LMFDB - Embedded newform 738.2.ba.d.17.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(17,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,0,0,0,-4,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$4$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	738.17
Dual form			738.2.ba.d.521.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.987688 - 0.156434i) q^{2} +(0.951057 - 0.309017i) q^{4} +(1.06405 - 2.08832i) q^{5} +(-1.59404 - 0.976830i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.724268 - 2.22907i) q^{10} +(-2.43855 + 0.191918i) q^{11} +(1.53962 - 6.41296i) q^{13} +(-1.72723 - 0.715440i) q^{14} +(0.809017 - 0.587785i) q^{16} +(-0.438953 + 0.513948i) q^{17} +(0.468536 + 1.95159i) q^{19} +(0.366648 - 2.31493i) q^{20} +(-2.37851 + 0.571029i) q^{22} +(-0.837387 - 0.608397i) q^{23} +(-0.289962 - 0.399098i) q^{25} +(0.517452 - 6.57486i) q^{26} +(-1.81788 - 0.436434i) q^{28} +(-6.03260 - 7.06326i) q^{29} +(9.30139 + 3.02221i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.353150 + 0.576288i) q^{34} +(-3.73608 + 2.28948i) q^{35} +(1.48034 + 4.55602i) q^{37} +(0.768064 + 1.85427i) q^{38} -2.34378i q^{40} +(5.69026 - 2.93614i) q^{41} +(0.303537 + 1.91646i) q^{43} +(-2.25990 + 0.936079i) q^{44} +(-0.922252 - 0.469911i) q^{46} +(1.67861 + 2.73924i) q^{47} +(-1.59116 - 3.12283i) q^{49} +(-0.348825 - 0.348825i) q^{50} +(-0.517452 - 6.57486i) q^{52} +(-1.20437 + 1.02863i) q^{53} +(-2.19397 + 5.29670i) q^{55} +(-1.86377 - 0.146682i) q^{56} +(-7.06326 - 6.03260i) q^{58} +(-5.80669 + 7.99222i) q^{59} +(1.75573 + 0.278080i) q^{61} +(9.65965 + 1.52994i) q^{62} +(0.587785 - 0.809017i) q^{64} +(-11.7541 - 10.0390i) q^{65} +(7.52800 + 0.592466i) q^{67} +(-0.258650 + 0.624437i) q^{68} +(-3.33193 + 2.84574i) q^{70} +(-0.392536 - 4.98765i) q^{71} +(5.81775 + 5.81775i) q^{73} +(2.17483 + 4.26835i) q^{74} +(1.04868 + 1.71129i) q^{76} +(4.07462 + 2.07613i) q^{77} +(14.7847 - 6.12403i) q^{79} +(-0.366648 - 2.31493i) q^{80} +(5.16089 - 3.79015i) q^{82} +9.15572i q^{83} +(0.606220 + 1.46354i) q^{85} +(0.599600 + 1.84538i) q^{86} +(-2.08564 + 1.27808i) q^{88} +(4.70364 - 7.67565i) q^{89} +(-8.71858 + 8.71858i) q^{91} +(-0.984407 - 0.319853i) q^{92} +(2.08646 + 2.44293i) q^{94} +(4.57411 + 1.09815i) q^{95} +(-1.16288 + 14.7757i) q^{97} +(-2.06009 - 2.83547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{7} + 8 q^{11} + 16 q^{13} - 4 q^{14} + 16 q^{16} + 16 q^{17} + 4 q^{19} - 4 q^{22} - 48 q^{23} + 40 q^{25} + 20 q^{26} + 4 q^{28} - 4 q^{29} + 40 q^{31} + 4 q^{34} + 52 q^{35} + 8 q^{37} - 16 q^{38}+ \cdots + 64 q^{97}+O(q^{100}) $ 64 * q - 4 * q^7 + 8 * q^11 + 16 * q^13 - 4 * q^14 + 16 * q^16 + 16 * q^17 + 4 * q^19 - 4 * q^22 - 48 * q^23 + 40 * q^25 + 20 * q^26 + 4 * q^28 - 4 * q^29 + 40 * q^31 + 4 * q^34 + 52 * q^35 + 8 * q^37 - 16 * q^38 - 12 * q^41 + 32 * q^43 + 4 * q^44 + 8 * q^47 + 48 * q^49 - 16 * q^50 - 20 * q^52 + 48 * q^53 - 36 * q^55 - 16 * q^56 - 20 * q^58 - 20 * q^59 + 24 * q^61 + 36 * q^62 - 60 * q^65 - 20 * q^67 - 12 * q^68 - 8 * q^70 + 8 * q^71 + 72 * q^73 + 12 * q^74 + 4 * q^76 + 76 * q^77 + 44 * q^79 - 68 * q^82 - 88 * q^85 + 32 * q^86 - 8 * q^88 - 84 * q^89 + 72 * q^91 + 12 * q^94 + 12 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{33}{40}\right)$

Coefficient data

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

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

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

$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$3$		0			0
$3$		0			0
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	1.06405	−	2.08832i	0.475860	−	0.933927i	−0.520910	−	0.853612i	$-0.674407\pi$
$5$	1.06405	−	2.08832i	0.475860	−	0.933927i	0.996769	−	0.0803155i	$-0.0255928\pi$
$6$		0			0
$7$	−1.59404	−	0.976830i	−0.602491	−	0.369207i	0.187555	−	0.982254i	$-0.439944\pi$
$7$	−1.59404	−	0.976830i	−0.602491	−	0.369207i	−0.790046	+	0.613047i	$0.789944\pi$
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$		0			0
$10$	0.724268	−	2.22907i	0.229034	−	0.704893i
$11$	−2.43855	+	0.191918i	−0.735251	+	0.0578655i	−0.440555	−	0.897725i	$-0.645218\pi$
$11$	−2.43855	+	0.191918i	−0.735251	+	0.0578655i	−0.294696	+	0.955591i	$0.595218\pi$
$12$		0			0
$13$	1.53962	−	6.41296i	0.427013	−	1.77864i	−0.179708	−	0.983720i	$-0.557515\pi$
$13$	1.53962	−	6.41296i	0.427013	−	1.77864i	0.606721	−	0.794915i	$-0.292485\pi$
$14$	−1.72723	−	0.715440i	−0.461620	−	0.191209i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.438953	+	0.513948i	−0.106462	+	0.124651i	−0.811078	−	0.584938i	$-0.801119\pi$
$17$	−0.438953	+	0.513948i	−0.106462	+	0.124651i	0.704617	+	0.709588i	$0.251119\pi$
$18$		0			0
$19$	0.468536	+	1.95159i	0.107490	+	0.447726i	0.999995	−	0.00331147i	$-0.00105408\pi$
$19$	0.468536	+	1.95159i	0.107490	+	0.447726i	−0.892505	+	0.451037i	$0.851054\pi$
$20$	0.366648	−	2.31493i	0.0819850	−	0.517633i
$21$		0			0
$22$	−2.37851	+	0.571029i	−0.507100	+	0.121744i
$23$	−0.837387	−	0.608397i	−0.174607	−	0.126860i	0.497049	−	0.867722i	$-0.334417\pi$
$23$	−0.837387	−	0.608397i	−0.174607	−	0.126860i	−0.671656	+	0.740863i	$0.734417\pi$
$24$		0			0
$25$	−0.289962	−	0.399098i	−0.0579924	−	0.0798197i
$26$	0.517452	−	6.57486i	0.101481	−	1.28944i
$27$		0			0
$28$	−1.81788	−	0.436434i	−0.343547	−	0.0824783i
$29$	−6.03260	−	7.06326i	−1.12022	−	1.31161i	−0.944994	−	0.327088i	$-0.893933\pi$
$29$	−6.03260	−	7.06326i	−1.12022	−	1.31161i	−0.175231	−	0.984527i	$-0.556067\pi$
$30$		0			0
$31$	9.30139	+	3.02221i	1.67058	+	0.542804i	0.983048	−	0.183350i	$-0.0586943\pi$
$31$	9.30139	+	3.02221i	1.67058	+	0.542804i	0.687532	+	0.726154i	$0.258694\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−0.353150	+	0.576288i	−0.0605646	+	0.0988325i
$35$	−3.73608	+	2.28948i	−0.631513	+	0.386992i
$36$		0			0
$37$	1.48034	+	4.55602i	0.243366	+	0.749004i	0.995901	+	0.0904516i	$0.0288311\pi$
$37$	1.48034	+	4.55602i	0.243366	+	0.749004i	−0.752535	+	0.658553i	$0.771169\pi$
$38$	0.768064	+	1.85427i	0.124596	+	0.300802i
$39$		0			0
$40$		−	2.34378i		−	0.370584i
$41$	5.69026	−	2.93614i	0.888669	−	0.458549i
$41$	5.69026	−	2.93614i	0.888669	−	0.458549i
$42$		0			0
$43$	0.303537	+	1.91646i	0.0462889	+	0.292257i	0.999963	−	0.00858448i	$-0.00273256\pi$
$43$	0.303537	+	1.91646i	0.0462889	+	0.292257i	−0.953674	+	0.300841i	$0.902733\pi$
$44$	−2.25990	+	0.936079i	−0.340692	+	0.141119i
$45$		0			0
$46$	−0.922252	−	0.469911i	−0.135979	−	0.0692846i
$47$	1.67861	+	2.73924i	0.244850	+	0.399560i	0.951330	−	0.308174i	$-0.0997178\pi$
$47$	1.67861	+	2.73924i	0.244850	+	0.399560i	−0.706480	+	0.707733i	$0.749718\pi$
$48$		0			0
$49$	−1.59116	−	3.12283i	−0.227309	−	0.446119i
$50$	−0.348825	−	0.348825i	−0.0493313	−	0.0493313i
$51$		0			0
$52$	−0.517452	−	6.57486i	−0.0717577	−	0.911768i
$53$	−1.20437	+	1.02863i	−0.165433	+	0.141293i	−0.728311	−	0.685247i	$-0.759694\pi$
$53$	−1.20437	+	1.02863i	−0.165433	+	0.141293i	0.562878	+	0.826540i	$0.309694\pi$
$54$		0			0
$55$	−2.19397	+	5.29670i	−0.295834	+	0.714207i
$56$	−1.86377	−	0.146682i	−0.249057	−	0.0196012i
$57$		0			0
$58$	−7.06326	−	6.03260i	−0.927452	−	0.792119i
$59$	−5.80669	+	7.99222i	−0.755966	+	1.04050i	0.241572	+	0.970383i	$0.422337\pi$
$59$	−5.80669	+	7.99222i	−0.755966	+	1.04050i	−0.997539	+	0.0701158i	$0.977663\pi$
$60$		0			0
$61$	1.75573	+	0.278080i	0.224798	+	0.0356045i	0.267817	−	0.963470i	$-0.413698\pi$
$61$	1.75573	+	0.278080i	0.224798	+	0.0356045i	−0.0430193	+	0.999074i	$0.513698\pi$
$62$	9.65965	+	1.52994i	1.22678	+	0.194302i
$63$		0			0
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−11.7541	−	10.0390i	−1.45792	−	1.24518i
$66$		0			0
$67$	7.52800	+	0.592466i	0.919691	+	0.0723813i	0.529459	−	0.848335i	$-0.322395\pi$
$67$	7.52800	+	0.592466i	0.919691	+	0.0723813i	0.390232	+	0.920717i	$0.372395\pi$
