LMFDB - Embedded newform 405.2.r.a.233.1

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			233.1
Character	$\chi$	$=$	405.233
Dual form			405.2.r.a.332.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.43892 + 2.05499i) q^{2} +(-1.46845 - 4.03452i) q^{4} +(0.953539 - 2.02256i) q^{5} +(-2.44940 + 1.14217i) q^{7} +(5.55747 + 1.48912i) q^{8} +(2.78428 + 4.86981i) q^{10} +(2.09979 + 2.50243i) q^{11} +(-2.57758 + 1.80484i) q^{13} +(1.17733 - 6.67697i) q^{14} +(-4.47891 + 3.75825i) q^{16} +(-5.88806 + 1.57770i) q^{17} +(-2.91796 + 1.68469i) q^{19} +(-9.56030 - 0.877047i) q^{20} +(-8.16389 + 0.714248i) q^{22} +(-2.10003 + 4.50352i) q^{23} +(-3.18153 - 3.85719i) q^{25} -7.89390i q^{26} +(8.20493 + 8.20493i) q^{28} +(0.541940 + 3.07349i) q^{29} +(0.346096 - 0.125969i) q^{31} +(-0.275472 - 3.14866i) q^{32} +(5.23028 - 14.3701i) q^{34} +(-0.0254777 + 6.04317i) q^{35} +(1.14721 + 4.28145i) q^{37} +(0.736698 - 8.42050i) q^{38} +(8.31110 - 9.82040i) q^{40} +(-7.54663 - 1.33068i) q^{41} +(4.42293 + 0.386956i) q^{43} +(7.01269 - 12.1463i) q^{44} +(-6.23291 - 10.7957i) q^{46} +(-2.90859 - 6.23750i) q^{47} +(0.195477 - 0.232960i) q^{49} +(12.5044 - 0.987828i) q^{50} +(11.0667 + 7.74898i) q^{52} +(3.48010 - 3.48010i) q^{53} +(7.06356 - 1.86079i) q^{55} +(-15.3133 + 2.70014i) q^{56} +(-7.09579 - 3.30882i) q^{58} +(5.87095 + 4.92631i) q^{59} +(-6.73344 - 2.45077i) q^{61} +(-0.239140 + 0.892481i) q^{62} +(-3.26012 - 1.88223i) q^{64} +(1.19258 + 6.93430i) q^{65} +(0.221089 + 0.315748i) q^{67} +(15.0116 + 21.4388i) q^{68} +(-12.3820 - 8.74797i) q^{70} +(8.46099 + 4.88495i) q^{71} +(0.00667095 - 0.0248963i) q^{73} +(-10.4491 - 3.80315i) q^{74} +(11.0818 + 9.29871i) q^{76} +(-8.00143 - 3.73113i) q^{77} +(-10.9549 + 1.93165i) q^{79} +(3.33049 + 12.6425i) q^{80} +(13.5935 - 13.5935i) q^{82} +(0.896484 + 0.627725i) q^{83} +(-2.42349 + 13.4134i) q^{85} +(-7.15941 + 8.53226i) q^{86} +(7.94310 + 17.0340i) q^{88} +(-3.93198 - 6.81039i) q^{89} +(4.25207 - 7.36481i) q^{91} +(21.2533 + 1.85943i) q^{92} +(17.0032 + 2.99812i) q^{94} +(0.624996 + 7.50818i) q^{95} +(-0.446850 + 5.10752i) q^{97} +(0.197455 + 0.736913i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.43892	+	2.05499i	−1.01747	+	1.45309i	−0.130396	+	0.991462i	$0.541625\pi$
$2$	−1.43892	+	2.05499i	−1.01747	+	1.45309i	−0.887071	+	0.461633i	$0.847264\pi$
$3$		0			0
$3$		0			0
$4$	−1.46845	−	4.03452i	−0.734223	−	2.01726i
$5$	0.953539	−	2.02256i	0.426435	−	0.904518i
$5$	0.953539	−	2.02256i	0.426435	−	0.904518i
$6$		0			0
$7$	−2.44940	+	1.14217i	−0.925785	+	0.431701i	−0.826231	−	0.563331i	$-0.809519\pi$
$7$	−2.44940	+	1.14217i	−0.925785	+	0.431701i	−0.0995542	+	0.995032i	$0.531742\pi$
$8$	5.55747	+	1.48912i	1.96486	+	0.526483i
$9$		0			0
$10$	2.78428	+	4.86981i	0.880466	+	1.53997i
$11$	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
$13$	−2.57758	+	1.80484i	−0.714891	+	0.500572i	−0.873534	−	0.486764i	$-0.838177\pi$
$13$	−2.57758	+	1.80484i	−0.714891	+	0.500572i	0.158642	+	0.987336i	$0.449288\pi$
$14$	1.17733	−	6.67697i	0.314655	−	1.78450i
$15$		0			0
$16$	−4.47891	+	3.75825i	−1.11973	+	0.939563i
$17$	−5.88806	+	1.57770i	−1.42807	+	0.382649i	−0.888338	−	0.459191i	$-0.848139\pi$
$17$	−5.88806	+	1.57770i	−1.42807	+	0.382649i	−0.539728	+	0.841840i	$0.681473\pi$
$18$		0			0
$19$	−2.91796	+	1.68469i	−0.669427	+	0.386494i	−0.795859	−	0.605481i	$-0.792981\pi$
$19$	−2.91796	+	1.68469i	−0.669427	+	0.386494i	0.126433	+	0.991975i	$0.459647\pi$
$20$	−9.56030	−	0.877047i	−2.13775	−	0.196114i
$21$		0			0
$22$	−8.16389	+	0.714248i	−1.74055	+	0.152278i
$23$	−2.10003	+	4.50352i	−0.437886	+	0.939049i	0.556261	+	0.831008i	$0.312236\pi$
$23$	−2.10003	+	4.50352i	−0.437886	+	0.939049i	−0.994146	+	0.108041i	$0.965542\pi$
$24$		0			0
$25$	−3.18153	−	3.85719i	−0.636306	−	0.771437i
$26$		−	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	$0.0380229\pi$
$29$	0.541940	+	3.07349i	0.100636	+	0.570733i	−0.892238	+	0.451565i	$0.850866\pi$
$30$		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	$0.378359\pi$
$32$	−0.275472	−	3.14866i	−0.0486971	−	0.556610i
$33$		0			0
$34$	5.23028	−	14.3701i	0.896985	−	2.46445i
$35$	−0.0254777	+	6.04317i	−0.00430652	+	1.02148i
$36$		0			0
$37$	1.14721	+	4.28145i	0.188600	+	0.703866i	0.993831	+	0.110904i	$0.0353747\pi$
$37$	1.14721	+	4.28145i	0.188600	+	0.703866i	−0.805231	+	0.592962i	$0.797959\pi$
$38$	0.736698	−	8.42050i	0.119508	−	1.36599i
$39$		0			0
$40$	8.31110	−	9.82040i	1.31410	−	1.55274i
$41$	−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
$43$	4.42293	+	0.386956i	0.674490	+	0.0590102i	0.419255	−	0.907869i	$-0.362291\pi$
$43$	4.42293	+	0.386956i	0.674490	+	0.0590102i	0.255236	+	0.966879i	$0.417847\pi$
$44$	7.01269	−	12.1463i	1.05720	−	1.83113i
$45$		0			0
$46$	−6.23291	−	10.7957i	−0.918992	−	1.59174i
$47$	−2.90859	−	6.23750i	−0.424262	−	0.909832i	−0.995996	−	0.0893938i	$-0.971507\pi$
$47$	−2.90859	−	6.23750i	−0.424262	−	0.909832i	0.571735	−	0.820439i	$-0.306271\pi$
$48$		0			0
$49$	0.195477	−	0.232960i	0.0279253	−	0.0332800i
$50$	12.5044	−	0.987828i	1.76839	−	0.139700i
$51$		0			0
$52$	11.0667	+	7.74898i	1.53467	+	1.07459i
$53$	3.48010	−	3.48010i	0.478029	−	0.478029i	−0.426472	−	0.904501i	$-0.640244\pi$
$53$	3.48010	−	3.48010i	0.478029	−	0.478029i	0.904501	+	0.426472i	$0.140244\pi$
$54$		0			0
$55$	7.06356	−	1.86079i	0.952450	−	0.250909i
$56$	−15.3133	+	2.70014i	−2.04632	+	0.360822i
$57$		0			0
$58$	−7.09579	−	3.30882i	−0.931723	−	0.434470i
$59$	5.87095	+	4.92631i	0.764332	+	0.641351i	0.939251	−	0.343232i	$-0.111522\pi$
$59$	5.87095	+	4.92631i	0.764332	+	0.641351i	−0.174918	+	0.984583i	$0.555966\pi$
$60$		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	$0.762806\pi$
$62$	−0.239140	+	0.892481i	−0.0303708	+	0.113345i
$63$		0			0
$64$	−3.26012	−	1.88223i	−0.407515	−	0.235279i
$65$	1.19258	+	6.93430i	0.147922	+	0.860094i
$66$		0			0
$67$	0.221089	+	0.315748i	0.0270103	+	0.0385747i	0.832430	−	0.554130i	$-0.186949\pi$
$67$	0.221089	+	0.315748i	0.0270103	+	0.0385747i	−0.805420	+	0.592705i	$0.798060\pi$
$68$	15.0116	+	21.4388i	1.82042	+	2.59983i
$69$		0			0
$70$	−12.3820	−	8.74797i	−1.47993	−	1.04558i
$71$	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
$73$	0.00667095	−	0.0248963i	0.000780776	−	0.00291389i	−0.965534	−	0.260276i	$-0.916187\pi$
$73$	0.00667095	−	0.0248963i	0.000780776	−	0.00291389i	0.966315	+	0.257362i	$0.0828532\pi$
$74$	−10.4491	−	3.80315i	−1.21468	−	0.442107i
$75$		0			0
$76$	11.0818	+	9.29871i	1.27117	+	1.06664i
$77$	−8.00143	−	3.73113i	−0.911848	−	0.425202i
$78$		0			0
$79$	−10.9549	+	1.93165i	−1.23253	+	0.217327i	−0.751710	−	0.659494i	$-0.770770\pi$
$79$	−10.9549	+	1.93165i	−1.23253	+	0.217327i	−0.480816	+	0.876822i	$0.659659\pi$
