LMFDB - Embedded newform 405.2.r.a.152.1

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			152.1
Character	$\chi$	$=$	405.152
Dual form			405.2.r.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05499 - 1.43892i) q^{2} +(1.46845 + 4.03452i) q^{4} +(1.82626 - 1.29027i) q^{5} +(-1.14217 - 2.44940i) q^{7} +(1.48912 - 5.55747i) q^{8} +(-5.60952 + 0.0236494i) q^{10} +(2.09979 + 2.50243i) q^{11} +(1.80484 + 2.57758i) q^{13} +(-1.17733 + 6.67697i) q^{14} +(-4.47891 + 3.75825i) q^{16} +(-1.57770 - 5.88806i) q^{17} +(2.91796 - 1.68469i) q^{19} +(7.88737 + 5.47338i) q^{20} +(-0.714248 - 8.16389i) q^{22} +(4.50352 + 2.10003i) q^{23} +(1.67042 - 4.71272i) q^{25} -7.89390i q^{26} +(8.20493 - 8.20493i) q^{28} +(-0.541940 - 3.07349i) q^{29} +(0.346096 - 0.125969i) q^{31} +(3.14866 - 0.275472i) q^{32} +(-5.23028 + 14.3701i) q^{34} +(-5.24628 - 2.99952i) q^{35} +(-4.28145 + 1.14721i) q^{37} +(-8.42050 - 0.736698i) q^{38} +(-4.45110 - 12.0707i) q^{40} +(-7.54663 - 1.33068i) q^{41} +(0.386956 - 4.42293i) q^{43} +(-7.01269 + 12.1463i) q^{44} +(-6.23291 - 10.7957i) q^{46} +(6.23750 - 2.90859i) q^{47} +(-0.195477 + 0.232960i) q^{49} +(-10.2139 + 7.28096i) q^{50} +(-7.74898 + 11.0667i) q^{52} +(-3.48010 - 3.48010i) q^{53} +(7.06356 + 1.86079i) q^{55} +(-15.3133 + 2.70014i) q^{56} +(-3.30882 + 7.09579i) q^{58} +(-5.87095 - 4.92631i) q^{59} +(-6.73344 - 2.45077i) q^{61} +(-0.892481 - 0.239140i) q^{62} +(3.26012 + 1.88223i) q^{64} +(6.62186 + 2.37859i) q^{65} +(-0.315748 + 0.221089i) q^{67} +(21.4388 - 15.0116i) q^{68} +(6.46497 + 13.7129i) q^{70} +(8.46099 + 4.88495i) q^{71} +(-0.0248963 - 0.00667095i) q^{73} +(10.4491 + 3.80315i) q^{74} +(11.0818 + 9.29871i) q^{76} +(3.73113 - 8.00143i) q^{77} +(10.9549 - 1.93165i) q^{79} +(-3.33049 + 12.6425i) q^{80} +(13.5935 + 13.5935i) q^{82} +(0.627725 - 0.896484i) q^{83} +(-10.4785 - 8.71746i) q^{85} +(-7.15941 + 8.53226i) q^{86} +(17.0340 - 7.94310i) q^{88} +(3.93198 + 6.81039i) q^{89} +(4.25207 - 7.36481i) q^{91} +(-1.85943 + 21.2533i) q^{92} +(-17.0032 - 2.99812i) q^{94} +(3.15525 - 6.84162i) q^{95} +(-5.10752 - 0.446850i) q^{97} +(0.736913 - 0.197455i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−2.05499	−	1.43892i	−1.45309	−	1.01747i	−0.991462	−	0.130396i	$-0.958375\pi$
$2$	−2.05499	−	1.43892i	−1.45309	−	1.01747i	−0.461633	−	0.887071i	$-0.652736\pi$
$3$		0			0
$3$		0			0
$4$	1.46845	+	4.03452i	0.734223	+	2.01726i
$5$	1.82626	−	1.29027i	0.816727	−	0.577025i
$5$	1.82626	−	1.29027i	0.816727	−	0.577025i
$6$		0			0
$7$	−1.14217	−	2.44940i	−0.431701	−	0.925785i	−0.995032	−	0.0995542i	$-0.968258\pi$
$7$	−1.14217	−	2.44940i	−0.431701	−	0.925785i	0.563331	−	0.826231i	$-0.309519\pi$
$8$	1.48912	−	5.55747i	0.526483	−	1.96486i
$9$		0			0
$10$	−5.60952	+	0.0236494i	−1.77389	+	0.00747861i
$11$	2.09979	+	2.50243i	0.633111	+	0.754512i	0.983265	−	0.182180i	$-0.0583154\pi$
$11$	2.09979	+	2.50243i	0.633111	+	0.754512i	−0.350155	+	0.936692i	$0.613871\pi$
$12$		0			0
$13$	1.80484	+	2.57758i	0.500572	+	0.714891i	0.987336	−	0.158642i	$-0.0507117\pi$
$13$	1.80484	+	2.57758i	0.500572	+	0.714891i	−0.486764	+	0.873534i	$0.661823\pi$
$14$	−1.17733	+	6.67697i	−0.314655	+	1.78450i
$15$		0			0
$16$	−4.47891	+	3.75825i	−1.11973	+	0.939563i
$17$	−1.57770	−	5.88806i	−0.382649	−	1.42807i	−0.841840	−	0.539728i	$-0.818527\pi$
$17$	−1.57770	−	5.88806i	−0.382649	−	1.42807i	0.459191	−	0.888338i	$-0.348139\pi$
$18$		0			0
$19$	2.91796	−	1.68469i	0.669427	−	0.386494i	−0.126433	−	0.991975i	$-0.540353\pi$
$19$	2.91796	−	1.68469i	0.669427	−	0.386494i	0.795859	+	0.605481i	$0.207019\pi$
$20$	7.88737	+	5.47338i	1.76367	+	1.22389i
$21$		0			0
$22$	−0.714248	−	8.16389i	−0.152278	−	1.74055i
$23$	4.50352	+	2.10003i	0.939049	+	0.437886i	0.831008	−	0.556261i	$-0.187764\pi$
$23$	4.50352	+	2.10003i	0.939049	+	0.437886i	0.108041	+	0.994146i	$0.465542\pi$
$24$		0			0
$25$	1.67042	−	4.71272i	0.334085	−	0.942543i
$26$		−	7.89390i		−	1.54812i
$27$		0			0
$28$	8.20493	−	8.20493i	1.55059	−	1.55059i
$29$	−0.541940	−	3.07349i	−0.100636	−	0.570733i	−0.992874	−	0.119169i	$-0.961977\pi$
$29$	−0.541940	−	3.07349i	−0.100636	−	0.570733i	0.892238	−	0.451565i	$-0.149134\pi$
$30$		0			0
$31$	0.346096	−	0.125969i	0.0621607	−	0.0226246i	−0.310753	−	0.950491i	$-0.600581\pi$
$31$	0.346096	−	0.125969i	0.0621607	−	0.0226246i	0.372913	+	0.927866i	$0.378359\pi$
$32$	3.14866	−	0.275472i	0.556610	−	0.0486971i
$33$		0			0
$34$	−5.23028	+	14.3701i	−0.896985	+	2.46445i
$35$	−5.24628	−	2.99952i	−0.886783	−	0.507011i
$36$		0			0
$37$	−4.28145	+	1.14721i	−0.703866	+	0.188600i	−0.592962	−	0.805231i	$-0.702041\pi$
$37$	−4.28145	+	1.14721i	−0.703866	+	0.188600i	−0.110904	+	0.993831i	$0.535375\pi$
$38$	−8.42050	−	0.736698i	−1.36599	−	0.119508i
$39$		0			0
$40$	−4.45110	−	12.0707i	−0.703781	−	1.90855i
$41$	−7.54663	−	1.33068i	−1.17859	−	0.207817i	−0.450164	−	0.892946i	$-0.648635\pi$
$41$	−7.54663	−	1.33068i	−1.17859	−	0.207817i	−0.728422	+	0.685129i	$0.759746\pi$
$42$		0			0
$43$	0.386956	−	4.42293i	0.0590102	−	0.674490i	−0.907869	−	0.419255i	$-0.862291\pi$
$43$	0.386956	−	4.42293i	0.0590102	−	0.674490i	0.966879	−	0.255236i	$-0.0821530\pi$
$44$	−7.01269	+	12.1463i	−1.05720	+	1.83113i
$45$		0			0
$46$	−6.23291	−	10.7957i	−0.918992	−	1.59174i
$47$	6.23750	−	2.90859i	0.909832	−	0.424262i	0.0893938	−	0.995996i	$-0.471507\pi$
$47$	6.23750	−	2.90859i	0.909832	−	0.424262i	0.820439	+	0.571735i	$0.193729\pi$
$48$		0			0
$49$	−0.195477	+	0.232960i	−0.0279253	+	0.0332800i
$50$	−10.2139	+	7.28096i	−1.44446	+	1.02968i
$51$		0			0
$52$	−7.74898	+	11.0667i	−1.07459	+	1.53467i
$53$	−3.48010	−	3.48010i	−0.478029	−	0.478029i	0.426472	−	0.904501i	$-0.359756\pi$
$53$	−3.48010	−	3.48010i	−0.478029	−	0.478029i	−0.904501	+	0.426472i	$0.859756\pi$
$54$		0			0
$55$	7.06356	+	1.86079i	0.952450	+	0.250909i
$56$	−15.3133	+	2.70014i	−2.04632	+	0.360822i
$57$		0			0
$58$	−3.30882	+	7.09579i	−0.434470	+	0.931723i
$59$	−5.87095	−	4.92631i	−0.764332	−	0.641351i	0.174918	−	0.984583i	$-0.444034\pi$
$59$	−5.87095	−	4.92631i	−0.764332	−	0.641351i	−0.939251	+	0.343232i	$0.888478\pi$
$60$		0			0
$61$	−6.73344	−	2.45077i	−0.862128	−	0.313789i	−0.127153	−	0.991883i	$-0.540584\pi$
$61$	−6.73344	−	2.45077i	−0.862128	−	0.313789i	−0.734975	+	0.678094i	$0.762806\pi$
$62$	−0.892481	−	0.239140i	−0.113345	−	0.0303708i
$63$		0			0
$64$	3.26012	+	1.88223i	0.407515	+	0.235279i
$65$	6.62186	+	2.37859i	0.821341	+	0.295028i
$66$		0			0
$67$	−0.315748	+	0.221089i	−0.0385747	+	0.0270103i	−0.592705	−	0.805420i	$-0.701940\pi$
$67$	−0.315748	+	0.221089i	−0.0385747	+	0.0270103i	0.554130	+	0.832430i	$0.313051\pi$
$68$	21.4388	−	15.0116i	2.59983	−	1.82042i
$69$		0			0
$70$	6.46497	+	13.7129i	0.772711	+	1.63901i
$71$	8.46099	+	4.88495i	1.00413	+	0.579737i	0.909469	−	0.415772i	$-0.136489\pi$
$71$	8.46099	+	4.88495i	1.00413	+	0.579737i	0.0946655	+	0.995509i	$0.469822\pi$
$72$		0			0
$73$	−0.0248963	−	0.00667095i	−0.00291389	−	0.000780776i	0.257362	−	0.966315i	$-0.417147\pi$
$73$	−0.0248963	−	0.00667095i	−0.00291389	−	0.000780776i	−0.260276	+	0.965534i	$0.583813\pi$
$74$	10.4491	+	3.80315i	1.21468	+	0.442107i
$75$		0			0
$76$	11.0818	+	9.29871i	1.27117	+	1.06664i
$77$	3.73113	−	8.00143i	0.425202	−	0.911848i
$78$		0			0
$79$	10.9549	−	1.93165i	1.23253	−	0.217327i	0.480816	−	0.876822i	$-0.340341\pi$
$79$	10.9549	−	1.93165i	1.23253	−	0.217327i	0.751710	+	0.659494i	$0.229230\pi$
$80$	−3.33049	+	12.6425i	−0.372360	+	1.41348i
$81$		0			0
$82$	13.5935	+	13.5935i	1.50115	+	1.50115i
$83$	0.627725	−	0.896484i	0.0689018	−	0.0984019i	−0.783222	−	0.621742i	$-0.786425\pi$
