103510i) q^{25} +(-2.48609 - 5.92636i) q^{26} +(1.86958 + 1.83622i) q^{28} +(3.16586 - 3.77293i) q^{29} +(-2.87863 + 0.507580i) q^{31} +(5.64449 - 0.373857i) q^{32} +(-1.51741 - 6.70172i) q^{34} +(1.48831 - 2.57783i) q^{35} +(-3.86074 - 6.68701i) q^{37} +(-6.53415 + 6.04178i) q^{38} +(-2.01478 - 6.10155i) q^{40} +(2.55335 + 3.04297i) q^{41} +(-2.90911 - 7.99270i) q^{43} +(-5.23705 - 1.35286i) q^{44} +(-3.55932 - 0.452305i) q^{46} +(2.07927 - 11.7921i) q^{47} +(-4.96462 - 1.80697i) q^{49} +(-0.191517 + 0.123225i) q^{50} +(-9.04663 + 0.873603i) q^{52} +3.84281i q^{53} +6.14402i q^{55} +(3.26381 - 1.75545i) q^{56} +(-3.76885 - 5.85756i) q^{58} +(10.7689 + 3.91958i) q^{59} +(0.00682825 - 0.0387249i) q^{61} +(-0.521117 + 4.10082i) q^{62} +(1.86114 - 7.78050i) q^{64} +(3.53096 + 9.70123i) q^{65} +(7.67125 + 9.14224i) q^{67} +(-9.68782 - 0.759767i) q^{68} +(-2.85789 - 3.09079i) q^{70} +(1.22570 + 2.12297i) q^{71} +(3.09175 - 5.35507i) q^{73} +(-10.6502 + 2.41144i) q^{74} +(5.42135 + 11.3581i) q^{76} +(-3.48972 + 0.615332i) q^{77} +(3.87187 - 4.61431i) q^{79} +(-9.08569 + 0.163591i) q^{80} +(5.18035 - 2.17314i) q^{82} +(7.31283 + 6.13619i) q^{83} +(1.91675 + 10.8704i) q^{85} +(-12.0149 + 0.578772i) q^{86} +(-4.02256 + 6.50638i) q^{88} +(-5.99050 - 3.45862i) q^{89} +(-5.15653 + 2.97713i) q^{91} +(-2.10293 + 4.61783i) q^{92} +(-15.0555 - 7.75149i) q^{94} +(10.9513 - 9.18922i) q^{95} +(8.22759 - 2.99460i) q^{97} +(-4.52172 + 5.94806i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) $ 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 + 33 * q^14 + 3 * q^16 - 18 * q^17 - 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 30 * q^29 + 33 * q^32 + 15 * q^34 - 6 * q^37 - 63 * q^38 + 33 * q^40 - 24 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 21 * q^50 + 57 * q^52 - 18 * q^56 + 57 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 + 30 * q^65 - 102 * q^68 + 51 * q^70 - 6 * q^73 + 75 * q^74 + 27 * q^76 - 42 * q^77 - 12 * q^82 - 24 * q^85 - 111 * q^86 + 27 * q^88 + 147 * q^92 + 30 * q^94 - 12 * q^97 - 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	0.419187	−	1.35066i	0.296410	−	0.955061i
$2$	0.419187	−	1.35066i	0.296410	−	0.955061i
$3$		0			0
$3$		0			0
$4$	−1.64856	−	1.13236i	−0.824282	−	0.566180i
$5$	−0.776998	+	2.13478i	−0.347484	+	0.954705i	0.635676	+	0.771956i	$0.280722\pi$
$5$	−0.776998	+	2.13478i	−0.347484	+	0.954705i	−0.983160	+	0.182748i	$0.941501\pi$
$6$		0			0
$7$	−1.29035	−	0.227523i	−0.487705	−	0.0859955i	−0.0756119	−	0.997137i	$-0.524091\pi$
$7$	−1.29035	−	0.227523i	−0.487705	−	0.0859955i	−0.412093	+	0.911142i	$0.635202\pi$
$8$	−2.22049	+	1.75198i	−0.785061	+	0.619418i
$9$		0			0
$10$	2.55766	+	1.94434i	0.808803	+	0.614853i
$11$	2.54138	−	0.924988i	0.766256	−	0.278894i	0.0708265	−	0.997489i	$-0.477436\pi$
$11$	2.54138	−	0.924988i	0.766256	−	0.278894i	0.695430	+	0.718594i	$0.255214\pi$
$12$		0			0
$13$	3.48118	−	2.92106i	0.965506	−	0.810156i	−0.0163342	−	0.999867i	$-0.505200\pi$
$13$	3.48118	−	2.92106i	0.965506	−	0.810156i	0.981840	+	0.189711i	$0.0607551\pi$
$14$	−0.848202	+	1.64744i	−0.226692	+	0.440298i
$15$		0			0
$16$	1.43553	+	3.73353i	0.358881	+	0.933383i
$17$	4.20783	−	2.42939i	1.02055	−	0.589214i	0.106286	−	0.994336i	$-0.466104\pi$
$17$	4.20783	−	2.42939i	1.02055	−	0.589214i	0.914263	+	0.405122i	$0.132771\pi$
$18$		0			0
$19$	−5.44971	−	3.14639i	−1.25025	−	0.721832i	−0.279090	−	0.960265i	$-0.590033\pi$
$19$	−5.44971	−	3.14639i	−1.25025	−	0.721832i	−0.971159	+	0.238433i	$0.923366\pi$
$20$	3.69827	−	2.63949i	0.826959	−	0.590208i
$21$		0			0
$22$	−0.184028	−	3.82029i	−0.0392349	−	0.814488i
$23$	−0.440555	−	2.49851i	−0.0918622	−	0.520976i	−0.995664	−	0.0930246i	$-0.970346\pi$
$23$	−0.440555	−	2.49851i	−0.0918622	−	0.520976i	0.903802	−	0.427952i	$-0.140765\pi$
$24$		0			0
$25$	−0.123358	−	0.103510i	−0.0246716	−	0.0207019i
$26$	−2.48609	−	5.92636i	−0.487562	−	1.16226i
$27$		0			0
$28$	1.86958	+	1.83622i	0.353317	+	0.347013i
$29$	3.16586	−	3.77293i	0.587886	−	0.700615i	−0.387313	−	0.921948i	$-0.626597\pi$
$29$	3.16586	−	3.77293i	0.587886	−	0.700615i	0.975198	+	0.221334i	$0.0710410\pi$
$30$		0			0
$31$	−2.87863	+	0.507580i	−0.517017	+	0.0911641i	−0.426068	−	0.904691i	$-0.640101\pi$
$31$	−2.87863	+	0.507580i	−0.517017	+	0.0911641i	−0.0909499	+	0.995855i	$0.528990\pi$
$32$	5.64449	−	0.373857i	0.997814	−	0.0660893i
$33$		0			0
$34$	−1.51741	−	6.70172i	−0.260234	−	1.14933i
$35$	1.48831	−	2.57783i	0.251570	−	0.435732i
$36$		0			0
$37$	−3.86074	−	6.68701i	−0.634703	−	1.09934i	−0.986578	−	0.163290i	$-0.947789\pi$
$37$	−3.86074	−	6.68701i	−0.634703	−	1.09934i	0.351876	−	0.936047i	$-0.385544\pi$
$38$	−6.53415	+	6.04178i	−1.05998	+	0.980105i
$39$		0			0
$40$	−2.01478	−	6.10155i	−0.318565	−	0.964740i
$41$	2.55335	+	3.04297i	0.398767	+	0.475232i	0.927643	−	0.373467i	$-0.121831\pi$
$41$	2.55335	+	3.04297i	0.398767	+	0.475232i	−0.528877	+	0.848699i	$0.677387\pi$
$42$		0			0
$43$	−2.90911	−	7.99270i	−0.443634	−	1.21888i	−0.937085	−	0.349102i	$-0.886487\pi$
$43$	−2.90911	−	7.99270i	−0.443634	−	1.21888i	0.493450	−	0.869774i	$-0.335735\pi$
$44$	−5.23705	−	1.35286i	−0.789515	−	0.203951i
$45$		0			0
$46$	−3.55932	−	0.452305i	−0.524793	−	0.0666887i
$47$	2.07927	−	11.7921i	0.303293	−	1.72006i	−0.328142	−	0.944629i	$-0.606422\pi$
$47$	2.07927	−	11.7921i	0.303293	−	1.72006i	0.631434	−	0.775429i	$-0.282467\pi$
$48$		0			0
$49$	−4.96462	−	1.80697i	−0.709232	−	0.258139i
$50$	−0.191517	+	0.123225i	−0.0270845	+	0.0174266i
$51$		0			0
$52$	−9.04663	+	0.873603i	−1.25454	+	0.121147i
$53$			3.84281i			0.527851i	0.964543	+	0.263925i	$0.0850173\pi$
$53$			3.84281i			0.527851i	−0.964543	+	0.263925i	$0.914983\pi$
$54$		0			0
$55$			6.14402i			0.828460i
$56$	3.26381	−	1.75545i	0.436145	−	0.234581i
$57$		0			0
$58$	−3.76885	−	5.85756i	−0.494874	−	0.769136i
$59$	10.7689	+	3.91958i	1.40200	+	0.510285i	0.928771	−	0.370655i	$-0.120867\pi$
$59$	10.7689	+	3.91958i	1.40200	+	0.510285i	0.473227	+	0.880941i	$0.343089\pi$
$60$		0			0
$61$	0.00682825	−	0.0387249i	0.000874268	−	0.00495822i	−0.984367	−	0.176127i	$-0.943643\pi$
$61$	0.00682825	−	0.0387249i	0.000874268	−	0.00495822i	0.985242	+	0.171169i	$0.0547543\pi$
$62$	−0.521117	+	4.10082i	−0.0661820	+	0.520805i
$63$		0			0
$64$	1.86114	−	7.78050i	0.232643	−	0.972562i
$65$	3.53096	+	9.70123i	0.437961	+	1.20329i
$66$		0			0
$67$	7.67125	+	9.14224i	0.937193	+	1.11690i	0.992959	+	0.118459i	$0.0377954\pi$
$67$	7.67125	+	9.14224i	0.937193	+	1.11690i	−0.0557663	+	0.998444i	$0.517760\pi$
$68$	−9.68782	−	0.759767i	−1.17482	−	0.0921352i
$69$		0			0
$70$	−2.85789	−	3.09079i	−0.341583	−	0.369420i
$71$	1.22570	+	2.12297i	0.145463	+	0.251950i	0.929546	−	0.368707i	$-0.120199\pi$
$71$	1.22570	+	2.12297i	0.145463	+	0.251950i	−0.784082	+	0.620657i	$0.786866\pi$
$72$		0			0
$73$	3.09175	−	5.35507i	0.361862	−	0.626764i	−0.626405	−	0.779498i	$-0.715474\pi$
$73$	3.09175	−	5.35507i	0.361862	−	0.626764i	0.988267	+	0.152734i	$0.0488077\pi$
$74$	−10.6502	+	2.41144i	−1.23807	+	0.280325i
$75$		0			0
$76$	5.42135	+	11.3581i	0.621871	+	1.30286i
$77$	−3.48972	+	0.615332i	−0.397690	+	0.0701236i
$78$		0			0
$79$	3.87187	−	4.61431i	0.435619	−	0.519151i	−0.502915	−	0.864336i	$-0.667739\pi$
$79$	3.87187	−	4.61431i	0.435619	−	0.519151i	0.938535	+	0.345185i	$0.112184\pi$
$80$	−9.08569	+	0.163591i	−1.01581	+	0.0182900i
$81$		0			0
$82$	5.18035	−	2.17314i	0.572074	−	0.239983i
$83$	7.31283	+	6.13619i	0.802687	+	0.673534i	0.948850	−	0.315726i	$-0.102248\pi$
$83$	7.31283	+	6.13619i	0.802687	+	0.673534i	−0.146163	+	0.989260i	$0.546693\pi$
$84$		0			0
$85$	1.91675	+	10.8704i	0.207901	+	1.17906i
$86$	−12.0149	+	0.578772i	−1.29560	+	0.0624106i
$87$		0			0
$88$	−4.02256	+	6.50638i	−0.428806	+	0.693582i