$80$	3.33049	+	12.6425i	0.372360	+	1.41348i
$81$		0			0
$82$	13.5935	−	13.5935i	1.50115	−	1.50115i
$83$	0.896484	+	0.627725i	0.0984019	+	0.0689018i	0.621742	−	0.783222i	$-0.286425\pi$
$83$	0.896484	+	0.627725i	0.0984019	+	0.0689018i	−0.523340	+	0.852124i	$0.675314\pi$
$84$		0			0
$85$	−2.42349	+	13.4134i	−0.262865	+	1.45489i
$86$	−7.15941	+	8.53226i	−0.772019	+	0.920057i
$87$		0			0
$88$	7.94310	+	17.0340i	0.846737	+	1.81583i
$89$	−3.93198	−	6.81039i	−0.416789	−	0.721900i	0.578825	−	0.815452i	$-0.303511\pi$
$89$	−3.93198	−	6.81039i	−0.416789	−	0.721900i	−0.995614	+	0.0935515i	$0.970178\pi$
$90$		0			0
$91$	4.25207	−	7.36481i	0.445738	−	0.772042i
$92$	21.2533	+	1.85943i	2.21581	+	0.193858i
$93$		0			0
$94$	17.0032	+	2.99812i	1.75375	+	0.309233i
$95$	0.624996	+	7.50818i	0.0641232	+	0.770323i
$96$		0			0
$97$	−0.446850	+	5.10752i	−0.0453707	+	0.518590i	0.939172	+	0.343447i	$0.111594\pi$
$97$	−0.446850	+	5.10752i	−0.0453707	+	0.518590i	−0.984543	+	0.175143i	$0.943961\pi$
$98$	0.197455	+	0.736913i	0.0199460	+	0.0744394i
$99$		0			0
$100$	−10.8900	+	18.5000i	−1.08900	+	1.85000i
$101$	−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
$103$	0.0163965	+	0.187413i	0.00161560	+	0.0184664i	0.996960	−	0.0779188i	$-0.0248275\pi$
$103$	0.0163965	+	0.187413i	0.00161560	+	0.0184664i	−0.995344	+	0.0963852i	$0.969272\pi$
$104$	−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	$-0.288544\pi$
$107$	−1.76707	−	1.76707i	−0.170829	−	0.170829i	−0.787344	+	0.616515i	$0.788544\pi$
$108$		0			0
$109$			7.80745i			0.747818i	0.927465	+	0.373909i	$0.121983\pi$
$109$			7.80745i			0.747818i	−0.927465	+	0.373909i	$0.878017\pi$
$110$	−6.33997	+	17.1930i	−0.604492	+	1.63929i
$111$		0			0
$112$	6.67806	−	14.3211i	0.631017	−	1.35322i
$113$	−19.4214	+	1.69916i	−1.82701	+	0.159843i	−0.948273	−	0.317455i	$-0.897172\pi$
$113$	−19.4214	+	1.69916i	−1.82701	+	0.159843i	−0.878741	+	0.477298i	$0.841616\pi$
$114$		0			0
$115$	7.10620	+	8.54172i	0.662657	+	0.796519i
$116$	11.6043	−	6.69973i	1.07743	−	0.622054i
$117$		0			0
$118$	−18.5713	+	4.97617i	−1.70963	+	0.458093i
$119$	12.6202	−	10.5896i	1.15689	−	0.970748i
$120$		0			0
$121$	0.0570802	−	0.323718i	0.00518911	−	0.0294289i
$122$	14.7252	−	10.3107i	1.33315	−	0.933484i
$123$		0			0
$124$	−1.01645	−	1.21135i	−0.0912796	−	0.108783i
$125$	−10.8351	+	2.75687i	−0.969122	+	0.246582i
$126$		0			0
$127$	20.6263	+	5.52679i	1.83028	+	0.490423i	0.997959	−	0.0638628i	$-0.0203420\pi$
$127$	20.6263	+	5.52679i	1.83028	+	0.490423i	0.832326	+	0.554286i	$0.187009\pi$
$128$	14.2881	−	6.66265i	1.26290	−	0.588901i
$129$		0			0
$130$	−15.9659	−	7.52714i	−1.40030	−	0.660174i
$131$	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
$133$	5.22305	−	7.45929i	0.452896	−	0.646802i
$134$	−0.966985			−0.0835348
$135$		0			0
$136$	−35.0721			−3.00741
$137$	11.4989	−	16.4221i	0.982418	−	1.40304i	0.0682654	−	0.997667i	$-0.478254\pi$
$137$	11.4989	−	16.4221i	0.982418	−	1.40304i	0.914152	−	0.405371i	$-0.132858\pi$
$138$		0			0
$139$	−6.07923	−	16.7026i	−0.515634	−	1.41669i	−0.875286	−	0.483606i	$-0.839327\pi$
$139$	−6.07923	−	16.7026i	−0.515634	−	1.41669i	0.359652	−	0.933087i	$-0.382895\pi$
$140$	24.4187	−	8.77128i	2.06376	−	0.741308i
$141$		0			0
$142$	−22.2132	+	10.3582i	−1.86409	+	0.869238i
$143$	−9.92886	−	2.66043i	−0.830293	−	0.222476i
$144$		0			0
$145$	6.73310	+	1.83459i	0.559153	+	0.152354i
$146$	0.0415627	+	0.0495324i	0.00343975	+	0.00409933i
$147$		0			0
$148$	15.5890	−	10.9155i	1.28141	−	0.897250i
$149$	−0.147586	+	0.837002i	−0.0120907	+	0.0685699i	−0.990256	−	0.139258i	$-0.955528\pi$
$149$	−0.147586	+	0.837002i	−0.0120907	+	0.0685699i	0.978165	+	0.207828i	$0.0666394\pi$
$150$		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	$0.0720246\pi$
$152$	−18.7252	+	5.01740i	−1.51881	+	0.406965i
$153$		0			0
$154$	19.1808	−	11.0740i	1.54563	−	0.892372i
$155$	0.0752363	−	0.820118i	0.00604313	−	0.0658734i
$156$		0			0
$157$	10.1875	−	0.891290i	0.813051	−	0.0711327i	0.326957	−	0.945039i	$-0.393977\pi$
$157$	10.1875	−	0.891290i	0.813051	−	0.0711327i	0.486094	+	0.873907i	$0.338421\pi$
$158$	11.7937	−	25.2917i	0.938257	−	2.01210i
$159$		0			0
$160$	−6.63104	−	2.44521i	−0.524230	−	0.193311i
$161$		−	13.4295i		−	1.05839i
$162$		0			0
$163$	−9.20802	−	9.20802i	−0.721228	−	0.721228i	0.247628	−	0.968855i	$-0.420349\pi$
$163$	−9.20802	−	9.20802i	−0.721228	−	0.721228i	−0.968855	+	0.247628i	$0.920349\pi$
$164$	5.71318	+	32.4011i	0.446125	+	2.53010i
$165$		0			0
$166$	−2.57993	+	0.939019i	−0.200242	+	0.0728820i
$167$	0.420214	+	4.80307i	0.0325171	+	0.371672i	0.994966	+	0.100210i	$0.0319516\pi$
$167$	0.420214	+	4.80307i	0.0325171	+	0.371672i	−0.962449	+	0.271462i	$0.912493\pi$
$168$		0			0
$169$	−1.05980	+	2.91178i	−0.0815232	+	0.223983i
$170$	−24.0771	−	24.2810i	−1.84663	−	1.86227i
$171$		0			0
$172$	−4.93365	−	18.4126i	−0.376187	−	1.40395i
$173$	0.561923	−	6.42280i	0.0427222	−	0.488317i	−0.944450	−	0.328656i	$-0.893404\pi$
$173$	0.561923	−	6.42280i	0.0427222	−	0.488317i	0.987172	−	0.159661i	$-0.0510401\pi$
$174$		0			0
$175$	12.1984	+	5.81393i	0.922112	+	0.439491i
$176$	−18.8095	−	3.31663i	−1.41782	−	0.250000i
$177$		0			0
$178$	19.6531	+	1.71942i	1.47306	+	0.128876i
$179$	1.30891	−	2.26710i	0.0978327	−	0.169451i	−0.812955	−	0.582327i	$-0.802142\pi$
$179$	1.30891	−	2.26710i	0.0978327	−	0.169451i	0.910787	+	0.412876i	$0.135476\pi$
$180$		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	$0.602832\pi$
$182$	9.01620	+	19.3353i	0.668325	+	1.43323i
$183$		0			0
$184$	−18.3771	+	21.9010i	−1.35478	+	1.61456i
$185$	9.75341	+	1.76222i	0.717085	+	0.129561i
$186$		0			0
$187$	−16.3118	−	11.4216i	−1.19284	−	0.835233i
$188$	−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
$193$	1.10994	+	0.517574i	0.0798952	+	0.0372558i	0.462155	−	0.886799i	$-0.347076\pi$
$193$	1.10994	+	0.517574i	0.0798952	+	0.0372558i	−0.382260	+	0.924055i	$0.624854\pi$
$194$	−9.85290	−	8.26756i	−0.707397	−	0.593576i
$195$		0			0
$196$	−1.22693	−	0.446566i	−0.0876379	−	0.0318976i
$197$	−3.63461	+	13.5645i	−0.258955	+	0.966434i	0.706892	+	0.707321i	$0.250097\pi$
$197$	−3.63461	+	13.5645i	−0.258955	+	0.966434i	−0.965847	+	0.259112i	$0.916570\pi$
$198$		0			0
$199$	11.1726	+	6.45050i	0.792004	+	0.457264i	0.840668	−	0.541552i	$-0.182163\pi$
$199$	11.1726	+	6.45050i	0.792004	+	0.457264i	−0.0486637	+	0.998815i	$0.515496\pi$
$200$	−11.9374	−	26.1739i	−0.844104	−	1.85077i
$201$		0			0
$202$	−1.71106	−	2.44365i	−0.120390	−	0.171934i
$203$	−4.83789	−	6.90922i	−0.339553	−	0.484932i
$204$		0			0
$205$	−9.88738	+	13.9947i	−0.690565	+	0.977432i
$206$	−0.408725	−	0.235978i	−0.0284772	−	0.0164413i
$207$		0			0
$208$	4.76170	−	17.7709i	0.330164	−	1.23219i
