LMFDB - Embedded newform 396.2.r.b.271.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(19,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("396.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.r (of order $10$, degree $4$, 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			271.4
Character	$\chi$	$=$	396.271
Dual form			396.2.r.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690263 + 1.23432i) q^{2} +(-1.04707 - 1.70401i) q^{4} +(-0.725620 + 0.527194i) q^{5} +(0.489790 + 1.50742i) q^{7} +(2.82604 - 0.116210i) q^{8} +O(q^{10})$	\(q+(-0.690263 + 1.23432i) q^{2} +(-1.04707 - 1.70401i) q^{4} +(-0.725620 + 0.527194i) q^{5} +(0.489790 + 1.50742i) q^{7} +(2.82604 - 0.116210i) q^{8} +(-0.149856 - 1.25955i) q^{10} +(2.62111 + 2.03219i) q^{11} +(-0.605536 + 0.833449i) q^{13} +(-2.19871 - 0.435959i) q^{14} +(-1.80727 + 3.56844i) q^{16} +(-2.49130 - 3.42898i) q^{17} +(-1.32556 + 4.07966i) q^{19} +(1.65812 + 0.684449i) q^{20} +(-4.31762 + 1.83254i) q^{22} +8.34003i q^{23} +(-1.29649 + 3.99020i) q^{25} +(-0.610761 - 1.32272i) q^{26} +(2.05580 - 2.41298i) q^{28} +(-0.588090 + 0.191082i) q^{29} +(-3.11863 + 4.29243i) q^{31} +(-3.15710 - 4.69391i) q^{32} +(5.95210 - 0.708155i) q^{34} +(-1.15010 - 0.835598i) q^{35} +(-0.924210 - 2.84443i) q^{37} +(-4.12061 - 4.45220i) q^{38} +(-1.98937 + 1.57419i) q^{40} +(0.0662322 + 0.0215201i) q^{41} +6.67734 q^{43} +(0.718360 - 6.59424i) q^{44} +(-10.2942 - 5.75681i) q^{46} +(1.49099 + 0.484451i) q^{47} +(3.63071 - 2.63786i) q^{49} +(-4.03025 - 4.35457i) q^{50} +(2.05424 + 0.159154i) q^{52} +(9.74373 + 7.07923i) q^{53} +(-2.97329 - 0.0927624i) q^{55} +(1.55934 + 4.20310i) q^{56} +(0.170081 - 0.857787i) q^{58} +(-7.81130 + 2.53804i) q^{59} +(-7.51474 - 10.3431i) q^{61} +(-3.14554 - 6.81229i) q^{62} +(7.97299 - 0.656828i) q^{64} -0.924002i q^{65} -13.8430i q^{67} +(-3.23442 + 7.83559i) q^{68} +(1.82526 - 0.842808i) q^{70} +(3.76717 + 5.18506i) q^{71} +(-4.25213 + 1.38160i) q^{73} +(4.14887 + 0.822634i) q^{74} +(8.33973 - 2.01294i) q^{76} +(-1.77956 + 4.94645i) q^{77} +(6.25795 + 4.54667i) q^{79} +(-0.569869 - 3.54211i) q^{80} +(-0.0722803 + 0.0668969i) q^{82} +(12.5105 - 9.08942i) q^{83} +(3.61547 + 1.17474i) q^{85} +(-4.60912 + 8.24196i) q^{86} +(7.64352 + 5.43844i) q^{88} -3.00882 q^{89} +(-1.55294 - 0.504581i) q^{91} +(14.2114 - 8.73263i) q^{92} +(-1.62714 + 1.50595i) q^{94} +(-1.18892 - 3.65911i) q^{95} +(11.6217 + 8.44368i) q^{97} +(0.749816 + 6.30226i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} + 14 q^{14} - 24 q^{16} + 22 q^{20} - 26 q^{22} - 20 q^{25} + 38 q^{26} - 10 q^{28} - 48 q^{37} - 58 q^{38} + 70 q^{40} + 40 q^{41} - 34 q^{44} + 70 q^{46} - 28 q^{49} - 70 q^{50} + 30 q^{52} + 64 q^{53} - 60 q^{56} - 54 q^{58} - 40 q^{64} + 4 q^{70} + 20 q^{73} - 50 q^{74} + 8 q^{77} - 58 q^{80} + 62 q^{82} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 48 q^{89} - 42 q^{92} - 10 q^{94} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 14 * q^14 - 24 * q^16 + 22 * q^20 - 26 * q^22 - 20 * q^25 + 38 * q^26 - 10 * q^28 - 48 * q^37 - 58 * q^38 + 70 * q^40 + 40 * q^41 - 34 * q^44 + 70 * q^46 - 28 * q^49 - 70 * q^50 + 30 * q^52 + 64 * q^53 - 60 * q^56 - 54 * q^58 - 40 * q^64 + 4 * q^70 + 20 * q^73 - 50 * q^74 + 8 * q^77 - 58 * q^80 + 62 * q^82 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 48 * q^89 - 42 * q^92 - 10 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.690263	+	1.23432i	−0.488089	+	0.872794i
$2$	−0.690263	+	1.23432i	−0.488089	+	0.872794i
$3$		0			0
$3$		0			0
$4$	−1.04707	−	1.70401i	−0.523537	−	0.852003i
$5$	−0.725620	+	0.527194i	−0.324507	+	0.235768i	−0.738096	−	0.674695i	$-0.764275\pi$
$5$	−0.725620	+	0.527194i	−0.324507	+	0.235768i	0.413589	+	0.910464i	$0.364275\pi$
$6$		0			0
$7$	0.489790	+	1.50742i	0.185123	+	0.569750i	0.999950	−	0.00995348i	$-0.00316834\pi$
$7$	0.489790	+	1.50742i	0.185123	+	0.569750i	−0.814827	+	0.579704i	$0.803168\pi$
$8$	2.82604	−	0.116210i	0.999156	−	0.0410864i
$9$		0			0
$10$	−0.149856	−	1.25955i	−0.0473885	−	0.398304i
$11$	2.62111	+	2.03219i	0.790294	+	0.612727i
$11$	2.62111	+	2.03219i	0.790294	+	0.612727i
$12$		0			0
$13$	−0.605536	+	0.833449i	−0.167945	+	0.231157i	−0.884691	−	0.466177i	$-0.845631\pi$
$13$	−0.605536	+	0.833449i	−0.167945	+	0.231157i	0.716746	+	0.697335i	$0.245631\pi$
$14$	−2.19871	−	0.435959i	−0.587631	−	0.116515i
$15$		0			0
$16$	−1.80727	+	3.56844i	−0.451817	+	0.892110i
$17$	−2.49130	−	3.42898i	−0.604229	−	0.831650i	0.391858	−	0.920026i	$-0.371832\pi$
$17$	−2.49130	−	3.42898i	−0.604229	−	0.831650i	−0.996087	+	0.0883758i	$0.971832\pi$
$18$		0			0
$19$	−1.32556	+	4.07966i	−0.304105	+	0.935938i	0.675905	+	0.736989i	$0.263753\pi$
$19$	−1.32556	+	4.07966i	−0.304105	+	0.935938i	−0.980010	+	0.198950i	$0.936247\pi$
$20$	1.65812	+	0.684449i	0.370767	+	0.153047i
$21$		0			0
$22$	−4.31762	+	1.83254i	−0.920519	+	0.390698i
$23$			8.34003i			1.73902i	0.493919	+	0.869508i	$0.335564\pi$
$23$			8.34003i			1.73902i	−0.493919	+	0.869508i	$0.664436\pi$
$24$		0			0
$25$	−1.29649	+	3.99020i	−0.259299	+	0.798040i
$26$	−0.610761	−	1.32272i	−0.119780	−	0.259407i
$27$		0			0
$28$	2.05580	−	2.41298i	0.388510	−	0.456011i
$29$	−0.588090	+	0.191082i	−0.109206	+	0.0354831i	−0.363110	−	0.931746i	$-0.618285\pi$
$29$	−0.588090	+	0.191082i	−0.109206	+	0.0354831i	0.253904	+	0.967229i	$0.418285\pi$
$30$		0			0
$31$	−3.11863	+	4.29243i	−0.560123	+	0.770943i	−0.991342	−	0.131304i	$-0.958084\pi$
$31$	−3.11863	+	4.29243i	−0.560123	+	0.770943i	0.431219	+	0.902247i	$0.358084\pi$
$32$	−3.15710	−	4.69391i	−0.558101	−	0.829773i
$33$		0			0
$34$	5.95210	−	0.708155i	1.02078	−	0.121448i
$35$	−1.15010	−	0.835598i	−0.194403	−	0.141242i
$36$		0			0
$37$	−0.924210	−	2.84443i	−0.151939	−	0.467621i	0.845899	−	0.533344i	$-0.179065\pi$
$37$	−0.924210	−	2.84443i	−0.151939	−	0.467621i	−0.997838	+	0.0657227i	$0.979065\pi$
$38$	−4.12061	−	4.45220i	−0.668451	−	0.722242i
$39$		0			0
$40$	−1.98937	+	1.57419i	−0.314546	+	0.248902i
$41$	0.0662322	+	0.0215201i	0.0103437	+	0.00336088i	0.314184	−	0.949362i	$-0.398269\pi$
$41$	0.0662322	+	0.0215201i	0.0103437	+	0.00336088i	−0.303841	+	0.952723i	$0.598269\pi$
$42$		0			0
$43$	6.67734			1.01829			0.509143	−	0.860682i	$-0.329963\pi$
$43$	6.67734			1.01829			0.509143	+	0.860682i	$0.329963\pi$
$44$	0.718360	−	6.59424i	0.108297	−	0.994119i
$45$		0			0
$46$	−10.2942	−	5.75681i	−1.51780	−	0.848795i
$47$	1.49099	+	0.484451i	0.217483	+	0.0706644i	0.415732	−	0.909487i	$-0.363525\pi$
$47$	1.49099	+	0.484451i	0.217483	+	0.0706644i	−0.198249	+	0.980152i	$0.563525\pi$
$48$		0			0
$49$	3.63071	−	2.63786i	0.518672	−	0.376838i
$50$	−4.03025	−	4.35457i	−0.569963	−	0.615829i
$51$		0			0
$52$	2.05424	+	0.159154i	0.284872	+	0.0220706i
$53$	9.74373	+	7.07923i	1.33840	+	0.972407i	0.999501	+	0.0315858i	$0.0100557\pi$
$53$	9.74373	+	7.07923i	1.33840	+	0.972407i	0.338903	+	0.940821i	$0.389944\pi$
$54$		0			0
$55$	−2.97329	−	0.0927624i	−0.400918	−	0.0125081i
$56$	1.55934	+	4.20310i	0.208376	+	0.561663i
$57$		0			0
$58$	0.170081	−	0.857787i	0.0223327	−	0.112633i
$59$	−7.81130	+	2.53804i	−1.01694	+	0.330425i	−0.769616	−	0.638507i	$-0.779553\pi$
$59$	−7.81130	+	2.53804i	−1.01694	+	0.330425i	−0.247328	+	0.968932i	$0.579553\pi$
$60$		0			0
$61$	−7.51474	−	10.3431i	−0.962163	−	1.32430i	−0.945908	−	0.324436i	$-0.894825\pi$
$61$	−7.51474	−	10.3431i	−0.962163	−	1.32430i	−0.0162558	−	0.999868i	$-0.505175\pi$
$62$	−3.14554	−	6.81229i	−0.399484	−	0.865161i
$63$		0			0
$64$	7.97299	−	0.656828i	0.996624	−	0.0821034i
$65$		−	0.924002i		−	0.114608i
$66$		0			0
$67$		−	13.8430i		−	1.69120i	−0.533820	−	0.845598i	$-0.679244\pi$
$67$		−	13.8430i		−	1.69120i	0.533820	−	0.845598i	$-0.320756\pi$
$68$	−3.23442	+	7.83559i	−0.392232	+	0.950204i
