LMFDB - Embedded newform 819.2.fm.e.622.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			622.4
Character	$\chi$	$=$	819.622
Dual form			819.2.fm.e.370.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0473445 + 0.176692i) q^{2} +(1.70307 + 0.983269i) q^{4} +(-2.80040 + 2.80040i) q^{5} +(-0.467560 + 2.60411i) q^{7} +(-0.513062 + 0.513062i) q^{8} +O(q^{10})$	\(q+(-0.0473445 + 0.176692i) q^{2} +(1.70307 + 0.983269i) q^{4} +(-2.80040 + 2.80040i) q^{5} +(-0.467560 + 2.60411i) q^{7} +(-0.513062 + 0.513062i) q^{8} +(-0.362225 - 0.627392i) q^{10} +(2.53602 + 0.679524i) q^{11} +(1.37067 - 3.33485i) q^{13} +(-0.437989 - 0.205904i) q^{14} +(1.90018 + 3.29120i) q^{16} +(1.43204 - 2.48037i) q^{17} +(0.759707 + 2.83527i) q^{19} +(-7.52284 + 2.01574i) q^{20} +(-0.240133 + 0.415922i) q^{22} +(-7.27090 + 4.19786i) q^{23} -10.6845i q^{25} +(0.524348 + 0.400074i) q^{26} +(-3.35683 + 3.97525i) q^{28} +(-1.66138 - 2.87760i) q^{29} +(-6.75045 + 6.75045i) q^{31} +(-2.07320 + 0.555513i) q^{32} +(0.370463 + 0.370463i) q^{34} +(-5.98320 - 8.60192i) q^{35} +(-6.77592 - 1.81560i) q^{37} -0.536937 q^{38} -2.87356i q^{40} +(2.79099 + 0.747843i) q^{41} +(-2.43132 - 1.40372i) q^{43} +(3.65087 + 3.65087i) q^{44} +(-0.397491 - 1.48346i) q^{46} +(4.85765 + 4.85765i) q^{47} +(-6.56278 - 2.43516i) q^{49} +(1.88787 + 0.505853i) q^{50} +(5.61342 - 4.33176i) q^{52} +5.43259 q^{53} +(-9.00481 + 5.19893i) q^{55} +(-1.09618 - 1.57596i) q^{56} +(0.587105 - 0.157314i) q^{58} +(0.00666592 - 0.00178613i) q^{59} +(5.65469 + 3.26474i) q^{61} +(-0.873154 - 1.51235i) q^{62} +7.20808i q^{64} +(5.50050 + 13.1774i) q^{65} +(2.10207 - 7.84504i) q^{67} +(4.87775 - 2.81617i) q^{68} +(1.80316 - 0.649930i) q^{70} +(14.5933 - 3.91026i) q^{71} +(0.321617 + 0.321617i) q^{73} +(0.641604 - 1.11129i) q^{74} +(-1.49399 + 5.57566i) q^{76} +(-2.95530 + 6.28635i) q^{77} +0.280448 q^{79} +(-14.5379 - 3.89543i) q^{80} +(-0.264276 + 0.457739i) q^{82} +(2.42973 - 2.42973i) q^{83} +(2.93575 + 10.9564i) q^{85} +(0.363136 - 0.363136i) q^{86} +(-1.64977 + 0.952496i) q^{88} +(-0.0536096 + 0.200074i) q^{89} +(8.04346 + 5.12863i) q^{91} -16.5105 q^{92} +(-1.08829 + 0.628324i) q^{94} +(-10.0674 - 5.81240i) q^{95} +(0.197356 + 0.736543i) q^{97} +(0.740984 - 1.04430i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$

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 $

$2$	−0.0473445	+	0.176692i	−0.0334776	+	0.124940i	−0.980642	−	0.195807i	$-0.937267\pi$
$2$	−0.0473445	+	0.176692i	−0.0334776	+	0.124940i	0.947165	+	0.320747i	$0.103934\pi$
$3$		0			0
$3$		0			0
$4$	1.70307	+	0.983269i	0.851536	+	0.491635i
$5$	−2.80040	+	2.80040i	−1.25238	+	1.25238i	−0.297728	+	0.954651i	$0.596229\pi$
$5$	−2.80040	+	2.80040i	−1.25238	+	1.25238i	−0.954651	+	0.297728i	$0.903771\pi$
$6$		0			0
$7$	−0.467560	+	2.60411i	−0.176721	+	0.984261i
$7$	−0.467560	+	2.60411i	−0.176721	+	0.984261i
$8$	−0.513062	+	0.513062i	−0.181395	+	0.181395i
$9$		0			0
$10$	−0.362225	−	0.627392i	−0.114546	−	0.198399i
$11$	2.53602	+	0.679524i	0.764638	+	0.204884i	0.620001	−	0.784601i	$-0.287132\pi$
$11$	2.53602	+	0.679524i	0.764638	+	0.204884i	0.144637	+	0.989485i	$0.453799\pi$
$12$		0			0
$13$	1.37067	−	3.33485i	0.380156	−	0.924922i
$13$	1.37067	−	3.33485i	0.380156	−	0.924922i
$14$	−0.437989	−	0.205904i	−0.117057	−	0.0550302i
$15$		0			0
$16$	1.90018	+	3.29120i	0.475044	+	0.822800i
$17$	1.43204	−	2.48037i	0.347322	−	0.601579i	−0.638451	−	0.769663i	$-0.720424\pi$
$17$	1.43204	−	2.48037i	0.347322	−	0.601579i	0.985773	+	0.168083i	$0.0537578\pi$
$18$		0			0
$19$	0.759707	+	2.83527i	0.174289	+	0.650455i	0.996672	+	0.0815202i	$0.0259775\pi$
$19$	0.759707	+	2.83527i	0.174289	+	0.650455i	−0.822383	+	0.568934i	$0.807356\pi$
$20$	−7.52284	+	2.01574i	−1.68216	+	0.450733i
$21$		0			0
$22$	−0.240133	+	0.415922i	−0.0511965	+	0.0886749i
$23$	−7.27090	+	4.19786i	−1.51609	+	0.875314i	−0.516266	+	0.856428i	$0.672679\pi$
$23$	−7.27090	+	4.19786i	−1.51609	+	0.875314i	−0.999822	+	0.0188857i	$0.993988\pi$
$24$		0			0
$25$		−	10.6845i		−	2.13690i
$26$	0.524348	+	0.400074i	0.102833	+	0.0784609i
$27$		0			0
$28$	−3.35683	+	3.97525i	−0.634381	+	0.751252i
$29$	−1.66138	−	2.87760i	−0.308511	−	0.534356i	0.669526	−	0.742789i	$-0.266497\pi$
$29$	−1.66138	−	2.87760i	−0.308511	−	0.534356i	−0.978037	+	0.208432i	$0.933164\pi$
$30$		0			0
$31$	−6.75045	+	6.75045i	−1.21242	+	1.21242i	−0.242188	+	0.970229i	$0.577865\pi$
$31$	−6.75045	+	6.75045i	−1.21242	+	1.21242i	−0.970229	+	0.242188i	$0.922135\pi$
$32$	−2.07320	+	0.555513i	−0.366494	+	0.0982017i
$33$		0			0
$34$	0.370463	+	0.370463i	0.0635339	+	0.0635339i
$35$	−5.98320	−	8.60192i	−1.01135	−	1.45399i
$36$		0			0
$37$	−6.77592	−	1.81560i	−1.11395	−	0.298483i	−0.345519	−	0.938412i	$-0.612297\pi$
$37$	−6.77592	−	1.81560i	−1.11395	−	0.298483i	−0.768434	+	0.639929i	$0.778964\pi$
$38$	−0.536937			−0.0871026
$39$		0			0
$40$		−	2.87356i		−	0.454350i
$41$	2.79099	+	0.747843i	0.435879	+	0.116793i	0.470085	−	0.882621i	$-0.344223\pi$
$41$	2.79099	+	0.747843i	0.435879	+	0.116793i	−0.0342056	+	0.999415i	$0.510890\pi$
$42$		0			0
$43$	−2.43132	−	1.40372i	−0.370773	−	0.214066i	0.303023	−	0.952983i	$-0.402004\pi$
$43$	−2.43132	−	1.40372i	−0.370773	−	0.214066i	−0.673796	+	0.738917i	$0.735337\pi$
$44$	3.65087	+	3.65087i	0.550389	+	0.550389i
$45$		0			0
$46$	−0.397491	−	1.48346i	−0.0586068	−	0.218724i
$47$	4.85765	+	4.85765i	0.708561	+	0.708561i	0.966232	−	0.257672i	$-0.0829554\pi$
$47$	4.85765	+	4.85765i	0.708561	+	0.708561i	−0.257672	+	0.966232i	$0.582955\pi$
$48$		0			0
$49$	−6.56278	−	2.43516i	−0.937539	−	0.347879i
$50$	1.88787	+	0.505853i	0.266985	+	0.0715384i
$51$		0			0
$52$	5.61342	−	4.33176i	0.778441	−	0.600707i
$53$	5.43259			0.746224			0.373112	−	0.927786i	$-0.378291\pi$
$53$	5.43259			0.746224			0.373112	+	0.927786i	$0.378291\pi$
$54$		0			0
$55$	−9.00481	+	5.19893i	−1.21421	+	0.701024i
$56$	−1.09618	−	1.57596i	−0.146483	−	0.210596i
$57$		0			0
$58$	0.587105	−	0.157314i	0.0770907	−	0.0206564i
$59$	0.00666592	−	0.00178613i	0.000867829	−	0.000232534i	−0.258385	−	0.966042i	$-0.583190\pi$
$59$	0.00666592	−	0.00178613i	0.000867829	−	0.000232534i	0.259253	+	0.965809i	$0.416524\pi$
$60$		0			0
$61$	5.65469	+	3.26474i	0.724009	+	0.418007i	0.816226	−	0.577732i	$-0.196062\pi$
$61$	5.65469	+	3.26474i	0.724009	+	0.418007i	−0.0922177	+	0.995739i	$0.529396\pi$
$62$	−0.873154	−	1.51235i	−0.110891	−	0.192068i
$63$		0			0
$64$			7.20808i			0.901010i
$65$	5.50050	+	13.1774i	0.682253	+	1.63445i
$66$		0			0
$67$	2.10207	−	7.84504i	0.256809	−	0.958424i	−0.710266	−	0.703933i	$-0.751425\pi$
$67$	2.10207	−	7.84504i	0.256809	−	0.958424i	0.967075	−	0.254491i	$-0.0819079\pi$
$68$	4.87775	−	2.81617i	0.591514	−	0.341511i
$69$		0			0
$70$	1.80316	−	0.649930i	0.215519	−	0.0776815i
$71$	14.5933	−	3.91026i	1.73191	−	0.464063i	0.751286	−	0.659977i	$-0.229434\pi$
$71$	14.5933	−	3.91026i	1.73191	−	0.464063i	0.980621	+	0.195914i	$0.0627675\pi$
$72$		0			0
$73$	0.321617	+	0.321617i	0.0376425	+	0.0376425i	0.725677	−	0.688035i	$-0.241526\pi$
$73$	0.321617	+	0.321617i	0.0376425	+	0.0376425i	−0.688035	+	0.725677i	$0.741526\pi$
$74$	0.641604	−	1.11129i	0.0745850	−	0.129185i
$75$		0			0
$76$	−1.49399	+	5.57566i	−0.171373	+	0.639572i
$77$	−2.95530	+	6.28635i	−0.336787	+	0.716396i
$78$		0			0
$79$	0.280448			0.0315529			0.0157764	−	0.999876i	$-0.494978\pi$
$79$	0.280448			0.0315529			0.0157764	+	0.999876i	$0.494978\pi$
$80$	−14.5379	−	3.89543i	−1.62539	−	0.435522i