$68$	−0.258650	+	0.624437i	−0.0313660	+	0.0757241i
$69$		0			0
$70$	−3.33193	+	2.84574i	−0.398242	+	0.340131i
$71$	−0.392536	−	4.98765i	−0.0465855	−	0.591925i	−0.975265	−	0.221041i	$-0.929055\pi$
$71$	−0.392536	−	4.98765i	−0.0465855	−	0.591925i	0.928679	−	0.370884i	$-0.120945\pi$
$72$		0			0
$73$	5.81775	+	5.81775i	0.680916	+	0.680916i	0.960207	−	0.279291i	$-0.0900993\pi$
$73$	5.81775	+	5.81775i	0.680916	+	0.680916i	−0.279291	+	0.960207i	$0.590099\pi$
$74$	2.17483	+	4.26835i	0.252819	+	0.496185i
$75$		0			0
$76$	1.04868	+	1.71129i	0.120292	+	0.196298i
$77$	4.07462	+	2.07613i	0.464347	+	0.236596i
$78$		0			0
$79$	14.7847	−	6.12403i	1.66341	−	0.689008i	0.665081	−	0.746771i	$-0.268397\pi$
$79$	14.7847	−	6.12403i	1.66341	−	0.689008i	0.998330	+	0.0577634i	$0.0183969\pi$
$80$	−0.366648	−	2.31493i	−0.0409925	−	0.258817i
$81$		0			0
$82$	5.16089	−	3.79015i	0.569925	−	0.418552i
$83$			9.15572i			1.00497i	0.864586	+	0.502486i	$0.167581\pi$
$83$			9.15572i			1.00497i	−0.864586	+	0.502486i	$0.832419\pi$
$84$		0			0
$85$	0.606220	+	1.46354i	0.0657538	+	0.158744i
$86$	0.599600	+	1.84538i	0.0646565	+	0.198992i
$87$		0			0
$88$	−2.08564	+	1.27808i	−0.222330	+	0.136244i
$89$	4.70364	−	7.67565i	0.498585	−	0.813617i	−0.500042	−	0.866001i	$-0.666682\pi$
$89$	4.70364	−	7.67565i	0.498585	−	0.813617i	0.998627	+	0.0523842i	$0.0166821\pi$
$90$		0			0
$91$	−8.71858	+	8.71858i	−0.913955	+	0.913955i
$92$	−0.984407	−	0.319853i	−0.102632	−	0.0333470i
$93$		0			0
$94$	2.08646	+	2.44293i	0.215201	+	0.251969i
$95$	4.57411	+	1.09815i	0.469293	+	0.112667i
$96$		0			0
$97$	−1.16288	+	14.7757i	−0.118072	+	1.50025i	0.597589	+	0.801802i	$0.296125\pi$
$97$	−1.16288	+	14.7757i	−0.118072	+	1.50025i	−0.715661	+	0.698447i	$0.753875\pi$
$98$	−2.06009	−	2.83547i	−0.208101	−	0.286426i
$99$		0			0
$100$	−0.399098	−	0.289962i	−0.0399098	−	0.0289962i
$101$	−5.09166	+	1.22240i	−0.506639	+	0.121633i	−0.478704	−	0.877977i	$-0.658893\pi$
$101$	−5.09166	+	1.22240i	−0.506639	+	0.121633i	−0.0279350	+	0.999610i	$0.508893\pi$
$102$		0			0
$103$	2.16284	−	13.6556i	0.213111	−	1.34553i	−0.616574	−	0.787297i	$-0.711480\pi$
$103$	2.16284	−	13.6556i	0.213111	−	1.34553i	0.829685	−	0.558232i	$-0.188520\pi$
$104$	−1.53962	−	6.41296i	−0.150972	−	0.628843i
$105$		0			0
$106$	−1.02863	+	1.20437i	−0.0999095	+	0.116979i
$107$	−3.34533	+	2.43053i	−0.323406	+	0.234968i	−0.737627	−	0.675208i	$-0.764054\pi$
$107$	−3.34533	+	2.43053i	−0.323406	+	0.234968i	0.414222	+	0.910176i	$0.364054\pi$
$108$		0			0
$109$	−3.98800	−	1.65188i	−0.381981	−	0.158222i	0.183426	−	0.983033i	$-0.441281\pi$
$109$	−3.98800	−	1.65188i	−0.381981	−	0.158222i	−0.565407	+	0.824812i	$0.691281\pi$
$110$	−1.33837	+	5.57470i	−0.127608	+	0.531527i
$111$		0			0
$112$	−1.86377	+	0.146682i	−0.176110	+	0.0138602i
$113$	−4.15993	+	12.8030i	−0.391333	+	1.20440i	0.540447	+	0.841378i	$0.318255\pi$
$113$	−4.15993	+	12.8030i	−0.391333	+	1.20440i	−0.931780	+	0.363022i	$0.881745\pi$
$114$		0			0
$115$	−2.16156	+	1.10137i	−0.201566	+	0.102703i
$116$	−7.92001	−	4.85339i	−0.735354	−	0.450626i
$117$		0			0
$118$	−4.48494	+	8.80219i	−0.412872	+	0.810307i
$119$	1.20175	−	0.390472i	0.110164	−	0.0357945i
$120$		0			0
$121$	−4.95486	+	0.784773i	−0.450442	+	0.0713430i
$122$	1.77761			0.160938
$123$		0			0
$124$	9.78006			0.878275
$125$	10.4326	−	1.65237i	0.933124	−	0.147792i
$126$		0			0
$127$	5.24751	−	1.70502i	0.465641	−	0.151296i	−0.0667941	−	0.997767i	$-0.521277\pi$
$127$	5.24751	−	1.70502i	0.465641	−	0.151296i	0.532435	+	0.846471i	$0.321277\pi$
$128$	0.453990	−	0.891007i	0.0401275	−	0.0787546i
$129$		0			0
$130$	−13.1798	−	8.07661i	−1.15595	−	0.708366i
$131$	−7.78361	+	3.96595i	−0.680057	+	0.346506i	−0.759660	−	0.650320i	$-0.774635\pi$
$131$	−7.78361	+	3.96595i	−0.680057	+	0.346506i	0.0796032	+	0.996827i	$0.474635\pi$
$132$		0			0
$133$	1.15951	−	3.56860i	0.100542	−	0.309437i
$134$	7.52800	−	0.592466i	0.650320	−	0.0511813i
$135$		0			0
$136$	−0.157782	+	0.657211i	−0.0135297	+	0.0563554i
$137$	10.6518	+	4.41213i	0.910047	+	0.376954i	0.788074	−	0.615580i	$-0.211078\pi$
$137$	10.6518	+	4.41213i	0.910047	+	0.376954i	0.121972	+	0.992534i	$0.461078\pi$
$138$		0			0
$139$	−16.2288	+	11.7909i	−1.37651	+	1.00009i	−0.379308	+	0.925270i	$0.623838\pi$
$139$	−16.2288	+	11.7909i	−1.37651	+	1.00009i	−0.997197	+	0.0748194i	$0.976162\pi$
$140$	−2.84574	+	3.33193i	−0.240509	+	0.281600i
$141$		0			0
$142$	−1.16794	−	4.86483i	−0.0980116	−	0.408248i
$143$	−2.52367	+	15.9338i	−0.211040	+	1.33245i
$144$		0			0
$145$	−21.1694	+	5.08232i	−1.75802	+	0.422064i
$146$	6.65622	+	4.83603i	0.550873	+	0.400232i
$147$		0			0
$148$	2.81577	+	3.87558i	0.231455	+	0.318571i
$149$	−0.848452	+	10.7806i	−0.0695079	+	0.883181i	0.859026	+	0.511933i	$0.171070\pi$
$149$	−0.848452	+	10.7806i	−0.0695079	+	0.883181i	−0.928534	+	0.371249i	$0.878930\pi$
$150$		0			0
$151$	1.73061	+	0.415483i	0.140835	+	0.0338115i	0.303250	−	0.952911i	$-0.401928\pi$
$151$	1.73061	+	0.415483i	0.140835	+	0.0338115i	−0.162415	+	0.986723i	$0.551928\pi$
$152$	1.30347	+	1.52617i	0.105726	+	0.123789i
$153$		0			0
$154$	4.34924	+	1.41315i	0.350471	+	0.113875i
$155$	16.2085	−	16.2085i	1.30190	−	1.30190i
$156$		0			0
$157$	−0.150656	+	0.245849i	−0.0120237	+	0.0196209i	−0.858596	−	0.512654i	$-0.828663\pi$
$157$	−0.150656	+	0.245849i	−0.0120237	+	0.0196209i	0.846572	+	0.532274i	$0.178663\pi$
$158$	13.6447	−	8.36148i	1.08551	−	0.665203i
$159$		0			0
$160$	−0.724268	−	2.22907i	−0.0572584	−	0.176223i
$161$	0.740529	+	1.78779i	0.0583618	+	0.140898i
$162$		0			0
$163$			15.4940i			1.21358i	0.794861	+	0.606792i	$0.207544\pi$
$163$			15.4940i			1.21358i	−0.794861	+	0.606792i	$0.792456\pi$
$164$	4.50444	−	4.55083i	0.351738	−	0.355360i
$165$		0			0
$166$	1.43227	+	9.04300i	0.111166	+	0.701873i
$167$	−21.2819	+	8.81526i	−1.64685	+	0.682146i	−0.996962	−	0.0778885i	$-0.975182\pi$
$167$	−21.2819	+	8.81526i	−1.64685	+	0.682146i	−0.649883	+	0.760034i	$0.725182\pi$
$168$		0			0
$169$	−27.1726	−	13.8451i	−2.09020	−	1.06501i
$170$	0.827705	+	1.35069i	0.0634821	+	0.103593i
$171$		0			0
$172$	0.880898	+	1.72886i	0.0671679	+	0.131824i
$173$	8.60874	+	8.60874i	0.654511	+	0.654511i	0.954076	−	0.299565i	$-0.0968416\pi$
$173$	8.60874	+	8.60874i	0.654511	+	0.654511i	−0.299565	+	0.954076i	$0.596842\pi$
$174$		0			0
$175$	0.0723601	+	0.919423i	0.00546991	+	0.0695018i
$176$	−1.86002	+	1.58861i	−0.140205	+	0.119746i
$177$		0			0
$178$	3.44500	−	8.31696i	0.258213	−	0.623382i
$179$	12.6936	+	0.999009i	0.948765	+	0.0746695i	0.543390	−	0.839481i	$-0.317141\pi$
$179$	12.6936	+	0.999009i	0.948765	+	0.0746695i	0.405376	+	0.914150i	$0.367141\pi$
$180$		0			0
$181$	−1.94237	−	1.65894i	−0.144375	−	0.123308i	0.574327	−	0.818626i	$-0.305264\pi$
$181$	−1.94237	−	1.65894i	−0.144375	−	0.123308i	−0.718702	+	0.695318i	$0.755264\pi$
$182$	−7.24735	+	9.97513i	−0.537210	+	0.739406i
$183$		0			0
$184$	−1.02232	−	0.161920i	−0.0753667	−	0.0119369i
$185$	11.0896	+	1.75642i	0.815324	+	0.129135i
$186$		0			0
$187$	0.971774	−	1.33753i	0.0710631	−	0.0978100i
$188$	2.44293	+	2.08646i	0.178169	+	0.152170i
$189$		0			0
$190$	4.68958	+	0.369078i	0.340218	+	0.0267757i
$191$	3.23068	−	7.79955i	0.233764	−	0.564356i	−0.762850	−	0.646575i	$-0.776201\pi$
$191$	3.23068	−	7.79955i	0.233764	−	0.564356i	0.996614	+	0.0822191i	$0.0262007\pi$
$192$		0			0
$193$	10.1075	−	8.63262i	0.727554	−	0.621390i	−0.206531	−	0.978440i	$-0.566217\pi$
$193$	10.1075	−	8.63262i	0.727554	−	0.621390i	0.934085	+	0.357050i	$0.116217\pi$
$194$	1.16288	+	14.7757i	0.0834897	+	1.06084i
$195$		0			0
$196$	−2.47829	−	2.47829i	−0.177021	−	0.177021i
$197$	−0.724660	−	1.42223i	−0.0516299	−	0.101329i	0.863750	−	0.503921i	$-0.168110\pi$
$197$	−0.724660	−	1.42223i	−0.0516299	−	0.101329i	−0.915380	+	0.402591i	$0.868110\pi$
$198$		0			0
$199$	8.61190	+	14.0533i	0.610481	+	0.996215i	0.997255	+	0.0740401i	$0.0235893\pi$
