LMFDB - Embedded newform 400.2.l.i.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(101,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("400.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			301.1
Root			$-1.40501 - 0.161069i$ of defining polynomial
Character	$\chi$	$=$	400.301
Dual form			400.2.l.i.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40501 + 0.161069i) q^{2} +(0.734294 + 0.734294i) q^{3} +(1.94811 - 0.452606i) q^{4} +(-1.14996 - 0.913419i) q^{6} -1.71452i q^{7} +(-2.66422 + 0.949697i) q^{8} -1.92163i q^{9} +(2.82684 - 2.82684i) q^{11} +(1.76283 + 1.09814i) q^{12} +(-2.59462 - 2.59462i) q^{13} +(0.276156 + 2.40893i) q^{14} +(3.59030 - 1.76346i) q^{16} +1.89939 q^{17} +(0.309513 + 2.69991i) q^{18} +(-2.89623 - 2.89623i) q^{19} +(1.25896 - 1.25896i) q^{21} +(-3.51643 + 4.42705i) q^{22} +2.00613i q^{23} +(-2.65368 - 1.25896i) q^{24} +(4.06338 + 3.22756i) q^{26} +(3.61392 - 3.61392i) q^{27} +(-0.776005 - 3.34009i) q^{28} +(6.72307 + 6.72307i) q^{29} -7.11778 q^{31} +(-4.76037 + 3.05596i) q^{32} +4.15146 q^{33} +(-2.66867 + 0.305932i) q^{34} +(-0.869740 - 3.74355i) q^{36} +(2.25207 - 2.25207i) q^{37} +(4.53572 + 3.60274i) q^{38} -3.81042i q^{39} +1.59630i q^{41} +(-1.56608 + 1.97164i) q^{42} +(8.06886 - 8.06886i) q^{43} +(4.22756 - 6.78645i) q^{44} +(-0.323124 - 2.81863i) q^{46} +4.43823 q^{47} +(3.93123 + 1.34144i) q^{48} +4.06040 q^{49} +(1.39471 + 1.39471i) q^{51} +(-6.22896 - 3.88027i) q^{52} +(-0.481758 + 0.481758i) q^{53} +(-4.49551 + 5.65968i) q^{54} +(1.62828 + 4.56787i) q^{56} -4.25336i q^{57} +(-10.5289 - 8.36311i) q^{58} +(-3.08580 + 3.08580i) q^{59} +(3.46410 + 3.46410i) q^{61} +(10.0006 - 1.14645i) q^{62} -3.29468 q^{63} +(6.19615 - 5.06040i) q^{64} +(-5.83285 + 0.668669i) q^{66} +(-1.80454 - 1.80454i) q^{67} +(3.70023 - 0.859677i) q^{68} +(-1.47309 + 1.47309i) q^{69} +0.379150i q^{71} +(1.82496 + 5.11964i) q^{72} +8.37718i q^{73} +(-2.80144 + 3.52691i) q^{74} +(-6.95303 - 4.33133i) q^{76} +(-4.84668 - 4.84668i) q^{77} +(0.613739 + 5.35369i) q^{78} -11.2566 q^{79} -0.457524 q^{81} +(-0.257114 - 2.24282i) q^{82} +(-8.24890 - 8.24890i) q^{83} +(1.88279 - 3.02242i) q^{84} +(-10.0372 + 12.6365i) q^{86} +9.87341i q^{87} +(-4.84668 + 10.2160i) q^{88} +11.9820i q^{89} +(-4.44854 + 4.44854i) q^{91} +(0.907986 + 3.90816i) q^{92} +(-5.22654 - 5.22654i) q^{93} +(-6.23577 + 0.714859i) q^{94} +(-5.73948 - 1.25154i) q^{96} +6.50543 q^{97} +(-5.70491 + 0.654003i) q^{98} +(-5.43213 - 5.43213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{6} + 8 q^{11} + 4 q^{14} + 16 q^{16} + 8 q^{19} - 16 q^{21} + 32 q^{24} + 32 q^{26} + 16 q^{29} + 16 q^{31} - 48 q^{34} + 60 q^{36} + 8 q^{44} - 28 q^{46} - 16 q^{49} - 16 q^{51} - 40 q^{54}+ \cdots - 88 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^6 + 8 * q^11 + 4 * q^14 + 16 * q^16 + 8 * q^19 - 16 * q^21 + 32 * q^24 + 32 * q^26 + 16 * q^29 + 16 * q^31 - 48 * q^34 + 60 * q^36 + 8 * q^44 - 28 * q^46 - 16 * q^49 - 16 * q^51 - 40 * q^54 - 56 * q^56 + 24 * q^59 + 16 * q^64 - 72 * q^66 - 32 * q^69 - 88 * q^76 - 16 * q^79 - 16 * q^81 + 80 * q^84 - 28 * q^86 - 16 * q^91 - 12 * q^94 + 56 * q^96 - 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.40501	+	0.161069i	−0.993493	+	0.113893i
$2$	−1.40501	+	0.161069i	−0.993493	+	0.113893i
$3$	0.734294	+	0.734294i	0.423945	+	0.423945i	0.886559	−	0.462615i	$-0.153089\pi$
$3$	0.734294	+	0.734294i	0.423945	+	0.423945i	−0.462615	+	0.886559i	$0.653089\pi$
$4$	1.94811	−	0.452606i	0.974057	−	0.226303i
$5$		0			0
$5$		0			0
$6$	−1.14996	−	0.913419i	−0.469470	−	0.372902i
$7$		−	1.71452i		−	0.648029i	−0.946052	−	0.324015i	$-0.894967\pi$
$7$		−	1.71452i		−	0.648029i	0.946052	−	0.324015i	$-0.105033\pi$
$8$	−2.66422	+	0.949697i	−0.941945	+	0.335768i
$9$		−	1.92163i		−	0.640542i
$10$		0			0
$11$	2.82684	−	2.82684i	0.852324	−	0.852324i	−0.138095	−	0.990419i	$-0.544098\pi$
$11$	2.82684	−	2.82684i	0.852324	−	0.852324i	0.990419	+	0.138095i	$0.0440980\pi$
$12$	1.76283	+	1.09814i	0.508886	+	0.317006i
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	0.248909	−	0.968527i	$-0.419928\pi$
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	−0.968527	+	0.248909i	$0.919928\pi$
$14$	0.276156	+	2.40893i	0.0738058	+	0.643813i
$15$		0			0
$16$	3.59030	−	1.76346i	0.897574	−	0.440864i
$17$	1.89939			0.460671			0.230335	−	0.973111i	$-0.426018\pi$
$17$	1.89939			0.460671			0.230335	+	0.973111i	$0.426018\pi$
$18$	0.309513	+	2.69991i	0.0729530	+	0.636374i
$19$	−2.89623	−	2.89623i	−0.664440	−	0.664440i	0.291983	−	0.956423i	$-0.405685\pi$
$19$	−2.89623	−	2.89623i	−0.664440	−	0.664440i	−0.956423	+	0.291983i	$0.905685\pi$
$20$		0			0
$21$	1.25896	−	1.25896i	0.274729	−	0.274729i
$22$	−3.51643	+	4.42705i	−0.749704	+	0.943851i
$23$			2.00613i			0.418306i	0.977883	+	0.209153i	$0.0670707\pi$
$23$			2.00613i			0.418306i	−0.977883	+	0.209153i	$0.932929\pi$
$24$	−2.65368	−	1.25896i	−0.541680	−	0.256985i
$25$		0			0
$26$	4.06338	+	3.22756i	0.796895	+	0.632976i
$27$	3.61392	−	3.61392i	0.695499	−	0.695499i
$28$	−0.776005	−	3.34009i	−0.146651	−	0.631218i
$29$	6.72307	+	6.72307i	1.24844	+	1.24844i	0.956408	+	0.292034i	$0.0943321\pi$
$29$	6.72307	+	6.72307i	1.24844	+	1.24844i	0.292034	+	0.956408i	$0.405668\pi$
$30$		0			0
$31$	−7.11778			−1.27839			−0.639195	−	0.769044i	$-0.720732\pi$
$31$	−7.11778			−1.27839			−0.639195	+	0.769044i	$0.720732\pi$
$32$	−4.76037	+	3.05596i	−0.841522	+	0.540223i
$33$	4.15146			0.722676
$34$	−2.66867	+	0.305932i	−0.457673	+	0.0524670i
$35$		0			0
$36$	−0.869740	−	3.74355i	−0.144957	−	0.623924i
$37$	2.25207	−	2.25207i	0.370237	−	0.370237i	−0.497326	−	0.867564i	$-0.665685\pi$
$37$	2.25207	−	2.25207i	0.370237	−	0.370237i	0.867564	+	0.497326i	$0.165685\pi$
$38$	4.53572	+	3.60274i	0.735792	+	0.584442i
$39$		−	3.81042i		−	0.610156i
$40$		0			0
$41$			1.59630i			0.249301i	0.992201	+	0.124650i	$0.0397809\pi$
$41$			1.59630i			0.249301i	−0.992201	+	0.124650i	$0.960219\pi$
$42$	−1.56608	+	1.97164i	−0.241651	+	0.304231i
$43$	8.06886	−	8.06886i	1.23049	−	1.23049i	0.266715	−	0.963776i	$-0.414062\pi$
$43$	8.06886	−	8.06886i	1.23049	−	1.23049i	0.963776	−	0.266715i	$-0.0859381\pi$
$44$	4.22756	−	6.78645i	0.637328	−	1.02310i
$45$		0			0
$46$	−0.323124	−	2.81863i	−0.0476420	−	0.415585i
$47$	4.43823			0.647383			0.323691	−	0.946163i	$-0.395076\pi$
$47$	4.43823			0.647383			0.323691	+	0.946163i	$0.395076\pi$
$48$	3.93123	+	1.34144i	0.567424	+	0.193620i
$49$	4.06040			0.580058
$50$		0			0
$51$	1.39471	+	1.39471i	0.195299	+	0.195299i
$52$	−6.22896	−	3.88027i	−0.863801	−	0.538097i
$53$	−0.481758	+	0.481758i	−0.0661746	+	0.0661746i	−0.739420	−	0.673245i	$-0.764900\pi$
$53$	−0.481758	+	0.481758i	−0.0661746	+	0.0661746i	0.673245	+	0.739420i	$0.264900\pi$
$54$	−4.49551	+	5.65968i	−0.611761	+	0.770186i
$55$		0			0
$56$	1.62828	+	4.56787i	0.217588	+	0.610408i
$57$		−	4.25336i		−	0.563372i
$58$	−10.5289	−	8.36311i	−1.38251	−	1.09813i
$59$	−3.08580	+	3.08580i	−0.401737	+	0.401737i	−0.878845	−	0.477108i	$-0.841685\pi$
$59$	−3.08580	+	3.08580i	−0.401737	+	0.401737i	0.477108	+	0.878845i	$0.341685\pi$
$60$		0			0
$61$	3.46410	+	3.46410i	0.443533	+	0.443533i	0.893197	−	0.449665i	$-0.148457\pi$
$61$	3.46410	+	3.46410i	0.443533	+	0.443533i	−0.449665	+	0.893197i	$0.648457\pi$
$62$	10.0006	−	1.14645i	1.27007	−	0.145599i
$63$	−3.29468			−0.415090
$64$	6.19615	−	5.06040i	0.774519	−	0.632551i
$65$		0			0
$66$	−5.83285	+	0.668669i	−0.717974	+	0.0823075i
