LMFDB - Embedded newform 792.2.br.b.685.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [792,2,Mod(37,792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(792, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 0, 2]))

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

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

chi := DirichletCharacter("792.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.br (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:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			685.6
Character	$\chi$	$=$	792.685
Dual form			792.2.br.b.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.321268 + 1.37724i) q^{2} +(-1.79357 + 0.884925i) q^{4} +(-0.858340 + 1.18140i) q^{5} +(1.36837 - 4.21140i) q^{7} +(-1.79497 - 2.18588i) q^{8} +(-1.90283 - 0.802592i) q^{10} +(2.69217 - 1.93706i) q^{11} +(3.27580 + 4.50875i) q^{13} +(6.23972 + 0.531582i) q^{14} +(2.43382 - 3.17436i) q^{16} +(-2.06951 - 1.50359i) q^{17} +(2.87209 - 0.933198i) q^{19} +(0.494043 - 2.87850i) q^{20} +(3.53270 + 3.08545i) q^{22} +3.70783 q^{23} +(0.886118 + 2.72719i) q^{25} +(-5.15722 + 5.96007i) q^{26} +(1.27250 + 8.76436i) q^{28} +(3.48036 + 1.13084i) q^{29} +(-1.20678 + 0.876776i) q^{31} +(5.15375 + 2.33213i) q^{32} +(1.40593 - 3.33327i) q^{34} +(3.80084 + 5.23141i) q^{35} +(-1.41593 - 0.460065i) q^{37} +(2.20795 + 3.65575i) q^{38} +(4.12310 - 0.244353i) q^{40} +(-0.970962 - 2.98831i) q^{41} -6.25559i q^{43} +(-3.11446 + 5.85663i) q^{44} +(1.19121 + 5.10657i) q^{46} +(0.821652 + 2.52878i) q^{47} +(-10.2003 - 7.41099i) q^{49} +(-3.47131 + 2.09655i) q^{50} +(-9.86529 - 5.18794i) q^{52} +(5.75943 + 7.92717i) q^{53} +(-0.0223497 + 4.84320i) q^{55} +(-11.6618 + 4.56825i) q^{56} +(-0.439307 + 5.15659i) q^{58} +(-2.45147 - 0.796531i) q^{59} +(3.28347 - 4.51930i) q^{61} +(-1.59523 - 1.38034i) q^{62} +(-1.55617 + 7.84719i) q^{64} -8.13840 q^{65} +11.5059i q^{67} +(5.04238 + 0.865435i) q^{68} +(-5.98381 + 6.91535i) q^{70} +(0.909086 + 0.660489i) q^{71} +(4.36398 - 13.4310i) q^{73} +(0.178725 - 2.09788i) q^{74} +(-4.32550 + 4.21534i) q^{76} +(-4.47386 - 13.9884i) q^{77} +(-0.619910 + 0.450391i) q^{79} +(1.66115 + 5.60000i) q^{80} +(3.80368 - 2.29729i) q^{82} +(5.03379 - 6.92841i) q^{83} +(3.55269 - 1.15434i) q^{85} +(8.61544 - 2.00972i) q^{86} +(-9.06656 - 2.40781i) q^{88} +8.84290 q^{89} +(23.4706 - 7.62607i) q^{91} +(-6.65026 + 3.28115i) q^{92} +(-3.21877 + 1.94403i) q^{94} +(-1.36275 + 4.19410i) q^{95} +(0.241317 - 0.175327i) q^{97} +(6.92966 - 16.4292i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - q^{4} - 10 q^{7} + 5 q^{8} - 20 q^{10} - 2 q^{14} + 15 q^{16} + 6 q^{17} - 8 q^{20} - 35 q^{22} + 8 q^{23} - 4 q^{25} + 10 q^{26} + 32 q^{28} - 6 q^{31} - 20 q^{32} + 10 q^{34} - 12 q^{38}+ \cdots + 144 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 - q^4 - 10 * q^7 + 5 * q^8 - 20 * q^10 - 2 * q^14 + 15 * q^16 + 6 * q^17 - 8 * q^20 - 35 * q^22 + 8 * q^23 - 4 * q^25 + 10 * q^26 + 32 * q^28 - 6 * q^31 - 20 * q^32 + 10 * q^34 - 12 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 18 * q^46 + 6 * q^47 - 4 * q^49 - 61 * q^50 + 20 * q^52 - 2 * q^55 + 32 * q^56 + 4 * q^58 - 48 * q^62 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 - 22 * q^71 - 6 * q^73 - 54 * q^74 - 134 * q^76 + 74 * q^79 + 44 * q^80 - 31 * q^82 + 15 * q^86 - 73 * q^88 + 16 * q^89 + 4 * q^92 - 100 * q^94 - 66 * q^95 + 10 * q^97 + 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$	$-1$

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 $

$2$	0.321268	+	1.37724i	0.227171	+	0.973855i
$2$	0.321268	+	1.37724i	0.227171	+	0.973855i
$3$		0			0
$3$		0			0
$4$	−1.79357	+	0.884925i	−0.896787	+	0.442462i
$5$	−0.858340	+	1.18140i	−0.383861	+	0.528340i	−0.956602	−	0.291397i	$-0.905880\pi$
$5$	−0.858340	+	1.18140i	−0.383861	+	0.528340i	0.572741	+	0.819736i	$0.305880\pi$
$6$		0			0
$7$	1.36837	−	4.21140i	0.517194	−	1.59176i	−0.262060	−	0.965052i	$-0.584402\pi$
$7$	1.36837	−	4.21140i	0.517194	−	1.59176i	0.779254	−	0.626708i	$-0.215598\pi$
$8$	−1.79497	−	2.18588i	−0.634618	−	0.772826i
$9$		0			0
$10$	−1.90283	−	0.802592i	−0.601728	−	0.253802i
$11$	2.69217	−	1.93706i	0.811721	−	0.584046i
$11$	2.69217	−	1.93706i	0.811721	−	0.584046i
$12$		0			0
$13$	3.27580	+	4.50875i	0.908543	+	1.25050i	0.967662	+	0.252251i	$0.0811708\pi$
$13$	3.27580	+	4.50875i	0.908543	+	1.25050i	−0.0591193	+	0.998251i	$0.518829\pi$
$14$	6.23972	+	0.531582i	1.66763	+	0.142071i
$15$		0			0
$16$	2.43382	−	3.17436i	0.608454	−	0.793589i
$17$	−2.06951	−	1.50359i	−0.501930	−	0.364674i	0.307824	−	0.951443i	$-0.400399\pi$
$17$	−2.06951	−	1.50359i	−0.501930	−	0.364674i	−0.809754	+	0.586770i	$0.800399\pi$
$18$		0			0
$19$	2.87209	−	0.933198i	0.658902	−	0.214090i	0.0395671	−	0.999217i	$-0.487402\pi$
$19$	2.87209	−	0.933198i	0.658902	−	0.214090i	0.619335	+	0.785127i	$0.287402\pi$
$20$	0.494043	−	2.87850i	0.110471	−	0.643652i
$21$		0			0
$22$	3.53270	+	3.08545i	0.753175	+	0.657820i
$23$	3.70783			0.773136			0.386568	−	0.922261i	$-0.373661\pi$
$23$	3.70783			0.773136			0.386568	+	0.922261i	$0.373661\pi$
$24$		0			0
$25$	0.886118	+	2.72719i	0.177224	+	0.545438i
$26$	−5.15722	+	5.96007i	−1.01141	+	1.16887i
$27$		0			0
$28$	1.27250	+	8.76436i	0.240481	+	1.65631i
$29$	3.48036	+	1.13084i	0.646287	+	0.209991i	0.613776	−	0.789480i	$-0.289650\pi$
$29$	3.48036	+	1.13084i	0.646287	+	0.209991i	0.0325108	+	0.999471i	$0.489650\pi$
$30$		0			0
$31$	−1.20678	+	0.876776i	−0.216744	+	0.157474i	−0.690860	−	0.722989i	$-0.742768\pi$
$31$	−1.20678	+	0.876776i	−0.216744	+	0.157474i	0.474116	+	0.880462i	$0.342768\pi$
$32$	5.15375	+	2.33213i	0.911063	+	0.412266i
$33$		0			0
$34$	1.40593	−	3.33327i	0.241116	−	0.571650i
$35$	3.80084	+	5.23141i	0.642459	+	0.884269i
$36$		0			0
$37$	−1.41593	−	0.460065i	−0.232778	−	0.0756342i	0.190305	−	0.981725i	$-0.439052\pi$
$37$	−1.41593	−	0.460065i	−0.232778	−	0.0756342i	−0.423083	+	0.906091i	$0.639052\pi$
$38$	2.20795	+	3.65575i	0.358176	+	0.593040i
$39$		0			0
$40$	4.12310	−	0.244353i	0.651920	−	0.0386357i
$41$	−0.970962	−	2.98831i	−0.151639	−	0.466696i	0.846166	−	0.532919i	$-0.178905\pi$
$41$	−0.970962	−	2.98831i	−0.151639	−	0.466696i	−0.997805	+	0.0662232i	$0.978905\pi$
$42$		0			0
$43$		−	6.25559i		−	0.953968i	−0.878912	−	0.476984i	$-0.841730\pi$
$43$		−	6.25559i		−	0.953968i	0.878912	−	0.476984i	$-0.158270\pi$
$44$	−3.11446	+	5.85663i	−0.469523	+	0.882920i
$45$		0			0
$46$	1.19121	+	5.10657i	0.175634	+	0.752922i
$47$	0.821652	+	2.52878i	0.119850	+	0.368861i	0.992928	−	0.118720i	$-0.0378792\pi$
$47$	0.821652	+	2.52878i	0.119850	+	0.368861i	−0.873077	+	0.487582i	$0.837879\pi$
$48$		0			0
$49$	−10.2003	−	7.41099i	−1.45719	−	1.05871i
$50$	−3.47131	+	2.09655i	−0.490918	+	0.296498i
$51$		0			0
$52$	−9.86529	−	5.18794i	−1.36807	−	0.719438i
$53$	5.75943	+	7.92717i	0.791118	+	1.08888i	0.993968	+	0.109671i	$0.0349797\pi$
$53$	5.75943	+	7.92717i	0.791118	+	1.08888i	−0.202850	+	0.979210i	$0.565020\pi$
$54$		0			0
$55$	−0.0223497	+	4.84320i	−0.00301363	+	0.653057i
$56$	−11.6618	+	4.56825i	−1.55837	+	0.610458i
$57$		0			0
$58$	−0.439307	+	5.15659i	−0.0576838	+	0.677094i
$59$	−2.45147	−	0.796531i	−0.319154	−	0.103700i	0.145059	−	0.989423i	$-0.453663\pi$
$59$	−2.45147	−	0.796531i	−0.319154	−	0.103700i	−0.464213	+	0.885723i	$0.653663\pi$
$60$		0			0
$61$	3.28347	−	4.51930i	0.420405	−	0.578638i	−0.545313	−	0.838233i	$-0.683589\pi$
$61$	3.28347	−	4.51930i	0.420405	−	0.578638i	0.965718	+	0.259595i	$0.0835891\pi$
$62$	−1.59523	−	1.38034i	−0.202594	−	0.175304i
$63$		0			0
$64$	−1.55617	+	7.84719i	−0.194521	+	0.980898i
$65$	−8.13840			−1.00944
$66$		0			0
$67$			11.5059i			1.40566i	0.711356	+	0.702832i	$0.248081\pi$
$67$			11.5059i			1.40566i	−0.711356	+	0.702832i	$0.751919\pi$
$68$	5.04238	+	0.865435i	0.611479	+	0.104949i
$69$		0			0
$70$	−5.98381	+	6.91535i	−0.715202	+	0.826542i
$71$	0.909086	+	0.660489i	0.107889	+	0.0783857i	0.640421	−	0.768024i	$-0.278760\pi$
