LMFDB - Embedded newform 405.2.r.a.332.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			332.5
Character	$\chi$	$=$	405.332
Dual form			405.2.r.a.233.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.606324 - 0.865920i) q^{2} +(0.301851 - 0.829330i) q^{4} +(1.02123 - 1.98924i) q^{5} +(-2.61975 - 1.22161i) q^{7} +(-2.94330 + 0.788655i) q^{8} +(-2.34172 + 0.321816i) q^{10} +(-1.51740 + 1.80836i) q^{11} +(-4.45519 - 3.11956i) q^{13} +(0.530600 + 3.00918i) q^{14} +(1.11535 + 0.935892i) q^{16} +(2.67549 + 0.716894i) q^{17} +(5.35751 + 3.09316i) q^{19} +(-1.34148 - 1.44740i) q^{20} +(2.48593 + 0.217491i) q^{22} +(0.301527 + 0.646627i) q^{23} +(-2.91416 - 4.06296i) q^{25} +5.74930i q^{26} +(-1.80389 + 1.80389i) q^{28} +(0.623300 - 3.53491i) q^{29} +(-5.18043 - 1.88552i) q^{31} +(-0.397007 + 4.53781i) q^{32} +(-1.00144 - 2.75143i) q^{34} +(-5.10545 + 3.96376i) q^{35} +(1.14193 - 4.26173i) q^{37} +(-0.569956 - 6.51463i) q^{38} +(-1.43698 + 6.66033i) q^{40} +(-5.70140 + 1.00531i) q^{41} +(1.44271 - 0.126221i) q^{43} +(1.04170 + 1.80428i) q^{44} +(0.377104 - 0.653164i) q^{46} +(4.38688 - 9.40770i) q^{47} +(0.871236 + 1.03830i) q^{49} +(-1.75128 + 4.98690i) q^{50} +(-3.93195 + 2.75318i) q^{52} +(-7.22940 - 7.22940i) q^{53} +(2.04765 + 4.86523i) q^{55} +(8.67413 + 1.52948i) q^{56} +(-3.43887 + 1.60357i) q^{58} +(6.27320 - 5.26384i) q^{59} +(2.64019 - 0.960952i) q^{61} +(1.50831 + 5.62907i) q^{62} +(6.69194 - 3.86359i) q^{64} +(-10.7553 + 5.67665i) q^{65} +(-4.28254 + 6.11610i) q^{67} +(1.40214 - 2.00246i) q^{68} +(6.52785 + 2.01759i) q^{70} +(4.24004 - 2.44799i) q^{71} +(1.80353 + 6.73088i) q^{73} +(-4.38269 + 1.59517i) q^{74} +(4.18242 - 3.50947i) q^{76} +(6.18430 - 2.88379i) q^{77} +(12.8661 + 2.26863i) q^{79} +(3.00075 - 1.26294i) q^{80} +(4.32741 + 4.32741i) q^{82} +(3.90587 - 2.73492i) q^{83} +(4.15837 - 4.59007i) q^{85} +(-0.984048 - 1.17274i) q^{86} +(3.03998 - 6.51925i) q^{88} +(3.33276 - 5.77251i) q^{89} +(7.86060 + 13.6150i) q^{91} +(0.627283 - 0.0548802i) q^{92} +(-10.8062 + 1.90542i) q^{94} +(11.6243 - 7.49853i) q^{95} +(-1.59893 - 18.2758i) q^{97} +(0.370833 - 1.38397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.606324	−	0.865920i	−0.428736	−	0.612298i	0.545424	−	0.838161i	$-0.316369\pi$
$2$	−0.606324	−	0.865920i	−0.428736	−	0.612298i	−0.974159	+	0.225863i	$0.927480\pi$
$3$		0			0
$3$		0			0
$4$	0.301851	−	0.829330i	0.150926	−	0.414665i
$5$	1.02123	−	1.98924i	0.456710	−	0.889616i
$5$	1.02123	−	1.98924i	0.456710	−	0.889616i
$6$		0			0
$7$	−2.61975	−	1.22161i	−0.990171	−	0.461725i	−0.141096	−	0.989996i	$-0.545063\pi$
$7$	−2.61975	−	1.22161i	−0.990171	−	0.461725i	−0.849076	+	0.528271i	$0.822840\pi$
$8$	−2.94330	+	0.788655i	−1.04061	+	0.278832i
$9$		0			0
$10$	−2.34172	+	0.321816i	−0.740518	+	0.101767i
$11$	−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
$13$	−4.45519	−	3.11956i	−1.23565	−	0.865210i	−0.241203	−	0.970475i	$-0.577542\pi$
$13$	−4.45519	−	3.11956i	−1.23565	−	0.865210i	−0.994444	+	0.105265i	$0.966431\pi$
$14$	0.530600	+	3.00918i	0.141809	+	0.804238i
$15$		0			0
$16$	1.11535	+	0.935892i	0.278838	+	0.233973i
$17$	2.67549	+	0.716894i	0.648901	+	0.173872i	0.568232	−	0.822869i	$-0.307628\pi$
$17$	2.67549	+	0.716894i	0.648901	+	0.173872i	0.0806688	+	0.996741i	$0.474294\pi$
$18$		0			0
$19$	5.35751	+	3.09316i	1.22910	+	0.709619i	0.966841	−	0.255379i	$-0.0822003\pi$
$19$	5.35751	+	3.09316i	1.22910	+	0.709619i	0.262256	+	0.964998i	$0.415534\pi$
$20$	−1.34148	−	1.44740i	−0.299963	−	0.323647i
$21$		0			0
$22$	2.48593	+	0.217491i	0.530002	+	0.0463692i
$23$	0.301527	+	0.646627i	0.0628728	+	0.134831i	0.935233	−	0.354032i	$-0.115190\pi$
$23$	0.301527	+	0.646627i	0.0628728	+	0.134831i	−0.872361	+	0.488863i	$0.837412\pi$
$24$		0			0
$25$	−2.91416	−	4.06296i	−0.582832	−	0.812593i
$26$			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	$-0.836292\pi$
$29$	0.623300	−	3.53491i	0.115744	−	0.656416i	0.986379	−	0.164487i	$-0.0525969\pi$
$30$		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	$0.775970\pi$
$32$	−0.397007	+	4.53781i	−0.0701815	+	0.802178i
$33$		0			0
$34$	−1.00144	−	2.75143i	−0.171745	−	0.471866i
$35$	−5.10545	+	3.96376i	−0.862979	+	0.669998i
$36$		0			0
$37$	1.14193	−	4.26173i	0.187732	−	0.700624i	−0.806298	−	0.591510i	$-0.798532\pi$
$37$	1.14193	−	4.26173i	0.187732	−	0.700624i	0.994029	−	0.109114i	$-0.0348013\pi$
$38$	−0.569956	−	6.51463i	−0.0924591	−	1.05681i
$39$		0			0
$40$	−1.43698	+	6.66033i	−0.227206	+	1.05309i
$41$	−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
$43$	1.44271	−	0.126221i	0.220012	−	0.0192485i	0.0233831	−	0.999727i	$-0.492556\pi$
$43$	1.44271	−	0.126221i	0.220012	−	0.0192485i	0.196629	+	0.980478i	$0.437001\pi$
$44$	1.04170	+	1.80428i	0.157042	+	0.272005i
$45$		0			0
$46$	0.377104	−	0.653164i	0.0556010	−	0.0963037i
$47$	4.38688	−	9.40770i	0.639893	−	1.37225i	−0.272188	−	0.962244i	$-0.587747\pi$
$47$	4.38688	−	9.40770i	0.639893	−	1.37225i	0.912081	−	0.410010i	$-0.134475\pi$
$48$		0			0
$49$	0.871236	+	1.03830i	0.124462	+	0.148328i
$50$	−1.75128	+	4.98690i	−0.247668	+	0.705254i
$51$		0			0
$52$	−3.93195	+	2.75318i	−0.545263	+	0.381797i
$53$	−7.22940	−	7.22940i	−0.993035	−	0.993035i	0.00694140	−	0.999976i	$-0.497790\pi$
$53$	−7.22940	−	7.22940i	−0.993035	−	0.993035i	−0.999976	+	0.00694140i	$0.997790\pi$
$54$		0			0
$55$	2.04765	+	4.86523i	0.276105	+	0.656027i
$56$	8.67413	+	1.52948i	1.15913	+	0.204386i
$57$		0			0
$58$	−3.43887	+	1.60357i	−0.451546	+	0.210559i
$59$	6.27320	−	5.26384i	0.816701	−	0.685293i	−0.135496	−	0.990778i	$-0.543263\pi$
$59$	6.27320	−	5.26384i	0.816701	−	0.685293i	0.952197	+	0.305484i	$0.0988184\pi$
$60$		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	$0.331322\pi$
$62$	1.50831	+	5.62907i	0.191555	+	0.714893i
$63$		0			0
$64$	6.69194	−	3.86359i	0.836493	−	0.482949i
$65$	−10.7553	+	5.67665i	−1.33404	+	0.704101i
$66$		0			0
$67$	−4.28254	+	6.11610i	−0.523196	+	0.747201i	−0.990592	−	0.136847i	$-0.956303\pi$
$67$	−4.28254	+	6.11610i	−0.523196	+	0.747201i	0.467396	+	0.884048i	$0.345192\pi$
$68$	1.40214	−	2.00246i	0.170034	−	0.242834i
$69$		0			0
$70$	6.52785	+	2.01759i	0.780228	+	0.241148i
$71$	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
$73$	1.80353	+	6.73088i	0.211088	+	0.787790i	0.987507	+	0.157574i	$0.0503671\pi$
$73$	1.80353	+	6.73088i	0.211088	+	0.787790i	−0.776420	+	0.630216i	$0.782966\pi$
$74$	−4.38269	+	1.59517i	−0.509478	+	0.185435i
$75$		0			0
$76$	4.18242	−	3.50947i	0.479756	−	0.402563i
$77$	6.18430	−	2.88379i	0.704767	−	0.328638i
$78$		0			0
$79$	12.8661	+	2.26863i	1.44754	+	0.255241i	0.841529	−	0.540212i	$-0.181656\pi$
$79$	12.8661	+	2.26863i	1.44754	+	0.255241i	0.606015	+	0.795453i	$0.292767\pi$