$67$	−1.80454	−	1.80454i	−0.220460	−	0.220460i	0.588232	−	0.808692i	$-0.299824\pi$
$67$	−1.80454	−	1.80454i	−0.220460	−	0.220460i	−0.808692	+	0.588232i	$0.799824\pi$
$68$	3.70023	−	0.859677i	0.448719	−	0.104251i
$69$	−1.47309	+	1.47309i	−0.177339	+	0.177339i
$70$		0			0
$71$			0.379150i			0.0449969i	0.999747	+	0.0224984i	$0.00716208\pi$
$71$			0.379150i			0.0449969i	−0.999747	+	0.0224984i	$0.992838\pi$
$72$	1.82496	+	5.11964i	0.215074	+	0.603355i
$73$			8.37718i			0.980475i	0.871589	+	0.490237i	$0.163090\pi$
$73$			8.37718i			0.980475i	−0.871589	+	0.490237i	$0.836910\pi$
$74$	−2.80144	+	3.52691i	−0.325661	+	0.409995i
$75$		0			0
$76$	−6.95303	−	4.33133i	−0.797567	−	0.496838i
$77$	−4.84668	−	4.84668i	−0.552331	−	0.552331i
$78$	0.613739	+	5.35369i	0.0694923	+	0.606186i
$79$	−11.2566			−1.26646			−0.633231	−	0.773963i	$-0.718272\pi$
$79$	−11.2566			−1.26646			−0.633231	+	0.773963i	$0.718272\pi$
$80$		0			0
$81$	−0.457524			−0.0508360
$82$	−0.257114	−	2.24282i	−0.0283935	−	0.247678i
$83$	−8.24890	−	8.24890i	−0.905435	−	0.905435i	0.0904649	−	0.995900i	$-0.471165\pi$
$83$	−8.24890	−	8.24890i	−0.905435	−	0.905435i	−0.995900	+	0.0904649i	$0.971165\pi$
$84$	1.88279	−	3.02242i	0.205429	−	0.329773i
$85$		0			0
$86$	−10.0372	+	12.6365i	−1.08234	+	1.36263i
$87$			9.87341i			1.05854i
$88$	−4.84668	+	10.2160i	−0.516658	+	1.08903i
$89$			11.9820i			1.27009i	0.772474	+	0.635046i	$0.219019\pi$
$89$			11.9820i			1.27009i	−0.772474	+	0.635046i	$0.780981\pi$
$90$		0			0
$91$	−4.44854	+	4.44854i	−0.466334	+	0.466334i
$92$	0.907986	+	3.90816i	0.0946640	+	0.407454i
$93$	−5.22654	−	5.22654i	−0.541967	−	0.541967i
$94$	−6.23577	+	0.714859i	−0.643170	+	0.0737321i
$95$		0			0
$96$	−5.73948	−	1.25154i	−0.585783	−	0.127734i
$97$	6.50543			0.660526			0.330263	−	0.943889i	$-0.392863\pi$
$97$	6.50543			0.660526			0.330263	+	0.943889i	$0.392863\pi$
$98$	−5.70491	+	0.654003i	−0.576283	+	0.0660643i
$99$	−5.43213	−	5.43213i	−0.545949	−	0.545949i
$100$		0			0
$101$	−6.72307	+	6.72307i	−0.668970	+	0.668970i	−0.957478	−	0.288508i	$-0.906841\pi$
$101$	−6.72307	+	6.72307i	−0.668970	+	0.668970i	0.288508	+	0.957478i	$0.406841\pi$
$102$	−2.18423	−	1.73494i	−0.216271	−	0.171785i
$103$			15.1733i			1.49506i	0.664225	+	0.747532i	$0.268762\pi$
$103$			15.1733i			1.49506i	−0.664225	+	0.747532i	$0.731238\pi$
$104$	9.37674	+	4.44854i	0.919465	+	0.436215i
$105$		0			0
$106$	0.599280	−	0.754472i	0.0582072	−	0.0732808i
$107$	−1.69781	+	1.69781i	−0.164134	+	0.164134i	−0.784395	−	0.620262i	$-0.787026\pi$
$107$	−1.69781	+	1.69781i	−0.164134	+	0.164134i	0.620262	+	0.784395i	$0.287026\pi$
$108$	5.40464	−	8.67601i	0.520062	−	0.834849i
$109$	−3.11120	−	3.11120i	−0.297999	−	0.297999i	0.542231	−	0.840230i	$-0.317580\pi$
$109$	−3.11120	−	3.11120i	−0.297999	−	0.297999i	−0.840230	+	0.542231i	$0.817580\pi$
$110$		0			0
$111$	3.30735			0.313920
$112$	−3.02349	−	6.15565i	−0.285693	−	0.581654i
$113$	15.8259			1.48877			0.744387	−	0.667748i	$-0.232742\pi$
$113$	15.8259			1.48877			0.744387	+	0.667748i	$0.232742\pi$
$114$	0.685083	+	5.97602i	0.0641639	+	0.559706i
$115$		0			0
$116$	16.1402	+	10.0544i	1.49858	+	0.933527i
$117$	−4.98589	+	4.98589i	−0.460946	+	0.460946i
$118$	3.83856	−	4.83261i	0.353368	−	0.444878i
$119$		−	3.25656i		−	0.298528i
$120$		0			0
$121$		−	4.98203i		−	0.452912i
$122$	−5.42506	−	4.30914i	−0.491162	−	0.390132i
$123$	−1.17216	+	1.17216i	−0.105690	+	0.105690i
$124$	−13.8662	+	3.22155i	−1.24523	+	0.289304i
$125$		0			0
$126$	4.62906	−	0.530669i	0.412389	−	0.0472757i
$127$	−18.3239			−1.62598			−0.812991	−	0.582276i	$-0.802162\pi$
$127$	−18.3239			−1.62598			−0.812991	+	0.582276i	$0.802162\pi$
$128$	−7.89059	+	8.10793i	−0.697436	+	0.716647i
$129$	11.8498			1.04332
$130$		0			0
$131$	−10.2036	−	10.2036i	−0.891491	−	0.891491i	0.103172	−	0.994663i	$-0.467101\pi$
$131$	−10.2036	−	10.2036i	−0.891491	−	0.891491i	−0.994663	+	0.103172i	$0.967101\pi$
$132$	8.08751	−	1.87898i	0.703928	−	0.163544i
$133$	−4.96565	+	4.96565i	−0.430577	+	0.430577i
$134$	2.82606	+	2.24475i	0.244134	+	0.193917i
$135$		0			0
$136$	−5.06040	+	1.80385i	−0.433926	+	0.154679i
$137$			14.9845i			1.28021i	0.768286	+	0.640107i	$0.221110\pi$
$137$			14.9845i			1.28021i	−0.768286	+	0.640107i	$0.778890\pi$
$138$	1.83244	−	2.30697i	0.155987	−	0.196382i
$139$	8.29094	−	8.29094i	0.703228	−	0.703228i	−0.261874	−	0.965102i	$-0.584340\pi$
$139$	8.29094	−	8.29094i	0.703228	−	0.703228i	0.965102	+	0.261874i	$0.0843404\pi$
$140$		0			0
$141$	3.25896	+	3.25896i	0.274454	+	0.274454i
$142$	−0.0610692	−	0.532711i	−0.00512481	−	0.0447041i
$143$	−14.6691			−1.22670
$144$	−3.38870	−	6.89920i	−0.282392	−	0.574934i
$145$		0			0
$146$	−1.34930	−	11.7700i	−0.111669	−	0.974095i
$147$	2.98153	+	2.98153i	0.245912	+	0.245912i
$148$	3.36798	−	5.40658i	0.276846	−	0.444418i
$149$	7.30735	−	7.30735i	0.598642	−	0.598642i	−0.341309	−	0.939951i	$-0.610870\pi$
$149$	7.30735	−	7.30735i	0.598642	−	0.598642i	0.939951	+	0.341309i	$0.110870\pi$
$150$		0			0
$151$		−	4.56873i		−	0.371798i	−0.982569	−	0.185899i	$-0.940480\pi$
$151$		−	4.56873i		−	0.371798i	0.982569	−	0.185899i	$-0.0595197\pi$
$152$	10.4667	+	4.96565i	0.848964	+	0.402768i
$153$		−	3.64992i		−	0.295079i
$154$	7.59030	+	6.02900i	0.611643	+	0.485831i
$155$		0			0
$156$	−1.72462	−	7.42314i	−0.138080	−	0.594327i
$157$	1.52966	+	1.52966i	0.122080	+	0.122080i	0.765507	−	0.643427i	$-0.222488\pi$
$157$	1.52966	+	1.52966i	0.122080	+	0.122080i	−0.643427	+	0.765507i	$0.722488\pi$
$158$	15.8156	−	1.81308i	1.25822	−	0.144241i
$159$	−0.707504			−0.0561087
$160$		0			0
$161$	3.43955			0.271075
$162$	0.642827	−	0.0736928i	0.0505053	−	0.00578985i
$163$	10.1361	+	10.1361i	0.793918	+	0.793918i	0.982129	−	0.188211i	$-0.0602689\pi$
$163$	10.1361	+	10.1361i	0.793918	+	0.793918i	−0.188211	+	0.982129i	$0.560269\pi$
$164$	0.722497	+	3.10978i	0.0564175	+	0.242833i
$165$		0			0
$166$	12.9184	+	10.2612i	1.00267	+	0.796421i
$167$		−	2.57967i		−	0.199621i	−0.995006	−	0.0998105i	$-0.968176\pi$
$167$		−	2.57967i		−	0.199621i	0.995006	−	0.0998105i	$-0.0318237\pi$
$168$	−2.15853	+	4.54979i	−0.166534	+	0.351024i
$169$			0.464102i			0.0357001i
$170$		0			0
$171$	−5.56547	+	5.56547i	−0.425602	+	0.425602i
$172$	12.0670	−	19.3711i	0.920104	−	1.47703i
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.996700	−	0.0811779i	$-0.974132\pi$
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.0811779	−	0.996700i	$-0.525868\pi$
$174$	−1.59030	−	13.8723i	−0.120560	−	1.05165i
$175$		0			0
$176$	5.16418	−	15.1342i	0.389264	−	1.14078i
$177$	−4.53177			−0.340629
$178$	−1.92993	−	16.8349i	−0.144654	−	1.26183i
$179$	9.88067	+	9.88067i	0.738516	+	0.738516i	0.972291	−	0.233775i	$-0.0751079\pi$
$179$	9.88067	+	9.88067i	0.738516	+	0.738516i	−0.233775	+	0.972291i	$0.575108\pi$
$180$		0			0
$181$	6.20514	−	6.20514i	0.461224	−	0.461224i	−0.437832	−	0.899057i	$-0.644254\pi$
$181$	6.20514	−	6.20514i	0.461224	−	0.461224i	0.899057	+	0.437832i	$0.144254\pi$
$182$	5.53373	−	6.96677i	0.410187	−	0.516411i
$183$			5.08733i			0.376067i
$184$	−1.90521	−	5.34477i	−0.140454	−	0.394021i
$185$		0			0
$186$	8.18518	+	6.50152i	0.600166	+	0.476714i
$187$	5.36928	−	5.36928i	0.392641	−	0.392641i
$188$	8.64618	−	2.00877i	0.630587	−	0.146505i
$189$	−6.19615	−	6.19615i	−0.450704	−	0.450704i
$190$		0			0
$191$	18.9282			1.36960			0.684798	−	0.728733i	$-0.259890\pi$
$191$	18.9282			1.36960			0.684798	+	0.728733i	$0.259890\pi$
$192$	8.26562	+	0.833972i	0.596520	+	0.0601868i
$193$	4.42987			0.318869			0.159434	−	0.987209i	$-0.449033\pi$
