LMFDB - Embedded newform 864.2.bn.a.35.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(35,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.3
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36587 + 0.366606i) q^{2} +(1.73120 - 1.00147i) q^{4} +(-0.924826 - 0.709644i) q^{5} +(1.85343 - 0.496625i) q^{7} +(-1.99745 + 2.00255i) q^{8} +(1.52335 + 0.630235i) q^{10} +(0.637333 - 4.84102i) q^{11} +(-2.65706 + 0.349808i) q^{13} +(-2.34948 + 1.35780i) q^{14} +(1.99411 - 3.46749i) q^{16} -4.48513 q^{17} +(1.00431 + 0.415998i) q^{19} +(-2.31175 - 0.302350i) q^{20} +(0.904232 + 6.84586i) q^{22} +(0.0881758 - 0.329076i) q^{23} +(-0.942386 - 3.51703i) q^{25} +(3.50095 - 1.45188i) q^{26} +(2.71130 - 2.71591i) q^{28} +(3.56729 + 4.64898i) q^{29} +(-4.83932 + 2.79398i) q^{31} +(-1.45250 + 5.46720i) q^{32} +(6.12611 - 1.64427i) q^{34} +(-2.06653 - 0.855983i) q^{35} +(-2.90428 - 7.01154i) q^{37} +(-1.52426 - 0.200014i) q^{38} +(3.26839 - 0.434529i) q^{40} +(3.68584 + 0.987619i) q^{41} +(-11.7865 - 1.55172i) q^{43} +(-3.74479 - 9.01905i) q^{44} +(0.000204623 + 0.481801i) q^{46} +(3.25721 + 1.88055i) q^{47} +(-2.87362 + 1.65908i) q^{49} +(2.57654 + 4.45833i) q^{50} +(-4.24958 + 3.26655i) q^{52} +(-3.91618 - 9.45448i) q^{53} +(-4.02483 + 4.02483i) q^{55} +(-2.70762 + 4.70356i) q^{56} +(-6.57680 - 5.04212i) q^{58} +(-0.584963 + 0.762339i) q^{59} +(9.47057 - 7.26703i) q^{61} +(5.58560 - 5.59034i) q^{62} +(-0.0203858 - 7.99997i) q^{64} +(2.70555 + 1.56205i) q^{65} +(-2.51153 + 0.330649i) q^{67} +(-7.76466 + 4.49173i) q^{68} +(3.13641 + 0.411562i) q^{70} +(-6.68291 + 6.68291i) q^{71} +(-0.787037 - 0.787037i) q^{73} +(6.53733 + 8.51213i) q^{74} +(2.15527 - 0.285609i) q^{76} +(-1.22292 - 9.28901i) q^{77} +(3.18314 - 5.51337i) q^{79} +(-4.30489 + 1.79172i) q^{80} +(-5.39645 + 0.00229190i) q^{82} +(-11.0027 - 14.3389i) q^{83} +(4.14797 + 3.18285i) q^{85} +(16.6676 - 2.20154i) q^{86} +(8.42133 + 10.9460i) q^{88} +(-2.96906 - 2.96906i) q^{89} +(-4.75094 + 1.96790i) q^{91} +(-0.176911 - 0.658003i) q^{92} +(-5.13835 - 1.37448i) q^{94} +(-0.633600 - 1.09743i) q^{95} +(-1.67561 + 2.90224i) q^{97} +(3.31676 - 3.31958i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.36587	+	0.366606i	−0.965816	+	0.259229i
$2$	−1.36587	+	0.366606i	−0.965816	+	0.259229i
$3$		0			0
$3$		0			0
$4$	1.73120	−	1.00147i	0.865600	−	0.500735i
$5$	−0.924826	−	0.709644i	−0.413595	−	0.317363i	0.380919	−	0.924608i	$-0.375608\pi$
$5$	−0.924826	−	0.709644i	−0.413595	−	0.317363i	−0.794514	+	0.607246i	$0.792274\pi$
$6$		0			0
$7$	1.85343	−	0.496625i	0.700530	−	0.187706i	0.109062	−	0.994035i	$-0.465215\pi$
$7$	1.85343	−	0.496625i	0.700530	−	0.187706i	0.591468	+	0.806328i	$0.298549\pi$
$8$	−1.99745	+	2.00255i	−0.706205	+	0.708007i
$9$		0			0
$10$	1.52335	+	0.630235i	0.481726	+	0.199298i
$11$	0.637333	−	4.84102i	0.192163	−	1.45962i	−0.574990	−	0.818160i	$-0.694994\pi$
$11$	0.637333	−	4.84102i	0.192163	−	1.45962i	0.767154	−	0.641463i	$-0.221672\pi$
$12$		0			0
$13$	−2.65706	+	0.349808i	−0.736935	+	0.0970193i	−0.489645	−	0.871922i	$-0.662873\pi$
$13$	−2.65706	+	0.349808i	−0.736935	+	0.0970193i	−0.247290	+	0.968941i	$0.579540\pi$
$14$	−2.34948	+	1.35780i	−0.627924	+	0.362888i
$15$		0			0
$16$	1.99411	−	3.46749i	0.498528	−	0.866874i
$17$	−4.48513			−1.08780			−0.543902	−	0.839149i	$-0.683054\pi$
$17$	−4.48513			−1.08780			−0.543902	+	0.839149i	$0.683054\pi$
$18$		0			0
$19$	1.00431	+	0.415998i	0.230404	+	0.0954365i	0.494899	−	0.868951i	$-0.335205\pi$
$19$	1.00431	+	0.415998i	0.230404	+	0.0954365i	−0.264495	+	0.964387i	$0.585205\pi$
$20$	−2.31175	−	0.302350i	−0.516923	−	0.0676075i
$21$		0			0
$22$	0.904232	+	6.84586i	0.192783	+	1.45954i
$23$	0.0881758	−	0.329076i	0.0183859	−	0.0686172i	−0.956123	−	0.292964i	$-0.905358\pi$
$23$	0.0881758	−	0.329076i	0.0183859	−	0.0686172i	0.974509	+	0.224347i	$0.0720249\pi$
$24$		0			0
$25$	−0.942386	−	3.51703i	−0.188477	−	0.703407i
$26$	3.50095	−	1.45188i	0.686593	−	0.284738i
$27$		0			0
$28$	2.71130	−	2.71591i	0.512388	−	0.513259i
$29$	3.56729	+	4.64898i	0.662429	+	0.863295i	0.996865	−	0.0791239i	$-0.0252123\pi$
$29$	3.56729	+	4.64898i	0.662429	+	0.863295i	−0.334435	+	0.942419i	$0.608546\pi$
$30$		0			0
$31$	−4.83932	+	2.79398i	−0.869168	+	0.501814i	−0.867072	−	0.498183i	$-0.834001\pi$
$31$	−4.83932	+	2.79398i	−0.869168	+	0.501814i	−0.00209645	+	0.999998i	$0.500667\pi$
$32$	−1.45250	+	5.46720i	−0.256767	+	0.966473i
$33$		0			0
$34$	6.12611	−	1.64427i	1.05062	−	0.281991i
$35$	−2.06653	−	0.855983i	−0.349307	−	0.144688i
$36$		0			0
$37$	−2.90428	−	7.01154i	−0.477460	−	1.15269i	−0.960796	−	0.277255i	$-0.910575\pi$
$37$	−2.90428	−	7.01154i	−0.477460	−	1.15269i	0.483336	−	0.875435i	$-0.339425\pi$
$38$	−1.52426	−	0.200014i	−0.247268	−	0.0324466i
$39$		0			0
$40$	3.26839	−	0.434529i	0.516778	−	0.0687051i
$41$	3.68584	+	0.987619i	0.575632	+	0.154240i	0.534878	−	0.844929i	$-0.320357\pi$
$41$	3.68584	+	0.987619i	0.575632	+	0.154240i	0.0407537	+	0.999169i	$0.487024\pi$
$42$		0			0
$43$	−11.7865	−	1.55172i	−1.79742	−	0.236635i	−0.843591	−	0.536986i	$-0.819563\pi$
$43$	−11.7865	−	1.55172i	−1.79742	−	0.236635i	−0.953829	+	0.300352i	$0.902896\pi$
$44$	−3.74479	−	9.01905i	−0.564549	−	1.35967i
$45$		0			0
$46$	0.000204623		0.481801i	3.01700e−5		0.0710377i
$47$	3.25721	+	1.88055i	0.475114	+	0.274307i	0.718378	−	0.695653i	$-0.244885\pi$
$47$	3.25721	+	1.88055i	0.475114	+	0.274307i	−0.243264	+	0.969960i	$0.578218\pi$
$48$		0			0
$49$	−2.87362	+	1.65908i	−0.410517	+	0.237012i
$50$	2.57654	+	4.45833i	0.364378	+	0.630503i
$51$		0			0
$52$	−4.24958	+	3.26655i	−0.589310	+	0.452989i
$53$	−3.91618	−	9.45448i	−0.537928	−	1.29867i	−0.926167	−	0.377114i	$-0.876916\pi$
$53$	−3.91618	−	9.45448i	−0.537928	−	1.29867i	0.388239	−	0.921559i	$-0.373084\pi$
$54$		0			0
$55$	−4.02483	+	4.02483i	−0.542708	+	0.542708i
$56$	−2.70762	+	4.70356i	−0.361821	+	0.628540i
$57$		0			0
$58$	−6.57680	−	5.04212i	−0.863576	−	0.662063i
$59$	−0.584963	+	0.762339i	−0.0761557	+	0.0992480i	−0.829878	−	0.557945i	$-0.811590\pi$
$59$	−0.584963	+	0.762339i	−0.0761557	+	0.0992480i	0.753722	+	0.657193i	$0.228257\pi$
$60$		0			0
$61$	9.47057	−	7.26703i	1.21258	−	0.930447i	0.213662	−	0.976908i	$-0.431461\pi$
$61$	9.47057	−	7.26703i	1.21258	−	0.930447i	0.998920	+	0.0464603i	$0.0147941\pi$
$62$	5.58560	−	5.59034i	0.709371	−	0.709974i
$63$		0			0
$64$	−0.0203858	−	7.99997i	−0.00254822	−	0.999997i
$65$	2.70555	+	1.56205i	0.335583	+	0.193749i
$66$		0			0
$67$	−2.51153	+	0.330649i	−0.306832	+	0.0403952i	−0.282370	−	0.959306i	$-0.591121\pi$
$67$	−2.51153	+	0.330649i	−0.306832	+	0.0403952i	−0.0244620	+	0.999701i	$0.507787\pi$
$68$	−7.76466	+	4.49173i	−0.941604	+	0.544702i
$69$		0			0
$70$	3.13641	+	0.411562i	0.374873	+	0.0491910i
$71$	−6.68291	+	6.68291i	−0.793115	+	0.793115i	−0.981999	−	0.188884i	$-0.939513\pi$
$71$	−6.68291	+	6.68291i	−0.793115	+	0.793115i	0.188884	+	0.981999i	$0.439513\pi$
$72$		0			0
$73$	−0.787037	−	0.787037i	−0.0921157	−	0.0921157i	0.659547	−	0.751663i	$-0.270748\pi$
$73$	−0.787037	−	0.787037i	−0.0921157	−	0.0921157i	−0.751663	+	0.659547i	$0.770748\pi$
$74$	6.53733	+	8.51213i	0.759949	+	0.989515i
$75$		0			0
$76$	2.15527	−	0.285609i	0.247226	−	0.0327616i
$77$	−1.22292	−	9.28901i	−0.139365	−	1.05858i
$78$		0			0
$79$	3.18314	−	5.51337i	0.358132	−	0.620302i	−0.629517	−	0.776987i	$-0.716747\pi$
$79$	3.18314	−	5.51337i	0.358132	−	0.620302i	0.987649	+	0.156684i	$0.0500805\pi$
$80$	−4.30489	+	1.79172i	−0.481302	+	0.200320i
$81$		0			0
$82$	−5.39645	+	0.00229190i	−0.595938	+	0.000253098i
$83$	−11.0027	−	14.3389i	−1.20770	−	1.57390i	−0.704432	−	0.709772i	$-0.748798\pi$