$80$	3.00075	−	1.26294i	0.335494	−	0.141201i
$81$		0			0
$82$	4.32741	+	4.32741i	0.477883	+	0.477883i
$83$	3.90587	−	2.73492i	0.428724	−	0.300196i	−0.339227	−	0.940705i	$-0.610165\pi$
$83$	3.90587	−	2.73492i	0.428724	−	0.300196i	0.767951	+	0.640509i	$0.221276\pi$
$84$		0			0
$85$	4.15837	−	4.59007i	0.451039	−	0.497863i
$86$	−0.984048	−	1.17274i	−0.106113	−	0.126460i
$87$		0			0
$88$	3.03998	−	6.51925i	0.324063	−	0.694955i
$89$	3.33276	−	5.77251i	0.353272	−	0.611885i	−0.633549	−	0.773703i	$-0.718402\pi$
$89$	3.33276	−	5.77251i	0.353272	−	0.611885i	0.986821	+	0.161818i	$0.0517357\pi$
$90$		0			0
$91$	7.86060	+	13.6150i	0.824014	+	1.42723i
$92$	0.627283	−	0.0548802i	0.0653988	−	0.00572165i
$93$		0			0
$94$	−10.8062	+	1.90542i	−1.11457	+	0.196529i
$95$	11.6243	−	7.49853i	1.19263	−	0.769333i
$96$		0			0
$97$	−1.59893	−	18.2758i	−0.162346	−	1.85563i	−0.443894	−	0.896079i	$-0.646403\pi$
$97$	−1.59893	−	18.2758i	−0.162346	−	1.85563i	0.281548	−	0.959547i	$-0.409152\pi$
$98$	0.370833	−	1.38397i	0.0374597	−	0.139802i
$99$		0			0
$100$	−4.24918	+	1.19039i	−0.424918	+	0.119039i
$101$	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
$103$	−0.316137	+	3.61346i	−0.0311499	+	0.356045i	0.964584	+	0.263775i	$0.0849677\pi$
$103$	−0.316137	+	3.61346i	−0.0311499	+	0.356045i	−0.995734	+	0.0922694i	$0.970588\pi$
$104$	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	$-0.838943\pi$
$107$	−4.03460	+	4.03460i	−0.390039	+	0.390039i	0.484662	+	0.874701i	$0.338943\pi$
$108$		0			0
$109$		−	15.8226i		−	1.51553i	−0.652527	−	0.757765i	$-0.726291\pi$
$109$		−	15.8226i		−	1.51553i	0.652527	−	0.757765i	$-0.273709\pi$
$110$	2.97136	−	4.72301i	0.283308	−	0.450321i
$111$		0			0
$112$	−1.77865	−	3.81433i	−0.168067	−	0.360420i
$113$	−2.65880	−	0.232615i	−0.250119	−	0.0218825i	−0.0385931	−	0.999255i	$-0.512288\pi$
$113$	−2.65880	−	0.232615i	−0.250119	−	0.0218825i	−0.211526	+	0.977372i	$0.567843\pi$
$114$		0			0
$115$	1.59423	+	0.0605481i	0.148662	+	0.00564614i
$116$	−2.74346	−	1.58394i	−0.254724	−	0.147065i
$117$		0			0
$118$	−8.36165	−	2.24050i	−0.769753	−	0.206255i
$119$	−6.13333	−	5.14648i	−0.562242	−	0.471777i
$120$		0			0
$121$	0.942447	+	5.34488i	0.0856770	+	0.485898i
$122$	−2.43292	−	1.70355i	−0.220266	−	0.154232i
$123$		0			0
$124$	−3.12744	+	3.72713i	−0.280852	+	0.334707i
$125$	−11.0583	+	1.64772i	−0.989080	+	0.147377i
$126$		0			0
$127$	3.15881	−	0.846401i	0.280299	−	0.0751059i	−0.115931	−	0.993257i	$-0.536985\pi$
$127$	3.15881	−	0.846401i	0.280299	−	0.0751059i	0.396230	+	0.918151i	$0.370318\pi$
$128$	0.853671	+	0.398073i	0.0754546	+	0.0351850i
$129$		0			0
$130$	11.4367	+	5.87139i	1.00307	+	0.514955i
$131$	−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
$133$	−10.2567	−	14.6481i	−0.889368	−	1.27015i
$134$	7.89266			0.681822
$135$		0			0
$136$	−8.44014			−0.723736
$137$	9.15193	+	13.0703i	0.781902	+	1.11667i	0.990343	+	0.138637i	$0.0442720\pi$
$137$	9.15193	+	13.0703i	0.781902	+	1.11667i	−0.208442	+	0.978035i	$0.566839\pi$
$138$		0			0
$139$	3.12149	−	8.57623i	0.264762	−	0.727426i	−0.734069	−	0.679075i	$-0.762381\pi$
$139$	3.12149	−	8.57623i	0.264762	−	0.727426i	0.998830	−	0.0483514i	$-0.0153967\pi$
$140$	1.74618	+	5.43057i	0.147579	+	0.458967i
$141$		0			0
$142$	−4.69060	−	2.18726i	−0.393626	−	0.183551i
$143$	12.4016	−	3.32299i	1.03707	−	0.277883i
$144$		0			0
$145$	−6.39525	−	4.84987i	−0.531097	−	0.402760i
$146$	4.73488	−	5.64281i	0.391861	−	0.467002i
$147$		0			0
$148$	−3.18968	−	2.23344i	−0.262190	−	0.183588i
$149$	1.63395	+	9.26659i	0.133858	+	0.759149i	0.975648	+	0.219343i	$0.0703913\pi$
$149$	1.63395	+	9.26659i	0.133858	+	0.759149i	−0.841789	+	0.539806i	$0.818498\pi$
$150$		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	$0.735901\pi$
$152$	−18.2082	−	4.87887i	−1.47688	−	0.395729i
$153$		0			0
$154$	−6.24682	−	3.60660i	−0.503383	−	0.290628i
$155$	−9.04119	+	8.37956i	−0.726206	+	0.673062i
$156$		0			0
$157$	22.2338	+	1.94520i	1.77445	+	0.155244i	0.926860	−	0.375408i	$-0.122497\pi$
$157$	22.2338	+	1.94520i	1.77445	+	0.155244i	0.847590	+	0.530652i	$0.178053\pi$
$158$	−5.83654	−	12.5165i	−0.464330	−	0.995759i
$159$		0			0
$160$	8.62135	+	5.42391i	0.681578	+	0.428798i
$161$		−	2.06235i		−	0.162536i
$162$		0			0
$163$	−1.74889	+	1.74889i	−0.136983	+	0.136983i	−0.772274	−	0.635290i	$-0.780881\pi$
$163$	−1.74889	+	1.74889i	−0.136983	+	0.136983i	0.635290	+	0.772274i	$0.280881\pi$
$164$	−0.887241	+	5.03179i	−0.0692819	+	0.392917i
$165$		0			0
$166$	−4.73644	−	1.72392i	−0.367619	−	0.133802i
$167$	0.634893	−	7.25686i	0.0491295	−	0.561553i	−0.931243	−	0.364399i	$-0.881275\pi$
$167$	0.634893	−	7.25686i	0.0491295	−	0.561553i	0.980373	−	0.197154i	$-0.0631699\pi$
$168$		0			0
$169$	5.67082	+	15.5805i	0.436217	+	1.19850i
$170$	−6.49595	−	0.817753i	−0.498217	−	0.0627188i
$171$		0			0
$172$	0.330806	−	1.23458i	0.0252237	−	0.0941362i
$173$	1.78680	+	20.4232i	0.135848	+	1.55275i	0.692143	+	0.721760i	$0.256667\pi$
$173$	1.78680	+	20.4232i	0.135848	+	1.55275i	−0.556295	+	0.830985i	$0.687778\pi$
$174$		0			0
$175$	2.67101	+	14.2039i	0.201909	+	1.07371i
$176$	−3.38487	+	0.596843i	−0.255144	+	0.0449887i
$177$		0			0
$178$	−7.01926	+	0.614106i	−0.526116	+	0.0460292i
$179$	7.17079	+	12.4202i	0.535970	+	0.928327i	0.999116	+	0.0420450i	$0.0133873\pi$
$179$	7.17079	+	12.4202i	0.535970	+	0.928327i	−0.463146	+	0.886282i	$0.653279\pi$
$180$		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	$0.142161\pi$
$182$	7.02339	−	15.0617i	0.520609	−	1.11645i
$183$		0			0
$184$	−1.39745	−	1.66542i	−0.103021	−	0.122776i
$185$	−7.31143	−	6.62379i	−0.537547	−	0.486991i
$186$		0			0
$187$	−5.35618	+	3.75043i	−0.391682	+	0.274259i
$188$	−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
$193$	−0.282417	+	0.131693i	−0.0203288	+	0.00947948i	−0.432756	−	0.901511i	$-0.642459\pi$
$193$	−0.282417	+	0.131693i	−0.0203288	+	0.00947948i	0.412427	+	0.910991i	$0.364681\pi$
$194$	−14.8559	+	12.4656i	−1.06659	+	0.894977i
$195$		0			0
$196$	1.12408	−	0.409130i	0.0802911	−	0.0292236i
$197$	0.840756	+	3.13774i	0.0599014	+	0.223555i	0.989387	−	0.145303i	$-0.0464156\pi$
$197$	0.840756	+	3.13774i	0.0599014	+	0.223555i	−0.929486	+	0.368858i	$0.879749\pi$
$198$		0			0
$199$	−5.52277	+	3.18857i	−0.391499	+	0.226032i	−0.682809	−	0.730596i	$-0.739242\pi$
$199$	−5.52277	+	3.18857i	−0.391499	+	0.226032i	0.291310	+	0.956629i	$0.405909\pi$
$200$	11.7815	+	9.66026i	0.833079	+	0.683083i
$201$		0			0
$202$	2.04207	−	2.91638i	0.143679	−	0.205196i
$203$	−5.95116	+	8.49914i	−0.417690	+	0.596523i
$204$		0			0
$205$	−3.82266	+	12.3681i	−0.266986	+	0.863827i
$206$	3.32065	−	1.91718i	0.231360	−	0.133576i
$207$		0			0
$208$	−2.04954	−	7.64899i	−0.142110	−	0.530362i
$209$	−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	$0.206905\pi$