$83$	0.627725	−	0.896484i	0.0689018	−	0.0984019i	0.852124	+	0.523340i	$0.175314\pi$
$84$		0			0
$85$	−10.4785	−	8.71746i	−1.13655	−	0.945541i
$86$	−7.15941	+	8.53226i	−0.772019	+	0.920057i
$87$		0			0
$88$	17.0340	−	7.94310i	1.81583	−	0.846737i
$89$	3.93198	+	6.81039i	0.416789	+	0.721900i	0.995614	−	0.0935515i	$-0.0298220\pi$
$89$	3.93198	+	6.81039i	0.416789	+	0.721900i	−0.578825	+	0.815452i	$0.696489\pi$
$90$		0			0
$91$	4.25207	−	7.36481i	0.445738	−	0.772042i
$92$	−1.85943	+	21.2533i	−0.193858	+	2.21581i
$93$		0			0
$94$	−17.0032	−	2.99812i	−1.75375	−	0.309233i
$95$	3.15525	−	6.84162i	0.323722	−	0.701936i
$96$		0			0
$97$	−5.10752	−	0.446850i	−0.518590	−	0.0453707i	−0.175143	−	0.984543i	$-0.556039\pi$
$97$	−5.10752	−	0.446850i	−0.518590	−	0.0453707i	−0.343447	+	0.939172i	$0.611594\pi$
$98$	0.736913	−	0.197455i	0.0744394	−	0.0199460i
$99$		0			0
$100$	21.4665	−	0.181006i	2.14665	−	0.0181006i
$101$	−0.406707	+	1.11742i	−0.0404688	+	0.111187i	−0.958281	−	0.285827i	$-0.907732\pi$
$101$	−0.406707	+	1.11742i	−0.0404688	+	0.111187i	0.917812	+	0.397015i	$0.129954\pi$
$102$		0			0
$103$	0.187413	−	0.0163965i	0.0184664	−	0.00161560i	−0.0779188	−	0.996960i	$-0.524827\pi$
$103$	0.187413	−	0.0163965i	0.0184664	−	0.00161560i	0.0963852	+	0.995344i	$0.469272\pi$
$104$	17.0124	−	6.19202i	1.66821	−	0.607177i
$105$		0			0
$106$	2.14398	+	12.1591i	0.208242	+	1.18100i
$107$	1.76707	−	1.76707i	0.170829	−	0.170829i	−0.616515	−	0.787344i	$-0.711456\pi$
$107$	1.76707	−	1.76707i	0.170829	−	0.170829i	0.787344	+	0.616515i	$0.211456\pi$
$108$		0			0
$109$		−	7.80745i		−	0.747818i	−0.927465	−	0.373909i	$-0.878017\pi$
$109$		−	7.80745i		−	0.747818i	0.927465	−	0.373909i	$-0.121983\pi$
$110$	−11.8380	−	13.9878i	−1.12871	−	1.33368i
$111$		0			0
$112$	14.3211	+	6.67806i	1.35322	+	0.631017i
$113$	1.69916	+	19.4214i	0.159843	+	1.82701i	0.477298	+	0.878741i	$0.341616\pi$
$113$	1.69916	+	19.4214i	0.159843	+	1.82701i	−0.317455	+	0.948273i	$0.602828\pi$
$114$		0			0
$115$	10.9342	−	1.97556i	1.01962	−	0.184222i
$116$	11.6043	−	6.69973i	1.07743	−	0.622054i
$117$		0			0
$118$	4.97617	+	18.5713i	0.458093	+	1.70963i
$119$	−12.6202	+	10.5896i	−1.15689	+	0.970748i
$120$		0			0
$121$	0.0570802	−	0.323718i	0.00518911	−	0.0294289i
$122$	10.3107	+	14.7252i	0.933484	+	1.33315i
$123$		0			0
$124$	1.01645	+	1.21135i	0.0912796	+	0.108783i
$125$	−3.03004	−	10.7619i	−0.271015	−	0.962575i
$126$		0			0
$127$	−5.52679	+	20.6263i	−0.490423	+	1.83028i	0.0638628	+	0.997959i	$0.479658\pi$
$127$	−5.52679	+	20.6263i	−0.490423	+	1.83028i	−0.554286	+	0.832326i	$0.687009\pi$
$128$	−6.66265	−	14.2881i	−0.588901	−	1.26290i
$129$		0			0
$130$	−10.1852	−	14.4163i	−0.893304	−	1.26439i
$131$	5.67190	+	15.5834i	0.495556	+	1.36153i	0.895529	+	0.445003i	$0.146797\pi$
$131$	5.67190	+	15.5834i	0.495556	+	1.36153i	−0.399973	+	0.916527i	$0.630980\pi$
$132$		0			0
$133$	−7.45929	−	5.22305i	−0.646802	−	0.452896i
$134$	0.966985			0.0835348
$135$		0			0
$136$	−35.0721			−3.00741
$137$	16.4221	+	11.4989i	1.40304	+	0.982418i	0.997667	+	0.0682654i	$0.0217465\pi$
$137$	16.4221	+	11.4989i	1.40304	+	0.982418i	0.405371	+	0.914152i	$0.367142\pi$
$138$		0			0
$139$	6.07923	+	16.7026i	0.515634	+	1.41669i	0.875286	+	0.483606i	$0.160673\pi$
$139$	6.07923	+	16.7026i	0.515634	+	1.41669i	−0.359652	+	0.933087i	$0.617105\pi$
$140$	4.39776	−	25.5708i	0.371678	−	2.16113i
$141$		0			0
$142$	−10.3582	−	22.2132i	−0.869238	−	1.86409i
$143$	−2.66043	+	9.92886i	−0.222476	+	0.830293i
$144$		0			0
$145$	−4.95535	−	4.91374i	−0.411519	−	0.408064i
$146$	0.0415627	+	0.0495324i	0.00343975	+	0.00409933i
$147$		0			0
$148$	−10.9155	−	15.5890i	−0.897250	−	1.28141i
$149$	0.147586	−	0.837002i	0.0120907	−	0.0685699i	−0.978165	−	0.207828i	$-0.933361\pi$
$149$	0.147586	−	0.837002i	0.0120907	−	0.0685699i	0.990256	+	0.139258i	$0.0444717\pi$
$150$		0			0
$151$	11.3395	−	9.51495i	0.922794	−	0.774316i	−0.0517160	−	0.998662i	$-0.516469\pi$
$151$	11.3395	−	9.51495i	0.922794	−	0.774316i	0.974510	+	0.224346i	$0.0720246\pi$
$152$	−5.01740	−	18.7252i	−0.406965	−	1.51881i
$153$		0			0
$154$	−19.1808	+	11.0740i	−1.54563	+	0.892372i
$155$	0.469527	−	0.676607i	0.0377133	−	0.0543464i
$156$		0			0
$157$	0.891290	+	10.1875i	0.0711327	+	0.813051i	0.945039	+	0.326957i	$0.106023\pi$
$157$	0.891290	+	10.1875i	0.0711327	+	0.813051i	−0.873907	+	0.486094i	$0.838421\pi$
$158$	−25.2917	−	11.7937i	−2.01210	−	0.938257i
$159$		0			0
$160$	5.39483	−	4.56570i	0.426499	−	0.360950i
$161$		−	13.4295i		−	1.05839i
$162$		0			0
$163$	−9.20802	+	9.20802i	−0.721228	+	0.721228i	−0.968855	−	0.247628i	$-0.920349\pi$
$163$	−9.20802	+	9.20802i	−0.721228	+	0.721228i	0.247628	+	0.968855i	$0.420349\pi$
$164$	−5.71318	−	32.4011i	−0.446125	−	2.53010i
$165$		0			0
$166$	−2.57993	+	0.939019i	−0.200242	+	0.0728820i
$167$	−4.80307	+	0.420214i	−0.371672	+	0.0325171i	−0.271462	−	0.962449i	$-0.587507\pi$
$167$	−4.80307	+	0.420214i	−0.371672	+	0.0325171i	−0.100210	+	0.994966i	$0.531952\pi$
$168$		0			0
$169$	1.05980	−	2.91178i	0.0815232	−	0.223983i
$170$	8.98940	+	32.9919i	0.689455	+	2.53036i
$171$		0			0
$172$	18.4126	−	4.93365i	1.40395	−	0.376187i
$173$	−6.42280	−	0.561923i	−0.488317	−	0.0427222i	−0.159661	−	0.987172i	$-0.551040\pi$
$173$	−6.42280	−	0.561923i	−0.488317	−	0.0427222i	−0.328656	+	0.944450i	$0.606596\pi$
$174$		0			0
$175$	−13.4512	+	1.29120i	−1.01682	+	0.0976058i
$176$	−18.8095	−	3.31663i	−1.41782	−	0.250000i
$177$		0			0
$178$	1.71942	−	19.6531i	0.128876	−	1.47306i
$179$	−1.30891	+	2.26710i	−0.0978327	+	0.169451i	−0.910787	−	0.412876i	$-0.864524\pi$
$179$	−1.30891	+	2.26710i	−0.0978327	+	0.169451i	0.812955	+	0.582327i	$0.197858\pi$
$180$		0			0
$181$	8.91293	+	15.4376i	0.662493	+	1.14747i	0.979959	+	0.199202i	$0.0638348\pi$
$181$	8.91293	+	15.4376i	0.662493	+	1.14747i	−0.317466	+	0.948270i	$0.602832\pi$
$182$	−19.3353	+	9.01620i	−1.43323	+	0.668325i
$183$		0			0
$184$	18.3771	−	21.9010i	1.35478	−	1.61456i
$185$	−6.33881	+	7.61931i	−0.466039	+	0.560183i
$186$		0			0
$187$	11.4216	−	16.3118i	0.835233	−	1.19284i
$188$	20.8942	+	20.8942i	1.52387	+	1.52387i
$189$		0			0
$190$	−16.3285	+	9.51929i	−1.18460	+	0.690602i
$191$	8.64200	−	1.52382i	0.625313	−	0.110260i	0.147992	−	0.988989i	$-0.452719\pi$
$191$	8.64200	−	1.52382i	0.625313	−	0.110260i	0.477321	+	0.878729i	$0.341608\pi$
$192$		0			0
$193$	0.517574	−	1.10994i	0.0372558	−	0.0798952i	−0.886799	−	0.462155i	$-0.847076\pi$
$193$	0.517574	−	1.10994i	0.0372558	−	0.0798952i	0.924055	+	0.382260i	$0.124854\pi$
$194$	9.85290	+	8.26756i	0.707397	+	0.593576i
$195$		0			0
$196$	−1.22693	−	0.446566i	−0.0876379	−	0.0318976i
$197$	−13.5645	−	3.63461i	−0.966434	−	0.258955i	−0.259112	−	0.965847i	$-0.583430\pi$
$197$	−13.5645	−	3.63461i	−0.966434	−	0.258955i	−0.707321	+	0.706892i	$0.750097\pi$
$198$		0			0
$199$	−11.1726	−	6.45050i	−0.792004	−	0.457264i	0.0486637	−	0.998815i	$-0.484504\pi$
$199$	−11.1726	−	6.45050i	−0.792004	−	0.457264i	−0.840668	+	0.541552i	$0.817837\pi$
$200$	−23.7033	−	16.3011i	−1.67608	−	1.15266i
$201$		0			0
$202$	2.44365	−	1.71106i	0.171934	−	0.120390i
$203$	−6.90922	+	4.83789i	−0.484932	+	0.339553i
$204$		0			0
$205$	−15.4990	+	7.30702i	−1.08250	+	0.510344i
$206$	−0.408725	−	0.235978i	−0.0284772	−	0.0164413i
$207$		0			0
$208$	−17.7709	−	4.76170i	−1.23219	−	0.330164i
$209$	10.3429	+	3.76452i	0.715435	+	0.260397i
$210$		0			0
$211$	−0.0983096	−	0.0824916i	−0.00676791	−	0.00567895i	0.639397	−	0.768876i	$-0.279184\pi$
$211$	−0.0983096	−	0.0824916i	−0.00676791	−	0.00567895i	−0.646165	+	0.763197i	$0.723628\pi$
$212$	8.93021	−	19.1509i	0.613329	−	1.31529i
$213$		0			0
