LMFDB - Embedded newform 864.2.w.a.107.13

Newspace parameters

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.13
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.13

$q$-expansion

$f(q)$	$=$	$q+(-0.394008 - 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(-2.44724 - 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(2.11938 + 1.87302i) q^{8} +O(q^{10})$	\(q+(-0.394008 - 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(-2.44724 - 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(2.11938 + 1.87302i) q^{8} +(-0.412566 + 3.72328i) q^{10} +(4.19398 + 1.73720i) q^{11} +(2.12813 + 5.13777i) q^{13} +(-5.93786 - 3.26747i) q^{14} +(1.70892 - 3.61657i) q^{16} -3.78123 q^{17} +(6.01757 - 2.49256i) q^{19} +(5.21959 - 0.906648i) q^{20} +(0.707039 - 6.38081i) q^{22} +(0.521933 - 0.521933i) q^{23} +(1.42590 + 1.42590i) q^{25} +(6.13971 - 4.91479i) q^{26} +(-2.09837 + 9.35232i) q^{28} +(-1.96141 - 4.73526i) q^{29} -2.30887i q^{31} +(-5.58542 - 0.896134i) q^{32} +(1.48984 + 5.13574i) q^{34} +(-11.7282 + 4.85798i) q^{35} +(0.301775 - 0.728548i) q^{37} +(-5.75641 - 7.19109i) q^{38} +(-3.28799 - 6.73211i) q^{40} +(5.11319 + 5.11319i) q^{41} +(-1.04025 + 2.51140i) q^{43} +(-8.94511 + 1.55378i) q^{44} +(-0.914544 - 0.503253i) q^{46} -6.05530i q^{47} -15.9673i q^{49} +(1.37487 - 2.49850i) q^{50} +(-9.09446 - 6.40260i) q^{52} +(3.39385 - 8.19348i) q^{53} +(-8.50270 - 8.50270i) q^{55} +(13.5293 - 0.834842i) q^{56} +(-5.65871 + 4.52976i) q^{58} +(3.61257 - 8.72153i) q^{59} +(-0.171884 + 0.0711965i) q^{61} +(-3.13594 + 0.909712i) q^{62} +(0.983556 + 7.93931i) q^{64} -14.7306i q^{65} +(0.155362 + 0.375078i) q^{67} +(6.38845 - 4.04705i) q^{68} +(11.2192 + 14.0154i) q^{70} +(-4.96412 - 4.96412i) q^{71} +(-1.96331 + 1.96331i) q^{73} +(-1.10843 - 0.122822i) q^{74} +(-7.49899 + 10.6518i) q^{76} +(20.0993 - 8.32540i) q^{77} -8.19131 q^{79} +(-7.84819 + 7.11831i) q^{80} +(4.93019 - 8.95946i) q^{82} +(4.85181 + 11.7133i) q^{83} +(9.25358 + 3.83296i) q^{85} +(3.82089 + 0.423382i) q^{86} +(5.63482 + 11.5372i) q^{88} +(-6.59205 + 6.59205i) q^{89} +(24.6223 + 10.1989i) q^{91} +(-0.323190 + 1.44044i) q^{92} +(-8.22442 + 2.38584i) q^{94} -17.2531 q^{95} -6.02797 q^{97} +(-21.6870 + 6.29123i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.394008	−	1.35822i	−0.278606	−	0.960406i
$2$	−0.394008	−	1.35822i	−0.278606	−	0.960406i
$3$		0			0
$3$		0			0
$4$	−1.68952	+	1.07030i	−0.844758	+	0.535149i
$5$	−2.44724	−	1.01368i	−1.09444	−	0.453331i	−0.238886	−	0.971048i	$-0.576782\pi$
$5$	−2.44724	−	1.01368i	−1.09444	−	0.453331i	−0.855552	+	0.517716i	$0.826782\pi$
$6$		0			0
$7$	3.38875	−	3.38875i	1.28083	−	1.28083i	0.340630	−	0.940197i	$-0.389360\pi$
$7$	3.38875	−	3.38875i	1.28083	−	1.28083i	0.940197	−	0.340630i	$-0.110640\pi$
$8$	2.11938	+	1.87302i	0.749315	+	0.662214i
$9$		0			0
$10$	−0.412566	+	3.72328i	−0.130465	+	1.17741i
$11$	4.19398	+	1.73720i	1.26453	+	0.523786i	0.911297	−	0.411749i	$-0.135082\pi$
$11$	4.19398	+	1.73720i	1.26453	+	0.523786i	0.353234	+	0.935535i	$0.385082\pi$
$12$		0			0
$13$	2.12813	+	5.13777i	0.590238	+	1.42496i	0.883273	+	0.468859i	$0.155335\pi$
$13$	2.12813	+	5.13777i	0.590238	+	1.42496i	−0.293035	+	0.956102i	$0.594665\pi$
$14$	−5.93786	−	3.26747i	−1.58696	−	0.873268i
$15$		0			0
$16$	1.70892	−	3.61657i	0.427231	−	0.904143i
$17$	−3.78123			−0.917084			−0.458542	−	0.888673i	$-0.651628\pi$
$17$	−3.78123			−0.917084			−0.458542	+	0.888673i	$0.651628\pi$
$18$		0			0
$19$	6.01757	−	2.49256i	1.38053	−	0.571832i	0.435903	−	0.899993i	$-0.356429\pi$
$19$	6.01757	−	2.49256i	1.38053	−	0.571832i	0.944622	+	0.328161i	$0.106429\pi$
$20$	5.21959	−	0.906648i	1.16714	−	0.202733i
$21$		0			0
$22$	0.707039	−	6.38081i	0.150741	−	1.36039i
$23$	0.521933	−	0.521933i	0.108830	−	0.108830i	−0.650595	−	0.759425i	$-0.725480\pi$
$23$	0.521933	−	0.521933i	0.108830	−	0.108830i	0.759425	+	0.650595i	$0.225480\pi$
$24$		0			0
$25$	1.42590	+	1.42590i	0.285180	+	0.285180i
$26$	6.13971	−	4.91479i	1.20410	−	0.963871i
$27$		0			0
$28$	−2.09837	+	9.35232i	−0.396555	+	1.76742i
$29$	−1.96141	−	4.73526i	−0.364225	−	0.879316i	−0.994673	−	0.103085i	$-0.967129\pi$
$29$	−1.96141	−	4.73526i	−0.364225	−	0.879316i	0.630448	−	0.776232i	$-0.282871\pi$
$30$		0			0
$31$		−	2.30887i		−	0.414684i	−0.978268	−	0.207342i	$-0.933519\pi$
$31$		−	2.30887i		−	0.414684i	0.978268	−	0.207342i	$-0.0664814\pi$
$32$	−5.58542	−	0.896134i	−0.987373	−	0.158416i
$33$		0			0
$34$	1.48984	+	5.13574i	0.255505	+	0.880773i
$35$	−11.7282	+	4.85798i	−1.98243	+	0.821148i
$36$		0			0
$37$	0.301775	−	0.728548i	0.0496114	−	0.119773i	−0.897131	−	0.441765i	$-0.854353\pi$
$37$	0.301775	−	0.728548i	0.0496114	−	0.119773i	0.946742	+	0.321992i	$0.104353\pi$
$38$	−5.75641	−	7.19109i	−0.933813	−	1.16655i
$39$		0			0
$40$	−3.28799	−	6.73211i	−0.519876	−	1.06444i
$41$	5.11319	+	5.11319i	0.798546	+	0.798546i	0.982866	−	0.184321i	$-0.0590084\pi$
$41$	5.11319	+	5.11319i	0.798546	+	0.798546i	−0.184321	+	0.982866i	$0.559008\pi$
$42$		0			0
$43$	−1.04025	+	2.51140i	−0.158637	+	0.382984i	−0.983135	−	0.182881i	$-0.941458\pi$
$43$	−1.04025	+	2.51140i	−0.158637	+	0.382984i	0.824498	+	0.565865i	$0.191458\pi$
$44$	−8.94511	+	1.55378i	−1.34853	+	0.234241i
$45$		0			0
$46$	−0.914544	−	0.503253i	−0.134842	−	0.0742006i
$47$		−	6.05530i		−	0.883256i	−0.897198	−	0.441628i	$-0.854401\pi$
$47$		−	6.05530i		−	0.883256i	0.897198	−	0.441628i	$-0.145599\pi$
$48$		0			0
$49$		−	15.9673i		−	2.28104i
$50$	1.37487	−	2.49850i	0.194436	−	0.353341i
$51$		0			0
$52$	−9.09446	−	6.40260i	−1.26117	−	0.887881i
$53$	3.39385	−	8.19348i	0.466181	−	1.12546i	−0.499635	−	0.866236i	$-0.666533\pi$
$53$	3.39385	−	8.19348i	0.466181	−	1.12546i	0.965817	−	0.259226i	$-0.0834673\pi$
$54$		0			0
$55$	−8.50270	−	8.50270i	−1.14650	−	1.14650i
$56$	13.5293	−	0.834842i	1.80792	−	0.111560i
$57$		0			0
$58$	−5.65871	+	4.52976i	−0.743025	+	0.594786i