$71$	0.909086	+	0.660489i	0.107889	+	0.0783857i	−0.532533	+	0.846409i	$0.678760\pi$
$72$		0			0
$73$	4.36398	−	13.4310i	0.510765	−	1.57197i	−0.280091	−	0.959973i	$-0.590365\pi$
$73$	4.36398	−	13.4310i	0.510765	−	1.57197i	0.790857	−	0.612001i	$-0.209635\pi$
$74$	0.178725	−	2.09788i	0.0207764	−	0.243874i
$75$		0			0
$76$	−4.32550	+	4.21534i	−0.496168	+	0.483533i
$77$	−4.47386	−	13.9884i	−0.509843	−	1.59413i
$78$		0			0
$79$	−0.619910	+	0.450391i	−0.0697454	+	0.0506730i	−0.622112	−	0.782929i	$-0.713725\pi$
$79$	−0.619910	+	0.450391i	−0.0697454	+	0.0506730i	0.552366	+	0.833602i	$0.313725\pi$
$80$	1.66115	+	5.60000i	0.185723	+	0.626099i
$81$		0			0
$82$	3.80368	−	2.29729i	0.420046	−	0.253694i
$83$	5.03379	−	6.92841i	0.552530	−	0.760492i	−0.437823	−	0.899061i	$-0.644250\pi$
$83$	5.03379	−	6.92841i	0.552530	−	0.760492i	0.990353	+	0.138569i	$0.0442503\pi$
$84$		0			0
$85$	3.55269	−	1.15434i	0.385343	−	0.125206i
$86$	8.61544	−	2.00972i	0.929027	−	0.216713i
$87$		0			0
$88$	−9.06656	−	2.40781i	−0.966498	−	0.256673i
$89$	8.84290			0.937346			0.468673	−	0.883372i	$-0.344732\pi$
$89$	8.84290			0.937346			0.468673	+	0.883372i	$0.344732\pi$
$90$		0			0
$91$	23.4706	−	7.62607i	2.46039	−	0.799430i
$92$	−6.65026	+	3.28115i	−0.693338	+	0.342083i
$93$		0			0
$94$	−3.21877	+	1.94403i	−0.331991	+	0.200511i
$95$	−1.36275	+	4.19410i	−0.139815	+	0.430305i
$96$		0			0
$97$	0.241317	−	0.175327i	0.0245021	−	0.0178018i	−0.575467	−	0.817825i	$-0.695180\pi$
$97$	0.241317	−	0.175327i	0.0245021	−	0.0178018i	0.599969	+	0.800023i	$0.295180\pi$
$98$	6.92966	−	16.4292i	0.700001	−	1.65960i
$99$		0			0
$100$	−4.00268	−	4.10727i	−0.400268	−	0.410727i
$101$	1.54671	+	2.12886i	0.153903	+	0.211830i	0.879006	−	0.476812i	$-0.158208\pi$
$101$	1.54671	+	2.12886i	0.153903	+	0.211830i	−0.725102	+	0.688641i	$0.758208\pi$
$102$		0			0
$103$	−0.699506	+	2.15286i	−0.0689243	+	0.212127i	−0.979586	−	0.201026i	$-0.935573\pi$
$103$	−0.699506	+	2.15286i	−0.0689243	+	0.212127i	0.910662	+	0.413153i	$0.135573\pi$
$104$	3.97564	−	15.2536i	0.389843	−	1.49574i
$105$		0			0
$106$	−9.06729	+	10.4789i	−0.880693	+	1.01780i
$107$	5.74970	−	1.86819i	0.555845	−	0.180605i	−0.0176059	−	0.999845i	$-0.505604\pi$
$107$	5.74970	−	1.86819i	0.555845	−	0.180605i	0.573451	+	0.819240i	$0.305604\pi$
$108$		0			0
$109$			11.9381i			1.14346i	0.820440	+	0.571732i	$0.193728\pi$
$109$			11.9381i			1.14346i	−0.820440	+	0.571732i	$0.806272\pi$
$110$	−6.67742	+	1.52518i	−0.636667	+	0.145420i
$111$		0			0
$112$	−10.0381	−	14.5935i	−0.948514	−	1.37895i
$113$	−3.83483	−	11.8024i	−0.360750	−	1.11028i	−0.952600	−	0.304227i	$-0.901602\pi$
$113$	−3.83483	−	11.8024i	−0.360750	−	1.11028i	0.591849	−	0.806049i	$-0.298398\pi$
$114$		0			0
$115$	−3.18258	+	4.38044i	−0.296777	+	0.408478i
$116$	−7.24300	+	1.05162i	−0.672495	+	0.0976401i
$117$		0			0
$118$	0.309436	−	3.63216i	0.0284859	−	0.334368i
$119$	−9.16406	+	6.65808i	−0.840068	+	0.610345i
$120$		0			0
$121$	3.49559	−	10.4298i	0.317781	−	0.948164i
$122$	7.27903	+	3.07021i	0.659013	+	0.277964i
$123$		0			0
$124$	1.38857	−	2.64047i	0.124697	−	0.237121i
$125$	−10.9266	−	3.55027i	−0.977307	−	0.317546i
$126$		0			0
$127$	7.20921	+	5.23780i	0.639714	+	0.464780i	0.859752	−	0.510712i	$-0.170618\pi$
$127$	7.20921	+	5.23780i	0.639714	+	0.464780i	−0.220038	+	0.975491i	$0.570618\pi$
$128$	−11.3074	+	0.377835i	−0.999442	+	0.0333962i
$129$		0			0
$130$	−2.61460	−	11.2085i	−0.229316	−	0.983052i
$131$			8.30263i			0.725404i	0.931905	+	0.362702i	$0.118146\pi$
$131$			8.30263i			0.725404i	−0.931905	+	0.362702i	$0.881854\pi$
$132$		0			0
$133$		−	13.3725i		−	1.15954i
$134$	−15.8463	+	3.69646i	−1.36891	+	0.319325i
$135$		0			0
$136$	0.428044	+	7.22260i	0.0367044	+	0.619333i
$137$	−13.3743	−	9.71699i	−1.14264	−	0.830179i	−0.155158	−	0.987890i	$-0.549589\pi$
$137$	−13.3743	−	9.71699i	−1.14264	−	0.830179i	−0.987485	+	0.157711i	$0.949589\pi$
$138$		0			0
$139$	−16.0635	−	5.21936i	−1.36249	−	0.442701i	−0.465618	−	0.884986i	$-0.654168\pi$
$139$	−16.0635	−	5.21936i	−1.36249	−	0.442701i	−0.896874	+	0.442285i	$0.854168\pi$
$140$	−11.4465	−	6.01946i	−0.967405	−	0.508737i
$141$		0			0
$142$	−0.617592	+	1.46422i	−0.0518272	+	0.122875i
$143$	17.5527	+	5.79291i	1.46783	+	0.484428i
$144$		0			0
$145$	−4.32331	+	3.14107i	−0.359031	+	0.260852i
$146$	19.8996	+	1.69531i	1.64691	+	0.140305i
$147$		0			0
$148$	2.94670	−	0.427834i	0.242218	−	0.0351678i
$149$	−11.1867	+	15.3972i	−0.916451	+	1.26139i	0.0484646	+	0.998825i	$0.484567\pi$
$149$	−11.1867	+	15.3972i	−0.916451	+	1.26139i	−0.964915	+	0.262561i	$0.915433\pi$
$150$		0			0
$151$	−3.14001	−	9.66396i	−0.255530	−	0.786442i	−0.993725	−	0.111854i	$-0.964321\pi$
$151$	−3.14001	−	9.66396i	−0.255530	−	0.786442i	0.738194	−	0.674588i	$-0.235679\pi$
$152$	−7.19518	−	4.60299i	−0.583606	−	0.373352i
$153$		0			0
$154$	17.8281	−	10.6556i	1.43663	−	0.858653i
$155$		−	2.17826i		−	0.174962i
$156$		0			0
$157$	−15.9290	+	5.17566i	−1.27128	+	0.413063i	−0.865499	−	0.500910i	$-0.832999\pi$
$157$	−15.9290	+	5.17566i	−1.27128	+	0.413063i	−0.405776	+	0.913972i	$0.632999\pi$
$158$	−0.819453	−	0.709069i	−0.0651922	−	0.0564105i
$159$		0			0
$160$	−7.17886	+	4.08690i	−0.567539	+	0.323098i
$161$	5.07367	−	15.6151i	0.399861	−	1.23065i
$162$		0			0
$163$	4.09770	+	5.64001i	0.320957	+	0.441759i	0.938759	−	0.344574i	$-0.111977\pi$
$163$	4.09770	+	5.64001i	0.320957	+	0.441759i	−0.617802	+	0.786334i	$0.711977\pi$
$164$	4.38592	+	4.50053i	0.342483	+	0.351433i
$165$		0			0
$166$	11.1593	+	4.70685i	0.866127	+	0.365323i
$167$	8.08495	−	5.87406i	0.625632	−	0.454548i	−0.229252	−	0.973367i	$-0.573628\pi$
$167$	8.08495	−	5.87406i	0.625632	−	0.454548i	0.854884	+	0.518819i	$0.173628\pi$
$168$		0			0
$169$	−5.58074	+	17.1758i	−0.429288	+	1.32121i
$170$	2.73116	+	4.52205i	0.209471	+	0.346825i
$171$		0			0
$172$	5.53572	+	11.2199i	0.422095	+	0.855506i
$173$	−3.38147	+	1.09871i	−0.257088	+	0.0835331i	−0.434726	−	0.900563i	$-0.643155\pi$
$173$	−3.38147	+	1.09871i	−0.257088	+	0.0835331i	0.177637	+	0.984096i	$0.443155\pi$
$174$		0			0
$175$	12.6978			0.959866
$176$	0.403338	−	13.2604i	0.0304027	−	0.999538i
$177$		0			0
$178$	2.84094	+	12.1788i	0.212937	+	0.912839i
$179$	−5.12791	+	1.66616i	−0.383278	+	0.124535i	−0.494318	−	0.869281i	$-0.664582\pi$
$179$	−5.12791	+	1.66616i	−0.383278	+	0.124535i	0.111039	+	0.993816i	$0.464582\pi$
$180$		0			0
$181$	2.35732	−	3.24458i	0.175219	−	0.241168i	−0.712371	−	0.701803i	$-0.752379\pi$
$181$	2.35732	−	3.24458i	0.175219	−	0.241168i	0.887589	+	0.460636i	$0.152379\pi$
$182$	18.0433	+	29.8747i	1.33746	+	2.21446i
$183$		0			0
$184$	−6.65544	−	8.10488i	−0.490646	−	0.597499i
$185$	1.75887	−	1.27790i	0.129315	−	0.0939529i
$186$		0			0
$187$	−8.48402	−	0.0391508i	−0.620413	−	0.00286299i
$188$	−3.71148	−	3.80846i	−0.270687	−	0.277761i
$189$		0			0
$190$	−6.21408	−	0.529398i	−0.450817	−	0.0384065i
$191$	−0.175918	+	0.541421i	−0.0127290	+	0.0391759i	−0.957219	−	0.289364i	$-0.906556\pi$
$191$	−0.175918	+	0.541421i	−0.0127290	+	0.0391759i	0.944490	+	0.328539i	$0.106556\pi$
$192$		0			0
$193$	−5.75741	−	4.18300i	−0.414428	−	0.301099i	0.360964	−	0.932580i	$-0.382448\pi$
$193$	−5.75741	−	4.18300i	−0.414428	−	0.301099i	−0.775392	+	0.631480i	$0.782448\pi$
$194$	0.318995	+	0.276025i	0.0229025	+	0.0198174i
$195$		0			0
$196$	24.8532	+	4.26562i	1.77523	+	0.304687i
$197$			1.44252i			0.102775i	0.998679	+	0.0513876i	$0.0163644\pi$
$197$			1.44252i			0.102775i	−0.998679	+	0.0513876i	$0.983636\pi$
$198$		0			0
$199$	0.847005			0.0600426			0.0300213	−	0.999549i	$-0.490442\pi$
$199$	0.847005			0.0600426			0.0300213	+	0.999549i	$0.490442\pi$
$200$	4.37076	−	6.83218i	0.309060	−	0.483108i
$201$		0			0
$202$	−2.43504	+	2.81412i	−0.171329	+	0.198001i
$203$	9.52483	−	13.1098i	0.668512	−	0.920127i
$204$		0			0
$205$	4.36382	+	1.41789i	0.304782	+	0.0990298i
$206$	−3.18973	−	0.271743i	−0.222239	−	0.0189332i
$207$		0			0
