LMFDB - Embedded newform 405.2.r.a.8.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] 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("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			8.5
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.865920 + 0.606324i) q^{2} +(-0.301851 + 0.829330i) q^{4} +(-2.13636 + 0.660292i) q^{5} +(-1.22161 + 2.61975i) q^{7} +(-0.788655 - 2.94330i) q^{8} +(1.44956 - 1.86708i) q^{10} +(-1.51740 + 1.80836i) q^{11} +(3.11956 - 4.45519i) q^{13} +(-0.530600 - 3.00918i) q^{14} +(1.11535 + 0.935892i) q^{16} +(0.716894 - 2.67549i) q^{17} +(-5.35751 - 3.09316i) q^{19} +(0.0972619 - 1.97105i) q^{20} +(0.217491 - 2.48593i) q^{22} +(-0.646627 + 0.301527i) q^{23} +(4.12803 - 2.82124i) q^{25} +5.74930i q^{26} +(-1.80389 - 1.80389i) q^{28} +(-0.623300 + 3.53491i) q^{29} +(-5.18043 - 1.88552i) q^{31} +(4.53781 + 0.397007i) q^{32} +(1.00144 + 2.75143i) q^{34} +(0.879991 - 6.40333i) q^{35} +(-4.26173 - 1.14193i) q^{37} +(6.51463 - 0.569956i) q^{38} +(3.62828 + 5.76719i) q^{40} +(-5.70140 + 1.00531i) q^{41} +(0.126221 + 1.44271i) q^{43} +(-1.04170 - 1.80428i) q^{44} +(0.377104 - 0.653164i) q^{46} +(-9.40770 - 4.38688i) q^{47} +(-0.871236 - 1.03830i) q^{49} +(-1.86396 + 4.94589i) q^{50} +(2.75318 + 3.93195i) q^{52} +(7.22940 - 7.22940i) q^{53} +(2.04765 - 4.86523i) q^{55} +(8.67413 + 1.52948i) q^{56} +(-1.60357 - 3.43887i) q^{58} +(-6.27320 + 5.26384i) q^{59} +(2.64019 - 0.960952i) q^{61} +(5.62907 - 1.50831i) q^{62} +(-6.69194 + 3.86359i) q^{64} +(-3.72276 + 11.5777i) q^{65} +(6.11610 + 4.28254i) q^{67} +(2.00246 + 1.40214i) q^{68} +(3.12049 + 6.07833i) q^{70} +(4.24004 - 2.44799i) q^{71} +(-6.73088 + 1.80353i) q^{73} +(4.38269 - 1.59517i) q^{74} +(4.18242 - 3.50947i) q^{76} +(-2.88379 - 6.18430i) q^{77} +(-12.8661 - 2.26863i) q^{79} +(-3.00075 - 1.26294i) q^{80} +(4.32741 - 4.32741i) q^{82} +(2.73492 + 3.90587i) q^{83} +(0.235061 + 6.18915i) q^{85} +(-0.984048 - 1.17274i) q^{86} +(6.51925 + 3.03998i) q^{88} +(-3.33276 + 5.77251i) q^{89} +(7.86060 + 13.6150i) q^{91} +(-0.0548802 - 0.627283i) q^{92} +(10.8062 - 1.90542i) q^{94} +(13.4879 + 3.07057i) q^{95} +(-18.2758 + 1.59893i) q^{97} +(1.38397 + 0.370833i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−0.865920	+	0.606324i	−0.612298	+	0.428736i	−0.838161	−	0.545424i	$-0.816369\pi$
$2$	−0.865920	+	0.606324i	−0.612298	+	0.428736i	0.225863	+	0.974159i	$0.427480\pi$
$3$		0			0
$3$		0			0
$4$	−0.301851	+	0.829330i	−0.150926	+	0.414665i
$5$	−2.13636	+	0.660292i	−0.955407	+	0.295292i
$5$	−2.13636	+	0.660292i	−0.955407	+	0.295292i
$6$		0			0
$7$	−1.22161	+	2.61975i	−0.461725	+	0.990171i	0.528271	+	0.849076i	$0.322840\pi$
$7$	−1.22161	+	2.61975i	−0.461725	+	0.990171i	−0.989996	+	0.141096i	$0.954937\pi$
$8$	−0.788655	−	2.94330i	−0.278832	−	1.04061i
$9$		0			0
$10$	1.44956	−	1.86708i	0.458392	−	0.590424i
$11$	−1.51740	+	1.80836i	−0.457512	+	0.545242i	−0.944648	−	0.328084i	$-0.893597\pi$
$11$	−1.51740	+	1.80836i	−0.457512	+	0.545242i	0.487136	+	0.873326i	$0.338041\pi$
$12$		0			0
$13$	3.11956	−	4.45519i	0.865210	−	1.23565i	−0.105265	−	0.994444i	$-0.533569\pi$
$13$	3.11956	−	4.45519i	0.865210	−	1.23565i	0.970475	−	0.241203i	$-0.0775421\pi$
$14$	−0.530600	−	3.00918i	−0.141809	−	0.804238i
$15$		0			0
$16$	1.11535	+	0.935892i	0.278838	+	0.233973i
$17$	0.716894	−	2.67549i	0.173872	−	0.648901i	−0.822869	−	0.568232i	$-0.807628\pi$
$17$	0.716894	−	2.67549i	0.173872	−	0.648901i	0.996741	−	0.0806688i	$-0.0257056\pi$
$18$		0			0
$19$	−5.35751	−	3.09316i	−1.22910	−	0.709619i	−0.262256	−	0.964998i	$-0.584466\pi$
$19$	−5.35751	−	3.09316i	−1.22910	−	0.709619i	−0.966841	+	0.255379i	$0.917800\pi$
$20$	0.0972619	−	1.97105i	0.0217484	−	0.440741i
$21$		0			0
$22$	0.217491	−	2.48593i	0.0463692	−	0.530002i
$23$	−0.646627	+	0.301527i	−0.134831	+	0.0628728i	−0.488863	−	0.872361i	$-0.662588\pi$
$23$	−0.646627	+	0.301527i	−0.134831	+	0.0628728i	0.354032	+	0.935233i	$0.384810\pi$
$24$		0			0
$25$	4.12803	−	2.82124i	0.825606	−	0.564247i
$26$			5.74930i			1.12753i
$27$		0			0
$28$	−1.80389	−	1.80389i	−0.340903	−	0.340903i
$29$	−0.623300	+	3.53491i	−0.115744	+	0.656416i	0.870635	+	0.491929i	$0.163708\pi$
$29$	−0.623300	+	3.53491i	−0.115744	+	0.656416i	−0.986379	+	0.164487i	$0.947403\pi$
$30$		0			0
$31$	−5.18043	−	1.88552i	−0.930432	−	0.338650i	−0.168051	−	0.985778i	$-0.553747\pi$
$31$	−5.18043	−	1.88552i	−0.930432	−	0.338650i	−0.762381	+	0.647129i	$0.775970\pi$
$32$	4.53781	+	0.397007i	0.802178	+	0.0701815i
$33$		0			0
$34$	1.00144	+	2.75143i	0.171745	+	0.471866i
$35$	0.879991	−	6.40333i	0.148746	−	1.08236i
$36$		0			0
$37$	−4.26173	−	1.14193i	−0.700624	−	0.187732i	−0.109114	−	0.994029i	$-0.534801\pi$
$37$	−4.26173	−	1.14193i	−0.700624	−	0.187732i	−0.591510	+	0.806298i	$0.701468\pi$
$38$	6.51463	−	0.569956i	1.05681	−	0.0924591i
$39$		0			0
$40$	3.62828	+	5.76719i	0.573682	+	0.911873i
$41$	−5.70140	+	1.00531i	−0.890409	+	0.157003i	−0.600095	−	0.799928i	$-0.704871\pi$
$41$	−5.70140	+	1.00531i	−0.890409	+	0.157003i	−0.290314	+	0.956932i	$0.593760\pi$
$42$		0			0
$43$	0.126221	+	1.44271i	0.0192485	+	0.220012i	0.999727	+	0.0233831i	$0.00744375\pi$
$43$	0.126221	+	1.44271i	0.0192485	+	0.220012i	−0.980478	+	0.196629i	$0.937001\pi$
$44$	−1.04170	−	1.80428i	−0.157042	−	0.272005i
$45$		0			0
$46$	0.377104	−	0.653164i	0.0556010	−	0.0963037i
$47$	−9.40770	−	4.38688i	−1.37225	−	0.639893i	−0.410010	−	0.912081i	$-0.634475\pi$
$47$	−9.40770	−	4.38688i	−1.37225	−	0.639893i	−0.962244	+	0.272188i	$0.912253\pi$
$48$		0			0
$49$	−0.871236	−	1.03830i	−0.124462	−	0.148328i
$50$	−1.86396	+	4.94589i	−0.263604	+	0.699454i
$51$		0			0
$52$	2.75318	+	3.93195i	0.381797	+	0.545263i
$53$	7.22940	−	7.22940i	0.993035	−	0.993035i	−0.00694140	−	0.999976i	$-0.502210\pi$
$53$	7.22940	−	7.22940i	0.993035	−	0.993035i	0.999976	+	0.00694140i	$0.00220953\pi$
$54$		0			0
$55$	2.04765	−	4.86523i	0.276105	−	0.656027i
$56$	8.67413	+	1.52948i	1.15913	+	0.204386i
$57$		0			0
$58$	−1.60357	−	3.43887i	−0.210559	−	0.451546i
$59$	−6.27320	+	5.26384i	−0.816701	+	0.685293i	−0.952197	−	0.305484i	$-0.901182\pi$
$59$	−6.27320	+	5.26384i	−0.816701	+	0.685293i	0.135496	+	0.990778i	$0.456737\pi$
$60$		0			0
$61$	2.64019	−	0.960952i	0.338042	−	0.123037i	−0.167421	−	0.985885i	$-0.553544\pi$
$61$	2.64019	−	0.960952i	0.338042	−	0.123037i	0.505463	+	0.862848i	$0.331322\pi$
$62$	5.62907	−	1.50831i	0.714893	−	0.191555i
$63$		0			0
$64$	−6.69194	+	3.86359i	−0.836493	+	0.482949i
$65$	−3.72276	+	11.5777i	−0.461751	+	1.43604i
$66$		0			0
$67$	6.11610	+	4.28254i	0.747201	+	0.523196i	0.884048	−	0.467396i	$-0.154808\pi$
$67$	6.11610	+	4.28254i	0.747201	+	0.523196i	−0.136847	+	0.990592i	$0.543697\pi$
$68$	2.00246	+	1.40214i	0.242834	+	0.170034i
$69$		0			0
$70$	3.12049	+	6.07833i	0.372970	+	0.726499i
$71$	4.24004	−	2.44799i	0.503200	−	0.290523i	−0.226834	−	0.973933i	$-0.572838\pi$
$71$	4.24004	−	2.44799i	0.503200	−	0.290523i	0.730034	+	0.683411i	$0.239504\pi$
$72$		0			0
$73$	−6.73088	+	1.80353i	−0.787790	+	0.211088i	−0.630216	−	0.776420i	$-0.717034\pi$
$73$	−6.73088	+	1.80353i	−0.787790	+	0.211088i	−0.157574	+	0.987507i	$0.550367\pi$
$74$	4.38269	−	1.59517i	0.509478	−	0.185435i
$75$		0			0
$76$	4.18242	−	3.50947i	0.479756	−	0.402563i
$77$	−2.88379	−	6.18430i	−0.328638	−	0.704767i
$78$		0			0
$79$	−12.8661	−	2.26863i	−1.44754	−	0.255241i	−0.606015	−	0.795453i	$-0.707233\pi$
$79$	−12.8661	−	2.26863i	−1.44754	−	0.255241i	−0.841529	+	0.540212i	$0.818344\pi$
$80$	−3.00075	−	1.26294i	−0.335494	−	0.141201i
$81$		0			0
$82$	4.32741	−	4.32741i	0.477883	−	0.477883i
$83$	2.73492	+	3.90587i	0.300196	+	0.428724i	0.940705	−	0.339227i	$-0.110165\pi$