$69$		0			0
$70$	1.82526	−	0.842808i	0.218161	−	0.100735i
$71$	3.76717	+	5.18506i	0.447081	+	0.615354i	0.971767	−	0.235942i	$-0.0758175\pi$
$71$	3.76717	+	5.18506i	0.447081	+	0.615354i	−0.524687	+	0.851296i	$0.675817\pi$
$72$		0			0
$73$	−4.25213	+	1.38160i	−0.497674	+	0.161704i	−0.547090	−	0.837074i	$-0.684264\pi$
$73$	−4.25213	+	1.38160i	−0.497674	+	0.161704i	0.0494151	+	0.998778i	$0.484264\pi$
$74$	4.14887	+	0.822634i	0.482296	+	0.0956293i
$75$		0			0
$76$	8.33973	−	2.01294i	0.956632	−	0.230901i
$77$	−1.77956	+	4.94645i	−0.202800	+	0.563700i
$78$		0			0
$79$	6.25795	+	4.54667i	0.704075	+	0.511540i	0.881257	−	0.472638i	$-0.156698\pi$
$79$	6.25795	+	4.54667i	0.704075	+	0.511540i	−0.177182	+	0.984178i	$0.556698\pi$
$80$	−0.569869	−	3.54211i	−0.0637133	−	0.396020i
$81$		0			0
$82$	−0.0722803	+	0.0668969i	−0.00798202	+	0.00738753i
$83$	12.5105	−	9.08942i	1.37321	−	0.997694i	0.375729	−	0.926730i	$-0.377392\pi$
$83$	12.5105	−	9.08942i	1.37321	−	0.997694i	0.997479	−	0.0709643i	$-0.0226076\pi$
$84$		0			0
$85$	3.61547	+	1.17474i	0.392153	+	0.127418i
$86$	−4.60912	+	8.24196i	−0.497014	+	0.888753i
$87$		0			0
$88$	7.64352	+	5.43844i	0.814802	+	0.579740i
$89$	−3.00882			−0.318935			−0.159467	−	0.987203i	$-0.550978\pi$
$89$	−3.00882			−0.318935			−0.159467	+	0.987203i	$0.550978\pi$
$90$		0			0
$91$	−1.55294	−	0.504581i	−0.162792	−	0.0528944i
$92$	14.2114	−	8.73263i	1.48165	−	0.910439i
$93$		0			0
$94$	−1.62714	+	1.50595i	−0.167827	+	0.155327i
$95$	−1.18892	−	3.65911i	−0.121980	−	0.375417i
$96$		0			0
$97$	11.6217	+	8.44368i	1.18001	+	0.857326i	0.992173	−	0.124874i	$-0.0398528\pi$
$97$	11.6217	+	8.44368i	1.18001	+	0.857326i	0.187836	+	0.982200i	$0.439853\pi$
$98$	0.749816	+	6.30226i	0.0757428	+	0.636624i
$99$		0			0
$100$	8.15685	−	1.96880i	0.815685	−	0.196880i
$101$	−4.90138	+	6.74617i	−0.487706	+	0.671269i	−0.979963	−	0.199180i	$-0.936172\pi$
$101$	−4.90138	+	6.74617i	−0.487706	+	0.671269i	0.492257	+	0.870450i	$0.336172\pi$
$102$		0			0
$103$	14.9233	−	4.84888i	1.47044	−	0.477775i	0.539198	−	0.842179i	$-0.318727\pi$
$103$	14.9233	−	4.84888i	1.47044	−	0.477775i	0.931241	+	0.364404i	$0.118727\pi$
$104$	−1.61441	+	2.42573i	−0.158306	+	0.237862i
$105$		0			0
$106$	−15.4637	+	7.14031i	−1.50197	+	0.693528i
$107$	2.22580	−	6.85031i	0.215176	−	0.662244i	−0.783965	−	0.620805i	$-0.786806\pi$
$107$	2.22580	−	6.85031i	0.215176	−	0.662244i	0.999141	−	0.0414391i	$-0.0131942\pi$
$108$		0			0
$109$			1.57116i			0.150490i	0.997165	+	0.0752449i	$0.0239738\pi$
$109$			1.57116i			0.150490i	−0.997165	+	0.0752449i	$0.976026\pi$
$110$	2.16685	−	3.60595i	0.206601	−	0.343813i
$111$		0			0
$112$	−6.26431	−	0.976524i	−0.591922	−	0.0922728i
$113$	3.51144	−	10.8071i	0.330328	−	1.01665i	−0.638649	−	0.769498i	$-0.720506\pi$
$113$	3.51144	−	10.8071i	0.330328	−	1.01665i	0.968978	−	0.247148i	$-0.0794935\pi$
$114$		0			0
$115$	−4.39681	−	6.05169i	−0.410005	−	0.564323i
$116$	0.941380	+	0.802032i	0.0874049	+	0.0744668i
$117$		0			0
$118$	2.25910	−	11.3935i	0.207967	−	1.04886i
$119$	3.94869	−	5.43491i	0.361976	−	0.498217i
$120$		0			0
$121$	2.74043	+	10.6532i	0.249130	+	0.968470i
$122$	17.9539	−	2.13607i	1.62547	−	0.193391i
$123$		0			0
$124$	10.5798	+	0.819674i	0.950091	+	0.0736089i
$125$	−2.54866	−	7.84396i	−0.227959	−	0.701585i
$126$		0			0
$127$	−7.90865	+	5.74597i	−0.701780	+	0.509873i	−0.880511	−	0.474025i	$-0.842801\pi$
$127$	−7.90865	+	5.74597i	−0.701780	+	0.509873i	0.178732	+	0.983898i	$0.442801\pi$
$128$	−4.69273	+	10.2946i	−0.414782	+	0.909921i
$129$		0			0
$130$	1.14051	+	0.637804i	0.100029	+	0.0559391i
$131$	−10.1612			−0.887790			−0.443895	−	0.896079i	$-0.646404\pi$
$131$	−10.1612			−0.887790			−0.443895	+	0.896079i	$0.646404\pi$
$132$		0			0
$133$	−6.79900			−0.589548
$134$	17.0867	+	9.55533i	1.47606	+	0.825455i
$135$		0			0
$136$	−7.43899	−	9.40092i	−0.637888	−	0.806122i
$137$	8.09097	−	5.87844i	0.691258	−	0.502229i	−0.185815	−	0.982585i	$-0.559493\pi$
$137$	8.09097	−	5.87844i	0.691258	−	0.502229i	0.877074	+	0.480356i	$0.159493\pi$
$138$		0			0
$139$	−4.63670	−	14.2703i	−0.393280	−	1.21039i	−0.930293	−	0.366817i	$-0.880447\pi$
$139$	−4.63670	−	14.2703i	−0.393280	−	1.21039i	0.537013	−	0.843574i	$-0.319553\pi$
$140$	−0.219621	+	2.83471i	−0.0185614	+	0.239577i
$141$		0			0
$142$	−9.00034	+	1.07082i	−0.755292	+	0.0898614i
$143$	−3.28090	+	0.953999i	−0.274363	+	0.0797774i
$144$		0			0
$145$	0.325993	−	0.448691i	0.0270722	−	0.0372617i
$146$	1.22976	−	6.20215i	0.101775	−	0.513293i
$147$		0			0
$148$	−3.87920	+	4.55319i	−0.318868	+	0.374270i
$149$	−10.1802	−	14.0119i	−0.833996	−	1.14790i	−0.987166	−	0.159697i	$-0.948948\pi$
$149$	−10.1802	−	14.0119i	−0.833996	−	1.14790i	0.153170	−	0.988200i	$-0.451052\pi$
$150$		0			0
$151$	−2.57768	+	7.93327i	−0.209768	+	0.645600i	0.789715	+	0.613473i	$0.210228\pi$
$151$	−2.57768	+	7.93327i	−0.209768	+	0.645600i	−0.999484	+	0.0321272i	$0.989772\pi$
$152$	−3.27199	+	11.6833i	−0.265394	+	0.947643i
$153$		0			0
$154$	−4.87712	−	5.61089i	−0.393010	−	0.452139i
$155$		−	4.75880i		−	0.382236i
$156$		0			0
$157$	0.00331991	−	0.0102176i	0.000264958	−	0.000815457i	−0.950924	−	0.309425i	$-0.899864\pi$
$157$	0.00331991	−	0.0102176i	0.000264958	−	0.000815457i	0.951189	+	0.308609i	$0.0998635\pi$
$158$	−9.93166	+	4.58590i	−0.790120	+	0.364834i
$159$		0			0
$160$	4.76545	+	1.74159i	0.376742	+	0.137685i
$161$	−12.5719	+	4.08486i	−0.990804	+	0.321932i
$162$		0			0
$163$	−7.50140	+	10.3248i	−0.587555	+	0.808700i	−0.994498	−	0.104754i	$-0.966595\pi$
$163$	−7.50140	+	10.3248i	−0.587555	+	0.808700i	0.406943	+	0.913453i	$0.366595\pi$
$164$	−0.0326796	−	0.135393i	−0.00255185	−	0.0105724i
$165$		0			0
$166$	2.58368	+	21.7160i	0.200533	+	1.68549i
$167$	−14.6932	−	10.6752i	−1.13699	−	0.826072i	−0.150294	−	0.988641i	$-0.548022\pi$
$167$	−14.6932	−	10.6752i	−1.13699	−	0.826072i	−0.986697	+	0.162569i	$0.948022\pi$
$168$		0			0
$169$	3.68926	+	11.3544i	0.283789	+	0.873413i
$170$	−3.94563	+	3.65176i	−0.302616	+	0.280077i
$171$		0			0
$172$	−6.99168	−	11.3782i	−0.533110	−	0.867582i
$173$	18.1923	+	5.91103i	1.38313	+	0.449407i	0.903698	−	0.428171i	$-0.140842\pi$
$173$	18.1923	+	5.91103i	1.38313	+	0.449407i	0.479435	+	0.877578i	$0.340842\pi$
$174$		0			0
$175$	−6.64990			−0.502685
$176$	−11.9888	+	5.68057i	−0.903689	+	0.428189i
$177$		0			0
$178$	2.07688	−	3.71384i	0.155669	−	0.278364i
$179$	−2.24104	−	0.728158i	−0.167503	−	0.0544251i	0.224065	−	0.974574i	$-0.428067\pi$
$179$	−2.24104	−	0.728158i	−0.167503	−	0.0544251i	−0.391568	+	0.920149i	$0.628067\pi$
$180$		0			0
$181$	19.0177	−	13.8171i	1.41357	−	1.02702i	0.420780	−	0.907163i	$-0.361756\pi$
$181$	19.0177	−	13.8171i	1.41357	−	1.02702i	0.992791	−	0.119857i	$-0.0382436\pi$
$182$	1.69475	−	1.56853i	0.125623	−	0.116267i
$183$		0			0
$184$	0.969194	+	23.5692i	0.0714499	+	1.73755i
$185$	2.17019	+	1.57674i	0.159556	+	0.115924i
$186$		0			0
$187$	0.438357	−	14.0505i	0.0320558	−	1.02748i
$188$	−0.735667	−	3.04791i	−0.0536541	−	0.222291i
$189$		0			0
$190$	5.33717	+	1.05825i	0.387199	+	0.0767734i
$191$	−7.43763	+	2.41663i	−0.538168	+	0.174861i	−0.565474	−	0.824766i	$-0.691307\pi$
$191$	−7.43763	+	2.41663i	−0.538168	+	0.174861i	0.0273067	+	0.999627i	$0.491307\pi$
$192$		0			0
$193$	−15.0239	−	20.6786i	−1.08144	−	1.48848i	−0.857924	−	0.513776i	$-0.828246\pi$
$193$	−15.0239	−	20.6786i	−1.08144	−	1.48848i	−0.223517	−	0.974700i	$-0.571754\pi$
$194$	−18.4442	+	8.51654i	−1.32422	+	0.611452i
$195$		0			0
$196$	−8.29655	−	3.42470i	−0.592611	−	0.244622i
$197$			11.3865i			0.811251i	0.914039	+	0.405626i	$0.132946\pi$
$197$			11.3865i			0.811251i	−0.914039	+	0.405626i	$0.867054\pi$
$198$		0			0
$199$			16.7427i			1.18686i	0.804887	+	0.593428i	$0.202226\pi$