$208$	22.2851	+	0.574922i	1.54519	+	0.0398636i
$209$	5.92450	−	8.07574i	0.409806	−	0.558611i
$210$		0			0
$211$	−8.88066	−	12.2232i	−0.611370	−	0.841478i	0.385320	−	0.922783i	$-0.374091\pi$
$211$	−8.88066	−	12.2232i	−0.611370	−	0.841478i	−0.996689	+	0.0813050i	$0.974091\pi$
$212$	−17.3449	−	9.12131i	−1.19125	−	0.626454i
$213$		0			0
$214$	4.42014	+	7.31852i	0.302155	+	0.500284i
$215$	7.39037	+	5.36942i	0.504019	+	0.366191i
$216$		0			0
$217$	2.04114	+	6.28198i	0.138562	+	0.426449i
$218$	−16.4416	+	3.83533i	−1.11357	+	0.259761i
$219$		0			0
$220$	−4.24578	−	8.70642i	−0.286250	−	0.586986i
$221$		−	14.2564i		−	0.958986i
$222$		0			0
$223$	−5.78093	−	17.7919i	−0.387120	−	1.19143i	−0.934931	−	0.354830i	$-0.884539\pi$
$223$	−5.78093	−	17.7919i	−0.387120	−	1.19143i	0.547811	−	0.836602i	$-0.315461\pi$
$224$	16.8738	−	18.5133i	1.12743	−	1.23697i
$225$		0			0
$226$	15.0227	−	9.07320i	0.999296	−	0.603541i
$227$	−25.7744	−	8.37460i	−1.71071	−	0.555842i	−0.720255	−	0.693710i	$-0.755975\pi$
$227$	−25.7744	−	8.37460i	−1.71071	−	0.555842i	−0.990451	+	0.137868i	$0.955975\pi$
$228$		0			0
$229$	−6.83211	−	9.40359i	−0.451479	−	0.621407i	0.521236	−	0.853413i	$-0.325471\pi$
$229$	−6.83211	−	9.40359i	−0.451479	−	0.621407i	−0.972714	+	0.232006i	$0.925471\pi$
$230$	−7.05537	−	2.97587i	−0.465218	−	0.196223i
$231$		0			0
$232$	−3.77527	−	9.63748i	−0.247858	−	0.632732i
$233$	−21.1297	+	15.3516i	−1.38425	+	1.00572i	−0.387781	+	0.921751i	$0.626758\pi$
$233$	−21.1297	+	15.3516i	−1.38425	+	1.00572i	−0.996469	+	0.0839651i	$0.973242\pi$
$234$		0			0
$235$	−3.69277	−	1.19985i	−0.240890	−	0.0782699i
$236$	5.10177	−	0.740729i	0.332097	−	0.0482174i
$237$		0			0
$238$	−12.1139	−	10.4821i	−0.785227	−	0.679452i
$239$	4.38468	+	13.4946i	0.283621	+	0.872896i	0.986809	+	0.161892i	$0.0517595\pi$
$239$	4.38468	+	13.4946i	0.283621	+	0.872896i	−0.703187	+	0.711005i	$0.748241\pi$
$240$		0			0
$241$	17.2505			1.11120			0.555602	−	0.831448i	$-0.312488\pi$
$241$	17.2505			1.11120			0.555602	+	0.831448i	$0.312488\pi$
$242$	15.4874	+	1.46351i	0.995565	+	0.0940779i
$243$		0			0
$244$	−1.88990	+	11.0113i	−0.120988	+	0.704928i
$245$	17.5107	−	5.68958i	1.11872	−	0.363494i
$246$		0			0
$247$	13.6159	+	9.89256i	0.866361	+	0.629448i
$248$	4.08266	+	1.06409i	0.259249	+	0.0675698i
$249$		0			0
$250$	1.37921	−	16.1892i	0.0872287	−	1.02389i
$251$	−11.9442	−	16.4398i	−0.753912	−	1.03767i	−0.997696	−	0.0678411i	$-0.978389\pi$
$251$	−11.9442	−	16.4398i	−0.753912	−	1.03767i	0.243784	−	0.969829i	$-0.421611\pi$
$252$		0			0
$253$	9.98212	−	7.18229i	0.627570	−	0.451547i
$254$	−4.89762	+	11.6115i	−0.307304	+	0.728573i
$255$		0			0
$256$	−4.15307	−	15.4516i	−0.259567	−	0.965725i
$257$	−4.66258	+	14.3499i	−0.290844	+	0.895125i	0.693742	+	0.720223i	$0.255961\pi$
$257$	−4.66258	+	14.3499i	−0.290844	+	0.895125i	−0.984586	+	0.174901i	$0.944039\pi$
$258$		0			0
$259$	−3.87503	+	5.33353i	−0.240783	+	0.331409i
$260$	14.5968	−	7.20187i	0.905256	−	0.446641i
$261$		0			0
$262$	−11.4347	+	2.66737i	−0.706439	+	0.164790i
$263$	10.8242			0.667448			0.333724	−	0.942671i	$-0.391695\pi$
$263$	10.8242			0.667448			0.333724	+	0.942671i	$0.391695\pi$
$264$		0			0
$265$	−14.3087			−0.878979
$266$	18.4171	−	4.29614i	1.12922	−	0.263413i
$267$		0			0
$268$	−10.1818	−	20.6366i	−0.621953	−	1.26058i
$269$	−11.5070	+	15.8381i	−0.701595	+	0.965663i	0.298342	+	0.954459i	$0.403566\pi$
$269$	−11.5070	+	15.8381i	−0.701595	+	0.965663i	−0.999937	+	0.0112040i	$0.996434\pi$
$270$		0			0
$271$	−7.98985	+	24.5902i	−0.485349	+	1.49375i	0.346127	+	0.938188i	$0.387497\pi$
$271$	−7.98985	+	24.5902i	−0.485349	+	1.49375i	−0.831475	+	0.555562i	$0.812503\pi$
$272$	−9.80974	+	2.90991i	−0.594803	+	0.176439i
$273$		0			0
$274$	9.08589	−	21.5413i	0.548899	−	1.30136i
$275$	7.66832	+	5.62561i	0.462417	+	0.339237i
$276$		0			0
$277$	14.4008	+	19.8210i	0.865261	+	1.19093i	0.980289	+	0.197567i	$0.0633042\pi$
$277$	14.4008	+	19.8210i	0.865261	+	1.19093i	−0.115028	+	0.993362i	$0.536696\pi$
$278$	2.02761	−	23.8002i	0.121608	−	1.42744i
$279$		0			0
$280$	4.61285	−	17.6984i	0.275670	−	1.05768i
$281$	7.54411	+	5.48112i	0.450044	+	0.326976i	0.789613	−	0.613605i	$-0.210281\pi$
$281$	7.54411	+	5.48112i	0.450044	+	0.326976i	−0.339569	+	0.940581i	$0.610281\pi$
$282$		0			0
$283$	18.0621	−	5.86872i	1.07368	−	0.348859i	0.281759	−	0.959485i	$-0.409082\pi$
$283$	18.0621	−	5.86872i	1.07368	−	0.348859i	0.791919	+	0.610626i	$0.209082\pi$
$284$	−2.21500	−	0.380165i	−0.131436	−	0.0225586i
$285$		0			0
$286$	−2.33910	+	26.0354i	−0.138314	+	1.53950i
$287$	−13.9136			−0.821295
$288$		0			0
$289$	−3.23119	−	9.94458i	−0.190070	−	0.584975i
$290$	−5.71494	−	4.94511i	−0.335593	−	0.290387i
$291$		0			0
$292$	4.05826	+	27.9512i	0.237492	+	1.63572i
$293$	5.62395	+	1.82733i	0.328555	+	0.106754i	0.468650	−	0.883384i	$-0.344741\pi$
$293$	5.62395	+	1.82733i	0.328555	+	0.106754i	−0.140095	+	0.990138i	$0.544741\pi$
$294$		0			0
$295$	3.04522	−	2.21248i	0.177300	−	0.128816i
$296$	1.53591	+	3.92087i	0.0892730	+	0.227896i
$297$		0			0
$298$	−24.7995	−	10.4602i	−1.43660	−	0.605940i
$299$	12.1461	+	16.7177i	0.702427	+	0.966807i
$300$		0			0
$301$	−26.3448	−	8.55994i	−1.51849	−	0.493387i
$302$	12.3008	−	7.42926i	0.707831	−	0.427506i
$303$		0			0
$304$	4.02784	−	11.3883i	0.231012	−	0.653162i
$305$	2.52079	+	7.75820i	0.144340	+	0.444233i
$306$		0			0
$307$			13.6216i			0.777423i	0.921360	+	0.388711i	$0.127080\pi$
$307$			13.6216i			0.777423i	−0.921360	+	0.388711i	$0.872920\pi$
$308$	20.4029	+	21.1303i	1.16256	+	1.20401i
$309$		0			0
$310$	2.99999	−	0.699806i	0.170388	−	0.0397463i
$311$	−4.38316	−	13.4900i	−0.248546	−	0.764946i	−0.995033	−	0.0995459i	$-0.968261\pi$
$311$	−4.38316	−	13.4900i	−0.248546	−	0.764946i	0.746487	−	0.665400i	$-0.231739\pi$
$312$		0			0
$313$	1.75411	+	1.27444i	0.0991482	+	0.0720354i	0.636255	−	0.771479i	$-0.280483\pi$
$313$	1.75411	+	1.27444i	0.0991482	+	0.0720354i	−0.537107	+	0.843514i	$0.680483\pi$
$314$	−12.2456	−	20.2753i	−0.691059	−	1.14420i
$315$		0			0
$316$	0.713293	−	1.35638i	0.0401259	−	0.0763026i
$317$	−8.32633	−	11.4602i	−0.467653	−	0.643669i	0.508421	−	0.861109i	$-0.330229\pi$
$317$	−8.32633	−	11.4602i	−0.467653	−	0.643669i	−0.976074	+	0.217440i	$0.930229\pi$
$318$		0			0
$319$	11.5602	−	3.69726i	0.647249	−	0.207007i
$320$	−7.93498	−	8.57401i	−0.443579	−	0.479302i
$321$		0			0
$322$	23.1358	+	1.97101i	1.28931	+	0.109840i
$323$	−7.34697	−	2.38717i	−0.408796	−	0.132826i
$324$		0			0
$325$	−9.39347	+	12.9290i	−0.521056	+	0.717172i
$326$	−6.45118	+	7.45547i	−0.357298	+	0.412920i
$327$		0			0
$328$	−4.78925	+	7.48634i	−0.264442	+	0.413364i
$329$	11.7740			0.649124
$330$		0			0
$331$			10.7862i			0.592865i	0.955054	+	0.296433i	$0.0957970\pi$
$331$			10.7862i			0.592865i	−0.955054	+	0.296433i	$0.904203\pi$
$332$	−2.89735	+	16.8811i	−0.159013	+	0.926473i
$333$		0			0
$334$	10.6874	+	9.24776i	0.584789	+	0.506015i
$335$	−13.5931	−	9.87594i	−0.742668	−	0.539580i
$336$		0			0
$337$	−1.94211	+	5.97720i	−0.105793	+	0.325599i	−0.989916	−	0.141657i	$-0.954757\pi$
$337$	−1.94211	+	5.97720i	−0.105793	+	0.325599i	0.884122	+	0.467255i	$0.154757\pi$
$338$	−25.4480	−	2.16800i	−1.38419	−	0.117924i
$339$		0			0
$340$	−5.35051	+	5.21425i	−0.290172	+	0.282783i
$341$	−1.55049	+	4.69804i	−0.0839637	+	0.254413i
$342$		0			0
$343$	−20.0914	+	14.5973i	−1.08484	+	0.788179i
$344$	−13.6740	+	11.2286i	−0.737252	+	0.605405i
$345$		0			0
$346$	−2.59954	−	4.30411i	−0.139752	−	0.231391i
$347$	−10.2014	+	14.0410i	−0.547640	+	0.753762i	−0.989690	−	0.143229i	$-0.954252\pi$
$347$	−10.2014	+	14.0410i	−0.547640	+	0.753762i	0.442050	+	0.896991i	$0.354252\pi$
$348$		0			0
$349$	−23.6261	+	7.67659i	−1.26468	+	0.410918i	−0.863159	−	0.504933i	$-0.831517\pi$
$349$	−23.6261	+	7.67659i	−1.26468	+	0.410918i	−0.401518	+	0.915851i	$0.631517\pi$
$350$	4.07940	+	17.4879i	0.218053	+	0.934770i
$351$		0			0
$352$	18.3923	−	3.70463i	0.980311	−	0.197458i