$59$	3.61257	−	8.72153i	0.470317	−	1.13545i	−0.493706	−	0.869629i	$-0.664358\pi$
$59$	3.61257	−	8.72153i	0.470317	−	1.13545i	0.964023	−	0.265817i	$-0.0856418\pi$
$60$		0			0
$61$	−0.171884	+	0.0711965i	−0.0220074	+	0.00911578i	−0.393660	−	0.919256i	$-0.628791\pi$
$61$	−0.171884	+	0.0711965i	−0.0220074	+	0.00911578i	0.371653	+	0.928372i	$0.378791\pi$
$62$	−3.13594	+	0.909712i	−0.398265	+	0.115533i
$63$		0			0
$64$	0.983556	+	7.93931i	0.122945	+	0.992414i
$65$		−	14.7306i		−	1.82711i
$66$		0			0
$67$	0.155362	+	0.375078i	0.0189805	+	0.0458231i	0.933086	−	0.359654i	$-0.117105\pi$
$67$	0.155362	+	0.375078i	0.0189805	+	0.0458231i	−0.914105	+	0.405477i	$0.867105\pi$
$68$	6.38845	−	4.04705i	0.774714	−	0.490777i
$69$		0			0
$70$	11.2192	+	14.0154i	1.34095	+	1.67516i
$71$	−4.96412	−	4.96412i	−0.589132	−	0.589132i	0.348264	−	0.937396i	$-0.386771\pi$
$71$	−4.96412	−	4.96412i	−0.589132	−	0.589132i	−0.937396	+	0.348264i	$0.886771\pi$
$72$		0			0
$73$	−1.96331	+	1.96331i	−0.229788	+	0.229788i	−0.812604	−	0.582816i	$-0.801951\pi$
$73$	−1.96331	+	1.96331i	−0.229788	+	0.229788i	0.582816	+	0.812604i	$0.301951\pi$
$74$	−1.10843	−	0.122822i	−0.128852	−	0.0142778i
$75$		0			0
$76$	−7.49899	+	10.6518i	−0.860194	+	1.22185i
$77$	20.0993	−	8.32540i	2.29053	−	0.948767i
$78$		0			0
$79$	−8.19131			−0.921594			−0.460797	−	0.887505i	$-0.652436\pi$
$79$	−8.19131			−0.921594			−0.460797	+	0.887505i	$0.652436\pi$
$80$	−7.84819	+	7.11831i	−0.877454	+	0.795851i
$81$		0			0
$82$	4.93019	−	8.95946i	0.544448	−	0.989407i
$83$	4.85181	+	11.7133i	0.532555	+	1.28570i	0.929826	+	0.368000i	$0.119957\pi$
$83$	4.85181	+	11.7133i	0.532555	+	1.28570i	−0.397271	+	0.917701i	$0.630043\pi$
$84$		0			0
$85$	9.25358	+	3.83296i	1.00369	+	0.415743i
$86$	3.82089	+	0.423382i	0.412017	+	0.0456545i
$87$		0			0
$88$	5.63482	+	11.5372i	0.600673	+	1.22987i
$89$	−6.59205	+	6.59205i	−0.698756	+	0.698756i	−0.964142	−	0.265386i	$-0.914501\pi$
$89$	−6.59205	+	6.59205i	−0.698756	+	0.698756i	0.265386	+	0.964142i	$0.414501\pi$
$90$		0			0
$91$	24.6223	+	10.1989i	2.58112	+	1.06914i
$92$	−0.323190	+	1.44044i	−0.0336948	+	0.150176i
$93$		0			0
$94$	−8.22442	+	2.38584i	−0.848284	+	0.246080i
$95$	−17.2531			−1.77013
$96$		0			0
$97$	−6.02797			−0.612048			−0.306024	−	0.952024i	$-0.598999\pi$
$97$	−6.02797			−0.612048			−0.306024	+	0.952024i	$0.598999\pi$
$98$	−21.6870	+	6.29123i	−2.19072	+	0.635510i
$99$		0			0
$100$	−3.93522	−	0.882941i	−0.393522	−	0.0882941i
$101$	1.74724	+	0.723731i	0.173857	+	0.0720140i	0.467914	−	0.883774i	$-0.345006\pi$
$101$	1.74724	+	0.723731i	0.173857	+	0.0720140i	−0.294057	+	0.955788i	$0.595006\pi$
$102$		0			0
$103$	5.68112	−	5.68112i	0.559777	−	0.559777i	−0.369467	−	0.929244i	$-0.620460\pi$
$103$	5.68112	−	5.68112i	0.559777	−	0.559777i	0.929244	+	0.369467i	$0.120460\pi$
$104$	−5.11284	+	14.8749i	−0.501356	+	1.45861i
$105$		0			0
$106$	−12.4657	−	1.38129i	−1.21078	−	0.134163i
$107$	11.3023	+	4.68159i	1.09264	+	0.452586i	0.854926	−	0.518749i	$-0.173602\pi$
$107$	11.3023	+	4.68159i	1.09264	+	0.452586i	0.237713	+	0.971335i	$0.423602\pi$
$108$		0			0
$109$	−2.63231	−	6.35496i	−0.252130	−	0.608695i	0.746246	−	0.665670i	$-0.231854\pi$
$109$	−2.63231	−	6.35496i	−0.252130	−	0.608695i	−0.998376	+	0.0569753i	$0.981854\pi$
$110$	−8.19839	+	14.8987i	−0.781686	+	1.42053i
$111$		0			0
$112$	−6.46454	−	18.0468i	−0.610842	−	1.70526i
$113$	16.8015			1.58055			0.790276	−	0.612751i	$-0.209937\pi$
$113$	16.8015			1.58055			0.790276	+	0.612751i	$0.209937\pi$
$114$		0			0
$115$	−1.80637	+	0.748222i	−0.168445	+	0.0697720i
$116$	8.38198	+	5.90101i	0.778247	+	0.547895i
$117$		0			0
$118$	−13.2691	−	1.47031i	−1.22152	−	0.135353i
$119$	−12.8137	+	12.8137i	−1.17463	+	1.17463i
$120$		0			0
$121$	6.79340	+	6.79340i	0.617582	+	0.617582i
$122$	0.164424	+	0.205403i	0.0148862	+	0.0185964i
$123$		0			0
$124$	2.47117	+	3.90086i	0.221918	+	0.350308i
$125$	3.02429	+	7.30128i	0.270500	+	0.653046i
$126$		0			0
$127$			9.50016i			0.843003i	0.906828	+	0.421501i	$0.138497\pi$
$127$			9.50016i			0.843003i	−0.906828	+	0.421501i	$0.861503\pi$
$128$	10.3958	−	4.46404i	0.918866	−	0.394569i
$129$		0			0
$130$	−20.0074	+	5.80398i	−1.75476	+	0.509042i
$131$	−19.3884	+	8.03093i	−1.69397	+	0.701666i	−0.999835	−	0.0181772i	$-0.994214\pi$
$131$	−19.3884	+	8.03093i	−1.69397	+	0.701666i	−0.694137	+	0.719843i	$0.744214\pi$
$132$		0			0
$133$	11.9454	−	28.8387i	1.03580	−	2.50063i
$134$	0.448224	−	0.358800i	0.0387206	−	0.0309956i
$135$		0			0
$136$	−8.01388	−	7.08235i	−0.687184	−	0.607306i
$137$	−10.5560	−	10.5560i	−0.901864	−	0.901864i	0.0937337	−	0.995597i	$-0.470120\pi$
$137$	−10.5560	−	10.5560i	−0.901864	−	0.901864i	−0.995597	+	0.0937337i	$0.970120\pi$
$138$		0			0
$139$	−0.124526	+	0.300633i	−0.0105622	+	0.0254994i	−0.929073	−	0.369897i	$-0.879393\pi$
$139$	−0.124526	+	0.300633i	−0.0105622	+	0.0254994i	0.918510	+	0.395397i	$0.129393\pi$
$140$	14.6155	−	20.7603i	1.23523	−	1.75456i
$141$		0			0
$142$	−4.78645	+	8.69826i	−0.401670	+	0.729942i
$143$			25.2447i			2.11107i
$144$		0			0
$145$			13.5766i			1.12747i
$146$	3.44017	+	1.89305i	0.284710	+	0.156670i
$147$		0			0
$148$	0.269911	+	1.55388i	0.0221866	+	0.127728i
$149$	−2.37298	+	5.72888i	−0.194402	+	0.469328i	−0.990782	−	0.135469i	$-0.956746\pi$
$149$	−2.37298	+	5.72888i	−0.194402	+	0.469328i	0.796380	+	0.604797i	$0.206746\pi$
$150$		0			0
$151$	−9.09870	−	9.09870i	−0.740442	−	0.740442i	0.232221	−	0.972663i	$-0.425401\pi$
$151$	−9.09870	−	9.09870i	−0.740442	−	0.740442i	−0.972663	+	0.232221i	$0.925401\pi$
$152$	17.4222	+	5.98837i	1.41312	+	0.485721i
$153$		0			0
$154$	−19.2270	−	24.0190i	−1.54936	−	1.93550i
$155$	−2.34045	+	5.65035i	−0.187989	+	0.453847i
$156$		0			0
$157$	14.6827	−	6.08178i	1.17181	−	0.485379i	0.290018	−	0.957021i	$-0.406339\pi$
$157$	14.6827	−	6.08178i	1.17181	−	0.485379i	0.881790	+	0.471642i	$0.156339\pi$
$158$	3.22744	+	11.1256i	0.256762	+	0.885104i
$159$		0			0
$160$	12.7605	+	7.85488i	1.00880	+	0.620983i
