LMFDB - Embedded newform 220.2.t.a.49.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(9,220)] 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("220.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.t (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.6
Character	$\chi$	$=$	220.49
Dual form			220.2.t.a.9.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.60349 - 2.20702i) q^{3} +(-1.89499 - 1.18702i) q^{5} +(-1.00600 - 1.38464i) q^{7} +(-1.37268 - 4.22469i) q^{9} +(-1.49354 + 2.96131i) q^{11} +(4.52263 - 1.46949i) q^{13} +(-5.65837 + 2.27889i) q^{15} +(0.621741 + 0.202016i) q^{17} +(3.20263 + 2.32684i) q^{19} -4.66902 q^{21} -0.675167i q^{23} +(2.18197 + 4.49878i) q^{25} +(-3.74152 - 1.21569i) q^{27} +(4.55804 - 3.31161i) q^{29} +(-1.98216 - 6.10045i) q^{31} +(4.14077 + 8.04469i) q^{33} +(0.262763 + 3.81801i) q^{35} +(0.653775 + 0.899844i) q^{37} +(4.00881 - 12.3378i) q^{39} +(9.28765 + 6.74788i) q^{41} -5.72146i q^{43} +(-2.41357 + 9.63513i) q^{45} +(-5.42888 + 7.47221i) q^{47} +(1.25793 - 3.87151i) q^{49} +(1.44281 - 1.04826i) q^{51} +(-12.5493 + 4.07753i) q^{53} +(6.34537 - 3.83878i) q^{55} +(10.2708 - 3.33717i) q^{57} +(-4.79516 + 3.48389i) q^{59} +(-4.68840 + 14.4294i) q^{61} +(-4.46874 + 6.15069i) q^{63} +(-10.3147 - 2.58378i) q^{65} +10.6913i q^{67} +(-1.49010 - 1.08262i) q^{69} +(-0.466178 + 1.43475i) q^{71} +(4.90121 + 6.74593i) q^{73} +(13.4276 + 2.39812i) q^{75} +(5.60284 - 0.911054i) q^{77} +(-2.67995 - 8.24805i) q^{79} +(2.09864 - 1.52475i) q^{81} +(-11.6443 - 3.78345i) q^{83} +(-0.938396 - 1.12084i) q^{85} -15.3698i q^{87} +1.80271 q^{89} +(-6.58448 - 4.78390i) q^{91} +(-16.6422 - 5.40736i) q^{93} +(-3.30693 - 8.21092i) q^{95} +(10.1851 - 3.30935i) q^{97} +(14.5607 + 2.24481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{5} + 14 q^{9} - 2 q^{11} - q^{15} + 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} - 26 q^{31} + 17 q^{35} + 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} - 12 q^{51} - 33 q^{55} - 48 q^{59} - 10 q^{61}+ \cdots + 156 q^{99}+O(q^{100}) $ 24 * q + q^5 + 14 * q^9 - 2 * q^11 - q^15 + 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 - 26 * q^31 + 17 * q^35 + 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 - 12 * q^51 - 33 * q^55 - 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 + 42 * q^71 - 17 * q^75 - 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 + 10 * q^91 + 67 * q^95 + 156 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	1.60349	−	2.20702i	0.925776	−	1.27422i	−0.0357091	−	0.999362i	$-0.511369\pi$
$3$	1.60349	−	2.20702i	0.925776	−	1.27422i	0.961485	−	0.274859i	$-0.0886310\pi$
$4$		0			0
$5$	−1.89499	−	1.18702i	−0.847465	−	0.530852i
$5$	−1.89499	−	1.18702i	−0.847465	−	0.530852i
$6$		0			0
$7$	−1.00600	−	1.38464i	−0.380232	−	0.523344i	0.575414	−	0.817862i	$-0.304841\pi$
$7$	−1.00600	−	1.38464i	−0.380232	−	0.523344i	−0.955646	+	0.294518i	$0.904841\pi$
$8$		0			0
$9$	−1.37268	−	4.22469i	−0.457561	−	1.40823i
$10$		0			0
$11$	−1.49354	+	2.96131i	−0.450320	+	0.892867i
$11$	−1.49354	+	2.96131i	−0.450320	+	0.892867i
$12$		0			0
$13$	4.52263	−	1.46949i	1.25435	−	0.407564i	0.394874	−	0.918735i	$-0.370788\pi$
$13$	4.52263	−	1.46949i	1.25435	−	0.407564i	0.859479	+	0.511171i	$0.170788\pi$
$14$		0			0
$15$	−5.65837	+	2.27889i	−1.46098	+	0.588408i
$16$		0			0
$17$	0.621741	+	0.202016i	0.150794	+	0.0489961i	0.383442	−	0.923565i	$-0.374739\pi$
$17$	0.621741	+	0.202016i	0.150794	+	0.0489961i	−0.232647	+	0.972561i	$0.574739\pi$
$18$		0			0
$19$	3.20263	+	2.32684i	0.734733	+	0.533815i	0.891057	−	0.453891i	$-0.149965\pi$
$19$	3.20263	+	2.32684i	0.734733	+	0.533815i	−0.156324	+	0.987706i	$0.549965\pi$
$20$		0			0
$21$	−4.66902			−1.01886
$22$		0			0
$23$		−	0.675167i		−	0.140782i	−0.997519	−	0.0703910i	$-0.977575\pi$
$23$		−	0.675167i		−	0.140782i	0.997519	−	0.0703910i	$-0.0224247\pi$
$24$		0			0
$25$	2.18197	+	4.49878i	0.436393	+	0.899756i
$26$		0			0
$27$	−3.74152	−	1.21569i	−0.720056	−	0.233961i
$28$		0			0
$29$	4.55804	−	3.31161i	0.846408	−	0.614951i	−0.0777456	−	0.996973i	$-0.524772\pi$
$29$	4.55804	−	3.31161i	0.846408	−	0.614951i	0.924153	+	0.382022i	$0.124772\pi$
$30$		0			0
$31$	−1.98216	−	6.10045i	−0.356006	−	1.09567i	−0.955424	−	0.295237i	$-0.904601\pi$
$31$	−1.98216	−	6.10045i	−0.356006	−	1.09567i	0.599418	−	0.800436i	$-0.295399\pi$
$32$		0			0
$33$	4.14077	+	8.04469i	0.720815	+	1.40040i
$34$		0			0
$35$	0.262763	+	3.81801i	0.0444150	+	0.645362i
$36$		0			0
$37$	0.653775	+	0.899844i	0.107480	+	0.147933i	0.859369	−	0.511357i	$-0.170857\pi$
$37$	0.653775	+	0.899844i	0.107480	+	0.147933i	−0.751889	+	0.659290i	$0.770857\pi$
$38$		0			0
$39$	4.00881	−	12.3378i	0.641923	−	1.97564i
$40$		0			0
$41$	9.28765	+	6.74788i	1.45049	+	1.05384i	0.985717	+	0.168410i	$0.0538633\pi$
$41$	9.28765	+	6.74788i	1.45049	+	1.05384i	0.464771	+	0.885431i	$0.346137\pi$
$42$		0			0
$43$		−	5.72146i		−	0.872515i	−0.899822	−	0.436257i	$-0.856304\pi$
$43$		−	5.72146i		−	0.872515i	0.899822	−	0.436257i	$-0.143696\pi$
$44$		0			0
$45$	−2.41357	+	9.63513i	−0.359793	+	1.43632i
$46$		0			0
$47$	−5.42888	+	7.47221i	−0.791883	+	1.08993i	0.201988	+	0.979388i	$0.435260\pi$
$47$	−5.42888	+	7.47221i	−0.791883	+	1.08993i	−0.993871	+	0.110546i	$0.964740\pi$
$48$		0			0
$49$	1.25793	−	3.87151i	0.179704	−	0.553073i
$50$		0			0
$51$	1.44281	−	1.04826i	0.202034	−	0.146786i
$52$		0			0
$53$	−12.5493	+	4.07753i	−1.72379	+	0.560092i	−0.992529	−	0.122011i	$-0.961066\pi$
$53$	−12.5493	+	4.07753i	−1.72379	+	0.560092i	−0.731257	+	0.682102i	$0.761066\pi$
$54$		0			0
$55$	6.34537	−	3.83878i	0.855610	−	0.517621i
$56$		0			0
$57$	10.2708	−	3.33717i	1.36040	−	0.442019i
$58$		0			0
$59$	−4.79516	+	3.48389i	−0.624277	+	0.453564i	−0.854413	−	0.519595i	$-0.826083\pi$
$59$	−4.79516	+	3.48389i	−0.624277	+	0.453564i	0.230136	+	0.973159i	$0.426083\pi$
$60$		0			0
$61$	−4.68840	+	14.4294i	−0.600288	+	1.84750i	−0.0738722	+	0.997268i	$0.523536\pi$
$61$	−4.68840	+	14.4294i	−0.600288	+	1.84750i	−0.526415	+	0.850227i	$0.676464\pi$
$62$		0			0
$63$	−4.46874	+	6.15069i	−0.563009	+	0.774915i
$64$		0			0
$65$	−10.3147	−	2.58378i	−1.27938	−	0.320479i
$66$		0			0
$67$			10.6913i			1.30615i	0.757293	+	0.653076i	$0.226522\pi$
$67$			10.6913i			1.30615i	−0.757293	+	0.653076i	$0.773478\pi$
$68$		0			0
$69$	−1.49010	−	1.08262i	−0.179387	−	0.130333i
$70$		0			0
$71$	−0.466178	+	1.43475i	−0.0553251	+	0.170273i	−0.974901	−	0.222640i	$-0.928533\pi$
$71$	−0.466178	+	1.43475i	−0.0553251	+	0.170273i	0.919576	+	0.392913i	$0.128533\pi$
$72$		0			0
$73$	4.90121	+	6.74593i	0.573643	+	0.789552i	0.992980	−	0.118279i	$-0.0377376\pi$
$73$	4.90121	+	6.74593i	0.573643	+	0.789552i	−0.419337	+	0.907830i	$0.637738\pi$
$74$		0			0
$75$	13.4276	+	2.39812i	1.55049	+	0.276911i
$76$		0			0
