LMFDB - Embedded newform 972.2.l.d.863.15

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			863.15
Character	$\chi$	$=$	972.863
Dual form			972.2.l.d.107.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25735 + 0.647359i) q^{2} +(1.16185 + 1.62791i) q^{4} +(-0.776998 - 2.13478i) q^{5} +(1.29035 - 0.227523i) q^{7} +(0.407013 + 2.79899i) q^{8} +(0.405013 - 3.18717i) q^{10} +(-2.54138 - 0.924988i) q^{11} +(3.48118 + 2.92106i) q^{13} +(1.76970 + 0.549241i) q^{14} +(-1.30019 + 3.78279i) q^{16} +(4.20783 + 2.42939i) q^{17} +(5.44971 - 3.14639i) q^{19} +(2.57248 - 3.74519i) q^{20} +(-2.59661 - 2.80822i) q^{22} +(0.440555 - 2.49851i) q^{23} +(-0.123358 + 0.103510i) q^{25} +(2.48609 + 5.92636i) q^{26} +(1.86958 + 1.83622i) q^{28} +(3.16586 + 3.77293i) q^{29} +(2.87863 + 0.507580i) q^{31} +(-4.08362 + 3.91460i) q^{32} +(3.71802 + 5.77857i) q^{34} +(-1.48831 - 2.57783i) q^{35} +(-3.86074 + 6.68701i) q^{37} +(8.88903 - 0.428196i) q^{38} +(5.65899 - 3.04370i) q^{40} +(2.55335 - 3.04297i) q^{41} +(2.90911 - 7.99270i) q^{43} +(-1.44692 - 5.21185i) q^{44} +(2.17137 - 2.85631i) q^{46} +(-2.07927 - 11.7921i) q^{47} +(-4.96462 + 1.80697i) q^{49} +(-0.222112 + 0.0502909i) q^{50} +(-0.710600 + 9.06090i) q^{52} -3.84281i q^{53} +6.14402i q^{55} +(1.16202 + 3.51906i) q^{56} +(1.53816 + 6.79333i) q^{58} +(-10.7689 + 3.91958i) q^{59} +(0.00682825 + 0.0387249i) q^{61} +(3.29086 + 2.50171i) q^{62} +(-7.66868 + 2.27845i) q^{64} +(3.53096 - 9.70123i) q^{65} +(-7.67125 + 9.14224i) q^{67} +(0.934048 + 9.67257i) q^{68} +(-0.202546 - 4.20470i) q^{70} +(-1.22570 + 2.12297i) q^{71} +(3.09175 + 5.35507i) q^{73} +(-9.18319 + 5.90861i) q^{74} +(11.4538 + 5.21600i) q^{76} +(-3.48972 - 0.615332i) q^{77} +(-3.87187 - 4.61431i) q^{79} +(9.08569 - 0.163591i) q^{80} +(5.18035 - 2.17314i) q^{82} +(-7.31283 + 6.13619i) q^{83} +(1.91675 - 10.8704i) q^{85} +(8.83191 - 8.16638i) q^{86} +(1.55465 - 7.48979i) q^{88} +(-5.99050 + 3.45862i) q^{89} +(5.15653 + 2.97713i) q^{91} +(4.57922 - 2.18572i) q^{92} +(5.01936 - 16.1728i) q^{94} +(-10.9513 - 9.18922i) q^{95} +(8.22759 + 2.99460i) q^{97} +(-7.41203 - 0.941893i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	1.25735	+	0.647359i	0.889080	+	0.457752i
$2$	1.25735	+	0.647359i	0.889080	+	0.457752i
$3$		0			0
$3$		0			0
$4$	1.16185	+	1.62791i	0.580927	+	0.813956i
$5$	−0.776998	−	2.13478i	−0.347484	−	0.954705i	−0.983160	−	0.182748i	$-0.941501\pi$
$5$	−0.776998	−	2.13478i	−0.347484	−	0.954705i	0.635676	−	0.771956i	$-0.280722\pi$
$6$		0			0
$7$	1.29035	−	0.227523i	0.487705	−	0.0859955i	0.0756119	−	0.997137i	$-0.475909\pi$
$7$	1.29035	−	0.227523i	0.487705	−	0.0859955i	0.412093	+	0.911142i	$0.364798\pi$
$8$	0.407013	+	2.79899i	0.143901	+	0.989592i
$9$		0			0
$10$	0.405013	−	3.18717i	0.128076	−	1.00787i
$11$	−2.54138	−	0.924988i	−0.766256	−	0.278894i	−0.0708265	−	0.997489i	$-0.522564\pi$
$11$	−2.54138	−	0.924988i	−0.766256	−	0.278894i	−0.695430	+	0.718594i	$0.744786\pi$
$12$		0			0
$13$	3.48118	+	2.92106i	0.965506	+	0.810156i	0.981840	−	0.189711i	$-0.0607551\pi$
$13$	3.48118	+	2.92106i	0.965506	+	0.810156i	−0.0163342	+	0.999867i	$0.505200\pi$
$14$	1.76970	+	0.549241i	0.472973	+	0.146791i
$15$		0			0
$16$	−1.30019	+	3.78279i	−0.325048	+	0.945698i
$17$	4.20783	+	2.42939i	1.02055	+	0.589214i	0.914263	−	0.405122i	$-0.132771\pi$
$17$	4.20783	+	2.42939i	1.02055	+	0.589214i	0.106286	+	0.994336i	$0.466104\pi$
$18$		0			0
$19$	5.44971	−	3.14639i	1.25025	−	0.721832i	0.279090	−	0.960265i	$-0.409967\pi$
$19$	5.44971	−	3.14639i	1.25025	−	0.721832i	0.971159	+	0.238433i	$0.0766339\pi$
$20$	2.57248	−	3.74519i	0.575225	−	0.837450i
$21$		0			0
$22$	−2.59661	−	2.80822i	−0.553599	−	0.598714i
$23$	0.440555	−	2.49851i	0.0918622	−	0.520976i	−0.903802	−	0.427952i	$-0.859235\pi$
$23$	0.440555	−	2.49851i	0.0918622	−	0.520976i	0.995664	−	0.0930246i	$-0.0296535\pi$
$24$		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	0.975198	−	0.221334i	$-0.0710410\pi$
$29$	3.16586	+	3.77293i	0.587886	+	0.700615i	−0.387313	+	0.921948i	$0.626597\pi$
$30$		0			0
$31$	2.87863	+	0.507580i	0.517017	+	0.0911641i	0.426068	−	0.904691i	$-0.359899\pi$
$31$	2.87863	+	0.507580i	0.517017	+	0.0911641i	0.0909499	+	0.995855i	$0.471010\pi$
$32$	−4.08362	+	3.91460i	−0.721888	+	0.692010i
$33$		0			0
$34$	3.71802	+	5.77857i	0.637636	+	0.991016i
$35$	−1.48831	−	2.57783i	−0.251570	−	0.435732i
$36$		0			0
$37$	−3.86074	+	6.68701i	−0.634703	+	1.09934i	0.351876	+	0.936047i	$0.385544\pi$
$37$	−3.86074	+	6.68701i	−0.634703	+	1.09934i	−0.986578	+	0.163290i	$0.947789\pi$
$38$	8.88903	−	0.428196i	1.44199	−	0.0694626i
$39$		0			0
$40$	5.65899	−	3.04370i	0.894765	−	0.481250i
$41$	2.55335	−	3.04297i	0.398767	−	0.475232i	−0.528877	−	0.848699i	$-0.677387\pi$
$41$	2.55335	−	3.04297i	0.398767	−	0.475232i	0.927643	+	0.373467i	$0.121831\pi$
$42$		0			0
$43$	2.90911	−	7.99270i	0.443634	−	1.21888i	−0.493450	−	0.869774i	$-0.664265\pi$
$43$	2.90911	−	7.99270i	0.443634	−	1.21888i	0.937085	−	0.349102i	$-0.113513\pi$
$44$	−1.44692	−	5.21185i	−0.218131	−	0.785716i
$45$		0			0
$46$	2.17137	−	2.85631i	0.320151	−	0.421140i
$47$	−2.07927	−	11.7921i	−0.303293	−	1.72006i	−0.631434	−	0.775429i	$-0.717533\pi$
$47$	−2.07927	−	11.7921i	−0.303293	−	1.72006i	0.328142	−	0.944629i	$-0.393578\pi$
$48$		0			0
$49$	−4.96462	+	1.80697i	−0.709232	+	0.258139i
$50$	−0.222112	+	0.0502909i	−0.0314114	+	0.00711221i
$51$		0			0
$52$	−0.710600	+	9.06090i	−0.0985425	+	1.25652i
$53$		−	3.84281i		−	0.527851i	−0.964543	−	0.263925i	$-0.914983\pi$
$53$		−	3.84281i		−	0.527851i	0.964543	−	0.263925i	$-0.0850173\pi$
$54$		0			0
$55$			6.14402i			0.828460i
$56$	1.16202	+	3.51906i	0.155282	+	0.470254i
$57$		0			0
$58$	1.53816	+	6.79333i	0.201970	+	0.892008i
$59$	−10.7689	+	3.91958i	−1.40200	+	0.510285i	−0.928771	−	0.370655i	$-0.879133\pi$
$59$	−10.7689	+	3.91958i	−1.40200	+	0.510285i	−0.473227	+	0.880941i	$0.656911\pi$
$60$		0			0
$61$	0.00682825	+	0.0387249i	0.000874268	+	0.00495822i	0.985242	−	0.171169i	$-0.0547543\pi$
$61$	0.00682825	+	0.0387249i	0.000874268	+	0.00495822i	−0.984367	+	0.176127i	$0.943643\pi$
$62$	3.29086	+	2.50171i	0.417939	+	0.317718i
$63$		0			0
$64$	−7.66868	+	2.27845i	−0.958585	+	0.284806i
$65$	3.53096	−	9.70123i	0.437961	−	1.20329i
$66$		0			0
$67$	−7.67125	+	9.14224i	−0.937193	+	1.11690i	0.0557663	+	0.998444i	$0.482240\pi$
$67$	−7.67125	+	9.14224i	−0.937193	+	1.11690i	−0.992959	+	0.118459i	$0.962205\pi$
$68$	0.934048	+	9.67257i	0.113270	+	1.17297i
$69$		0			0
$70$	−0.202546	−	4.20470i	−0.0242088	−	0.502557i
$71$	−1.22570	+	2.12297i	−0.145463	+	0.251950i	−0.929546	−	0.368707i	$-0.879801\pi$
$71$	−1.22570	+	2.12297i	−0.145463	+	0.251950i	0.784082	+	0.620657i	$0.213134\pi$
$72$		0			0
$73$	3.09175	+	5.35507i	0.361862	+	0.626764i	0.988267	−	0.152734i	$-0.0488077\pi$
$73$	3.09175	+	5.35507i	0.361862	+	0.626764i	−0.626405	+	0.779498i	$0.715474\pi$
$74$	−9.18319	+	5.90861i	−1.06752	+	0.686863i
$75$		0			0
$76$	11.4538	+	5.21600i	1.31384	+	0.598316i
$77$	−3.48972	−	0.615332i	−0.397690	−	0.0701236i
$78$		0			0
$79$	−3.87187	−	4.61431i	−0.435619	−	0.519151i	0.502915	−	0.864336i	$-0.332261\pi$
$79$	−3.87187	−	4.61431i	−0.435619	−	0.519151i	−0.938535	+	0.345185i	$0.887816\pi$