$83$	2.73492	+	3.90587i	0.300196	+	0.428724i	−0.640509	+	0.767951i	$0.721276\pi$
$84$		0			0
$85$	0.235061	+	6.18915i	0.0254960	+	0.671307i
$86$	−0.984048	−	1.17274i	−0.106113	−	0.126460i
$87$		0			0
$88$	6.51925	+	3.03998i	0.694955	+	0.324063i
$89$	−3.33276	+	5.77251i	−0.353272	+	0.611885i	−0.986821	−	0.161818i	$-0.948264\pi$
$89$	−3.33276	+	5.77251i	−0.353272	+	0.611885i	0.633549	+	0.773703i	$0.281598\pi$
$90$		0			0
$91$	7.86060	+	13.6150i	0.824014	+	1.42723i
$92$	−0.0548802	−	0.627283i	−0.00572165	−	0.0653988i
$93$		0			0
$94$	10.8062	−	1.90542i	1.11457	−	0.196529i
$95$	13.4879	+	3.07057i	1.38383	+	0.315033i
$96$		0			0
$97$	−18.2758	+	1.59893i	−1.85563	+	0.162346i	−0.959547	−	0.281548i	$-0.909152\pi$
$97$	−18.2758	+	1.59893i	−1.85563	+	0.162346i	−0.896079	+	0.443894i	$0.853597\pi$
$98$	1.38397	+	0.370833i	0.139802	+	0.0374597i
$99$		0			0
$100$	1.09368	+	4.27509i	0.109368	+	0.427509i
$101$	1.15191	+	3.16484i	0.114619	+	0.314913i	0.983716	−	0.179728i	$-0.0575217\pi$
$101$	1.15191	+	3.16484i	0.114619	+	0.314913i	−0.869097	+	0.494641i	$0.835299\pi$
$102$		0			0
$103$	−3.61346	−	0.316137i	−0.356045	−	0.0311499i	−0.0922694	−	0.995734i	$-0.529412\pi$
$103$	−3.61346	−	0.316137i	−0.356045	−	0.0311499i	−0.263775	+	0.964584i	$0.584968\pi$
$104$	−15.5732	−	5.66819i	−1.52708	−	0.555812i
$105$		0			0
$106$	−1.87673	+	10.6434i	−0.182284	+	1.03378i
$107$	4.03460	+	4.03460i	0.390039	+	0.390039i	0.874701	−	0.484662i	$-0.161057\pi$
$107$	4.03460	+	4.03460i	0.390039	+	0.390039i	−0.484662	+	0.874701i	$0.661057\pi$
$108$		0			0
$109$			15.8226i			1.51553i	0.652527	+	0.757765i	$0.273709\pi$
$109$			15.8226i			1.51553i	−0.652527	+	0.757765i	$0.726291\pi$
$110$	1.17680	+	5.45444i	0.112204	+	0.520060i
$111$		0			0
$112$	−3.81433	+	1.77865i	−0.360420	+	0.168067i
$113$	0.232615	−	2.65880i	0.0218825	−	0.250119i	−0.977372	−	0.211526i	$-0.932157\pi$
$113$	0.232615	−	2.65880i	0.0218825	−	0.250119i	0.999255	−	0.0385931i	$-0.0122876\pi$
$114$		0			0
$115$	1.18233	−	1.07113i	0.110253	−	0.0998836i
$116$	−2.74346	−	1.58394i	−0.254724	−	0.147065i
$117$		0			0
$118$	2.24050	−	8.36165i	0.206255	−	0.769753i
$119$	6.13333	+	5.14648i	0.562242	+	0.471777i
$120$		0			0
$121$	0.942447	+	5.34488i	0.0856770	+	0.485898i
$122$	−1.70355	+	2.43292i	−0.154232	+	0.220266i
$123$		0			0
$124$	3.12744	−	3.72713i	0.280852	−	0.334707i
$125$	−6.95610	+	8.75287i	−0.622172	+	0.782880i
$126$		0			0
$127$	−0.846401	−	3.15881i	−0.0751059	−	0.280299i	0.918151	−	0.396230i	$-0.129682\pi$
$127$	−0.846401	−	3.15881i	−0.0751059	−	0.280299i	−0.993257	+	0.115931i	$0.963015\pi$
$128$	−0.398073	+	0.853671i	−0.0351850	+	0.0754546i
$129$		0			0
$130$	−3.79622	−	12.2826i	−0.332950	−	1.07725i
$131$	−0.497235	+	1.36614i	−0.0434436	+	0.119360i	−0.959517	−	0.281649i	$-0.909118\pi$
$131$	−0.497235	+	1.36614i	−0.0434436	+	0.119360i	0.916074	+	0.401010i	$0.131341\pi$
$132$		0			0
$133$	14.6481	−	10.2567i	1.27015	−	0.889368i
$134$	−7.89266			−0.681822
$135$		0			0
$136$	−8.44014			−0.723736
$137$	13.0703	−	9.15193i	1.11667	−	0.781902i	0.138637	−	0.990343i	$-0.455728\pi$
$137$	13.0703	−	9.15193i	1.11667	−	0.781902i	0.978035	+	0.208442i	$0.0668391\pi$
$138$		0			0
$139$	−3.12149	+	8.57623i	−0.264762	+	0.727426i	0.734069	+	0.679075i	$0.237619\pi$
$139$	−3.12149	+	8.57623i	−0.264762	+	0.727426i	−0.998830	+	0.0483514i	$0.984603\pi$
$140$	5.04484	+	2.66266i	0.426367	+	0.225035i
$141$		0			0
$142$	−2.18726	+	4.69060i	−0.183551	+	0.393626i
$143$	3.32299	+	12.4016i	0.277883	+	1.03707i
$144$		0			0
$145$	−1.00248	−	7.96338i	−0.0832517	−	0.661323i
$146$	4.73488	−	5.64281i	0.391861	−	0.467002i
$147$		0			0
$148$	2.23344	−	3.18968i	0.183588	−	0.262190i
$149$	−1.63395	−	9.26659i	−0.133858	−	0.759149i	−0.975648	−	0.219343i	$-0.929609\pi$
$149$	−1.63395	−	9.26659i	−0.133858	−	0.759149i	0.841789	−	0.539806i	$-0.181502\pi$
$150$		0			0
$151$	−0.808803	−	0.678666i	−0.0658194	−	0.0552291i	0.609284	−	0.792952i	$-0.291457\pi$
$151$	−0.808803	−	0.678666i	−0.0658194	−	0.0552291i	−0.675104	+	0.737723i	$0.735901\pi$
$152$	−4.87887	+	18.2082i	−0.395729	+	1.47688i
$153$		0			0
$154$	6.24682	+	3.60660i	0.503383	+	0.290628i
$155$	12.3122	+	0.607549i	0.988942	+	0.0487995i
$156$		0			0
$157$	1.94520	−	22.2338i	0.155244	−	1.77445i	−0.375408	−	0.926860i	$-0.622497\pi$
$157$	1.94520	−	22.2338i	0.155244	−	1.77445i	0.530652	−	0.847590i	$-0.321947\pi$
$158$	12.5165	−	5.83654i	0.995759	−	0.464330i
$159$		0			0
$160$	−9.95651	+	2.14813i	−0.787131	+	0.169825i
$161$		−	2.06235i		−	0.162536i
$162$		0			0
$163$	−1.74889	−	1.74889i	−0.136983	−	0.136983i	0.635290	−	0.772274i	$-0.280881\pi$
$163$	−1.74889	−	1.74889i	−0.136983	−	0.136983i	−0.772274	+	0.635290i	$0.780881\pi$
$164$	0.887241	−	5.03179i	0.0692819	−	0.392917i
$165$		0			0
$166$	−4.73644	−	1.72392i	−0.367619	−	0.133802i
$167$	−7.25686	−	0.634893i	−0.561553	−	0.0491295i	−0.197154	−	0.980373i	$-0.563170\pi$
$167$	−7.25686	−	0.634893i	−0.561553	−	0.0491295i	−0.364399	+	0.931243i	$0.618725\pi$
$168$		0			0
$169$	−5.67082	−	15.5805i	−0.436217	−	1.19850i
$170$	−3.95617	−	5.21678i	−0.303424	−	0.400109i
$171$		0			0
$172$	−1.23458	−	0.330806i	−0.0941362	−	0.0252237i
$173$	−20.4232	+	1.78680i	−1.55275	+	0.135848i	−0.830985	−	0.556295i	$-0.812222\pi$
$173$	−20.4232	+	1.78680i	−1.55275	+	0.135848i	−0.721760	+	0.692143i	$0.756667\pi$
$174$		0			0
$175$	2.34809	+	14.2608i	0.177499	+	1.07802i
$176$	−3.38487	+	0.596843i	−0.255144	+	0.0449887i
$177$		0			0
$178$	−0.614106	−	7.01926i	−0.0460292	−	0.526116i
$179$	−7.17079	−	12.4202i	−0.535970	−	0.928327i	−0.999116	−	0.0420450i	$-0.986613\pi$
$179$	−7.17079	−	12.4202i	−0.535970	−	0.928327i	0.463146	−	0.886282i	$-0.346721\pi$
$180$		0			0
$181$	1.03474	−	1.79221i	0.0769112	−	0.133214i	−0.825005	−	0.565126i	$-0.808828\pi$
$181$	1.03474	−	1.79221i	0.0769112	−	0.133214i	0.901916	+	0.431912i	$0.142161\pi$
$182$	−15.0617	−	7.02339i	−1.11645	−	0.520609i
$183$		0			0
$184$	1.39745	+	1.66542i	0.103021	+	0.122776i
$185$	9.85857	−	0.374424i	0.724816	−	0.0275282i
$186$		0			0
$187$	3.75043	+	5.35618i	0.274259	+	0.391682i
$188$	6.47790	−	6.47790i	0.472449	−	0.472449i
$189$		0			0
$190$	−13.5412	+	5.51919i	−0.982384	+	0.400404i
$191$	−22.9618	−	4.04878i	−1.66145	−	0.292959i	−0.737467	−	0.675383i	$-0.763978\pi$
$191$	−22.9618	−	4.04878i	−1.66145	−	0.292959i	−0.923987	+	0.382424i	$0.875089\pi$
$192$		0			0
$193$	−0.131693	−	0.282417i	−0.00947948	−	0.0203288i	0.901511	−	0.432756i	$-0.142459\pi$
$193$	−0.131693	−	0.282417i	−0.00947948	−	0.0203288i	−0.910991	+	0.412427i	$0.864681\pi$
$194$	14.8559	−	12.4656i	1.06659	−	0.894977i
$195$		0			0
$196$	1.12408	−	0.409130i	0.0802911	−	0.0292236i
$197$	3.13774	−	0.840756i	0.223555	−	0.0599014i	−0.145303	−	0.989387i	$-0.546416\pi$
$197$	3.13774	−	0.840756i	0.223555	−	0.0599014i	0.368858	+	0.929486i	$0.379749\pi$
$198$		0			0
$199$	5.52277	−	3.18857i	0.391499	−	0.226032i	−0.291310	−	0.956629i	$-0.594091\pi$
$199$	5.52277	−	3.18857i	0.391499	−	0.226032i	0.682809	+	0.730596i	$0.260758\pi$
$200$	−11.5593	−	9.92504i	−0.817369	−	0.701807i
$201$		0			0
$202$	−2.91638	−	2.04207i	−0.205196	−	0.143679i
$203$	−8.49914	−	5.95116i	−0.596523	−	0.417690i
$204$		0			0
$205$	11.5164	−	5.91229i	0.804342	−	0.412932i
$206$	3.32065	−	1.91718i	0.231360	−	0.133576i
$207$		0			0
$208$	7.64899	−	2.04954i	0.530362	−	0.142110i
$209$	13.7230	−	4.99477i	0.949241	−	0.345495i
$210$		0			0
$211$	4.91430	−	4.12359i	0.338314	−	0.283879i	−0.457763	−	0.889074i	$-0.651349\pi$
$211$	4.91430	−	4.12359i	0.338314	−	0.283879i	0.796077	+	0.605195i	$0.206905\pi$
$212$	3.81335	+	8.17776i	0.261902	+	0.561651i