$77$	5.60284	−	0.911054i	0.638502	−	0.103824i
$78$		0			0
$79$	−2.67995	−	8.24805i	−0.301518	−	0.927978i	−0.980953	−	0.194243i	$-0.937775\pi$
$79$	−2.67995	−	8.24805i	−0.301518	−	0.927978i	0.679435	−	0.733736i	$-0.262225\pi$
$80$		0			0
$81$	2.09864	−	1.52475i	0.233183	−	0.169417i
$82$		0			0
$83$	−11.6443	−	3.78345i	−1.27812	−	0.415288i	−0.410205	−	0.911993i	$-0.634543\pi$
$83$	−11.6443	−	3.78345i	−1.27812	−	0.415288i	−0.867919	+	0.496706i	$0.834543\pi$
$84$		0			0
$85$	−0.938396	−	1.12084i	−0.101783	−	0.121572i
$86$		0			0
$87$		−	15.3698i		−	1.64782i
$88$		0			0
$89$	1.80271			0.191087			0.0955436	−	0.995425i	$-0.469541\pi$
$89$	1.80271			0.191087			0.0955436	+	0.995425i	$0.469541\pi$
$90$		0			0
$91$	−6.58448	−	4.78390i	−0.690241	−	0.501489i
$92$		0			0
$93$	−16.6422	−	5.40736i	−1.72571	−	0.560717i
$94$		0			0
$95$	−3.30693	−	8.21092i	−0.339284	−	0.842423i
$96$		0			0
$97$	10.1851	−	3.30935i	1.03414	−	0.336013i	0.257716	−	0.966221i	$-0.417030\pi$
$97$	10.1851	−	3.30935i	1.03414	−	0.336013i	0.776427	+	0.630207i	$0.217030\pi$
$98$		0			0
$99$	14.5607	+	2.24481i	1.46341	+	0.225612i
$100$		0			0
$101$	−2.81593	−	8.66654i	−0.280196	−	0.862353i	−0.987798	−	0.155742i	$-0.950223\pi$
$101$	−2.81593	−	8.66654i	−0.280196	−	0.862353i	0.707602	−	0.706611i	$-0.249777\pi$
$102$		0			0
$103$	−4.51151	−	6.20957i	−0.444533	−	0.611847i	0.526679	−	0.850064i	$-0.323437\pi$
$103$	−4.51151	−	6.20957i	−0.444533	−	0.611847i	−0.971212	+	0.238217i	$0.923437\pi$
$104$		0			0
$105$	8.84775	+	5.54223i	0.863452	+	0.540866i
$106$		0			0
$107$	−6.44743	+	8.87413i	−0.623297	+	0.857894i	−0.997588	−	0.0694170i	$-0.977886\pi$
$107$	−6.44743	+	8.87413i	−0.623297	+	0.857894i	0.374291	+	0.927311i	$0.377886\pi$
$108$		0			0
$109$	9.84961			0.943422			0.471711	−	0.881753i	$-0.343637\pi$
$109$	9.84961			0.943422			0.471711	+	0.881753i	$0.343637\pi$
$110$		0			0
$111$	3.03429			0.288002
$112$		0			0
$113$	3.50202	−	4.82012i	0.329442	−	0.453439i	−0.611878	−	0.790952i	$-0.709586\pi$
$113$	3.50202	−	4.82012i	0.329442	−	0.453439i	0.941321	+	0.337513i	$0.109586\pi$
$114$		0			0
$115$	−0.801436	+	1.27943i	−0.0747343	+	0.119308i
$116$		0			0
$117$	−12.4163	−	17.0896i	−1.14789	−	1.57993i
$118$		0			0
$119$	−0.345752	−	1.06411i	−0.0316950	−	0.0975472i
$120$		0			0
$121$	−6.53867	−	8.84567i	−0.594424	−	0.804152i
$122$		0			0
$123$	29.7853	−	9.67784i	2.68565	−	0.872621i
$124$		0			0
$125$	1.20534	−	11.1152i	0.107809	−	0.994172i
$126$		0			0
$127$	16.5263	+	5.36973i	1.46647	+	0.476486i	0.930041	−	0.367457i	$-0.119771\pi$
$127$	16.5263	+	5.36973i	1.46647	+	0.476486i	0.536433	+	0.843943i	$0.319771\pi$
$128$		0			0
$129$	−12.6274	−	9.17431i	−1.11178	−	0.807753i
$130$		0			0
$131$	3.84691			0.336106			0.168053	−	0.985778i	$-0.446252\pi$
$131$	3.84691			0.336106			0.168053	+	0.985778i	$0.446252\pi$
$132$		0			0
$133$		−	6.77528i		−	0.587491i
$134$		0			0
$135$	5.64709	+	6.74499i	0.486024	+	0.580516i
$136$		0			0
$137$	−7.70919	−	2.50487i	−0.658641	−	0.214005i	−0.0394205	−	0.999223i	$-0.512551\pi$
$137$	−7.70919	−	2.50487i	−0.658641	−	0.214005i	−0.619220	+	0.785217i	$0.712551\pi$
$138$		0			0
$139$	−16.1882	+	11.7614i	−1.37306	+	0.997589i	−0.375572	+	0.926793i	$0.622554\pi$
$139$	−16.1882	+	11.7614i	−1.37306	+	0.997589i	−0.997491	+	0.0707957i	$0.977446\pi$
$140$		0			0
$141$	7.78613	+	23.9632i	0.655710	+	2.01807i
$142$		0			0
$143$	−2.40312	+	15.5876i	−0.200959	+	1.30350i
$144$		0			0
$145$	−12.5684	+	0.864980i	−1.04375	+	0.0718327i
$146$		0			0
$147$	−6.52740	−	8.98420i	−0.538371	−	0.741004i
$148$		0			0
$149$	−1.41102	+	4.34268i	−0.115596	+	0.355766i	−0.992071	−	0.125680i	$-0.959889\pi$
$149$	−1.41102	+	4.34268i	−0.115596	+	0.355766i	0.876475	+	0.481447i	$0.159889\pi$
$150$		0			0
$151$	−11.1394	−	8.09328i	−0.906515	−	0.658621i	0.0336163	−	0.999435i	$-0.489298\pi$
$151$	−11.1394	−	8.09328i	−0.906515	−	0.658621i	−0.940131	+	0.340813i	$0.889298\pi$
$152$		0			0
$153$		−	2.90396i		−	0.234772i
$154$		0			0
$155$	−3.48519	+	13.9131i	−0.279937	+	1.11753i
$156$		0			0
$157$	−2.55560	+	3.51748i	−0.203959	+	0.280725i	−0.898727	−	0.438508i	$-0.855507\pi$
$157$	−2.55560	+	3.51748i	−0.203959	+	0.280725i	0.694768	+	0.719234i	$0.255507\pi$
$158$		0			0
$159$	−11.1236	+	34.2349i	−0.882158	+	2.71500i
$160$		0			0
$161$	−0.934861	+	0.679216i	−0.0736774	+	0.0535297i
$162$		0			0
$163$	0.529107	−	0.171917i	0.0414429	−	0.0134656i	−0.288222	−	0.957564i	$-0.593064\pi$
$163$	0.529107	−	0.171917i	0.0414429	−	0.0134656i	0.329665	+	0.944098i	$0.393064\pi$
$164$		0			0
$165$	1.70251	−	20.1598i	0.132540	−	1.56944i
$166$		0			0
$167$	−4.46642	+	1.45123i	−0.345622	+	0.112299i	−0.476684	−	0.879075i	$-0.658161\pi$
$167$	−4.46642	+	1.45123i	−0.345622	+	0.112299i	0.131062	+	0.991374i	$0.458161\pi$
$168$		0			0
$169$	7.77758	−	5.65074i	0.598276	−	0.434673i
$170$		0			0
$171$	5.43399	−	16.7241i	0.415548	−	1.27892i
$172$		0			0
$173$	7.33369	−	10.0940i	0.557570	−	0.767429i	−0.433445	−	0.901180i	$-0.642702\pi$
$173$	7.33369	−	10.0940i	0.557570	−	0.767429i	0.991015	+	0.133751i	$0.0427022\pi$
$174$		0			0
$175$	4.03413	−	7.54700i	0.304951	−	0.570499i
$176$		0			0
$177$			16.1694i			1.21537i
$178$		0			0
$179$	−15.5655	−	11.3090i	−1.16342	−	0.845277i	−0.173217	−	0.984884i	$-0.555416\pi$
$179$	−15.5655	−	11.3090i	−1.16342	−	0.845277i	−0.990207	+	0.139607i	$0.955416\pi$
$180$		0			0
$181$	−0.193540	+	0.595656i	−0.0143857	+	0.0442748i	−0.957992	−	0.286796i	$-0.907410\pi$
$181$	−0.193540	+	0.595656i	−0.0143857	+	0.0442748i	0.943606	+	0.331071i	$0.107410\pi$
$182$		0			0
$183$	24.3281	+	33.4848i	1.79839	+	2.47526i
$184$		0			0
$185$	−0.170763	−	2.48124i	−0.0125548	−	0.182424i
$186$		0			0
$187$	−1.52683	+	1.53945i	−0.111653	+	0.112575i
$188$		0			0
$189$	2.08067	+	6.40364i	0.151346	+	0.465796i
$190$		0			0
$191$	6.71370	−	4.87779i	0.485786	−	0.352944i	−0.317775	−	0.948166i	$-0.602936\pi$
$191$	6.71370	−	4.87779i	0.485786	−	0.352944i	0.803561	+	0.595222i	$0.202936\pi$
$192$		0			0
$193$	−0.0179897	−	0.00584521i	−0.00129493	−	0.000420747i	0.308369	−	0.951267i	$-0.400217\pi$
$193$	−0.0179897	−	0.00584521i	−0.00129493	−	0.000420747i	−0.309664	+	0.950846i	$0.600217\pi$
$194$		0			0
$195$	−22.2419	+	18.6215i	−1.59278	+	1.33352i
$196$		0			0
$197$			2.53495i			0.180608i	0.995914	+	0.0903040i	$0.0287839\pi$
$197$			2.53495i			0.180608i	−0.995914	+	0.0903040i	$0.971216\pi$
$198$		0			0
$199$	14.6101			1.03568			0.517841	−	0.855477i	$-0.326736\pi$
$199$	14.6101			1.03568			0.517841	+	0.855477i	$0.326736\pi$
$200$		0			0
$201$	23.5959	+	17.1434i	1.66433	+	1.20920i
$202$		0			0
$203$	−9.17077	−	2.97976i	−0.643662	−	0.209138i
$204$		0			0
$205$	−9.59014	−	23.8118i	−0.669804	−	1.66309i
$206$		0			0
$207$	−2.85237	+	0.926790i	−0.198253	+	0.0644164i
$208$		0			0
$209$	−11.6738	+	6.00872i	−0.807490	+	0.415632i