$80$	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	$-0.897752\pi$
$83$	−7.31283	+	6.13619i	−0.802687	+	0.673534i	0.146163	+	0.989260i	$0.453307\pi$
$84$		0			0
$85$	1.91675	−	10.8704i	0.207901	−	1.17906i
$86$	8.83191	−	8.16638i	0.952369	−	0.880604i
$87$		0			0
$88$	1.55465	−	7.48979i	0.165727	−	0.798414i
$89$	−5.99050	+	3.45862i	−0.634991	+	0.366613i	−0.782683	−	0.622421i	$-0.786149\pi$
$89$	−5.99050	+	3.45862i	−0.634991	+	0.366613i	0.147691	+	0.989034i	$0.452816\pi$
$90$		0			0
$91$	5.15653	+	2.97713i	0.540552	+	0.312088i
$92$	4.57922	−	2.18572i	0.477417	−	0.227877i
$93$		0			0
$94$	5.01936	−	16.1728i	0.517708	−	1.66810i
$95$	−10.9513	−	9.18922i	−1.12358	−	0.942794i
$96$		0			0
$97$	8.22759	+	2.99460i	0.835385	+	0.304055i	0.724067	−	0.689729i	$-0.242270\pi$
$97$	8.22759	+	2.99460i	0.835385	+	0.304055i	0.111318	+	0.993785i	$0.464493\pi$
$98$	−7.41203	−	0.941893i	−0.748728	−	0.0951455i
$99$		0			0
$100$	−0.311829	−	0.0805529i	−0.0311829	−	0.00805529i
$101$	−2.16848	+	0.382362i	−0.215772	+	0.0380465i	−0.280489	−	0.959857i	$-0.590497\pi$
$101$	−2.16848	+	0.382362i	−0.215772	+	0.0380465i	0.0647169	+	0.997904i	$0.479386\pi$
$102$		0			0
$103$	0.672781	+	1.84845i	0.0662911	+	0.182133i	0.968415	−	0.249344i	$-0.0802149\pi$
$103$	0.672781	+	1.84845i	0.0662911	+	0.182133i	−0.902124	+	0.431477i	$0.857993\pi$
$104$	−6.75912	+	10.9327i	−0.662786	+	1.07204i
$105$		0			0
$106$	2.48768	−	4.83176i	0.241625	−	0.469302i
$107$	−4.06709			−0.393180			−0.196590	−	0.980486i	$-0.562987\pi$
$107$	−4.06709			−0.393180			−0.196590	+	0.980486i	$0.562987\pi$
$108$		0			0
$109$	−1.81021			−0.173387			−0.0866934	−	0.996235i	$-0.527630\pi$
$109$	−1.81021			−0.173387			−0.0866934	+	0.996235i	$0.527630\pi$
$110$	−3.97739	+	7.72518i	−0.379229	+	0.736567i
$111$		0			0
$112$	−0.817026	+	5.17693i	−0.0772017	+	0.489174i
$113$	−1.20062	−	3.29869i	−0.112945	−	0.310314i	0.870322	−	0.492483i	$-0.163911\pi$
$113$	−1.20062	−	3.29869i	−0.112945	−	0.310314i	−0.983267	+	0.182168i	$0.941688\pi$
$114$		0			0
$115$	−5.67610	+	1.00085i	−0.529299	+	0.0933297i
$116$	−2.46372	+	9.53733i	−0.228751	+	0.885519i
$117$		0			0
$118$	−16.0777	−	2.04309i	−1.48007	−	0.188082i
$119$	5.98230	+	2.17738i	0.548396	+	0.199600i
$120$		0			0
$121$	−2.82346	−	2.36916i	−0.256678	−	0.215379i
$122$	−0.0164834	+	0.0531111i	−0.00149234	+	0.00480845i
$123$		0			0
$124$	2.51825	+	5.27589i	0.226146	+	0.473789i
$125$	−9.52032	−	5.49656i	−0.851523	−	0.491627i
$126$		0			0
$127$	9.71588	−	5.60947i	0.862145	−	0.497760i	−0.00258477	−	0.999997i	$-0.500823\pi$
$127$	9.71588	−	5.60947i	0.862145	−	0.497760i	0.864730	+	0.502237i	$0.167489\pi$
$128$	−11.1172	−	2.09958i	−0.982630	−	0.185578i
$129$		0			0
$130$	10.7198	−	9.91203i	0.940190	−	0.869343i
$131$	−0.890936	+	5.05275i	−0.0778415	+	0.441461i	0.920832	+	0.389961i	$0.127511\pi$
$131$	−0.890936	+	5.05275i	−0.0778415	+	0.441461i	−0.998673	+	0.0515002i	$0.983600\pi$
$132$		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	0.714100	−	0.700043i	$-0.246836\pi$
$137$	−1.16239	−	1.38529i	−0.0993100	−	0.118353i	−0.813410	+	0.581690i	$0.802392\pi$
$138$		0			0
$139$	−12.8033	−	2.25758i	−1.08597	−	0.191485i	−0.398114	−	0.917336i	$-0.630335\pi$
$139$	−12.8033	−	2.25758i	−1.08597	−	0.191485i	−0.687852	+	0.725851i	$0.741446\pi$
$140$	2.46728	−	5.41789i	0.208523	−	0.457895i
$141$		0			0
$142$	−2.91545	+	1.87585i	−0.244659	+	0.157418i
$143$	−6.14507	−	10.6436i	−0.513877	−	0.890061i
$144$		0			0
$145$	5.59452	−	9.68999i	0.464599	−	0.804710i
$146$	0.420760	+	8.73467i	0.0348224	+	0.722887i
$147$		0			0
$148$	−15.3715	+	1.48437i	−1.26353	+	0.122015i
$149$	−1.65428	+	1.97150i	−0.135524	+	0.161511i	−0.829538	−	0.558450i	$-0.811396\pi$
$149$	−1.65428	+	1.97150i	−0.135524	+	0.161511i	0.694014	+	0.719962i	$0.255841\pi$
$150$		0			0
$151$	−1.79566	+	4.93353i	−0.146128	+	0.401485i	−0.991065	−	0.133382i	$-0.957416\pi$
$151$	−1.79566	+	4.93353i	−0.146128	+	0.401485i	0.844936	+	0.534867i	$0.179638\pi$
$152$	11.0248	+	13.9731i	0.894231	+	1.13336i
$153$		0			0
$154$	−3.98946	−	3.03279i	−0.321479	−	0.244389i
$155$	−1.15312	−	6.53965i	−0.0926205	−	0.525277i
$156$		0			0
$157$	−19.6331	+	7.14587i	−1.56689	+	0.570302i	−0.972302	−	0.233727i	$-0.924908\pi$
$157$	−19.6331	+	7.14587i	−1.56689	+	0.570302i	−0.594590	+	0.804029i	$0.702686\pi$
$158$	−1.88118	−	8.30829i	−0.149658	−	0.660972i
$159$		0			0
$160$	11.5298	+	5.67601i	0.911510	+	0.448728i
$161$		−	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	$0.958960\pi$
$164$	7.92030	+	0.621150i	0.618472	+	0.0485036i
$165$		0			0
$166$	−13.1671	+	2.98131i	−1.02196	+	0.231395i
$167$	17.9950	−	6.54965i	1.39250	−	0.506827i	0.466553	−	0.884493i	$-0.345496\pi$
$167$	17.9950	−	6.54965i	1.39250	−	0.506827i	0.925942	+	0.377666i	$0.123273\pi$
$168$		0			0
$169$	1.32862	+	7.53496i	0.102201	+	0.579612i
$170$	9.44710	−	12.4271i	0.724560	−	0.953116i
$171$		0			0
$172$	16.3914	−	4.55058i	1.24983	−	0.346979i
$173$	2.98997	−	8.21488i	0.227323	−	0.624566i	−0.772624	−	0.634864i	$-0.781056\pi$
$173$	2.98997	−	8.21488i	0.227323	−	0.624566i	0.999947	+	0.0102987i	$0.00327824\pi$
$174$		0			0
$175$	−0.135624	+	0.161630i	−0.0102522	+	0.0122181i
$176$	6.80332	−	8.41086i	0.512820	−	0.633992i
$177$		0			0
$178$	−9.77111	+	0.470687i	−0.732376	+	0.0352795i
$179$	3.03371	−	5.25454i	0.226750	−	0.392743i	−0.730093	−	0.683348i	$-0.760523\pi$
$179$	3.03371	−	5.25454i	0.226750	−	0.392743i	0.956843	+	0.290605i	$0.0938565\pi$
$180$		0			0
$181$	−8.01419	−	13.8810i	−0.595690	−	1.03177i	−0.993449	−	0.114276i	$-0.963545\pi$
$181$	−8.01419	−	13.8810i	−0.595690	−	1.03177i	0.397759	−	0.917490i	$-0.369788\pi$
$182$	4.55629	+	7.08141i	0.337735	+	0.524909i
$183$		0			0
$184$	7.17263	+	0.216182i	0.528773	+	0.0159371i
$185$	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	$-0.861312\pi$
$191$	−8.96056	+	7.51880i	−0.648363	+	0.544042i	0.258210	+	0.966089i	$0.416867\pi$
$192$		0			0
$193$	3.05125	−	17.3045i	0.219633	−	1.24560i	−0.653049	−	0.757315i	$-0.726511\pi$
$193$	3.05125	−	17.3045i	0.219633	−	1.24560i	0.872683	−	0.488288i	$-0.162378\pi$
$194$	8.40638	+	9.09146i	0.603543	+	0.652729i
$195$		0			0
$196$	−8.70976	−	5.98253i	−0.622126	−	0.427323i
$197$	19.9607	−	11.5243i	1.42214	−	0.821074i	0.425660	−	0.904883i	$-0.360042\pi$
$197$	19.9607	−	11.5243i	1.42214	−	0.821074i	0.996482	+	0.0838089i	$0.0267085\pi$
$198$		0			0
$199$	2.70763	+	1.56325i	0.191939	+	0.110816i	0.592890	−	0.805284i	$-0.297987\pi$
$199$	2.70763	+	1.56325i	0.191939	+	0.110816i	−0.400951	+	0.916099i	$0.631320\pi$
$200$	−0.339931	−	0.303148i	−0.0240367	−	0.0214358i
$201$		0			0
$202$	−2.97407	−	0.923024i	−0.209255	−	0.0649438i
$203$	4.94348	+	4.14807i	0.346964	+	0.291138i
$204$		0			0
$205$	−8.48003	−	3.08648i	−0.592271	−	0.215569i
$206$	−0.350690	+	2.75968i	−0.0244337	+	0.192276i
$207$		0			0
$208$	−15.5760	+	9.37064i	−1.08000	+	0.649737i
$209$	−16.7602	+	2.95527i	−1.15933	+	0.204420i
$210$		0			0
$211$	−4.39608	−	12.0781i	−0.302639	−	0.831493i	−0.994039	−	0.109022i	$-0.965228\pi$
$211$	−4.39608	−	12.0781i	−0.302639	−	0.831493i	0.691401	−	0.722472i	$-0.256994\pi$
$212$	6.25576	−	4.46479i	0.429647	−	0.306643i
$213$		0			0
$214$	−5.11375	−	2.63287i	−0.349569	−	0.179979i