$199$	8.61190	+	14.0533i	0.610481	+	0.996215i	−0.386774	+	0.922174i	$0.626411\pi$
$200$	−0.439545	−	0.223959i	−0.0310805	−	0.0158363i
$201$		0			0
$202$	−4.83774	+	2.00386i	−0.340382	+	0.140991i
$203$	2.71660	+	17.1519i	0.190668	+	1.20383i
$204$		0			0
$205$	−0.0768749	−	15.0073i	−0.00536918	−	1.04816i
$206$		−	13.8258i		−	0.963293i
$207$		0			0
$208$	−2.52387	−	6.09316i	−0.174999	−	0.422484i
$209$	−1.51710	−	4.66914i	−0.104940	−	0.322971i
$210$		0			0
$211$	3.30131	−	2.02304i	0.227271	−	0.139272i	−0.404202	−	0.914670i	$-0.632451\pi$
$211$	3.30131	−	2.02304i	0.227271	−	0.139272i	0.631473	+	0.775398i	$0.282451\pi$
$212$	−0.827562	+	1.35046i	−0.0568372	+	0.0927498i
$213$		0			0
$214$	−2.92393	+	2.92393i	−0.199876	+	0.199876i
$215$	4.32516	+	1.40533i	0.294974	+	0.0958427i
$216$		0			0
$217$	−11.8746	−	13.9034i	−0.806102	−	0.943824i
$218$	−4.19731	−	1.00769i	−0.284278	−	0.0682491i
$219$		0			0
$220$	−0.449815	+	5.71544i	−0.0303265	+	0.385335i
$221$	2.62011	+	3.60627i	0.176248	+	0.242584i
$222$		0			0
$223$	−9.50051	−	6.90253i	−0.636201	−	0.462227i	0.222342	−	0.974969i	$-0.428630\pi$
$223$	−9.50051	−	6.90253i	−0.636201	−	0.462227i	−0.858543	+	0.512741i	$0.828630\pi$
$224$	−1.81788	+	0.436434i	−0.121462	+	0.0291605i
$225$		0			0
$226$	−2.10589	+	13.2961i	−0.140082	+	0.884442i
$227$	−0.457727	−	1.90657i	−0.0303804	−	0.126543i	0.955119	−	0.296222i	$-0.0957269\pi$
$227$	−0.457727	−	1.90657i	−0.0303804	−	0.126543i	−0.985499	+	0.169679i	$0.945727\pi$
$228$		0			0
$229$	0.649097	−	0.759995i	0.0428935	−	0.0502219i	−0.738544	−	0.674205i	$-0.764487\pi$
$229$	0.649097	−	0.759995i	0.0428935	−	0.0502219i	0.781438	+	0.623983i	$0.214487\pi$
$230$	−1.96265	+	1.42595i	−0.129413	+	0.0940244i
$231$		0			0
$232$	−8.58174	−	3.55467i	−0.563419	−	0.233376i
$233$	2.47050	−	10.2904i	0.161848	−	0.674144i	−0.831154	−	0.556043i	$-0.812319\pi$
$233$	2.47050	−	10.2904i	0.161848	−	0.674144i	0.993002	−	0.118102i	$-0.0376808\pi$
$234$		0			0
$235$	7.50656	−	0.590779i	0.489674	−	0.0385382i
$236$	−3.05276	+	9.39542i	−0.198718	+	0.611590i
$237$		0			0
$238$	1.12587	−	0.573659i	0.0729793	−	0.0371848i
$239$	−3.44794	−	2.11290i	−0.223029	−	0.136672i	0.406496	−	0.913653i	$-0.366750\pi$
$239$	−3.44794	−	2.11290i	−0.223029	−	0.136672i	−0.629525	+	0.776980i	$0.716750\pi$
$240$		0			0
$241$	10.8848	−	21.3626i	0.701151	−	1.37609i	−0.215543	−	0.976494i	$-0.569152\pi$
$241$	10.8848	−	21.3626i	0.701151	−	1.37609i	0.916693	−	0.399591i	$-0.130848\pi$
$242$	−4.77110	+	1.55022i	−0.306698	+	0.0996521i
$243$		0			0
$244$	1.75573	−	0.278080i	0.112399	−	0.0178022i
$245$	−8.21457			−0.524810
$246$		0			0
$247$	13.2369			0.842241
$248$	9.65965	−	1.52994i	0.613389	−	0.0971512i
$249$		0			0
$250$	10.0457	−	3.26405i	0.635347	−	0.206437i
$251$	9.90370	−	19.4371i	0.625116	−	1.22686i	−0.333660	−	0.942694i	$-0.608284\pi$
$251$	9.90370	−	19.4371i	0.625116	−	1.22686i	0.958775	−	0.284165i	$-0.0917164\pi$
$252$		0			0
$253$	2.15878	+	1.32290i	0.135721	+	0.0831700i
$254$	4.91618	−	2.50492i	0.308468	−	0.157173i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−3.97955	+	0.313197i	−0.248237	+	0.0195367i	−0.201967	−	0.979392i	$-0.564733\pi$
$257$	−3.97955	+	0.313197i	−0.248237	+	0.0195367i	−0.0462700	+	0.998929i	$0.514733\pi$
$258$		0			0
$259$	2.09073	−	8.70851i	0.129912	−	0.541121i
$260$	−14.2810	−	5.91540i	−0.885672	−	0.366857i
$261$		0			0
$262$	−7.06737	+	5.13474i	−0.436623	+	0.317225i
$263$	5.40619	−	6.32983i	0.333360	−	0.390314i	−0.568256	−	0.822852i	$-0.692382\pi$
$263$	5.40619	−	6.32983i	0.333360	−	0.390314i	0.901616	+	0.432538i	$0.142382\pi$
$264$		0			0
$265$	0.866598	+	3.60964i	0.0532347	+	0.221738i
$266$	0.586981	−	3.70605i	0.0359901	−	0.227232i
$267$		0			0
$268$	7.34263	−	1.76281i	0.448523	−	0.107681i
$269$	16.5789	+	12.0453i	1.01083	+	0.734413i	0.964384	−	0.264508i	$-0.0852094\pi$
$269$	16.5789	+	12.0453i	1.01083	+	0.734413i	0.0464493	+	0.998921i	$0.485209\pi$
$270$		0			0
$271$	5.07588	+	6.98635i	0.308338	+	0.424391i	0.934862	−	0.355011i	$-0.115523\pi$
$271$	5.07588	+	6.98635i	0.308338	+	0.424391i	−0.626524	+	0.779402i	$0.715523\pi$
$272$	−0.0530294	+	0.673803i	−0.00321538	+	0.0408553i
$273$		0			0
$274$	11.2109	+	2.69150i	0.677275	+	0.162599i
$275$	0.783682	+	0.917574i	0.0472578	+	0.0553318i
$276$		0			0
$277$	−18.3442	−	5.96039i	−1.10220	−	0.358125i	−0.299248	−	0.954175i	$-0.596736\pi$
$277$	−18.3442	−	5.96039i	−1.10220	−	0.358125i	−0.802947	+	0.596050i	$0.796736\pi$
$278$	−14.1845	+	14.1845i	−0.850727	+	0.850727i
$279$		0			0
$280$	−2.28948	+	3.73608i	−0.136822	+	0.223274i
$281$	25.8060	−	15.8139i	1.53946	−	0.943379i	0.544975	−	0.838452i	$-0.316539\pi$
$281$	25.8060	−	15.8139i	1.53946	−	0.943379i	0.994480	−	0.104927i	$-0.0334610\pi$
$282$		0			0
$283$	−7.33793	−	22.5838i	−0.436194	−	1.34247i	−0.891858	−	0.452316i	$-0.850598\pi$
$283$	−7.33793	−	22.5838i	−0.436194	−	1.34247i	0.455663	−	0.890152i	$-0.349402\pi$
$284$	−1.91459	−	4.62223i	−0.113610	−	0.274279i
$285$		0			0
$286$			16.1324i			0.953931i
$287$	−11.9386	−	0.878080i	−0.704714	−	0.0518314i
$288$		0			0
$289$	2.58792	+	16.3395i	0.152231	+	0.961147i
$290$	−20.1137	+	8.33137i	−1.18112	+	0.489235i
$291$		0			0
$292$	7.33079	+	3.73523i	0.429002	+	0.218588i
$293$	−10.3803	−	16.9391i	−0.606425	−	0.989595i	−0.997597	−	0.0692779i	$-0.977930\pi$
$293$	−10.3803	−	16.9391i	−0.606425	−	0.989595i	0.391173	−	0.920317i	$-0.372070\pi$
$294$		0			0
$295$	10.5117	+	20.6304i	0.612016	+	1.20115i
$296$	3.38738	+	3.38738i	0.196887	+	0.196887i
$297$		0			0
$298$	0.848452	+	10.7806i	0.0491495	+	0.624503i
$299$	−5.19088	+	4.43343i	−0.300196	+	0.256392i
$300$		0			0
$301$	1.38820	−	3.35141i	0.0800146	−	0.193172i
$302$	1.77430	+	0.139640i	0.102099	+	0.00803540i
$303$		0			0
$304$	1.52617	+	1.30347i	0.0875319	+	0.0747593i
$305$	2.44891	−	3.37064i	0.140224	−	0.193002i
$306$		0			0
$307$	−19.1046	−	3.02588i	−1.09036	−	0.172696i	−0.414735	−	0.909942i	$-0.636126\pi$
$307$	−19.1046	−	3.02588i	−1.09036	−	0.172696i	−0.675624	+	0.737246i	$0.736126\pi$
$308$	4.51676	+	0.715384i	0.257366	+	0.0407628i
$309$		0			0
$310$	13.4734	−	18.5446i	0.765238	−	1.05326i
$311$	−21.6034	−	18.4510i	−1.22501	−	1.04626i	−0.997367	−	0.0725173i	$-0.976897\pi$
$311$	−21.6034	−	18.4510i	−1.22501	−	1.04626i	−0.227647	−	0.973744i	$-0.573103\pi$
$312$		0			0
$313$	−12.8356	−	1.01018i	−0.725510	−	0.0570989i	−0.289675	−	0.957125i	$-0.593547\pi$
$313$	−12.8356	−	1.01018i	−0.725510	−	0.0570989i	−0.435836	+	0.900026i	$0.643547\pi$
$314$	−0.110342	+	0.266390i	−0.00622698	+	0.0150332i
$315$		0			0
$316$	12.1687	−	10.3930i	0.684542	−	0.584654i
$317$	−1.70237	−	21.6306i	−0.0956145	−	1.21490i	−0.838282	−	0.545237i	$-0.816440\pi$
$317$	−1.70237	−	21.6306i	−0.0956145	−	1.21490i	0.742667	−	0.669660i	$-0.233560\pi$
$318$		0			0
$319$	16.0664	+	16.0664i	0.899544	+	0.899544i
$320$	−1.06405	−	2.08832i	−0.0594825	−	0.116741i
$321$		0			0
$322$	1.01108	+	1.64994i	0.0563455	+	0.0919475i
$323$	−1.20868	−	0.615854i	−0.0672529	−	0.0342670i
$324$		0			0
$325$	−3.00583	+	1.24506i	−0.166734	+	0.0690633i
$326$	2.42379	+	15.3032i	0.134242	+	0.847568i
$327$		0			0
$328$	3.73708	−	5.19945i	0.206346	−	0.287091i
$329$		−	6.00618i		−	0.331131i
$330$		0			0
$331$	2.07805	+	5.01686i	0.114220	+	0.275752i	0.970644	−	0.240522i	$-0.0773187\pi$
$331$	2.07805	+	5.01686i	0.114220	+	0.275752i	−0.856424	+	0.516274i	$0.827319\pi$
$332$	2.82927	+	8.70761i	0.155277	+	0.477892i
$333$		0			0
$334$	−19.6409	+	12.0360i	−1.07470	+	0.658578i
$335$	9.24746	−	15.0905i	0.505243	−	0.824482i
$336$		0			0
$337$	−9.63812	+	9.63812i	−0.525022	+	0.525022i	−0.919084	−	0.394062i	$-0.871070\pi$
$337$	−9.63812	+	9.63812i	−0.525022	+	0.525022i	0.394062	+	0.919084i	$0.371070\pi$
$338$	−29.0039	−	9.42393i	−1.57760	−	0.512594i
$339$		0			0