$89$	−5.99050	−	3.45862i	−0.634991	−	0.366613i	0.147691	−	0.989034i	$-0.452816\pi$
$89$	−5.99050	−	3.45862i	−0.634991	−	0.366613i	−0.782683	+	0.622421i	$0.786149\pi$
$90$		0			0
$91$	−5.15653	+	2.97713i	−0.540552	+	0.312088i
$92$	−2.10293	+	4.61783i	−0.219246	+	0.481442i
$93$		0			0
$94$	−15.0555	−	7.75149i	−1.55286	−	0.799506i
$95$	10.9513	−	9.18922i	1.12358	−	0.942794i
$96$		0			0
$97$	8.22759	−	2.99460i	0.835385	−	0.304055i	0.111318	−	0.993785i	$-0.464493\pi$
$97$	8.22759	−	2.99460i	0.835385	−	0.304055i	0.724067	+	0.689729i	$0.242270\pi$
$98$	−4.52172	+	5.94806i	−0.456762	+	0.600844i
$99$		0			0
$100$	0.0861535	+	0.310328i	0.00861535	+	0.0310328i
$101$	−2.16848	−	0.382362i	−0.215772	−	0.0380465i	0.0647169	−	0.997904i	$-0.479386\pi$
$101$	−2.16848	−	0.382362i	−0.215772	−	0.0380465i	−0.280489	+	0.959857i	$0.590497\pi$
$102$		0			0
$103$	−0.672781	+	1.84845i	−0.0662911	+	0.182133i	−0.968415	−	0.249344i	$-0.919785\pi$
$103$	−0.672781	+	1.84845i	−0.0662911	+	0.182133i	0.902124	+	0.431477i	$0.142007\pi$
$104$	−2.61229	+	12.5851i	−0.256157	+	1.23407i
$105$		0			0
$106$	5.19033	+	1.61086i	0.504130	+	0.156460i
$107$	4.06709			0.393180			0.196590	−	0.980486i	$-0.437013\pi$
$107$	4.06709			0.393180			0.196590	+	0.980486i	$0.437013\pi$
$108$		0			0
$109$	−1.81021			−0.173387			−0.0866934	−	0.996235i	$-0.527630\pi$
$109$	−1.81021			−0.173387			−0.0866934	+	0.996235i	$0.527630\pi$
$110$	8.29848	+	2.57550i	0.791229	+	0.245564i
$111$		0			0
$112$	−1.00286	−	5.14416i	−0.0947615	−	0.486078i
$113$	−1.20062	+	3.29869i	−0.112945	+	0.310314i	−0.983267	−	0.182168i	$-0.941688\pi$
$113$	−1.20062	+	3.29869i	−0.112945	+	0.310314i	0.870322	+	0.492483i	$0.163911\pi$
$114$		0			0
$115$	5.67610	+	1.00085i	0.529299	+	0.0933297i
$116$	−9.49143	+	2.63502i	−0.881257	+	0.244655i
$117$		0			0
$118$	9.80822	−	12.9021i	0.902920	−	1.18774i
$119$	−5.98230	+	2.17738i	−0.548396	+	0.199600i
$120$		0			0
$121$	−2.82346	+	2.36916i	−0.256678	+	0.215379i
$122$	−0.0494419	−	0.0254557i	−0.00447626	−	0.00230465i
$123$		0			0
$124$	5.32037	+	2.42287i	0.477783	+	0.217580i
$125$	−9.52032	+	5.49656i	−0.851523	+	0.491627i
$126$		0			0
$127$	−9.71588	−	5.60947i	−0.862145	−	0.497760i	0.00258477	−	0.999997i	$-0.499177\pi$
$127$	−9.71588	−	5.60947i	−0.862145	−	0.497760i	−0.864730	+	0.502237i	$0.832511\pi$
$128$	−9.72864	−	5.77526i	−0.859898	−	0.510466i
$129$		0			0
$130$	14.5832	−	0.702491i	1.27903	−	0.0616126i
$131$	0.890936	+	5.05275i	0.0778415	+	0.441461i	0.998673	+	0.0515002i	$0.0164003\pi$
$131$	0.890936	+	5.05275i	0.0778415	+	0.441461i	−0.920832	+	0.389961i	$0.872489\pi$
$132$		0			0
$133$	6.31613	+	5.29986i	0.547678	+	0.459557i
$134$	15.5638	−	6.52894i	1.34450	−	0.564015i
$135$		0			0
$136$	−5.08720	+	12.7665i	−0.436224	+	1.09472i
$137$	−1.16239	+	1.38529i	−0.0993100	+	0.118353i	−0.813410	−	0.581690i	$-0.802392\pi$
$137$	−1.16239	+	1.38529i	−0.0993100	+	0.118353i	0.714100	+	0.700043i	$0.246836\pi$
$138$		0			0
$139$	12.8033	−	2.25758i	1.08597	−	0.191485i	0.398114	−	0.917336i	$-0.369665\pi$
$139$	12.8033	−	2.25758i	1.08597	−	0.191485i	0.687852	+	0.725851i	$0.258554\pi$
$140$	−5.37260	+	2.56441i	−0.454067	+	0.216732i
$141$		0			0
$142$	3.38120	−	0.765577i	0.283744	−	0.0642458i
$143$	6.14507	−	10.6436i	0.513877	−	0.890061i
$144$		0			0
$145$	5.59452	+	9.68999i	0.464599	+	0.804710i
$146$	−5.93686	−	6.42069i	−0.491338	−	0.531380i
$147$		0			0
$148$	−1.20741	+	15.3957i	−0.0992483	+	1.26552i
$149$	−1.65428	−	1.97150i	−0.135524	−	0.161511i	0.694014	−	0.719962i	$-0.255841\pi$
$149$	−1.65428	−	1.97150i	−0.135524	−	0.161511i	−0.829538	+	0.558450i	$0.811396\pi$
$150$		0			0
$151$	1.79566	+	4.93353i	0.146128	+	0.401485i	0.991065	−	0.133382i	$-0.0425839\pi$
$151$	1.79566	+	4.93353i	0.146128	+	0.401485i	−0.844936	+	0.534867i	$0.820362\pi$
$152$	17.6134	−	2.56125i	1.42864	−	0.207744i
$153$		0			0
$154$	−0.631743	+	4.97136i	−0.0509073	+	0.400604i
$155$	1.15312	−	6.53965i	0.0926205	−	0.525277i
$156$		0			0
$157$	−19.6331	−	7.14587i	−1.56689	−	0.570302i	−0.594590	−	0.804029i	$-0.702686\pi$
$157$	−19.6331	−	7.14587i	−1.56689	−	0.570302i	−0.972302	+	0.233727i	$0.924908\pi$
$158$	−4.60933	−	7.16384i	−0.366699	−	0.569925i
$159$		0			0
$160$	−3.58765	+	12.3403i	−0.283629	+	0.975583i
$161$			3.32418i			0.261982i
$162$		0			0
$163$			3.28308i			0.257151i	0.991700	+	0.128575i	$0.0410404\pi$
$163$			3.28308i			0.257151i	−0.991700	+	0.128575i	$0.958960\pi$
$164$	−0.763634	−	7.90784i	−0.0596298	−	0.617498i
$165$		0			0
$166$	11.3533	−	7.30493i	0.881191	−	0.566972i
$167$	−17.9950	−	6.54965i	−1.39250	−	0.506827i	−0.466553	−	0.884493i	$-0.654504\pi$
$167$	−17.9950	−	6.54965i	−1.39250	−	0.506827i	−0.925942	+	0.377666i	$0.876727\pi$
$168$		0			0
$169$	1.32862	−	7.53496i	0.102201	−	0.579612i
$170$	15.4857	+	1.96787i	1.18770	+	0.150929i
$171$		0			0
$172$	−4.25476	+	16.4706i	−0.324423	+	1.25587i
$173$	2.98997	+	8.21488i	0.227323	+	0.624566i	0.999947	−	0.0102987i	$-0.00327824\pi$
$173$	2.98997	+	8.21488i	0.227323	+	0.624566i	−0.772624	+	0.634864i	$0.781056\pi$
$174$		0			0
$175$	0.135624	+	0.161630i	0.0102522	+	0.0122181i
$176$	7.10170	+	8.16049i	0.535310	+	0.615120i
$177$		0			0
$178$	−7.18255	+	6.64132i	−0.538355	+	0.497788i
$179$	−3.03371	−	5.25454i	−0.226750	−	0.392743i	0.730093	−	0.683348i	$-0.239477\pi$
$179$	−3.03371	−	5.25454i	−0.226750	−	0.392743i	−0.956843	+	0.290605i	$0.906143\pi$
$180$		0			0
$181$	−8.01419	+	13.8810i	−0.595690	+	1.03177i	0.397759	+	0.917490i	$0.369788\pi$
$181$	−8.01419	+	13.8810i	−0.595690	+	1.03177i	−0.993449	+	0.114276i	$0.963545\pi$
$182$	1.85953	+	8.21270i	0.137838	+	0.608766i
$183$		0			0
$184$	5.35559	+	4.77608i	0.394819	+	0.352097i
$185$	17.2751	−	3.04607i	1.27009	−	0.223951i
$186$		0			0
$187$	8.44655	−	10.0662i	0.617673	−	0.736114i
$188$	−16.7807	+	17.0856i	−1.22386	+	1.24609i
$189$		0			0
$190$	−7.82087	−	18.6435i	−0.567385	−	1.35254i
$191$	8.96056	+	7.51880i	0.648363	+	0.544042i	0.906574	−	0.422047i	$-0.138688\pi$
$191$	8.96056	+	7.51880i	0.648363	+	0.544042i	−0.258210	+	0.966089i	$0.583133\pi$
$192$		0			0
$193$	3.05125	+	17.3045i	0.219633	+	1.24560i	0.872683	+	0.488288i	$0.162378\pi$
$193$	3.05125	+	17.3045i	0.219633	+	1.24560i	−0.653049	+	0.757315i	$0.726511\pi$
$194$	−0.595781	−	12.3680i	−0.0427746	−	0.887969i
$195$		0			0
$196$	6.13835	+	8.60065i	0.438454	+	0.614332i
$197$	19.9607	+	11.5243i	1.42214	+	0.821074i	0.996482	−	0.0838089i	$-0.0267085\pi$
$197$	19.9607	+	11.5243i	1.42214	+	0.821074i	0.425660	+	0.904883i	$0.360042\pi$
$198$		0			0
$199$	−2.70763	+	1.56325i	−0.191939	+	0.110816i	−0.592890	−	0.805284i	$-0.702013\pi$
$199$	−2.70763	+	1.56325i	−0.191939	+	0.110816i	0.400951	+	0.916099i	$0.368680\pi$
$200$	0.455262	+	0.0137215i	0.0321919	+	0.000970257i
$201$		0			0
$202$	−1.42544	+	2.76860i	−0.100294	+	0.194798i
$203$	−4.94348	+	4.14807i	−0.346964	+	0.291138i
$204$		0			0
$205$	−8.48003	+	3.08648i	−0.592271	+	0.215569i
$206$	2.21461	+	1.68355i	0.154299	+	0.117298i
$207$		0			0
$208$	15.9032	+	8.80385i	1.10269	+	0.610437i
$209$	−16.7602	−	2.95527i	−1.15933	−	0.204420i
$210$		0			0
$211$	4.39608	−	12.0781i	0.302639	−	0.831493i	−0.691401	−	0.722472i	$-0.743006\pi$
$211$	4.39608	−	12.0781i	0.302639	−	0.831493i	0.994039	−	0.109022i	$-0.0347718\pi$
$212$	4.35144	−	6.33512i	0.298858	−	0.435098i
$213$		0			0
$214$	1.70487	−	5.49326i	0.116543	−	0.375511i
$215$	19.3231			1.31782
$216$		0			0
$217$	3.82992			0.259992
$218$	−0.758818	+	2.44498i	−0.0513936	+	0.165595i
$219$		0			0
$220$	6.95724	−	10.1288i	0.469057	−	0.682884i
$221$	7.55182	−	20.7485i	0.507991	−	1.39569i
$222$		0			0
$223$	−10.1821	−	1.79539i	−0.681846	−	0.120228i	−0.178012	−	0.984028i	$-0.556967\pi$
$223$	−10.1821	−	1.79539i	−0.681846	−	0.120228i	−0.503834	+	0.863800i	$0.668078\pi$