$161$		−	3.53740i		−	0.278786i
$162$		0			0
$163$	2.81351	+	6.79241i	0.220371	+	0.532023i	0.994940	−	0.100466i	$-0.0320334\pi$
$163$	2.81351	+	6.79241i	0.220371	+	0.532023i	−0.774569	+	0.632489i	$0.782033\pi$
$164$	−14.1114	−	3.16617i	−1.10192	−	0.247237i
$165$		0			0
$166$	13.9976	−	11.2049i	1.08642	−	0.869673i
$167$	10.4693	+	10.4693i	0.810140	+	0.810140i	0.984655	−	0.174515i	$-0.0558356\pi$
$167$	10.4693	+	10.4693i	0.810140	+	0.810140i	−0.174515	+	0.984655i	$0.555836\pi$
$168$		0			0
$169$	−12.6753	+	12.6753i	−0.975026	+	0.975026i
$170$	1.56001	−	14.0786i	0.119647	−	1.07978i
$171$		0			0
$172$	−0.930417	−	5.35642i	−0.0709436	−	0.408423i
$173$	14.7918	−	6.12697i	1.12460	−	0.465825i	0.258658	−	0.965969i	$-0.416720\pi$
$173$	14.7918	−	6.12697i	1.12460	−	0.465825i	0.865942	+	0.500144i	$0.166720\pi$
$174$		0			0
$175$	9.66403			0.730532
$176$	13.4499	−	12.1991i	1.01382	−	0.919539i
$177$		0			0
$178$	11.5508	+	6.35612i	0.865766	+	0.476412i
$179$	2.32212	+	5.60609i	0.173563	+	0.419019i	0.986592	−	0.163204i	$-0.0521830\pi$
$179$	2.32212	+	5.60609i	0.173563	+	0.419019i	−0.813029	+	0.582223i	$0.802183\pi$
$180$		0			0
$181$	9.25503	+	3.83356i	0.687921	+	0.284946i	0.699134	−	0.714991i	$-0.253569\pi$
$181$	9.25503	+	3.83356i	0.687921	+	0.284946i	−0.0112129	+	0.999937i	$0.503569\pi$
$182$	4.15094	−	37.4610i	0.307688	−	2.77679i
$183$		0			0
$184$	2.08377	−	0.128582i	0.153617	−	0.00947916i
$185$	−1.47703	+	1.47703i	−0.108593	+	0.108593i
$186$		0			0
$187$	−15.8584	−	6.56877i	−1.15968	−	0.480356i
$188$	6.48098	+	10.2305i	0.472674	+	0.746137i
$189$		0			0
$190$	6.79786	+	23.4335i	0.493168	+	1.70004i
$191$	7.97826			0.577287			0.288643	−	0.957437i	$-0.406796\pi$
$191$	7.97826			0.577287			0.288643	+	0.957437i	$0.406796\pi$
$192$		0			0
$193$	−11.9488			−0.860091			−0.430045	−	0.902807i	$-0.641502\pi$
$193$	−11.9488			−0.860091			−0.430045	+	0.902807i	$0.641502\pi$
$194$	2.37507	+	8.18731i	0.170520	+	0.587814i
$195$		0			0
$196$	17.0897	+	26.9769i	1.22070	+	1.92692i
$197$	−4.88423	−	2.02312i	−0.347987	−	0.144141i	0.201842	−	0.979418i	$-0.435307\pi$
$197$	−4.88423	−	2.02312i	−0.347987	−	0.144141i	−0.549829	+	0.835277i	$0.685307\pi$
$198$		0			0
$199$	15.8193	−	15.8193i	1.12140	−	1.12140i	0.129871	−	0.991531i	$-0.458544\pi$
$199$	15.8193	−	15.8193i	1.12140	−	1.12140i	0.991531	−	0.129871i	$-0.0414563\pi$
$200$	0.351280	+	5.69277i	0.0248392	+	0.402539i
$201$		0			0
$202$	0.294558	−	2.65829i	0.0207250	−	0.187037i
$203$	−22.6934	−	9.39990i	−1.59276	−	0.659743i
$204$		0			0
$205$	−7.33006	−	17.6963i	−0.511953	−	1.23596i
$206$	−9.95461	−	5.47779i	−0.693570	−	0.381656i
$207$		0			0
$208$	22.2179	+	1.08351i	1.54054	+	0.0751279i
$209$	29.5676			2.04524
$210$		0			0
$211$	−25.3944	+	10.5187i	−1.74823	+	0.724139i	−0.750207	+	0.661202i	$0.770046\pi$
$211$	−25.3944	+	10.5187i	−1.74823	+	0.724139i	−0.998018	+	0.0629360i	$0.979954\pi$
$212$	3.03551	+	17.4754i	0.208479	+	1.20022i
$213$		0			0
$214$	1.90540	−	17.1956i	0.130250	−	1.17547i
$215$	5.09150	−	5.09150i	0.347237	−	0.347237i
$216$		0			0
$217$	−7.82417	−	7.82417i	−0.531139	−	0.531139i
$218$	−7.59428	+	6.07916i	−0.514349	+	0.411733i
$219$		0			0
$220$	23.4659	+	5.26502i	1.58207	+	0.354967i
$221$	−8.04697	−	19.4271i	−0.541298	−	1.30681i
$222$		0			0
$223$		−	11.8736i		−	0.795117i	−0.917577	−	0.397558i	$-0.869858\pi$
$223$		−	11.8736i		−	0.795117i	0.917577	−	0.397558i	$-0.130142\pi$
$224$	−21.9644	+	15.8908i	−1.46756	+	1.06175i
$225$		0			0
$226$	−6.61992	−	22.8201i	−0.440351	−	1.51797i
$227$	16.0487	−	6.64758i	1.06519	−	0.441215i	0.219898	−	0.975523i	$-0.429428\pi$
$227$	16.0487	−	6.64758i	1.06519	−	0.441215i	0.845290	+	0.534308i	$0.179428\pi$
$228$		0			0
$229$	−0.190035	+	0.458786i	−0.0125579	+	0.0303174i	−0.930034	−	0.367473i	$-0.880223\pi$
$229$	−0.190035	+	0.458786i	−0.0125579	+	0.0303174i	0.917476	+	0.397791i	$0.130223\pi$
$230$	1.72797	+	2.15864i	0.113939	+	0.142336i
$231$		0			0
$232$	4.71229	−	13.7096i	0.309377	−	0.900079i
$233$	−4.46281	−	4.46281i	−0.292369	−	0.292369i	0.545647	−	0.838015i	$-0.316284\pi$
$233$	−4.46281	−	4.46281i	−0.292369	−	0.292369i	−0.838015	+	0.545647i	$0.816284\pi$
$234$		0			0
$235$	−6.13813	+	14.8188i	−0.400408	+	0.966670i
$236$	3.23113	+	18.6017i	0.210329	+	1.21087i
$237$		0			0
$238$	22.4524	+	12.3551i	1.45538	+	0.800860i
$239$			8.12218i			0.525380i	0.964880	+	0.262690i	$0.0846096\pi$
$239$			8.12218i			0.525380i	−0.964880	+	0.262690i	$0.915390\pi$
$240$		0			0
$241$			3.91627i			0.252269i	0.992013	+	0.126135i	$0.0402571\pi$
$241$			3.91627i			0.252269i	−0.992013	+	0.126135i	$0.959743\pi$
$242$	6.55027	−	11.9036i	0.421067	−	0.765191i
$243$		0			0
$244$	0.214198	−	0.304254i	0.0137126	−	0.0194779i
$245$	−16.1857	+	39.0757i	−1.03407	+	2.49646i
$246$		0			0
$247$	25.6124	+	25.6124i	1.62968	+	1.62968i
$248$	4.32456	−	4.89337i	0.274610	−	0.310729i
$249$		0			0
$250$	8.72513	−	6.98440i	0.551826	−	0.441733i
$251$	3.33165	−	8.04332i	0.210292	−	0.507690i	−0.783176	−	0.621800i	$-0.786402\pi$
$251$	3.33165	−	8.04332i	0.210292	−	0.507690i	0.993468	+	0.114110i	$0.0364017\pi$
$252$		0			0
$253$	3.09568	−	1.28227i	0.194624	−	0.0806157i
$254$	12.9033	−	3.74314i	0.809625	−	0.234865i
$255$		0			0
$256$	−10.1592	−	12.3609i	−0.634948	−	0.772555i
$257$			4.79986i			0.299407i	0.988731	+	0.149704i	$0.0478319\pi$
$257$			4.79986i			0.299407i	−0.988731	+	0.149704i	$0.952168\pi$
$258$		0			0
$259$	−1.44623	−	3.49151i	−0.0898643	−	0.216952i
$260$	15.7661	+	24.8876i	0.977774	+	1.54346i
$261$		0			0
$262$	18.5469	+	23.1694i	1.14583	+	1.43141i
$263$	−6.41988	−	6.41988i	−0.395867	−	0.395867i	0.480906	−	0.876772i	$-0.340308\pi$
$263$	−6.41988	−	6.41988i	−0.395867	−	0.395867i	−0.876772	+	0.480906i	$0.840308\pi$
$264$		0			0
$265$	−16.6111	+	16.6111i	−1.02041	+	1.02041i
$266$	−43.8758	−	4.86176i	−2.69020	−	0.298093i
$267$		0			0
$268$	−0.663932	−	0.467416i	−0.0405561	−	0.0285520i
$269$	−24.9505	+	10.3349i	−1.52126	+	0.630127i	−0.977844	−	0.209335i	$-0.932870\pi$