$340$	1.02881	+	1.20458i	0.0557950	+	0.0653276i
$341$	−23.2620	−	5.58470i	−1.25971	−	0.302429i
$342$		0			0
$343$	−1.54087	+	19.5786i	−0.0831992	+	1.05715i
$344$	1.14051	+	1.56977i	0.0614920	+	0.0846364i
$345$		0			0
$346$	9.84946	+	7.15605i	0.529510	+	0.384712i
$347$	−27.6510	+	6.63842i	−1.48438	+	0.356369i	−0.893013	−	0.450031i	$-0.851413\pi$
$347$	−27.6510	+	6.63842i	−1.48438	+	0.356369i	−0.591371	+	0.806400i	$0.701413\pi$
$348$		0			0
$349$	0.423743	−	2.67541i	0.0226824	−	0.143211i	−0.973748	−	0.227628i	$-0.926903\pi$
$349$	0.423743	−	2.67541i	0.0226824	−	0.143211i	0.996431	+	0.0844172i	$0.0269028\pi$
$350$	0.215299	+	0.896783i	0.0115082	+	0.0479351i
$351$		0			0
$352$	−1.58861	+	1.86002i	−0.0846732	+	0.0991396i
$353$	−1.51453	+	1.10037i	−0.0806106	+	0.0585670i	−0.627361	−	0.778729i	$-0.715865\pi$
$353$	−1.51453	+	1.10037i	−0.0806106	+	0.0585670i	0.546750	+	0.837296i	$0.315865\pi$
$354$		0			0
$355$	−10.8335	−	4.48739i	−0.574983	−	0.238166i
$356$	2.10152	−	8.75348i	0.111381	−	0.463934i
$357$		0			0
$358$	12.6936	−	0.999009i	0.670878	−	0.0527993i
$359$	−7.19685	+	22.1496i	−0.379835	+	1.16901i	0.560323	+	0.828274i	$0.310677\pi$
$359$	−7.19685	+	22.1496i	−0.379835	+	1.16901i	−0.940158	+	0.340738i	$0.889323\pi$
$360$		0			0
$361$	13.3399	−	6.79704i	0.702102	−	0.357739i
$362$	−2.17797	−	1.33466i	−0.114472	−	0.0701483i
$363$		0			0
$364$	−5.59767	+	10.9861i	−0.293398	+	0.575826i
$365$	18.3398	−	5.95895i	0.959947	−	0.311906i
$366$		0			0
$367$	27.1174	−	4.29498i	1.41552	−	0.224196i	0.598646	−	0.801014i	$-0.295706\pi$
$367$	27.1174	−	4.29498i	1.41552	−	0.224196i	0.816873	+	0.576818i	$0.195706\pi$
$368$	−1.03507			−0.0539566
$369$		0			0
$370$	11.2278			0.583707
$371$	2.92462	−	0.463214i	0.151839	−	0.0240489i
$372$		0			0
$373$	−6.46737	+	2.10138i	−0.334868	+	0.108805i	−0.471624	−	0.881799i	$-0.656332\pi$
$373$	−6.46737	+	2.10138i	−0.334868	+	0.108805i	0.136757	+	0.990605i	$0.456332\pi$
$374$	0.750574	−	1.47308i	0.0388112	−	0.0761713i
$375$		0			0
$376$	2.73924	+	1.67861i	0.141266	+	0.0865677i
$377$	−54.5843	+	27.8121i	−2.81123	+	1.43240i
$378$		0			0
$379$	1.06475	−	3.27696i	0.0546924	−	0.168326i	−0.919979	−	0.391968i	$-0.871795\pi$
$379$	1.06475	−	3.27696i	0.0546924	−	0.168326i	0.974671	+	0.223642i	$0.0717945\pi$
$380$	4.68958	−	0.369078i	0.240570	−	0.0189333i
$381$		0			0
$382$	1.97079	−	8.20892i	0.100834	−	0.420005i
$383$	26.5589	+	11.0011i	1.35710	+	0.562129i	0.938260	−	0.345932i	$-0.112437\pi$
$383$	26.5589	+	11.0011i	1.35710	+	0.562129i	0.418839	+	0.908061i	$0.362437\pi$
$384$		0			0
$385$	8.67125	−	6.30003i	0.441928	−	0.321079i
$386$	8.63262	−	10.1075i	0.439389	−	0.514458i
$387$		0			0
$388$	3.46000	+	14.4119i	0.175655	+	0.731654i
$389$	2.41753	−	15.2637i	0.122574	−	0.773900i	−0.847447	−	0.530880i	$-0.821862\pi$
$389$	2.41753	−	15.2637i	0.122574	−	0.773900i	0.970021	−	0.243021i	$-0.0781384\pi$
$390$		0			0
$391$	0.680258	−	0.163315i	0.0344021	−	0.00825922i
$392$	−2.83547	−	2.06009i	−0.143213	−	0.104050i
$393$		0			0
$394$	−0.938224	−	1.29135i	−0.0472670	−	0.0650575i
$395$	2.94278	−	37.3916i	0.148068	−	1.88138i
$396$		0			0
$397$	−36.4180	−	8.74318i	−1.82777	−	0.438808i	−0.834142	−	0.551550i	$-0.814036\pi$
$397$	−36.4180	−	8.74318i	−1.82777	−	0.438808i	−0.993624	+	0.112743i	$0.964036\pi$
$398$	10.7043	+	12.5331i	0.536558	+	0.628228i
$399$		0			0
$400$	−0.469168	−	0.152442i	−0.0234584	−	0.00762210i
$401$	5.37453	−	5.37453i	0.268391	−	0.268391i	−0.560061	−	0.828452i	$-0.689222\pi$
$401$	5.37453	−	5.37453i	0.268391	−	0.268391i	0.828452	+	0.560061i	$0.189222\pi$
$402$		0			0
$403$	33.7019	−	54.9964i	1.67881	−	2.73957i
$404$	−4.46471	+	2.73598i	−0.222128	+	0.136120i
$405$		0			0
$406$	5.36631	+	16.5158i	0.266326	+	0.819666i
$407$	−4.48427	−	10.8260i	−0.222277	−	0.536624i
$408$		0			0
$409$		−	17.1920i		−	0.850090i	−0.905172	−	0.425045i	$-0.860258\pi$
$409$		−	17.1920i		−	0.850090i	0.905172	−	0.425045i	$-0.139742\pi$
$410$	−2.42359	−	14.8105i	−0.119693	−	0.731440i
$411$		0			0
$412$	−2.16284	−	13.6556i	−0.106555	−	0.672765i
$413$	17.0631	−	7.06778i	0.839622	−	0.347783i
$414$		0			0
$415$	19.1201	+	9.74219i	0.938570	+	0.478225i
$416$	−3.44598	−	5.62332i	−0.168953	−	0.275706i
$417$		0			0
$418$	−2.22883	−	4.37433i	−0.109016	−	0.213955i
$419$	7.31893	+	7.31893i	0.357553	+	0.357553i	0.862910	−	0.505357i	$-0.168639\pi$
$419$	7.31893	+	7.31893i	0.357553	+	0.357553i	−0.505357	+	0.862910i	$0.668639\pi$
$420$		0			0
$421$	1.84081	+	23.3897i	0.0897156	+	1.13995i	0.862767	+	0.505602i	$0.168729\pi$
$421$	1.84081	+	23.3897i	0.0897156	+	1.13995i	−0.773051	+	0.634343i	$0.781271\pi$
$422$	2.94419	−	2.51458i	0.143321	−	0.122408i
$423$		0			0
$424$	−0.606115	+	1.46329i	−0.0294355	+	0.0710637i
$425$	0.332395	+	0.0261601i	0.0161235	+	0.00126895i
$426$		0			0
$427$	−2.52706	−	2.15832i	−0.122293	−	0.104448i
$428$	−2.43053	+	3.34533i	−0.117484	+	0.161703i
$429$		0			0
$430$	4.49175	+	0.711424i	0.216612	+	0.0343079i
$431$	−15.1672	−	2.40225i	−0.730577	−	0.115712i	−0.219946	−	0.975512i	$-0.570588\pi$
$431$	−15.1672	−	2.40225i	−0.730577	−	0.115712i	−0.510631	+	0.859800i	$0.670588\pi$
$432$		0			0
$433$	6.74841	−	9.28839i	0.324308	−	0.446372i	−0.615468	−	0.788162i	$-0.711033\pi$
$433$	6.74841	−	9.28839i	0.324308	−	0.446372i	0.939776	+	0.341790i	$0.111033\pi$
$434$	−13.9034	−	11.8746i	−0.667384	−	0.570000i
$435$		0			0
$436$	−4.30327	−	0.338675i	−0.206089	−	0.0162196i
$437$	0.794998	−	1.91929i	0.0380299	−	0.0918123i
$438$		0			0
$439$	28.5463	−	24.3809i	1.36244	−	1.16364i	0.392654	−	0.919686i	$-0.371557\pi$
$439$	28.5463	−	24.3809i	1.36244	−	1.16364i	0.969788	−	0.243949i	$-0.0784429\pi$
$440$	0.449815	+	5.71544i	0.0214441	+	0.272473i
$441$		0			0
$442$	3.15200	+	3.15200i	0.149925	+	0.149925i
$443$	11.8854	+	23.3264i	0.564691	+	1.10827i	0.980076	+	0.198623i	$0.0636470\pi$
$443$	11.8854	+	23.3264i	0.564691	+	1.10827i	−0.415385	+	0.909646i	$0.636353\pi$
$444$		0			0
$445$	−11.0243	−	17.9900i	−0.522603	−	0.852810i
$446$	−10.4633	−	5.33134i	−0.495453	−	0.252446i
$447$		0			0
$448$	−1.72723	+	0.715440i	−0.0816037	+	0.0338014i
$449$	−6.16329	−	38.9135i	−0.290864	−	1.83644i	−0.509300	−	0.860589i	$-0.670096\pi$
$449$	−6.16329	−	38.9135i	−0.290864	−	1.83644i	0.218436	−	0.975851i	$-0.429904\pi$
$450$		0			0
$451$	−13.3125	+	8.25201i	−0.626861	+	0.388572i
$452$			13.4618i			0.633191i
$453$		0			0
$454$	−0.750345	−	1.81149i	−0.0352154	−	0.0850176i
$455$	8.93018	+	27.4843i	0.418653	+	1.28848i
$456$		0			0
$457$	−12.9539	+	7.93814i	−0.605956	+	0.371330i	−0.791377	−	0.611329i	$-0.790635\pi$
$457$	−12.9539	+	7.93814i	−0.605956	+	0.371330i	0.185421	+	0.982659i	$0.440635\pi$
$458$	0.522216	−	0.852179i	0.0244015	−	0.0398197i
$459$		0			0
$460$	−1.71542	+	1.71542i	−0.0799819	+	0.0799819i
$461$	−15.0701	−	4.89657i	−0.701884	−	0.228056i	−0.0637330	−	0.997967i	$-0.520301\pi$
$461$	−15.0701	−	4.89657i	−0.701884	−	0.228056i	−0.638151	+	0.769911i	$0.720301\pi$
$462$		0			0
$463$	−0.888764	−	1.04061i	−0.0413044	−	0.0483612i	0.739369	−	0.673300i	$-0.235124\pi$
$463$	−0.888764	−	1.04061i	−0.0413044	−	0.0483612i	−0.780674	+	0.624939i	$0.785124\pi$
$464$	−9.03215	−	2.16843i	−0.419307	−	0.100667i
$465$		0			0
$466$	0.830314	−	10.5501i	0.0384636	−	0.488726i
$467$	10.5470	+	14.5167i	0.488057	+	0.671753i	0.980028	−	0.198859i	$-0.0637235\pi$
$467$	10.5470	+	14.5167i	0.488057	+	0.671753i	−0.491971	+	0.870611i	$0.663723\pi$
$468$		0			0
$469$	−11.4212	−	8.29799i	−0.527382	−	0.383165i
$470$	7.32172	−	1.75779i	0.337726	−	0.0810808i
$471$		0			0
$472$	−1.54540	+	9.75730i	−0.0711330	+	0.449116i
$473$	−1.10799	−	4.61513i	−0.0509456	−	0.212204i
$474$		0			0
$475$	0.643020	−	0.752880i	0.0295038	−	0.0345445i
$476$	1.02227	−	0.742721i	0.0468556	−	0.0340426i
$477$		0			0
$478$	−3.73602	−	1.54751i	−0.170882	−	0.0707816i