$212$	−8.17776	+	3.81335i	−0.561651	+	0.261902i
$213$		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
$218$	−13.7011	+	9.59362i	−0.927956	+	0.649762i
$219$		0			0
$220$	4.65296	−	0.229601i	0.313703	−	0.0154797i
$221$	−9.68341	−	11.5402i	−0.651376	−	0.776280i
$222$		0			0
$223$	−4.39023	+	9.41489i	−0.293992	+	0.630467i	−0.996714	−	0.0809965i	$-0.974190\pi$
$223$	−4.39023	+	9.41489i	−0.293992	+	0.630467i	0.702723	+	0.711464i	$0.251968\pi$
$224$	6.58348	−	11.4029i	0.439877	−	0.761889i
$225$		0			0
$226$	1.41067	+	2.44335i	0.0938361	+	0.162529i
$227$	3.11245	−	0.272304i	0.206580	−	0.0180734i	0.0166042	−	0.999862i	$-0.494714\pi$
$227$	3.11245	−	0.272304i	0.206580	−	0.0180734i	0.189976	+	0.981789i	$0.439159\pi$
$228$		0			0
$229$	−23.1368	+	4.07964i	−1.52892	+	0.269590i	−0.873933	−	0.486047i	$-0.838438\pi$
$229$	−23.1368	+	4.07964i	−1.52892	+	0.269590i	−0.654990	+	0.755638i	$0.727327\pi$
$230$	−0.914188	−	1.41718i	−0.0602798	−	0.0934464i
$231$		0			0
$232$	0.953265	+	10.8959i	0.0625849	+	0.715349i
$233$	0.858538	−	3.20411i	0.0562447	−	0.209908i	−0.932085	−	0.362241i	$-0.882012\pi$
$233$	0.858538	−	3.20411i	0.0562447	−	0.209908i	0.988329	+	0.152333i	$0.0486785\pi$
$234$		0			0
$235$	−14.2341	−	18.3340i	−0.928533	−	1.19598i
$236$	−2.47188	−	6.79145i	−0.160906	−	0.442085i
$237$		0			0
$238$	−0.737653	+	8.43141i	−0.0478149	+	0.546527i
$239$	−15.9837	−	5.81759i	−1.03390	−	0.376309i	−0.231335	−	0.972874i	$-0.574309\pi$
$239$	−15.9837	−	5.81759i	−1.03390	−	0.376309i	−0.802564	+	0.596566i	$0.796532\pi$
$240$		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
$245$	2.95516	−	0.672751i	0.188798	−	0.0429805i
$246$		0			0
$247$	−14.2194	−	30.4937i	−0.904761	−	1.94027i
$248$	16.7346	+	1.46409i	1.06265	+	0.0929695i
$249$		0			0
$250$	8.13168	+	8.57651i	0.514292	+	0.542426i
$251$	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
$253$	−1.62687	−	0.435919i	−0.102281	−	0.0274060i
$254$	−2.64818	−	2.22208i	−0.166161	−	0.139426i
$255$		0			0
$256$	−2.85653	−	16.2002i	−0.178533	−	1.01251i
$257$	−7.11815	−	4.98418i	−0.444018	−	0.310905i	0.330100	−	0.943946i	$-0.392917\pi$
$257$	−7.11815	−	4.98418i	−0.444018	−	0.310905i	−0.774118	+	0.633041i	$0.781806\pi$
$258$		0			0
$259$	−8.19772	+	9.76966i	−0.509382	+	0.607057i
$260$	1.46129	+	10.6332i	0.0906256	+	0.659445i
$261$		0			0
$262$	1.48446	−	0.397759i	0.0917099	−	0.0245736i
$263$	21.3889	+	9.97382i	1.31890	+	0.615012i	0.949356	−	0.314203i	$-0.101737\pi$
$263$	21.3889	+	9.97382i	1.31890	+	0.615012i	0.369541	+	0.929214i	$0.379515\pi$
$264$		0			0
$265$	−21.7639	+	6.99810i	−1.33695	+	0.429890i
$266$	−6.46518	+	17.7629i	−0.396406	+	1.08912i
$267$		0			0
$268$	3.77957	+	5.39779i	0.230874	+	0.329723i
$269$	10.2124			0.622659			0.311330	−	0.950302i	$-0.399226\pi$
$269$	10.2124			0.622659			0.311330	+	0.950302i	$0.399226\pi$
$270$		0			0
$271$	4.84409			0.294258			0.147129	−	0.989117i	$-0.452997\pi$
$271$	4.84409			0.294258			0.147129	+	0.989117i	$0.452997\pi$
$272$	2.31318	+	3.30356i	0.140257	+	0.200308i
$273$		0			0
$274$	5.76881	−	15.8497i	0.348506	−	0.957514i
$275$	11.7692	+	0.895273i	0.709712	+	0.0539870i
$276$		0			0
$277$	−12.2491	−	5.71185i	−0.735978	−	0.343192i	0.0182248	−	0.999834i	$-0.494199\pi$
$277$	−12.2491	−	5.71185i	−0.735978	−	0.343192i	−0.754203	+	0.656642i	$0.771976\pi$
$278$	−9.31897	+	2.49701i	−0.558914	+	0.149761i
$279$		0			0
$280$	11.9008	−	15.6930i	0.711211	−	0.937834i
$281$	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
$283$	24.7001	+	17.2952i	1.46827	+	1.02809i	0.988587	+	0.150648i	$0.0481361\pi$
$283$	24.7001	+	17.2952i	1.46827	+	1.02809i	0.479680	+	0.877443i	$0.340753\pi$
$284$	−0.750327	−	4.25532i	−0.0445237	−	0.252507i
$285$		0			0
$286$	−10.3968	−	8.72397i	−0.614777	−	0.515859i
$287$	16.1643	+	4.33122i	0.954150	+	0.255664i
$288$		0			0
$289$	−8.07815	−	4.66392i	−0.475185	−	0.274348i
$290$	−0.322005	+	8.47837i	−0.0189088	+	0.497867i
$291$		0			0
$292$	6.12652	+	0.536001i	0.358527	+	0.0313671i
$293$	−3.10333	−	6.65512i	−0.181299	−	0.388796i	0.794564	−	0.607180i	$-0.207699\pi$
$293$	−3.10333	−	6.65512i	−0.181299	−	0.388796i	−0.975863	+	0.218384i	$0.929922\pi$
$294$		0			0
$295$	−4.06463	−	17.8545i	−0.236652	−	1.03953i
$296$			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
$302$	−0.0972742	+	1.11185i	−0.00559750	+	0.0639798i
$303$		0			0
$304$	3.08065	+	8.46402i	0.176687	+	0.485445i
$305$	0.784693	−	6.23334i	0.0449314	−	0.356920i
$306$		0			0
$307$	−3.54038	+	13.2129i	−0.202060	+	0.754099i	0.788265	+	0.615336i	$0.210980\pi$
$307$	−3.54038	+	13.2129i	−0.202060	+	0.754099i	−0.990326	+	0.138764i	$0.955687\pi$
$308$	−0.524871	−	5.99930i	−0.0299073	−	0.341842i
$309$		0			0
$310$	12.7379	+	2.74822i	0.723465	+	0.156089i
$311$	−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
$313$	24.5081	−	2.14418i	1.38528	−	0.121196i	0.629997	−	0.776597i	$-0.283056\pi$
$313$	24.5081	−	2.14418i	1.38528	−	0.121196i	0.755281	+	0.655401i	$0.227500\pi$
$314$	−11.7965	−	20.4321i	−0.665714	−	1.15305i
$315$		0			0
$316$	5.76508	−	9.98541i	0.324311	−	0.561723i
$317$	6.97386	−	14.9555i	0.391691	−	0.839984i	−0.607274	−	0.794493i	$-0.707737\pi$
$317$	6.97386	−	14.9555i	0.391691	−	0.839984i	0.998965	−	0.0454916i	$-0.0144854\pi$
$318$		0			0
$319$	5.44660	+	6.49101i	0.304951	+	0.363427i
$320$	−0.851574	−	17.2575i	−0.0476045	−	0.964725i
$321$		0			0
$322$	−1.78583	+	1.25045i	−0.0995203	+	0.0696849i
$323$	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
$328$	15.9881	−	7.45537i	0.882794	−	0.411654i
$329$	−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	$0.580901\pi$
$332$	−1.08916	−	4.06479i	−0.0597752	−	0.223084i
$333$		0			0
$334$	−6.66881	+	3.85024i	−0.364901	+	0.210676i
$335$	7.79292	+	14.7650i	0.425773	+	0.806697i
$336$		0			0
$337$	6.00115	−	8.57053i	0.326904	−	0.466867i	−0.621735	−	0.783227i	$-0.713572\pi$
$337$	6.00115	−	8.57053i	0.326904	−	0.466867i	0.948639	+	0.316361i	$0.102461\pi$
$338$	10.0531	−	14.3573i	0.546815	−	0.780933i
$339$		0			0
$340$	−2.55147	−	4.83418i	−0.138373	−	0.262170i
$341$	11.2705	−	6.50701i	0.610330	−	0.352374i
$342$		0			0
$343$	4.22292	+	15.7602i	0.228016	+	0.850968i
$344$	−4.14679	+	1.50931i	−0.223580	+	0.0813765i
$345$		0			0
$346$	16.6015	−	13.9303i	0.892500	−	0.748896i
$347$	−10.4146	+	4.85639i	−0.559083	+	0.260705i	−0.681554	−	0.731767i	$-0.738696\pi$
$347$	−10.4146	+	4.85639i	−0.559083	+	0.260705i	0.122472	+	0.992472i	$0.460918\pi$
$348$		0			0
$349$	−15.6377	−	2.75735i	−0.837067	−	0.147597i	−0.261347	−	0.965245i	$-0.584167\pi$
$349$	−15.6377	−	2.75735i	−0.837067	−	0.147597i	−0.575719	+	0.817647i	$0.695278\pi$
$350$	10.6799	−	10.9250i	0.570867	−	0.583968i
$351$		0			0