$81$		0			0
$82$	−0.264276	+	0.457739i	−0.0291844	+	0.0505488i
$83$	2.42973	−	2.42973i	0.266698	−	0.266698i	−0.561070	−	0.827768i	$-0.689610\pi$
$83$	2.42973	−	2.42973i	0.266698	−	0.266698i	0.827768	+	0.561070i	$0.189610\pi$
$84$		0			0
$85$	2.93575	+	10.9564i	0.318426	+	1.18838i
$86$	0.363136	−	0.363136i	0.0391580	−	0.0391580i
$87$		0			0
$88$	−1.64977	+	0.952496i	−0.175866	+	0.101536i
$89$	−0.0536096	+	0.200074i	−0.00568261	+	0.0212078i	−0.968709	−	0.248200i	$-0.920161\pi$
$89$	−0.0536096	+	0.200074i	−0.00568261	+	0.0212078i	0.963026	+	0.269407i	$0.0868278\pi$
$90$		0			0
$91$	8.04346	+	5.12863i	0.843183	+	0.537626i
$92$	−16.5105			−1.72134
$93$		0			0
$94$	−1.08829	+	0.628324i	−0.112249	+	0.0648067i
$95$	−10.0674	−	5.81240i	−1.03289	−	0.596340i
$96$		0			0
$97$	0.197356	+	0.736543i	0.0200385	+	0.0747847i	0.975221	−	0.221233i	$-0.0710080\pi$
$97$	0.197356	+	0.736543i	0.0200385	+	0.0747847i	−0.955183	+	0.296017i	$0.904341\pi$
$98$	0.740984	−	1.04430i	0.0748506	−	0.105490i
$99$		0			0
$100$	10.5058	−	18.1965i	1.05058	−	1.81965i
$101$	−0.682084	−	1.18140i	−0.0678699	−	0.117554i	0.830094	−	0.557624i	$-0.188287\pi$
$101$	−0.682084	−	1.18140i	−0.0678699	−	0.117554i	−0.897963	+	0.440070i	$0.854954\pi$
$102$		0			0
$103$	−4.43543			−0.437036			−0.218518	−	0.975833i	$-0.570122\pi$
$103$	−4.43543			−0.437036			−0.218518	+	0.975833i	$0.570122\pi$
$104$	1.00775	+	2.41423i	0.0988177	+	0.236734i
$105$		0			0
$106$	−0.257203	+	0.959895i	−0.0249818	+	0.0932333i
$107$	1.81150	+	3.13761i	0.175124	+	0.303324i	0.940204	−	0.340611i	$-0.110634\pi$
$107$	1.81150	+	3.13761i	0.175124	+	0.303324i	−0.765080	+	0.643935i	$0.777301\pi$
$108$		0			0
$109$	11.1249	+	11.1249i	1.06557	+	1.06557i	0.997694	+	0.0678792i	$0.0216232\pi$
$109$	11.1249	+	11.1249i	1.06557	+	1.06557i	0.0678792	+	0.997694i	$0.478377\pi$
$110$	−0.492281	−	1.83722i	−0.0469372	−	0.175172i
$111$		0			0
$112$	−9.45909	+	3.40943i	−0.893800	+	0.322161i
$113$	2.74763	−	4.75903i	0.258475	−	0.447692i	−0.707358	−	0.706855i	$-0.750113\pi$
$113$	2.74763	−	4.75903i	0.258475	−	0.447692i	0.965834	+	0.259163i	$0.0834466\pi$
$114$		0			0
$115$	8.60577	−	32.1172i	0.802492	−	2.99494i
$116$		−	6.53434i		−	0.606698i
$117$		0			0
$118$			0.00126238i			0.000116211i
$119$	5.78960	+	4.88893i	0.530732	+	0.448167i
$120$		0			0
$121$	−3.55665	−	2.05343i	−0.323331	−	0.186675i
$122$	−0.844571	+	0.844571i	−0.0764638	+	0.0764638i
$123$		0			0
$124$	−18.1340	+	4.85900i	−1.62848	+	0.436351i
$125$	15.9190	+	15.9190i	1.42383	+	1.42383i
$126$		0			0
$127$	8.80555	−	5.08389i	0.781367	−	0.451122i	−0.0555478	−	0.998456i	$-0.517691\pi$
$127$	8.80555	−	5.08389i	0.781367	−	0.451122i	0.836914	+	0.547334i	$0.184357\pi$
$128$	−5.42001	−	1.45229i	−0.479066	−	0.128365i
$129$		0			0
$130$	−2.58875	+	0.348018i	−0.227049	+	0.0305232i
$131$			19.5230i			1.70573i	0.522129	+	0.852867i	$0.325138\pi$
$131$			19.5230i			1.70573i	−0.522129	+	0.852867i	$0.674862\pi$
$132$		0			0
$133$	−7.73855	+	0.652704i	−0.671018	+	0.0565966i
$134$	1.28663	+	0.742838i	0.111148	+	0.0641715i
$135$		0			0
$136$	0.537858	+	2.00731i	0.0461209	+	0.172126i
$137$	3.09421	+	11.5477i	0.264356	+	0.986590i	0.962643	+	0.270773i	$0.0872791\pi$
$137$	3.09421	+	11.5477i	0.264356	+	0.986590i	−0.698287	+	0.715818i	$0.746054\pi$
$138$		0			0
$139$	14.4291	+	8.33062i	1.22386	+	0.706594i	0.965738	−	0.259519i	$-0.0835640\pi$
$139$	14.4291	+	8.33062i	1.22386	+	0.706594i	0.258119	+	0.966113i	$0.416897\pi$
$140$	−1.73183	−	20.5328i	−0.146366	−	1.73534i
$141$		0			0
$142$			2.76365i			0.231920i
$143$	5.74217	−	7.52585i	0.480184	−	0.629343i
$144$		0			0
$145$	12.7110	+	3.40589i	1.05559	+	0.282844i
$146$	−0.0720540	+	0.0416004i	−0.00596323	+	0.00344287i
$147$		0			0
$148$	−9.75465	−	9.75465i	−0.801827	−	0.801827i
$149$	−14.7603	+	3.95502i	−1.20921	+	0.324008i	−0.806454	−	0.591297i	$-0.798616\pi$
$149$	−14.7603	+	3.95502i	−1.20921	+	0.324008i	−0.402761	+	0.915305i	$0.631949\pi$
$150$		0			0
$151$	−7.50367	+	7.50367i	−0.610640	+	0.610640i	−0.943113	−	0.332473i	$-0.892117\pi$
$151$	−7.50367	+	7.50367i	−0.610640	+	0.610640i	0.332473	+	0.943113i	$0.392117\pi$
$152$	−1.84444	−	1.06489i	−0.149604	−	0.0863740i
$153$		0			0
$154$	−0.970831	−	0.819801i	−0.0782318	−	0.0660614i
$155$		−	37.8080i		−	3.03681i
$156$		0			0
$157$			13.4871i			1.07639i	0.842820	+	0.538195i	$0.180894\pi$
$157$			13.4871i			1.07639i	−0.842820	+	0.538195i	$0.819106\pi$
$158$	−0.0132777	+	0.0495530i	−0.00105632	+	0.00394222i
$159$		0			0
$160$	4.25014	−	7.36146i	0.336003	−	0.581975i
$161$	−7.53210	−	20.8970i	−0.593612	−	1.64691i
$162$		0			0
$163$	−1.07320	−	4.00525i	−0.0840598	−	0.313716i	0.911075	−	0.412241i	$-0.135254\pi$
$163$	−1.07320	−	4.00525i	−0.0840598	−	0.313716i	−0.995134	+	0.0985258i	$0.968587\pi$
$164$	4.01792	+	4.01792i	0.313747	+	0.313747i
$165$		0			0
$166$	0.314280	+	0.544349i	0.0243928	+	0.0422496i
$167$	−3.62497	+	13.5286i	−0.280508	+	1.04687i	0.671551	+	0.740958i	$0.265628\pi$
$167$	−3.62497	+	13.5286i	−0.280508	+	1.04687i	−0.952059	+	0.305913i	$0.901038\pi$
$168$		0			0
$169$	−9.24251	−	9.14199i	−0.710962	−	0.703230i
$170$	−2.07489			−0.159137
$171$		0			0
$172$	−2.76048	−	4.78129i	−0.210484	−	0.364570i
$173$	7.63123	−	13.2177i	0.580192	−	1.00492i	−0.415265	−	0.909701i	$-0.636311\pi$
$173$	7.63123	−	13.2177i	0.580192	−	1.00492i	0.995456	−	0.0952206i	$-0.0303556\pi$
$174$		0			0
$175$	27.8237	+	4.99566i	2.10327	+	0.377636i
$176$	2.58243	+	9.63776i	0.194658	+	0.726473i
$177$		0			0
$178$	−0.0328133	−	0.0189448i	−0.00245946	−	0.00141997i
$179$	−6.94881	+	4.01190i	−0.519379	+	0.299863i	−0.736680	−	0.676241i	$-0.763608\pi$
$179$	−6.94881	+	4.01190i	−0.519379	+	0.299863i	0.217302	+	0.976104i	$0.430274\pi$
$180$		0			0
$181$	9.08130			0.675008			0.337504	−	0.941324i	$-0.390417\pi$
$181$	9.08130			0.675008			0.337504	+	0.941324i	$0.390417\pi$
$182$	−1.28700	+	1.17840i	−0.0953988	+	0.0873489i
$183$		0			0
$184$	1.57666	−	5.88418i	0.116233	−	0.433788i
$185$	24.0597	−	13.8909i	1.76891	−	1.02128i
$186$		0			0
$187$	5.31717	−	5.31717i	0.388830	−	0.388830i
$188$	3.49655	+	13.0493i	0.255012	+	0.951718i
$189$		0			0
$190$	1.50364	−	1.50364i	0.109085	−	0.109085i
$191$	10.2571	−	17.7658i	0.742179	−	1.28549i	−0.209323	−	0.977847i	$-0.567126\pi$
$191$	10.2571	−	17.7658i	0.742179	−	1.28549i	0.951501	−	0.307645i	$-0.0995408\pi$
$192$		0			0
$193$	14.0081	+	3.75346i	1.00832	+	0.270180i	0.724929	−	0.688823i	$-0.241872\pi$
$193$	14.0081	+	3.75346i	1.00832	+	0.270180i	0.283396	+	0.959003i	$0.408539\pi$
$194$	−0.139485			−0.0100144
$195$		0			0
$196$	−8.78247	−	10.6002i	−0.627319	−	0.757159i
$197$	−4.65346	+	17.3669i	−0.331545	+	1.23734i	0.576022	+	0.817434i	$0.304604\pi$
$197$	−4.65346	+	17.3669i	−0.331545	+	1.23734i	−0.907567	+	0.419908i	$0.862062\pi$
$198$		0			0
$199$	1.63893	−	2.83871i	0.116181	−	0.201231i	−0.802070	−	0.597230i	$-0.796268\pi$
$199$	1.63893	−	2.83871i	0.116181	−	0.201231i	0.918251	+	0.395999i	$0.129601\pi$
$200$	5.48182	+	5.48182i	0.387623	+	0.387623i
$201$		0			0
$202$	0.241037	−	0.0645858i	0.0169593	−	0.00454424i
$203$	8.27037	−	2.98097i	0.580466	−	0.209223i
$204$		0			0
$205$	−9.91015	+	5.72163i	−0.692155	+	0.399616i
$206$	0.209993	−	0.783706i	0.0146309	−	0.0546034i
$207$		0			0
$208$	13.5802	−	1.82565i	0.941617	−	0.126586i
$209$			7.70652i			0.533071i
$210$		0			0
$211$	12.5254	+	21.6946i	0.862283	+	1.49352i	0.869719	+	0.493546i	$0.164300\pi$
$211$	12.5254	+	21.6946i	0.862283	+	1.49352i	−0.00743594	+	0.999972i	$0.502367\pi$