$193$	4.42987			0.318869			0.159434	+	0.987209i	$0.449033\pi$
$194$	−9.14020	+	1.04782i	−0.656228	+	0.0752291i
$195$		0			0
$196$	7.91013	−	1.83776i	0.565009	−	0.131269i
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	−0.897179	−	0.441667i	$-0.854387\pi$
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	0.441667	+	0.897179i	$0.354387\pi$
$198$	8.50714	+	6.75725i	0.604576	+	0.480217i
$199$			5.85641i			0.415150i	0.978219	+	0.207575i	$0.0665570\pi$
$199$			5.85641i			0.415150i	−0.978219	+	0.207575i	$0.933443\pi$
$200$		0			0
$201$		−	2.65013i		−	0.186926i
$202$	8.36311	−	10.5289i	0.588426	−	0.740808i
$203$	11.5269	−	11.5269i	0.809027	−	0.809027i
$204$	3.34831	+	2.08580i	0.234429	+	0.146035i
$205$		0			0
$206$	−2.44393	−	21.3186i	−0.170277	−	1.48534i
$207$	3.85503			0.267943
$208$	−13.8910	−	4.73995i	−0.963164	−	0.328656i
$209$	−16.3743			−1.13264
$210$		0			0
$211$	7.60373	+	7.60373i	0.523462	+	0.523462i	0.918615	−	0.395153i	$-0.129308\pi$
$211$	7.60373	+	7.60373i	0.523462	+	0.523462i	−0.395153	+	0.918615i	$0.629308\pi$
$212$	−0.720473	+	1.15657i	−0.0494823	+	0.0794334i
$213$	−0.278408	+	0.278408i	−0.0190762	+	0.0190762i
$214$	2.11198	−	2.65891i	0.144372	−	0.181759i
$215$		0			0
$216$	−6.19615	+	13.0604i	−0.421595	+	0.888648i
$217$			12.2036i			0.828435i
$218$	4.87239	+	3.87016i	0.330000	+	0.262120i
$219$	−6.15131	+	6.15131i	−0.415667	+	0.415667i
$220$		0			0
$221$	−4.92820	−	4.92820i	−0.331507	−	0.331507i
$222$	−4.64687	+	0.532711i	−0.311877	+	0.0357532i
$223$	9.22430			0.617705			0.308853	−	0.951110i	$-0.400055\pi$
$223$	9.22430			0.617705			0.308853	+	0.951110i	$0.400055\pi$
$224$	5.23952	+	8.16177i	0.350080	+	0.545331i
$225$		0			0
$226$	−22.2356	+	2.54905i	−1.47909	+	0.169560i
$227$	−9.21725	−	9.21725i	−0.611770	−	0.611770i	0.331637	−	0.943407i	$-0.392399\pi$
$227$	−9.21725	−	9.21725i	−0.611770	−	0.611770i	−0.943407	+	0.331637i	$0.892399\pi$
$228$	−1.92510	−	8.28603i	−0.127493	−	0.548756i
$229$	−1.63811	+	1.63811i	−0.108250	+	0.108250i	−0.759157	−	0.650907i	$-0.774389\pi$
$229$	−1.63811	+	1.63811i	−0.108250	+	0.108250i	0.650907	+	0.759157i	$0.274389\pi$
$230$		0			0
$231$		−	7.11778i		−	0.468315i
$232$	−24.2966	−	11.5269i	−1.59515	−	0.756776i
$233$			12.3798i			0.811026i	0.914089	+	0.405513i	$0.132907\pi$
$233$			12.3798i			0.811026i	−0.914089	+	0.405513i	$0.867093\pi$
$234$	6.20216	−	7.80830i	0.405448	−	0.510445i
$235$		0			0
$236$	−4.61484	+	7.40815i	−0.300401	+	0.482229i
$237$	−8.26562	−	8.26562i	−0.536910	−	0.536910i
$238$	0.524529	+	4.57550i	0.0340002	+	0.296586i
$239$	7.77449			0.502890			0.251445	−	0.967872i	$-0.419094\pi$
$239$	7.77449			0.502890			0.251445	+	0.967872i	$0.419094\pi$
$240$		0			0
$241$	−3.47068			−0.223566			−0.111783	−	0.993733i	$-0.535656\pi$
$241$	−3.47068			−0.223566			−0.111783	+	0.993733i	$0.535656\pi$
$242$	0.802448	+	6.99981i	0.0515833	+	0.449965i
$243$	−11.1777	−	11.1777i	−0.717051	−	0.717051i
$244$	8.31634	+	5.18059i	0.532399	+	0.331653i
$245$		0			0
$246$	1.45809	−	1.83569i	0.0929647	−	0.117039i
$247$			15.0292i			0.956286i
$248$	18.9633	−	6.75973i	1.20417	−	0.429243i
$249$		−	12.1142i		−	0.767708i
$250$		0			0
$251$	8.94765	−	8.94765i	0.564771	−	0.564771i	−0.365888	−	0.930659i	$-0.619235\pi$
$251$	8.94765	−	8.94765i	0.564771	−	0.564771i	0.930659	+	0.365888i	$0.119235\pi$
$252$	−6.41840	+	1.49119i	−0.404321	+	0.0939362i
$253$	5.67100	+	5.67100i	0.356533	+	0.356533i
$254$	25.7453	−	2.95140i	1.61540	−	0.185187i
$255$		0			0
$256$	9.78044	−	12.6627i	0.611277	−	0.791416i
$257$	−3.62228			−0.225952			−0.112976	−	0.993598i	$-0.536038\pi$
$257$	−3.62228			−0.225952			−0.112976	+	0.993598i	$0.536038\pi$
$258$	−16.6491	+	1.90863i	−1.03653	+	0.118826i
$259$	−3.86122	−	3.86122i	−0.239925	−	0.239925i
$260$		0			0
$261$	12.9192	−	12.9192i	0.799680	−	0.799680i
$262$	15.9796	+	12.6927i	0.987224	+	0.784156i
$263$			13.7416i			0.847345i	0.905815	+	0.423673i	$0.139259\pi$
$263$			13.7416i			0.847345i	−0.905815	+	0.423673i	$0.860741\pi$
$264$	−11.0604	+	3.94263i	−0.680721	+	0.242652i
$265$		0			0
$266$	6.17699	−	7.77661i	0.378736	−	0.476815i
$267$	−8.79833	+	8.79833i	−0.538449	+	0.538449i
$268$	−4.33221	−	2.69871i	−0.264632	−	0.164850i
$269$	4.22240	+	4.22240i	0.257444	+	0.257444i	0.824014	−	0.566570i	$-0.191730\pi$
$269$	4.22240	+	4.22240i	0.257444	+	0.257444i	−0.566570	+	0.824014i	$0.691730\pi$
$270$		0			0
$271$	−5.40015			−0.328036			−0.164018	−	0.986457i	$-0.552445\pi$
$271$	−5.40015			−0.328036			−0.164018	+	0.986457i	$0.552445\pi$
$272$	6.81938	−	3.34950i	0.413486	−	0.203093i
$273$	−6.53307			−0.395399
$274$	−2.41353	−	21.0534i	−0.145807	−	1.27188i
$275$		0			0
$276$	−2.20301	+	3.53647i	−0.132606	+	0.212870i
$277$	5.08733	−	5.08733i	0.305668	−	0.305668i	−0.537558	−	0.843227i	$-0.680653\pi$
$277$	5.08733	−	5.08733i	0.305668	−	0.305668i	0.843227	+	0.537558i	$0.180653\pi$
$278$	−10.3135	+	12.9843i	−0.618560	+	0.778745i
$279$			13.6777i			0.818863i
$280$		0			0
$281$			21.2780i			1.26934i	0.772784	+	0.634669i	$0.218864\pi$
$281$			21.2780i			1.26934i	−0.772784	+	0.634669i	$0.781136\pi$
$282$	−5.10380	−	4.05397i	−0.303927	−	0.241410i
$283$	4.08521	−	4.08521i	0.242840	−	0.242840i	−0.575184	−	0.818024i	$-0.695069\pi$
$283$	4.08521	−	4.08521i	0.242840	−	0.242840i	0.818024	+	0.575184i	$0.195069\pi$
$284$	0.171606	+	0.738628i	0.0101829	+	0.0438295i
$285$		0			0
$286$	20.6103	−	2.36274i	1.21871	−	0.139712i
$287$	2.73690			0.161554
$288$	5.87241	+	9.14765i	0.346035	+	0.539030i
$289$	−13.3923			−0.787783
$290$		0			0
$291$	4.77689	+	4.77689i	0.280026	+	0.280026i
$292$	3.79156	+	16.3197i	0.221884	+	0.955038i
$293$	−7.40400	+	7.40400i	−0.432547	+	0.432547i	−0.889494	−	0.456947i	$-0.848943\pi$
$293$	−7.40400	+	7.40400i	−0.432547	+	0.432547i	0.456947	+	0.889494i	$0.348943\pi$
$294$	−4.66931	−	3.70885i	−0.272320	−	0.216305i
$295$		0			0
$296$	−3.86122	+	8.13878i	−0.224429	+	0.473057i
$297$		−	20.4319i		−	1.18558i
$298$	−9.08993	+	11.4439i	−0.526566	+	0.662927i
$299$	5.20514	−	5.20514i	0.301021	−	0.301021i
$300$		0			0
$301$	−13.8343	−	13.8343i	−0.797394	−	0.797394i
$302$	0.735878	+	6.41911i	0.0423450	+	0.369378i
$303$	−9.87341			−0.567212
$304$	−15.5057	−	5.29094i	−0.889312	−	0.303456i
$305$		0			0
$306$	0.587888	+	5.12818i	0.0336073	+	0.293159i
$307$	16.6634	+	16.6634i	0.951030	+	0.951030i	0.998856	−	0.0478262i	$-0.0152294\pi$
$307$	16.6634	+	16.6634i	0.951030	+	0.951030i	−0.0478262	+	0.998856i	$0.515229\pi$
$308$	−11.6355	−	7.24825i	−0.662996	−	0.413008i
$309$	−11.1416	+	11.1416i	−0.633825	+	0.633825i
$310$		0			0
$311$			21.9072i			1.24224i	0.783714	+	0.621122i	$0.213323\pi$
$311$			21.9072i			1.24224i	−0.783714	+	0.621122i	$0.786677\pi$
$312$	3.61875	+	10.1518i	0.204871	+	0.574733i
$313$			12.4820i			0.705525i	0.935713	+	0.352763i	$0.114758\pi$
$313$			12.4820i			0.705525i	−0.935713	+	0.352763i	$0.885242\pi$
$314$	−2.39556	−	1.90280i	−0.135189	−	0.107381i
$315$		0			0
$316$	−21.9291	+	5.09479i	−1.23361	+	0.286604i
$317$	4.24325	+	4.24325i	0.238324	+	0.238324i	0.816156	−	0.577832i	$-0.196101\pi$
$317$	4.24325	+	4.24325i	0.238324	+	0.238324i	−0.577832	+	0.816156i	$0.696101\pi$
$318$	0.994051	−	0.113957i	0.0557436	−	0.00639037i
$319$	38.0100			2.12815
$320$		0			0
$321$	−2.49338			−0.139167
$322$	−4.83261	+	0.554004i	−0.269311	+	0.0308734i
$323$	−5.50108	−	5.50108i	−0.306088	−	0.306088i
$324$	−0.891310	+	0.207078i	−0.0495172	+	0.0115044i
$325$		0			0
$326$	−15.8739	−	12.6087i	−0.879173	−	0.698330i
