LMFDB - Embedded newform 405.2.r.a.233.5

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			233.5
Character	$\chi$	$=$	405.233
Dual form			405.2.r.a.332.5

$q$-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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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	−0.974159	−	0.225863i	$-0.927480\pi$
$2$	−0.606324	+	0.865920i	−0.428736	+	0.612298i	0.545424	+	0.838161i	$0.316369\pi$
$3$		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	−0.849076	−	0.528271i	$-0.822840\pi$
$7$	−2.61975	+	1.22161i	−0.990171	+	0.461725i	−0.141096	+	0.989996i	$0.545063\pi$
$8$	−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	0.487136	−	0.873326i	$-0.338041\pi$
$11$	−1.51740	−	1.80836i	−0.457512	−	0.545242i	−0.944648	+	0.328084i	$0.893597\pi$
$12$		0			0
$13$	−4.45519	+	3.11956i	−1.23565	+	0.865210i	−0.994444	−	0.105265i	$-0.966431\pi$
$13$	−4.45519	+	3.11956i	−1.23565	+	0.865210i	−0.241203	+	0.970475i	$0.577542\pi$
$14$	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	0.0806688	−	0.996741i	$-0.474294\pi$
$17$	2.67549	−	0.716894i	0.648901	−	0.173872i	0.568232	+	0.822869i	$0.307628\pi$
$18$		0			0
$19$	5.35751	−	3.09316i	1.22910	−	0.709619i	0.262256	−	0.964998i	$-0.415534\pi$
$19$	5.35751	−	3.09316i	1.22910	−	0.709619i	0.966841	+	0.255379i	$0.0822003\pi$
$20$	−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	−0.872361	−	0.488863i	$-0.837412\pi$
$23$	0.301527	−	0.646627i	0.0628728	−	0.134831i	0.935233	+	0.354032i	$0.115190\pi$
$24$		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	0.986379	+	0.164487i	$0.0525969\pi$
$29$	0.623300	+	3.53491i	0.115744	+	0.656416i	−0.870635	+	0.491929i	$0.836292\pi$
$30$		0			0
$31$	−5.18043	+	1.88552i	−0.930432	+	0.338650i	−0.762381	−	0.647129i	$-0.775970\pi$
$31$	−5.18043	+	1.88552i	−0.930432	+	0.338650i	−0.168051	+	0.985778i	$0.553747\pi$
$32$	−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	0.994029	+	0.109114i	$0.0348013\pi$
$37$	1.14193	+	4.26173i	0.187732	+	0.700624i	−0.806298	+	0.591510i	$0.798532\pi$
$38$	−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	−0.290314	−	0.956932i	$-0.593760\pi$
$41$	−5.70140	−	1.00531i	−0.890409	−	0.157003i	−0.600095	+	0.799928i	$0.704871\pi$
$42$		0			0
$43$	1.44271	+	0.126221i	0.220012	+	0.0192485i	0.196629	−	0.980478i	$-0.437001\pi$
$43$	1.44271	+	0.126221i	0.220012	+	0.0192485i	0.0233831	+	0.999727i	$0.492556\pi$
$44$	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	0.912081	+	0.410010i	$0.134475\pi$
$47$	4.38688	+	9.40770i	0.639893	+	1.37225i	−0.272188	+	0.962244i	$0.587747\pi$
$48$		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	−0.999976	−	0.00694140i	$-0.997790\pi$
$53$	−7.22940	+	7.22940i	−0.993035	+	0.993035i	0.00694140	+	0.999976i	$0.497790\pi$
$54$		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	0.952197	−	0.305484i	$-0.0988184\pi$
$59$	6.27320	+	5.26384i	0.816701	+	0.685293i	−0.135496	+	0.990778i	$0.543263\pi$
$60$		0			0
$61$	2.64019	+	0.960952i	0.338042	+	0.123037i	0.505463	−	0.862848i	$-0.331322\pi$
$61$	2.64019	+	0.960952i	0.338042	+	0.123037i	−0.167421	+	0.985885i	$0.553544\pi$
$62$	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	0.467396	−	0.884048i	$-0.345192\pi$
$67$	−4.28254	−	6.11610i	−0.523196	−	0.747201i	−0.990592	+	0.136847i	$0.956303\pi$
$68$	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	0.730034	−	0.683411i	$-0.239504\pi$
$71$	4.24004	+	2.44799i	0.503200	+	0.290523i	−0.226834	+	0.973933i	$0.572838\pi$
$72$		0			0
$73$	1.80353	−	6.73088i	0.211088	−	0.787790i	−0.776420	−	0.630216i	$-0.782966\pi$
$73$	1.80353	−	6.73088i	0.211088	−	0.787790i	0.987507	−	0.157574i	$-0.0503671\pi$
$74$	−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	0.606015	−	0.795453i	$-0.292767\pi$
