LMFDB - Embedded newform 405.2.r.a.197.4

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			197.4
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85978 + 0.162710i) q^{2} +(1.46269 - 0.257912i) q^{4} +(2.23266 - 0.123434i) q^{5} +(-2.56418 + 1.79546i) q^{7} +(0.928224 - 0.248717i) q^{8} +O(q^{10})$	\(q+(-1.85978 + 0.162710i) q^{2} +(1.46269 - 0.257912i) q^{4} +(2.23266 - 0.123434i) q^{5} +(-2.56418 + 1.79546i) q^{7} +(0.928224 - 0.248717i) q^{8} +(-4.13217 + 0.592836i) q^{10} +(1.21790 + 3.34616i) q^{11} +(0.165875 - 1.89596i) q^{13} +(4.47667 - 3.75637i) q^{14} +(-4.47719 + 1.62956i) q^{16} +(-3.30982 - 0.886863i) q^{17} +(5.00990 + 2.89247i) q^{19} +(3.23385 - 0.756375i) q^{20} +(-2.80948 - 6.02495i) q^{22} +(-0.749079 + 1.06979i) q^{23} +(4.96953 - 0.551173i) q^{25} +3.55306i q^{26} +(-3.28753 + 3.28753i) q^{28} +(-0.0144398 - 0.0121164i) q^{29} +(0.260357 + 1.47656i) q^{31} +(6.31958 - 2.94687i) q^{32} +(6.29984 + 1.11083i) q^{34} +(-5.50331 + 4.32515i) q^{35} +(-2.61962 + 9.77656i) q^{37} +(-9.78795 - 4.56420i) q^{38} +(2.04171 - 0.669874i) q^{40} +(6.39065 + 7.61608i) q^{41} +(-3.23518 + 6.93786i) q^{43} +(2.64443 + 4.58028i) q^{44} +(1.21906 - 2.11147i) q^{46} +(6.31914 + 9.02466i) q^{47} +(0.957202 - 2.62989i) q^{49} +(-9.15255 + 1.83365i) q^{50} +(-0.246367 - 2.81599i) q^{52} +(-3.54041 - 3.54041i) q^{53} +(3.13219 + 7.32049i) q^{55} +(-1.93357 + 2.30434i) q^{56} +(0.0288263 + 0.0201844i) q^{58} +(5.27046 + 1.91829i) q^{59} +(1.47697 - 8.37633i) q^{61} +(-0.724458 - 2.70371i) q^{62} +(-3.02114 + 1.74425i) q^{64} +(0.136316 - 4.25351i) q^{65} +(0.222695 + 0.0194833i) q^{67} +(-5.06998 - 0.443565i) q^{68} +(9.53121 - 8.93927i) q^{70} +(0.428964 - 0.247662i) q^{71} +(-2.07694 - 7.75123i) q^{73} +(3.28118 - 18.6085i) q^{74} +(8.07394 + 2.93867i) q^{76} +(-9.13079 - 6.39345i) q^{77} +(1.13950 - 1.35801i) q^{79} +(-9.79489 + 4.19090i) q^{80} +(-13.1244 - 13.1244i) q^{82} +(-0.643650 - 7.35695i) q^{83} +(-7.49916 - 1.57152i) q^{85} +(4.88786 - 13.4293i) q^{86} +(1.96273 + 2.80307i) q^{88} +(-4.43260 + 7.67748i) q^{89} +(2.97878 + 5.15940i) q^{91} +(-0.819758 + 1.75798i) q^{92} +(-13.2206 - 15.7557i) q^{94} +(11.5424 + 5.83950i) q^{95} +(6.93643 + 3.23451i) q^{97} +(-1.35228 + 5.04676i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.85978	+	0.162710i	−1.31506	+	0.115053i	−0.723005	−	0.690842i	$-0.757240\pi$
$2$	−1.85978	+	0.162710i	−1.31506	+	0.115053i	−0.592058	+	0.805896i	$0.701684\pi$
$3$		0			0
$3$		0			0
$4$	1.46269	−	0.257912i	0.731346	−	0.128956i
$5$	2.23266	−	0.123434i	0.998475	−	0.0552015i
$5$	2.23266	−	0.123434i	0.998475	−	0.0552015i
$6$		0			0
$7$	−2.56418	+	1.79546i	−0.969168	+	0.678619i	−0.947033	−	0.321136i	$-0.895935\pi$
$7$	−2.56418	+	1.79546i	−0.969168	+	0.678619i	−0.0221350	+	0.999755i	$0.507046\pi$
$8$	0.928224	−	0.248717i	0.328177	−	0.0879347i
$9$		0			0
$10$	−4.13217	+	0.592836i	−1.30671	+	0.187471i
$11$	1.21790	+	3.34616i	0.367211	+	1.00890i	0.976417	+	0.215892i	$0.0692660\pi$
$11$	1.21790	+	3.34616i	0.367211	+	1.00890i	−0.609206	+	0.793012i	$0.708512\pi$
$12$		0			0
$13$	0.165875	−	1.89596i	0.0460055	−	0.525845i	−0.937870	−	0.346988i	$-0.887205\pi$
$13$	0.165875	−	1.89596i	0.0460055	−	0.525845i	0.983875	−	0.178857i	$-0.0572399\pi$
$14$	4.47667	−	3.75637i	1.19644	−	1.00393i
$15$		0			0
$16$	−4.47719	+	1.62956i	−1.11930	+	0.407391i
$17$	−3.30982	−	0.886863i	−0.802749	−	0.215096i	−0.165958	−	0.986133i	$-0.553072\pi$
$17$	−3.30982	−	0.886863i	−0.802749	−	0.215096i	−0.636791	+	0.771037i	$0.719738\pi$
$18$		0			0
$19$	5.00990	+	2.89247i	1.14935	+	0.663578i	0.948729	−	0.316091i	$-0.102371\pi$
$19$	5.00990	+	2.89247i	1.14935	+	0.663578i	0.200622	+	0.979669i	$0.435704\pi$
$20$	3.23385	−	0.756375i	0.723112	−	0.169131i
$21$		0			0
$22$	−2.80948	−	6.02495i	−0.598983	−	1.28452i
$23$	−0.749079	+	1.06979i	−0.156194	+	0.223068i	−0.889620	−	0.456701i	$-0.849031\pi$
$23$	−0.749079	+	1.06979i	−0.156194	+	0.223068i	0.733427	+	0.679769i	$0.237920\pi$
$24$		0			0
$25$	4.96953	−	0.551173i	0.993906	−	0.110235i
$26$			3.55306i			0.696812i
$27$		0			0
$28$	−3.28753	+	3.28753i	−0.621285	+	0.621285i
$29$	−0.0144398	−	0.0121164i	−0.00268140	−	0.00224996i	0.641446	−	0.767168i	$-0.278335\pi$
$29$	−0.0144398	−	0.0121164i	−0.00268140	−	0.00224996i	−0.644127	+	0.764918i	$0.722779\pi$
$30$		0			0
$31$	0.260357	+	1.47656i	0.0467616	+	0.265198i	0.999221	−	0.0394679i	$-0.0125663\pi$
$31$	0.260357	+	1.47656i	0.0467616	+	0.265198i	−0.952459	+	0.304666i	$0.901455\pi$
$32$	6.31958	−	2.94687i	1.11715	−	0.520938i
$33$		0			0
$34$	6.29984	+	1.11083i	1.08041	+	0.190506i
$35$	−5.50331	+	4.32515i	−0.930230	+	0.731084i
$36$		0			0
$37$	−2.61962	+	9.77656i	−0.430663	+	1.60726i	0.320574	+	0.947224i	$0.396124\pi$
$37$	−2.61962	+	9.77656i	−0.430663	+	1.60726i	−0.751237	+	0.660033i	$0.770542\pi$
$38$	−9.78795	−	4.56420i	−1.58781	−	0.740410i
$39$		0			0
$40$	2.04171	−	0.669874i	0.322822	−	0.105916i
$41$	6.39065	+	7.61608i	0.998051	+	1.18943i	0.981869	+	0.189562i	$0.0607069\pi$
$41$	6.39065	+	7.61608i	0.998051	+	1.18943i	0.0161828	+	0.999869i	$0.494849\pi$
$42$		0			0
$43$	−3.23518	+	6.93786i	−0.493360	+	1.05801i	0.489218	+	0.872162i	$0.337282\pi$
$43$	−3.23518	+	6.93786i	−0.493360	+	1.05801i	−0.982578	+	0.185852i	$0.940495\pi$
$44$	2.64443	+	4.58028i	0.398662	+	0.690503i
$45$		0			0
$46$	1.21906	−	2.11147i	0.179740	−	0.311319i
$47$	6.31914	+	9.02466i	0.921741	+	1.31638i	0.948512	+	0.316741i	$0.102589\pi$
$47$	6.31914	+	9.02466i	0.921741	+	1.31638i	−0.0267711	+	0.999642i	$0.508523\pi$
$48$		0			0
$49$	0.957202	−	2.62989i	0.136743	−	0.375699i
$50$	−9.15255	+	1.83365i	−1.29437	+	0.259317i
$51$		0			0
$52$	−0.246367	−	2.81599i	−0.0341649	−	0.390507i
$53$	−3.54041	−	3.54041i	−0.486312	−	0.486312i	0.420828	−	0.907140i	$-0.361740\pi$
$53$	−3.54041	−	3.54041i	−0.486312	−	0.486312i	−0.907140	+	0.420828i	$0.861740\pi$
$54$		0			0
$55$	3.13219	+	7.32049i	0.422344	+	0.987095i
$56$	−1.93357	+	2.30434i	−0.258384	+	0.307930i
$57$		0			0
$58$	0.0288263	+	0.0201844i	0.00378507	+	0.00265034i
$59$	5.27046	+	1.91829i	0.686155	+	0.249740i	0.661488	−	0.749956i	$-0.269925\pi$
$59$	5.27046	+	1.91829i	0.686155	+	0.249740i	0.0246670	+	0.999696i	$0.492147\pi$
$60$		0			0
$61$	1.47697	−	8.37633i	0.189107	−	1.07248i	−0.731457	−	0.681887i	$-0.761159\pi$
$61$	1.47697	−	8.37633i	0.189107	−	1.07248i	0.920564	−	0.390591i	$-0.127729\pi$
$62$	−0.724458	−	2.70371i	−0.0920063	−	0.343372i
$63$		0			0
$64$	−3.02114	+	1.74425i	−0.377642	+	0.218032i
$65$	0.136316	−	4.25351i	0.0169079	−	0.527583i
$66$		0			0
$67$	0.222695	+	0.0194833i	0.0272065	+	0.00238026i	0.100751	−	0.994912i	$-0.467876\pi$
$67$	0.222695	+	0.0194833i	0.0272065	+	0.00238026i	−0.0735444	+	0.997292i	$0.523431\pi$
$68$	−5.06998	−	0.443565i	−0.614825	−	0.0537902i
$69$		0			0
$70$	9.53121	−	8.93927i	1.13920	−	1.06845i
$71$	0.428964	−	0.247662i	0.0509086	−	0.0293921i	−0.474330	−	0.880347i	$-0.657310\pi$
$71$	0.428964	−	0.247662i	0.0509086	−	0.0293921i	0.525238	+	0.850955i	$0.323976\pi$
$72$		0			0
$73$	−2.07694	−	7.75123i	−0.243087	−	0.907213i	−0.974335	−	0.225102i	$-0.927729\pi$
$73$	−2.07694	−	7.75123i	−0.243087	−	0.907213i	0.731248	−	0.682111i	$-0.238938\pi$
$74$	3.28118	−	18.6085i	0.381429	−	2.16319i
$75$		0			0
$76$	8.07394	+	2.93867i	0.926145	+	0.337089i
$77$	−9.13079	−	6.39345i	−1.04055	−	0.728601i
$78$		0			0
$79$	1.13950	−	1.35801i	0.128204	−	0.152788i	−0.698124	−	0.715977i	$-0.745981\pi$
$79$	1.13950	−	1.35801i	0.128204	−	0.152788i	0.826328	+	0.563190i	$0.190426\pi$
$80$	−9.79489	+	4.19090i	−1.09510	+	0.468557i
$81$		0			0
$82$	−13.1244	−	13.1244i	−1.44935	−	1.44935i