$479$	−4.98866	+	20.7793i	−0.227938	+	0.949429i	0.734647	+	0.678449i	$0.237348\pi$
$479$	−4.98866	+	20.7793i	−0.227938	+	0.949429i	−0.962585	+	0.270980i	$0.912652\pi$
$480$		0			0
$481$	31.4967	−	2.47884i	1.43613	−	0.113026i
$482$	7.40893	−	22.8023i	0.337468	−	1.03862i
$483$		0			0
$484$	−4.46985	+	2.27750i	−0.203175	+	0.103523i
$485$	29.6192	+	18.1507i	1.34494	+	0.824179i
$486$		0			0
$487$	−8.78084	+	17.2334i	−0.397898	+	0.780919i	−0.999845	−	0.0176174i	$-0.994392\pi$
$487$	−8.78084	+	17.2334i	−0.397898	+	0.780919i	0.601947	+	0.798536i	$0.294392\pi$
$488$	1.69061	−	0.549313i	0.0765303	−	0.0248662i
$489$		0			0
$490$	−8.11344	+	1.28504i	−0.366528	+	0.0580523i
$491$	24.0558			1.08563			0.542813	−	0.839854i	$-0.317359\pi$
$491$	24.0558			1.08563			0.542813	+	0.839854i	$0.317359\pi$
$492$		0			0
$493$	6.27817			0.282755
$494$	13.0739	−	2.07070i	0.588222	−	0.0931652i
$495$		0			0
$496$	9.30139	−	3.02221i	0.417645	−	0.135701i
$497$	−4.24636	+	8.33396i	−0.190475	+	0.373829i
$498$		0			0
$499$	−18.8040	−	11.5231i	−0.841781	−	0.515844i	0.0335110	−	0.999438i	$-0.489331\pi$
$499$	−18.8040	−	11.5231i	−0.841781	−	0.515844i	−0.875292	+	0.483594i	$0.839331\pi$
$500$	9.41143	−	4.79536i	0.420892	−	0.214455i
$501$		0			0
$502$	6.74113	−	20.7471i	0.300871	−	0.925987i
$503$	−29.9427	+	2.35654i	−1.33508	+	0.105073i	−0.725813	−	0.687892i	$-0.758536\pi$
$503$	−29.9427	+	2.35654i	−1.33508	+	0.105073i	−0.609267	+	0.792965i	$0.708536\pi$
$504$		0			0
$505$	−2.86503	+	11.9337i	−0.127492	+	0.531044i
$506$	2.33914	+	0.968905i	0.103988	+	0.0430731i
$507$		0			0
$508$	4.46380	−	3.24314i	0.198049	−	0.143891i
$509$	−5.43511	+	6.36370i	−0.240907	+	0.282066i	−0.867666	−	0.497147i	$-0.834381\pi$
$509$	−5.43511	+	6.36370i	−0.240907	+	0.282066i	0.626759	+	0.779213i	$0.284381\pi$
$510$		0			0
$511$	−3.59078	−	14.9567i	−0.158847	−	0.661645i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$		0			0
$514$	−3.88156	+	0.931879i	−0.171208	+	0.0411034i
$515$	−26.2160	−	19.0470i	−1.15522	−	0.839313i
$516$		0			0
$517$	−4.61909	−	6.35763i	−0.203147	−	0.279608i
$518$	0.702677	−	8.92836i	0.0308739	−	0.392290i
$519$		0			0
$520$	−15.0306	−	3.60852i	−0.659135	−	0.158244i
$521$	13.1104	+	15.3503i	0.574376	+	0.672508i	0.969208	−	0.246245i	$-0.0791969\pi$
$521$	13.1104	+	15.3503i	0.574376	+	0.672508i	−0.394831	+	0.918754i	$0.629197\pi$
$522$		0			0
$523$	−0.0117671	−	0.00382336i	−0.000514539	−	0.000167184i	0.308760	−	0.951140i	$-0.400086\pi$
$523$	−0.0117671	−	0.00382336i	−0.000514539	−	0.000167184i	−0.309274	+	0.950973i	$0.600086\pi$
$524$	−6.17711	+	6.17711i	−0.269848	+	0.269848i
$525$		0			0
$526$	4.34942	−	7.09761i	0.189644	−	0.309471i
$527$	−5.63613	+	3.45382i	−0.245514	+	0.150451i
$528$		0			0
$529$	−6.77632	−	20.8554i	−0.294623	−	0.906755i
$530$	1.42060	+	3.42963i	0.0617070	+	0.148974i
$531$		0			0
$532$		−	3.75225i		−	0.162680i
$533$	−10.0686	−	41.0119i	−0.436118	−	1.77642i
$534$		0			0
$535$	1.51611	+	9.57236i	0.0655473	+	0.413849i
$536$	6.97647	−	2.88975i	0.301338	−	0.124818i
$537$		0			0
$538$	18.2591	+	9.30346i	0.787205	+	0.401101i
$539$	4.47946	+	7.30982i	0.192944	+	0.314856i
$540$		0			0
$541$	11.6032	+	22.7725i	0.498860	+	0.979067i	0.993909	+	0.110203i	$0.0351500\pi$
$541$	11.6032	+	22.7725i	0.498860	+	0.979067i	−0.495049	+	0.868865i	$0.664850\pi$
$542$	6.10630	+	6.10630i	0.262288	+	0.262288i
$543$		0			0
$544$	0.0530294	+	0.673803i	0.00227362	+	0.0288890i
$545$	−7.69312	+	6.57054i	−0.329537	+	0.281451i
$546$		0			0
$547$	−7.96968	+	19.2405i	−0.340759	+	0.822665i	0.656880	+	0.753995i	$0.271876\pi$
$547$	−7.96968	+	19.2405i	−0.340759	+	0.822665i	−0.997639	+	0.0686702i	$0.978124\pi$
$548$	11.4939	+	0.904590i	0.490995	+	0.0386422i
$549$		0			0
$550$	0.917574	+	0.783682i	0.0391255	+	0.0334163i
$551$	10.9581	−	15.0826i	0.466832	−	0.642539i
$552$		0			0
$553$	−29.5496	−	4.68020i	−1.25658	−	0.199022i
$554$	−19.0507	−	3.01734i	−0.809389	−	0.128195i
$555$		0			0
$556$	−11.7909	+	16.2288i	−0.500045	+	0.688253i
$557$	5.27262	+	4.50324i	0.223408	+	0.190809i	0.754106	−	0.656752i	$-0.228070\pi$
$557$	5.27262	+	4.50324i	0.223408	+	0.190809i	−0.530698	+	0.847561i	$0.678070\pi$
$558$		0			0
$559$	12.7575	+	1.00404i	0.539584	+	0.0424662i
$560$	−1.67684	+	4.04824i	−0.0708592	+	0.171069i
$561$		0			0
$562$	23.0144	−	19.6562i	0.970805	−	0.829145i
$563$	−1.85704	−	23.5960i	−0.0782651	−	0.994452i	−0.903199	−	0.429222i	$-0.858788\pi$
$563$	−1.85704	−	23.5960i	−0.0782651	−	0.994452i	0.824934	−	0.565229i	$-0.191212\pi$
$564$		0			0
$565$	22.3103	+	22.3103i	0.938603	+	0.938603i
$566$	−10.7805	−	21.1579i	−0.453137	−	0.889332i
$567$		0			0
$568$	−2.61410	−	4.26582i	−0.109685	−	0.178990i
$569$	16.7865	+	8.55315i	0.703727	+	0.358567i	0.768954	−	0.639304i	$-0.220777\pi$
$569$	16.7865	+	8.55315i	0.703727	+	0.358567i	−0.0652274	+	0.997870i	$0.520777\pi$
$570$		0			0
$571$	−31.3264	+	12.9758i	−1.31097	+	0.543020i	−0.925166	−	0.379562i	$-0.876075\pi$
$571$	−31.3264	+	12.9758i	−1.31097	+	0.543020i	−0.385801	+	0.922582i	$0.626075\pi$
$572$	2.52367	+	15.9338i	0.105520	+	0.666227i
$573$		0			0
$574$	−11.9290	+	1.00034i	−0.497907	+	0.0417535i
$575$			0.510612i			0.0212940i
$576$		0			0
$577$	15.4218	+	37.2316i	0.642020	+	1.54997i	0.823951	+	0.566662i	$0.191765\pi$
$577$	15.4218	+	37.2316i	0.642020	+	1.54997i	−0.181931	+	0.983311i	$0.558235\pi$
$578$	5.11212	+	15.7335i	0.212636	+	0.654427i
$579$		0			0
$580$	−18.5628	+	11.3753i	−0.770777	+	0.472333i
$581$	8.94358	−	14.5946i	0.371042	−	0.605486i
$582$		0			0
$583$	2.73951	−	2.73951i	0.113459	−	0.113459i
$584$	7.82486	+	2.54245i	0.323795	+	0.105207i
$585$		0			0
$586$	−12.9024	−	15.1068i	−0.532993	−	0.624054i
$587$	4.73968	+	1.13790i	0.195628	+	0.0469660i	0.330075	−	0.943955i	$-0.392926\pi$
$587$	4.73968	+	1.13790i	0.195628	+	0.0469660i	−0.134447	+	0.990921i	$0.542926\pi$
$588$		0			0
$589$	−1.54008	+	19.5685i	−0.0634578	+	0.806308i
$590$	13.6096	+	18.7320i	0.560299	+	0.771185i
$591$		0			0
$592$	3.87558	+	2.81577i	0.159285	+	0.115728i
$593$	12.0898	−	2.90250i	0.496467	−	0.119191i	0.0225233	−	0.999746i	$-0.492830\pi$
$593$	12.0898	−	2.90250i	0.496467	−	0.119191i	0.473944	+	0.880555i	$0.342830\pi$
$594$		0			0
$595$	0.463294	−	2.92512i	0.0189932	−	0.119918i
$596$	2.52446	+	10.5151i	0.103406	+	0.430717i
$597$		0			0
$598$	−4.43343	+	5.19088i	−0.181297	+	0.212271i
$599$	9.53529	−	6.92780i	0.389601	−	0.283062i	−0.375691	−	0.926745i	$-0.622594\pi$
$599$	9.53529	−	6.92780i	0.389601	−	0.283062i	0.765292	+	0.643683i	$0.222594\pi$
$600$		0			0
$601$	−24.7967	−	10.2711i	−1.01148	−	0.418968i	−0.185485	−	0.982647i	$-0.559386\pi$
$601$	−24.7967	−	10.2711i	−1.01148	−	0.418968i	−0.825994	+	0.563679i	$0.809386\pi$
$602$	0.846833	−	3.52731i	0.0345143	−	0.143763i
$603$		0			0
$604$	1.77430	−	0.139640i	0.0721952	−	0.00568189i
$605$	−3.63338	+	11.1824i	−0.147718	+	0.454629i
$606$		0			0
$607$	−10.0572	+	5.12439i	−0.408208	+	0.207993i	−0.646023	−	0.763318i	$-0.723569\pi$
$607$	−10.0572	+	5.12439i	−0.408208	+	0.207993i	0.237815	+	0.971311i	$0.423569\pi$
$608$	1.71129	+	1.04868i	0.0694019	+	0.0425296i
$609$		0			0
$610$	1.89148	−	3.71223i	0.0765837	−	0.150304i
$611$	20.1511	−	6.54748i	0.815225	−	0.264883i
$612$		0			0
$613$	23.7239	−	3.75750i	0.958201	−	0.151764i	0.342303	−	0.939590i	$-0.388793\pi$
$613$	23.7239	−	3.75750i	0.958201	−	0.151764i	0.615898	+	0.787826i	$0.288793\pi$
$614$	−19.3428			−0.780611
$615$		0			0
$616$	4.57306			0.184254
$617$	22.5934	−	3.57844i	0.909576	−	0.144063i	0.315924	−	0.948784i	$-0.397685\pi$
$617$	22.5934	−	3.57844i	0.909576	−	0.144063i	0.593652	+	0.804722i	$0.297685\pi$
$618$		0			0
$619$	−18.9948	+	6.17177i	−0.763464	+	0.248064i	−0.664765	−	0.747053i	$-0.731468\pi$
$619$	−18.9948	+	6.17177i	−0.763464	+	0.248064i	−0.0986991	+	0.995117i	$0.531468\pi$
$620$	10.4065	−	20.4239i	0.417936	−	0.820245i
$621$		0			0