$210$		0			0
$211$	0.642557	+	1.97759i	0.0442355	+	0.136143i	0.970735	−	0.240153i	$-0.0771976\pi$
$211$	0.642557	+	1.97759i	0.0442355	+	0.136143i	−0.926500	+	0.376296i	$0.877198\pi$
$212$		0			0
$213$	2.41900	+	3.32947i	0.165747	+	0.228131i
$214$		0			0
$215$	−6.79149	+	10.8421i	−0.463176	+	0.739425i
$216$		0			0
$217$	−6.45287	+	8.88161i	−0.438049	+	0.602923i
$218$		0			0
$219$	22.7474			1.53713
$220$		0			0
$221$	3.10877			0.209118
$222$		0			0
$223$	−2.74866	+	3.78320i	−0.184064	+	0.253342i	−0.891071	−	0.453865i	$-0.850045\pi$
$223$	−2.74866	+	3.78320i	−0.184064	+	0.253342i	0.707007	+	0.707207i	$0.250045\pi$
$224$		0			0
$225$	16.0108	−	15.3935i	1.06739	−	1.02623i
$226$		0			0
$227$	8.93440	+	12.2971i	0.592997	+	0.816190i	0.995045	−	0.0994287i	$-0.0317015\pi$
$227$	8.93440	+	12.2971i	0.592997	+	0.816190i	−0.402048	+	0.915619i	$0.631702\pi$
$228$		0			0
$229$	2.18447	+	6.72309i	0.144354	+	0.444274i	0.996927	−	0.0783324i	$-0.0249596\pi$
$229$	2.18447	+	6.72309i	0.144354	+	0.444274i	−0.852574	+	0.522607i	$0.824960\pi$
$230$		0			0
$231$	6.97338	−	13.8264i	0.458815	−	0.909711i
$232$		0			0
$233$	21.8099	−	7.08647i	1.42881	−	0.464250i	0.510423	−	0.859923i	$-0.329489\pi$
$233$	21.8099	−	7.08647i	1.42881	−	0.464250i	0.918391	+	0.395673i	$0.129489\pi$
$234$		0			0
$235$	19.1573	−	7.71557i	1.24969	−	0.503308i
$236$		0			0
$237$	−22.5009	−	7.31097i	−1.46159	−	0.474899i
$238$		0			0
$239$	15.4399	+	11.2177i	0.998722	+	0.725614i	0.961814	−	0.273705i	$-0.0882491\pi$
$239$	15.4399	+	11.2177i	0.998722	+	0.725614i	0.0369082	+	0.999319i	$0.488249\pi$
$240$		0			0
$241$	−11.5798			−0.745917			−0.372959	−	0.927848i	$-0.621657\pi$
$241$	−11.5798			−0.745917			−0.372959	+	0.927848i	$0.621657\pi$
$242$		0			0
$243$		−	18.8789i		−	1.21108i
$244$		0			0
$245$	−6.97932	+	5.84328i	−0.445893	+	0.373313i
$246$		0			0
$247$	17.9036	+	5.81723i	1.13918	+	0.370141i
$248$		0			0
$249$	−27.0216	+	19.6323i	−1.71242	+	1.24415i
$250$		0			0
$251$	−5.27876	−	16.2463i	−0.333192	−	1.02546i	−0.967606	−	0.252466i	$-0.918758\pi$
$251$	−5.27876	−	16.2463i	−0.333192	−	1.02546i	0.634414	−	0.772994i	$-0.281242\pi$
$252$		0			0
$253$	1.99937	+	1.00839i	0.125700	+	0.0633969i
$254$		0			0
$255$	−3.97841	+	0.273802i	−0.249138	+	0.0171461i
$256$		0			0
$257$	7.96319	+	10.9604i	0.496730	+	0.683690i	0.981611	−	0.190890i	$-0.0611373\pi$
$257$	7.96319	+	10.9604i	0.496730	+	0.683690i	−0.484881	+	0.874580i	$0.661137\pi$
$258$		0			0
$259$	0.588261	−	1.81048i	0.0365528	−	0.112498i
$260$		0			0
$261$	−20.2473	−	14.7105i	−1.25327	−	0.910557i
$262$		0			0
$263$			1.28142i			0.0790155i	0.999219	+	0.0395077i	$0.0125790\pi$
$263$			1.28142i			0.0790155i	−0.999219	+	0.0395077i	$0.987421\pi$
$264$		0			0
$265$	28.6210	+	7.16945i	1.75817	+	0.440416i
$266$		0			0
$267$	2.89063	−	3.97862i	0.176904	−	0.243487i
$268$		0			0
$269$	−4.43132	+	13.6382i	−0.270183	+	0.831537i	0.720271	+	0.693692i	$0.244017\pi$
$269$	−4.43132	+	13.6382i	−0.270183	+	0.831537i	−0.990454	+	0.137844i	$0.955983\pi$
$270$		0			0
$271$	−7.64657	+	5.55556i	−0.464496	+	0.337476i	−0.795292	−	0.606226i	$-0.792683\pi$
$271$	−7.64657	+	5.55556i	−0.464496	+	0.337476i	0.330796	+	0.943702i	$0.392683\pi$
$272$		0			0
$273$	−21.1163	+	6.86110i	−1.27802	+	0.415253i
$274$		0			0
$275$	−16.5811	−	0.257645i	−0.999879	−	0.0155366i
$276$		0			0
$277$	−11.1368	+	3.61857i	−0.669147	+	0.217419i	−0.623838	−	0.781554i	$-0.714427\pi$
$277$	−11.1368	+	3.61857i	−0.669147	+	0.217419i	−0.0453094	+	0.998973i	$0.514427\pi$
$278$		0			0
$279$	−23.0516	+	16.7480i	−1.38006	+	1.00267i
$280$		0			0
$281$	−0.871465	+	2.68209i	−0.0519873	+	0.160000i	−0.973679	−	0.227922i	$-0.926807\pi$
$281$	−0.871465	+	2.68209i	−0.0519873	+	0.160000i	0.921692	+	0.387922i	$0.126807\pi$
$282$		0			0
$283$	−1.08445	+	1.49262i	−0.0644639	+	0.0887269i	−0.840032	−	0.542537i	$-0.817464\pi$
$283$	−1.08445	+	1.49262i	−0.0644639	+	0.0887269i	0.775568	+	0.631264i	$0.217464\pi$
$284$		0			0
$285$	−23.4243	−	5.86769i	−1.38753	−	0.347572i
$286$		0			0
$287$		−	19.6484i		−	1.15981i
$288$		0			0
$289$	−13.4075	−	9.74115i	−0.788679	−	0.573009i
$290$		0			0
$291$	9.02797	−	27.7852i	0.529229	−	1.62880i
$292$		0			0
$293$	2.20510	+	3.03506i	0.128823	+	0.177310i	0.868556	−	0.495590i	$-0.165048\pi$
$293$	2.20510	+	3.03506i	0.128823	+	0.177310i	−0.739733	+	0.672901i	$0.765048\pi$
$294$		0			0
$295$	13.2222	−	0.909979i	0.769828	−	0.0529810i
$296$		0			0
$297$	9.18816	−	9.26410i	0.533151	−	0.537558i
$298$		0			0
$299$	−0.992152	−	3.05353i	−0.0573776	−	0.176590i
$300$		0			0
$301$	−7.92215	+	5.75578i	−0.456625	+	0.331758i
$302$		0			0
$303$	−23.6425	−	7.68192i	−1.35823	−	0.441315i
$304$		0			0
$305$	26.0124	−	21.7783i	1.48947	−	1.24702i
$306$		0			0
$307$		−	7.99801i		−	0.456470i	−0.973606	−	0.228235i	$-0.926705\pi$
$307$		−	7.99801i		−	0.456470i	0.973606	−	0.228235i	$-0.0732955\pi$
$308$		0			0
$309$	−20.9388			−1.19117
$310$		0			0
$311$	10.2107	+	7.41849i	0.578994	+	0.420664i	0.838361	−	0.545115i	$-0.183514\pi$
$311$	10.2107	+	7.41849i	0.578994	+	0.420664i	−0.259367	+	0.965779i	$0.583514\pi$
$312$		0			0
$313$	−11.7949	−	3.83241i	−0.666690	−	0.216621i	−0.0439310	−	0.999035i	$-0.513988\pi$
$313$	−11.7949	−	3.83241i	−0.666690	−	0.216621i	−0.622759	+	0.782414i	$0.713988\pi$
$314$		0			0
$315$	15.7692	−	6.35101i	0.888495	−	0.357839i
$316$		0			0
$317$	2.69675	−	0.876229i	0.151465	−	0.0492139i	−0.232303	−	0.972643i	$-0.574626\pi$
$317$	2.69675	−	0.876229i	0.151465	−	0.0492139i	0.383768	+	0.923429i	$0.374626\pi$
$318$		0			0
$319$	2.99907	+	18.4438i	0.167916	+	1.03265i
$320$		0			0
$321$	9.24694	+	28.4592i	0.516114	+	1.58844i
$322$		0			0
$323$	1.52114	+	2.09368i	0.0846387	+	0.116495i
$324$		0			0
$325$	16.4792	+	17.1399i	0.914099	+	0.950753i
$326$		0			0
$327$	15.7938	−	21.7382i	0.873397	−	1.20213i
$328$		0			0
$329$	15.8077			0.871509
$330$		0			0
$331$	−14.0009			−0.769562			−0.384781	−	0.923008i	$-0.625723\pi$
$331$	−14.0009			−0.769562			−0.384781	+	0.923008i	$0.625723\pi$
$332$		0			0
$333$	2.90413	−	3.99719i	0.159145	−	0.219045i
$334$		0			0
$335$	12.6908	−	20.2599i	0.693372	−	1.10692i
$336$		0			0
$337$	−8.18748	−	11.2691i	−0.446000	−	0.613867i	0.525532	−	0.850774i	$-0.323866\pi$
$337$	−8.18748	−	11.2691i	−0.446000	−	0.613867i	−0.971532	+	0.236907i	$0.923866\pi$
$338$		0			0
$339$	−5.02262	−	15.4580i	−0.272791	−	0.839565i
$340$		0			0
$341$	21.0257	+	3.24151i	1.13861	+	0.175537i
$342$		0			0
$343$	−18.0203	+	5.85515i	−0.973004	+	0.316148i
$344$		0			0
$345$	1.53863	+	3.82034i	0.0828372	+	0.205680i
$346$		0			0
$347$	29.8076	+	9.68506i	1.60015	+	0.519921i	0.967145	−	0.254224i	$-0.0818199\pi$
$347$	29.8076	+	9.68506i	1.60015	+	0.519921i	0.633008	+	0.774145i	$0.281820\pi$
$348$		0			0
$349$	17.1026	+	12.4258i	0.915482	+	0.665137i	0.942395	−	0.334501i	$-0.108568\pi$