$213$		0			0
$214$	−5.93991	−	1.04737i	−0.406044	−	0.0715965i
$215$	−1.22226	−	2.99880i	−0.0833578	−	0.204517i
$216$		0			0
$217$	11.2680	−	11.2680i	0.764925	−	0.764925i
$218$	−9.59362	−	13.7011i	−0.649762	−	0.927956i
$219$		0			0
$220$	3.41679	+	3.16675i	0.230360	+	0.213502i
$221$	−9.68341	−	11.5402i	−0.651376	−	0.776280i
$222$		0			0
$223$	−9.41489	−	4.39023i	−0.630467	−	0.293992i	0.0809965	−	0.996714i	$-0.474190\pi$
$223$	−9.41489	−	4.39023i	−0.630467	−	0.293992i	−0.711464	+	0.702723i	$0.751968\pi$
$224$	−6.58348	+	11.4029i	−0.439877	+	0.761889i
$225$		0			0
$226$	1.41067	+	2.44335i	0.0938361	+	0.162529i
$227$	−0.272304	−	3.11245i	−0.0180734	−	0.206580i	−0.999862	−	0.0166042i	$-0.994714\pi$
$227$	−0.272304	−	3.11245i	−0.0180734	−	0.206580i	0.981789	−	0.189976i	$-0.0608411\pi$
$228$		0			0
$229$	23.1368	−	4.07964i	1.52892	−	0.269590i	0.654990	−	0.755638i	$-0.272673\pi$
$229$	23.1368	−	4.07964i	1.52892	−	0.269590i	0.873933	+	0.486047i	$0.161562\pi$
$230$	−0.374350	+	1.64439i	−0.0246839	+	0.108428i
$231$		0			0
$232$	10.8959	−	0.953265i	0.715349	−	0.0625849i
$233$	3.20411	+	0.858538i	0.209908	+	0.0562447i	0.362241	−	0.932085i	$-0.382012\pi$
$233$	3.20411	+	0.858538i	0.209908	+	0.0562447i	−0.152333	+	0.988329i	$0.548679\pi$
$234$		0			0
$235$	22.9948	+	3.16011i	1.50002	+	0.206143i
$236$	−2.47188	−	6.79145i	−0.160906	−	0.442085i
$237$		0			0
$238$	−8.43141	−	0.737653i	−0.546527	−	0.0478149i
$239$	15.9837	+	5.81759i	1.03390	+	0.376309i	0.802564	−	0.596566i	$-0.203468\pi$
$239$	15.9837	+	5.81759i	1.03390	+	0.376309i	0.231335	+	0.972874i	$0.425691\pi$
$240$		0			0
$241$	3.22231	−	18.2746i	0.207567	−	1.17717i	−0.685782	−	0.727807i	$-0.740540\pi$
$241$	3.22231	−	18.2746i	0.207567	−	1.17717i	0.893349	−	0.449364i	$-0.148349\pi$
$242$	−4.05681	−	4.05681i	−0.260782	−	0.260782i
$243$		0			0
$244$			2.47965i			0.158744i
$245$	2.54685	+	1.64290i	0.162712	+	0.104961i
$246$		0			0
$247$	−30.4937	+	14.2194i	−1.94027	+	0.904761i
$248$	−1.46409	+	16.7346i	−0.0929695	+	1.06265i
$249$		0			0
$250$	0.716350	−	11.7969i	0.0453060	−	0.746103i
$251$	13.1493	+	7.59178i	0.829979	+	0.479189i	0.853846	−	0.520527i	$-0.174264\pi$
$251$	13.1493	+	7.59178i	0.829979	+	0.479189i	−0.0238664	+	0.999715i	$0.507598\pi$
$252$		0			0
$253$	0.435919	−	1.62687i	0.0274060	−	0.102281i
$254$	2.64818	+	2.22208i	0.166161	+	0.139426i
$255$		0			0
$256$	−2.85653	−	16.2002i	−0.178533	−	1.01251i
$257$	−4.98418	+	7.11815i	−0.310905	+	0.444018i	−0.943946	−	0.330100i	$-0.892917\pi$
$257$	−4.98418	+	7.11815i	−0.310905	+	0.444018i	0.633041	+	0.774118i	$0.281806\pi$
$258$		0			0
$259$	8.19772	−	9.76966i	0.509382	−	0.607057i
$260$	−8.47800	−	6.58213i	−0.525783	−	0.408207i
$261$		0			0
$262$	−0.397759	−	1.48446i	−0.0245736	−	0.0917099i
$263$	−9.97382	+	21.3889i	−0.615012	+	1.31890i	0.314203	+	0.949356i	$0.398263\pi$
$263$	−9.97382	+	21.3889i	−0.615012	+	1.31890i	−0.929214	+	0.369541i	$0.879515\pi$
$264$		0			0
$265$	−10.6711	+	20.2181i	−0.655518	+	1.24199i
$266$	−6.46518	+	17.7629i	−0.396406	+	1.08912i
$267$		0			0
$268$	−5.39779	+	3.77957i	−0.329723	+	0.230874i
$269$	−10.2124			−0.622659			−0.311330	−	0.950302i	$-0.600774\pi$
$269$	−10.2124			−0.622659			−0.311330	+	0.950302i	$0.600774\pi$
$270$		0			0
$271$	4.84409			0.294258			0.147129	−	0.989117i	$-0.452997\pi$
$271$	4.84409			0.294258			0.147129	+	0.989117i	$0.452997\pi$
$272$	3.30356	−	2.31318i	0.200308	−	0.140257i
$273$		0			0
$274$	−5.76881	+	15.8497i	−0.348506	+	0.957514i
$275$	−1.16204	+	11.7459i	−0.0700734	+	0.708305i
$276$		0			0
$277$	−5.71185	+	12.2491i	−0.343192	+	0.735978i	−0.999834	−	0.0182248i	$-0.994199\pi$
$277$	−5.71185	+	12.2491i	−0.343192	+	0.735978i	0.656642	+	0.754203i	$0.271976\pi$
$278$	−2.49701	−	9.31897i	−0.149761	−	0.558914i
$279$		0			0
$280$	−19.5409	+	2.45994i	−1.16779	+	0.147010i
$281$	10.1156	−	12.0553i	0.603445	−	0.719158i	−0.374685	−	0.927152i	$-0.622249\pi$
$281$	10.1156	−	12.0553i	0.603445	−	0.719158i	0.978130	+	0.207994i	$0.0666936\pi$
$282$		0			0
$283$	−17.2952	+	24.7001i	−1.02809	+	1.46827i	−0.150648	+	0.988587i	$0.548136\pi$
$283$	−17.2952	+	24.7001i	−1.02809	+	1.46827i	−0.877443	+	0.479680i	$0.840753\pi$
$284$	0.750327	+	4.25532i	0.0445237	+	0.252507i
$285$		0			0
$286$	−10.3968	−	8.72397i	−0.614777	−	0.515859i
$287$	4.33122	−	16.1643i	0.255664	−	0.954150i
$288$		0			0
$289$	8.07815	+	4.66392i	0.475185	+	0.274348i
$290$	5.69646	+	6.28782i	0.334508	+	0.369234i
$291$		0			0
$292$	0.536001	−	6.12652i	0.0313671	−	0.358527i
$293$	6.65512	−	3.10333i	0.388796	−	0.181299i	−0.218384	−	0.975863i	$-0.570078\pi$
$293$	6.65512	−	3.10333i	0.388796	−	0.181299i	0.607180	+	0.794564i	$0.292301\pi$
$294$		0			0
$295$	9.92611	−	15.3876i	0.577921	−	0.895899i
$296$			13.4441i			0.781424i
$297$		0			0
$298$	7.03343	+	7.03343i	0.407435	+	0.407435i
$299$	−0.673830	+	3.82148i	−0.0389686	+	0.221002i
$300$		0			0
$301$	−3.93374	−	1.43176i	−0.226737	−	0.0825254i
$302$	1.11185	+	0.0972742i	0.0639798	+	0.00559750i
$303$		0			0
$304$	−3.08065	−	8.46402i	−0.176687	−	0.485445i
$305$	−5.00588	+	3.79623i	−0.286636	+	0.217372i
$306$		0			0
$307$	13.2129	+	3.54038i	0.754099	+	0.202060i	0.615336	−	0.788265i	$-0.289020\pi$
$307$	13.2129	+	3.54038i	0.754099	+	0.202060i	0.138764	+	0.990326i	$0.455687\pi$
$308$	5.99930	−	0.524871i	0.341842	−	0.0299073i
$309$		0			0
$310$	−11.0298	+	6.93911i	−0.626449	+	0.394115i
$311$	−3.80231	+	0.670449i	−0.215609	+	0.0380177i	−0.280409	−	0.959881i	$-0.590470\pi$
$311$	−3.80231	+	0.670449i	−0.215609	+	0.0380177i	0.0648001	+	0.997898i	$0.479359\pi$
$312$		0			0
$313$	2.14418	+	24.5081i	0.121196	+	1.38528i	0.776597	+	0.629997i	$0.216944\pi$
$313$	2.14418	+	24.5081i	0.121196	+	1.38528i	−0.655401	+	0.755281i	$0.727500\pi$
$314$	11.7965	+	20.4321i	0.665714	+	1.15305i
$315$		0			0
$316$	5.76508	−	9.98541i	0.324311	−	0.561723i
$317$	−14.9555	−	6.97386i	−0.839984	−	0.391691i	−0.0454916	−	0.998965i	$-0.514485\pi$
$317$	−14.9555	−	6.97386i	−0.839984	−	0.391691i	−0.794493	+	0.607274i	$0.792263\pi$
$318$		0			0
$319$	−5.44660	−	6.49101i	−0.304951	−	0.363427i
$320$	11.7453	−	12.6726i	0.656580	−	0.708422i
$321$		0			0
$322$	1.25045	+	1.78583i	0.0696849	+	0.0995203i
$323$	−12.1165	+	12.1165i	−0.674178	+	0.674178i
$324$		0			0
$325$	0.308476	−	27.1922i	0.0171112	−	1.50835i
$326$	2.57479	+	0.454005i	0.142604	+	0.0251450i
$327$		0			0
$328$	7.45537	+	15.9881i	0.411654	+	0.882794i
$329$	22.9851	−	19.2867i	1.26721	−	1.06331i
$330$		0			0
$331$	−19.3973	+	7.06005i	−1.06617	+	0.388056i	−0.814744	−	0.579820i	$-0.803123\pi$
$331$	−19.3973	+	7.06005i	−1.06617	+	0.388056i	−0.251429	+	0.967876i	$0.580901\pi$
$332$	−4.06479	+	1.08916i	−0.223084	+	0.0597752i
$333$		0			0
$334$	6.66881	−	3.85024i	0.364901	−	0.210676i
$335$	−15.8939	−	5.11062i	−0.868377	−	0.279223i
$336$		0			0
$337$	−8.57053	−	6.00115i	−0.466867	−	0.326904i	0.316361	−	0.948639i	$-0.397539\pi$
$337$	−8.57053	−	6.00115i	−0.466867	−	0.326904i	−0.783227	+	0.621735i	$0.786428\pi$
$338$	14.3573	+	10.0531i	0.780933	+	0.546815i
$339$		0			0
$340$	−5.20380	−	1.67326i	−0.282215	−	0.0907452i
$341$	11.2705	−	6.50701i	0.610330	−	0.352374i
$342$		0			0
$343$	−15.7602	+	4.22292i	−0.850968	+	0.228016i
$344$	4.14679	−	1.50931i	0.223580	−	0.0813765i
$345$		0			0
$346$	16.6015	−	13.9303i	0.892500	−	0.748896i
$347$	4.85639	+	10.4146i	0.260705	+	0.559083i	0.992472	−	0.122472i	$-0.0390821\pi$
$347$	4.85639	+	10.4146i	0.260705	+	0.559083i	−0.731767	+	0.681554i	$0.761304\pi$
$348$		0			0
$349$	15.6377	+	2.75735i	0.837067	+	0.147597i	0.575719	−	0.817647i	$-0.304722\pi$
$349$	15.6377	+	2.75735i	0.837067	+	0.147597i	0.261347	+	0.965245i	$0.415833\pi$