$622$	−24.2238	−	14.8443i	−0.971284	−	0.595204i
$623$	−14.9956	+	7.64064i	−0.600786	+	0.306116i
$624$		0			0
$625$	8.41243	−	25.8908i	0.336497	−	1.03563i
$626$	−12.8356	+	1.01018i	−0.513013	+	0.0403750i
$627$		0			0
$628$	−0.0673112	+	0.280371i	−0.00268601	+	0.0111880i
$629$	−2.99135	−	1.23906i	−0.119273	−	0.0494045i
$630$		0			0
$631$	13.8279	−	10.0466i	0.550482	−	0.399948i	−0.277481	−	0.960731i	$-0.589500\pi$
$631$	13.8279	−	10.0466i	0.550482	−	0.399948i	0.827963	+	0.560783i	$0.189500\pi$
$632$	10.3930	−	12.1687i	0.413413	−	0.484044i
$633$		0			0
$634$	−5.06518	−	21.0980i	−0.201164	−	0.837909i
$635$	2.02300	−	12.7727i	0.0802804	−	0.506870i
$636$		0			0
$637$	−22.4764	+	5.39610i	−0.890547	+	0.213801i
$638$	18.3819	+	13.3552i	0.727747	+	0.528739i
$639$		0			0
$640$	−1.37764	−	1.89616i	−0.0544560	−	0.0749523i
$641$	0.838993	−	10.6604i	0.0331382	−	0.421061i	−0.957865	−	0.287220i	$-0.907269\pi$
$641$	0.838993	−	10.6604i	0.0331382	−	0.421061i	0.991003	−	0.133841i	$-0.0427312\pi$
$642$		0			0
$643$	−37.6510	−	9.03919i	−1.48481	−	0.356471i	−0.591644	−	0.806200i	$-0.701521\pi$
$643$	−37.6510	−	9.03919i	−1.48481	−	0.356471i	−0.893165	+	0.449729i	$0.851521\pi$
$644$	1.25674	+	1.47146i	0.0495226	+	0.0579836i
$645$		0			0
$646$	−1.29014	−	0.419192i	−0.0507599	−	0.0164929i
$647$	−32.8897	+	32.8897i	−1.29303	+	1.29303i	−0.360125	+	0.932904i	$0.617266\pi$
$647$	−32.8897	+	32.8897i	−1.29303	+	1.29303i	−0.932904	+	0.360125i	$0.882734\pi$
$648$		0			0
$649$	12.6261	−	20.6039i	0.495616	−	0.808772i
$650$	−2.77406	+	1.69994i	−0.108807	+	0.0666773i
$651$		0			0
$652$	4.78791	+	14.7357i	0.187509	+	0.577093i
$653$	14.5796	+	35.1983i	0.570544	+	1.37742i	0.901093	+	0.433627i	$0.142766\pi$
$653$	14.5796	+	35.1983i	0.570544	+	1.37742i	−0.330548	+	0.943789i	$0.607234\pi$
$654$		0			0
$655$			20.4747i			0.800012i
$656$	2.87769	−	5.72004i	0.112355	−	0.223330i
$657$		0			0
$658$	−0.939574	−	5.93223i	−0.0366284	−	0.231263i
$659$	−37.1213	+	15.3761i	−1.44604	+	0.598970i	−0.961254	−	0.275663i	$-0.911103\pi$
$659$	−37.1213	+	15.3761i	−1.44604	+	0.598970i	−0.484786	+	0.874633i	$0.661103\pi$
$660$		0			0
$661$	15.1700	+	7.72950i	0.590044	+	0.300643i	0.723404	−	0.690425i	$-0.242576\pi$
$661$	15.1700	+	7.72950i	0.590044	+	0.300643i	−0.133359	+	0.991068i	$0.542576\pi$
$662$	2.83728	+	4.63002i	0.110274	+	0.179951i
$663$		0			0
$664$	4.15661	+	8.15781i	0.161308	+	0.316584i
$665$	−6.21861	−	6.21861i	−0.241147	−	0.241147i
$666$		0			0
$667$	0.754348	+	9.58490i	0.0292085	+	0.371129i
$668$	−17.5163	+	14.9603i	−0.677724	+	0.578831i
$669$		0			0
$670$	6.77294	−	16.3513i	0.261661	−	0.631707i
$671$	−4.33480	−	0.341156i	−0.167343	−	0.0131702i
$672$		0			0
$673$	15.4996	+	13.2379i	0.597464	+	0.510283i	0.895964	−	0.444127i	$-0.146486\pi$
$673$	15.4996	+	13.2379i	0.597464	+	0.510283i	−0.298499	+	0.954410i	$0.596486\pi$
$674$	−8.01173	+	11.0272i	−0.308600	+	0.424752i
$675$		0			0
$676$	−30.1210	−	4.77070i	−1.15850	−	0.183488i
$677$	−1.62364	−	0.257159i	−0.0624015	−	0.00988342i	0.125156	−	0.992137i	$-0.460057\pi$
$677$	−1.62364	−	0.257159i	−0.0624015	−	0.00988342i	−0.187557	+	0.982254i	$0.560057\pi$
$678$		0			0
$679$	16.2871	−	22.4172i	0.625040	−	0.860294i
$680$	1.20458	+	1.02881i	0.0461936	+	0.0394531i
$681$		0			0
$682$	−23.8492	−	1.87697i	−0.913233	−	0.0718730i
$683$	1.40971	−	3.40335i	0.0539412	−	0.130225i	−0.894612	−	0.446845i	$-0.852548\pi$
$683$	1.40971	−	3.40335i	0.0539412	−	0.130225i	0.948553	+	0.316619i	$0.102548\pi$
$684$		0			0
$685$	20.5481	−	17.5497i	0.785102	−	0.670540i
$686$	1.54087	+	19.5786i	0.0588307	+	0.747515i
$687$		0			0
$688$	1.37203	+	1.37203i	0.0523082	+	0.0523082i
$689$	4.74230	+	9.30729i	0.180667	+	0.354579i
$690$		0			0
$691$	3.26695	+	5.33117i	0.124281	+	0.202807i	0.908729	−	0.417387i	$-0.137054\pi$
$691$	3.26695	+	5.33117i	0.124281	+	0.202807i	−0.784449	+	0.620194i	$0.787054\pi$
$692$	10.8477	+	5.52715i	0.412366	+	0.210111i
$693$		0			0
$694$	−26.2721	+	10.8823i	−0.997275	+	0.413085i
$695$	7.35491	+	46.4371i	0.278988	+	1.76146i
$696$		0			0
$697$	−0.988731	+	4.21333i	−0.0374509	+	0.159591i
$698$		−	2.70876i		−	0.102528i
$699$		0			0
$700$	0.352936	+	0.852062i	0.0133397	+	0.0322049i
$701$	15.6243	+	48.0868i	0.590123	+	1.81621i	0.577642	+	0.816290i	$0.303973\pi$
$701$	15.6243	+	48.0868i	0.590123	+	1.81621i	0.0124806	+	0.999922i	$0.496027\pi$
$702$		0			0
$703$	−8.19789	+	5.02368i	−0.309189	+	0.189472i
$704$	−1.27808	+	2.08564i	−0.0481695	+	0.0786054i
$705$		0			0
$706$	−1.32375	+	1.32375i	−0.0498201	+	0.0498201i
$707$	9.31038	+	3.02513i	0.350153	+	0.113772i
$708$		0			0
$709$	−10.5698	−	12.3756i	−0.396956	−	0.464776i	0.525547	−	0.850764i	$-0.323861\pi$
$709$	−10.5698	−	12.3756i	−0.396956	−	0.464776i	−0.922504	+	0.385988i	$0.873861\pi$
$710$	−11.4021	−	2.73740i	−0.427914	−	0.102733i
$711$		0			0
$712$	0.706305	−	8.97446i	0.0264699	−	0.336332i
$713$	−5.95016	−	8.18970i	−0.222835	−	0.306707i
$714$		0			0
$715$	30.5897	+	22.2247i	1.14399	+	0.831157i
$716$	12.3811	−	2.97243i	0.462702	−	0.111085i
$717$		0			0
$718$	−3.64328	+	23.0028i	−0.135966	+	0.858455i
$719$	11.1897	+	46.6083i	0.417304	+	1.73820i	0.644739	+	0.764403i	$0.276966\pi$
$719$	11.1897	+	46.6083i	0.417304	+	1.73820i	−0.227435	+	0.973793i	$0.573034\pi$
$720$		0			0
$721$	−16.7869	+	19.6549i	−0.625176	+	0.731987i
$722$	12.1124	−	8.80018i	0.450777	−	0.327509i
$723$		0			0
$724$	−2.35994	−	0.977520i	−0.0877066	−	0.0363293i
$725$	−1.06971	+	4.45568i	−0.0397282	+	0.165480i
$726$		0			0
$727$	−48.0671	+	3.78296i	−1.78271	+	0.140302i	−0.926492	−	0.376315i	$-0.877191\pi$
$727$	−48.0671	+	3.78296i	−1.78271	+	0.140302i	−0.856217	+	0.516617i	$0.827191\pi$
$728$	−3.81016	+	11.7265i	−0.141214	+	0.434612i
$729$		0			0
$730$	17.1818	−	8.75455i	0.635926	−	0.324021i
$731$	−1.11820	−	0.685232i	−0.0413580	−	0.0253442i
$732$		0			0
$733$	10.1557	−	19.9317i	0.375110	−	0.736195i	−0.623862	−	0.781535i	$-0.714437\pi$
$733$	10.1557	−	19.9317i	0.375110	−	0.736195i	0.998972	+	0.0453401i	$0.0144372\pi$
$734$	26.1117	−	8.48421i	0.963800	−	0.313158i
$735$		0			0
$736$	−1.02232	+	0.161920i	−0.0376834	+	0.00596846i
$737$	−18.4711			−0.680393
$738$		0			0
$739$	0.864088			0.0317860			0.0158930	−	0.999874i	$-0.494941\pi$
$739$	0.864088			0.0317860			0.0158930	+	0.999874i	$0.494941\pi$
$740$	11.0896	−	1.75642i	0.407662	−	0.0645673i
$741$		0			0
$742$	2.81615	−	0.915021i	0.103384	−	0.0335915i
$743$	13.1351	−	25.7791i	0.481881	−	0.945745i	−0.514231	−	0.857652i	$-0.671923\pi$
$743$	13.1351	−	25.7791i	0.481881	−	0.945745i	0.996112	−	0.0880933i	$-0.0280774\pi$
$744$		0			0
$745$	21.6106	+	13.2430i	0.791751	+	0.485186i
$746$	−6.05902	+	3.08723i	−0.221837	+	0.113031i
$747$		0			0
$748$	0.510892	−	1.57236i	0.0186801	−	0.0574913i
$749$	7.70681	−	0.606539i	0.281601	−	0.0221625i
$750$		0			0
$751$	−11.4154	+	47.5486i	−0.416554	+	1.73507i	0.230908	+	0.972976i	$0.425830\pi$
$751$	−11.4154	+	47.5486i	−0.416554	+	1.73507i	−0.647462	+	0.762098i	$0.724170\pi$
$752$	2.96811	+	1.22943i	0.108236	+	0.0448328i
$753$		0			0
$754$	−49.5615	+	36.0085i	−1.80492	+	1.31135i
$755$	2.70913	−	3.17198i	0.0985952	−	0.115440i
$756$		0			0
$757$	0.0914912	+	0.381088i	0.00332530	+	0.0138509i	0.974008	−	0.226514i	$-0.0727329\pi$
$757$	0.0914912	+	0.381088i	0.00332530	+	0.0138509i	−0.970683	+	0.240365i	$0.922733\pi$
$758$	0.539010	−	3.40318i	0.0195777	−	0.123609i
$759$		0			0
$760$	4.57411	−	1.09815i	0.165920	−	0.0398339i
$761$	−23.6216	−	17.1621i	−0.856284	−	0.622126i	0.0705877	−	0.997506i	$-0.477513\pi$
$761$	−23.6216	−	17.1621i	−0.856284	−	0.622126i	−0.926871	+	0.375379i	$0.877513\pi$
$762$		0			0
$763$	4.74343	+	6.52876i	0.171724	+	0.236357i
$764$	0.662365	−	8.41615i	0.0239635	−	0.304486i
$765$		0			0
$766$	27.9529	+	6.71090i	1.00998	+	0.242475i
$767$	42.3137	+	49.5430i	1.52786	+	1.78889i