$224$	−7.36840	−	0.801844i	−0.492322	−	0.0535754i
$225$		0			0
$226$	3.95212	+	3.00440i	0.262891	+	0.199850i
$227$	0.0902519	−	0.0328490i	0.00599023	−	0.00218027i	−0.339023	−	0.940778i	$-0.610097\pi$
$227$	0.0902519	−	0.0328490i	0.00599023	−	0.00218027i	0.345014	+	0.938598i	$0.387874\pi$
$228$		0			0
$229$	20.5858	−	17.2735i	1.36035	−	1.14147i	0.384474	−	0.923136i	$-0.374383\pi$
$229$	20.5858	−	17.2735i	1.36035	−	1.14147i	0.975874	−	0.218332i	$-0.0700617\pi$
$230$	3.73116	−	7.24694i	0.246025	−	0.477849i
$231$		0			0
$232$	−0.419674	+	13.9243i	−0.0275530	+	0.914172i
$233$	6.26494	−	3.61706i	0.410430	−	0.236962i	−0.280545	−	0.959841i	$-0.590515\pi$
$233$	6.26494	−	3.61706i	0.410430	−	0.236962i	0.690974	+	0.722879i	$0.257182\pi$
$234$		0			0
$235$	23.5581	+	13.6013i	1.53676	+	0.887248i
$236$	−13.3149	−	18.6560i	−0.866728	−	1.21440i
$237$		0			0
$238$	0.433194	+	8.99278i	0.0280798	+	0.582915i
$239$	−2.21525	−	12.5633i	−0.143293	−	0.812653i	−0.968722	−	0.248148i	$-0.920178\pi$
$239$	−2.21525	−	12.5633i	−0.143293	−	0.812653i	0.825430	−	0.564505i	$-0.190933\pi$
$240$		0			0
$241$	−5.80114	−	4.86773i	−0.373684	−	0.313558i	0.436533	−	0.899688i	$-0.356206\pi$
$241$	−5.80114	−	4.86773i	−0.373684	−	0.313558i	−0.810217	+	0.586130i	$0.800651\pi$
$242$	2.01638	+	4.80666i	0.129618	+	0.308984i
$243$		0			0
$244$	−0.0551074	+	0.0561085i	−0.00352789	+	0.00359198i
$245$	7.71501	−	9.19439i	0.492894	−	0.587408i
$246$		0			0
$247$	−28.1622	+	4.96576i	−1.79192	+	0.315964i
$248$	5.50270	−	6.17038i	0.349422	−	0.391819i
$249$		0			0
$250$	3.43318	+	15.1628i	0.217134	+	0.958980i
$251$	−5.95007	+	10.3058i	−0.375565	+	0.650498i	−0.990411	−	0.138149i	$-0.955885\pi$
$251$	−5.95007	+	10.3058i	−0.375565	+	0.650498i	0.614846	+	0.788647i	$0.289218\pi$
$252$		0			0
$253$	−3.43072	−	5.94217i	−0.215687	−	0.373581i
$254$	−11.6493	+	10.7714i	−0.730940	+	0.675860i
$255$		0			0
$256$	−11.8785	+	10.7192i	−0.742408	+	0.669948i
$257$	−3.50902	−	4.18189i	−0.218887	−	0.260859i	0.645416	−	0.763832i	$-0.276684\pi$
$257$	−3.50902	−	4.18189i	−0.218887	−	0.260859i	−0.864302	+	0.502972i	$0.832240\pi$
$258$		0			0
$259$	3.46025	+	9.50696i	0.215009	+	0.590734i
$260$	5.16426	−	19.9914i	0.320274	−	1.23981i
$261$		0			0
$262$	7.19802	+	0.914698i	0.444695	+	0.0565102i
$263$	−3.53693	+	20.0589i	−0.218097	+	1.23689i	0.657355	+	0.753581i	$0.271675\pi$
$263$	−3.53693	+	20.0589i	−0.218097	+	1.23689i	−0.875451	+	0.483306i	$0.839436\pi$
$264$		0			0
$265$	−8.20358	−	2.98586i	−0.503942	−	0.183420i
$266$	9.80596	−	6.30931i	0.601242	−	0.386849i
$267$		0			0
$268$	−2.29425	−	23.7582i	−0.140144	−	1.45126i
$269$		−	9.12305i		−	0.556242i	−0.960546	−	0.278121i	$-0.910288\pi$
$269$		−	9.12305i		−	0.556242i	0.960546	−	0.278121i	$-0.0897116\pi$
$270$		0			0
$271$		−	21.2629i		−	1.29163i	−0.763495	−	0.645813i	$-0.776518\pi$
$271$		−	21.2629i		−	1.29163i	0.763495	−	0.645813i	$-0.223482\pi$
$272$	15.1107	+	12.2226i	0.916218	+	0.741105i
$273$		0			0
$274$	1.38379	+	2.15069i	0.0835979	+	0.129928i
$275$	−0.409245	−	0.148953i	−0.0246784	−	0.00898221i
$276$		0			0
$277$	−4.43224	+	25.1365i	−0.266308	+	1.51031i	0.498977	+	0.866615i	$0.333709\pi$
$277$	−4.43224	+	25.1365i	−0.266308	+	1.51031i	−0.765285	+	0.643691i	$0.777402\pi$
$278$	2.31779	−	18.2393i	0.139012	−	1.09392i
$279$		0			0
$280$	1.21152	+	8.33152i	0.0724023	+	0.497903i
$281$	−4.21589	−	11.5831i	−0.251499	−	0.690987i	−0.999624	−	0.0274292i	$-0.991268\pi$
$281$	−4.21589	−	11.5831i	−0.251499	−	0.690987i	0.748125	−	0.663558i	$-0.230954\pi$
$282$		0			0
$283$	10.7391	+	12.7984i	0.638374	+	0.760784i	0.984112	−	0.177547i	$-0.0568161\pi$
$283$	10.7391	+	12.7984i	0.638374	+	0.760784i	−0.345739	+	0.938331i	$0.612372\pi$
$284$	0.383324	−	4.88778i	0.0227461	−	0.290036i
$285$		0			0
$286$	−11.7999	−	12.7616i	−0.697744	−	0.754607i
$287$	−2.60236	−	4.50743i	−0.153613	−	0.266065i
$288$		0			0
$289$	3.30388	−	5.72249i	0.194346	−	0.336617i
$290$	15.4330	−	3.49437i	0.906259	−	0.205196i
$291$		0			0
$292$	−11.1608	+	5.32721i	−0.653138	+	0.311751i
$293$	−13.1269	+	2.31463i	−0.766884	+	0.135222i	−0.543387	−	0.839482i	$-0.682858\pi$
$293$	−13.1269	+	2.31463i	−0.766884	+	0.135222i	−0.223497	+	0.974705i	$0.571747\pi$
$294$		0			0
$295$	−16.7349	+	19.9439i	−0.974344	+	1.16118i
$296$	20.2882	+	8.08448i	1.17923	+	0.469901i
$297$		0			0
$298$	−3.35627	+	1.40794i	−0.194424	+	0.0815601i
$299$	−8.83196	−	7.41089i	−0.510765	−	0.428583i
$300$		0			0
$301$	1.93523	+	10.9752i	0.111545	+	0.632602i
$302$	7.41623	−	0.357249i	0.426756	−	0.0205574i
$303$		0			0
$304$	3.92395	−	24.8634i	0.225054	−	1.42601i
$305$	0.0773639	+	0.0446661i	0.00442984	+	0.00255757i
$306$		0			0
$307$	18.8505	−	10.8833i	1.07585	−	0.621144i	0.146078	−	0.989273i	$-0.453335\pi$
$307$	18.8505	−	10.8833i	1.07585	−	0.621144i	0.929775	+	0.368129i	$0.120002\pi$
$308$	6.44980	+	2.93720i	0.367512	+	0.167363i
$309$		0			0
$310$	−8.34947	−	4.29881i	−0.474218	−	0.244156i
$311$	−10.9280	+	9.16969i	−0.619671	+	0.519966i	−0.897700	−	0.440607i	$-0.854763\pi$
$311$	−10.9280	+	9.16969i	−0.619671	+	0.519966i	0.278029	+	0.960573i	$0.410319\pi$
$312$		0			0
$313$	−19.9926	+	7.27672i	−1.13005	+	0.411304i	−0.838310	−	0.545194i	$-0.816456\pi$
$313$	−19.9926	+	7.27672i	−1.13005	+	0.411304i	−0.291739	+	0.956498i	$0.594234\pi$
$314$	−17.8816	+	23.5222i	−1.00912	+	1.32743i
$315$		0			0
$316$	−11.6081	+	3.22265i	−0.653006	+	0.181288i
$317$	6.63831	+	1.17051i	0.372845	+	0.0657426i	0.356931	−	0.934131i	$-0.383823\pi$
$317$	6.63831	+	1.17051i	0.372845	+	0.0657426i	0.0159138	+	0.999873i	$0.494934\pi$
$318$		0			0
$319$	4.55576	−	12.5168i	0.255073	−	0.700808i
$320$	15.1636	+	10.0186i	0.847670	+	0.560055i
$321$		0			0
$322$	4.48984	+	1.39346i	0.250209	+	0.0776542i
$323$	−30.5753			−1.70125
$324$		0			0
$325$	−0.731790			−0.0405924
$326$	4.43433	+	1.37623i	0.245595	+	0.0762222i
$327$		0			0
$328$	−11.0009	−	2.28346i	−0.607423	−	0.126083i
$329$	−5.36595	+	14.7428i	−0.295835	+	0.812799i
$330$		0			0
$331$	23.8297	+	4.20182i	1.30980	+	0.230953i	0.784587	−	0.620019i	$-0.212875\pi$
$331$	23.8297	+	4.20182i	1.30980	+	0.230953i	0.525212	+	0.850972i	$0.323986\pi$
$332$	−5.10729	−	18.3966i	−0.280299	−	1.00965i
$333$		0			0
$334$	−16.3896	+	21.5596i	−0.896800	+	1.17969i
$335$	−25.4773	+	9.27297i	−1.39197	+	0.506636i
$336$		0			0
$337$	16.7397	−	14.0463i	0.911869	−	0.765149i	−0.0606043	−	0.998162i	$-0.519303\pi$
$337$	16.7397	−	14.0463i	0.911869	−	0.765149i	0.972474	+	0.233013i	$0.0748583\pi$
$338$	−9.62022	−	4.95307i	−0.523271	−	0.269411i
$339$		0			0
$340$	9.14936	−	20.0911i	0.496193	−	1.08959i
$341$	−6.84620	+	3.95266i	−0.370743	+	0.214048i
$342$		0			0
$343$	13.9379	+	8.04707i	0.752577	+	0.434501i
$344$	20.4627	+	12.6510i	1.10327	+	0.682097i
$345$		0			0
$346$	12.3489	−	0.594861i	0.663879	−	0.0319799i
$347$	2.24912	+	12.7554i	0.120739	+	0.684745i	0.983748	+	0.179556i	$0.0574661\pi$
$347$	2.24912	+	12.7554i	0.120739	+	0.684745i	−0.863009	+	0.505189i	$0.831423\pi$
$348$		0			0
$349$	−2.96273	−	2.48603i	−0.158591	−	0.133074i	0.560039	−	0.828466i	$-0.310786\pi$
$349$	−2.96273	−	2.48603i	−0.158591	−	0.133074i	−0.718630	+	0.695392i	$0.755231\pi$
$350$	0.275159	−	0.115428i	0.0147079	−	0.00616990i
$351$		0			0
$352$	13.9990	−	6.17120i	0.746149	−	0.328926i
$353$	−1.95578	+	2.33080i	−0.104095	+	0.124056i	−0.815577	−	0.578649i	$-0.803580\pi$
$353$	−1.95578	+	2.33080i	−0.104095	+	0.124056i	0.711481	+	0.702705i	$0.248025\pi$
$354$		0			0
$355$	−5.48444	+	0.967055i	−0.291084	+	0.0513260i
$356$	5.95932	+	12.4851i	0.315844	+	0.661711i
$357$		0			0
$358$	−8.36880	+	1.89488i	−0.442305	+	0.100147i
$359$	−8.27544	+	14.3335i	−0.436761	+	0.756492i	−0.997438	−	0.0715425i	$-0.977208\pi$
$359$	−8.27544	+	14.3335i	−0.436761	+	0.756492i	0.560676	+	0.828035i	$0.310541\pi$