$212$	9.25209	+	5.34170i	0.635436	+	0.366869i
$213$		0			0
$214$	−0.640155	+	0.171529i	−0.0437601	+	0.0117255i
$215$	10.7397	−	2.87769i	0.732440	−	0.196257i
$216$		0			0
$217$	−14.4227	−	20.7352i	−0.979075	−	1.40759i
$218$	−2.49238	+	1.43898i	−0.168806	+	0.0974599i
$219$		0			0
$220$	−20.4478			−1.37859
$221$	−6.30882	−	8.17544i	−0.424377	−	0.549940i
$222$		0			0
$223$	9.63125	+	2.58069i	0.644956	+	0.172816i	0.566447	−	0.824098i	$-0.308317\pi$
$223$	9.63125	+	2.58069i	0.644956	+	0.172816i	0.0785089	+	0.996913i	$0.474984\pi$
$224$	−0.477270	−	5.65858i	−0.0318889	−	0.378080i
$225$		0			0
$226$	0.710798	+	0.710798i	0.0472816	+	0.0472816i
$227$	−4.05289	−	15.1256i	−0.269000	−	1.00392i	−0.959757	−	0.280833i	$-0.909389\pi$
$227$	−4.05289	−	15.1256i	−0.269000	−	1.00392i	0.690757	−	0.723087i	$-0.257278\pi$
$228$		0			0
$229$	−1.59130	−	1.59130i	−0.105156	−	0.105156i	0.652571	−	0.757727i	$-0.273690\pi$
$229$	−1.59130	−	1.59130i	−0.105156	−	0.105156i	−0.757727	+	0.652571i	$0.773690\pi$
$230$	5.26741	+	3.04114i	0.347323	+	0.200527i
$231$		0			0
$232$	2.32878	+	0.623994i	0.152892	+	0.0409672i
$233$		−	8.49682i		−	0.556645i	−0.960488	−	0.278323i	$-0.910222\pi$
$233$		−	8.49682i		−	0.556645i	0.960488	−	0.278323i	$-0.0897784\pi$
$234$		0			0
$235$	−27.2067			−1.77477
$236$	0.0131088	+	0.00351249i	0.000853310	+	0.000228644i
$237$		0			0
$238$	−1.13794	+	0.791512i	−0.0737617	+	0.0513061i
$239$	6.87958	+	6.87958i	0.445003	+	0.445003i	0.893689	−	0.448686i	$-0.148108\pi$
$239$	6.87958	+	6.87958i	0.445003	+	0.445003i	−0.448686	+	0.893689i	$0.648108\pi$
$240$		0			0
$241$	19.8128	−	5.30883i	1.27626	−	0.341972i	0.443831	−	0.896110i	$-0.353619\pi$
$241$	19.8128	−	5.30883i	1.27626	−	0.341972i	0.832424	+	0.554139i	$0.186952\pi$
$242$	0.531212	−	0.531212i	0.0341476	−	0.0341476i
$243$		0			0
$244$	6.42023	+	11.1202i	0.411013	+	0.711895i
$245$	25.1978	−	11.5590i	1.60983	−	0.738477i
$246$		0			0
$247$	10.4965	+	1.35271i	0.667877	+	0.0860709i
$248$		−	6.92680i		−	0.439852i
$249$		0			0
$250$	−3.56642	+	2.05908i	−0.225561	+	0.130227i
$251$	−4.35546	+	7.54388i	−0.274914	+	0.476165i	−0.970113	−	0.242652i	$-0.921983\pi$
$251$	−4.35546	+	7.54388i	−0.274914	+	0.476165i	0.695199	+	0.718817i	$0.255316\pi$
$252$		0			0
$253$	−21.2917	+	5.70509i	−1.33860	+	0.358676i
$254$	0.481388	+	1.79656i	0.0302050	+	0.112726i
$255$		0			0
$256$	−6.69487	+	11.5958i	−0.418429	+	0.724741i
$257$	−6.96099	−	12.0568i	−0.434215	−	0.752082i	0.563016	−	0.826446i	$-0.309641\pi$
$257$	−6.96099	−	12.0568i	−0.434215	−	0.752082i	−0.997231	+	0.0743637i	$0.976307\pi$
$258$		0			0
$259$	7.89617	−	16.7963i	0.490644	−	1.04367i
$260$	−3.58916	+	27.8505i	−0.222590	+	1.72721i
$261$		0			0
$262$	−3.44956	−	0.924307i	−0.213114	−	0.0571039i
$263$	5.34924	+	9.26516i	0.329848	+	0.571314i	0.982482	−	0.186360i	$-0.0596690\pi$
$263$	5.34924	+	9.26516i	0.329848	+	0.571314i	−0.652633	+	0.757674i	$0.726336\pi$
$264$		0			0
$265$	−15.2134	+	15.2134i	−0.934555	+	0.934555i
$266$	0.251050	−	1.39824i	0.0153929	−	0.0857317i
$267$		0			0
$268$	11.2938	−	11.2938i	0.689877	−	0.689877i
$269$	−7.98188	−	4.60834i	−0.486664	−	0.280976i	0.236526	−	0.971625i	$-0.423991\pi$
$269$	−7.98188	−	4.60834i	−0.486664	−	0.280976i	−0.723189	+	0.690650i	$0.757325\pi$
$270$		0			0
$271$	−0.262832	+	0.980903i	−0.0159659	+	0.0595856i	−0.973449	−	0.228903i	$-0.926486\pi$
$271$	−0.262832	+	0.980903i	−0.0159659	+	0.0595856i	0.957483	+	0.288489i	$0.0931528\pi$
$272$	10.8845			0.659972
$273$		0			0
$274$	−2.18689			−0.132115
$275$	7.26039	−	27.0961i	0.437818	−	1.63396i
$276$		0			0
$277$	0.795438	+	0.459247i	0.0477933	+	0.0275935i	0.523706	−	0.851899i	$-0.324549\pi$
$277$	0.795438	+	0.459247i	0.0477933	+	0.0275935i	−0.475913	+	0.879492i	$0.657882\pi$
$278$	−2.15509	+	2.15509i	−0.129254	+	0.129254i
$279$		0			0
$280$	7.48307	+	1.34356i	0.447199	+	0.0802932i
$281$	−3.41893	+	3.41893i	−0.203956	+	0.203956i	−0.801693	−	0.597737i	$-0.796067\pi$
$281$	−3.41893	+	3.41893i	−0.203956	+	0.203956i	0.597737	+	0.801693i	$0.296067\pi$
$282$		0			0
$283$	7.94500	+	13.7611i	0.472281	+	0.818015i	0.999497	−	0.0317167i	$-0.0100974\pi$
$283$	7.94500	+	13.7611i	0.472281	+	0.818015i	−0.527216	+	0.849731i	$0.676764\pi$
$284$	28.6983	+	7.68968i	1.70293	+	0.456299i
$285$		0			0
$286$	1.05790	+	1.37090i	0.0625547	+	0.0810631i
$287$	−3.25242	+	6.91838i	−0.191984	+	0.408379i
$288$		0			0
$289$	4.39849	+	7.61842i	0.258735	+	0.448142i
$290$	−1.20359	+	2.08468i	−0.0706771	+	0.122416i
$291$		0			0
$292$	0.231501	+	0.863974i	0.0135476	+	0.0505603i
$293$	14.2807	−	3.82651i	0.834288	−	0.223547i	0.183705	−	0.982981i	$-0.441191\pi$
$293$	14.2807	−	3.82651i	0.834288	−	0.223547i	0.650584	+	0.759435i	$0.274524\pi$
$294$		0			0
$295$	−0.0136654	+	0.0236692i	−0.000795630	+	0.00137807i
$296$	4.40798	−	2.54495i	0.256209	−	0.147922i
$297$		0			0
$298$		−	2.79528i		−	0.161926i
$299$	4.03321	+	30.0013i	0.233247	+	1.73502i
$300$		0			0
$301$	4.79224	−	5.67510i	0.276220	−	0.327107i
$302$	−0.970581	−	1.68110i	−0.0558506	−	0.0967362i
$303$		0			0
$304$	−7.88785	+	7.88785i	−0.452399	+	0.452399i
$305$	−24.9780	+	6.69283i	−1.43024	+	0.383230i
$306$		0			0
$307$	−11.9699	−	11.9699i	−0.683157	−	0.683157i	0.277553	−	0.960710i	$-0.410477\pi$
$307$	−11.9699	−	11.9699i	−0.683157	−	0.683157i	−0.960710	+	0.277553i	$0.910477\pi$
$308$	−11.2143	+	7.80026i	−0.638992	+	0.444461i
$309$		0			0
$310$	6.68037	+	1.79000i	0.379419	+	0.101665i
$311$	−22.3022			−1.26464			−0.632322	−	0.774706i	$-0.717898\pi$
$311$	−22.3022			−1.26464			−0.632322	+	0.774706i	$0.717898\pi$
$312$		0			0
$313$		−	21.7630i		−	1.23012i	−0.788481	−	0.615059i	$-0.789132\pi$
$313$		−	21.7630i		−	1.23012i	0.788481	−	0.615059i	$-0.210868\pi$
$314$	−2.38307	−	0.638541i	−0.134484	−	0.0360349i
$315$		0			0
$316$	0.477624	+	0.275756i	0.0268684	+	0.0155125i
$317$	−3.88719	−	3.88719i	−0.218327	−	0.218327i	0.589466	−	0.807793i	$-0.299338\pi$
$317$	−3.88719	−	3.88719i	−0.218327	−	0.218327i	−0.807793	+	0.589466i	$0.799338\pi$
$318$		0			0
$319$	−2.25790	−	8.42659i	−0.126418	−	0.471798i
$320$	−20.1855	−	20.1855i	−1.12841	−	1.12841i
$321$		0			0
$322$	4.04893	−	0.341505i	0.225638	−	0.0190313i
$323$	8.12046	+	2.17587i	0.451834	+	0.121069i
$324$		0			0
$325$	−35.6313	−	14.6450i	−1.97647	−	0.812358i
$326$	0.758506			0.0420098
$327$		0			0
$328$	−1.81564	+	1.04826i	−0.100252	+	0.0578804i
$329$	−14.9211	+	10.3786i	−0.822626	+	0.572191i
$330$		0			0
$331$	−17.6440	+	4.72770i	−0.969802	+	0.259858i	−0.708744	−	0.705466i	$-0.750738\pi$
$331$	−17.6440	+	4.72770i	−0.969802	+	0.259858i	−0.261058	+	0.965323i	$0.584071\pi$
$332$	6.52709	−	1.74893i	0.358221	−	0.0959849i
$333$		0			0
$334$	−2.21877	−	1.28101i	−0.121406	−	0.0700935i
$335$	16.0826	+	27.8559i	0.878688	+	1.52193i
$336$		0			0
$337$		−	12.4905i		−	0.680402i	−0.940353	−	0.340201i	$-0.889505\pi$
$337$		−	12.4905i		−	0.680402i	0.940353	−	0.340201i	$-0.110495\pi$
$338$	2.05290	−	1.20025i	0.111663	−	0.0652852i
$339$		0			0
$340$	−5.77326	+	21.5461i	−0.313099	+	1.16850i
$341$	−21.7064	+	12.5322i	−1.17547	+	0.678655i
$342$		0			0
$343$	9.40990	−	15.9516i	0.508087	−	0.861306i
$344$	1.96762	−	0.527221i	0.106087	−	0.0284258i
$345$		0			0
$346$	1.97416	+	1.97416i	0.106132	+	0.106132i
$347$	2.70509	−	4.68534i	0.145217	−	0.251522i	−0.784237	−	0.620461i	$-0.786945\pi$
$347$	2.70509	−	4.68534i	0.145217	−	0.251522i	0.929454	+	0.368939i	$0.120279\pi$
$348$		0			0