$352$	−7.60358	−	7.60358i	−0.405272	−	0.405272i
$353$	−7.10893	+	4.97772i	−0.378370	+	0.264938i	−0.747255	−	0.664538i	$-0.768629\pi$
$353$	−7.10893	+	4.97772i	−0.378370	+	0.264938i	0.368885	+	0.929475i	$0.379740\pi$
$354$		0			0
$355$	−0.539561	−	10.9344i	−0.0286369	−	0.580339i
$356$	−3.78131	−	4.50640i	−0.200409	−	0.238838i
$357$		0			0
$358$	6.40706	−	13.7400i	0.338623	−	0.726180i
$359$	10.2032	−	17.6725i	0.538505	−	0.932718i	−0.460480	−	0.887670i	$-0.652323\pi$
$359$	10.2032	−	17.6725i	0.538505	−	0.932718i	0.998985	−	0.0450476i	$-0.0143439\pi$
$360$		0			0
$361$	9.63526	+	16.6888i	0.507119	+	0.878356i
$362$	−2.17930	+	0.190664i	−0.114541	+	0.0100211i
$363$		0			0
$364$	13.6640	−	2.40933i	0.716189	−	0.126283i
$365$	15.2312	+	3.28615i	0.797236	+	0.172005i
$366$		0			0
$367$	2.26163	+	25.8506i	0.118056	+	1.34939i	0.791962	+	0.610571i	$0.209060\pi$
$367$	2.26163	+	25.8506i	0.118056	+	1.34939i	−0.673906	+	0.738818i	$0.735385\pi$
$368$	−0.268864	+	1.00341i	−0.0140155	+	0.0523066i
$369$		0			0
$370$	−1.30258	+	10.3473i	−0.0677180	+	0.537929i
$371$	10.1077	+	27.7707i	0.524766	+	1.44178i
$372$		0			0
$373$	0.416402	−	4.75950i	0.0215605	−	0.246438i	−0.977765	−	0.209705i	$-0.932750\pi$
$373$	0.416402	−	4.75950i	0.0215605	−	0.246438i	0.999325	−	0.0367323i	$-0.0116949\pi$
$374$	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	$-0.774856\pi$
$379$		−	25.3002i		−	1.29958i	0.760112	−	0.649792i	$-0.225144\pi$
$380$	−2.70994	−	11.9038i	−0.139017	−	0.610653i
$381$		0			0
$382$	10.4163	+	22.3379i	0.532946	+	1.14291i
$383$	−12.2766	−	1.07406i	−0.627303	−	0.0548819i	−0.230929	−	0.972971i	$-0.574176\pi$
$383$	−12.2766	−	1.07406i	−0.627303	−	0.0548819i	−0.396375	+	0.918089i	$0.629732\pi$
$384$		0			0
$385$	0.579078	−	15.2471i	0.0295126	−	0.777064i
$386$	0.285272	+	0.164702i	0.0145200	+	0.00838310i
$387$		0			0
$388$	−15.6393	−	4.19054i	−0.793965	−	0.212742i
$389$	6.83430	+	5.73466i	0.346513	+	0.290759i	0.799388	−	0.600815i	$-0.205157\pi$
$389$	6.83430	+	5.73466i	0.346513	+	0.290759i	−0.452875	+	0.891574i	$0.649602\pi$
$390$		0			0
$391$	0.343168	+	1.94620i	0.0173548	+	0.0984238i
$392$	−3.38317	−	2.36892i	−0.170876	−	0.119649i
$393$		0			0
$394$	2.20727	−	2.63052i	0.111200	−	0.132524i
$395$	17.6521	−	23.2769i	0.888175	−	1.17119i
$396$		0			0
$397$	−13.1660	+	3.52782i	−0.660782	+	0.177056i	−0.573599	−	0.819136i	$-0.694453\pi$
$397$	−13.1660	+	3.52782i	−0.660782	+	0.177056i	−0.0871833	+	0.996192i	$0.527787\pi$
$398$	6.10964	+	2.84897i	0.306249	+	0.142806i
$399$		0			0
$400$	0.552182	−	7.25898i	0.0276091	−	0.362949i
$401$	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
$403$	17.1978	+	24.5610i	0.856683	+	1.22347i
$404$	2.97240			0.147882
$405$		0			0
$406$	10.9679			0.544328
$407$	5.97399	+	8.53175i	0.296120	+	0.422903i
$408$		0			0
$409$	−9.80467	+	26.9381i	−0.484810	+	1.33200i	0.420515	+	0.907285i	$0.361849\pi$
$409$	−9.80467	+	26.9381i	−0.484810	+	1.33200i	−0.905325	+	0.424719i	$0.860373\pi$
$410$	13.0276	−	4.18896i	0.643386	−	0.206878i
$411$		0			0
$412$	2.90132	+	1.35291i	0.142938	+	0.0666530i
$413$	−22.8645	+	6.12654i	−1.12509	+	0.301467i
$414$		0			0
$415$	−1.45160	−	10.5627i	−0.0712563	−	0.518503i
$416$	15.9247	−	18.9783i	0.780772	−	0.930488i
$417$		0			0
$418$	12.6457	+	8.85459i	0.618519	+	0.433092i
$419$	−2.30839	−	13.0915i	−0.112772	−	0.639563i	−0.987829	−	0.155543i	$-0.950287\pi$
$419$	−2.30839	−	13.0915i	−0.112772	−	0.639563i	0.875057	−	0.484020i	$-0.160824\pi$
$420$		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	$0.651425\pi$
$422$	−6.55035	−	1.75516i	−0.318866	−	0.0854399i
$423$		0			0
$424$	26.9798	+	15.5768i	1.31025	+	0.756476i
$425$	−4.88407	−	12.9595i	−0.236912	−	0.628630i
$426$		0			0
$427$	−8.09054	−	0.707831i	−0.391529	−	0.0342543i
$428$	2.12816	+	4.56386i	0.102869	+	0.220602i
$429$		0			0
$430$	−3.33781	+	0.759863i	−0.160964	+	0.0366438i
$431$			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	−0.328541	−	0.944490i	$-0.606557\pi$
$433$	12.8171	−	12.8171i	0.615949	−	0.615949i	0.944490	+	0.328541i	$0.106557\pi$
$434$	2.92514	−	16.5893i	0.140411	−	0.796312i
$435$		0			0
$436$	−13.1221	−	4.77607i	−0.628437	−	0.228732i
$437$	−0.384686	+	4.39698i	−0.0184020	+	0.210336i
$438$		0			0
$439$	9.75841	+	26.8110i	0.465743	+	1.27962i	0.921105	+	0.389313i	$0.127288\pi$
$439$	9.75841	+	26.8110i	0.465743	+	1.27962i	−0.455362	+	0.890306i	$0.650490\pi$
$440$	−9.86383	−	12.7049i	−0.470240	−	0.605684i
$441$		0			0
$442$	−4.12164	+	15.3822i	−0.196046	+	0.731655i
$443$	−3.51399	−	40.1651i	−0.166955	−	1.90830i	−0.369833	−	0.929098i	$-0.620585\pi$
$443$	−3.51399	−	40.1651i	−0.166955	−	1.90830i	0.202878	−	0.979204i	$-0.434970\pi$
$444$		0			0
$445$	−8.07938	−	12.5248i	−0.382999	−	0.593730i
$446$	10.8144	−	1.90688i	0.512079	−	0.0902933i
$447$		0			0
$448$	−22.2510	+	1.94671i	−1.05126	+	0.0919734i
$449$	−3.91232	−	6.77634i	−0.184634	−	0.319795i	0.758819	−	0.651301i	$-0.225777\pi$
$449$	−3.91232	−	6.77634i	−0.184634	−	0.319795i	−0.943453	+	0.331506i	$0.892443\pi$
$450$		0			0
$451$	6.83332	−	11.8357i	0.321768	−	0.557319i
$452$	−0.995476	+	2.13480i	−0.0468232	+	0.100413i
$453$		0			0
$454$	−2.12294	−	2.53003i	−0.0996347	−	0.118740i
$455$	35.1109	−	1.73255i	1.64603	−	0.0812234i
$456$		0			0
$457$	4.48957	−	3.14363i	0.210013	−	0.147053i	−0.463838	−	0.885920i	$-0.653528\pi$
$457$	4.48957	−	3.14363i	0.210013	−	0.147053i	0.673851	+	0.738867i	$0.264639\pi$
$458$	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
$463$	0.163397	−	0.0761934i	0.00759371	−	0.00354101i	−0.418818	−	0.908070i	$-0.637555\pi$
$463$	0.163397	−	0.0761934i	0.00759371	−	0.00354101i	0.426411	+	0.904529i	$0.359778\pi$
$464$	4.00350	−	3.35933i	0.185858	−	0.155953i
$465$		0			0
$466$	−3.29505	+	1.19930i	−0.152640	+	0.0555566i
$467$	3.26672	+	12.1916i	0.151166	+	0.564158i	0.999403	+	0.0345422i	$0.0109973\pi$
$467$	3.26672	+	12.1916i	0.151166	+	0.564158i	−0.848238	+	0.529616i	$0.822336\pi$
$468$		0			0
$469$	18.6907	−	10.7911i	0.863055	−	0.498285i
$470$	−7.24531	+	23.4420i	−0.334201	+	1.08130i
$471$		0			0
$472$	−14.3126	+	20.4404i	−0.658789	+	0.940848i
$473$	−1.96091	+	2.80048i	−0.0901629	+	0.128766i
$474$		0			0
$475$	−3.04523	−	30.7813i	−0.139725	−	1.41234i
$476$	−6.11948	+	3.53308i	−0.280486	+	0.161939i
$477$		0			0
$478$	4.65373	+	17.3679i	0.212857	+	0.794391i
$479$	−33.4923	+	12.1902i	−1.53030	+	0.556985i	−0.963696	−	0.267003i	$-0.913966\pi$
$479$	−33.4923	+	12.1902i	−1.53030	+	0.556985i	−0.566607	+	0.823988i	$0.691744\pi$
$480$		0			0
$481$	−18.3822	+	15.4245i	−0.838157	+	0.703297i
$482$	−17.7781	+	8.29007i	−0.809771	+	0.377602i
$483$		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	0.809149	−	0.587604i	$-0.199929\pi$
$487$	4.88907	+	4.88907i	0.221545	+	0.221545i	−0.587604	+	0.809149i	$0.699929\pi$