$360$		0			0
$361$	10.2995	+	17.8393i	0.542082	+	0.938913i
$362$	15.3890	+	16.6432i	0.808830	+	0.874746i
$363$		0			0
$364$	11.8721	+	0.931065i	0.622265	+	0.0488011i
$365$	9.02965	+	10.7611i	0.472633	+	0.563262i
$366$		0			0
$367$	−0.754802	−	2.07380i	−0.0394003	−	0.108252i	0.918432	−	0.395578i	$-0.129456\pi$
$367$	−0.754802	−	2.07380i	−0.0394003	−	0.108252i	−0.957833	+	0.287327i	$0.907234\pi$
$368$	8.69586	−	5.23151i	0.453303	−	0.272711i
$369$		0			0
$370$	3.12731	−	24.6097i	0.162581	−	1.27940i
$371$	0.874327	−	4.95856i	0.0453928	−	0.257435i
$372$		0			0
$373$	9.85493	+	3.58690i	0.510269	+	0.185723i	0.584307	−	0.811533i	$-0.301366\pi$
$373$	9.85493	+	3.58690i	0.510269	+	0.185723i	−0.0740382	+	0.997255i	$0.523589\pi$
$374$	−10.0553	−	15.6280i	−0.519949	−	0.808107i
$375$		0			0
$376$	16.0425	+	29.8271i	0.827331	+	1.53822i
$377$		−	22.3819i		−	1.15273i
$378$		0			0
$379$		−	3.08694i		−	0.158565i	−0.996852	−	0.0792826i	$-0.974737\pi$
$379$		−	3.08694i		−	0.158565i	0.996852	−	0.0792826i	$-0.0252630\pi$
$380$	−28.4594	+	2.74823i	−1.45994	+	0.140981i
$381$		0			0
$382$	13.9115	−	8.95088i	0.711774	−	0.457967i
$383$	15.0967	+	5.49476i	0.771406	+	0.280769i	0.697585	−	0.716503i	$-0.254258\pi$
$383$	15.0967	+	5.49476i	0.771406	+	0.280769i	0.0738218	+	0.997271i	$0.476480\pi$
$384$		0			0
$385$	1.39790	−	7.92791i	0.0712438	−	0.404044i
$386$	24.6515	+	3.13262i	1.25473	+	0.159446i
$387$		0			0
$388$	−16.9547	−	4.37980i	−0.860743	−	0.222351i
$389$	−6.03724	−	16.5872i	−0.306100	−	0.841004i	−0.993407	−	0.114637i	$-0.963430\pi$
$389$	−6.03724	−	16.5872i	−0.306100	−	0.841004i	0.687307	−	0.726367i	$-0.258793\pi$
$390$		0			0
$391$	−7.92365	−	9.44304i	−0.400716	−	0.477555i
$392$	14.1897	−	4.68554i	0.716687	−	0.236656i
$393$		0			0
$394$	23.9327	−	22.1293i	1.20571	−	1.11486i
$395$	6.84213	+	11.8509i	0.344265	+	0.596285i
$396$		0			0
$397$	6.73828	−	11.6710i	0.338185	−	0.585753i	−0.645907	−	0.763416i	$-0.723520\pi$
$397$	6.73828	−	11.6710i	0.338185	−	0.585753i	0.984091	+	0.177663i	$0.0568538\pi$
$398$	0.976415	+	4.31238i	0.0489433	+	0.216160i
$399$		0			0
$400$	0.209373	−	0.609152i	0.0104687	−	0.0304576i
$401$	−6.65594	+	1.17362i	−0.332382	+	0.0586079i	−0.337349	−	0.941380i	$-0.609530\pi$
$401$	−6.65594	+	1.17362i	−0.332382	+	0.0586079i	0.00496671	+	0.999988i	$0.498419\pi$
$402$		0			0
$403$	−8.53836	+	10.1756i	−0.425326	+	0.506884i
$404$	3.14191	+	3.08585i	0.156316	+	0.153527i
$405$		0			0
$406$	3.53039	+	8.41578i	0.175210	+	0.417668i
$407$	−15.9970	−	13.4231i	−0.792944	−	0.665359i
$408$		0			0
$409$	3.27211	+	18.5570i	0.161795	+	0.917586i	0.952307	+	0.305140i	$0.0987033\pi$
$409$	3.27211	+	18.5570i	0.161795	+	0.917586i	−0.790512	+	0.612446i	$0.790186\pi$
$410$	0.614061	+	12.7475i	0.0303263	+	0.629552i
$411$		0			0
$412$	3.20223	−	2.28546i	0.157763	−	0.112597i
$413$	−13.0039	−	7.50779i	−0.639879	−	0.369434i
$414$		0			0
$415$	−18.7815	+	10.8435i	−0.921947	+	0.532287i
$416$	18.5574	−	17.7893i	0.909852	−	0.872194i
$417$		0			0
$418$	−11.0172	+	21.3985i	−0.538870	+	1.04663i
$419$	−14.6271	+	12.2736i	−0.714582	+	0.599606i	−0.925881	−	0.377816i	$-0.876675\pi$
$419$	−14.6271	+	12.2736i	−0.714582	+	0.599606i	0.211299	+	0.977422i	$0.432231\pi$
$420$		0			0
$421$	21.1833	−	7.71011i	1.03241	−	0.375768i	0.230414	−	0.973093i	$-0.425992\pi$
$421$	21.1833	−	7.71011i	1.03241	−	0.375768i	0.801999	+	0.597325i	$0.203770\pi$
$422$	−14.4707	−	11.0006i	−0.704421	−	0.535502i
$423$		0			0
$424$	−6.73252	−	8.53292i	−0.326960	−	0.414395i
$425$	−0.770535	−	0.135866i	−0.0373765	−	0.00659048i
$426$		0			0
$427$	−0.0176216	+	0.0484150i	−0.000852770	+	0.00234297i
$428$	−6.70486	−	4.60541i	−0.324092	−	0.222611i
$429$		0			0
$430$	8.09999	−	26.0989i	0.390616	−	1.25860i
$431$	−10.8059			−0.520500			−0.260250	−	0.965541i	$-0.583805\pi$
$431$	−10.8059			−0.520500			−0.260250	+	0.965541i	$0.583805\pi$
$432$		0			0
$433$	−37.5914			−1.80653			−0.903264	−	0.429084i	$-0.858836\pi$
$433$	−37.5914			−1.80653			−0.903264	+	0.429084i	$0.858836\pi$
$434$	1.60545	−	5.17291i	0.0770642	−	0.248308i
$435$		0			0
$436$	2.98425	+	2.04981i	0.142920	+	0.0981681i
$437$	−5.46040	+	15.0023i	−0.261206	+	0.717659i
$438$		0			0
$439$	−31.4487	−	5.54525i	−1.50096	−	0.264660i	−0.638043	−	0.770000i	$-0.720256\pi$
$439$	−31.4487	−	5.54525i	−1.50096	−	0.264660i	−0.862920	+	0.505340i	$0.831367\pi$
$440$	−10.7642	−	13.6427i	−0.513163	−	0.650392i
$441$		0			0
$442$	−24.8585	−	18.8974i	−1.18240	−	0.898859i
$443$	35.3150	−	12.8536i	1.67786	−	0.610693i	0.684850	−	0.728684i	$-0.259868\pi$
$443$	35.3150	−	12.8536i	1.67786	−	0.610693i	0.993015	+	0.117992i	$0.0376456\pi$
$444$		0			0
$445$	12.0380	−	10.1011i	0.570656	−	0.478837i
$446$	−6.69318	+	13.0000i	−0.316931	+	0.615568i
$447$		0			0
$448$	−4.17176	+	9.61608i	−0.197097	+	0.454317i
$449$	−6.99926	+	4.04102i	−0.330315	+	0.190708i	−0.655981	−	0.754777i	$-0.727745\pi$
$449$	−6.99926	+	4.04102i	−0.330315	+	0.190708i	0.325666	+	0.945485i	$0.394412\pi$
$450$		0			0
$451$	9.30376	+	5.37153i	0.438097	+	0.252935i
$452$	5.71460	−	4.07856i	0.268792	−	0.191839i
$453$		0			0
$454$	−0.00653538	−	0.135670i	−0.000306720	−	0.00636729i
$455$	−2.34891	−	13.3213i	−0.110118	−	0.624513i
$456$		0			0
$457$	−1.89531	−	1.59036i	−0.0886590	−	0.0743937i	0.597381	−	0.801958i	$-0.296208\pi$
$457$	−1.89531	−	1.59036i	−0.0886590	−	0.0743937i	−0.686040	+	0.727564i	$0.740652\pi$
$458$	−14.7014	−	35.0453i	−0.686950	−	1.63756i
$459$		0			0
$460$	−8.22409	−	8.07735i	−0.383450	−	0.376608i
$461$	−5.80793	+	6.92163i	−0.270502	+	0.322372i	−0.884146	−	0.467211i	$-0.845259\pi$
$461$	−5.80793	+	6.92163i	−0.270502	+	0.322372i	0.613643	+	0.789583i	$0.289703\pi$
$462$		0			0
$463$	−1.37343	+	0.242173i	−0.0638287	+	0.0112547i	−0.205471	−	0.978663i	$-0.565873\pi$
$463$	−1.37343	+	0.242173i	−0.0638287	+	0.0112547i	0.141643	+	0.989918i	$0.454762\pi$
$464$	18.6310	+	6.40371i	0.864923	+	0.297285i
$465$		0			0
$466$	−2.25924	−	9.97803i	−0.104657	−	0.462223i
$467$	−10.5492	+	18.2717i	−0.488158	+	0.845515i	−0.999907	−	0.0136203i	$-0.995664\pi$
$467$	−10.5492	+	18.2717i	−0.488158	+	0.845515i	0.511749	+	0.859135i	$0.328998\pi$
$468$		0			0
$469$	−7.81850	−	13.5420i	−0.361025	−	0.625313i
$470$	28.2459	−	26.1174i	1.30289	−	1.20471i
$471$		0			0
$472$	−30.7793	+	10.1636i	−1.41673	+	0.467817i
$473$	−14.7863	−	17.6216i	−0.679875	−	0.810244i
$474$		0			0
$475$	0.346584	+	0.952230i	0.0159023	+	0.0436913i
$476$	12.3278	+	3.18456i	0.565042	+	0.145964i
$477$		0			0
$478$	−17.8974	−	2.27433i	−0.818606	−	0.104025i
$479$	−2.53604	+	14.3826i	−0.115874	+	0.657156i	0.870439	+	0.492276i	$0.163835\pi$
$479$	−2.53604	+	14.3826i	−0.115874	+	0.657156i	−0.986314	+	0.164880i	$0.947276\pi$
$480$		0			0
$481$	−32.9731	−	12.0012i	−1.50344	−	0.547208i
$482$	−9.00641	+	5.79487i	−0.410231	+	0.263949i
$483$		0			0
$484$	7.33740	−	0.708548i	0.333518	−	0.0322067i
$485$			19.8909i			0.903201i
$486$		0			0
$487$		−	0.282541i		−	0.0128032i	−0.999980	−	0.00640158i	$-0.997962\pi$
$487$		−	0.282541i		−	0.0128032i	0.999980	−	0.00640158i	$-0.00203770\pi$
$488$	0.0526832	+	0.0979513i	0.00238486	+	0.00443405i
$489$		0			0
$490$	−9.18445	−	14.2745i	−0.414911	−	0.644857i
$491$	−14.5642	−	5.30093i	−0.657273	−	0.239228i	−0.00821432	−	0.999966i	$-0.502615\pi$
$491$	−14.5642	−	5.30093i	−0.657273	−	0.239228i	−0.649058	+	0.760739i	$0.724837\pi$
$492$		0			0
$493$	4.15549	−	23.5669i	0.187154	−	1.06140i
$494$	−5.09819	+	40.1191i	−0.229379	+	1.80505i
$495$		0			0
$496$	−6.02742	−	10.0188i	−0.270639	−	0.449858i
$497$	−1.09855	−	3.01824i	−0.0492766	−	0.135386i
$498$		0			0
$499$	−26.2876	−	31.3283i	−1.17679	−	1.40245i	−0.896794	−	0.442448i	$-0.854110\pi$
$499$	−26.2876	−	31.3283i	−1.17679	−	1.40245i	−0.279999	−	0.960000i	$-0.590334\pi$