$209$	−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	$0.723628\pi$
$212$	−19.1509	−	8.93021i	−1.31529	−	0.613329i
$213$		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
$218$	−16.0442	−	11.2343i	−1.08665	−	0.760881i
$219$		0			0
$220$	−17.8799	−	25.7656i	−1.20546	−	1.73712i
$221$	12.3294	−	14.6937i	0.829368	−	0.988402i
$222$		0			0
$223$	−3.54033	−	7.59226i	−0.237078	−	0.508415i	0.751388	−	0.659861i	$-0.229385\pi$
$223$	−3.54033	−	7.59226i	−0.237078	−	0.508415i	−0.988466	+	0.151446i	$0.951607\pi$
$224$	4.27106	+	7.39769i	0.285372	+	0.494279i
$225$		0			0
$226$	24.4541	−	42.3557i	1.62666	−	2.81746i
$227$	3.59601	+	0.314610i	0.238675	+	0.0208814i	0.205866	−	0.978580i	$-0.433999\pi$
$227$	3.59601	+	0.314610i	0.238675	+	0.0208814i	0.0328096	+	0.999462i	$0.489555\pi$
$228$		0			0
$229$	1.22130	+	0.215349i	0.0807059	+	0.0142306i	0.213855	−	0.976865i	$-0.431398\pi$
$229$	1.22130	+	0.215349i	0.0807059	+	0.0142306i	−0.133149	+	0.991096i	$0.542509\pi$
$230$	−27.7783	+	2.31233i	−1.83165	+	0.152470i
$231$		0			0
$232$	−1.56498	+	17.8879i	−0.102746	+	1.17440i
$233$	5.37571	+	20.0624i	0.352175	+	1.31433i	0.884003	+	0.467481i	$0.154839\pi$
$233$	5.37571	+	20.0624i	0.352175	+	1.31433i	−0.531828	+	0.846852i	$0.678495\pi$
$234$		0			0
$235$	−15.3892	−	0.0648800i	−1.00388	−	0.00423231i
$236$	11.2541	−	30.9205i	0.732582	−	2.01275i
$237$		0			0
$238$	3.60207	+	41.1719i	0.233488	+	2.66878i
$239$	−11.3730	+	4.13943i	−0.735658	+	0.267758i	−0.682558	−	0.730831i	$-0.739133\pi$
$239$	−11.3730	+	4.13943i	−0.735658	+	0.267758i	−0.0531004	+	0.998589i	$0.516910\pi$
$240$		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
$245$	−0.284782	−	0.617501i	−0.0181941	−	0.0394507i
$246$		0			0
$247$	4.48069	−	9.60887i	0.285099	−	0.611397i
$248$	2.11100	−	0.184689i	0.134049	−	0.0117277i
$249$		0			0
$250$	9.92550	−	26.2329i	0.627744	−	1.65911i
$251$	−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
$253$	−15.6794	+	4.20128i	−0.985754	+	0.264132i
$254$	−41.0369	+	34.4341i	−2.57489	+	2.16059i
$255$		0			0
$256$	−5.56035	+	31.5343i	−0.347522	+	1.97090i
$257$	−9.21372	+	6.45152i	−0.574736	+	0.402435i	−0.824491	−	0.565874i	$-0.808539\pi$
$257$	−9.21372	+	6.45152i	−0.574736	+	0.402435i	0.249755	+	0.968309i	$0.419650\pi$
$258$		0			0
$259$	−7.70013	−	9.17666i	−0.478463	−	0.570210i
$260$	26.2253	−	14.9941i	1.62643	−	0.929897i
$261$		0			0
$262$	−40.1851	−	10.7676i	−2.48264	−	0.665222i
$263$	7.46977	−	3.48321i	0.460606	−	0.214784i	−0.178443	−	0.983950i	$-0.557106\pi$
$263$	7.46977	−	3.48321i	0.460606	−	0.214784i	0.639049	+	0.769166i	$0.279328\pi$
$264$		0			0
$265$	−3.72032	−	10.3571i	−0.228537	−	0.636234i
$266$	7.81320	+	21.4666i	0.479058	+	1.31620i
$267$		0			0
$268$	0.949234	−	1.35565i	0.0579837	−	0.0828093i
$269$	21.3745			1.30322			0.651612	−	0.758553i	$-0.274093\pi$
$269$	21.3745			1.30322			0.651612	+	0.758553i	$0.274093\pi$
$270$		0			0
$271$	−16.0063			−0.972313			−0.486157	−	0.873872i	$-0.661602\pi$
$271$	−16.0063			−0.972313			−0.486157	+	0.873872i	$0.661602\pi$
$272$	20.4427	−	29.1952i	1.23952	−	1.77022i
$273$		0			0
$274$	17.2013	+	47.2602i	1.03917	+	2.85509i
$275$	2.97180	−	16.0608i	0.179207	−	0.968505i
$276$		0			0
$277$	13.0267	−	6.07443i	0.782696	−	0.364977i	0.0101600	−	0.999948i	$-0.496766\pi$
$277$	13.0267	−	6.07443i	0.782696	−	0.364977i	0.772536	+	0.634971i	$0.218988\pi$
$278$	43.0710	+	11.5408i	2.58323	+	0.692174i
$279$		0			0
$280$	−9.14059	+	33.5468i	−0.546255	+	2.00480i
$281$	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
$283$	−20.1559	+	14.1133i	−1.19815	+	0.838951i	−0.990264	−	0.139203i	$-0.955546\pi$
$283$	−20.1559	+	14.1133i	−1.19815	+	0.838951i	−0.207882	+	0.978154i	$0.566657\pi$
$284$	7.28395	−	41.3093i	0.432223	−	2.45126i
$285$		0			0
$286$	19.7539	−	16.5755i	1.16808	−	0.980132i
$287$	20.0046	−	5.36021i	1.18083	−	0.316403i
$288$		0			0
$289$	17.4577	−	10.0792i	1.02692	−	0.592895i
$290$	−13.4584	+	11.1966i	−0.790305	+	0.657487i
$291$		0			0
$292$	−0.110241	+	0.00964481i	−0.00645135	+	0.000564420i
$293$	10.1452	−	21.7565i	0.592691	−	1.27103i	−0.349809	−	0.936821i	$-0.613753\pi$
$293$	10.1452	−	21.7565i	0.592691	−	1.27103i	0.942499	−	0.334208i	$-0.108469\pi$
$294$		0			0
$295$	15.5620	−	7.17694i	0.906052	−	0.417858i
$296$			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
$302$	3.23653	+	36.9937i	0.186241	+	2.12875i
$303$		0			0
$304$	6.73782	−	18.5120i	0.386440	−	1.06174i
$305$	−11.3774	+	11.2819i	−0.651470	+	0.646000i
$306$		0			0
$307$	1.05256	+	3.92820i	0.0600726	+	0.224194i	0.989436	−	0.144973i	$-0.0463096\pi$
$307$	1.05256	+	3.92820i	0.0600726	+	0.224194i	−0.929363	+	0.369167i	$0.879643\pi$
$308$	−3.30365	+	37.7609i	−0.188243	+	2.15163i
$309$		0			0
$310$	1.57707	+	1.33469i	0.0895716	+	0.0758053i
$311$	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
$313$	−29.3680	−	2.56936i	−1.65998	−	0.145229i	−0.781787	−	0.623545i	$-0.785692\pi$
$313$	−29.3680	−	2.56936i	−1.65998	−	0.145229i	−0.878188	+	0.478316i	$0.841247\pi$
$314$	−12.8274	+	22.2177i	−0.723890	+	1.25381i
$315$		0			0
$316$	23.8800	+	41.3614i	1.34335	+	2.32676i
$317$	1.32127	+	2.83348i	0.0742101	+	0.159144i	0.939913	−	0.341414i	$-0.110906\pi$
$317$	1.32127	+	2.83348i	0.0742101	+	0.159144i	−0.865703	+	0.500558i	$0.833128\pi$
$318$		0			0
$319$	−6.55325	+	7.80986i	−0.366912	+	0.437268i
$320$	−6.91558	+	4.79902i	−0.386593	+	0.268273i
$321$		0			0
$322$	27.5975	+	19.3239i	1.53795	+	1.07688i
$323$	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
$328$	−39.9586	−	18.6330i	−2.20635	−	1.02884i
$329$	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	$0.312432\pi$
$332$	1.21613	−	4.53867i	0.0667439	−	0.249092i
$333$		0			0
$334$	−10.4749	−	6.04768i	−0.573160	−	0.330914i
$335$	0.849436	−	0.146089i	0.0464097	−	0.00798168i
$336$		0			0
$337$	−9.18427	−	13.1165i	−0.500299	−	0.714501i	0.486995	−	0.873405i	$-0.338093\pi$
$337$	−9.18427	−	13.1165i	−0.500299	−	0.714501i	−0.987294	+	0.158904i	$0.949204\pi$
$338$	−4.45870	−	6.36769i	−0.242521	−	0.346356i
$339$		0			0
$340$	57.6754	−	9.91919i	3.12789	−	0.537944i
$341$	1.04196	+	0.601574i	0.0564252	+	0.0325771i
$342$		0			0
$343$	4.68369	−	17.4798i	0.252896	−	0.943819i
$344$	24.0041	+	8.73676i	1.29421	+	0.471055i
$345$		0			0
$346$	12.3902	+	10.3966i	0.666102	+	0.558926i
$347$	1.87163	+	0.872755i	0.100474	+	0.0468520i	0.472206	−	0.881488i	$-0.343458\pi$
$347$	1.87163	+	0.872755i	0.100474	+	0.0468520i	−0.371731	+	0.928340i	$0.621236\pi$
$348$		0			0
$349$	−0.561803	+	0.0990609i	−0.0300726	+	0.00530261i	−0.188664	−	0.982042i	$-0.560416\pi$
$349$	−0.561803	+	0.0990609i	−0.0300726	+	0.00530261i	0.158592	+	0.987344i	$0.449305\pi$
$350$	−29.5000	+	16.7018i	−1.57684	+	0.892748i