$350$	−10.6799	−	10.9250i	−0.570867	−	0.583968i
$351$		0			0
$352$	−7.60358	+	7.60358i	−0.405272	+	0.405272i
$353$	−4.97772	−	7.10893i	−0.264938	−	0.378370i	0.664538	−	0.747255i	$-0.268629\pi$
$353$	−4.97772	−	7.10893i	−0.264938	−	0.378370i	−0.929475	+	0.368885i	$0.879740\pi$
$354$		0			0
$355$	−7.44184	+	8.02943i	−0.394972	+	0.426158i
$356$	−3.78131	−	4.50640i	−0.200409	−	0.238838i
$357$		0			0
$358$	13.7400	+	6.40706i	0.726180	+	0.338623i
$359$	−10.2032	+	17.6725i	−0.538505	+	0.932718i	0.460480	+	0.887670i	$0.347677\pi$
$359$	−10.2032	+	17.6725i	−0.538505	+	0.932718i	−0.998985	+	0.0450476i	$0.985656\pi$
$360$		0			0
$361$	9.63526	+	16.6888i	0.507119	+	0.878356i
$362$	0.190664	+	2.17930i	0.0100211	+	0.114541i
$363$		0			0
$364$	−13.6640	+	2.40933i	−0.716189	+	0.126283i
$365$	13.1887	−	8.29733i	0.690328	−	0.434302i
$366$		0			0
$367$	25.8506	−	2.26163i	1.34939	−	0.118056i	0.610571	−	0.791962i	$-0.290940\pi$
$367$	25.8506	−	2.26163i	1.34939	−	0.118056i	0.738818	+	0.673906i	$0.235385\pi$
$368$	−1.00341	−	0.268864i	−0.0523066	−	0.0140155i
$369$		0			0
$370$	−8.30971	+	6.30171i	−0.432001	+	0.327610i
$371$	10.1077	+	27.7707i	0.524766	+	1.44178i
$372$		0			0
$373$	4.75950	+	0.416402i	0.246438	+	0.0215605i	0.209705	−	0.977765i	$-0.432750\pi$
$373$	4.75950	+	0.416402i	0.246438	+	0.0215605i	0.0367323	+	0.999325i	$0.488305\pi$
$374$	−6.49515	−	2.36404i	−0.335856	−	0.122242i
$375$		0			0
$376$	−5.49248	+	31.1494i	−0.283253	+	1.60641i
$377$	13.8043	+	13.8043i	0.710956	+	0.710956i
$378$		0			0
$379$			25.3002i			1.29958i	0.760112	+	0.649792i	$0.225144\pi$
$379$			25.3002i			1.29958i	−0.760112	+	0.649792i	$0.774856\pi$
$380$	−6.61786	+	10.2591i	−0.339489	+	0.526280i
$381$		0			0
$382$	22.3379	−	10.4163i	1.14291	−	0.532946i
$383$	1.07406	−	12.2766i	0.0548819	−	0.627303i	−0.918089	−	0.396375i	$-0.870268\pi$
$383$	1.07406	−	12.2766i	0.0548819	−	0.627303i	0.972971	−	0.230929i	$-0.0741764\pi$
$384$		0			0
$385$	10.2442	+	11.3077i	0.522095	+	0.576295i
$386$	0.285272	+	0.164702i	0.0145200	+	0.00838310i
$387$		0			0
$388$	4.19054	−	15.6393i	0.212742	−	0.793965i
$389$	−6.83430	−	5.73466i	−0.346513	−	0.290759i	0.452875	−	0.891574i	$-0.350398\pi$
$389$	−6.83430	−	5.73466i	−0.346513	−	0.290759i	−0.799388	+	0.600815i	$0.794843\pi$
$390$		0			0
$391$	0.343168	+	1.94620i	0.0173548	+	0.0984238i
$392$	−2.36892	+	3.38317i	−0.119649	+	0.170876i
$393$		0			0
$394$	−2.20727	+	2.63052i	−0.111200	+	0.132524i
$395$	28.9844	−	3.64875i	1.45836	−	0.183588i
$396$		0			0
$397$	3.52782	+	13.1660i	0.177056	+	0.660782i	0.996192	+	0.0871833i	$0.0277866\pi$
$397$	3.52782	+	13.1660i	0.177056	+	0.660782i	−0.819136	+	0.573599i	$0.805547\pi$
$398$	−2.84897	+	6.10964i	−0.142806	+	0.306249i
$399$		0			0
$400$	7.24458	+	0.716715i	0.362229	+	0.0358358i
$401$	1.00354	−	2.75721i	0.0501146	−	0.137689i	−0.912110	−	0.409945i	$-0.865548\pi$
$401$	1.00354	−	2.75721i	0.0501146	−	0.137689i	0.962225	+	0.272257i	$0.0877700\pi$
$402$		0			0
$403$	−24.5610	+	17.1978i	−1.22347	+	0.856683i
$404$	−2.97240			−0.147882
$405$		0			0
$406$	10.9679			0.544328
$407$	8.53175	−	5.97399i	0.422903	−	0.296120i
$408$		0			0
$409$	9.80467	−	26.9381i	0.484810	−	1.33200i	−0.420515	−	0.907285i	$-0.638151\pi$
$409$	9.80467	−	26.9381i	0.484810	−	1.33200i	0.905325	−	0.424719i	$-0.139627\pi$
$410$	−6.38754	+	12.1022i	−0.315458	+	0.597687i
$411$		0			0
$412$	1.35291	−	2.90132i	0.0666530	−	0.142938i
$413$	−6.12654	−	22.8645i	−0.301467	−	1.12509i
$414$		0			0
$415$	−8.42177	−	6.53847i	−0.413408	−	0.320961i
$416$	15.9247	−	18.9783i	0.780772	−	0.930488i
$417$		0			0
$418$	−8.85459	+	12.6457i	−0.433092	+	0.618519i
$419$	2.30839	+	13.0915i	0.112772	+	0.639563i	0.987829	+	0.155543i	$0.0497127\pi$
$419$	2.30839	+	13.0915i	0.112772	+	0.639563i	−0.875057	+	0.484020i	$0.839176\pi$
$420$		0			0
$421$	6.93437	+	5.81863i	0.337960	+	0.283582i	0.795934	−	0.605383i	$-0.206980\pi$
$421$	6.93437	+	5.81863i	0.337960	+	0.283582i	−0.457974	+	0.888966i	$0.651425\pi$
$422$	−1.75516	+	6.55035i	−0.0854399	+	0.318866i
$423$		0			0
$424$	−26.9798	−	15.5768i	−1.31025	−	0.756476i
$425$	−4.58882	−	13.0670i	−0.222590	−	0.633843i
$426$		0			0
$427$	−0.707831	+	8.09054i	−0.0342543	+	0.391529i
$428$	−4.56386	+	2.12816i	−0.220602	+	0.102869i
$429$		0			0
$430$	2.87663	+	1.85564i	0.138723	+	0.0894868i
$431$			0.295969i			0.0142563i	0.999975	+	0.00712817i	$0.00226899\pi$
$431$			0.295969i			0.0142563i	−0.999975	+	0.00712817i	$0.997731\pi$
$432$		0			0
$433$	12.8171	+	12.8171i	0.615949	+	0.615949i	0.944490	−	0.328541i	$-0.106557\pi$
$433$	12.8171	+	12.8171i	0.615949	+	0.615949i	−0.328541	+	0.944490i	$0.606557\pi$
$434$	−2.92514	+	16.5893i	−0.140411	+	0.796312i
$435$		0			0
$436$	−13.1221	−	4.77607i	−0.628437	−	0.228732i
$437$	4.39698	+	0.384686i	0.210336	+	0.0184020i
$438$		0			0
$439$	−9.75841	−	26.8110i	−0.465743	−	1.27962i	−0.921105	−	0.389313i	$-0.872712\pi$
$439$	−9.75841	−	26.8110i	−0.465743	−	1.27962i	0.455362	−	0.890306i	$-0.349510\pi$
$440$	−15.9347	−	2.18986i	−0.759658	−	0.104398i
$441$		0			0
$442$	15.3822	+	4.12164i	0.731655	+	0.196046i
$443$	40.1651	−	3.51399i	1.90830	−	0.166955i	0.929098	−	0.369833i	$-0.120585\pi$
$443$	40.1651	−	3.51399i	1.90830	−	0.166955i	0.979204	+	0.202878i	$0.0650296\pi$
$444$		0			0
$445$	3.30842	−	14.5327i	0.156834	−	0.688917i
$446$	10.8144	−	1.90688i	0.512079	−	0.0902933i
$447$		0			0
$448$	−1.94671	−	22.2510i	−0.0919734	−	1.05126i
$449$	3.91232	+	6.77634i	0.184634	+	0.319795i	0.943453	−	0.331506i	$-0.107557\pi$
$449$	3.91232	+	6.77634i	0.184634	+	0.319795i	−0.758819	+	0.651301i	$0.774223\pi$
$450$		0			0
$451$	6.83332	−	11.8357i	0.321768	−	0.557319i
$452$	2.13480	+	0.995476i	0.100413	+	0.0468232i
$453$		0			0
$454$	2.12294	+	2.53003i	0.0996347	+	0.118740i
$455$	−25.7829	−	23.8961i	−1.20872	−	1.12027i
$456$		0			0
$457$	−3.14363	−	4.48957i	−0.147053	−	0.210013i	0.738867	−	0.673851i	$-0.235361\pi$
$457$	−3.14363	−	4.48957i	−0.147053	−	0.210013i	−0.885920	+	0.463838i	$0.846472\pi$
$458$	−17.5610	+	17.5610i	−0.820573	+	0.820573i
$459$		0			0
$460$	0.531434	+	1.30386i	0.0247782	+	0.0607929i
$461$	−29.6880	−	5.23480i	−1.38271	−	0.243809i	−0.567689	−	0.823243i	$-0.692163\pi$
$461$	−29.6880	−	5.23480i	−1.38271	−	0.243809i	−0.815019	+	0.579434i	$0.803274\pi$
$462$		0			0
$463$	0.0761934	+	0.163397i	0.00354101	+	0.00759371i	0.908070	−	0.418818i	$-0.137555\pi$
$463$	0.0761934	+	0.163397i	0.00354101	+	0.00759371i	−0.904529	+	0.426411i	$0.859778\pi$
$464$	−4.00350	+	3.35933i	−0.185858	+	0.155953i
$465$		0			0
$466$	−3.29505	+	1.19930i	−0.152640	+	0.0555566i
$467$	12.1916	−	3.26672i	0.564158	−	0.151166i	0.0345422	−	0.999403i	$-0.489003\pi$
$467$	12.1916	−	3.26672i	0.564158	−	0.151166i	0.529616	+	0.848238i	$0.322336\pi$
$468$		0			0
$469$	−18.6907	+	10.7911i	−0.863055	+	0.498285i
$470$	−21.8277	+	11.2059i	−1.00684	+	0.516890i
$471$		0			0
$472$	20.4404	+	14.3126i	0.940848	+	0.658789i
$473$	−2.80048	−	1.96091i	−0.128766	−	0.0901629i
$474$		0			0
$475$	−30.8425	+	2.34615i	−1.41515	+	0.107649i
$476$	−6.11948	+	3.53308i	−0.280486	+	0.161939i
$477$		0			0
$478$	−17.3679	+	4.65373i	−0.794391	+	0.212857i
$479$	33.4923	−	12.1902i	1.53030	−	0.556985i	0.566607	−	0.823988i	$-0.308256\pi$
$479$	33.4923	−	12.1902i	1.53030	−	0.556985i	0.963696	+	0.267003i	$0.0860335\pi$
$480$		0			0
$481$	−18.3822	+	15.4245i	−0.838157	+	0.703297i
$482$	8.29007	+	17.7781i	0.377602	+	0.809771i
$483$		0			0
$484$	−4.71715	−	0.831760i	−0.214416	−	0.0378073i
$485$	37.9878	−	15.4832i	1.72494	−	0.703058i
$486$		0			0
$487$	4.88907	−	4.88907i	0.221545	−	0.221545i	−0.587604	−	0.809149i	$-0.699929\pi$