$83$	−0.643650	−	7.35695i	−0.0706498	−	0.807531i	−0.946027	−	0.324089i	$-0.894942\pi$
$83$	−0.643650	−	7.35695i	−0.0706498	−	0.807531i	0.875377	−	0.483441i	$-0.160613\pi$
$84$		0			0
$85$	−7.49916	−	1.57152i	−0.813399	−	0.170455i
$86$	4.88786	−	13.4293i	0.527072	−	1.44812i
$87$		0			0
$88$	1.96273	+	2.80307i	0.209228	+	0.298808i
$89$	−4.43260	+	7.67748i	−0.469854	+	0.813812i	−0.999406	−	0.0344662i	$-0.989027\pi$
$89$	−4.43260	+	7.67748i	−0.469854	+	0.813812i	0.529552	+	0.848278i	$0.322360\pi$
$90$		0			0
$91$	2.97878	+	5.15940i	0.312261	+	0.540852i
$92$	−0.819758	+	1.75798i	−0.0854656	+	0.183282i
$93$		0			0
$94$	−13.2206	−	15.7557i	−1.36360	−	1.62508i
$95$	11.5424	+	5.83950i	1.18423	+	0.599120i
$96$		0			0
$97$	6.93643	+	3.23451i	0.704288	+	0.328415i	0.741556	−	0.670890i	$-0.234088\pi$
$97$	6.93643	+	3.23451i	0.704288	+	0.328415i	−0.0372686	+	0.999305i	$0.511866\pi$
$98$	−1.35228	+	5.04676i	−0.136601	+	0.509800i
$99$		0			0
$100$	7.12673	−	2.08790i	0.712673	−	0.208790i
$101$	−16.6975	−	2.94423i	−1.66147	−	0.292961i	−0.737475	−	0.675374i	$-0.763982\pi$
$101$	−16.6975	−	2.94423i	−1.66147	−	0.292961i	−0.923992	+	0.382413i	$0.875093\pi$
$102$		0			0
$103$	1.99712	−	0.931271i	0.196782	−	0.0917609i	−0.321730	−	0.946832i	$-0.604264\pi$
$103$	1.99712	−	0.931271i	0.196782	−	0.0917609i	0.518511	+	0.855071i	$0.326486\pi$
$104$	−0.317588	−	1.80113i	−0.0311421	−	0.176616i
$105$		0			0
$106$	7.16044	+	6.00832i	0.695483	+	0.583579i
$107$	13.8021	−	13.8021i	1.33430	−	1.33430i	0.432826	−	0.901477i	$-0.357516\pi$
$107$	13.8021	−	13.8021i	1.33430	−	1.33430i	0.901477	−	0.432826i	$-0.142484\pi$
$108$		0			0
$109$		−	14.9196i		−	1.42903i	−0.699618	−	0.714517i	$-0.746646\pi$
$109$		−	14.9196i		−	1.42903i	0.699618	−	0.714517i	$-0.253354\pi$
$110$	−7.01629	−	13.1049i	−0.668977	−	1.24950i
$111$		0			0
$112$	8.55450	−	12.2171i	0.808324	−	1.15441i
$113$	−2.98979	−	6.41164i	−0.281256	−	0.603156i	0.714032	−	0.700113i	$-0.246867\pi$
$113$	−2.98979	−	6.41164i	−0.281256	−	0.603156i	−0.995289	+	0.0969568i	$0.969089\pi$
$114$		0			0
$115$	−1.54039	+	2.48095i	−0.143642	+	0.231350i
$116$	−0.0242459	−	0.0139984i	−0.00225118	−	0.00129972i
$117$		0			0
$118$	−10.1140	−	2.71004i	−0.931070	−	0.249480i
$119$	10.0793	−	3.66856i	0.923967	−	0.336296i
$120$		0			0
$121$	−1.28699	+	1.07991i	−0.116999	+	0.0981738i
$122$	−1.38393	+	15.8184i	−0.125296	+	1.43213i
$123$		0			0
$124$	0.761645	+	2.09260i	0.0683978	+	0.187921i
$125$	11.0272	−	1.84399i	0.986305	−	0.164932i
$126$		0			0
$127$	−1.38335	+	0.370667i	−0.122752	+	0.0328914i	−0.319672	−	0.947528i	$-0.603573\pi$
$127$	−1.38335	+	0.370667i	−0.122752	+	0.0328914i	0.196920	+	0.980420i	$0.436906\pi$
$128$	−6.08886	+	4.26347i	−0.538184	+	0.376841i
$129$		0			0
$130$	0.438569	+	7.93277i	0.0384651	+	0.695750i
$131$	5.99175	−	1.05651i	0.523502	−	0.0923075i	0.0943485	−	0.995539i	$-0.469923\pi$
$131$	5.99175	−	1.05651i	0.523502	−	0.0923075i	0.429153	+	0.903232i	$0.358812\pi$
$132$		0			0
$133$	−18.0396	+	1.57826i	−1.56423	+	0.136852i
$134$	−0.417333			−0.0360521
$135$		0			0
$136$	−3.29283			−0.282358
$137$	1.03468	−	0.0905225i	0.0883984	−	0.00773386i	−0.0428707	−	0.999081i	$-0.513650\pi$
$137$	1.03468	−	0.0905225i	0.0883984	−	0.00773386i	0.131269	+	0.991347i	$0.458095\pi$
$138$		0			0
$139$	−18.7473	+	3.30565i	−1.59012	+	0.280381i	−0.897532	−	0.440950i	$-0.854642\pi$
$139$	−18.7473	+	3.30565i	−1.59012	+	0.280381i	−0.692590	+	0.721331i	$0.743531\pi$
$140$	−6.93414	+	7.74573i	−0.586042	+	0.654633i
$141$		0			0
$142$	−0.757481	+	0.530394i	−0.0635664	+	0.0445097i
$143$	6.54620	−	1.75405i	0.547421	−	0.146681i
$144$		0			0
$145$	−0.0337347	−	0.0252694i	−0.00280151	−	0.00209851i
$146$	5.12385	+	14.0777i	0.424052	+	1.16507i
$147$		0			0
$148$	−1.31021	+	14.9757i	−0.107698	+	1.23100i
$149$	−2.25551	+	1.89260i	−0.184779	+	0.155048i	−0.730485	−	0.682929i	$-0.760706\pi$
$149$	−2.25551	+	1.89260i	−0.184779	+	0.155048i	0.545706	+	0.837977i	$0.316261\pi$
$150$		0			0
$151$	−16.5766	+	6.03340i	−1.34899	+	0.490992i	−0.912632	−	0.408782i	$-0.865953\pi$
$151$	−16.5766	+	6.03340i	−1.34899	+	0.490992i	−0.436356	+	0.899774i	$0.643731\pi$
$152$	5.36972	+	1.43881i	0.435542	+	0.116703i
$153$		0			0
$154$	18.0215	+	10.4047i	1.45222	+	0.838438i
$155$	0.763547	+	3.26452i	0.0613296	+	0.262212i
$156$		0			0
$157$	3.65003	+	7.82751i	0.291304	+	0.624703i	0.996434	−	0.0843747i	$-0.0268893\pi$
$157$	3.65003	+	7.82751i	0.291304	+	0.624703i	−0.705130	+	0.709078i	$0.749111\pi$
$158$	−1.89826	+	2.71100i	−0.151018	+	0.215676i
$159$		0			0
$160$	13.7457	−	7.35940i	1.08669	−	0.581812i
$161$		−	4.08808i		−	0.322186i
$162$		0			0
$163$	7.31819	−	7.31819i	0.573205	−	0.573205i	−0.359818	−	0.933023i	$-0.617161\pi$
$163$	7.31819	−	7.31819i	0.573205	−	0.573205i	0.933023	+	0.359818i	$0.117161\pi$
$164$	11.3118	+	9.49174i	0.883305	+	0.741181i
$165$		0			0
$166$	2.39409	+	13.5776i	0.185818	+	1.05382i
$167$	−6.39434	+	2.98173i	−0.494809	+	0.230733i	−0.653971	−	0.756519i	$-0.726898\pi$
$167$	−6.39434	+	2.98173i	−0.494809	+	0.230733i	0.159163	+	0.987252i	$0.449121\pi$
$168$		0			0
$169$	9.23535	+	1.62844i	0.710411	+	0.125265i
$170$	14.2025	+	1.70249i	1.08928	+	0.130575i
$171$		0			0
$172$	−2.94271	+	10.9823i	−0.224379	+	0.837396i
$173$	3.36346	+	1.56841i	0.255719	+	0.119244i	0.546251	−	0.837622i	$-0.316055\pi$
$173$	3.36346	+	1.56841i	0.255719	+	0.119244i	−0.290532	+	0.956865i	$0.593832\pi$
$174$		0			0
$175$	−11.7531	+	10.3359i	−0.888454	+	0.781319i
$176$	−10.9056	−	12.9967i	−0.822037	−	0.979666i
$177$		0			0
$178$	6.99445	−	14.9997i	0.524256	−	1.12427i
$179$	−2.76656	−	4.79182i	−0.206782	−	0.358157i	0.743917	−	0.668272i	$-0.232966\pi$
$179$	−2.76656	−	4.79182i	−0.206782	−	0.358157i	−0.950699	+	0.310115i	$0.899632\pi$
$180$		0			0
$181$	7.47188	−	12.9417i	0.555381	−	0.961948i	−0.442493	−	0.896772i	$-0.645906\pi$
$181$	7.47188	−	12.9417i	0.555381	−	0.961948i	0.997874	−	0.0651757i	$-0.0207608\pi$
$182$	−6.37936	−	9.11067i	−0.472870	−	0.675328i
$183$		0			0
$184$	−0.429237	+	1.17932i	−0.0316437	+	0.0869405i
$185$	−4.64196	+	22.1511i	−0.341283	+	1.62858i
$186$		0			0
$187$	−1.06345	−	12.1553i	−0.0777671	−	0.888882i
$188$	11.5705	+	11.5705i	0.843867	+	0.843867i
$189$		0			0
$190$	−22.4165	−	8.98212i	−1.62627	−	0.651632i
$191$	1.79674	−	2.14127i	0.130008	−	0.154937i	−0.697113	−	0.716961i	$-0.745533\pi$
$191$	1.79674	−	2.14127i	0.130008	−	0.154937i	0.827121	+	0.562024i	$0.189977\pi$
$192$		0			0
$193$	9.74863	+	6.82607i	0.701722	+	0.491351i	0.869160	−	0.494532i	$-0.164660\pi$
$193$	9.74863	+	6.82607i	0.701722	+	0.491351i	−0.167438	+	0.985883i	$0.553549\pi$
$194$	−13.4265	−	4.88685i	−0.963968	−	0.350856i
$195$		0			0
$196$	0.721811	−	4.09359i	0.0515579	−	0.292399i
$197$	−5.07629	−	18.9450i	−0.361671	−	1.34977i	−0.871879	−	0.489722i	$-0.837098\pi$
$197$	−5.07629	−	18.9450i	−0.361671	−	1.34977i	0.510208	−	0.860051i	$-0.329568\pi$
$198$		0			0
$199$	10.1682	−	5.87060i	0.720802	−	0.416156i	−0.0942455	−	0.995549i	$-0.530044\pi$
$199$	10.1682	−	5.87060i	0.720802	−	0.416156i	0.815048	+	0.579393i	$0.196711\pi$
$200$	4.47575	−	1.74762i	0.316483	−	0.123575i
$201$		0			0
$202$	31.5328	+	2.75876i	2.21864	+	0.194106i
$203$	0.0587806	+	0.00514264i	0.00412559	+	0.000360943i
$204$		0			0
$205$	15.2082	+	16.2153i	1.06219	+	1.13252i
$206$	−3.56267	+	2.05691i	−0.248223	+	0.143312i
$207$		0			0
$208$	2.34694	+	8.75888i	0.162731	+	0.607319i
$209$	−3.57709	+	20.2867i	−0.247432	+	1.40326i
$210$		0			0
$211$	−5.77638	−	2.10243i	−0.397662	−	0.144737i	0.135445	−	0.990785i	$-0.456754\pi$
$211$	−5.77638	−	2.10243i	−0.397662	−	0.144737i	−0.533107	+	0.846048i	$0.678976\pi$
$212$	−6.09163	−	4.26541i	−0.418375	−	0.292949i
$213$		0			0