$83$	−11.0027	−	14.3389i	−1.20770	−	1.57390i	−0.503266	−	0.864131i	$-0.667869\pi$
$84$		0			0
$85$	4.14797	+	3.18285i	0.449910	+	0.345228i
$86$	16.6676	−	2.20154i	1.79732	−	0.237398i
$87$		0			0
$88$	8.42133	+	10.9460i	0.897717	+	1.16685i
$89$	−2.96906	−	2.96906i	−0.314720	−	0.314720i	0.532015	−	0.846735i	$-0.321435\pi$
$89$	−2.96906	−	2.96906i	−0.314720	−	0.314720i	−0.846735	+	0.532015i	$0.821435\pi$
$90$		0			0
$91$	−4.75094	+	1.96790i	−0.498034	+	0.206292i
$92$	−0.176911	−	0.658003i	−0.0184442	−	0.0686015i
$93$		0			0
$94$	−5.13835	−	1.37448i	−0.529981	−	0.141767i
$95$	−0.633600	−	1.09743i	−0.0650060	−	0.112594i
$96$		0			0
$97$	−1.67561	+	2.90224i	−0.170132	+	0.294678i	−0.938466	−	0.345372i	$-0.887753\pi$
$97$	−1.67561	+	2.90224i	−0.170132	+	0.294678i	0.768334	+	0.640049i	$0.221086\pi$
$98$	3.31676	−	3.31958i	0.335043	−	0.335328i
$99$		0			0
$100$	−5.15367	−	5.14492i	−0.515367	−	0.514492i
$101$	1.63476	−	12.4173i	0.162665	−	1.23556i	−0.694108	−	0.719871i	$-0.744201\pi$
$101$	1.63476	−	12.4173i	0.162665	−	1.23556i	0.856773	−	0.515694i	$-0.172466\pi$
$102$		0			0
$103$	1.01900	−	3.80296i	0.100405	−	0.374717i	−0.897378	−	0.441262i	$-0.854531\pi$
$103$	1.01900	−	3.80296i	0.100405	−	0.374717i	0.997783	+	0.0665452i	$0.0211977\pi$
$104$	4.60683	−	6.01960i	0.451737	−	0.590271i
$105$		0			0
$106$	8.81505	+	11.4779i	0.856194	+	1.11483i
$107$	10.9410	−	4.53190i	1.05770	−	0.438115i	0.215068	−	0.976599i	$-0.431003\pi$
$107$	10.9410	−	4.53190i	1.05770	−	0.438115i	0.842636	+	0.538484i	$0.181003\pi$
$108$		0			0
$109$	5.21100	−	12.5805i	0.499124	−	1.20499i	−0.450833	−	0.892608i	$-0.648873\pi$
$109$	5.21100	−	12.5805i	0.499124	−	1.20499i	0.949956	−	0.312383i	$-0.101127\pi$
$110$	4.02187	−	6.97291i	0.383470	−	0.664841i
$111$		0			0
$112$	1.97390	−	7.41708i	0.186516	−	0.700848i
$113$	−1.89610	−	3.28415i	−0.178370	−	0.308947i	0.762952	−	0.646455i	$-0.223749\pi$
$113$	−1.89610	−	3.28415i	−0.178370	−	0.308947i	−0.941323	+	0.337508i	$0.890416\pi$
$114$		0			0
$115$	−0.315074	+	0.241765i	−0.0293808	+	0.0225447i
$116$	10.8315	+	4.47579i	1.00568	+	0.415566i
$117$		0			0
$118$	0.519506	−	1.25571i	0.0478244	−	0.115597i
$119$	−8.31287	+	2.22743i	−0.762040	+	0.204188i
$120$		0			0
$121$	−12.4041	−	3.32368i	−1.12765	−	0.302152i
$122$	−10.2714	+	13.3978i	−0.929932	+	1.21298i
$123$		0			0
$124$	−5.57975	+	9.68339i	−0.501076	+	0.869594i
$125$	−3.85480	+	9.30632i	−0.344784	+	0.832383i
$126$		0			0
$127$		−	0.602538i		−	0.0534666i	−0.999643	−	0.0267333i	$-0.991490\pi$
$127$		−	0.602538i		−	0.0534666i	0.999643	−	0.0267333i	$-0.00851049\pi$
$128$	2.96068	+	10.9194i	0.261690	+	0.965152i
$129$		0			0
$130$	−4.26809	−	1.14169i	−0.374337	−	0.100133i
$131$	0.922112	+	7.00414i	0.0805653	+	0.611954i	0.983331	+	0.181823i	$0.0581996\pi$
$131$	0.922112	+	7.00414i	0.0805653	+	0.611954i	−0.902766	+	0.430132i	$0.858467\pi$
$132$		0			0
$133$	2.06801	+	0.272258i	0.179319	+	0.0236078i
$134$	3.30920	−	1.37236i	0.285872	−	0.118554i
$135$		0			0
$136$	8.95883	−	8.98168i	0.768213	−	0.770173i
$137$	−3.69237	−	13.7801i	−0.315461	−	1.17731i	−0.923560	−	0.383454i	$-0.874734\pi$
$137$	−3.69237	−	13.7801i	−0.315461	−	1.17731i	0.608099	−	0.793861i	$-0.291932\pi$
$138$		0			0
$139$	−4.76751	+	6.21314i	−0.404375	+	0.526992i	−0.950505	−	0.310708i	$-0.899434\pi$
$139$	−4.76751	+	6.21314i	−0.404375	+	0.526992i	0.546130	+	0.837700i	$0.316100\pi$
$140$	−4.43481	+	0.587687i	−0.374810	+	0.0496686i
$141$		0			0
$142$	6.67799	−	11.5780i	0.560405	−	0.971602i
$143$			13.0858i			1.09429i
$144$		0			0
$145$		−	6.83101i		−	0.567285i
$146$	1.36352	+	0.786458i	0.112846	+	0.0650877i
$147$		0			0
$148$	−12.0497	−	9.22984i	−0.990482	−	0.758688i
$149$	10.1226	−	13.1920i	0.829274	−	1.08073i	−0.166237	−	0.986086i	$-0.553162\pi$
$149$	10.1226	−	13.1920i	0.829274	−	1.08073i	0.995511	−	0.0946449i	$-0.0301716\pi$
$150$		0			0
$151$	2.59500	+	9.68466i	0.211178	+	0.788127i	0.987477	+	0.157762i	$0.0504279\pi$
$151$	2.59500	+	9.68466i	0.211178	+	0.788127i	−0.776299	+	0.630365i	$0.782905\pi$
$152$	−2.83911	+	1.18024i	−0.230282	+	0.0957300i
$153$		0			0
$154$	5.07575	+	12.2392i	0.409016	+	0.986266i
$155$	6.45827	+	0.850247i	0.518741	+	0.0682935i
$156$		0			0
$157$	2.93301	+	22.2784i	0.234080	+	1.77801i	0.555936	+	0.831225i	$0.312360\pi$
$157$	2.93301	+	22.2784i	0.234080	+	1.77801i	−0.321856	+	0.946789i	$0.604307\pi$
$158$	−2.32653	+	8.69750i	−0.185089	+	0.691936i
$159$		0			0
$160$	5.22307	−	4.02545i	0.412920	−	0.318240i
$161$		−	0.653710i		−	0.0515196i
$162$		0			0
$163$	−3.18448	+	7.68801i	−0.249428	+	0.602171i	−0.998156	−	0.0607058i	$-0.980665\pi$
$163$	−3.18448	+	7.68801i	−0.249428	+	0.602171i	0.748728	+	0.662877i	$0.230665\pi$
$164$	7.37001	−	1.98150i	0.575501	−	0.154729i
$165$		0			0
$166$	20.2849	+	15.5515i	1.57442	+	1.20703i
$167$	6.67910	+	1.78966i	0.516844	+	0.138488i	0.507806	−	0.861471i	$-0.330457\pi$
$167$	6.67910	+	1.78966i	0.516844	+	0.138488i	0.00903759	+	0.999959i	$0.497123\pi$
$168$		0			0
$169$	−5.61945	+	1.50573i	−0.432266	+	0.115825i
$170$	−6.83243	−	2.82669i	−0.524024	−	0.216797i
$171$		0			0
$172$	−21.9587	+	9.11747i	−1.67434	+	0.695200i
$173$	−5.99572	+	4.60068i	−0.455847	+	0.349783i	−0.811021	−	0.585017i	$-0.801088\pi$
$173$	−5.99572	+	4.60068i	−0.455847	+	0.349783i	0.355175	+	0.934800i	$0.384421\pi$
$174$		0			0
$175$	−3.49329	−	6.05056i	−0.264068	−	0.457379i
$176$	−15.5153	−	11.8635i	−1.16951	−	0.894244i
$177$		0			0
$178$	5.14382	+	2.96688i	0.385546	+	0.222377i
$179$	−8.90629	+	21.5017i	−0.665688	+	1.60711i	0.123063	+	0.992399i	$0.460728\pi$
$179$	−8.90629	+	21.5017i	−0.665688	+	1.60711i	−0.788751	+	0.614713i	$0.789272\pi$
$180$		0			0
$181$	23.2328	−	9.62335i	1.72688	−	0.715298i	0.727302	−	0.686318i	$-0.240774\pi$
$181$	23.2328	−	9.62335i	1.72688	−	0.715298i	0.999580	−	0.0289797i	$-0.00922581\pi$
$182$	5.76772	−	4.42962i	0.427532	−	0.328345i
$183$		0			0
$184$	0.482864	+	0.833890i	0.0355972	+	0.0614752i
$185$	−2.28975	+	8.54546i	−0.168346	+	0.628275i
$186$		0			0
$187$	−2.85852	+	21.7126i	−0.209036	+	1.58778i
$188$	7.52221	−	0.00638943i	0.548614	−	0.000465997i
$189$		0			0
$190$	1.26774	+	1.26666i	0.0919714	+	0.0918933i
$191$	−2.34881	+	4.06825i	−0.169954	+	0.294369i	−0.938403	−	0.345542i	$-0.887695\pi$
$191$	−2.34881	+	4.06825i	−0.169954	+	0.294369i	0.768450	+	0.639910i	$0.221029\pi$
$192$		0			0
$193$	5.59933	+	9.69833i	0.403049	+	0.698101i	0.994092	−	0.108539i	$-0.0346171\pi$
$193$	5.59933	+	9.69833i	0.403049	+	0.698101i	−0.591043	+	0.806640i	$0.701284\pi$
$194$	1.22469	−	4.57837i	0.0879273	−	0.328708i
$195$		0			0
$196$	−3.31328	+	5.75005i	−0.236663	+	0.410718i
$197$	−10.2796	+	4.25796i	−0.732394	+	0.303367i	−0.717535	−	0.696522i	$-0.754730\pi$
$197$	−10.2796	+	4.25796i	−0.732394	+	0.303367i	−0.0148585	+	0.999890i	$0.504730\pi$
$198$		0			0
$199$	12.0444	+	12.0444i	0.853803	+	0.853803i	0.990599	−	0.136796i	$-0.0436806\pi$
$199$	12.0444	+	12.0444i	0.853803	+	0.853803i	−0.136796	+	0.990599i	$0.543681\pi$
$200$	8.92539	+	5.13793i	0.631121	+	0.363306i
$201$		0			0
$202$	2.31936	+	17.5597i	0.163190	+	1.23550i
$203$	8.92052	+	6.84496i	0.626098	+	0.480422i
$204$		0			0
$205$	−2.70791	−	3.52901i	−0.189128	−	0.246477i
$206$	0.00236472	+	5.56792i	0.000164758	+	0.387935i
$207$		0			0
$208$	−4.08551	+	9.91088i	−0.283279	+	0.687196i
$209$	2.65393	−	4.59675i	0.183576	−	0.317964i
$210$		0			0
$211$	−2.66573	−	20.2482i	−0.183516	−	1.39394i	−0.796877	−	0.604141i	$-0.793516\pi$
$211$	−2.66573	−	20.2482i	−0.183516	−	1.39394i	0.613361	−	0.789802i	$-0.289817\pi$
$212$	−16.2481	−	12.4457i	−1.11592	−	0.854773i