$349$	−1.60376	+	5.98531i	−0.0858472	+	0.320386i	−0.995473	−	0.0950418i	$-0.969702\pi$
$349$	−1.60376	+	5.98531i	−0.0858472	+	0.320386i	0.909626	+	0.415428i	$0.136368\pi$
$350$	−2.19999	+	4.67970i	−0.117594	+	0.250141i
$351$		0			0
$352$	−5.63516			−0.300355
$353$	−34.1022	−	9.13766i	−1.81508	−	0.486348i	−0.818918	−	0.573911i	$-0.805425\pi$
$353$	−34.1022	−	9.13766i	−1.81508	−	0.486348i	−0.996159	+	0.0875628i	$0.972092\pi$
$354$		0			0
$355$	−29.9168	+	51.8175i	−1.58782	+	2.75019i
$356$	−0.288028	+	0.288028i	−0.0152654	+	0.0152654i
$357$		0			0
$358$	−0.379882	−	1.41774i	−0.0200774	−	0.0749299i
$359$	−7.81387	+	7.81387i	−0.412400	+	0.412400i	−0.882574	−	0.470174i	$-0.844191\pi$
$359$	−7.81387	+	7.81387i	−0.412400	+	0.412400i	0.470174	+	0.882574i	$0.344191\pi$
$360$		0			0
$361$	8.99290	−	5.19206i	0.473311	−	0.273266i
$362$	−0.429949	+	1.60459i	−0.0225976	+	0.0843355i
$363$		0			0
$364$	8.65576	+	16.6433i	0.453685	+	0.872346i
$365$	−1.80132			−0.0942852
$366$		0			0
$367$	19.4308	−	11.2184i	1.01428	−	0.585593i	0.101836	−	0.994801i	$-0.467528\pi$
$367$	19.4308	−	11.2184i	1.01428	−	0.585593i	0.912441	+	0.409208i	$0.134195\pi$
$368$	−27.6320	−	15.9533i	−1.44042	−	0.831625i
$369$		0			0
$370$	1.31531	+	4.90882i	0.0683799	+	0.255197i
$371$	−2.54006	+	14.1471i	−0.131873	+	0.734479i
$372$		0			0
$373$	−3.45623	+	5.98637i	−0.178957	+	0.309962i	−0.941523	−	0.336947i	$-0.890606\pi$
$373$	−3.45623	+	5.98637i	−0.178957	+	0.309962i	0.762567	+	0.646910i	$0.223939\pi$
$374$	0.687762	+	1.19124i	0.0355633	+	0.0615975i
$375$		0			0
$376$	−4.98455			−0.257058
$377$	−11.8736	+	1.59622i	−0.611520	+	0.0822095i
$378$		0			0
$379$	2.16569	−	8.08246i	0.111244	−	0.415168i	−0.887735	−	0.460356i	$-0.847722\pi$
$379$	2.16569	−	8.08246i	0.111244	−	0.415168i	0.998979	+	0.0451875i	$0.0143885\pi$
$380$	−11.4303	−	19.7979i	−0.586363	−	1.01561i
$381$		0			0
$382$	2.65346	+	2.65346i	0.135763	+	0.135763i
$383$	0.572661	+	2.13720i	0.0292616	+	0.109206i	0.979012	−	0.203802i	$-0.0653300\pi$
$383$	0.572661	+	2.13720i	0.0292616	+	0.109206i	−0.949750	+	0.313008i	$0.898663\pi$
$384$		0			0
$385$	−9.32830	−	25.8803i	−0.475414	−	1.31898i
$386$	−1.32641	+	2.29741i	−0.0675126	+	0.116935i
$387$		0			0
$388$	−0.388109	+	1.44844i	−0.0197032	+	0.0735334i
$389$			24.7852i			1.25666i	0.777946	+	0.628331i	$0.216262\pi$
$389$			24.7852i			1.25666i	−0.777946	+	0.628331i	$0.783738\pi$
$390$		0			0
$391$			24.0461i			1.21606i
$392$	4.61649	−	2.11772i	0.233168	−	0.106961i
$393$		0			0
$394$	−2.84828	−	1.64446i	−0.143494	−	0.0828465i
$395$	−0.785368	+	0.785368i	−0.0395162	+	0.0395162i
$396$		0			0
$397$	11.9456	−	3.20082i	0.599534	−	0.160645i	0.0537271	−	0.998556i	$-0.482890\pi$
$397$	11.9456	−	3.20082i	0.599534	−	0.160645i	0.545807	+	0.837911i	$0.316223\pi$
$398$	0.423983	+	0.423983i	0.0212524	+	0.0212524i
$399$		0			0
$400$	35.1649	−	20.3025i	1.75824	−	1.01512i
$401$	27.4395	+	7.35239i	1.37026	+	0.367161i	0.867575	−	0.497307i	$-0.165678\pi$
$401$	27.4395	+	7.35239i	1.37026	+	0.367161i	0.502688	+	0.864468i	$0.332344\pi$
$402$		0			0
$403$	13.2591	+	31.7644i	0.660484	+	1.58230i
$404$		−	2.68269i		−	0.133469i
$405$		0			0
$406$	0.135157	+	1.60244i	0.00670773	+	0.0795278i
$407$	−15.9501	−	9.20880i	−0.790617	−	0.456463i
$408$		0			0
$409$	−8.06083	−	30.0834i	−0.398583	−	1.48753i	−0.815592	−	0.578628i	$-0.803588\pi$
$409$	−8.06083	−	30.0834i	−0.398583	−	1.48753i	0.417009	−	0.908902i	$-0.363078\pi$
$410$	−0.541775	−	2.02193i	−0.0267564	−	0.0998561i
$411$		0			0
$412$	−7.55386	−	4.36123i	−0.372152	−	0.214862i
$413$	0.00153456	+	0.0181939i	7.55105e−5	+	0.000895264i
$414$		0			0
$415$			13.6085i			0.668013i
$416$	−0.989128	+	7.67525i	−0.0484960	+	0.376310i
$417$		0			0
$418$	−1.36168	−	0.364861i	−0.0666020	−	0.0178460i
$419$	15.4180	−	8.90159i	0.753219	−	0.434871i	−0.0736368	−	0.997285i	$-0.523461\pi$
$419$	15.4180	−	8.90159i	0.753219	−	0.434871i	0.826856	+	0.562414i	$0.190127\pi$
$420$		0			0
$421$	−7.27536	−	7.27536i	−0.354579	−	0.354579i	0.507231	−	0.861810i	$-0.330669\pi$
$421$	−7.27536	−	7.27536i	−0.354579	−	0.354579i	−0.861810	+	0.507231i	$0.830669\pi$
$422$	−4.42627	+	1.18602i	−0.215468	+	0.0577344i
$423$		0			0
$424$	−2.78725	+	2.78725i	−0.135361	+	0.135361i
$425$	−26.5016	−	15.3007i	−1.28552	−	0.742194i
$426$		0			0
$427$	−11.1456	+	13.1990i	−0.539375	+	0.638743i
$428$			7.12477i			0.344389i
$429$		0			0
$430$			2.03386i			0.0980813i
$431$	5.92484	−	22.1118i	0.285389	−	1.06509i	−0.663165	−	0.748473i	$-0.730787\pi$
$431$	5.92484	−	22.1118i	0.285389	−	1.06509i	0.948554	−	0.316615i	$-0.102546\pi$
$432$		0			0
$433$	3.70820	−	6.42278i	0.178205	−	0.308659i	−0.763061	−	0.646326i	$-0.776304\pi$
$433$	3.70820	−	6.42278i	0.178205	−	0.308659i	0.941266	+	0.337667i	$0.109638\pi$
$434$	4.34657	−	1.56668i	0.208642	−	0.0752029i
$435$		0			0
$436$	8.00774	+	29.8853i	0.383501	+	1.43125i
$437$	−17.4258	−	17.4258i	−0.833589	−	0.833589i
$438$		0			0
$439$	−18.4110	−	31.8888i	−0.878709	−	1.52197i	−0.852758	−	0.522306i	$-0.825072\pi$
$439$	−18.4110	−	31.8888i	−0.878709	−	1.52197i	−0.0259510	−	0.999663i	$-0.508261\pi$
$440$	1.95265	−	7.28740i	0.0930891	−	0.347413i
$441$		0			0
$442$	1.74322	−	0.727656i	0.0829167	−	0.0346111i
$443$	−25.6906			−1.22060			−0.610298	−	0.792172i	$-0.708950\pi$
$443$	−25.6906			−1.22060			−0.610298	+	0.792172i	$0.708950\pi$
$444$		0			0
$445$	−0.410159	−	0.710416i	−0.0194434	−	0.0336770i
$446$	−0.911973	+	1.57958i	−0.0431832	+	0.0747955i
$447$		0			0
$448$	−18.7706	−	3.37021i	−0.886829	−	0.159228i
$449$	1.26128	+	4.70715i	0.0595234	+	0.222144i	0.989280	−	0.146030i	$-0.0466496\pi$
$449$	1.26128	+	4.70715i	0.0595234	+	0.222144i	−0.929757	+	0.368174i	$0.879983\pi$
$450$		0			0
$451$	6.56982	+	3.79308i	0.309361	+	0.178609i
$452$	9.35882	−	5.40332i	0.440202	−	0.254151i
$453$		0			0
$454$	2.86445			0.134435
$455$	−36.8871	+	8.16269i	−1.72930	+	0.382673i
$456$		0			0
$457$	−1.32032	+	4.92751i	−0.0617621	+	0.230499i	−0.989907	−	0.141721i	$-0.954737\pi$
$457$	−1.32032	+	4.92751i	−0.0617621	+	0.230499i	0.928145	+	0.372220i	$0.121403\pi$
$458$	0.356509	−	0.205830i	0.0166586	−	0.00961783i
$459$		0			0
$460$	46.2361	−	46.2361i	2.15577	−	2.15577i
$461$	2.21189	+	8.25490i	0.103018	+	0.384469i	0.998113	−	0.0614071i	$-0.0195588\pi$
$461$	2.21189	+	8.25490i	0.103018	+	0.384469i	−0.895095	+	0.445876i	$0.852892\pi$
$462$		0			0
$463$	0.176712	−	0.176712i	0.00821253	−	0.00821253i	−0.702989	−	0.711201i	$-0.748152\pi$
$463$	0.176712	−	0.176712i	0.00821253	−	0.00821253i	0.711201	+	0.702989i	$0.248152\pi$
$464$	6.31383	−	10.9359i	0.293112	−	0.507685i
$465$		0			0
$466$	1.50132	+	0.402277i	0.0695473	+	0.0186351i
$467$	23.3883			1.08228			0.541140	−	0.840932i	$-0.317993\pi$
$467$	23.3883			1.08228			0.541140	+	0.840932i	$0.317993\pi$
$468$		0			0
$469$	19.4465	+	9.14205i	0.897956	+	0.422141i
$470$	1.28809	−	4.80721i	0.0594151	−	0.221740i
$471$		0			0
$472$	−0.00250364	+	0.00433642i	−0.000115239	+	0.000199600i
$473$	−5.21201	−	5.21201i	−0.239648	−	0.239648i
$474$		0			0
$475$	30.2935	−	8.11711i	1.38996	−	0.372438i
$476$	5.05298	+	14.0189i	0.231603	+	0.642557i
$477$		0			0
$478$	−1.54128	+	0.889857i	−0.0704964	+	0.0407011i
$479$	8.63573	−	32.2290i	0.394577	−	1.47258i	−0.427924	−	0.903815i	$-0.640755\pi$
$479$	8.63573	−	32.2290i	0.394577	−	1.47258i	0.822500	−	0.568765i	$-0.192579\pi$
$480$		0			0
$481$	−15.3423	+	20.1081i	−0.699550	+	0.916851i
$482$			3.75211i			0.170904i
$483$		0			0
$484$	−4.03815	−	6.99428i	−0.183552	−	0.317922i