$500$	21.9189	+	1.71899i	0.980245	+	0.0768757i
$501$		0			0
$502$	11.4255	+	12.3566i	0.509944	+	0.551502i
$503$	9.96192	+	17.2546i	0.444180	+	0.769343i	0.997995	−	0.0632975i	$-0.0201617\pi$
$503$	9.96192	+	17.2546i	0.444180	+	0.769343i	−0.553815	+	0.832640i	$0.686828\pi$
$504$		0			0
$505$	2.50117	−	4.33215i	0.111301	−	0.192778i
$506$	−9.46397	+	2.14285i	−0.420725	+	0.0952611i
$507$		0			0
$508$	9.66532	+	20.2494i	0.428829	+	0.898424i
$509$	−27.8835	+	4.91661i	−1.23591	+	0.217925i	−0.753164	−	0.657833i	$-0.771473\pi$
$509$	−27.8835	+	4.91661i	−1.23591	+	0.217925i	−0.482750	+	0.875758i	$0.660362\pi$
$510$		0			0
$511$	−5.20783	+	6.20645i	−0.230381	+	0.274557i
$512$	9.49862	+	20.5372i	0.419783	+	0.907624i
$513$		0			0
$514$	−7.11925	+	2.98650i	−0.314017	+	0.131729i
$515$	−3.42330	−	2.87249i	−0.150848	−	0.126577i
$516$		0			0
$517$	−5.62335	−	31.8916i	−0.247315	−	1.40259i
$518$	14.2912	−	0.688423i	0.627917	−	0.0302476i
$519$		0			0
$520$	−24.8368	−	15.3553i	−1.08917	−	0.673375i
$521$	−18.4642	−	10.6603i	−0.808931	−	0.467036i	0.0376537	−	0.999291i	$-0.488012\pi$
$521$	−18.4642	−	10.6603i	−0.808931	−	0.467036i	−0.846584	+	0.532255i	$0.821345\pi$
$522$		0			0
$523$	17.0213	−	9.82725i	0.744289	−	0.429716i	−0.0793376	−	0.996848i	$-0.525281\pi$
$523$	17.0213	−	9.82725i	0.744289	−	0.429716i	0.823627	+	0.567132i	$0.191947\pi$
$524$	4.25276	−	9.33864i	0.185783	−	0.407961i
$525$		0			0
$526$	25.6102	+	13.1856i	1.11666	+	0.574922i
$527$	−10.8797	+	9.12913i	−0.473926	+	0.397671i
$528$		0			0
$529$	15.5644	−	5.66500i	0.676715	−	0.246304i
$530$	−7.47171	+	9.82861i	−0.324551	+	0.426927i
$531$		0			0
$532$	−4.41120	−	15.8893i	−0.191250	−	0.688888i
$533$	17.7774	+	3.13463i	0.770023	+	0.135776i
$534$		0			0
$535$	−3.16012	+	8.68236i	−0.136624	+	0.375371i
$536$	−33.0509	−	6.86038i	−1.42758	−	0.296323i
$537$		0			0
$538$	−12.3221	−	3.82427i	−0.531245	−	0.164876i
$539$	−14.2884			−0.615447
$540$		0			0
$541$	41.1619			1.76969			0.884844	−	0.465888i	$-0.154265\pi$
$541$	41.1619			1.76969			0.884844	+	0.465888i	$0.154265\pi$
$542$	−28.7189	−	8.91312i	−1.23358	−	0.382851i
$543$		0			0
$544$	22.8428	−	15.2858i	0.979377	−	0.655373i
$545$	1.40653	−	3.86441i	0.0602492	−	0.165533i
$546$		0			0
$547$	7.15368	+	1.26139i	0.305869	+	0.0539330i	0.324476	−	0.945894i	$-0.394812\pi$
$547$	7.15368	+	1.26139i	0.305869	+	0.0539330i	−0.0186069	+	0.999827i	$0.505923\pi$
$548$	3.48492	−	0.967487i	0.148869	−	0.0413290i
$549$		0			0
$550$	−0.372736	+	0.490312i	−0.0158935	+	0.0209070i
$551$	−29.1241	+	10.6003i	−1.24073	+	0.451588i
$552$		0			0
$553$	−6.04591	+	5.07312i	−0.257098	+	0.215731i
$554$	32.0929	+	16.5234i	1.36350	+	0.702010i
$555$		0			0
$556$	−23.6635	−	10.7762i	−1.00356	−	0.457014i
$557$	32.2123	−	18.5978i	1.36488	−	0.788012i	0.374609	−	0.927183i	$-0.377777\pi$
$557$	32.2123	−	18.5978i	1.36488	−	0.788012i	0.990268	+	0.139170i	$0.0444436\pi$
$558$		0			0
$559$	−33.4743	−	19.3264i	−1.41581	−	0.817419i
$560$	11.7609	+	1.85611i	0.496989	+	0.0784351i
$561$		0			0
$562$	−17.4120	+	0.838759i	−0.734481	+	0.0353809i
$563$	7.70741	+	43.7109i	0.324829	+	1.84219i	0.510876	+	0.859654i	$0.329321\pi$
$563$	7.70741	+	43.7109i	0.324829	+	1.84219i	−0.186048	+	0.982541i	$0.559568\pi$
$564$		0			0
$565$	−6.10911	−	5.12615i	−0.257012	−	0.215659i
$566$	21.7879	−	9.13997i	0.915816	−	0.384181i
$567$		0			0
$568$	−6.44104	−	2.56663i	−0.270260	−	0.107694i
$569$	−18.9577	+	22.5929i	−0.794749	+	0.947144i	−0.999498	−	0.0316699i	$-0.989917\pi$
$569$	−18.9577	+	22.5929i	−0.794749	+	0.947144i	0.204750	+	0.978814i	$0.434362\pi$
$570$		0			0
$571$	−12.9011	+	2.27481i	−0.539893	+	0.0951977i	−0.436944	−	0.899489i	$-0.643939\pi$
$571$	−12.9011	+	2.27481i	−0.539893	+	0.0951977i	−0.102949	+	0.994687i	$0.532828\pi$
$572$	−22.1829	+	10.5882i	−0.927514	+	0.442714i
$573$		0			0
$574$	−7.17888	+	1.62545i	−0.299641	+	0.0678450i
$575$	−0.204274	+	0.353814i	−0.00851883	+	0.0147550i
$576$		0			0
$577$	2.02124	+	3.50090i	0.0841455	+	0.145744i	0.905027	−	0.425355i	$-0.139851\pi$
$577$	2.02124	+	3.50090i	0.0841455	+	0.145744i	−0.820881	+	0.571099i	$0.806517\pi$
$578$	−6.34420	−	6.86122i	−0.263884	−	0.285389i
$579$		0			0
$580$	1.74963	−	22.3096i	0.0726493	−	0.926354i
$581$	−8.03995	−	9.58164i	−0.333553	−	0.397513i
$582$		0			0
$583$	3.55456	+	9.76606i	0.147215	+	0.404469i
$584$	2.51677	+	17.3076i	0.104145	+	0.716192i
$585$		0			0
$586$	−2.37637	+	18.7003i	−0.0981667	+	0.772502i
$587$	−1.26345	+	7.16540i	−0.0521483	+	0.295748i	−0.999717	−	0.0238055i	$-0.992422\pi$
$587$	−1.26345	+	7.16540i	−0.0521483	+	0.295748i	0.947568	+	0.319553i	$0.103533\pi$
$588$		0			0
$589$	17.2847	+	6.29113i	0.712206	+	0.259222i
$590$	19.9223	+	30.9634i	0.820190	+	1.27474i
$591$		0			0
$592$	19.4240	−	24.0136i	0.798320	−	0.986952i
$593$			2.93118i			0.120369i	0.998187	+	0.0601846i	$0.0191689\pi$
$593$			2.93118i			0.120369i	−0.998187	+	0.0601846i	$0.980831\pi$
$594$		0			0
$595$		−	14.4627i		−	0.592914i
$596$	0.494747	+	5.12338i	0.0202656	+	0.209862i
$597$		0			0
$598$	−13.7118	+	8.82242i	−0.560719	+	0.360775i
$599$	−1.27568	−	0.464311i	−0.0521230	−	0.0189712i	0.315827	−	0.948817i	$-0.397718\pi$
$599$	−1.27568	−	0.464311i	−0.0521230	−	0.0189712i	−0.367950	+	0.929846i	$0.619940\pi$
$600$		0			0
$601$	1.34379	−	7.62101i	0.0548144	−	0.310868i	−0.945057	−	0.326906i	$-0.893994\pi$
$601$	1.34379	−	7.62101i	0.0548144	−	0.310868i	0.999871	+	0.0160378i	$0.00510522\pi$
$602$	15.6350	+	1.98684i	0.637236	+	0.0809777i
$603$		0			0
$604$	2.62627	−	10.1666i	0.106861	−	0.413672i
$605$	−2.86383	−	7.86832i	−0.116431	−	0.319893i
$606$		0			0
$607$	−7.34402	−	8.75226i	−0.298085	−	0.355243i	0.596125	−	0.802891i	$-0.296706\pi$
$607$	−7.34402	−	8.75226i	−0.298085	−	0.355243i	−0.894210	+	0.447648i	$0.852262\pi$
$608$	−31.9371	−	15.7223i	−1.29522	−	0.637625i
$609$		0			0
$610$	0.0927586	−	0.0857688i	0.00375569	−	0.00347268i
$611$	−27.2072	−	47.1242i	−1.10068	−	1.90644i
$612$		0			0
$613$	−12.0261	+	20.8298i	−0.485729	+	0.841307i	−0.999865	−	0.0164015i	$-0.994779\pi$
$613$	−12.0261	+	20.8298i	−0.485729	+	0.841307i	0.514137	+	0.857708i	$0.328112\pi$
$614$	−6.79779	−	30.0227i	−0.274336	−	1.21162i
$615$		0			0
$616$	6.67084	−	7.48025i	0.268776	−	0.301388i
$617$	47.5174	−	8.37860i	1.91298	−	0.337310i	0.915147	−	0.403119i	$-0.132074\pi$
$617$	47.5174	−	8.37860i	1.91298	−	0.337310i	0.997832	+	0.0658095i	$0.0209630\pi$
$618$		0			0
$619$	2.89879	−	3.45464i	0.116512	−	0.138854i	−0.704636	−	0.709569i	$-0.748890\pi$
$619$	2.89879	−	3.45464i	0.116512	−	0.138854i	0.821148	+	0.570715i	$0.193334\pi$
$620$	−9.30621	+	9.47528i	−0.373747	+	0.380537i
$621$		0			0
$622$	7.80425	+	18.6038i	0.312922	+	0.745946i
$623$	6.94290	+	5.82578i	0.278161	+	0.233405i
$624$		0			0
$625$	−4.47652	−	25.3876i	−0.179061	−	1.01550i
$626$	1.44772	+	30.0535i	0.0578624	+	1.20118i
$627$		0			0
$628$	24.2747	+	34.0121i	0.968668	+	1.35723i
$629$	−32.4907	−	18.7585i	−1.29549	−	0.747951i
$630$		0			0
$631$	−9.73065	+	5.61799i	−0.387371	+	0.223649i	−0.681020	−	0.732264i	$-0.738464\pi$
$631$	−9.73065	+	5.61799i	−0.387371	+	0.223649i	0.293649	+	0.955913i	$0.405130\pi$
$632$	−0.513265	+	17.0295i	−0.0204166	+	0.677396i
$633$		0			0
$634$	4.36366	−	8.47544i	0.173303	−	0.336603i
$635$	19.5242	−	16.3828i	0.774796	−	0.650131i
$636$		0			0
$637$	−22.5610	+	8.21154i	−0.893900	+	0.325353i
$638$	−14.9963	−	11.4002i	−0.593708	−	0.451337i
$639$		0			0
$640$	19.8881	−	16.2812i	0.786145	−	0.643570i
$641$	39.8883	+	7.03338i	1.57549	+	0.277802i	0.891958	−	0.452118i	$-0.149331\pi$
$641$	39.8883	+	7.03338i	1.57549	+	0.277802i	0.683533	+	0.729919i	$0.260442\pi$
$642$		0			0
$643$	11.0345	−	30.3169i	0.435157	−	1.19558i	−0.507451	−	0.861681i	$-0.669412\pi$