$349$	17.1026	+	12.4258i	0.915482	+	0.665137i	−0.0269132	+	0.999638i	$0.508568\pi$
$350$		0			0
$351$	−18.7080			−0.998559
$352$		0			0
$353$		−	18.6583i		−	0.993084i	−0.868013	−	0.496542i	$-0.834603\pi$
$353$		−	18.6583i		−	0.993084i	0.868013	−	0.496542i	$-0.165397\pi$
$354$		0			0
$355$	2.58648	−	2.16547i	0.137276	−	0.114931i
$356$		0			0
$357$	−2.90292	−	0.943217i	−0.153639	−	0.0499204i
$358$		0			0
$359$	9.43404	−	6.85423i	0.497910	−	0.361752i	−0.310308	−	0.950636i	$-0.600432\pi$
$359$	9.43404	−	6.85423i	0.497910	−	0.361752i	0.808218	+	0.588883i	$0.200432\pi$
$360$		0			0
$361$	−1.02871	−	3.16605i	−0.0541428	−	0.166634i
$362$		0			0
$363$	−30.0072	+	0.246989i	−1.57497	+	0.0129635i
$364$		0			0
$365$	−1.28018	−	18.6013i	−0.0670075	−	0.973637i
$366$		0			0
$367$	−20.2757	−	27.9070i	−1.05838	−	1.45674i	−0.881311	−	0.472537i	$-0.843338\pi$
$367$	−20.2757	−	27.9070i	−1.05838	−	1.45674i	−0.177070	−	0.984198i	$-0.556662\pi$
$368$		0			0
$369$	15.7586	−	48.5001i	0.820362	−	2.52481i
$370$		0			0
$371$	18.2705	+	13.2743i	0.948558	+	0.689168i
$372$		0			0
$373$			23.3283i			1.20789i	0.797025	+	0.603947i	$0.206406\pi$
$373$			23.3283i			1.20789i	−0.797025	+	0.603947i	$0.793594\pi$
$374$		0			0
$375$	−22.5986	−	20.4833i	−1.16699	−	1.05775i
$376$		0			0
$377$	15.7480	−	21.6752i	0.811062	−	1.11633i
$378$		0			0
$379$	−3.82655	+	11.7769i	−0.196557	+	0.604940i	0.803398	+	0.595442i	$0.203023\pi$
$379$	−3.82655	+	11.7769i	−0.196557	+	0.604940i	−0.999955	+	0.00949730i	$0.996977\pi$
$380$		0			0
$381$	38.3509	−	27.8635i	1.96477	−	1.42749i
$382$		0			0
$383$	−10.1594	+	3.30098i	−0.519120	+	0.168672i	−0.556846	−	0.830616i	$-0.687989\pi$
$383$	−10.1594	+	3.30098i	−0.519120	+	0.168672i	0.0377259	+	0.999288i	$0.487989\pi$
$384$		0			0
$385$	−11.6988	−	4.92424i	−0.596224	−	0.250963i
$386$		0			0
$387$	−24.1714	+	7.85375i	−1.22870	+	0.399229i
$388$		0			0
$389$	−4.99450	+	3.62872i	−0.253231	+	0.183983i	−0.707158	−	0.707056i	$-0.750023\pi$
$389$	−4.99450	+	3.62872i	−0.253231	+	0.183983i	0.453926	+	0.891039i	$0.350023\pi$
$390$		0			0
$391$	0.136394	−	0.419779i	0.00689776	−	0.0212291i
$392$		0			0
$393$	6.16849	−	8.49019i	0.311159	−	0.428274i
$394$		0			0
$395$	−4.71212	+	18.8111i	−0.237092	+	0.946491i
$396$		0			0
$397$			23.6084i			1.18487i	0.805618	+	0.592436i	$0.201834\pi$
$397$			23.6084i			1.18487i	−0.805618	+	0.592436i	$0.798166\pi$
$398$		0			0
$399$	−14.9531	−	10.8641i	−0.748593	−	0.543885i
$400$		0			0
$401$	−1.25044	+	3.84845i	−0.0624438	+	0.192182i	−0.977412	−	0.211344i	$-0.932216\pi$
$401$	−1.25044	+	3.84845i	−0.0624438	+	0.192182i	0.914968	+	0.403527i	$0.132216\pi$
$402$		0			0
$403$	−17.9291	−	24.6773i	−0.893114	−	1.22927i
$404$		0			0
$405$	−5.78682	+	0.398260i	−0.287549	+	0.0197897i
$406$		0			0
$407$	−3.64115	+	0.592073i	−0.180485	+	0.0293480i
$408$		0			0
$409$	1.71104	+	5.26604i	0.0846055	+	0.260389i	0.984406	−	0.175913i	$-0.0562878\pi$
$409$	1.71104	+	5.26604i	0.0846055	+	0.260389i	−0.899800	+	0.436302i	$0.856288\pi$
$410$		0			0
$411$	−17.8899	+	12.9978i	−0.882444	+	0.641133i
$412$		0			0
$413$	9.64785	+	3.13478i	0.474740	+	0.154252i
$414$		0			0
$415$	17.5747	+	20.9916i	0.862709	+	1.03044i
$416$		0			0
$417$			54.5868i			2.67313i
$418$		0			0
$419$	−6.68772			−0.326716			−0.163358	−	0.986567i	$-0.552233\pi$
$419$	−6.68772			−0.326716			−0.163358	+	0.986567i	$0.552233\pi$
$420$		0			0
$421$	−14.0535	−	10.2105i	−0.684925	−	0.497627i	0.190063	−	0.981772i	$-0.439131\pi$
$421$	−14.0535	−	10.2105i	−0.684925	−	0.497627i	−0.874988	+	0.484145i	$0.839131\pi$
$422$		0			0
$423$	39.0199	+	12.6783i	1.89721	+	0.616441i
$424$		0			0
$425$	0.447793	+	3.23787i	0.0217212	+	0.157060i
$426$		0			0
$427$	24.6960	−	8.02422i	1.19512	−	0.388319i
$428$		0			0
$429$	30.5488	+	30.2984i	1.47491	+	1.46282i
$430$		0			0
$431$	0.854246	+	2.62910i	0.0411476	+	0.126639i	0.969520	−	0.245012i	$-0.0787918\pi$
$431$	0.854246	+	2.62910i	0.0411476	+	0.126639i	−0.928373	+	0.371651i	$0.878792\pi$
$432$		0			0
$433$	13.1027	+	18.0344i	0.629677	+	0.866676i	0.998012	−	0.0630170i	$-0.0200722\pi$
$433$	13.1027	+	18.0344i	0.629677	+	0.866676i	−0.368335	+	0.929693i	$0.620072\pi$
$434$		0			0
$435$	−18.2443	+	29.1256i	−0.874746	+	1.39647i
$436$		0			0
$437$	1.57101	−	2.16231i	0.0751515	−	0.103437i
$438$		0			0
$439$	5.68059			0.271120			0.135560	−	0.990769i	$-0.456717\pi$
$439$	5.68059			0.271120			0.135560	+	0.990769i	$0.456717\pi$
$440$		0			0
$441$	−18.0826			−0.861078
$442$		0			0
$443$	14.2207	−	19.5732i	0.675647	−	0.929949i	−0.324224	−	0.945980i	$-0.605103\pi$
$443$	14.2207	−	19.5732i	0.675647	−	0.929949i	0.999871	+	0.0160315i	$0.00510320\pi$
$444$		0			0
$445$	−3.41612	−	2.13986i	−0.161940	−	0.101439i
$446$		0			0
$447$	7.32181	+	10.0776i	0.346310	+	0.476654i
$448$		0			0
$449$	−11.2633	−	34.6648i	−0.531548	−	1.63594i	−0.750993	−	0.660310i	$-0.770425\pi$
$449$	−11.2633	−	34.6648i	−0.531548	−	1.63594i	0.219445	−	0.975625i	$-0.429575\pi$
$450$		0			0
$451$	−33.8540	+	17.4253i	−1.59412	+	0.820528i
$452$		0			0
$453$	−35.7240	+	11.6074i	−1.67846	+	0.545364i
$454$		0			0
$455$	6.79892	+	16.8813i	0.318738	+	0.791410i
$456$		0			0
$457$	−30.4602	−	9.89713i	−1.42487	−	0.462968i	−0.507724	−	0.861520i	$-0.669513\pi$
$457$	−30.4602	−	9.89713i	−1.42487	−	0.462968i	−0.917146	+	0.398552i	$0.869513\pi$
$458$		0			0
$459$	−2.08067	−	1.51169i	−0.0971173	−	0.0705599i
$460$		0			0
$461$	−10.4043			−0.484577			−0.242289	−	0.970204i	$-0.577898\pi$
$461$	−10.4043			−0.484577			−0.242289	+	0.970204i	$0.577898\pi$
$462$		0			0
$463$			13.9916i			0.650245i	0.945672	+	0.325123i	$0.105406\pi$
$463$			13.9916i			0.650245i	−0.945672	+	0.325123i	$0.894594\pi$
$464$		0			0
$465$	25.1180	+	30.0015i	1.16482	+	1.39128i
$466$		0			0
$467$	−4.92912	−	1.60157i	−0.228092	−	0.0741117i	0.192741	−	0.981250i	$-0.438262\pi$
$467$	−4.92912	−	1.60157i	−0.228092	−	0.0741117i	−0.420833	+	0.907138i	$0.638262\pi$
$468$		0			0
$469$	14.8036	−	10.7554i	0.683566	−	0.496640i
$470$		0			0
$471$	3.66525	+	11.2805i	0.168886	+	0.519777i
$472$		0			0
$473$	16.9430	+	8.54524i	0.779040	+	0.392911i
$474$		0			0
$475$	−3.47994	+	19.4850i	−0.159670	+	0.894033i
$476$		0			0
$477$	34.4526	+	47.4199i	1.57747	+	2.17121i
$478$		0			0
$479$	−1.43170	+	4.40633i	−0.0654162	+	0.201330i	−0.978422	−	0.206616i	$-0.933755\pi$
$479$	−1.43170	+	4.40633i	−0.0654162	+	0.201330i	0.913006	+	0.407946i	$0.133755\pi$
$480$		0			0
$481$	4.27910	+	3.10895i	0.195110	+	0.141756i
$482$		0			0
$483$			3.15237i			0.143438i
$484$		0			0
$485$	−23.2290	−	5.81877i	−1.05477	−	0.264217i
$486$		0			0
$487$	−17.9264	+	24.6735i	−0.812322	+	1.11807i	0.178639	+	0.983915i	$0.442831\pi$
$487$	−17.9264	+	24.6735i	−0.812322	+	1.11807i	−0.990961	+	0.134151i	$0.957169\pi$
$488$		0			0