$351$		0			0
$352$	7.30088	−	7.30088i	0.389138	−	0.389138i
$353$	−6.18882	−	4.33346i	−0.329398	−	0.230647i	0.397165	−	0.917747i	$-0.369994\pi$
$353$	−6.18882	−	4.33346i	−0.329398	−	0.230647i	−0.726562	+	0.687101i	$0.758883\pi$
$354$		0			0
$355$	17.9480	−	12.4549i	0.952581	−	0.661037i
$356$	−21.7028	+	25.8644i	−1.15024	+	1.37081i
$357$		0			0
$358$	2.77545	+	5.95197i	0.146687	+	0.314571i
$359$	7.12655	+	12.3435i	0.376125	+	0.651467i	0.990495	−	0.137551i	$-0.0439231\pi$
$359$	7.12655	+	12.3435i	0.376125	+	0.651467i	−0.614370	+	0.789018i	$0.710590\pi$
$360$		0			0
$361$	−3.82366	+	6.62277i	−0.201245	+	0.348567i
$362$	−44.5491	−	3.89754i	−2.34145	−	0.204850i
$363$		0			0
$364$	−35.9574	−	6.34026i	−1.88468	−	0.332320i
$365$	−0.0439934	−	0.0372320i	−0.00230272	−	0.00194881i
$366$		0			0
$367$	−1.57285	+	17.9778i	−0.0821024	+	0.938434i	0.837720	+	0.546100i	$0.183888\pi$
$367$	−1.57285	+	17.9778i	−0.0821024	+	0.938434i	−0.919823	+	0.392335i	$0.871668\pi$
$368$	−7.51954	−	28.0633i	−0.391983	−	1.46290i
$369$		0			0
$370$	−17.6557	+	17.5074i	−0.917875	+	0.910168i
$371$	−4.54928	+	12.4990i	−0.236187	+	0.648918i
$372$		0			0
$373$	−0.475246	−	5.43209i	−0.0246073	−	0.281263i	−0.998522	−	0.0543485i	$-0.982692\pi$
$373$	−0.475246	−	5.43209i	−0.0246073	−	0.281263i	0.973915	−	0.226914i	$-0.0728638\pi$
$374$	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	$0.0330888\pi$
$379$			4.04015i			0.207529i	−0.994602	+	0.103764i	$0.966911\pi$
$380$	29.3741	−	13.5469i	1.50686	−	0.694942i
$381$		0			0
$382$	−9.30369	+	19.9518i	−0.476018	+	1.02082i
$383$	−30.5793	+	2.67534i	−1.56253	+	0.136704i	−0.835341	−	0.549732i	$-0.814730\pi$
$383$	−30.5793	+	2.67534i	−1.56253	+	0.136704i	−0.727190	+	0.686436i	$0.759174\pi$
$384$		0			0
$385$	−15.1761	+	12.6256i	−0.773447	+	0.643462i
$386$	−2.66072	+	1.53617i	−0.135427	+	0.0781888i
$387$		0			0
$388$	21.2626	−	5.69729i	1.07944	−	0.289236i
$389$	−23.0823	+	19.3684i	−1.17032	+	0.982014i	−0.999994	−	0.00337359i	$-0.998926\pi$
$389$	−23.0823	+	19.3684i	−1.17032	+	0.982014i	−0.170325	+	0.985388i	$0.554482\pi$
$390$		0			0
$391$	5.25988	−	29.8302i	0.266003	−	1.50858i
$392$	1.43326	−	1.00358i	0.0723907	−	0.0506885i
$393$		0			0
$394$	−22.6451	−	26.9873i	−1.14084	−	1.35960i
$395$	−6.53906	+	23.9989i	−0.329016	+	1.20752i
$396$		0			0
$397$	−27.5321	−	7.37720i	−1.38180	−	0.370251i	−0.510023	−	0.860161i	$-0.670363\pi$
$397$	−27.5321	−	7.37720i	−1.38180	−	0.370251i	−0.871773	+	0.489910i	$0.837030\pi$
$398$	−29.3321	+	13.6778i	−1.47029	+	0.685605i
$399$		0			0
$400$	28.7460	+	5.31900i	1.43730	+	0.265950i
$401$	−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
$403$	−0.664736	+	0.949342i	−0.0331129	+	0.0472901i
$404$	5.10547			0.254007
$405$		0			0
$406$	21.1597			1.05014
$407$	−8.30514	+	11.8610i	−0.411670	+	0.587926i
$408$		0			0
$409$	−6.83310	−	18.7738i	−0.337875	−	0.928304i	−0.985996	−	0.166767i	$-0.946667\pi$
$409$	−6.83310	−	18.7738i	−0.337875	−	0.928304i	0.648121	−	0.761537i	$-0.275555\pi$
$410$	−14.5318	−	40.4556i	−0.717674	−	1.99796i
$411$		0			0
$412$	0.732046	−	0.341359i	0.0360653	−	0.0168175i
$413$	−20.0070	−	5.36086i	−0.984479	−	0.263790i
$414$		0			0
$415$	2.12445	−	1.21464i	0.104285	−	0.0596242i
$416$	6.39288	+	7.61873i	0.313437	+	0.373539i
$417$		0			0
$418$	22.6186	−	15.8377i	1.10631	−	0.774649i
$419$	1.26780	−	7.19003i	0.0619359	−	0.351256i	−0.938053	−	0.346492i	$-0.887373\pi$
$419$	1.26780	−	7.19003i	0.0619359	−	0.351256i	0.999989	−	0.00476336i	$-0.00151623\pi$
$420$		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	$0.529015\pi$
$422$	0.310978	−	0.0833264i	0.0151382	−	0.00405627i
$423$		0			0
$424$	24.5229	−	14.1583i	1.19094	−	0.687587i
$425$	24.8185	+	17.6918i	1.20388	+	0.858181i
$426$		0			0
$427$	19.2921	−	1.68784i	0.933609	−	0.0816802i
$428$	−4.53443	+	9.72412i	−0.219180	+	0.470033i
$429$		0			0
$430$	10.4303	+	22.6162i	0.502992	+	1.09065i
$431$			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	0.980316	−	0.197435i	$-0.0632612\pi$
$433$	16.2907	+	16.2907i	0.782881	+	0.782881i	−0.197435	+	0.980316i	$0.563261\pi$
$434$	−0.433620	−	2.45918i	−0.0208144	−	0.118044i
$435$		0			0
$436$	31.4993	−	11.4648i	1.50854	−	0.549065i
$437$	−1.45922	−	16.6790i	−0.0698041	−	0.797865i
$438$		0			0
$439$	−6.36027	+	17.4747i	−0.303559	+	0.834021i	0.690316	+	0.723508i	$0.257472\pi$
$439$	−6.36027	+	17.4747i	−0.303559	+	0.834021i	−0.993875	+	0.110513i	$0.964751\pi$
$440$	42.0265	+	0.177181i	2.00353	+	0.00844679i
$441$		0			0
$442$	12.4542	+	46.4798i	0.592387	+	2.21082i
$443$	2.37273	−	27.1205i	0.112732	−	1.28853i	−0.703453	−	0.710741i	$-0.748360\pi$
$443$	2.37273	−	27.1205i	0.112732	−	1.28853i	0.816185	−	0.577790i	$-0.196085\pi$
$444$		0			0
$445$	−17.5238	+	1.45871i	−0.830705	+	0.0691496i
$446$	20.6962	+	3.64930i	0.979994	+	0.172799i
$447$		0			0
$448$	10.1352	+	0.886712i	0.478841	+	0.0418932i
$449$	15.3860	−	26.6493i	0.726109	−	1.25766i	−0.232407	−	0.972619i	$-0.574660\pi$
$449$	15.3860	−	26.6493i	0.726109	−	1.25766i	0.958516	−	0.285039i	$-0.0920064\pi$
$450$		0			0
$451$	−12.5164	−	21.6791i	−0.589375	−	1.02083i
$452$	35.3746	+	75.8611i	1.66388	+	3.56820i
$453$		0			0
$454$	−5.82087	+	6.93705i	−0.273187	+	0.325572i
$455$	−10.8413	−	15.6227i	−0.508247	−	0.732404i
$456$		0			0
$457$	−19.1830	−	13.4321i	−0.897344	−	0.628327i	0.0312144	−	0.999513i	$-0.490063\pi$
$457$	−19.1830	−	13.4321i	−0.897344	−	0.628327i	−0.928559	+	0.371185i	$0.878951\pi$
$458$	−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
$463$	26.5805	+	12.3947i	1.23530	+	0.576030i	0.926929	−	0.375236i	$-0.122438\pi$
$463$	26.5805	+	12.3947i	1.23530	+	0.576030i	0.308371	+	0.951266i	$0.400216\pi$
$464$	−13.9783	−	11.7292i	−0.648924	−	0.544512i
$465$		0			0
$466$	−48.9632	−	17.8212i	−2.26818	−	0.825549i
$467$	5.36199	−	20.0112i	0.248123	−	0.926008i	−0.723665	−	0.690152i	$-0.757544\pi$
$467$	5.36199	−	20.0112i	0.248123	−	0.926008i	0.971788	−	0.235857i	$-0.0757896\pi$
$468$		0			0
$469$	−0.902173	−	0.520870i	−0.0416585	−	0.0240515i
$470$	22.2771	−	31.5312i	1.02757	−	1.45443i
$471$		0			0
$472$	25.2917	+	36.1204i	1.16415	+	1.66257i
$473$	8.31889	+	11.8806i	0.382503	+	0.546271i
$474$		0			0
$475$	15.7817	+	5.89525i	0.724116	+	0.270492i
$476$	−61.2561	−	35.3662i	−2.80767	−	1.62101i
$477$		0			0
$478$	7.85832	−	29.3277i	0.359431	−	1.34142i
$479$	7.18880	+	2.61651i	0.328465	+	0.119551i	0.500988	−	0.865454i	$-0.332970\pi$
$479$	7.18880	+	2.61651i	0.328465	+	0.119551i	−0.172524	+	0.985005i	$0.555192\pi$
$480$		0			0
$481$	−10.6843	−	8.96523i	−0.487164	−	0.408779i
$482$	15.6055	+	7.27698i	0.710813	+	0.331458i
$483$		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	−0.475832	−	0.879536i	$-0.657853\pi$