$269$	−24.9505	+	10.3349i	−1.52126	+	0.630127i	−0.543418	+	0.839462i	$0.682870\pi$
$270$		0			0
$271$	−13.2069			−0.802264			−0.401132	−	0.916020i	$-0.631383\pi$
$271$	−13.2069			−0.802264			−0.401132	+	0.916020i	$0.631383\pi$
$272$	−6.46184	+	13.6751i	−0.391807	+	0.829175i
$273$		0			0
$274$	−10.1782	+	18.4966i	−0.614890	+	1.11742i
$275$	3.50311	+	8.45726i	0.211246	+	0.509992i
$276$		0			0
$277$	24.2560	+	10.0471i	1.45740	+	0.603675i	0.963946	−	0.266098i	$-0.0857344\pi$
$277$	24.2560	+	10.0471i	1.45740	+	0.603675i	0.493453	+	0.869772i	$0.335734\pi$
$278$	0.457390	+	0.0506821i	0.0274324	+	0.00303971i
$279$		0			0
$280$	−33.9556	−	11.6713i	−2.02924	−	0.697493i
$281$	4.07978	−	4.07978i	0.243379	−	0.243379i	−0.574867	−	0.818247i	$-0.694946\pi$
$281$	4.07978	−	4.07978i	0.243379	−	0.243379i	0.818247	+	0.574867i	$0.194946\pi$
$282$		0			0
$283$	22.5628	+	9.34580i	1.34122	+	0.555550i	0.933834	−	0.357707i	$-0.116441\pi$
$283$	22.5628	+	9.34580i	1.34122	+	0.555550i	0.407383	+	0.913257i	$0.366441\pi$
$284$	13.7000	+	3.07387i	0.812948	+	0.182400i
$285$		0			0
$286$	34.2878	−	9.94661i	2.02748	−	0.588156i
$287$	34.6546			2.04560
$288$		0			0
$289$	−2.70227			−0.158957
$290$	18.4399	−	5.34928i	1.08283	−	0.314120i
$291$		0			0
$292$	1.21572	−	5.41837i	0.0711444	−	0.317086i
$293$	18.8574	+	7.81101i	1.10166	+	0.456324i	0.858059	−	0.513551i	$-0.171670\pi$
$293$	18.8574	+	7.81101i	1.10166	+	0.456324i	0.243604	+	0.969875i	$0.421670\pi$
$294$		0			0
$295$	−17.6817	+	17.6817i	−1.02947	+	1.02947i
$296$	2.00416	−	0.978841i	0.116490	−	0.0568940i
$297$		0			0
$298$	8.71604	+	0.965800i	0.504907	+	0.0559473i
$299$	3.79231	+	1.57083i	0.219315	+	0.0908433i
$300$		0			0
$301$	4.98533	+	12.0357i	0.287350	+	0.693724i
$302$	−8.77306	+	15.9430i	−0.504833	+	0.917416i
$303$		0			0
$304$	1.26905	−	26.0226i	0.0727851	−	1.49250i
$305$	0.492811			0.0282182
$306$		0			0
$307$	−8.73142	+	3.61667i	−0.498328	+	0.206414i	−0.617668	−	0.786439i	$-0.711922\pi$
$307$	−8.73142	+	3.61667i	−0.498328	+	0.206414i	0.119339	+	0.992854i	$0.461922\pi$
$308$	−25.0474	+	35.5781i	−1.42721	+	2.02725i
$309$		0			0
$310$	8.59656	+	0.952560i	0.488252	+	0.0541018i
$311$	−1.57810	+	1.57810i	−0.0894860	+	0.0894860i	−0.750433	−	0.660947i	$-0.770155\pi$
$311$	−1.57810	+	1.57810i	−0.0894860	+	0.0894860i	0.660947	+	0.750433i	$0.270155\pi$
$312$		0			0
$313$	−11.4730	−	11.4730i	−0.648492	−	0.648492i	0.304137	−	0.952628i	$-0.401632\pi$
$313$	−11.4730	−	11.4730i	−0.648492	−	0.648492i	−0.952628	+	0.304137i	$0.901632\pi$
$314$	−14.0455	−	17.5461i	−0.792633	−	0.990182i
$315$		0			0
$316$	13.8393	−	8.76714i	0.778524	−	0.493190i
$317$	−9.79160	−	23.6390i	−0.549951	−	1.32770i	−0.917515	−	0.397701i	$-0.869808\pi$
$317$	−9.79160	−	23.6390i	−0.549951	−	1.32770i	0.367564	−	0.929998i	$-0.380192\pi$
$318$		0			0
$319$		−	23.2670i		−	1.30270i
$320$	5.64092	−	20.4264i	0.315337	−	1.14187i
$321$		0			0
$322$	−4.80456	+	1.39376i	−0.267748	+	0.0776714i
$323$	−22.7538	+	9.42495i	−1.26606	+	0.524418i
$324$		0			0
$325$	−4.29144	+	10.3604i	−0.238046	+	0.574694i
$326$	8.11703	−	6.49762i	0.449561	−	0.359870i
$327$		0			0
$328$	1.25967	+	20.4139i	0.0695535	+	1.12717i
$329$	−20.5199	−	20.5199i	−1.13130	−	1.13130i
$330$		0			0
$331$	0.460135	−	1.11086i	0.0252913	−	0.0610586i	−0.910729	−	0.413004i	$-0.864480\pi$
$331$	0.460135	−	1.11086i	0.0252913	−	0.0610586i	0.936021	+	0.351945i	$0.114480\pi$
$332$	−20.7339	−	14.5969i	−1.13792	−	0.801110i
$333$		0			0
$334$	10.0946	−	18.3446i	0.552353	−	1.00377i
$335$		−	1.07539i		−	0.0587550i
$336$		0			0
$337$			28.2686i			1.53989i	0.638110	+	0.769945i	$0.279716\pi$
$337$			28.2686i			1.53989i	−0.638110	+	0.769945i	$0.720284\pi$
$338$	22.2101	+	12.2217i	1.20807	+	0.664773i
$339$		0			0
$340$	−19.7365	+	3.42825i	−1.07036	+	0.185923i
$341$	4.01097	−	9.68333i	0.217206	−	0.524382i
$342$		0			0
$343$	−30.3878	−	30.3878i	−1.64079	−	1.64079i
$344$	−6.90860	+	3.37418i	−0.372487	+	0.181924i
$345$		0			0
$346$	−14.1498	−	17.6764i	−0.760701	−	0.950291i
$347$	−3.19400	+	7.71101i	−0.171463	+	0.413949i	−0.986129	−	0.165982i	$-0.946920\pi$
$347$	−3.19400	+	7.71101i	−0.171463	+	0.413949i	0.814666	+	0.579931i	$0.196920\pi$
$348$		0			0
$349$	−15.0741	+	6.24391i	−0.806900	+	0.334229i	−0.747716	−	0.664018i	$-0.768850\pi$
$349$	−15.0741	+	6.24391i	−0.806900	+	0.334229i	−0.0591837	+	0.998247i	$0.518850\pi$
$350$	−3.80771	−	13.1259i	−0.203531	−	0.701607i
$351$		0			0
$352$	−21.8684	−	13.4614i	−1.16559	−	0.717494i
$353$			25.0652i			1.33409i	0.745019	+	0.667043i	$0.232440\pi$
$353$			25.0652i			1.33409i	−0.745019	+	0.667043i	$0.767560\pi$
$354$		0			0
$355$	7.11636	+	17.1804i	0.377697	+	0.911841i
$356$	4.08191	−	18.1928i	0.216341	−	0.964218i
$357$		0			0
$358$	6.69936	−	5.36279i	0.354072	−	0.283432i
$359$	−12.3171	−	12.3171i	−0.650069	−	0.650069i	0.302940	−	0.953010i	$-0.402032\pi$
$359$	−12.3171	−	12.3171i	−0.650069	−	0.650069i	−0.953010	+	0.302940i	$0.902032\pi$
$360$		0			0
$361$	16.5633	−	16.5633i	0.871751	−	0.871751i
$362$	1.56025	−	14.0808i	0.0820051	−	0.740070i
$363$		0			0
$364$	−52.5157	+	9.12204i	−2.75257	+	0.478125i
$365$	6.79486	−	2.81452i	0.355659	−	0.147319i
$366$		0			0
$367$	1.24387			0.0649297			0.0324649	−	0.999473i	$-0.489664\pi$
$367$	1.24387			0.0649297			0.0324649	+	0.999473i	$0.489664\pi$
$368$	−0.995663	−	2.77955i	−0.0519025	−	0.144894i
$369$		0			0
$370$	2.58809	+	1.42417i	0.134548	+	0.0740389i
$371$	−16.2648	−	39.2666i	−0.844424	−	2.03862i
$372$		0			0
$373$	−14.2613	−	5.90724i	−0.738424	−	0.305865i	−0.0184154	−	0.999830i	$-0.505862\pi$
$373$	−14.2613	−	5.90724i	−0.738424	−	0.305865i	−0.720009	+	0.693965i	$0.755862\pi$
$374$	−2.67348	+	24.1273i	−0.138242	+	1.24759i
$375$		0			0
$376$	11.3417	−	12.8335i	0.584905	−	0.661837i
$377$	20.1546	−	20.1546i	1.03801	−	1.03801i
$378$		0			0
$379$	−6.21100	−	2.57268i	−0.319037	−	0.132150i	0.217417	−	0.976079i	$-0.430237\pi$