$213$		0			0
$214$	−13.2825	+	10.2010i	−0.907975	+	0.697327i
$215$	9.79927	+	9.79927i	0.668305	+	0.668305i
$216$		0			0
$217$	−7.58178	+	7.58178i	−0.514685	+	0.514685i
$218$	−2.50548	+	19.0937i	−0.169693	+	1.29319i
$219$		0			0
$220$	−2.93704	+	10.9985i	−0.198015	+	0.741521i
$221$	11.9172	−	1.56894i	0.801641	−	0.105538i
$222$		0			0
$223$	11.0201	+	6.36245i	0.737960	+	0.426061i	0.821327	−	0.570457i	$-0.193234\pi$
$223$	11.0201	+	6.36245i	0.737960	+	0.426061i	−0.0833671	+	0.996519i	$0.526567\pi$
$224$	0.0230496	+	10.8544i	0.00154007	+	0.725241i
$225$		0			0
$226$	3.79382	+	3.79060i	0.252361	+	0.252147i
$227$	18.2169	−	13.9783i	1.20910	−	0.927772i	0.210340	−	0.977628i	$-0.432543\pi$
$227$	18.2169	−	13.9783i	1.20910	−	0.927772i	0.998756	+	0.0498561i	$0.0158763\pi$
$228$		0			0
$229$	9.10025	−	11.8597i	0.601362	−	0.783710i	−0.389145	−	0.921177i	$-0.627229\pi$
$229$	9.10025	−	11.8597i	0.601362	−	0.783710i	0.990506	+	0.137467i	$0.0438961\pi$
$230$	0.341718	−	0.445728i	0.0225322	−	0.0293904i
$231$		0			0
$232$	−16.4353	−	2.14245i	−1.07903	−	0.140659i
$233$	7.68982	−	7.68982i	0.503777	−	0.503777i	−0.408833	−	0.912609i	$-0.634064\pi$
$233$	7.68982	−	7.68982i	0.503777	−	0.503777i	0.912609	+	0.408833i	$0.134064\pi$
$234$		0			0
$235$	−1.67783	−	4.05065i	−0.109450	−	0.264235i
$236$	−0.249228	+	1.90558i	−0.0162234	+	0.124043i
$237$		0			0
$238$	10.5377	−	6.08992i	0.683058	−	0.394751i
$239$	−3.38369	+	1.95358i	−0.218873	+	0.126366i	−0.605428	−	0.795900i	$-0.706998\pi$
$239$	−3.38369	+	1.95358i	−0.218873	+	0.126366i	0.386555	+	0.922266i	$0.373665\pi$
$240$		0			0
$241$	24.7577	+	14.2939i	1.59479	+	0.920751i	0.992469	+	0.122494i	$0.0390892\pi$
$241$	24.7577	+	14.2939i	1.59479	+	0.920751i	0.602318	+	0.798257i	$0.294244\pi$
$242$	18.1609	−	0.00771302i	1.16743	−	0.000495812i
$243$		0			0
$244$	9.11775	−	22.0652i	0.583704	−	1.41258i
$245$	3.83495	+	0.504881i	0.245006	+	0.0322557i
$246$		0			0
$247$	−2.81402	−	0.754015i	−0.179052	−	0.0479768i
$248$	4.07122	−	15.2718i	0.258523	−	0.969761i
$249$		0			0
$250$	1.85341	−	14.1244i	0.117220	−	0.893306i
$251$	−2.34809	−	5.66878i	−0.148210	−	0.357810i	0.832287	−	0.554345i	$-0.187031\pi$
$251$	−2.34809	−	5.66878i	−0.148210	−	0.357810i	−0.980497	+	0.196535i	$0.937031\pi$
$252$		0			0
$253$	−1.53687	−	0.636592i	−0.0966222	−	0.0400222i
$254$	0.220894	+	0.822989i	0.0138601	+	0.0516389i
$255$		0			0
$256$	−8.04703	−	13.8291i	−0.502940	−	0.864322i
$257$	8.35257	−	4.82236i	0.521019	−	0.300810i	−0.216333	−	0.976320i	$-0.569410\pi$
$257$	8.35257	−	4.82236i	0.521019	−	0.300810i	0.737351	+	0.675509i	$0.236076\pi$
$258$		0			0
$259$	−8.86497	−	11.5531i	−0.550843	−	0.717872i
$260$	6.24821	−	0.00530728i	0.387497	−	0.000329144i
$261$		0			0
$262$	−3.82724	−	9.22869i	−0.236448	−	0.570150i
$263$	8.17454	+	30.5078i	0.504063	+	1.88119i	0.471789	+	0.881712i	$0.343608\pi$
$263$	8.17454	+	30.5078i	0.504063	+	1.88119i	0.0322745	+	0.999479i	$0.489725\pi$
$264$		0			0
$265$	−3.08754	+	11.5228i	−0.189666	+	0.707843i
$266$	−2.92444	+	0.386274i	−0.179309	+	0.0236840i
$267$		0			0
$268$	−4.01682	+	3.08764i	−0.245367	+	0.188608i
$269$	21.1423	+	8.75744i	1.28907	+	0.533951i	0.918708	−	0.394937i	$-0.129233\pi$
$269$	21.1423	+	8.75744i	1.28907	+	0.533951i	0.370362	+	0.928887i	$0.379233\pi$
$270$		0			0
$271$	−11.0776			−0.672917			−0.336459	−	0.941698i	$-0.609229\pi$
$271$	−11.0776			−0.672917			−0.336459	+	0.941698i	$0.609229\pi$
$272$	−8.94386	+	15.5522i	−0.542301	+	0.942989i
$273$		0			0
$274$	10.0952	+	17.4682i	0.609871	+	1.05529i
$275$	−17.6267	+	2.32059i	−1.06293	+	0.139937i
$276$		0			0
$277$	−0.689862	+	5.24003i	−0.0414498	+	0.314843i	0.958143	+	0.286292i	$0.0924226\pi$
$277$	−0.689862	+	5.24003i	−0.0414498	+	0.314843i	−0.999592	+	0.0285510i	$0.990911\pi$
$278$	4.23403	−	10.2341i	0.253940	−	0.613803i
$279$		0			0
$280$	5.84193	−	2.42853i	0.349122	−	0.145133i
$281$	−28.0589	+	7.51836i	−1.67385	+	0.448508i	−0.966146	−	0.257997i	$-0.916938\pi$
$281$	−28.0589	+	7.51836i	−1.67385	+	0.448508i	−0.707708	+	0.706505i	$0.750271\pi$
$282$		0			0
$283$	9.47185	+	7.26801i	0.563043	+	0.432038i	0.850667	−	0.525705i	$-0.176199\pi$
$283$	9.47185	+	7.26801i	0.563043	+	0.432038i	−0.287624	+	0.957744i	$0.592865\pi$
$284$	−4.87672	+	18.2622i	−0.289380	+	1.08366i
$285$		0			0
$286$	−4.79733	−	17.8735i	−0.283672	−	1.05688i
$287$	7.32192			0.432200
$288$		0			0
$289$	3.11640			0.183318
$290$	2.50429	+	9.33027i	0.147057	+	0.547892i
$291$		0			0
$292$	−2.15071	−	0.574324i	−0.125861	−	0.0336098i
$293$	9.05940	+	6.95152i	0.529256	+	0.406112i	0.838526	−	0.544862i	$-0.183418\pi$
$293$	9.05940	+	6.95152i	0.529256	+	0.406112i	−0.309270	+	0.950974i	$0.600085\pi$
$294$		0			0
$295$	1.08198	−	0.289915i	0.0629952	−	0.0168795i
$296$	19.8421	+	8.18926i	1.15330	+	0.475991i
$297$		0			0
$298$	−8.98986	+	21.7295i	−0.520769	+	1.25876i
$299$	−0.119174	+	0.905219i	−0.00689203	+	0.0523502i
$300$		0			0
$301$	−22.6160	+	2.97745i	−1.30356	+	0.171618i
$302$	−7.09488	−	12.2767i	−0.408265	−	0.706442i
$303$		0			0
$304$	3.44517	−	2.65289i	0.197594	−	0.152153i
$305$	−13.9156			−0.796807
$306$		0			0
$307$	−30.1275	−	12.4792i	−1.71947	−	0.712228i	−0.999840	−	0.0178696i	$-0.994312\pi$
$307$	−30.1275	−	12.4792i	−1.71947	−	0.712228i	−0.719630	−	0.694358i	$-0.755688\pi$
$308$	−11.4198	−	14.8564i	−0.650703	−	0.846523i
$309$		0			0
$310$	−9.13286	+	1.20631i	−0.518712	+	0.0685138i
$311$	−0.958889	+	3.57862i	−0.0543736	+	0.202925i	−0.987769	−	0.155925i	$-0.950164\pi$
$311$	−0.958889	+	3.57862i	−0.0543736	+	0.202925i	0.933395	+	0.358850i	$0.116831\pi$
$312$		0			0
$313$	1.23426	+	4.60631i	0.0697643	+	0.260364i	0.991995	−	0.126276i	$-0.0403024\pi$
$313$	1.23426	+	4.60631i	0.0697643	+	0.260364i	−0.922231	+	0.386640i	$0.873636\pi$
$314$	−12.1735	−	29.3542i	−0.686991	−	1.65655i
$315$		0			0
$316$	−0.0108152	−	12.7326i	−0.000608400	−	0.716263i
$317$	1.92143	+	2.50405i	0.107918	+	0.140642i	0.844190	−	0.536044i	$-0.180082\pi$
$317$	1.92143	+	2.50405i	0.107918	+	0.140642i	−0.736272	+	0.676686i	$0.763415\pi$
$318$		0			0
$319$	24.7794	−	14.3064i	1.38738	−	0.801004i
$320$	−5.65828	+	7.41305i	−0.316308	+	0.414402i
$321$		0			0
$322$	0.239654	+	0.892883i	0.0133554	+	0.0497584i
$323$	−4.50445	−	1.86581i	−0.250634	−	0.103816i
$324$		0			0
$325$	3.73426	+	9.01530i	0.207139	+	0.500079i
$326$	1.53112	−	11.6683i	0.0848006	−	0.646245i
$327$		0			0
$328$	−9.34004	+	5.40835i	−0.515718	+	0.298626i
$329$	6.97094	+	1.86786i	0.384321	+	0.102978i
$330$		0			0
$331$	−17.8399	−	2.34867i	−0.980571	−	0.129095i	−0.376836	−	0.926280i	$-0.622988\pi$
$331$	−17.8399	−	2.34867i	−0.980571	−	0.129095i	−0.603735	+	0.797185i	$0.706321\pi$
$332$	−33.4078	−	13.8047i	−1.83349	−	0.757634i
$333$		0			0
$334$	−9.77887	+	0.00415313i	−0.535076	+	0.000227249i
$335$	2.55737	+	1.47650i	0.139724	+	0.0806697i
$336$		0			0
$337$	21.5782	−	12.4582i	1.17544	−	0.678641i	0.220485	−	0.975390i	$-0.429236\pi$
$337$	21.5782	−	12.4582i	1.17544	−	0.678641i	0.954955	+	0.296750i	$0.0959027\pi$
$338$	7.12343	−	4.11675i	0.387464	−	0.223922i
$339$		0			0
$340$	10.3685	+	1.35608i	0.562311	+	0.0735437i
$341$	10.4415	+	25.2080i	0.565438	+	1.36509i
$342$		0			0
$343$	−13.9997	+	13.9997i	−0.755914	+	0.755914i
$344$	26.6503	−	20.5035i	1.43689	−	1.10547i
$345$		0			0
$346$	6.50274	−	8.48200i	0.349590	−	0.455995i
$347$	14.4898	−	18.8835i	0.777853	−	1.01372i	−0.221404	−	0.975182i	$-0.571064\pi$
$347$	14.4898	−	18.8835i	0.777853	−	1.01372i	0.999257	−	0.0385355i	$-0.0122693\pi$
$348$		0			0
$349$	5.69606	−	4.37074i	0.304903	−	0.233960i	−0.444965	−	0.895548i	$-0.646784\pi$