$214$	−6.17397	+	1.08864i	−0.422044	+	0.0744177i
$215$	−5.00008	−	8.57668i	−0.341002	−	0.584924i
$216$		0			0
$217$	−0.703849	−	0.703849i	−0.0477804	−	0.0477804i
$218$	−11.2343	+	16.0442i	−0.760881	+	1.08665i
$219$		0			0
$220$	2.86504	+	31.2306i	0.193161	+	2.10556i
$221$	12.3294	−	14.6937i	0.829368	−	0.988402i
$222$		0			0
$223$	−7.59226	+	3.54033i	−0.508415	+	0.237078i	−0.659861	−	0.751388i	$-0.729385\pi$
$223$	−7.59226	+	3.54033i	−0.508415	+	0.237078i	0.151446	+	0.988466i	$0.451607\pi$
$224$	−4.27106	−	7.39769i	−0.285372	−	0.494279i
$225$		0			0
$226$	24.4541	−	42.3557i	1.62666	−	2.81746i
$227$	−0.314610	+	3.59601i	−0.0208814	+	0.238675i	0.978580	+	0.205866i	$0.0660010\pi$
$227$	−0.314610	+	3.59601i	−0.0208814	+	0.238675i	−0.999462	+	0.0328096i	$0.989555\pi$
$228$		0			0
$229$	−1.22130	−	0.215349i	−0.0807059	−	0.0142306i	0.133149	−	0.991096i	$-0.457491\pi$
$229$	−1.22130	−	0.215349i	−0.0807059	−	0.0142306i	−0.213855	+	0.976865i	$0.568602\pi$
$230$	−25.3122	−	11.6736i	−1.66904	−	0.769736i
$231$		0			0
$232$	−17.8879	−	1.56498i	−1.17440	−	0.102746i
$233$	20.0624	−	5.37571i	1.31433	−	0.352175i	0.467481	−	0.884003i	$-0.345161\pi$
$233$	20.0624	−	5.37571i	1.31433	−	0.352175i	0.846852	+	0.531828i	$0.178495\pi$
$234$		0			0
$235$	7.63841	−	13.3599i	0.498275	−	0.871502i
$236$	11.2541	−	30.9205i	0.732582	−	2.01275i
$237$		0			0
$238$	41.1719	−	3.60207i	2.66878	−	0.233488i
$239$	11.3730	−	4.13943i	0.735658	−	0.267758i	0.0531004	−	0.998589i	$-0.483090\pi$
$239$	11.3730	−	4.13943i	0.735658	−	0.267758i	0.682558	+	0.730831i	$0.260867\pi$
$240$		0			0
$241$	−1.19187	−	6.75943i	−0.0767751	−	0.435413i	−0.998830	−	0.0483548i	$-0.984602\pi$
$241$	−1.19187	−	6.75943i	−0.0767751	−	0.435413i	0.922055	−	0.387059i	$-0.126509\pi$
$242$	−0.583102	+	0.583102i	−0.0374832	+	0.0374832i
$243$		0			0
$244$		−	30.7650i		−	1.96953i
$245$	−0.0564100	+	0.677662i	−0.00360390	+	0.0432943i
$246$		0			0
$247$	9.60887	+	4.48069i	0.611397	+	0.285099i
$248$	−0.184689	−	2.11100i	−0.0117277	−	0.134049i
$249$		0			0
$250$	−9.25882	+	26.4756i	−0.585579	+	1.67446i
$251$	−8.53784	+	4.92932i	−0.538904	+	0.311136i	−0.744634	−	0.667472i	$-0.767376\pi$
$251$	−8.53784	+	4.92932i	−0.538904	+	0.311136i	0.205731	+	0.978609i	$0.434043\pi$
$252$		0			0
$253$	4.20128	+	15.6794i	0.264132	+	0.985754i
$254$	41.0369	−	34.4341i	2.57489	−	2.16059i
$255$		0			0
$256$	−5.56035	+	31.5343i	−0.347522	+	1.97090i
$257$	−6.45152	−	9.21372i	−0.402435	−	0.574736i	0.565874	−	0.824491i	$-0.308539\pi$
$257$	−6.45152	−	9.21372i	−0.402435	−	0.574736i	−0.968309	+	0.249755i	$0.919650\pi$
$258$		0			0
$259$	7.70013	+	9.17666i	0.478463	+	0.570210i
$260$	0.127359	+	30.2089i	0.00789847	+	1.87347i
$261$		0			0
$262$	10.7676	−	40.1851i	0.665222	−	2.48264i
$263$	−3.48321	−	7.46977i	−0.214784	−	0.460606i	0.769166	−	0.639049i	$-0.220672\pi$
$263$	−3.48321	−	7.46977i	−0.214784	−	0.460606i	−0.983950	+	0.178443i	$0.942894\pi$
$264$		0			0
$265$	−10.8458	−	1.86530i	−0.666254	−	0.114584i
$266$	7.81320	+	21.4666i	0.479058	+	1.31620i
$267$		0			0
$268$	−1.35565	−	0.949234i	−0.0828093	−	0.0579837i
$269$	−21.3745			−1.30322			−0.651612	−	0.758553i	$-0.725907\pi$
$269$	−21.3745			−1.30322			−0.651612	+	0.758553i	$0.725907\pi$
$270$		0			0
$271$	−16.0063			−0.972313			−0.486157	−	0.873872i	$-0.661602\pi$
$271$	−16.0063			−0.972313			−0.486157	+	0.873872i	$0.661602\pi$
$272$	29.1952	+	20.4427i	1.77022	+	1.23952i
$273$		0			0
$274$	−17.2013	−	47.2602i	−1.03917	−	2.85509i
$275$	15.3008	−	5.71559i	0.922672	−	0.344663i
$276$		0			0
$277$	6.07443	+	13.0267i	0.364977	+	0.782696i	0.999948	+	0.0101600i	$0.00323409\pi$
$277$	6.07443	+	13.0267i	0.364977	+	0.782696i	−0.634971	+	0.772536i	$0.718988\pi$
$278$	11.5408	−	43.0710i	0.692174	−	2.58323i
$279$		0			0
$280$	−24.4821	+	24.6894i	−1.46308	+	1.47547i
$281$	6.85563	+	8.17022i	0.408973	+	0.487395i	0.930734	−	0.365697i	$-0.119169\pi$
$281$	6.85563	+	8.17022i	0.408973	+	0.487395i	−0.521761	+	0.853091i	$0.674725\pi$
$282$		0			0
$283$	14.1133	+	20.1559i	0.838951	+	1.19815i	0.978154	+	0.207882i	$0.0666570\pi$
$283$	14.1133	+	20.1559i	0.838951	+	1.19815i	−0.139203	+	0.990264i	$0.544454\pi$
$284$	−7.28395	+	41.3093i	−0.432223	+	2.45126i
$285$		0			0
$286$	19.7539	−	16.5755i	1.16808	−	0.980132i
$287$	5.36021	+	20.0046i	0.316403	+	1.18083i
$288$		0			0
$289$	−17.4577	+	10.0792i	−1.02692	+	0.592895i
$290$	3.11271	+	17.2280i	0.182784	+	1.01166i
$291$		0			0
$292$	−0.00964481	−	0.110241i	−0.000564420	−	0.00645135i
$293$	−21.7565	−	10.1452i	−1.27103	−	0.592691i	−0.334208	−	0.942499i	$-0.608469\pi$
$293$	−21.7565	−	10.1452i	−1.27103	−	0.592691i	−0.936821	+	0.349809i	$0.886247\pi$
$294$		0			0
$295$	−17.0781	−	1.42162i	−0.994326	−	0.0827697i
$296$			25.5023i			1.48229i
$297$		0			0
$298$	−1.50766	+	1.50766i	−0.0873366	+	0.0873366i
$299$	2.71515	+	15.3984i	0.157021	+	0.890512i
$300$		0			0
$301$	−11.2755	+	4.10394i	−0.649908	+	0.236547i
$302$	−36.9937	+	3.23653i	−2.12875	+	0.186241i
$303$		0			0
$304$	−6.73782	+	18.5120i	−0.386440	+	1.06174i
$305$	−15.4591	+	4.21219i	−0.885187	+	0.241190i
$306$		0			0
$307$	−3.92820	+	1.05256i	−0.224194	+	0.0600726i	−0.369167	−	0.929363i	$-0.620357\pi$
$307$	−3.92820	+	1.05256i	−0.224194	+	0.0600726i	0.144973	+	0.989436i	$0.453690\pi$
$308$	37.7609	+	3.30365i	2.15163	+	0.188243i
$309$		0			0
$310$	−1.93845	+	0.714808i	−0.110097	+	0.0405984i
$311$	9.98381	+	1.76041i	0.566130	+	0.0998239i	0.449385	−	0.893338i	$-0.351643\pi$
$311$	9.98381	+	1.76041i	0.566130	+	0.0998239i	0.116744	+	0.993162i	$0.462754\pi$
$312$		0			0
$313$	−2.56936	+	29.3680i	−0.145229	+	1.65998i	0.478316	+	0.878188i	$0.341247\pi$
$313$	−2.56936	+	29.3680i	−0.145229	+	1.65998i	−0.623545	+	0.781787i	$0.714308\pi$
$314$	12.8274	−	22.2177i	0.723890	−	1.25381i
$315$		0			0
$316$	23.8800	+	41.3614i	1.34335	+	2.32676i
$317$	−2.83348	+	1.32127i	−0.159144	+	0.0742101i	−0.500558	−	0.865703i	$-0.666872\pi$
$317$	−2.83348	+	1.32127i	−0.159144	+	0.0742101i	0.341414	+	0.939913i	$0.389094\pi$
$318$		0			0
$319$	6.55325	−	7.80986i	0.366912	−	0.437268i
$320$	8.38239	−	0.768988i	0.468590	−	0.0429877i
$321$		0			0
$322$	−19.3239	+	27.5975i	−1.07688	+	1.53795i
$323$	−14.5232	−	14.5232i	−0.808094	−	0.808094i
$324$		0			0
$325$	15.1622	−	4.20005i	0.841049	−	0.232977i
$326$	32.1719	−	5.67278i	1.78184	−	0.314186i
$327$		0			0
$328$	−18.6330	+	39.9586i	−1.02884	+	2.20635i
$329$	−14.2486	−	11.9560i	−0.785551	−	0.659155i
$330$		0			0
$331$	27.5786	+	10.0378i	1.51586	+	0.551727i	0.960109	−	0.279624i	$-0.0902099\pi$
$331$	27.5786	+	10.0378i	1.51586	+	0.551727i	0.555747	+	0.831351i	$0.312432\pi$
$332$	4.53867	+	1.21613i	0.249092	+	0.0667439i
$333$		0			0
$334$	10.4749	+	6.04768i	0.573160	+	0.330914i
$335$	−0.291372	+	0.811164i	−0.0159194	+	0.0443186i
$336$		0			0
$337$	13.1165	−	9.18427i	0.714501	−	0.500299i	−0.158904	−	0.987294i	$-0.550796\pi$
$337$	13.1165	−	9.18427i	0.714501	−	0.500299i	0.873405	+	0.486995i	$0.161907\pi$
$338$	−6.36769	+	4.45870i	−0.346356	+	0.242521i
$339$		0			0
$340$	19.7837	−	55.0767i	1.07292	−	2.98695i
$341$	1.04196	+	0.601574i	0.0564252	+	0.0325771i
$342$		0			0
$343$	−17.4798	−	4.68369i	−0.943819	−	0.252896i
$344$	−24.0041	−	8.73676i	−1.29421	−	0.471055i
$345$		0			0
$346$	12.3902	+	10.3966i	0.666102	+	0.558926i
$347$	−0.872755	+	1.87163i	−0.0468520	+	0.100474i	−0.928340	−	0.371731i	$-0.878764\pi$
$347$	−0.872755	+	1.87163i	−0.0468520	+	0.100474i	0.881488	+	0.472206i	$0.156542\pi$
$348$		0			0
$349$	0.561803	−	0.0990609i	0.0300726	−	0.00530261i	−0.158592	−	0.987344i	$-0.550695\pi$
$349$	0.561803	−	0.0990609i	0.0300726	−	0.00530261i	0.188664	+	0.982042i	$0.439584\pi$