$379$	−6.21100	−	2.57268i	−0.319037	−	0.132150i	−0.536455	+	0.843929i	$0.680237\pi$
$380$	29.1494	−	18.4659i	1.49533	−	0.947283i
$381$		0			0
$382$	−3.14350	−	10.8362i	−0.160835	−	0.554429i
$383$	13.6072			0.695296			0.347648	−	0.937625i	$-0.386980\pi$
$383$	13.6072			0.695296			0.347648	+	0.937625i	$0.386980\pi$
$384$		0			0
$385$	−57.6271			−2.93695
$386$	4.70791	+	16.2290i	0.239626	+	0.826036i
$387$		0			0
$388$	10.1844	−	6.45173i	0.517032	−	0.327537i
$389$	2.68660	+	1.11283i	0.136216	+	0.0564226i	0.449750	−	0.893154i	$-0.351513\pi$
$389$	2.68660	+	1.11283i	0.136216	+	0.0564226i	−0.313534	+	0.949577i	$0.601513\pi$
$390$		0			0
$391$	−1.97355	+	1.97355i	−0.0998067	+	0.0998067i
$392$	29.9071	−	33.8407i	1.51054	−	1.70921i
$393$		0			0
$394$	−0.823406	+	7.43098i	−0.0414826	+	0.374367i
$395$	20.0461	+	8.30336i	1.00863	+	0.417788i
$396$		0			0
$397$	2.81875	+	6.80507i	0.141469	+	0.341537i	0.978695	−	0.205321i	$-0.0658239\pi$
$397$	2.81875	+	6.80507i	0.141469	+	0.341537i	−0.837226	+	0.546858i	$0.815824\pi$
$398$	−27.7190	−	15.2532i	−1.38943	−	0.764572i
$399$		0			0
$400$	7.59362	−	2.72011i	0.379681	−	0.136006i
$401$	33.3220			1.66402			0.832012	−	0.554758i	$-0.187189\pi$
$401$	33.3220			1.66402			0.832012	+	0.554758i	$0.187189\pi$
$402$		0			0
$403$	11.8624	−	4.91358i	0.590909	−	0.244763i
$404$	−3.72660	+	0.647315i	−0.185405	+	0.0322051i
$405$		0			0
$406$	−3.82575	+	34.5262i	−0.189869	+	1.71351i
$407$	2.53127	−	2.53127i	0.125470	−	0.125470i
$408$		0			0
$409$	8.50034	+	8.50034i	0.420315	+	0.420315i	0.885312	−	0.464997i	$-0.153945\pi$
$409$	8.50034	+	8.50034i	0.420315	+	0.420315i	−0.464997	+	0.885312i	$0.653945\pi$
$410$	−21.1474	+	16.9283i	−1.04439	+	0.836030i
$411$		0			0
$412$	−3.51785	+	15.6788i	−0.173312	+	0.772440i
$413$	−17.3130	−	41.7972i	−0.851915	−	2.05671i
$414$		0			0
$415$		−	33.5834i		−	1.64855i
$416$	−7.28240	−	30.6037i	−0.357049	−	1.50047i
$417$		0			0
$418$	−11.6499	−	40.1593i	−0.569815	−	1.96426i
$419$	−8.90474	+	3.68846i	−0.435025	+	0.180193i	−0.589439	−	0.807813i	$-0.700651\pi$
$419$	−8.90474	+	3.68846i	−0.435025	+	0.180193i	0.154414	+	0.988006i	$0.450651\pi$
$420$		0			0
$421$	−9.24819	+	22.3271i	−0.450729	+	1.08816i	0.521316	+	0.853363i	$0.325441\pi$
$421$	−9.24819	+	22.3271i	−0.450729	+	1.08816i	−0.972045	+	0.234793i	$0.924559\pi$
$422$	24.2923	+	30.3467i	1.18253	+	1.47726i
$423$		0			0
$424$	22.5395	−	11.0083i	1.09461	−	0.534613i
$425$	−5.39166	−	5.39166i	−0.261534	−	0.261534i
$426$		0			0
$427$	−0.341203	+	0.823738i	−0.0165120	+	0.0398635i
$428$	−24.1062	+	4.18727i	−1.16522	+	0.202399i
$429$		0			0
$430$	−8.92146	−	4.90928i	−0.430231	−	0.236746i
$431$			34.2686i			1.65066i	0.564650	+	0.825331i	$0.309011\pi$
$431$			34.2686i			1.65066i	−0.564650	+	0.825331i	$0.690989\pi$
$432$		0			0
$433$		−	0.323021i		−	0.0155234i	−0.999970	−	0.00776171i	$-0.997529\pi$
$433$		−	0.323021i		−	0.0155234i	0.999970	−	0.00776171i	$-0.00247065\pi$
$434$	−7.54415	+	13.7097i	−0.362131	+	0.658088i
$435$		0			0
$436$	11.2490	+	7.91945i	0.538731	+	0.379273i
$437$	1.83982	−	4.44171i	0.0880104	−	0.212476i
$438$		0			0
$439$	−1.22080	−	1.22080i	−0.0582654	−	0.0582654i	0.677374	−	0.735639i	$-0.263118\pi$
$439$	−1.22080	−	1.22080i	−0.0582654	−	0.0582654i	−0.735639	+	0.677374i	$0.763118\pi$
$440$	−2.09470	−	33.9462i	−0.0998608	−	1.61832i
$441$		0			0
$442$	−23.2157	+	18.5840i	−1.10426	+	0.883950i
$443$	−3.37120	+	8.13880i	−0.160171	+	0.386686i	−0.983508	−	0.180867i	$-0.942110\pi$
$443$	−3.37120	+	8.13880i	−0.160171	+	0.386686i	0.823337	+	0.567553i	$0.192110\pi$
$444$		0			0
$445$	22.8145	−	9.45009i	1.08151	−	0.447977i
$446$	−16.1270	+	4.67830i	−0.763635	+	0.221524i
$447$		0			0
$448$	30.2374	+	23.5713i	1.42858	+	1.11364i
$449$		−	4.83707i		−	0.228276i	−0.993465	−	0.114138i	$-0.963589\pi$
$449$		−	4.83707i		−	0.228276i	0.993465	−	0.114138i	$-0.0364105\pi$
$450$		0			0
$451$	12.5620	+	30.3272i	0.591519	+	1.42805i
$452$	−28.3864	+	17.9826i	−1.33518	+	0.845831i
$453$		0			0
$454$	−15.3522	−	19.1784i	−0.720513	−	0.900087i
$455$	−49.9183	−	49.9183i	−2.34021	−	2.34021i
$456$		0			0
$457$	−7.23423	+	7.23423i	−0.338403	+	0.338403i	−0.855766	−	0.517363i	$-0.826914\pi$
$457$	−7.23423	+	7.23423i	−0.338403	+	0.338403i	0.517363	+	0.855766i	$0.326914\pi$
$458$	0.698006	+	0.0773441i	0.0326157	+	0.00361405i
$459$		0			0
$460$	2.25106	−	3.19748i	0.104956	−	0.149083i
$461$	−4.04570	+	1.67578i	−0.188427	+	0.0780490i	−0.474902	−	0.880039i	$-0.657516\pi$
$461$	−4.04570	+	1.67578i	−0.188427	+	0.0780490i	0.286475	+	0.958088i	$0.407516\pi$
$462$		0			0
$463$	−39.1299			−1.81852			−0.909261	−	0.416227i	$-0.863352\pi$
$463$	−39.1299			−1.81852			−0.909261	+	0.416227i	$0.863352\pi$
$464$	−20.4773	−	0.998625i	−0.950635	−	0.0463600i
$465$		0			0
$466$	−4.30309	+	7.81986i	−0.199337	+	0.362248i
$467$	2.71550	+	6.55579i	0.125658	+	0.303366i	0.974172	−	0.225808i	$-0.0725021\pi$
$467$	2.71550	+	6.55579i	0.125658	+	0.303366i	−0.848514	+	0.529173i	$0.822502\pi$
$468$		0			0
$469$	1.79753	+	0.744561i	0.0830022	+	0.0343807i
$470$	22.5456	+	2.49821i	1.03995	+	0.115234i
$471$		0			0
$472$	23.9921	−	11.7178i	1.10432	−	0.539356i
$473$	−8.72560	+	8.72560i	−0.401204	+	0.401204i
$474$		0			0
$475$	12.1346	+	5.02631i	0.556773	+	0.230623i
$476$	7.93444	−	35.3633i	0.363674	−	1.62087i
$477$		0			0
$478$	11.0317	−	3.20020i	0.504578	−	0.146374i
$479$	19.3768			0.885349			0.442674	−	0.896682i	$-0.354030\pi$
$479$	19.3768			0.885349			0.442674	+	0.896682i	$0.354030\pi$
$480$		0			0
$481$	4.38533			0.199954
$482$	5.31915	−	1.54304i	0.242281	−	0.0702837i
$483$		0			0
$484$	−18.7485	−	4.20659i	−0.852206	−	0.191209i
$485$	14.7519	+	6.11044i	0.669849	+	0.277461i
$486$		0			0
$487$	−28.1905	+	28.1905i	−1.27743	+	1.27743i	−0.335334	+	0.942099i	$0.608849\pi$
$487$	−28.1905	+	28.1905i	−1.27743	+	1.27743i	−0.942099	+	0.335334i	$0.891151\pi$
$488$	−0.497640	−	0.171050i	−0.0225271	−	0.00774305i
$489$		0			0
$490$	59.4507	+	6.58756i	2.68571	+	0.297596i