$79$	12.8661	−	2.26863i	1.44754	−	0.255241i	0.841529	+	0.540212i	$0.181656\pi$
$80$	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	0.767951	−	0.640509i	$-0.221276\pi$
$83$	3.90587	+	2.73492i	0.428724	+	0.300196i	−0.339227	+	0.940705i	$0.610165\pi$
$84$		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	0.986821	−	0.161818i	$-0.0517357\pi$
$89$	3.33276	+	5.77251i	0.353272	+	0.611885i	−0.633549	+	0.773703i	$0.718402\pi$
$90$		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	0.281548	+	0.959547i	$0.409152\pi$
$97$	−1.59893	+	18.2758i	−0.162346	+	1.85563i	−0.443894	+	0.896079i	$0.646403\pi$
$98$	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	−0.869097	−	0.494641i	$-0.835299\pi$
$101$	1.15191	−	3.16484i	0.114619	−	0.314913i	0.983716	+	0.179728i	$0.0575217\pi$
$102$		0			0
$103$	−0.316137	−	3.61346i	−0.0311499	−	0.356045i	−0.995734	−	0.0922694i	$-0.970588\pi$
$103$	−0.316137	−	3.61346i	−0.0311499	−	0.356045i	0.964584	−	0.263775i	$-0.0849677\pi$
$104$	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	0.484662	−	0.874701i	$-0.338943\pi$
$107$	−4.03460	−	4.03460i	−0.390039	−	0.390039i	−0.874701	+	0.484662i	$0.838943\pi$
$108$		0			0
$109$			15.8226i			1.51553i	0.652527	+	0.757765i	$0.273709\pi$
$109$			15.8226i			1.51553i	−0.652527	+	0.757765i	$0.726291\pi$
$110$	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	−0.211526	−	0.977372i	$-0.567843\pi$
$113$	−2.65880	+	0.232615i	−0.250119	+	0.0218825i	−0.0385931	+	0.999255i	$0.512288\pi$
$114$		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	0.396230	−	0.918151i	$-0.370318\pi$
$127$	3.15881	+	0.846401i	0.280299	+	0.0751059i	−0.115931	+	0.993257i	$0.536985\pi$
$128$	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	0.916074	−	0.401010i	$-0.131341\pi$
$131$	−0.497235	−	1.36614i	−0.0434436	−	0.119360i	−0.959517	+	0.281649i	$0.909118\pi$
$132$		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	−0.208442	−	0.978035i	$-0.566839\pi$
$137$	9.15193	−	13.0703i	0.781902	−	1.11667i	0.990343	−	0.138637i	$-0.0442720\pi$
$138$		0			0
$139$	3.12149	+	8.57623i	0.264762	+	0.727426i	0.998830	+	0.0483514i	$0.0153967\pi$
$139$	3.12149	+	8.57623i	0.264762	+	0.727426i	−0.734069	+	0.679075i	$0.762381\pi$
$140$	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	−0.841789	−	0.539806i	$-0.818498\pi$
$149$	1.63395	−	9.26659i	0.133858	−	0.759149i	0.975648	−	0.219343i	$-0.0703913\pi$
$150$		0			0
$151$	−0.808803	+	0.678666i	−0.0658194	+	0.0552291i	−0.675104	−	0.737723i	$-0.735901\pi$
$151$	−0.808803	+	0.678666i	−0.0658194	+	0.0552291i	0.609284	+	0.792952i	$0.291457\pi$
$152$	−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	0.847590	−	0.530652i	$-0.178053\pi$
$157$	22.2338	−	1.94520i	1.77445	−	0.155244i	0.926860	+	0.375408i	$0.122497\pi$
$158$	−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	0.635290	−	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
$167$	0.634893	+	7.25686i	0.0491295	+	0.561553i	0.980373	+	0.197154i	$0.0631699\pi$
$167$	0.634893	+	7.25686i	0.0491295	+	0.561553i	−0.931243	+	0.364399i	$0.881275\pi$
$168$		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	−0.556295	−	0.830985i	$-0.687778\pi$
$173$	1.78680	−	20.4232i	0.135848	−	1.55275i	0.692143	−	0.721760i	$-0.256667\pi$
$174$		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	−0.463146	−	0.886282i	$-0.653279\pi$
$179$	7.17079	−	12.4202i	0.535970	−	0.928327i	0.999116	−	0.0420450i	$-0.0133873\pi$
$180$		0			0
$181$	1.03474	+	1.79221i	0.0769112	+	0.133214i	0.901916	−	0.431912i	$-0.142161\pi$
$181$	1.03474	+	1.79221i	0.0769112	+	0.133214i	−0.825005	+	0.565126i	$0.808828\pi$
$182$	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	−0.923987	−	0.382424i	$-0.875089\pi$
$191$	−22.9618	+	4.04878i	−1.66145	+	0.292959i	−0.737467	+	0.675383i	$0.763978\pi$