$768$		0			0
$769$	35.6289	+	11.5765i	1.28481	+	0.417461i	0.870272	−	0.492571i	$-0.163943\pi$
$769$	35.6289	+	11.5765i	1.28481	+	0.417461i	0.414539	+	0.910031i	$0.363943\pi$
$770$	7.57895	−	7.57895i	0.273126	−	0.273126i
$771$		0			0
$772$	6.94518	−	11.3335i	0.249962	−	0.407902i
$773$	6.12840	−	3.75549i	0.220423	−	0.135076i	−0.407904	−	0.913025i	$-0.633740\pi$
$773$	6.12840	−	3.75549i	0.220423	−	0.135076i	0.628327	+	0.777949i	$0.283740\pi$
$774$		0			0
$775$	−1.49089	−	4.58850i	−0.0535544	−	0.164824i
$776$	5.67192	+	13.6932i	0.203610	+	0.491558i
$777$		0			0
$778$		−	15.4540i		−	0.554052i
$779$	8.39625	+	9.72938i	0.300827	+	0.348591i
$780$		0			0
$781$	1.91444	+	12.0873i	0.0685041	+	0.432518i
$782$	0.646335	−	0.267721i	0.0231129	−	0.00957367i
$783$		0			0
$784$	−3.12283	−	1.59116i	−0.111530	−	0.0568272i
$785$	0.353106	+	0.576216i	0.0126029	+	0.0205660i
$786$		0			0
$787$	8.38653	+	16.4595i	0.298948	+	0.586718i	0.990802	−	0.135319i	$-0.0432060\pi$
$787$	8.38653	+	16.4595i	0.298948	+	0.586718i	−0.691854	+	0.722037i	$0.743206\pi$
$788$	−1.12868	−	1.12868i	−0.0402077	−	0.0402077i
$789$		0			0
$790$	−2.94278	−	37.3916i	−0.104700	−	1.33033i
$791$	19.1374	−	16.3449i	0.680448	−	0.581157i
$792$		0			0
$793$	4.48646	−	10.8313i	0.159319	−	0.384630i
$794$	−37.3373	−	2.93851i	−1.32505	−	0.104284i
$795$		0			0
$796$	12.5331	+	10.7043i	0.444225	+	0.379404i
$797$	−15.0776	+	20.7525i	−0.534076	+	0.735092i	−0.987745	−	0.156078i	$-0.950115\pi$
$797$	−15.0776	+	20.7525i	−0.534076	+	0.735092i	0.453669	+	0.891170i	$0.350115\pi$
$798$		0			0
$799$	−2.14466	−	0.339681i	−0.0758726	−	0.0120170i
$800$	−0.487239	−	0.0771711i	−0.0172265	−	0.00272841i
$801$		0			0
$802$	4.46760	−	6.14912i	0.157756	−	0.217133i
$803$	−15.3034	−	13.0704i	−0.540046	−	0.461243i
$804$		0			0
$805$	4.52146	+	0.355847i	0.159360	+	0.0125419i
$806$	24.6836	−	59.5915i	0.869442	−	2.09902i
$807$		0			0
$808$	−3.98174	+	3.40073i	−0.140077	+	0.119637i
$809$	3.89378	+	49.4752i	0.136898	+	1.73946i	0.555705	+	0.831380i	$0.312449\pi$
$809$	3.89378	+	49.4752i	0.136898	+	1.73946i	−0.418806	+	0.908076i	$0.637551\pi$
$810$		0			0
$811$	−18.5814	−	18.5814i	−0.652481	−	0.652481i	0.301109	−	0.953590i	$-0.402643\pi$
$811$	−18.5814	−	18.5814i	−0.652481	−	0.652481i	−0.953590	+	0.301109i	$0.902643\pi$
$812$	7.88389	+	15.4730i	0.276670	+	0.542996i
$813$		0			0
$814$	−6.12262	−	9.99120i	−0.214598	−	0.350191i
$815$	32.3565	+	16.4865i	1.13340	+	0.577495i
$816$		0			0
$817$	−3.59792	+	1.49031i	−0.125875	+	0.0521393i
$818$	−2.68942	−	16.9803i	−0.0940335	−	0.593704i
$819$		0			0
$820$	−4.71063	−	14.2491i	−0.164502	−	0.497599i
$821$		−	53.1876i		−	1.85626i	−0.372256	−	0.928130i	$-0.621416\pi$
$821$		−	53.1876i		−	1.85626i	0.372256	−	0.928130i	$-0.378584\pi$
$822$		0			0
$823$	14.1511	+	34.1639i	0.493278	+	1.19088i	0.953042	+	0.302837i	$0.0979337\pi$
$823$	14.1511	+	34.1639i	0.493278	+	1.19088i	−0.459765	+	0.888041i	$0.652066\pi$
$824$	−4.27242	−	13.1492i	−0.148837	−	0.458073i
$825$		0			0
$826$	15.7474	−	9.65003i	0.547923	−	0.335767i
$827$	18.1999	−	29.6996i	0.632874	−	1.03276i	−0.362053	−	0.932157i	$-0.617924\pi$
$827$	18.1999	−	29.6996i	0.632874	−	1.03276i	0.994927	−	0.100599i	$-0.0320759\pi$
$828$		0			0
$829$	−26.6511	+	26.6511i	−0.925630	+	0.925630i	−0.997420	−	0.0717900i	$-0.977129\pi$
$829$	−26.6511	+	26.6511i	−0.925630	+	0.925630i	0.0717900	+	0.997420i	$0.477129\pi$
$830$	20.4087	+	6.63120i	0.708398	+	0.230172i
$831$		0			0
$832$	−4.28323	−	5.01502i	−0.148494	−	0.173864i
$833$	2.30342	+	0.553002i	0.0798087	+	0.0191604i
$834$		0			0
$835$	−4.23600	+	53.8235i	−0.146593	+	1.86264i
$836$	−2.88569	−	3.97181i	−0.0998036	−	0.137368i
$837$		0			0
$838$	8.37375	+	6.08389i	0.289267	+	0.210164i
$839$	−24.0245	+	5.76778i	−0.829419	+	0.199126i	−0.625859	−	0.779937i	$-0.715251\pi$
$839$	−24.0245	+	5.76778i	−0.829419	+	0.199126i	−0.203560	+	0.979062i	$0.565251\pi$
$840$		0			0
$841$	−8.96086	+	56.5767i	−0.308995	+	1.95092i
$842$	5.47710	+	22.8138i	0.188754	+	0.786215i
$843$		0			0
$844$	2.51458	−	2.94419i	0.0865552	−	0.101343i
$845$	−57.8262	+	42.0132i	−1.98928	+	1.44530i
$846$		0			0
$847$	8.66484	+	3.58910i	0.297728	+	0.123323i
$848$	−0.369743	+	1.54009i	−0.0126970	+	0.0528870i
$849$		0			0
$850$	0.332395	−	0.0261601i	0.0114011	−	0.000897284i
$851$	1.53225	−	4.71578i	0.0525249	−	0.161655i
$852$		0			0
$853$	5.50774	−	2.80634i	0.188582	−	0.0960871i	−0.357150	−	0.934047i	$-0.616252\pi$
$853$	5.50774	−	2.80634i	0.188582	−	0.0960871i	0.545732	+	0.837960i	$0.316252\pi$
$854$	−2.83359	−	1.73642i	−0.0969634	−	0.0594192i
$855$		0			0
$856$	−1.87728	+	3.68437i	−0.0641641	+	0.125929i
$857$	−20.7231	+	6.73334i	−0.707887	+	0.230006i	−0.640764	−	0.767738i	$-0.721382\pi$
$857$	−20.7231	+	6.73334i	−0.707887	+	0.230006i	−0.0671233	+	0.997745i	$0.521382\pi$
$858$		0			0
$859$	−18.4687	+	2.92516i	−0.630145	+	0.0998051i	−0.463334	−	0.886184i	$-0.653347\pi$
$859$	−18.4687	+	2.92516i	−0.630145	+	0.0998051i	−0.166811	+	0.985989i	$0.553347\pi$
$860$	4.54774			0.155077
$861$		0			0
$862$	−15.3562			−0.523036
$863$	−10.1249	+	1.60362i	−0.344655	+	0.0545880i	−0.326363	−	0.945245i	$-0.605823\pi$
$863$	−10.1249	+	1.60362i	−0.344655	+	0.0545880i	−0.0182925	+	0.999833i	$0.505823\pi$
$864$		0			0
$865$	27.1380	−	8.81768i	0.922721	−	0.299810i
$866$	5.21230	−	10.2297i	0.177121	−	0.347620i
$867$		0			0
$868$	−15.5898	−	9.55345i	−0.529153	−	0.324265i
$869$	−34.8780	+	17.7712i	−1.18316	+	0.602848i
$870$		0			0
$871$	15.3897	−	47.3646i	0.521460	−	1.60489i
$872$	−4.30327	+	0.338675i	−0.145727	+	0.0114690i
$873$		0			0
$874$	0.484966	−	2.02003i	0.0164042	−	0.0683285i
$875$	−18.2441	−	7.55697i	−0.616765	−	0.255472i
$876$		0			0
$877$	−21.0913	+	15.3237i	−0.712203	+	0.517445i	−0.883883	−	0.467707i	$-0.845080\pi$
$877$	−21.0913	+	15.3237i	−0.712203	+	0.517445i	0.171681	+	0.985153i	$0.445080\pi$
$878$	24.3809	−	28.5463i	0.822814	−	0.963392i
$879$		0			0
$880$	1.33837	+	5.57470i	0.0451164	+	0.187923i
$881$	−5.33957	+	33.7127i	−0.179895	+	1.13581i	0.718144	+	0.695894i	$0.244992\pi$
$881$	−5.33957	+	33.7127i	−0.179895	+	1.13581i	−0.898039	+	0.439916i	$0.855008\pi$
$882$		0			0
$883$	12.9648	−	3.11258i	0.436302	−	0.104747i	−0.00934362	−	0.999956i	$-0.502974\pi$
$883$	12.9648	−	3.11258i	0.436302	−	0.104747i	0.445645	+	0.895210i	$0.352974\pi$
$884$	3.60627	+	2.62011i	0.121292	+	0.0881238i
$885$		0			0
$886$	15.3881	+	21.1799i	0.516973	+	0.711553i
$887$	−4.16570	+	52.9303i	−0.139871	+	1.77722i	0.381963	+	0.924178i	$0.375248\pi$
$887$	−4.16570	+	52.9303i	−0.139871	+	1.77722i	−0.521834	+	0.853047i	$0.674752\pi$
$888$		0			0
$889$	−10.0303	−	2.40805i	−0.336404	−	0.0807634i
$890$	−13.7028	−	16.0440i	−0.459320	−	0.537795i
$891$		0			0
$892$	−11.1685	−	3.62887i	−0.373950	−	0.121504i
$893$	−4.55940	+	4.55940i	−0.152574	+	0.152574i
$894$		0			0
$895$	15.5930	−	25.4454i	0.521215	−	0.850546i
$896$	−1.59404	+	0.976830i	−0.0532532	+	0.0326336i
$897$		0			0
$898$	−12.1748	−	37.4702i	−0.406279	−	1.25040i
$899$	−34.7649	−	83.9299i	−1.15947	−	2.79922i
$900$		0			0
$901$		−	1.07051i		−	0.0356637i
$902$	−11.8577	+	10.2329i	−0.394818	+	0.340720i
$903$		0			0
$904$	2.10589	+	13.2961i	0.0700409	+	0.442221i
$905$	−5.53119	+	2.29109i	−0.183863	+	0.0761586i
$906$		0			0
$907$	−45.1866	−	23.0237i	−1.50040	−	0.764490i	−0.505257	−	0.862969i	$-0.668602\pi$
$907$	−45.1866	−	23.0237i	−1.50040	−	0.764490i	−0.995139	+	0.0984792i	$0.968602\pi$
$908$	−1.02449	−	1.67181i	−0.0339988	−	0.0554810i
$909$		0			0
$910$	13.1197	+	25.7489i	0.434915	+	0.853568i
$911$	−35.6505	−	35.6505i	−1.18115	−	1.18115i	−0.979446	−	0.201708i	$-0.935351\pi$
$911$	−35.6505	−	35.6505i	−1.18115	−	1.18115i	−0.201708	−	0.979446i	$-0.564649\pi$
$912$		0			0
$913$	−1.75715	−	22.3267i	−0.0581532	−	0.738906i
$914$	−11.5526	+	9.86683i	−0.382125	+	0.326366i
$915$		0			0