$214$	−23.4232	+	27.9147i	−1.60118	+	1.90821i
$215$	−6.36668	+	15.8892i	−0.434204	+	1.08364i
$216$		0			0
$217$	−3.31870	−	3.31870i	−0.225288	−	0.225288i
$218$	2.42756	+	27.7471i	0.164415	+	1.87927i
$219$		0			0
$220$	6.46947	+	9.89979i	0.436171	+	0.667444i
$221$	−2.23047	+	6.12818i	−0.150038	+	0.412226i
$222$		0			0
$223$	5.53001	+	7.89767i	0.370317	+	0.528867i	0.960455	−	0.278435i	$-0.0898156\pi$
$223$	5.53001	+	7.89767i	0.370317	+	0.528867i	−0.590138	+	0.807302i	$0.700927\pi$
$224$	−10.9135	+	18.9028i	−0.729192	+	1.26300i
$225$		0			0
$226$	6.60360	+	11.4378i	0.439265	+	0.760829i
$227$	−0.386431	+	0.828704i	−0.0256483	+	0.0550030i	−0.918715	−	0.394922i	$-0.870772\pi$
$227$	−0.386431	+	0.828704i	−0.0256483	+	0.0550030i	0.893066	+	0.449925i	$0.148549\pi$
$228$		0			0
$229$	3.03966	+	3.62252i	0.200866	+	0.239383i	0.857069	−	0.515201i	$-0.172283\pi$
$229$	3.03966	+	3.62252i	0.200866	+	0.239383i	−0.656203	+	0.754585i	$0.727838\pi$
$230$	2.46111	−	4.86465i	0.162281	−	0.320766i
$231$		0			0
$232$	−0.0164169	−	0.00765533i	−0.00107782	−	0.000502597i
$233$	1.04784	−	3.91060i	0.0686464	−	0.256192i	−0.923071	−	0.384629i	$-0.874329\pi$
$233$	1.04784	−	3.91060i	0.0686464	−	0.256192i	0.991718	+	0.128437i	$0.0409961\pi$
$234$		0			0
$235$	15.2224	+	19.3690i	0.993002	+	1.26349i
$236$	8.20380	+	1.44655i	0.534022	+	0.0941625i
$237$		0			0
$238$	−18.1483	+	8.46271i	−1.17638	+	0.548556i
$239$	−2.52463	−	14.3179i	−0.163305	−	0.926146i	−0.950795	−	0.309820i	$-0.899731\pi$
$239$	−2.52463	−	14.3179i	−0.163305	−	0.926146i	0.787491	−	0.616327i	$-0.211380\pi$
$240$		0			0
$241$	−12.3103	−	10.3295i	−0.792974	−	0.665384i	0.153506	−	0.988148i	$-0.450944\pi$
$241$	−12.3103	−	10.3295i	−0.792974	−	0.665384i	−0.946480	+	0.322764i	$0.895388\pi$
$242$	2.21780	−	2.21780i	0.142566	−	0.142566i
$243$		0			0
$244$		−	12.6329i		−	0.808739i
$245$	1.81249	−	5.98980i	0.115796	−	0.382674i
$246$		0			0
$247$	6.31502	−	9.01879i	0.401815	−	0.573852i
$248$	0.608915	+	1.30582i	0.0386662	+	0.0829199i
$249$		0			0
$250$	−20.2082	+	5.22365i	−1.27808	+	0.330373i
$251$	−5.03670	−	2.90794i	−0.317914	−	0.183547i	0.332549	−	0.943086i	$-0.392091\pi$
$251$	−5.03670	−	2.90794i	−0.317914	−	0.183547i	−0.650462	+	0.759539i	$0.725425\pi$
$252$		0			0
$253$	−4.49200	−	1.20363i	−0.282410	−	0.0756715i
$254$	2.51241	−	0.914443i	0.157643	−	0.0573773i
$255$		0			0
$256$	15.9749	−	13.4046i	0.998434	−	0.837785i
$257$	−0.946469	+	10.8182i	−0.0590391	+	0.674820i	0.907795	+	0.419414i	$0.137765\pi$
$257$	−0.946469	+	10.8182i	−0.0590391	+	0.674820i	−0.966834	+	0.255406i	$0.917791\pi$
$258$		0			0
$259$	−10.8362	−	29.7722i	−0.673329	−	1.84996i
$260$	−0.897642	−	6.25673i	−0.0556694	−	0.388026i
$261$		0			0
$262$	−10.9714	+	2.93979i	−0.677817	+	0.181621i
$263$	10.3433	−	7.24249i	0.637798	−	0.446591i	−0.209428	−	0.977824i	$-0.567160\pi$
$263$	10.3433	−	7.24249i	0.637798	−	0.446591i	0.847226	+	0.531233i	$0.178271\pi$
$264$		0			0
$265$	−8.34153	−	7.46751i	−0.512416	−	0.458726i
$266$	33.2929	−	5.87043i	2.04132	−	0.359939i
$267$		0			0
$268$	0.330759	−	0.0289376i	0.0202043	−	0.00176765i
$269$	0.247995			0.0151205			0.00756025	−	0.999971i	$-0.497593\pi$
$269$	0.247995			0.0151205			0.00756025	+	0.999971i	$0.497593\pi$
$270$		0			0
$271$	10.3307			0.627548			0.313774	−	0.949498i	$-0.398407\pi$
$271$	10.3307			0.627548			0.313774	+	0.949498i	$0.398407\pi$
$272$	16.2639	−	1.42291i	0.986143	−	0.0862764i
$273$		0			0
$274$	−1.90954	+	0.336704i	−0.115360	+	0.0203410i
$275$	7.89671	+	15.9575i	0.476189	+	0.962276i
$276$		0			0
$277$	−11.7965	+	8.26002i	−0.708785	+	0.496297i	−0.871512	−	0.490375i	$-0.836860\pi$
$277$	−11.7965	+	8.26002i	−0.708785	+	0.496297i	0.162727	+	0.986671i	$0.447971\pi$
$278$	34.3279	−	9.19814i	2.05885	−	0.551668i
$279$		0			0
$280$	−4.03257	+	5.38347i	−0.240992	+	0.321724i
$281$	−3.43244	−	9.43056i	−0.204762	−	0.562580i	0.794223	−	0.607627i	$-0.207878\pi$
$281$	−3.43244	−	9.43056i	−0.204762	−	0.562580i	−0.998985	+	0.0450472i	$0.985656\pi$
$282$		0			0
$283$	−1.88728	+	21.5718i	−0.112187	+	1.28231i	0.706353	+	0.707860i	$0.250339\pi$
$283$	−1.88728	+	21.5718i	−0.112187	+	1.28231i	−0.818541	+	0.574449i	$0.805217\pi$
$284$	0.563566	−	0.472888i	0.0334415	−	0.0280608i
$285$		0			0
$286$	−11.8891	+	4.32727i	−0.703017	+	0.255877i
$287$	−30.0611	−	8.05485i	−1.77445	−	0.475462i
$288$		0			0
$289$	−4.55406	−	2.62929i	−0.267886	−	0.154664i
$290$	0.0668506	+	0.0415066i	0.00392560	+	0.00243735i
$291$		0			0
$292$	−5.03705	−	10.8020i	−0.294771	−	0.632139i
$293$	8.21615	−	11.7339i	0.479992	−	0.685500i	−0.504001	−	0.863703i	$-0.668139\pi$
$293$	8.21615	−	11.7339i	0.479992	−	0.685500i	0.983994	+	0.178203i	$0.0570283\pi$
$294$		0			0
$295$	12.0039	+	3.63233i	0.698895	+	0.211482i
$296$			9.72638i			0.565334i
$297$		0			0
$298$	3.88681	−	3.88681i	0.225157	−	0.225157i
$299$	1.90404	+	1.59768i	0.110113	+	0.0923960i
$300$		0			0
$301$	−4.16106	−	23.5985i	−0.239839	−	1.36020i
$302$	29.8472	−	13.9180i	1.71751	−	0.800890i
$303$		0			0
$304$	−27.1438	−	4.78618i	−1.55680	−	0.274506i
$305$	2.26365	−	18.8838i	0.129616	−	1.08128i
$306$		0			0
$307$	−3.02613	+	11.2937i	−0.172710	+	0.644564i	0.824220	+	0.566270i	$0.191614\pi$
$307$	−3.02613	+	11.2937i	−0.172710	+	0.644564i	−0.996930	+	0.0782941i	$0.975053\pi$
$308$	−15.0045	−	6.99670i	−0.854959	−	0.398674i
$309$		0			0
$310$	−1.95120	−	5.94705i	−0.110821	−	0.337770i
$311$	−16.3947	−	19.5384i	−0.929657	−	1.10792i	−0.993933	−	0.109990i	$-0.964918\pi$
$311$	−16.3947	−	19.5384i	−0.929657	−	1.10792i	0.0642755	−	0.997932i	$-0.479526\pi$
$312$		0			0
$313$	12.5926	−	27.0049i	0.711775	−	1.52641i	−0.132902	−	0.991129i	$-0.542430\pi$
$313$	12.5926	−	27.0049i	0.711775	−	1.52641i	0.844677	−	0.535276i	$-0.179793\pi$
$314$	−8.06186	−	13.9635i	−0.454957	−	0.788008i
$315$		0			0
$316$	1.31649	−	2.28023i	0.0740586	−	0.128273i
$317$	14.4521	+	20.6398i	0.811713	+	1.15925i	0.984689	+	0.174321i	$0.0557729\pi$
$317$	14.4521	+	20.6398i	0.811713	+	1.15925i	−0.172976	+	0.984926i	$0.555338\pi$
$318$		0			0
$319$	0.0229572	−	0.0630743i	0.00128536	−	0.00353148i
$320$	−6.52987	+	4.26724i	−0.365031	+	0.238546i
$321$		0			0
$322$	0.665170	+	7.60293i	0.0370685	+	0.423695i
$323$	−14.0166	−	14.0166i	−0.779907	−	0.779907i
$324$		0			0
$325$	−0.220682	−	9.51346i	−0.0122412	−	0.527712i
$326$	−12.4195	+	14.8010i	−0.687852	+	0.819750i
$327$		0			0
$328$	7.82620	+	5.47996i	0.432130	+	0.302580i
$329$	−32.4068	−	11.7951i	−1.78664	−	0.650285i
$330$		0			0
$331$	4.41876	−	25.0600i	0.242877	−	1.37742i	−0.582495	−	0.812834i	$-0.697924\pi$
$331$	4.41876	−	25.0600i	0.242877	−	1.37742i	0.825372	−	0.564589i	$-0.190965\pi$
$332$	−2.83891	−	10.5949i	−0.155805	−	0.581473i
$333$		0			0
$334$	11.4069	−	6.58578i	0.624158	−	0.360358i
$335$	0.499606	+	0.0160113i	0.0272964	+	0.000874792i
$336$		0			0
$337$	−15.7115	−	1.37458i	−0.855859	−	0.0748780i	−0.349225	−	0.937039i	$-0.613555\pi$
$337$	−15.7115	−	1.37458i	−0.855859	−	0.0748780i	−0.506634	+	0.862161i	$0.669111\pi$
$338$	−17.4407	−	1.52586i	−0.948648	−	0.0829959i
$339$		0			0
$340$	−11.3743	−	0.364521i	−0.616857	−	0.0197689i
$341$	−4.62371	+	2.66950i	−0.250388	+	0.144562i
$342$		0			0
$343$	−3.40382	−	12.7032i	−0.183789	−	0.685910i
$344$	−1.27741	+	7.24453i	−0.0688731	+	0.390599i
$345$		0			0
$346$	−6.51048	−	2.36962i	−0.350006	−	0.127392i
$347$	9.12375	+	6.38852i	0.489788	+	0.342954i	0.792238	−	0.610212i	$-0.208916\pi$
$347$	9.12375	+	6.38852i	0.489788	+	0.342954i	−0.302450	+	0.953165i	$0.597805\pi$
$348$		0			0
$349$	−0.156572	+	0.186596i	−0.00838112	+	0.00998823i	−0.770219	−	0.637780i	$-0.779853\pi$
$349$	−0.156572	+	0.186596i	−0.00838112	+	0.00998823i	0.761838	+	0.647768i	$0.224297\pi$