$353$	−17.9063			−0.953056			−0.476528	−	0.879159i	$-0.658105\pi$
$353$	−17.9063			−0.953056			−0.476528	+	0.879159i	$0.658105\pi$
$354$		0			0
$355$	−1.56061	+	0.507073i	−0.0828285	+	0.0269126i
$356$	−15.8604	+	7.82530i	−0.840600	+	0.414740i
$357$		0			0
$358$	−3.94213	−	6.52708i	−0.208348	−	0.344967i
$359$	−4.54688	+	13.9939i	−0.239975	+	0.738568i	0.756447	+	0.654055i	$0.226934\pi$
$359$	−4.54688	+	13.9939i	−0.239975	+	0.738568i	−0.996422	+	0.0845133i	$0.973066\pi$
$360$		0			0
$361$	−7.99328	+	5.80746i	−0.420699	+	0.305656i
$362$	5.22589	+	2.20422i	0.274667	+	0.115851i
$363$		0			0
$364$	−35.3478	+	34.4477i	−1.85273	+	1.80555i
$365$	12.1216	+	16.6839i	0.634473	+	0.873278i
$366$		0			0
$367$	−9.71617	+	29.9033i	−0.507180	+	1.56094i	0.289894	+	0.957059i	$0.406380\pi$
$367$	−9.71617	+	29.9033i	−0.507180	+	1.56094i	−0.797074	+	0.603881i	$0.793620\pi$
$368$	9.02417	−	11.7700i	0.470418	−	0.613552i
$369$		0			0
$370$	2.32504	+	2.01184i	0.120873	+	0.104591i
$371$	41.2655	−	13.4080i	2.14240	−	0.696107i
$372$		0			0
$373$			20.5892i			1.06607i	0.846094	+	0.533034i	$0.178948\pi$
$373$			20.5892i			1.06607i	−0.846094	+	0.533034i	$0.821052\pi$
$374$	−2.67172	−	11.6971i	−0.138151	−	0.604843i
$375$		0			0
$376$	4.05279	−	6.33513i	0.209006	−	0.326709i
$377$	6.30230	+	19.3965i	0.324585	+	0.998969i
$378$		0			0
$379$	7.64489	−	10.5223i	0.392692	−	0.540494i	−0.566199	−	0.824268i	$-0.691587\pi$
$379$	7.64489	−	10.5223i	0.392692	−	0.540494i	0.958891	+	0.283775i	$0.0915868\pi$
$380$	−1.26728	−	8.72835i	−0.0650099	−	0.447755i
$381$		0			0
$382$	−0.802183	−	0.0683406i	−0.0410433	−	0.00349661i
$383$	30.0437	−	21.8280i	1.53516	−	1.11536i	0.581883	−	0.813272i	$-0.302316\pi$
$383$	30.0437	−	21.8280i	1.53516	−	1.11536i	0.953280	−	0.302089i	$-0.0976839\pi$
$384$		0			0
$385$	20.3661	+	6.72140i	1.03795	+	0.342554i
$386$	3.91133	−	9.27319i	0.199081	−	0.471993i
$387$		0			0
$388$	−0.277669	+	0.528010i	−0.0140965	+	0.0268057i
$389$	−3.37583	−	1.09687i	−0.171161	−	0.0556137i	0.222183	−	0.975005i	$-0.428682\pi$
$389$	−3.37583	−	1.09687i	−0.171161	−	0.0556137i	−0.393344	+	0.919391i	$0.628682\pi$
$390$		0			0
$391$	−7.67339	−	5.57505i	−0.388060	−	0.281942i
$392$	2.10977	+	35.5993i	0.106560	+	1.79803i
$393$		0			0
$394$	−1.98669	+	0.463434i	−0.100088	+	0.0233475i
$395$		−	1.11895i		−	0.0563006i
$396$		0			0
$397$		−	35.1583i		−	1.76454i	−0.470742	−	0.882271i	$-0.656014\pi$
$397$		−	35.1583i		−	1.76454i	0.470742	−	0.882271i	$-0.343986\pi$
$398$	0.272115	+	1.16653i	0.0136399	+	0.0584728i
$399$		0			0
$400$	10.8137	+	3.82463i	0.540686	+	0.191231i
$401$	11.5283	+	8.37578i	0.575694	+	0.418266i	0.837169	−	0.546944i	$-0.184209\pi$
$401$	11.5283	+	8.37578i	0.575694	+	0.418266i	−0.261475	+	0.965210i	$0.584209\pi$
$402$		0			0
$403$	−7.90632	−	2.56892i	−0.393842	−	0.127967i
$404$	−4.65802	−	2.44955i	−0.231745	−	0.121870i
$405$		0			0
$406$	21.1153	+	8.90621i	1.04794	+	0.442008i
$407$	−4.70311	+	1.50418i	−0.233125	+	0.0745592i
$408$		0			0
$409$	−8.40619	+	6.10746i	−0.415660	+	0.301994i	−0.775889	−	0.630869i	$-0.782698\pi$
$409$	−8.40619	+	6.10746i	−0.415660	+	0.301994i	0.360230	+	0.932864i	$0.382698\pi$
$410$	−0.550821	+	6.46554i	−0.0272031	+	0.319310i
$411$		0			0
$412$	−0.650501	−	4.48032i	−0.0320479	−	0.220729i
$413$	−6.70902	+	9.23418i	−0.330130	+	0.454384i
$414$		0			0
$415$	3.86455	+	11.8939i	0.189703	+	0.583847i
$416$	6.36766	+	30.8766i	0.312200	+	1.51385i
$417$		0			0
$418$	13.0256	+	5.56498i	0.637102	+	0.272192i
$419$			20.7586i			1.01412i	0.861910	+	0.507062i	$0.169268\pi$
$419$			20.7586i			1.01412i	−0.861910	+	0.507062i	$0.830732\pi$
$420$		0			0
$421$	0.157132	−	0.0510554i	0.00765817	−	0.00248829i	−0.305185	−	0.952293i	$-0.598718\pi$
$421$	0.157132	−	0.0510554i	0.00765817	−	0.00248829i	0.312844	+	0.949805i	$0.398718\pi$
$422$	13.9812	−	16.1577i	0.680593	−	0.786544i
$423$		0			0
$424$	6.98987	−	26.8185i	0.339458	−	1.30242i
$425$	2.26674	−	6.97631i	0.109953	−	0.338401i
$426$		0			0
$427$	−14.5396	−	20.0121i	−0.703621	−	0.968451i
$428$	−8.65931	+	8.43879i	−0.418564	+	0.407904i
$429$		0			0
$430$	−5.02069	+	11.9033i	−0.242119	+	0.574030i
$431$	−27.3557	+	19.8751i	−1.31768	+	0.957350i	−0.317721	+	0.948184i	$0.602918\pi$
$431$	−27.3557	+	19.8751i	−1.31768	+	0.957350i	−0.999958	+	0.00916561i	$0.997082\pi$
$432$		0			0
$433$	−1.66699	+	5.13046i	−0.0801103	+	0.246554i	−0.983088	−	0.183133i	$-0.941376\pi$
$433$	−1.66699	+	5.13046i	−0.0801103	+	0.246554i	0.902978	+	0.429687i	$0.141376\pi$
$434$	−7.99604	+	4.82933i	−0.383822	+	0.231815i
$435$		0			0
$436$	−10.5643	−	21.4119i	−0.505940	−	1.02544i
$437$	10.6492	−	3.46014i	0.509421	−	0.165521i
$438$		0			0
$439$	0.0455090			0.00217203			0.00108601	−	0.999999i	$-0.499654\pi$
$439$	0.0455090			0.00217203			0.00108601	+	0.999999i	$0.499654\pi$
$440$	10.6268	−	8.64454i	0.506612	−	0.412112i
$441$		0			0
$442$	19.6344	−	4.58011i	0.933913	−	0.217853i
$443$	0.0831509	−	0.0270174i	0.00395062	−	0.00128363i	−0.307041	−	0.951696i	$-0.599339\pi$
$443$	0.0831509	−	0.0270174i	0.00395062	−	0.00128363i	0.310992	+	0.950413i	$0.399339\pi$
$444$		0			0
$445$	−7.59022	+	10.4470i	−0.359811	+	0.495237i
$446$	22.6464	−	13.6777i	1.07234	−	0.647657i
$447$		0			0
$448$	30.9182	+	17.2915i	1.46075	+	0.816945i
$449$	24.1983	−	17.5811i	1.14199	−	0.829702i	0.154592	−	0.987978i	$-0.450594\pi$
$449$	24.1983	−	17.5811i	1.14199	−	0.829702i	0.987395	+	0.158276i	$0.0505937\pi$
$450$		0			0
$451$	−8.40254	−	6.16424i	−0.395660	−	0.290263i
$452$	17.3223	+	17.7749i	0.814771	+	0.836062i
$453$		0			0
$454$	3.25336	−	38.1880i	0.152688	−	1.79225i
$455$	−11.1363	+	34.2741i	−0.522079	+	1.60679i
$456$		0			0
$457$	17.4004	+	12.6421i	0.813957	+	0.591375i	0.914975	−	0.403510i	$-0.132210\pi$
$457$	17.4004	+	12.6421i	0.813957	+	0.591375i	−0.101018	+	0.994885i	$0.532210\pi$
$458$	10.7561	−	12.4305i	0.502598	−	0.580840i
$459$		0			0
$460$	1.83183	−	10.6730i	0.0854094	−	0.497631i
$461$		−	7.88518i		−	0.367250i	−0.982996	−	0.183625i	$-0.941217\pi$
$461$		−	7.88518i		−	0.367250i	0.982996	−	0.183625i	$-0.0587832\pi$
$462$		0			0
$463$	5.12007			0.237950			0.118975	−	0.992897i	$-0.462039\pi$
$463$	5.12007			0.237950			0.118975	+	0.992897i	$0.462039\pi$
$464$	12.0602	−	8.29566i	0.559883	−	0.385116i
$465$		0			0
$466$	−27.9311	−	24.1686i	−1.29388	−	1.11959i
$467$	−10.9476	+	15.0681i	−0.506596	+	0.697270i	−0.983341	−	0.181772i	$-0.941817\pi$
$467$	−10.9476	+	15.0681i	−0.506596	+	0.697270i	0.476745	+	0.879042i	$0.341817\pi$
$468$		0			0
$469$	48.4558	+	15.7442i	2.23748	+	0.727001i
$470$	0.466118	−	5.47130i	0.0215004	−	0.252372i
$471$		0			0
$472$	2.65919	+	6.78838i	0.122399	+	0.312460i
$473$	−12.1174	−	16.8411i	−0.557161	−	0.774356i
$474$		0			0
$475$	5.09002	+	7.00581i	0.233546	+	0.321449i
$476$	10.5445	−	20.0513i	0.483308	−	0.919048i
$477$		0			0
$478$	−17.1767	+	10.3741i	−0.785644	+	0.474502i
$479$	−31.7897	−	23.0965i	−1.45251	−	1.05531i	−0.985238	−	0.171192i	$-0.945238\pi$
$479$	−31.7897	−	23.0965i	−1.45251	−	1.05531i	−0.467269	−	0.884115i	$-0.654762\pi$
$480$		0			0
$481$	−2.56400	−	7.89117i	−0.116908	−	0.359806i
$482$	5.54204	+	23.7581i	0.252433	+	1.08215i
$483$		0			0
$484$	2.95998	+	21.8000i	0.134545	+	0.990908i
$485$			0.435584i			0.0197788i
$486$		0			0
$487$	−5.64965	−	17.3878i	−0.256010	−	0.787918i	−0.993629	−	0.112701i	$-0.964050\pi$
$487$	−5.64965	−	17.3878i	−0.256010	−	0.787918i	0.737619	−	0.675217i	$-0.235950\pi$
$488$	−15.7724	+	0.934742i	−0.713983	+	0.0423138i
$489$		0			0
$490$	13.4615	+	22.2886i	0.608131	+	1.00690i
$491$	3.90141	+	1.26765i	0.176068	+	0.0572081i	0.395724	−	0.918369i	$-0.370494\pi$
$491$	3.90141	+	1.26765i	0.176068	+	0.0572081i	−0.219656	+	0.975577i	$0.570494\pi$
$492$		0			0
$493$	−5.50234	−	7.57331i	−0.247813	−	0.341085i
$494$	−9.25006	+	21.9306i	−0.416180	+	0.986702i
$495$		0			0
$496$	−0.153879	+	5.96466i	−0.00690939	+	0.267821i
$497$	4.02555	−	2.92473i	0.180571	−	0.131192i
$498$		0			0