$215$	−19.3231			−1.31782
$216$		0			0
$217$	3.82992			0.259992
$218$	−2.27607	−	1.17186i	−0.154155	−	0.0793681i
$219$		0			0
$220$	−10.0019	+	7.13845i	−0.674330	+	0.481274i
$221$	7.55182	+	20.7485i	0.507991	+	1.39569i
$222$		0			0
$223$	10.1821	−	1.79539i	0.681846	−	0.120228i	0.178012	−	0.984028i	$-0.443033\pi$
$223$	10.1821	−	1.79539i	0.681846	−	0.120228i	0.503834	+	0.863800i	$0.331922\pi$
$224$	−4.37862	+	5.98030i	−0.292559	+	0.399576i
$225$		0			0
$226$	0.625830	−	4.92484i	0.0416296	−	0.327595i
$227$	−0.0902519	−	0.0328490i	−0.00599023	−	0.00218027i	0.339023	−	0.940778i	$-0.389903\pi$
$227$	−0.0902519	−	0.0328490i	−0.00599023	−	0.00218027i	−0.345014	+	0.938598i	$0.612126\pi$
$228$		0			0
$229$	20.5858	+	17.2735i	1.36035	+	1.14147i	0.975874	+	0.218332i	$0.0700617\pi$
$229$	20.5858	+	17.2735i	1.36035	+	1.14147i	0.384474	+	0.923136i	$0.374383\pi$
$230$	−7.78475	−	2.41606i	−0.513311	−	0.159310i
$231$		0			0
$232$	−9.27183	+	10.3968i	−0.608726	+	0.682586i
$233$	6.26494	+	3.61706i	0.410430	+	0.236962i	0.690974	−	0.722879i	$-0.257182\pi$
$233$	6.26494	+	3.61706i	0.410430	+	0.236962i	−0.280545	+	0.959841i	$0.590515\pi$
$234$		0			0
$235$	−23.5581	+	13.6013i	−1.53676	+	0.887248i
$236$	−18.8927	−	12.9769i	−1.22981	−	0.844725i
$237$		0			0
$238$	6.11229	+	6.61041i	0.396201	+	0.428490i
$239$	2.21525	−	12.5633i	0.143293	−	0.812653i	−0.825430	−	0.564505i	$-0.809067\pi$
$239$	2.21525	−	12.5633i	0.143293	−	0.812653i	0.968722	−	0.248148i	$-0.0798218\pi$
$240$		0			0
$241$	−5.80114	+	4.86773i	−0.373684	+	0.313558i	−0.810217	−	0.586130i	$-0.800651\pi$
$241$	−5.80114	+	4.86773i	−0.373684	+	0.313558i	0.436533	+	0.899688i	$0.356206\pi$
$242$	−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
$248$	−0.249071	+	8.26385i	−0.0158160	+	0.524755i
$249$		0			0
$250$	−8.41212	−	13.0742i	−0.532029	−	0.826882i
$251$	5.95007	+	10.3058i	0.375565	+	0.650498i	0.990411	−	0.138149i	$-0.0441153\pi$
$251$	5.95007	+	10.3058i	0.375565	+	0.650498i	−0.614846	+	0.788647i	$0.710782\pi$
$252$		0			0
$253$	−3.43072	+	5.94217i	−0.215687	+	0.373581i
$254$	15.8476	−	0.763399i	0.994367	−	0.0478999i
$255$		0			0
$256$	−12.6190	−	9.83671i	−0.788688	−	0.614794i
$257$	−3.50902	+	4.18189i	−0.218887	+	0.260859i	−0.864302	−	0.502972i	$-0.832240\pi$
$257$	−3.50902	+	4.18189i	−0.218887	+	0.260859i	0.645416	+	0.763832i	$0.276684\pi$
$258$		0			0
$259$	−3.46025	+	9.50696i	−0.215009	+	0.590734i
$260$	19.8952	−	5.52332i	1.23385	−	0.342542i
$261$		0			0
$262$	−4.39116	+	5.77632i	−0.271287	+	0.356862i
$263$	3.53693	+	20.0589i	0.218097	+	1.23689i	0.875451	+	0.483306i	$0.160564\pi$
$263$	3.53693	+	20.0589i	0.218097	+	1.23689i	−0.657355	+	0.753581i	$0.728325\pi$
$264$		0			0
$265$	−8.20358	+	2.98586i	−0.503942	+	0.183420i
$266$	11.3725	−	2.57498i	0.697292	−	0.157882i
$267$		0			0
$268$	−23.7956	−	1.86617i	−1.45355	−	0.113995i
$269$			9.12305i			0.556242i	0.960546	+	0.278121i	$0.0897116\pi$
$269$			9.12305i			0.556242i	−0.960546	+	0.278121i	$0.910288\pi$
$270$		0			0
$271$		−	21.2629i		−	1.29163i	−0.763495	−	0.645813i	$-0.776518\pi$
$271$		−	21.2629i		−	1.29163i	0.763495	−	0.645813i	$-0.223482\pi$
$272$	−14.6609	+	12.7587i	−0.888945	+	0.773607i
$273$		0			0
$274$	−0.564757	−	2.49428i	−0.0341182	−	0.150685i
$275$	0.409245	−	0.148953i	0.0246784	−	0.00898221i
$276$		0			0
$277$	−4.43224	−	25.1365i	−0.266308	−	1.51031i	−0.765285	−	0.643691i	$-0.777402\pi$
$277$	−4.43224	−	25.1365i	−0.266308	−	1.51031i	0.498977	−	0.866615i	$-0.333709\pi$
$278$	−14.6368	−	11.1269i	−0.877858	−	0.667348i
$279$		0			0
$280$	6.60954	−	5.21497i	0.394996	−	0.311654i
$281$	−4.21589	+	11.5831i	−0.251499	+	0.690987i	0.748125	+	0.663558i	$0.230954\pi$
$281$	−4.21589	+	11.5831i	−0.251499	+	0.690987i	−0.999624	+	0.0274292i	$0.991268\pi$
$282$		0			0
$283$	−10.7391	+	12.7984i	−0.638374	+	0.760784i	−0.984112	−	0.177547i	$-0.943184\pi$
$283$	−10.7391	+	12.7984i	−0.638374	+	0.760784i	0.345739	+	0.938331i	$0.387628\pi$
$284$	−4.88008	+	0.471253i	−0.289580	+	0.0279637i
$285$		0			0
$286$	−0.836290	−	17.3608i	−0.0494509	−	1.02656i
$287$	2.60236	−	4.50743i	0.153613	−	0.266065i
$288$		0			0
$289$	3.30388	+	5.72249i	0.194346	+	0.336617i
$290$	13.3072	−	8.56204i	0.781423	−	0.502780i
$291$		0			0
$292$	−5.12542	+	11.2549i	−0.299943	+	0.658644i
$293$	−13.1269	−	2.31463i	−0.766884	−	0.135222i	−0.223497	−	0.974705i	$-0.571747\pi$
$293$	−13.1269	−	2.31463i	−0.766884	−	0.135222i	−0.543387	+	0.839482i	$0.682858\pi$
$294$		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
$302$	−5.45153	+	5.04073i	−0.313700	+	0.290061i
$303$		0			0
$304$	4.81647	+	24.7060i	0.276243	+	1.41699i
$305$	0.0773639	−	0.0446661i	0.00442984	−	0.00255757i
$306$		0			0
$307$	−18.8505	−	10.8833i	−1.07585	−	0.621144i	−0.146078	−	0.989273i	$-0.546665\pi$
$307$	−18.8505	−	10.8833i	−1.07585	−	0.621144i	−0.929775	+	0.368129i	$0.879998\pi$
$308$	−3.05284	−	6.39588i	−0.173952	−	0.364439i
$309$		0			0
$310$	2.78363	−	8.96910i	0.158099	−	0.509411i
$311$	10.9280	+	9.16969i	0.619671	+	0.519966i	0.897700	−	0.440607i	$-0.145237\pi$
$311$	10.9280	+	9.16969i	0.619671	+	0.519966i	−0.278029	+	0.960573i	$0.589681\pi$
$312$		0			0
$313$	−19.9926	−	7.27672i	−1.13005	−	0.411304i	−0.291739	−	0.956498i	$-0.594234\pi$
$313$	−19.9926	−	7.27672i	−1.13005	−	0.411304i	−0.838310	+	0.545194i	$0.816456\pi$
$314$	−29.3116	−	3.72481i	−1.65415	−	0.210203i
$315$		0			0
$316$	3.01315	−	11.6642i	0.169503	−	0.656164i
$317$	6.63831	−	1.17051i	0.372845	−	0.0657426i	0.0159138	−	0.999873i	$-0.494934\pi$
$317$	6.63831	−	1.17051i	0.372845	−	0.0657426i	0.356931	+	0.934131i	$0.383823\pi$
$318$		0			0
$319$	−4.55576	−	12.5168i	−0.255073	−	0.700808i
$320$	10.8226	+	14.6006i	0.604999	+	0.816200i
$321$		0			0
$322$	2.15194	−	4.17966i	0.119923	−	0.232923i
$323$	30.5753			1.70125
$324$		0			0
$325$	−0.731790			−0.0405924
$326$	−2.12533	+	4.12798i	−0.117711	+	0.228628i
$327$		0			0
$328$	9.55648	+	5.90828i	0.527668	+	0.326230i
$329$	−5.36595	−	14.7428i	−0.295835	−	0.812799i
$330$		0			0
$331$	−23.8297	+	4.20182i	−1.30980	+	0.230953i	−0.784587	−	0.620019i	$-0.787125\pi$
$331$	−23.8297	+	4.20182i	−1.30980	+	0.230953i	−0.525212	+	0.850972i	$0.676014\pi$
$332$	−18.4856	−	4.77528i	−1.01453	−	0.262077i
$333$		0			0
$334$	26.8660	+	3.41403i	1.47004	+	0.186807i
$335$	25.4773	+	9.27297i	1.39197	+	0.506636i
$336$		0			0
$337$	16.7397	+	14.0463i	0.911869	+	0.765149i	0.972474	−	0.233013i	$-0.0748583\pi$
$337$	16.7397	+	14.0463i	0.911869	+	0.765149i	−0.0606043	+	0.998162i	$0.519303\pi$
$338$	−3.20728	+	10.3342i	−0.174453	+	0.562104i
$339$		0			0
$340$	19.9231	−	9.50956i	1.08048	−	0.515728i
$341$	−6.84620	−	3.95266i	−0.370743	−	0.214048i
$342$		0			0
$343$	−13.9379	+	8.04707i	−0.752577	+	0.434501i
$344$	23.5555	+	4.88942i	1.27003	+	0.263620i
$345$		0			0
$346$	9.07741	−	8.39338i	0.488004	−	0.451231i
$347$	−2.24912	+	12.7554i	−0.120739	+	0.684745i	0.863009	+	0.505189i	$0.168577\pi$
$347$	−2.24912	+	12.7554i	−0.120739	+	0.684745i	−0.983748	+	0.179556i	$0.942534\pi$
$348$		0			0
$349$	−2.96273	+	2.48603i	−0.158591	+	0.133074i	−0.718630	−	0.695392i	$-0.755231\pi$
$349$	−2.96273	+	2.48603i	−0.158591	+	0.133074i	0.560039	+	0.828466i	$0.310786\pi$