$487$	8.90898	−	8.90898i	0.403704	−	0.403704i	0.879536	+	0.475832i	$0.157853\pi$
$488$	−33.7714	−	23.6470i	−1.52876	−	1.07045i
$489$		0			0
$490$	1.67873	+	0.303309i	0.0758375	+	0.0137021i
$491$	−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
$493$	−8.04003	−	17.2419i	−0.362105	−	0.776536i
$494$	13.2987	+	23.0341i	0.598339	+	1.03635i
$495$		0			0
$496$	−1.07671	+	1.86492i	−0.0483458	+	0.0837373i
$497$	−26.3038	−	2.30128i	−1.17989	−	0.103227i
$498$		0			0
$499$	0.621729	+	0.109628i	0.0278324	+	0.00490760i	0.187547	−	0.982256i	$-0.439946\pi$
$499$	0.621729	+	0.109628i	0.0278324	+	0.00490760i	−0.159715	+	0.987163i	$0.551057\pi$
$500$	27.0334	+	39.6662i	1.20897	+	1.77393i
$501$		0			0
$502$	2.15555	−	24.6380i	0.0962068	−	1.09965i
$503$	9.79612	+	36.5596i	0.436788	+	1.63011i	0.736752	+	0.676163i	$0.236359\pi$
$503$	9.79612	+	36.5596i	0.436788	+	1.63011i	−0.299964	+	0.953950i	$0.596975\pi$
$504$		0			0
$505$	1.87224	+	1.88809i	0.0833135	+	0.0840190i
$506$	13.9278	−	38.2662i	0.619164	−	1.70114i
$507$		0			0
$508$	−7.99059	−	91.3329i	−0.354525	−	4.05224i
$509$	−27.9791	+	10.1836i	−1.24015	+	0.451378i	−0.877063	−	0.480376i	$-0.840500\pi$
$509$	−27.9791	+	10.1836i	−1.24015	+	0.451378i	−0.363089	+	0.931754i	$0.618278\pi$
$510$		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
$515$	0.394690	+	0.145543i	0.0173921	+	0.00641338i
$516$		0			0
$517$	9.50148	−	20.3760i	0.417875	−	0.896135i
$518$	29.9377	−	2.61921i	1.31539	−	0.115082i
$519$		0			0
$520$	−3.69826	+	40.3130i	−0.162179	+	1.76784i
$521$	−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
$523$	−31.8316	+	8.52925i	−1.39190	+	0.372958i	−0.875429	−	0.483347i	$-0.839421\pi$
$523$	−31.8316	+	8.52925i	−1.39190	+	0.372958i	−0.516470	+	0.856305i	$0.672754\pi$
$524$	54.5428	−	45.7668i	2.38271	−	1.99933i
$525$		0			0
$526$	−3.59043	+	20.3623i	−0.156550	+	0.887840i
$527$	−1.83910	+	1.28775i	−0.0801122	+	0.0560952i
$528$		0			0
$529$	−1.08748	−	1.29601i	−0.0472817	−	0.0563482i
$530$	26.6370	+	7.25787i	1.15704	+	0.315262i
$531$		0			0
$532$	−37.7644	−	10.1189i	−1.63730	−	0.438712i
$533$	21.8537	−	10.1905i	0.946588	−	0.441401i
$534$		0			0
$535$	−5.25898	+	1.88904i	−0.227365	+	0.0816704i
$536$	0.758509	+	2.08399i	0.0327626	+	0.0900144i
$537$		0			0
$538$	−30.7561	+	43.9242i	−1.32599	+	1.89371i
$539$	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	$0.640279\pi$
$542$	23.0317	−	32.8927i	0.989297	−	1.41286i
$543$		0			0
$544$	6.58965	+	18.1049i	0.282529	+	0.776241i
$545$	15.7911	+	7.44471i	0.676415	+	0.318896i
$546$		0			0
$547$	15.7916	−	7.36373i	0.675199	−	0.314851i	−0.0546038	−	0.998508i	$-0.517390\pi$
$547$	15.7916	−	7.36373i	0.675199	−	0.314851i	0.729803	+	0.683658i	$0.239612\pi$
$548$	−83.1410	−	22.2776i	−3.55161	−	0.951650i
$549$		0			0
$550$	28.7286	+	29.2172i	1.22499	+	1.24583i
$551$	−6.75924	−	8.05534i	−0.287953	−	0.343169i
$552$		0			0
$553$	24.6267	−	17.2438i	1.04723	−	0.733281i
$554$	−6.26140	+	35.5102i	−0.266022	+	1.50868i
$555$		0			0
$556$	−58.4598	+	49.0536i	−2.47925	+	2.08034i
$557$	9.77513	−	2.61924i	0.414185	−	0.110981i	−0.0457078	−	0.998955i	$-0.514554\pi$
$557$	9.77513	−	2.61924i	0.414185	−	0.110981i	0.459893	+	0.887974i	$0.347888\pi$
$558$		0			0
$559$	−12.0988	+	6.98526i	−0.511726	+	0.295445i
$560$	−22.5976	−	27.1626i	−0.954924	−	1.14783i
$561$		0			0
$562$	−26.6544	+	2.33196i	−1.12435	+	0.0983676i
$563$	−15.7891	+	33.8599i	−0.665432	+	1.42702i	0.226118	+	0.974100i	$0.427397\pi$
$563$	−15.7891	+	33.8599i	−0.665432	+	1.42702i	−0.891550	+	0.452923i	$0.850381\pi$
$564$		0			0
$565$	−15.0824	+	40.9013i	−0.634523	+	1.72073i
$566$		−	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	0.998220	−	0.0596413i	$-0.0189957\pi$
$569$	0.949414	+	5.38439i	0.0398015	+	0.225725i	−0.958418	+	0.285367i	$0.907885\pi$
$570$		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	$0.595893\pi$
$572$	3.84643	+	43.9649i	0.160827	+	1.83826i
$573$		0			0
$574$	−17.7698	+	48.8220i	−0.741695	+	2.03779i
$575$	24.0522	−	6.22789i	1.00305	−	0.259721i
$576$		0			0
$577$	3.56601	+	13.3085i	0.148455	+	0.554041i	0.999577	+	0.0290738i	$0.00925578\pi$
$577$	3.56601	+	13.3085i	0.148455	+	0.554041i	−0.851122	+	0.524967i	$0.824078\pi$
$578$	−4.40755	+	50.3785i	−0.183330	+	2.09547i
$579$		0			0
$580$	−2.48551	−	29.8588i	−0.103205	−	1.23982i
$581$	−2.91282	−	0.513608i	−0.120844	−	0.0213081i
$582$		0			0
$583$	16.0162	+	1.40124i	0.663324	+	0.0580333i
$584$	0.0741472	−	0.128427i	0.00306823	−	0.00531433i
$585$		0			0
$586$	30.1112	+	52.1541i	1.24388	+	2.15447i
$587$	−8.99405	−	19.2878i	−0.371224	−	0.796093i	−0.999831	−	0.0183698i	$-0.994152\pi$
$587$	−8.99405	−	19.2878i	−0.371224	−	0.796093i	0.628607	−	0.777723i	$-0.283625\pi$
$588$		0			0
$589$	−0.797678	+	0.950636i	−0.0328678	+	0.0391703i
$590$	−7.64384	+	42.3066i	−0.314692	+	1.74174i
$591$		0			0
$592$	−21.2290	−	14.8647i	−0.872507	−	0.610936i
$593$	−9.84862	+	9.84862i	−0.404434	+	0.404434i	−0.879792	−	0.475358i	$-0.842319\pi$
$593$	−9.84862	+	9.84862i	−0.404434	+	0.404434i	0.475358	+	0.879792i	$0.342319\pi$
$594$		0			0
$595$	−9.38431	−	35.6228i	−0.384719	−	1.46039i
$596$	3.59362	−	0.633653i	0.147201	−	0.0259554i
$597$		0			0
$598$	35.5503	+	16.5774i	1.45376	+	0.677900i
$599$	7.79546	+	6.54117i	0.318514	+	0.267265i	0.788000	−	0.615675i	$-0.211116\pi$
$599$	7.79546	+	6.54117i	0.318514	+	0.267265i	−0.469486	+	0.882940i	$0.655561\pi$
$600$		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	$0.393341\pi$
$602$	7.79094	−	29.0762i	0.317535	−	1.18506i
$603$		0			0
$604$	−55.0397	−	31.7772i	−2.23953	−	1.29299i
$605$	−0.600311	−	0.424126i	−0.0244061	−	0.0172432i
$606$		0			0
$607$	17.4264	+	24.8874i	0.707315	+	1.01015i	0.998568	+	0.0535038i	$0.0170389\pi$
$607$	17.4264	+	24.8874i	0.707315	+	1.01015i	−0.291253	+	0.956646i	$0.594072\pi$
$608$	6.10833	+	8.72359i	0.247725	+	0.353788i
$609$		0			0
$610$	−6.81297	−	39.6142i	−0.275849	−	1.60393i
$611$	18.7548	+	10.8281i	0.758738	+	0.438058i
$612$		0			0
$613$	−0.956834	+	3.57095i	−0.0386462	+	0.144229i	−0.982553	−	0.185982i	$-0.940453\pi$
$613$	−0.956834	+	3.57095i	−0.0386462	+	0.144229i	0.943907	+	0.330211i	$0.107120\pi$
$614$	−9.58694	−	3.48936i	−0.386897	−	0.140819i
$615$		0			0
$616$	−38.9116	−	32.6507i	−1.56779	−	1.31553i
$617$	14.6652	+	6.83850i	0.590399	+	0.275308i	0.694771	−	0.719231i	$-0.255506\pi$
$617$	14.6652	+	6.83850i	0.590399	+	0.275308i	−0.104372	+	0.994538i	$0.533283\pi$
$618$		0			0
$619$	20.5670	−	3.62651i	0.826656	−	0.145762i	0.255714	−	0.966752i	$-0.417689\pi$
$619$	20.5670	−	3.62651i	0.826656	−	0.145762i	0.570942	+	0.820991i	$0.306578\pi$
$620$	−3.41926	+	0.900756i	−0.137321	+	0.0361752i
$621$		0			0
$622$	−17.9835	+	17.9835i	−0.721072	+	0.721072i
$623$	17.4096	+	12.1904i	0.697502	+	0.488396i