$485$	−2.61530	−	1.50994i	−0.118754	−	0.0685629i
$486$		0			0
$487$	−14.6137	+	3.91573i	−0.662211	+	0.177439i	−0.574243	−	0.818685i	$-0.694704\pi$
$487$	−14.6137	+	3.91573i	−0.662211	+	0.177439i	−0.0879671	+	0.996123i	$0.528037\pi$
$488$	−4.57622	+	1.22619i	−0.207156	+	0.0555072i
$489$		0			0
$490$	0.849404	+	4.99951i	0.0383722	+	0.225855i
$491$	11.7579	−	6.78843i	0.530627	−	0.306357i	−0.210645	−	0.977563i	$-0.567556\pi$
$491$	11.7579	−	6.78843i	0.530627	−	0.306357i	0.741272	+	0.671205i	$0.234223\pi$
$492$		0			0
$493$	−9.51669			−0.428610
$494$	−0.735965	+	1.79061i	−0.0331126	+	0.0805632i
$495$		0			0
$496$	−35.0441	−	9.39005i	−1.57353	−	0.421626i
$497$	3.35951	+	39.8308i	0.150695	+	1.78666i
$498$		0			0
$499$	9.45211	+	9.45211i	0.423135	+	0.423135i	0.886282	−	0.463147i	$-0.153280\pi$
$499$	9.45211	+	9.45211i	0.423135	+	0.423135i	−0.463147	+	0.886282i	$0.653280\pi$
$500$	11.4585	+	42.7637i	0.512440	+	1.91245i
$501$		0			0
$502$	−1.12674	−	1.12674i	−0.0502887	−	0.0502887i
$503$	−1.20476	−	0.695570i	−0.0537177	−	0.0310140i	0.472901	−	0.881116i	$-0.343207\pi$
$503$	−1.20476	−	0.695570i	−0.0537177	−	0.0310140i	−0.526618	+	0.850102i	$0.676540\pi$
$504$		0			0
$505$	5.21852	+	1.39830i	0.232221	+	0.0622234i
$506$		−	4.03217i		−	0.179252i
$507$		0			0
$508$	19.9953			0.887149
$509$	22.4834	+	6.02441i	0.996559	+	0.267027i	0.720003	−	0.693971i	$-0.244140\pi$
$509$	22.4834	+	6.02441i	0.996559	+	0.267027i	0.276556	+	0.960998i	$0.410807\pi$
$510$		0			0
$511$	−0.987902	+	0.687152i	−0.0437022	+	0.0303978i
$512$	−9.66738	−	9.66738i	−0.427242	−	0.427242i
$513$		0			0
$514$	2.45990	−	0.659129i	0.108502	−	0.0290729i
$515$	12.4210	−	12.4210i	0.547335	−	0.547335i
$516$		0			0
$517$	9.01819	+	15.6200i	0.396620	+	0.686965i
$518$	2.59394	+	2.19040i	0.113971	+	0.0962408i
$519$		0			0
$520$	−9.58291	−	3.93871i	−0.420238	−	0.172724i
$521$			6.02463i			0.263944i	0.991253	+	0.131972i	$0.0421309\pi$
$521$			6.02463i			0.263944i	−0.991253	+	0.131972i	$0.957869\pi$
$522$		0			0
$523$	2.29311	−	1.32393i	0.100271	−	0.0578914i	−0.449026	−	0.893519i	$-0.648229\pi$
$523$	2.29311	−	1.32393i	0.100271	−	0.0578914i	0.549297	+	0.835627i	$0.314896\pi$
$524$	−19.1964	+	33.2491i	−0.838598	+	1.45249i
$525$		0			0
$526$	−1.89034	+	0.506514i	−0.0824226	+	0.0220851i
$527$	7.07670	+	26.4106i	0.308266	+	1.15046i
$528$		0			0
$529$	23.7440	−	41.1258i	1.03235	−	1.78808i
$530$	−1.96782	−	3.40837i	−0.0854767	−	0.148050i
$531$		0			0
$532$	−13.8211	−	6.49748i	−0.599221	−	0.281701i
$533$	6.31948	−	8.28249i	0.273727	−	0.358754i
$534$		0			0
$535$	−13.8595	−	3.71364i	−0.599199	−	0.160555i
$536$	2.94650	+	5.10348i	0.127269	+	0.220437i
$537$		0			0
$538$	1.19215	−	1.19215i	0.0513974	−	0.0513974i
$539$	−14.9886	−	10.6352i	−0.645603	−	0.458089i
$540$		0			0
$541$	−22.5427	+	22.5427i	−0.969185	+	0.969185i	−0.999539	−	0.0303542i	$-0.990336\pi$
$541$	−22.5427	+	22.5427i	−0.969185	+	0.969185i	0.0303542	+	0.999539i	$0.490336\pi$
$542$	−0.160874	−	0.0928807i	−0.00691013	−	0.00398957i
$543$		0			0
$544$	−1.59104	+	5.93784i	−0.0682152	+	0.254583i
$545$	−62.3085			−2.66900
$546$		0			0
$547$	24.3001			1.03900			0.519500	−	0.854471i	$-0.326118\pi$
$547$	24.3001			1.03900			0.519500	+	0.854471i	$0.326118\pi$
$548$	−6.08488	+	22.7091i	−0.259933	+	0.970084i
$549$		0			0
$550$	4.44393	+	2.56570i	0.189490	+	0.109402i
$551$	6.89659	−	6.89659i	0.293805	−	0.293805i
$552$		0			0
$553$	−0.131126	+	0.730318i	−0.00557606	+	0.0310563i
$554$	−0.118805	+	0.118805i	−0.00504753	+	0.00504753i
$555$		0			0
$556$	16.3825	+	28.3753i	0.694772	+	1.20338i
$557$	4.94226	+	1.32427i	0.209410	+	0.0561113i	0.361999	−	0.932178i	$-0.382094\pi$
$557$	4.94226	+	1.32427i	0.209410	+	0.0561113i	−0.152589	+	0.988290i	$0.548761\pi$
$558$		0			0
$559$	−8.01376	+	6.18406i	−0.338946	+	0.261558i
$560$	16.9415	−	36.0371i	0.715909	−	1.52284i
$561$		0			0
$562$	−0.442230	−	0.765964i	−0.0186543	−	0.0323102i
$563$	10.0206	−	17.3563i	0.422320	−	0.731480i	−0.573846	−	0.818963i	$-0.694549\pi$
$563$	10.0206	−	17.3563i	0.422320	−	0.731480i	0.996166	+	0.0874837i	$0.0278826\pi$
$564$		0			0
$565$	5.63274	+	21.0217i	0.236971	+	0.884389i
$566$	−2.80763	+	0.752303i	−0.118014	+	0.0316217i
$567$		0			0
$568$	−5.48106	+	9.49347i	−0.229980	+	0.398337i
$569$	29.3938	−	16.9705i	1.23225	−	0.711441i	0.264754	−	0.964316i	$-0.414709\pi$
$569$	29.3938	−	16.9705i	1.23225	−	0.711441i	0.967499	+	0.252875i	$0.0813760\pi$
$570$		0			0
$571$			19.5735i			0.819124i	0.912282	+	0.409562i	$0.134319\pi$
$571$			19.5735i			0.819124i	−0.912282	+	0.409562i	$0.865681\pi$
$572$	17.1793	−	7.17096i	0.718301	−	0.299833i
$573$		0			0
$574$	−1.06844	−	0.902223i	−0.0445957	−	0.0376581i
$575$	44.8521	+	77.6861i	1.87046	+	3.23973i
$576$		0			0
$577$	−32.3003	+	32.3003i	−1.34468	+	1.34468i	−0.453345	+	0.891335i	$0.649769\pi$
$577$	−32.3003	+	32.3003i	−1.34468	+	1.34468i	−0.891335	+	0.453345i	$0.850231\pi$
$578$	−1.55436	+	0.416489i	−0.0646527	+	0.0173237i
$579$		0			0
$580$	18.2988	+	18.2988i	0.759816	+	0.759816i
$581$	5.19124	+	7.46334i	0.215369	+	0.309631i
$582$		0			0
$583$	13.7771	+	3.69158i	0.570591	+	0.152889i
$584$	−0.330019			−0.0136563
$585$		0			0
$586$			2.70445i			0.111720i
$587$	12.7987	+	3.42941i	0.528260	+	0.141547i	0.513084	−	0.858338i	$-0.328503\pi$
$587$	12.7987	+	3.42941i	0.528260	+	0.141547i	0.0151751	+	0.999885i	$0.495169\pi$
$588$		0			0
$589$	−24.2677	−	14.0110i	−0.999933	−	0.577312i
$590$	−0.00353517	−	0.00353517i	−0.000145541	−	0.000145541i
$591$		0			0
$592$	−6.89992	−	25.7509i	−0.283585	−	1.05835i
$593$	−28.9194	−	28.9194i	−1.18758	−	1.18758i	−0.977735	−	0.209843i	$-0.932705\pi$
$593$	−28.9194	−	28.9194i	−1.18758	−	1.18758i	−0.209843	−	0.977735i	$-0.567295\pi$
$594$		0			0
$595$	−29.9042	+	2.52225i	−1.22595	+	0.103402i
$596$	−29.0268	−	7.77770i	−1.18898	−	0.318587i
$597$		0			0
$598$	−5.49194	−	0.707759i	−0.224582	−	0.0289424i
$599$	−10.2540			−0.418967			−0.209484	−	0.977812i	$-0.567178\pi$
$599$	−10.2540			−0.418967			−0.209484	+	0.977812i	$0.567178\pi$
$600$		0			0
$601$	27.4693	−	15.8594i	1.12050	−	0.646919i	0.178969	−	0.983855i	$-0.442724\pi$
$601$	27.4693	−	15.8594i	1.12050	−	0.646919i	0.941528	+	0.336936i	$0.109390\pi$
$602$	0.775859	+	1.11544i	0.0316216	+	0.0454617i
$603$		0			0
$604$	−20.1574	+	5.40116i	−0.820194	+	0.219770i
$605$	15.7105	−	4.20961i	0.638722	−	0.171145i
$606$		0			0
$607$	−23.1914	−	13.3895i	−0.941309	−	0.543465i	−0.0509383	−	0.998702i	$-0.516221\pi$
$607$	−23.1914	−	13.3895i	−0.941309	−	0.543465i	−0.890370	+	0.455237i	$0.849555\pi$
$608$	−3.15005	−	5.45605i	−0.127752	−	0.221272i
$609$		0			0
$610$		−	4.73028i		−	0.191523i
$611$	22.8578	−	9.54130i	0.924727	−	0.386000i
$612$		0			0
$613$	8.17678	−	30.5162i	0.330257	−	1.23254i	−0.578663	−	0.815567i	$-0.696425\pi$
$613$	8.17678	−	30.5162i	0.330257	−	1.23254i	0.908920	−	0.416970i	$-0.136908\pi$
$614$	2.68169	−	1.54827i	0.108224	−	0.0624833i
$615$		0			0
$616$	−1.70904	−	4.74154i	−0.0688591	−	0.191042i
$617$	−35.9374	+	9.62939i	−1.44678	+	0.387665i	−0.894904	−	0.446259i	$-0.852756\pi$
$617$	−35.9374	+	9.62939i	−1.44678	+	0.387665i	−0.551880	+	0.833923i	$0.686089\pi$
$618$		0			0
$619$	13.9520	+	13.9520i	0.560777	+	0.560777i	0.929528	−	0.368751i	$-0.120215\pi$
$619$	13.9520	+	13.9520i	0.560777	+	0.560777i	−0.368751	+	0.929528i	$0.620215\pi$
$620$	37.1754	−	64.3897i	1.49300	−	2.58595i
$621$		0			0
$622$	1.05589	−	3.94062i	0.0423372	−	0.158005i