$350$	−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	0.711481	−	0.702705i	$-0.248025\pi$
$353$	−1.95578	−	2.33080i	−0.104095	−	0.124056i	−0.815577	+	0.578649i	$0.803580\pi$
$354$		0			0
$355$	5.48444	+	0.967055i	0.291084	+	0.0513260i
$356$	−12.5904	−	5.73359i	−0.667290	−	0.303880i
$357$		0			0
$358$	7.21601	−	4.64290i	0.381378	−	0.245385i
$359$	8.27544	+	14.3335i	0.436761	+	0.756492i	0.997438	−	0.0715425i	$-0.0227922\pi$
$359$	8.27544	+	14.3335i	0.436761	+	0.756492i	−0.560676	+	0.828035i	$0.689459\pi$
$360$		0			0
$361$	10.2995	−	17.8393i	0.542082	−	0.938913i
$362$	−1.09066	−	22.6413i	−0.0573239	−	1.19000i
$363$		0			0
$364$	1.14464	+	11.8534i	0.0599954	+	0.621285i
$365$	9.02965	−	10.7611i	0.472633	−	0.563262i
$366$		0			0
$367$	0.754802	−	2.07380i	0.0394003	−	0.108252i	−0.918432	−	0.395578i	$-0.870544\pi$
$367$	0.754802	−	2.07380i	0.0394003	−	0.108252i	0.957833	+	0.287327i	$0.0927665\pi$
$368$	8.87855	+	4.91508i	0.462826	+	0.256216i
$369$		0			0
$370$	19.7489	+	15.0132i	1.02670	+	0.780497i
$371$	−0.874327	−	4.95856i	−0.0453928	−	0.257435i
$372$		0			0
$373$	9.85493	−	3.58690i	0.510269	−	0.185723i	−0.0740382	−	0.997255i	$-0.523589\pi$
$373$	9.85493	−	3.58690i	0.510269	−	0.185723i	0.584307	+	0.811533i	$0.301366\pi$
$374$	−4.10382	−	18.1247i	−0.212203	−	0.937205i
$375$		0			0
$376$	32.1597	−	10.6194i	1.65851	−	0.547654i
$377$			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	$-0.0252630\pi$
$380$	2.23544	−	28.5042i	0.114676	−	1.46224i
$381$		0			0
$382$	−16.1339	+	3.65306i	−0.825483	+	0.186907i
$383$	−15.0967	+	5.49476i	−0.771406	+	0.280769i	−0.697585	−	0.716503i	$-0.745742\pi$
$383$	−15.0967	+	5.49476i	−0.771406	+	0.280769i	−0.0738218	+	0.997271i	$0.523520\pi$
$384$		0			0
$385$	1.39790	+	7.92791i	0.0712438	+	0.404044i
$386$	15.0387	−	19.7825i	0.765449	−	1.00690i
$387$		0			0
$388$	4.68432	+	16.8731i	0.237810	+	0.856601i
$389$	−6.03724	+	16.5872i	−0.306100	+	0.841004i	0.687307	+	0.726367i	$0.258793\pi$
$389$	−6.03724	+	16.5872i	−0.306100	+	0.841004i	−0.993407	+	0.114637i	$0.963430\pi$
$390$		0			0
$391$	7.92365	−	9.44304i	0.400716	−	0.477555i
$392$	−7.07837	−	13.1605i	−0.357512	−	0.664704i
$393$		0			0
$394$	32.5580	−	1.56836i	1.64025	−	0.0790128i
$395$	−6.84213	+	11.8509i	−0.344265	+	0.596285i
$396$		0			0
$397$	6.73828	+	11.6710i	0.338185	+	0.585753i	0.984091	−	0.177663i	$-0.0568538\pi$
$397$	6.73828	+	11.6710i	0.338185	+	0.585753i	−0.645907	+	0.763416i	$0.723520\pi$
$398$	2.39245	+	3.71836i	0.119923	+	0.186384i
$399$		0			0
$400$	−0.231166	−	0.601220i	−0.0115583	−	0.0300610i
$401$	−6.65594	−	1.17362i	−0.332382	−	0.0586079i	0.00496671	−	0.999988i	$-0.498419\pi$
$401$	−6.65594	−	1.17362i	−0.332382	−	0.0586079i	−0.337349	+	0.941380i	$0.609530\pi$
$402$		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	−0.790512	−	0.612446i	$-0.790186\pi$
$409$	3.27211	−	18.5570i	0.161795	−	0.917586i	0.952307	−	0.305140i	$-0.0987033\pi$
$410$	−8.66430	−	9.37040i	−0.427899	−	0.462771i
$411$		0			0
$412$	−2.22744	+	3.24286i	−0.109738	+	0.159764i
$413$	−13.0039	+	7.50779i	−0.639879	+	0.369434i
$414$		0			0
$415$	18.7815	+	10.8435i	0.921947	+	0.532287i
$416$	−25.6506	+	1.69894i	−1.25762	+	0.0832975i
$417$		0			0
$418$	−22.9865	−	7.13404i	−1.12431	−	0.348937i
$419$	14.6271	+	12.2736i	0.714582	+	0.599606i	0.925881	−	0.377816i	$-0.123325\pi$
$419$	14.6271	+	12.2736i	0.714582	+	0.599606i	−0.211299	+	0.977422i	$0.567769\pi$
$420$		0			0
$421$	21.1833	+	7.71011i	1.03241	+	0.375768i	0.801999	−	0.597325i	$-0.203770\pi$
$421$	21.1833	+	7.71011i	1.03241	+	0.375768i	0.230414	+	0.973093i	$0.425992\pi$
$422$	2.29148	−	18.0323i	0.111547	−	0.877797i
$423$		0			0
$424$	10.7560	−	1.56408i	0.522357	−	0.0759582i
$425$	−0.770535	+	0.135866i	−0.0373765	+	0.00659048i
$426$		0			0
$427$	0.0176216	+	0.0484150i	0.000852770	+	0.00234297i
$428$	−4.72536	−	6.62086i	−0.228409	−	0.320032i
$429$		0			0
$430$	−24.2958	−	12.5090i	−1.17165	−	0.603235i
$431$	10.8059			0.520500			0.260250	−	0.965541i	$-0.416195\pi$
$431$	10.8059			0.520500			0.260250	+	0.965541i	$0.416195\pi$
$432$		0			0
$433$	−37.5914			−1.80653			−0.903264	−	0.429084i	$-0.858836\pi$
$433$	−37.5914			−1.80653			−0.903264	+	0.429084i	$0.858836\pi$
$434$	4.81554	+	2.47933i	0.231153	+	0.119012i
$435$		0			0
$436$	−2.10320	−	2.94686i	−0.100725	−	0.141129i
$437$	−5.46040	−	15.0023i	−0.261206	−	0.717659i
$438$		0			0
$439$	31.4487	−	5.54525i	1.50096	−	0.264660i	0.638043	−	0.770000i	$-0.279744\pi$
$439$	31.4487	−	5.54525i	1.50096	−	0.264660i	0.862920	+	0.505340i	$0.168633\pi$
$440$	−17.1970	+	2.50070i	−0.819837	+	0.119216i
$441$		0			0
$442$	−3.93642	+	30.9768i	−0.187236	+	1.47342i
$443$	−35.3150	−	12.8536i	−1.67786	−	0.610693i	−0.684850	−	0.728684i	$-0.740132\pi$
$443$	−35.3150	−	12.8536i	−1.67786	−	0.610693i	−0.993015	+	0.117992i	$0.962354\pi$
$444$		0			0
$445$	12.0380	+	10.1011i	0.570656	+	0.478837i
$446$	13.9648	+	4.33407i	0.661250	+	0.205224i
$447$		0			0
$448$	−9.37685	+	4.68479i	−0.443014	+	0.221335i
$449$	−6.99926	−	4.04102i	−0.330315	−	0.190708i	0.325666	−	0.945485i	$-0.394412\pi$
$449$	−6.99926	−	4.04102i	−0.330315	−	0.190708i	−0.655981	+	0.754777i	$0.727745\pi$
$450$		0			0
$451$	−9.30376	+	5.37153i	−0.438097	+	0.252935i
$452$	3.97502	−	5.78710i	0.186969	−	0.272202i
$453$		0			0
$454$	−0.0922131	−	0.0997280i	−0.00432777	−	0.00468047i
$455$	2.34891	−	13.3213i	0.110118	−	0.624513i
$456$		0			0
$457$	−1.89531	+	1.59036i	−0.0886590	+	0.0743937i	−0.686040	−	0.727564i	$-0.740652\pi$
$457$	−1.89531	+	1.59036i	−0.0886590	+	0.0743937i	0.597381	+	0.801958i	$0.296208\pi$
$458$	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	0.613643	−	0.789583i	$-0.289703\pi$
$461$	−5.80793	−	6.92163i	−0.270502	−	0.322372i	−0.884146	+	0.467211i	$0.845259\pi$
$462$		0			0
$463$	1.37343	+	0.242173i	0.0638287	+	0.0112547i	0.205471	−	0.978663i	$-0.434127\pi$
$463$	1.37343	+	0.242173i	0.0638287	+	0.0112547i	−0.141643	+	0.989918i	$0.545238\pi$
$464$	−18.3884	+	7.07026i	−0.853661	+	0.328229i
$465$		0			0
$466$	5.53568	+	8.60357i	0.256435	+	0.398553i
$467$	10.5492	+	18.2717i	0.488158	+	0.845515i	0.999907	−	0.0136203i	$-0.00433561\pi$
$467$	10.5492	+	18.2717i	0.488158	+	0.845515i	−0.511749	+	0.859135i	$0.671002\pi$
$468$		0			0
$469$	−7.81850	+	13.5420i	−0.361025	+	0.625313i
$470$	−38.4256	+	1.85101i	−1.77244	+	0.0853807i
$471$		0			0
$472$	−15.3540	−	28.5468i	−0.706723	−	1.31398i
$473$	−14.7863	+	17.6216i	−0.679875	+	0.810244i
$474$		0			0
$475$	−0.346584	+	0.952230i	−0.0159023	+	0.0436913i
$476$	3.40597	+	12.2684i	0.156113	+	0.562323i
$477$		0			0
$478$	10.9183	−	14.3624i	0.499392	−	0.656921i
$479$	2.53604	+	14.3826i	0.115874	+	0.657156i	0.986314	+	0.164880i	$0.0527238\pi$
$479$	2.53604	+	14.3826i	0.115874	+	0.657156i	−0.870439	+	0.492276i	$0.836165\pi$
$480$		0			0
$481$	−32.9731	+	12.0012i	−1.50344	+	0.547208i
$482$	−10.4452	+	2.36502i	−0.475767	+	0.107724i
$483$		0			0
$484$	0.576342	−	7.34897i	0.0261974	−	0.334044i
$485$		−	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	$-0.00203770\pi$
$488$	−0.105612	+	0.0348738i	−0.00478081	+	0.00157866i
$489$		0			0
$490$	3.74839	+	16.5549i	0.169335	+	0.747875i
$491$	14.5642	−	5.30093i	0.657273	−	0.239228i	0.00821432	−	0.999966i	$-0.497385\pi$