$624$		0			0
$625$	−4.75575	+	24.5435i	−0.190230	+	0.981740i
$626$	47.5380	−	56.6536i	1.90000	−	2.26433i
$627$		0			0
$628$	−18.5557	−	39.7929i	−0.740454	−	1.58791i
$629$	−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	$0.0653454\pi$
$632$	−63.7581	−	5.57811i	−2.53616	−	0.221885i
$633$		0			0
$634$	−7.72396	−	1.36194i	−0.306758	−	0.0540897i
$635$	30.8462	−	36.4479i	1.22410	−	1.44639i
$636$		0			0
$637$	−0.0834010	+	0.953277i	−0.00330447	+	0.0377702i
$638$	−6.61957	−	24.7046i	−0.262071	−	0.978063i
$639$		0			0
$640$	0.148619	−	35.2517i	0.00587470	−	1.39345i
$641$	−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
$643$	2.25900	+	25.8204i	0.0890861	+	1.01826i	0.900809	+	0.434216i	$0.142974\pi$
$643$	2.25900	+	25.8204i	0.0890861	+	1.01826i	−0.811723	+	0.584043i	$0.801470\pi$
$644$	−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	$-0.0270935\pi$
$647$	23.1817	+	23.1817i	0.911366	+	0.911366i	−0.0850141	+	0.996380i	$0.527094\pi$
$648$		0			0
$649$			25.0359i			0.982744i
$650$	−30.4482	+	25.1147i	−1.19428	+	0.985078i
$651$		0			0
$652$	−23.6285	+	50.6714i	−0.925362	+	1.98445i
$653$	32.8699	−	2.87574i	1.28630	−	0.112537i	0.576591	−	0.817033i	$-0.304383\pi$
$653$	32.8699	−	2.87574i	1.28630	−	0.112537i	0.709708	+	0.704496i	$0.248827\pi$
$654$		0			0
$655$	36.9268	+	3.38761i	1.44285	+	0.132365i
$656$	38.8017	−	22.4022i	1.51495	−	0.874658i
$657$		0			0
$658$	−45.0720	+	12.0770i	−1.75709	+	0.470810i
$659$	12.5302	−	10.5141i	0.488108	−	0.409571i	−0.365240	−	0.930914i	$-0.619013\pi$
$659$	12.5302	−	10.5141i	0.488108	−	0.409571i	0.853348	+	0.521342i	$0.174568\pi$
$660$		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	$-0.127097\pi$
$662$	−60.3108	+	42.2301i	−2.34405	+	1.64132i
$663$		0			0
$664$	4.04743	+	4.82353i	0.157071	+	0.187189i
$665$	−10.1065	−	17.6767i	−0.391913	−	0.685472i
$666$		0			0
$667$	−14.9796	−	4.01378i	−0.580014	−	0.155414i
$668$	18.7610	−	8.74840i	0.725885	−	0.338486i
$669$		0			0
$670$	−0.922058	+	1.95579i	−0.0356222	+	0.0755587i
$671$	−8.00592	−	21.9961i	−0.309065	−	0.849149i
$672$		0			0
$673$	20.3600	−	29.0771i	0.784821	−	1.12084i	−0.205034	−	0.978755i	$-0.565730\pi$
$673$	20.3600	−	29.0771i	0.784821	−	1.12084i	0.989854	−	0.142085i	$-0.0453807\pi$
$674$	40.1696			1.54728
$675$		0			0
$676$	13.3039			0.511688
$677$	1.17325	−	1.67557i	0.0450916	−	0.0643975i	−0.795973	−	0.605332i	$-0.793040\pi$
$677$	1.17325	−	1.67557i	0.0450916	−	0.0643975i	0.841065	+	0.540934i	$0.181929\pi$
$678$		0			0
$679$	−4.73916	−	13.0207i	−0.181872	−	0.499689i
$680$	−33.4426	+	70.9356i	−1.28247	+	2.72026i
$681$		0			0
$682$	−2.73552	+	1.27559i	−0.104748	+	0.0488450i
$683$	−8.66609	−	2.32207i	−0.331599	−	0.0888516i	0.0891783	−	0.996016i	$-0.471576\pi$
$683$	−8.66609	−	2.32207i	−0.331599	−	0.0888516i	−0.420777	+	0.907164i	$0.638243\pi$
$684$		0			0
$685$	−22.2502	−	38.9164i	−0.850135	−	1.48692i
$686$	29.1812	+	34.7769i	1.11415	+	1.32779i
$687$		0			0
$688$	−21.2642	+	14.8893i	−0.810689	+	0.567650i
$689$	−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	$0.463650\pi$
$692$	−26.7381	+	7.16445i	−1.01643	+	0.272352i
$693$		0			0
$694$	−4.48662	+	2.59035i	−0.170310	+	0.0983284i
$695$	−39.5788	−	3.63090i	−1.50131	−	0.137728i
$696$		0			0
$697$	46.5345	−	4.07124i	1.76262	−	0.154209i
$698$	0.604818	−	1.29704i	0.0228927	−	0.0490936i
$699$		0			0
$700$	5.54372	−	57.7521i	0.209533	−	2.18283i
$701$			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
$707$	−0.280098	−	3.20153i	−0.0105342	−	0.120406i
$708$		0			0
$709$	8.05475	−	22.1303i	0.302503	−	0.831119i	−0.691561	−	0.722318i	$-0.743077\pi$
$709$	8.05475	−	22.1303i	0.302503	−	0.831119i	0.994064	−	0.108801i	$-0.0347011\pi$
$710$	−0.231053	+	54.8045i	−0.00867125	+	2.05677i
$711$		0			0
$712$	−11.7104	−	43.7037i	−0.438865	−	1.63787i
$713$	−0.159508	+	1.82319i	−0.00597364	+	0.0682790i
$714$		0			0
$715$	−14.8484	+	17.5449i	−0.555300	+	0.656143i
$716$	−11.0687	−	1.95172i	−0.413658	−	0.0729391i
$717$		0			0
$718$	−35.6203	−	3.11637i	−1.32934	−	0.116302i
$719$	−3.55440	+	6.15640i	−0.132557	+	0.229595i	−0.924661	−	0.380790i	$-0.875652\pi$
$719$	−3.55440	+	6.15640i	−0.132557	+	0.229595i	0.792105	+	0.610385i	$0.208985\pi$
$720$		0			0
$721$	−0.254220	−	0.440322i	−0.00946765	−	0.0163985i
$722$	−8.10778	−	17.3872i	−0.301740	−	0.647084i
$723$		0			0
$724$	49.1954	−	58.6288i	1.82833	−	2.17892i
$725$	10.1308	−	11.8688i	0.376250	−	0.440795i
$726$		0			0
$727$	−15.9661	−	11.1796i	−0.592148	−	0.414627i	0.238726	−	0.971087i	$-0.423270\pi$
$727$	−15.9661	−	11.1796i	−0.592148	−	0.414627i	−0.830874	+	0.556460i	$0.812159\pi$
$728$	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
$733$	33.2213	+	15.4914i	1.22706	+	0.572186i	0.924587	−	0.380972i	$-0.124411\pi$
$733$	33.2213	+	15.4914i	1.22706	+	0.572186i	0.302471	+	0.953159i	$0.402188\pi$
$734$	−34.6809	−	29.1008i	−1.28010	−	1.07413i
$735$		0			0
$736$	14.7586	+	5.37168i	0.544008	+	0.198003i
$737$	−0.325897	+	1.21626i	−0.0120046	+	0.0448017i
$738$		0			0
$739$	39.9362	+	23.0572i	1.46908	+	0.848172i	0.999399	−	0.0346657i	$-0.0110366\pi$
$739$	39.9362	+	23.0572i	1.46908	+	0.848172i	0.469678	+	0.882838i	$0.344370\pi$
$740$	−7.21264	−	41.9381i	−0.265142	−	1.54167i
$741$		0			0
$742$	−19.1393	−	27.3338i	−0.702626	−	1.00345i
$743$	−4.00223	−	5.71577i	−0.146828	−	0.209691i	0.739001	−	0.673705i	$-0.235298\pi$
$743$	−4.00223	−	5.71577i	−0.146828	−	0.209691i	−0.885828	+	0.464013i	$0.846409\pi$
$744$		0			0
$745$	1.55216	+	1.09662i	0.0568668	+	0.0401769i
$746$	11.8467	+	6.83970i	0.433739	+	0.250419i
$747$		0			0
$748$	−22.1279	+	82.5823i	−0.809075	+	3.01951i
$749$	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	$0.606013\pi$
$752$	36.4694	+	17.0060i	1.32990	+	0.620144i
$753$		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	−0.912350	−	0.409411i	$-0.865734\pi$
$757$	−13.8377	+	13.8377i	−0.502940	+	0.502940i	0.409411	+	0.912350i	$0.365734\pi$
$758$	−8.30245	−	5.81344i	−0.301559	−	0.211154i
$759$		0			0
$760$	−7.70718	+	42.6572i	−0.279569	+	1.54734i
$761$	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
$763$	−8.91746	−	19.1236i	−0.322834	−	0.692319i
$764$	−18.8382	−	32.6287i	−0.681542	−	1.18046i
$765$		0			0
$766$	38.5033	−	66.6897i	1.39118	−	2.40960i
$767$	−24.0240	−	2.10183i	−0.867457	−	0.0758927i
$768$		0			0
$769$	43.7099	+	7.70724i	1.57622	+	0.277930i	0.892237	−	0.451567i	$-0.149135\pi$
$769$	43.7099	+	7.70724i	1.57622	+	0.277930i	0.683983	+	0.729498i	$0.260246\pi$
$770$	−4.10832	−	49.3539i	−0.148054	−	1.77859i
$771$		0			0
$772$	0.458275	−	5.23811i	0.0164937	−	0.188524i
$773$	−4.60315	−	17.1792i	−0.165564	−	0.617893i	−0.997968	−	0.0637231i	$-0.979703\pi$