$350$	20.1765	−	21.1348i	1.07848	−	1.12970i
$351$		0			0
$352$	17.5573	+	17.5573i	0.935807	+	0.935807i
$353$	−1.23061	−	14.0660i	−0.0654989	−	0.748656i	−0.955941	−	0.293559i	$-0.905160\pi$
$353$	−1.23061	−	14.0660i	−0.0654989	−	0.748656i	0.890442	−	0.455097i	$-0.150395\pi$
$354$		0			0
$355$	0.927160	−	0.605894i	0.0492085	−	0.0321575i
$356$	−4.50341	+	12.3730i	−0.238680	+	0.655768i
$357$		0			0
$358$	5.92486	+	8.46158i	0.313139	+	0.447208i
$359$	0.501469	−	0.868570i	0.0264665	−	0.0458414i	−0.852489	−	0.522746i	$-0.824908\pi$
$359$	0.501469	−	0.868570i	0.0264665	−	0.0458414i	0.878955	+	0.476904i	$0.158241\pi$
$360$		0			0
$361$	7.23275	+	12.5275i	0.380671	+	0.659341i
$362$	−11.7903	+	25.2844i	−0.619686	+	1.32892i
$363$		0			0
$364$	5.68771	+	6.77835i	0.298117	+	0.355282i
$365$	−5.59386	−	17.0495i	−0.292796	−	0.892411i
$366$		0			0
$367$	−13.1991	−	6.15484i	−0.688987	−	0.321280i	0.0464043	−	0.998923i	$-0.485224\pi$
$367$	−13.1991	−	6.15484i	−0.688987	−	0.321280i	−0.735391	+	0.677643i	$0.763002\pi$
$368$	1.61047	−	6.01035i	0.0839514	−	0.313311i
$369$		0			0
$370$	5.02883	−	41.9514i	0.261436	−	2.18095i
$371$	15.4349	+	2.72159i	0.801339	+	0.141298i
$372$		0			0
$373$	32.3578	−	15.0887i	1.67542	−	0.781262i	0.676423	−	0.736513i	$-0.263529\pi$
$373$	32.3578	−	15.0887i	1.67542	−	0.781262i	0.998998	−	0.0447484i	$-0.0142486\pi$
$374$	3.95556	+	22.4331i	0.204537	+	1.15999i
$375$		0			0
$376$	8.11016	+	6.80523i	0.418250	+	0.350953i
$377$	−0.0253674	+	0.0253674i	−0.00130649	+	0.00130649i
$378$		0			0
$379$			33.2247i			1.70664i	0.521388	+	0.853320i	$0.325415\pi$
$379$			33.2247i			1.70664i	−0.521388	+	0.853320i	$0.674585\pi$
$380$	18.3891	+	5.56446i	0.943340	+	0.285451i
$381$		0			0
$382$	−2.99314	+	4.27464i	−0.153142	+	0.218710i
$383$	13.8723	+	29.7492i	0.708842	+	1.52012i	0.848087	+	0.529858i	$0.177755\pi$
$383$	13.8723	+	29.7492i	0.708842	+	1.52012i	−0.139245	+	0.990258i	$0.544468\pi$
$384$		0			0
$385$	−21.1751	−	13.1473i	−1.07918	−	0.670050i
$386$	−19.2410	−	11.1088i	−0.979340	−	0.565422i
$387$		0			0
$388$	10.9801	+	2.94210i	0.557429	+	0.149363i
$389$	5.02600	−	1.82931i	0.254828	−	0.0927498i	−0.211447	−	0.977389i	$-0.567818\pi$
$389$	5.02600	−	1.82931i	0.254828	−	0.0927498i	0.466276	+	0.884640i	$0.345596\pi$
$390$		0			0
$391$	3.42808	−	2.87650i	0.173365	−	0.145471i
$392$	0.234400	−	2.67920i	0.0118390	−	0.135320i
$393$		0			0
$394$	12.5233	+	34.4075i	0.630915	+	1.73343i
$395$	2.37650	−	3.17262i	0.119574	−	0.159632i
$396$		0			0
$397$	29.6681	−	7.94953i	1.48900	−	0.398976i	0.579599	−	0.814902i	$-0.303209\pi$
$397$	29.6681	−	7.94953i	1.48900	−	0.398976i	0.909398	+	0.415926i	$0.136542\pi$
$398$	−17.9554	+	12.5725i	−0.900021	+	0.630201i
$399$		0			0
$400$	−21.3514	+	10.5659i	−1.06757	+	0.528294i
$401$	0.473405	−	0.0834740i	0.0236407	−	0.00416849i	−0.161815	−	0.986821i	$-0.551735\pi$
$401$	0.473405	−	0.0834740i	0.0236407	−	0.00416849i	0.185456	+	0.982653i	$0.440624\pi$
$402$		0			0
$403$	2.84269	−	0.248703i	0.141604	−	0.0123888i
$404$	−25.1827			−1.25289
$405$		0			0
$406$	−0.110156			−0.00546694
$407$	−35.9043	+	3.14122i	−1.77971	+	0.155705i
$408$		0			0
$409$	22.3819	−	3.94653i	1.10671	−	0.195144i	0.409714	−	0.912214i	$-0.365629\pi$
$409$	22.3819	−	3.94653i	1.10671	−	0.195144i	0.697000	+	0.717071i	$0.254518\pi$
$410$	−30.9223	−	27.6823i	−1.52714	−	1.36713i
$411$		0			0
$412$	2.68098	−	1.87724i	0.132082	−	0.0924851i
$413$	−16.9586	+	4.54404i	−0.834478	+	0.223598i
$414$		0			0
$415$	−2.34515	−	16.3461i	−0.115119	−	0.802399i
$416$	−4.53888	−	12.4705i	−0.222537	−	0.611416i
$417$		0			0
$418$	3.35176	−	38.3107i	0.163940	−	1.87384i
$419$	8.25865	−	6.92983i	0.403462	−	0.338544i	−0.418368	−	0.908277i	$-0.637398\pi$
$419$	8.25865	−	6.92983i	0.403462	−	0.338544i	0.821830	+	0.569733i	$0.192953\pi$
$420$		0			0
$421$	−23.5375	+	8.56694i	−1.14715	+	0.417527i	−0.844489	−	0.535572i	$-0.820096\pi$
$421$	−23.5375	+	8.56694i	−1.14715	+	0.417527i	−0.302657	+	0.953099i	$0.597874\pi$
$422$	11.0849	+	2.97018i	0.539603	+	0.144586i
$423$		0			0
$424$	−4.16685	−	2.40573i	−0.202360	−	0.116833i
$425$	−16.9371	−	2.58301i	−0.821568	−	0.125294i
$426$		0			0
$427$	11.2521	+	24.1302i	0.544528	+	1.16774i
$428$	16.6285	−	23.7480i	0.803771	−	1.14790i
$429$		0			0
$430$	9.25529	−	30.5864i	0.446330	−	1.47500i
$431$			14.1259i			0.680421i	0.940349	+	0.340210i	$0.110498\pi$
$431$			14.1259i			0.680421i	−0.940349	+	0.340210i	$0.889502\pi$
$432$		0			0
$433$	1.82757	−	1.82757i	0.0878275	−	0.0878275i	−0.661828	−	0.749656i	$-0.730219\pi$
$433$	1.82757	−	1.82757i	0.0878275	−	0.0878275i	0.749656	+	0.661828i	$0.230219\pi$
$434$	6.71204	+	5.63207i	0.322188	+	0.270348i
$435$		0			0
$436$	−3.84793	−	21.8227i	−0.184283	−	1.04512i
$437$	−6.84716	+	3.19288i	−0.327544	+	0.152736i
$438$		0			0
$439$	24.0637	+	4.24307i	1.14850	+	0.202511i	0.715319	−	0.698798i	$-0.246281\pi$
$439$	24.0637	+	4.24307i	1.14850	+	0.202511i	0.433177	+	0.901309i	$0.357393\pi$
$440$	4.72810	+	6.01603i	0.225403	+	0.286803i
$441$		0			0
$442$	3.15108	−	11.7600i	0.149881	−	0.559365i
$443$	26.8103	+	12.5019i	1.27380	+	0.593981i	0.937569	−	0.347800i	$-0.113071\pi$
$443$	26.8103	+	12.5019i	1.27380	+	0.593981i	0.336227	+	0.941781i	$0.390849\pi$
$444$		0			0
$445$	−8.94881	+	17.6883i	−0.424214	+	0.838507i
$446$	−11.5696	−	13.7881i	−0.547838	−	0.652888i
$447$		0			0
$448$	4.61500	−	9.89690i	0.218038	−	0.467584i
$449$	15.2444	+	26.4040i	0.719426	+	1.24608i	0.961228	+	0.275756i	$0.0889283\pi$
$449$	15.2444	+	26.4040i	0.719426	+	1.24608i	−0.241802	+	0.970326i	$0.577738\pi$
$450$		0			0
$451$	−17.7014	+	30.6597i	−0.833527	+	1.44371i
$452$	−6.02678	−	8.60714i	−0.283476	−	0.404846i
$453$		0			0
$454$	0.583838	−	1.60408i	0.0274009	−	0.0752833i
$455$	7.28745	+	11.1515i	0.341641	+	0.522790i
$456$		0			0
$457$	0.815525	+	9.32149i	0.0381486	+	0.436041i	0.991119	+	0.132978i	$0.0424538\pi$
$457$	0.815525	+	9.32149i	0.0381486	+	0.436041i	−0.952970	+	0.303063i	$0.901991\pi$
$458$	−6.24252	−	6.24252i	−0.291694	−	0.291694i
$459$		0			0
$460$	−1.61324	+	4.02615i	−0.0752179	+	0.187720i
$461$	4.16189	−	4.95995i	0.193839	−	0.231008i	−0.660367	−	0.750943i	$-0.729599\pi$
$461$	4.16189	−	4.95995i	0.193839	−	0.231008i	0.854206	+	0.519935i	$0.174044\pi$
$462$		0			0
$463$	−10.8905	−	7.62562i	−0.506125	−	0.354393i	0.292457	−	0.956279i	$-0.405527\pi$
$463$	−10.8905	−	7.62562i	−0.506125	−	0.354393i	−0.798582	+	0.601886i	$0.794416\pi$
$464$	0.0843941	+	0.0307169i	0.00391790	+	0.00142600i
$465$		0			0
$466$	−1.31246	+	7.44335i	−0.0607987	+	0.344806i
$467$	5.67127	+	21.1655i	0.262435	+	0.979421i	0.963802	+	0.266620i	$0.0859069\pi$
$467$	5.67127	+	21.1655i	0.262435	+	0.979421i	−0.701367	+	0.712801i	$0.747426\pi$
$468$		0			0
$469$	−0.606010	+	0.349880i	−0.0279829	+	0.0161560i
$470$	−31.4619	−	33.5452i	−1.45123	−	1.54733i
$471$		0			0
$472$	5.36927	+	0.469751i	0.247141	+	0.0216220i
$473$	−27.1553	−	2.37578i	−1.24860	−	0.109239i
$474$		0			0
$475$	26.4911	+	11.6129i	1.21550	+	0.532835i
$476$	13.7967	−	7.96554i	0.632372	−	0.365100i
$477$		0			0
$478$	7.02491	+	26.2173i	0.321312	+	1.19915i
$479$	2.75645	−	15.6326i	0.125945	−	0.714272i	−0.854796	−	0.518964i	$-0.826318\pi$
$479$	2.75645	−	15.6326i	0.125945	−	0.714272i	0.980742	−	0.195309i	$-0.0625709\pi$
$480$		0			0
$481$	18.1014	+	6.58839i	0.825355	+	0.300405i
$482$	24.5751	+	17.2077i	1.11936	+	0.783788i
$483$		0			0
$484$	−1.60395	+	1.91151i	−0.0729066	+	0.0868867i
$485$	15.8859	+	6.36537i	0.721343	+	0.289036i
$486$		0			0
$487$	−9.67948	−	9.67948i	−0.438619	−	0.438619i	0.452928	−	0.891547i	$-0.350379\pi$
$487$	−9.67948	−	9.67948i	−0.438619	−	0.438619i	−0.891547	+	0.452928i	$0.850379\pi$