$349$	5.69606	−	4.37074i	0.304903	−	0.233960i	0.749868	+	0.661588i	$0.230117\pi$
$350$	6.98955	+	6.98362i	0.373607	+	0.373290i
$351$		0			0
$352$	25.5411	+	10.5160i	1.36135	+	0.560504i
$353$	−4.86328	−	2.80781i	−0.258846	−	0.149445i	0.364962	−	0.931022i	$-0.381082\pi$
$353$	−4.86328	−	2.80781i	−0.258846	−	0.149445i	−0.623808	+	0.781578i	$0.714415\pi$
$354$		0			0
$355$	10.9230	−	1.43804i	0.579733	−	0.0763234i
$356$	−8.11347	−	2.16661i	−0.430013	−	0.114830i
$357$		0			0
$358$	4.28220	−	32.6336i	0.226321	−	1.72474i
$359$	10.4889	−	10.4889i	0.553582	−	0.553582i	−0.373891	−	0.927473i	$-0.621977\pi$
$359$	10.4889	−	10.4889i	0.553582	−	0.553582i	0.927473	+	0.373891i	$0.121977\pi$
$360$		0			0
$361$	−12.5994	−	12.5994i	−0.663129	−	0.663129i
$362$	−28.2050	+	21.6615i	−1.48242	+	1.13850i
$363$		0			0
$364$	−6.25403	+	8.16477i	−0.327800	+	0.427950i
$365$	0.169356	+	1.28639i	0.00886451	+	0.0673326i
$366$		0			0
$367$	4.13255	−	7.15779i	0.215718	−	0.373634i	−0.737777	−	0.675045i	$-0.764124\pi$
$367$	4.13255	−	7.15779i	0.215718	−	0.373634i	0.953494	+	0.301411i	$0.0974576\pi$
$368$	−0.965238	−	0.961964i	−0.0503165	−	0.0501459i
$369$		0			0
$370$	−0.00531366	−	12.5114i	−0.000276244	−	0.650438i
$371$	−11.9537	−	15.5783i	−0.620604	−	0.808787i
$372$		0			0
$373$	−17.0254	−	13.0640i	−0.881540	−	0.676430i	0.0653931	−	0.997860i	$-0.479170\pi$
$373$	−17.0254	−	13.0640i	−0.881540	−	0.676430i	−0.946933	+	0.321430i	$0.895837\pi$
$374$	−4.05560	−	30.7046i	−0.209710	−	1.58770i
$375$		0			0
$376$	−10.2720	+	2.76641i	−0.529739	+	0.142667i
$377$	−11.1047	−	11.1047i	−0.571924	−	0.571924i
$378$		0			0
$379$	15.8866	−	6.58044i	0.816039	−	0.338015i	0.0646786	−	0.997906i	$-0.479398\pi$
$379$	15.8866	−	6.58044i	0.816039	−	0.338015i	0.751361	+	0.659892i	$0.229398\pi$
$380$	−2.19593	−	1.26533i	−0.112649	−	0.0649103i
$381$		0			0
$382$	1.71672	−	6.41779i	0.0878351	−	0.328363i
$383$	2.44422	+	4.23351i	0.124894	+	0.216322i	0.921691	−	0.387924i	$-0.126808\pi$
$383$	2.44422	+	4.23351i	0.124894	+	0.216322i	−0.796798	+	0.604246i	$0.793474\pi$
$384$		0			0
$385$	−5.46090	+	9.45856i	−0.278313	+	0.482053i
$386$	−11.2034	−	11.1939i	−0.570239	−	0.569755i
$387$		0			0
$388$	0.00569310	+	6.70243i	0.000289024	+	0.340264i
$389$	3.68256	−	27.9719i	0.186713	−	1.41823i	−0.599550	−	0.800338i	$-0.704654\pi$
$389$	3.68256	−	27.9719i	0.186713	−	1.41823i	0.786263	−	0.617892i	$-0.212013\pi$
$390$		0			0
$391$	−0.395480	+	1.47595i	−0.0200003	+	0.0746420i
$392$	2.41751	−	9.06849i	0.122103	−	0.458028i
$393$		0			0
$394$	12.4797	−	9.58440i	0.628716	−	0.482855i
$395$	−6.85638	+	2.84001i	−0.344982	+	0.142896i
$396$		0			0
$397$	3.45578	−	8.34299i	0.173441	−	0.418723i	−0.813125	−	0.582089i	$-0.802235\pi$
$397$	3.45578	−	8.34299i	0.173441	−	0.418723i	0.986565	+	0.163367i	$0.0522354\pi$
$398$	−20.8666	−	12.0355i	−1.04595	−	0.603286i
$399$		0			0
$400$	−14.0745	−	3.74564i	−0.703726	−	0.187282i
$401$	−8.90316	−	15.4207i	−0.444602	−	0.770074i	0.553422	−	0.832901i	$-0.313322\pi$
$401$	−8.90316	−	15.4207i	−0.444602	−	0.770074i	−0.998024	+	0.0628271i	$0.979988\pi$
$402$		0			0
$403$	11.8810	−	9.11661i	0.591835	−	0.454131i
$404$	−9.60543	−	23.1340i	−0.477888	−	1.15096i
$405$		0			0
$406$	−14.6937	−	6.07901i	−0.729235	−	0.301696i
$407$	−35.7940	+	9.59098i	−1.77424	+	0.475407i
$408$		0			0
$409$	−2.12454	−	0.569267i	−0.105052	−	0.0281485i	0.205910	−	0.978571i	$-0.433984\pi$
$409$	−2.12454	−	0.569267i	−0.105052	−	0.0281485i	−0.310962	+	0.950422i	$0.600651\pi$
$410$	4.99241	+	3.82744i	0.246557	+	0.189024i
$411$		0			0
$412$	−2.04446	−	7.60418i	−0.100723	−	0.374631i
$413$	−0.705591	+	1.70345i	−0.0347199	+	0.0838212i
$414$		0			0
$415$			21.0690i			1.03424i
$416$	1.94689	−	15.0347i	0.0954542	−	0.737139i
$417$		0			0
$418$	−1.93974	+	7.25151i	−0.0948756	+	0.354683i
$419$	3.34453	+	25.4042i	0.163391	+	1.24108i	0.854932	+	0.518740i	$0.173599\pi$
$419$	3.34453	+	25.4042i	0.163391	+	1.24108i	−0.691541	+	0.722337i	$0.743068\pi$
$420$		0			0
$421$	7.72051	+	1.01642i	0.376275	+	0.0495375i	0.316292	−	0.948662i	$-0.397562\pi$
$421$	7.72051	+	1.01642i	0.376275	+	0.0495375i	0.0599828	+	0.998199i	$0.480895\pi$
$422$	11.0641	+	26.6791i	0.538594	+	1.29872i
$423$		0			0
$424$	26.7554	+	11.0425i	1.29936	+	0.536273i
$425$	4.22673	+	15.7744i	0.205026	+	0.765169i
$426$		0			0
$427$	13.9440	−	18.1722i	0.674800	−	0.879416i
$428$	14.4025	−	18.8027i	0.696169	−	0.908863i
$429$		0			0
$430$	−16.9770	−	9.79206i	−0.818703	−	0.472215i
$431$			5.95516i			0.286850i	0.989661	+	0.143425i	$0.0458116\pi$
$431$			5.95516i			0.286850i	−0.989661	+	0.143425i	$0.954188\pi$
$432$		0			0
$433$		−	0.651090i		−	0.0312894i	−0.999878	−	0.0156447i	$-0.995020\pi$
$433$		−	0.651090i		−	0.0312894i	0.999878	−	0.0156447i	$-0.00498007\pi$
$434$	7.57620	−	13.1352i	0.363669	−	0.630512i
$435$		0			0
$436$	−3.57769	−	26.9980i	−0.171340	−	1.29297i
$437$	0.225451	−	0.293813i	0.0107848	−	0.0140550i
$438$		0			0
$439$	−9.13069	−	34.0762i	−0.435784	−	1.62637i	−0.739183	−	0.673505i	$-0.764788\pi$
$439$	−9.13069	−	34.0762i	−0.435784	−	1.62637i	0.303399	−	0.952864i	$-0.401879\pi$
$440$	−0.0205123	−	16.0993i	−0.000977887	−	0.767504i
$441$		0			0
$442$	−15.7022	+	6.51189i	−0.746879	+	0.309739i
$443$	−13.5187	−	1.77978i	−0.642295	−	0.0845597i	−0.197658	−	0.980271i	$-0.563334\pi$
$443$	−13.5187	−	1.77978i	−0.642295	−	0.0845597i	−0.444636	+	0.895711i	$0.646667\pi$
$444$		0			0
$445$	0.638889	+	4.85284i	0.0302862	+	0.230047i
$446$	−17.3845	−	4.65026i	−0.823181	−	0.220196i
$447$		0			0
$448$	−4.01077	−	14.8173i	−0.189491	−	0.700050i
$449$		−	26.8384i		−	1.26658i	−0.773914	−	0.633291i	$-0.781704\pi$
$449$		−	26.8384i		−	1.26658i	0.773914	−	0.633291i	$-0.218296\pi$
$450$		0			0
$451$	7.13020	−	17.2138i	0.335748	−	0.810567i
$452$	−6.57152	−	3.78663i	−0.309098	−	0.178108i
$453$		0			0
$454$	−19.7574	+	25.7709i	−0.927259	+	1.20949i
$455$	5.79031	+	1.55151i	0.271454	+	0.0727358i
$456$		0			0
$457$	16.7058	−	4.47630i	0.781463	−	0.209392i	0.154033	−	0.988066i	$-0.450774\pi$
$457$	16.7058	−	4.47630i	0.781463	−	0.209392i	0.627430	+	0.778673i	$0.284107\pi$
$458$	−8.08193	+	19.5350i	−0.377644	+	0.912810i
$459$		0			0
$460$	−0.303336	+	0.734082i	−0.0141431	+	0.0342267i
$461$	−2.59860	+	1.99398i	−0.121029	+	0.0928688i	−0.667502	−	0.744608i	$-0.732637\pi$
$461$	−2.59860	+	1.99398i	−0.121029	+	0.0928688i	0.546473	+	0.837476i	$0.315970\pi$
$462$		0			0
$463$	13.4759	+	23.3409i	0.626277	+	1.08474i	0.988293	+	0.152571i	$0.0487552\pi$
$463$	13.4759	+	23.3409i	0.626277	+	1.08474i	−0.362016	+	0.932172i	$0.617911\pi$
$464$	23.2339	−	3.09897i	1.07861	−	0.143866i
$465$		0			0
$466$	−7.68416	+	13.3224i	−0.355962	+	0.617149i
$467$	6.67811	−	16.1224i	0.309026	−	0.746055i	−0.690711	−	0.723131i	$-0.742702\pi$
$467$	6.67811	−	16.1224i	0.309026	−	0.746055i	0.999737	−	0.0229242i	$-0.00729765\pi$
$468$		0			0
$469$	−4.49073	+	1.86012i	−0.207363	+	0.0858924i
$470$	3.77669	+	4.91756i	0.174206	+	0.226830i
$471$		0			0
$472$	−0.358184	−	2.69415i	−0.0164868	−	0.124008i
$473$	−15.0238	+	56.0696i	−0.690795	+	2.57808i
$474$		0			0
$475$	0.516633	−	3.92422i	0.0237047	−	0.180055i
$476$	−12.1605	+	12.1812i	−0.557378	+	0.558325i
$477$		0			0
$478$	3.90549	−	3.90881i	0.178633	−	0.178785i
$479$	9.05406	−	15.6821i	0.413691	−	0.716533i	−0.581599	−	0.813475i	$-0.697573\pi$
$479$	9.05406	−	15.6821i	0.413691	−	0.716533i	0.995290	+	0.0969423i	$0.0309062\pi$
$480$		0			0
$481$	10.1695	+	17.6141i	0.463690	+	0.803135i
$482$	−39.0561	−	10.4473i	−1.77896	−	0.475860i
$483$		0			0
$484$	−24.8026	+	6.66842i	−1.12739	+	0.303110i
$485$	3.60920	−	1.49498i	0.163885	−	0.0678836i