$773$	−4.60315	−	17.1792i	−0.165564	−	0.617893i	0.832404	−	0.554170i	$-0.186964\pi$
$774$		0			0
$775$	−1.58700	−	0.934184i	−0.0570067	−	0.0335569i
$776$	−10.0891	+	27.7195i	−0.362176	+	0.995071i
$777$		0			0
$778$	−6.58818	−	75.3032i	−0.236198	−	2.69975i
$779$	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
$785$	7.91148	−	21.4547i	0.282373	−	0.765752i
$786$		0			0
$787$	−12.6422	+	27.1112i	−0.450644	+	0.966410i	0.541429	+	0.840747i	$0.317884\pi$
$787$	−12.6422	+	27.1112i	−0.450644	+	0.966410i	−0.992073	+	0.125663i	$0.959894\pi$
$788$	60.0637	−	5.25489i	2.13968	−	0.187198i
$789$		0			0
$790$	−39.9083	−	47.9701i	−1.41987	−	1.70670i
$791$	45.6301	−	26.3445i	1.62242	−	0.936704i
$792$		0			0
$793$	21.7792	−	5.83572i	0.773402	−	0.207232i
$794$	54.7764	−	45.9629i	1.94394	−	1.63116i
$795$		0			0
$796$	9.61833	−	54.5483i	0.340913	−	1.93341i
$797$	20.3795	−	14.2699i	0.721880	−	0.505466i	−0.153954	−	0.988078i	$-0.549201\pi$
$797$	20.3795	−	14.2699i	0.721880	−	0.505466i	0.875834	+	0.482612i	$0.160312\pi$
$798$		0			0
$799$	26.9669	+	32.1379i	0.954020	+	1.13696i
$800$	−11.2685	+	11.0801i	−0.398403	+	0.391741i
$801$		0			0
$802$	68.4155	+	18.3319i	2.41584	+	0.647321i
$803$	0.0763090	−	0.0355835i	0.00269289	−	0.00125571i
$804$		0			0
$805$	−27.1620	−	12.8056i	−0.957336	−	0.451337i
$806$	−0.994384	−	2.73205i	−0.0350257	−	0.0962323i
$807$		0			0
$808$	−3.92423	+	5.60438i	−0.138054	+	0.197161i
$809$	−27.7036			−0.974006			−0.487003	−	0.873400i	$-0.661910\pi$
$809$	−27.7036			−0.974006			−0.487003	+	0.873400i	$0.661910\pi$
$810$		0			0
$811$	−16.0245			−0.562695			−0.281347	−	0.959606i	$-0.590781\pi$
$811$	−16.0245			−0.562695			−0.281347	+	0.959606i	$0.590781\pi$
$812$	−20.7712	+	29.6644i	−0.728927	+	1.04102i
$813$		0			0
$814$	−12.4237	−	34.1339i	−0.435451	−	1.19639i
$815$	−27.4040	+	9.84360i	−0.959920	+	0.344806i
$816$		0			0
$817$	−13.5578	+	6.32213i	−0.474329	+	0.221183i
$818$	48.4121	+	12.9720i	1.69269	+	0.453555i
$819$		0			0
$820$	70.9810	+	19.3404i	2.47876	+	0.675396i
$821$	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
$823$	−42.9536	+	30.0764i	−1.49727	+	1.04840i	−0.515815	+	0.856700i	$0.672511\pi$
$823$	−42.9536	+	30.0764i	−1.49727	+	1.04840i	−0.981454	+	0.191699i	$0.938600\pi$
$824$	−0.187958	+	1.06596i	−0.00654781	+	0.0371345i
$825$		0			0
$826$	39.8049	−	33.4002i	1.38499	−	1.16214i
$827$	20.7603	−	5.56271i	0.721907	−	0.193434i	0.120885	−	0.992667i	$-0.461427\pi$
$827$	20.7603	−	5.56271i	0.721907	−	0.193434i	0.601023	+	0.799232i	$0.294760\pi$
$828$		0			0
$829$	27.5695	−	15.9172i	0.957527	−	0.552828i	0.0621158	−	0.998069i	$-0.480215\pi$
$829$	27.5695	−	15.9172i	0.957527	−	0.552828i	0.895411	+	0.445241i	$0.146882\pi$
$830$	−0.560840	+	6.11347i	−0.0194670	+	0.212202i
$831$		0			0
$832$	11.8003	−	1.03240i	0.409103	−	0.0357919i
$833$	−0.783438	+	1.68009i	−0.0271445	+	0.0582116i
$834$		0			0
$835$	10.1152	+	3.73000i	0.350051	+	0.129082i
$836$			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	$0.125283\pi$
$839$	5.41257	+	30.6962i	0.186863	+	1.05975i	−0.736676	+	0.676246i	$0.763606\pi$
$840$		0			0
$841$	18.0984	−	6.58729i	0.624084	−	0.227148i
$842$	−6.36910	−	72.7991i	−0.219494	−	2.50882i
$843$		0			0
$844$	−0.188452	+	0.517767i	−0.00648677	+	0.0178223i
$845$	4.87870	+	4.92001i	0.167832	+	0.169254i
$846$		0			0
$847$	0.229930	+	0.858109i	0.00790047	+	0.0294850i
$848$	−2.50796	+	28.6662i	−0.0861239	+	0.984400i
$849$		0			0
$850$	−72.0683	+	25.5446i	−2.47192	+	0.876174i
$851$	−21.6908	−	3.82467i	−0.743550	−	0.131108i
$852$		0			0
$853$	34.9235	+	3.05541i	1.19576	+	0.104615i	0.667593	−	0.744526i	$-0.267325\pi$
$853$	34.9235	+	3.05541i	1.19576	+	0.104615i	0.528165	+	0.849142i	$0.322880\pi$
$854$	−24.2912	+	42.0736i	−0.831228	+	1.43973i
$855$		0			0
$856$	−7.18905	−	12.4518i	−0.245717	−	0.425594i
$857$	−23.5835	−	50.5751i	−0.805599	−	1.72761i	−0.677086	−	0.735904i	$-0.736758\pi$
$857$	−23.5835	−	50.5751i	−0.805599	−	1.72761i	−0.128512	−	0.991708i	$-0.541020\pi$
$858$		0			0
$859$	−18.4923	+	22.0383i	−0.630949	+	0.751936i	−0.982912	−	0.184078i	$-0.941070\pi$
$859$	−18.4923	+	22.0383i	−0.630949	+	0.751936i	0.351962	+	0.936014i	$0.385514\pi$
$860$	−41.9451	−	7.57853i	−1.43032	−	0.258426i
$861$		0			0
$862$	−29.4666	−	20.6328i	−1.00364	−	0.702754i
$863$	−20.3595	+	20.3595i	−0.693044	+	0.693044i	−0.962901	−	0.269856i	$-0.913024\pi$
$863$	−20.3595	+	20.3595i	−0.693044	+	0.693044i	0.269856	+	0.962901i	$0.413024\pi$
$864$		0			0
$865$	−12.4547	−	7.26092i	−0.423473	−	0.246879i
$866$	−56.9181	+	10.0362i	−1.93416	+	0.341044i
$867$		0			0
$868$	3.87326	+	1.80613i	0.131467	+	0.0613040i
$869$	−27.8369	−	23.3579i	−0.944301	−	0.792363i
$870$		0			0
$871$	−1.13975	−	0.414834i	−0.0386189	−	0.0140561i
$872$	−11.6262	+	43.3897i	−0.393714	+	1.46936i
$873$		0			0
$874$	36.3748	+	21.0010i	1.23040	+	0.710370i
$875$	23.3907	−	19.1282i	0.790749	−	0.646653i
$876$		0			0
$877$	−24.2499	−	34.6324i	−0.818860	−	1.16945i	−0.983107	−	0.183034i	$-0.941408\pi$
$877$	−24.2499	−	34.6324i	−0.818860	−	1.16945i	0.164247	−	0.986419i	$-0.447481\pi$
$878$	−26.7583	−	38.2149i	−0.903050	−	1.28969i
$879$		0			0
$880$	−24.6437	+	34.8810i	−0.830739	+	1.17584i
$881$	−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
$883$	−4.93007	+	18.3993i	−0.165910	+	0.619185i	0.832012	+	0.554757i	$0.187189\pi$
$883$	−4.93007	+	18.3993i	−0.165910	+	0.619185i	−0.997922	+	0.0644275i	$0.979478\pi$
$884$	−77.3870	−	28.1666i	−2.60281	−	0.947344i
$885$		0			0
$886$	52.3180	+	43.9000i	1.75766	+	1.47485i
$887$	33.0811	+	15.4260i	1.11076	+	0.517954i	0.889350	−	0.457228i	$-0.151158\pi$
$887$	33.0811	+	15.4260i	1.11076	+	0.517954i	0.221406	+	0.975182i	$0.428935\pi$
$888$		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
$893$	18.9954	+	13.3007i	0.635657	+	0.445092i
$894$		0			0
$895$	−3.33726	−	4.80913i	−0.111552	−	0.160751i
$896$	−27.3874	+	32.6390i	−0.914947	+	1.09039i
$897$		0			0
$898$	32.6248	+	69.9640i	1.08870	+	2.33473i
$899$	0.574727	+	0.995457i	0.0191682	+	0.0332003i
$900$		0			0
$901$	−15.0005	+	25.9816i	−0.499739	+	0.865574i
$902$	62.5603	+	5.47332i	2.08303	+	0.182242i
$903$		0			0
$904$	−110.464	−	19.4778i	−3.67399	−	0.647823i
$905$	39.7224	−	3.30658i	1.32042	−	0.109914i
$906$		0			0
$907$	3.14986	−	36.0031i	0.104589	−	1.19546i	−0.744650	−	0.667455i	$-0.767384\pi$
$907$	3.14986	−	36.0031i	0.104589	−	1.19546i	0.849240	−	0.528008i	$-0.177061\pi$
$908$	−4.01124	−	14.9702i	−0.133118	−	0.496802i
$909$		0			0
$910$	47.7042	+	0.201118i	1.58138	+	0.00666701i
$911$	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
$913$	0.311589	+	3.56148i	0.0103121	+	0.117868i
$914$	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	$0.173538\pi$
$919$			31.4414i			1.03716i	−0.855030	+	0.518578i	$0.826462\pi$