$488$	−0.712372	−	8.14245i	−0.0322476	−	0.368592i
$489$		0			0
$490$	−2.39623	+	11.4346i	−0.108251	+	0.516563i
$491$	−9.36638	+	25.7339i	−0.422699	+	1.16136i	0.527458	+	0.849581i	$0.323145\pi$
$491$	−9.36638	+	25.7339i	−0.422699	+	1.16136i	−0.950156	+	0.311774i	$0.899077\pi$
$492$		0			0
$493$	0.0370474	+	0.0529092i	0.00166853	+	0.00238291i
$494$	−10.2771	+	17.8005i	−0.462389	+	0.800881i
$495$		0			0
$496$	−3.57182	−	6.18657i	−0.160379	−	0.277785i
$497$	−0.655272	+	1.40524i	−0.0293930	+	0.0630335i
$498$		0			0
$499$	2.84438	+	3.38980i	0.127332	+	0.151749i	0.825944	−	0.563753i	$-0.190643\pi$
$499$	2.84438	+	3.38980i	0.127332	+	0.151749i	−0.698612	+	0.715501i	$0.746198\pi$
$500$	15.6538	−	5.54124i	0.700061	−	0.247812i
$501$		0			0
$502$	9.84030	+	4.58861i	0.439194	+	0.204800i
$503$	−5.44875	+	20.3350i	−0.242948	+	0.906693i	0.731456	+	0.681889i	$0.238841\pi$
$503$	−5.44875	+	20.3350i	−0.242948	+	0.906693i	−0.974404	+	0.224805i	$0.927826\pi$
$504$		0			0
$505$	−37.6433	−	4.51240i	−1.67511	−	0.200799i
$506$	8.54998	+	1.50759i	0.380093	+	0.0670207i
$507$		0			0
$508$	−1.92781	+	0.898953i	−0.0855328	+	0.0398846i
$509$	−3.28136	−	18.6095i	−0.145444	−	0.824851i	−0.967010	−	0.254739i	$-0.918011\pi$
$509$	−3.28136	−	18.6095i	−0.145444	−	0.824851i	0.821566	−	0.570113i	$-0.193101\pi$
$510$		0			0
$511$	19.2426	+	16.1465i	0.851244	+	0.714279i
$512$	−17.0168	+	17.0168i	−0.752043	+	0.752043i
$513$		0			0
$514$		−	20.2735i		−	0.894224i
$515$	4.34393	−	2.32572i	0.191416	−	0.102484i
$516$		0			0
$517$	−22.5018	+	32.1360i	−0.989630	+	1.41334i
$518$	24.9972	+	53.6067i	1.09831	+	2.35534i
$519$		0			0
$520$	−0.931387	−	3.98211i	−0.0408440	−	0.174627i
$521$	20.9815	+	12.1137i	0.919216	+	0.530709i	0.883385	−	0.468648i	$-0.155259\pi$
$521$	20.9815	+	12.1137i	0.919216	+	0.530709i	0.0358309	+	0.999358i	$0.488592\pi$
$522$		0			0
$523$	−31.3165	−	8.39124i	−1.36938	−	0.366923i	−0.502125	−	0.864795i	$-0.667448\pi$
$523$	−31.3165	−	8.39124i	−1.36938	−	0.366923i	−0.867251	+	0.497872i	$0.834115\pi$
$524$	8.49159	−	3.09069i	0.370957	−	0.135017i
$525$		0			0
$526$	−18.0579	+	15.1524i	−0.787363	+	0.660676i
$527$	0.447771	−	5.11805i	0.0195052	−	0.222946i
$528$		0			0
$529$	7.28312	+	20.0102i	0.316657	+	0.870009i
$530$	16.7284	+	12.5307i	0.726637	+	0.544298i
$531$		0			0
$532$	−25.9793	+	6.96113i	−1.12634	+	0.301803i
$533$	15.4998	−	10.8531i	0.671372	−	0.470100i
$534$		0			0
$535$	29.1118	−	32.5191i	1.25861	−	1.40592i
$536$	0.211556	−	0.0373031i	0.00913784	−	0.00161125i
$537$		0			0
$538$	−0.461216	+	0.0403511i	−0.0198844	+	0.00173966i
$539$	9.96580			0.429258
$540$		0			0
$541$	−31.6739			−1.36177			−0.680885	−	0.732391i	$-0.738404\pi$
$541$	−31.6739			−1.36177			−0.680885	+	0.732391i	$0.738404\pi$
$542$	−19.2129	+	1.68091i	−0.825265	+	0.0722013i
$543$		0			0
$544$	−23.5301	+	4.14900i	−1.00885	+	0.177887i
$545$	−1.84159	−	33.3103i	−0.0788848	−	1.42686i
$546$		0			0
$547$	4.35939	−	3.05247i	0.186394	−	0.130514i	−0.476655	−	0.879090i	$-0.658151\pi$
$547$	4.35939	−	3.05247i	0.186394	−	0.130514i	0.663049	+	0.748576i	$0.269262\pi$
$548$	1.49007	−	0.399262i	0.0636525	−	0.0170556i
$549$		0			0
$550$	−17.2826	−	28.3926i	−0.736932	−	1.21067i
$551$	−0.0372955	−	0.102469i	−0.00158884	−	0.00436531i
$552$		0			0
$553$	−0.483646	+	5.52810i	−0.0205667	+	0.235079i
$554$	20.5950	−	17.2812i	0.874996	−	0.734209i
$555$		0			0
$556$	−26.5689	+	9.67029i	−1.12677	+	0.410111i
$557$	5.85880	+	1.56986i	0.248245	+	0.0665171i	0.380796	−	0.924659i	$-0.375650\pi$
$557$	5.85880	+	1.56986i	0.248245	+	0.0665171i	−0.132551	+	0.991176i	$0.542317\pi$
$558$		0			0
$559$	12.6173	+	7.28459i	0.533654	+	0.308105i
$560$	17.5913	−	28.3325i	0.743367	−	1.19727i
$561$		0			0
$562$	7.91803	+	16.9803i	0.334002	+	0.716269i
$563$	−7.27648	+	10.3919i	−0.306667	+	0.437966i	−0.942673	−	0.333718i	$-0.891697\pi$
$563$	−7.27648	+	10.3919i	−0.306667	+	0.437966i	0.636006	+	0.771684i	$0.280585\pi$
$564$		0			0
$565$	−7.46661	−	13.9459i	−0.314122	−	0.586711i
$566$		−	40.4258i		−	1.69922i
$567$		0			0
$568$	0.336577	−	0.336577i	0.0141224	−	0.0141224i
$569$	−10.4685	−	8.78410i	−0.438862	−	0.368249i	0.396421	−	0.918069i	$-0.370252\pi$
$569$	−10.4685	−	8.78410i	−0.438862	−	0.368249i	−0.835283	+	0.549820i	$0.814696\pi$
$570$		0			0
$571$	0.567607	+	3.21906i	0.0237536	+	0.134713i	0.994378	−	0.105885i	$-0.0337675\pi$
$571$	0.567607	+	3.21906i	0.0237536	+	0.134713i	−0.970625	+	0.240598i	$0.922656\pi$
$572$	9.12268	−	4.25397i	0.381438	−	0.177868i
$573$		0			0
$574$	57.2176	+	10.0890i	2.38822	+	0.421107i
$575$	−3.13292	+	5.72925i	−0.130652	+	0.238926i
$576$		0			0
$577$	3.86877	−	14.4385i	0.161059	−	0.601081i	−0.837451	−	0.546513i	$-0.815955\pi$
$577$	3.86877	−	14.4385i	0.161059	−	0.601081i	0.998510	−	0.0545684i	$-0.0173783\pi$
$578$	8.89735	+	4.14890i	0.370081	+	0.172572i
$579$		0			0
$580$	−0.0558607	−	0.0282608i	−0.00231949	−	0.00117347i
$581$	14.8595	+	17.7089i	0.616477	+	0.734689i
$582$		0			0
$583$	7.53489	−	16.1586i	0.312063	−	0.669222i
$584$	−3.85572	−	6.67831i	−0.159551	−	0.276350i
$585$		0			0
$586$	−13.3710	+	23.1593i	−0.552351	+	0.956700i
$587$	−16.4912	−	23.5519i	−0.680666	−	0.972091i	−0.999704	−	0.0243494i	$-0.992249\pi$
$587$	−16.4912	−	23.5519i	−0.680666	−	0.972091i	0.319038	−	0.947742i	$-0.396640\pi$
$588$		0			0
$589$	−2.96654	+	8.15050i	−0.122234	+	0.335836i
$590$	−22.9157	−	4.80218i	−0.943422	−	0.197703i
$591$		0			0
$592$	−4.20299	−	48.0404i	−0.172742	−	1.97445i
$593$	21.0591	+	21.0591i	0.864795	+	0.864795i	0.991891	−	0.127095i	$-0.0405654\pi$
$593$	21.0591	+	21.0591i	0.864795	+	0.864795i	−0.127095	+	0.991891i	$0.540565\pi$
$594$		0			0
$595$	22.0508	−	9.43477i	0.903994	−	0.386788i
$596$	−2.81099	+	3.35001i	−0.115143	+	0.137222i
$597$		0			0
$598$	−3.80104	−	2.66152i	−0.155436	−	0.108838i
$599$	−18.9188	−	6.88587i	−0.773000	−	0.281349i	−0.0747495	−	0.997202i	$-0.523816\pi$
$599$	−18.9188	−	6.88587i	−0.773000	−	0.281349i	−0.698251	+	0.715853i	$0.746038\pi$
$600$		0			0
$601$	3.78086	−	21.4423i	0.154225	−	0.874652i	−0.805267	−	0.592913i	$-0.797978\pi$
$601$	3.78086	−	21.4423i	0.154225	−	0.874652i	0.959491	−	0.281739i	$-0.0909111\pi$
$602$	11.5784	+	43.2110i	0.471899	+	1.76115i
$603$		0			0
$604$	−22.6904	+	13.1003i	−0.923260	+	0.533045i
$605$	−2.74011	+	2.56993i	−0.111401	+	0.104483i
$606$		0			0
$607$	−25.1503	−	2.20037i	−1.02082	−	0.0893101i	−0.435563	−	0.900158i	$-0.643451\pi$
$607$	−25.1503	−	2.20037i	−1.02082	−	0.0893101i	−0.585257	+	0.810848i	$0.699006\pi$
$608$	40.1842	+	3.51566i	1.62968	+	0.142579i
$609$		0			0
$610$	−1.13732	+	35.4880i	−0.0460485	+	1.43687i
$611$	18.1586	−	10.4839i	0.734618	−	0.424132i
$612$		0			0
$613$	−7.34719	−	27.4201i	−0.296750	−	1.10749i	−0.939817	−	0.341677i	$-0.889005\pi$
$613$	−7.34719	−	27.4201i	−0.296750	−	1.10749i	0.643067	−	0.765810i	$-0.277662\pi$
$614$	3.79035	−	21.4961i	0.152966	−	0.867513i
$615$		0			0
$616$	−10.0656	−	3.66357i	−0.405554	−	0.147609i
$617$	−18.7465	−	13.1265i	−0.754707	−	0.528452i	0.131738	−	0.991285i	$-0.457944\pi$
$617$	−18.7465	−	13.1265i	−0.754707	−	0.528452i	−0.886446	+	0.462833i	$0.846833\pi$
$618$		0			0
$619$	−18.4274	+	21.9609i	−0.740658	+	0.882682i	−0.996462	−	0.0840469i	$-0.973215\pi$
$619$	−18.4274	+	21.9609i	−0.740658	+	0.882682i	0.255804	+	0.966729i	$0.417660\pi$
$620$	1.95879	+	4.57805i	0.0786670	+	0.183859i
$621$		0			0
$622$	33.6696	+	33.6696i	1.35003	+	1.35003i
$623$	−2.41862	−	27.6450i	−0.0969000	−	1.10757i
$624$		0			0
$625$	24.3924	−	5.47814i	0.975697	−	0.219126i
$626$	−19.0255	+	52.2720i	−0.760411	+	2.08921i
$627$		0			0
$628$	7.35767	+	10.5078i	0.293603	+	0.419308i
$629$	17.3409	−	30.0354i	0.691429	−	1.19759i
$630$		0			0