$487$	4.88907	−	4.88907i	0.221545	−	0.221545i	0.809149	+	0.587604i	$0.199929\pi$
$488$	−4.91057	−	7.01302i	−0.222291	−	0.317464i
$489$		0			0
$490$	−3.20150	+	0.121592i	−0.144629	+	0.00549295i
$491$	16.6934	+	19.8944i	0.753361	+	0.897821i	0.997409	−	0.0719426i	$-0.0229198\pi$
$491$	16.6934	+	19.8944i	0.753361	+	0.897821i	−0.244048	+	0.969763i	$0.578475\pi$
$492$		0			0
$493$	9.01076	+	4.20179i	0.405824	+	0.189239i
$494$	17.7835	−	30.8019i	0.800117	−	1.38584i
$495$		0			0
$496$	−4.01336	−	6.95135i	−0.180205	−	0.312125i
$497$	1.23344	+	14.0983i	0.0553275	+	0.632396i
$498$		0			0
$499$	11.0477	−	1.94801i	0.494564	−	0.0872050i	0.0791972	−	0.996859i	$-0.474764\pi$
$499$	11.0477	−	1.94801i	0.494564	−	0.0872050i	0.415367	+	0.909654i	$0.363653\pi$
$500$	−5.15931	−	8.41096i	−0.230731	−	0.376150i
$501$		0			0
$502$	−15.9894	+	1.39889i	−0.713640	+	0.0624354i
$503$	−29.1890	−	7.82118i	−1.30147	−	0.348729i	−0.459467	−	0.888195i	$-0.651960\pi$
$503$	−29.1890	−	7.82118i	−1.30147	−	0.348729i	−0.842008	+	0.539466i	$0.818626\pi$
$504$		0			0
$505$	−4.55060	−	6.00063i	−0.202499	−	0.267024i
$506$	0.608940	+	1.67305i	0.0270707	+	0.0743761i
$507$		0			0
$508$	2.87518	+	0.251546i	0.127566	+	0.0111605i
$509$	−22.0511	−	8.02596i	−0.977399	−	0.355744i	−0.196571	−	0.980490i	$-0.562981\pi$
$509$	−22.0511	−	8.02596i	−0.977399	−	0.355744i	−0.780829	+	0.624745i	$0.785203\pi$
$510$		0			0
$511$	3.49769	−	19.8364i	0.154729	−	0.877511i
$512$	10.9640	+	10.9640i	0.484544	+	0.484544i
$513$		0			0
$514$		−	9.18578i		−	0.405167i
$515$	7.92837	−	1.71056i	0.349366	−	0.0753762i
$516$		0			0
$517$	22.2083	−	10.3559i	0.976719	−	0.455452i
$518$	−1.17499	+	13.4302i	−0.0516262	+	0.590090i
$519$		0			0
$520$	37.0126	+	1.82639i	1.62311	+	0.0800925i
$521$	14.2319	+	8.21681i	0.623512	+	0.359985i	0.778235	−	0.627973i	$-0.216115\pi$
$521$	14.2319	+	8.21681i	0.623512	+	0.359985i	−0.154723	+	0.987958i	$0.549449\pi$
$522$		0			0
$523$	3.78176	−	14.1137i	0.165365	−	0.617150i	−0.832629	−	0.553832i	$-0.813165\pi$
$523$	3.78176	−	14.1137i	0.165365	−	0.617150i	0.997993	−	0.0633182i	$-0.0201683\pi$
$524$	−0.982891	−	0.824743i	−0.0429378	−	0.0360291i
$525$		0			0
$526$	−4.33208	−	24.5685i	−0.188888	−	1.07124i
$527$	−8.75850	+	12.5084i	−0.381526	+	0.544876i
$528$		0			0
$529$	−14.4569	+	17.2291i	−0.628561	+	0.749090i
$530$	−3.01843	−	23.9774i	−0.131112	−	1.04151i
$531$		0			0
$532$	4.08464	+	15.2441i	0.177091	+	0.660914i
$533$	−13.3070	+	28.5370i	−0.576390	+	1.23607i
$534$		0			0
$535$	−11.2833	−	5.95532i	−0.487822	−	0.257471i
$536$	7.78131	−	21.3790i	0.336101	−	0.923431i
$537$		0			0
$538$	8.84309	−	6.19200i	0.381253	−	0.266956i
$539$	3.19963			0.137818
$540$		0			0
$541$	−28.4337			−1.22246			−0.611230	−	0.791453i	$-0.709325\pi$
$541$	−28.4337			−1.22246			−0.611230	+	0.791453i	$0.709325\pi$
$542$	−4.19460	+	2.93709i	−0.180173	+	0.126159i
$543$		0			0
$544$	4.31531	−	11.8562i	0.185017	−	0.508331i
$545$	−10.4475	−	33.8027i	−0.447523	−	1.44795i
$546$		0			0
$547$	4.44356	−	9.52924i	0.189993	−	0.407441i	−0.788118	−	0.615524i	$-0.788945\pi$
$547$	4.44356	−	9.52924i	0.189993	−	0.407441i	0.978111	+	0.208083i	$0.0667224\pi$
$548$	3.64467	+	13.6021i	0.155693	+	0.581053i
$549$		0			0
$550$	−6.11559	−	10.8756i	−0.260770	−	0.463737i
$551$	14.2734	−	17.0103i	0.608066	−	0.724665i
$552$		0			0
$553$	21.6605	−	30.9344i	0.921099	−	1.31547i
$554$	−2.48092	−	14.0700i	−0.105404	−	0.597776i
$555$		0			0
$556$	−6.17030	−	5.17749i	−0.261679	−	0.219575i
$557$	4.48926	−	16.7541i	0.190216	−	0.709896i	−0.803238	−	0.595659i	$-0.796891\pi$
$557$	4.48926	−	16.7541i	0.190216	−	0.709896i	0.993454	−	0.114237i	$-0.0364423\pi$
$558$		0			0
$559$	6.82132	+	3.93829i	0.288511	+	0.166572i
$560$	6.97433	−	6.31840i	0.294719	−	0.267001i
$561$		0			0
$562$	−1.44988	+	16.5722i	−0.0611596	+	0.699057i
$563$	−21.2542	+	9.91099i	−0.895758	+	0.417699i	−0.815286	−	0.579058i	$-0.803420\pi$
$563$	−21.2542	+	9.91099i	−0.895758	+	0.417699i	−0.0804714	+	0.996757i	$0.525643\pi$
$564$		0			0
$565$	1.25864	+	5.83373i	0.0529512	+	0.245427i
$566$		−	31.8748i		−	1.33980i
$567$		0			0
$568$	−10.5491	−	10.5491i	−0.442630	−	0.442630i
$569$	−6.84027	+	38.7931i	−0.286759	+	1.62629i	0.412175	+	0.911105i	$0.364769\pi$
$569$	−6.84027	+	38.7931i	−0.286759	+	1.62629i	−0.698934	+	0.715186i	$0.746342\pi$
$570$		0			0
$571$	31.4980	+	11.4643i	1.31815	+	0.479767i	0.902865	−	0.429924i	$-0.141460\pi$
$571$	31.4980	+	11.4643i	1.31815	+	0.479767i	0.415285	+	0.909691i	$0.363682\pi$
$572$	−11.2880	−	0.987576i	−0.471977	−	0.0412926i
$573$		0			0
$574$	6.05032	+	16.6231i	0.252536	+	0.693836i
$575$	−1.81862	+	3.06900i	−0.0758415	+	0.127986i
$576$		0			0
$577$	−21.0819	−	5.64888i	−0.877651	−	0.235166i	−0.208257	−	0.978074i	$-0.566779\pi$
$577$	−21.0819	−	5.64888i	−0.877651	−	0.235166i	−0.669393	+	0.742908i	$0.733446\pi$
$578$	−9.82287	+	0.859390i	−0.408578	+	0.0357459i
$579$		0			0
$580$	6.90687	+	1.57237i	0.286792	+	0.0652891i
$581$	−13.5734	+	2.39335i	−0.563119	+	0.0992930i
$582$		0			0
$583$	2.10351	+	24.0432i	0.0871185	+	0.995769i
$584$	10.6167	+	18.3886i	0.439321	+	0.760927i
$585$		0			0
$586$	−3.88117	+	6.72239i	−0.160330	+	0.277699i
$587$	22.1244	+	10.3168i	0.913173	+	0.425819i	0.821656	−	0.569984i	$-0.193051\pi$
$587$	22.1244	+	10.3168i	0.913173	+	0.425819i	0.0915170	+	0.995804i	$0.470828\pi$
$588$		0			0
$589$	21.9220	+	26.1256i	0.903279	+	1.07649i
$590$	0.734633	+	19.3428i	0.0302444	+	0.796332i
$591$		0			0
$592$	−3.68461	−	5.26217i	−0.151437	−	0.216274i
$593$	4.09490	−	4.09490i	0.168157	−	0.168157i	−0.618012	−	0.786169i	$-0.712062\pi$
$593$	4.09490	−	4.09490i	0.168157	−	0.168157i	0.786169	+	0.618012i	$0.212062\pi$
$594$		0			0
$595$	−16.5012	−	6.94491i	−0.676481	−	0.284714i
$596$	8.17827	+	1.44205i	0.334995	+	0.0590687i
$597$		0			0
$598$	−1.73357	−	3.71765i	−0.0708910	−	0.152026i
$599$	−30.3866	+	25.4974i	−1.24156	+	1.04180i	−0.244163	+	0.969734i	$0.578513\pi$
$599$	−30.3866	+	25.4974i	−1.24156	+	1.04180i	−0.997400	+	0.0720615i	$0.977042\pi$
$600$		0			0
$601$	−22.4811	+	8.18244i	−0.917022	+	0.333769i	−0.757053	−	0.653353i	$-0.773362\pi$
$601$	−22.4811	+	8.18244i	−0.917022	+	0.333769i	−0.159969	+	0.987122i	$0.551139\pi$
$602$	4.27441	−	1.14533i	0.174212	−	0.0466800i
$603$		0			0
$604$	0.806976	−	0.465908i	0.0328354	−	0.0189575i
$605$	−5.54258	−	10.7963i	−0.225338	−	0.438931i
$606$		0			0
$607$	−26.5308	−	18.5771i	−1.07685	−	0.754020i	−0.106160	−	0.994349i	$-0.533856\pi$
$607$	−26.5308	−	18.5771i	−1.07685	−	0.754020i	−0.970691	+	0.240329i	$0.922745\pi$
$608$	−23.0833	−	16.1631i	−0.936152	−	0.655501i
$609$		0			0
$610$	2.03295	−	6.32242i	0.0823116	−	0.255987i
$611$	−48.8923	+	28.2280i	−1.97797	+	1.14198i
$612$		0			0
$613$	14.7737	−	3.95860i	0.596704	−	0.159886i	0.0521885	−	0.998637i	$-0.483380\pi$
$613$	14.7737	−	3.95860i	0.596704	−	0.159886i	0.544515	+	0.838751i	$0.316714\pi$
$614$	−13.5879	+	4.94560i	−0.548364	+	0.199588i
$615$		0			0
$616$	−15.9279	+	13.3651i	−0.641755	+	0.538497i
$617$	−11.3221	−	24.2804i	−0.455812	−	0.977492i	−0.991137	−	0.132845i	$-0.957589\pi$
$617$	−11.3221	−	24.2804i	−0.455812	−	0.977492i	0.535325	−	0.844646i	$-0.320189\pi$
$618$		0			0
$619$	18.6300	+	3.28497i	0.748802	+	0.132034i	0.535011	−	0.844845i	$-0.320308\pi$
$619$	18.6300	+	3.28497i	0.748802	+	0.132034i	0.213792	+	0.976879i	$0.431419\pi$
$620$	−4.22032	+	10.0275i	−0.169492	+	0.402714i
$621$		0			0
$622$	2.88598	−	2.88598i	0.115717	−	0.115717i
$623$	−11.0512	−	15.7827i	−0.442757	−	0.632322i
$624$		0			0
$625$	9.08124	−	23.2923i	0.363250	−	0.931692i
$626$	−16.7165	−	19.9220i	−0.668126	−	0.796242i
$627$		0			0
$628$	17.8520	+	8.32451i	0.712371	+	0.332184i