$920$	26.7729	+	58.0523i	0.882675	+	1.91393i
$921$		0			0
$922$	33.4873	−	71.8138i	1.10285	−	2.36506i
$923$	−30.6254	+	2.67938i	−1.00805	+	0.0881927i
$924$		0			0
$925$	12.8645	−	18.0466i	0.422981	−	0.593367i
$926$	−63.7180	+	36.7876i	−2.09390	+	1.20892i
$927$		0			0
$928$	9.52810	−	2.55305i	0.312775	−	0.0838079i
$929$	−35.9403	+	30.1575i	−1.17916	+	0.989435i	−0.179178	+	0.983817i	$0.557344\pi$
$929$	−35.9403	+	30.1575i	−1.17916	+	0.989435i	−0.999984	+	0.00561833i	$0.998212\pi$
$930$		0			0
$931$	−0.177929	+	1.00909i	−0.00583140	+	0.0330715i
$932$	73.0484	−	51.1490i	2.39278	−	1.67544i
$933$		0			0
$934$	33.4073	+	39.8133i	1.09312	+	1.30273i
$935$	−38.6549	+	22.1007i	−1.26415	+	0.722769i
$936$		0			0
$937$	45.8184	+	12.2770i	1.49682	+	0.401072i	0.912034	−	0.410114i	$-0.134511\pi$
$937$	45.8184	+	12.2770i	1.49682	+	0.401072i	0.584788	+	0.811186i	$0.301178\pi$
$938$	2.36853	−	1.10446i	0.0773353	−	0.0360620i
$939$		0			0
$940$	22.3364	+	62.1833i	0.728534	+	2.02820i
$941$	−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
$943$	21.8409	−	31.1920i	0.711236	−	1.01575i
$944$	−44.8097			−1.45843
$945$		0			0
$946$	−36.3847			−1.18297
$947$	−16.1599	+	23.0787i	−0.525126	+	0.749958i	−0.990849	−	0.134973i	$-0.956905\pi$
$947$	−16.1599	+	23.0787i	−0.525126	+	0.749958i	0.465723	+	0.884930i	$0.345794\pi$
$948$		0			0
$949$	0.0277390	+	0.0762122i	0.000900445	+	0.00247395i
$950$	−34.8232	+	23.9485i	−1.12982	+	0.776991i
$951$		0			0
$952$	85.9056	−	40.0584i	2.78422	−	1.29830i
$953$	−0.146858	−	0.0393504i	−0.00475719	−	0.00127468i	0.256440	−	0.966560i	$-0.417451\pi$
$953$	−0.146858	−	0.0393504i	−0.00475719	−	0.00127468i	−0.261197	+	0.965286i	$0.584117\pi$
$954$		0			0
$955$	5.15846	−	18.9320i	0.166924	−	0.612626i
$956$	33.4013	+	39.8061i	1.08027	+	1.28742i
$957$		0			0
$958$	−15.7210	+	11.0079i	−0.507922	+	0.355651i
$959$	−9.40847	+	53.3581i	−0.303815	+	1.72302i
$960$		0			0
$961$	−23.6435	+	19.8392i	−0.762692	+	0.639975i
$962$	33.7973	−	9.05596i	1.08967	−	0.291976i
$963$		0			0
$964$	−25.5209	+	14.7345i	−0.821972	+	0.474566i
$965$	2.10520	−	1.75140i	0.0677687	−	0.0563795i
$966$		0			0
$967$	−39.1584	+	3.42592i	−1.25925	+	0.110170i	−0.697165	−	0.716910i	$-0.745556\pi$
$967$	−39.1584	+	3.42592i	−1.25925	+	0.110170i	−0.562084	+	0.827080i	$0.690000\pi$
$968$	0.799275	−	1.71405i	0.0256897	−	0.0550917i
$969$		0			0
$970$	−26.1168	+	12.0447i	−0.838560	+	0.386731i
$971$		−	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
$977$	3.90528	+	44.6375i	0.124941	+	1.42808i	0.757129	+	0.653266i	$0.226602\pi$
$977$	3.90528	+	44.6375i	0.124941	+	1.42808i	−0.632188	+	0.774815i	$0.717843\pi$
$978$		0			0
$979$	8.78621	−	24.1399i	0.280809	−	0.771515i
$980$	−2.07313	+	2.05573i	−0.0662238	+	0.0656678i
$981$		0			0
$982$	−2.32792	−	8.68793i	−0.0742871	−	0.277243i
$983$	−0.145188	+	1.65951i	−0.00463078	+	0.0529300i	−0.998158	−	0.0606600i	$-0.980679\pi$
$983$	−0.145188	+	1.65951i	−0.00463078	+	0.0529300i	0.993528	+	0.113590i	$0.0362350\pi$
$984$		0			0
$985$	23.9694	+	20.2855i	0.763729	+	0.646351i
$986$	47.0008	+	8.28751i	1.49681	+	0.263928i
$987$		0			0
$988$	−45.3468	−	3.96733i	−1.44267	−	0.126218i
$989$	−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	$0.608977\pi$
$992$	−0.491973	−	1.05504i	−0.0156201	−	0.0334975i
$993$		0			0
$994$	42.5781	−	50.7425i	1.35049	−	1.60946i
$995$	23.7000	−	16.4465i	0.751342	−	0.521388i
$996$		0			0
$997$	46.5404	+	32.5879i	1.47395	+	1.03207i	0.987370	+	0.158432i	$0.0506439\pi$
$997$	46.5404	+	32.5879i	1.47395	+	1.03207i	0.486578	+	0.873637i	$0.338245\pi$
$998$	−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.233.1		192
3.2	odd	2		135.2.q.a.68.16	yes	192
5.2	odd	4	inner	405.2.r.a.152.1		192
15.2	even	4		135.2.q.a.122.16	yes	192
15.8	even	4		675.2.ba.b.257.1		192
15.14	odd	2		675.2.ba.b.68.1		192
27.2	odd	18	inner	405.2.r.a.8.1		192
27.25	even	9		135.2.q.a.83.16	yes	192
135.2	even	36	inner	405.2.r.a.332.1		192
135.52	odd	36		135.2.q.a.2.16	✓	192
135.79	even	18		675.2.ba.b.218.1		192
135.133	odd	36		675.2.ba.b.407.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.16	✓	192	135.52	odd	36
135.2.q.a.68.16	yes	192	3.2	odd	2
135.2.q.a.83.16	yes	192	27.25	even	9
135.2.q.a.122.16	yes	192	15.2	even	4
405.2.r.a.8.1		192	27.2	odd	18	inner
405.2.r.a.152.1		192	5.2	odd	4	inner
405.2.r.a.233.1		192	1.1	even	1	trivial
405.2.r.a.332.1		192	135.2	even	36	inner
675.2.ba.b.68.1		192	15.14	odd	2
675.2.ba.b.218.1		192	135.79	even	18
675.2.ba.b.257.1		192	15.8	even	4
675.2.ba.b.407.1		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)

\(f(q)\)	\(=\)	\(q+(-1.43892 + 2.05499i) q^{2} +(-1.46845 - 4.03452i) q^{4} +(0.953539 - 2.02256i) q^{5} +(-2.44940 + 1.14217i) q^{7} +(5.55747 + 1.48912i) q^{8} +(2.78428 + 4.86981i) q^{10} +(2.09979 + 2.50243i) q^{11} +(-2.57758 + 1.80484i) q^{13} +(1.17733 - 6.67697i) q^{14} +(-4.47891 + 3.75825i) q^{16} +(-5.88806 + 1.57770i) q^{17} +(-2.91796 + 1.68469i) q^{19} +(-9.56030 - 0.877047i) q^{20} +(-8.16389 + 0.714248i) q^{22} +(-2.10003 + 4.50352i) q^{23} +(-3.18153 - 3.85719i) q^{25} -7.89390i q^{26} +(8.20493 + 8.20493i) q^{28} +(0.541940 + 3.07349i) q^{29} +(0.346096 - 0.125969i) q^{31} +(-0.275472 - 3.14866i) q^{32} +(5.23028 - 14.3701i) q^{34} +(-0.0254777 + 6.04317i) q^{35} +(1.14721 + 4.28145i) q^{37} +(0.736698 - 8.42050i) q^{38} +(8.31110 - 9.82040i) q^{40} +(-7.54663 - 1.33068i) q^{41} +(4.42293 + 0.386956i) q^{43} +(7.01269 - 12.1463i) q^{44} +(-6.23291 - 10.7957i) q^{46} +(-2.90859 - 6.23750i) q^{47} +(0.195477 - 0.232960i) q^{49} +(12.5044 - 0.987828i) q^{50} +(11.0667 + 7.74898i) q^{52} +(3.48010 - 3.48010i) q^{53} +(7.06356 - 1.86079i) q^{55} +(-15.3133 + 2.70014i) q^{56} +(-7.09579 - 3.30882i) q^{58} +(5.87095 + 4.92631i) q^{59} +(-6.73344 - 2.45077i) q^{61} +(-0.239140 + 0.892481i) q^{62} +(-3.26012 - 1.88223i) q^{64} +(1.19258 + 6.93430i) q^{65} +(0.221089 + 0.315748i) q^{67} +(15.0116 + 21.4388i) q^{68} +(-12.3820 - 8.74797i) q^{70} +(8.46099 + 4.88495i) q^{71} +(0.00667095 - 0.0248963i) q^{73} +(-10.4491 - 3.80315i) q^{74} +(11.0818 + 9.29871i) q^{76} +(-8.00143 - 3.73113i) q^{77} +(-10.9549 + 1.93165i) q^{79} +(3.33049 + 12.6425i) q^{80} +(13.5935 - 13.5935i) q^{82} +(0.896484 + 0.627725i) q^{83} +(-2.42349 + 13.4134i) q^{85} +(-7.15941 + 8.53226i) q^{86} +(7.94310 + 17.0340i) q^{88} +(-3.93198 - 6.81039i) q^{89} +(4.25207 - 7.36481i) q^{91} +(21.2533 + 1.85943i) q^{92} +(17.0032 + 2.99812i) q^{94} +(0.624996 + 7.50818i) q^{95} +(-0.446850 + 5.10752i) q^{97} +(0.197455 + 0.736913i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 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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