$491$	14.5642	−	5.30093i	0.657273	−	0.239228i	0.649058	+	0.760739i	$0.275163\pi$
$492$		0			0
$493$	4.15549	+	23.5669i	0.187154	+	1.06140i
$494$	32.1951	+	24.4747i	1.44853	+	1.10117i
$495$		0			0
$496$	−5.66284	+	10.2293i	−0.254269	+	0.459309i
$497$	−1.09855	+	3.01824i	−0.0492766	+	0.135386i
$498$		0			0
$499$	26.2876	−	31.3283i	1.17679	−	1.40245i	0.279999	−	0.960000i	$-0.409666\pi$
$499$	26.2876	−	31.3283i	1.17679	−	1.40245i	0.896794	−	0.442448i	$-0.145890\pi$
$500$	−2.11331	−	21.8844i	−0.0945100	−	0.978702i
$501$		0			0
$502$	0.809752	+	16.8099i	0.0361410	+	0.750260i
$503$	−9.96192	+	17.2546i	−0.444180	+	0.769343i	−0.997995	−	0.0632975i	$-0.979838\pi$
$503$	−9.96192	+	17.2546i	−0.444180	+	0.769343i	0.553815	+	0.832640i	$0.313172\pi$
$504$		0			0
$505$	2.50117	+	4.33215i	0.111301	+	0.192778i
$506$	−8.16033	+	5.25048i	−0.362771	+	0.233413i
$507$		0			0
$508$	20.4202	+	9.29922i	0.905998	+	0.412586i
$509$	−27.8835	−	4.91661i	−1.23591	−	0.217925i	−0.482750	−	0.875758i	$-0.660362\pi$
$509$	−27.8835	−	4.91661i	−1.23591	−	0.217925i	−0.753164	+	0.657833i	$0.771473\pi$
$510$		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
$518$	−10.5052	+	9.71354i	−0.461570	+	0.426789i
$519$		0			0
$520$	28.5908	+	5.93459i	1.25379	+	0.260249i
$521$	−18.4642	+	10.6603i	−0.808931	+	0.467036i	−0.846584	−	0.532255i	$-0.821345\pi$
$521$	−18.4642	+	10.6603i	−0.808931	+	0.467036i	0.0376537	+	0.999291i	$0.488012\pi$
$522$		0			0
$523$	−17.0213	−	9.82725i	−0.744289	−	0.429716i	0.0793376	−	0.996848i	$-0.474719\pi$
$523$	−17.0213	−	9.82725i	−0.744289	−	0.429716i	−0.823627	+	0.567132i	$0.808053\pi$
$524$	−9.26057	+	4.42019i	−0.404550	+	0.193097i
$525$		0			0
$526$	−8.53817	+	27.5108i	−0.372282	+	1.19953i
$527$	10.8797	+	9.12913i	0.473926	+	0.397671i
$528$		0			0
$529$	15.5644	+	5.66500i	0.676715	+	0.246304i
$530$	−12.2477	−	1.55639i	−0.532005	−	0.0676053i
$531$		0			0
$532$	15.9661	+	4.12444i	0.692220	+	0.178817i
$533$	17.7774	−	3.13463i	0.770023	−	0.135776i
$534$		0			0
$535$	3.16012	+	8.68236i	0.136624	+	0.375371i
$536$	−28.7113	−	17.7507i	−1.24014	−	0.766715i
$537$		0			0
$538$	−5.90588	+	11.4709i	−0.254621	+	0.494544i
$539$	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	$0.154265\pi$
$542$	13.7647	−	26.7348i	0.591244	−	1.14836i
$543$		0			0
$544$	−26.6933	+	6.55125i	−1.14446	+	0.280883i
$545$	1.40653	+	3.86441i	0.0602492	+	0.165533i
$546$		0			0
$547$	−7.15368	+	1.26139i	−0.305869	+	0.0539330i	−0.324476	−	0.945894i	$-0.605188\pi$
$547$	−7.15368	+	1.26139i	−0.305869	+	0.0539330i	0.0186069	+	0.999827i	$0.494077\pi$
$548$	0.904593	−	3.50178i	0.0386423	−	0.149588i
$549$		0			0
$550$	0.610991	+	0.0776424i	0.0260527	+	0.00331068i
$551$	29.1241	+	10.6003i	1.24073	+	0.451588i
$552$		0			0
$553$	−6.04591	−	5.07312i	−0.257098	−	0.215731i
$554$	10.6995	−	34.4746i	0.454576	−	1.46469i
$555$		0			0
$556$	−11.2005	−	23.4657i	−0.475006	−	0.995167i
$557$	32.2123	+	18.5978i	1.36488	+	0.788012i	0.990268	−	0.139170i	$-0.0444436\pi$
$557$	32.2123	+	18.5978i	1.36488	+	0.788012i	0.374609	+	0.927183i	$0.377777\pi$
$558$		0			0
$559$	33.4743	−	19.3264i	1.41581	−	0.817419i
$560$	11.6865	−	2.27829i	0.493843	−	0.0962753i
$561$		0			0
$562$	−12.7992	+	11.8348i	−0.539903	+	0.499219i
$563$	−7.70741	+	43.7109i	−0.324829	+	1.84219i	0.186048	+	0.982541i	$0.440432\pi$
$563$	−7.70741	+	43.7109i	−0.324829	+	1.84219i	−0.510876	+	0.859654i	$0.670679\pi$
$564$		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	0.204750	−	0.978814i	$-0.434362\pi$
$569$	−18.9577	−	22.5929i	−0.794749	−	0.947144i	−0.999498	+	0.0316699i	$0.989917\pi$
$570$		0			0
$571$	12.9011	+	2.27481i	0.539893	+	0.0951977i	0.436944	−	0.899489i	$-0.356061\pi$
$571$	12.9011	+	2.27481i	0.539893	+	0.0951977i	0.102949	+	0.994687i	$0.467172\pi$
$572$	10.1871	−	22.3699i	0.425945	−	0.935333i
$573$		0			0
$574$	6.19000	−	3.98275i	0.258366	−	0.166237i
$575$	0.204274	+	0.353814i	0.00851883	+	0.0147550i
$576$		0			0
$577$	2.02124	−	3.50090i	0.0841455	−	0.145744i	−0.820881	−	0.571099i	$-0.806517\pi$
$577$	2.02124	−	3.50090i	0.0841455	−	0.145744i	0.905027	+	0.425355i	$0.139851\pi$
$578$	0.449629	+	9.33397i	0.0187021	+	0.388242i
$579$		0			0
$580$	22.2745	−	2.15097i	0.924896	−	0.0893141i
$581$	−8.03995	+	9.58164i	−0.333553	+	0.397513i
$582$		0			0
$583$	−3.55456	+	9.76606i	−0.147215	+	0.404469i
$584$	−13.7304	+	10.8334i	−0.568168	+	0.448288i
$585$		0			0
$586$	−15.0068	−	11.4081i	−0.619923	−	0.471266i
$587$	1.26345	+	7.16540i	0.0521483	+	0.295748i	0.999717	−	0.0238055i	$-0.00757823\pi$
$587$	1.26345	+	7.16540i	0.0521483	+	0.295748i	−0.947568	+	0.319553i	$0.896467\pi$
$588$		0			0
$589$	17.2847	−	6.29113i	0.712206	−	0.259222i
$590$	8.13077	+	35.9099i	0.334739	+	1.47839i
$591$		0			0
$592$	−20.2758	−	23.2988i	−0.833332	−	0.957574i
$593$		−	2.93118i		−	0.120369i	−0.998187	−	0.0601846i	$-0.980831\pi$
$593$		−	2.93118i		−	0.120369i	0.998187	−	0.0601846i	$-0.0191689\pi$
$594$		0			0
$595$		−	14.4627i		−	0.592914i
$596$	−5.13145	−	0.402434i	−0.210192	−	0.0164843i
$597$		0			0
$598$	15.9024	−	3.60064i	0.650296	−	0.147241i
$599$	1.27568	−	0.464311i	0.0521230	−	0.0189712i	−0.315827	−	0.948817i	$-0.602282\pi$
$599$	1.27568	−	0.464311i	0.0521230	−	0.0189712i	0.367950	+	0.929846i	$0.380060\pi$
$600$		0			0
$601$	1.34379	+	7.62101i	0.0548144	+	0.310868i	0.999871	−	0.0160378i	$-0.00510522\pi$
$601$	1.34379	+	7.62101i	0.0548144	+	0.310868i	−0.945057	+	0.326906i	$0.893994\pi$
$602$	9.53817	−	12.5469i	0.388747	−	0.511374i
$603$		0			0
$604$	−10.1176	+	2.80887i	−0.411681	+	0.114291i
$605$	−2.86383	+	7.86832i	−0.116431	+	0.319893i
$606$		0			0
$607$	7.34402	−	8.75226i	0.298085	−	0.355243i	−0.596125	−	0.802891i	$-0.703294\pi$
$607$	7.34402	−	8.75226i	0.298085	−	0.355243i	0.894210	+	0.447648i	$0.147738\pi$
$608$	−9.93767	+	34.1821i	−0.403026	+	1.38627i
$609$		0			0
$610$	0.126188	−	0.00607866i	0.00510922	−	0.000246118i
$611$	27.2072	−	47.1242i	1.10068	−	1.90644i
$612$		0			0
$613$	−12.0261	−	20.8298i	−0.485729	−	0.841307i	0.514137	−	0.857708i	$-0.328112\pi$
$613$	−12.0261	−	20.8298i	−0.485729	−	0.841307i	−0.999865	+	0.0164015i	$0.994779\pi$
$614$	−16.6562	−	25.8871i	−0.672190	−	1.04472i
$615$		0			0
$616$	0.301945	−	10.0181i	0.0121657	−	0.403642i
$617$	47.5174	+	8.37860i	1.91298	+	0.337310i	0.997832	−	0.0658095i	$-0.0209630\pi$
$617$	47.5174	+	8.37860i	1.91298	+	0.337310i	0.915147	+	0.403119i	$0.132074\pi$
$618$		0			0
$619$	−2.89879	−	3.45464i	−0.116512	−	0.138854i	0.704636	−	0.709569i	$-0.251110\pi$
$619$	−2.89879	−	3.45464i	−0.116512	−	0.138854i	−0.821148	+	0.570715i	$0.806666\pi$
$620$	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
$626$	−20.4270	−	22.0918i	−0.816429	−	0.882964i
$627$		0			0
$628$	−34.4436	−	23.6585i	−1.37445	−	0.944077i
$629$	−32.4907	+	18.7585i	−1.29549	+	0.747951i
$630$		0			0
$631$	9.73065	+	5.61799i	0.387371	+	0.223649i	0.681020	−	0.732264i	$-0.261536\pi$
$631$	9.73065	+	5.61799i	0.387371	+	0.223649i	−0.293649	+	0.955913i	$0.594870\pi$
$632$	11.3395	−	12.7154i	0.451062	−	0.505792i
$633$		0			0
$634$	9.10442	+	2.82562i	0.361583	+	0.112220i
$635$	−19.5242	−	16.3828i	−0.774796	−	0.650131i
$636$		0			0
$637$	−22.5610	−	8.21154i	−0.893900	−	0.325353i
$638$	2.37471	−	18.6872i	0.0940155	−	0.739835i