$491$	−21.4812	−	8.89781i	−0.969434	−	0.401553i	−0.158933	−	0.987289i	$-0.550805\pi$
$491$	−21.4812	−	8.89781i	−0.969434	−	0.401553i	−0.810501	+	0.585737i	$0.800805\pi$
$492$		0			0
$493$	7.41655	+	17.9051i	0.334025	+	0.806407i
$494$	24.6957	−	44.8787i	1.11111	−	2.01919i
$495$		0			0
$496$	−8.35017	−	3.94567i	−0.374934	−	0.177166i
$497$	−33.6443			−1.50915
$498$		0			0
$499$	24.2391	−	10.0402i	1.08509	−	0.449459i	0.232798	−	0.972525i	$-0.425212\pi$
$499$	24.2391	−	10.0402i	1.08509	−	0.449459i	0.852292	+	0.523066i	$0.175212\pi$
$500$	−12.9241	−	9.09873i	−0.577984	−	0.406907i
$501$		0			0
$502$	−12.2373	−	1.35598i	−0.546177	−	0.0605203i
$503$	8.27072	−	8.27072i	0.368773	−	0.368773i	−0.498256	−	0.867030i	$-0.666026\pi$
$503$	8.27072	−	8.27072i	0.368773	−	0.368773i	0.867030	+	0.498256i	$0.166026\pi$
$504$		0			0
$505$	−3.54229	−	3.54229i	−0.157630	−	0.157630i
$506$	−2.96133	−	3.69938i	−0.131647	−	0.164458i
$507$		0			0
$508$	−10.1680	−	16.0507i	−0.451132	−	0.712133i
$509$	14.1181	+	34.0841i	0.625774	+	1.51075i	0.844827	+	0.535039i	$0.179703\pi$
$509$	14.1181	+	34.0841i	0.625774	+	1.51075i	−0.219054	+	0.975713i	$0.570297\pi$
$510$		0			0
$511$			13.3063i			0.588638i
$512$	−12.7860	+	18.6686i	−0.565066	+	0.825046i
$513$		0			0
$514$	6.51926	−	1.89118i	0.287552	−	0.0834166i
$515$	−19.6619	+	8.14422i	−0.866406	+	0.358877i
$516$		0			0
$517$	10.5193	−	25.3958i	0.462637	−	1.11691i
$518$	−4.17240	+	3.33998i	−0.183325	+	0.146750i
$519$		0			0
$520$	27.5908	−	31.2198i	1.20994	−	1.36908i
$521$	−6.11354	−	6.11354i	−0.267839	−	0.267839i	0.560390	−	0.828229i	$-0.310651\pi$
$521$	−6.11354	−	6.11354i	−0.267839	−	0.267839i	−0.828229	+	0.560390i	$0.810651\pi$
$522$		0			0
$523$	−10.2211	+	24.6760i	−0.446939	+	1.07901i	0.526524	+	0.850160i	$0.323495\pi$
$523$	−10.2211	+	24.6760i	−0.446939	+	1.07901i	−0.973463	+	0.228846i	$0.926505\pi$
$524$	24.1615	−	34.3197i	1.05550	−	1.49926i
$525$		0			0
$526$	−6.19012	+	11.2491i	−0.269902	+	0.490483i
$527$			8.73036i			0.380300i
$528$		0			0
$529$			22.4552i			0.976312i
$530$	29.1065	+	16.0166i	1.26430	+	0.695718i
$531$		0			0
$532$	10.6841	+	61.5086i	0.463215	+	2.66673i
$533$	−15.3888	+	37.1519i	−0.666564	+	1.60923i
$534$		0			0
$535$	−22.9139	−	22.9139i	−0.990655	−	0.990655i
$536$	−0.373258	+	1.08593i	−0.0161223	+	0.0469051i
$537$		0			0
$538$	23.8677	+	29.8163i	1.02901	+	1.28547i
$539$	27.7384	−	66.9664i	1.19478	−	2.88445i
$540$		0			0
$541$	−26.2040	+	10.8540i	−1.12660	+	0.466652i	−0.866623	−	0.498964i	$-0.833714\pi$
$541$	−26.2040	+	10.8540i	−1.12660	+	0.466652i	−0.259974	+	0.965616i	$0.583714\pi$
$542$	5.20364	+	17.9379i	0.223515	+	0.770498i
$543$		0			0
$544$	21.1198	+	3.38849i	0.905504	+	0.145280i
$545$			18.2204i			0.780478i
$546$		0			0
$547$	−2.86307	−	6.91207i	−0.122416	−	0.295539i	0.850777	−	0.525526i	$-0.176131\pi$
$547$	−2.86307	−	6.91207i	−0.122416	−	0.295539i	−0.973194	+	0.229987i	$0.926131\pi$
$548$	29.1327	+	6.53648i	1.24449	+	0.279225i
$549$		0			0
$550$	10.1066	−	8.09022i	0.430945	−	0.344968i
$551$	−23.6058	−	23.6058i	−1.00564	−	1.00564i
$552$		0			0
$553$	−27.7583	+	27.7583i	−1.18040	+	1.18040i
$554$	4.08918	−	36.9035i	0.173733	−	1.56788i
$555$		0			0
$556$	−0.111378	−	0.641205i	−0.00472348	−	0.0271931i
$557$	−9.83837	+	4.07519i	−0.416865	+	0.172671i	−0.581250	−	0.813725i	$-0.697436\pi$
$557$	−9.83837	+	4.07519i	−0.416865	+	0.172671i	0.164385	+	0.986396i	$0.447436\pi$
$558$		0			0
$559$	−15.1168			−0.639371
$560$	−2.47337	+	50.7177i	−0.104519	+	2.14322i
$561$		0			0
$562$	−7.14870	−	3.93377i	−0.301550	−	0.165936i
$563$	1.54232	+	3.72350i	0.0650012	+	0.156927i	0.953042	−	0.302837i	$-0.0979339\pi$
$563$	1.54232	+	3.72350i	0.0650012	+	0.156927i	−0.888041	+	0.459764i	$0.847934\pi$
$564$		0			0
$565$	−41.1173	−	17.0313i	−1.72982	−	0.716513i
$566$	3.80373	−	34.3275i	0.159883	−	1.44289i
$567$		0			0
$568$	−1.22294	−	19.8188i	−0.0513136	−	0.831577i
$569$	−8.57127	+	8.57127i	−0.359327	+	0.359327i	−0.863565	−	0.504238i	$-0.831773\pi$
$569$	−8.57127	+	8.57127i	−0.359327	+	0.359327i	0.504238	+	0.863565i	$0.331773\pi$
$570$		0			0
$571$	−26.2074	−	10.8554i	−1.09674	−	0.454286i	−0.240390	−	0.970676i	$-0.577275\pi$
$571$	−26.2074	−	10.8554i	−1.09674	−	0.454286i	−0.856353	+	0.516390i	$0.827275\pi$
$572$	−27.0194	−	42.6513i	−1.12974	−	1.78334i
$573$		0			0
$574$	−13.6542	−	47.0686i	−0.569916	−	1.96460i
$575$	1.48845			0.0620725
$576$		0			0
$577$	40.8448			1.70039			0.850196	−	0.526466i	$-0.176483\pi$
$577$	40.8448			1.70039			0.850196	+	0.526466i	$0.176483\pi$
$578$	1.06472	+	3.67027i	0.0442863	+	0.152663i
$579$		0			0
$580$	−14.5310	−	22.9378i	−0.603366	−	0.952441i
$581$	56.1350	+	23.2519i	2.32887	+	0.964651i
$582$		0			0
$583$	28.4675	−	28.4675i	1.17900	−	1.17900i
$584$	−7.83834	+	0.483675i	−0.324353	+	0.0200146i
$585$		0			0
$586$	3.17907	−	28.6901i	0.131326	−	1.18518i
$587$	30.3985	+	12.5915i	1.25468	+	0.519705i	0.908273	−	0.418379i	$-0.137402\pi$
$587$	30.3985	+	12.5915i	1.25468	+	0.519705i	0.346407	+	0.938084i	$0.387402\pi$
$588$		0			0
$589$	−5.75498	−	13.8938i	−0.237130	−	0.572482i
$590$	30.9823	+	17.0488i	1.27552	+	0.701890i
$591$		0			0
$592$	−2.11914	−	2.33642i	−0.0870960	−	0.0960264i
$593$	−5.64301			−0.231731			−0.115865	−	0.993265i	$-0.536964\pi$
$593$	−5.64301			−0.231731			−0.115865	+	0.993265i	$0.536964\pi$
$594$		0			0
$595$	44.3470	−	18.3691i	1.81805	−	0.753062i
$596$	−2.12242	−	12.2188i	−0.0869379	−	0.500502i
$597$		0			0
$598$	0.639325	−	5.76971i	0.0261439	−	0.235941i
$599$	5.75089	−	5.75089i	0.234975	−	0.234975i	−0.579790	−	0.814766i	$-0.696866\pi$
$599$	5.75089	−	5.75089i	0.234975	−	0.234975i	0.814766	+	0.579790i	$0.196866\pi$
$600$		0			0
$601$	−22.4340	−	22.4340i	−0.915102	−	0.915102i	0.0815662	−	0.996668i	$-0.474008\pi$
$601$	−22.4340	−	22.4340i	−0.915102	−	0.915102i	−0.996668	+	0.0815662i	$0.974008\pi$
$602$	14.3828	−	11.5133i	0.586199	−	0.469248i
$603$		0			0