$199$			16.7427i			1.18686i	−0.804887	+	0.593428i	$0.797774\pi$
$200$	−3.20024	+	11.4271i	−0.226291	+	0.808019i
$201$		0			0
$202$	−4.94367	−	10.7065i	−0.347836	−	0.753306i
$203$	−0.576081	−	0.792907i	−0.0404330	−	0.0556512i
$204$		0			0
$205$	−0.0594047	+	0.0193018i	−0.00414900	+	0.00134809i
$206$	−4.31596	+	21.7671i	−0.300707	+	1.51659i
$207$		0			0
$208$	−1.87975	−	3.66709i	−0.130337	−	0.254267i
$209$	−11.7651	+	7.99945i	−0.813807	+	0.553334i
$210$		0			0
$211$	1.82420	+	1.32536i	0.125583	+	0.0912412i	0.648804	−	0.760956i	$-0.275270\pi$
$211$	1.82420	+	1.32536i	0.125583	+	0.0912412i	−0.523221	+	0.852197i	$0.675270\pi$
$212$	1.86064	−	24.0158i	0.127789	−	1.64942i
$213$		0			0
$214$	6.91906	+	7.47585i	0.472977	+	0.511039i
$215$	−4.84521	+	3.52025i	−0.330441	+	0.240079i
$216$		0			0
$217$	−7.99796	−	2.59869i	−0.542937	−	0.176411i
$218$	−1.93931	−	1.08451i	−0.131347	−	0.0734525i
$219$		0			0
$220$	2.95518	+	5.16362i	0.199238	+	0.348132i
$221$	4.36645			0.293719
$222$		0			0
$223$	−4.97253	−	1.61567i	−0.332985	−	0.108193i	0.137752	−	0.990467i	$-0.456012\pi$
$223$	−4.97253	−	1.61567i	−0.332985	−	0.108193i	−0.470738	+	0.882273i	$0.656012\pi$
$224$	5.52936	−	7.05809i	0.369446	−	0.471588i
$225$		0			0
$226$	10.9156	+	11.7940i	0.726093	+	0.784523i
$227$	−1.26953	−	3.90721i	−0.0842616	−	0.259330i	0.900045	−	0.435797i	$-0.143533\pi$
$227$	−1.26953	−	3.90721i	−0.0842616	−	0.259330i	−0.984307	+	0.176466i	$0.943533\pi$
$228$		0			0
$229$	−1.29997	−	0.944481i	−0.0859042	−	0.0624131i	0.544004	−	0.839083i	$-0.316908\pi$
$229$	−1.29997	−	0.944481i	−0.0859042	−	0.0624131i	−0.629908	+	0.776669i	$0.716908\pi$
$230$	10.5047	−	1.24980i	0.692656	−	0.0824093i
$231$		0			0
$232$	−1.63976	+	0.608348i	−0.107656	+	0.0399400i
$233$	6.61953	−	9.11100i	0.433660	−	0.596882i	−0.535129	−	0.844771i	$-0.679737\pi$
$233$	6.61953	−	9.11100i	0.433660	−	0.596882i	0.968788	+	0.247889i	$0.0797369\pi$
$234$		0			0
$235$	−1.33729	+	0.434512i	−0.0872351	+	0.0283444i
$236$	12.5039	+	10.6530i	0.813932	+	0.693449i
$237$		0			0
$238$	3.98276	+	8.62545i	0.258164	+	0.559105i
$239$	−1.23014	+	3.78599i	−0.0795713	+	0.244895i	−0.982927	−	0.183997i	$-0.941096\pi$
$239$	−1.23014	+	3.78599i	−0.0795713	+	0.244895i	0.903355	+	0.428893i	$0.141096\pi$
$240$		0			0
$241$		−	10.6165i		−	0.683870i	−0.939724	−	0.341935i	$-0.888918\pi$
$241$		−	10.6165i		−	0.683870i	0.939724	−	0.341935i	$-0.111082\pi$
$242$	−15.0410	−	3.97092i	−0.966872	−	0.255261i
$243$		0			0
$244$	−9.75629	+	23.6352i	−0.624582	+	1.51309i
$245$	−1.24385	+	3.82817i	−0.0794666	+	0.244573i
$246$		0			0
$247$	−2.59751	−	3.57517i	−0.165276	−	0.227483i
$248$	−8.31456	+	12.4930i	−0.527975	+	0.793306i
$249$		0			0
$250$	11.4412	+	2.26854i	0.723603	+	0.143475i
$251$	5.28407	−	7.27290i	0.333528	−	0.459061i	−0.609010	−	0.793163i	$-0.708433\pi$
$251$	5.28407	−	7.27290i	0.333528	−	0.459061i	0.942537	+	0.334102i	$0.108433\pi$
$252$		0			0
$253$	−16.9485	+	21.8601i	−1.06554	+	1.37433i
$254$	−1.63330	−	13.7280i	−0.102482	−	0.861372i
$255$		0			0
$256$	−9.46755	−	12.8983i	−0.591722	−	0.806142i
$257$	5.82270	+	17.9204i	0.363210	+	1.11784i	0.951094	+	0.308900i	$0.0999609\pi$
$257$	5.82270	+	17.9204i	0.363210	+	1.11784i	−0.587885	+	0.808945i	$0.700039\pi$
$258$		0			0
$259$	3.83507	−	2.78634i	0.238300	−	0.173135i
$260$	−1.57450	+	0.967499i	−0.0976466	+	0.0600017i
$261$		0			0
$262$	7.01391	−	12.5422i	0.433321	−	0.774858i
$263$	17.5390			1.08150			0.540750	−	0.841183i	$-0.318140\pi$
$263$	17.5390			1.08150			0.540750	+	0.841183i	$0.318140\pi$
$264$		0			0
$265$	−10.8024			−0.663584
$266$	4.69309	−	8.39212i	0.287752	−	0.514554i
$267$		0			0
$268$	−23.5886	+	14.4947i	−1.44090	+	0.885404i
$269$	10.2497	−	7.44686i	0.624936	−	0.454043i	−0.229706	−	0.973260i	$-0.573776\pi$
$269$	10.2497	−	7.44686i	0.624936	−	0.454043i	0.854642	+	0.519217i	$0.173776\pi$
$270$		0			0
$271$	7.47193	+	22.9962i	0.453888	+	1.39692i	0.872436	+	0.488728i	$0.162539\pi$
$271$	7.47193	+	22.9962i	0.453888	+	1.39692i	−0.418549	+	0.908194i	$0.637461\pi$
$272$	16.7386	−	2.69297i	1.01492	−	0.163285i
$273$		0			0
$274$	1.67095	+	14.0445i	0.100946	+	0.848459i
$275$	−11.5071	+	7.82403i	−0.693903	+	0.471807i
$276$		0			0
$277$	6.66973	−	9.18010i	0.400745	−	0.551579i	−0.560185	−	0.828367i	$-0.689270\pi$
$277$	6.66973	−	9.18010i	0.400745	−	0.551579i	0.960931	+	0.276789i	$0.0892701\pi$
$278$	20.8146	+	4.12710i	1.24838	+	0.247527i
$279$		0			0
$280$	−3.34734	−	2.22778i	−0.200042	−	0.133135i
$281$	−7.96394	−	10.9614i	−0.475089	−	0.653903i	0.502463	−	0.864599i	$-0.332427\pi$
$281$	−7.96394	−	10.9614i	−0.475089	−	0.653903i	−0.977552	+	0.210695i	$0.932427\pi$
$282$		0			0
$283$	7.59280	−	23.3682i	0.451345	−	1.38910i	−0.424028	−	0.905649i	$-0.639384\pi$
$283$	7.59280	−	23.3682i	0.451345	−	1.38910i	0.875373	−	0.483449i	$-0.160616\pi$
$284$	4.89087	−	11.8484i	0.290220	−	0.703075i
$285$		0			0
$286$	1.08715	−	4.70818i	0.0642843	−	0.278400i
$287$			0.110380i			0.00651552i
$288$		0			0
$289$	−0.298041	+	0.917276i	−0.0175318	+	0.0539574i
$290$	0.328806	+	0.712093i	0.0193081	+	0.0418155i
$291$		0			0
$292$	6.80656	+	5.79902i	0.398324	+	0.339362i
$293$	5.43709	−	1.76662i	0.317638	−	0.103207i	−0.145859	−	0.989305i	$-0.546595\pi$
$293$	5.43709	−	1.76662i	0.317638	−	0.103207i	0.463497	+	0.886099i	$0.346595\pi$
$294$		0			0
$295$	4.32999	−	5.95972i	0.252102	−	0.346989i
$296$	−2.94240	−	7.93106i	−0.171024	−	0.460983i
$297$		0			0
$298$	24.3221	−	2.89374i	1.40894	−	0.167630i
$299$	−6.95098	−	5.05019i	−0.401986	−	0.292060i
$300$		0			0
$301$	3.27049	+	10.0655i	0.188508	+	0.580168i
$302$	−8.01289	−	8.65771i	−0.461090	−	0.498195i
$303$		0			0
$304$	−12.1624	−	12.1032i	−0.697561	−	0.694168i
$305$	10.9057	+	3.54347i	0.624458	+	0.202899i
$306$		0			0
$307$	−7.63441			−0.435719			−0.217859	−	0.975980i	$-0.569907\pi$
$307$	−7.63441			−0.435719			−0.217859	+	0.975980i	$0.569907\pi$
$308$	10.2921	−	2.14692i	0.586447	−	0.122332i
$309$		0			0
$310$	5.87386	+	3.28482i	0.333613	+	0.186565i
$311$	20.1706	+	6.55383i	1.14377	+	0.371634i	0.818794	−	0.574088i	$-0.194643\pi$
$311$	20.1706	+	6.55383i	1.14377	+	0.371634i	0.324978	+	0.945722i	$0.394643\pi$
$312$		0			0
$313$	−3.49829	+	2.54166i	−0.197735	+	0.143663i	−0.682247	−	0.731122i	$-0.738997\pi$
$313$	−3.49829	+	2.54166i	−0.197735	+	0.143663i	0.484512	+	0.874785i	$0.338997\pi$
$314$	0.0103202	+	0.0111507i	0.000582402	+	0.000629269i
$315$		0			0
$316$	1.19501	−	15.4243i	0.0672243	−	0.867684i
$317$	−5.71480	−	4.15205i	−0.320975	−	0.233202i	0.415616	−	0.909540i	$-0.363566\pi$
$317$	−5.71480	−	4.15205i	−0.320975	−	0.233202i	−0.736592	+	0.676338i	$0.763566\pi$
$318$		0			0
$319$	−1.92976	−	0.694262i	−0.108046	−	0.0388712i
$320$	−5.43909	+	4.67992i	−0.304054	+	0.261615i
$321$		0			0
$322$	3.63591	−	18.3373i	0.202621	−	1.02190i
$323$	17.2915	−	5.61833i	0.962122	−	0.312612i
$324$		0			0
$325$	−2.54055	−	3.49677i	−0.140924	−	0.193966i
$326$	−7.56612	−	16.3859i	−0.419049	−	0.907532i
$327$		0			0
$328$	0.189676	+	0.0531199i	0.0104731	+	0.00293306i
$329$			2.48482i			0.136992i
$330$		0			0
$331$		−	7.22121i		−	0.396914i	−0.980110	−	0.198457i	$-0.936407\pi$
$331$		−	7.22121i		−	0.396914i	0.980110	−	0.198457i	$-0.0635929\pi$
$332$	−28.5879	−	11.8007i	−1.56896	−	0.647647i
$333$		0			0
$334$	23.3187	−	10.7673i	1.27594	−	0.589161i
$335$	7.29796	+	10.0448i	0.398730	+	0.548805i
$336$		0			0
$337$	27.9259	−	9.07368i	1.52122	−	0.494275i	0.575100	−	0.818083i	$-0.304963\pi$
$337$	27.9259	−	9.07368i	1.52122	−	0.494275i	0.946123	+	0.323808i	$0.104963\pi$
$338$	−16.5614	−	3.28379i	−0.900824	−	0.178614i
$339$		0			0
$340$	−1.78391	−	7.39083i	−0.0967461	−	0.400824i
$341$	−16.8973	+	4.91329i	−0.915040	+	0.266069i
$342$		0			0
$343$	14.7306	+	10.7024i	0.795380	+	0.577877i