$643$	11.0345	−	30.3169i	0.435157	−	1.19558i	0.942608	−	0.333902i	$-0.108366\pi$
$644$	3.76417	−	5.48013i	0.148329	−	0.215947i
$645$		0			0
$646$	−12.8168	+	41.2968i	−0.504269	+	1.62480i
$647$	7.00490			0.275391			0.137696	−	0.990475i	$-0.456030\pi$
$647$	7.00490			0.275391			0.137696	+	0.990475i	$0.456030\pi$
$648$		0			0
$649$	30.9936			1.21660
$650$	−0.306757	+	0.988399i	−0.0120320	+	0.0387682i
$651$		0			0
$652$	3.71763	−	5.41237i	0.145594	−	0.211965i
$653$	12.0075	−	32.9903i	0.469889	−	1.29101i	−0.447951	−	0.894058i	$-0.647846\pi$
$653$	12.0075	−	32.9903i	0.469889	−	1.29101i	0.917840	−	0.396951i	$-0.129932\pi$
$654$		0			0
$655$	−11.4788	−	2.02402i	−0.448514	−	0.0790850i
$656$	−7.69561	+	13.9013i	−0.300463	+	0.542754i
$657$		0			0
$658$	17.6632	+	13.4276i	0.688584	+	0.523462i
$659$	8.41721	−	3.06361i	0.327888	−	0.119341i	−0.172831	−	0.984952i	$-0.555291\pi$
$659$	8.41721	−	3.06361i	0.327888	−	0.119341i	0.500719	+	0.865610i	$0.333069\pi$
$660$		0			0
$661$	−27.2876	+	22.8970i	−1.06137	+	0.890592i	−0.994243	−	0.107153i	$-0.965826\pi$
$661$	−27.2876	+	22.8970i	−1.06137	+	0.890592i	−0.0671232	+	0.997745i	$0.521382\pi$
$662$	15.6643	−	30.4245i	0.608812	−	1.18248i
$663$		0			0
$664$	−26.9885	−	0.813429i	−1.04736	−	0.0315672i
$665$	−16.2217	+	9.36560i	−0.629050	+	0.363182i
$666$		0			0
$667$	−10.8214	−	6.24776i	−0.419008	−	0.241914i
$668$	22.2494	+	31.1743i	0.860854	+	1.20617i
$669$		0			0
$670$	1.84488	+	38.2982i	0.0712738	+	1.47959i
$671$	−0.0184669	−	0.104731i	−0.000712907	−	0.00404310i
$672$		0			0
$673$	−2.58660	−	2.17042i	−0.0997062	−	0.0836634i	0.591572	−	0.806252i	$-0.298508\pi$
$673$	−2.58660	−	2.17042i	−0.0997062	−	0.0836634i	−0.691278	+	0.722589i	$0.742952\pi$
$674$	−11.9547	−	28.4977i	−0.460477	−	1.09769i
$675$		0			0
$676$	−10.7226	+	10.9174i	−0.412407	+	0.419900i
$677$	0.742831	−	0.885272i	0.0285493	−	0.0340238i	−0.751581	−	0.659641i	$-0.770708\pi$
$677$	0.742831	−	0.885272i	0.0285493	−	0.0340238i	0.780130	+	0.625617i	$0.215153\pi$
$678$		0			0
$679$	−11.2978	+	1.99210i	−0.433569	+	0.0764499i
$680$	−23.3009	−	20.7796i	−0.893549	−	0.796861i
$681$		0			0
$682$	2.46885	+	10.9038i	0.0945372	+	0.417528i
$683$	21.5897	−	37.3945i	0.826107	−	1.43086i	−0.0749630	−	0.997186i	$-0.523884\pi$
$683$	21.5897	−	37.3945i	0.826107	−	1.43086i	0.901070	−	0.433673i	$-0.142783\pi$
$684$		0			0
$685$	−2.05411	−	3.55783i	−0.0784836	−	0.135938i
$686$	16.7115	−	15.4522i	0.638046	−	0.589967i
$687$		0			0
$688$	25.6649	−	22.3350i	0.978466	−	0.851513i
$689$	11.2251	+	13.3775i	0.427641	+	0.509643i
$690$		0			0
$691$	4.39185	+	12.0665i	0.167074	+	0.459031i	0.994769	−	0.102146i	$-0.0325709\pi$
$691$	4.39185	+	12.0665i	0.167074	+	0.459031i	−0.827696	+	0.561177i	$0.810349\pi$
$692$	4.37303	−	16.9285i	0.166238	−	0.643524i
$693$		0			0
$694$	18.1710	+	2.30910i	0.689761	+	0.0876523i
$695$	−5.12874	+	29.0865i	−0.194544	+	1.10331i
$696$		0			0
$697$	18.1366	+	6.60119i	0.686974	+	0.250038i
$698$	−4.59971	+	2.95953i	−0.174102	+	0.112020i
$699$		0			0
$700$	−0.0405611	−	0.420032i	−0.00153307	−	0.0158757i
$701$		−	3.10248i		−	0.117179i	−0.998282	−	0.0585896i	$-0.981340\pi$
$701$		−	3.10248i		−	0.117179i	0.998282	−	0.0585896i	$-0.0186603\pi$
$702$		0			0
$703$			48.5896i			1.83259i
$704$	−2.46699	−	21.4948i	−0.0929781	−	0.810114i
$705$		0			0
$706$	2.32828	+	3.61863i	0.0876262	+	0.136189i
$707$	2.71110	+	0.986759i	0.101961	+	0.0371109i
$708$		0			0
$709$	1.67631	−	9.50681i	0.0629550	−	0.357036i	−0.937015	−	0.349289i	$-0.886423\pi$
$709$	1.67631	−	9.50681i	0.0629550	−	0.357036i	0.999970	−	0.00774652i	$-0.00246582\pi$
$710$	−0.992846	+	7.81299i	−0.0372609	+	0.293216i
$711$		0			0
$712$	19.3613	−	2.81540i	0.725594	−	0.105512i
$713$	2.53639	+	6.96868i	0.0949887	+	0.260979i
$714$		0			0
$715$	17.9470	+	21.3884i	0.671181	+	0.799883i
$716$	−0.948762	+	12.0977i	−0.0354569	+	0.452112i
$717$		0			0
$718$	15.8907	+	17.1857i	0.593036	+	0.641365i
$719$	20.9190	+	36.2327i	0.780146	+	1.35125i	0.931856	+	0.362827i	$0.118188\pi$
$719$	20.9190	+	36.2327i	0.780146	+	1.35125i	−0.151711	+	0.988425i	$0.548478\pi$
$720$		0			0
$721$	1.28869	−	2.23207i	0.0479931	−	0.0831266i
$722$	28.4123	−	6.43316i	1.05740	−	0.239417i
$723$		0			0
$724$	28.9302	−	13.8088i	1.07518	−	0.513198i
$725$	−0.781069	+	0.137724i	−0.0290082	+	0.00511492i
$726$		0			0
$727$	−0.315311	+	0.375773i	−0.0116942	+	0.0139367i	−0.771860	−	0.635793i	$-0.780673\pi$
$727$	−0.315311	+	0.375773i	−0.0116942	+	0.0139367i	0.760166	+	0.649729i	$0.225118\pi$
$728$	6.23417	−	15.6448i	0.231054	−	0.579835i
$729$		0			0
$730$	18.3197	−	7.68506i	0.678043	−	0.284437i
$731$	−31.6584	−	26.5646i	−1.17093	−	0.982526i
$732$		0			0
$733$	5.08882	+	28.8601i	0.187960	+	1.06597i	0.922093	+	0.386967i	$0.126477\pi$
$733$	5.08882	+	28.8601i	0.187960	+	1.06597i	−0.734134	+	0.679005i	$0.762411\pi$
$734$	−3.11740	+	0.150169i	−0.115065	+	0.00554285i
$735$		0			0
$736$	−3.42080	−	13.9381i	−0.126092	−	0.513766i
$737$	27.9521	+	16.1381i	1.02963	+	0.594456i
$738$		0			0
$739$	34.8536	−	20.1228i	1.28211	−	0.740227i	0.304877	−	0.952392i	$-0.401384\pi$
$739$	34.8536	−	20.1228i	1.28211	−	0.740227i	0.977234	+	0.212164i	$0.0680512\pi$
$740$	−31.9284	−	14.5400i	−1.17371	−	0.534501i
$741$		0			0
$742$	−6.33082	−	3.25948i	−0.232412	−	0.119659i
$743$	30.1377	−	25.2885i	1.10564	−	0.927746i	0.107853	−	0.994167i	$-0.465603\pi$
$743$	30.1377	−	25.2885i	1.10564	−	0.927746i	0.997792	+	0.0664212i	$0.0211581\pi$
$744$		0			0
$745$	5.49409	−	1.99969i	0.201288	−	0.0732628i
$746$	8.97574	−	11.8071i	0.328625	−	0.432287i
$747$		0			0
$748$	−25.3232	+	7.03026i	−0.925909	+	0.257052i
$749$	−5.24795	−	0.925356i	−0.191756	−	0.0338118i
$750$		0			0
$751$	−9.37903	+	25.7687i	−0.342246	+	0.940312i	0.642496	+	0.766289i	$0.277899\pi$
$751$	−9.37903	+	25.7687i	−0.342246	+	0.940312i	−0.984742	+	0.174023i	$0.944323\pi$
$752$	47.0111	−	9.16488i	1.71432	−	0.334209i
$753$		0			0
$754$	−30.2303	−	9.38221i	−1.10092	−	0.341680i
$755$	−11.9272			−0.434077
$756$		0			0
$757$	−13.2822			−0.482750			−0.241375	−	0.970432i	$-0.577598\pi$
$757$	−13.2822			−0.482750			−0.241375	+	0.970432i	$0.577598\pi$
$758$	−4.16940	−	1.29400i	−0.151439	−	0.0470004i
$759$		0			0
$760$	−8.21789	+	39.5910i	−0.298094	+	1.43612i
$761$	−4.40238	+	12.0954i	−0.159586	+	0.438459i	−0.993555	−	0.113353i	$-0.963841\pi$
$761$	−4.40238	+	12.0954i	−0.159586	+	0.438459i	0.833969	+	0.551812i	$0.186063\pi$
$762$		0			0
$763$	2.33580	+	0.411864i	0.0845616	+	0.0149105i
$764$	−6.25807	−	22.5418i	−0.226409	−	0.815534i
$765$		0			0
$766$	13.7499	−	18.0872i	0.496804	−	0.653517i
$767$	48.9380	−	17.8120i	1.76705	−	0.643153i
$768$		0			0
$769$	22.2691	−	18.6860i	0.803045	−	0.673835i	−0.145892	−	0.989301i	$-0.546605\pi$
$769$	22.2691	−	18.6860i	0.803045	−	0.673835i	0.948937	+	0.315466i	$0.102161\pi$
$770$	−10.1219	−	5.21137i	−0.364769	−	0.187805i
$771$		0			0
$772$	14.5647	−	31.9826i	0.524195	−	1.15108i
$773$	4.16046	−	2.40204i	0.149641	−	0.0863954i	−0.423310	−	0.905985i	$-0.639132\pi$
$773$	4.16046	−	2.40204i	0.149641	−	0.0863954i	0.572951	+	0.819590i	$0.305798\pi$
$774$		0			0
$775$	0.407642	+	0.235352i	0.0146429	+	0.00845410i
$776$	−13.0228	+	21.0640i	−0.467492	+	0.756155i
$777$		0			0
$778$	−24.9344	+	1.20112i	−0.893941	+	0.0430623i
$779$	−4.34066	−	24.6171i	−0.155520	−	0.882000i
$780$		0			0
$781$	5.07868	+	4.26152i	0.181730	+	0.152489i
$782$	−16.0758	+	6.74375i	−0.574870	+	0.241156i
$783$		0			0
$784$	−0.380445	−	21.1295i	−0.0135873	−	0.754626i
$785$	30.5098	−	36.3601i	1.08894	−	1.29775i
$786$		0			0
$787$	39.5137	−	6.96732i	1.40851	−	0.248358i	0.582874	−	0.812562i	$-0.301928\pi$
$787$	39.5137	−	6.96732i	1.40851	−	0.248358i	0.825635	+	0.564204i	$0.190817\pi$
$788$	−19.8568	−	41.6013i	−0.707371	−	1.48198i