$488$	−7.01302	+	4.91057i	−0.317464	+	0.222291i
$489$		0			0
$490$	−2.37433	−	2.15103i	−0.107262	−	0.0971736i
$491$	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
$493$	4.20179	−	9.01076i	0.189239	−	0.405824i
$494$	−17.7835	+	30.8019i	−0.800117	+	1.38584i
$495$		0			0
$496$	−4.01336	−	6.95135i	−0.180205	−	0.312125i
$497$	−14.0983	+	1.23344i	−0.632396	+	0.0553275i
$498$		0			0
$499$	−11.0477	+	1.94801i	−0.494564	+	0.0872050i	−0.415367	−	0.909654i	$-0.636347\pi$
$499$	−11.0477	+	1.94801i	−0.494564	+	0.0872050i	−0.0791972	+	0.996859i	$0.525236\pi$
$500$	−1.97144	+	9.66830i	−0.0881657	+	0.432380i
$501$		0			0
$502$	−1.39889	−	15.9894i	−0.0624354	−	0.713640i
$503$	−7.82118	+	29.1890i	−0.348729	+	1.30147i	0.539466	+	0.842008i	$0.318626\pi$
$503$	−7.82118	+	29.1890i	−0.348729	+	1.30147i	−0.888195	+	0.459467i	$0.848040\pi$
$504$		0			0
$505$	7.47200	+	0.940624i	0.332499	+	0.0418572i
$506$	0.608940	+	1.67305i	0.0270707	+	0.0743761i
$507$		0			0
$508$	0.251546	−	2.87518i	0.0111605	−	0.127566i
$509$	22.0511	+	8.02596i	0.977399	+	0.355744i	0.780829	−	0.624745i	$-0.214797\pi$
$509$	22.0511	+	8.02596i	0.977399	+	0.355744i	0.196571	+	0.980490i	$0.437019\pi$
$510$		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
$515$	6.86519	+	4.31906i	0.302516	+	0.190321i
$516$		0			0
$517$	10.3559	+	22.2083i	0.455452	+	0.976719i
$518$	13.4302	+	1.17499i	0.590090	+	0.0516262i
$519$		0			0
$520$	27.1793	−	25.1903i	1.19189	−	1.10467i
$521$	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
$523$	−14.1137	−	3.78176i	−0.617150	−	0.165365i	−0.0633182	−	0.997993i	$-0.520168\pi$
$523$	−14.1137	−	3.78176i	−0.617150	−	0.165365i	−0.553832	+	0.832629i	$0.686835\pi$
$524$	0.982891	+	0.824743i	0.0429378	+	0.0360291i
$525$		0			0
$526$	−4.33208	−	24.5685i	−0.188888	−	1.07124i
$527$	−12.5084	−	8.75850i	−0.544876	−	0.381526i
$528$		0			0
$529$	14.4569	−	17.2291i	0.628561	−	0.749090i
$530$	19.2558	+	14.6027i	0.836418	+	0.634301i
$531$		0			0
$532$	−15.2441	+	4.08464i	−0.660914	+	0.177091i
$533$	28.5370	+	13.3070i	1.23607	+	0.576390i
$534$		0			0
$535$	3.90551	+	12.1461i	0.168850	+	0.525120i
$536$	7.78131	−	21.3790i	0.336101	−	0.923431i
$537$		0			0
$538$	−6.19200	−	8.84309i	−0.266956	−	0.381253i
$539$	−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	$0.709325\pi$
$542$	−2.93709	−	4.19460i	−0.126159	−	0.180173i
$543$		0			0
$544$	−4.31531	+	11.8562i	−0.185017	+	0.508331i
$545$	−31.4750	−	16.1586i	−1.34824	−	0.692158i
$546$		0			0
$547$	9.52924	+	4.44356i	0.407441	+	0.189993i	0.615524	−	0.788118i	$-0.288945\pi$
$547$	9.52924	+	4.44356i	0.407441	+	0.189993i	−0.208083	+	0.978111i	$0.566722\pi$
$548$	13.6021	−	3.64467i	0.581053	−	0.155693i
$549$		0			0
$550$	−6.36074	−	10.7340i	−0.271223	−	0.457701i
$551$	14.2734	−	17.0103i	0.608066	−	0.724665i
$552$		0			0
$553$	−30.9344	−	21.6605i	−1.31547	−	0.921099i
$554$	2.48092	+	14.0700i	0.105404	+	0.597776i
$555$		0			0
$556$	−6.17030	−	5.17749i	−0.261679	−	0.219575i
$557$	16.7541	+	4.48926i	0.709896	+	0.190216i	0.595659	−	0.803238i	$-0.296891\pi$
$557$	16.7541	+	4.48926i	0.709896	+	0.190216i	0.114237	+	0.993454i	$0.463558\pi$
$558$		0			0
$559$	−6.82132	−	3.93829i	−0.288511	−	0.166572i
$560$	−9.40403	−	0.357161i	−0.397393	−	0.0150928i
$561$		0			0
$562$	−16.5722	−	1.44988i	−0.699057	−	0.0611596i
$563$	9.91099	+	21.2542i	0.417699	+	0.895758i	0.996757	+	0.0804714i	$0.0256426\pi$
$563$	9.91099	+	21.2542i	0.417699	+	0.895758i	−0.579058	+	0.815286i	$0.696580\pi$
$564$		0			0
$565$	−3.17798	+	5.05144i	−0.133699	+	0.212515i
$566$		−	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	$-0.635231\pi$
$569$	6.84027	−	38.7931i	0.286759	−	1.62629i	0.698934	−	0.715186i	$-0.253658\pi$
$570$		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	$0.363682\pi$
$572$	0.987576	−	11.2880i	0.0412926	−	0.471977i
$573$		0			0
$574$	−6.05032	−	16.6231i	−0.252536	−	0.693836i
$575$	1.74853	−	3.10947i	0.0729185	−	0.129674i
$576$		0			0
$577$	5.64888	−	21.0819i	0.235166	−	0.877651i	−0.742908	−	0.669393i	$-0.766554\pi$
$577$	5.64888	−	21.0819i	0.235166	−	0.877651i	0.978074	−	0.208257i	$-0.0667792\pi$
$578$	0.859390	+	9.82287i	0.0357459	+	0.408578i
$579$		0			0
$580$	−5.95255	+	3.83983i	−0.247166	+	0.159440i
$581$	−13.5734	+	2.39335i	−0.563119	+	0.0992930i
$582$		0			0
$583$	24.0432	−	2.10351i	0.995769	−	0.0871185i
$584$	−10.6167	−	18.3886i	−0.439321	−	0.760927i
$585$		0			0
$586$	−3.88117	+	6.72239i	−0.160330	+	0.277699i
$587$	−10.3168	+	22.1244i	−0.425819	+	0.913173i	0.569984	+	0.821656i	$0.306949\pi$
$587$	−10.3168	+	22.1244i	−0.425819	+	0.913173i	−0.995804	+	0.0915170i	$0.970828\pi$
$588$		0			0
$589$	−21.9220	−	26.1256i	−0.903279	−	1.07649i
$590$	−12.9961	+	14.3453i	−0.535041	+	0.590585i
$591$		0			0
$592$	5.26217	−	3.68461i	0.216274	−	0.151437i
$593$	−4.09490	−	4.09490i	−0.168157	−	0.168157i	0.618012	−	0.786169i	$-0.287938\pi$
$593$	−4.09490	−	4.09490i	−0.168157	−	0.168157i	−0.786169	+	0.618012i	$0.787938\pi$
$594$		0			0
$595$	−16.5012	+	6.94491i	−0.676481	+	0.284714i
$596$	8.17827	+	1.44205i	0.334995	+	0.0590687i
$597$		0			0
$598$	−3.71765	+	1.73357i	−0.152026	+	0.0708910i
$599$	30.3866	−	25.4974i	1.24156	−	1.04180i	0.244163	−	0.969734i	$-0.421487\pi$
$599$	30.3866	−	25.4974i	1.24156	−	1.04180i	0.997400	−	0.0720615i	$-0.0229578\pi$
$600$		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	$0.551139\pi$
$602$	1.14533	+	4.27441i	0.0466800	+	0.174212i
$603$		0			0
$604$	−0.806976	+	0.465908i	−0.0328354	+	0.0189575i
$605$	11.5947	+	3.58363i	0.471392	+	0.145695i
$606$		0			0
$607$	18.5771	−	26.5308i	0.754020	−	1.07685i	−0.240329	−	0.970691i	$-0.577255\pi$
$607$	18.5771	−	26.5308i	0.754020	−	1.07685i	0.994349	−	0.106160i	$-0.0338557\pi$
$608$	−16.1631	+	23.0833i	−0.655501	+	0.936152i
$609$		0			0
$610$	−5.87335	+	3.09994i	−0.237805	+	0.125513i
$611$	−48.8923	+	28.2280i	−1.97797	+	1.14198i
$612$		0			0
$613$	−3.95860	−	14.7737i	−0.159886	−	0.596704i	−0.998637	−	0.0521885i	$-0.983380\pi$
$613$	−3.95860	−	14.7737i	−0.159886	−	0.596704i	0.838751	−	0.544515i	$-0.183286\pi$
$614$	13.5879	−	4.94560i	0.548364	−	0.199588i
$615$		0			0
$616$	−15.9279	+	13.3651i	−0.641755	+	0.538497i
$617$	24.2804	−	11.3221i	0.977492	−	0.455812i	0.132845	−	0.991137i	$-0.457589\pi$
$617$	24.2804	−	11.3221i	0.977492	−	0.455812i	0.844646	+	0.535325i	$0.179811\pi$
$618$		0			0
$619$	−18.6300	−	3.28497i	−0.748802	−	0.132034i	−0.213792	−	0.976879i	$-0.568581\pi$
$619$	−18.6300	−	3.28497i	−0.748802	−	0.132034i	−0.535011	+	0.844845i	$0.679692\pi$
$620$	4.22032	+	10.0275i	0.169492	+	0.402714i
$621$		0			0
$622$	2.88598	+	2.88598i	0.115717	+	0.115717i
$623$	−15.7827	+	11.0512i	−0.632322	+	0.442757i
$624$		0			0