$327$		−	4.56907i		−	0.252670i
$328$	−1.51600	−	4.25290i	−0.0837073	−	0.234827i
$329$		−	7.60946i		−	0.419523i
$330$		0			0
$331$	1.10377	−	1.10377i	0.0606688	−	0.0606688i	−0.676121	−	0.736790i	$-0.736341\pi$
$331$	1.10377	−	1.10377i	0.0606688	−	0.0606688i	0.736790	+	0.676121i	$0.236341\pi$
$332$	−19.8033	−	12.3363i	−1.08685	−	0.677042i
$333$	−4.32763	−	4.32763i	−0.237152	−	0.237152i
$334$	0.415504	+	3.62447i	0.0227354	+	0.198322i
$335$		0			0
$336$	2.29992	−	6.74018i	0.125471	−	0.367707i
$337$	7.47635			0.407263			0.203631	−	0.979048i	$-0.434726\pi$
$337$	7.47635			0.407263			0.203631	+	0.979048i	$0.434726\pi$
$338$	−0.0747522	−	0.652068i	−0.00406598	−	0.0354678i
$339$	11.6208	+	11.6208i	0.631158	+	0.631158i
$340$		0			0
$341$	−20.1208	+	20.1208i	−1.08960	+	1.08960i
$342$	6.92312	−	8.71597i	0.374360	−	0.471305i
$343$		−	18.9633i		−	1.02392i
$344$	−13.8343	+	29.1602i	−0.745894	+	1.57221i
$345$		0			0
$346$	22.2027	+	17.6357i	1.19363	+	0.948102i
$347$	8.56074	−	8.56074i	0.459565	−	0.459565i	−0.438948	−	0.898512i	$-0.644649\pi$
$347$	8.56074	−	8.56074i	0.459565	−	0.459565i	0.898512	+	0.438948i	$0.144649\pi$
$348$	4.46877	+	19.2345i	0.239551	+	1.03108i
$349$	−7.91567	−	7.91567i	−0.423716	−	0.423716i	0.462765	−	0.886481i	$-0.346857\pi$
$349$	−7.91567	−	7.91567i	−0.423716	−	0.423716i	−0.886481	+	0.462765i	$0.846857\pi$
$350$		0			0
$351$	−18.7535			−1.00099
$352$	−4.81809	+	22.0955i	−0.256805	+	1.17769i
$353$	−9.67314			−0.514849			−0.257425	−	0.966298i	$-0.582874\pi$
$353$	−9.67314			−0.514849			−0.257425	+	0.966298i	$0.582874\pi$
$354$	6.36719	−	0.729926i	0.338412	−	0.0387951i
$355$		0			0
$356$	5.42314	+	23.3424i	0.287426	+	1.23714i
$357$	2.39127	−	2.39127i	0.126559	−	0.126559i
$358$	−15.4739	−	12.2910i	−0.817822	−	0.649599i
$359$		−	17.0867i		−	0.901799i	−0.892575	−	0.450900i	$-0.851103\pi$
$359$		−	17.0867i		−	0.901799i	0.892575	−	0.450900i	$-0.148897\pi$
$360$		0			0
$361$		−	2.22373i		−	0.117038i
$362$	−7.71884	+	9.71774i	−0.405693	+	0.510753i
$363$	3.65827	−	3.65827i	0.192010	−	0.192010i
$364$	−6.65283	+	10.6797i	−0.348703	+	0.559768i
$365$		0			0
$366$	−0.819410	−	7.14776i	−0.0428312	−	0.373620i
$367$	13.4500			0.702086			0.351043	−	0.936359i	$-0.385827\pi$
$367$	13.4500			0.702086			0.351043	+	0.936359i	$0.385827\pi$
$368$	3.53772	+	7.20259i	0.184416	+	0.375461i
$369$	3.06750			0.159688
$370$		0			0
$371$	0.825987	+	0.825987i	0.0428831	+	0.0428831i
$372$	−12.5475	−	7.81633i	−0.650555	−	0.405258i
$373$	12.0271	−	12.0271i	0.622740	−	0.622740i	−0.323491	−	0.946231i	$-0.604857\pi$
$373$	12.0271	−	12.0271i	0.622740	−	0.622740i	0.946231	+	0.323491i	$0.104857\pi$
$374$	−6.67908	+	8.40872i	−0.345367	+	0.434804i
$375$		0			0
$376$	−11.8244	+	4.21497i	−0.609798	+	0.217371i
$377$		−	34.8876i		−	1.79680i
$378$	9.70367	+	7.70766i	0.499103	+	0.396439i
$379$	−19.1552	+	19.1552i	−0.983936	+	0.983936i	−0.999873	−	0.0159369i	$-0.994927\pi$
$379$	−19.1552	+	19.1552i	−0.983936	+	0.983936i	0.0159369	+	0.999873i	$0.494927\pi$
$380$		0			0
$381$	−13.4551	−	13.4551i	−0.689327	−	0.689327i
$382$	−26.5943	+	3.04874i	−1.36068	+	0.155987i
$383$	17.7503			0.907000			0.453500	−	0.891256i	$-0.350175\pi$
$383$	17.7503			0.907000			0.453500	+	0.891256i	$0.350175\pi$
$384$	−11.7476	+	0.159590i	−0.599493	+	0.00814406i
$385$		0			0
$386$	−6.22401	+	0.713512i	−0.316794	+	0.0363168i
$387$	−15.5053	−	15.5053i	−0.788181	−	0.788181i
$388$	12.6733	−	2.94440i	0.643390	−	0.149479i
$389$	1.18654	−	1.18654i	0.0601602	−	0.0601602i	−0.676387	−	0.736547i	$-0.736455\pi$
$389$	1.18654	−	1.18654i	0.0601602	−	0.0601602i	0.736547	+	0.676387i	$0.236455\pi$
$390$		0			0
$391$			3.81042i			0.192701i
$392$	−10.8178	+	3.85615i	−0.546382	+	0.194765i
$393$		−	14.9848i		−	0.755886i
$394$	7.95303	−	10.0126i	0.400668	−	0.504427i
$395$		0			0
$396$	−13.0410	−	8.12379i	−0.655336	−	0.408236i
$397$	4.74478	+	4.74478i	0.238134	+	0.238134i	0.816077	−	0.577943i	$-0.196145\pi$
$397$	4.74478	+	4.74478i	0.238134	+	0.238134i	−0.577943	+	0.816077i	$0.696145\pi$
$398$	−0.943283	−	8.22832i	−0.0472825	−	0.412448i
$399$	−7.29250			−0.365081
$400$		0			0
$401$	0.632677			0.0315944			0.0157972	−	0.999875i	$-0.494971\pi$
$401$	0.632677			0.0315944			0.0157972	+	0.999875i	$0.494971\pi$
$402$	0.426853	+	3.72346i	0.0212895	+	0.185709i
$403$	18.4679	+	18.4679i	0.919953	+	0.919953i
$404$	−10.0544	+	16.1402i	−0.500225	+	0.803005i
$405$		0			0
$406$	−14.3388	+	18.0520i	−0.711621	+	0.895905i
$407$		−	12.7324i		−	0.631124i
$408$	−5.04038	−	2.39127i	−0.249536	−	0.118385i
$409$		−	26.3809i		−	1.30445i	−0.758024	−	0.652226i	$-0.773835\pi$
$409$		−	26.3809i		−	1.30445i	0.758024	−	0.652226i	$-0.226165\pi$
$410$		0			0
$411$	−11.0030	+	11.0030i	−0.542739	+	0.542739i
$412$	6.86751	+	29.5592i	0.338338	+	1.45628i
$413$	5.29069	+	5.29069i	0.260338	+	0.260338i
$414$	−5.41636	+	0.620923i	−0.266199	+	0.0305167i
$415$		0			0
$416$	20.2804	+	4.42229i	0.994328	+	0.216821i
$417$	12.1760			0.596260
$418$	23.0061	−	2.63739i	1.12527	−	0.128999i
$419$	1.37589	+	1.37589i	0.0672167	+	0.0672167i	0.739916	−	0.672699i	$-0.234865\pi$
$419$	1.37589	+	1.37589i	0.0672167	+	0.0672167i	−0.672699	+	0.739916i	$0.734865\pi$
$420$		0			0
$421$	6.65671	−	6.65671i	0.324428	−	0.324428i	−0.526035	−	0.850463i	$-0.676322\pi$
$421$	6.65671	−	6.65671i	0.324428	−	0.324428i	0.850463	+	0.526035i	$0.176322\pi$
$422$	−11.9081	−	9.45861i	−0.579675	−	0.460438i
$423$		−	8.52862i		−	0.414676i
$424$	0.825987	−	1.74104i	0.0401135	−	0.0845522i
$425$		0			0
$426$	0.346323	−	0.436009i	0.0167794	−	0.0211247i
$427$	5.93929	−	5.93929i	0.287422	−	0.287422i
$428$	−2.53909	+	4.07597i	−0.122731	+	0.197019i
$429$	−10.7715	−	10.7715i	−0.520051	−	0.520051i
$430$		0			0
$431$	4.08798			0.196911			0.0984556	−	0.995141i	$-0.468610\pi$
$431$	4.08798			0.196911			0.0984556	+	0.995141i	$0.468610\pi$
$432$	6.60204	−	19.3480i	0.317641	−	0.930882i
$433$	29.2913			1.40765			0.703826	−	0.710373i	$-0.251474\pi$
$433$	29.2913			1.40765			0.703826	+	0.710373i	$0.251474\pi$
$434$	−1.96562	−	17.1462i	−0.0943526	−	0.823044i
$435$		0			0
$436$	−7.46912	−	4.65283i	−0.357706	−	0.222830i
$437$	5.81020	−	5.81020i	0.277940	−	0.277940i
$438$	7.65188	−	9.63344i	0.365621	−	0.460304i
$439$			26.9790i			1.28764i	0.765178	+	0.643819i	$0.222651\pi$
$439$			26.9790i			1.28764i	−0.765178	+	0.643819i	$0.777349\pi$
$440$		0			0
$441$		−	7.80258i		−	0.371551i
$442$	7.71796	+	6.13040i	0.367106	+	0.291594i
$443$	−14.5286	+	14.5286i	−0.690276	+	0.690276i	−0.962293	−	0.272017i	$-0.912309\pi$
$443$	−14.5286	+	14.5286i	−0.690276	+	0.690276i	0.272017	+	0.962293i	$0.412309\pi$
$444$	6.44310	−	1.49693i	0.305776	−	0.0710411i
$445$		0			0
$446$	−12.9603	+	1.48575i	−0.613686	+	0.0703521i
$447$	10.7315			0.507582
$448$	−8.67619	−	10.6235i	−0.409911	−	0.501911i
$449$	−23.1572			−1.09286			−0.546428	−	0.837506i	$-0.684013\pi$
$449$	−23.1572			−1.09286			−0.546428	+	0.837506i	$0.684013\pi$
$450$		0			0
$451$	4.51249	+	4.51249i	0.212485	+	0.212485i
$452$	30.8306	−	7.16290i	1.45015	−	0.336914i
$453$	3.35479	−	3.35479i	0.157622	−	0.157622i
$454$	14.4349	+	11.4657i	0.677466	+	0.538113i
$455$		0			0
$456$	4.03940	+	11.3319i	0.189162	+	0.530665i
$457$			37.7026i			1.76365i	0.471572	+	0.881827i	$0.343687\pi$
$457$			37.7026i			1.76365i	−0.471572	+	0.881827i	$0.656313\pi$
$458$	2.03772	−	2.56542i	0.0952165	−	0.119874i
$459$	6.86425	−	6.86425i	0.320396	−	0.320396i
$460$		0			0
$461$	11.3737	+	11.3737i	0.529727	+	0.529727i	0.920491	−	0.390764i	$-0.127789\pi$