$350$	29.5000	+	16.7018i	1.57684	+	0.892748i
$351$		0			0
$352$	7.30088	+	7.30088i	0.389138	+	0.389138i
$353$	−4.33346	+	6.18882i	−0.230647	+	0.329398i	−0.917747	−	0.397165i	$-0.869994\pi$
$353$	−4.33346	+	6.18882i	−0.230647	+	0.329398i	0.687101	+	0.726562i	$0.258883\pi$
$354$		0			0
$355$	21.7548	−	1.99575i	1.15463	−	0.105924i
$356$	−21.7028	+	25.8644i	−1.15024	+	1.37081i
$357$		0			0
$358$	5.95197	−	2.77545i	0.314571	−	0.146687i
$359$	−7.12655	−	12.3435i	−0.376125	−	0.651467i	0.614370	−	0.789018i	$-0.289410\pi$
$359$	−7.12655	−	12.3435i	−0.376125	−	0.651467i	−0.990495	+	0.137551i	$0.956077\pi$
$360$		0			0
$361$	−3.82366	+	6.62277i	−0.201245	+	0.348567i
$362$	3.89754	−	44.5491i	0.204850	−	2.34145i
$363$		0			0
$364$	35.9574	+	6.34026i	1.88468	+	0.332320i
$365$	−0.0540744	+	0.0199400i	−0.00283038	+	0.00104371i
$366$		0			0
$367$	−17.9778	−	1.57285i	−0.938434	−	0.0821024i	−0.392335	−	0.919823i	$-0.628332\pi$
$367$	−17.9778	−	1.57285i	−0.938434	−	0.0821024i	−0.546100	+	0.837720i	$0.683888\pi$
$368$	−28.0633	+	7.51954i	−1.46290	+	0.391983i
$369$		0			0
$370$	23.9897	−	6.53655i	1.24717	−	0.339819i
$371$	−4.54928	+	12.4990i	−0.236187	+	0.648918i
$372$		0			0
$373$	−5.43209	+	0.475246i	−0.281263	+	0.0246073i	−0.226914	−	0.973915i	$-0.572864\pi$
$373$	−5.43209	+	0.475246i	−0.281263	+	0.0246073i	−0.0543485	+	0.998522i	$0.517308\pi$
$374$	−46.9426	+	17.0857i	−2.42735	+	0.883481i
$375$		0			0
$376$	−6.87604	−	38.9959i	−0.354604	−	2.01106i
$377$	6.94405	−	6.94405i	0.357637	−	0.357637i
$378$		0			0
$379$		−	4.04015i		−	0.207529i	−0.994602	−	0.103764i	$-0.966911\pi$
$379$		−	4.04015i		−	0.207529i	0.994602	−	0.103764i	$-0.0330888\pi$
$380$	32.2360	+	2.68339i	1.65367	+	0.137655i
$381$		0			0
$382$	−19.9518	−	9.30369i	−1.02082	−	0.476018i
$383$	2.67534	+	30.5793i	0.136704	+	1.56253i	0.686436	+	0.727190i	$0.259174\pi$
$383$	2.67534	+	30.5793i	0.136704	+	1.56253i	−0.549732	+	0.835341i	$0.685270\pi$
$384$		0			0
$385$	−3.50998	−	19.4268i	−0.178885	−	0.990082i
$386$	−2.66072	+	1.53617i	−0.135427	+	0.0781888i
$387$		0			0
$388$	−5.69729	−	21.2626i	−0.289236	−	1.07944i
$389$	23.0823	−	19.3684i	1.17032	−	0.982014i	0.170325	−	0.985388i	$-0.445518\pi$
$389$	23.0823	−	19.3684i	1.17032	−	0.982014i	0.999994	+	0.00337359i	$0.00107385\pi$
$390$		0			0
$391$	5.25988	−	29.8302i	0.266003	−	1.50858i
$392$	1.00358	+	1.43326i	0.0506885	+	0.0723907i
$393$		0			0
$394$	22.6451	+	26.9873i	1.14084	+	1.35960i
$395$	17.5142	−	17.6625i	0.881233	−	0.888695i
$396$		0			0
$397$	7.37720	−	27.5321i	0.370251	−	1.38180i	−0.489910	−	0.871773i	$-0.662970\pi$
$397$	7.37720	−	27.5321i	0.370251	−	1.38180i	0.860161	−	0.510023i	$-0.170363\pi$
$398$	13.6778	+	29.3321i	0.685605	+	1.47029i
$399$		0			0
$400$	10.2299	+	27.3857i	0.511494	+	1.36928i
$401$	−9.65646	−	26.5309i	−0.482221	−	1.32489i	−0.907585	−	0.419868i	$-0.862076\pi$
$401$	−9.65646	−	26.5309i	−0.482221	−	1.32489i	0.425364	−	0.905022i	$-0.360146\pi$
$402$		0			0
$403$	0.949342	+	0.664736i	0.0472901	+	0.0331129i
$404$	−5.10547			−0.254007
$405$		0			0
$406$	21.1597			1.05014
$407$	−11.8610	−	8.30514i	−0.587926	−	0.411670i
$408$		0			0
$409$	6.83310	+	18.7738i	0.337875	+	0.928304i	0.985996	+	0.166767i	$0.0533328\pi$
$409$	6.83310	+	18.7738i	0.337875	+	0.928304i	−0.648121	+	0.761537i	$0.724445\pi$
$410$	42.3644	+	7.28597i	2.09223	+	0.359828i
$411$		0			0
$412$	0.341359	+	0.732046i	0.0168175	+	0.0360653i
$413$	−5.36086	+	20.0070i	−0.263790	+	0.984479i
$414$		0			0
$415$	−0.0103170	−	2.44714i	−0.000506443	−	0.120126i
$416$	6.39288	+	7.61873i	0.313437	+	0.373539i
$417$		0			0
$418$	−15.8377	−	22.6186i	−0.774649	−	1.10631i
$419$	−1.26780	+	7.19003i	−0.0619359	+	0.351256i	0.938053	+	0.346492i	$0.112627\pi$
$419$	−1.26780	+	7.19003i	−0.0619359	+	0.351256i	−0.999989	+	0.00476336i	$0.998484\pi$
$420$		0			0
$421$	−22.3147	+	18.7243i	−1.08755	+	0.912566i	−0.996526	−	0.0832827i	$-0.973460\pi$
$421$	−22.3147	+	18.7243i	−1.08755	+	0.912566i	−0.0910275	+	0.995848i	$0.529015\pi$
$422$	0.0833264	+	0.310978i	0.00405627	+	0.0151382i
$423$		0			0
$424$	−24.5229	+	14.1583i	−1.19094	+	0.687587i
$425$	−30.3842	−	2.40030i	−1.47385	−	0.116432i
$426$		0			0
$427$	1.68784	+	19.2921i	0.0816802	+	0.933609i
$428$	9.72412	+	4.53443i	0.470033	+	0.219180i
$429$		0			0
$430$	−2.06604	+	24.8196i	−0.0996331	+	1.19691i
$431$			14.3391i			0.690690i	0.938476	+	0.345345i	$0.112238\pi$
$431$			14.3391i			0.690690i	−0.938476	+	0.345345i	$0.887762\pi$
$432$		0			0
$433$	16.2907	−	16.2907i	0.782881	−	0.782881i	−0.197435	−	0.980316i	$-0.563261\pi$
$433$	16.2907	−	16.2907i	0.782881	−	0.782881i	0.980316	+	0.197435i	$0.0632612\pi$
$434$	0.433620	+	2.45918i	0.0208144	+	0.118044i
$435$		0			0
$436$	31.4993	−	11.4648i	1.50854	−	0.549065i
$437$	16.6790	−	1.45922i	0.797865	−	0.0698041i
$438$		0			0
$439$	6.36027	−	17.4747i	0.303559	−	0.834021i	−0.690316	−	0.723508i	$-0.742528\pi$
$439$	6.36027	−	17.4747i	0.303559	−	0.834021i	0.993875	−	0.110513i	$-0.0352494\pi$
$440$	20.8598	−	36.4846i	0.994451	−	1.73933i
$441$		0			0
$442$	−46.4798	+	12.4542i	−2.21082	+	0.592387i
$443$	−27.1205	−	2.37273i	−1.28853	−	0.112732i	−0.577790	−	0.816185i	$-0.696085\pi$
$443$	−27.1205	−	2.37273i	−1.28853	−	0.112732i	−0.710741	+	0.703453i	$0.751640\pi$
$444$		0			0
$445$	15.9680	+	7.36422i	0.756957	+	0.349097i
$446$	20.6962	+	3.64930i	0.979994	+	0.172799i
$447$		0			0
$448$	0.886712	−	10.1352i	0.0418932	−	0.478841i
$449$	−15.3860	+	26.6493i	−0.726109	+	1.25766i	0.232407	+	0.972619i	$0.425340\pi$
$449$	−15.3860	+	26.6493i	−0.726109	+	1.25766i	−0.958516	+	0.285039i	$0.907994\pi$
$450$		0			0
$451$	−12.5164	−	21.6791i	−0.589375	−	1.02083i
$452$	−75.8611	+	35.3746i	−3.56820	+	1.66388i
$453$		0			0
$454$	5.82087	−	6.93705i	0.273187	−	0.325572i
$455$	−1.73719	−	18.9363i	−0.0814407	−	0.887749i
$456$		0			0
$457$	13.4321	−	19.1830i	0.628327	−	0.897344i	−0.371185	−	0.928559i	$-0.621049\pi$
$457$	13.4321	−	19.1830i	0.628327	−	0.897344i	0.999513	+	0.0312144i	$0.00993748\pi$
$458$	2.19989	+	2.19989i	0.102794	+	0.102794i
$459$		0			0
$460$	24.0267	+	41.2132i	1.12025	+	1.92157i
$461$	−31.1056	+	5.48476i	−1.44873	+	0.255451i	−0.842010	−	0.539462i	$-0.818628\pi$
$461$	−31.1056	+	5.48476i	−1.44873	+	0.255451i	−0.606724	+	0.794913i	$0.707517\pi$
$462$		0			0
$463$	12.3947	−	26.5805i	0.576030	−	1.23530i	−0.375236	−	0.926929i	$-0.622438\pi$
$463$	12.3947	−	26.5805i	0.576030	−	1.23530i	0.951266	−	0.308371i	$-0.0997839\pi$
$464$	13.9783	+	11.7292i	0.648924	+	0.544512i
$465$		0			0
$466$	−48.9632	−	17.8212i	−2.26818	−	0.825549i
$467$	20.0112	+	5.36199i	0.926008	+	0.248123i	0.690152	−	0.723665i	$-0.257544\pi$
$467$	20.0112	+	5.36199i	0.926008	+	0.248123i	0.235857	+	0.971788i	$0.424210\pi$
$468$		0			0
$469$	0.902173	+	0.520870i	0.0416585	+	0.0240515i
$470$	−34.9206	+	16.4633i	−1.61077	+	0.759396i
$471$		0			0
$472$	−36.1204	+	25.2917i	−1.66257	+	1.16415i
$473$	11.8806	−	8.31889i	0.546271	−	0.382503i
$474$		0			0
$475$	−3.06521	−	16.5657i	−0.140642	−	0.760085i
$476$	−61.2561	−	35.3662i	−2.80767	−	1.62101i
$477$		0			0
$478$	−29.3277	−	7.85832i	−1.34142	−	0.359431i
$479$	−7.18880	−	2.61651i	−0.328465	−	0.119551i	0.172524	−	0.985005i	$-0.444808\pi$
$479$	−7.18880	−	2.61651i	−0.328465	−	0.119551i	−0.500988	+	0.865454i	$0.667030\pi$
$480$		0			0
$481$	−10.6843	−	8.96523i	−0.487164	−	0.408779i
$482$	−7.27698	+	15.6055i	−0.331458	+	0.710813i
$483$		0			0
$484$	1.38986	−	0.245071i	0.0631757	−	0.0111396i
$485$	−9.90419	+	5.77400i	−0.449726	+	0.262184i
$486$		0			0
$487$	8.90898	+	8.90898i	0.403704	+	0.403704i	0.879536	−	0.475832i	$-0.157853\pi$