$499$	8.91593	+	2.89696i	0.399132	+	0.129686i	0.501703	−	0.865040i	$-0.332707\pi$
$499$	8.91593	+	2.89696i	0.399132	+	0.129686i	−0.102571	+	0.994726i	$0.532707\pi$
$500$	22.7394	−	3.30155i	1.01694	−	0.147650i
$501$		0			0
$502$	18.8042	−	21.7316i	0.839274	−	0.969929i
$503$	4.47159	+	13.7621i	0.199378	+	0.613624i	0.999898	+	0.0143165i	$0.00455723\pi$
$503$	4.47159	+	13.7621i	0.199378	+	0.613624i	−0.800519	+	0.599307i	$0.795443\pi$
$504$		0			0
$505$	−3.84264			−0.170995
$506$	13.0987	+	11.4403i	0.582306	+	0.508584i
$507$		0			0
$508$	−17.5653	−	3.01477i	−0.779335	−	0.133759i
$509$	−5.42967	+	1.76421i	−0.240666	+	0.0781971i	−0.426867	−	0.904315i	$-0.640383\pi$
$509$	−5.42967	+	1.76421i	−0.240666	+	0.0781971i	0.186201	+	0.982512i	$0.440383\pi$
$510$		0			0
$511$	−50.5916	−	36.7570i	−2.23804	−	1.62603i
$512$	19.9463	−	10.6839i	0.881510	−	0.472165i
$513$		0			0
$514$	−21.2612	−	1.81131i	−0.937793	−	0.0798936i
$515$	−1.94298	−	2.67428i	−0.0856179	−	0.117843i
$516$		0			0
$517$	7.11044	+	5.21634i	0.312717	+	0.229414i
$518$	−8.59046	−	3.62336i	−0.377443	−	0.159201i
$519$		0			0
$520$	14.6082	+	17.7896i	0.640611	+	0.780125i
$521$	−10.5048	+	32.3304i	−0.460222	+	1.41642i	0.404671	+	0.914463i	$0.367386\pi$
$521$	−10.5048	+	32.3304i	−0.460222	+	1.41642i	−0.864893	+	0.501956i	$0.832614\pi$
$522$		0			0
$523$	−20.3248	+	27.9746i	−0.888740	+	1.22325i	0.0851828	+	0.996365i	$0.472853\pi$
$523$	−20.3248	+	27.9746i	−0.888740	+	1.22325i	−0.973923	+	0.226880i	$0.927147\pi$
$524$	−7.34720	−	14.8914i	−0.320964	−	0.650533i
$525$		0			0
$526$	3.47746	+	14.9075i	0.151625	+	0.649998i
$527$	3.81575			0.166217
$528$		0			0
$529$	−9.25201			−0.402261
$530$	−4.59693	−	19.7065i	−0.199678	−	0.855998i
$531$		0			0
$532$	11.8336	+	23.9845i	0.513053	+	1.03986i
$533$	10.2929	−	14.1669i	0.445834	−	0.613638i
$534$		0			0
$535$	−2.72811	+	8.39626i	−0.117947	+	0.363002i
$536$	25.1504	−	20.6527i	1.08633	−	0.892059i
$537$		0			0
$538$	−25.5096	−	10.7597i	−1.09980	−	0.463882i
$539$	−41.8166	−	0.192969i	−1.80117	−	0.00831177i
$540$		0			0
$541$	−17.0845	−	23.5148i	−0.734520	−	1.01098i	−0.998915	−	0.0465653i	$-0.985172\pi$
$541$	−17.0845	−	23.5148i	−0.734520	−	1.01098i	0.264396	−	0.964414i	$-0.414828\pi$
$542$	−36.4335	−	3.10389i	−1.56495	−	0.133323i
$543$		0			0
$544$	−7.15919	−	12.5755i	−0.306948	−	0.539170i
$545$	−14.1037	−	10.2470i	−0.604138	−	0.438932i
$546$		0			0
$547$	12.7447	−	4.14101i	0.544925	−	0.177057i	−0.0236019	−	0.999721i	$-0.507513\pi$
$547$	12.7447	−	4.14101i	0.544925	−	0.177057i	0.568527	+	0.822664i	$0.307513\pi$
$548$	32.5866	+	5.59291i	1.39203	+	0.238917i
$549$		0			0
$550$	−5.28422	+	12.3684i	−0.225320	+	0.527392i
$551$	11.0512			0.470797
$552$		0			0
$553$	1.04851	+	3.22699i	0.0445873	+	0.137226i
$554$	−22.6718	+	26.2012i	−0.963231	+	1.11318i
$555$		0			0
$556$	33.4299	−	4.85371i	1.41774	−	0.205843i
$557$	−0.872304	−	0.283429i	−0.0369607	−	0.0120093i	0.290478	−	0.956882i	$-0.406186\pi$
$557$	−0.872304	−	0.283429i	−0.0369607	−	0.0120093i	−0.327439	+	0.944872i	$0.606186\pi$
$558$		0			0
$559$	28.2049	−	20.4920i	1.19294	−	0.866721i
$560$	25.8569	+	0.667070i	1.09265	+	0.0281888i
$561$		0			0
$562$	−5.12513	+	12.1510i	−0.216191	+	0.512557i
$563$	−14.4004	−	19.8205i	−0.606906	−	0.835334i	0.389413	−	0.921063i	$-0.372678\pi$
$563$	−14.4004	−	19.8205i	−0.606906	−	0.835334i	−0.996318	+	0.0857291i	$0.972678\pi$
$564$		0			0
$565$	17.2350	+	5.59998i	0.725081	+	0.235593i
$566$	13.8854	+	22.9904i	0.583646	+	0.966357i
$567$		0			0
$568$	−0.188029	−	3.17271i	−0.00788953	−	0.133124i
$569$	−1.14323	−	3.51851i	−0.0479268	−	0.147503i	0.924229	−	0.381838i	$-0.124709\pi$
$569$	−1.14323	−	3.51851i	−0.0479268	−	0.147503i	−0.972156	+	0.234335i	$0.924709\pi$
$570$		0			0
$571$			22.3627i			0.935849i	0.883768	+	0.467925i	$0.154998\pi$
$571$			22.3627i			0.935849i	−0.883768	+	0.467925i	$0.845002\pi$
$572$	−36.6084	+	5.14282i	−1.53067	+	0.215032i
$573$		0			0
$574$	−4.46999	−	19.1624i	−0.186574	−	0.799822i
$575$	3.28557	+	10.1120i	0.137018	+	0.421698i
$576$		0			0
$577$	27.3646	+	19.8815i	1.13920	+	0.827678i	0.987008	−	0.160672i	$-0.0513662\pi$
$577$	27.3646	+	19.8815i	1.13920	+	0.827678i	0.152194	+	0.988351i	$0.451366\pi$
$578$	12.6580	−	7.64499i	0.526503	−	0.317990i
$579$		0			0
$580$	4.97457	−	9.45954i	0.206558	−	0.392786i
$581$	−22.2903	−	30.6799i	−0.924755	−	1.27282i
$582$		0			0
$583$	30.8608	+	10.1850i	1.27812	+	0.421818i
$584$	−37.1917	+	14.5690i	−1.53900	+	0.602870i
$585$		0			0
$586$	−0.709880	+	8.33259i	−0.0293249	+	0.344216i
$587$	42.0044	+	13.6481i	1.73371	+	0.563316i	0.993977	−	0.109588i	$-0.0349531\pi$
$587$	42.0044	+	13.6481i	1.73371	+	0.563316i	0.739730	+	0.672904i	$0.234953\pi$
$588$		0			0
$589$	−2.64777	+	3.64434i	−0.109099	+	0.150163i
$590$	4.02545	+	3.48320i	0.165725	+	0.143401i
$591$		0			0
$592$	−4.90653	+	3.37496i	−0.201657	+	0.138710i
$593$	13.4081			0.550605			0.275303	−	0.961358i	$-0.411222\pi$
$593$	13.4081			0.550605			0.275303	+	0.961358i	$0.411222\pi$
$594$		0			0
$595$		−	16.5414i		−	0.678129i
$596$	6.43884	−	37.5154i	0.263745	−	1.53669i
$597$		0			0
$598$	−19.1221	+	22.0989i	−0.781960	+	0.903692i
$599$	−30.8401	−	22.4066i	−1.26009	−	0.915511i	−0.261330	−	0.965249i	$-0.584161\pi$
$599$	−30.8401	−	22.4066i	−1.26009	−	0.915511i	−0.998762	+	0.0497386i	$0.984161\pi$
$600$		0			0
$601$	1.54690	−	4.76086i	0.0630992	−	0.194199i	−0.914537	−	0.404502i	$-0.867445\pi$
$601$	1.54690	−	4.76086i	0.0630992	−	0.194199i	0.977636	+	0.210303i	$0.0674449\pi$
$602$	3.32536	−	39.0331i	0.135531	−	1.59087i
$603$		0			0
$604$	14.1837	+	14.5544i	0.577127	+	0.592208i
$605$	9.32140	+	13.0820i	0.378969	+	0.531860i
$606$		0			0
$607$	23.8596	−	17.3350i	0.968430	−	0.703606i	0.0133371	−	0.999911i	$-0.495755\pi$
$607$	23.8596	−	17.3350i	0.968430	−	0.703606i	0.955093	+	0.296305i	$0.0957545\pi$
$608$	16.9784	+	1.88861i	0.688564	+	0.0765933i
$609$		0			0
$610$	−9.87504	+	5.96419i	−0.399829	+	0.241483i
$611$	−8.71009	+	11.9884i	−0.352372	+	0.484999i
$612$		0			0
$613$	18.0106	−	5.85201i	0.727443	−	0.236360i	0.0781956	−	0.996938i	$-0.475084\pi$
$613$	18.0106	−	5.85201i	0.727443	−	0.236360i	0.649247	+	0.760578i	$0.275084\pi$
$614$	−18.7601	+	4.37616i	−0.757097	+	0.176608i
$615$		0			0
$616$	−22.5466	+	34.8881i	−0.908429	+	1.40568i
$617$	22.1947			0.893524			0.446762	−	0.894653i	$-0.352577\pi$
$617$	22.1947			0.893524			0.446762	+	0.894653i	$0.352577\pi$
$618$		0			0
$619$	−39.4857	+	12.8297i	−1.58707	+	0.515669i	−0.963864	−	0.266393i	$-0.914168\pi$
$619$	−39.4857	+	12.8297i	−1.58707	+	0.515669i	−0.623201	+	0.782062i	$0.714168\pi$
$620$	1.92760	+	3.90688i	0.0774143	+	0.156904i
$621$		0			0
$622$	17.1707	−	10.3705i	0.688484	−	0.415821i
$623$	12.1003	−	37.2410i	0.484790	−	1.49203i
$624$		0			0
$625$	1.97363	−	1.43392i	0.0789450	−	0.0573569i
$626$	−1.19166	+	2.82527i	−0.0476285	+	0.112920i
$627$		0			0
$628$	23.9898	−	23.3789i	0.957299	−	0.932921i
$629$	2.23854	+	3.08109i	0.0892566	+	0.122851i
$630$		0			0
$631$	6.66284	−	20.5061i	0.265244	−	0.816336i	−0.726394	−	0.687279i	$-0.758805\pi$
$631$	6.66284	−	20.5061i	0.265244	−	0.816336i	0.991637	−	0.129057i	$-0.0411950\pi$
$632$	2.09722	+	0.546613i	0.0834230	+	0.0217431i
$633$		0			0
$634$	13.1085	−	15.1491i	0.520603	−	0.601649i
$635$	−12.3759	+	4.02118i	−0.491123	+	0.159576i
$636$		0			0
$637$		−	70.2677i		−	2.78411i
$638$	8.80594	+	14.7334i	0.348631	+	0.583301i
$639$		0			0
$640$	9.25922	−	13.6829i	0.366003	−	0.540865i
$641$	3.11203	+	9.57784i	0.122918	+	0.378302i	0.993516	−	0.113693i	$-0.0362680\pi$
$641$	3.11203	+	9.57784i	0.122918	+	0.378302i	−0.870598	+	0.491995i	$0.836268\pi$
$642$		0			0
$643$	18.0424	−	24.8333i	0.711525	−	0.979330i	−0.288238	−	0.957559i	$-0.593070\pi$
$643$	18.0424	−	24.8333i	0.711525	−	0.979330i	0.999763	−	0.0217709i	$-0.00693044\pi$
$644$	4.71823	+	32.4967i	0.185924	+	1.28055i
$645$		0			0
$646$	0.927367	−	10.8855i	0.0364868	−	0.428282i