$344$	18.8704	−	0.775974i	1.01743	−	0.0418377i
$345$		0			0
$346$	−19.8535	+	18.3749i	−1.06733	+	0.987838i
$347$	3.88937	−	2.82580i	0.208793	−	0.151697i	−0.478475	−	0.878101i	$-0.658810\pi$
$347$	3.88937	−	2.82580i	0.208793	−	0.151697i	0.687267	+	0.726405i	$0.258810\pi$
$348$		0			0
$349$	19.9638	+	6.48663i	1.06864	+	0.347221i	0.789957	−	0.613163i	$-0.210103\pi$
$349$	19.9638	+	6.48663i	1.06864	+	0.347221i	0.278681	+	0.960384i	$0.410103\pi$
$350$	4.59018	−	8.20808i	0.245355	−	0.438741i
$351$		0			0
$352$	1.26380	−	18.7190i	0.0673606	−	0.997729i
$353$	−7.06506			−0.376035			−0.188018	−	0.982166i	$-0.560206\pi$
$353$	−7.06506			−0.376035			−0.188018	+	0.982166i	$0.560206\pi$
$354$		0			0
$355$	−5.46707	−	1.77636i	−0.290162	−	0.0942793i
$356$	3.15046	+	5.12705i	0.166974	+	0.271733i
$357$		0			0
$358$	2.44568	−	2.26353i	0.129258	−	0.119631i
$359$	4.34491	+	13.3723i	0.229316	+	0.705761i	0.997825	+	0.0659221i	$0.0209989\pi$
$359$	4.34491	+	13.3723i	0.229316	+	0.705761i	−0.768509	+	0.639839i	$0.779001\pi$
$360$		0			0
$361$	0.484803	+	0.352230i	0.0255159	+	0.0185384i
$362$	3.92754	+	33.0113i	0.206427	+	1.73503i
$363$		0			0
$364$	0.766236	+	3.17455i	0.0401617	+	0.166392i
$365$	2.35706	−	3.24422i	0.123374	−	0.169810i
$366$		0			0
$367$	−17.0875	+	5.55207i	−0.891961	+	0.289816i	−0.718915	−	0.695098i	$-0.755361\pi$
$367$	−17.0875	+	5.55207i	−0.891961	+	0.289816i	−0.173046	+	0.984914i	$0.555361\pi$
$368$	−29.7609	−	15.0727i	−1.55139	−	0.785717i
$369$		0			0
$370$	−3.44419	+	1.59034i	−0.179055	+	0.0826778i
$371$	−5.89898	+	18.1552i	−0.306260	+	0.942571i
$372$		0			0
$373$			23.1319i			1.19773i	0.800851	+	0.598863i	$0.204381\pi$
$373$			23.1319i			1.19773i	−0.800851	+	0.598863i	$0.795619\pi$
$374$	17.0402	+	10.2396i	0.881128	+	0.529478i
$375$		0			0
$376$	4.26989	+	1.19581i	0.220203	+	0.0616692i
$377$	0.196853	−	0.605850i	0.0101384	−	0.0312029i
$378$		0			0
$379$	20.1247	+	27.6993i	1.03374	+	1.42281i	0.902105	+	0.431516i	$0.142021\pi$
$379$	20.1247	+	27.6993i	1.03374	+	1.42281i	0.131630	+	0.991299i	$0.457979\pi$
$380$	−4.99026	+	5.85729i	−0.255995	+	0.300472i
$381$		0			0
$382$	2.15103	−	10.8485i	0.110056	−	0.555057i
$383$	−9.21636	+	12.6852i	−0.470934	+	0.648185i	−0.976731	−	0.214467i	$-0.931198\pi$
$383$	−9.21636	+	12.6852i	−0.470934	+	0.648185i	0.505797	+	0.862653i	$0.331198\pi$
$384$		0			0
$385$	−1.31645	−	4.52742i	−0.0670926	−	0.230738i
$386$	35.8943	−	4.27055i	1.82697	−	0.217365i
$387$		0			0
$388$	2.21926	−	28.6447i	0.112666	−	1.45421i
$389$	0.579547	+	1.78366i	0.0293842	+	0.0904353i	0.964673	−	0.263450i	$-0.0848604\pi$
$389$	0.579547	+	1.78366i	0.0293842	+	0.0904353i	−0.935289	+	0.353885i	$0.884860\pi$
$390$		0			0
$391$	28.5978	−	20.7775i	1.44625	−	1.05076i
$392$	9.95397	−	7.87663i	0.502751	−	0.397830i
$393$		0			0
$394$	−14.0545	−	7.85965i	−0.708055	−	0.395963i
$395$	−6.93787			−0.349082
$396$		0			0
$397$	−19.8246			−0.994971			−0.497485	−	0.867472i	$-0.665743\pi$
$397$	−19.8246			−0.994971			−0.497485	+	0.867472i	$0.665743\pi$
$398$	−20.6657	−	11.5568i	−1.03588	−	0.579292i
$399$		0			0
$400$	−11.8957	−	11.8378i	−0.594784	−	0.591891i
$401$	−8.74238	+	6.35171i	−0.436574	+	0.317189i	−0.784272	−	0.620417i	$-0.786963\pi$
$401$	−8.74238	+	6.35171i	−0.436574	+	0.317189i	0.347698	+	0.937606i	$0.386963\pi$
$402$		0			0
$403$	−1.68908	−	5.19844i	−0.0841389	−	0.258953i
$404$	16.6276	+	1.28823i	0.827255	+	0.0640921i
$405$		0			0
$406$	1.37635	−	0.163752i	0.0683069	−	0.00812687i
$407$	3.35795	−	9.33372i	0.166447	−	0.462656i
$408$		0			0
$409$	2.42257	−	3.33439i	0.119789	−	0.164875i	−0.744912	−	0.667163i	$-0.767508\pi$
$409$	2.42257	−	3.33439i	0.119789	−	0.164875i	0.864700	+	0.502288i	$0.167508\pi$
$410$	0.0171804	−	0.0866475i	0.000848478	−	0.00427921i
$411$		0			0
$412$	−23.8884	−	20.3523i	−1.17689	−	1.00269i
$413$	−7.65178	−	10.5318i	−0.376520	−	0.518235i
$414$		0			0
$415$	−4.28599	+	13.1909i	−0.210391	+	0.647518i
$416$	5.82386	+	0.211051i	0.285538	+	0.0103476i
$417$		0			0
$418$	−1.75286	−	20.0436i	−0.0857351	−	0.980362i
$419$		−	7.40916i		−	0.361961i	−0.983487	−	0.180981i	$-0.942073\pi$
$419$		−	7.40916i		−	0.361961i	0.983487	−	0.180981i	$-0.0579271\pi$
$420$		0			0
$421$	−0.377897	+	1.16305i	−0.0184176	+	0.0566834i	−0.959843	−	0.280538i	$-0.909487\pi$
$421$	−0.377897	+	1.16305i	−0.0184176	+	0.0566834i	0.941425	+	0.337221i	$0.109487\pi$
$422$	−2.89508	+	1.33679i	−0.140930	+	0.0650740i
$423$		0			0
$424$	28.3588	+	18.8739i	1.37723	+	0.916596i
$425$	16.9123	−	5.49513i	0.820365	−	0.266553i
$426$		0			0
$427$	11.9108	−	16.3938i	0.576404	−	0.793352i
$428$	−14.0035	+	3.38001i	−0.676887	+	0.163379i
$429$		0			0
$430$	−1.00064	−	8.41043i	−0.0482550	−	0.405587i
$431$	15.7477	+	11.4413i	0.758538	+	0.551110i	0.898462	−	0.439052i	$-0.144686\pi$
$431$	15.7477	+	11.4413i	0.758538	+	0.551110i	−0.139923	+	0.990162i	$0.544686\pi$
$432$		0			0
$433$	5.05505	+	15.5578i	0.242930	+	0.747662i	0.995970	+	0.0896872i	$0.0285867\pi$
$433$	5.05505	+	15.5578i	0.242930	+	0.747662i	−0.753040	+	0.657975i	$0.771413\pi$
$434$	8.72830	−	8.07823i	0.418972	−	0.387767i
$435$		0			0
$436$	2.67726	−	1.64512i	0.128218	−	0.0787870i
$437$	−34.0245	−	11.0552i	−1.62761	−	0.528843i
$438$		0			0
$439$	−14.7044			−0.701804			−0.350902	−	0.936412i	$-0.614125\pi$
$439$	−14.7044			−0.701804			−0.350902	+	0.936412i	$0.614125\pi$
$440$	−8.41340	+	0.0833751i	−0.401093	+	0.00397475i
$441$		0			0
$442$	−3.01400	+	5.38958i	−0.143361	+	0.256356i
$443$	7.00255	+	2.27527i	0.332701	+	0.108101i	0.470604	−	0.882345i	$-0.344036\pi$
$443$	7.00255	+	2.27527i	0.332701	+	0.108101i	−0.137903	+	0.990446i	$0.544036\pi$
$444$		0			0
$445$	2.18326	−	1.58623i	0.103497	−	0.0751946i
$446$	5.42660	−	5.02244i	0.256957	−	0.237819i
$447$		0			0
$448$	4.89520	+	11.6969i	0.231276	+	0.552627i
$449$	4.51170	+	3.27794i	0.212920	+	0.154696i	0.689134	−	0.724634i	$-0.257991\pi$
$449$	4.51170	+	3.27794i	0.212920	+	0.154696i	−0.476214	+	0.879330i	$0.657991\pi$
$450$		0			0
$451$	0.129869	+	0.191003i	0.00611529	+	0.00899397i
$452$	−22.0921	+	5.33233i	−1.03912	+	0.250812i
$453$		0			0
$454$	5.69904	+	1.13000i	0.267469	+	0.0530335i
$455$	1.39286	−	0.452566i	0.0652981	−	0.0212166i
$456$		0			0
$457$	−10.8622	−	14.9505i	−0.508113	−	0.699357i	0.475487	−	0.879723i	$-0.342272\pi$
$457$	−10.8622	−	14.9505i	−0.508113	−	0.699357i	−0.983600	+	0.180366i	$0.942272\pi$
$458$	2.06311	−	0.952630i	0.0964027	−	0.0445135i
$459$		0			0
$460$	−5.70832	+	13.8288i	−0.266152	+	0.644769i
$461$		−	17.6315i		−	0.821182i	−0.911820	−	0.410591i	$-0.865322\pi$
$461$		−	17.6315i		−	0.821182i	0.911820	−	0.410591i	$-0.134678\pi$
$462$		0			0
$463$			13.2658i			0.616515i	0.951303	+	0.308257i	$0.0997458\pi$
$463$			13.2658i			0.616515i	−0.951303	+	0.308257i	$0.900254\pi$
$464$	0.380972	−	2.44390i	0.0176862	−	0.113455i
$465$		0			0
$466$	6.67664	+	14.4596i	0.309290	+	0.669827i
$467$	−12.8463	−	17.6814i	−0.594456	−	0.818198i	0.400731	−	0.916196i	$-0.368756\pi$
$467$	−12.8463	−	17.6814i	−0.594456	−	0.818198i	−0.995187	+	0.0979976i	$0.968756\pi$
$468$		0			0
$469$	20.8672	−	6.78017i	0.963559	−	0.313079i
$470$	0.386756	−	1.95057i	0.0178397	−	0.0899729i
$471$		0			0
$472$	−21.7801	+	8.08036i	−1.00251	+	0.371929i
$473$	17.5021	+	13.5696i	0.804745	+	0.623931i
$474$		0			0
$475$	−14.5601	−	10.5785i	−0.668062	−	0.485375i
$476$	−13.3957	−	1.03784i	−0.613990	−	0.0475692i
$477$		0			0
$478$	−3.82399	−	4.13171i	−0.174905	−	0.188980i
$479$	−28.7819	+	20.9113i	−1.31508	+	0.955462i	−0.315101	+	0.949058i	$0.602038\pi$
$479$	−28.7819	+	20.9113i	−1.31508	+	0.955462i	−0.999979	+	0.00640328i	$0.997962\pi$
$480$		0			0
$481$	2.93033	+	0.952121i	0.133611	+	0.0434130i
$482$	13.1041	+	7.32819i	0.596877	+	0.333790i