$625$	−8.01536	+	23.6802i	−0.320615	+	0.947210i
$626$	−16.7165	−	19.9220i	−0.668126	−	0.796242i
$627$		0			0
$628$	8.32451	−	17.8520i	0.332184	−	0.712371i
$629$	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	$0.833172\pi$
$632$	−39.6578	+	3.46961i	−1.57750	+	0.138014i
$633$		0			0
$634$	−17.1787	+	3.02907i	−0.682253	+	0.120300i
$635$	1.54219	−	7.14801i	0.0612001	−	0.283660i
$636$		0			0
$637$	−0.642490	−	7.34369i	−0.0254564	−	0.290968i
$638$	2.31829	−	8.65198i	0.0917820	−	0.342535i
$639$		0			0
$640$	1.66366	−	1.29163i	0.0657620	−	0.0510562i
$641$	−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
$643$	−0.152914	+	1.74781i	−0.00603033	+	0.0689270i	−0.998614	−	0.0526401i	$-0.983236\pi$
$643$	−0.152914	+	1.74781i	−0.00603033	+	0.0689270i	0.992583	+	0.121567i	$0.0387920\pi$
$644$	−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	$-0.615669\pi$
$647$	14.7341	−	14.7341i	0.579259	−	0.579259i	0.934699	+	0.355440i	$0.115669\pi$
$648$		0			0
$649$			19.3315i			0.758830i
$650$	23.3592	−	16.7544i	0.916223	−	0.657161i
$651$		0			0
$652$	0.922501	+	1.97831i	0.0361279	+	0.0774766i
$653$	9.28810	+	0.812604i	0.363471	+	0.0317996i	0.267429	−	0.963578i	$-0.413826\pi$
$653$	9.28810	+	0.812604i	0.363471	+	0.0317996i	0.0960426	+	0.995377i	$0.469382\pi$
$654$		0			0
$655$	2.20979	+	2.38427i	0.0863437	+	0.0931612i
$656$	−7.29994	−	4.21462i	−0.285015	−	0.164553i
$657$		0			0
$658$	30.6372	+	8.20920i	1.19436	+	0.320028i
$659$	−14.0775	−	11.8125i	−0.548383	−	0.460148i	0.326010	−	0.945366i	$-0.394296\pi$
$659$	−14.0775	−	11.8125i	−0.548383	−	0.460148i	−0.874393	+	0.485218i	$0.838740\pi$
$660$		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	$0.779070\pi$
$662$	17.8745	+	12.5159i	0.694712	+	0.486443i
$663$		0			0
$664$	−9.33923	+	11.1301i	−0.362432	+	0.431930i
$665$	−39.6130	+	5.44390i	−1.53613	+	0.211106i
$666$		0			0
$667$	2.47371	−	0.662829i	0.0957825	−	0.0256648i
$668$	−5.82669	−	2.71703i	−0.225441	−	0.105125i
$669$		0			0
$670$	8.06026	−	15.7004i	0.311395	−	0.606560i
$671$	−2.26847	+	6.23257i	−0.0875733	+	0.240606i
$672$		0			0
$673$	−2.68248	−	3.83098i	−0.103402	−	0.147673i	0.764117	−	0.645078i	$-0.223175\pi$
$673$	−2.68248	−	3.83098i	−0.103402	−	0.147673i	−0.867518	+	0.497405i	$0.834286\pi$
$674$	−11.0600			−0.426017
$675$		0			0
$676$	14.6331			0.562810
$677$	22.5105	+	32.1483i	0.865147	+	1.23556i	0.970495	+	0.241123i	$0.0775158\pi$
$677$	22.5105	+	32.1483i	0.865147	+	1.23556i	−0.105347	+	0.994436i	$0.533595\pi$
$678$		0			0
$679$	−18.1371	+	49.8312i	−0.696038	+	1.91235i
$680$	−8.61936	+	16.7895i	−0.330538	+	0.643847i
$681$		0			0
$682$	−12.4681	−	5.81397i	−0.477428	−	0.222628i
$683$	−36.4765	+	9.77386i	−1.39574	+	0.373986i	−0.876812	−	0.480834i	$-0.840334\pi$
$683$	−36.4765	+	9.77386i	−1.39574	+	0.373986i	−0.518924	+	0.854820i	$0.673667\pi$
$684$		0			0
$685$	35.3462	−	4.85753i	1.35051	−	0.185597i
$686$	11.0866	−	13.2125i	0.423287	−	0.504454i
$687$		0			0
$688$	1.72726	+	1.20944i	0.0658513	+	0.0461096i
$689$	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	$0.641144\pi$
$692$	17.4769	+	4.68292i	0.664372	+	0.178018i
$693$		0			0
$694$	10.5198	+	6.07363i	0.399327	+	0.230552i
$695$	−13.8724	−	14.9677i	−0.526211	−	0.567759i
$696$		0			0
$697$	−15.9747	−	1.39761i	−0.605086	−	0.0529381i
$698$	7.09386	+	15.2128i	0.268507	+	0.575814i
$699$		0			0
$700$	12.5860	+	2.07232i	0.475705	+	0.0783263i
$701$			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
$707$	0.848488	−	9.69826i	0.0319107	−	0.364741i
$708$		0			0
$709$	−12.4901	−	34.3163i	−0.469077	−	1.28878i	−0.918487	−	0.395452i	$-0.870588\pi$
$709$	−12.4901	−	34.3163i	−0.469077	−	1.28878i	0.449410	−	0.893325i	$-0.351634\pi$
$710$	−9.14119	+	7.09702i	−0.343063	+	0.266346i
$711$		0			0
$712$	−5.25679	+	19.6186i	−0.197007	+	0.735239i
$713$	−0.342810	−	3.91834i	−0.0128384	−	0.146743i
$714$		0			0
$715$	6.05469	−	28.0633i	0.226433	−	1.04951i
$716$	12.4649	−	2.19790i	0.465836	−	0.0821395i
$717$		0			0
$718$	−21.4894	+	1.88008i	−0.801977	+	0.0701639i
$719$	12.9014	+	22.3459i	0.481142	+	0.833363i	0.999766	−	0.0216398i	$-0.00688871\pi$
$719$	12.9014	+	22.3459i	0.481142	+	0.833363i	−0.518624	+	0.855003i	$0.673555\pi$
$720$		0			0
$721$	5.24243	−	9.08015i	0.195238	−	0.338162i
$722$	8.60904	−	18.4622i	0.320395	−	0.687090i
$723$		0			0
$724$	−1.17400	−	1.39912i	−0.0436314	−	0.0519978i
$725$	−16.1786	+	7.76884i	−0.600858	+	0.288528i
$726$		0			0
$727$	1.32255	−	0.926059i	0.0490507	−	0.0343456i	−0.548794	−	0.835958i	$-0.684913\pi$
$727$	1.32255	−	0.926059i	0.0490507	−	0.0343456i	0.597845	+	0.801612i	$0.296024\pi$
$728$	−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
$733$	−12.0574	+	5.62244i	−0.445349	+	0.207669i	−0.632338	−	0.774692i	$-0.717905\pi$
$733$	−12.0574	+	5.62244i	−0.445349	+	0.207669i	0.186990	+	0.982362i	$0.440127\pi$
$734$	21.0132	−	17.6322i	0.775613	−	0.650816i
$735$		0			0
$736$	−3.05398	+	1.11156i	−0.112571	+	0.0409725i
$737$	−4.56182	−	17.0249i	−0.168037	−	0.627122i
$738$		0			0
$739$	−30.9063	+	17.8437i	−1.13691	+	0.656393i	−0.945663	−	0.325150i	$-0.894585\pi$
$739$	−30.9063	+	17.8437i	−1.13691	+	0.656393i	−0.191243	+	0.981543i	$0.561252\pi$
$740$	−7.70027	+	4.06418i	−0.283068	+	0.149402i
$741$		0			0
$742$	17.9187	−	25.5905i	0.657815	−	0.939457i
$743$	20.1985	−	28.8465i	0.741012	−	1.05828i	−0.254813	−	0.966990i	$-0.582014\pi$
$743$	20.1985	−	28.8465i	0.741012	−	1.05828i	0.995825	−	0.0912848i	$-0.0290974\pi$
$744$		0			0
$745$	20.1021	+	6.21305i	0.736485	+	0.227629i
$746$	−4.37382	+	2.52523i	−0.160137	+	0.0924551i
$747$		0			0
$748$	1.49358	+	5.57411i	0.0546106	+	0.203810i
$749$	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	$0.128076\pi$
$752$	13.6975	−	6.38726i	0.499497	−	0.232919i
$753$		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	0.952263	−	0.305278i	$-0.0987493\pi$
$757$	17.8009	+	17.8009i	0.646986	+	0.646986i	−0.305278	+	0.952263i	$0.598749\pi$
$758$	−21.9080	+	15.3401i	−0.795733	+	0.557178i
$759$		0			0
$760$	−28.3001	+	31.2380i	−1.02655	+	1.13312i
$761$	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
$763$	−19.3290	+	41.4512i	−0.699757	+	1.50063i
$764$	−10.2888	+	17.8207i	−0.372236	+	0.644731i
$765$		0			0
$766$	6.51352	+	11.2818i	0.235343	+	0.407626i
$767$	−44.3691	+	3.88180i	−1.60208	+	0.140164i
$768$		0			0
$769$	43.1365	−	7.60612i	1.55554	−	0.274284i	0.671254	−	0.741227i	$-0.265756\pi$
$769$	43.1365	−	7.60612i	1.55554	−	0.274284i	0.884287	+	0.466944i	$0.154645\pi$
$770$	−13.5539	+	8.74324i	−0.488448	+	0.315085i
$771$		0			0
$772$	0.0239691	+	0.273968i	0.000862668	+	0.00986034i
$773$	5.91076	−	22.0592i	0.212595	−	0.793416i	−0.774404	−	0.632691i	$-0.781950\pi$
$773$	5.91076	−	22.0592i	0.212595	−	0.793416i	0.986999	−	0.160725i	$-0.0513831\pi$