$489$	0.468994	−	1.44341i	0.0212086	−	0.0652735i
$490$		0			0
$491$	17.4600	−	12.6854i	0.787958	−	0.572485i	−0.119399	−	0.992846i	$-0.538097\pi$
$491$	17.4600	−	12.6854i	0.787958	−	0.572485i	0.907357	+	0.420362i	$0.138097\pi$
$492$		0			0
$493$	3.50292	−	1.13817i	0.157764	−	0.0512605i
$494$		0			0
$495$	−24.9278	−	21.5378i	−1.12042	−	0.968051i
$496$		0			0
$497$	2.45558	−	0.797867i	0.110148	−	0.0357892i
$498$		0			0
$499$	11.0681	−	8.04142i	0.495475	−	0.359983i	−0.311811	−	0.950144i	$-0.600936\pi$
$499$	11.0681	−	8.04142i	0.495475	−	0.359983i	0.807286	+	0.590161i	$0.200936\pi$
$500$		0			0
$501$	−3.95898	+	12.1845i	−0.176874	+	0.544362i
$502$		0			0
$503$	−4.78142	+	6.58106i	−0.213193	+	0.293435i	−0.902198	−	0.431321i	$-0.858048\pi$
$503$	−4.78142	+	6.58106i	−0.213193	+	0.293435i	0.689006	+	0.724756i	$0.258048\pi$
$504$		0			0
$505$	−4.95120	+	19.7656i	−0.220326	+	0.879556i
$506$		0			0
$507$		−	26.2262i		−	1.16474i
$508$		0			0
$509$	−25.7114	−	18.6804i	−1.13964	−	0.827996i	−0.152569	−	0.988293i	$-0.548755\pi$
$509$	−25.7114	−	18.6804i	−1.13964	−	0.827996i	−0.987069	+	0.160297i	$0.948755\pi$
$510$		0			0
$511$	4.41007	−	13.5728i	0.195090	−	0.600425i
$512$		0			0
$513$	−9.15397	−	12.5994i	−0.404158	−	0.556275i
$514$		0			0
$515$	1.17839	+	17.1223i	0.0519261	+	0.754500i
$516$		0			0
$517$	−14.0192	−	27.2366i	−0.616566	−	1.19787i
$518$		0			0
$519$	−10.5180	−	32.3711i	−0.461690	−	1.42093i
$520$		0			0
$521$	7.18170	−	5.21781i	0.314636	−	0.228596i	−0.419247	−	0.907872i	$-0.637706\pi$
$521$	7.18170	−	5.21781i	0.314636	−	0.228596i	0.733883	+	0.679276i	$0.237706\pi$
$522$		0			0
$523$	28.5567	+	9.27864i	1.24870	+	0.405727i	0.857454	−	0.514560i	$-0.172045\pi$
$523$	28.5567	+	9.27864i	1.24870	+	0.405727i	0.391244	+	0.920287i	$0.372045\pi$
$524$		0			0
$525$	−10.1877	−	21.0049i	−0.444626	−	0.916730i
$526$		0			0
$527$		−	4.19333i		−	0.182664i
$528$		0			0
$529$	22.5442			0.980180
$530$		0			0
$531$	21.3006	+	15.4758i	0.924367	+	0.671592i
$532$		0			0
$533$	51.9206	+	16.8700i	2.24893	+	0.730722i
$534$		0			0
$535$	22.7516	−	9.16314i	0.983636	−	0.396157i
$536$		0			0
$537$	−49.9184	+	16.2195i	−2.15414	+	0.699922i
$538$		0			0
$539$	9.58595	+	9.50738i	0.412896	+	0.409512i
$540$		0			0
$541$	−8.98551	−	27.6545i	−0.386317	−	1.18896i	−0.935520	−	0.353273i	$-0.885069\pi$
$541$	−8.98551	−	27.6545i	−0.386317	−	1.18896i	0.549203	−	0.835689i	$-0.314931\pi$
$542$		0			0
$543$	1.00428	+	1.38228i	0.0430979	+	0.0593191i
$544$		0			0
$545$	−18.6649	−	11.6917i	−0.799517	−	0.500817i
$546$		0			0
$547$	3.71206	−	5.10921i	0.158716	−	0.218454i	−0.722251	−	0.691631i	$-0.756893\pi$
$547$	3.71206	−	5.10921i	0.158716	−	0.218454i	0.880968	+	0.473176i	$0.156893\pi$
$548$		0			0
$549$	67.3954			2.87636
$550$		0			0
$551$	22.3033			0.950153
$552$		0			0
$553$	−8.72454	+	12.0083i	−0.371005	+	0.510645i
$554$		0			0
$555$	−5.74995	−	3.60176i	−0.244072	−	0.152886i
$556$		0			0
$557$	18.4284	+	25.3645i	0.780836	+	1.07473i	0.995189	+	0.0979718i	$0.0312355\pi$
$557$	18.4284	+	25.3645i	0.780836	+	1.07473i	−0.214354	+	0.976756i	$0.568765\pi$
$558$		0			0
$559$	−8.40764	−	25.8761i	−0.355605	−	1.09444i
$560$		0			0
$561$	0.949328	+	5.83822i	0.0400807	+	0.246490i
$562$		0			0
$563$	−13.9824	+	4.54315i	−0.589287	+	0.191471i	−0.588457	−	0.808529i	$-0.700264\pi$
$563$	−13.9824	+	4.54315i	−0.589287	+	0.191471i	−0.000830194		1.00000i	$0.500264\pi$
$564$		0			0
$565$	−12.3579	+	4.97710i	−0.519899	+	0.209388i
$566$		0			0
$567$	−4.22246	−	1.37196i	−0.177327	−	0.0576170i
$568$		0			0
$569$	−18.9361	−	13.7578i	−0.793841	−	0.576759i	0.115260	−	0.993335i	$-0.463230\pi$
$569$	−18.9361	−	13.7578i	−0.793841	−	0.576759i	−0.909101	+	0.416576i	$0.863230\pi$
$570$		0			0
$571$	−9.67155			−0.404742			−0.202371	−	0.979309i	$-0.564865\pi$
$571$	−9.67155			−0.404742			−0.202371	+	0.979309i	$0.564865\pi$
$572$		0			0
$573$		−	22.6387i		−	0.945746i
$574$		0			0
$575$	3.03743	−	1.47319i	0.126669	−	0.0614363i
$576$		0			0
$577$	25.3831	+	8.24747i	1.05671	+	0.343347i	0.785299	−	0.619116i	$-0.212509\pi$
$577$	25.3831	+	8.24747i	1.05671	+	0.343347i	0.271413	+	0.962463i	$0.412509\pi$
$578$		0			0
$579$	−0.0417468	+	0.0303308i	−0.00173494	+	0.00126051i
$580$		0			0
$581$	6.47540	+	19.9292i	0.268645	+	0.826804i
$582$		0			0
$583$	6.66816	−	43.2524i	0.276167	−	1.79133i
$584$		0			0
$585$	3.24309	+	47.1229i	0.134085	+	1.94829i
$586$		0			0
$587$	−19.9125	−	27.4073i	−0.821878	−	1.13122i	−0.989381	−	0.145347i	$-0.953570\pi$
$587$	−19.9125	−	27.4073i	−0.821878	−	1.13122i	0.167502	−	0.985872i	$-0.446430\pi$
$588$		0			0
$589$	7.84669	−	24.1496i	0.323317	−	0.995068i
$590$		0			0
$591$	5.59468	+	4.06477i	0.230134	+	0.167202i
$592$		0			0
$593$		−	7.43914i		−	0.305489i	−0.988266	−	0.152745i	$-0.951189\pi$
$593$		−	7.43914i		−	0.305489i	0.988266	−	0.152745i	$-0.0488112\pi$
$594$		0			0
$595$	−0.607929	+	2.42690i	−0.0249227	+	0.0994931i
$596$		0			0
$597$	23.4271	−	32.2447i	0.958809	−	1.31969i
$598$		0			0
$599$	6.30588	−	19.4075i	0.257651	−	0.792969i	−0.735644	−	0.677368i	$-0.763121\pi$
$599$	6.30588	−	19.4075i	0.257651	−	0.792969i	0.993296	−	0.115601i	$-0.0368794\pi$
$600$		0			0
$601$	−34.7579	+	25.2531i	−1.41780	+	1.03009i	−0.425673	+	0.904877i	$0.639963\pi$
$601$	−34.7579	+	25.2531i	−1.41780	+	1.03009i	−0.992129	+	0.125217i	$0.960037\pi$
$602$		0			0
$603$	45.1674	−	14.6758i	1.83936	−	0.597644i
$604$		0			0
$605$	1.89071	+	24.5240i	0.0768684	+	0.997041i
$606$		0			0
$607$	−42.1420	+	13.6928i	−1.71049	+	0.555772i	−0.990415	−	0.138122i	$-0.955893\pi$
$607$	−42.1420	+	13.6928i	−1.71049	+	0.555772i	−0.720076	+	0.693895i	$0.755893\pi$
$608$		0			0
$609$	−21.2816	+	15.4620i	−0.862375	+	0.626552i
$610$		0			0
$611$	−13.5725	+	41.7718i	−0.549083	+	1.68990i
$612$		0			0
$613$	14.2472	−	19.6096i	0.575439	−	0.792025i	−0.417747	−	0.908564i	$-0.637180\pi$
$613$	14.2472	−	19.6096i	0.575439	−	0.792025i	0.993186	+	0.116539i	$0.0371800\pi$
$614$		0			0
$615$	−67.9307	−	17.0164i	−2.73923	−	0.686167i
$616$		0			0
$617$		−	39.5457i		−	1.59205i	−0.605264	−	0.796025i	$-0.706932\pi$
$617$		−	39.5457i		−	1.59205i	0.605264	−	0.796025i	$-0.293068\pi$
$618$		0			0
$619$	2.98508	+	2.16879i	0.119981	+	0.0871710i	0.646157	−	0.763204i	$-0.276375\pi$
$619$	2.98508	+	2.16879i	0.119981	+	0.0871710i	−0.526177	+	0.850375i	$0.676375\pi$
$620$		0			0
$621$	−0.820796	+	2.52615i	−0.0329374	+	0.101371i
$622$		0			0
$623$	−1.81353	−	2.49610i	−0.0726574	−	0.100004i
$624$		0			0
$625$	−15.4780	+	19.6324i	−0.619122	+	0.785295i
$626$		0			0
$627$	−5.45742	+	35.3991i	−0.217948	+	1.41370i
$628$		0			0
$629$	0.224696	+	0.691543i	0.00895921	+	0.0275736i
$630$		0			0
$631$	21.8127	−	15.8478i	0.868349	−	0.630893i	−0.0617944	−	0.998089i	$-0.519682\pi$
$631$	21.8127	−	15.8478i	0.868349	−	0.630893i	0.930143	+	0.367196i	$0.119682\pi$