$461$	11.3737	+	11.3737i	0.529727	+	0.529727i	−0.390764	+	0.920491i	$0.627789\pi$
$462$	1.14645	+	10.0006i	0.0533377	+	0.465268i
$463$	−7.94895			−0.369419			−0.184710	−	0.982793i	$-0.559134\pi$
$463$	−7.94895			−0.369419			−0.184710	+	0.982793i	$0.559134\pi$
$464$	35.9936	+	12.2820i	1.67096	+	0.570175i
$465$		0			0
$466$	−1.99399	−	17.3937i	−0.0923699	−	0.805749i
$467$	−5.34999	−	5.34999i	−0.247568	−	0.247568i	0.572404	−	0.819972i	$-0.306011\pi$
$467$	−5.34999	−	5.34999i	−0.247568	−	0.247568i	−0.819972	+	0.572404i	$0.806011\pi$
$468$	−7.45643	+	11.9697i	−0.344674	+	0.553301i
$469$	−3.09394	+	3.09394i	−0.142865	+	0.142865i
$470$		0			0
$471$			2.24643i			0.103510i
$472$	5.29069	−	11.1518i	0.243524	−	0.513305i
$473$		−	45.6187i		−	2.09755i
$474$	12.9446	+	10.2820i	0.594566	+	0.472266i
$475$		0			0
$476$	−1.47394	−	6.34414i	−0.0675578	−	0.290783i
$477$	0.925759	+	0.925759i	0.0423876	+	0.0423876i
$478$	−10.9232	+	1.25222i	−0.499617	+	0.0572754i
$479$	9.58973			0.438166			0.219083	−	0.975706i	$-0.429693\pi$
$479$	9.58973			0.438166			0.219083	+	0.975706i	$0.429693\pi$
$480$		0			0
$481$	−11.6865			−0.532859
$482$	4.87634	−	0.559017i	0.222111	−	0.0254625i
$483$	2.52564	+	2.52564i	0.114921	+	0.114921i
$484$	−2.25490	−	9.70556i	−0.102495	−	0.441162i
$485$		0			0
$486$	17.5052	+	13.9044i	0.794052	+	0.630718i
$487$		−	36.6487i		−	1.66071i	−0.557232	−	0.830357i	$-0.688137\pi$
$487$		−	36.6487i		−	1.66071i	0.557232	−	0.830357i	$-0.311863\pi$
$488$	−12.5190	−	5.93929i	−0.566708	−	0.268859i
$489$			14.8857i			0.673154i
$490$		0			0
$491$	23.4273	−	23.4273i	1.05726	−	1.05726i	0.0590019	−	0.998258i	$-0.481208\pi$
$491$	23.4273	−	23.4273i	1.05726	−	1.05726i	0.998258	−	0.0590019i	$-0.0187918\pi$
$492$	−1.75297	+	2.81402i	−0.0790298	+	0.126866i
$493$	12.7697	+	12.7697i	0.575120	+	0.575120i
$494$	−2.42073	−	21.1162i	−0.108914	−	0.950064i
$495$		0			0
$496$	−25.5549	+	12.5519i	−1.14745	+	0.563597i
$497$	0.650063			0.0291593
$498$	1.95122	+	17.0206i	0.0874363	+	0.762713i
$499$	9.50152	+	9.50152i	0.425346	+	0.425346i	0.887040	−	0.461693i	$-0.152758\pi$
$499$	9.50152	+	9.50152i	0.425346	+	0.425346i	−0.461693	+	0.887040i	$0.652758\pi$
$500$		0			0
$501$	1.89424	−	1.89424i	0.0846283	−	0.0846283i
$502$	−11.1304	+	14.0127i	−0.496772	+	0.625419i
$503$		−	20.6875i		−	0.922411i	−0.887293	−	0.461206i	$-0.847417\pi$
$503$		−	20.6875i		−	0.922411i	0.887293	−	0.461206i	$-0.152583\pi$
$504$	8.77775	−	3.12894i	0.390992	−	0.139374i
$505$		0			0
$506$	−8.88124	−	7.05440i	−0.394819	−	0.313606i
$507$	−0.340787	+	0.340787i	−0.0151349	+	0.0151349i
$508$	−35.6970	+	8.29351i	−1.58380	+	0.367965i
$509$	−11.6381	−	11.6381i	−0.515850	−	0.515850i	0.400463	−	0.916313i	$-0.368849\pi$
$509$	−11.6381	−	11.6381i	−0.515850	−	0.515850i	−0.916313	+	0.400463i	$0.868849\pi$
$510$		0			0
$511$	14.3629			0.635377
$512$	−11.7021	+	19.3665i	−0.517163	+	0.855887i
$513$	−20.9335			−0.924235
$514$	5.08935	−	0.583436i	0.224482	−	0.0257343i
$515$		0			0
$516$	23.0848	−	5.36331i	1.01625	−	0.236106i
$517$	12.5462	−	12.5462i	0.551780	−	0.551780i
$518$	6.04698	+	4.80314i	0.265689	+	0.211038i
$519$		−	20.8205i		−	0.913921i
$520$		0			0
$521$		−	5.18654i		−	0.227227i	−0.993525	−	0.113613i	$-0.963758\pi$
$521$		−	5.18654i		−	0.227227i	0.993525	−	0.113613i	$-0.0362425\pi$
$522$	−16.0708	+	20.2325i	−0.703398	+	0.885554i
$523$	−26.9589	+	26.9589i	−1.17883	+	1.17883i	−0.198788	+	0.980043i	$0.563700\pi$
$523$	−26.9589	+	26.9589i	−1.17883	+	1.17883i	−0.980043	+	0.198788i	$0.936300\pi$
$524$	−24.4959	−	15.2595i	−1.07011	−	0.666616i
$525$		0			0
$526$	−2.21334	−	19.3071i	−0.0965064	−	0.841832i
$527$	−13.5195			−0.588917
$528$	14.9050	−	7.32092i	0.648655	−	0.318602i
$529$	18.9755			0.825020
$530$		0			0
$531$	5.92976	+	5.92976i	0.257330	+	0.257330i
$532$	−7.42617	+	11.9211i	−0.321965	+	0.516847i
$533$	4.14180	−	4.14180i	0.179401	−	0.179401i
$534$	10.9446	−	13.7789i	0.473620	−	0.596271i
$535$		0			0
$536$	6.52148	+	3.09394i	0.281685	+	0.133638i
$537$			14.5106i			0.626179i
$538$	−6.61262	−	5.25243i	−0.285090	−	0.226448i
$539$	11.4781	−	11.4781i	0.494397	−	0.494397i
$540$		0			0
$541$	27.4945	+	27.4945i	1.18208	+	1.18208i	0.979204	+	0.202878i	$0.0650294\pi$
$541$	27.4945	+	27.4945i	1.18208	+	1.18208i	0.202878	+	0.979204i	$0.434971\pi$
$542$	7.58727	−	0.869794i	0.325901	−	0.0373609i
$543$	9.11278			0.391067
$544$	−9.04181	+	5.80447i	−0.387664	+	0.248865i
$545$		0			0
$546$	9.17903	−	1.05227i	0.392826	−	0.0450331i
$547$	22.5197	+	22.5197i	0.962873	+	0.962873i	0.999335	−	0.0364619i	$-0.0116088\pi$
$547$	22.5197	+	22.5197i	0.962873	+	0.962873i	−0.0364619	+	0.999335i	$0.511609\pi$
$548$	6.78208	+	29.1915i	0.289716	+	1.24700i
$549$	6.65671	−	6.65671i	0.284101	−	0.284101i
$550$		0			0
$551$		−	38.9431i		−	1.65903i
$552$	2.52564	−	5.32361i	0.107499	−	0.226588i
$553$			19.2996i			0.820704i
$554$	−6.32835	+	7.96717i	−0.268866	+	0.338493i
$555$		0			0
$556$	12.3992	−	19.9042i	0.525842	−	0.844127i
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	0.935424	−	0.353527i	$-0.115018\pi$
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	−0.353527	+	0.935424i	$0.615018\pi$
$558$	−2.20305	−	19.2173i	−0.0932625	−	0.813535i
$559$	−41.8713			−1.77097
$560$		0			0
$561$	7.88525			0.332916
$562$	−3.42721	−	29.8958i	−0.144568	−	1.26108i
$563$	0.229223	+	0.229223i	0.00966061	+	0.00966061i	0.711921	−	0.702260i	$-0.247826\pi$
$563$	0.229223	+	0.229223i	0.00966061	+	0.00966061i	−0.702260	+	0.711921i	$0.747826\pi$
$564$	7.82386	+	4.87381i	0.329444	+	0.205224i
$565$		0			0
$566$	−5.08177	+	6.39776i	−0.213603	+	0.268918i
$567$			0.784437i			0.0329433i
$568$	−0.360078	−	1.01014i	−0.0151085	−	0.0423846i
$569$			23.0376i			0.965787i	0.875679	+	0.482894i	$0.160414\pi$
$569$			23.0376i			0.965787i	−0.875679	+	0.482894i	$0.839586\pi$
$570$		0			0
$571$	−11.8610	+	11.8610i	−0.496367	+	0.496367i	−0.910305	−	0.413938i	$-0.864153\pi$
$571$	−11.8610	+	11.8610i	−0.496367	+	0.496367i	0.413938	+	0.910305i	$0.364153\pi$
$572$	−28.5772	+	6.63934i	−1.19487	+	0.277605i
$573$	13.8989	+	13.8989i	0.580633	+	0.580633i
$574$	−3.84538	+	0.440829i	−0.160503	+	0.0183998i
$575$		0			0
$576$	−9.72421	−	11.9067i	−0.405175	−	0.496112i
$577$	−39.7168			−1.65343			−0.826715	−	0.562621i	$-0.809793\pi$
$577$	−39.7168			−1.65343			−0.826715	+	0.562621i	$0.809793\pi$
$578$	18.8163	−	2.15708i	0.782657	−	0.0897226i
$579$	3.25282	+	3.25282i	0.135183	+	0.135183i
$580$		0			0
$581$	−14.1429	+	14.1429i	−0.586748	+	0.586748i
$582$	−7.48100	−	5.94218i	−0.310097	−	0.246311i
$583$			2.72371i			0.112804i
$584$	−7.95578	−	22.3187i	−0.329213	−	0.923553i
$585$		0			0
$586$	9.21016	−	11.5953i	0.380468	−	0.478996i
$587$	−8.63887	+	8.63887i	−0.356564	+	0.356564i	−0.862545	−	0.505980i	$-0.831131\pi$
$587$	−8.63887	+	8.63887i	−0.356564	+	0.356564i	0.505980	+	0.862545i	$0.331131\pi$
$588$	7.15782	+	4.45890i	0.295183	+	0.183882i
$589$	20.6147	+	20.6147i	0.849414	+	0.849414i
$590$		0			0
$591$	−9.38927			−0.386223
$592$	4.11416	−	12.0570i	0.169091	−	0.495540i
$593$	−45.8229			−1.88172			−0.940860	−	0.338795i	$-0.889981\pi$
$593$	−45.8229			−1.88172			−0.940860	+	0.338795i	$0.889981\pi$
$594$	3.29094	+	28.7071i	0.135029	+	1.17787i
$595$		0			0
$596$	10.9282	−	17.5429i	0.447637	−	0.718586i
$597$	−4.30032	+	4.30032i	−0.176000	+	0.176000i
$598$	−6.47489	+	8.15166i	−0.264778	+	0.333346i
$599$			17.0609i			0.697090i	0.937292	+	0.348545i	$0.113324\pi$
$599$			17.0609i			0.697090i	−0.937292	+	0.348545i	$0.886676\pi$