$486$		0			0
$487$	22.7577	+	22.7577i	1.03125	+	1.03125i	0.999496	+	0.0317527i	$0.0101089\pi$
$487$	22.7577	+	22.7577i	1.03125	+	1.03125i	0.0317527	+	0.999496i	$0.489891\pi$
$488$	−4.36444	+	33.4808i	−0.197569	+	1.51560i
$489$		0			0
$490$	−5.42314	+	0.716313i	−0.244993	+	0.0323597i
$491$	8.12295	+	6.23296i	0.366584	+	0.281290i	0.775584	−	0.631245i	$-0.217456\pi$
$491$	8.12295	+	6.23296i	0.366584	+	0.281290i	−0.409000	+	0.912534i	$0.634122\pi$
$492$		0			0
$493$	−15.9998	−	20.8513i	−0.720593	−	0.939096i
$494$	4.12001	−	0.00174979i	0.185368	−	7.87267e-5i
$495$		0			0
$496$	0.0379717	+	22.3518i	0.00170498	+	1.00363i
$497$	−9.06740	+	15.7052i	−0.406728	+	0.704474i
$498$		0			0
$499$	−1.10083	−	8.36162i	−0.0492798	−	0.374318i	−0.998259	−	0.0589794i	$-0.981215\pi$
$499$	−1.10083	−	8.36162i	−0.0492798	−	0.374318i	0.948979	−	0.315338i	$-0.102118\pi$
$500$	2.64657	+	19.9716i	0.118358	+	0.893156i
$501$		0			0
$502$	5.28538	+	6.88199i	0.235898	+	0.307158i
$503$	−23.0958	−	23.0958i	−1.02979	−	1.02979i	−0.999542	−	0.0302472i	$-0.990371\pi$
$503$	−23.0958	−	23.0958i	−1.02979	−	1.02979i	−0.0302472	−	0.999542i	$-0.509629\pi$
$504$		0			0
$505$	−10.3237	+	10.3237i	−0.459399	+	0.459399i
$506$	2.33254	+	0.306077i	0.103694	+	0.0136068i
$507$		0			0
$508$	−0.603425	−	1.04311i	−0.0267726	−	0.0462807i
$509$	33.5101	−	4.41168i	1.48531	−	0.195544i	0.656180	−	0.754605i	$-0.272171\pi$
$509$	33.5101	−	4.41168i	1.48531	−	0.195544i	0.829127	+	0.559060i	$0.188838\pi$
$510$		0			0
$511$	−1.84958	−	1.06785i	−0.0818205	−	0.0472391i
$512$	16.0610	+	15.9387i	0.709804	+	0.704399i
$513$		0			0
$514$	−9.64062	+	9.64881i	−0.425229	+	0.425591i
$515$	−3.64115	+	2.79395i	−0.160448	+	0.123116i
$516$		0			0
$517$	11.1797	−	14.5697i	0.491684	−	0.640775i
$518$	16.3438	+	12.5300i	0.718106	+	0.550538i
$519$		0			0
$520$	−8.53229	+	2.29788i	−0.374166	+	0.100769i
$521$	−6.84957	+	6.84957i	−0.300085	+	0.300085i	−0.841047	−	0.540962i	$-0.818060\pi$
$521$	−6.84957	+	6.84957i	−0.300085	+	0.300085i	0.540962	+	0.841047i	$0.318060\pi$
$522$		0			0
$523$	15.0066	+	36.2292i	0.656193	+	1.58419i	0.803637	+	0.595120i	$0.202896\pi$
$523$	15.0066	+	36.2292i	0.656193	+	1.58419i	−0.147443	+	0.989071i	$0.547104\pi$
$524$	8.61080	+	11.2021i	0.376165	+	0.489366i
$525$		0			0
$526$	−22.3497	−	38.6728i	−0.974492	−	1.68622i
$527$	21.7050	−	12.5314i	0.945485	−	0.545876i
$528$		0			0
$529$	19.8181	+	11.4420i	0.861655	+	0.497477i
$530$	−0.00716503	−	16.8706i	−0.000311229	−	0.732813i
$531$		0			0
$532$	3.85280	−	1.59972i	0.167040	−	0.0693565i
$533$	−10.1390	−	1.33482i	−0.439168	−	0.0578175i
$534$		0			0
$535$	−13.3345	−	3.57298i	−0.576503	−	0.154473i
$536$	4.35451	−	5.68991i	0.188086	−	0.245767i
$537$		0			0
$538$	−32.0882	−	4.21063i	−1.38342	−	0.181533i
$539$	6.20021	+	14.9686i	0.267062	+	0.644745i
$540$		0			0
$541$	16.0481	+	6.64736i	0.689963	+	0.285792i	0.699985	−	0.714158i	$-0.253190\pi$
$541$	16.0481	+	6.64736i	0.689963	+	0.285792i	−0.0100216	+	0.999950i	$0.503190\pi$
$542$	15.1306	−	4.06111i	0.649914	−	0.174440i
$543$		0			0
$544$	6.51463	−	24.5211i	0.279313	−	1.05133i
$545$	−13.7469	+	7.93680i	−0.588854	+	0.339975i
$546$		0			0
$547$	11.0225	+	14.3647i	0.471286	+	0.614192i	0.967149	−	0.254208i	$-0.0818149\pi$
$547$	11.0225	+	14.3647i	0.471286	+	0.614192i	−0.495863	+	0.868401i	$0.665148\pi$
$548$	−20.1926	−	20.1583i	−0.862586	−	0.861122i
$549$		0			0
$550$	23.2250	−	9.63166i	0.990316	−	0.410695i
$551$	1.64869	+	6.15300i	0.0702366	+	0.262127i
$552$		0			0
$553$	3.16166	−	11.7995i	0.134447	−	0.501764i
$554$	−0.978760	−	7.41010i	−0.0415835	−	0.314825i
$555$		0			0
$556$	−2.03124	+	15.5307i	−0.0861438	+	0.658650i
$557$	−5.47199	−	2.26657i	−0.231856	−	0.0960377i	0.263731	−	0.964596i	$-0.415047\pi$
$557$	−5.47199	−	2.26657i	−0.231856	−	0.0960377i	−0.495587	+	0.868559i	$0.665047\pi$
$558$		0			0
$559$	31.8601			1.34754
$560$	−7.08900	+	5.45874i	−0.299565	+	0.230674i
$561$		0			0
$562$	35.5685	−	20.5557i	1.50037	−	0.867088i
$563$	−3.00069	+	0.395049i	−0.126464	+	0.0166493i	−0.193493	−	0.981102i	$-0.561982\pi$
$563$	−3.00069	+	0.395049i	−0.126464	+	0.0166493i	0.0670284	+	0.997751i	$0.478648\pi$
$564$		0			0
$565$	−0.577010	+	4.38283i	−0.0242750	+	0.184387i
$566$	−15.6018	−	6.45472i	−0.655793	−	0.271312i
$567$		0			0
$568$	−0.0340591	−	26.7316i	−0.00142909	−	1.12163i
$569$	4.93731	−	1.32295i	0.206983	−	0.0554608i	−0.153838	−	0.988096i	$-0.549163\pi$
$569$	4.93731	−	1.32295i	0.206983	−	0.0554608i	0.360821	+	0.932635i	$0.382497\pi$
$570$		0			0
$571$	17.1849	+	13.1864i	0.719166	+	0.551836i	0.902225	−	0.431266i	$-0.141933\pi$
$571$	17.1849	+	13.1864i	0.719166	+	0.551836i	−0.183058	+	0.983102i	$0.558600\pi$
$572$	13.1051	+	22.6542i	0.547950	+	0.947219i
$573$		0			0
$574$	−10.0008	+	2.68426i	−0.417425	+	0.112039i
$575$	−1.24047			−0.0517311
$576$		0			0
$577$	−14.1206			−0.587847			−0.293924	−	0.955829i	$-0.594961\pi$
$577$	−14.1206			−0.587847			−0.293924	+	0.955829i	$0.594961\pi$
$578$	−4.25660	+	1.14249i	−0.177051	+	0.0475213i
$579$		0			0
$580$	−6.84106	−	11.8259i	−0.284059	−	0.491042i
$581$	−27.5137	−	21.1120i	−1.14146	−	0.875874i
$582$		0			0
$583$	−48.2653	+	12.9326i	−1.99894	+	0.535615i
$584$	3.14814	−	0.00401109i	0.130271	−	0.000165980i
$585$		0			0
$586$	−14.9224	−	6.17365i	−0.616440	−	0.255031i
$587$	3.27791	−	24.8982i	0.135294	−	1.02766i	−0.780258	−	0.625458i	$-0.784912\pi$
$587$	3.27791	−	24.8982i	0.135294	−	1.02766i	0.915552	−	0.402200i	$-0.131754\pi$
$588$		0			0
$589$	−6.02246	+	0.792872i	−0.248151	+	0.0326697i
$590$	−1.37156	+	0.792646i	−0.0564661	+	0.0326327i
$591$		0			0
$592$	−30.1039	−	3.91124i	−1.23726	−	0.160751i
$593$	7.37102			0.302692			0.151346	−	0.988481i	$-0.451639\pi$
$593$	7.37102			0.302692			0.151346	+	0.988481i	$0.451639\pi$
$594$		0			0
$595$	9.26864	+	3.83920i	0.379977	+	0.157392i
$596$	4.31281	−	32.9755i	0.176660	−	1.35073i
$597$		0			0
$598$	−0.169082	−	1.28010i	−0.00691426	−	0.0523472i
$599$	−2.27969	+	8.50790i	−0.0931454	+	0.347623i	−0.996732	−	0.0807826i	$-0.974258\pi$
$599$	−2.27969	+	8.50790i	−0.0931454	+	0.347623i	0.903586	+	0.428406i	$0.140925\pi$
$600$		0			0
$601$	−2.82530	−	10.5441i	−0.115246	−	0.430105i	0.884059	−	0.467375i	$-0.154800\pi$
$601$	−2.82530	−	10.5441i	−0.115246	−	0.430105i	−0.999305	+	0.0372706i	$0.988134\pi$
$602$	29.7990	−	12.3580i	1.21451	−	0.503673i
$603$		0			0
$604$	14.1914	+	14.1673i	0.577439	+	0.576459i
$605$	9.11304	+	11.8763i	0.370498	+	0.482842i
$606$		0			0
$607$	28.7961	−	16.6254i	1.16880	−	0.674805i	0.215400	−	0.976526i	$-0.430894\pi$
$607$	28.7961	−	16.6254i	1.16880	−	0.674805i	0.953396	+	0.301721i	$0.0975611\pi$
$608$	−3.73310	+	4.88652i	−0.151397	+	0.198174i
$609$		0			0
$610$	19.0069	−	5.10155i	0.769569	−	0.206556i
$611$	−9.31243	−	3.85734i	−0.376741	−	0.156051i
$612$		0			0
$613$	−14.8026	−	35.7366i	−0.597871	−	1.44339i	−0.875747	−	0.482770i	$-0.839631\pi$
$613$	−14.8026	−	35.7366i	−0.597871	−	1.44339i	0.277876	−	0.960617i	$-0.410369\pi$
$614$	45.7253	+	6.00009i	1.84532	+	0.242144i
$615$		0			0
$616$	21.0444	+	16.1054i	0.847903	+	0.648904i
$617$	−32.7075	−	8.76394i	−1.31675	−	0.352823i	−0.468992	−	0.883202i	$-0.655383\pi$
$617$	−32.7075	−	8.76394i	−1.31675	−	0.352823i	−0.847760	+	0.530380i	$0.822049\pi$
$618$		0			0
$619$	−42.0543	−	5.53655i	−1.69030	−	0.222533i	−0.776911	−	0.629610i	$-0.783215\pi$
$619$	−42.0543	−	5.53655i	−1.69030	−	0.222533i	−0.913394	+	0.407078i	$0.866548\pi$
$620$	12.0321	−	4.99582i	0.483219	−	0.200637i
$621$		0			0
$622$	−0.00222522	−	5.23947i	−8.92234e−5	−	0.210083i
$623$	−6.97745	−	4.02843i	−0.279546	−	0.161396i
$624$		0			0