$192$		0			0
$193$	−0.282417	−	0.131693i	−0.0203288	−	0.00947948i	0.412427	−	0.910991i	$-0.364681\pi$
$193$	−0.282417	−	0.131693i	−0.0203288	−	0.00947948i	−0.432756	+	0.901511i	$0.642459\pi$
$194$	−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	−0.929486	−	0.368858i	$-0.879749\pi$
$197$	0.840756	−	3.13774i	0.0599014	−	0.223555i	0.989387	+	0.145303i	$0.0464156\pi$
$198$		0			0
$199$	−5.52277	−	3.18857i	−0.391499	−	0.226032i	0.291310	−	0.956629i	$-0.405909\pi$
$199$	−5.52277	−	3.18857i	−0.391499	−	0.226032i	−0.682809	+	0.730596i	$0.739242\pi$
$200$	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	0.796077	−	0.605195i	$-0.206905\pi$
$211$	4.91430	+	4.12359i	0.338314	+	0.283879i	−0.457763	+	0.889074i	$0.651349\pi$
$212$	−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	0.702723	−	0.711464i	$-0.251968\pi$
$223$	−4.39023	−	9.41489i	−0.293992	−	0.630467i	−0.996714	+	0.0809965i	$0.974190\pi$
$224$	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	0.189976	−	0.981789i	$-0.439159\pi$
$227$	3.11245	+	0.272304i	0.206580	+	0.0180734i	0.0166042	+	0.999862i	$0.494714\pi$
$228$		0			0
$229$	−23.1368	−	4.07964i	−1.52892	−	0.269590i	−0.654990	−	0.755638i	$-0.727327\pi$
$229$	−23.1368	−	4.07964i	−1.52892	−	0.269590i	−0.873933	+	0.486047i	$0.838438\pi$
$230$	−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	0.988329	−	0.152333i	$-0.0486785\pi$
$233$	0.858538	+	3.20411i	0.0562447	+	0.209908i	−0.932085	+	0.362241i	$0.882012\pi$
$234$		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	−0.802564	−	0.596566i	$-0.796532\pi$
$239$	−15.9837	+	5.81759i	−1.03390	+	0.376309i	−0.231335	+	0.972874i	$0.574309\pi$
$240$		0			0
$241$	3.22231	+	18.2746i	0.207567	+	1.17717i	0.893349	+	0.449364i	$0.148349\pi$
$241$	3.22231	+	18.2746i	0.207567	+	1.17717i	−0.685782	+	0.727807i	$0.740540\pi$
$242$	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	−0.0238664	−	0.999715i	$-0.507598\pi$
$251$	13.1493	−	7.59178i	0.829979	−	0.479189i	0.853846	+	0.520527i	$0.174264\pi$
$252$		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	−0.774118	−	0.633041i	$-0.781806\pi$
$257$	−7.11815	+	4.98418i	−0.444018	+	0.310905i	0.330100	+	0.943946i	$0.392917\pi$
$258$		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	0.369541	−	0.929214i	$-0.379515\pi$
$263$	21.3889	−	9.97382i	1.31890	−	0.615012i	0.949356	+	0.314203i	$0.101737\pi$
$264$		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	−0.754203	−	0.656642i	$-0.771976\pi$
$277$	−12.2491	+	5.71185i	−0.735978	+	0.343192i	0.0182248	+	0.999834i	$0.494199\pi$
$278$	−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	0.978130	−	0.207994i	$-0.0666936\pi$
$281$	10.1156	+	12.0553i	0.603445	+	0.719158i	−0.374685	+	0.927152i	$0.622249\pi$
$282$		0			0
$283$	24.7001	−	17.2952i	1.46827	−	1.02809i	0.479680	−	0.877443i	$-0.340753\pi$
$283$	24.7001	−	17.2952i	1.46827	−	1.02809i	0.988587	−	0.150648i	$-0.0481361\pi$
$284$	−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	−0.975863	−	0.218384i	$-0.929922\pi$
$293$	−3.10333	+	6.65512i	−0.181299	+	0.388796i	0.794564	+	0.607180i	$0.207699\pi$
$294$		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	−0.990326	−	0.138764i	$-0.955687\pi$
$307$	−3.54038	−	13.2129i	−0.202060	−	0.754099i	0.788265	−	0.615336i	$-0.210980\pi$
$308$	−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	0.0648001	−	0.997898i	$-0.479359\pi$
$311$	−3.80231	−	0.670449i	−0.215609	−	0.0380177i	−0.280409	+	0.959881i	$0.590470\pi$
$312$		0			0
$313$	24.5081	+	2.14418i	1.38528	+	0.121196i	0.755281	−	0.655401i	$-0.227500\pi$
$313$	24.5081	+	2.14418i	1.38528	+	0.121196i	0.629997	+	0.776597i	$0.283056\pi$
$314$	−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	0.998965	+	0.0454916i	$0.0144854\pi$