$632$		0			0
$633$	5.39490	+	1.75291i	0.214428	+	0.0696719i
$634$		0			0
$635$	−24.9432	−	29.7926i	−0.989842	−	1.18229i
$636$		0			0
$637$		−	19.3579i		−	0.766989i
$638$		0			0
$639$	6.70127			0.265098
$640$		0			0
$641$	−8.59512	−	6.24472i	−0.339487	−	0.246652i	0.404958	−	0.914335i	$-0.367286\pi$
$641$	−8.59512	−	6.24472i	−0.339487	−	0.246652i	−0.744445	+	0.667683i	$0.767286\pi$
$642$		0			0
$643$	7.53543	+	2.44841i	0.297169	+	0.0965559i	0.453807	−	0.891100i	$-0.350066\pi$
$643$	7.53543	+	2.44841i	0.297169	+	0.0965559i	−0.156638	+	0.987656i	$0.550066\pi$
$644$		0			0
$645$	13.0386	+	32.3741i	0.513395	+	1.27473i
$646$		0			0
$647$	−1.05242	+	0.341951i	−0.0413748	+	0.0134435i	−0.329631	−	0.944110i	$-0.606924\pi$
$647$	−1.05242	+	0.341951i	−0.0413748	+	0.0134435i	0.288257	+	0.957553i	$0.406924\pi$
$648$		0			0
$649$	−3.15509	−	19.4033i	−0.123848	−	0.761646i
$650$		0			0
$651$	9.25474	+	28.4831i	0.362722	+	1.11634i
$652$		0			0
$653$	3.29765	+	4.53883i	0.129047	+	0.177618i	0.868651	−	0.495424i	$-0.164987\pi$
$653$	3.29765	+	4.53883i	0.129047	+	0.177618i	−0.739604	+	0.673042i	$0.764987\pi$
$654$		0			0
$655$	−7.28986	−	4.56636i	−0.284838	−	0.178422i
$656$		0			0
$657$	21.7716	−	29.9661i	0.849393	−	1.16909i
$658$		0			0
$659$	12.6847			0.494124			0.247062	−	0.969000i	$-0.420535\pi$
$659$	12.6847			0.494124			0.247062	+	0.969000i	$0.420535\pi$
$660$		0			0
$661$	−35.1508			−1.36721			−0.683604	−	0.729853i	$-0.739589\pi$
$661$	−35.1508			−1.36721			−0.683604	+	0.729853i	$0.739589\pi$
$662$		0			0
$663$	4.98488	−	6.86110i	0.193597	−	0.266463i
$664$		0			0
$665$	−8.04239	+	12.8391i	−0.311871	+	0.497878i
$666$		0			0
$667$	−2.23589	−	3.07744i	−0.0865740	−	0.119159i
$668$		0			0
$669$	3.94214	+	12.1326i	0.152412	+	0.469075i
$670$		0			0
$671$	−35.7275	−	35.4347i	−1.37925	−	1.36794i
$672$		0			0
$673$	−34.9096	+	11.3428i	−1.34567	+	0.437234i	−0.891233	−	0.453546i	$-0.850159\pi$
$673$	−34.9096	+	11.3428i	−1.34567	+	0.437234i	−0.454435	+	0.890780i	$0.650159\pi$
$674$		0			0
$675$	−2.69474	−	19.4849i	−0.103720	−	0.749974i
$676$		0			0
$677$	−14.8944	−	4.83948i	−0.572438	−	0.185996i	0.00847232	−	0.999964i	$-0.497303\pi$
$677$	−14.8944	−	4.83948i	−0.572438	−	0.185996i	−0.580910	+	0.813968i	$0.697303\pi$
$678$		0			0
$679$	−14.8285	−	10.7735i	−0.569064	−	0.413449i
$680$		0			0
$681$	41.4662			1.58899
$682$		0			0
$683$			14.0291i			0.536808i	0.963306	+	0.268404i	$0.0864962\pi$
$683$			14.0291i			0.536808i	−0.963306	+	0.268404i	$0.913504\pi$
$684$		0			0
$685$	11.6355	+	13.8977i	0.444570	+	0.531002i
$686$		0			0
$687$	18.3407	+	5.95927i	0.699743	+	0.227360i
$688$		0			0
$689$	−50.7642	+	36.8823i	−1.93396	+	1.40511i
$690$		0			0
$691$	−3.31456	−	10.2012i	−0.126092	−	0.388071i	0.868007	−	0.496553i	$-0.165401\pi$
$691$	−3.31456	−	10.2012i	−0.126092	−	0.388071i	−0.994098	+	0.108482i	$0.965401\pi$
$692$		0			0
$693$	−11.5398	−	22.4196i	−0.438362	−	0.851651i
$694$		0			0
$695$	44.6374	−	3.07203i	1.69319	−	0.116529i
$696$		0			0
$697$	4.41134	+	6.07169i	0.167091	+	0.229981i
$698$		0			0
$699$	19.3320	−	59.4979i	0.731205	−	2.25042i
$700$		0			0
$701$	0.940147	+	0.683057i	0.0355088	+	0.0257987i	0.605398	−	0.795923i	$-0.293014\pi$
$701$	0.940147	+	0.683057i	0.0355088	+	0.0257987i	−0.569889	+	0.821721i	$0.693014\pi$
$702$		0			0
$703$			4.40309i			0.166066i
$704$		0			0
$705$	13.6902	−	54.6524i	0.515603	−	2.05833i
$706$		0			0
$707$	−9.16720	+	12.6176i	−0.344768	+	0.474533i
$708$		0			0
$709$	−11.3880	+	35.0488i	−0.427687	+	1.31628i	0.472711	+	0.881217i	$0.343275\pi$
$709$	−11.3880	+	35.0488i	−0.427687	+	1.31628i	−0.900398	+	0.435067i	$0.856725\pi$
$710$		0			0
$711$	−31.1667	+	22.6439i	−1.16884	+	0.849214i
$712$		0			0
$713$	−4.11882	+	1.33829i	−0.154251	+	0.0501192i
$714$		0			0
$715$	23.0567	−	26.6859i	0.862273	−	0.997995i
$716$		0			0
$717$	49.5154	−	16.0885i	1.84918	−	0.600837i
$718$		0			0
$719$	33.8568	−	24.5984i	1.26265	−	0.917366i	0.263761	−	0.964588i	$-0.415037\pi$
$719$	33.8568	−	24.5984i	1.26265	−	0.917366i	0.998884	+	0.0472225i	$0.0150370\pi$
$720$		0			0
$721$	−4.05943	+	12.4936i	−0.151181	+	0.465287i
$722$		0			0
$723$	−18.5680	+	25.5567i	−0.690552	+	0.950463i
$724$		0			0
$725$	24.8437	+	13.2798i	0.922672	+	0.493200i
$726$		0			0
$727$		−	25.1900i		−	0.934245i	−0.884193	−	0.467122i	$-0.845291\pi$
$727$		−	25.1900i		−	0.934245i	0.884193	−	0.467122i	$-0.154709\pi$
$728$		0			0
$729$	−35.3700	−	25.6978i	−1.31000	−	0.951772i
$730$		0			0
$731$	1.15583	−	3.55727i	0.0427498	−	0.131570i
$732$		0			0
$733$	−23.3513	−	32.1404i	−0.862501	−	1.18713i	−0.980967	−	0.194173i	$-0.937798\pi$
$733$	−23.3513	−	32.1404i	−0.862501	−	1.18713i	0.118466	−	0.992958i	$-0.462202\pi$
$734$		0			0
$735$	1.70493	+	24.7731i	0.0628873	+	0.913770i
$736$		0			0
$737$	−31.6602	−	15.9679i	−1.16622	−	0.588186i
$738$		0			0
$739$	7.89240	+	24.2903i	0.290327	+	0.893534i	0.984751	+	0.173968i	$0.0556590\pi$
$739$	7.89240	+	24.2903i	0.290327	+	0.893534i	−0.694425	+	0.719566i	$0.744341\pi$
$740$		0			0
$741$	41.5469	−	30.1856i	1.52626	−	1.10890i
$742$		0			0
$743$	−15.2722	−	4.96223i	−0.560281	−	0.182046i	0.0151663	−	0.999885i	$-0.495172\pi$
$743$	−15.2722	−	4.96223i	−0.560281	−	0.182046i	−0.575448	+	0.817838i	$0.695172\pi$
$744$		0			0
$745$	7.82873	−	6.55442i	0.286822	−	0.240136i
$746$		0			0
$747$			54.3868i			1.98991i
$748$		0			0
$749$	18.7736			0.685971
$750$		0			0
$751$	1.58907	+	1.15452i	0.0579859	+	0.0421292i	0.616401	−	0.787433i	$-0.288590\pi$
$751$	1.58907	+	1.15452i	0.0579859	+	0.0421292i	−0.558415	+	0.829562i	$0.688590\pi$
$752$		0			0
$753$	−44.3204	−	14.4006i	−1.61512	−	0.524786i
$754$		0			0
$755$	11.5022	+	28.5594i	0.418609	+	1.03938i
$756$		0			0
$757$	30.8321	−	10.0180i	1.12061	−	0.364109i	0.310612	−	0.950537i	$-0.399466\pi$
$757$	30.8321	−	10.0180i	1.12061	−	0.364109i	0.810002	+	0.586428i	$0.199466\pi$
$758$		0			0
$759$	5.43151	−	2.79571i	0.197151	−	0.101478i
$760$		0			0
$761$	−14.6289	−	45.0230i	−0.530296	−	1.63208i	−0.753599	−	0.657334i	$-0.771684\pi$
$761$	−14.6289	−	45.0230i	−0.530296	−	1.63208i	0.223303	−	0.974749i	$-0.428316\pi$
$762$		0			0
$763$	−9.90869	−	13.6381i	−0.358719	−	0.493734i
$764$		0			0
$765$	−3.44706	+	5.50298i	−0.124629	+	0.198961i
$766$		0			0
$767$	−16.5672	+	22.8028i	−0.598208	+	0.823362i
$768$		0			0
$769$	17.6637			0.636969			0.318485	−	0.947928i	$-0.396826\pi$
$769$	17.6637			0.636969			0.318485	+	0.947928i	$0.396826\pi$
$770$		0			0
$771$	36.9586			1.33103
$772$		0			0
$773$	−17.8124	+	24.5166i	−0.640666	+	0.881801i	−0.998651	−	0.0519265i	$-0.983464\pi$
$773$	−17.8124	+	24.5166i	−0.640666	+	0.881801i	0.357985	+	0.933727i	$0.383464\pi$
$774$		0			0
$775$	23.1196	−	22.2283i	0.830480	−	0.798463i
$776$		0			0
$777$	−3.05249	−	4.20139i	−0.109507	−	0.150724i
$778$		0			0