$600$		0			0
$601$		−	38.0363i		−	1.55153i	−0.631020	−	0.775766i	$-0.717364\pi$
$601$		−	38.0363i		−	1.55153i	0.631020	−	0.775766i	$-0.282636\pi$
$602$	21.6656	+	17.2090i	0.883023	+	0.701388i
$603$	−3.46766	+	3.46766i	−0.141214	+	0.141214i
$604$	−2.06783	−	8.90040i	−0.0841390	−	0.362152i
$605$		0			0
$606$	13.8723	−	1.59030i	0.563522	−	0.0646013i
$607$	−8.67169			−0.351973			−0.175987	−	0.984393i	$-0.556312\pi$
$607$	−8.67169			−0.351973			−0.175987	+	0.984393i	$0.556312\pi$
$608$	22.6379	+	4.93635i	0.918087	+	0.200196i
$609$	16.9282			0.685965
$610$		0			0
$611$	−11.5155	−	11.5155i	−0.465868	−	0.465868i
$612$	−1.65198	−	7.11047i	−0.0667773	−	0.287424i
$613$	13.9739	−	13.9739i	0.564401	−	0.564401i	−0.366153	−	0.930554i	$-0.619325\pi$
$613$	13.9739	−	13.9739i	0.564401	−	0.564401i	0.930554	+	0.366153i	$0.119325\pi$
$614$	−26.0962	−	20.7283i	−1.05316	−	0.836526i
$615$		0			0
$616$	17.5155	+	8.30976i	0.705720	+	0.334810i
$617$		−	37.3904i		−	1.50528i	−0.658431	−	0.752641i	$-0.728780\pi$
$617$		−	37.3904i		−	1.50528i	0.658431	−	0.752641i	$-0.271220\pi$
$618$	13.8595	−	17.4487i	0.557512	−	0.701888i
$619$	23.2754	−	23.2754i	0.935516	−	0.935516i	−0.0625269	−	0.998043i	$-0.519916\pi$
$619$	23.2754	−	23.2754i	0.935516	−	0.935516i	0.998043	+	0.0625269i	$0.0199159\pi$
$620$		0			0
$621$	7.24998	+	7.24998i	0.290932	+	0.290932i
$622$	−3.52856	−	30.7799i	−0.141482	−	1.23416i
$623$	20.5435			0.823058
$624$	−6.71952	−	13.6806i	−0.268996	−	0.547660i
$625$		0			0
$626$	−2.01046	−	17.5374i	−0.0803541	−	0.700934i
$627$	−12.0236	−	12.0236i	−0.480175	−	0.480175i
$628$	3.67228	+	2.28761i	0.146540	+	0.0912857i
$629$	4.27756	−	4.27756i	0.170557	−	0.170557i
$630$		0			0
$631$			19.1834i			0.763680i	0.924228	+	0.381840i	$0.124710\pi$
$631$			19.1834i			0.763680i	−0.924228	+	0.381840i	$0.875290\pi$
$632$	29.9900	−	10.6903i	1.19294	−	0.425238i
$633$			11.1667i			0.443838i
$634$	−6.64526	−	5.27835i	−0.263917	−	0.209630i
$635$		0			0
$636$	−1.37830	+	0.320221i	−0.0546531	+	0.0126976i
$637$	−10.5352	−	10.5352i	−0.417420	−	0.417420i
$638$	−53.4045	+	6.12222i	−2.11431	+	0.242381i
$639$	0.728585			0.0288224
$640$		0			0
$641$	−16.1765			−0.638933			−0.319466	−	0.947598i	$-0.603504\pi$
$641$	−16.1765			−0.638933			−0.319466	+	0.947598i	$0.603504\pi$
$642$	3.50323	−	0.401605i	0.138261	−	0.0158501i
$643$	−15.0289	−	15.0289i	−0.592681	−	0.592681i	0.345674	−	0.938355i	$-0.387650\pi$
$643$	−15.0289	−	15.0289i	−0.592681	−	0.592681i	−0.938355	+	0.345674i	$0.887650\pi$
$644$	6.70064	−	1.55676i	0.264042	−	0.0613451i
$645$		0			0
$646$	8.61512	+	6.84302i	0.338958	+	0.269235i
$647$			49.3812i			1.94138i	0.240345	+	0.970688i	$0.422739\pi$
$647$			49.3812i			1.94138i	−0.240345	+	0.970688i	$0.577261\pi$
$648$	1.21895	−	0.434509i	0.0478847	−	0.0170691i
$649$			17.4461i			0.684821i
$650$		0			0
$651$	−8.96103	+	8.96103i	−0.351210	+	0.351210i
$652$	24.3338	+	15.1586i	0.952987	+	0.593655i
$653$	19.8685	+	19.8685i	0.777514	+	0.777514i	0.979408	−	0.201893i	$-0.0647094\pi$
$653$	19.8685	+	19.8685i	0.777514	+	0.777514i	−0.201893	+	0.979408i	$0.564709\pi$
$654$	0.735933	+	6.41960i	0.0287773	+	0.251026i
$655$		0			0
$656$	2.81501	+	5.73120i	0.109908	+	0.223766i
$657$	16.0978			0.628035
$658$	1.22564	+	10.6914i	0.0477806	+	0.416793i
$659$	−4.94765	−	4.94765i	−0.192733	−	0.192733i	0.604143	−	0.796876i	$-0.293516\pi$
$659$	−4.94765	−	4.94765i	−0.192733	−	0.192733i	−0.796876	+	0.604143i	$0.793516\pi$
$660$		0			0
$661$	12.1602	−	12.1602i	0.472977	−	0.472977i	−0.429899	−	0.902877i	$-0.641451\pi$
$661$	12.1602	−	12.1602i	0.472977	−	0.472977i	0.902877	+	0.429899i	$0.141451\pi$
$662$	−1.37303	+	1.72860i	−0.0533643	+	0.0671838i
$663$		−	7.23750i		−	0.281081i
$664$	29.8109	+	14.1429i	1.15689	+	0.548853i
$665$		0			0
$666$	6.77741	+	5.38332i	0.262619	+	0.208599i
$667$	−13.4873	+	13.4873i	−0.522231	+	0.522231i
$668$	−1.16758	−	5.02550i	−0.0451749	−	0.194442i
$669$	6.77335	+	6.77335i	0.261873	+	0.261873i
$670$		0			0
$671$	19.5849			0.756067
$672$	−2.14579	+	9.84048i	−0.0827756	+	0.379605i
$673$	−32.9882			−1.27160			−0.635801	−	0.771853i	$-0.719330\pi$
$673$	−32.9882			−1.27160			−0.635801	+	0.771853i	$0.719330\pi$
$674$	−10.5044	+	1.20420i	−0.404613	+	0.0463842i
$675$		0			0
$676$	0.210055	+	0.904123i	0.00807905	+	0.0347740i
$677$	−18.4610	+	18.4610i	−0.709513	+	0.709513i	−0.966433	−	0.256920i	$-0.917292\pi$
$677$	−18.4610	+	18.4610i	−0.709513	+	0.709513i	0.256920	+	0.966433i	$0.417292\pi$
$678$	−18.1992	−	14.4557i	−0.698935	−	0.555167i
$679$		−	11.1537i		−	0.428040i
$680$		0			0
$681$		−	13.5363i		−	0.518713i
$682$	25.0291	−	31.5108i	0.958415	−	1.20661i
$683$	−12.2374	+	12.2374i	−0.468251	+	0.468251i	−0.901347	−	0.433097i	$-0.857421\pi$
$683$	−12.2374	+	12.2374i	−0.468251	+	0.468251i	0.433097	+	0.901347i	$0.357421\pi$
$684$	−8.32320	+	13.3611i	−0.318245	+	0.510875i
$685$		0			0
$686$	3.05440	+	26.6437i	0.116617	+	1.01726i
$687$	−2.40571			−0.0917837
$688$	14.7405	−	43.1987i	0.561977	−	1.64693i
$689$	2.49996			0.0952409
$690$		0			0
$691$	−9.46014	−	9.46014i	−0.359881	−	0.359881i	0.503888	−	0.863769i	$-0.331902\pi$
$691$	−9.46014	−	9.46014i	−0.359881	−	0.359881i	−0.863769	+	0.503888i	$0.831902\pi$
$692$	−34.0356	−	21.2022i	−1.29384	−	0.805987i
$693$	−9.31352	+	9.31352i	−0.353791	+	0.353791i
$694$	−10.6491	+	13.4068i	−0.404233	+	0.508915i
$695$		0			0
$696$	−9.37674	−	26.3049i	−0.355425	−	0.997086i
$697$			3.03201i			0.114845i
$698$	12.3966	+	9.84664i	0.469217	+	0.372701i
$699$	−9.09039	+	9.09039i	−0.343830	+	0.343830i
$700$		0			0
$701$	−5.14714	−	5.14714i	−0.194405	−	0.194405i	0.603192	−	0.797596i	$-0.293895\pi$
$701$	−5.14714	−	5.14714i	−0.194405	−	0.194405i	−0.797596	+	0.603192i	$0.793895\pi$
$702$	26.3489	−	3.02060i	0.994474	−	0.114005i
$703$	−13.0450			−0.492001
$704$	3.21058	−	31.8205i	0.121003	−	1.19928i
$705$		0			0
$706$	13.5909	−	1.55804i	0.511499	−	0.0586375i
$707$	11.5269	+	11.5269i	0.433512	+	0.433512i
$708$	−8.82840	+	2.05111i	−0.331792	+	0.0770853i
$709$	18.0125	−	18.0125i	0.676472	−	0.676472i	−0.282728	−	0.959200i	$-0.591239\pi$
$709$	18.0125	−	18.0125i	0.676472	−	0.676472i	0.959200	+	0.282728i	$0.0912395\pi$
$710$		0			0
$711$			21.6309i			0.811222i
$712$	−11.3793	−	31.9228i	−0.426457	−	1.19636i
$713$		−	14.2792i		−	0.534759i
$714$	−2.97460	+	3.74492i	−0.111322	+	0.140150i
$715$		0			0
$716$	23.7207	+	14.7766i	0.886485	+	0.552228i
$717$	5.70875	+	5.70875i	0.213197	+	0.213197i
$718$	2.75212	+	24.0069i	0.102708	+	0.895931i
$719$	−34.5017			−1.28669			−0.643347	−	0.765574i	$-0.722455\pi$
$719$	−34.5017			−1.28669			−0.643347	+	0.765574i	$0.722455\pi$
$720$		0			0
$721$	26.0149			0.968846
$722$	0.358173	+	3.12437i	0.0133298	+	0.116277i
$723$	−2.54850	−	2.54850i	−0.0947796	−	0.0947796i
$724$	9.27983	−	14.8968i	0.344882	−	0.553635i
$725$		0			0
$726$	−4.55068	+	5.72915i	−0.168892	+	0.212629i
$727$		−	12.8421i		−	0.476288i	−0.971230	−	0.238144i	$-0.923461\pi$
$727$		−	12.8421i		−	0.476288i	0.971230	−	0.238144i	$-0.0765391\pi$
$728$	7.62713	−	16.0767i	0.282680	−	0.595841i
$729$		−	15.0429i		−	0.557143i
$730$		0			0
$731$	15.3259	−	15.3259i	0.566851	−	0.566851i
$732$	2.30256	+	9.91071i	0.0851050	+	0.366310i
$733$	24.1490	+	24.1490i	0.891965	+	0.891965i	0.994708	−	0.102743i	$-0.0327618\pi$
$733$	24.1490	+	24.1490i	0.891965	+	0.891965i	−0.102743	+	0.994708i	$0.532762\pi$
$734$	−18.8974	+	2.16638i	−0.697517	+	0.0799624i
$735$		0			0
$736$	−6.13065	−	9.54990i	−0.225979	−	0.352014i