$623$	−0.495949	−	0.233152i	−0.0198698	−	0.00934104i
$624$		0			0
$625$	−35.7364			−1.42945
$626$	3.84535	+	1.03036i	0.153691	+	0.0411814i
$627$		0			0
$628$	−13.2615	+	22.9695i	−0.529190	+	0.916585i
$629$	−14.2068	+	14.2068i	−0.566462	+	0.566462i
$630$		0			0
$631$	−2.16532	−	8.08109i	−0.0862001	−	0.321703i	0.909339	−	0.416057i	$-0.136588\pi$
$631$	−2.16532	−	8.08109i	−0.0862001	−	0.321703i	−0.995539	+	0.0943536i	$0.969922\pi$
$632$	−0.143887	+	0.143887i	−0.00572353	+	0.00572353i
$633$		0			0
$634$	0.870873	−	0.502799i	0.0345868	−	0.0199687i
$635$	−10.4222	+	38.8960i	−0.413591	+	1.54354i
$636$		0			0
$637$	−17.1163	+	18.5481i	−0.678173	+	0.734902i
$638$	1.59581			0.0631787
$639$		0			0
$640$	19.2452	−	11.1112i	0.760734	−	0.439210i
$641$	19.7158	+	11.3829i	0.778726	+	0.449598i	0.835979	−	0.548762i	$-0.184901\pi$
$641$	19.7158	+	11.3829i	0.778726	+	0.449598i	−0.0572524	+	0.998360i	$0.518234\pi$
$642$		0			0
$643$	−3.68359	−	13.7474i	−0.145267	−	0.542143i	−0.999743	−	0.0226531i	$-0.992789\pi$
$643$	−3.68359	−	13.7474i	−0.145267	−	0.542143i	0.854477	−	0.519490i	$-0.173878\pi$
$644$	7.71965	−	42.9951i	0.304197	−	1.69425i
$645$		0			0
$646$	−0.768917	+	1.33180i	−0.0302527	+	0.0523991i
$647$	22.6826	+	39.2874i	0.891744	+	1.54455i	0.837783	+	0.546003i	$0.183851\pi$
$647$	22.6826	+	39.2874i	0.891744	+	1.54455i	0.0539612	+	0.998543i	$0.482815\pi$
$648$		0			0
$649$	0.0181186			0.000711218
$650$	4.27460	−	5.60241i	0.167663	−	0.219745i
$651$		0			0
$652$	2.11050	−	7.87648i	0.0826534	−	0.308467i
$653$	−5.43437	−	9.41260i	−0.212663	−	0.368344i	0.739884	−	0.672735i	$-0.234880\pi$
$653$	−5.43437	−	9.41260i	−0.212663	−	0.368344i	−0.952547	+	0.304391i	$0.901547\pi$
$654$		0			0
$655$	−54.6723	−	54.6723i	−2.13622	−	2.13622i
$656$	2.84206	+	10.6067i	0.110964	+	0.414123i
$657$		0			0
$658$	−1.12738	−	3.12781i	−0.0439500	−	0.121935i
$659$	4.13172	−	7.15635i	0.160949	−	0.278772i	−0.774260	−	0.632867i	$-0.781878\pi$
$659$	4.13172	−	7.15635i	0.160949	−	0.278772i	0.935209	+	0.354096i	$0.115211\pi$
$660$		0			0
$661$	0.844712	−	3.15251i	0.0328555	−	0.122618i	−0.947550	−	0.319606i	$-0.896449\pi$
$661$	0.844712	−	3.15251i	0.0328555	−	0.122618i	0.980406	+	0.196988i	$0.0631160\pi$
$662$		−	3.34138i		−	0.129867i
$663$		0			0
$664$			2.49321i			0.0967552i
$665$	19.8432	−	23.4989i	0.769488	−	0.911248i
$666$		0			0
$667$	24.1595	+	13.9485i	0.935459	+	0.540088i
$668$	−19.4758	+	19.4758i	−0.753542	+	0.753542i
$669$		0			0
$670$	−5.68334	+	1.52285i	−0.219567	+	0.0588327i
$671$	12.1219	+	12.1219i	0.467962	+	0.467962i
$672$		0			0
$673$	−29.2655	+	16.8964i	−1.12810	+	0.651310i	−0.943457	−	0.331495i	$-0.892447\pi$
$673$	−29.2655	+	16.8964i	−1.12810	+	0.651310i	−0.184645	+	0.982805i	$0.559114\pi$
$674$	2.20697	+	0.591357i	0.0850095	+	0.0227782i
$675$		0			0
$676$	−6.75162	−	24.6573i	−0.259678	−	0.948360i
$677$			26.7526i			1.02819i	0.857734	+	0.514093i	$0.171871\pi$
$677$			26.7526i			1.02819i	−0.857734	+	0.514093i	$0.828129\pi$
$678$		0			0
$679$	−2.01032	+	0.169559i	−0.0771488	+	0.00650707i
$680$	−7.12751	−	4.11507i	−0.273327	−	0.157806i
$681$		0			0
$682$	−1.18666	−	4.42867i	−0.0454395	−	0.169583i
$683$	4.61892	+	17.2380i	0.176738	+	0.659595i	0.996249	+	0.0865317i	$0.0275784\pi$
$683$	4.61892	+	17.2380i	0.176738	+	0.659595i	−0.819511	+	0.573063i	$0.805755\pi$
$684$		0			0
$685$	−41.0034	−	23.6733i	−1.56666	−	0.904511i
$686$	2.37301	+	2.41787i	0.0906021	+	0.0923149i
$687$		0			0
$688$		−	10.6693i		−	0.406763i
$689$	7.44631	−	18.1169i	0.283682	−	0.690199i
$690$		0			0
$691$	28.7650	+	7.70756i	1.09427	+	0.293209i	0.760430	−	0.649420i	$-0.224988\pi$
$691$	28.7650	+	7.70756i	1.09427	+	0.293209i	0.333842	+	0.942629i	$0.391655\pi$
$692$	25.9931	−	15.0071i	0.988108	−	0.570484i
$693$		0			0
$694$	0.699792	+	0.699792i	0.0265637	+	0.0265637i
$695$	−63.7363	+	17.0781i	−2.41766	+	0.647809i
$696$		0			0
$697$	5.85175	−	5.85175i	0.221651	−	0.221651i
$698$	−0.981627	−	0.566743i	−0.0371551	−	0.0214515i
$699$		0			0
$700$	42.4736	+	35.8661i	1.60535	+	1.35561i
$701$		−	23.3038i		−	0.880172i	−0.897956	−	0.440086i	$-0.854948\pi$
$701$		−	23.3038i		−	0.880172i	0.897956	−	0.440086i	$-0.145052\pi$
$702$		0			0
$703$		−	20.5909i		−	0.776599i
$704$	−4.89806	+	18.2798i	−0.184603	+	0.688947i
$705$		0			0
$706$	3.22910	−	5.59297i	0.121529	−	0.210494i
$707$	3.39542	−	1.22384i	0.127698	−	0.0460274i
$708$		0			0
$709$	2.40630	+	8.98045i	0.0903706	+	0.337268i	0.996277	−	0.0862104i	$-0.0274757\pi$
$709$	2.40630	+	8.98045i	0.0903706	+	0.337268i	−0.905906	+	0.423478i	$0.860809\pi$
$710$	−7.73933	−	7.73933i	−0.290452	−	0.290452i
$711$		0			0
$712$	−0.0751452	−	0.130155i	−0.00281619	−	0.00487778i
$713$	20.7444	−	77.4193i	0.776886	−	2.89938i
$714$		0			0
$715$	4.99502	+	37.1558i	0.186803	+	1.38955i
$716$	−15.7791			−0.589693
$717$		0			0
$718$	−1.01070	−	1.75059i	−0.0377191	−	0.0653315i
$719$	−7.87045	+	13.6320i	−0.293518	+	0.508388i	−0.974639	−	0.223783i	$-0.928159\pi$
$719$	−7.87045	+	13.6320i	−0.293518	+	0.508388i	0.681121	+	0.732171i	$0.261493\pi$
$720$		0			0
$721$	2.07383	−	11.5504i	0.0772335	−	0.430158i
$722$	0.491630	+	1.83479i	0.0182966	+	0.0682838i
$723$		0			0
$724$	15.4661	+	8.92936i	0.574793	+	0.331857i
$725$	−30.7457	+	17.7511i	−1.14187	+	0.659258i
$726$		0			0
$727$	5.72068			0.212168			0.106084	−	0.994357i	$-0.466169\pi$
$727$	5.72068			0.212168			0.106084	+	0.994357i	$0.466169\pi$
$728$	−6.75809	+	1.49549i	−0.250472	+	0.0554264i
$729$		0			0
$730$	0.0852824	−	0.318278i	0.00315644	−	0.0117800i
$731$	−6.96352	+	4.02039i	−0.257555	+	0.148700i
$732$		0			0
$733$	12.5077	−	12.5077i	0.461982	−	0.461982i	−0.437322	−	0.899305i	$-0.644073\pi$
$733$	12.5077	−	12.5077i	0.461982	−	0.461982i	0.899305	+	0.437322i	$0.144073\pi$
$734$	1.06225	+	3.96439i	0.0392085	+	0.146328i
$735$		0			0
$736$	12.7421	−	12.7421i	0.469680	−	0.469680i
$737$	10.6618	−	18.4668i	0.392732	−	0.680232i
$738$		0			0
$739$	34.5884	+	9.26794i	1.27236	+	0.340927i	0.830933	−	0.556372i	$-0.187807\pi$
$739$	34.5884	+	9.26794i	1.27236	+	0.340927i	0.441423	+	0.897299i	$0.354474\pi$
$740$	54.6339			2.00838
$741$		0			0
$742$	−2.37941	−	1.11859i	−0.0873510	−	0.0410649i
$743$	1.35076	−	5.04112i	0.0495547	−	0.184941i	−0.936712	−	0.350101i	$-0.886147\pi$
$743$	1.35076	−	5.04112i	0.0495547	−	0.184941i	0.986267	+	0.165160i	$0.0528140\pi$
$744$		0			0
$745$	30.2593	−	52.4106i	1.10861	−	1.92017i
$746$	−0.894109	−	0.894109i	−0.0327357	−	0.0327357i
$747$		0			0
$748$	14.2837	−	3.82731i	0.522265	−	0.139940i
$749$	−9.01766	+	3.25032i	−0.329498	+	0.118764i
$750$		0			0
$751$	24.9221	−	14.3888i	0.909421	−	0.525055i	0.0291764	−	0.999574i	$-0.490712\pi$
$751$	24.9221	−	14.3888i	0.909421	−	0.525055i	0.880245	+	0.474520i	$0.157378\pi$
$752$	−6.75711	+	25.2179i	−0.246406	+	0.919601i
$753$		0			0
$754$	0.280109	−	2.17354i	0.0102010	−	0.0791556i
$755$		−	42.0266i		−	1.52950i
$756$		0			0
$757$	8.90997	+	15.4325i	0.323838	+	0.560905i	0.981277	−	0.192604i	$-0.0616933\pi$
$757$	8.90997	+	15.4325i	0.323838	+	0.560905i	−0.657438	+	0.753508i	$0.728360\pi$
$758$	1.32557	+	0.765320i	0.0481470	+	0.0277977i
$759$		0			0
$760$	8.14731	−	2.18306i	0.295534	−	0.0791881i
$761$	52.7426	−	14.1323i	1.91192	−	0.512296i	0.918872	−	0.394556i	$-0.129101\pi$
$761$	52.7426	−	14.1323i	1.91192	−	0.512296i	0.993044	−	0.117741i	$-0.0375652\pi$
$762$		0			0
$763$	−34.1720	+	23.7689i	−1.23711	+	0.860492i
$764$	34.9372	−	20.1710i	1.26398	−	0.729761i
$765$		0			0
$766$	−0.404738			−0.0146238