$779$	14.0436	+	43.2218i	0.503165	+	1.54858i
$780$		0			0
$781$	−3.55247	−	3.52335i	−0.127117	−	0.126075i
$782$		0			0
$783$	−21.0799	+	6.84929i	−0.753335	+	0.244774i
$784$		0			0
$785$	9.01814	−	3.63204i	0.321871	−	0.129633i
$786$		0			0
$787$	40.1295	+	13.0389i	1.43046	+	0.464785i	0.918910	−	0.394467i	$-0.129071\pi$
$787$	40.1295	+	13.0389i	1.43046	+	0.464785i	0.511552	+	0.859252i	$0.329071\pi$
$788$		0			0
$789$	2.82810	+	2.05474i	0.100683	+	0.0731506i
$790$		0			0
$791$	−10.1971			−0.362569
$792$		0			0
$793$			72.1484i			2.56207i
$794$		0			0
$795$	61.7166	−	51.6708i	2.18886	−	1.83257i
$796$		0			0
$797$	−20.3023	−	6.59662i	−0.719145	−	0.233664i	−0.0734924	−	0.997296i	$-0.523414\pi$
$797$	−20.3023	−	6.59662i	−0.719145	−	0.233664i	−0.645652	+	0.763632i	$0.723414\pi$
$798$		0			0
$799$	−4.88486	+	3.54906i	−0.172814	+	0.125557i
$800$		0			0
$801$	−2.47455	−	7.61590i	−0.0874341	−	0.269094i
$802$		0			0
$803$	−27.2969	+	4.43864i	−0.963288	+	0.156636i
$804$		0			0
$805$	2.57780	−	0.177409i	0.0908553	−	0.00625283i
$806$		0			0
$807$	22.9942	+	31.6487i	0.809433	+	1.11409i
$808$		0			0
$809$	6.33703	−	19.5034i	0.222798	−	0.685702i	−0.775710	−	0.631090i	$-0.782608\pi$
$809$	6.33703	−	19.5034i	0.222798	−	0.685702i	0.998508	−	0.0546119i	$-0.0173922\pi$
$810$		0			0
$811$	−2.20327	−	1.60077i	−0.0773674	−	0.0562107i	0.548429	−	0.836197i	$-0.315226\pi$
$811$	−2.20327	−	1.60077i	−0.0773674	−	0.0562107i	−0.625797	+	0.779986i	$0.715226\pi$
$812$		0			0
$813$			25.7844i			0.904298i
$814$		0			0
$815$	−1.20672	−	0.302279i	−0.0422696	−	0.0105884i
$816$		0			0
$817$	13.3129	−	18.3237i	0.465761	−	0.641065i
$818$		0			0
$819$	−11.1721	+	34.3841i	−0.390384	+	1.20148i
$820$		0			0
$821$	9.22131	−	6.69968i	0.321826	−	0.233820i	−0.415128	−	0.909763i	$-0.636263\pi$
$821$	9.22131	−	6.69968i	0.321826	−	0.233820i	0.736954	+	0.675943i	$0.236263\pi$
$822$		0			0
$823$	45.1364	−	14.6657i	1.57336	−	0.511215i	0.613023	−	0.790065i	$-0.289953\pi$
$823$	45.1364	−	14.6657i	1.57336	−	0.511215i	0.960335	+	0.278850i	$0.0899533\pi$
$824$		0			0
$825$	−27.1563	+	36.1817i	−0.945461	+	1.25968i
$826$		0			0
$827$	19.1572	−	6.22456i	0.666162	−	0.216449i	0.0436349	−	0.999048i	$-0.486106\pi$
$827$	19.1572	−	6.22456i	0.666162	−	0.216449i	0.622527	+	0.782598i	$0.286106\pi$
$828$		0			0
$829$	−5.35298	+	3.88917i	−0.185917	+	0.135076i	−0.676851	−	0.736120i	$-0.736656\pi$
$829$	−5.35298	+	3.88917i	−0.185917	+	0.135076i	0.490934	+	0.871197i	$0.336656\pi$
$830$		0			0
$831$	−9.87154	+	30.3815i	−0.342440	+	1.05392i
$832$		0			0
$833$	1.56421	−	2.15295i	0.0541968	−	0.0745955i
$834$		0			0
$835$	10.1864	+	2.55167i	0.352517	+	0.0883041i
$836$		0			0
$837$			25.2347i			0.872238i
$838$		0			0
$839$	8.05951	+	5.85558i	0.278245	+	0.202157i	0.718152	−	0.695887i	$-0.244988\pi$
$839$	8.05951	+	5.85558i	0.278245	+	0.202157i	−0.439906	+	0.898044i	$0.644988\pi$
$840$		0			0
$841$	0.847493	−	2.60831i	0.0292239	−	0.0899419i
$842$		0			0
$843$	4.52204	+	6.22405i	0.155747	+	0.214368i
$844$		0			0
$845$	−21.4460	+	1.47595i	−0.737764	+	0.0507743i
$846$		0			0
$847$	−5.67016	+	17.9524i	−0.194829	+	0.616852i
$848$		0			0
$849$	1.55532	+	4.78679i	0.0533786	+	0.164282i
$850$		0			0
$851$	0.607544	−	0.441407i	0.0208264	−	0.0151312i
$852$		0			0
$853$	24.1549	+	7.84842i	0.827049	+	0.268725i	0.691802	−	0.722087i	$-0.256817\pi$
$853$	24.1549	+	7.84842i	0.827049	+	0.268725i	0.135247	+	0.990812i	$0.456817\pi$
$854$		0			0
$855$	−30.1492	+	25.2417i	−1.03108	+	0.863249i
$856$		0			0
$857$		−	43.5351i		−	1.48713i	−0.668663	−	0.743566i	$-0.733133\pi$
$857$		−	43.5351i		−	1.48713i	0.668663	−	0.743566i	$-0.266867\pi$
$858$		0			0
$859$	−41.3539			−1.41098			−0.705489	−	0.708721i	$-0.749272\pi$
$859$	−41.3539			−1.41098			−0.705489	+	0.708721i	$0.749272\pi$
$860$		0			0
$861$	−43.3643	−	31.5060i	−1.47785	−	1.07372i
$862$		0			0
$863$	−15.3460	−	4.98621i	−0.522383	−	0.169733i	0.0359435	−	0.999354i	$-0.488556\pi$
$863$	−15.3460	−	4.98621i	−0.522383	−	0.169733i	−0.558327	+	0.829621i	$0.688556\pi$
$864$		0			0
$865$	−25.8790	+	10.4227i	−0.879912	+	0.354382i
$866$		0			0
$867$	−42.9977	+	13.9708i	−1.46028	+	0.474473i
$868$		0			0
$869$	28.4276	+	4.38265i	0.964341	+	0.148671i
$870$		0			0
$871$	15.7108	+	48.3529i	0.532340	+	1.63837i
$872$		0			0
$873$	−27.9619	−	38.4863i	−0.946367	−	1.30256i
$874$		0			0
$875$	−16.6031	+	9.51289i	−0.561286	+	0.321594i
$876$		0			0
$877$	−25.6803	+	35.3458i	−0.867161	+	1.19354i	0.112654	+	0.993634i	$0.464065\pi$
$877$	−25.6803	+	35.3458i	−0.867161	+	1.19354i	−0.979814	+	0.199910i	$0.935935\pi$
$878$		0			0
$879$	10.2343			0.345194
$880$		0			0
$881$	51.4721			1.73414			0.867069	−	0.498187i	$-0.166001\pi$
$881$	51.4721			1.73414			0.867069	+	0.498187i	$0.166001\pi$
$882$		0			0
$883$	−24.7534	+	34.0702i	−0.833019	+	1.14655i	0.154334	+	0.988019i	$0.450677\pi$
$883$	−24.7534	+	34.0702i	−0.833019	+	1.14655i	−0.987354	+	0.158534i	$0.949323\pi$
$884$		0			0
$885$	19.1934	−	30.6408i	0.645179	−	1.02998i
$886$		0			0
$887$	23.2383	+	31.9847i	0.780265	+	1.07394i	0.995253	+	0.0973254i	$0.0310288\pi$
$887$	23.2383	+	31.9847i	0.780265	+	1.07394i	−0.214988	+	0.976617i	$0.568971\pi$
$888$		0			0
$889$	−9.19032	−	28.2849i	−0.308233	−	0.948645i
$890$		0			0
$891$	1.38085	+	8.49201i	0.0462602	+	0.284493i
$892$		0			0
$893$	−34.7733	+	11.2985i	−1.16365	+	0.378091i
$894$		0			0
$895$	16.0725	+	39.9071i	0.537244	+	1.33395i
$896$		0			0
$897$	−8.33010	−	2.70661i	−0.278134	−	0.0903711i
$898$		0			0
$899$	−29.2371	−	21.2420i	−0.975111	−	0.708460i
$900$		0			0
$901$	−8.62617			−0.287379
$902$		0			0
$903$			26.7136i			0.888974i
$904$		0			0
$905$	1.07381	−	0.899026i	0.0356948	−	0.0298846i
$906$		0			0
$907$	−0.0864398	−	0.0280860i	−0.00287018	−	0.000932580i	0.307582	−	0.951522i	$-0.400480\pi$
$907$	−0.0864398	−	0.0280860i	−0.00287018	−	0.000932580i	−0.310452	+	0.950589i	$0.600480\pi$
$908$		0			0
$909$	−32.7480	+	23.7928i	−1.08618	+	0.789159i
$910$		0			0
$911$	14.4946	+	44.6097i	0.480227	+	1.47799i	0.838777	+	0.544476i	$0.183271\pi$
$911$	14.4946	+	44.6097i	0.480227	+	1.47799i	−0.358550	+	0.933511i	$0.616729\pi$
$912$		0			0
$913$	28.5951	−	28.8315i	0.946361	−	0.954183i
$914$		0			0
$915$	−6.35440	−	92.3312i	−0.210070	−	3.05238i
$916$		0			0
$917$	−3.86999	−	5.32658i	−0.127798	−	0.175899i
$918$		0			0
$919$	−7.67481	+	23.6206i	−0.253169	+	0.779173i	0.741016	+	0.671487i	$0.234344\pi$
$919$	−7.67481	+	23.6206i	−0.253169	+	0.779173i	−0.994185	+	0.107686i	$0.965656\pi$
$920$		0			0
$921$	−17.6517	−	12.8247i	−0.581644	−	0.422589i
$922$		0			0
$923$			7.17388i			0.236131i
$924$		0			0
$925$	−2.62168	+	4.90462i	−0.0862004	+	0.161263i
$926$		0			0
$927$	−20.0406	+	27.5835i	−0.658219	+	0.905961i
$928$		0			0
$929$	−14.7623	+	45.4336i	−0.484334	+	1.49063i	0.348608	+	0.937268i	$0.386654\pi$