$737$	−10.2023			−0.375807
$738$	−4.30987	+	0.494077i	−0.158648	+	0.0181872i
$739$	−35.9398	−	35.9398i	−1.32207	−	1.32207i	−0.912101	−	0.409966i	$-0.865540\pi$
$739$	−35.9398	−	35.9398i	−1.32207	−	1.32207i	−0.409966	−	0.912101i	$-0.634460\pi$
$740$		0			0
$741$	−11.0359	+	11.0359i	−0.405412	+	0.405412i
$742$	−1.29356	−	1.02748i	−0.0474881	−	0.0377200i
$743$		−	45.9502i		−	1.68575i	−0.538109	−	0.842875i	$-0.680861\pi$
$743$		−	45.9502i		−	1.68575i	0.538109	−	0.842875i	$-0.319139\pi$
$744$	18.8883	+	8.96103i	0.692478	+	0.328527i
$745$		0			0
$746$	−14.9610	+	18.8354i	−0.547762	+	0.689613i
$747$	−15.8513	+	15.8513i	−0.579969	+	0.579969i
$748$	8.02980	−	12.8901i	0.293598	−	0.471310i
$749$	2.91094	+	2.91094i	0.106363	+	0.106363i
$750$		0			0
$751$	−24.4820			−0.893361			−0.446680	−	0.894694i	$-0.647394\pi$
$751$	−24.4820			−0.893361			−0.446680	+	0.894694i	$0.647394\pi$
$752$	15.9346	−	7.82663i	0.581074	−	0.285408i
$753$	13.1404			0.478863
$754$	5.61929	+	49.0175i	0.204643	+	1.78511i
$755$		0			0
$756$	−14.8752	−	9.26639i	−0.541007	−	0.337015i
$757$	17.0328	−	17.0328i	0.619067	−	0.619067i	−0.326225	−	0.945292i	$-0.605777\pi$
$757$	17.0328	−	17.0328i	0.619067	−	0.619067i	0.945292	+	0.326225i	$0.105777\pi$
$758$	23.8280	−	29.9986i	0.865471	−	1.08960i
$759$			8.32835i			0.302300i
$760$		0			0
$761$			8.53590i			0.309426i	0.987959	+	0.154713i	$0.0494453\pi$
$761$			8.53590i			0.309426i	−0.987959	+	0.154713i	$0.950555\pi$
$762$	21.0718	+	16.7374i	0.763350	+	0.606332i
$763$	−5.33423	+	5.33423i	−0.193112	+	0.193112i
$764$	36.8743	−	8.56702i	1.33407	−	0.309944i
$765$		0			0
$766$	−24.9394	+	2.85902i	−0.901099	+	0.103301i
$767$	16.0130			0.578195
$768$	16.4798	−	2.11640i	0.594664	−	0.0763689i
$769$	1.87438			0.0675917			0.0337959	−	0.999429i	$-0.489240\pi$
$769$	1.87438			0.0675917			0.0337959	+	0.999429i	$0.489240\pi$
$770$		0			0
$771$	−2.65982	−	2.65982i	−0.0957911	−	0.0957911i
$772$	8.62988	−	2.00498i	0.310596	−	0.0721610i
$773$	−21.5374	+	21.5374i	−0.774645	+	0.774645i	−0.978915	−	0.204270i	$-0.934518\pi$
$773$	−21.5374	+	21.5374i	−0.774645	+	0.774645i	0.204270	+	0.978915i	$0.434518\pi$
$774$	24.2826	+	19.2878i	0.872820	+	0.693284i
$775$		0			0
$776$	−17.3319	+	6.17818i	−0.622179	+	0.221784i
$777$		−	5.67054i		−	0.203429i
$778$	−1.47599	+	1.85822i	−0.0529169	+	0.0666205i
$779$	4.62326	−	4.62326i	0.165645	−	0.165645i
$780$		0			0
$781$	1.07180	+	1.07180i	0.0383519	+	0.0383519i
$782$	−0.613739	−	5.35369i	−0.0219473	−	0.191448i
$783$	48.5932			1.73658
$784$	14.5781	−	7.16035i	0.520645	−	0.255727i
$785$		0			0
$786$	2.41359	+	21.0539i	0.0860898	+	0.750967i
$787$	7.03687	+	7.03687i	0.250837	+	0.250837i	0.821314	−	0.570477i	$-0.193241\pi$
$787$	7.03687	+	7.03687i	0.250837	+	0.250837i	−0.570477	+	0.821314i	$0.693241\pi$
$788$	−9.56139	+	15.3488i	−0.340610	+	0.546778i
$789$	−10.0904	+	10.0904i	−0.359227	+	0.359227i
$790$		0			0
$791$		−	27.1339i		−	0.964770i
$792$	19.6313	+	9.31352i	0.697566	+	0.330941i
$793$		−	17.9761i		−	0.638348i
$794$	−7.43071	−	5.90224i	−0.263706	−	0.209463i
$795$		0			0
$796$	2.65065	+	11.4089i	0.0939497	+	0.404379i
$797$	8.07933	+	8.07933i	0.286185	+	0.286185i	0.835569	−	0.549385i	$-0.185138\pi$
$797$	8.07933	+	8.07933i	0.286185	+	0.286185i	−0.549385	+	0.835569i	$0.685138\pi$
$798$	10.2460	−	1.17459i	0.362706	−	0.0415801i
$799$	8.42995			0.298230
$800$		0			0
$801$	23.0250			0.813548
$802$	−0.888918	+	0.101904i	−0.0313888	+	0.00359837i
$803$	23.6809	+	23.6809i	0.835682	+	0.835682i
$804$	−1.19947	−	5.16276i	−0.0423019	−	0.182076i
$805$		0			0
$806$	−28.9222	−	22.9730i	−1.01874	−	0.809191i
$807$			6.20097i			0.218284i
$808$	11.5269	−	24.2966i	0.405514	−	0.854752i
$809$		−	5.40185i		−	0.189919i	−0.995481	−	0.0949595i	$-0.969728\pi$
$809$		−	5.40185i		−	0.189919i	0.995481	−	0.0949595i	$-0.0302722\pi$
$810$		0			0
$811$	−10.3478	+	10.3478i	−0.363360	+	0.363360i	−0.865049	−	0.501688i	$-0.832712\pi$
$811$	−10.3478	+	10.3478i	−0.363360	+	0.363360i	0.501688	+	0.865049i	$0.332712\pi$
$812$	17.2385	−	27.6728i	0.604953	−	0.971124i
$813$	−3.96530	−	3.96530i	−0.139069	−	0.139069i
$814$	2.05080	+	17.8892i	0.0718804	+	0.627017i
$815$		0			0
$816$	7.46694	+	2.54791i	0.261395	+	0.0891948i
$817$	−46.7385			−1.63517
$818$	4.24913	+	37.0655i	0.148568	+	1.29596i
$819$	8.54843	+	8.54843i	0.298706	+	0.298706i
$820$		0			0
$821$	10.7321	−	10.7321i	0.374551	−	0.374551i	−0.494581	−	0.869132i	$-0.664678\pi$
$821$	10.7321	−	10.7321i	0.374551	−	0.374551i	0.869132	+	0.494581i	$0.164678\pi$
$822$	13.6871	−	17.2316i	0.477394	−	0.601022i
$823$		−	3.51588i		−	0.122556i	−0.998121	−	0.0612780i	$-0.980482\pi$
$823$		−	3.51588i		−	0.122556i	0.998121	−	0.0612780i	$-0.0195176\pi$
$824$	−14.4100	−	40.4249i	−0.501996	−	1.40827i
$825$		0			0
$826$	−8.28564	−	6.58131i	−0.288294	−	0.228993i
$827$	−27.7375	+	27.7375i	−0.964529	+	0.964529i	−0.999392	−	0.0348631i	$-0.988900\pi$
$827$	−27.7375	+	27.7375i	−0.964529	+	0.964529i	0.0348631	+	0.999392i	$0.488900\pi$
$828$	7.51003	−	1.74481i	0.260992	−	0.0606363i
$829$	19.5849	+	19.5849i	0.680212	+	0.680212i	0.960048	−	0.279836i	$-0.0902800\pi$
$829$	19.5849	+	19.5849i	0.680212	+	0.680212i	−0.279836	+	0.960048i	$0.590280\pi$
$830$		0			0
$831$	7.47119			0.259173
$832$	−29.2065	−	2.94683i	−1.01255	−	0.102163i
$833$	7.71231			0.267216
$834$	−17.1074	+	1.96117i	−0.592380	+	0.0679096i
$835$		0			0
$836$	−31.8991	+	7.41113i	−1.10325	+	0.256319i
$837$	−25.7231	+	25.7231i	−0.889119	+	0.889119i
$838$	−2.15476	−	1.71153i	−0.0744348	−	0.0591238i
$839$		−	40.0520i		−	1.38275i	−0.722496	−	0.691375i	$-0.757005\pi$
$839$		−	40.0520i		−	1.38275i	0.722496	−	0.691375i	$-0.242995\pi$
$840$		0			0
$841$			61.3992i			2.11722i
$842$	−8.28056	+	10.4249i	−0.285367	+	0.359267i
$843$	−15.6243	+	15.6243i	−0.538129	+	0.538129i
$844$	18.2544	+	11.3714i	0.628343	+	0.391421i
$845$		0			0
$846$	1.37369	+	11.9828i	0.0472285	+	0.411977i
$847$	−8.54182			−0.293500
$848$	−0.880095	+	2.57922i	−0.0302226	+	0.0885706i
$849$	5.99948			0.205902
$850$		0			0
$851$	4.51793	+	4.51793i	0.154873	+	0.154873i
$852$	−0.416361	+	0.668379i	−0.0142643	+	0.0228983i
$853$	13.7328	−	13.7328i	0.470202	−	0.470202i	−0.431778	−	0.901980i	$-0.642114\pi$
$853$	13.7328	−	13.7328i	0.470202	−	0.470202i	0.901980	+	0.431778i	$0.142114\pi$
$854$	−7.38814	+	9.30140i	−0.252817	+	0.318287i
$855$		0			0
$856$	2.91094	−	6.13575i	0.0994938	−	0.209716i
$857$			39.9485i			1.36462i	0.731065	+	0.682308i	$0.239024\pi$
$857$			39.9485i			1.36462i	−0.731065	+	0.682308i	$0.760976\pi$
$858$	16.8690	+	13.3991i	0.575897	+	0.457437i
$859$	−33.6366	+	33.6366i	−1.14766	+	1.14766i	−0.160654	+	0.987011i	$0.551360\pi$
$859$	−33.6366	+	33.6366i	−1.14766	+	1.14766i	−0.987011	+	0.160654i	$0.948640\pi$
$860$		0			0
$861$	2.00969	+	2.00969i	0.0684900	+	0.0684900i
$862$	−5.74366	+	0.658445i	−0.195630	+	0.0224267i
$863$	−16.5303			−0.562697			−0.281349	−	0.959606i	$-0.590782\pi$
$863$	−16.5303			−0.562697			−0.281349	+	0.959606i	$0.590782\pi$
$864$	−6.15959	+	28.2476i	−0.209554	+	0.961002i
$865$		0			0
$866$	−41.1546	+	4.71791i	−1.39849	+	0.160321i
$867$	−9.83388	−	9.83388i	−0.333976	−	0.333976i
$868$	5.52343	+	23.7740i	0.187477	+	0.806943i
$869$	−31.8205	+	31.8205i	−1.07944	+	1.07944i
$870$		0			0
$871$			9.36421i			0.317294i
$872$	11.2436	+	5.33423i	0.380757	+	0.180640i
$873$		−	12.5010i		−	0.423095i
$874$	−7.22756	+	9.09924i	−0.244476	+	0.307786i
$875$		0			0
$876$	−9.19933	+	14.7676i	−0.310817	+	0.498950i