$629$	−6.11042	+	10.5836i	−0.243638	+	0.421994i
$630$		0			0
$631$	0.0126965	+	0.0219910i	0.000505440	+	0.000875448i	0.866278	−	0.499562i	$-0.166506\pi$
$631$	0.0126965	+	0.0219910i	0.000505440	+	0.000875448i	−0.865773	+	0.500438i	$0.833172\pi$
$632$	3.46961	+	39.6578i	0.138014	+	1.57750i
$633$		0			0
$634$	17.1787	−	3.02907i	0.682253	−	0.120300i
$635$	3.89395	+	6.18947i	0.154527	+	0.245622i
$636$		0			0
$637$	−7.34369	+	0.642490i	−0.290968	+	0.0254564i
$638$	8.65198	+	2.31829i	0.342535	+	0.0917820i
$639$		0			0
$640$	0.286754	−	2.08659i	0.0113349	−	0.0824797i
$641$	−9.97230	−	27.3987i	−0.393882	−	1.08218i	−0.965214	−	0.261463i	$-0.915795\pi$
$641$	−9.97230	−	27.3987i	−0.393882	−	1.08218i	0.571331	−	0.820720i	$-0.306427\pi$
$642$		0			0
$643$	−1.74781	−	0.152914i	−0.0689270	−	0.00603033i	0.0526401	−	0.998614i	$-0.483236\pi$
$643$	−1.74781	−	0.152914i	−0.0689270	−	0.00603033i	−0.121567	+	0.992583i	$0.538792\pi$
$644$	1.71037	+	0.622522i	0.0673979	+	0.0245308i
$645$		0			0
$646$	3.14539	−	17.8384i	0.123754	−	0.701842i
$647$	−14.7341	−	14.7341i	−0.579259	−	0.579259i	0.355440	−	0.934699i	$-0.384331\pi$
$647$	−14.7341	−	14.7341i	−0.579259	−	0.579259i	−0.934699	+	0.355440i	$0.884331\pi$
$648$		0			0
$649$		−	19.3315i		−	0.758830i
$650$	16.2201	+	23.7333i	0.636206	+	0.930896i
$651$		0			0
$652$	1.97831	−	0.922501i	0.0774766	−	0.0361279i
$653$	−0.812604	+	9.28810i	−0.0317996	+	0.363471i	0.963578	+	0.267429i	$0.0861741\pi$
$653$	−0.812604	+	9.28810i	−0.0317996	+	0.363471i	−0.995377	+	0.0960426i	$0.969382\pi$
$654$		0			0
$655$	0.160218	−	3.24688i	0.00626023	−	0.126866i
$656$	−7.29994	−	4.21462i	−0.285015	−	0.164553i
$657$		0			0
$658$	−8.20920	+	30.6372i	−0.320028	+	1.19436i
$659$	14.0775	+	11.8125i	0.548383	+	0.460148i	0.874393	−	0.485218i	$-0.161260\pi$
$659$	14.0775	+	11.8125i	0.548383	+	0.460148i	−0.326010	+	0.945366i	$0.605704\pi$
$660$		0			0
$661$	4.43306	+	25.1412i	0.172426	+	0.977878i	0.941073	+	0.338204i	$0.109819\pi$
$661$	4.43306	+	25.1412i	0.172426	+	0.977878i	−0.768647	+	0.639674i	$0.779070\pi$
$662$	12.5159	−	17.8745i	0.486443	−	0.694712i
$663$		0			0
$664$	9.33923	−	11.1301i	0.362432	−	0.431930i
$665$	−24.5211	+	31.5839i	−0.950886	+	1.22477i
$666$		0			0
$667$	−0.662829	−	2.47371i	−0.0256648	−	0.0957825i
$668$	2.71703	−	5.82669i	0.105125	−	0.225441i
$669$		0			0
$670$	16.8615	−	5.21146i	0.651418	−	0.201336i
$671$	−2.26847	+	6.23257i	−0.0875733	+	0.240606i
$672$		0			0
$673$	3.83098	−	2.68248i	0.147673	−	0.103402i	−0.497405	−	0.867518i	$-0.665714\pi$
$673$	3.83098	−	2.68248i	0.147673	−	0.103402i	0.645078	+	0.764117i	$0.276825\pi$
$674$	11.0600			0.426017
$675$		0			0
$676$	14.6331			0.562810
$677$	32.1483	−	22.5105i	1.23556	−	0.865147i	0.241123	−	0.970495i	$-0.422484\pi$
$677$	32.1483	−	22.5105i	1.23556	−	0.865147i	0.994436	+	0.105347i	$0.0335953\pi$
$678$		0			0
$679$	18.1371	−	49.8312i	0.696038	−	1.91235i
$680$	18.0311	−	5.57296i	0.691462	−	0.213713i
$681$		0			0
$682$	−5.81397	+	12.4681i	−0.222628	+	0.477428i
$683$	−9.77386	−	36.4765i	−0.373986	−	1.39574i	−0.854820	−	0.518924i	$-0.826333\pi$
$683$	−9.77386	−	36.4765i	−0.373986	−	1.39574i	0.480834	−	0.876812i	$-0.340334\pi$
$684$		0			0
$685$	−21.8799	+	28.1820i	−0.835987	+	1.07678i
$686$	11.0866	−	13.2125i	0.423287	−	0.504454i
$687$		0			0
$688$	−1.20944	+	1.72726i	−0.0461096	+	0.0658513i
$689$	−9.65582	−	54.7609i	−0.367858	−	2.08622i
$690$		0			0
$691$	10.1478	+	8.51501i	0.386040	+	0.323926i	0.815068	−	0.579365i	$-0.196699\pi$
$691$	10.1478	+	8.51501i	0.386040	+	0.323926i	−0.429028	+	0.903291i	$0.641144\pi$
$692$	4.68292	−	17.4769i	0.178018	−	0.664372i
$693$		0			0
$694$	−10.5198	−	6.07363i	−0.399327	−	0.230552i
$695$	1.00580	−	20.3830i	0.0381522	−	0.773170i
$696$		0			0
$697$	−1.39761	+	15.9747i	−0.0529381	+	0.605086i
$698$	−15.2128	+	7.09386i	−0.575814	+	0.268507i
$699$		0			0
$700$	−12.5357	−	2.35731i	−0.473805	−	0.0890979i
$701$			1.42181i			0.0537011i	0.999639	+	0.0268505i	$0.00854782\pi$
$701$			1.42181i			0.0537011i	−0.999639	+	0.0268505i	$0.991452\pi$
$702$		0			0
$703$	19.3001	+	19.3001i	0.727916	+	0.727916i
$704$	3.16755	−	17.9641i	0.119381	−	0.677046i
$705$		0			0
$706$	8.62062	+	3.13765i	0.324441	+	0.118087i
$707$	−9.69826	−	0.848488i	−0.364741	−	0.0319107i
$708$		0			0
$709$	12.4901	+	34.3163i	0.469077	+	1.28878i	0.918487	+	0.395452i	$0.129412\pi$
$709$	12.4901	+	34.3163i	0.469077	+	1.28878i	−0.449410	+	0.893325i	$0.648366\pi$
$710$	1.57560	−	11.4650i	0.0591313	−	0.430274i
$711$		0			0
$712$	19.6186	+	5.25679i	0.735239	+	0.197007i
$713$	3.91834	−	0.342810i	0.146743	−	0.0128384i
$714$		0			0
$715$	−15.2878	−	24.3000i	−0.571730	−	0.908770i
$716$	12.4649	−	2.19790i	0.465836	−	0.0821395i
$717$		0			0
$718$	−1.88008	−	21.4894i	−0.0701639	−	0.801977i
$719$	−12.9014	−	22.3459i	−0.481142	−	0.833363i	0.518624	−	0.855003i	$-0.326445\pi$
$719$	−12.9014	−	22.3459i	−0.481142	−	0.833363i	−0.999766	+	0.0216398i	$0.993111\pi$
$720$		0			0
$721$	5.24243	−	9.08015i	0.195238	−	0.338162i
$722$	−18.4622	−	8.60904i	−0.687090	−	0.320395i
$723$		0			0
$724$	1.17400	+	1.39912i	0.0436314	+	0.0519978i
$725$	7.39982	+	16.3507i	0.274822	+	0.607249i
$726$		0			0
$727$	−0.926059	−	1.32255i	−0.0343456	−	0.0490507i	0.801612	−	0.597845i	$-0.203976\pi$
$727$	−0.926059	−	1.32255i	−0.0343456	−	0.0490507i	−0.835958	+	0.548794i	$0.815087\pi$
$728$	33.8736	−	33.8736i	1.25544	−	1.25544i
$729$		0			0
$730$	−6.38948	+	15.1814i	−0.236485	+	0.561890i
$731$	3.95045	+	0.696570i	0.146112	+	0.0257636i
$732$		0			0
$733$	−5.62244	−	12.0574i	−0.207669	−	0.445349i	0.774692	−	0.632338i	$-0.217905\pi$
$733$	−5.62244	−	12.0574i	−0.207669	−	0.445349i	−0.982362	+	0.186990i	$0.940127\pi$
$734$	−21.0132	+	17.6322i	−0.775613	+	0.650816i
$735$		0			0
$736$	−3.05398	+	1.11156i	−0.112571	+	0.0409725i
$737$	−17.0249	+	4.56182i	−0.627122	+	0.168037i
$738$		0			0
$739$	30.9063	−	17.8437i	1.13691	−	0.656393i	0.191243	−	0.981543i	$-0.438748\pi$
$739$	30.9063	−	17.8437i	1.13691	−	0.656393i	0.945663	+	0.325150i	$0.105415\pi$
$740$	−2.66530	+	8.28902i	−0.0979784	+	0.304711i
$741$		0			0
$742$	−25.5905	−	17.9187i	−0.939457	−	0.657815i
$743$	28.8465	+	20.1985i	1.05828	+	0.741012i	0.966990	−	0.254813i	$-0.0820138\pi$
$743$	28.8465	+	20.1985i	1.05828	+	0.741012i	0.0912848	+	0.995825i	$0.470903\pi$
$744$		0			0
$745$	9.60936	+	18.7179i	0.352060	+	0.685769i
$746$	−4.37382	+	2.52523i	−0.160137	+	0.0924551i
$747$		0			0
$748$	−5.57411	+	1.49358i	−0.203810	+	0.0546106i
$749$	−15.4983	+	5.64093i	−0.566296	+	0.206115i
$750$		0			0
$751$	19.0262	−	15.9649i	0.694275	−	0.582566i	−0.225864	−	0.974159i	$-0.572520\pi$
$751$	19.0262	−	15.9649i	0.694275	−	0.582566i	0.920138	+	0.391593i	$0.128076\pi$
$752$	−6.38726	−	13.6975i	−0.232919	−	0.499497i
$753$		0			0
$754$	−20.3233	−	3.58354i	−0.740130	−	0.130505i
$755$	2.17601	+	0.915826i	0.0791930	+	0.0333303i
$756$		0			0
$757$	17.8009	−	17.8009i	0.646986	−	0.646986i	−0.305278	−	0.952263i	$-0.598749\pi$
$757$	17.8009	−	17.8009i	0.646986	−	0.646986i	0.952263	+	0.305278i	$0.0987493\pi$
$758$	−15.3401	−	21.9080i	−0.557178	−	0.795733i
$759$		0			0
$760$	−1.59972	−	42.1206i	−0.0580281	−	1.52788i
$761$	31.3105	+	37.3144i	1.13500	+	1.35265i	0.927240	+	0.374467i	$0.122174\pi$
$761$	31.3105	+	37.3144i	1.13500	+	1.35265i	0.207765	+	0.978179i	$0.433381\pi$
$762$		0			0
$763$	−41.4512	−	19.3290i	−1.50063	−	0.699757i
$764$	10.2888	−	17.8207i	0.372236	−	0.644731i
$765$		0			0
$766$	6.51352	+	11.2818i	0.235343	+	0.407626i
$767$	3.88180	+	44.3691i	0.140164	+	1.60208i
$768$		0			0
$769$	−43.1365	+	7.60612i	−1.55554	+	0.274284i	−0.884287	−	0.466944i	$-0.845355\pi$