$625$	−5.59723	+	3.23156i	−0.223889	+	0.129263i
$626$	−3.37453	−	5.83913i	−0.134873	−	0.233379i
$627$		0			0
$628$	27.3889	+	35.6311i	1.09293	+	1.42184i
$629$	13.0261	+	31.4477i	0.519383	+	1.25390i
$630$		0			0
$631$	12.5592	−	12.5592i	0.499973	−	0.499973i	−0.411457	−	0.911429i	$-0.634980\pi$
$631$	12.5592	−	12.5592i	0.499973	−	0.499973i	0.911429	+	0.411457i	$0.134980\pi$
$632$	4.68260	+	17.3871i	0.186264	+	0.691621i
$633$		0			0
$634$	−3.54242	−	2.71581i	−0.140688	−	0.107858i
$635$	−0.427588	+	0.557243i	−0.0169683	+	0.0221135i
$636$		0			0
$637$	7.05500	−	5.41349i	0.279529	−	0.214490i
$638$	−28.6006	+	28.6249i	−1.13231	+	1.13327i
$639$		0			0
$640$	5.01081	−	12.1996i	0.198070	−	0.482232i
$641$	28.9745	+	16.7284i	1.14442	+	0.660733i	0.947522	−	0.319690i	$-0.103579\pi$
$641$	28.9745	+	16.7284i	1.14442	+	0.660733i	0.196901	+	0.980423i	$0.436912\pi$
$642$		0			0
$643$	−22.3466	+	2.94198i	−0.881263	+	0.116021i	−0.557559	−	0.830138i	$-0.688262\pi$
$643$	−22.3466	+	2.94198i	−0.881263	+	0.116021i	−0.323705	+	0.946158i	$0.604928\pi$
$644$	−0.654671	−	1.13170i	−0.0257977	−	0.0445954i
$645$		0			0
$646$	6.83651	+	0.897090i	0.268979	+	0.0352955i
$647$	6.25883	−	6.25883i	0.246060	−	0.246060i	−0.573291	−	0.819352i	$-0.694334\pi$
$647$	6.25883	−	6.25883i	0.246060	−	0.246060i	0.819352	+	0.573291i	$0.194334\pi$
$648$		0			0
$649$	3.31768	+	3.31768i	0.130230	+	0.130230i
$650$	−8.40557	−	10.9447i	−0.329694	−	0.429288i
$651$		0			0
$652$	2.18635	+	16.4986i	0.0856239	+	0.646137i
$653$	6.33253	+	48.1003i	0.247811	+	1.88231i	0.435658	+	0.900112i	$0.356516\pi$
$653$	6.33253	+	48.1003i	0.247811	+	1.88231i	−0.187847	+	0.982198i	$0.560151\pi$
$654$		0			0
$655$	4.11765	−	7.13198i	0.160890	−	0.278670i
$656$	10.7745	−	10.8112i	0.420675	−	0.422107i
$657$		0			0
$658$	−10.2062	+	0.00433460i	−0.397878	+	0.000168980i
$659$	−3.84152	−	5.00637i	−0.149644	−	0.195020i	0.712516	−	0.701656i	$-0.247556\pi$
$659$	−3.84152	−	5.00637i	−0.149644	−	0.195020i	−0.862160	+	0.506636i	$0.830889\pi$
$660$		0			0
$661$	−11.4845	−	8.81236i	−0.446695	−	0.342761i	0.360792	−	0.932646i	$-0.382506\pi$
$661$	−11.4845	−	8.81236i	−0.446695	−	0.342761i	−0.807487	+	0.589885i	$0.799173\pi$
$662$	25.2281	−	3.33224i	0.980516	−	0.129511i
$663$		0			0
$664$	50.6916	+	6.60799i	1.96722	+	0.256440i
$665$	−1.71934	−	1.71934i	−0.0666732	−	0.0666732i
$666$		0			0
$667$	1.84442	−	0.763984i	0.0714162	−	0.0295816i
$668$	13.3551	−	3.59066i	0.516726	−	0.138927i
$669$		0			0
$670$	−4.03433	−	1.07916i	−0.155860	−	0.0416915i
$671$	−29.1439	−	50.4788i	−1.12509	−	1.94871i
$672$		0			0
$673$	−15.4497	+	26.7596i	−0.595541	+	1.03151i	0.397930	+	0.917416i	$0.369729\pi$
$673$	−15.4497	+	26.7596i	−0.595541	+	1.03151i	−0.993470	+	0.114091i	$0.963605\pi$
$674$	−24.9058	+	24.9270i	−0.959335	+	0.960150i
$675$		0			0
$676$	−8.22046	+	8.23444i	−0.316172	+	0.316709i
$677$	−0.102675	+	0.779896i	−0.00394613	+	0.0299738i	−0.993305	−	0.115524i	$-0.963145\pi$
$677$	−0.102675	+	0.779896i	−0.00394613	+	0.0299738i	0.989359	+	0.145498i	$0.0464785\pi$
$678$		0			0
$679$	−1.66430	+	6.21124i	−0.0638698	+	0.238366i
$680$	−14.6592	+	1.94892i	−0.562153	+	0.0747376i
$681$		0			0
$682$	−23.5031	−	30.6029i	−0.899980	−	1.17185i
$683$	−23.0089	+	9.53060i	−0.880411	+	0.364678i	−0.776656	−	0.629925i	$-0.783086\pi$
$683$	−23.0089	+	9.53060i	−0.880411	+	0.364678i	−0.103755	+	0.994603i	$0.533086\pi$
$684$		0			0
$685$	−6.36418	+	15.3645i	−0.243163	+	0.587047i
$686$	13.9894	−	24.2542i	0.534119	−	0.926029i
$687$		0			0
$688$	−28.8841	+	37.7752i	−1.10120	+	1.44017i
$689$	13.7128	+	23.7512i	0.522414	+	0.904848i
$690$		0			0
$691$	8.12020	−	6.23085i	0.308907	−	0.237033i	−0.442660	−	0.896690i	$-0.645965\pi$
$691$	8.12020	−	6.23085i	0.308907	−	0.237033i	0.751567	+	0.659657i	$0.229298\pi$
$692$	−5.77235	+	13.9692i	−0.219432	+	0.531031i
$693$		0			0
$694$	−12.8684	+	31.1044i	−0.488477	+	1.18071i
$695$	8.81824	−	2.36284i	0.334495	−	0.0896277i
$696$		0			0
$697$	−16.5315	−	4.42960i	−0.626175	−	0.167783i
$698$	−6.17774	+	8.05807i	−0.233831	+	0.305002i
$699$		0			0
$700$	−12.1070	−	6.97630i	−0.457603	−	0.263679i
$701$	−9.41659	+	22.7336i	−0.355660	+	0.858638i	0.640240	+	0.768175i	$0.278835\pi$
$701$	−9.41659	+	22.7336i	−0.355660	+	0.858638i	−0.995900	+	0.0904633i	$0.971165\pi$
$702$		0			0
$703$		−	8.24992i		−	0.311152i
$704$	−38.7411	−	4.99996i	−1.46011	−	0.188443i
$705$		0			0
$706$	7.67196	+	2.05220i	0.288738	+	0.0772357i
$707$	−3.13680	−	23.8264i	−0.117972	−	0.896084i
$708$		0			0
$709$	−4.29982	−	0.566082i	−0.161483	−	0.0212597i	0.0493510	−	0.998781i	$-0.484285\pi$
$709$	−4.29982	−	0.566082i	−0.161483	−	0.0212597i	−0.210834	+	0.977522i	$0.567618\pi$
$710$	−14.3922	+	5.96862i	−0.540131	+	0.223998i
$711$		0			0
$712$	11.8762	−	0.0151317i	0.445081	−	0.000567083i
$713$	0.492723	+	1.83887i	0.0184526	+	0.0688662i
$714$		0			0
$715$	9.28627	−	12.1021i	0.347287	−	0.452593i
$716$	6.11474	+	46.1431i	0.228518	+	1.72445i
$717$		0			0
$718$	−10.4812	+	18.1717i	−0.391153	+	0.678162i
$719$		−	31.9312i		−	1.19083i	−0.803418	−	0.595416i	$-0.796987\pi$
$719$		−	31.9312i		−	1.19083i	0.803418	−	0.595416i	$-0.203013\pi$
$720$		0			0
$721$		−	7.55457i		−	0.281347i
$722$	21.8282	+	12.5902i	0.812363	+	0.468558i
$723$		0			0
$724$	30.5832	−	39.9269i	1.13661	−	1.48387i
$725$	12.9889	−	16.9274i	0.482394	−	0.628669i
$726$		0			0
$727$	9.11768	+	34.0277i	0.338156	+	1.26202i	0.900407	+	0.435049i	$0.143269\pi$
$727$	9.11768	+	34.0277i	0.338156	+	1.26202i	−0.562251	+	0.826967i	$0.690064\pi$
$728$	5.54895	−	13.4448i	0.205658	−	0.498296i
$729$		0			0
$730$	−0.702916	−	1.69495i	−0.0260161	−	0.0627330i
$731$	52.8639	+	6.95966i	1.95524	+	0.257412i
$732$		0			0
$733$	2.70865	+	20.5742i	0.100046	+	0.759927i	0.965769	+	0.259403i	$0.0835258\pi$
$733$	2.70865	+	20.5742i	0.100046	+	0.759927i	−0.865723	+	0.500524i	$0.833141\pi$
$734$	−3.02044	+	11.2916i	−0.111487	+	0.416782i
$735$		0			0
$736$	1.67105	+	0.960056i	0.0615958	+	0.0353881i
$737$			12.3691i			0.455622i
$738$		0			0
$739$	4.30694	−	10.3979i	0.158433	−	0.382492i	−0.824652	−	0.565641i	$-0.808629\pi$
$739$	4.30694	−	10.3979i	0.158433	−	0.382492i	0.983085	+	0.183149i	$0.0586289\pi$
$740$	4.59401	+	17.0870i	0.168879	+	0.628131i
$741$		0			0
$742$	22.0383	+	16.8957i	0.809051	+	0.620261i
$743$	−22.4653	−	6.01956i	−0.824172	−	0.220836i	−0.178003	−	0.984030i	$-0.556964\pi$
$743$	−22.4653	−	6.01956i	−0.824172	−	0.220836i	−0.646170	+	0.763194i	$0.723630\pi$
$744$		0			0
$745$	−18.7233	+	5.01688i	−0.685967	+	0.183804i
$746$	28.0438	+	11.6022i	1.02676	+	0.424785i
$747$		0			0
$748$	16.7959	+	40.4516i	0.614118	+	1.47906i
$749$	18.0277	−	13.8331i	0.658717	−	0.505451i
$750$		0			0
$751$	23.4640	+	40.6409i	0.856214	+	1.48301i	0.875514	+	0.483192i	$0.160523\pi$
$751$	23.4640	+	40.6409i	0.856214	+	1.48301i	−0.0193005	+	0.999814i	$0.506144\pi$
$752$	13.0161	−	7.54434i	0.474647	−	0.275114i
$753$		0			0
$754$	19.2387	+	11.0966i	0.700632	+	0.404113i
$755$	4.47274	−	10.7982i	0.162780	−	0.392985i
$756$		0			0
$757$	−23.1447	+	9.58685i	−0.841209	+	0.348440i	−0.761330	−	0.648364i	$-0.775453\pi$
$757$	−23.1447	+	9.58685i	−0.841209	+	0.348440i	−0.0798788	+	0.996805i	$0.525453\pi$
$758$	−19.2866	+	14.8121i	−0.700521	+	0.538001i
$759$		0			0
$760$	3.46323	+	0.923243i	0.125625	+	0.0334895i
$761$	−0.0262675	+	0.0980316i	−0.000952196	+	0.00355364i	−0.966400	−	0.257042i	$-0.917252\pi$
$761$	−0.0262675	+	0.0980316i	−0.000952196	+	0.00355364i	0.965448	+	0.260595i	$0.0839189\pi$
$762$		0			0
$763$	3.41045	−	25.9049i	0.123467	−	0.937821i
$764$	0.00798039	+	9.39523i	0.000288720	+	0.339907i
$765$		0			0