$487$	8.90898	+	8.90898i	0.403704	+	0.403704i	−0.475832	+	0.879536i	$0.657853\pi$
$488$	−23.6470	+	33.7714i	−1.07045	+	1.52876i
$489$		0			0
$490$	1.09102	−	1.31142i	0.0492873	−	0.0592438i
$491$	−2.30460	+	2.74652i	−0.104005	+	0.123949i	−0.815536	−	0.578706i	$-0.803558\pi$
$491$	−2.30460	+	2.74652i	−0.104005	+	0.123949i	0.711531	+	0.702655i	$0.248002\pi$
$492$		0			0
$493$	−17.2419	+	8.04003i	−0.776536	+	0.362105i
$494$	−13.2987	−	23.0341i	−0.598339	−	1.03635i
$495$		0			0
$496$	−1.07671	+	1.86492i	−0.0483458	+	0.0837373i
$497$	2.30128	−	26.3038i	0.103227	−	1.17989i
$498$		0			0
$499$	−0.621729	−	0.109628i	−0.0278324	−	0.00490760i	0.159715	−	0.987163i	$-0.448943\pi$
$499$	−0.621729	−	0.109628i	−0.0278324	−	0.00490760i	−0.187547	+	0.982256i	$0.560054\pi$
$500$	38.9697	−	28.0280i	1.74278	−	1.25345i
$501$		0			0
$502$	24.6380	+	2.15555i	1.09965	+	0.0962068i
$503$	36.5596	−	9.79612i	1.63011	−	0.436788i	0.676163	−	0.736752i	$-0.263641\pi$
$503$	36.5596	−	9.79612i	1.63011	−	0.436788i	0.953950	+	0.299964i	$0.0969748\pi$
$504$		0			0
$505$	0.699016	+	2.56545i	0.0311058	+	0.114161i
$506$	13.9278	−	38.2662i	0.619164	−	1.70114i
$507$		0			0
$508$	−91.3329	+	7.99059i	−4.05224	+	0.354525i
$509$	27.9791	−	10.1836i	1.24015	−	0.451378i	0.363089	−	0.931754i	$-0.381722\pi$
$509$	27.9791	−	10.1836i	1.24015	−	0.451378i	0.877063	+	0.480376i	$0.159500\pi$
$510$		0			0
$511$	0.0120961	+	0.0686004i	0.000535100	+	0.00303470i
$512$	34.5064	−	34.5064i	1.52498	−	1.52498i
$513$		0			0
$514$			28.2173i			1.24461i
$515$	0.321109	−	0.271757i	0.0141497	−	0.0119751i
$516$		0			0
$517$	20.3760	+	9.50148i	0.896135	+	0.417875i
$518$	−2.61921	−	29.9377i	−0.115082	−	1.31539i
$519$		0			0
$520$	23.0797	−	33.2588i	1.01211	−	1.45849i
$521$	−27.1230	+	15.6595i	−1.18828	+	0.686054i	−0.957915	−	0.287050i	$-0.907325\pi$
$521$	−27.1230	+	15.6595i	−1.18828	+	0.686054i	−0.230365	+	0.973104i	$0.573992\pi$
$522$		0			0
$523$	8.52925	+	31.8316i	0.372958	+	1.39190i	0.856305	+	0.516470i	$0.172754\pi$
$523$	8.52925	+	31.8316i	0.372958	+	1.39190i	−0.483347	+	0.875429i	$0.660579\pi$
$524$	−54.5428	+	45.7668i	−2.38271	+	1.99933i
$525$		0			0
$526$	−3.59043	+	20.3623i	−0.156550	+	0.887840i
$527$	−1.28775	−	1.83910i	−0.0560952	−	0.0801122i
$528$		0			0
$529$	1.08748	+	1.29601i	0.0472817	+	0.0563482i
$530$	19.6040	+	19.4394i	0.851543	+	0.844394i
$531$		0			0
$532$	10.1189	−	37.7644i	0.438712	−	1.63730i
$533$	−10.1905	−	21.8537i	−0.441401	−	0.946588i
$534$		0			0
$535$	0.947130	−	5.50711i	0.0409480	−	0.238093i
$536$	0.758509	+	2.08399i	0.0327626	+	0.0900144i
$537$		0			0
$538$	43.9242	+	30.7561i	1.89371	+	1.32599i
$539$	−0.993428			−0.0427900
$540$		0			0
$541$	−19.8436			−0.853142			−0.426571	−	0.904454i	$-0.640279\pi$
$541$	−19.8436			−0.853142			−0.426571	+	0.904454i	$0.640279\pi$
$542$	32.8927	+	23.0317i	1.41286	+	0.989297i
$543$		0			0
$544$	−6.58965	−	18.1049i	−0.282529	−	0.776241i
$545$	−10.0737	−	14.2584i	−0.431510	−	0.610763i
$546$		0			0
$547$	7.36373	+	15.7916i	0.314851	+	0.675199i	0.998508	−	0.0546038i	$-0.0173896\pi$
$547$	7.36373	+	15.7916i	0.314851	+	0.675199i	−0.683658	+	0.729803i	$0.739612\pi$
$548$	−22.2776	+	83.1410i	−0.951650	+	3.55161i
$549$		0			0
$550$	−39.6672	−	10.2711i	−1.69141	−	0.437961i
$551$	−6.75924	−	8.05534i	−0.287953	−	0.343169i
$552$		0			0
$553$	−17.2438	−	24.6267i	−0.733281	−	1.04723i
$554$	6.26140	−	35.5102i	0.266022	−	1.50868i
$555$		0			0
$556$	−58.4598	+	49.0536i	−2.47925	+	2.08034i
$557$	2.61924	+	9.77513i	0.110981	+	0.414185i	0.998955	−	0.0457078i	$-0.0145543\pi$
$557$	2.61924	+	9.77513i	0.110981	+	0.414185i	−0.887974	+	0.459893i	$0.847888\pi$
$558$		0			0
$559$	12.0988	−	6.98526i	0.511726	−	0.295445i
$560$	34.7705	−	6.28225i	1.46932	−	0.265473i
$561$		0			0
$562$	−2.33196	−	26.6544i	−0.0983676	−	1.12435i
$563$	33.8599	+	15.7891i	1.42702	+	0.665432i	0.974100	−	0.226118i	$-0.0726034\pi$
$563$	33.8599	+	15.7891i	1.42702	+	0.665432i	0.452923	+	0.891550i	$0.350381\pi$
$564$		0			0
$565$	28.1619	+	33.2761i	1.18478	+	1.39994i
$566$		−	61.7281i		−	2.59462i
$567$		0			0
$568$	39.7474	−	39.7474i	1.66776	−	1.66776i
$569$	−0.949414	−	5.38439i	−0.0398015	−	0.225725i	0.958418	−	0.285367i	$-0.0921154\pi$
$569$	−0.949414	−	5.38439i	−0.0398015	−	0.225725i	−0.998220	+	0.0596413i	$0.981004\pi$
$570$		0			0
$571$	−27.1899	+	9.89631i	−1.13786	+	0.414148i	−0.841141	−	0.540817i	$-0.818115\pi$
$571$	−27.1899	+	9.89631i	−1.13786	+	0.414148i	−0.296721	+	0.954964i	$0.595893\pi$
$572$	−43.9649	+	3.84643i	−1.83826	+	0.160827i
$573$		0			0
$574$	17.7698	−	48.8220i	0.741695	−	2.03779i
$575$	17.4196	−	17.7159i	0.726448	−	0.738803i
$576$		0			0
$577$	−13.3085	+	3.56601i	−0.554041	+	0.148455i	−0.524967	−	0.851122i	$-0.675922\pi$
$577$	−13.3085	+	3.56601i	−0.554041	+	0.148455i	−0.0290738	+	0.999577i	$0.509256\pi$
$578$	50.3785	+	4.40755i	2.09547	+	0.183330i
$579$		0			0
$580$	12.5479	−	27.2080i	0.521024	−	1.12975i
$581$	−2.91282	−	0.513608i	−0.120844	−	0.0213081i
$582$		0			0
$583$	1.40124	−	16.0162i	0.0580333	−	0.663324i
$584$	−0.0741472	+	0.128427i	−0.00306823	+	0.00531433i
$585$		0			0
$586$	30.1112	+	52.1541i	1.24388	+	2.15447i
$587$	19.2878	−	8.99405i	0.796093	−	0.371224i	0.0183698	−	0.999831i	$-0.494152\pi$
$587$	19.2878	−	8.99405i	0.796093	−	0.371224i	0.777723	+	0.628607i	$0.216375\pi$
$588$		0			0
$589$	0.797678	−	0.950636i	0.0328678	−	0.0391703i
$590$	33.0497	+	27.4954i	1.36063	+	1.13197i
$591$		0			0
$592$	14.8647	−	21.2290i	0.610936	−	0.872507i
$593$	9.84862	+	9.84862i	0.404434	+	0.404434i	0.879792	−	0.475358i	$-0.157681\pi$
$593$	9.84862	+	9.84862i	0.404434	+	0.404434i	−0.475358	+	0.879792i	$0.657681\pi$
$594$		0			0
$595$	−9.38431	+	35.6228i	−0.384719	+	1.46039i
$596$	3.59362	−	0.633653i	0.147201	−	0.0259554i
$597$		0			0
$598$	16.5774	−	35.5503i	0.677900	−	1.45376i
$599$	−7.79546	−	6.54117i	−0.318514	−	0.267265i	0.469486	−	0.882940i	$-0.344439\pi$
$599$	−7.79546	−	6.54117i	−0.318514	−	0.267265i	−0.788000	+	0.615675i	$0.788884\pi$
$600$		0			0
$601$	29.1191	+	10.5985i	1.18779	+	0.432321i	0.858948	−	0.512063i	$-0.171119\pi$
$601$	29.1191	+	10.5985i	1.18779	+	0.432321i	0.328845	+	0.944384i	$0.393341\pi$
$602$	29.0762	+	7.79094i	1.18506	+	0.317535i
$603$		0			0
$604$	55.0397	+	31.7772i	2.23953	+	1.29299i
$605$	−0.313439	−	0.664840i	−0.0127431	−	0.0270296i
$606$		0			0
$607$	−24.8874	+	17.4264i	−1.01015	+	0.707315i	−0.956646	−	0.291253i	$-0.905928\pi$
$607$	−24.8874	+	17.4264i	−1.01015	+	0.707315i	−0.0535038	+	0.998568i	$0.517039\pi$
$608$	8.72359	−	6.10833i	0.353788	−	0.247725i
$609$		0			0
$610$	37.8293	+	13.5884i	1.53166	+	0.550178i
$611$	18.7548	+	10.8281i	0.758738	+	0.438058i
$612$		0			0
$613$	3.57095	+	0.956834i	0.144229	+	0.0386462i	0.330211	−	0.943907i	$-0.392880\pi$
$613$	3.57095	+	0.956834i	0.144229	+	0.0386462i	−0.185982	+	0.982553i	$0.559547\pi$
$614$	9.58694	+	3.48936i	0.386897	+	0.140819i
$615$		0			0
$616$	−38.9116	−	32.6507i	−1.56779	−	1.31553i
$617$	−6.83850	+	14.6652i	−0.275308	+	0.590399i	−0.994538	−	0.104372i	$-0.966717\pi$
$617$	−6.83850	+	14.6652i	−0.275308	+	0.590399i	0.719231	+	0.694771i	$0.244494\pi$
$618$		0			0
$619$	−20.5670	+	3.62651i	−0.826656	+	0.145762i	−0.570942	−	0.820991i	$-0.693422\pi$
$619$	−20.5670	+	3.62651i	−0.826656	+	0.145762i	−0.255714	+	0.966752i	$0.582311\pi$
$620$	3.41926	+	0.900756i	0.137321	+	0.0361752i
$621$		0			0
$622$	−17.9835	−	17.9835i	−0.721072	−	0.721072i
$623$	12.1904	−	17.4096i	0.488396	−	0.697502i
$624$		0			0
$625$	−19.4194	−	15.7445i	−0.776775	−	0.629778i
$626$	47.5380	−	56.6536i	1.90000	−	2.26433i
$627$		0			0