$767$	0.00318032	−	0.0246781i	0.000114835	−	0.000891074i
$768$		0			0
$769$	−23.1319	−	6.19819i	−0.834159	−	0.223512i	−0.183632	−	0.982995i	$-0.558785\pi$
$769$	−23.1319	−	6.19819i	−0.834159	−	0.223512i	−0.650527	+	0.759483i	$0.725452\pi$
$770$	5.01449	−	0.422944i	0.180710	−	0.0152419i
$771$		0			0
$772$	20.1661	+	20.1661i	0.725795	+	0.725795i
$773$	−10.0708	−	37.5846i	−0.362221	−	1.35183i	−0.871150	−	0.491017i	$-0.836625\pi$
$773$	−10.0708	−	37.5846i	−0.362221	−	1.35183i	0.508929	−	0.860808i	$-0.330042\pi$
$774$		0			0
$775$	72.1254	+	72.1254i	2.59082	+	2.59082i
$776$	−0.479148	−	0.276636i	−0.0172004	−	0.00993067i
$777$		0			0
$778$	−4.37935	−	1.17344i	−0.157007	−	0.0420700i
$779$			8.48133i			0.303875i
$780$		0			0
$781$	39.6660			1.41936
$782$	−4.24875	−	1.13845i	−0.151935	−	0.0407109i
$783$		0			0
$784$	−4.45584	−	26.2266i	−0.159137	−	0.936665i
$785$	−37.7694	−	37.7694i	−1.34805	−	1.34805i
$786$		0			0
$787$	−17.8194	+	4.77470i	−0.635194	+	0.170200i	−0.562026	−	0.827120i	$-0.689978\pi$
$787$	−17.8194	+	4.77470i	−0.635194	+	0.170200i	−0.0731686	+	0.997320i	$0.523311\pi$
$788$	−25.0015	+	25.0015i	−0.890643	+	0.890643i
$789$		0			0
$790$	−0.101585	−	0.175951i	−0.00361425	−	0.00626006i
$791$	11.1084	+	9.38026i	0.394968	+	0.333524i
$792$		0			0
$793$	18.6381	−	14.3827i	0.661860	−	0.510744i
$794$			2.26224i			0.0802838i
$795$		0			0
$796$	5.58244	−	3.22302i	0.197864	−	0.114237i
$797$	0.444897	−	0.770584i	0.0157591	−	0.0272955i	−0.858038	−	0.513586i	$-0.828317\pi$
$797$	0.444897	−	0.770584i	0.0157591	−	0.0272955i	0.873797	+	0.486290i	$0.161650\pi$
$798$		0			0
$799$	19.0051	−	5.09241i	0.672354	−	0.180157i
$800$	5.93539	+	22.1512i	0.209848	+	0.783162i
$801$		0			0
$802$	−2.59822	+	4.50024i	−0.0917462	+	0.158909i
$803$	0.597081	+	1.03417i	0.0210705	+	0.0364952i
$804$		0			0
$805$	79.6129	+	37.4271i	2.80599	+	1.31913i
$806$	−6.24027	+	0.838908i	−0.219804	+	0.0295493i
$807$		0			0
$808$	0.956084	+	0.256182i	0.0336349	+	0.00901245i
$809$	−22.3601	−	38.7288i	−0.786138	−	1.36163i	−0.928317	−	0.371790i	$-0.878744\pi$
$809$	−22.3601	−	38.7288i	−0.786138	−	1.36163i	0.142179	−	0.989841i	$-0.454589\pi$
$810$		0			0
$811$	−28.1862	+	28.1862i	−0.989753	+	0.989753i	−0.999948	−	0.0101954i	$-0.996755\pi$
$811$	−28.1862	+	28.1862i	−0.989753	+	0.989753i	0.0101954	+	0.999948i	$0.496755\pi$
$812$	17.0161	+	3.05520i	0.597149	+	0.107216i
$813$		0			0
$814$	2.38227	−	2.38227i	0.0834985	−	0.0834985i
$815$	14.2217	+	8.21092i	0.498165	+	0.287616i
$816$		0			0
$817$	2.13284	−	7.95986i	0.0746186	−	0.278480i
$818$	5.69714			0.199196
$819$		0			0
$820$	−22.5036			−0.785860
$821$	−0.320911	+	1.19766i	−0.0111999	+	0.0417986i	−0.971300	−	0.237859i	$-0.923554\pi$
$821$	−0.320911	+	1.19766i	−0.0111999	+	0.0417986i	0.960100	+	0.279658i	$0.0902210\pi$
$822$		0			0
$823$	−25.3229	−	14.6202i	−0.882701	−	0.509628i	−0.0111531	−	0.999938i	$-0.503550\pi$
$823$	−25.3229	−	14.6202i	−0.882701	−	0.509628i	−0.871548	+	0.490310i	$0.836884\pi$
$824$	2.27565	−	2.27565i	0.0792761	−	0.0792761i
$825$		0			0
$826$	−0.00328737		0.000590238i	−0.000114382		2.05370e-5i
$827$	27.0221	−	27.0221i	0.939649	−	0.939649i	−0.0586310	−	0.998280i	$-0.518674\pi$
$827$	27.0221	−	27.0221i	0.939649	−	0.939649i	0.998280	+	0.0586310i	$0.0186735\pi$
$828$		0			0
$829$	9.30153	+	16.1107i	0.323055	+	0.559548i	0.981117	−	0.193416i	$-0.0619567\pi$
$829$	9.30153	+	16.1107i	0.323055	+	0.559548i	−0.658061	+	0.752964i	$0.728623\pi$
$830$	−2.40451	−	0.644285i	−0.0834616	−	0.0223635i
$831$		0			0
$832$	24.0379	+	9.87993i	0.833364	+	0.342525i
$833$	−15.4383	+	12.7909i	−0.534905	+	0.443178i
$834$		0			0
$835$	−27.7341	−	48.0368i	−0.959777	−	1.66238i
$836$	−7.57759	+	13.1248i	−0.262076	+	0.453930i
$837$		0			0
$838$	0.842882	+	3.14568i	0.0291169	+	0.108666i
$839$	−17.3070	+	4.63740i	−0.597504	+	0.160101i	−0.544881	−	0.838514i	$-0.683425\pi$
$839$	−17.3070	+	4.63740i	−0.597504	+	0.160101i	−0.0526236	+	0.998614i	$0.516758\pi$
$840$		0			0
$841$	8.97962	−	15.5532i	0.309642	−	0.536316i
$842$	1.62995	−	0.941050i	0.0561716	−	0.0324307i
$843$		0			0
$844$			49.2633i			1.69571i
$845$	51.4840	−	0.281491i	1.77110	−	0.00968359i
$846$		0			0
$847$	7.01030	−	8.30179i	0.240877	−	0.285253i
$848$	10.3229	+	17.8797i	0.354489	+	0.613993i
$849$		0			0
$850$	3.95822	−	3.95822i	0.135766	−	0.135766i
$851$	56.8887	−	15.2433i	1.95012	−	0.522533i
$852$		0			0
$853$	−36.5250	−	36.5250i	−1.25059	−	1.25059i	−0.955455	−	0.295137i	$-0.904635\pi$
$853$	−36.5250	−	36.5250i	−1.25059	−	1.25059i	−0.295137	−	0.955455i	$-0.595365\pi$
$854$	−1.80447	−	2.59424i	−0.0617476	−	0.0887731i
$855$		0			0
$856$	−2.53920	−	0.680376i	−0.0867880	−	0.0232548i
$857$	36.8519			1.25884			0.629418	−	0.777067i	$-0.283293\pi$
$857$	36.8519			1.25884			0.629418	+	0.777067i	$0.283293\pi$
$858$		0			0
$859$		−	29.0833i		−	0.992310i	−0.868234	−	0.496155i	$-0.834745\pi$
$859$		−	29.0833i		−	0.992310i	0.868234	−	0.496155i	$-0.165255\pi$
$860$	21.1200	+	5.65908i	0.720185	+	0.192973i
$861$		0			0
$862$	3.62647	+	2.09374i	0.123518	+	0.0713132i
$863$	0.584660	+	0.584660i	0.0199021	+	0.0199021i	0.716988	−	0.697086i	$-0.245520\pi$
$863$	0.584660	+	0.584660i	0.0199021	+	0.0199021i	−0.697086	+	0.716988i	$0.745520\pi$
$864$		0			0
$865$	15.6443	+	58.3853i	0.531922	+	1.98516i
$866$	0.959292	+	0.959292i	0.0325981	+	0.0325981i
$867$		0			0
$868$	−4.17462	−	49.4949i	−0.141696	−	1.67997i
$869$	0.711222	+	0.190571i	0.0241266	+	0.00646469i
$870$		0			0
$871$	−23.2808	−	17.7631i	−0.788840	−	0.601879i
$872$	−11.4155			−0.386579
$873$		0			0
$874$	3.90401	−	2.25398i	0.132055	−	0.0762421i
$875$	−48.8978	+	34.0116i	−1.65305	+	1.14980i
$876$		0			0
$877$	24.9512	−	6.68566i	0.842543	−	0.225759i	0.188365	−	0.982099i	$-0.439681\pi$
$877$	24.9512	−	6.68566i	0.842543	−	0.225759i	0.654178	+	0.756340i	$0.273015\pi$
$878$	6.50615	−	1.74332i	0.219572	−	0.0588341i
$879$		0			0
$880$	−34.2215	−	19.7578i	−1.15360	−	0.666034i
$881$	−16.3924	−	28.3925i	−0.552275	−	0.956568i	−0.998110	−	0.0614526i	$-0.980427\pi$
$881$	−16.3924	−	28.3925i	−0.552275	−	0.956568i	0.445835	−	0.895115i	$-0.352907\pi$
$882$		0			0
$883$		−	51.9581i		−	1.74853i	−0.485450	−	0.874265i	$-0.661344\pi$
$883$		−	51.9581i		−	1.74853i	0.485450	−	0.874265i	$-0.338656\pi$
$884$	−2.70572	−	20.1266i	−0.0910031	−	0.676932i
$885$		0			0
$886$	1.21631	−	4.53932i	0.0408627	−	0.152501i
$887$	−28.3210	+	16.3512i	−0.950928	+	0.549018i	−0.893369	−	0.449324i	$-0.851665\pi$
$887$	−28.3210	+	16.3512i	−0.950928	+	0.549018i	−0.0575587	+	0.998342i	$0.518332\pi$
$888$		0			0
$889$	9.12188	+	25.3077i	0.305938	+	0.848791i
$890$	0.144944	−	0.0388375i	0.00485852	−	0.00130184i
$891$		0			0
$892$	13.8652	+	13.8652i	0.464242	+	0.464242i
$893$	−10.0823	+	17.4631i	−0.337392	+	0.584381i
$894$		0			0
$895$	8.22454	−	30.6944i	0.274916	−	1.02600i
$896$	6.31610	−	13.4353i	0.211006	−	0.448841i
$897$		0			0
$898$	−0.891430			−0.0297474
$899$	30.6402	+	8.21001i	1.02191	+	0.273819i
$900$		0			0
$901$	7.77971	−	13.4749i	0.259180	−	0.448913i
$902$	−0.981252	+	0.981252i	−0.0326721	+	0.0326721i
$903$		0			0
$904$	1.03197	+	3.85138i	0.0343230	+	0.128095i
$905$	−25.4313	+	25.4313i	−0.845365	+	0.845365i
$906$		0			0
$907$	−17.5633	+	10.1402i	−0.583178	+	0.336698i	−0.762395	−	0.647111i	$-0.775977\pi$
$907$	−17.5633	+	10.1402i	−0.583178	+	0.336698i	0.179217	+	0.983810i	$0.442644\pi$
$908$	7.97016	−	29.7451i	0.264499	−	0.987124i
$909$		0			0
$910$	0.304121	−	6.90412i	0.0100815	−	0.228869i