$647$	33.3683	−	24.2435i	1.31184	−	0.953111i	0.311849	−	0.950132i	$-0.399052\pi$
$647$	33.3683	−	24.2435i	1.31184	−	0.953111i	0.999996	−	0.00297890i	$-0.000948215\pi$
$648$		0			0
$649$	−8.14271	+	2.60425i	−0.319630	+	0.102226i
$650$	−20.8241	−	8.78339i	−0.816790	−	0.344513i
$651$		0			0
$652$	−12.3405	−	6.48961i	−0.483292	−	0.254153i
$653$	23.0914	+	7.50286i	0.903638	+	0.293610i	0.723738	−	0.690075i	$-0.242423\pi$
$653$	23.0914	+	7.50286i	0.903638	+	0.293610i	0.179900	+	0.983685i	$0.442423\pi$
$654$		0			0
$655$	−9.80876	−	7.12648i	−0.383260	−	0.278455i
$656$	−11.8491	−	4.19083i	−0.462630	−	0.163624i
$657$		0			0
$658$	3.78262	+	16.2157i	0.147462	+	0.632153i
$659$			2.24471i			0.0874413i	0.999044	+	0.0437207i	$0.0139212\pi$
$659$			2.24471i			0.0874413i	−0.999044	+	0.0437207i	$0.986079\pi$
$660$		0			0
$661$			21.5996i			0.840129i	0.907494	+	0.420064i	$0.137993\pi$
$661$			21.5996i			0.840129i	−0.907494	+	0.420064i	$0.862007\pi$
$662$	−14.8552	+	3.46527i	−0.577365	+	0.134681i
$663$		0			0
$664$	−24.1802	+	1.43303i	−0.938373	+	0.0556122i
$665$	15.7983	+	11.4781i	0.612631	+	0.445103i
$666$		0			0
$667$	12.9046	+	4.19295i	0.499668	+	0.162352i
$668$	−9.30286	+	17.6901i	−0.359938	+	0.684452i
$669$		0			0
$670$	9.23451	−	21.8937i	0.356760	−	0.845828i
$671$	0.0854957	−	18.5270i	0.00330053	−	0.715228i
$672$		0			0
$673$	17.6776	−	12.8435i	0.681421	−	0.495082i	−0.192408	−	0.981315i	$-0.561630\pi$
$673$	17.6776	−	12.8435i	0.681421	−	0.495082i	0.873829	+	0.486234i	$0.161630\pi$
$674$	−8.85597	−	0.754469i	−0.341119	−	0.0290610i
$675$		0			0
$676$	−5.18977	−	35.7445i	−0.199607	−	1.37479i
$677$	23.3056	−	32.0775i	0.895708	−	1.23284i	−0.0761084	−	0.997100i	$-0.524249\pi$
$677$	23.3056	−	32.0775i	0.895708	−	1.23284i	0.971817	−	0.235737i	$-0.0757505\pi$
$678$		0			0
$679$	−0.408163	−	1.25620i	−0.0156639	−	0.0482084i
$680$	−8.90022	−	5.69376i	−0.341308	−	0.218346i
$681$		0			0
$682$	−6.96844	−	0.626067i	−0.266835	−	0.0239733i
$683$		−	5.22481i		−	0.199922i	−0.994991	−	0.0999610i	$-0.968128\pi$
$683$		−	5.22481i		−	0.199922i	0.994991	−	0.0999610i	$-0.0318718\pi$
$684$		0			0
$685$	22.9594	−	7.45995i	0.877233	−	0.285030i
$686$	−26.5587	−	22.9811i	−1.01401	−	0.877421i
$687$		0			0
$688$	−19.8575	−	15.2250i	−0.757058	−	0.580446i
$689$	−16.8749	+	51.9356i	−0.642883	+	1.97859i
$690$		0			0
$691$	−0.0482807	−	0.0664526i	−0.00183668	−	0.00252798i	0.808098	−	0.589049i	$-0.200497\pi$
$691$	−0.0482807	−	0.0664526i	−0.00183668	−	0.00252798i	−0.809934	+	0.586521i	$0.800497\pi$
$692$	5.09265	−	4.96296i	0.193593	−	0.188663i
$693$		0			0
$694$	−22.6152	−	9.53884i	−0.858463	−	0.362090i
$695$	19.9542	−	14.4975i	0.756904	−	0.549923i
$696$		0			0
$697$	−2.48377	+	7.64427i	−0.0940797	+	0.289548i
$698$	−18.1628	−	30.0725i	−0.687472	−	1.13826i
$699$		0			0
$700$	−22.7745	+	11.2366i	−0.860795	+	0.424704i
$701$	20.8676	−	6.78030i	0.788159	−	0.256088i	0.112839	−	0.993613i	$-0.464006\pi$
$701$	20.8676	−	6.78030i	0.788159	−	0.256088i	0.675320	+	0.737525i	$0.264006\pi$
$702$		0			0
$703$	−4.49602			−0.169571
$704$	11.0110	+	24.1404i	0.414993	+	0.909825i
$705$		0			0
$706$	−5.75271	−	24.6612i	−0.216506	−	0.928138i
$707$	11.0819	−	3.60074i	0.416780	−	0.135420i
$708$		0			0
$709$	−24.0097	+	33.0466i	−0.901705	+	1.24109i	0.0682161	+	0.997671i	$0.478269\pi$
$709$	−24.0097	+	33.0466i	−0.901705	+	1.24109i	−0.969921	+	0.243420i	$0.921731\pi$
$710$	−1.19973	−	1.98643i	−0.0450252	−	0.0745492i
$711$		0			0
$712$	−15.8727	−	19.3296i	−0.594856	−	0.724406i
$713$	−4.47453	+	3.25094i	−0.167572	+	0.121748i
$714$		0			0
$715$	−21.9100	+	15.7646i	−0.819387	+	0.589561i
$716$	7.72287	−	7.52620i	0.288617	−	0.281267i
$717$		0			0
$718$	−20.7337	−	1.76637i	−0.773774	−	0.0659203i
$719$	13.1613	−	40.5064i	0.490834	−	1.51063i	−0.332515	−	0.943098i	$-0.607897\pi$
$719$	13.1613	−	40.5064i	0.490834	−	1.51063i	0.823349	−	0.567535i	$-0.192103\pi$
$720$		0			0
$721$	8.10936	+	5.89180i	0.302008	+	0.219422i
$722$	−10.5662	−	9.14291i	−0.393235	−	0.340264i
$723$		0			0
$724$	−1.35683	+	7.90545i	−0.0504261	+	0.293804i
$725$			10.4937i			0.389725i
$726$		0			0
$727$	−26.7043			−0.990408			−0.495204	−	0.868777i	$-0.664907\pi$
$727$	−26.7043			−0.990408			−0.495204	+	0.868777i	$0.664907\pi$
$728$	−58.7988	−	37.6155i	−2.17923	−	1.39412i
$729$		0			0
$730$	−19.0835	+	22.0544i	−0.706312	+	0.816268i
$731$	−9.40583	+	12.9460i	−0.347887	+	0.478825i
$732$		0			0
$733$	−22.6501	−	7.35947i	−0.836602	−	0.271828i	−0.140778	−	0.990041i	$-0.544960\pi$
$733$	−22.6501	−	7.35947i	−0.836602	−	0.271828i	−0.695823	+	0.718213i	$0.744960\pi$
$734$	−44.3055	−	3.77453i	−1.63535	−	0.139320i
$735$		0			0
$736$	19.1092	+	8.64714i	0.704376	+	0.318738i
$737$	22.2875	+	30.9758i	0.820972	+	1.14101i
$738$		0			0
$739$	0.413968	+	0.569778i	0.0152281	+	0.0209596i	0.816563	−	0.577256i	$-0.195877\pi$
$739$	0.413968	+	0.569778i	0.0152281	+	0.0209596i	−0.801335	+	0.598216i	$0.795877\pi$
$740$	−2.02383	+	3.84847i	−0.0743974	+	0.141473i
$741$		0			0
$742$	31.7233	+	52.5249i	1.16460	+	1.92825i
$743$	1.01396	+	0.736685i	0.0371986	+	0.0270264i	0.606229	−	0.795290i	$-0.292681\pi$
$743$	1.01396	+	0.736685i	0.0371986	+	0.0270264i	−0.569031	+	0.822316i	$0.692681\pi$
$744$		0			0
$745$	−8.58829	−	26.4320i	−0.314650	−	0.968395i
$746$	−28.3562	+	6.61464i	−1.03819	+	0.242179i
$747$		0			0
$748$	15.2514	−	7.43750i	0.557645	−	0.271942i
$749$		−	26.7707i		−	0.978179i
$750$		0			0
$751$	9.91130	+	30.5038i	0.361668	+	1.11310i	0.952041	+	0.305970i	$0.0989808\pi$
$751$	9.91130	+	30.5038i	0.361668	+	1.11310i	−0.590373	+	0.807131i	$0.701019\pi$
$752$	10.0270	+	3.54638i	0.365648	+	0.129323i
$753$		0			0
$754$	−24.6889	+	14.9112i	−0.899115	+	0.543035i
$755$	14.1122	+	4.58534i	0.513597	+	0.166878i
$756$		0			0
$757$	18.2609	+	25.1340i	0.663703	+	0.913509i	0.999597	−	0.0283908i	$-0.00903828\pi$
$757$	18.2609	+	25.1340i	0.663703	+	0.913509i	−0.335894	+	0.941900i	$0.609038\pi$
$758$	16.9478	+	7.14837i	0.615571	+	0.259641i
$759$		0			0
$760$	11.6139	−	4.54948i	0.421280	−	0.165027i
$761$	12.3987	−	9.00817i	0.449452	−	0.326546i	−0.339928	−	0.940452i	$-0.610403\pi$
$761$	12.3987	−	9.00817i	0.449452	−	0.326546i	0.789379	+	0.613906i	$0.210403\pi$
$762$		0			0
$763$	50.2762	+	16.3357i	1.82012	+	0.591393i
$764$	−0.163594	−	1.12675i	−0.00591863	−	0.0407645i
$765$		0			0
$766$	39.7145	+	34.3648i	1.43494	+	1.24165i
$767$	−4.43916	−	13.6623i	−0.160289	−	0.493319i
$768$		0			0
$769$	−42.6201			−1.53692			−0.768460	−	0.639898i	$-0.778977\pi$
$769$	−42.6201			−1.53692			−0.768460	+	0.639898i	$0.778977\pi$
$770$	−2.71401	+	30.2083i	−0.0978062	+	1.08863i
$771$		0			0
$772$	14.0280	+	2.40765i	0.504878	+	0.0866534i
$773$	−32.9733	+	10.7137i	−1.18597	+	0.385345i	−0.834581	−	0.550885i	$-0.814290\pi$
$773$	−32.9733	+	10.7137i	−1.18597	+	0.385345i	−0.351388	+	0.936230i	$0.614290\pi$
$774$		0			0
$775$	−3.46048	−	2.51419i	−0.124304	−	0.0903123i
$776$	−0.816402	−	0.212784i	−0.0293071	−	0.00763851i
$777$		0			0
$778$	0.426112	−	5.00172i	0.0152769	−	0.179320i
$779$	−5.57738	−	7.67660i	−0.199830	−	0.275043i
$780$		0			0
$781$	3.72682	+	0.0171980i	0.133356	+	0.000615393i
$782$	5.21296	−	12.3592i	0.186415	−	0.441963i
$783$		0			0
$784$	−48.3509	+	14.3425i	−1.72682	+	0.512234i
$785$	7.55799	−	23.2611i	0.269756	−	0.830224i
$786$		0			0
$787$	23.5270	−	32.3822i	0.838648	−	1.15430i	−0.147603	−	0.989047i	$-0.547156\pi$
$787$	23.5270	−	32.3822i	0.838648	−	1.15430i	0.986251	−	0.165253i	$-0.0528441\pi$
$788$	−1.27652	−	2.58726i	−0.0454741	−	0.0921674i
$789$		0			0
$790$	1.54107	−	0.359483i	0.0548287	−	0.0127898i
$791$	−54.9521			−1.95387
$792$		0			0
$793$	31.1324			1.10554
$794$	48.4213	−	11.2952i	1.71841	−	0.400852i
$795$		0			0
$796$	−1.51917	+	0.749536i	−0.0538454	+	0.0265666i
$797$	−21.2428	+	29.2383i	−0.752460	+	1.03567i	0.245344	+	0.969436i	$0.421099\pi$
$797$	−21.2428	+	29.2383i	−0.752460	+	1.03567i	−0.997804	+	0.0662363i	$0.978901\pi$
$798$		0			0