$317$	6.97386	+	14.9555i	0.391691	+	0.839984i	−0.607274	+	0.794493i	$0.707737\pi$
$318$		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	−0.251429	−	0.967876i	$-0.580901\pi$
$331$	−19.3973	−	7.06005i	−1.06617	−	0.388056i	−0.814744	+	0.579820i	$0.803123\pi$
$332$	−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	0.948639	−	0.316361i	$-0.102461\pi$
$337$	6.00115	+	8.57053i	0.326904	+	0.466867i	−0.621735	+	0.783227i	$0.713572\pi$
$338$	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	0.122472	−	0.992472i	$-0.460918\pi$
$347$	−10.4146	−	4.85639i	−0.559083	−	0.260705i	−0.681554	+	0.731767i	$0.738696\pi$
$348$		0			0
$349$	−15.6377	+	2.75735i	−0.837067	+	0.147597i	−0.575719	−	0.817647i	$-0.695278\pi$
$349$	−15.6377	+	2.75735i	−0.837067	+	0.147597i	−0.261347	+	0.965245i	$0.584167\pi$
$350$	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	0.368885	−	0.929475i	$-0.379740\pi$
$353$	−7.10893	−	4.97772i	−0.378370	−	0.264938i	−0.747255	+	0.664538i	$0.768629\pi$
$354$		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	0.998985	+	0.0450476i	$0.0143439\pi$
$359$	10.2032	+	17.6725i	0.538505	+	0.932718i	−0.460480	+	0.887670i	$0.652323\pi$
$360$		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	−0.673906	−	0.738818i	$-0.735385\pi$
$367$	2.26163	−	25.8506i	0.118056	−	1.34939i	0.791962	−	0.610571i	$-0.209060\pi$
$368$	−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	0.999325	+	0.0367323i	$0.0116949\pi$
$373$	0.416402	+	4.75950i	0.0215605	+	0.246438i	−0.977765	+	0.209705i	$0.932750\pi$
$374$	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	$0.774856\pi$
$380$	−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	−0.396375	−	0.918089i	$-0.629732\pi$
$383$	−12.2766	+	1.07406i	−0.627303	+	0.0548819i	−0.230929	+	0.972971i	$0.574176\pi$
$384$		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	−0.452875	−	0.891574i	$-0.649602\pi$
$389$	6.83430	−	5.73466i	0.346513	−	0.290759i	0.799388	+	0.600815i	$0.205157\pi$
$390$		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	−0.0871833	−	0.996192i	$-0.527787\pi$
$397$	−13.1660	−	3.52782i	−0.660782	−	0.177056i	−0.573599	+	0.819136i	$0.694453\pi$
$398$	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	0.962225	−	0.272257i	$-0.0877700\pi$
$401$	1.00354	+	2.75721i	0.0501146	+	0.137689i	−0.912110	+	0.409945i	$0.865548\pi$
$402$		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	−0.905325	−	0.424719i	$-0.860373\pi$
$409$	−9.80467	−	26.9381i	−0.484810	−	1.33200i	0.420515	−	0.907285i	$-0.361849\pi$
$410$	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	0.875057	+	0.484020i	$0.160824\pi$
$419$	−2.30839	+	13.0915i	−0.112772	+	0.639563i	−0.987829	+	0.155543i	$0.950287\pi$
$420$		0			0
$421$	6.93437	−	5.81863i	0.337960	−	0.283582i	−0.457974	−	0.888966i	$-0.651425\pi$
$421$	6.93437	−	5.81863i	0.337960	−	0.283582i	0.795934	+	0.605383i	$0.206980\pi$
$422$	−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	$-0.997731\pi$
$431$		−	0.295969i		−	0.0142563i	0.999975	−	0.00712817i	$-0.00226899\pi$
$432$		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
$437$	−0.384686	−	4.39698i	−0.0184020	−	0.210336i
$438$		0			0
$439$	9.75841	−	26.8110i	0.465743	−	1.27962i	−0.455362	−	0.890306i	$-0.650490\pi$
$439$	9.75841	−	26.8110i	0.465743	−	1.27962i	0.921105	−	0.389313i	$-0.127288\pi$
$440$	−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	0.202878	+	0.979204i	$0.434970\pi$
$443$	−3.51399	+	40.1651i	−0.166955	+	1.90830i	−0.369833	+	0.929098i	$0.620585\pi$
$444$		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	−0.943453	−	0.331506i	$-0.892443\pi$
$449$	−3.91232	+	6.77634i	−0.184634	+	0.319795i	0.758819	+	0.651301i	$0.225777\pi$
$450$		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	0.673851	−	0.738867i	$-0.264639\pi$