$628$	−39.7929	+	18.5557i	−1.58791	+	0.740454i
$629$	13.5097	+	23.3995i	0.538667	+	0.932999i
$630$		0			0
$631$	7.86152	−	13.6165i	0.312962	−	0.542066i	−0.666040	−	0.745916i	$-0.732012\pi$
$631$	7.86152	−	13.6165i	0.312962	−	0.542066i	0.979002	+	0.203850i	$0.0653454\pi$
$632$	5.57811	−	63.7581i	0.221885	−	2.53616i
$633$		0			0
$634$	7.72396	+	1.36194i	0.306758	+	0.0540897i
$635$	16.5200	+	44.7999i	0.655578	+	1.77783i
$636$		0			0
$637$	−0.953277	−	0.0834010i	−0.0377702	−	0.00330447i
$638$	−24.7046	+	6.61957i	−0.978063	+	0.262071i
$639$		0			0
$640$	−30.6032	−	17.4971i	−1.20970	−	0.691635i
$641$	−13.8355	+	38.0128i	−0.546471	+	1.50142i	0.291971	+	0.956427i	$0.405689\pi$
$641$	−13.8355	+	38.0128i	−0.546471	+	1.50142i	−0.838443	+	0.544990i	$0.816533\pi$
$642$		0			0
$643$	25.8204	−	2.25900i	1.01826	−	0.0890861i	0.434216	−	0.900809i	$-0.357026\pi$
$643$	25.8204	−	2.25900i	1.01826	−	0.0890861i	0.584043	+	0.811723i	$0.301470\pi$
$644$	54.1816	−	19.7205i	2.13506	−	0.777097i
$645$		0			0
$646$	8.94731	+	50.7427i	0.352027	+	1.99645i
$647$	−23.1817	+	23.1817i	−0.911366	+	0.911366i	−0.996380	−	0.0850141i	$-0.972906\pi$
$647$	−23.1817	+	23.1817i	−0.911366	+	0.911366i	0.0850141	+	0.996380i	$0.472906\pi$
$648$		0			0
$649$		−	25.0359i		−	0.982744i
$650$	−37.2017	−	13.1862i	−1.45917	−	0.517203i
$651$		0			0
$652$	−50.6714	−	23.6285i	−1.98445	−	0.925362i
$653$	−2.87574	−	32.8699i	−0.112537	−	1.28630i	−0.817033	−	0.576591i	$-0.804383\pi$
$653$	−2.87574	−	32.8699i	−0.112537	−	1.28630i	0.704496	−	0.709708i	$-0.251173\pi$
$654$		0			0
$655$	30.4651	+	21.1411i	1.19037	+	0.826049i
$656$	38.8017	−	22.4022i	1.51495	−	0.874658i
$657$		0			0
$658$	12.0770	+	45.0720i	0.470810	+	1.75709i
$659$	−12.5302	+	10.5141i	−0.488108	+	0.409571i	−0.853348	−	0.521342i	$-0.825432\pi$
$659$	−12.5302	+	10.5141i	−0.488108	+	0.409571i	0.365240	+	0.930914i	$0.380987\pi$
$660$		0			0
$661$	4.84704	−	27.4889i	0.188528	−	1.06920i	−0.732810	−	0.680433i	$-0.761792\pi$
$661$	4.84704	−	27.4889i	0.188528	−	1.06920i	0.921338	−	0.388762i	$-0.127097\pi$
$662$	−42.2301	−	60.3108i	−1.64132	−	2.34405i
$663$		0			0
$664$	−4.04743	−	4.82353i	−0.157071	−	0.187189i
$665$	−20.3617	+	0.0858439i	−0.789593	+	0.00332888i
$666$		0			0
$667$	4.01378	−	14.9796i	0.155414	−	0.580014i
$668$	−8.74840	−	18.7610i	−0.338486	−	0.725885i
$669$		0			0
$670$	1.76596	−	1.24767i	0.0682251	−	0.0482017i
$671$	−8.00592	−	21.9961i	−0.309065	−	0.849149i
$672$		0			0
$673$	−29.0771	−	20.3600i	−1.12084	−	0.784821i	−0.142085	−	0.989854i	$-0.545381\pi$
$673$	−29.0771	−	20.3600i	−1.12084	−	0.784821i	−0.978755	+	0.205034i	$0.934270\pi$
$674$	−40.1696			−1.54728
$675$		0			0
$676$	13.3039			0.511688
$677$	1.67557	+	1.17325i	0.0643975	+	0.0450916i	0.605332	−	0.795973i	$-0.293040\pi$
$677$	1.67557	+	1.17325i	0.0643975	+	0.0450916i	−0.540934	+	0.841065i	$0.681929\pi$
$678$		0			0
$679$	4.73916	+	13.0207i	0.181872	+	0.499689i
$680$	−64.0507	+	45.2524i	−2.45623	+	1.73535i
$681$		0			0
$682$	−1.27559	−	2.73552i	−0.0488450	−	0.104748i
$683$	−2.32207	+	8.66609i	−0.0888516	+	0.331599i	−0.996016	−	0.0891783i	$-0.971576\pi$
$683$	−2.32207	+	8.66609i	−0.0888516	+	0.331599i	0.907164	+	0.420777i	$0.138243\pi$
$684$		0			0
$685$	44.8277	−	0.188991i	1.71278	−	0.00722098i
$686$	29.1812	+	34.7769i	1.11415	+	1.32779i
$687$		0			0
$688$	14.8893	+	21.2642i	0.567650	+	0.810689i
$689$	2.68921	−	15.2513i	0.102451	−	0.581027i
$690$		0			0
$691$	−22.2034	+	18.6309i	−0.844657	+	0.708752i	−0.958606	−	0.284735i	$-0.908094\pi$
$691$	−22.2034	+	18.6309i	−0.844657	+	0.708752i	0.113949	+	0.993487i	$0.463650\pi$
$692$	−7.16445	−	26.7381i	−0.272352	−	1.01643i
$693$		0			0
$694$	4.48662	−	2.59035i	0.170310	−	0.0983284i
$695$	32.6530	+	22.6593i	1.23860	+	0.859517i
$696$		0			0
$697$	4.07124	+	46.5345i	0.154209	+	1.76262i
$698$	−1.29704	−	0.604818i	−0.0490936	−	0.0228927i
$699$		0			0
$700$	−24.9618	−	52.3732i	−0.943467	−	1.97952i
$701$			4.40189i			0.166257i	0.996539	+	0.0831285i	$0.0264912\pi$
$701$			4.40189i			0.166257i	−0.996539	+	0.0831285i	$0.973509\pi$
$702$		0			0
$703$	−10.5604	+	10.5604i	−0.398294	+	0.398294i
$704$	2.13541	+	12.1105i	0.0804813	+	0.456432i
$705$		0			0
$706$	17.8104	−	6.48245i	0.670303	−	0.243970i
$707$	3.20153	−	0.280098i	0.120406	−	0.0105342i
$708$		0			0
$709$	−8.05475	+	22.1303i	−0.302503	+	0.831119i	0.691561	+	0.722318i	$0.256923\pi$
$709$	−8.05475	+	22.1303i	−0.302503	+	0.831119i	−0.994064	+	0.108801i	$0.965299\pi$
$710$	−47.5776	−	27.2021i	−1.78555	−	1.02088i
$711$		0			0
$712$	43.7037	−	11.7104i	1.63787	−	0.438865i
$713$	1.82319	+	0.159508i	0.0682790	+	0.00597364i
$714$		0			0
$715$	7.95225	+	21.5653i	0.297397	+	0.806497i
$716$	−11.0687	−	1.95172i	−0.413658	−	0.0729391i
$717$		0			0
$718$	−3.11637	+	35.6203i	−0.116302	+	1.32934i
$719$	3.55440	−	6.15640i	0.132557	−	0.229595i	−0.792105	−	0.610385i	$-0.791015\pi$
$719$	3.55440	−	6.15640i	0.132557	−	0.229595i	0.924661	+	0.380790i	$0.124348\pi$
$720$		0			0
$721$	−0.254220	−	0.440322i	−0.00946765	−	0.0163985i
$722$	17.3872	−	8.10778i	0.647084	−	0.301740i
$723$		0			0
$724$	−49.1954	+	58.6288i	−1.82833	+	2.17892i
$725$	−15.3898	−	2.58003i	−0.571562	−	0.0958198i
$726$		0			0
$727$	11.1796	−	15.9661i	0.414627	−	0.592148i	−0.556460	−	0.830874i	$-0.687841\pi$
$727$	11.1796	−	15.9661i	0.414627	−	0.592148i	0.971087	+	0.238726i	$0.0767298\pi$
$728$	−34.5978	−	34.5978i	−1.28228	−	1.28228i
$729$		0			0
$730$	0.139814	+	0.0368320i	0.00517475	+	0.00136321i
$731$	−26.6530	+	4.69964i	−0.985796	+	0.173822i
$732$		0			0
$733$	15.4914	−	33.2213i	0.572186	−	1.22706i	−0.380972	−	0.924587i	$-0.624411\pi$
$733$	15.4914	−	33.2213i	0.572186	−	1.22706i	0.953159	−	0.302471i	$-0.0978116\pi$
$734$	34.6809	+	29.1008i	1.28010	+	1.07413i
$735$		0			0
$736$	14.7586	+	5.37168i	0.544008	+	0.198003i
$737$	−1.21626	−	0.325897i	−0.0448017	−	0.0120046i
$738$		0			0
$739$	−39.9362	−	23.0572i	−1.46908	−	0.848172i	−0.469678	−	0.882838i	$-0.655630\pi$
$739$	−39.9362	−	23.0572i	−1.46908	−	0.848172i	−0.999399	+	0.0346657i	$0.988963\pi$
$740$	−40.0485	−	14.3855i	−1.47221	−	0.528823i
$741$		0			0
$742$	27.3338	−	19.1393i	1.00345	−	0.702626i
$743$	−5.71577	+	4.00223i	−0.209691	+	0.146828i	−0.673705	−	0.739001i	$-0.735298\pi$
$743$	−5.71577	+	4.00223i	−0.209691	+	0.146828i	0.464013	+	0.885828i	$0.346409\pi$
$744$		0			0
$745$	−0.810426	−	1.71901i	−0.0296917	−	0.0629795i
$746$	11.8467	+	6.83970i	0.433739	+	0.250419i
$747$		0			0
$748$	82.5823	+	22.1279i	3.01951	+	0.809075i
$749$	−6.34655	−	2.30996i	−0.231898	−	0.0844040i
$750$		0			0
$751$	14.9900	+	12.5781i	0.546995	+	0.458983i	0.873922	−	0.486067i	$-0.161569\pi$
$751$	14.9900	+	12.5781i	0.546995	+	0.458983i	−0.326927	+	0.945050i	$0.606013\pi$
$752$	−17.0060	+	36.4694i	−0.620144	+	1.32990i
$753$		0			0
$754$	−24.2618	+	4.27802i	−0.883564	+	0.155796i
$755$	8.43197	−	32.0077i	0.306871	−	1.16488i
$756$		0			0
$757$	−13.8377	−	13.8377i	−0.502940	−	0.502940i	0.409411	−	0.912350i	$-0.365734\pi$
$757$	−13.8377	−	13.8377i	−0.502940	−	0.502940i	−0.912350	+	0.409411i	$0.865734\pi$
$758$	−5.81344	+	8.30245i	−0.211154	+	0.301559i
$759$		0			0
$760$	−33.3235	−	27.7232i	−1.20877	−	1.00563i
$761$	4.04597	−	4.82180i	0.146666	−	0.174790i	−0.687710	−	0.725986i	$-0.741384\pi$
$761$	4.04597	−	4.82180i	0.146666	−	0.174790i	0.834376	+	0.551196i	$0.185828\pi$
$762$		0			0
$763$	−19.1236	+	8.91746i	−0.692319	+	0.322834i
$764$	18.8382	+	32.6287i	0.681542	+	1.18046i
$765$		0			0
$766$	38.5033	−	66.6897i	1.39118	−	2.40960i
$767$	2.10183	−	24.0240i	0.0758927	−	0.867457i
$768$		0			0
$769$	−43.7099	−	7.70724i	−1.57622	−	0.277930i	−0.683983	−	0.729498i	$-0.739754\pi$