$631$	−3.00683	−	5.20799i	−0.119700	−	0.207327i	0.799949	−	0.600068i	$-0.204860\pi$
$631$	−3.00683	−	5.20799i	−0.119700	−	0.207327i	−0.919649	+	0.392742i	$0.871527\pi$
$632$	0.719954	−	1.54395i	0.0286382	−	0.0614149i
$633$		0			0
$634$	−30.2361	−	36.0340i	−1.20083	−	1.43109i
$635$	−3.04279	+	0.998325i	−0.120749	+	0.0396173i
$636$		0			0
$637$	−4.82739	−	2.25105i	−0.191268	−	0.0891899i
$638$	−0.0324325	+	0.121040i	−0.00128401	+	0.00479201i
$639$		0			0
$640$	−13.0681	+	10.2704i	−0.516561	+	0.405975i
$641$	7.56572	+	1.33404i	0.298828	+	0.0526914i	0.321052	−	0.947062i	$-0.395964\pi$
$641$	7.56572	+	1.33404i	0.298828	+	0.0526914i	−0.0222240	+	0.999753i	$0.507075\pi$
$642$		0			0
$643$	−26.3895	+	12.3056i	−1.04070	+	0.485286i	−0.866370	−	0.499402i	$-0.833553\pi$
$643$	−26.3895	+	12.3056i	−1.04070	+	0.485286i	−0.174328	+	0.984688i	$0.555775\pi$
$644$	−1.05437	−	5.97960i	−0.0415478	−	0.235629i
$645$		0			0
$646$	28.3485	+	23.7872i	1.11536	+	0.935896i
$647$	−12.6122	+	12.6122i	−0.495836	+	0.495836i	−0.910139	−	0.414303i	$-0.864025\pi$
$647$	−12.6122	+	12.6122i	−0.495836	+	0.495836i	0.414303	+	0.910139i	$0.364025\pi$
$648$		0			0
$649$			19.9721i			0.783972i
$650$	1.95835	+	17.6570i	0.0768128	+	0.692566i
$651$		0			0
$652$	8.81681	−	12.5917i	0.345293	−	0.493129i
$653$	1.21466	+	2.60484i	0.0475332	+	0.101935i	0.928640	−	0.370982i	$-0.120979\pi$
$653$	1.21466	+	2.60484i	0.0475332	+	0.101935i	−0.881107	+	0.472917i	$0.843201\pi$
$654$		0			0
$655$	13.2471	−	3.09841i	0.517608	−	0.121065i
$656$	−41.0230	−	23.6847i	−1.60168	−	0.924731i
$657$		0			0
$658$	62.1887	+	16.6634i	2.42437	+	0.649607i
$659$	27.2829	−	9.93016i	1.06279	−	0.386824i	0.249314	−	0.968423i	$-0.419795\pi$
$659$	27.2829	−	9.93016i	1.06279	−	0.386824i	0.813476	+	0.581599i	$0.197573\pi$
$660$		0			0
$661$	−1.29090	+	1.08319i	−0.0502100	+	0.0421312i	−0.667547	−	0.744567i	$-0.732656\pi$
$661$	−1.29090	+	1.08319i	−0.0502100	+	0.0421312i	0.617337	+	0.786699i	$0.288211\pi$
$662$	−4.14041	+	47.3251i	−0.160922	+	1.83934i
$663$		0			0
$664$	−2.42725	−	6.66881i	−0.0941955	−	0.258800i
$665$	−40.0814	+	5.75042i	−1.55429	+	0.222992i
$666$		0			0
$667$	0.0237786	−	0.00637146i	0.000920711	−	0.000246704i
$668$	−8.58392	+	6.01053i	−0.332122	+	0.232554i
$669$		0			0
$670$	−0.931762	+	0.0515132i	−0.0359971	+	0.00199013i
$671$	29.8273	−	5.25936i	1.15147	−	0.203035i
$672$		0			0
$673$	21.4142	−	1.87350i	0.825458	−	0.0722182i	0.333405	−	0.942784i	$-0.391802\pi$
$673$	21.4142	−	1.87350i	0.825458	−	0.0722182i	0.492053	+	0.870565i	$0.336247\pi$
$674$	29.4436			1.13412
$675$		0			0
$676$	13.9285			0.535710
$677$	11.6890	−	1.02266i	0.449245	−	0.0393039i	0.139711	−	0.990192i	$-0.455383\pi$
$677$	11.6890	−	1.02266i	0.449245	−	0.0393039i	0.309534	+	0.950888i	$0.399827\pi$
$678$		0			0
$679$	−23.5937	+	4.16020i	−0.905442	+	0.159654i
$680$	−7.35177	+	0.406448i	−0.281927	+	0.0155866i
$681$		0			0
$682$	8.16473	−	5.71701i	0.312644	−	0.218916i
$683$	−32.6999	+	8.76191i	−1.25123	+	0.335265i	−0.822810	−	0.568316i	$-0.807595\pi$
$683$	−32.6999	+	8.76191i	−1.25123	+	0.335265i	−0.428416	+	0.903581i	$0.640928\pi$
$684$		0			0
$685$	2.29891	−	0.329820i	0.0878367	−	0.0126018i
$686$	8.39729	+	23.0714i	0.320610	+	0.880869i
$687$		0			0
$688$	3.17882	−	36.3341i	0.121191	−	1.38522i
$689$	−7.29974	+	6.12521i	−0.278098	+	0.233352i
$690$		0			0
$691$	26.6550	−	9.70163i	1.01400	−	0.369067i	0.219035	−	0.975717i	$-0.429709\pi$
$691$	26.6550	−	9.70163i	1.01400	−	0.369067i	0.794969	+	0.606650i	$0.207487\pi$
$692$	5.32421	+	1.42662i	0.202396	+	0.0542318i
$693$		0			0
$694$	−18.0076	−	10.3967i	−0.683561	−	0.394654i
$695$	−41.4482	+	9.69444i	−1.57222	+	0.367731i
$696$		0			0
$697$	−14.3975	−	30.8755i	−0.545343	−	1.16949i
$698$	0.260829	−	0.372502i	0.00987252	−	0.0140994i
$699$		0			0
$700$	−14.5255	+	18.1495i	−0.549011	+	0.685986i
$701$		−	44.1563i		−	1.66776i	−0.551945	−	0.833880i	$-0.686114\pi$
$701$		−	44.1563i		−	1.66776i	0.551945	−	0.833880i	$-0.313886\pi$
$702$		0			0
$703$	−41.4024	+	41.4024i	−1.56152	+	1.56152i
$704$	−9.51599	−	7.98487i	−0.358648	−	0.300941i
$705$		0			0
$706$	4.57734	+	25.9594i	0.172270	+	0.976994i
$707$	48.1017	−	22.4302i	1.80905	−	0.843574i
$708$		0			0
$709$	−16.3732	−	2.88704i	−0.614909	−	0.108425i	−0.142486	−	0.989797i	$-0.545510\pi$
$709$	−16.3732	−	2.88704i	−0.614909	−	0.108425i	−0.472423	+	0.881372i	$0.656621\pi$
$710$	−1.62573	+	1.27769i	−0.0610125	+	0.0479508i
$711$		0			0
$712$	−2.20492	+	8.22888i	−0.0826330	+	0.308390i
$713$	−1.77465	−	0.827531i	−0.0664610	−	0.0309913i
$714$		0			0
$715$	14.3989	−	4.72422i	0.538489	−	0.176676i
$716$	−5.28248	−	6.29542i	−0.197416	−	0.235271i
$717$		0			0
$718$	−0.791297	+	1.69694i	−0.0295310	+	0.0633293i
$719$	24.0796	+	41.7071i	0.898017	+	1.55541i	0.830026	+	0.557725i	$0.188326\pi$
$719$	24.0796	+	41.7071i	0.898017	+	1.55541i	0.0679908	+	0.997686i	$0.478341\pi$
$720$		0			0
$721$	−3.44891	+	5.97368i	−0.128444	+	0.222472i
$722$	−15.4897	−	22.1215i	−0.576466	−	0.823278i
$723$		0			0
$724$	7.59124	−	20.8568i	0.282126	−	0.775136i
$725$	−0.0784371	−	0.0522540i	−0.00291308	−	0.00194067i
$726$		0			0
$727$	−2.20894	−	25.2483i	−0.0819250	−	0.936407i	−0.920274	−	0.391274i	$-0.872035\pi$
$727$	−2.20894	−	25.2483i	−0.0819250	−	0.936407i	0.838349	−	0.545133i	$-0.183521\pi$
$728$	4.04821	+	4.04821i	0.150037	+	0.150037i
$729$		0			0
$730$	13.1775	+	30.7981i	0.487720	+	1.13989i
$731$	16.8608	−	20.0939i	0.623619	−	0.743200i
$732$		0			0
$733$	−12.1951	−	8.53910i	−0.450436	−	0.315399i	0.326253	−	0.945282i	$-0.394214\pi$
$733$	−12.1951	−	8.53910i	−0.450436	−	0.315399i	−0.776690	+	0.629883i	$0.783103\pi$
$734$	25.5488	+	9.29902i	0.943025	+	0.343233i
$735$		0			0
$736$	−1.58132	+	8.96809i	−0.0582881	+	0.330568i
$737$	0.206026	+	0.768900i	0.00758907	+	0.0283228i
$738$		0			0
$739$	23.0919	−	13.3321i	0.849450	−	0.490430i	−0.0110150	−	0.999939i	$-0.503506\pi$
$739$	23.0919	−	13.3321i	0.849450	−	0.490430i	0.860465	+	0.509509i	$0.170173\pi$
$740$	−1.07673	+	33.5974i	−0.0395812	+	1.23506i
$741$		0			0
$742$	−29.1483	−	2.55015i	−1.07007	−	0.0936188i
$743$	0.669700	+	0.0585912i	0.0245689	+	0.00214950i	0.0994336	−	0.995044i	$-0.468297\pi$
$743$	0.669700	+	0.0585912i	0.0245689	+	0.00214950i	−0.0748647	+	0.997194i	$0.523852\pi$
$744$		0			0
$745$	−4.80218	+	4.50393i	−0.175938	+	0.165011i
$746$	−57.7232	+	33.3265i	−2.11340	+	1.22017i
$747$		0			0
$748$	−4.69049	−	17.5051i	−0.171501	−	0.640052i
$749$	−10.6100	+	60.1723i	−0.387681	+	2.19865i
$750$		0			0
$751$	9.08514	+	3.30672i	0.331521	+	0.120664i	0.502417	−	0.864625i	$-0.332444\pi$
$751$	9.08514	+	3.30672i	0.331521	+	0.120664i	−0.170896	+	0.985289i	$0.554666\pi$
$752$	−42.9983	−	30.1077i	−1.56799	−	1.09791i
$753$		0			0
$754$	0.0430503	−	0.0513054i	0.00156780	−	0.00186843i
$755$	−36.2653	+	15.5167i	−1.31983	+	0.564709i
$756$		0			0
$757$	17.1950	+	17.1950i	0.624963	+	0.624963i	0.946796	−	0.321833i	$-0.104299\pi$
$757$	17.1950	+	17.1950i	0.624963	+	0.624963i	−0.321833	+	0.946796i	$0.604299\pi$
$758$	−5.40599	−	61.7907i	−0.196354	−	2.24434i
$759$		0			0
$760$	12.1663	+	2.54957i	0.441320	+	0.0924825i
$761$	13.4878	−	37.0575i	0.488933	−	1.34333i	−0.412715	−	0.910860i	$-0.635419\pi$
$761$	13.4878	−	37.0575i	0.488933	−	1.34333i	0.901647	−	0.432472i	$-0.142358\pi$
$762$		0			0
$763$	26.7874	+	38.2564i	0.969770	+	1.38498i
$764$	2.07582	−	3.59542i	0.0751005	−	0.130078i
$765$		0			0
$766$	−30.6399	−	53.0699i	−1.10707	−	1.91749i
$767$	4.51124	−	9.67438i	0.162891	−	0.349322i
$768$		0			0
$769$	33.2031	+	39.5700i	1.19734	+	1.42693i	0.877580	+	0.479429i	$0.159156\pi$
$769$	33.2031	+	39.5700i	1.19734	+	1.42693i	0.319756	+	0.947500i	$0.396399\pi$