$457$	4.48957	+	3.14363i	0.210013	+	0.147053i	−0.463838	+	0.885920i	$0.653528\pi$
$458$	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	−0.815019	−	0.579434i	$-0.803274\pi$
$461$	−29.6880	+	5.23480i	−1.38271	+	0.243809i	−0.567689	+	0.823243i	$0.692163\pi$
$462$		0			0
$463$	0.163397	+	0.0761934i	0.00759371	+	0.00354101i	0.426411	−	0.904529i	$-0.359778\pi$
$463$	0.163397	+	0.0761934i	0.00759371	+	0.00354101i	−0.418818	+	0.908070i	$0.637555\pi$
$464$	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	−0.848238	−	0.529616i	$-0.822336\pi$
$467$	3.26672	−	12.1916i	0.151166	−	0.564158i	0.999403	−	0.0345422i	$-0.0109973\pi$
$468$		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	−0.566607	−	0.823988i	$-0.691744\pi$
$479$	−33.4923	−	12.1902i	−1.53030	−	0.556985i	−0.963696	+	0.267003i	$0.913966\pi$
$480$		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	−0.587604	−	0.809149i	$-0.699929\pi$
$487$	4.88907	−	4.88907i	0.221545	−	0.221545i	0.809149	+	0.587604i	$0.199929\pi$
$488$	−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	−0.244048	−	0.969763i	$-0.578475\pi$
$491$	16.6934	−	19.8944i	0.753361	−	0.897821i	0.997409	+	0.0719426i	$0.0229198\pi$
$492$		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	−0.0791972	−	0.996859i	$-0.525236\pi$
$499$	−11.0477	−	1.94801i	−0.494564	−	0.0872050i	−0.415367	+	0.909654i	$0.636347\pi$
$500$	−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	−0.888195	−	0.459467i	$-0.848040\pi$
$503$	−7.82118	−	29.1890i	−0.348729	−	1.30147i	0.539466	−	0.842008i	$-0.318626\pi$
$504$		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	0.196571	−	0.980490i	$-0.437019\pi$
$509$	22.0511	−	8.02596i	0.977399	−	0.355744i	0.780829	+	0.624745i	$0.214797\pi$
$510$		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	−0.154723	−	0.987958i	$-0.549449\pi$
$521$	14.2319	−	8.21681i	0.623512	−	0.359985i	0.778235	+	0.627973i	$0.216115\pi$
$522$		0			0
$523$	−14.1137	+	3.78176i	−0.617150	+	0.165365i	−0.553832	−	0.832629i	$-0.686835\pi$
$523$	−14.1137	+	3.78176i	−0.617150	+	0.165365i	−0.0633182	+	0.997993i	$0.520168\pi$
$524$	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	−0.208083	−	0.978111i	$-0.566722\pi$
$547$	9.52924	−	4.44356i	0.407441	−	0.189993i	0.615524	+	0.788118i	$0.288945\pi$
$548$	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	0.114237	−	0.993454i	$-0.463558\pi$
$557$	16.7541	−	4.48926i	0.709896	−	0.190216i	0.595659	+	0.803238i	$0.296891\pi$
$558$		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	−0.579058	−	0.815286i	$-0.696580\pi$
$563$	9.91099	−	21.2542i	0.417699	−	0.895758i	0.996757	−	0.0804714i	$-0.0256426\pi$
$564$		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	0.698934	+	0.715186i	$0.253658\pi$
$569$	6.84027	+	38.7931i	0.286759	+	1.62629i	−0.412175	+	0.911105i	$0.635231\pi$
$570$		0			0
$571$	31.4980	−	11.4643i	1.31815	−	0.479767i	0.415285	−	0.909691i	$-0.363682\pi$
$571$	31.4980	−	11.4643i	1.31815	−	0.479767i	0.902865	+	0.429924i	$0.141460\pi$
$572$	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	0.978074	+	0.208257i	$0.0667792\pi$
$577$	5.64888	+	21.0819i	0.235166	+	0.877651i	−0.742908	+	0.669393i	$0.766554\pi$
$578$	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	−0.995804	−	0.0915170i	$-0.970828\pi$
$587$	−10.3168	−	22.1244i	−0.425819	−	0.913173i	0.569984	−	0.821656i	$-0.306949\pi$
$588$		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	−0.786169	−	0.618012i	$-0.787938\pi$
$593$	−4.09490	+	4.09490i	−0.168157	+	0.168157i	0.618012	+	0.786169i	$0.287938\pi$
$594$		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	0.997400	+	0.0720615i	$0.0229578\pi$
$599$	30.3866	+	25.4974i	1.24156	+	1.04180i	0.244163	+	0.969734i	$0.421487\pi$
$600$		0			0
$601$	−22.4811	−	8.18244i	−0.917022	−	0.333769i	−0.159969	−	0.987122i	$-0.551139\pi$