$769$	−43.1365	+	7.60612i	−1.55554	+	0.274284i	−0.671254	+	0.741227i	$0.734244\pi$
$770$	−15.7268	−	3.58026i	−0.566756	−	0.129024i
$771$		0			0
$772$	0.273968	−	0.0239691i	0.00986034	−	0.000862668i
$773$	22.0592	+	5.91076i	0.793416	+	0.212595i	0.632691	−	0.774404i	$-0.281950\pi$
$773$	22.0592	+	5.91076i	0.793416	+	0.212595i	0.160725	+	0.986999i	$0.448617\pi$
$774$		0			0
$775$	−26.7045	+	6.83173i	−0.959252	+	0.245403i
$776$	19.1194	+	52.5302i	0.686347	+	1.88572i
$777$		0			0
$778$	9.39502	+	0.821958i	0.336828	+	0.0294686i
$779$	33.6549	+	12.2494i	1.20581	+	0.438879i
$780$		0			0
$781$	−2.00697	+	11.3821i	−0.0718150	+	0.407283i
$782$	−1.47719	−	1.47719i	−0.0528241	−	0.0528241i
$783$		0			0
$784$		−	1.97345i		−	0.0704805i
$785$	10.5251	+	48.7837i	0.375659	+	1.74116i
$786$		0			0
$787$	−15.6093	+	7.27876i	−0.556413	+	0.259460i	−0.680421	−	0.732822i	$-0.738203\pi$
$787$	−15.6093	+	7.27876i	−0.556413	+	0.259460i	0.124008	+	0.992281i	$0.460425\pi$
$788$	−0.249868	+	2.85601i	−0.00890119	+	0.101741i
$789$		0			0
$790$	−22.8859	+	20.7335i	−0.814243	+	0.737664i
$791$	6.68122	+	3.85740i	0.237557	+	0.137153i
$792$		0			0
$793$	3.95501	−	14.7603i	0.140447	−	0.524154i
$794$	−11.0377	−	9.26170i	−0.391712	−	0.328685i
$795$		0			0
$796$	0.977323	+	5.54267i	0.0346403	+	0.196455i
$797$	−18.8617	+	26.9373i	−0.668115	+	0.954166i	0.331827	+	0.943340i	$0.392335\pi$
$797$	−18.8617	+	26.9373i	−0.668115	+	0.954166i	−0.999941	+	0.0108262i	$0.996554\pi$
$798$		0			0
$799$	−18.4814	+	22.0252i	−0.653824	+	0.779197i
$800$	19.8522	−	11.1634i	0.701883	−	0.394685i
$801$		0			0
$802$	0.802775	+	2.99600i	0.0283470	+	0.105792i
$803$	6.95197	−	14.9085i	0.245330	−	0.526111i
$804$		0			0
$805$	1.36175	+	4.40591i	0.0479954	+	0.155288i
$806$	10.8404	−	29.7838i	0.381838	−	1.04909i
$807$		0			0
$808$	8.40661	−	5.88637i	0.295744	−	0.207082i
$809$	0.589848			0.0207379			0.0103690	−	0.999946i	$-0.496699\pi$
$809$	0.589848			0.0207379			0.0103690	+	0.999946i	$0.496699\pi$
$810$		0			0
$811$	−48.5224			−1.70385			−0.851925	−	0.523664i	$-0.824565\pi$
$811$	−48.5224			−1.70385			−0.851925	+	0.523664i	$0.824565\pi$
$812$	7.50095	−	5.25222i	0.263232	−	0.184317i
$813$		0			0
$814$	−3.76564	+	10.3460i	−0.131985	+	0.362627i
$815$	4.89102	+	2.58147i	0.171325	+	0.0904249i
$816$		0			0
$817$	3.78631	−	8.11977i	0.132466	−	0.284075i
$818$	7.84316	+	29.2711i	0.274230	+	1.02344i
$819$		0			0
$820$	1.42699	+	11.3355i	0.0498327	+	0.395854i
$821$	−12.3182	+	14.6802i	−0.429907	+	0.512343i	−0.936895	−	0.349610i	$-0.886314\pi$
$821$	−12.3182	+	14.6802i	−0.429907	+	0.512343i	0.506989	+	0.861953i	$0.330759\pi$
$822$		0			0
$823$	−0.358433	+	0.511895i	−0.0124942	+	0.0178435i	−0.825351	−	0.564621i	$-0.809022\pi$
$823$	−0.358433	+	0.511895i	−0.0124942	+	0.0178435i	0.812856	+	0.582464i	$0.197911\pi$
$824$	1.91929	+	10.8848i	0.0668615	+	0.379190i
$825$		0			0
$826$	19.1684	+	16.0842i	0.666954	+	0.559641i
$827$	−3.05127	+	11.3875i	−0.106103	+	0.395981i	−0.998468	−	0.0553328i	$-0.982378\pi$
$827$	−3.05127	+	11.3875i	−0.106103	+	0.395981i	0.892365	+	0.451314i	$0.149045\pi$
$828$		0			0
$829$	−38.0844	−	21.9880i	−1.32272	−	0.763675i	−0.338562	−	0.940944i	$-0.609941\pi$
$829$	−38.0844	−	21.9880i	−1.32272	−	0.763675i	−0.984163	+	0.177269i	$0.943274\pi$
$830$	11.2570	+	0.555479i	0.390736	+	0.0192809i
$831$		0			0
$832$	−3.66285	+	41.8666i	−0.126986	+	1.45146i
$833$	−3.40254	+	1.58663i	−0.117891	+	0.0549735i
$834$		0			0
$835$	15.9225	−	3.43529i	0.551019	−	0.118883i
$836$			12.8886i			0.445761i
$837$		0			0
$838$	−9.93659	−	9.93659i	−0.343254	−	0.343254i
$839$	−0.173429	+	0.983567i	−0.00598745	+	0.0339565i	−0.987655	−	0.156644i	$-0.949932\pi$
$839$	−0.173429	+	0.983567i	−0.00598745	+	0.0339565i	0.981668	+	0.190601i	$0.0610435\pi$
$840$		0			0
$841$	15.1440	+	5.51197i	0.522207	+	0.190068i
$842$	−9.53258	−	0.833993i	−0.328514	−	0.0287413i
$843$		0			0
$844$	1.93642	+	5.32028i	0.0666545	+	0.183132i
$845$	22.4025	+	29.5410i	0.770671	+	1.01624i
$846$		0			0
$847$	−15.1535	−	4.06038i	−0.520682	−	0.139516i
$848$	14.8293	−	1.29739i	0.509239	−	0.0445527i
$849$		0			0
$850$	11.8964	+	8.53268i	0.408043	+	0.292668i
$851$	3.10007	−	0.546626i	0.106269	−	0.0187381i
$852$		0			0
$853$	0.394403	+	4.50805i	0.0135041	+	0.154353i	0.999953	−	0.00971747i	$-0.00309322\pi$
$853$	0.394403	+	4.50805i	0.0135041	+	0.154353i	−0.986449	+	0.164070i	$0.947538\pi$
$854$	−4.29256	−	7.43494i	−0.146889	−	0.254418i
$855$		0			0
$856$	8.69313	−	15.0569i	0.297125	−	0.514635i
$857$	−51.8892	−	24.1963i	−1.77250	−	0.826531i	−0.974670	−	0.223650i	$-0.928203\pi$
$857$	−51.8892	−	24.1963i	−1.77250	−	0.826531i	−0.797831	−	0.602881i	$-0.794019\pi$
$858$		0			0
$859$	20.9711	+	24.9924i	0.715526	+	0.852730i	0.994188	−	0.107659i	$-0.0343354\pi$
$859$	20.9711	+	24.9924i	0.715526	+	0.852730i	−0.278662	+	0.960389i	$0.589891\pi$
$860$	2.85594	−	0.108467i	0.0973867	−	0.00369871i
$861$		0			0
$862$	−0.179453	−	0.256286i	−0.00611220	−	0.00872913i
$863$	−28.5706	+	28.5706i	−0.972554	+	0.972554i	−0.999633	−	0.0270792i	$-0.991379\pi$
$863$	−28.5706	+	28.5706i	−0.972554	+	0.972554i	0.0270792	+	0.999633i	$0.491379\pi$
$864$		0			0
$865$	42.4513	−	17.3025i	1.44339	−	0.588302i
$866$	−18.8698	−	3.32726i	−0.641223	−	0.113065i
$867$		0			0
$868$	5.94365	+	12.7462i	0.201741	+	0.432634i
$869$	23.6254	−	19.8241i	0.801437	−	0.672486i
$870$		0			0
$871$	38.1591	−	13.8888i	1.29297	−	0.470603i
$872$	46.5707	−	12.4786i	1.57708	−	0.422578i
$873$		0			0
$874$	−4.04068	+	2.33289i	−0.136678	+	0.0789111i
$875$	−14.4327	−	28.9158i	−0.487914	−	0.977532i
$876$		0			0
$877$	−29.1215	−	20.3911i	−0.983364	−	0.688559i	−0.0329214	−	0.999458i	$-0.510481\pi$
$877$	−29.1215	−	20.3911i	−0.983364	−	0.688559i	−0.950443	+	0.310899i	$0.899370\pi$
$878$	24.7062	+	17.2994i	0.833792	+	0.583828i
$879$		0			0
$880$	6.83718	−	3.51007i	0.230481	−	0.118324i
$881$	30.9752	−	17.8836i	1.04358	−	0.602512i	0.122736	−	0.992439i	$-0.460833\pi$
$881$	30.9752	−	17.8836i	1.04358	−	0.602512i	0.920846	+	0.389927i	$0.127500\pi$
$882$		0			0
$883$	−3.38029	+	0.905746i	−0.113756	+	0.0304808i	−0.315248	−	0.949009i	$-0.602088\pi$
$883$	−3.38029	+	0.905746i	−0.113756	+	0.0304808i	0.201492	+	0.979490i	$0.435421\pi$
$884$	12.4936	−	4.54730i	0.420205	−	0.152942i
$885$		0			0
$886$	−32.6492	+	27.3959i	−1.09687	+	0.920383i
$887$	−12.0260	−	25.7899i	−0.403794	−	0.865939i	−0.998095	−	0.0616962i	$-0.980349\pi$
$887$	−12.0260	−	25.7899i	−0.403794	−	0.865939i	0.594301	−	0.804243i	$-0.297429\pi$
$888$		0			0
$889$	9.30926	+	1.64147i	0.312222	+	0.0550532i
$890$	5.94671	+	14.5902i	0.199334	+	0.489063i
$891$		0			0
$892$	6.48285	−	6.48285i	0.217062	−	0.217062i
$893$	36.8325	+	52.6023i	1.23255	+	1.76027i
$894$		0			0
$895$	23.5203	+	21.7991i	0.786197	+	0.728663i
$896$	−1.75011	−	2.08570i	−0.0584672	−	0.0696785i
$897$		0			0
$898$	−7.49641	−	3.49564i	−0.250159	−	0.116651i
$899$	9.89411	−	17.1371i	0.329987	−	0.571554i
$900$		0			0
$901$	−14.1594	−	24.5249i	−0.471719	−	0.817042i
$902$	1.25913	+	14.3919i	0.0419245	+	0.479199i
$903$		0			0
$904$	−8.00909	+	1.41222i	−0.266378	+	0.0469697i
$905$	−1.02718	+	4.51203i	−0.0341445	+	0.149985i
$906$		0			0
$907$	32.6761	−	2.85879i	1.08499	−	0.0949246i	0.469398	−	0.882987i	$-0.344471\pi$
$907$	32.6761	−	2.85879i	1.08499	−	0.0949246i	0.615596	+	0.788062i	$0.288915\pi$
$908$	2.66344	+	0.713667i	0.0883894	+	0.0236839i
$909$		0			0
$910$	36.8147	+	5.05933i	1.22039	+	0.167715i
$911$	−9.92857	−	27.2785i	−0.328948	−	0.903778i	−0.988379	−	0.152012i	$-0.951425\pi$
$911$	−9.92857	−	27.2785i	−0.328948	−	0.903778i	0.659430	−	0.751766i	$-0.270798\pi$
$912$		0			0