$483$		0			0
$484$	15.2836	−	15.8244i	0.694710	−	0.719290i
$485$	−12.8844			−0.585051
$486$		0			0
$487$	13.0159	+	4.22912i	0.589806	+	0.191640i	0.588689	−	0.808360i	$-0.299644\pi$
$487$	13.0159	+	4.22912i	0.589806	+	0.191640i	0.00111710	+	0.999999i	$0.499644\pi$
$488$	−22.4389	−	28.3568i	−1.01576	−	1.28365i
$489$		0			0
$490$	−3.86659	−	4.17775i	−0.174675	−	0.188731i
$491$	3.07565	+	9.46588i	0.138802	+	0.427189i	0.996162	−	0.0875283i	$-0.0278968\pi$
$491$	3.07565	+	9.46588i	0.138802	+	0.427189i	−0.857360	+	0.514717i	$0.827897\pi$
$492$		0			0
$493$	2.12033	+	1.54051i	0.0954947	+	0.0693810i
$494$	6.20586	−	0.738347i	0.279215	−	0.0332198i
$495$		0			0
$496$	−9.68108	−	18.8862i	−0.434693	−	0.848017i
$497$	−5.97093	+	8.21828i	−0.267833	+	0.368640i
$498$		0			0
$499$	−16.9602	+	5.51072i	−0.759245	+	0.246694i	−0.662954	−	0.748660i	$-0.730698\pi$
$499$	−16.9602	+	5.51072i	−0.759245	+	0.246694i	−0.0962903	+	0.995353i	$0.530698\pi$
$500$	−10.6975	+	12.5561i	−0.478407	+	0.561527i
$501$		0			0
$502$	5.32966	+	11.5424i	0.237874	+	0.515164i
$503$	−0.0583996	+	0.179735i	−0.00260391	+	0.00801401i	−0.952350	−	0.305007i	$-0.901341\pi$
$503$	−0.0583996	+	0.179735i	−0.00260391	+	0.00801401i	0.949746	+	0.313021i	$0.101341\pi$
$504$		0			0
$505$		−	7.47914i		−	0.332817i
$506$	−15.2834	−	36.0090i	−0.679430	−	1.60080i
$507$		0			0
$508$	18.0721	+	7.45993i	0.801821	+	0.330981i
$509$	4.30669	−	13.2546i	0.190891	−	0.587501i	−0.809109	−	0.587658i	$-0.800050\pi$
$509$	4.30669	−	13.2546i	0.190891	−	0.587501i	1.00000		0.000157233i	$5.00489e-5\pi$
$510$		0			0
$511$	−4.16530	−	5.73304i	−0.184262	−	0.253615i
$512$	22.4557	−	2.78276i	0.992409	−	0.122982i
$513$		0			0
$514$	−26.1387	−	5.18275i	−1.15293	−	0.228601i
$515$	−8.27236	+	11.3859i	−0.364524	+	0.501724i
$516$		0			0
$517$	2.92355	+	4.29976i	0.128577	+	0.189103i
$518$	0.792021	+	6.65700i	0.0347994	+	0.292492i
$519$		0			0
$520$	−0.107378	−	2.61127i	−0.00470885	−	0.114512i
$521$	5.64640	+	17.3778i	0.247373	+	0.761337i	0.995237	+	0.0974844i	$0.0310796\pi$
$521$	5.64640	+	17.3778i	0.247373	+	0.761337i	−0.747864	+	0.663852i	$0.768920\pi$
$522$		0			0
$523$	−15.0953	+	10.9674i	−0.660070	+	0.479569i	−0.866687	−	0.498853i	$-0.833755\pi$
$523$	−15.0953	+	10.9674i	−0.660070	+	0.479569i	0.206617	+	0.978422i	$0.433755\pi$
$524$	10.6396	+	17.3148i	0.464791	+	0.756400i
$525$		0			0
$526$	−12.1065	+	21.6487i	−0.527869	+	0.943926i
$527$	22.4881			0.979598
$528$		0			0
$529$	−46.5560			−2.02417
$530$	7.45647	−	13.3335i	0.323889	−	0.579172i
$531$		0			0
$532$	7.11906	+	11.5855i	0.308650	+	0.502296i
$533$	−0.0580419	+	0.0421699i	−0.00251407	+	0.00182658i
$534$		0			0
$535$	1.99635	+	6.14415i	0.0863100	+	0.265635i
$536$	−1.60870	−	39.1210i	−0.0694852	−	1.68977i
$537$		0			0
$538$	2.11678	+	17.7917i	0.0912608	+	0.767054i
$539$	14.8771	+	0.464145i	0.640802	+	0.0199922i
$540$		0			0
$541$	−6.76205	+	9.30716i	−0.290723	+	0.400146i	−0.929249	−	0.369454i	$-0.879545\pi$
$541$	−6.76205	+	9.30716i	−0.290723	+	0.400146i	0.638526	+	0.769600i	$0.279545\pi$
$542$	−33.5422	−	6.65072i	−1.44076	−	0.285673i
$543$		0			0
$544$	−8.23004	+	22.5195i	−0.352860	+	0.965518i
$545$	−0.828305	−	1.14006i	−0.0354807	−	0.0488350i
$546$		0			0
$547$	3.33782	−	10.2727i	0.142715	−	0.439231i	−0.853995	−	0.520281i	$-0.825827\pi$
$547$	3.33782	−	10.2727i	0.142715	−	0.439231i	0.996710	+	0.0810500i	$0.0258273\pi$
$548$	−18.4887	−	7.63190i	−0.789800	−	0.326019i
$549$		0			0
$550$	−1.71442	−	19.6040i	−0.0731031	−	0.835918i
$551$		−	2.65250i		−	0.113000i
$552$		0			0
$553$	−3.78865	+	11.6603i	−0.161110	+	0.495844i
$554$	6.72728	+	14.5692i	0.285815	+	0.618988i
$555$		0			0
$556$	−19.4617	+	22.8430i	−0.825360	+	0.968760i
$557$	32.1819	−	10.4565i	1.36359	−	0.443057i	0.466350	−	0.884600i	$-0.345569\pi$
$557$	32.1819	−	10.4565i	1.36359	−	0.443057i	0.897240	+	0.441543i	$0.145569\pi$
$558$		0			0
$559$	−4.04337	+	5.56522i	−0.171016	+	0.235384i
$560$	5.06033	−	2.59392i	0.213838	−	0.109613i
$561$		0			0
$562$	19.0271	−	2.26376i	0.802609	−	0.0954909i
$563$	31.7142	+	23.0417i	1.33659	+	0.971092i	0.999562	+	0.0295994i	$0.00942314\pi$
$563$	31.7142	+	23.0417i	1.33659	+	0.971092i	0.337032	+	0.941493i	$0.390577\pi$
$564$		0			0
$565$	3.14946	+	9.69306i	0.132499	+	0.407790i
$566$	23.6028	+	25.5021i	0.992099	+	1.07194i
$567$		0			0
$568$	11.2487	+	14.2154i	0.471986	+	0.596465i
$569$	21.6670	+	7.04003i	0.908328	+	0.295134i	0.725670	−	0.688043i	$-0.241530\pi$
$569$	21.6670	+	7.04003i	0.908328	+	0.295134i	0.182658	+	0.983177i	$0.441530\pi$
$570$		0			0
$571$	19.5463			0.817989			0.408994	−	0.912537i	$-0.365880\pi$
$571$	19.5463			0.817989			0.408994	+	0.912537i	$0.365880\pi$
$572$	5.06097	+	4.59176i	0.211610	+	0.191991i
$573$		0			0
$574$	−0.136244	−	0.0761911i	−0.00568670	−	0.00318016i
$575$	−33.2784	−	10.8128i	−1.38780	−	0.450925i
$576$		0			0
$577$	26.3692	−	19.1583i	1.09776	−	0.797572i	0.117071	−	0.993124i	$-0.462650\pi$
$577$	26.3692	−	19.1583i	1.09776	−	0.797572i	0.980693	+	0.195551i	$0.0626496\pi$
$578$	−0.926482	−	1.00104i	−0.0385366	−	0.0416377i
$579$		0			0
$580$	−1.10591	−	0.0856810i	−0.0459204	−	0.00355771i
$581$	19.8291	+	14.4067i	0.822649	+	0.597689i
$582$		0			0
$583$	11.1531	+	38.3565i	0.461912	+	1.58856i
$584$	−11.8561	+	4.39860i	−0.490610	+	0.182015i
$585$		0			0
$586$	−1.57245	+	7.93052i	−0.0649575	+	0.327607i
$587$	22.7419	−	7.38928i	0.938658	−	0.304988i	0.200559	−	0.979682i	$-0.435724\pi$
$587$	22.7419	−	7.38928i	0.938658	−	0.304988i	0.738098	+	0.674693i	$0.235724\pi$
$588$		0			0
$589$	−13.3777	−	18.4129i	−0.551219	−	0.758688i
$590$	4.36735	+	9.45836i	0.179801	+	0.389394i
$591$		0			0
$592$	11.8205	+	1.84266i	0.485818	+	0.0757327i
$593$			10.8950i			0.447405i	0.974658	+	0.223702i	$0.0718143\pi$
$593$			10.8950i			0.447405i	−0.974658	+	0.223702i	$0.928186\pi$
$594$		0			0
$595$			6.02540i			0.247017i
$596$	−13.2168	+	32.0186i	−0.541383	+	1.31153i
$597$		0			0
$598$	11.0315	−	5.09376i	0.451113	−	0.208299i
$599$	−4.33733	−	5.96983i	−0.177219	−	0.243921i	0.711162	−	0.703028i	$-0.248169\pi$
$599$	−4.33733	−	5.96983i	−0.177219	−	0.243921i	−0.888381	+	0.459108i	$0.848169\pi$
$600$		0			0
$601$	16.2181	−	5.26959i	0.661552	−	0.214951i	0.0410510	−	0.999157i	$-0.486929\pi$
$601$	16.2181	−	5.26959i	0.661552	−	0.214951i	0.620501	+	0.784206i	$0.286929\pi$
$602$	−14.6816	−	2.91105i	−0.598376	−	0.118645i
$603$		0			0
$604$	16.2174	−	3.91435i	0.659875	−	0.159273i
$605$	−7.60480	−	6.28541i	−0.309179	−	0.255538i
$606$		0			0
$607$	−26.3836	−	19.1688i	−1.07088	−	0.778039i	−0.0948089	−	0.995495i	$-0.530224\pi$
$607$	−26.3836	−	19.1688i	−1.07088	−	0.778039i	−0.976070	+	0.217456i	$0.930224\pi$
$608$	23.3345	−	6.65782i	0.946338	−	0.270010i
$609$		0			0
$610$	−11.9016	+	11.0151i	−0.481880	+	0.445990i
$611$	−1.30661	+	0.949309i	−0.0528598	+	0.0384049i
$612$		0			0
$613$	−33.4699	−	10.8750i	−1.35183	−	0.439238i	−0.458526	−	0.888681i	$-0.651622\pi$
$613$	−33.4699	−	10.8750i	−1.35183	−	0.439238i	−0.893309	+	0.449443i	$0.851622\pi$
$614$	5.26975	−	9.42327i	0.212670	−	0.380292i
$615$		0			0
$616$	−4.45428	+	14.1857i	−0.179468	+	0.571557i
$617$	−12.4123			−0.499701			−0.249850	−	0.968284i	$-0.580381\pi$
$617$	−12.4123			−0.499701			−0.249850	+	0.968284i	$0.580381\pi$
$618$		0			0
$619$	20.1287	+	6.54020i	0.809039	+	0.262873i	0.684191	−	0.729303i	$-0.260156\pi$
$619$	20.1287	+	6.54020i	0.809039	+	0.262873i	0.124848	+	0.992176i	$0.460156\pi$
$620$	−8.10902	+	4.98282i	−0.325666	+	0.200115i
$621$		0			0
$622$	−22.0125	+	20.3731i	−0.882622	+	0.816886i
$623$	−1.47369	−	4.53555i	−0.0590421	−	0.181713i
$624$		0			0
$625$	−10.9867	−	7.98229i	−0.439467	−	0.319292i
$626$	−0.722469	−	6.07241i	−0.0288757	−	0.242702i
$627$		0			0