$604$	25.1107	+	5.63407i	1.02174	+	0.229247i
$605$	−9.73875	−	23.5114i	−0.395936	−	0.955875i
$606$		0			0
$607$			7.67228i			0.311408i	0.987804	+	0.155704i	$0.0497647\pi$
$607$			7.67228i			0.311408i	−0.987804	+	0.155704i	$0.950235\pi$
$608$	−35.8443	+	8.52945i	−1.45368	+	0.345915i
$609$		0			0
$610$	−0.194171	−	0.669344i	−0.00786177	−	0.0271010i
$611$	31.1107	−	12.8865i	1.25861	−	0.521332i
$612$		0			0
$613$	−3.65989	+	8.83576i	−0.147822	+	0.356873i	−0.980395	−	0.197042i	$-0.936867\pi$
$613$	−3.65989	+	8.83576i	−0.147822	+	0.356873i	0.832573	+	0.553915i	$0.186867\pi$
$614$	8.35248	+	10.4342i	0.337079	+	0.421089i
$615$		0			0
$616$	58.1918	+	20.0018i	2.34461	+	0.805895i
$617$	−7.16767	−	7.16767i	−0.288560	−	0.288560i	0.547951	−	0.836511i	$-0.315408\pi$
$617$	−7.16767	−	7.16767i	−0.288560	−	0.288560i	−0.836511	+	0.547951i	$0.815408\pi$
$618$		0			0
$619$	−13.8565	+	33.4525i	−0.556939	+	1.34457i	0.355239	+	0.934776i	$0.384400\pi$
$619$	−13.8565	+	33.4525i	−0.556939	+	1.34457i	−0.912178	+	0.409794i	$0.865600\pi$
$620$	−2.09333	−	12.0513i	−0.0840701	−	0.483993i
$621$		0			0
$622$	2.76519	+	1.52162i	0.110874	+	0.0610115i
$623$			44.6776i			1.78997i
$624$		0			0
$625$		−	31.0163i		−	1.24065i
$626$	−11.0624	+	20.1033i	−0.442141	+	0.803488i
$627$		0			0
$628$	−18.2973	+	25.9901i	−0.730144	+	1.03712i
$629$	−1.14108	+	2.75481i	−0.0454979	+	0.109842i
$630$		0			0
$631$	4.00538	+	4.00538i	0.159452	+	0.159452i	0.782324	−	0.622872i	$-0.214034\pi$
$631$	4.00538	+	4.00538i	0.159452	+	0.159452i	−0.622872	+	0.782324i	$0.714034\pi$
$632$	−17.3605	−	15.3425i	−0.690564	−	0.610293i
$633$		0			0
$634$	−28.2490	+	22.6131i	−1.12191	+	0.898081i
$635$	9.63012	−	23.2492i	0.382160	−	0.922615i
$636$		0			0
$637$	82.0361	−	33.9805i	3.25039	−	1.34636i
$638$	−31.6016	+	9.16737i	−1.25112	+	0.362940i
$639$		0			0
$640$	−29.9661	+	0.386566i	−1.18451	+	0.0152804i
$641$		−	0.320061i		−	0.0126416i	−0.999980	−	0.00632082i	$-0.997988\pi$
$641$		−	0.320061i		−	0.0126416i	0.999980	−	0.00632082i	$-0.00201199\pi$
$642$		0			0
$643$	15.3875	+	37.1487i	0.606824	+	1.46500i	0.866435	+	0.499289i	$0.166405\pi$
$643$	15.3875	+	37.1487i	0.606824	+	1.46500i	−0.259612	+	0.965713i	$0.583595\pi$
$644$	3.78607	+	5.97649i	0.149192	+	0.235507i
$645$		0			0
$646$	21.7663	+	27.1912i	0.856385	+	1.06982i
$647$	−11.1884	−	11.1884i	−0.439863	−	0.439863i	0.452103	−	0.891966i	$-0.350674\pi$
$647$	−11.1884	−	11.1884i	−0.439863	−	0.439863i	−0.891966	+	0.452103i	$0.850674\pi$
$648$		0			0
$649$	30.3021	−	30.3021i	1.18946	−	1.18946i
$650$	15.7626	+	1.74661i	0.618260	+	0.0685077i
$651$		0			0
$652$	−12.0234	−	8.46459i	−0.470871	−	0.331499i
$653$	−44.2880	+	18.3447i	−1.73312	+	0.717884i	−0.733870	+	0.679290i	$0.762288\pi$
$653$	−44.2880	+	18.3447i	−1.73312	+	0.717884i	−0.999255	+	0.0385936i	$0.987712\pi$
$654$		0			0
$655$	55.5888			2.17203
$656$	27.2302	−	9.75415i	1.06316	−	0.380836i
$657$		0			0
$658$	−19.7855	+	35.9555i	−0.771319	+	1.40169i
$659$	7.81320	+	18.8627i	0.304359	+	0.734788i	0.999868	+	0.0162701i	$0.00517915\pi$
$659$	7.81320	+	18.8627i	0.304359	+	0.734788i	−0.695509	+	0.718518i	$0.744821\pi$
$660$		0			0
$661$	−19.8609	−	8.22666i	−0.772500	−	0.319980i	−0.0386153	−	0.999254i	$-0.512295\pi$
$661$	−19.8609	−	8.22666i	−0.772500	−	0.319980i	−0.733885	+	0.679274i	$0.762295\pi$
$662$	−1.69009	−	0.187274i	−0.0656873	−	0.00727863i
$663$		0			0
$664$	−11.6565	+	33.9125i	−0.452359	+	1.31606i
$665$	−58.4664	+	58.4664i	−2.26723	+	2.26723i
$666$		0			0
$667$	−3.49521	−	1.44776i	−0.135335	−	0.0560577i
$668$	−28.8934	−	6.48278i	−1.11792	−	0.250826i
$669$		0			0
$670$	−1.46062	+	0.423714i	−0.0564286	+	0.0163695i
$671$	−0.844558			−0.0326038
$672$		0			0
$673$	43.3143			1.66964			0.834821	−	0.550522i	$-0.185571\pi$
$673$	43.3143			1.66964			0.834821	+	0.550522i	$0.185571\pi$
$674$	38.3950	−	11.1381i	1.47892	−	0.429022i
$675$		0			0
$676$	7.84879	−	34.9816i	0.301876	−	1.34545i
$677$	−39.7727	−	16.4744i	−1.52859	−	0.633162i	−0.549298	−	0.835626i	$-0.685105\pi$
$677$	−39.7727	−	16.4744i	−1.52859	−	0.633162i	−0.979290	+	0.202465i	$0.935105\pi$
$678$		0			0
$679$	−20.4273	+	20.4273i	−0.783928	+	0.783928i
$680$	12.4326	+	25.4557i	0.476770	+	0.976181i
$681$		0			0
$682$	−14.7324	−	1.63246i	−0.564134	−	0.0625101i
$683$	5.40622	+	2.23933i	0.206863	+	0.0856856i	0.483709	−	0.875229i	$-0.339289\pi$
$683$	5.40622	+	2.23933i	0.206863	+	0.0856856i	−0.276846	+	0.960914i	$0.589289\pi$
$684$		0			0
$685$	15.1327	+	36.5336i	0.578191	+	1.39588i
$686$	−29.3003	+	53.2464i	−1.11869	+	2.03296i
$687$		0			0
$688$	7.30492	+	8.05393i	0.278498	+	0.307053i
$689$	49.3188			1.87890
$690$		0			0
$691$	−17.4054	+	7.20955i	−0.662132	+	0.274264i	−0.688336	−	0.725392i	$-0.741658\pi$
$691$	−17.4054	+	7.20955i	−0.662132	+	0.274264i	0.0262032	+	0.999657i	$0.491658\pi$
$692$	−18.4333	+	26.1832i	−0.700729	+	0.995338i
$693$		0			0
$694$	11.7317	+	1.29996i	0.445329	+	0.0493457i
$695$	0.609492	−	0.609492i	0.0231193	−	0.0231193i
$696$		0			0
$697$	−19.3342	−	19.3342i	−0.732333	−	0.732333i
$698$	14.4199	+	18.0138i	0.545802	+	0.681833i
$699$		0			0
$700$	−16.3275	+	10.3434i	−0.617123	+	0.390944i
$701$	10.6696	+	25.7586i	0.402984	+	0.972889i	0.986938	+	0.161102i	$0.0515048\pi$
$701$	10.6696	+	25.7586i	0.402984	+	0.972889i	−0.583954	+	0.811787i	$0.698495\pi$
$702$		0			0
$703$		−	5.13628i		−	0.193719i
$704$	−9.66717	+	35.0059i	−0.364345	+	1.31934i
$705$		0			0
$706$	34.0440	−	9.87589i	1.28126	−	0.371684i
$707$	8.37351	−	3.46842i	0.314918	−	0.130443i
$708$		0			0
$709$	−0.671243	+	1.62052i	−0.0252091	+	0.0608601i	−0.935983	−	0.352046i	$-0.885486\pi$
$709$	−0.671243	+	1.62052i	−0.0252091	+	0.0608601i	0.910774	+	0.412906i	$0.135486\pi$
$710$	20.5308	−	16.4348i	0.770509	−	0.616787i
$711$		0			0
$712$	−26.3181	+	1.62400i	−0.986314	+	0.0608618i
$713$	−1.20507	−	1.20507i	−0.0451303	−	0.0451303i
$714$		0			0
$715$	25.5900	−	61.7798i	0.957013	−	2.31043i
$716$	−9.92344	−	6.98622i	−0.370857	−	0.261087i