$769$	−43.7099	−	7.70724i	−1.57622	−	0.277930i	−0.892237	+	0.451567i	$0.850865\pi$
$770$	−20.7406	+	44.9724i	−0.747439	+	1.62069i
$771$		0			0
$772$	5.23811	+	0.458275i	0.188524	+	0.0164937i
$773$	−17.1792	+	4.60315i	−0.617893	+	0.165564i	−0.554170	−	0.832404i	$-0.686964\pi$
$773$	−17.1792	+	4.60315i	−0.617893	+	0.165564i	−0.0637231	+	0.997968i	$0.520297\pi$
$774$		0			0
$775$	−0.0155274	−	1.84147i	−0.000557760	−	0.0661477i
$776$	−10.0891	+	27.7195i	−0.362176	+	0.995071i
$777$		0			0
$778$	−75.3032	+	6.58818i	−2.69975	+	0.236198i
$779$	−24.2626	+	8.83085i	−0.869297	+	0.316398i
$780$		0			0
$781$	5.54203	+	31.4304i	0.198310	+	1.12467i
$782$	−53.7322	+	53.7322i	−1.92146	+	1.92146i
$783$		0			0
$784$		−	1.77806i		−	0.0635021i
$785$	14.7723	+	17.4550i	0.527246	+	0.622995i
$786$		0			0
$787$	−27.1112	−	12.6422i	−0.966410	−	0.450644i	−0.125663	−	0.992073i	$-0.540106\pi$
$787$	−27.1112	−	12.6422i	−0.966410	−	0.450644i	−0.840747	+	0.541429i	$0.817884\pi$
$788$	−5.25489	−	60.0637i	−0.187198	−	2.13968i
$789$		0			0
$790$	−61.4062	+	11.0947i	−2.18473	+	0.394731i
$791$	45.6301	−	26.3445i	1.62242	−	0.936704i
$792$		0			0
$793$	−5.83572	−	21.7792i	−0.207232	−	0.773402i
$794$	−54.7764	+	45.9629i	−1.94394	+	1.63116i
$795$		0			0
$796$	9.61833	−	54.5483i	0.340913	−	1.93341i
$797$	14.2699	+	20.3795i	0.505466	+	0.721880i	0.988078	−	0.153954i	$-0.0492008\pi$
$797$	14.2699	+	20.3795i	0.505466	+	0.721880i	−0.482612	+	0.875834i	$0.660312\pi$
$798$		0			0
$799$	−26.9669	−	32.1379i	−0.954020	−	1.13696i
$800$	3.96138	−	15.2989i	0.140056	−	0.540898i
$801$		0			0
$802$	−18.3319	+	68.4155i	−0.647321	+	2.41584i
$803$	−0.0355835	−	0.0763090i	−0.00125571	−	0.00269289i
$804$		0			0
$805$	−17.3276	−	24.5257i	−0.610719	−	0.864418i
$806$	−0.994384	−	2.73205i	−0.0350257	−	0.0962323i
$807$		0			0
$808$	5.60438	+	3.92423i	0.197161	+	0.138054i
$809$	27.7036			0.974006			0.487003	−	0.873400i	$-0.338090\pi$
$809$	27.7036			0.974006			0.487003	+	0.873400i	$0.338090\pi$
$810$		0			0
$811$	−16.0245			−0.562695			−0.281347	−	0.959606i	$-0.590781\pi$
$811$	−16.0245			−0.562695			−0.281347	+	0.959606i	$0.590781\pi$
$812$	−29.6644	−	20.7712i	−1.04102	−	0.728927i
$813$		0			0
$814$	12.4237	+	34.1339i	0.435451	+	1.19639i
$815$	−4.93540	+	28.6970i	−0.172880	+	1.00521i
$816$		0			0
$817$	−6.32213	−	13.5578i	−0.221183	−	0.474329i
$818$	12.9720	−	48.4121i	0.453555	−	1.69269i
$819$		0			0
$820$	−52.2398	−	51.8011i	−1.82429	−	1.80897i
$821$	36.5832	+	43.5982i	1.27676	+	1.52159i	0.727920	+	0.685663i	$0.240487\pi$
$821$	36.5832	+	43.5982i	1.27676	+	1.52159i	0.548844	+	0.835925i	$0.315068\pi$
$822$		0			0
$823$	30.0764	+	42.9536i	1.04840	+	1.49727i	0.856700	+	0.515815i	$0.172511\pi$
$823$	30.0764	+	42.9536i	1.04840	+	1.49727i	0.191699	+	0.981454i	$0.438600\pi$
$824$	0.187958	−	1.06596i	0.00654781	−	0.0371345i
$825$		0			0
$826$	39.8049	−	33.4002i	1.38499	−	1.16214i
$827$	5.56271	+	20.7603i	0.193434	+	0.721907i	0.992667	+	0.120885i	$0.0385731\pi$
$827$	5.56271	+	20.7603i	0.193434	+	0.721907i	−0.799232	+	0.601023i	$0.794760\pi$
$828$		0			0
$829$	−27.5695	+	15.9172i	−0.957527	+	0.552828i	−0.895411	−	0.445241i	$-0.853118\pi$
$829$	−27.5695	+	15.9172i	−0.957527	+	0.552828i	−0.0621158	+	0.998069i	$0.519785\pi$
$830$	−3.50003	+	5.04369i	−0.121488	+	0.175069i
$831$		0			0
$832$	1.03240	+	11.8003i	0.0357919	+	0.409103i
$833$	1.68009	+	0.783438i	0.0582116	+	0.0271445i
$834$		0			0
$835$	−8.22944	+	6.96465i	−0.284792	+	0.241022i
$836$			47.2568i			1.63441i
$837$		0			0
$838$	12.9511	−	12.9511i	0.447390	−	0.447390i
$839$	−5.41257	−	30.6962i	−0.186863	−	1.05975i	−0.923539	−	0.383505i	$-0.874717\pi$
$839$	−5.41257	−	30.6962i	−0.186863	−	1.05975i	0.736676	−	0.676246i	$-0.236394\pi$
$840$		0			0
$841$	18.0984	−	6.58729i	0.624084	−	0.227148i
$842$	72.7991	−	6.36910i	2.50882	−	0.219494i
$843$		0			0
$844$	0.188452	−	0.517767i	0.00648677	−	0.0178223i
$845$	−1.82150	−	6.68508i	−0.0626617	−	0.229974i
$846$		0			0
$847$	−0.858109	+	0.229930i	−0.0294850	+	0.00790047i
$848$	28.6662	+	2.50796i	0.984400	+	0.0861239i
$849$		0			0
$850$	58.9853	+	48.6529i	2.02318	+	1.66878i
$851$	−21.6908	−	3.82467i	−0.743550	−	0.131108i
$852$		0			0
$853$	3.05541	−	34.9235i	0.104615	−	1.19576i	−0.744526	−	0.667593i	$-0.767325\pi$
$853$	3.05541	−	34.9235i	0.104615	−	1.19576i	0.849142	−	0.528165i	$-0.177120\pi$
$854$	24.2912	−	42.0736i	0.831228	−	1.43973i
$855$		0			0
$856$	−7.18905	−	12.4518i	−0.245717	−	0.425594i
$857$	50.5751	−	23.5835i	1.72761	−	0.805599i	0.735904	−	0.677086i	$-0.236758\pi$
$857$	50.5751	−	23.5835i	1.72761	−	0.805599i	0.991708	−	0.128512i	$-0.0410202\pi$
$858$		0			0
$859$	18.4923	−	22.0383i	0.630949	−	0.751936i	−0.351962	−	0.936014i	$-0.614486\pi$
$859$	18.4923	−	22.0383i	0.630949	−	0.751936i	0.982912	+	0.184078i	$0.0589300\pi$
$860$	27.2604	−	32.7673i	0.929573	−	1.11736i
$861$		0			0
$862$	20.6328	−	29.4666i	0.702754	−	1.00364i
$863$	20.3595	+	20.3595i	0.693044	+	0.693044i	0.962901	−	0.269856i	$-0.0869762\pi$
$863$	20.3595	+	20.3595i	0.693044	+	0.693044i	−0.269856	+	0.962901i	$0.586976\pi$
$864$		0			0
$865$	−12.4547	+	7.26092i	−0.423473	+	0.246879i
$866$	−56.9181	+	10.0362i	−1.93416	+	0.341044i
$867$		0			0
$868$	1.80613	−	3.87326i	0.0613040	−	0.131467i
$869$	27.8369	+	23.3579i	0.944301	+	0.792363i
$870$		0			0
$871$	−1.13975	−	0.414834i	−0.0386189	−	0.0140561i
$872$	−43.3897	−	11.6262i	−1.46936	−	0.393714i
$873$		0			0
$874$	−36.3748	−	21.0010i	−1.23040	−	0.710370i
$875$	−22.8994	+	19.7137i	−0.774141	+	0.666446i
$876$		0			0
$877$	34.6324	−	24.2499i	1.16945	−	0.818860i	0.183034	−	0.983107i	$-0.441408\pi$
$877$	34.6324	−	24.2499i	1.16945	−	0.818860i	0.986419	+	0.164247i	$0.0525193\pi$
$878$	−38.2149	+	26.7583i	−1.28969	+	0.903050i
$879$		0			0
$880$	−38.6304	+	18.2123i	−1.30223	+	0.613937i
$881$	−17.8875	−	10.3273i	−0.602644	−	0.347936i	0.167437	−	0.985883i	$-0.446451\pi$
$881$	−17.8875	−	10.3273i	−0.602644	−	0.347936i	−0.770081	+	0.637946i	$0.779784\pi$
$882$		0			0
$883$	18.3993	+	4.93007i	0.619185	+	0.165910i	0.554757	−	0.832012i	$-0.312811\pi$
$883$	18.3993	+	4.93007i	0.619185	+	0.165910i	0.0644275	+	0.997922i	$0.479478\pi$
$884$	77.3870	+	28.1666i	2.60281	+	0.947344i
$885$		0			0
$886$	52.3180	+	43.9000i	1.75766	+	1.47485i
$887$	−15.4260	+	33.0811i	−0.517954	+	1.11076i	0.457228	+	0.889350i	$0.348842\pi$
$887$	−15.4260	+	33.0811i	−0.517954	+	1.11076i	−0.975182	+	0.221406i	$0.928935\pi$
$888$		0			0
$889$	56.8345	−	10.0215i	1.90617	−	0.336109i
$890$	−22.2176	−	38.1100i	−0.744735	−	1.27745i
$891$		0			0
$892$	−25.4323	−	25.4323i	−0.851538	−	0.851538i
$893$	13.3007	−	18.9954i	0.445092	−	0.635657i
$894$		0			0
$895$	0.534758	+	5.82916i	0.0178750	+	0.194847i
$896$	−27.3874	+	32.6390i	−0.914947	+	1.09039i
$897$		0			0
$898$	69.9640	−	32.6248i	2.33473	−	1.08870i
$899$	−0.574727	−	0.995457i	−0.0191682	−	0.0332003i
$900$		0			0
$901$	−15.0005	+	25.9816i	−0.499739	+	0.865574i
$902$	−5.47332	+	62.5603i	−0.182242	+	2.08303i
$903$		0			0
$904$	110.464	+	19.4778i	3.67399	+	0.647823i
$905$	36.1960	+	16.6930i	1.20319	+	0.554896i
$906$		0			0
$907$	36.0031	+	3.14986i	1.19546	+	0.104589i	0.667455	−	0.744650i	$-0.267384\pi$
$907$	36.0031	+	3.14986i	1.19546	+	0.104589i	0.528008	+	0.849240i	$0.322939\pi$
$908$	−14.9702	+	4.01124i	−0.496802	+	0.133118i
$909$		0			0
$910$	−23.6779	+	41.4136i	−0.784915	+	1.37285i
$911$	1.01321	−	2.78377i	0.0335691	−	0.0922304i	−0.921776	−	0.387723i	$-0.873262\pi$
$911$	1.01321	−	2.78377i	0.0335691	−	0.0922304i	0.955345	+	0.295493i	$0.0954838\pi$
$912$		0			0
$913$	3.56148	−	0.311589i	0.117868	−	0.0103121i