$639$		0			0
$640$	4.15589	+	25.3642i	0.164276	+	1.00261i
$641$	39.8883	−	7.03338i	1.57549	−	0.277802i	0.683533	−	0.729919i	$-0.260442\pi$
$641$	39.8883	−	7.03338i	1.57549	−	0.277802i	0.891958	+	0.452118i	$0.149331\pi$
$642$		0			0
$643$	−11.0345	−	30.3169i	−0.435157	−	1.19558i	−0.942608	−	0.333902i	$-0.891634\pi$
$643$	−11.0345	−	30.3169i	−0.435157	−	1.19558i	0.507451	−	0.861681i	$-0.330588\pi$
$644$	5.41148	−	3.86221i	0.213242	−	0.152193i
$645$		0			0
$646$	38.4438	+	19.7932i	1.51255	+	0.778751i
$647$	−7.00490			−0.275391			−0.137696	−	0.990475i	$-0.543970\pi$
$647$	−7.00490			−0.275391			−0.137696	+	0.990475i	$0.543970\pi$
$648$		0			0
$649$	30.9936			1.21660
$650$	−0.920115	−	0.473730i	−0.0360899	−	0.0185812i
$651$		0			0
$652$	−5.34457	+	3.81446i	−0.209309	+	0.149386i
$653$	12.0075	+	32.9903i	0.469889	+	1.29101i	0.917840	+	0.396951i	$0.129932\pi$
$653$	12.0075	+	32.9903i	0.469889	+	1.29101i	−0.447951	+	0.894058i	$0.647846\pi$
$654$		0			0
$655$	11.4788	−	2.02402i	0.448514	−	0.0790850i
$656$	8.19106	+	13.6152i	0.319807	+	0.531586i
$657$		0			0
$658$	2.79702	−	22.0106i	0.109039	−	0.858062i
$659$	−8.41721	−	3.06361i	−0.327888	−	0.119341i	0.172831	−	0.984952i	$-0.444709\pi$
$659$	−8.41721	−	3.06361i	−0.327888	−	0.119341i	−0.500719	+	0.865610i	$0.666931\pi$
$660$		0			0
$661$	−27.2876	−	22.8970i	−1.06137	−	0.890592i	−0.0671232	−	0.997745i	$-0.521382\pi$
$661$	−27.2876	−	22.8970i	−1.06137	−	0.890592i	−0.994243	+	0.107153i	$0.965826\pi$
$662$	−32.6823	−	10.1432i	−1.27024	−	0.394227i
$663$		0			0
$664$	−20.1515	−	17.9710i	−0.782032	−	0.697410i
$665$	−16.2217	−	9.36560i	−0.629050	−	0.363182i
$666$		0			0
$667$	10.8214	−	6.24776i	0.419008	−	0.241914i
$668$	31.5698	+	21.6845i	1.22147	+	0.839000i
$669$		0			0
$670$	26.0309	+	28.1523i	1.00566	+	1.08762i
$671$	0.0184669	−	0.104731i	0.000712907	−	0.00404310i
$672$		0			0
$673$	−2.58660	+	2.17042i	−0.0997062	+	0.0836634i	−0.691278	−	0.722589i	$-0.742952\pi$
$673$	−2.58660	+	2.17042i	−0.0997062	+	0.0836634i	0.591572	+	0.806252i	$0.298508\pi$
$674$	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	0.780130	−	0.625617i	$-0.215153\pi$
$677$	0.742831	+	0.885272i	0.0285493	+	0.0340238i	−0.751581	+	0.659641i	$0.770708\pi$
$678$		0			0
$679$	11.2978	+	1.99210i	0.433569	+	0.0764499i
$680$	31.2064	+	0.940555i	1.19671	+	0.0360686i
$681$		0			0
$682$	−6.04928	−	9.40182i	−0.231639	−	0.360014i
$683$	−21.5897	−	37.3945i	−0.826107	−	1.43086i	−0.901070	−	0.433673i	$-0.857217\pi$
$683$	−21.5897	−	37.3945i	−0.826107	−	1.43086i	0.0749630	−	0.997186i	$-0.476116\pi$
$684$		0			0
$685$	−2.05411	+	3.55783i	−0.0784836	+	0.135938i
$686$	−22.7342	+	1.09513i	−0.867995	+	0.0418124i
$687$		0			0
$688$	26.4523	+	21.3966i	1.00849	+	0.815737i
$689$	11.2251	−	13.3775i	0.427641	−	0.509643i
$690$		0			0
$691$	−4.39185	+	12.0665i	−0.167074	+	0.459031i	−0.994769	−	0.102146i	$-0.967429\pi$
$691$	−4.39185	+	12.0665i	−0.167074	+	0.459031i	0.827696	+	0.561177i	$0.189651\pi$
$692$	16.8470	−	4.67708i	0.640427	−	0.177796i
$693$		0			0
$694$	−11.0852	+	14.5820i	−0.420790	+	0.553525i
$695$	5.12874	+	29.0865i	0.194544	+	1.10331i
$696$		0			0
$697$	18.1366	−	6.60119i	0.686974	−	0.250038i
$698$	−5.33454	+	1.20785i	−0.201915	+	0.0457179i
$699$		0			0
$700$	−0.420694	−	0.0329929i	−0.0159008	−	0.00124702i
$701$			3.10248i			0.117179i	0.998282	+	0.0585896i	$0.0186603\pi$
$701$			3.10248i			0.117179i	−0.998282	+	0.0585896i	$0.981340\pi$
$702$		0			0
$703$			48.5896i			1.83259i
$704$	21.5966	+	1.30302i	0.813952	+	0.0491093i
$705$		0			0
$706$	−0.950228	−	4.19672i	−0.0357623	−	0.157946i
$707$	−2.71110	+	0.986759i	−0.101961	+	0.0371109i
$708$		0			0
$709$	1.67631	+	9.50681i	0.0629550	+	0.357036i	0.999970	+	0.00774652i	$0.00246582\pi$
$709$	1.67631	+	9.50681i	0.0629550	+	0.357036i	−0.937015	+	0.349289i	$0.886423\pi$
$710$	6.26983	+	4.76633i	0.235302	+	0.178877i
$711$		0			0
$712$	−12.1188	−	15.3596i	−0.454173	−	0.575627i
$713$	2.53639	−	6.96868i	0.0949887	−	0.260979i
$714$		0			0
$715$	−17.9470	+	21.3884i	−0.671181	+	0.799883i
$716$	12.0787	−	1.16640i	0.451401	−	0.0435903i
$717$		0			0
$718$	1.12621	+	23.3794i	0.0420300	+	0.872510i
$719$	−20.9190	+	36.2327i	−0.780146	+	1.35125i	0.151711	+	0.988425i	$0.451522\pi$
$719$	−20.9190	+	36.2327i	−0.780146	+	1.35125i	−0.931856	+	0.362827i	$0.881812\pi$
$720$		0			0
$721$	1.28869	+	2.23207i	0.0479931	+	0.0831266i
$722$	24.4986	−	15.7628i	0.911743	−	0.586630i
$723$		0			0
$724$	13.2857	−	29.1741i	0.493759	−	1.08425i
$725$	−0.781069	−	0.137724i	−0.0290082	−	0.00511492i
$726$		0			0
$727$	0.315311	+	0.375773i	0.0116942	+	0.0139367i	0.771860	−	0.635793i	$-0.219327\pi$
$727$	0.315311	+	0.375773i	0.0116942	+	0.0139367i	−0.760166	+	0.649729i	$0.774882\pi$
$728$	−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	−0.734134	−	0.679005i	$-0.762411\pi$
$733$	5.08882	−	28.8601i	0.187960	−	1.06597i	0.922093	−	0.386967i	$-0.126477\pi$
$734$	2.29154	−	2.11886i	0.0845823	−	0.0782087i
$735$		0			0
$736$	7.98162	+	11.9276i	0.294206	+	0.439656i
$737$	27.9521	−	16.1381i	1.02963	−	0.594456i
$738$		0			0
$739$	−34.8536	−	20.1228i	−1.28211	−	0.740227i	−0.304877	−	0.952392i	$-0.598616\pi$
$739$	−34.8536	−	20.1228i	−1.28211	−	0.740227i	−0.977234	+	0.212164i	$0.931949\pi$
$740$	15.1124	+	31.6614i	0.555544	+	1.16390i
$741$		0			0
$742$	2.11063	−	6.80064i	0.0774836	−	0.249659i
$743$	−30.1377	−	25.2885i	−1.10564	−	0.927746i	−0.107853	−	0.994167i	$-0.534397\pi$
$743$	−30.1377	−	25.2885i	−1.10564	−	0.927746i	−0.997792	+	0.0664212i	$0.978842\pi$
$744$		0			0
$745$	5.49409	+	1.99969i	0.201288	+	0.0732628i
$746$	14.7131	+	1.86969i	0.538685	+	0.0684541i
$747$		0			0
$748$	6.57324	−	25.4457i	0.240341	−	0.930387i
$749$	−5.24795	+	0.925356i	−0.191756	+	0.0338118i
$750$		0			0
$751$	9.37903	+	25.7687i	0.342246	+	0.940312i	0.984742	+	0.174023i	$0.0556767\pi$
$751$	9.37903	+	25.7687i	0.342246	+	0.940312i	−0.642496	+	0.766289i	$0.722101\pi$
$752$	47.3106	+	7.46658i	1.72524	+	0.272278i
$753$		0			0
$754$	−14.4891	+	28.1419i	−0.527662	+	1.02487i
$755$	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	$0.577598\pi$
$758$	1.99835	−	3.88136i	0.0725835	−	0.140977i
$759$		0			0
$760$	21.2632	−	34.3926i	0.771297	−	1.24755i
$761$	−4.40238	−	12.0954i	−0.159586	−	0.438459i	0.833969	−	0.551812i	$-0.186063\pi$
$761$	−4.40238	−	12.0954i	−0.159586	−	0.438459i	−0.993555	+	0.113353i	$0.963841\pi$
$762$		0			0
$763$	−2.33580	+	0.411864i	−0.0845616	+	0.0149105i
$764$	−22.6508	−	5.85125i	−0.819477	−	0.211691i
$765$		0			0
$766$	−22.5389	−	2.86416i	−0.814364	−	0.103486i
$767$	−48.9380	−	17.8120i	−1.76705	−	0.643153i
$768$		0			0
$769$	22.2691	+	18.6860i	0.803045	+	0.673835i	0.948937	−	0.315466i	$-0.102161\pi$
$769$	22.2691	+	18.6860i	0.803045	+	0.673835i	−0.145892	+	0.989301i	$0.546605\pi$
$770$	−3.37455	+	10.8731i	−0.121610	+	0.391839i
$771$		0			0
$772$	31.7153	−	15.1381i	1.14146	−	0.544832i
$773$	4.16046	+	2.40204i	0.149641	+	0.0863954i	0.572951	−	0.819590i	$-0.305798\pi$
$773$	4.16046	+	2.40204i	0.149641	+	0.0863954i	−0.423310	+	0.905985i	$0.639132\pi$
$774$		0			0
$775$	−0.407642	+	0.235352i	−0.0146429	+	0.00845410i
$776$	−5.03311	+	24.2478i	−0.180678	+	0.870445i
$777$		0			0