$601$	−22.4811	−	8.18244i	−0.917022	−	0.333769i	−0.757053	+	0.653353i	$0.773362\pi$
$602$	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	0.994349	+	0.106160i	$0.0338557\pi$
$607$	18.5771	+	26.5308i	0.754020	+	1.07685i	−0.240329	+	0.970691i	$0.577255\pi$
$608$	−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	0.838751	+	0.544515i	$0.183286\pi$
$613$	−3.95860	+	14.7737i	−0.159886	+	0.596704i	−0.998637	+	0.0521885i	$0.983380\pi$
$614$	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	0.844646	−	0.535325i	$-0.179811\pi$
$617$	24.2804	+	11.3221i	0.977492	+	0.455812i	0.132845	+	0.991137i	$0.457589\pi$
$618$		0			0
$619$	−18.6300	+	3.28497i	−0.748802	+	0.132034i	−0.535011	−	0.844845i	$-0.679692\pi$
$619$	−18.6300	+	3.28497i	−0.748802	+	0.132034i	−0.213792	+	0.976879i	$0.568581\pi$
$620$	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	−0.865773	−	0.500438i	$-0.833172\pi$
$631$	0.0126965	−	0.0219910i	0.000505440	−	0.000875448i	0.866278	+	0.499562i	$0.166506\pi$
$632$	−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	0.571331	+	0.820720i	$0.306427\pi$
$641$	−9.97230	+	27.3987i	−0.393882	+	1.08218i	−0.965214	+	0.261463i	$0.915795\pi$
$642$		0			0
$643$	−0.152914	−	1.74781i	−0.00603033	−	0.0689270i	0.992583	−	0.121567i	$-0.0387920\pi$
$643$	−0.152914	−	1.74781i	−0.00603033	−	0.0689270i	−0.998614	+	0.0526401i	$0.983236\pi$
$644$	−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	0.934699	−	0.355440i	$-0.115669\pi$
$647$	14.7341	+	14.7341i	0.579259	+	0.579259i	−0.355440	+	0.934699i	$0.615669\pi$
$648$		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	0.0960426	−	0.995377i	$-0.469382\pi$
$653$	9.28810	−	0.812604i	0.363471	−	0.0317996i	0.267429	+	0.963578i	$0.413826\pi$
$654$		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	−0.874393	−	0.485218i	$-0.838740\pi$
$659$	−14.0775	+	11.8125i	−0.548383	+	0.460148i	0.326010	+	0.945366i	$0.394296\pi$
$660$		0			0
$661$	4.43306	−	25.1412i	0.172426	−	0.977878i	−0.768647	−	0.639674i	$-0.779070\pi$
$661$	4.43306	−	25.1412i	0.172426	−	0.977878i	0.941073	−	0.338204i	$-0.109819\pi$
$662$	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	−0.867518	−	0.497405i	$-0.834286\pi$
$673$	−2.68248	+	3.83098i	−0.103402	+	0.147673i	0.764117	+	0.645078i	$0.223175\pi$
$674$	−11.0600			−0.426017
$675$		0			0
$676$	14.6331			0.562810
$677$	22.5105	−	32.1483i	0.865147	−	1.23556i	−0.105347	−	0.994436i	$-0.533595\pi$
$677$	22.5105	−	32.1483i	0.865147	−	1.23556i	0.970495	−	0.241123i	$-0.0775158\pi$
$678$		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	−0.518924	−	0.854820i	$-0.673667\pi$
$683$	−36.4765	−	9.77386i	−1.39574	−	0.373986i	−0.876812	+	0.480834i	$0.840334\pi$
$684$		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	−0.429028	−	0.903291i	$-0.641144\pi$
$691$	10.1478	−	8.51501i	0.386040	−	0.323926i	0.815068	+	0.579365i	$0.196699\pi$
$692$	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	$-0.991452\pi$
$701$		−	1.42181i		−	0.0537011i	0.999639	−	0.0268505i	$-0.00854782\pi$
$702$		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	0.449410	+	0.893325i	$0.351634\pi$
$709$	−12.4901	+	34.3163i	−0.469077	+	1.28878i	−0.918487	+	0.395452i	$0.870588\pi$
$710$	−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	−0.518624	−	0.855003i	$-0.673555\pi$
$719$	12.9014	−	22.3459i	0.481142	−	0.833363i	0.999766	+	0.0216398i	$0.00688871\pi$
$720$		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	0.597845	−	0.801612i	$-0.296024\pi$
$727$	1.32255	+	0.926059i	0.0490507	+	0.0343456i	−0.548794	+	0.835958i	$0.684913\pi$
$728$	−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	0.186990	−	0.982362i	$-0.440127\pi$
$733$	−12.0574	−	5.62244i	−0.445349	−	0.207669i	−0.632338	+	0.774692i	$0.717905\pi$