$774$		0			0
$775$	7.43578	+	26.5426i	0.267101	+	0.953438i
$776$	19.1194	+	52.5302i	0.686347	+	1.88572i
$777$		0			0
$778$	0.821958	−	9.39502i	0.0294686	−	0.336828i
$779$	−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
$785$	26.5754	−	42.2419i	0.948517	−	1.50768i
$786$		0			0
$787$	−7.27876	−	15.6093i	−0.259460	−	0.556413i	0.732822	−	0.680421i	$-0.238203\pi$
$787$	−7.27876	−	15.6093i	−0.259460	−	0.556413i	−0.992281	+	0.124008i	$0.960425\pi$
$788$	2.85601	+	0.249868i	0.101741	+	0.00890119i
$789$		0			0
$790$	−30.8588	−	1.17200i	−1.09791	−	0.0416980i
$791$	6.68122	+	3.85740i	0.237557	+	0.137153i
$792$		0			0
$793$	−14.7603	−	3.95501i	−0.524154	−	0.140447i
$794$	11.0377	+	9.26170i	0.391712	+	0.328685i
$795$		0			0
$796$	0.977323	+	5.54267i	0.0346403	+	0.196455i
$797$	−26.9373	−	18.8617i	−0.954166	−	0.668115i	−0.0108262	−	0.999941i	$-0.503446\pi$
$797$	−26.9373	−	18.8617i	−0.954166	−	0.668115i	−0.943340	+	0.331827i	$0.892335\pi$
$798$		0			0
$799$	18.4814	−	22.0252i	0.653824	−	0.779197i
$800$	19.5939	−	11.6109i	0.692748	−	0.410506i
$801$		0			0
$802$	−2.99600	+	0.802775i	−0.105792	+	0.0283470i
$803$	−14.9085	−	6.95197i	−0.526111	−	0.245330i
$804$		0			0
$805$	−4.10251	−	2.10614i	−0.144594	−	0.0742317i
$806$	10.8404	−	29.7838i	0.381838	−	1.04909i
$807$		0			0
$808$	−5.88637	−	8.40661i	−0.207082	−	0.295744i
$809$	−0.589848			−0.0207379			−0.0103690	−	0.999946i	$-0.503301\pi$
$809$	−0.589848			−0.0207379			−0.0103690	+	0.999946i	$0.503301\pi$
$810$		0			0
$811$	−48.5224			−1.70385			−0.851925	−	0.523664i	$-0.824565\pi$
$811$	−48.5224			−1.70385			−0.851925	+	0.523664i	$0.824565\pi$
$812$	5.25222	+	7.50095i	0.184317	+	0.263232i
$813$		0			0
$814$	3.76564	−	10.3460i	0.131985	−	0.362627i
$815$	1.69293	+	5.26499i	0.0593009	+	0.184424i
$816$		0			0
$817$	8.11977	+	3.78631i	0.284075	+	0.132466i
$818$	29.2711	−	7.84316i	1.02344	−	0.274230i
$819$		0			0
$820$	9.10337	+	6.90358i	0.317903	+	0.241083i
$821$	−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
$823$	0.511895	+	0.358433i	0.0178435	+	0.0124942i	0.582464	−	0.812856i	$-0.302089\pi$
$823$	0.511895	+	0.358433i	0.0178435	+	0.0124942i	−0.564621	+	0.825351i	$0.690978\pi$
$824$	−1.91929	−	10.8848i	−0.0668615	−	0.379190i
$825$		0			0
$826$	19.1684	+	16.0842i	0.666954	+	0.559641i
$827$	−11.3875	−	3.05127i	−0.395981	−	0.106103i	0.0553328	−	0.998468i	$-0.482378\pi$
$827$	−11.3875	−	3.05127i	−0.395981	−	0.106103i	−0.451314	+	0.892365i	$0.649045\pi$
$828$		0			0
$829$	38.0844	+	21.9880i	1.32272	+	0.763675i	0.984163	−	0.177269i	$-0.0567261\pi$
$829$	38.0844	+	21.9880i	1.32272	+	0.763675i	0.338562	+	0.940944i	$0.390059\pi$
$830$	−8.26631	+	7.66139i	−0.286928	+	0.265931i
$831$		0			0
$832$	−41.8666	−	3.66285i	−1.45146	−	0.126986i
$833$	1.58663	+	3.40254i	0.0549735	+	0.117891i
$834$		0			0
$835$	−13.7873	−	8.67392i	−0.477128	−	0.300173i
$836$			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	−0.981668	−	0.190601i	$-0.938956\pi$
$839$	0.173429	−	0.983567i	0.00598745	−	0.0339565i	0.987655	+	0.156644i	$0.0500676\pi$
$840$		0			0
$841$	15.1440	+	5.51197i	0.522207	+	0.190068i
$842$	0.833993	−	9.53258i	0.0287413	−	0.328514i
$843$		0			0
$844$	−1.93642	−	5.32028i	−0.0666545	−	0.183132i
$845$	36.7845	+	4.63067i	1.26543	+	0.159300i
$846$		0			0
$847$	4.06038	−	15.1535i	0.139516	−	0.520682i
$848$	−1.29739	−	14.8293i	−0.0445527	−	0.509239i
$849$		0			0
$850$	−8.26060	+	12.0869i	−0.283336	+	0.414577i
$851$	3.10007	−	0.546626i	0.106269	−	0.0187381i
$852$		0			0
$853$	4.50805	−	0.394403i	0.154353	−	0.0135041i	−0.00971747	−	0.999953i	$-0.503093\pi$
$853$	4.50805	−	0.394403i	0.154353	−	0.0135041i	0.164070	+	0.986449i	$0.447538\pi$
$854$	4.29256	+	7.43494i	0.146889	+	0.254418i
$855$		0			0
$856$	8.69313	−	15.0569i	0.297125	−	0.514635i
$857$	24.1963	−	51.8892i	0.826531	−	1.77250i	0.223650	−	0.974670i	$-0.428203\pi$
$857$	24.1963	−	51.8892i	0.826531	−	1.77250i	0.602881	−	0.797831i	$-0.294019\pi$
$858$		0			0
$859$	−20.9711	−	24.9924i	−0.715526	−	0.852730i	0.278662	−	0.960389i	$-0.410109\pi$
$859$	−20.9711	−	24.9924i	−0.715526	−	0.852730i	−0.994188	+	0.107659i	$0.965665\pi$
$860$	−2.11806	−	1.91885i	−0.0722251	−	0.0654324i
$861$		0			0
$862$	0.256286	−	0.179453i	0.00872913	−	0.00611220i
$863$	28.5706	+	28.5706i	0.972554	+	0.972554i	0.999633	−	0.0270792i	$-0.00862062\pi$
$863$	28.5706	+	28.5706i	0.972554	+	0.972554i	−0.0270792	+	0.999633i	$0.508621\pi$
$864$		0			0
$865$	42.4513	+	17.3025i	1.44339	+	0.588302i
$866$	−18.8698	−	3.32726i	−0.641223	−	0.113065i
$867$		0			0
$868$	12.7462	−	5.94365i	0.432634	−	0.201741i
$869$	−23.6254	+	19.8241i	−0.801437	+	0.672486i
$870$		0			0
$871$	38.1591	−	13.8888i	1.29297	−	0.470603i
$872$	12.4786	+	46.5707i	0.422578	+	1.57708i
$873$		0			0
$874$	4.04068	−	2.33289i	0.136678	−	0.0789111i
$875$	30.9827	+	9.19224i	1.04741	+	0.310755i
$876$		0			0
$877$	20.3911	−	29.1215i	0.688559	−	0.983364i	−0.310899	−	0.950443i	$-0.600630\pi$
$877$	20.3911	−	29.1215i	0.688559	−	0.983364i	0.999458	−	0.0329214i	$-0.0104811\pi$
$878$	17.2994	−	24.7062i	0.583828	−	0.833792i
$879$		0			0
$880$	−2.26948	+	7.34283i	−0.0765041	+	0.247527i
$881$	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
$883$	0.905746	+	3.38029i	0.0304808	+	0.113756i	0.979490	−	0.201492i	$-0.0645790\pi$
$883$	0.905746	+	3.38029i	0.0304808	+	0.113756i	−0.949009	+	0.315248i	$0.897912\pi$
$884$	−12.4936	+	4.54730i	−0.420205	+	0.152942i
$885$		0			0
$886$	−32.6492	+	27.3959i	−1.09687	+	0.920383i
$887$	25.7899	−	12.0260i	0.865939	−	0.403794i	0.0616962	−	0.998095i	$-0.480349\pi$
$887$	25.7899	−	12.0260i	0.865939	−	0.403794i	0.804243	+	0.594301i	$0.202571\pi$
$888$		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
$893$	52.6023	−	36.8325i	1.76027	−	1.23255i
$894$		0			0
$895$	32.0298	−	1.58051i	1.07064	−	0.0528307i
$896$	−1.75011	−	2.08570i	−0.0584672	−	0.0696785i
$897$		0			0
$898$	−3.49564	+	7.49641i	−0.116651	+	0.250159i
$899$	−9.89411	+	17.1371i	−0.329987	+	0.571554i
$900$		0			0
$901$	−14.1594	−	24.5249i	−0.471719	−	0.817042i
$902$	−14.3919	+	1.25913i	−0.479199	+	0.0419245i
$903$		0			0
$904$	8.00909	−	1.41222i	0.266378	−	0.0469697i
$905$	−2.50844	−	3.88861i	−0.0833833	−	0.129262i
$906$		0			0
$907$	2.85879	+	32.6761i	0.0949246	+	1.08499i	0.882987	+	0.469398i	$0.155529\pi$
$907$	2.85879	+	32.6761i	0.0949246	+	1.08499i	−0.788062	+	0.615596i	$0.788915\pi$
$908$	0.713667	−	2.66344i	0.0236839	−	0.0883894i
$909$		0			0
$910$	−22.7888	−	29.3528i	−0.755443	−	0.973035i
$911$	−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
$913$	−0.981025	+	11.2132i	−0.0324672	+	0.371102i
$914$	−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	$-0.845460\pi$
$919$		−	28.2931i		−	0.933302i	0.884442	−	0.466651i	$-0.154540\pi$