$799$	2.10183	−	6.46878i	0.0743575	−	0.228849i
$800$	−1.79333	+	16.1218i	−0.0634038	+	0.569992i
$801$		0			0
$802$	−7.83179	+	18.5680i	−0.276550	+	0.655660i
$803$	−14.2680	−	44.6118i	−0.503506	−	1.57431i
$804$		0			0
$805$	14.0929	+	19.3972i	0.496708	+	0.683660i
$806$	0.997971	−	11.7142i	0.0351520	−	0.412615i
$807$		0			0
$808$	1.87715	−	7.20216i	0.0660378	−	0.253371i
$809$	−5.20574	−	3.78219i	−0.183024	−	0.132975i	0.492501	−	0.870312i	$-0.336083\pi$
$809$	−5.20574	−	3.78219i	−0.183024	−	0.132975i	−0.675525	+	0.737337i	$0.736083\pi$
$810$		0			0
$811$	9.09860	−	2.95631i	0.319495	−	0.103810i	−0.144879	−	0.989449i	$-0.546279\pi$
$811$	9.09860	−	2.95631i	0.319495	−	0.103810i	0.464374	+	0.885639i	$0.346279\pi$
$812$	−5.48230	+	31.9421i	−0.192391	+	1.12095i
$813$		0			0
$814$	−3.58257	−	5.99407i	−0.125569	−	0.210092i
$815$	−10.1803			−0.356602
$816$		0			0
$817$	−5.83770	−	17.9666i	−0.204235	−	0.628572i
$818$	−11.1121	−	9.61521i	−0.388524	−	0.336188i
$819$		0			0
$820$	−9.08156	+	1.31856i	−0.317142	+	0.0460460i
$821$	16.3544	+	5.31387i	0.570772	+	0.185455i	0.580163	−	0.814501i	$-0.302989\pi$
$821$	16.3544	+	5.31387i	0.570772	+	0.185455i	−0.00939014	+	0.999956i	$0.502989\pi$
$822$		0			0
$823$	31.0609	−	22.5671i	1.08272	−	0.786639i	0.104561	−	0.994518i	$-0.466656\pi$
$823$	31.0609	−	22.5671i	1.08272	−	0.786639i	0.978154	+	0.207880i	$0.0666563\pi$
$824$	5.96148	−	2.33528i	0.207678	−	0.0813532i
$825$		0			0
$826$	−14.8731	−	6.27329i	−0.517500	−	0.218276i
$827$	−10.3457	−	14.2396i	−0.359754	−	0.495159i	0.590326	−	0.807165i	$-0.298999\pi$
$827$	−10.3457	−	14.2396i	−0.359754	−	0.495159i	−0.950080	+	0.312006i	$0.898999\pi$
$828$		0			0
$829$	−27.1880	−	8.83392i	−0.944279	−	0.306815i	−0.203890	−	0.978994i	$-0.565359\pi$
$829$	−27.1880	−	8.83392i	−0.944279	−	0.306815i	−0.740389	+	0.672179i	$0.765359\pi$
$830$	−15.1391	+	9.14352i	−0.525487	+	0.317376i
$831$		0			0
$832$	−40.4787	+	18.6894i	−1.40335	+	0.647939i
$833$	9.96666	+	30.6742i	0.345324	+	1.06280i
$834$		0			0
$835$			14.5935i			0.505030i
$836$	−3.47961	+	19.7272i	−0.120345	+	0.682279i
$837$		0			0
$838$	−28.5895	+	6.66906i	−0.987609	+	0.230379i
$839$	−16.3891	−	50.4404i	−0.565814	−	1.74140i	−0.665520	−	0.746380i	$-0.731790\pi$
$839$	−16.3891	−	50.4404i	−0.565814	−	1.74140i	0.0997063	−	0.995017i	$-0.468210\pi$
$840$		0			0
$841$	−12.6274	−	9.17432i	−0.435426	−	0.316356i
$842$	0.120797	+	0.200006i	0.00416294	+	0.00689268i
$843$		0			0
$844$	26.7447	+	14.0645i	0.920591	+	0.484119i
$845$	−15.5013	−	21.3357i	−0.533262	−	0.733972i
$846$		0			0
$847$	−39.1408	−	28.9931i	−1.34489	−	0.996216i
$848$	39.1811	+	1.01081i	1.34548	+	0.0347115i
$849$		0			0
$850$	10.3363	+	0.880581i	0.354531	+	0.0302037i
$851$	−5.25004	−	1.70584i	−0.179969	−	0.0584755i
$852$		0			0
$853$	2.39168	−	3.29187i	0.0818896	−	0.112711i	−0.766107	−	0.642713i	$-0.777809\pi$
$853$	2.39168	−	3.29187i	0.0818896	−	0.112711i	0.847997	+	0.530002i	$0.177809\pi$
$854$	22.8903	−	26.4537i	0.783289	−	0.905229i
$855$		0			0
$856$	−14.4042	−	9.21483i	−0.492325	−	0.314956i
$857$	−23.5570			−0.804692			−0.402346	−	0.915488i	$-0.631805\pi$
$857$	−23.5570			−0.804692			−0.402346	+	0.915488i	$0.631805\pi$
$858$		0			0
$859$		−	21.8683i		−	0.746138i	−0.927804	−	0.373069i	$-0.878306\pi$
$859$		−	21.8683i		−	0.746138i	0.927804	−	0.373069i	$-0.121694\pi$
$860$	−18.0067	−	3.09053i	−0.614024	−	0.105386i
$861$		0			0
$862$	−36.1613	−	31.2901i	−1.23166	−	1.06575i
$863$	18.1407	+	13.1800i	0.617517	+	0.448653i	0.852053	−	0.523455i	$-0.175357\pi$
$863$	18.1407	+	13.1800i	0.617517	+	0.448653i	−0.234536	+	0.972107i	$0.575357\pi$
$864$		0			0
$865$	1.60444	−	4.93794i	0.0545524	−	0.167895i
$866$	−7.60142	−	0.647590i	−0.258307	−	0.0220060i
$867$		0			0
$868$	−9.22001	−	9.46094i	−0.312948	−	0.321125i
$869$	−0.796471	+	2.41334i	−0.0270184	+	0.0818668i
$870$		0			0
$871$	−51.8770	+	37.6908i	−1.75779	+	1.27711i
$872$	26.0953	−	21.4286i	0.883700	−	0.725663i
$873$		0			0
$874$	8.18669	+	13.5549i	0.276919	+	0.458501i
$875$	−29.9033	+	41.1583i	−1.01091	+	1.39140i
$876$		0			0
$877$	17.3825	−	5.64793i	0.586967	−	0.190717i	−0.000452412	−	1.00000i	$-0.500144\pi$
$877$	17.3825	−	5.64793i	0.586967	−	0.190717i	0.587419	+	0.809283i	$0.300144\pi$
$878$	0.0146206	+	0.0626768i	0.000493420	+	0.00211524i
$879$		0			0
$880$	15.3196	+	11.8584i	0.516425	+	0.399747i
$881$	6.65131			0.224088			0.112044	−	0.993703i	$-0.464260\pi$
$881$	6.65131			0.224088			0.112044	+	0.993703i	$0.464260\pi$
$882$		0			0
$883$	−24.2520	+	7.87997i	−0.816146	+	0.265182i	−0.687199	−	0.726469i	$-0.741160\pi$
$883$	−24.2520	+	7.87997i	−0.816146	+	0.265182i	−0.128947	+	0.991651i	$0.541160\pi$
$884$	12.6158	+	25.5698i	0.424315	+	0.860006i
$885$		0			0
$886$	0.0639230	+	0.105839i	0.00214754	+	0.00355572i
$887$	−6.95549	+	21.4068i	−0.233543	+	0.718770i	0.763769	+	0.645490i	$0.223347\pi$
$887$	−6.95549	+	21.4068i	−0.233543	+	0.718770i	−0.997311	+	0.0732803i	$0.976653\pi$
$888$		0			0
$889$	31.9233	−	23.1937i	1.07067	−	0.777890i
$890$	−16.8266	−	7.09725i	−0.564028	−	0.237900i
$891$		0			0
$892$	26.1130	+	26.7954i	0.874328	+	0.897175i
$893$	4.71972	+	6.49613i	0.157939	+	0.217385i
$894$		0			0
$895$	2.43309	−	7.48827i	0.0813291	−	0.250305i
$896$	−13.8815	+	48.1370i	−0.463747	+	1.60814i
$897$		0			0
$898$	31.9875	+	27.6786i	1.06744	+	0.923646i
$899$	−5.19152	+	1.68683i	−0.173147	+	0.0562588i
$900$		0			0
$901$		−	25.0652i		−	0.835042i
$902$	5.79017	−	13.5527i	0.192792	−	0.451255i
$903$		0			0
$904$	−18.9152	+	29.5674i	−0.629112	+	0.983398i
$905$	1.80977	+	5.56990i	0.0601588	+	0.185150i
$906$		0			0
$907$	8.05465	−	11.0863i	0.267450	−	0.368114i	−0.654077	−	0.756428i	$-0.726943\pi$
$907$	8.05465	−	11.0863i	0.267450	−	0.368114i	0.921527	+	0.388315i	$0.126943\pi$
$908$	53.6391	−	7.78791i	1.78008	−	0.258451i
$909$		0			0
$910$	−50.7813	−	4.32622i	−1.68338	−	0.143413i
$911$	−35.8407	+	26.0398i	−1.18746	+	0.862737i	−0.992993	−	0.118173i	$-0.962296\pi$
$911$	−35.8407	+	26.0398i	−1.18746	+	0.862737i	−0.194462	+	0.980910i	$0.562296\pi$
$912$		0			0
$913$	0.131071	−	28.4032i	0.00433782	−	0.940010i
$914$	−11.8211	+	28.0260i	−0.391006	+	0.927019i
$915$		0			0
$916$	20.5754	+	10.8201i	0.679829	+	0.357508i
$917$	34.9657	+	11.3610i	1.15467	+	0.375175i
$918$		0			0
$919$	−36.1252	−	26.2465i	−1.19166	−	0.865791i	−0.198221	−	0.980157i	$-0.563516\pi$
$919$	−36.1252	−	26.2465i	−1.19166	−	0.865791i	−0.993439	+	0.114366i	$0.963516\pi$
$920$	15.2878	−	0.906021i	0.504023	−	0.0298706i
$921$		0			0
$922$	10.8598	−	2.53325i	0.357648	−	0.0834283i
$923$			6.26247i			0.206132i
$924$		0			0
$925$		−	4.26919i		−	0.140370i
$926$	1.64491	+	7.05157i	0.0540552	+	0.231729i
$927$		0			0
$928$	15.2997	+	13.9447i	0.502236	+	0.457758i
$929$	−30.6162	−	22.2440i	−1.00449	−	0.729802i	−0.0414410	−	0.999141i	$-0.513195\pi$
$929$	−30.6162	−	22.2440i	−1.00449	−	0.729802i	−0.963045	+	0.269339i	$0.913195\pi$
$930$		0			0
$931$	−36.2122	−	11.7661i	−1.18681	−	0.385617i
$932$	24.3126	−	46.2324i	0.796386	−	1.51439i
$933$		0			0
$934$	−24.2695	−	10.2366i	−0.794123	−	0.334952i
$935$	7.32843	−	9.98945i	0.239665	−	0.326690i
$936$		0			0
$937$	−13.8071	+	10.0315i	−0.451059	+	0.327713i	−0.790014	−	0.613089i	$-0.789927\pi$
$937$	−13.8071	+	10.0315i	−0.451059	+	0.327713i	0.338955	+	0.940803i	$0.389927\pi$
$938$	−6.11630	+	71.7933i	−0.199704	+	2.34413i
$939$		0			0
$940$	7.68504	−	1.11580i	0.250658	−	0.0363933i
$941$	−2.74175	+	3.77370i	−0.0893785	+	0.123019i	−0.851365	−	0.524574i	$-0.824224\pi$
$941$	−2.74175	+	3.77370i	−0.0893785	+	0.123019i	0.761986	+	0.647593i	$0.224224\pi$
$942$		0			0
$943$	−3.60016	−	11.0801i	−0.117237	−	0.360819i
$944$	−8.49491	+	5.84323i	−0.276486	+	0.190181i
$945$		0			0
$946$	19.3013	−	22.0991i	0.627540	−	0.718505i
$947$		−	52.8254i		−	1.71659i	−0.513153	−	0.858297i	$-0.671523\pi$
$947$		−	52.8254i		−	1.71659i	0.513153	−	0.858297i	$-0.328477\pi$
$948$		0			0
$949$	74.8523	−	24.3210i	2.42981	−	0.789493i