$766$	−4.89051	−	4.88636i	−0.176701	−	0.176551i
$767$	1.28761	−	2.23020i	0.0464928	−	0.0805279i
$768$		0			0
$769$	−15.1755	−	26.2847i	−0.547241	−	0.947850i	−0.998462	−	0.0554374i	$-0.982345\pi$
$769$	−15.1755	−	26.2847i	−0.547241	−	0.947850i	0.451221	−	0.892412i	$-0.350989\pi$
$770$	3.99132	−	14.9212i	0.143837	−	0.537721i
$771$		0			0
$772$	19.4062	+	11.1822i	0.698443	+	0.402456i
$773$	10.1380	−	4.19928i	0.364637	−	0.151038i	−0.192839	−	0.981230i	$-0.561770\pi$
$773$	10.1380	−	4.19928i	0.364637	−	0.151038i	0.557477	+	0.830193i	$0.311770\pi$
$774$		0			0
$775$	14.3871	+	14.3871i	0.516798	+	0.516798i
$776$	−2.46492	−	9.15256i	−0.0884856	−	0.328558i
$777$		0			0
$778$	5.22473	+	39.5560i	0.187316	+	1.41815i
$779$	3.29087	+	2.52518i	0.117908	+	0.0904739i
$780$		0			0
$781$	28.0929	+	36.6114i	1.00524	+	1.31006i
$782$	−0.000917762	−	2.16094i	−3.28191e−5	−	0.0772751i
$783$		0			0
$784$	0.0225478	+	13.2726i	0.000805279	+	0.474023i
$785$	13.0972	−	22.6851i	0.467461	−	0.809666i
$786$		0			0
$787$	−2.32542	−	17.6633i	−0.0828924	−	0.629630i	−0.981581	−	0.191044i	$-0.938813\pi$
$787$	−2.32542	−	17.6633i	−0.0828924	−	0.629630i	0.898689	−	0.438586i	$-0.144521\pi$
$788$	−13.5319	+	17.6661i	−0.482053	+	0.629330i
$789$		0			0
$790$	8.32377	−	6.39267i	0.296146	−	0.227441i
$791$	−5.14528	−	5.14528i	−0.182945	−	0.182945i
$792$		0			0
$793$	−22.6218	+	22.6218i	−0.803323	+	0.803323i
$794$	−1.66156	+	12.6623i	−0.0589665	+	0.449370i
$795$		0			0
$796$	32.9133	+	8.78914i	1.16658	+	0.311523i
$797$	0.478432	−	0.0629867i	0.0169469	−	0.00223110i	−0.122048	−	0.992524i	$-0.538946\pi$
$797$	0.478432	−	0.0629867i	0.0169469	−	0.00223110i	0.138995	+	0.990293i	$0.455613\pi$
$798$		0			0
$799$	−14.6090	−	8.43453i	−0.516830	−	0.298392i
$800$	20.5971	−	0.0437385i	0.728219	−	0.00154639i
$801$		0			0
$802$	17.8139	+	17.7987i	0.629030	+	0.628496i
$803$	−4.31167	+	3.30846i	−0.152155	+	0.116753i
$804$		0			0
$805$	−0.463901	+	0.604568i	−0.0163504	+	0.0213082i
$806$	−12.8857	+	16.8077i	−0.453879	+	0.592027i
$807$		0			0
$808$	21.6008	+	28.0766i	0.759914	+	0.987730i
$809$	−2.96581	+	2.96581i	−0.104272	+	0.104272i	−0.757318	−	0.653046i	$-0.773491\pi$
$809$	−2.96581	+	2.96581i	−0.104272	+	0.104272i	0.653046	+	0.757318i	$0.273491\pi$
$810$		0			0
$811$	2.73876	+	6.61195i	0.0961709	+	0.232177i	0.964642	−	0.263562i	$-0.0848973\pi$
$811$	2.73876	+	6.61195i	0.0961709	+	0.232177i	−0.868472	+	0.495739i	$0.834897\pi$
$812$	22.2982	+	2.91635i	0.782515	+	0.102344i
$813$		0			0
$814$	45.3739	−	26.2223i	1.59035	−	0.919092i
$815$	8.40084	−	4.85023i	0.294269	−	0.169896i
$816$		0			0
$817$	−11.1917	−	6.46155i	−0.391549	−	0.226061i
$818$	3.11054	−	0.00132106i	0.108757	−	4.61897e-5i
$819$		0			0
$820$	−8.22214	−	3.39754i	−0.287129	−	0.118647i
$821$	−34.5764	−	4.55206i	−1.20672	−	0.158868i	−0.499789	−	0.866147i	$-0.666589\pi$
$821$	−34.5764	−	4.55206i	−1.20672	−	0.158868i	−0.706934	+	0.707279i	$0.749922\pi$
$822$		0			0
$823$	−36.1366	−	9.68278i	−1.25964	−	0.337520i	−0.433589	−	0.901111i	$-0.642753\pi$
$823$	−36.1366	−	9.68278i	−1.25964	−	0.337520i	−0.826054	+	0.563590i	$0.809420\pi$
$824$	5.58020	+	9.63681i	0.194395	+	0.335714i
$825$		0			0
$826$	0.339252	−	2.58536i	0.0118041	−	0.0899562i
$827$	−2.02392	−	4.88617i	−0.0703785	−	0.169909i	0.884776	−	0.466016i	$-0.154311\pi$
$827$	−2.02392	−	4.88617i	−0.0703785	−	0.169909i	−0.955155	+	0.296108i	$0.904311\pi$
$828$		0			0
$829$	−49.1995	−	20.3791i	−1.70877	−	0.707795i	−0.999997	−	0.00235766i	$-0.999250\pi$
$829$	−49.1995	−	20.3791i	−1.70877	−	0.707795i	−0.708772	−	0.705438i	$-0.750750\pi$
$830$	−7.72401	−	28.7775i	−0.268104	−	0.998882i
$831$		0			0
$832$	2.85262	+	21.2492i	0.0988969	+	0.736685i
$833$	12.8885	−	7.44121i	0.446562	−	0.257822i
$834$		0			0
$835$	−4.90698	−	6.39490i	−0.169813	−	0.221305i
$836$	−0.00901710	−	10.6157i	−0.000311863	−	0.367153i
$837$		0			0
$838$	−13.8815	−	33.4727i	−0.479529	−	1.15630i
$839$	7.01726	+	26.1888i	0.242263	+	0.904137i	0.974739	+	0.223345i	$0.0716976\pi$
$839$	7.01726	+	26.1888i	0.242263	+	0.904137i	−0.732477	+	0.680792i	$0.761636\pi$
$840$		0			0
$841$	−1.38174	+	5.15671i	−0.0476461	+	0.177818i
$842$	−10.9178	+	1.44208i	−0.376254	+	0.0496973i
$843$		0			0
$844$	−24.8929	−	32.3840i	−0.856848	−	1.11470i
$845$	6.26555	+	2.59528i	0.215541	+	0.0892802i
$846$		0			0
$847$	−24.6408			−0.846668
$848$	−40.5927	−	5.27399i	−1.39396	−	0.181109i
$849$		0			0
$850$	−11.5561	−	19.9962i	−0.396372	−	0.685863i
$851$	−2.56342	+	0.337481i	−0.0878729	+	0.0115687i
$852$		0			0
$853$	4.12534	−	31.3351i	0.141249	−	1.07289i	−0.763155	−	0.646216i	$-0.776351\pi$
$853$	4.12534	−	31.3351i	0.141249	−	1.07289i	0.904404	−	0.426678i	$-0.140316\pi$
$854$	−12.3837	+	29.9329i	−0.423762	+	1.02428i
$855$		0			0
$856$	−12.7787	+	30.9621i	−0.436767	+	1.05826i
$857$	23.9116	−	6.40709i	0.816804	−	0.218862i	0.173855	−	0.984771i	$-0.444378\pi$
$857$	23.9116	−	6.40709i	0.816804	−	0.218862i	0.642949	+	0.765909i	$0.277711\pi$
$858$		0			0
$859$	2.45003	+	1.87998i	0.0835940	+	0.0641439i	0.649713	−	0.760180i	$-0.274889\pi$
$859$	2.45003	+	1.87998i	0.0835940	+	0.0641439i	−0.566119	+	0.824324i	$0.691556\pi$
$860$	26.7782	+	7.15082i	0.913128	+	0.243841i
$861$		0			0
$862$	−2.18320	−	8.13398i	−0.0743599	−	0.277044i
$863$	38.7531			1.31917			0.659585	−	0.751630i	$-0.270732\pi$
$863$	38.7531			1.31917			0.659585	+	0.751630i	$0.270732\pi$
$864$		0			0
$865$	8.80985			0.299544
$866$	0.238693	+	0.889305i	0.00811113	+	0.0302198i
$867$		0			0
$868$	−5.53265	+	20.7185i	−0.187790	+	0.703232i
$869$	−24.6616	−	18.9235i	−0.836588	−	0.641937i
$870$		0			0
$871$	6.55761	−	1.75711i	0.222196	−	0.0595373i
$872$	14.7843	+	35.5641i	0.500658	+	1.20435i
$873$		0			0
$874$	−0.200223	+	0.483962i	−0.00677264	+	0.0163703i
$875$	−2.52286	+	19.1630i	−0.0852881	+	0.647827i
$876$		0			0
$877$	−11.0924	+	1.46034i	−0.374563	+	0.0493122i	−0.315458	−	0.948940i	$-0.602158\pi$
$877$	−11.0924	+	1.46034i	−0.374563	+	0.0493122i	−0.0591054	+	0.998252i	$0.518825\pi$
$878$	24.9639	+	43.1963i	0.842489	+	1.45780i
$879$		0			0
$880$	5.93011	+	21.9820i	0.199904	+	0.741014i
$881$	33.1806			1.11788			0.558941	−	0.829208i	$-0.311208\pi$
$881$	33.1806			1.11788			0.558941	+	0.829208i	$0.311208\pi$
$882$		0			0
$883$	−16.9677	−	7.02823i	−0.571007	−	0.236519i	0.0784488	−	0.996918i	$-0.475003\pi$
$883$	−16.9677	−	7.02823i	−0.571007	−	0.236519i	−0.649456	+	0.760399i	$0.725003\pi$
$884$	19.0599	−	14.6509i	0.641054	−	0.492764i
$885$		0			0
$886$	19.1173	−	2.52510i	0.642259	−	0.0848325i
$887$	−6.51728	+	24.3228i	−0.218829	+	0.816681i	0.765955	+	0.642895i	$0.222267\pi$
$887$	−6.51728	+	24.3228i	−0.218829	+	0.816681i	−0.984783	+	0.173786i	$0.944400\pi$
$888$		0			0
$889$	−0.299235	−	1.11676i	−0.0100360	−	0.0374550i
$890$	−2.65172	−	6.39413i	−0.0888858	−	0.214332i
$891$		0			0
$892$	25.4498	−	0.0216173i	0.852123	−	0.000723801i
$893$	2.48894	+	3.24365i	0.0832892	+	0.108545i
$894$		0			0
$895$	23.4953	−	13.5650i	0.785362	−	0.453429i
$896$	10.9103	+	18.7681i	0.364487	+	0.626997i
$897$		0			0
$898$	9.83910	+	36.6578i	0.328335	+	1.22329i
$899$	−30.2525	−	12.5310i	−1.00898	−	0.417932i
$900$		0			0
$901$	17.5646	+	42.4046i	0.585160	+	1.41270i
$902$	−3.42824	+	26.1258i	−0.114148	+	0.869894i
$903$		0			0
$904$	10.3640	+	2.76289i	0.344703	+	0.0918922i
$905$	−28.3155	−	7.58711i	−0.941238	−	0.252204i
$906$		0			0
$907$	3.68122	+	0.484642i	0.122233	+	0.0160923i	0.191394	−	0.981513i	$-0.438699\pi$
$907$	3.68122	+	0.484642i	0.122233	+	0.0160923i	−0.0691614	+	0.997605i	$0.522032\pi$
$908$	17.5382	−	42.4429i	0.582026	−	1.40852i
$909$		0			0