$628$	−0.0208871	+	0.00504148i	−0.000833487	+	0.000201177i
$629$	−7.45100	+	10.2554i	−0.297091	+	0.408910i
$630$		0			0
$631$	−12.1486	+	3.94731i	−0.483627	+	0.157140i	−0.540675	−	0.841231i	$-0.681831\pi$
$631$	−12.1486	+	3.94731i	−0.483627	+	0.157140i	0.0570479	+	0.998371i	$0.481831\pi$
$632$	18.2136	+	12.1218i	0.724497	+	0.482180i
$633$		0			0
$634$	9.06966	−	4.18787i	0.360202	−	0.166322i
$635$	2.70944	−	8.33879i	0.107521	−	0.330915i
$636$		0			0
$637$			4.62333i			0.183183i
$638$	2.18898	−	1.90272i	0.0866627	−	0.0753293i
$639$		0			0
$640$	−2.02210	−	9.94393i	−0.0799306	−	0.393068i
$641$	−12.4717	+	38.3840i	−0.492604	+	1.51608i	0.328055	+	0.944659i	$0.393607\pi$
$641$	−12.4717	+	38.3840i	−0.492604	+	1.51608i	−0.820658	+	0.571419i	$0.806393\pi$
$642$		0			0
$643$	−3.43492	−	4.72776i	−0.135460	−	0.186444i	0.735898	−	0.677092i	$-0.236760\pi$
$643$	−3.43492	−	4.72776i	−0.135460	−	0.186444i	−0.871358	+	0.490648i	$0.836760\pi$
$644$	20.1243	+	17.1454i	0.793010	+	0.675625i
$645$		0			0
$646$	−5.00084	+	25.2212i	−0.196756	+	0.992317i
$647$	−13.8164	+	19.0166i	−0.543179	+	0.747621i	−0.989067	−	0.147467i	$-0.952888\pi$
$647$	−13.8164	+	19.0166i	−0.543179	+	0.747621i	0.445888	+	0.895089i	$0.352888\pi$
$648$		0			0
$649$	−25.6321	−	9.22152i	−1.00615	−	0.361976i
$650$	6.06977	−	0.722155i	0.238076	−	0.0283253i
$651$		0			0
$652$	25.4480	+	1.97160i	0.996621	+	0.0772138i
$653$	−0.182276	−	0.560987i	−0.00713300	−	0.0219531i	0.947427	−	0.319973i	$-0.103674\pi$
$653$	−0.182276	−	0.560987i	−0.00713300	−	0.0219531i	−0.954560	+	0.298020i	$0.903674\pi$
$654$		0			0
$655$	7.37319	−	5.35693i	0.288094	−	0.209313i
$656$	−0.196493	+	0.197453i	−0.00767176	+	0.00770925i
$657$		0			0
$658$	−3.06705	−	1.71518i	−0.119566	−	0.0668646i
$659$	−45.0533			−1.75503			−0.877514	−	0.479550i	$-0.840800\pi$
$659$	−45.0533			−1.75503			−0.877514	+	0.479550i	$0.840800\pi$
$660$		0			0
$661$	14.0486			0.546425			0.273213	−	0.961954i	$-0.411914\pi$
$661$	14.0486			0.546425			0.273213	+	0.961954i	$0.411914\pi$
$662$	8.91326	+	4.98453i	0.346424	+	0.193729i
$663$		0			0
$664$	34.2989	−	27.1409i	1.33106	−	1.05327i
$665$	4.93349	−	3.58439i	0.191312	−	0.138997i
$666$		0			0
$667$	−1.59363	−	4.90469i	−0.0617056	−	0.189910i
$668$	−2.80577	+	36.2150i	−0.108559	+	1.40120i
$669$		0			0
$670$	−17.4360	+	2.07446i	−0.673610	+	0.0801432i
$671$	1.32226	−	42.3819i	0.0510451	−	1.63613i
$672$		0			0
$673$	18.5003	−	25.4634i	0.713133	−	0.981544i	−0.286591	−	0.958053i	$-0.592522\pi$
$673$	18.5003	−	25.4634i	0.713133	−	0.981544i	0.999724	−	0.0234905i	$-0.00747794\pi$
$674$	−8.07643	+	40.7327i	−0.311092	+	1.56896i
$675$		0			0
$676$	15.4850	−	18.1754i	0.595576	−	0.699053i
$677$	5.17890	+	7.12815i	0.199041	+	0.273957i	0.896857	−	0.442320i	$-0.145845\pi$
$677$	5.17890	+	7.12815i	0.199041	+	0.273957i	−0.697816	+	0.716277i	$0.745845\pi$
$678$		0			0
$679$	−7.03595	+	21.6544i	−0.270015	+	0.831021i
$680$	10.3540	+	2.89970i	0.397057	+	0.111199i
$681$		0			0
$682$	5.59903	−	24.2481i	0.214398	−	0.928507i
$683$		−	24.3800i		−	0.932875i	−0.884554	−	0.466438i	$-0.845537\pi$
$683$		−	24.3800i		−	0.932875i	0.884554	−	0.466438i	$-0.154463\pi$
$684$		0			0
$685$	−2.77190	+	8.53102i	−0.105909	+	0.325954i
$686$	−23.3782	+	10.7948i	−0.892584	+	0.412147i
$687$		0			0
$688$	−12.0678	+	23.8277i	−0.460079	+	0.908423i
$689$	−11.8004	+	3.83417i	−0.449558	+	0.146070i
$690$		0			0
$691$	−1.04830	+	1.44287i	−0.0398794	+	0.0548893i	−0.828491	−	0.560002i	$-0.810800\pi$
$691$	−1.04830	+	1.44287i	−0.0398794	+	0.0548893i	0.788612	+	0.614892i	$0.210800\pi$
$692$	−8.97624	−	37.1890i	−0.341225	−	1.41371i
$693$		0			0
$694$	0.803236	+	6.75126i	0.0304904	+	0.256274i
$695$	10.8877	+	7.91038i	0.412994	+	0.300058i
$696$		0			0
$697$	−0.0912121	−	0.280722i	−0.00345491	−	0.0106331i
$698$	−21.7868	+	20.1642i	−0.824643	+	0.763225i
$699$		0			0
$700$	6.96294	+	11.3315i	0.263175	+	0.428289i
$701$	−32.1497	−	10.4461i	−1.21428	−	0.394542i	−0.369282	−	0.929317i	$-0.620396\pi$
$701$	−32.1497	−	10.4461i	−1.21428	−	0.394542i	−0.844995	+	0.534775i	$0.820396\pi$
$702$		0			0
$703$	12.8294			0.483870
$704$	22.2329	+	14.4810i	0.837933	+	0.545773i
$705$		0			0
$706$	4.87675	−	8.72053i	0.183539	−	0.328201i
$707$	−12.5699	−	4.08422i	−0.472741	−	0.153603i
$708$		0			0
$709$	2.04093	−	1.48282i	0.0766487	−	0.0556886i	−0.548801	−	0.835953i	$-0.684916\pi$
$709$	2.04093	−	1.48282i	0.0766487	−	0.0556886i	0.625450	+	0.780264i	$0.284916\pi$
$710$	5.96630	−	5.52194i	0.223911	−	0.207235i
$711$		0			0
$712$	−8.50305	+	0.349655i	−0.318665	+	0.0131039i
$713$	−35.7990	−	26.0095i	−1.34068	−	0.974063i
$714$		0			0
$715$	1.87774	−	2.42191i	0.0702237	−	0.0905743i
$716$	1.10575	+	4.58118i	0.0413238	+	0.171207i
$717$		0			0
$718$	−19.5047	−	3.86738i	−0.727910	−	0.144329i
$719$	−35.8763	+	11.6569i	−1.33796	+	0.434730i	−0.888626	−	0.458633i	$-0.848339\pi$
$719$	−35.8763	+	11.6569i	−1.33796	+	0.434730i	−0.449335	+	0.893363i	$0.648339\pi$
$720$		0			0
$721$	14.6186	+	20.1207i	0.544424	+	0.749336i
$722$	−0.769404	+	0.355269i	−0.0286343	+	0.0132217i
$723$		0			0
$724$	−43.4574	−	17.9386i	−1.61508	−	0.666684i
$725$		−	2.59433i		−	0.0963511i
$726$		0			0
$727$		−	36.4726i		−	1.35269i	−0.736584	−	0.676347i	$-0.763562\pi$
$727$		−	36.4726i		−	1.35269i	0.736584	−	0.676347i	$-0.236438\pi$
$728$	−4.44731	−	1.24550i	−0.164828	−	0.0461612i
$729$		0			0
$730$	2.37740	+	5.14872i	0.0879914	+	0.190563i
$731$	−16.6353	−	22.8965i	−0.615278	−	0.846857i
$732$		0			0
$733$	10.7638	−	3.49738i	0.397571	−	0.129179i	−0.103406	−	0.994639i	$-0.532974\pi$
$733$	10.7638	−	3.49738i	0.397571	−	0.129179i	0.500977	+	0.865461i	$0.332974\pi$
$734$	4.94186	−	24.9238i	0.182408	−	0.919954i
$735$		0			0
$736$	39.1473	−	26.3303i	1.44299	−	0.970546i
$737$	28.1316	−	36.2841i	1.03624	−	1.33654i
$738$		0			0
$739$	−40.1538	−	29.1734i	−1.47708	−	1.07316i	−0.978483	−	0.206329i	$-0.933848\pi$
$739$	−40.1538	−	29.1734i	−1.47708	−	1.07316i	−0.498598	−	0.866833i	$-0.666152\pi$
$740$	0.414415	−	5.34897i	0.0152342	−	0.196632i
$741$		0			0
$742$	−18.3374	−	19.8131i	−0.673187	−	0.727360i
$743$	33.8825	−	24.6171i	1.24303	−	0.903113i	0.245232	−	0.969464i	$-0.421136\pi$
$743$	33.8825	−	24.6171i	1.24303	−	0.903113i	0.997796	+	0.0663513i	$0.0211358\pi$
$744$		0			0
$745$	14.7739	+	4.80034i	0.541275	+	0.175871i
$746$	−28.5521	−	15.9671i	−1.04537	−	0.584597i
$747$		0			0
$748$	−24.4012	+	13.9650i	−0.892195	+	0.510610i
$749$	11.4164			0.417148
$750$		0			0
$751$	−7.26705	−	2.36121i	−0.265178	−	0.0861616i	0.173410	−	0.984850i	$-0.444521\pi$
$751$	−7.26705	−	2.36121i	−0.265178	−	0.0861616i	−0.438588	+	0.898688i	$0.644521\pi$
$752$	−4.42335	+	4.44497i	−0.161303	+	0.162091i
$753$		0			0
$754$	0.611931	+	0.661175i	0.0222852	+	0.0240786i
$755$	−2.31196	−	7.11547i	−0.0841408	−	0.258959i
$756$		0			0
$757$	28.7250	+	20.8699i	1.04403	+	0.758531i	0.971068	−	0.238804i	$-0.0767553\pi$
$757$	28.7250	+	20.8699i	1.04403	+	0.758531i	0.0729604	+	0.997335i	$0.476755\pi$
$758$	−48.0810	+	5.72047i	−1.74638	+	0.207777i
$759$		0			0
$760$	−3.78515	−	10.2026i	−0.137302	−	0.370088i
$761$	27.8808	−	38.3747i	1.01068	−	1.39108i	0.0921424	−	0.995746i	$-0.470629\pi$
$761$	27.8808	−	38.3747i	1.01068	−	1.39108i	0.918537	−	0.395335i	$-0.129371\pi$
$762$		0			0
$763$	−2.36839	+	0.769537i	−0.0857416	+	0.0278591i
$764$	11.9057	+	10.1434i	0.430733	+	0.366974i
$765$		0			0
$766$	−9.29588	−	20.1321i	−0.335874	−	0.727401i
$767$	2.61469	−	8.04719i	0.0944111	−	0.290567i
$768$		0			0
$769$			18.3147i			0.660444i	0.943903	+	0.330222i	$0.107124\pi$
$769$			18.3147i			0.660444i	−0.943903	+	0.330222i	$0.892876\pi$
$770$	6.49696	+	1.50019i	0.234134	+	0.0540630i
$771$		0			0
$772$	−19.5053	+	47.2527i	−0.702011	+	1.70066i