$929$	−14.7623	+	45.4336i	−0.484334	+	1.49063i	−0.832943	+	0.553359i	$0.813346\pi$
$930$		0			0
$931$	13.0371	−	9.47199i	0.427273	−	0.310432i
$932$		0			0
$933$	32.7454	−	10.6396i	1.07204	−	0.348326i
$934$		0			0
$935$	4.72067	−	1.10486i	0.154383	−	0.0361328i
$936$		0			0
$937$	12.2414	−	3.97746i	0.399908	−	0.129938i	−0.102156	−	0.994768i	$-0.532574\pi$
$937$	12.2414	−	3.97746i	0.399908	−	0.129938i	0.502064	+	0.864830i	$0.332574\pi$
$938$		0			0
$939$	−27.3713	+	19.8864i	−0.893227	+	0.648968i
$940$		0			0
$941$	5.45583	−	16.7913i	0.177855	−	0.547381i	−0.821898	−	0.569635i	$-0.807084\pi$
$941$	5.45583	−	16.7913i	0.177855	−	0.547381i	0.999752	+	0.0222545i	$0.00708442\pi$
$942$		0			0
$943$	4.55594	−	6.27071i	0.148362	−	0.204203i
$944$		0			0
$945$	3.65841	−	14.6046i	0.119008	−	0.475088i
$946$		0			0
$947$		−	31.2112i		−	1.01423i	−0.861879	−	0.507114i	$-0.830712\pi$
$947$		−	31.2112i		−	1.01423i	0.861879	−	0.507114i	$-0.169288\pi$
$948$		0			0
$949$	32.0795	+	23.3071i	1.04134	+	0.756580i
$950$		0			0
$951$	2.39037	−	7.35680i	0.0775131	−	0.238561i
$952$		0			0
$953$	−16.2877	−	22.4181i	−0.527609	−	0.726192i	0.459154	−	0.888357i	$-0.348152\pi$
$953$	−16.2877	−	22.4181i	−0.527609	−	0.726192i	−0.986764	+	0.162164i	$0.948152\pi$
$954$		0			0
$955$	−18.5124	+	1.27406i	−0.599048	+	0.0412276i
$956$		0			0
$957$	45.5147	+	22.9555i	1.47128	+	0.742045i
$958$		0			0
$959$	4.28710	+	13.1943i	0.138438	+	0.426067i
$960$		0			0
$961$	−8.20701	+	5.96274i	−0.264742	+	0.192346i
$962$		0			0
$963$	46.3407	+	15.0570i	1.49331	+	0.485205i
$964$		0			0
$965$	0.0271519	+	0.0324307i	0.000874051	+	0.00104398i
$966$		0			0
$967$		−	30.3110i		−	0.974736i	−0.873197	−	0.487368i	$-0.837957\pi$
$967$		−	30.3110i		−	0.974736i	0.873197	−	0.487368i	$-0.162043\pi$
$968$		0			0
$969$	7.05991			0.226797
$970$		0			0
$971$	30.0208	+	21.8114i	0.963413	+	0.699961i	0.953941	−	0.299995i	$-0.0969849\pi$
$971$	30.0208	+	21.8114i	0.963413	+	0.699961i	0.00947210	+	0.999955i	$0.496985\pi$
$972$		0			0
$973$	32.5706	+	10.5828i	1.04416	+	0.339269i
$974$		0			0
$975$	64.2523	−	8.88601i	2.05772	−	0.284580i
$976$		0			0
$977$	−11.5190	+	3.74276i	−0.368527	+	0.119742i	−0.487425	−	0.873165i	$-0.662064\pi$
$977$	−11.5190	+	3.74276i	−0.368527	+	0.119742i	0.118898	+	0.992906i	$0.462064\pi$
$978$		0			0
$979$	−2.69243	+	5.33839i	−0.0860504	+	0.170616i
$980$		0			0
$981$	−13.5204	−	41.6115i	−0.431673	−	1.32855i
$982$		0			0
$983$	7.44647	+	10.2492i	0.237506	+	0.326898i	0.911087	−	0.412215i	$-0.135245\pi$
$983$	7.44647	+	10.2492i	0.237506	+	0.326898i	−0.673581	+	0.739113i	$0.735245\pi$
$984$		0			0
$985$	3.00904	−	4.80371i	0.0958760	−	0.153059i
$986$		0			0
$987$	25.3476	−	34.8879i	0.806822	−	1.11050i
$988$		0			0
$989$	−3.86294			−0.122834
$990$		0			0
$991$	8.30199			0.263721			0.131861	−	0.991268i	$-0.457905\pi$
$991$	8.30199			0.263721			0.131861	+	0.991268i	$0.457905\pi$
$992$		0			0
$993$	−22.4504	+	30.9003i	−0.712442	+	0.980592i
$994$		0			0
$995$	−27.6859	−	17.3425i	−0.877704	−	0.549793i
$996$		0			0
$997$	−22.2050	−	30.5626i	−0.703241	−	0.967928i	−0.999916	−	0.0129494i	$-0.995878\pi$
$997$	−22.2050	−	30.5626i	−0.703241	−	0.967928i	0.296676	−	0.954978i	$-0.404122\pi$
$998$		0			0
$999$	−1.35218	−	4.16158i	−0.0427810	−	0.131666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.t.a.49.6	yes	24
4.3	odd	2		880.2.cd.d.49.1		24
5.2	odd	4		1100.2.n.f.401.1		24
5.3	odd	4		1100.2.n.f.401.6		24
5.4	even	2	inner	220.2.t.a.49.1	yes	24
11.3	even	5		2420.2.b.i.969.11		12
11.8	odd	10		2420.2.b.h.969.11		12
11.9	even	5	inner	220.2.t.a.9.1	✓	24
20.19	odd	2		880.2.cd.d.49.6		24
44.31	odd	10		880.2.cd.d.449.6		24
55.9	even	10	inner	220.2.t.a.9.6	yes	24
55.14	even	10		2420.2.b.i.969.2		12
55.19	odd	10		2420.2.b.h.969.2		12
55.42	odd	20		1100.2.n.f.801.1		24
55.53	odd	20		1100.2.n.f.801.6		24
220.119	odd	10		880.2.cd.d.449.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.t.a.9.1	✓	24	11.9	even	5	inner
220.2.t.a.9.6	yes	24	55.9	even	10	inner
220.2.t.a.49.1	yes	24	5.4	even	2	inner
220.2.t.a.49.6	yes	24	1.1	even	1	trivial
880.2.cd.d.49.1		24	4.3	odd	2
880.2.cd.d.49.6		24	20.19	odd	2
880.2.cd.d.449.1		24	220.119	odd	10
880.2.cd.d.449.6		24	44.31	odd	10
1100.2.n.f.401.1		24	5.2	odd	4
1100.2.n.f.401.6		24	5.3	odd	4
1100.2.n.f.801.1		24	55.42	odd	20
1100.2.n.f.801.6		24	55.53	odd	20
2420.2.b.h.969.2		12	55.19	odd	10
2420.2.b.h.969.11		12	11.8	odd	10
2420.2.b.i.969.2		12	55.14	even	10
2420.2.b.i.969.11		12	11.3	even	5

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.t (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60349 - 2.20702i) q^{3} +(-1.89499 - 1.18702i) q^{5} +(-1.00600 - 1.38464i) q^{7} +(-1.37268 - 4.22469i) q^{9} +(-1.49354 + 2.96131i) q^{11} +(4.52263 - 1.46949i) q^{13} +(-5.65837 + 2.27889i) q^{15} +(0.621741 + 0.202016i) q^{17} +(3.20263 + 2.32684i) q^{19} -4.66902 q^{21} -0.675167i q^{23} +(2.18197 + 4.49878i) q^{25} +(-3.74152 - 1.21569i) q^{27} +(4.55804 - 3.31161i) q^{29} +(-1.98216 - 6.10045i) q^{31} +(4.14077 + 8.04469i) q^{33} +(0.262763 + 3.81801i) q^{35} +(0.653775 + 0.899844i) q^{37} +(4.00881 - 12.3378i) q^{39} +(9.28765 + 6.74788i) q^{41} -5.72146i q^{43} +(-2.41357 + 9.63513i) q^{45} +(-5.42888 + 7.47221i) q^{47} +(1.25793 - 3.87151i) q^{49} +(1.44281 - 1.04826i) q^{51} +(-12.5493 + 4.07753i) q^{53} +(6.34537 - 3.83878i) q^{55} +(10.2708 - 3.33717i) q^{57} +(-4.79516 + 3.48389i) q^{59} +(-4.68840 + 14.4294i) q^{61} +(-4.46874 + 6.15069i) q^{63} +(-10.3147 - 2.58378i) q^{65} +10.6913i q^{67} +(-1.49010 - 1.08262i) q^{69} +(-0.466178 + 1.43475i) q^{71} +(4.90121 + 6.74593i) q^{73} +(13.4276 + 2.39812i) q^{75} +(5.60284 - 0.911054i) q^{77} +(-2.67995 - 8.24805i) q^{79} +(2.09864 - 1.52475i) q^{81} +(-11.6443 - 3.78345i) q^{83} +(-0.938396 - 1.12084i) q^{85} -15.3698i q^{87} +1.80271 q^{89} +(-6.58448 - 4.78390i) q^{91} +(-16.6422 - 5.40736i) q^{93} +(-3.30693 - 8.21092i) q^{95} +(10.1851 - 3.30935i) q^{97} +(14.5607 + 2.24481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{5} + 14 q^{9} - 2 q^{11} - q^{15} + 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} - 26 q^{31} + 17 q^{35} + 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} - 12 q^{51} - 33 q^{55} - 48 q^{59} - 10 q^{61}+ \cdots + 156 q^{99}+O(q^{100}) \) 24 * q + q^5 + 14 * q^9 - 2 * q^11 - q^15 + 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 - 26 * q^31 + 17 * q^35 + 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 - 12 * q^51 - 33 * q^55 - 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 + 42 * q^71 - 17 * q^75 - 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 + 10 * q^91 + 67 * q^95 + 156 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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