$789$		0			0
$790$	18.8747	−	4.27364i	0.671532	−	0.152049i
$791$	2.29975	−	3.98328i	0.0817696	−	0.141629i
$792$		0			0
$793$	−0.0893474	−	0.154754i	−0.00317282	−	0.00549548i
$794$	−12.9390	−	13.9935i	−0.459188	−	0.496610i
$795$		0			0
$796$	6.23386	+	0.488890i	0.220953	+	0.0173283i
$797$	19.9816	+	23.8132i	0.707785	+	0.843505i	0.993384	−	0.114844i	$-0.0366368\pi$
$797$	19.9816	+	23.8132i	0.707785	+	0.843505i	−0.285599	+	0.958349i	$0.592192\pi$
$798$		0			0
$799$	−19.8985	−	54.6706i	−0.703957	−	1.93411i
$800$	−0.734991	−	0.538141i	−0.0259859	−	0.0190262i
$801$		0			0
$802$	−1.20492	+	9.48189i	−0.0425473	+	0.334817i
$803$	2.90395	−	16.4691i	0.102478	−	0.581183i
$804$		0			0
$805$	−7.09642	−	2.58288i	−0.250116	−	0.0910347i
$806$	10.1646	+	15.7979i	0.358034	+	0.556458i
$807$		0			0
$808$	5.48499	−	2.95011i	0.192961	−	0.103784i
$809$			26.7938i			0.942021i	0.882128	+	0.471010i	$0.156111\pi$
$809$			26.7938i			0.942021i	−0.882128	+	0.471010i	$0.843889\pi$
$810$		0			0
$811$			22.6335i			0.794769i	0.917652	+	0.397384i	$0.130082\pi$
$811$			22.6335i			0.794769i	−0.917652	+	0.397384i	$0.869918\pi$
$812$	12.8468	−	1.24057i	0.450833	−	0.0435354i
$813$		0			0
$814$	−24.8358	+	15.9798i	−0.870494	+	0.560090i
$815$	−7.00868	−	2.55095i	−0.245503	−	0.0893559i
$816$		0			0
$817$	−9.29439	+	52.7111i	−0.325169	+	1.84413i
$818$	26.4359	+	3.35937i	0.924309	+	0.117458i
$819$		0			0
$820$	17.4749	+	4.51418i	0.610249	+	0.157642i
$821$	4.37655	+	12.0245i	0.152743	+	0.419657i	0.992338	−	0.123556i	$-0.0394298\pi$
$821$	4.37655	+	12.0245i	0.152743	+	0.419657i	−0.839595	+	0.543213i	$0.817208\pi$
$822$		0			0
$823$	16.6888	+	19.8889i	0.581735	+	0.693284i	0.973995	−	0.226570i	$-0.0727512\pi$
$823$	16.6888	+	19.8889i	0.581735	+	0.693284i	−0.392260	+	0.919854i	$0.628307\pi$
$824$	−1.74454	−	5.28316i	−0.0607741	−	0.184048i
$825$		0			0
$826$	−15.5915	+	14.4166i	−0.542499	+	0.501619i
$827$	−9.69134	−	16.7859i	−0.337001	−	0.583703i	0.646866	−	0.762603i	$-0.276079\pi$
$827$	−9.69134	−	16.7859i	−0.337001	−	0.583703i	−0.983867	+	0.178901i	$0.942746\pi$
$828$		0			0
$829$	−15.3678	+	26.6178i	−0.533745	+	0.924474i	0.465478	+	0.885060i	$0.345883\pi$
$829$	−15.3678	+	26.6178i	−0.533745	+	0.924474i	−0.999223	+	0.0394143i	$0.987451\pi$
$830$	6.77292	+	29.9129i	0.235091	+	1.03829i
$831$		0			0
$832$	−16.2483	−	32.5218i	−0.563309	−	1.12749i
$833$	−25.2801	+	4.45757i	−0.875905	+	0.154446i
$834$		0			0
$835$	27.9642	−	33.3264i	0.967740	−	1.15331i
$836$	24.2838	+	23.8505i	0.839872	+	0.824886i
$837$		0			0
$838$	10.4460	+	24.9012i	0.360850	+	0.860199i
$839$	−8.37643	−	7.02866i	−0.289186	−	0.242656i	0.486640	−	0.873603i	$-0.338222\pi$
$839$	−8.37643	−	7.02866i	−0.289186	−	0.242656i	−0.775826	+	0.630946i	$0.782667\pi$
$840$		0			0
$841$	0.823502	+	4.67031i	0.0283966	+	0.161045i
$842$	−1.53394	−	31.8435i	−0.0528631	−	1.09740i
$843$		0			0
$844$	−20.9240	+	14.9336i	−0.720234	+	0.514037i
$845$	15.0532	+	8.69096i	0.517845	+	0.298978i
$846$		0			0
$847$	4.18228	−	2.41464i	0.143705	−	0.0829680i
$848$	−14.3473	+	5.51646i	−0.492687	+	0.189436i
$849$		0			0
$850$	−0.506508	+	0.983778i	−0.0173731	+	0.0337433i
$851$	−15.0067	+	12.5921i	−0.514423	+	0.431652i
$852$		0			0
$853$	−6.04290	+	2.19943i	−0.206905	+	0.0753072i	−0.443394	−	0.896327i	$-0.646226\pi$
$853$	−6.04290	+	2.19943i	−0.206905	+	0.0753072i	0.236489	+	0.971634i	$0.424003\pi$
$854$	0.0580054	+	0.0440958i	0.00198490	+	0.00150893i
$855$		0			0
$856$	−9.03093	+	7.12545i	−0.308671	+	0.243543i
$857$	3.12650	+	0.551287i	0.106799	+	0.0188316i	0.226792	−	0.973943i	$-0.427176\pi$
$857$	3.12650	+	0.551287i	0.106799	+	0.0188316i	−0.119993	+	0.992775i	$0.538287\pi$
$858$		0			0
$859$	−9.69336	+	26.6323i	−0.330733	+	0.908682i	0.657188	+	0.753727i	$0.271746\pi$
$859$	−9.69336	+	26.6323i	−0.330733	+	0.908682i	−0.987921	+	0.154956i	$0.950477\pi$
$860$	−31.8553	−	21.8807i	−1.08626	−	0.746124i
$861$		0			0
$862$	−4.52968	+	14.5950i	−0.154281	+	0.497109i
$863$	53.5310			1.82222			0.911108	−	0.412168i	$-0.135228\pi$
$863$	53.5310			1.82222			0.911108	+	0.412168i	$0.135228\pi$
$864$		0			0
$865$	−19.8602			−0.675267
$866$	−15.7579	+	50.7732i	−0.535474	+	1.72534i
$867$		0			0
$868$	−6.31386	−	4.33684i	−0.214306	−	0.147202i
$869$	5.57172	−	15.3082i	0.189008	−	0.519294i
$870$		0			0
$871$	53.4100	+	9.41763i	1.80973	+	0.319104i
$872$	4.01956	−	3.17145i	0.136119	−	0.107399i
$873$		0			0
$874$	17.9741	+	13.6639i	0.607984	+	0.462190i
$875$	13.5351	−	4.92637i	0.457570	−	0.166542i
$876$		0			0
$877$	−22.8969	+	19.2128i	−0.773175	+	0.648770i	−0.941520	−	0.336958i	$-0.890602\pi$
$877$	−22.8969	+	19.2128i	−0.773175	+	0.648770i	0.168345	+	0.985728i	$0.446158\pi$
$878$	−20.6726	+	40.1520i	−0.697668	+	1.35506i
$879$		0			0
$880$	−22.9389	+	8.81990i	−0.773270	+	0.297319i
$881$	14.9002	−	8.60262i	0.502000	−	0.289830i	−0.227539	−	0.973769i	$-0.573068\pi$
$881$	14.9002	−	8.60262i	0.502000	−	0.289830i	0.729539	+	0.683939i	$0.239735\pi$
$882$		0			0
$883$	19.9228	+	11.5024i	0.670455	+	0.387088i	0.796249	−	0.604969i	$-0.206814\pi$
$883$	19.9228	+	11.5024i	0.670455	+	0.387088i	−0.125794	+	0.992056i	$0.540148\pi$
$884$	−35.9444	+	25.6538i	−1.20894	+	0.862830i
$885$		0			0
$886$	−2.55725	−	53.0866i	−0.0859124	−	1.78348i
$887$	−4.95616	−	28.1078i	−0.166411	−	0.943766i	−0.947597	−	0.319468i	$-0.896496\pi$
$887$	−4.95616	−	28.1078i	−0.166411	−	0.943766i	0.781186	−	0.624299i	$-0.214615\pi$
$888$		0			0
$889$	11.2606	+	9.44874i	0.377667	+	0.316901i
$890$	−8.59695	−	20.4935i	−0.288170	−	0.686944i
$891$		0			0
$892$	14.7529	+	14.4896i	0.493963	+	0.485149i
$893$	−48.4340	+	57.7214i	−1.62078	+	1.93157i
$894$		0			0
$895$	13.5745	−	2.39355i	0.453746	−	0.0800076i
$896$	11.2393	+	9.66557i	0.375479	+	0.322904i
$897$		0			0
$898$	2.52405	+	11.1476i	0.0842285	+	0.371999i
$899$	−7.19828	+	12.4678i	−0.240076	+	0.415824i
$900$		0			0
$901$	9.33569	+	16.1699i	0.311017	+	0.538697i
$902$	11.1551	−	10.3145i	0.371425	−	0.343436i
$903$		0			0
$904$	−3.11326	−	9.42817i	−0.103545	−	0.313576i
$905$	−23.4059	−	27.8941i	−0.778039	−	0.927231i
$906$		0			0
$907$	19.9408	+	54.7868i	0.662123	+	1.81917i	0.567027	+	0.823699i	$0.308093\pi$
$907$	19.9408	+	54.7868i	0.662123	+	1.81917i	0.0950957	+	0.995468i	$0.469684\pi$
$908$	−0.185983	−	0.0480439i	−0.00617206	−	0.00159439i
$909$		0			0
$910$	−18.9772	−	2.41155i	−0.629088	−	0.0799422i
$911$	−0.684711	+	3.88319i	−0.0226855	+	0.128656i	−0.994047	−	0.108949i	$-0.965251\pi$
$911$	−0.684711	+	3.88319i	−0.0226855	+	0.128656i	0.971362	+	0.237605i	$0.0763625\pi$
$912$		0			0
$913$	24.2606	+	8.83014i	0.802909	+	0.292235i
$914$	−2.94252	+	1.89327i	−0.0973300	+	0.0626237i
$915$		0			0
$916$	−53.4969	+	5.16602i	−1.76759	+	0.170690i
$917$		−	6.72250i		−	0.221997i
$918$		0			0
$919$		−	6.45794i		−	0.213028i	−0.994311	−	0.106514i	$-0.966031\pi$
$919$		−	6.45794i		−	0.213028i	0.994311	−	0.106514i	$-0.0339689\pi$
$920$	−14.3572	+	7.72203i	−0.473342	+	0.254588i
$921$		0			0
$922$	6.91415	+	10.7460i	0.227705	+	0.353901i
$923$	10.4682	+	3.81011i	0.344564	+	0.125411i
$924$		0			0
$925$	−0.215916	+	1.22452i	−0.00709928	+	0.0402620i
$926$	−0.248631	+	1.95655i	−0.00817054	+	0.0642963i
$927$		0			0
$928$	16.4591	−	22.4798i	0.540297	−	0.737936i
$929$	−19.4892	−	53.5462i	−0.639420	−	1.75679i	−0.653539	−	0.756893i	$-0.726716\pi$
$929$	−19.4892	−	53.5462i	−0.639420	−	1.75679i	0.0141186	−	0.999900i	$-0.495506\pi$
$930$		0			0
$931$	21.3703	+	25.4681i	0.700383	+	0.834684i
$932$	−14.4240	−	1.13120i	−0.472473	−	0.0370537i
$933$		0			0
$934$	20.2568	+	21.9076i	0.662823	+	0.716840i
$935$	14.9262	+	25.8530i	0.488140	+	0.845483i
$936$		0			0
$937$	9.57464	−	16.5838i	0.312790	−	0.541768i	−0.666175	−	0.745795i	$-0.732070\pi$