$914$	−55.2056	+	20.0932i	−1.82604	+	0.664623i
$915$		0			0
$916$	−0.924588	−	5.24360i	−0.0305492	−	0.173253i
$917$	31.6917	−	31.6917i	1.04655	−	1.04655i
$918$		0			0
$919$		−	31.4414i		−	1.03716i	−0.855030	−	0.518578i	$-0.826462\pi$
$919$		−	31.4414i		−	1.03716i	0.855030	−	0.518578i	$-0.173538\pi$
$920$	5.30320	−	63.7082i	0.174841	−	2.10040i
$921$		0			0
$922$	71.8138	+	33.4873i	2.36506	+	1.10285i
$923$	2.67938	+	30.6254i	0.0881927	+	1.00805i
$924$		0			0
$925$	−1.74536	+	22.0936i	−0.0573869	+	0.726432i
$926$	−63.7180	+	36.7876i	−2.09390	+	1.20892i
$927$		0			0
$928$	−2.55305	−	9.52810i	−0.0838079	−	0.312775i
$929$	35.9403	−	30.1575i	1.17916	−	0.989435i	0.179178	−	0.983817i	$-0.442656\pi$
$929$	35.9403	−	30.1575i	1.17916	−	0.989435i	0.999984	−	0.00561833i	$-0.00178838\pi$
$930$		0			0
$931$	−0.177929	+	1.00909i	−0.00583140	+	0.0330715i
$932$	51.1490	+	73.0484i	1.67544	+	2.39278i
$933$		0			0
$934$	−33.4073	−	39.8133i	−1.09312	−	1.30273i
$935$	−0.187721	−	44.5265i	−0.00613914	−	1.45617i
$936$		0			0
$937$	−12.2770	+	45.8184i	−0.401072	+	1.49682i	0.410114	+	0.912034i	$0.365489\pi$
$937$	−12.2770	+	45.8184i	−0.401072	+	1.49682i	−0.811186	+	0.584788i	$0.801178\pi$
$938$	−1.10446	−	2.36853i	−0.0360620	−	0.0773353i
$939$		0			0
$940$	65.1173	+	11.1991i	2.12389	+	0.365274i
$941$	−3.46508	−	9.52023i	−0.112958	−	0.310351i	0.870313	−	0.492500i	$-0.163917\pi$
$941$	−3.46508	−	9.52023i	−0.112958	−	0.310351i	−0.983271	+	0.182149i	$0.941695\pi$
$942$		0			0
$943$	−31.1920	−	21.8409i	−1.01575	−	0.711236i
$944$	44.8097			1.45843
$945$		0			0
$946$	−36.3847			−1.18297
$947$	−23.0787	−	16.1599i	−0.749958	−	0.525126i	0.134973	−	0.990849i	$-0.456905\pi$
$947$	−23.0787	−	16.1599i	−0.749958	−	0.525126i	−0.884930	+	0.465723i	$0.845794\pi$
$948$		0			0
$949$	−0.0277390	−	0.0762122i	−0.000900445	−	0.00247395i
$950$	−17.5376	+	38.4528i	−0.568996	+	1.24757i
$951$		0			0
$952$	40.0584	+	85.9056i	1.29830	+	2.78422i
$953$	−0.0393504	+	0.146858i	−0.00127468	+	0.00475719i	−0.966560	−	0.256440i	$-0.917451\pi$
$953$	−0.0393504	+	0.146858i	−0.00127468	+	0.00475719i	0.965286	+	0.261197i	$0.0841172\pi$
$954$		0			0
$955$	13.8164	−	13.9334i	0.447087	−	0.450873i
$956$	33.4013	+	39.8061i	1.08027	+	1.28742i
$957$		0			0
$958$	11.0079	+	15.7210i	0.355651	+	0.507922i
$959$	9.40847	−	53.3581i	0.303815	−	1.72302i
$960$		0			0
$961$	−23.6435	+	19.8392i	−0.762692	+	0.639975i
$962$	9.05596	+	33.7973i	0.291976	+	1.08967i
$963$		0			0
$964$	25.5209	−	14.7345i	0.821972	−	0.474566i
$965$	−0.486897	−	2.69484i	−0.0156738	−	0.0867501i
$966$		0			0
$967$	−3.42592	−	39.1584i	−0.110170	−	1.25925i	−0.827080	−	0.562084i	$-0.810000\pi$
$967$	−3.42592	−	39.1584i	−0.110170	−	1.25925i	0.716910	−	0.697165i	$-0.245556\pi$
$968$	−1.71405	−	0.799275i	−0.0550917	−	0.0256897i
$969$		0			0
$970$	28.6613	+	2.38582i	0.920258	+	0.0766041i
$971$		−	16.2895i		−	0.522755i	−0.965237	−	0.261378i	$-0.915823\pi$
$971$		−	16.2895i		−	0.522755i	0.965237	−	0.261378i	$-0.0841768\pi$
$972$		0			0
$973$	33.9677	−	33.9677i	1.08895	−	1.08895i
$974$	−5.48855	−	31.1271i	−0.175864	−	0.997376i
$975$		0			0
$976$	39.3691	−	14.3292i	1.26017	−	0.458665i
$977$	−44.6375	+	3.90528i	−1.42808	+	0.124941i	−0.774815	−	0.632188i	$-0.782157\pi$
$977$	−44.6375	+	3.90528i	−1.42808	+	0.124941i	−0.653266	+	0.757129i	$0.726602\pi$
$978$		0			0
$979$	−8.78621	+	24.1399i	−0.280809	+	0.771515i
$980$	−2.81688	+	0.767523i	−0.0899819	+	0.0245176i
$981$		0			0
$982$	8.68793	−	2.32792i	0.277243	−	0.0742871i
$983$	1.65951	+	0.145188i	0.0529300	+	0.00463078i	0.113590	−	0.993528i	$-0.463765\pi$
$983$	1.65951	+	0.145188i	0.0529300	+	0.00463078i	−0.0606600	+	0.998158i	$0.519321\pi$
$984$		0			0
$985$	−29.4620	+	10.8642i	−0.938736	+	0.346161i
$986$	47.0008	+	8.28751i	1.49681	+	0.263928i
$987$		0			0
$988$	−3.96733	+	45.3468i	−0.126218	+	1.44267i
$989$	11.0309	−	19.1061i	0.350763	−	0.607540i
$990$		0			0
$991$	20.3962	+	35.3273i	0.647908	+	1.12221i	0.983622	+	0.180246i	$0.0576892\pi$
$991$	20.3962	+	35.3273i	0.647908	+	1.12221i	−0.335714	+	0.941964i	$0.608977\pi$
$992$	1.05504	−	0.491973i	0.0334975	−	0.0156201i
$993$		0			0
$994$	−42.5781	+	50.7425i	−1.35049	+	1.60946i
$995$	−28.7269	+	2.63536i	−0.910703	+	0.0835465i
$996$		0			0
$997$	−32.5879	+	46.5404i	−1.03207	+	1.47395i	−0.158432	+	0.987370i	$0.550644\pi$
$997$	−32.5879	+	46.5404i	−1.03207	+	1.47395i	−0.873637	+	0.486578i	$0.838245\pi$
$998$	1.11990	+	1.11990i	0.0354498	+	0.0354498i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.152.1		192
3.2	odd	2		135.2.q.a.122.16	yes	192
5.3	odd	4	inner	405.2.r.a.233.1		192
15.2	even	4		675.2.ba.b.68.1		192
15.8	even	4		135.2.q.a.68.16	yes	192
15.14	odd	2		675.2.ba.b.257.1		192
27.2	odd	18	inner	405.2.r.a.332.1		192
27.25	even	9		135.2.q.a.2.16	✓	192
135.52	odd	36		675.2.ba.b.218.1		192
135.79	even	18		675.2.ba.b.407.1		192
135.83	even	36	inner	405.2.r.a.8.1		192
135.133	odd	36		135.2.q.a.83.16	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.16	✓	192	27.25	even	9
135.2.q.a.68.16	yes	192	15.8	even	4
135.2.q.a.83.16	yes	192	135.133	odd	36
135.2.q.a.122.16	yes	192	3.2	odd	2
405.2.r.a.8.1		192	135.83	even	36	inner
405.2.r.a.152.1		192	1.1	even	1	trivial
405.2.r.a.233.1		192	5.3	odd	4	inner
405.2.r.a.332.1		192	27.2	odd	18	inner
675.2.ba.b.68.1		192	15.2	even	4
675.2.ba.b.218.1		192	135.52	odd	36
675.2.ba.b.257.1		192	15.14	odd	2
675.2.ba.b.407.1		192	135.79	even	18

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)

\(f(q)\)	\(=\)	\(q+(-2.05499 - 1.43892i) q^{2} +(1.46845 + 4.03452i) q^{4} +(1.82626 - 1.29027i) q^{5} +(-1.14217 - 2.44940i) q^{7} +(1.48912 - 5.55747i) q^{8} +(-5.60952 + 0.0236494i) q^{10} +(2.09979 + 2.50243i) q^{11} +(1.80484 + 2.57758i) q^{13} +(-1.17733 + 6.67697i) q^{14} +(-4.47891 + 3.75825i) q^{16} +(-1.57770 - 5.88806i) q^{17} +(2.91796 - 1.68469i) q^{19} +(7.88737 + 5.47338i) q^{20} +(-0.714248 - 8.16389i) q^{22} +(4.50352 + 2.10003i) q^{23} +(1.67042 - 4.71272i) q^{25} -7.89390i q^{26} +(8.20493 - 8.20493i) q^{28} +(-0.541940 - 3.07349i) q^{29} +(0.346096 - 0.125969i) q^{31} +(3.14866 - 0.275472i) q^{32} +(-5.23028 + 14.3701i) q^{34} +(-5.24628 - 2.99952i) q^{35} +(-4.28145 + 1.14721i) q^{37} +(-8.42050 - 0.736698i) q^{38} +(-4.45110 - 12.0707i) q^{40} +(-7.54663 - 1.33068i) q^{41} +(0.386956 - 4.42293i) q^{43} +(-7.01269 + 12.1463i) q^{44} +(-6.23291 - 10.7957i) q^{46} +(6.23750 - 2.90859i) q^{47} +(-0.195477 + 0.232960i) q^{49} +(-10.2139 + 7.28096i) q^{50} +(-7.74898 + 11.0667i) q^{52} +(-3.48010 - 3.48010i) q^{53} +(7.06356 + 1.86079i) q^{55} +(-15.3133 + 2.70014i) q^{56} +(-3.30882 + 7.09579i) q^{58} +(-5.87095 - 4.92631i) q^{59} +(-6.73344 - 2.45077i) q^{61} +(-0.892481 - 0.239140i) q^{62} +(3.26012 + 1.88223i) q^{64} +(6.62186 + 2.37859i) q^{65} +(-0.315748 + 0.221089i) q^{67} +(21.4388 - 15.0116i) q^{68} +(6.46497 + 13.7129i) q^{70} +(8.46099 + 4.88495i) q^{71} +(-0.0248963 - 0.00667095i) q^{73} +(10.4491 + 3.80315i) q^{74} +(11.0818 + 9.29871i) q^{76} +(3.73113 - 8.00143i) q^{77} +(10.9549 - 1.93165i) q^{79} +(-3.33049 + 12.6425i) q^{80} +(13.5935 + 13.5935i) q^{82} +(0.627725 - 0.896484i) q^{83} +(-10.4785 - 8.71746i) q^{85} +(-7.15941 + 8.53226i) q^{86} +(17.0340 - 7.94310i) q^{88} +(3.93198 + 6.81039i) q^{89} +(4.25207 - 7.36481i) q^{91} +(-1.85943 + 21.2533i) q^{92} +(-17.0032 - 2.99812i) q^{94} +(3.15525 - 6.84162i) q^{95} +(-5.10752 - 0.446850i) q^{97} +(0.736913 - 0.197455i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 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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