$773$	−0.791057	+	2.43462i	−0.0284524	+	0.0875674i	−0.964274	−	0.264906i	$-0.914659\pi$
$773$	−0.791057	+	2.43462i	−0.0284524	+	0.0875674i	0.935822	+	0.352473i	$0.114659\pi$
$774$		0			0
$775$	−13.0844	−	18.0091i	−0.470004	−	0.646905i
$776$	33.8247	+	22.5116i	1.21424	+	0.808120i
$777$		0			0
$778$	−2.60164	−	0.515851i	−0.0932734	−	0.0184942i
$779$	−0.175590	+	0.241679i	−0.00629116	+	0.00865904i
$780$		0			0
$781$	−0.662852	+	21.2462i	−0.0237187	+	0.760249i
$782$	5.90603	+	49.6407i	0.211199	+	1.77515i
$783$		0			0
$784$	2.85139	+	17.7233i	0.101836	+	0.632975i
$785$	0.00297768	+	0.00916436i	0.000106278	+	0.000327090i
$786$		0			0
$787$	−17.2890	+	12.5612i	−0.616285	+	0.447757i	−0.851622	−	0.524157i	$-0.824381\pi$
$787$	−17.2890	+	12.5612i	−0.616285	+	0.447757i	0.235337	+	0.971914i	$0.424381\pi$
$788$	19.4026	−	11.9225i	0.691188	−	0.424720i
$789$		0			0
$790$	4.78895	−	8.56353i	0.170383	−	0.304677i
$791$	18.0107			0.640386
$792$		0			0
$793$	13.1709			0.467713
$794$	13.6842	−	24.4699i	0.485635	−	0.868404i
$795$		0			0
$796$	28.5296	−	17.5308i	1.01120	−	0.621363i
$797$	−1.47840	+	1.07412i	−0.0523675	+	0.0380472i	−0.613661	−	0.789570i	$-0.710304\pi$
$797$	−1.47840	+	1.07412i	−0.0523675	+	0.0380472i	0.561294	+	0.827617i	$0.310304\pi$
$798$		0			0
$799$	−2.05332	−	6.31948i	−0.0726413	−	0.223567i
$800$	22.8228	−	6.51182i	0.806907	−	0.230228i
$801$		0			0
$802$	−1.80548	−	15.1752i	−0.0637538	−	0.535855i
$803$	−13.9530	−	5.01980i	−0.492390	−	0.177145i
$804$		0			0
$805$	6.96891	−	9.59188i	0.245622	−	0.338069i
$806$	7.58243	+	1.50344i	0.267080	+	0.0529563i
$807$		0			0
$808$	−13.0675	+	19.6345i	−0.459714	+	0.690741i
$809$	8.16002	+	11.2313i	0.286891	+	0.394872i	0.928001	−	0.372577i	$-0.121526\pi$
$809$	8.16002	+	11.2313i	0.286891	+	0.394872i	−0.641110	+	0.767449i	$0.721526\pi$
$810$		0			0
$811$	10.5825	−	32.5697i	0.371603	−	1.14368i	−0.574139	−	0.818758i	$-0.694663\pi$
$811$	10.5825	−	32.5697i	0.371603	−	1.14368i	0.945742	−	0.324919i	$-0.105337\pi$
$812$	−0.747919	+	1.81188i	−0.0262468	+	0.0635845i
$813$		0			0
$814$	9.20290	+	10.5875i	0.322562	+	0.371092i
$815$		−	11.4466i		−	0.400956i
$816$		0			0
$817$	−8.85124	+	27.2413i	−0.309666	+	0.953052i
$818$	2.44348	+	5.29183i	0.0854342	+	0.185024i
$819$		0			0
$820$	0.0950914	+	0.0810155i	0.00332074	+	0.00282919i
$821$	17.2622	−	5.60881i	0.602453	−	0.195749i	0.00811908	−	0.999967i	$-0.497416\pi$
$821$	17.2622	−	5.60881i	0.602453	−	0.195749i	0.594334	+	0.804218i	$0.297416\pi$
$822$		0			0
$823$	33.1901	−	45.6823i	1.15693	−	1.59238i	0.434987	−	0.900436i	$-0.356753\pi$
$823$	33.1901	−	45.6823i	1.15693	−	1.59238i	0.721947	−	0.691948i	$-0.243247\pi$
$824$	41.6104	−	15.4374i	1.44957	−	0.537786i
$825$		0			0
$826$	18.2813	−	2.17503i	0.636087	−	0.0756790i
$827$	3.49657	+	2.54041i	0.121588	+	0.0883387i	0.646917	−	0.762560i	$-0.276058\pi$
$827$	3.49657	+	2.54041i	0.121588	+	0.0883387i	−0.525329	+	0.850899i	$0.676058\pi$
$828$		0			0
$829$	0.143533	+	0.441750i	0.00498512	+	0.0153426i	0.953518	−	0.301336i	$-0.0974325\pi$
$829$	0.143533	+	0.441750i	0.00498512	+	0.0153426i	−0.948533	+	0.316678i	$0.897432\pi$
$830$	−13.3233	−	14.3955i	−0.462459	−	0.499675i
$831$		0			0
$832$	−4.28050	+	7.04281i	−0.148400	+	0.244166i
$833$	−18.0904	−	5.87791i	−0.626794	−	0.203658i
$834$		0			0
$835$	16.2895			0.563723
$836$	25.9500	+	11.6717i	0.897500	+	0.403675i
$837$		0			0
$838$	9.14525	+	5.11427i	0.315917	+	0.176669i
$839$	−46.8242	−	15.2141i	−1.61655	−	0.525249i	−0.645427	−	0.763822i	$-0.723320\pi$
$839$	−46.8242	−	15.2141i	−1.61655	−	0.525249i	−0.971125	+	0.238573i	$0.923320\pi$
$840$		0			0
$841$	−23.1522	+	16.8210i	−0.798350	+	0.580035i
$842$	−1.17472	−	1.26925i	−0.0404835	−	0.0437413i
$843$		0			0
$844$	0.348344	−	4.49618i	0.0119905	−	0.154765i
$845$	−8.66295	−	6.29400i	−0.298015	−	0.216520i
$846$		0			0
$847$	−14.7165	+	9.34879i	−0.505666	+	0.321228i
$848$	−42.8714	+	21.9758i	−1.47221	+	0.754653i
$849$		0			0
$850$	−4.89118	+	24.6682i	−0.167766	+	0.846111i
$851$	23.7226	−	7.70794i	0.813200	−	0.264225i
$852$		0			0
$853$	3.74183	+	5.15019i	0.128118	+	0.176339i	0.868257	−	0.496115i	$-0.165240\pi$
$853$	3.74183	+	5.15019i	0.128118	+	0.176339i	−0.740139	+	0.672454i	$0.765240\pi$
$854$	12.0136	+	26.0177i	0.411096	+	0.890308i
$855$		0			0
$856$	5.49412	−	19.6179i	0.187785	−	0.670526i
$857$		−	36.2659i		−	1.23882i	−0.785067	−	0.619410i	$-0.787372\pi$
$857$		−	36.2659i		−	1.23882i	0.785067	−	0.619410i	$-0.212628\pi$
$858$		0			0
$859$			7.69096i			0.262412i	0.991355	+	0.131206i	$0.0418850\pi$
$859$			7.69096i			0.262412i	−0.991355	+	0.131206i	$0.958115\pi$
$860$	11.0718	+	4.57030i	0.377546	+	0.155846i
$861$		0			0
$862$	−24.9923	+	11.5401i	−0.851240	+	0.393056i
$863$	19.8376	+	27.3041i	0.675280	+	0.929443i	0.999865	−	0.0164137i	$-0.00522487\pi$
$863$	19.8376	+	27.3041i	0.675280	+	0.929443i	−0.324586	+	0.945856i	$0.605225\pi$
$864$		0			0
$865$	−16.3169	+	5.30169i	−0.554792	+	0.180263i
$866$	−22.6926	−	4.49947i	−0.771126	−	0.152898i
$867$		0			0
$868$	3.94627	+	16.3496i	0.133945	+	0.554941i
$869$	7.16310	+	24.6346i	0.242992	+	0.835673i
$870$		0			0
$871$	11.5375	+	8.38246i	0.390932	+	0.284029i
$872$	0.182584	+	4.44016i	0.00618308	+	0.150363i
$873$		0			0
$874$	37.1315	−	34.3660i	1.25599	−	1.16245i
$875$	10.5758	−	7.68378i	0.357528	−	0.259759i
$876$		0			0
$877$	−17.3624	−	5.64139i	−0.586287	−	0.190496i	0.000827907	−	1.00000i	$-0.499736\pi$
$877$	−17.3624	−	5.64139i	−0.586287	−	0.190496i	−0.587115	+	0.809503i	$0.699736\pi$
$878$	10.1499	−	18.1499i	0.342543	−	0.612530i
$879$		0			0
$880$	5.70455	−	10.4424i	0.192300	−	0.352012i
$881$	−37.3245			−1.25749			−0.628747	−	0.777610i	$-0.716432\pi$
$881$	−37.3245			−1.25749			−0.628747	+	0.777610i	$0.716432\pi$
$882$		0			0
$883$	−7.36835	−	2.39412i	−0.247965	−	0.0805686i	0.182398	−	0.983225i	$-0.441614\pi$
$883$	−7.36835	−	2.39412i	−0.247965	−	0.0805686i	−0.430362	+	0.902656i	$0.641614\pi$
$884$	−4.57200	−	7.44046i	−0.153773	−	0.250250i
$885$		0			0
$886$	−7.64200	+	7.07283i	−0.256738	+	0.237616i
$887$	−12.3998	−	38.1626i	−0.416344	−	1.28138i	−0.911043	−	0.412311i	$-0.864722\pi$
$887$	−12.3998	−	38.1626i	−0.416344	−	1.28138i	0.494699	−	0.869065i	$-0.335278\pi$
$888$		0			0
$889$	−12.5352	−	9.10732i	−0.420416	−	0.305450i
$890$	0.450889	+	3.78975i	0.0151138	+	0.127033i
$891$		0			0
$892$	2.45349	+	10.1649i	0.0821491	+	0.340348i
$893$	−3.95279	+	5.44055i	−0.132275	+	0.182061i
$894$		0			0
$895$	2.01002	−	0.653096i	0.0671877	−	0.0218306i
$896$	−17.8167	−	2.03172i	−0.595213	−	0.0678750i
$897$		0			0
$898$	−7.16027	+	3.30622i	−0.238941	+	0.110330i
$899$	1.01383	−	3.12025i	0.0338132	−	0.104066i
$900$		0			0
$901$		−	51.0475i		−	1.70064i
$902$	−0.325402	+	0.0284572i	−0.0108347	+	0.000947521i
$903$		0			0
$904$	8.66757	−	30.9493i	0.288279	−	1.02936i
$905$	−6.51528	+	20.0520i	−0.216575	+	0.666550i
$906$		0			0
$907$	28.1825	+	38.7899i	0.935784	+	1.28800i	0.957560	+	0.288234i	$0.0930680\pi$
$907$	28.1825	+	38.7899i	0.935784	+	1.28800i	−0.0217756	+	0.999763i	$0.506932\pi$
$908$	−5.32861	+	6.25442i	−0.176836	+	0.207560i
$909$		0			0
$910$	−0.402827	+	2.03162i	−0.0133536	+	0.0673474i
$911$	12.8537	−	17.6916i	0.425863	−	0.586150i	−0.541135	−	0.840936i	$-0.682005\pi$
$911$	12.8537	−	17.6916i	0.425863	−	0.586150i	0.966997	+	0.254786i	$0.0820051\pi$
$912$		0			0
$913$	51.2629	+	1.59933i	1.69655	+	0.0529301i
$914$	25.9515	−	3.08760i	0.858399	−	0.102129i
$915$		0			0
$916$	−0.248239	+	3.20409i	−0.00820204	+	0.105866i
$917$	−4.97686	−	15.3172i	−0.164350	−	0.505819i
$918$		0			0
$919$	26.8892	−	19.5362i	0.886993	−	0.644438i	−0.0480990	−	0.998843i	$-0.515316\pi$
$919$	26.8892	−	19.5362i	0.886993	−	0.644438i	0.935092	+	0.354404i	$0.115316\pi$
$920$	−13.1288	−	16.5914i	−0.432844	−	0.547001i