$913$	−11.2132	−	0.981025i	−0.371102	−	0.0324672i
$914$	5.44427	+	1.98155i	0.180080	+	0.0655439i
$915$		0			0
$916$	−3.60050	+	20.4195i	−0.118964	+	0.674678i
$917$	−2.97152	−	2.97152i	−0.0981282	−	0.0981282i
$918$		0			0
$919$			28.2931i			0.933302i	0.884442	+	0.466651i	$0.154540\pi$
$919$			28.2931i			0.933302i	−0.884442	+	0.466651i	$0.845460\pi$
$920$	−4.08511	−	2.63520i	−0.134682	−	0.0868798i
$921$		0			0
$922$	28.8814	−	13.4676i	0.951159	−	0.443533i
$923$	2.32080	−	26.5268i	0.0763899	−	0.873141i
$924$		0			0
$925$	−20.8142	+	7.30944i	−0.684366	+	0.240333i
$926$	−0.165049	−	0.0952911i	−0.00542385	−	0.00313146i
$927$		0			0
$928$	−4.23180	+	15.7933i	−0.138916	+	0.518440i
$929$	−25.1788	−	21.1275i	−0.826089	−	0.693171i	0.128300	−	0.991735i	$-0.459048\pi$
$929$	−25.1788	−	21.1275i	−0.826089	−	0.693171i	−0.954390	+	0.298564i	$0.903492\pi$
$930$		0			0
$931$	1.45603	+	8.25757i	0.0477195	+	0.270631i
$932$	−1.67917	+	2.39811i	−0.0550032	+	0.0785527i
$933$		0			0
$934$	−8.57623	+	10.2208i	−0.280623	+	0.334433i
$935$	−11.5489	−	8.96631i	−0.377690	−	0.293230i
$936$		0			0
$937$	−1.30584	−	4.87347i	−0.0426600	−	0.159209i	0.941310	−	0.337543i	$-0.109596\pi$
$937$	−1.30584	−	4.87347i	−0.0426600	−	0.159209i	−0.983970	+	0.178334i	$0.942929\pi$
$938$	9.64174	−	20.6768i	0.314814	−	0.675121i
$939$		0			0
$940$	−9.56179	+	18.1164i	−0.311871	+	0.590892i
$941$	−19.6715	+	54.0471i	−0.641274	+	1.76189i	0.00641343	+	0.999979i	$0.497959\pi$
$941$	−19.6715	+	54.0471i	−0.641274	+	1.76189i	−0.647687	+	0.761906i	$0.724264\pi$
$942$		0			0
$943$	3.38355	−	2.36919i	0.110184	−	0.0771514i
$944$	−11.9232			−0.388068
$945$		0			0
$946$	3.61394			0.117499
$947$	26.3740	−	18.4673i	0.857041	−	0.600107i	−0.0603125	−	0.998180i	$-0.519210\pi$
$947$	26.3740	−	18.4673i	0.857041	−	0.600107i	0.917354	+	0.398073i	$0.130321\pi$
$948$		0			0
$949$	−12.9623	+	35.6136i	−0.420773	+	1.15607i
$950$	25.2846	−	20.7321i	0.820341	−	0.672638i
$951$		0			0
$952$	10.3105	−	22.1110i	0.334167	−	0.716623i
$953$	5.59819	+	20.8927i	0.181343	+	0.676782i	0.995384	+	0.0959743i	$0.0305967\pi$
$953$	5.59819	+	20.8927i	0.181343	+	0.676782i	−0.814041	+	0.580808i	$0.802737\pi$
$954$		0			0
$955$	51.7278	−	6.51184i	1.67387	−	0.210718i
$956$	−9.64940	+	11.4997i	−0.312084	+	0.371927i
$957$		0			0
$958$	−21.6105	+	30.8629i	−0.698202	+	0.997136i
$959$	8.00894	+	45.4210i	0.258622	+	1.46672i
$960$		0			0
$961$	−0.465741	−	0.390803i	−0.0150239	−	0.0126065i
$962$	6.56528	−	24.5020i	0.211673	−	0.789975i
$963$		0			0
$964$	14.1830	+	8.18857i	0.456804	+	0.263736i
$965$	0.467821	+	0.516387i	0.0150597	+	0.0166231i
$966$		0			0
$967$	0.961701	−	10.9923i	0.0309262	−	0.353488i	−0.964927	−	0.262517i	$-0.915447\pi$
$967$	0.961701	−	10.9923i	0.0309262	−	0.353488i	0.995854	−	0.0909711i	$-0.0289971\pi$
$968$	14.9883	−	6.98917i	0.481743	−	0.224640i
$969$		0			0
$970$	−23.5066	+	36.4402i	−0.754751	+	1.17002i
$971$		−	21.9387i		−	0.704047i	−0.935991	−	0.352023i	$-0.885494\pi$
$971$		−	21.9387i		−	0.704047i	0.935991	−	0.352023i	$-0.114506\pi$
$972$		0			0
$973$	−18.6543	−	18.6543i	−0.598030	−	0.598030i
$974$	−1.26918	+	7.19790i	−0.0406673	+	0.230635i
$975$		0			0
$976$	3.84410	+	1.39914i	0.123046	+	0.0447853i
$977$	5.48124	+	0.479546i	0.175360	+	0.0153420i	0.174498	−	0.984658i	$-0.444170\pi$
$977$	5.48124	+	0.479546i	0.175360	+	0.0153420i	0.000862648		1.00000i	$0.499725\pi$
$978$		0			0
$979$	−5.38167	−	14.7860i	−0.171999	−	0.472563i
$980$	−2.13128	+	1.61627i	−0.0680812	+	0.0516297i
$981$		0			0
$982$	−26.5176	−	7.10536i	−0.846209	−	0.226741i
$983$	27.3904	−	2.39635i	0.873618	−	0.0764316i	0.358478	−	0.933538i	$-0.383296\pi$
$983$	27.3904	−	2.39635i	0.873618	−	0.0764316i	0.515139	+	0.857106i	$0.327740\pi$
$984$		0			0
$985$	−6.14819	+	3.86798i	−0.195898	+	0.123244i
$986$	−10.3502	+	1.82503i	−0.329619	+	0.0581207i
$987$		0			0
$988$	−2.58804	−	29.5815i	−0.0823366	−	0.941111i
$989$	−0.516635	−	0.894838i	−0.0164280	−	0.0284542i
$990$		0			0
$991$	7.95205	−	13.7734i	0.252605	−	0.437525i	−0.711637	−	0.702547i	$-0.752046\pi$
$991$	7.95205	−	13.7734i	0.252605	−	0.437525i	0.964242	+	0.265022i	$0.0853793\pi$
$992$	−22.7592	−	10.6128i	−0.722606	−	0.336956i
$993$		0			0
$994$	−9.61620	−	11.4601i	−0.305007	−	0.363494i
$995$	−9.69322	+	10.4586i	−0.307296	+	0.331559i
$996$		0			0
$997$	−2.10376	−	3.00447i	−0.0666266	−	0.0951527i	0.784456	−	0.620185i	$-0.212942\pi$
$997$	−2.10376	−	3.00447i	−0.0666266	−	0.0951527i	−0.851083	+	0.525032i	$0.824053\pi$
$998$	−8.38532	+	8.38532i	−0.265433	+	0.265433i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.8.5		192
3.2	odd	2		135.2.q.a.83.12	yes	192
5.2	odd	4	inner	405.2.r.a.332.5		192
15.2	even	4		135.2.q.a.2.12	✓	192
15.8	even	4		675.2.ba.b.407.5		192
15.14	odd	2		675.2.ba.b.218.5		192
27.13	even	9		135.2.q.a.68.12	yes	192
27.14	odd	18	inner	405.2.r.a.233.5		192
135.13	odd	36		675.2.ba.b.257.5		192
135.67	odd	36		135.2.q.a.122.12	yes	192
135.94	even	18		675.2.ba.b.68.5		192
135.122	even	36	inner	405.2.r.a.152.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	15.2	even	4
135.2.q.a.68.12	yes	192	27.13	even	9
135.2.q.a.83.12	yes	192	3.2	odd	2
135.2.q.a.122.12	yes	192	135.67	odd	36
405.2.r.a.8.5		192	1.1	even	1	trivial
405.2.r.a.152.5		192	135.122	even	36	inner
405.2.r.a.233.5		192	27.14	odd	18	inner
405.2.r.a.332.5		192	5.2	odd	4	inner
675.2.ba.b.68.5		192	135.94	even	18
675.2.ba.b.218.5		192	15.14	odd	2
675.2.ba.b.257.5		192	135.13	odd	36
675.2.ba.b.407.5		192	15.8	even	4

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.865920 + 0.606324i) q^{2} +(-0.301851 + 0.829330i) q^{4} +(-2.13636 + 0.660292i) q^{5} +(-1.22161 + 2.61975i) q^{7} +(-0.788655 - 2.94330i) q^{8} +(1.44956 - 1.86708i) q^{10} +(-1.51740 + 1.80836i) q^{11} +(3.11956 - 4.45519i) q^{13} +(-0.530600 - 3.00918i) q^{14} +(1.11535 + 0.935892i) q^{16} +(0.716894 - 2.67549i) q^{17} +(-5.35751 - 3.09316i) q^{19} +(0.0972619 - 1.97105i) q^{20} +(0.217491 - 2.48593i) q^{22} +(-0.646627 + 0.301527i) q^{23} +(4.12803 - 2.82124i) q^{25} +5.74930i q^{26} +(-1.80389 - 1.80389i) q^{28} +(-0.623300 + 3.53491i) q^{29} +(-5.18043 - 1.88552i) q^{31} +(4.53781 + 0.397007i) q^{32} +(1.00144 + 2.75143i) q^{34} +(0.879991 - 6.40333i) q^{35} +(-4.26173 - 1.14193i) q^{37} +(6.51463 - 0.569956i) q^{38} +(3.62828 + 5.76719i) q^{40} +(-5.70140 + 1.00531i) q^{41} +(0.126221 + 1.44271i) q^{43} +(-1.04170 - 1.80428i) q^{44} +(0.377104 - 0.653164i) q^{46} +(-9.40770 - 4.38688i) q^{47} +(-0.871236 - 1.03830i) q^{49} +(-1.86396 + 4.94589i) q^{50} +(2.75318 + 3.93195i) q^{52} +(7.22940 - 7.22940i) q^{53} +(2.04765 - 4.86523i) q^{55} +(8.67413 + 1.52948i) q^{56} +(-1.60357 - 3.43887i) q^{58} +(-6.27320 + 5.26384i) q^{59} +(2.64019 - 0.960952i) q^{61} +(5.62907 - 1.50831i) q^{62} +(-6.69194 + 3.86359i) q^{64} +(-3.72276 + 11.5777i) q^{65} +(6.11610 + 4.28254i) q^{67} +(2.00246 + 1.40214i) q^{68} +(3.12049 + 6.07833i) q^{70} +(4.24004 - 2.44799i) q^{71} +(-6.73088 + 1.80353i) q^{73} +(4.38269 - 1.59517i) q^{74} +(4.18242 - 3.50947i) q^{76} +(-2.88379 - 6.18430i) q^{77} +(-12.8661 - 2.26863i) q^{79} +(-3.00075 - 1.26294i) q^{80} +(4.32741 - 4.32741i) q^{82} +(2.73492 + 3.90587i) q^{83} +(0.235061 + 6.18915i) q^{85} +(-0.984048 - 1.17274i) q^{86} +(6.51925 + 3.03998i) q^{88} +(-3.33276 + 5.77251i) q^{89} +(7.86060 + 13.6150i) q^{91} +(-0.0548802 - 0.627283i) q^{92} +(10.8062 - 1.90542i) q^{94} +(13.4879 + 3.07057i) q^{95} +(-18.2758 + 1.59893i) q^{97} +(1.38397 + 0.370833i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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Database

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