$734$	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	−0.191243	−	0.981543i	$-0.561252\pi$
$739$	−30.9063	−	17.8437i	−1.13691	−	0.656393i	−0.945663	+	0.325150i	$0.894585\pi$
$740$	−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	0.995825	+	0.0912848i	$0.0290974\pi$
$743$	20.1985	+	28.8465i	0.741012	+	1.05828i	−0.254813	+	0.966990i	$0.582014\pi$
$744$		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	0.920138	−	0.391593i	$-0.128076\pi$
$751$	19.0262	+	15.9649i	0.694275	+	0.582566i	−0.225864	+	0.974159i	$0.572520\pi$
$752$	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	−0.305278	−	0.952263i	$-0.598749\pi$
$757$	17.8009	−	17.8009i	0.646986	−	0.646986i	0.952263	+	0.305278i	$0.0987493\pi$
$758$	−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	0.207765	−	0.978179i	$-0.433381\pi$
$761$	31.3105	−	37.3144i	1.13500	−	1.35265i	0.927240	−	0.374467i	$-0.122174\pi$
$762$		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	0.884287	−	0.466944i	$-0.154645\pi$
$769$	43.1365	+	7.60612i	1.55554	+	0.274284i	0.671254	+	0.741227i	$0.265756\pi$
$770$	−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	0.986999	+	0.160725i	$0.0513831\pi$
$773$	5.91076	+	22.0592i	0.212595	+	0.793416i	−0.774404	+	0.632691i	$0.781950\pi$
$774$		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	−0.992281	−	0.124008i	$-0.960425\pi$
$787$	−7.27876	+	15.6093i	−0.259460	+	0.556413i	0.732822	+	0.680421i	$0.238203\pi$
$788$	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	−0.943340	−	0.331827i	$-0.892335\pi$
$797$	−26.9373	+	18.8617i	−0.954166	+	0.668115i	−0.0108262	+	0.999941i	$0.503446\pi$
$798$		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	0.506989	−	0.861953i	$-0.330759\pi$
$821$	−12.3182	−	14.6802i	−0.429907	−	0.512343i	−0.936895	+	0.349610i	$0.886314\pi$
$822$		0			0
$823$	0.511895	−	0.358433i	0.0178435	−	0.0124942i	−0.564621	−	0.825351i	$-0.690978\pi$
$823$	0.511895	−	0.358433i	0.0178435	−	0.0124942i	0.582464	+	0.812856i	$0.302089\pi$
$824$	−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	−0.451314	−	0.892365i	$-0.649045\pi$
$827$	−11.3875	+	3.05127i	−0.395981	+	0.106103i	0.0553328	+	0.998468i	$0.482378\pi$
$828$		0			0
$829$	38.0844	−	21.9880i	1.32272	−	0.763675i	0.338562	−	0.940944i	$-0.390059\pi$
$829$	38.0844	−	21.9880i	1.32272	−	0.763675i	0.984163	+	0.177269i	$0.0567261\pi$
$830$	−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	0.987655	−	0.156644i	$-0.0500676\pi$
$839$	0.173429	+	0.983567i	0.00598745	+	0.0339565i	−0.981668	+	0.190601i	$0.938956\pi$
$840$		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	0.164070	−	0.986449i	$-0.447538\pi$
$853$	4.50805	+	0.394403i	0.154353	+	0.0135041i	−0.00971747	+	0.999953i	$0.503093\pi$
$854$	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	0.602881	+	0.797831i	$0.294019\pi$
$857$	24.1963	+	51.8892i	0.826531	+	1.77250i	0.223650	+	0.974670i	$0.428203\pi$
$858$		0			0
$859$	−20.9711	+	24.9924i	−0.715526	+	0.852730i	−0.994188	−	0.107659i	$-0.965665\pi$
$859$	−20.9711	+	24.9924i	−0.715526	+	0.852730i	0.278662	+	0.960389i	$0.410109\pi$
$860$	−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	−0.0270792	−	0.999633i	$-0.508621\pi$
$863$	28.5706	−	28.5706i	0.972554	−	0.972554i	0.999633	+	0.0270792i	$0.00862062\pi$
$864$		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	0.999458	+	0.0329214i	$0.0104811\pi$
$877$	20.3911	+	29.1215i	0.688559	+	0.983364i	−0.310899	+	0.950443i	$0.600630\pi$
$878$	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	0.920846	−	0.389927i	$-0.127500\pi$
$881$	30.9752	+	17.8836i	1.04358	+	0.602512i	0.122736	+	0.992439i	$0.460833\pi$
$882$		0			0
$883$	0.905746	−	3.38029i	0.0304808	−	0.113756i	−0.949009	−	0.315248i	$-0.897912\pi$
$883$	0.905746	−	3.38029i	0.0304808	−	0.113756i	0.979490	+	0.201492i	$0.0645790\pi$