$778$	−18.3288	+	16.9476i	−0.657119	+	0.607602i
$779$	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	$-0.698072\pi$
$787$	−39.5137	−	6.96732i	−1.40851	−	0.248358i	−0.825635	+	0.564204i	$0.809183\pi$
$788$	41.9520	+	19.1047i	1.49448	+	0.680577i
$789$		0			0
$790$	−16.2747	+	10.4714i	−0.579030	+	0.372557i
$791$	−2.29975	−	3.98328i	−0.0817696	−	0.141629i
$792$		0			0
$793$	−0.0893474	+	0.154754i	−0.00317282	+	0.00549548i
$794$	0.917021	+	19.0367i	0.0325438	+	0.675586i
$795$		0			0
$796$	0.601035	+	6.22405i	0.0213031	+	0.220606i
$797$	19.9816	−	23.8132i	0.707785	−	0.843505i	−0.285599	−	0.958349i	$-0.592192\pi$
$797$	19.9816	−	23.8132i	0.707785	−	0.843505i	0.993384	+	0.114844i	$0.0366368\pi$
$798$		0			0
$799$	19.8985	−	54.6706i	0.703957	−	1.93411i
$800$	0.0985482	−	0.905591i	0.00348421	−	0.0320175i
$801$		0			0
$802$	−7.60909	−	5.78444i	−0.268686	−	0.204256i
$803$	−2.90395	−	16.4691i	−0.102478	−	0.581183i
$804$		0			0
$805$	−7.09642	+	2.58288i	−0.250116	+	0.0910347i
$806$	4.14843	+	18.3217i	0.146122	+	0.645354i
$807$		0			0
$808$	−1.95283	−	5.91394i	−0.0687003	−	0.208052i
$809$		−	26.7938i		−	0.942021i	−0.882128	−	0.471010i	$-0.843889\pi$
$809$		−	26.7938i		−	0.942021i	0.882128	−	0.471010i	$-0.156111\pi$
$810$		0			0
$811$			22.6335i			0.794769i	0.917652	+	0.397384i	$0.130082\pi$
$811$			22.6335i			0.794769i	−0.917652	+	0.397384i	$0.869918\pi$
$812$	−1.00909	+	12.8670i	−0.0354123	+	0.451543i
$813$		0			0
$814$	28.8034	−	6.52171i	1.00956	−	0.228586i
$815$	7.00868	−	2.55095i	0.245503	−	0.0893559i
$816$		0			0
$817$	−9.29439	−	52.7111i	−0.325169	−	1.84413i
$818$	16.1272	−	21.2144i	0.563876	−	0.741746i
$819$		0			0
$820$	−4.82804	−	17.3908i	−0.168603	−	0.607312i
$821$	4.37655	−	12.0245i	0.152743	−	0.419657i	−0.839595	−	0.543213i	$-0.817208\pi$
$821$	4.37655	−	12.0245i	0.152743	−	0.419657i	0.992338	+	0.123556i	$0.0394298\pi$
$822$		0			0
$823$	−16.6888	+	19.8889i	−0.581735	+	0.693284i	−0.973995	−	0.226570i	$-0.927249\pi$
$823$	−16.6888	+	19.8889i	−0.581735	+	0.693284i	0.392260	+	0.919854i	$0.371693\pi$
$824$	−4.89996	+	2.63545i	−0.170698	+	0.0918103i
$825$		0			0
$826$	−21.2106	+	1.02174i	−0.738012	+	0.0355510i
$827$	9.69134	−	16.7859i	0.337001	−	0.583703i	−0.646866	−	0.762603i	$-0.723921\pi$
$827$	9.69134	−	16.7859i	0.337001	−	0.583703i	0.983867	+	0.178901i	$0.0572542\pi$
$828$		0			0
$829$	−15.3678	−	26.6178i	−0.533745	−	0.924474i	−0.999223	−	0.0394143i	$-0.987451\pi$
$829$	−15.3678	−	26.6178i	−0.533745	−	0.924474i	0.465478	−	0.885060i	$-0.345883\pi$
$830$	16.5953	+	25.7924i	0.576030	+	0.895268i
$831$		0			0
$832$	−33.3516	−	14.4690i	−1.15626	−	0.501621i
$833$	−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	$-0.661778\pi$
$839$	8.37643	−	7.02866i	0.289186	−	0.242656i	0.775826	+	0.630946i	$0.217333\pi$
$840$		0			0
$841$	0.823502	−	4.67031i	0.0283966	−	0.161045i
$842$	21.6437	+	23.4075i	0.745890	+	0.806676i
$843$		0			0
$844$	14.5545	−	21.1895i	0.500988	−	0.729371i
$845$	15.0532	−	8.69096i	0.517845	−	0.298978i
$846$		0			0
$847$	−4.18228	−	2.41464i	−0.143705	−	0.0829680i
$848$	14.5366	+	4.99639i	0.499187	+	0.171577i
$849$		0			0
$850$	−1.05679	−	0.327981i	−0.0362475	−	0.0112497i
$851$	15.0067	+	12.5921i	0.514423	+	0.431652i
$852$		0			0
$853$	−6.04290	−	2.19943i	−0.206905	−	0.0753072i	0.236489	−	0.971634i	$-0.424003\pi$
$853$	−6.04290	−	2.19943i	−0.206905	−	0.0753072i	−0.443394	+	0.896327i	$0.646226\pi$
$854$	−0.00918534	+	0.0722820i	−0.000314316	+	0.00247344i
$855$		0			0
$856$	−1.65536	−	11.3837i	−0.0565790	−	0.389088i
$857$	3.12650	−	0.551287i	0.106799	−	0.0188316i	−0.119993	−	0.992775i	$-0.538287\pi$
$857$	3.12650	−	0.551287i	0.106799	−	0.0188316i	0.226792	+	0.973943i	$0.427176\pi$
$858$		0			0
$859$	9.69336	+	26.6323i	0.330733	+	0.908682i	0.987921	+	0.154956i	$0.0495235\pi$
$859$	9.69336	+	26.6323i	0.330733	+	0.908682i	−0.657188	+	0.753727i	$0.728254\pi$
$860$	−22.4506	−	31.4562i	−0.765558	−	1.07265i
$861$		0			0
$862$	13.5867	+	6.99526i	0.462766	+	0.238260i
$863$	−53.5310			−1.82222			−0.911108	−	0.412168i	$-0.864772\pi$
$863$	−53.5310			−1.82222			−0.911108	+	0.412168i	$0.864772\pi$
$864$		0			0
$865$	−19.8602			−0.675267
$866$	−47.2656	−	24.3351i	−1.60615	−	0.826942i
$867$		0			0
$868$	4.44980	+	6.23476i	0.151036	+	0.211622i
$869$	5.57172	+	15.3082i	0.189008	+	0.519294i
$870$		0			0
$871$	−53.4100	+	9.41763i	−1.80973	+	0.319104i
$872$	−0.736780	−	5.06676i	−0.0249505	−	0.171582i
$873$		0			0
$874$	2.84626	−	22.3980i	0.0962761	−	0.757624i
$875$	−13.5351	−	4.92637i	−0.457570	−	0.166542i
$876$		0			0
$877$	−22.8969	−	19.2128i	−0.773175	−	0.648770i	0.168345	−	0.985728i	$-0.446158\pi$
$877$	−22.8969	−	19.2128i	−0.773175	−	0.648770i	−0.941520	+	0.336958i	$0.890602\pi$
$878$	43.1317	+	13.3863i	1.45563	+	0.451764i
$879$		0			0
$880$	−23.2415	−	7.98841i	−0.783472	−	0.269289i
$881$	14.9002	+	8.60262i	0.502000	+	0.289830i	0.729539	−	0.683939i	$-0.239735\pi$
$881$	14.9002	+	8.60262i	0.502000	+	0.289830i	−0.227539	+	0.973769i	$0.573068\pi$
$882$		0			0
$883$	−19.9228	+	11.5024i	−0.670455	+	0.387088i	−0.796249	−	0.604969i	$-0.793186\pi$
$883$	−19.9228	+	11.5024i	−0.670455	+	0.387088i	0.125794	+	0.992056i	$0.459852\pi$
$884$	−25.0025	+	36.4004i	−0.840927	+	1.22428i
$885$		0			0
$886$	−36.0823	−	39.0229i	−1.21221	−	1.31100i
$887$	4.95616	−	28.1078i	0.166411	−	0.943766i	−0.781186	−	0.624299i	$-0.785385\pi$
$887$	4.95616	−	28.1078i	0.166411	−	0.943766i	0.947597	−	0.319468i	$-0.103504\pi$
$888$		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
$896$	−14.8227	−	0.179768i	−0.495192	−	0.00600563i
$897$		0			0
$898$	−6.18452	−	9.61200i	−0.206380	−	0.320757i
$899$	7.19828	+	12.4678i	0.240076	+	0.415824i
$900$		0			0
$901$	9.33569	−	16.1699i	0.311017	−	0.538697i
$902$	−15.1754	+	0.731017i	−0.505285	+	0.0243402i
$903$		0			0
$904$	8.74432	−	4.70314i	0.290832	−	0.156424i
$905$	−23.4059	+	27.8941i	−0.778039	+	0.927231i
$906$		0			0
$907$	−19.9408	+	54.7868i	−0.662123	+	1.81917i	−0.0950957	+	0.995468i	$0.530316\pi$
$907$	−19.9408	+	54.7868i	−0.662123	+	1.81917i	−0.567027	+	0.823699i	$0.691907\pi$
$908$	−0.0513842	−	0.185088i	−0.00170525	−	0.00614236i
$909$		0			0
$910$	11.5771	−	15.2290i	0.383776	−	0.504835i
$911$	0.684711	+	3.88319i	0.0226855	+	0.128656i	0.994047	−	0.108949i	$-0.0347487\pi$
$911$	0.684711	+	3.88319i	0.0226855	+	0.128656i	−0.971362	+	0.237605i	$0.923638\pi$
$912$		0			0
$913$	24.2606	−	8.83014i	0.802909	−	0.292235i
$914$	−3.41260	+	0.772686i	−0.112879	+	0.0255582i
$915$		0			0
$916$	−4.20210	+	53.5812i	−0.138841	+	1.77037i
$917$			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	$-0.0339689\pi$
$920$	−5.11162	−	15.4800i	−0.168525	−	0.510360i
$921$		0			0
$922$	−2.82183	−	12.4627i	−0.0929319	−	0.410438i
$923$	−10.4682	+	3.81011i	−0.344564	+	0.125411i
$924$		0			0
$925$	−0.215916	−	1.22452i	−0.00709928	−	0.0402620i
$926$	1.57011	+	1.19360i	0.0515970	+	0.0392240i
$927$		0			0
$928$	−27.6976	−	3.01411i	−0.909220	−	0.0989431i
$929$	−19.4892	+	53.5462i	−0.639420	+	1.75679i	0.0141186	+	0.999900i	$0.495506\pi$
$929$	−19.4892	+	53.5462i	−0.639420	+	1.75679i	−0.653539	+	0.756893i	$0.726716\pi$
$930$		0			0
$931$	−21.3703	+	25.4681i	−0.700383	+	0.834684i
$932$	1.39068	+	14.4013i	0.0455533	+	0.471729i