$921$		0			0
$922$	21.7629	+	12.1704i	0.716723	+	0.400810i
$923$	−6.60264			−0.217329
$924$		0			0
$925$	12.5481			0.412578
$926$	−16.3742	−	9.15690i	−0.538090	−	0.300914i
$927$		0			0
$928$	2.75358	+	2.15718i	0.0903907	+	0.0708128i
$929$	20.7577	−	15.0813i	0.681038	−	0.494803i	−0.192664	−	0.981265i	$-0.561713\pi$
$929$	20.7577	−	15.0813i	0.681038	−	0.494803i	0.873702	+	0.486462i	$0.161713\pi$
$930$		0			0
$931$	5.94886	+	18.3087i	0.194966	+	0.600044i
$932$	−22.4563	−	1.73982i	−0.735582	−	0.0569896i
$933$		0			0
$934$	30.6918	−	3.65158i	1.00427	−	0.119483i
$935$	7.08927	+	10.4264i	0.231844	+	0.340981i
$936$		0			0
$937$	0.340605	−	0.468802i	0.0111271	−	0.0153151i	−0.803417	−	0.595416i	$-0.796987\pi$
$937$	0.340605	−	0.468802i	0.0111271	−	0.0153151i	0.814544	+	0.580101i	$0.196987\pi$
$938$	−6.03499	+	30.4369i	−0.197049	+	0.993799i
$939$		0			0
$940$	2.14065	+	1.82378i	0.0698204	+	0.0594852i
$941$	29.1003	+	40.0531i	0.948643	+	1.30569i	0.952128	+	0.305701i	$0.0988907\pi$
$941$	29.1003	+	40.0531i	0.948643	+	1.30569i	−0.00348491	+	0.999994i	$0.501109\pi$
$942$		0			0
$943$	−0.179479	+	0.552378i	−0.00584463	+	0.0179879i
$944$	5.06026	−	32.4611i	0.164697	−	1.05652i
$945$		0			0
$946$	−28.8302	+	12.2365i	−0.937351	+	0.397842i
$947$			36.6649i			1.19145i	0.803189	+	0.595725i	$0.203135\pi$
$947$			36.6649i			1.19145i	−0.803189	+	0.595725i	$0.796865\pi$
$948$		0			0
$949$	1.42333	−	4.38054i	0.0462031	−	0.142198i
$950$	23.1075	−	10.6698i	0.749707	−	0.346174i
$951$		0			0
$952$	10.5276	−	15.8181i	0.341200	−	0.512669i
$953$	−29.3372	+	9.53224i	−0.950326	+	0.308780i	−0.742848	−	0.669460i	$-0.766526\pi$
$953$	−29.3372	+	9.53224i	−0.950326	+	0.308780i	−0.207478	+	0.978240i	$0.566526\pi$
$954$		0			0
$955$	4.12286	−	5.67463i	0.133413	−	0.183627i
$956$	7.73940	−	1.86804i	0.250310	−	0.0604168i
$957$		0			0
$958$	−5.94406	−	49.9603i	−0.192044	−	1.61414i
$959$	12.8241	+	9.31728i	0.414113	+	0.300871i
$960$		0			0
$961$	0.880437	+	2.70971i	0.0284012	+	0.0874099i
$962$	−3.19791	+	2.95974i	−0.103105	+	0.0954258i
$963$		0			0
$964$	−18.0906	+	11.1163i	−0.582659	+	0.358032i
$965$	21.8032	+	7.08430i	0.701871	+	0.228052i
$966$		0			0
$967$	−14.2448			−0.458082			−0.229041	−	0.973417i	$-0.573559\pi$
$967$	−14.2448			−0.458082			−0.229041	+	0.973417i	$0.573559\pi$
$968$	8.98258	+	29.7878i	0.288711	+	0.957416i
$969$		0			0
$970$	8.89363	−	15.9034i	0.285557	−	0.510629i
$971$	19.0385	+	6.18597i	0.610973	+	0.198517i	0.598128	−	0.801400i	$-0.295911\pi$
$971$	19.0385	+	6.18597i	0.610973	+	0.198517i	0.0128447	+	0.999918i	$0.495911\pi$
$972$		0			0
$973$	19.2403	−	13.9789i	0.616815	−	0.448143i
$974$	−14.2044	+	13.1465i	−0.455140	+	0.421241i
$975$		0			0
$976$	50.4901	−	8.12304i	1.61615	−	0.260012i
$977$	19.9486	+	14.4935i	0.638211	+	0.463687i	0.859235	−	0.511581i	$-0.170940\pi$
$977$	19.9486	+	14.4935i	0.638211	+	0.463687i	−0.221024	+	0.975268i	$0.570940\pi$
$978$		0			0
$979$	−7.88645	−	6.11449i	−0.252052	−	0.195420i
$980$	7.82563	−	1.88886i	0.249980	−	0.0603373i
$981$		0			0
$982$	−13.8069	−	2.73762i	−0.440596	−	0.0873609i
$983$	6.72347	−	2.18459i	0.214445	−	0.0696775i	−0.199824	−	0.979832i	$-0.564037\pi$
$983$	6.72347	−	2.18459i	0.214445	−	0.0696775i	0.414270	+	0.910154i	$0.364037\pi$
$984$		0			0
$985$	−6.00287	−	8.26224i	−0.191267	−	0.263257i
$986$	−3.36506	+	1.55380i	−0.107165	+	0.0494830i
$987$		0			0
$988$	−3.37232	+	8.16965i	−0.107288	+	0.259911i
$989$			55.6892i			1.77081i
$990$		0			0
$991$		−	22.2482i		−	0.706736i	−0.935484	−	0.353368i	$-0.885036\pi$
$991$		−	22.2482i		−	0.706736i	0.935484	−	0.353368i	$-0.114964\pi$
$992$	29.9941	+	1.08696i	0.952313	+	0.0345109i
$993$		0			0
$994$	−6.02245	−	13.0428i	−0.191021	−	0.413692i
$995$	−8.82662	−	12.1488i	−0.279823	−	0.385143i
$996$		0			0
$997$	−34.5506	+	11.2262i	−1.09423	+	0.355536i	−0.799878	−	0.600162i	$-0.795103\pi$
$997$	−34.5506	+	11.2262i	−1.09423	+	0.355536i	−0.294349	+	0.955698i	$0.595103\pi$
$998$	4.90506	−	24.7382i	0.155267	−	0.783073i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.r.b.271.4		48
3.2	odd	2		132.2.j.a.7.9	✓	48
4.3	odd	2	inner	396.2.r.b.271.3		48
11.8	odd	10	inner	396.2.r.b.19.3		48
12.11	even	2		132.2.j.a.7.10	yes	48
33.8	even	10		132.2.j.a.19.10	yes	48
44.19	even	10	inner	396.2.r.b.19.4		48
132.107	odd	10		132.2.j.a.19.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.9	✓	48	3.2	odd	2
132.2.j.a.7.10	yes	48	12.11	even	2
132.2.j.a.19.9	yes	48	132.107	odd	10
132.2.j.a.19.10	yes	48	33.8	even	10
396.2.r.b.19.3		48	11.8	odd	10	inner
396.2.r.b.19.4		48	44.19	even	10	inner
396.2.r.b.271.3		48	4.3	odd	2	inner
396.2.r.b.271.4		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.690263 + 1.23432i) q^{2} +(-1.04707 - 1.70401i) q^{4} +(-0.725620 + 0.527194i) q^{5} +(0.489790 + 1.50742i) q^{7} +(2.82604 - 0.116210i) q^{8} +O(q^{10})\)	\(q+(-0.690263 + 1.23432i) q^{2} +(-1.04707 - 1.70401i) q^{4} +(-0.725620 + 0.527194i) q^{5} +(0.489790 + 1.50742i) q^{7} +(2.82604 - 0.116210i) q^{8} +(-0.149856 - 1.25955i) q^{10} +(2.62111 + 2.03219i) q^{11} +(-0.605536 + 0.833449i) q^{13} +(-2.19871 - 0.435959i) q^{14} +(-1.80727 + 3.56844i) q^{16} +(-2.49130 - 3.42898i) q^{17} +(-1.32556 + 4.07966i) q^{19} +(1.65812 + 0.684449i) q^{20} +(-4.31762 + 1.83254i) q^{22} +8.34003i q^{23} +(-1.29649 + 3.99020i) q^{25} +(-0.610761 - 1.32272i) q^{26} +(2.05580 - 2.41298i) q^{28} +(-0.588090 + 0.191082i) q^{29} +(-3.11863 + 4.29243i) q^{31} +(-3.15710 - 4.69391i) q^{32} +(5.95210 - 0.708155i) q^{34} +(-1.15010 - 0.835598i) q^{35} +(-0.924210 - 2.84443i) q^{37} +(-4.12061 - 4.45220i) q^{38} +(-1.98937 + 1.57419i) q^{40} +(0.0662322 + 0.0215201i) q^{41} +6.67734 q^{43} +(0.718360 - 6.59424i) q^{44} +(-10.2942 - 5.75681i) q^{46} +(1.49099 + 0.484451i) q^{47} +(3.63071 - 2.63786i) q^{49} +(-4.03025 - 4.35457i) q^{50} +(2.05424 + 0.159154i) q^{52} +(9.74373 + 7.07923i) q^{53} +(-2.97329 - 0.0927624i) q^{55} +(1.55934 + 4.20310i) q^{56} +(0.170081 - 0.857787i) q^{58} +(-7.81130 + 2.53804i) q^{59} +(-7.51474 - 10.3431i) q^{61} +(-3.14554 - 6.81229i) q^{62} +(7.97299 - 0.656828i) q^{64} -0.924002i q^{65} -13.8430i q^{67} +(-3.23442 + 7.83559i) q^{68} +(1.82526 - 0.842808i) q^{70} +(3.76717 + 5.18506i) q^{71} +(-4.25213 + 1.38160i) q^{73} +(4.14887 + 0.822634i) q^{74} +(8.33973 - 2.01294i) q^{76} +(-1.77956 + 4.94645i) q^{77} +(6.25795 + 4.54667i) q^{79} +(-0.569869 - 3.54211i) q^{80} +(-0.0722803 + 0.0668969i) q^{82} +(12.5105 - 9.08942i) q^{83} +(3.61547 + 1.17474i) q^{85} +(-4.60912 + 8.24196i) q^{86} +(7.64352 + 5.43844i) q^{88} -3.00882 q^{89} +(-1.55294 - 0.504581i) q^{91} +(14.2114 - 8.73263i) q^{92} +(-1.62714 + 1.50595i) q^{94} +(-1.18892 - 3.65911i) q^{95} +(11.6217 + 8.44368i) q^{97} +(0.749816 + 6.30226i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} + 14 q^{14} - 24 q^{16} + 22 q^{20} - 26 q^{22} - 20 q^{25} + 38 q^{26} - 10 q^{28} - 48 q^{37} - 58 q^{38} + 70 q^{40} + 40 q^{41} - 34 q^{44} + 70 q^{46} - 28 q^{49} - 70 q^{50} + 30 q^{52} + 64 q^{53} - 60 q^{56} - 54 q^{58} - 40 q^{64} + 4 q^{70} + 20 q^{73} - 50 q^{74} + 8 q^{77} - 58 q^{80} + 62 q^{82} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 48 q^{89} - 42 q^{92} - 10 q^{94} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 14 * q^14 - 24 * q^16 + 22 * q^20 - 26 * q^22 - 20 * q^25 + 38 * q^26 - 10 * q^28 - 48 * q^37 - 58 * q^38 + 70 * q^40 + 40 * q^41 - 34 * q^44 + 70 * q^46 - 28 * q^49 - 70 * q^50 + 30 * q^52 + 64 * q^53 - 60 * q^56 - 54 * q^58 - 40 * q^64 + 4 * q^70 + 20 * q^73 - 50 * q^74 + 8 * q^77 - 58 * q^80 + 62 * q^82 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 48 * q^89 - 42 * q^92 - 10 * q^94 + 48 * q^97

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