$770$	41.5202	+	21.0058i	1.49629	+	0.756995i
$771$		0			0
$772$	16.0198	+	7.47014i	0.576564	+	0.268856i
$773$	8.14217	−	30.3870i	0.292853	−	1.09294i	−0.650054	−	0.759888i	$-0.725254\pi$
$773$	8.14217	−	30.3870i	0.292853	−	1.09294i	0.942907	−	0.333056i	$-0.108080\pi$
$774$		0			0
$775$	2.10769	+	7.19431i	0.0757106	+	0.258427i
$776$	7.24304	+	1.27714i	0.260010	+	0.0458468i
$777$		0			0
$778$	−9.04960	+	4.21990i	−0.324444	+	0.151291i
$779$	9.98726	+	56.6405i	0.357831	+	2.02936i
$780$		0			0
$781$	1.35115	+	1.13375i	0.0483480	+	0.0405688i
$782$	−5.90743	+	5.90743i	−0.211249	+	0.211249i
$783$		0			0
$784$			13.3343i			0.476227i
$785$	9.11545	+	17.0256i	0.325344	+	0.607670i
$786$		0			0
$787$	−13.4246	+	19.1723i	−0.478535	+	0.683419i	−0.983744	−	0.179579i	$-0.942527\pi$
$787$	−13.4246	+	19.1723i	−0.478535	+	0.683419i	0.505209	+	0.862997i	$0.331415\pi$
$788$	−12.3112	−	26.4014i	−0.438567	−	0.940511i
$789$		0			0
$790$	−3.90354	+	6.28705i	−0.138882	+	0.223683i
$791$	19.1782	+	11.0725i	0.681898	+	0.393694i
$792$		0			0
$793$	−15.6362	−	4.18971i	−0.555257	−	0.148781i
$794$	−53.8826	+	19.6117i	−1.91222	+	0.695992i
$795$		0			0
$796$	13.3588	−	11.2094i	0.473490	−	0.397305i
$797$	−0.552985	+	6.32065i	−0.0195877	+	0.223889i	0.980091	+	0.198548i	$0.0636226\pi$
$797$	−0.552985	+	6.32065i	−0.0195877	+	0.223889i	−0.999679	+	0.0253407i	$0.991933\pi$
$798$		0			0
$799$	−12.9116	−	35.4742i	−0.456778	−	1.25499i
$800$	29.7811	−	18.1277i	1.05292	−	0.640912i
$801$		0			0
$802$	−0.866846	+	0.232271i	−0.0306094	+	0.00820177i
$803$	23.4073	−	16.3900i	0.826027	−	0.578390i
$804$		0			0
$805$	−0.504609	−	9.12729i	−0.0177851	−	0.321695i
$806$	−5.24631	+	0.925065i	−0.184793	+	0.0325840i
$807$		0			0
$808$	−16.2313	+	1.42006i	−0.571016	+	0.0499574i
$809$	−2.19431			−0.0771479			−0.0385740	−	0.999256i	$-0.512282\pi$
$809$	−2.19431			−0.0771479			−0.0385740	+	0.999256i	$0.512282\pi$
$810$		0			0
$811$	6.26943			0.220149			0.110075	−	0.993923i	$-0.464891\pi$
$811$	6.26943			0.220149			0.110075	+	0.993923i	$0.464891\pi$
$812$	0.0873043	−	0.00763813i	0.00306378	−	0.000268046i
$813$		0			0
$814$	66.2630	−	11.6840i	2.32252	−	0.409523i
$815$	15.4357	−	17.2423i	0.540689	−	0.603973i
$816$		0			0
$817$	−36.2755	+	25.4004i	−1.26912	+	0.888646i
$818$	−40.9833	+	10.9814i	−1.43295	+	0.383957i
$819$		0			0
$820$	26.4270	+	19.7956i	0.922872	+	0.691291i
$821$	0.182595	+	0.501675i	0.00637260	+	0.0175086i	0.942838	−	0.333251i	$-0.108146\pi$
$821$	0.182595	+	0.501675i	0.00637260	+	0.0175086i	−0.936466	+	0.350760i	$0.885923\pi$
$822$		0			0
$823$	0.0403877	−	0.461633i	0.00140783	−	0.0160915i	−0.995458	−	0.0951987i	$-0.969651\pi$
$823$	0.0403877	−	0.461633i	0.00140783	−	0.0160915i	0.996866	+	0.0791071i	$0.0252069\pi$
$824$	1.62215	−	1.36115i	0.0565103	−	0.0474177i
$825$		0			0
$826$	30.7999	−	11.2102i	1.07167	−	0.390054i
$827$	29.9299	+	8.01968i	1.04076	+	0.278872i	0.738430	−	0.674331i	$-0.235568\pi$
$827$	29.9299	+	8.01968i	1.04076	+	0.278872i	0.302333	+	0.953202i	$0.402234\pi$
$828$		0			0
$829$	−35.8944	−	20.7236i	−1.24666	−	0.719761i	−0.276220	−	0.961094i	$-0.589082\pi$
$829$	−35.8944	−	20.7236i	−1.24666	−	0.719761i	−0.970442	+	0.241334i	$0.922415\pi$
$830$	7.02113	+	30.0186i	0.243707	+	1.04196i
$831$		0			0
$832$	2.80591	+	6.01729i	0.0972773	+	0.208612i
$833$	−5.50052	+	7.85556i	−0.190582	+	0.272179i
$834$		0			0
$835$	−13.9083	+	7.44647i	−0.481318	+	0.257696i
$836$			30.5957i			1.05817i
$837$		0			0
$838$	−14.2317	+	14.2317i	−0.491627	+	0.491627i
$839$	−23.3960	−	19.6316i	−0.807719	−	0.677757i	0.142343	−	0.989817i	$-0.454536\pi$
$839$	−23.3960	−	19.6316i	−0.807719	−	0.677757i	−0.950062	+	0.312060i	$0.898981\pi$
$840$		0			0
$841$	−5.03574	−	28.5591i	−0.173646	−	0.984796i
$842$	42.3806	−	19.7624i	1.46053	−	0.681057i
$843$		0			0
$844$	−8.99130	−	1.58541i	−0.309493	−	0.0545720i
$845$	20.8204	+	2.49579i	0.716243	+	0.0858579i
$846$		0			0
$847$	1.36113	−	5.07982i	0.0467691	−	0.174545i
$848$	21.6204	+	10.0818i	0.742447	+	0.346209i
$849$		0			0
$850$	31.9195	+	2.04801i	1.09483	+	0.0702460i
$851$	−8.49661	−	10.1259i	−0.291260	−	0.347110i
$852$		0			0
$853$	−17.7118	+	37.9830i	−0.606439	+	1.30051i	0.328097	+	0.944644i	$0.393593\pi$
$853$	−17.7118	+	37.9830i	−0.606439	+	1.30051i	−0.934536	+	0.355869i	$0.884185\pi$
$854$	−24.8527	−	43.0461i	−0.850441	−	1.47301i
$855$		0			0
$856$	9.37865	−	16.2443i	0.320556	−	0.555219i
$857$	0.814484	+	1.16320i	0.0278222	+	0.0397343i	0.832822	−	0.553541i	$-0.186724\pi$
$857$	0.814484	+	1.16320i	0.0278222	+	0.0397343i	−0.805000	+	0.593275i	$0.797835\pi$
$858$		0			0
$859$	7.27047	−	19.9755i	0.248065	−	0.681554i	−0.751692	−	0.659515i	$-0.770762\pi$
$859$	7.27047	−	19.9755i	0.248065	−	0.681554i	0.999757	−	0.0220394i	$-0.00701591\pi$
$860$	−5.21447	+	24.8830i	−0.177812	+	0.848505i
$861$		0			0
$862$	−2.29842	−	26.2711i	−0.0782845	−	0.894796i
$863$	−17.8190	−	17.8190i	−0.606565	−	0.606565i	0.335482	−	0.942047i	$-0.391101\pi$
$863$	−17.8190	−	17.8190i	−0.606565	−	0.606565i	−0.942047	+	0.335482i	$0.891101\pi$
$864$		0			0
$865$	7.70304	+	3.08655i	0.261911	+	0.104946i
$866$	−3.10152	+	3.69624i	−0.105394	+	0.125603i
$867$		0			0
$868$	−5.71017	−	3.99830i	−0.193816	−	0.135711i
$869$	5.93190	+	2.15904i	0.201226	+	0.0732403i
$870$		0			0
$871$	0.0738790	−	0.418989i	0.00250329	−	0.0141969i
$872$	−3.71075	−	13.8487i	−0.125662	−	0.468976i
$873$		0			0
$874$	12.2147	−	7.05216i	0.413168	−	0.238543i
$875$	−24.9650	+	24.5272i	−0.843970	+	0.829172i
$876$		0			0
$877$	48.5508	+	4.24765i	1.63944	+	0.143433i	0.869249	−	0.494375i	$-0.164603\pi$
$877$	48.5508	+	4.24765i	1.63944	+	0.143433i	0.770196	+	0.637808i	$0.220159\pi$
$878$	−45.4435	−	3.97579i	−1.53364	−	0.134176i
$879$		0			0
$880$	−25.9526	−	27.6711i	−0.874863	−	0.932794i
$881$	6.73697	−	3.88959i	0.226974	−	0.131044i	−0.382201	−	0.924079i	$-0.624834\pi$
$881$	6.73697	−	3.88959i	0.226974	−	0.131044i	0.609175	+	0.793036i	$0.291501\pi$
$882$		0			0
$883$	3.63385	+	13.5617i	0.122289	+	0.456388i	0.999729	−	0.0232990i	$-0.00741698\pi$
$883$	3.63385	+	13.5617i	0.122289	+	0.456388i	−0.877440	+	0.479687i	$0.840750\pi$
$884$	−1.68197	+	9.53890i	−0.0565706	+	0.320828i
$885$		0			0
$886$	−51.8954	−	18.8884i	−1.74346	−	0.634568i
$887$	−33.1326	−	23.1997i	−1.11248	−	0.778969i	−0.135182	−	0.990821i	$-0.543162\pi$
$887$	−33.1326	−	23.1997i	−1.11248	−	0.778969i	−0.977302	+	0.211851i	$0.932051\pi$
$888$		0			0
$889$	2.88163	−	3.43420i	0.0966469	−	0.115179i
$890$	13.7648	−	34.3525i	0.461396	−	1.15150i
$891$		0			0
$892$	10.1256	+	10.1256i	0.339030	+	0.339030i
$893$	5.55471	+	63.4906i	0.185881	+	2.12463i
$894$		0			0
$895$	−6.76825	−	10.3570i	−0.226238	−	0.346196i
$896$	7.95805	−	21.8646i	0.265860	−	0.730444i
$897$		0			0
$898$	−32.6473	−	46.6252i	−1.08946	−	1.55590i
$899$	0.0141311	−	0.0244758i	0.000471299	−	0.000816314i
$900$		0			0
$901$	8.57825	+	14.8580i	0.285783	+	0.494990i
$902$	27.9321	−	59.9005i	0.930037	−	1.99447i
$903$		0			0
$904$	−4.36988	−	5.20782i	−0.145340	−	0.173210i
$905$	15.0847	−	29.8166i	0.501433	−	0.991139i
$906$		0			0
$907$	−14.0475	−	6.55044i	−0.466438	−	0.217504i	0.175167	−	0.984539i	$-0.443953\pi$
$907$	−14.0475	−	6.55044i	−0.466438	−	0.217504i	−0.641605	+	0.767035i	$0.721731\pi$
$908$	−0.351496	+	1.31180i	−0.0116648	+	0.0435337i
$909$		0			0
$910$	−15.3675	−	19.5536i	−0.509428	−	0.648195i
$911$	−21.0612	−	3.71365i	−0.697788	−	0.123039i	−0.186508	−	0.982453i	$-0.559717\pi$
$911$	−21.0612	−	3.71365i	−0.697788	−	0.123039i	−0.511279	+	0.859415i	$0.670828\pi$
$912$		0			0
$913$	23.8336	−	11.1138i	0.788777	−	0.367813i
$914$	−3.03339	−	17.2032i	−0.100336	−	0.569032i
$915$		0			0
$916$	5.38037	+	4.51467i	0.177773	+	0.149169i