$933$		0			0
$934$	1.43565	+	29.8030i	0.0469759	+	0.975185i
$935$	−14.9262	+	25.8530i	−0.488140	+	0.845483i
$936$		0			0
$937$	9.57464	+	16.5838i	0.312790	+	0.541768i	0.978965	−	0.204027i	$-0.0654031\pi$
$937$	9.57464	+	16.5838i	0.312790	+	0.541768i	−0.666175	+	0.745795i	$0.732070\pi$
$938$	−18.5971	+	11.9657i	−0.607218	+	0.390694i
$939$		0			0
$940$	−49.5126	−	22.5478i	−1.61492	−	0.735427i
$941$	18.4077	+	3.24578i	0.600075	+	0.105809i	0.465430	−	0.885085i	$-0.345900\pi$
$941$	18.4077	+	3.24578i	0.600075	+	0.105809i	0.134645	+	0.990894i	$0.457011\pi$
$942$		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	$-0.875232\pi$
$947$	−21.8007	+	18.2930i	−0.708428	+	0.594442i	0.215729	+	0.976453i	$0.430787\pi$
$948$		0			0
$949$	−4.87953	+	27.6732i	−0.158396	+	0.898309i
$950$	−1.05221	+	0.972922i	−0.0341382	+	0.0315658i
$951$		0			0
$952$	−3.65958	+	17.6306i	−0.118608	+	0.571411i
$953$	39.0891	−	22.5681i	1.26622	−	0.731052i	0.291949	−	0.956434i	$-0.405696\pi$
$953$	39.0891	−	22.5681i	1.26622	−	0.731052i	0.974270	+	0.225382i	$0.0723630\pi$
$954$		0			0
$955$	23.0134	+	13.2868i	0.744695	+	0.429950i
$956$	23.0257	−	10.9905i	0.744706	−	0.355458i
$957$		0			0
$958$	−6.12200	+	19.7256i	−0.197793	+	0.637306i
$959$	−1.81507	−	1.52303i	−0.0586118	−	0.0491811i
$960$		0			0
$961$	−21.1016	−	7.68035i	−0.680697	−	0.247753i
$962$	−49.2278	−	6.25568i	−1.58717	−	0.201691i
$963$		0			0
$964$	−14.6643	−	3.78814i	−0.472305	−	0.122008i
$965$	−39.3121	+	6.93179i	−1.26550	+	0.223142i
$966$		0			0
$967$	3.13528	+	8.61412i	0.100824	+	0.277011i	0.979841	−	0.199779i	$-0.0640224\pi$
$967$	3.13528	+	8.61412i	0.100824	+	0.277011i	−0.879017	+	0.476790i	$0.841800\pi$
$968$	5.48208	−	8.86712i	0.176201	−	0.285000i
$969$		0			0
$970$	12.8766	−	25.0099i	0.413442	−	0.803018i
$971$	−10.7197			−0.344010			−0.172005	−	0.985096i	$-0.555025\pi$
$971$	−10.7197			−0.344010			−0.172005	+	0.985096i	$0.555025\pi$
$972$		0			0
$973$	−17.0344			−0.546098
$974$	0.182905	−	0.355253i	0.00586067	−	0.0113830i
$975$		0			0
$976$	−0.155366	−	0.0245200i	−0.00497316	−	0.000784866i
$977$	−17.0312	−	46.7929i	−0.544877	−	1.49704i	−0.840542	−	0.541746i	$-0.817763\pi$
$977$	−17.0312	−	46.7929i	−0.544877	−	1.49704i	0.295665	−	0.955292i	$-0.404459\pi$
$978$		0			0
$979$	18.4233	−	3.24853i	0.588812	−	0.103823i
$980$	−6.00394	+	23.2419i	−0.191789	+	0.742435i
$981$		0			0
$982$	21.7439	+	2.76313i	0.693875	+	0.0881751i
$983$	1.70953	+	0.622218i	0.0545255	+	0.0198457i	0.369139	−	0.929374i	$-0.379653\pi$
$983$	1.70953	+	0.622218i	0.0545255	+	0.0198457i	−0.314613	+	0.949220i	$0.601875\pi$
$984$		0			0
$985$	−40.1114	−	33.6575i	−1.27806	−	1.07242i
$986$	−10.0314	+	32.3220i	−0.319464	+	1.02934i
$987$		0			0
$988$	24.6366	+	51.6151i	0.783793	+	1.64209i
$989$	−18.6883	−	10.7897i	−0.594252	−	0.343092i
$990$		0			0
$991$	48.8792	−	28.2204i	1.55270	−	0.896451i	0.554777	−	0.831999i	$-0.312804\pi$
$991$	48.8792	−	28.2204i	1.55270	−	0.896451i	0.997921	−	0.0644516i	$-0.0205298\pi$
$992$	−13.7422	+	9.19592i	−0.436315	+	0.291971i
$993$		0			0
$994$	−3.33514	+	3.08382i	−0.105784	+	0.0978129i
$995$	1.23338	−	6.99485i	0.0391008	−	0.221752i
$996$		0			0
$997$	9.04342	−	7.58833i	0.286408	−	0.240325i	−0.488252	−	0.872703i	$-0.662365\pi$
$997$	9.04342	−	7.58833i	0.286408	−	0.240325i	0.774660	+	0.632378i	$0.217921\pi$
$998$	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.863.15		96
3.2	odd	2		972.2.l.a.863.2		96
4.3	odd	2	inner	972.2.l.d.863.10		96
9.2	odd	6		324.2.l.a.179.9		96
9.4	even	3		972.2.l.c.215.4		96
9.5	odd	6		972.2.l.b.215.13		96
9.7	even	3		108.2.l.a.23.8	✓	96
12.11	even	2		972.2.l.a.863.7		96
27.2	odd	18		108.2.l.a.47.13	yes	96
27.7	even	9		972.2.l.b.755.15		96
27.11	odd	18	inner	972.2.l.d.107.10		96
27.16	even	9		972.2.l.a.107.7		96
27.20	odd	18		972.2.l.c.755.2		96
27.25	even	9		324.2.l.a.143.4		96
36.7	odd	6		108.2.l.a.23.13	yes	96
36.11	even	6		324.2.l.a.179.4		96
36.23	even	6		972.2.l.b.215.15		96
36.31	odd	6		972.2.l.c.215.2		96
108.7	odd	18		972.2.l.b.755.13		96
108.11	even	18	inner	972.2.l.d.107.15		96
108.43	odd	18		972.2.l.a.107.2		96
108.47	even	18		972.2.l.c.755.4		96
108.79	odd	18		324.2.l.a.143.9		96
108.83	even	18		108.2.l.a.47.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.8	✓	96	9.7	even	3
108.2.l.a.23.13	yes	96	36.7	odd	6
108.2.l.a.47.8	yes	96	108.83	even	18
108.2.l.a.47.13	yes	96	27.2	odd	18
324.2.l.a.143.4		96	27.25	even	9
324.2.l.a.143.9		96	108.79	odd	18
324.2.l.a.179.4		96	36.11	even	6
324.2.l.a.179.9		96	9.2	odd	6
972.2.l.a.107.2		96	108.43	odd	18
972.2.l.a.107.7		96	27.16	even	9
972.2.l.a.863.2		96	3.2	odd	2
972.2.l.a.863.7		96	12.11	even	2
972.2.l.b.215.13		96	9.5	odd	6
972.2.l.b.215.15		96	36.23	even	6
972.2.l.b.755.13		96	108.7	odd	18
972.2.l.b.755.15		96	27.7	even	9
972.2.l.c.215.2		96	36.31	odd	6
972.2.l.c.215.4		96	9.4	even	3
972.2.l.c.755.2		96	27.20	odd	18
972.2.l.c.755.4		96	108.47	even	18
972.2.l.d.107.10		96	27.11	odd	18	inner
972.2.l.d.107.15		96	108.11	even	18	inner
972.2.l.d.863.10		96	4.3	odd	2	inner
972.2.l.d.863.15		96	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.25735 + 0.647359i) q^{2} +(1.16185 + 1.62791i) q^{4} +(-0.776998 - 2.13478i) q^{5} +(1.29035 - 0.227523i) q^{7} +(0.407013 + 2.79899i) q^{8} +(0.405013 - 3.18717i) q^{10} +(-2.54138 - 0.924988i) q^{11} +(3.48118 + 2.92106i) q^{13} +(1.76970 + 0.549241i) q^{14} +(-1.30019 + 3.78279i) q^{16} +(4.20783 + 2.42939i) q^{17} +(5.44971 - 3.14639i) q^{19} +(2.57248 - 3.74519i) q^{20} +(-2.59661 - 2.80822i) q^{22} +(0.440555 - 2.49851i) q^{23} +(-0.123358 + 0.103510i) q^{25} +(2.48609 + 5.92636i) q^{26} +(1.86958 + 1.83622i) q^{28} +(3.16586 + 3.77293i) q^{29} +(2.87863 + 0.507580i) q^{31} +(-4.08362 + 3.91460i) q^{32} +(3.71802 + 5.77857i) q^{34} +(-1.48831 - 2.57783i) q^{35} +(-3.86074 + 6.68701i) q^{37} +(8.88903 - 0.428196i) q^{38} +(5.65899 - 3.04370i) q^{40} +(2.55335 - 3.04297i) q^{41} +(2.90911 - 7.99270i) q^{43} +(-1.44692 - 5.21185i) q^{44} +(2.17137 - 2.85631i) q^{46} +(-2.07927 - 11.7921i) q^{47} +(-4.96462 + 1.80697i) q^{49} +(-0.222112 + 0.0502909i) q^{50} +(-0.710600 + 9.06090i) q^{52} -3.84281i q^{53} +6.14402i q^{55} +(1.16202 + 3.51906i) q^{56} +(1.53816 + 6.79333i) q^{58} +(-10.7689 + 3.91958i) q^{59} +(0.00682825 + 0.0387249i) q^{61} +(3.29086 + 2.50171i) q^{62} +(-7.66868 + 2.27845i) q^{64} +(3.53096 - 9.70123i) q^{65} +(-7.67125 + 9.14224i) q^{67} +(0.934048 + 9.67257i) q^{68} +(-0.202546 - 4.20470i) q^{70} +(-1.22570 + 2.12297i) q^{71} +(3.09175 + 5.35507i) q^{73} +(-9.18319 + 5.90861i) q^{74} +(11.4538 + 5.21600i) q^{76} +(-3.48972 - 0.615332i) q^{77} +(-3.87187 - 4.61431i) q^{79} +(9.08569 - 0.163591i) q^{80} +(5.18035 - 2.17314i) q^{82} +(-7.31283 + 6.13619i) q^{83} +(1.91675 - 10.8704i) q^{85} +(8.83191 - 8.16638i) q^{86} +(1.55465 - 7.48979i) q^{88} +(-5.99050 + 3.45862i) q^{89} +(5.15653 + 2.97713i) q^{91} +(4.57922 - 2.18572i) q^{92} +(5.01936 - 16.1728i) q^{94} +(-10.9513 - 9.18922i) q^{95} +(8.22759 + 2.99460i) q^{97} +(-7.41203 - 0.941893i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) \) 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

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