$911$	10.1023			0.334704			0.167352	−	0.985897i	$-0.446478\pi$
$911$	10.1023			0.334704			0.167352	+	0.985897i	$0.446478\pi$
$912$		0			0
$913$	7.81291	−	4.51078i	0.258569	−	0.149285i
$914$	−0.808142	−	0.466581i	−0.0267309	−	0.0154331i
$915$		0			0
$916$	−1.14542	−	4.27477i	−0.0378458	−	0.141242i
$917$	−50.8401	−	9.12818i	−1.67889	−	0.301439i
$918$		0			0
$919$	17.0100	−	29.4622i	0.561108	−	0.971867i	−0.436293	−	0.899805i	$-0.643709\pi$
$919$	17.0100	−	29.4622i	0.561108	−	0.971867i	0.997400	−	0.0720619i	$-0.0229579\pi$
$920$	12.0628	+	20.8934i	0.397699	+	0.688834i
$921$		0			0
$922$	−1.56330			−0.0514844
$923$	6.96249	−	54.0262i	0.229173	−	1.77830i
$924$		0			0
$925$	−19.3988	+	72.3974i	−0.637830	+	2.38041i
$926$	0.0228573	+	0.0395900i	0.000751138	+	0.00130101i
$927$		0			0
$928$	5.04292	+	5.04292i	0.165542	+	0.165542i
$929$	−1.74577	−	6.51529i	−0.0572768	−	0.213760i	0.931356	−	0.364110i	$-0.118627\pi$
$929$	−1.74577	−	6.51529i	−0.0572768	−	0.213760i	−0.988633	+	0.150350i	$0.951960\pi$
$930$		0			0
$931$	1.91853	−	20.4572i	0.0628772	−	0.670458i
$932$	8.35466	−	14.4707i	0.273666	−	0.474003i
$933$		0			0
$934$	−1.10731	+	4.13252i	−0.0362321	+	0.135220i
$935$			29.7804i			0.973924i
$936$		0			0
$937$			37.1803i			1.21463i	0.794461	+	0.607315i	$0.207753\pi$
$937$			37.1803i			1.21463i	−0.794461	+	0.607315i	$0.792247\pi$
$938$	−2.53601	+	3.00321i	−0.0828037	+	0.0980584i
$939$		0			0
$940$	−46.3350	−	26.7515i	−1.51128	−	0.872539i
$941$	−38.8786	+	38.8786i	−1.26741	+	1.26741i	−0.319981	+	0.947424i	$0.603677\pi$
$941$	−38.8786	+	38.8786i	−1.26741	+	1.26741i	−0.947424	+	0.319981i	$0.896323\pi$
$942$		0			0
$943$	−23.4323	+	6.27867i	−0.763062	+	0.204462i
$944$	0.0185449	+	0.0185449i	0.000603586	+	0.000603586i
$945$		0			0
$946$	1.16768	−	0.674160i	0.0379646	−	0.0219188i
$947$	20.0773	+	5.37969i	0.652424	+	0.174816i	0.569824	−	0.821766i	$-0.307011\pi$
$947$	20.0773	+	5.37969i	0.652424	+	0.174816i	0.0825993	+	0.996583i	$0.473678\pi$
$948$		0			0
$949$	1.51338	−	0.631715i	0.0491264	−	0.0205063i
$950$			5.73691i			0.186130i
$951$		0			0
$952$	−5.47874	+	0.462102i	−0.177567	+	0.0149768i
$953$	−23.9622	−	13.8346i	−0.776212	−	0.448146i	0.0588741	−	0.998265i	$-0.481249\pi$
$953$	−23.9622	−	13.8346i	−0.776212	−	0.448146i	−0.835086	+	0.550119i	$0.814582\pi$
$954$		0			0
$955$	21.0275	+	78.4756i	0.680433	+	2.53941i
$956$	4.95194	+	18.4809i	0.160157	+	0.597715i
$957$		0			0
$958$	5.28575	+	3.05173i	0.170775	+	0.0985968i
$959$	−31.5183	+	2.65839i	−1.01778	+	0.0858440i
$960$		0			0
$961$		−	60.1373i		−	1.93991i
$962$	−2.82657	−	3.66287i	−0.0911321	−	0.118096i
$963$		0			0
$964$	38.9627	+	10.4400i	1.25490	+	0.336250i
$965$	−49.7395	+	28.7171i	−1.60117	+	0.924437i
$966$		0			0
$967$	9.79059	+	9.79059i	0.314844	+	0.314844i	0.846783	−	0.531939i	$-0.178536\pi$
$967$	9.79059	+	9.79059i	0.314844	+	0.314844i	−0.531939	+	0.846783i	$0.678536\pi$
$968$	2.87832	−	0.771242i	0.0925126	−	0.0247887i
$969$		0			0
$970$	0.390614	−	0.390614i	0.0125419	−	0.0125419i
$971$	18.5031	+	10.6828i	0.593792	+	0.342826i	0.766596	−	0.642130i	$-0.221949\pi$
$971$	18.5031	+	10.6828i	0.593792	+	0.342826i	−0.172803	+	0.984956i	$0.555283\pi$
$972$		0			0
$973$	−28.4403	+	33.6798i	−0.911755	+	1.07972i
$974$		−	2.76751i		−	0.0886769i
$975$		0			0
$976$			24.8143i			0.794286i
$977$	9.16391	−	34.2002i	0.293179	−	1.09416i	−0.649473	−	0.760384i	$-0.725011\pi$
$977$	9.16391	−	34.2002i	0.293179	−	1.09416i	0.942653	−	0.333776i	$-0.108323\pi$
$978$		0			0
$979$	−0.271910	+	0.470962i	−0.00869028	+	0.0150520i
$980$	54.2793	+	5.09045i	1.73389	+	0.162608i
$981$		0			0
$982$	0.642789	+	2.39892i	0.0205122	+	0.0765526i
$983$	21.6097	+	21.6097i	0.689243	+	0.689243i	0.962065	−	0.272822i	$-0.0879570\pi$
$983$	21.6097	+	21.6097i	0.689243	+	0.689243i	−0.272822	+	0.962065i	$0.587957\pi$
$984$		0			0
$985$	−35.6029	−	61.6660i	−1.13440	−	1.96484i
$986$	0.450563	−	1.68152i	0.0143488	−	0.0535506i
$987$		0			0
$988$	16.5462	+	12.6247i	0.526406	+	0.401644i
$989$	23.5705			0.749499
$990$		0			0
$991$	0.414264	+	0.717526i	0.0131595	+	0.0227930i	0.872530	−	0.488560i	$-0.162478\pi$
$991$	0.414264	+	0.717526i	0.0131595	+	0.0227930i	−0.859371	+	0.511353i	$0.829144\pi$
$992$	10.2451	−	17.7450i	0.325282	−	0.563405i
$993$		0			0
$994$	−7.19684	−	1.29217i	−0.228270	−	0.0409852i
$995$	3.35987	+	12.5392i	0.106515	+	0.397520i
$996$		0			0
$997$	35.7880	+	20.6622i	1.13342	+	0.654379i	0.944792	−	0.327671i	$-0.106264\pi$
$997$	35.7880	+	20.6622i	1.13342	+	0.654379i	0.188625	+	0.982049i	$0.439597\pi$
$998$	−2.11762	+	1.22261i	−0.0670320	+	0.0387009i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.e.622.4		32
3.2	odd	2		273.2.by.d.76.5	yes	32
7.6	odd	2		819.2.fm.f.622.4		32
13.6	odd	12		819.2.fm.f.370.4		32
21.20	even	2		273.2.by.c.76.5	✓	32
39.32	even	12		273.2.by.c.97.5	yes	32
91.6	even	12	inner	819.2.fm.e.370.4		32
273.188	odd	12		273.2.by.d.97.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.5	✓	32	21.20	even	2
273.2.by.c.97.5	yes	32	39.32	even	12
273.2.by.d.76.5	yes	32	3.2	odd	2
273.2.by.d.97.5	yes	32	273.188	odd	12
819.2.fm.e.370.4		32	91.6	even	12	inner
819.2.fm.e.622.4		32	1.1	even	1	trivial
819.2.fm.f.370.4		32	13.6	odd	12
819.2.fm.f.622.4		32	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0473445 + 0.176692i) q^{2} +(1.70307 + 0.983269i) q^{4} +(-2.80040 + 2.80040i) q^{5} +(-0.467560 + 2.60411i) q^{7} +(-0.513062 + 0.513062i) q^{8} +O(q^{10})\)	\(q+(-0.0473445 + 0.176692i) q^{2} +(1.70307 + 0.983269i) q^{4} +(-2.80040 + 2.80040i) q^{5} +(-0.467560 + 2.60411i) q^{7} +(-0.513062 + 0.513062i) q^{8} +(-0.362225 - 0.627392i) q^{10} +(2.53602 + 0.679524i) q^{11} +(1.37067 - 3.33485i) q^{13} +(-0.437989 - 0.205904i) q^{14} +(1.90018 + 3.29120i) q^{16} +(1.43204 - 2.48037i) q^{17} +(0.759707 + 2.83527i) q^{19} +(-7.52284 + 2.01574i) q^{20} +(-0.240133 + 0.415922i) q^{22} +(-7.27090 + 4.19786i) q^{23} -10.6845i q^{25} +(0.524348 + 0.400074i) q^{26} +(-3.35683 + 3.97525i) q^{28} +(-1.66138 - 2.87760i) q^{29} +(-6.75045 + 6.75045i) q^{31} +(-2.07320 + 0.555513i) q^{32} +(0.370463 + 0.370463i) q^{34} +(-5.98320 - 8.60192i) q^{35} +(-6.77592 - 1.81560i) q^{37} -0.536937 q^{38} -2.87356i q^{40} +(2.79099 + 0.747843i) q^{41} +(-2.43132 - 1.40372i) q^{43} +(3.65087 + 3.65087i) q^{44} +(-0.397491 - 1.48346i) q^{46} +(4.85765 + 4.85765i) q^{47} +(-6.56278 - 2.43516i) q^{49} +(1.88787 + 0.505853i) q^{50} +(5.61342 - 4.33176i) q^{52} +5.43259 q^{53} +(-9.00481 + 5.19893i) q^{55} +(-1.09618 - 1.57596i) q^{56} +(0.587105 - 0.157314i) q^{58} +(0.00666592 - 0.00178613i) q^{59} +(5.65469 + 3.26474i) q^{61} +(-0.873154 - 1.51235i) q^{62} +7.20808i q^{64} +(5.50050 + 13.1774i) q^{65} +(2.10207 - 7.84504i) q^{67} +(4.87775 - 2.81617i) q^{68} +(1.80316 - 0.649930i) q^{70} +(14.5933 - 3.91026i) q^{71} +(0.321617 + 0.321617i) q^{73} +(0.641604 - 1.11129i) q^{74} +(-1.49399 + 5.57566i) q^{76} +(-2.95530 + 6.28635i) q^{77} +0.280448 q^{79} +(-14.5379 - 3.89543i) q^{80} +(-0.264276 + 0.457739i) q^{82} +(2.42973 - 2.42973i) q^{83} +(2.93575 + 10.9564i) q^{85} +(0.363136 - 0.363136i) q^{86} +(-1.64977 + 0.952496i) q^{88} +(-0.0536096 + 0.200074i) q^{89} +(8.04346 + 5.12863i) q^{91} -16.5105 q^{92} +(-1.08829 + 0.628324i) q^{94} +(-10.0674 - 5.81240i) q^{95} +(0.197356 + 0.736543i) q^{97} +(0.740984 - 1.04430i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

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