$910$	−8.47760	+	0.00360047i	−0.281030	+	0.000119355i
$911$	41.0434	+	23.6964i	1.35983	+	0.785098i	0.989601	−	0.143843i	$-0.0459460\pi$
$911$	41.0434	+	23.6964i	1.35983	+	0.785098i	0.370229	+	0.928941i	$0.379279\pi$
$912$		0			0
$913$	−76.4275	+	44.1254i	−2.52938	+	1.46034i
$914$	−21.1769	+	12.2385i	−0.700469	+	0.404813i
$915$		0			0
$916$	3.87724	−	29.6451i	0.128108	−	0.979502i
$917$	5.18750	+	12.5237i	0.171306	+	0.413570i
$918$		0			0
$919$	18.4084	−	18.4084i	0.607235	−	0.607235i	−0.334987	−	0.942223i	$-0.608732\pi$
$919$	18.4084	−	18.4084i	0.607235	−	0.607235i	0.942223	+	0.334987i	$0.108732\pi$
$920$	0.145200	−	1.11387i	0.00478709	−	0.0367230i
$921$		0			0
$922$	2.81835	−	3.67618i	0.0928174	−	0.121068i
$923$	15.4191	−	20.0946i	0.507527	−	0.661422i
$924$		0			0
$925$	−21.9229	+	16.8220i	−0.720820	+	0.553104i
$926$	−26.9632	−	26.9403i	−0.886065	−	0.885313i
$927$		0			0
$928$	−30.5984	+	12.7505i	−1.00444	+	0.418554i
$929$	16.1678	+	9.33448i	0.530448	+	0.306254i	0.741199	−	0.671285i	$-0.234258\pi$
$929$	16.1678	+	9.33448i	0.530448	+	0.306254i	−0.210751	+	0.977540i	$0.567591\pi$
$930$		0			0
$931$	−3.57617	+	0.470812i	−0.117204	+	0.0154302i
$932$	5.61149	−	21.0138i	0.183811	−	0.688328i
$933$		0			0
$934$	−3.21087	+	24.4693i	−0.105063	+	0.800660i
$935$	18.0519	−	18.0519i	0.590359	−	0.590359i
$936$		0			0
$937$	3.70266	+	3.70266i	0.120961	+	0.120961i	0.764996	−	0.644035i	$-0.222741\pi$
$937$	3.70266	+	3.70266i	0.120961	+	0.120961i	−0.644035	+	0.764996i	$0.722741\pi$
$938$	5.45182	−	4.18701i	0.178008	−	0.136711i
$939$		0			0
$940$	−6.96127	−	5.33218i	−0.227052	−	0.173917i
$941$	−6.11775	−	46.4689i	−0.199433	−	1.51484i	−0.739463	−	0.673197i	$-0.764920\pi$
$941$	−6.11775	−	46.4689i	−0.199433	−	1.51484i	0.540030	−	0.841646i	$-0.318413\pi$
$942$		0			0
$943$	0.650004	−	1.12584i	0.0211670	−	0.0366624i
$944$	1.47692	+	3.54854i	0.0480697	+	0.115495i
$945$		0			0
$946$	−0.0348647	−	82.0916i	−0.00113355	−	2.66903i
$947$	−13.8473	−	18.0462i	−0.449977	−	0.586422i	0.512193	−	0.858870i	$-0.328833\pi$
$947$	−13.8473	−	18.0462i	−0.449977	−	0.586422i	−0.962170	+	0.272449i	$0.912167\pi$
$948$		0			0
$949$	2.36651	+	1.81589i	0.0768202	+	0.0589462i
$950$	0.732986	+	5.54937i	0.0237812	+	0.180045i
$951$		0			0
$952$	12.1440	−	21.0961i	0.393590	−	0.683728i
$953$	−20.1825	−	20.1825i	−0.653774	−	0.653774i	0.300126	−	0.953900i	$-0.402971\pi$
$953$	−20.1825	−	20.1825i	−0.653774	−	0.653774i	−0.953900	+	0.300126i	$0.902971\pi$
$954$		0			0
$955$	5.05925	−	2.09561i	0.163714	−	0.0678124i
$956$	−3.90140	+	6.77070i	−0.126180	+	0.218980i
$957$		0			0
$958$	−6.61753	+	24.7390i	−0.213803	+	0.799280i
$959$	−13.6871	−	23.7067i	−0.441979	−	0.765531i
$960$		0			0
$961$	0.112702	−	0.195206i	0.00363555	−	0.00629696i
$962$	−20.3477	−	20.3304i	−0.656035	−	0.655478i
$963$		0			0
$964$	57.1756	−	0.0485654i	1.84150	−	0.00156419i
$965$	1.70395	−	12.9428i	0.0548522	−	0.416644i
$966$		0			0
$967$	4.79197	−	17.8839i	0.154100	−	0.575107i	−0.845081	−	0.534638i	$-0.820448\pi$
$967$	4.79197	−	17.8839i	0.154100	−	0.575107i	0.999181	−	0.0404694i	$-0.0128853\pi$
$968$	31.4325	−	18.2010i	1.01028	−	0.585001i
$969$		0			0
$970$	−4.38163	+	3.36510i	−0.140686	+	0.108047i
$971$	−38.0099	+	15.7442i	−1.21979	+	0.505255i	−0.897344	−	0.441331i	$-0.854506\pi$
$971$	−38.0099	+	15.7442i	−1.21979	+	0.505255i	−0.322450	+	0.946586i	$0.604506\pi$
$972$		0			0
$973$	−5.75065	+	13.8833i	−0.184357	+	0.445078i
$974$	−39.4271	−	22.7409i	−1.26333	−	0.728666i
$975$		0			0
$976$	−6.31299	−	47.3304i	−0.202074	−	1.51501i
$977$	−6.97197	−	12.0758i	−0.223053	−	0.386339i	0.732680	−	0.680573i	$-0.238269\pi$
$977$	−6.97197	−	12.0758i	−0.223053	−	0.386339i	−0.955734	+	0.294233i	$0.904936\pi$
$978$		0			0
$979$	−16.2656	+	12.4810i	−0.519850	+	0.398895i
$980$	7.14470	−	2.96654i	0.228229	−	0.0947628i
$981$		0			0
$982$	−13.3799	−	5.53549i	−0.426971	−	0.176645i
$983$	32.9007	−	8.81570i	1.04937	−	0.281177i	0.307377	−	0.951588i	$-0.400549\pi$
$983$	32.9007	−	8.81570i	1.04937	−	0.281177i	0.741990	+	0.670410i	$0.233882\pi$
$984$		0			0
$985$	12.5285	+	3.35701i	0.399192	+	0.106963i
$986$	29.4978	+	22.6146i	0.939402	+	0.720194i
$987$		0			0
$988$	−5.62676	+	1.51281i	−0.179011	+	0.0481289i
$989$	−1.54991	+	3.74182i	−0.0492844	+	0.118983i
$990$		0			0
$991$		−	18.4826i		−	0.587119i	−0.955941	−	0.293560i	$-0.905160\pi$
$991$		−	18.4826i		−	0.587119i	0.955941	−	0.293560i	$-0.0948399\pi$
$992$	−8.24617	−	30.5158i	−0.261816	−	0.968877i
$993$		0			0
$994$	6.62727	−	24.7754i	0.210204	−	0.785828i
$995$	−2.59173	−	19.6862i	−0.0821635	−	0.624093i
$996$		0			0
$997$	4.84617	+	0.638010i	0.153480	+	0.0202060i	0.206874	−	0.978367i	$-0.433671\pi$
$997$	4.84617	+	0.638010i	0.153480	+	0.0202060i	−0.0533947	+	0.998573i	$0.517004\pi$
$998$	4.56901	+	11.0173i	0.144629	+	0.348747i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.3		368
3.2	odd	2		288.2.bf.a.227.44	yes	368
9.4	even	3		288.2.bf.a.131.29	yes	368
9.5	odd	6	inner	864.2.bn.a.611.18		368
32.11	odd	8	inner	864.2.bn.a.683.18		368
96.11	even	8		288.2.bf.a.11.29	✓	368
288.139	odd	24		288.2.bf.a.203.44	yes	368
288.203	even	24	inner	864.2.bn.a.395.3		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.29	✓	368	96.11	even	8
288.2.bf.a.131.29	yes	368	9.4	even	3
288.2.bf.a.203.44	yes	368	288.139	odd	24
288.2.bf.a.227.44	yes	368	3.2	odd	2
864.2.bn.a.35.3		368	1.1	even	1	trivial
864.2.bn.a.395.3		368	288.203	even	24	inner
864.2.bn.a.611.18		368	9.5	odd	6	inner
864.2.bn.a.683.18		368	32.11	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36587 + 0.366606i) q^{2} +(1.73120 - 1.00147i) q^{4} +(-0.924826 - 0.709644i) q^{5} +(1.85343 - 0.496625i) q^{7} +(-1.99745 + 2.00255i) q^{8} +(1.52335 + 0.630235i) q^{10} +(0.637333 - 4.84102i) q^{11} +(-2.65706 + 0.349808i) q^{13} +(-2.34948 + 1.35780i) q^{14} +(1.99411 - 3.46749i) q^{16} -4.48513 q^{17} +(1.00431 + 0.415998i) q^{19} +(-2.31175 - 0.302350i) q^{20} +(0.904232 + 6.84586i) q^{22} +(0.0881758 - 0.329076i) q^{23} +(-0.942386 - 3.51703i) q^{25} +(3.50095 - 1.45188i) q^{26} +(2.71130 - 2.71591i) q^{28} +(3.56729 + 4.64898i) q^{29} +(-4.83932 + 2.79398i) q^{31} +(-1.45250 + 5.46720i) q^{32} +(6.12611 - 1.64427i) q^{34} +(-2.06653 - 0.855983i) q^{35} +(-2.90428 - 7.01154i) q^{37} +(-1.52426 - 0.200014i) q^{38} +(3.26839 - 0.434529i) q^{40} +(3.68584 + 0.987619i) q^{41} +(-11.7865 - 1.55172i) q^{43} +(-3.74479 - 9.01905i) q^{44} +(0.000204623 + 0.481801i) q^{46} +(3.25721 + 1.88055i) q^{47} +(-2.87362 + 1.65908i) q^{49} +(2.57654 + 4.45833i) q^{50} +(-4.24958 + 3.26655i) q^{52} +(-3.91618 - 9.45448i) q^{53} +(-4.02483 + 4.02483i) q^{55} +(-2.70762 + 4.70356i) q^{56} +(-6.57680 - 5.04212i) q^{58} +(-0.584963 + 0.762339i) q^{59} +(9.47057 - 7.26703i) q^{61} +(5.58560 - 5.59034i) q^{62} +(-0.0203858 - 7.99997i) q^{64} +(2.70555 + 1.56205i) q^{65} +(-2.51153 + 0.330649i) q^{67} +(-7.76466 + 4.49173i) q^{68} +(3.13641 + 0.411562i) q^{70} +(-6.68291 + 6.68291i) q^{71} +(-0.787037 - 0.787037i) q^{73} +(6.53733 + 8.51213i) q^{74} +(2.15527 - 0.285609i) q^{76} +(-1.22292 - 9.28901i) q^{77} +(3.18314 - 5.51337i) q^{79} +(-4.30489 + 1.79172i) q^{80} +(-5.39645 + 0.00229190i) q^{82} +(-11.0027 - 14.3389i) q^{83} +(4.14797 + 3.18285i) q^{85} +(16.6676 - 2.20154i) q^{86} +(8.42133 + 10.9460i) q^{88} +(-2.96906 - 2.96906i) q^{89} +(-4.75094 + 1.96790i) q^{91} +(-0.176911 - 0.658003i) q^{92} +(-5.13835 - 1.37448i) q^{94} +(-0.633600 - 1.09743i) q^{95} +(-1.67561 + 2.90224i) q^{97} +(3.31676 - 3.31958i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

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