$950$	−8.01342	+	9.26091i	−0.259990	+	0.300464i
$951$		0			0
$952$	31.0030	+	8.08051i	1.00481	+	0.261891i
$953$	11.9830	−	36.8800i	0.388168	−	1.19466i	−0.545988	−	0.837793i	$-0.683845\pi$
$953$	11.9830	−	36.8800i	0.388168	−	1.19466i	0.934156	−	0.356866i	$-0.116155\pi$
$954$		0			0
$955$	−0.488639	−	0.672554i	−0.0158120	−	0.0217633i
$956$	−19.8060	−	20.3235i	−0.640571	−	0.657310i
$957$		0			0
$958$	21.5965	−	51.2021i	0.697750	−	1.65427i
$959$	−59.2231	+	43.0281i	−1.91241	+	1.38945i
$960$		0			0
$961$	−8.89195	+	27.3666i	−0.286837	+	0.882794i
$962$	10.0443	−	6.06641i	0.323841	−	0.195589i
$963$		0			0
$964$	−30.9401	+	15.2654i	−0.996514	+	0.491666i
$965$	9.88363	−	3.21139i	0.318165	−	0.103378i
$966$		0			0
$967$	38.0583			1.22387			0.611937	−	0.790907i	$-0.290391\pi$
$967$	38.0583			1.22387			0.611937	+	0.790907i	$0.290391\pi$
$968$	−29.0728	+	11.0802i	−0.934436	+	0.356132i
$969$		0			0
$970$	−0.599903	+	0.139939i	−0.0192617	+	0.00449317i
$971$	5.43270	−	1.76519i	0.174344	−	0.0566476i	−0.220544	−	0.975377i	$-0.570783\pi$
$971$	5.43270	−	1.76519i	0.174344	−	0.0566476i	0.394888	+	0.918729i	$0.370783\pi$
$972$		0			0
$973$	−43.9617	+	60.5080i	−1.40935	+	1.93980i
$974$	22.1321	−	13.3671i	0.709160	−	0.428308i
$975$		0			0
$976$	−6.35452	−	21.4220i	−0.203403	−	0.685703i
$977$	0.460069	−	0.334259i	0.0147189	−	0.0106939i	−0.580401	−	0.814330i	$-0.697104\pi$
$977$	0.460069	−	0.334259i	0.0147189	−	0.0106939i	0.595120	+	0.803637i	$0.297104\pi$
$978$		0			0
$979$	23.8066	−	17.1292i	0.760863	−	0.547453i
$980$	−26.3719	+	25.7004i	−0.842421	+	0.820968i
$981$		0			0
$982$	−0.492454	+	5.78043i	−0.0157148	+	0.184461i
$983$	−0.678324	+	2.08767i	−0.0216352	+	0.0665863i	−0.961291	−	0.275534i	$-0.911145\pi$
$983$	−0.678324	+	2.08767i	−0.0216352	+	0.0665863i	0.939656	+	0.342121i	$0.111145\pi$
$984$		0			0
$985$	−1.70420	−	1.23817i	−0.0543002	−	0.0394514i
$986$	8.66254	−	10.0111i	0.275872	−	0.318818i
$987$		0			0
$988$	−33.1754	−	5.69396i	−1.05545	−	0.181149i
$989$		−	23.1946i		−	0.737547i
$990$		0			0
$991$	10.7399			0.341165			0.170582	−	0.985343i	$-0.445435\pi$
$991$	10.7399			0.341165			0.170582	+	0.985343i	$0.445435\pi$
$992$	−8.26420	+	1.70432i	−0.262388	+	0.0541123i
$993$		0			0
$994$	5.32133	+	4.60452i	0.168782	+	0.146047i
$995$	−0.727018	+	1.00065i	−0.0230480	+	0.0317229i
$996$		0			0
$997$	−4.99166	−	1.62189i	−0.158088	−	0.0513657i	0.228904	−	0.973449i	$-0.426486\pi$
$997$	−4.99166	−	1.62189i	−0.158088	−	0.0513657i	−0.386992	+	0.922083i	$0.626486\pi$
$998$	−1.12541	+	13.2101i	−0.0356242	+	0.418157i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.br.b.685.6		40
3.2	odd	2		88.2.o.a.69.5	yes	40
8.5	even	2	inner	792.2.br.b.685.2		40
11.4	even	5	inner	792.2.br.b.37.2		40
12.11	even	2		352.2.w.a.113.5		40
24.5	odd	2		88.2.o.a.69.9	yes	40
24.11	even	2		352.2.w.a.113.6		40
33.2	even	10		968.2.c.i.485.13		20
33.5	odd	10		968.2.o.j.493.8		40
33.8	even	10		968.2.o.d.269.10		40
33.14	odd	10		968.2.o.j.269.1		40
33.17	even	10		968.2.o.d.493.3		40
33.20	odd	10		968.2.c.h.485.8		20
33.26	odd	10		88.2.o.a.37.9	yes	40
33.29	even	10		968.2.o.i.565.2		40
33.32	even	2		968.2.o.i.245.6		40
88.37	even	10	inner	792.2.br.b.37.6		40
132.35	odd	10		3872.2.c.i.1937.13		20
132.59	even	10		352.2.w.a.81.6		40
132.119	even	10		3872.2.c.h.1937.13		20
264.5	odd	10		968.2.o.j.493.1		40
264.29	even	10		968.2.o.i.565.6		40
264.35	odd	10		3872.2.c.i.1937.8		20
264.53	odd	10		968.2.c.h.485.7		20
264.59	even	10		352.2.w.a.81.5		40
264.101	even	10		968.2.c.i.485.14		20
264.125	odd	10		88.2.o.a.37.5	✓	40
264.149	even	10		968.2.o.d.493.10		40
264.173	even	10		968.2.o.d.269.3		40
264.197	even	2		968.2.o.i.245.2		40
264.245	odd	10		968.2.o.j.269.8		40
264.251	even	10		3872.2.c.h.1937.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.5	✓	40	264.125	odd	10
88.2.o.a.37.9	yes	40	33.26	odd	10
88.2.o.a.69.5	yes	40	3.2	odd	2
88.2.o.a.69.9	yes	40	24.5	odd	2
352.2.w.a.81.5		40	264.59	even	10
352.2.w.a.81.6		40	132.59	even	10
352.2.w.a.113.5		40	12.11	even	2
352.2.w.a.113.6		40	24.11	even	2
792.2.br.b.37.2		40	11.4	even	5	inner
792.2.br.b.37.6		40	88.37	even	10	inner
792.2.br.b.685.2		40	8.5	even	2	inner
792.2.br.b.685.6		40	1.1	even	1	trivial
968.2.c.h.485.7		20	264.53	odd	10
968.2.c.h.485.8		20	33.20	odd	10
968.2.c.i.485.13		20	33.2	even	10
968.2.c.i.485.14		20	264.101	even	10
968.2.o.d.269.3		40	264.173	even	10
968.2.o.d.269.10		40	33.8	even	10
968.2.o.d.493.3		40	33.17	even	10
968.2.o.d.493.10		40	264.149	even	10
968.2.o.i.245.2		40	264.197	even	2
968.2.o.i.245.6		40	33.32	even	2
968.2.o.i.565.2		40	33.29	even	10
968.2.o.i.565.6		40	264.29	even	10
968.2.o.j.269.1		40	33.14	odd	10
968.2.o.j.269.8		40	264.245	odd	10
968.2.o.j.493.1		40	264.5	odd	10
968.2.o.j.493.8		40	33.5	odd	10
3872.2.c.h.1937.8		20	264.251	even	10
3872.2.c.h.1937.13		20	132.119	even	10
3872.2.c.i.1937.8		20	264.35	odd	10
3872.2.c.i.1937.13		20	132.35	odd	10

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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.br (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.321268 + 1.37724i) q^{2} +(-1.79357 + 0.884925i) q^{4} +(-0.858340 + 1.18140i) q^{5} +(1.36837 - 4.21140i) q^{7} +(-1.79497 - 2.18588i) q^{8} +(-1.90283 - 0.802592i) q^{10} +(2.69217 - 1.93706i) q^{11} +(3.27580 + 4.50875i) q^{13} +(6.23972 + 0.531582i) q^{14} +(2.43382 - 3.17436i) q^{16} +(-2.06951 - 1.50359i) q^{17} +(2.87209 - 0.933198i) q^{19} +(0.494043 - 2.87850i) q^{20} +(3.53270 + 3.08545i) q^{22} +3.70783 q^{23} +(0.886118 + 2.72719i) q^{25} +(-5.15722 + 5.96007i) q^{26} +(1.27250 + 8.76436i) q^{28} +(3.48036 + 1.13084i) q^{29} +(-1.20678 + 0.876776i) q^{31} +(5.15375 + 2.33213i) q^{32} +(1.40593 - 3.33327i) q^{34} +(3.80084 + 5.23141i) q^{35} +(-1.41593 - 0.460065i) q^{37} +(2.20795 + 3.65575i) q^{38} +(4.12310 - 0.244353i) q^{40} +(-0.970962 - 2.98831i) q^{41} -6.25559i q^{43} +(-3.11446 + 5.85663i) q^{44} +(1.19121 + 5.10657i) q^{46} +(0.821652 + 2.52878i) q^{47} +(-10.2003 - 7.41099i) q^{49} +(-3.47131 + 2.09655i) q^{50} +(-9.86529 - 5.18794i) q^{52} +(5.75943 + 7.92717i) q^{53} +(-0.0223497 + 4.84320i) q^{55} +(-11.6618 + 4.56825i) q^{56} +(-0.439307 + 5.15659i) q^{58} +(-2.45147 - 0.796531i) q^{59} +(3.28347 - 4.51930i) q^{61} +(-1.59523 - 1.38034i) q^{62} +(-1.55617 + 7.84719i) q^{64} -8.13840 q^{65} +11.5059i q^{67} +(5.04238 + 0.865435i) q^{68} +(-5.98381 + 6.91535i) q^{70} +(0.909086 + 0.660489i) q^{71} +(4.36398 - 13.4310i) q^{73} +(0.178725 - 2.09788i) q^{74} +(-4.32550 + 4.21534i) q^{76} +(-4.47386 - 13.9884i) q^{77} +(-0.619910 + 0.450391i) q^{79} +(1.66115 + 5.60000i) q^{80} +(3.80368 - 2.29729i) q^{82} +(5.03379 - 6.92841i) q^{83} +(3.55269 - 1.15434i) q^{85} +(8.61544 - 2.00972i) q^{86} +(-9.06656 - 2.40781i) q^{88} +8.84290 q^{89} +(23.4706 - 7.62607i) q^{91} +(-6.65026 + 3.28115i) q^{92} +(-3.21877 + 1.94403i) q^{94} +(-1.36275 + 4.19410i) q^{95} +(0.241317 - 0.175327i) q^{97} +(6.92966 - 16.4292i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - q^{4} - 10 q^{7} + 5 q^{8} - 20 q^{10} - 2 q^{14} + 15 q^{16} + 6 q^{17} - 8 q^{20} - 35 q^{22} + 8 q^{23} - 4 q^{25} + 10 q^{26} + 32 q^{28} - 6 q^{31} - 20 q^{32} + 10 q^{34} - 12 q^{38}+ \cdots + 144 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 - q^4 - 10 * q^7 + 5 * q^8 - 20 * q^10 - 2 * q^14 + 15 * q^16 + 6 * q^17 - 8 * q^20 - 35 * q^22 + 8 * q^23 - 4 * q^25 + 10 * q^26 + 32 * q^28 - 6 * q^31 - 20 * q^32 + 10 * q^34 - 12 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 18 * q^46 + 6 * q^47 - 4 * q^49 - 61 * q^50 + 20 * q^52 - 2 * q^55 + 32 * q^56 + 4 * q^58 - 48 * q^62 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 - 22 * q^71 - 6 * q^73 - 54 * q^74 - 134 * q^76 + 74 * q^79 + 44 * q^80 - 31 * q^82 + 15 * q^86 - 73 * q^88 + 16 * q^89 + 4 * q^92 - 100 * q^94 - 66 * q^95 + 10 * q^97 + 144 * q^98

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