$937$	9.57464	−	16.5838i	0.312790	−	0.541768i	0.978965	+	0.204027i	$0.0654031\pi$
$938$	−21.5681	+	4.88348i	−0.704224	+	0.159451i
$939$		0			0
$940$	−23.4355	−	49.0987i	−0.764381	−	1.60142i
$941$	18.4077	−	3.24578i	0.600075	−	0.105809i	0.134645	−	0.990894i	$-0.457011\pi$
$941$	18.4077	−	3.24578i	0.600075	−	0.105809i	0.465430	+	0.885085i	$0.345900\pi$
$942$		0			0
$943$	6.47800	−	7.72018i	0.210953	−	0.251404i
$944$	0.825237	+	45.8329i	0.0268592	+	1.49173i
$945$		0			0
$946$	−29.9991	+	12.5845i	−0.975354	+	0.409158i
$947$	21.8007	+	18.2930i	0.708428	+	0.594442i	0.924158	−	0.382011i	$-0.124768\pi$
$947$	21.8007	+	18.2930i	0.708428	+	0.594442i	−0.215729	+	0.976453i	$0.569213\pi$
$948$		0			0
$949$	−4.87953	−	27.6732i	−0.158396	−	0.898309i
$950$	1.43142	−	0.0689535i	0.0464415	−	0.00223715i
$951$		0			0
$952$	9.46890	−	15.3157i	0.306889	−	0.496385i
$953$	39.0891	+	22.5681i	1.26622	+	0.731052i	0.974270	−	0.225382i	$-0.0723630\pi$
$953$	39.0891	+	22.5681i	1.26622	+	0.731052i	0.291949	+	0.956434i	$0.405696\pi$
$954$		0			0
$955$	−23.0134	+	13.2868i	−0.744695	+	0.429950i
$956$	−10.5742	+	23.2199i	−0.341994	+	0.750984i
$957$		0			0
$958$	18.3629	+	9.45431i	0.593278	+	0.305455i
$959$	1.81507	−	1.52303i	0.0586118	−	0.0491811i
$960$		0			0
$961$	−21.1016	+	7.68035i	−0.680697	+	0.247753i
$962$	−30.0315	+	39.5047i	−0.968253	+	1.27368i
$963$		0			0
$964$	4.05152	+	14.5937i	0.130491	+	0.470032i
$965$	−39.3121	−	6.93179i	−1.26550	−	0.223142i
$966$		0			0
$967$	−3.13528	+	8.61412i	−0.100824	+	0.277011i	−0.979841	−	0.199779i	$-0.935978\pi$
$967$	−3.13528	+	8.61412i	−0.100824	+	0.277011i	0.879017	+	0.476790i	$0.158200\pi$
$968$	2.11874	−	10.2073i	0.0680988	−	0.328077i
$969$		0			0
$970$	26.8659	+	8.33803i	0.862612	+	0.267718i
$971$	10.7197			0.344010			0.172005	−	0.985096i	$-0.444975\pi$
$971$	10.7197			0.344010			0.172005	+	0.985096i	$0.444975\pi$
$972$		0			0
$973$	−17.0344			−0.546098
$974$	−0.381617	−	0.118438i	−0.0122278	−	0.00379499i
$975$		0			0
$976$	0.154383	−	0.0300972i	0.00494168	−	0.000963387i
$977$	−17.0312	+	46.7929i	−0.544877	+	1.49704i	0.295665	+	0.955292i	$0.404459\pi$
$977$	−17.0312	+	46.7929i	−0.544877	+	1.49704i	−0.840542	+	0.541746i	$0.817763\pi$
$978$		0			0
$979$	−18.4233	−	3.24853i	−0.588812	−	0.103823i
$980$	−23.1300	+	6.42138i	−0.738862	+	0.205123i
$981$		0			0
$982$	−13.2649	+	17.4492i	−0.423299	+	0.556826i
$983$	−1.70953	+	0.622218i	−0.0545255	+	0.0198457i	−0.369139	−	0.929374i	$-0.620347\pi$
$983$	−1.70953	+	0.622218i	−0.0545255	+	0.0198457i	0.314613	+	0.949220i	$0.398125\pi$
$984$		0			0
$985$	−40.1114	+	33.6575i	−1.27806	+	1.07242i
$986$	−30.0890	−	15.4916i	−0.958229	−	0.493353i
$987$		0			0
$988$	52.0502	+	23.7034i	1.65594	+	0.754104i
$989$	−18.6883	+	10.7897i	−0.594252	+	0.343092i
$990$		0			0
$991$	−48.8792	−	28.2204i	−1.55270	−	0.896451i	−0.997921	−	0.0644516i	$-0.979470\pi$
$991$	−48.8792	−	28.2204i	−1.55270	−	0.896451i	−0.554777	−	0.831999i	$-0.687196\pi$
$992$	−16.0586	+	3.94123i	−0.509862	+	0.125134i
$993$		0			0
$994$	−4.53711	+	0.218558i	−0.143908	+	0.00693225i
$995$	−1.23338	−	6.99485i	−0.0391008	−	0.221752i
$996$		0			0
$997$	9.04342	+	7.58833i	0.286408	+	0.240325i	0.774660	−	0.632378i	$-0.217921\pi$
$997$	9.04342	+	7.58833i	0.286408	+	0.240325i	−0.488252	+	0.872703i	$0.662365\pi$
$998$	−53.3333	+	22.3731i	−1.68824	+	0.708209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.d.107.10		96
3.2	odd	2		972.2.l.a.107.7		96
4.3	odd	2	inner	972.2.l.d.107.15		96
9.2	odd	6		972.2.l.b.755.15		96
9.4	even	3		108.2.l.a.47.13	yes	96
9.5	odd	6		324.2.l.a.143.4		96
9.7	even	3		972.2.l.c.755.2		96
12.11	even	2		972.2.l.a.107.2		96
27.4	even	9		972.2.l.b.215.13		96
27.5	odd	18	inner	972.2.l.d.863.15		96
27.13	even	9		324.2.l.a.179.9		96
27.14	odd	18		108.2.l.a.23.8	✓	96
27.22	even	9		972.2.l.a.863.2		96
27.23	odd	18		972.2.l.c.215.4		96
36.7	odd	6		972.2.l.c.755.4		96
36.11	even	6		972.2.l.b.755.13		96
36.23	even	6		324.2.l.a.143.9		96
36.31	odd	6		108.2.l.a.47.8	yes	96
108.23	even	18		972.2.l.c.215.2		96
108.31	odd	18		972.2.l.b.215.15		96
108.59	even	18	inner	972.2.l.d.863.10		96
108.67	odd	18		324.2.l.a.179.4		96
108.95	even	18		108.2.l.a.23.13	yes	96
108.103	odd	18		972.2.l.a.863.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.8	✓	96	27.14	odd	18
108.2.l.a.23.13	yes	96	108.95	even	18
108.2.l.a.47.8	yes	96	36.31	odd	6
108.2.l.a.47.13	yes	96	9.4	even	3
324.2.l.a.143.4		96	9.5	odd	6
324.2.l.a.143.9		96	36.23	even	6
324.2.l.a.179.4		96	108.67	odd	18
324.2.l.a.179.9		96	27.13	even	9
972.2.l.a.107.2		96	12.11	even	2
972.2.l.a.107.7		96	3.2	odd	2
972.2.l.a.863.2		96	27.22	even	9
972.2.l.a.863.7		96	108.103	odd	18
972.2.l.b.215.13		96	27.4	even	9
972.2.l.b.215.15		96	108.31	odd	18
972.2.l.b.755.13		96	36.11	even	6
972.2.l.b.755.15		96	9.2	odd	6
972.2.l.c.215.2		96	108.23	even	18
972.2.l.c.215.4		96	27.23	odd	18
972.2.l.c.755.2		96	9.7	even	3
972.2.l.c.755.4		96	36.7	odd	6
972.2.l.d.107.10		96	1.1	even	1	trivial
972.2.l.d.107.15		96	4.3	odd	2	inner
972.2.l.d.863.10		96	108.59	even	18	inner
972.2.l.d.863.15		96	27.5	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.419187 - 1.35066i) q^{2} +(-1.64856 - 1.13236i) q^{4} +(-0.776998 + 2.13478i) q^{5} +(-1.29035 - 0.227523i) q^{7} +(-2.22049 + 1.75198i) q^{8} +(2.55766 + 1.94434i) q^{10} +(2.54138 - 0.924988i) q^{11} +(3.48118 - 2.92106i) q^{13} +(-0.848202 + 1.64744i) q^{14} +(1.43553 + 3.73353i) q^{16} +(4.20783 - 2.42939i) q^{17} +(-5.44971 - 3.14639i) q^{19} +(3.69827 - 2.63949i) q^{20} +(-0.184028 - 3.82029i) q^{22} +(-0.440555 - 2.49851i) q^{23} +(-0.123358 - 0.103510i) q^{25} +(-2.48609 - 5.92636i) q^{26} +(1.86958 + 1.83622i) q^{28} +(3.16586 - 3.77293i) q^{29} +(-2.87863 + 0.507580i) q^{31} +(5.64449 - 0.373857i) q^{32} +(-1.51741 - 6.70172i) q^{34} +(1.48831 - 2.57783i) q^{35} +(-3.86074 - 6.68701i) q^{37} +(-6.53415 + 6.04178i) q^{38} +(-2.01478 - 6.10155i) q^{40} +(2.55335 + 3.04297i) q^{41} +(-2.90911 - 7.99270i) q^{43} +(-5.23705 - 1.35286i) q^{44} +(-3.55932 - 0.452305i) q^{46} +(2.07927 - 11.7921i) q^{47} +(-4.96462 - 1.80697i) q^{49} +(-0.191517 + 0.123225i) q^{50} +(-9.04663 + 0.873603i) q^{52} +3.84281i q^{53} +6.14402i q^{55} +(3.26381 - 1.75545i) q^{56} +(-3.76885 - 5.85756i) q^{58} +(10.7689 + 3.91958i) q^{59} +(0.00682825 - 0.0387249i) q^{61} +(-0.521117 + 4.10082i) q^{62} +(1.86114 - 7.78050i) q^{64} +(3.53096 + 9.70123i) q^{65} +(7.67125 + 9.14224i) q^{67} +(-9.68782 - 0.759767i) q^{68} +(-2.85789 - 3.09079i) q^{70} +(1.22570 + 2.12297i) q^{71} +(3.09175 - 5.35507i) q^{73} +(-10.6502 + 2.41144i) q^{74} +(5.42135 + 11.3581i) q^{76} +(-3.48972 + 0.615332i) q^{77} +(3.87187 - 4.61431i) q^{79} +(-9.08569 + 0.163591i) q^{80} +(5.18035 - 2.17314i) q^{82} +(7.31283 + 6.13619i) q^{83} +(1.91675 + 10.8704i) q^{85} +(-12.0149 + 0.578772i) q^{86} +(-4.02256 + 6.50638i) q^{88} +(-5.99050 - 3.45862i) q^{89} +(-5.15653 + 2.97713i) q^{91} +(-2.10293 + 4.61783i) q^{92} +(-15.0555 - 7.75149i) q^{94} +(10.9513 - 9.18922i) q^{95} +(8.22759 - 2.99460i) q^{97} +(-4.52172 + 5.94806i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) \) 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 + 33 * q^14 + 3 * q^16 - 18 * q^17 - 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 30 * q^29 + 33 * q^32 + 15 * q^34 - 6 * q^37 - 63 * q^38 + 33 * q^40 - 24 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 21 * q^50 + 57 * q^52 - 18 * q^56 + 57 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 + 30 * q^65 - 102 * q^68 + 51 * q^70 - 6 * q^73 + 75 * q^74 + 27 * q^76 - 42 * q^77 - 12 * q^82 - 24 * q^85 - 111 * q^86 + 27 * q^88 + 147 * q^92 + 30 * q^94 - 12 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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