$920$	−4.74004	+	1.07908i	−0.156274	+	0.0355763i
$921$		0			0
$922$	13.4676	+	28.8814i	0.443533	+	0.951159i
$923$	−26.5268	−	2.32080i	−0.873141	−	0.0763899i
$924$		0			0
$925$	−20.6430	+	7.77974i	−0.678738	+	0.255796i
$926$	−0.165049	−	0.0952911i	−0.00542385	−	0.00313146i
$927$		0			0
$928$	15.7933	+	4.23180i	0.518440	+	0.138916i
$929$	25.1788	+	21.1275i	0.826089	+	0.693171i	0.954390	−	0.298564i	$-0.0965076\pi$
$929$	25.1788	+	21.1275i	0.826089	+	0.693171i	−0.128300	+	0.991735i	$0.540952\pi$
$930$		0			0
$931$	1.45603	+	8.25757i	0.0477195	+	0.270631i
$932$	−2.39811	−	1.67917i	−0.0785527	−	0.0550032i
$933$		0			0
$934$	8.57623	−	10.2208i	0.280623	−	0.334433i
$935$	1.99060	+	14.4848i	0.0650997	+	0.473704i
$936$		0			0
$937$	4.87347	−	1.30584i	0.159209	−	0.0426600i	−0.178334	−	0.983970i	$-0.557071\pi$
$937$	4.87347	−	1.30584i	0.159209	−	0.0426600i	0.337543	+	0.941310i	$0.390404\pi$
$938$	−20.6768	−	9.64174i	−0.675121	−	0.314814i
$939$		0			0
$940$	−19.5016	+	6.27064i	−0.636071	+	0.204526i
$941$	−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
$943$	−2.36919	−	3.38355i	−0.0771514	−	0.110184i
$944$	11.9232			0.388068
$945$		0			0
$946$	3.61394			0.117499
$947$	18.4673	+	26.3740i	0.600107	+	0.857041i	0.998180	−	0.0603125i	$-0.0192097\pi$
$947$	18.4673	+	26.3740i	0.600107	+	0.857041i	−0.398073	+	0.917354i	$0.630321\pi$
$948$		0			0
$949$	12.9623	−	35.6136i	0.420773	−	1.15607i
$950$	−24.8078	+	21.3004i	−0.804870	+	0.691075i
$951$		0			0
$952$	22.1110	+	10.3105i	0.716623	+	0.334167i
$953$	20.8927	−	5.59819i	0.676782	−	0.181343i	0.0959743	−	0.995384i	$-0.469403\pi$
$953$	20.8927	−	5.59819i	0.676782	−	0.181343i	0.580808	+	0.814041i	$0.302737\pi$
$954$		0			0
$955$	−31.5033	+	41.5417i	−1.01942	+	1.34426i
$956$	−9.64940	+	11.4997i	−0.312084	+	0.371927i
$957$		0			0
$958$	30.8629	+	21.6105i	0.997136	+	0.698202i
$959$	−8.00894	−	45.4210i	−0.258622	−	1.46672i
$960$		0			0
$961$	−0.465741	−	0.390803i	−0.0150239	−	0.0126065i
$962$	24.5020	+	6.56528i	0.789975	+	0.211673i
$963$		0			0
$964$	−14.1830	−	8.18857i	−0.456804	−	0.263736i
$965$	−0.0264446	+	0.696285i	−0.000851282	+	0.0224142i
$966$		0			0
$967$	10.9923	+	0.961701i	0.353488	+	0.0309262i	0.262517	−	0.964927i	$-0.415447\pi$
$967$	10.9923	+	0.961701i	0.353488	+	0.0309262i	0.0909711	+	0.995854i	$0.471003\pi$
$968$	−6.98917	−	14.9883i	−0.224640	−	0.481743i
$969$		0			0
$970$	9.62569	+	42.2823i	0.309062	+	1.35760i
$971$		−	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
$977$	−0.479546	+	5.48124i	−0.0153420	+	0.175360i	0.984658	+	0.174498i	$0.0558301\pi$
$977$	−0.479546	+	5.48124i	−0.0153420	+	0.175360i	−1.00000		0.000862648i	$0.999725\pi$
$978$		0			0
$979$	5.38167	+	14.7860i	0.171999	+	0.472563i
$980$	0.334087	−	2.65388i	0.0106720	−	0.0847749i
$981$		0			0
$982$	7.10536	−	26.5176i	0.226741	−	0.846209i
$983$	−2.39635	−	27.3904i	−0.0764316	−	0.873618i	−0.933538	−	0.358478i	$-0.883296\pi$
$983$	−2.39635	−	27.3904i	−0.0764316	−	0.873618i	0.857106	−	0.515139i	$-0.172260\pi$
$984$		0			0
$985$	7.10034	+	1.53191i	0.226236	+	0.0488107i
$986$	−10.3502	+	1.82503i	−0.329619	+	0.0581207i
$987$		0			0
$988$	−29.5815	+	2.58804i	−0.941111	+	0.0823366i
$989$	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	$0.0853793\pi$
$992$	10.6128	−	22.7592i	0.336956	−	0.722606i
$993$		0			0
$994$	9.61620	+	11.4601i	0.305007	+	0.363494i
$995$	0.702794	+	14.2424i	0.0222801	+	0.451515i
$996$		0			0
$997$	3.00447	−	2.10376i	0.0951527	−	0.0666266i	−0.525032	−	0.851083i	$-0.675947\pi$
$997$	3.00447	−	2.10376i	0.0951527	−	0.0666266i	0.620185	+	0.784456i	$0.287058\pi$
$998$	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.332.5		192
3.2	odd	2		135.2.q.a.2.12	✓	192
5.3	odd	4	inner	405.2.r.a.8.5		192
15.2	even	4		675.2.ba.b.218.5		192
15.8	even	4		135.2.q.a.83.12	yes	192
15.14	odd	2		675.2.ba.b.407.5		192
27.13	even	9		135.2.q.a.122.12	yes	192
27.14	odd	18	inner	405.2.r.a.152.5		192
135.13	odd	36		135.2.q.a.68.12	yes	192
135.67	odd	36		675.2.ba.b.68.5		192
135.68	even	36	inner	405.2.r.a.233.5		192
135.94	even	18		675.2.ba.b.257.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	3.2	odd	2
135.2.q.a.68.12	yes	192	135.13	odd	36
135.2.q.a.83.12	yes	192	15.8	even	4
135.2.q.a.122.12	yes	192	27.13	even	9
405.2.r.a.8.5		192	5.3	odd	4	inner
405.2.r.a.152.5		192	27.14	odd	18	inner
405.2.r.a.233.5		192	135.68	even	36	inner
405.2.r.a.332.5		192	1.1	even	1	trivial
675.2.ba.b.68.5		192	135.67	odd	36
675.2.ba.b.218.5		192	15.2	even	4
675.2.ba.b.257.5		192	135.94	even	18
675.2.ba.b.407.5		192	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.606324 - 0.865920i) q^{2} +(0.301851 - 0.829330i) q^{4} +(1.02123 - 1.98924i) q^{5} +(-2.61975 - 1.22161i) q^{7} +(-2.94330 + 0.788655i) q^{8} +(-2.34172 + 0.321816i) q^{10} +(-1.51740 + 1.80836i) q^{11} +(-4.45519 - 3.11956i) q^{13} +(0.530600 + 3.00918i) q^{14} +(1.11535 + 0.935892i) q^{16} +(2.67549 + 0.716894i) q^{17} +(5.35751 + 3.09316i) q^{19} +(-1.34148 - 1.44740i) q^{20} +(2.48593 + 0.217491i) q^{22} +(0.301527 + 0.646627i) q^{23} +(-2.91416 - 4.06296i) q^{25} +5.74930i q^{26} +(-1.80389 + 1.80389i) q^{28} +(0.623300 - 3.53491i) q^{29} +(-5.18043 - 1.88552i) q^{31} +(-0.397007 + 4.53781i) q^{32} +(-1.00144 - 2.75143i) q^{34} +(-5.10545 + 3.96376i) q^{35} +(1.14193 - 4.26173i) q^{37} +(-0.569956 - 6.51463i) q^{38} +(-1.43698 + 6.66033i) q^{40} +(-5.70140 + 1.00531i) q^{41} +(1.44271 - 0.126221i) q^{43} +(1.04170 + 1.80428i) q^{44} +(0.377104 - 0.653164i) q^{46} +(4.38688 - 9.40770i) q^{47} +(0.871236 + 1.03830i) q^{49} +(-1.75128 + 4.98690i) q^{50} +(-3.93195 + 2.75318i) q^{52} +(-7.22940 - 7.22940i) q^{53} +(2.04765 + 4.86523i) q^{55} +(8.67413 + 1.52948i) q^{56} +(-3.43887 + 1.60357i) q^{58} +(6.27320 - 5.26384i) q^{59} +(2.64019 - 0.960952i) q^{61} +(1.50831 + 5.62907i) q^{62} +(6.69194 - 3.86359i) q^{64} +(-10.7553 + 5.67665i) q^{65} +(-4.28254 + 6.11610i) q^{67} +(1.40214 - 2.00246i) q^{68} +(6.52785 + 2.01759i) q^{70} +(4.24004 - 2.44799i) q^{71} +(1.80353 + 6.73088i) q^{73} +(-4.38269 + 1.59517i) q^{74} +(4.18242 - 3.50947i) q^{76} +(6.18430 - 2.88379i) q^{77} +(12.8661 + 2.26863i) q^{79} +(3.00075 - 1.26294i) q^{80} +(4.32741 + 4.32741i) q^{82} +(3.90587 - 2.73492i) q^{83} +(4.15837 - 4.59007i) q^{85} +(-0.984048 - 1.17274i) q^{86} +(3.03998 - 6.51925i) q^{88} +(3.33276 - 5.77251i) q^{89} +(7.86060 + 13.6150i) q^{91} +(0.627283 - 0.0548802i) q^{92} +(-10.8062 + 1.90542i) q^{94} +(11.6243 - 7.49853i) q^{95} +(-1.59893 - 18.2758i) q^{97} +(0.370833 - 1.38397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 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

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