$717$		0			0
$718$	−11.8762	+	21.5823i	−0.443217	+	0.805443i
$719$		−	22.7818i		−	0.849618i	−0.905283	−	0.424809i	$-0.860341\pi$
$719$		−	22.7818i		−	0.849618i	0.905283	−	0.424809i	$-0.139659\pi$
$720$		0			0
$721$		−	38.5038i		−	1.43396i
$722$	−29.0226	−	15.9705i	−1.08011	−	0.594359i
$723$		0			0
$724$	−19.7396	+	3.42878i	−0.733615	+	0.127430i
$725$	3.95523	−	9.54878i	0.146894	−	0.354633i
$726$		0			0
$727$	12.5833	+	12.5833i	0.466688	+	0.466688i	0.900840	−	0.434152i	$-0.142952\pi$
$727$	12.5833	+	12.5833i	0.466688	+	0.466688i	−0.434152	+	0.900840i	$0.642952\pi$
$728$	33.0813	+	67.7336i	1.22608	+	2.51038i
$729$		0			0
$730$	−6.49997	−	8.11996i	−0.240575	−	0.300533i
$731$	3.93344	−	9.49617i	0.145484	−	0.351229i
$732$		0			0
$733$	35.2843	−	14.6152i	1.30326	−	0.539826i	0.380347	−	0.924844i	$-0.375805\pi$
$733$	35.2843	−	14.6152i	1.30326	−	0.539826i	0.922909	+	0.385017i	$0.125805\pi$
$734$	−0.490096	−	1.68945i	−0.0180898	−	0.0623588i
$735$		0			0
$736$	−3.38294	+	2.44749i	−0.124697	+	0.0902158i
$737$			1.84296i			0.0678865i
$738$		0			0
$739$	14.2438	+	34.3875i	0.523965	+	1.26496i	0.935421	+	0.353535i	$0.115020\pi$
$739$	14.2438	+	34.3875i	0.523965	+	1.26496i	−0.411456	+	0.911430i	$0.634980\pi$
$740$	0.914602	−	4.07632i	0.0336214	−	0.149849i
$741$		0			0
$742$	−46.9242	+	37.5624i	−1.72264	+	1.37896i
$743$	−5.48927	−	5.48927i	−0.201382	−	0.201382i	0.599210	−	0.800592i	$-0.295481\pi$
$743$	−5.48927	−	5.48927i	−0.201382	−	0.201382i	−0.800592	+	0.599210i	$0.795481\pi$
$744$		0			0
$745$	11.6145	−	11.6145i	0.425522	−	0.425522i
$746$	−2.40424	+	21.6975i	−0.0880255	+	0.794402i
$747$		0			0
$748$	33.8236	−	5.87519i	1.23671	−	0.214818i
$749$	54.1656	−	22.4361i	1.97917	−	0.819798i
$750$		0			0
$751$	13.1151			0.478576			0.239288	−	0.970949i	$-0.423086\pi$
$751$	13.1151			0.478576			0.239288	+	0.970949i	$0.423086\pi$
$752$	−21.8994	−	10.3480i	−0.798590	−	0.377354i
$753$		0			0
$754$	−35.3153	−	19.4332i	−1.28611	−	0.707717i
$755$	13.0435	+	31.4899i	0.474702	+	1.14603i
$756$		0			0
$757$	24.2944	+	10.0631i	0.882994	+	0.365748i	0.777657	−	0.628689i	$-0.216408\pi$
$757$	24.2944	+	10.0631i	0.882994	+	0.365748i	0.105337	+	0.994437i	$0.466408\pi$
$758$	−1.04708	+	9.44955i	−0.0380316	+	0.343223i
$759$		0			0
$760$	−36.5659	−	32.3155i	−1.32638	−	1.17220i
$761$	−10.1791	+	10.1791i	−0.368993	+	0.368993i	−0.867110	−	0.498117i	$-0.834025\pi$
$761$	−10.1791	+	10.1791i	−0.368993	+	0.368993i	0.498117	+	0.867110i	$0.334025\pi$
$762$		0			0
$763$	−30.4556	−	12.6151i	−1.10257	−	0.456699i
$764$	−13.4794	+	8.53912i	−0.487667	+	0.308934i
$765$		0			0
$766$	−5.36135	−	18.4816i	−0.193713	−	0.667766i
$767$	52.4972			1.89557
$768$		0			0
$769$	10.7380			0.387221			0.193611	−	0.981078i	$-0.437980\pi$
$769$	10.7380			0.387221			0.193611	+	0.981078i	$0.437980\pi$
$770$	22.7055	+	78.2701i	0.818250	+	2.82066i
$771$		0			0
$772$	20.1876	−	12.7887i	0.726568	−	0.460277i
$773$	−27.6103	−	11.4366i	−0.993073	−	0.411344i	−0.173820	−	0.984777i	$-0.555611\pi$
$773$	−27.6103	−	11.4366i	−0.993073	−	0.411344i	−0.819252	+	0.573433i	$0.805611\pi$
$774$		0			0
$775$	3.29221	−	3.29221i	0.118260	−	0.118260i
$776$	−12.7756	−	11.2905i	−0.458617	−	0.405307i
$777$		0			0
$778$	0.452920	−	4.08746i	0.0162380	−	0.146543i
$779$	43.5139	+	18.0240i	1.55905	+	0.645778i
$780$		0			0
$781$	−12.1957	−	29.4431i	−0.436397	−	1.05356i
$782$	3.45811	+	1.90292i	0.123662	+	0.0680482i
$783$		0			0
$784$	−57.7467	−	27.2868i	−2.06238	−	0.974530i
$785$	−42.0971			−1.50251
$786$		0			0
$787$	−6.96385	+	2.88452i	−0.248234	+	0.102822i	−0.503331	−	0.864093i	$-0.667893\pi$
$787$	−6.96385	+	2.88452i	−0.248234	+	0.102822i	0.255097	+	0.966915i	$0.417893\pi$
$788$	10.4173	−	1.80950i	0.371102	−	0.0644608i
$789$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.394008 - 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(-2.44724 - 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(2.11938 + 1.87302i) q^{8} +O(q^{10})\)	\(q+(-0.394008 - 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(-2.44724 - 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(2.11938 + 1.87302i) q^{8} +(-0.412566 + 3.72328i) q^{10} +(4.19398 + 1.73720i) q^{11} +(2.12813 + 5.13777i) q^{13} +(-5.93786 - 3.26747i) q^{14} +(1.70892 - 3.61657i) q^{16} -3.78123 q^{17} +(6.01757 - 2.49256i) q^{19} +(5.21959 - 0.906648i) q^{20} +(0.707039 - 6.38081i) q^{22} +(0.521933 - 0.521933i) q^{23} +(1.42590 + 1.42590i) q^{25} +(6.13971 - 4.91479i) q^{26} +(-2.09837 + 9.35232i) q^{28} +(-1.96141 - 4.73526i) q^{29} -2.30887i q^{31} +(-5.58542 - 0.896134i) q^{32} +(1.48984 + 5.13574i) q^{34} +(-11.7282 + 4.85798i) q^{35} +(0.301775 - 0.728548i) q^{37} +(-5.75641 - 7.19109i) q^{38} +(-3.28799 - 6.73211i) q^{40} +(5.11319 + 5.11319i) q^{41} +(-1.04025 + 2.51140i) q^{43} +(-8.94511 + 1.55378i) q^{44} +(-0.914544 - 0.503253i) q^{46} -6.05530i q^{47} -15.9673i q^{49} +(1.37487 - 2.49850i) q^{50} +(-9.09446 - 6.40260i) q^{52} +(3.39385 - 8.19348i) q^{53} +(-8.50270 - 8.50270i) q^{55} +(13.5293 - 0.834842i) q^{56} +(-5.65871 + 4.52976i) q^{58} +(3.61257 - 8.72153i) q^{59} +(-0.171884 + 0.0711965i) q^{61} +(-3.13594 + 0.909712i) q^{62} +(0.983556 + 7.93931i) q^{64} -14.7306i q^{65} +(0.155362 + 0.375078i) q^{67} +(6.38845 - 4.04705i) q^{68} +(11.2192 + 14.0154i) q^{70} +(-4.96412 - 4.96412i) q^{71} +(-1.96331 + 1.96331i) q^{73} +(-1.10843 - 0.122822i) q^{74} +(-7.49899 + 10.6518i) q^{76} +(20.0993 - 8.32540i) q^{77} -8.19131 q^{79} +(-7.84819 + 7.11831i) q^{80} +(4.93019 - 8.95946i) q^{82} +(4.85181 + 11.7133i) q^{83} +(9.25358 + 3.83296i) q^{85} +(3.82089 + 0.423382i) q^{86} +(5.63482 + 11.5372i) q^{88} +(-6.59205 + 6.59205i) q^{89} +(24.6223 + 10.1989i) q^{91} +(-0.323190 + 1.44044i) q^{92} +(-8.22442 + 2.38584i) q^{94} -17.2531 q^{95} -6.02797 q^{97} +(-21.6870 + 6.29123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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