$917$	−13.4670	+	13.4670i	−0.444720	+	0.444720i
$918$		0			0
$919$		−	10.8447i		−	0.357733i	−0.983873	−	0.178867i	$-0.942757\pi$
$919$		−	10.8447i		−	0.357733i	0.983873	−	0.178867i	$-0.0572431\pi$
$920$	−0.812770	+	2.68600i	−0.0267962	+	0.0885547i
$921$		0			0
$922$	−6.93317	+	9.90159i	−0.228332	+	0.326091i
$923$	−0.398404	−	0.854379i	−0.0131136	−	0.0281222i
$924$		0			0
$925$	−7.62970	+	50.0287i	−0.250863	+	1.64494i
$926$	21.4947	+	12.4100i	0.706360	+	0.407817i
$927$		0			0
$928$	−0.126959	−	0.0340185i	−0.00416762	−	0.00111671i
$929$	−27.6616	+	10.0680i	−0.907549	+	0.330321i	−0.753274	−	0.657707i	$-0.771526\pi$
$929$	−27.6616	+	10.0680i	−0.907549	+	0.330321i	−0.154275	+	0.988028i	$0.549304\pi$
$930$		0			0
$931$	12.4024	−	10.4068i	0.406471	−	0.341070i
$932$	0.524079	−	5.99025i	0.0171668	−	0.196217i
$933$		0			0
$934$	−13.9911	−	38.4403i	−0.457804	−	1.25781i
$935$	−3.87470	−	27.0073i	−0.126716	−	0.883234i
$936$		0			0
$937$	9.22780	−	2.47258i	0.301459	−	0.0807757i	−0.104919	−	0.994481i	$-0.533458\pi$
$937$	9.22780	−	2.47258i	0.301459	−	0.0807757i	0.406378	+	0.913705i	$0.366792\pi$
$938$	1.07012	−	0.749304i	0.0349405	−	0.0244656i
$939$		0			0
$940$	27.2612	+	24.4048i	0.889163	+	0.795997i
$941$	−34.3869	+	6.06333i	−1.12098	+	0.197659i	−0.703271	−	0.710922i	$-0.748278\pi$
$941$	−34.3869	+	6.06333i	−1.12098	+	0.197659i	−0.417709	+	0.908581i	$0.637167\pi$
$942$		0			0
$943$	−12.9347	+	1.13164i	−0.421213	+	0.0368514i
$944$	−26.7228			−0.869754
$945$		0			0
$946$	50.8894			1.65456
$947$	9.06188	−	0.792811i	0.294471	−	0.0257629i	0.0610371	−	0.998135i	$-0.480559\pi$
$947$	9.06188	−	0.792811i	0.294471	−	0.0257629i	0.233434	+	0.972373i	$0.425004\pi$
$948$		0			0
$949$	−15.0405	+	2.65205i	−0.488237	+	0.0860893i
$950$	−51.1571	−	17.2870i	−1.65976	−	0.560866i
$951$		0			0
$952$	8.44340	−	5.91213i	0.273652	−	0.191613i
$953$	6.76251	−	1.81201i	0.219059	−	0.0586968i	−0.147620	−	0.989044i	$-0.547161\pi$
$953$	6.76251	−	1.81201i	0.219059	−	0.0586968i	0.366679	+	0.930347i	$0.380495\pi$
$954$		0			0
$955$	3.74720	−	5.00251i	0.121257	−	0.161877i
$956$	−7.38550	−	20.2915i	−0.238864	−	0.656274i
$957$		0			0
$958$	−2.58282	+	29.5217i	−0.0834470	+	0.953803i
$959$	−2.49057	+	2.08983i	−0.0804246	+	0.0674842i
$960$		0			0
$961$	27.0180	−	9.83376i	0.871549	−	0.317218i
$962$	−34.7367	−	9.30767i	−1.11996	−	0.300091i
$963$		0			0
$964$	−20.6702	−	11.9340i	−0.665743	−	0.384367i
$965$	22.6079	+	14.0370i	0.727775	+	0.451866i
$966$		0			0
$967$	5.53995	+	11.8805i	0.178153	+	0.382050i	0.975024	−	0.222099i	$-0.0712909\pi$
$967$	5.53995	+	11.8805i	0.178153	+	0.382050i	−0.796871	+	0.604149i	$0.793513\pi$
$968$	−0.926022	+	1.32250i	−0.0297635	+	0.0425066i
$969$		0			0
$970$	−30.5800	−	9.25338i	−0.981866	−	0.297108i
$971$			10.0161i			0.321431i	0.987001	+	0.160716i	$0.0513802\pi$
$971$			10.0161i			0.321431i	−0.987001	+	0.160716i	$0.948620\pi$
$972$		0			0
$973$	42.1362	−	42.1362i	1.35082	−	1.35082i
$974$	19.5766	+	16.4268i	0.627276	+	0.526347i
$975$		0			0
$976$	7.03707	+	39.9092i	0.225251	+	1.27746i
$977$	32.0639	−	14.9516i	1.02581	−	0.478345i	0.164479	−	0.986381i	$-0.447406\pi$
$977$	32.0639	−	14.9516i	1.02581	−	0.478345i	0.861336	+	0.508035i	$0.169628\pi$
$978$		0			0
$979$	−31.0885	−	5.48175i	−0.993594	−	0.175197i
$980$	1.10627	−	9.22869i	0.0353384	−	0.294800i
$981$		0			0
$982$	13.2322	−	49.3834i	0.422258	−	1.57589i
$983$	−39.3025	−	18.3271i	−1.25356	−	0.584543i	−0.321518	−	0.946903i	$-0.604193\pi$
$983$	−39.3025	−	18.3271i	−1.25356	−	0.584543i	−0.932038	+	0.362361i	$0.881971\pi$
$984$		0			0
$985$	−13.6721	−	41.6711i	−0.435629	−	1.32775i
$986$	−0.0775089	−	0.0923715i	−0.00246839	−	0.00294171i
$987$		0			0
$988$	6.91088	−	14.8204i	0.219864	−	0.471500i
$989$	−4.99869	−	8.65798i	−0.158949	−	0.275308i
$990$		0			0
$991$	−2.24550	+	3.88933i	−0.0713308	+	0.123549i	−0.899485	−	0.436952i	$-0.856058\pi$
$991$	−2.24550	+	3.88933i	−0.0713308	+	0.123549i	0.828154	+	0.560501i	$0.189391\pi$
$992$	5.99658	+	8.56400i	0.190392	+	0.271907i
$993$		0			0
$994$	0.990017	−	2.72005i	0.0314014	−	0.0862747i
$995$	21.9774	−	14.3621i	0.696731	−	0.455310i
$996$		0			0
$997$	1.90368	+	21.7592i	0.0602903	+	0.689121i	0.964855	+	0.262784i	$0.0846407\pi$
$997$	1.90368	+	21.7592i	0.0602903	+	0.689121i	−0.904564	+	0.426337i	$0.859804\pi$
$998$	−5.84148	−	5.84148i	−0.184909	−	0.184909i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.197.4		192
3.2	odd	2		135.2.q.a.92.13	yes	192
5.3	odd	4	inner	405.2.r.a.278.13		192
15.2	even	4		675.2.ba.b.443.13		192
15.8	even	4		135.2.q.a.38.4	yes	192
15.14	odd	2		675.2.ba.b.632.4		192
27.5	odd	18	inner	405.2.r.a.287.13		192
27.22	even	9		135.2.q.a.32.4	✓	192
135.22	odd	36		675.2.ba.b.518.4		192
135.49	even	18		675.2.ba.b.32.13		192
135.103	odd	36		135.2.q.a.113.13	yes	192
135.113	even	36	inner	405.2.r.a.368.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.4	✓	192	27.22	even	9
135.2.q.a.38.4	yes	192	15.8	even	4
135.2.q.a.92.13	yes	192	3.2	odd	2
135.2.q.a.113.13	yes	192	135.103	odd	36
405.2.r.a.197.4		192	1.1	even	1	trivial
405.2.r.a.278.13		192	5.3	odd	4	inner
405.2.r.a.287.13		192	27.5	odd	18	inner
405.2.r.a.368.4		192	135.113	even	36	inner
675.2.ba.b.32.13		192	135.49	even	18
675.2.ba.b.443.13		192	15.2	even	4
675.2.ba.b.518.4		192	135.22	odd	36
675.2.ba.b.632.4		192	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.85978 + 0.162710i) q^{2} +(1.46269 - 0.257912i) q^{4} +(2.23266 - 0.123434i) q^{5} +(-2.56418 + 1.79546i) q^{7} +(0.928224 - 0.248717i) q^{8} +O(q^{10})\)	\(q+(-1.85978 + 0.162710i) q^{2} +(1.46269 - 0.257912i) q^{4} +(2.23266 - 0.123434i) q^{5} +(-2.56418 + 1.79546i) q^{7} +(0.928224 - 0.248717i) q^{8} +(-4.13217 + 0.592836i) q^{10} +(1.21790 + 3.34616i) q^{11} +(0.165875 - 1.89596i) q^{13} +(4.47667 - 3.75637i) q^{14} +(-4.47719 + 1.62956i) q^{16} +(-3.30982 - 0.886863i) q^{17} +(5.00990 + 2.89247i) q^{19} +(3.23385 - 0.756375i) q^{20} +(-2.80948 - 6.02495i) q^{22} +(-0.749079 + 1.06979i) q^{23} +(4.96953 - 0.551173i) q^{25} +3.55306i q^{26} +(-3.28753 + 3.28753i) q^{28} +(-0.0144398 - 0.0121164i) q^{29} +(0.260357 + 1.47656i) q^{31} +(6.31958 - 2.94687i) q^{32} +(6.29984 + 1.11083i) q^{34} +(-5.50331 + 4.32515i) q^{35} +(-2.61962 + 9.77656i) q^{37} +(-9.78795 - 4.56420i) q^{38} +(2.04171 - 0.669874i) q^{40} +(6.39065 + 7.61608i) q^{41} +(-3.23518 + 6.93786i) q^{43} +(2.64443 + 4.58028i) q^{44} +(1.21906 - 2.11147i) q^{46} +(6.31914 + 9.02466i) q^{47} +(0.957202 - 2.62989i) q^{49} +(-9.15255 + 1.83365i) q^{50} +(-0.246367 - 2.81599i) q^{52} +(-3.54041 - 3.54041i) q^{53} +(3.13219 + 7.32049i) q^{55} +(-1.93357 + 2.30434i) q^{56} +(0.0288263 + 0.0201844i) q^{58} +(5.27046 + 1.91829i) q^{59} +(1.47697 - 8.37633i) q^{61} +(-0.724458 - 2.70371i) q^{62} +(-3.02114 + 1.74425i) q^{64} +(0.136316 - 4.25351i) q^{65} +(0.222695 + 0.0194833i) q^{67} +(-5.06998 - 0.443565i) q^{68} +(9.53121 - 8.93927i) q^{70} +(0.428964 - 0.247662i) q^{71} +(-2.07694 - 7.75123i) q^{73} +(3.28118 - 18.6085i) q^{74} +(8.07394 + 2.93867i) q^{76} +(-9.13079 - 6.39345i) q^{77} +(1.13950 - 1.35801i) q^{79} +(-9.79489 + 4.19090i) q^{80} +(-13.1244 - 13.1244i) q^{82} +(-0.643650 - 7.35695i) q^{83} +(-7.49916 - 1.57152i) q^{85} +(4.88786 - 13.4293i) q^{86} +(1.96273 + 2.80307i) q^{88} +(-4.43260 + 7.67748i) q^{89} +(2.97878 + 5.15940i) q^{91} +(-0.819758 + 1.75798i) q^{92} +(-13.2206 - 15.7557i) q^{94} +(11.5424 + 5.83950i) q^{95} +(6.93643 + 3.23451i) q^{97} +(-1.35228 + 5.04676i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 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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