$916$	0.382476	−	0.923380i	0.0126374	−	0.0305093i
$917$	16.2814	+	1.28138i	0.537661	+	0.0423148i
$918$		0			0
$919$	−23.8934	−	20.4069i	−0.788170	−	0.673161i	0.161340	−	0.986899i	$-0.448419\pi$
$919$	−23.8934	−	20.4069i	−0.788170	−	0.673161i	−0.949509	+	0.313738i	$0.898419\pi$
$920$	−1.42595	+	1.96265i	−0.0470122	+	0.0647067i
$921$		0			0
$922$	−15.6505	−	2.47880i	−0.515423	−	0.0816350i
$923$	−32.5899	−	5.16174i	−1.07271	−	0.169901i
$924$		0			0
$925$	1.38906	−	1.91187i	0.0456719	−	0.0628620i
$926$	−1.04061	−	0.888764i	−0.0341965	−	0.0292066i
$927$		0			0
$928$	−9.26017	−	0.728791i	−0.303980	−	0.0239237i
$929$	−14.8199	+	35.7785i	−0.486226	+	1.17385i	0.470378	+	0.882465i	$0.344117\pi$
$929$	−14.8199	+	35.7785i	−0.486226	+	1.17385i	−0.956605	+	0.291389i	$0.905883\pi$
$930$		0			0
$931$	5.34898	−	4.56846i	0.175306	−	0.149725i
$932$	−0.830314	−	10.5501i	−0.0271978	−	0.345581i
$933$		0			0
$934$	12.6881	+	12.6881i	0.415166	+	0.415166i
$935$	−1.75918	−	3.45259i	−0.0575314	−	0.112912i
$936$		0			0
$937$	21.0687	+	34.3810i	0.688285	+	1.12318i	0.985713	+	0.168435i	$0.0538712\pi$
$937$	21.0687	+	34.3810i	0.688285	+	1.12318i	−0.297428	+	0.954744i	$0.596129\pi$
$938$	−12.5787	−	6.40916i	−0.410708	−	0.209266i
$939$		0			0
$940$	6.95660	−	2.88152i	0.226899	−	0.0939848i
$941$	−9.05607	−	57.1777i	−0.295219	−	1.86394i	−0.474655	−	0.880172i	$-0.657427\pi$
$941$	−9.05607	−	57.1777i	−0.295219	−	1.86394i	0.179436	−	0.983770i	$-0.442573\pi$
$942$		0			0
$943$	−6.55129	−	1.00325i	−0.213339	−	0.0326703i
$944$			9.87893i			0.321532i
$945$		0			0
$946$	−1.81632	−	4.38498i	−0.0590536	−	0.142568i
$947$	3.62357	+	11.1522i	0.117750	+	0.362397i	0.992511	−	0.122158i	$-0.0389814\pi$
$947$	3.62357	+	11.1522i	0.117750	+	0.362397i	−0.874761	+	0.484555i	$0.838981\pi$
$948$		0			0
$949$	46.2661	−	28.3519i	1.50186	−	0.920342i
$950$	0.517327	−	0.844201i	0.0167843	−	0.0273895i
$951$		0			0
$952$	0.893495	−	0.893495i	0.0289583	−	0.0289583i
$953$	40.3558	+	13.1124i	1.30725	+	0.424752i	0.878099	−	0.478479i	$-0.158812\pi$
$953$	40.3558	+	13.1124i	1.30725	+	0.424752i	0.429154	+	0.903231i	$0.358812\pi$
$954$		0			0
$955$	−12.8504	−	15.0459i	−0.415829	−	0.486873i
$956$	−3.93211	−	0.944017i	−0.127174	−	0.0305317i
$957$		0			0
$958$	−1.67665	+	21.3038i	−0.0541700	+	0.688296i
$959$	−12.6695	−	17.4381i	−0.409121	−	0.563107i
$960$		0			0
$961$	52.3026	+	38.0001i	1.68718	+	1.22581i
$962$	30.7211	−	7.37550i	0.990490	−	0.237796i
$963$		0			0
$964$	3.75064	−	23.6806i	0.120800	−	0.762701i
$965$	−7.27279	−	30.2933i	−0.234119	−	0.975177i
$966$		0			0
$967$	−2.09524	+	2.45321i	−0.0673785	+	0.0788900i	−0.793071	−	0.609129i	$-0.791519\pi$
$967$	−2.09524	+	2.45321i	−0.0673785	+	0.0788900i	0.725693	+	0.688019i	$0.241519\pi$
$968$	−4.05854	+	2.94870i	−0.130446	+	0.0947748i
$969$		0			0
$970$	32.0939	+	13.2937i	1.03047	+	0.426836i
$971$	5.66635	−	23.6020i	0.181842	−	0.757425i	−0.804668	−	0.593725i	$-0.797657\pi$
$971$	5.66635	−	23.6020i	0.181842	−	0.757425i	0.986510	−	0.163701i	$-0.0523432\pi$
$972$		0			0
$973$	37.3870	−	2.94242i	1.19857	−	0.0943297i
$974$	−5.97684	+	18.3948i	−0.191510	+	0.589408i
$975$		0			0
$976$	1.58386	−	0.807019i	0.0506983	−	0.0258321i
$977$	−10.5296	−	6.45253i	−0.336871	−	0.206435i	0.343766	−	0.939055i	$-0.388297\pi$
$977$	−10.5296	−	6.45253i	−0.336871	−	0.206435i	−0.680638	+	0.732620i	$0.738297\pi$
$978$		0			0
$979$	−9.99699	+	19.6202i	−0.319505	+	0.627064i
$980$	−7.81252	+	2.53844i	−0.249562	+	0.0810876i
$981$		0			0
$982$	23.7597	−	3.76316i	0.758202	−	0.120087i
$983$	37.2264			1.18734			0.593668	−	0.804710i	$-0.297679\pi$
$983$	37.2264			1.18734			0.593668	+	0.804710i	$0.297679\pi$
$984$		0			0
$985$	−3.74115			−0.119203
$986$	6.20088	−	0.982123i	0.197476	−	0.0312772i
$987$		0			0
$988$	12.5890	−	4.09041i	0.400509	−	0.130133i
$989$	0.911789	−	1.78949i	0.0289932	−	0.0569024i
$990$		0			0
$991$	−9.54979	−	5.85212i	−0.303359	−	0.185899i	0.362485	−	0.931990i	$-0.381928\pi$
$991$	−9.54979	−	5.85212i	−0.303359	−	0.185899i	−0.665844	+	0.746091i	$0.731928\pi$
$992$	8.71410	−	4.44006i	0.276673	−	0.140972i
$993$		0			0
$994$	−2.89036	+	8.89563i	−0.0916768	+	0.282152i
$995$	38.5115	−	3.03092i	1.22090	−	0.0960865i
$996$		0			0
$997$	−9.99162	+	41.6181i	−0.316438	+	1.31806i	0.556752	+	0.830679i	$0.312047\pi$
$997$	−9.99162	+	41.6181i	−0.316438	+	1.31806i	−0.873190	+	0.487380i	$0.837953\pi$
$998$	−20.3751	−	8.43963i	−0.644962	−	0.267152i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.d.17.4	yes	64
3.2	odd	2		738.2.ba.c.17.1	✓	64
41.29	odd	40		738.2.ba.c.521.1	yes	64
123.29	even	40	inner	738.2.ba.d.521.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.c.17.1	✓	64	3.2	odd	2
738.2.ba.c.521.1	yes	64	41.29	odd	40
738.2.ba.d.17.4	yes	64	1.1	even	1	trivial
738.2.ba.d.521.4	yes	64	123.29	even	40	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 - 0.156434i) q^{2} +(0.951057 - 0.309017i) q^{4} +(1.06405 - 2.08832i) q^{5} +(-1.59404 - 0.976830i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.724268 - 2.22907i) q^{10} +(-2.43855 + 0.191918i) q^{11} +(1.53962 - 6.41296i) q^{13} +(-1.72723 - 0.715440i) q^{14} +(0.809017 - 0.587785i) q^{16} +(-0.438953 + 0.513948i) q^{17} +(0.468536 + 1.95159i) q^{19} +(0.366648 - 2.31493i) q^{20} +(-2.37851 + 0.571029i) q^{22} +(-0.837387 - 0.608397i) q^{23} +(-0.289962 - 0.399098i) q^{25} +(0.517452 - 6.57486i) q^{26} +(-1.81788 - 0.436434i) q^{28} +(-6.03260 - 7.06326i) q^{29} +(9.30139 + 3.02221i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.353150 + 0.576288i) q^{34} +(-3.73608 + 2.28948i) q^{35} +(1.48034 + 4.55602i) q^{37} +(0.768064 + 1.85427i) q^{38} -2.34378i q^{40} +(5.69026 - 2.93614i) q^{41} +(0.303537 + 1.91646i) q^{43} +(-2.25990 + 0.936079i) q^{44} +(-0.922252 - 0.469911i) q^{46} +(1.67861 + 2.73924i) q^{47} +(-1.59116 - 3.12283i) q^{49} +(-0.348825 - 0.348825i) q^{50} +(-0.517452 - 6.57486i) q^{52} +(-1.20437 + 1.02863i) q^{53} +(-2.19397 + 5.29670i) q^{55} +(-1.86377 - 0.146682i) q^{56} +(-7.06326 - 6.03260i) q^{58} +(-5.80669 + 7.99222i) q^{59} +(1.75573 + 0.278080i) q^{61} +(9.65965 + 1.52994i) q^{62} +(0.587785 - 0.809017i) q^{64} +(-11.7541 - 10.0390i) q^{65} +(7.52800 + 0.592466i) q^{67} +(-0.258650 + 0.624437i) q^{68} +(-3.33193 + 2.84574i) q^{70} +(-0.392536 - 4.98765i) q^{71} +(5.81775 + 5.81775i) q^{73} +(2.17483 + 4.26835i) q^{74} +(1.04868 + 1.71129i) q^{76} +(4.07462 + 2.07613i) q^{77} +(14.7847 - 6.12403i) q^{79} +(-0.366648 - 2.31493i) q^{80} +(5.16089 - 3.79015i) q^{82} +9.15572i q^{83} +(0.606220 + 1.46354i) q^{85} +(0.599600 + 1.84538i) q^{86} +(-2.08564 + 1.27808i) q^{88} +(4.70364 - 7.67565i) q^{89} +(-8.71858 + 8.71858i) q^{91} +(-0.984407 - 0.319853i) q^{92} +(2.08646 + 2.44293i) q^{94} +(4.57411 + 1.09815i) q^{95} +(-1.16288 + 14.7757i) q^{97} +(-2.06009 - 2.83547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{7} + 8 q^{11} + 16 q^{13} - 4 q^{14} + 16 q^{16} + 16 q^{17} + 4 q^{19} - 4 q^{22} - 48 q^{23} + 40 q^{25} + 20 q^{26} + 4 q^{28} - 4 q^{29} + 40 q^{31} + 4 q^{34} + 52 q^{35} + 8 q^{37} - 16 q^{38}+ \cdots + 64 q^{97}+O(q^{100}) \) 64 * q - 4 * q^7 + 8 * q^11 + 16 * q^13 - 4 * q^14 + 16 * q^16 + 16 * q^17 + 4 * q^19 - 4 * q^22 - 48 * q^23 + 40 * q^25 + 20 * q^26 + 4 * q^28 - 4 * q^29 + 40 * q^31 + 4 * q^34 + 52 * q^35 + 8 * q^37 - 16 * q^38 - 12 * q^41 + 32 * q^43 + 4 * q^44 + 8 * q^47 + 48 * q^49 - 16 * q^50 - 20 * q^52 + 48 * q^53 - 36 * q^55 - 16 * q^56 - 20 * q^58 - 20 * q^59 + 24 * q^61 + 36 * q^62 - 60 * q^65 - 20 * q^67 - 12 * q^68 - 8 * q^70 + 8 * q^71 + 72 * q^73 + 12 * q^74 + 4 * q^76 + 76 * q^77 + 44 * q^79 - 68 * q^82 - 88 * q^85 + 32 * q^86 - 8 * q^88 - 84 * q^89 + 72 * q^91 + 12 * q^94 + 12 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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