$884$	−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	0.804243	−	0.594301i	$-0.202571\pi$
$887$	25.7899	+	12.0260i	0.865939	+	0.403794i	0.0616962	+	0.998095i	$0.480349\pi$
$888$		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	−0.788062	−	0.615596i	$-0.788915\pi$
$907$	2.85879	−	32.6761i	0.0949246	−	1.08499i	0.882987	−	0.469398i	$-0.155529\pi$
$908$	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	0.659430	+	0.751766i	$0.270798\pi$
$911$	−9.92857	+	27.2785i	−0.328948	+	0.903778i	−0.988379	+	0.152012i	$0.951425\pi$
$912$		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	$0.154540\pi$
$919$			28.2931i			0.933302i	−0.884442	+	0.466651i	$0.845460\pi$
$920$	−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	−0.128300	−	0.991735i	$-0.540952\pi$
$929$	25.1788	−	21.1275i	0.826089	−	0.693171i	0.954390	+	0.298564i	$0.0965076\pi$
$930$		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	0.337543	−	0.941310i	$-0.390404\pi$
$937$	4.87347	+	1.30584i	0.159209	+	0.0426600i	−0.178334	+	0.983970i	$0.557071\pi$
$938$	−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	−0.647687	−	0.761906i	$-0.724264\pi$
$941$	−19.6715	−	54.0471i	−0.641274	−	1.76189i	0.00641343	−	0.999979i	$-0.497959\pi$
$942$		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	−0.398073	−	0.917354i	$-0.630321\pi$
$947$	18.4673	−	26.3740i	0.600107	−	0.857041i	0.998180	+	0.0603125i	$0.0192097\pi$
$948$		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	0.580808	−	0.814041i	$-0.302737\pi$
$953$	20.8927	+	5.59819i	0.676782	+	0.181343i	0.0959743	+	0.995384i	$0.469403\pi$
$954$		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	0.0909711	−	0.995854i	$-0.471003\pi$
$967$	10.9923	−	0.961701i	0.353488	−	0.0309262i	0.262517	+	0.964927i	$0.415447\pi$
$968$	−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	$0.114506\pi$
$971$			21.9387i			0.704047i	−0.935991	+	0.352023i	$0.885494\pi$
$972$		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	−1.00000		0.000862648i	$-0.999725\pi$
$977$	−0.479546	−	5.48124i	−0.0153420	−	0.175360i	0.984658	−	0.174498i	$-0.0558301\pi$
$978$		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	0.857106	+	0.515139i	$0.172260\pi$
$983$	−2.39635	+	27.3904i	−0.0764316	+	0.873618i	−0.933538	+	0.358478i	$0.883296\pi$
$984$		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	0.964242	−	0.265022i	$-0.0853793\pi$
$991$	7.95205	+	13.7734i	0.252605	+	0.437525i	−0.711637	+	0.702547i	$0.752046\pi$
$992$	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	0.620185	−	0.784456i	$-0.287058\pi$
$997$	3.00447	+	2.10376i	0.0951527	+	0.0666266i	−0.525032	+	0.851083i	$0.675947\pi$
$998$	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.233.5		192
3.2	odd	2		135.2.q.a.68.12	yes	192
5.2	odd	4	inner	405.2.r.a.152.5		192
15.2	even	4		135.2.q.a.122.12	yes	192
15.8	even	4		675.2.ba.b.257.5		192
15.14	odd	2		675.2.ba.b.68.5		192
27.2	odd	18	inner	405.2.r.a.8.5		192
27.25	even	9		135.2.q.a.83.12	yes	192
135.2	even	36	inner	405.2.r.a.332.5		192
135.52	odd	36		135.2.q.a.2.12	✓	192
135.79	even	18		675.2.ba.b.218.5		192
135.133	odd	36		675.2.ba.b.407.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.12	✓	192	135.52	odd	36
135.2.q.a.68.12	yes	192	3.2	odd	2
135.2.q.a.83.12	yes	192	27.25	even	9
135.2.q.a.122.12	yes	192	15.2	even	4
405.2.r.a.8.5		192	27.2	odd	18	inner
405.2.r.a.152.5		192	5.2	odd	4	inner
405.2.r.a.233.5		192	1.1	even	1	trivial
405.2.r.a.332.5		192	135.2	even	36	inner
675.2.ba.b.68.5		192	15.14	odd	2
675.2.ba.b.218.5		192	135.79	even	18
675.2.ba.b.257.5		192	15.8	even	4
675.2.ba.b.407.5		192	135.133	odd	36

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

L-functions

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