$877$	−9.66381	−	9.66381i	−0.326324	−	0.326324i	0.524863	−	0.851187i	$-0.324117\pi$
$877$	−9.66381	−	9.66381i	−0.326324	−	0.326324i	−0.851187	+	0.524863i	$0.824117\pi$
$878$	−4.34547	−	37.9058i	−0.146652	−	1.27926i
$879$	−10.8734			−0.366752
$880$		0			0
$881$	−43.4299			−1.46319			−0.731596	−	0.681739i	$-0.761224\pi$
$881$	−43.4299			−1.46319			−0.731596	+	0.681739i	$0.761224\pi$
$882$	1.25675	+	10.9627i	0.0423170	+	0.369134i
$883$	22.3879	+	22.3879i	0.753413	+	0.753413i	0.975115	−	0.221701i	$-0.0711610\pi$
$883$	22.3879	+	22.3879i	0.753413	+	0.753413i	−0.221701	+	0.975115i	$0.571161\pi$
$884$	−11.8312	−	7.37017i	−0.397928	−	0.247885i
$885$		0			0
$886$	18.0728	−	22.7530i	0.607167	−	0.764402i
$887$		−	31.6913i		−	1.06409i	−0.846716	−	0.532045i	$-0.821424\pi$
$887$		−	31.6913i		−	1.06409i	0.846716	−	0.532045i	$-0.178576\pi$
$888$	−8.81152	+	3.14098i	−0.295695	+	0.105404i
$889$			31.4168i			1.05368i
$890$		0			0
$891$	−1.29335	+	1.29335i	−0.0433288	+	0.0433288i
$892$	17.9700	−	4.17498i	0.601680	−	0.139789i
$893$	−12.8541	−	12.8541i	−0.430147	−	0.430147i
$894$	−15.0779	+	1.72850i	−0.504279	+	0.0578098i
$895$		0			0
$896$	13.9012	+	13.5286i	0.464408	+	0.451959i
$897$	7.64420			0.255232
$898$	32.5361	−	3.72989i	1.08574	−	0.124468i
$899$	−47.8533	−	47.8533i	−1.59600	−	1.59600i
$900$		0			0
$901$	−0.915049	+	0.915049i	−0.0304847	+	0.0304847i
$902$	−7.06692	−	5.61328i	−0.235303	−	0.186902i
$903$		−	20.3168i		−	0.676102i
$904$	−42.1637	+	15.0298i	−1.40234	+	0.499884i
$905$		0			0
$906$	−4.17316	+	5.25386i	−0.138644	+	0.174548i
$907$	24.9184	−	24.9184i	0.827401	−	0.827401i	−0.159755	−	0.987157i	$-0.551071\pi$
$907$	24.9184	−	24.9184i	0.827401	−	0.827401i	0.987157	+	0.159755i	$0.0510705\pi$
$908$	−22.1280	−	13.7845i	−0.734345	−	0.457454i
$909$	12.9192	+	12.9192i	0.428503	+	0.428503i
$910$		0			0
$911$	−47.0459			−1.55870			−0.779350	−	0.626589i	$-0.784451\pi$
$911$	−47.0459			−1.55870			−0.779350	+	0.626589i	$0.784451\pi$
$912$	−7.50062	−	15.2708i	−0.248370	−	0.505668i
$913$	−46.6366			−1.54345
$914$	−6.07271	−	52.9726i	−0.200867	−	1.75218i
$915$		0			0
$916$	−2.44981	+	3.93266i	−0.0809441	+	0.129939i
$917$	−17.4943	+	17.4943i	−0.577712	+	0.577712i
$918$	−8.53874	+	10.7500i	−0.281820	+	0.354802i
$919$		−	12.5442i		−	0.413796i	−0.978362	−	0.206898i	$-0.933663\pi$
$919$		−	12.5442i		−	0.413796i	0.978362	−	0.206898i	$-0.0663369\pi$
$920$		0			0
$921$			24.4716i			0.806368i
$922$	−17.8121	−	14.1482i	−0.586612	−	0.465948i
$923$	0.983751	−	0.983751i	0.0323806	−	0.0323806i
$924$	−3.22155	−	13.8662i	−0.105981	−	0.456166i
$925$		0			0
$926$	11.1684	−	1.28033i	0.367015	−	0.0420741i
$927$	29.1573			0.957652
$928$	−52.5497	−	11.4588i	−1.72503	−	0.376155i
$929$	26.7421			0.877380			0.438690	−	0.898639i	$-0.355443\pi$
$929$	26.7421			0.877380			0.438690	+	0.898639i	$0.355443\pi$
$930$		0			0
$931$	−11.7599	−	11.7599i	−0.385414	−	0.385414i
$932$	5.60316	+	24.1172i	0.183538	+	0.789986i
$933$	−16.0863	+	16.0863i	−0.526642	+	0.526642i
$934$	8.37851	+	6.65508i	0.274153	+	0.217761i
$935$		0			0
$936$	8.54843	−	18.0186i	0.279414	−	0.588956i
$937$			3.06580i			0.100155i	0.998745	+	0.0500777i	$0.0159469\pi$
$937$			3.06580i			0.100155i	−0.998745	+	0.0500777i	$0.984053\pi$
$938$	3.84868	−	4.84535i	0.125664	−	0.158206i
$939$	−9.16546	+	9.16546i	−0.299104	+	0.299104i
$940$		0			0
$941$	−14.6023	−	14.6023i	−0.476020	−	0.476020i	0.427836	−	0.903856i	$-0.359276\pi$
$941$	−14.6023	−	14.6023i	−0.476020	−	0.476020i	−0.903856	+	0.427836i	$0.859276\pi$
$942$	−0.361830	−	3.15626i	−0.0117890	−	0.102837i
$943$	−3.20239			−0.104284
$944$	−5.63726	+	16.5206i	−0.183477	+	0.537701i
$945$		0			0
$946$	7.34774	+	64.0949i	0.238896	+	2.08390i
$947$	−29.4872	−	29.4872i	−0.958204	−	0.958204i	0.0409570	−	0.999161i	$-0.486959\pi$
$947$	−29.4872	−	29.4872i	−0.958204	−	0.958204i	−0.999161	+	0.0409570i	$0.986959\pi$
$948$	−19.8434	−	12.3613i	−0.644485	−	0.401476i
$949$	21.7356	−	21.7356i	0.705567	−	0.705567i
$950$		0			0
$951$			6.23158i			0.202073i
$952$	3.09274	+	8.67619i	0.100236	+	0.281197i
$953$			33.6807i			1.09103i	0.838103	+	0.545513i	$0.183665\pi$
$953$			33.6807i			1.09103i	−0.838103	+	0.545513i	$0.816335\pi$
$954$	−1.44981	−	1.15159i	−0.0469394	−	0.0372842i
$955$		0			0
$956$	15.1456	−	3.51878i	0.489843	−	0.113805i
$957$	27.9105	+	27.9105i	0.902219	+	0.902219i
$958$	−13.4737	+	1.54460i	−0.435315	+	0.0499039i
$959$	25.6913			0.829616
$960$		0			0
$961$	19.6628			0.634283
$962$	16.4197	−	1.88233i	0.529391	−	0.0606887i
$963$	3.26256	+	3.26256i	0.105134	+	0.105134i
$964$	−6.76128	+	1.57085i	−0.217766	+	0.0505937i
$965$		0			0
$966$	−3.95536	−	3.14176i	−0.127262	−	0.101084i
$967$		−	8.70089i		−	0.279802i	−0.990166	−	0.139901i	$-0.955322\pi$
$967$		−	8.70089i		−	0.279802i	0.990166	−	0.139901i	$-0.0446784\pi$
$968$	4.73142	+	13.2732i	0.152074	+	0.426618i
$969$		−	8.07881i		−	0.259529i
$970$		0			0
$971$	−5.87523	+	5.87523i	−0.188545	+	0.188545i	−0.795067	−	0.606522i	$-0.792564\pi$
$971$	−5.87523	+	5.87523i	−0.188545	+	0.188545i	0.606522	+	0.795067i	$0.292564\pi$
$972$	−26.8346	−	16.7164i	−0.860719	−	0.536177i
$973$	−14.2150	−	14.2150i	−0.455713	−	0.455713i
$974$	5.90296	+	51.4919i	0.189143	+	1.64991i
$975$		0			0
$976$	18.5459	+	6.32835i	0.593641	+	0.202566i
$977$	41.8541			1.33903			0.669516	−	0.742798i	$-0.266502\pi$
$977$	41.8541			1.33903			0.669516	+	0.742798i	$0.266502\pi$
$978$	−2.39762	−	20.9146i	−0.0766673	−	0.668774i
$979$	33.8713	+	33.8713i	1.08253	+	1.08253i
$980$		0			0
$981$	−5.97856	+	5.97856i	−0.190881	+	0.190881i
$982$	−29.1422	+	36.6890i	−0.929966	+	1.17079i
$983$			57.4539i			1.83250i	0.400612	+	0.916248i	$0.368797\pi$
$983$			57.4539i			1.83250i	−0.400612	+	0.916248i	$0.631203\pi$
$984$	2.00969	−	4.23607i	0.0640665	−	0.135041i
$985$		0			0
$986$	−19.9984	−	15.8848i	−0.636880	−	0.505876i
$987$	5.58758	−	5.58758i	0.177854	−	0.177854i
$988$	6.80232	+	29.2786i	0.216411	+	0.931477i
$989$	16.1872	+	16.1872i	0.514722	+	0.514722i
$990$		0			0
$991$	12.8205			0.407258			0.203629	−	0.979048i	$-0.434726\pi$
$991$	12.8205			0.407258			0.203629	+	0.979048i	$0.434726\pi$
$992$	33.8832	−	21.7516i	1.07579	−	0.690616i
$993$	1.62099			0.0514404
$994$	−0.913345	+	0.104705i	−0.0289696	+	0.00332103i
$995$		0			0
$996$	−5.48298	−	23.5999i	−0.173735	−	0.747792i
$997$	15.0860	−	15.0860i	0.477777	−	0.477777i	−0.426643	−	0.904420i	$-0.640304\pi$
$997$	15.0860	−	15.0860i	0.477777	−	0.477777i	0.904420	+	0.426643i	$0.140304\pi$
$998$	−14.8801	−	11.8193i	−0.471022	−	0.374135i
$999$		−	16.2776i		−	0.514999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.i.301.1		16
4.3	odd	2		1600.2.l.h.401.3		16
5.2	odd	4		80.2.q.c.29.4	✓	16
5.3	odd	4		80.2.q.c.29.5	yes	16
5.4	even	2	inner	400.2.l.i.301.8		16
15.2	even	4		720.2.bm.f.109.5		16
15.8	even	4		720.2.bm.f.109.4		16
16.5	even	4	inner	400.2.l.i.101.1		16
16.11	odd	4		1600.2.l.h.1201.3		16
20.3	even	4		320.2.q.c.209.6		16
20.7	even	4		320.2.q.c.209.3		16
20.19	odd	2		1600.2.l.h.401.6		16
40.3	even	4		640.2.q.f.289.3		16
40.13	odd	4		640.2.q.e.289.6		16
40.27	even	4		640.2.q.f.289.6		16
40.37	odd	4		640.2.q.e.289.3		16
80.3	even	4		640.2.q.f.609.6		16
80.13	odd	4		640.2.q.e.609.3		16
80.27	even	4		320.2.q.c.49.6		16
80.37	odd	4		80.2.q.c.69.5	yes	16
80.43	even	4		320.2.q.c.49.3		16
80.53	odd	4		80.2.q.c.69.4	yes	16
80.59	odd	4		1600.2.l.h.1201.6		16
80.67	even	4		640.2.q.f.609.3		16
80.69	even	4	inner	400.2.l.i.101.8		16
80.77	odd	4		640.2.q.e.609.6		16
240.53	even	4		720.2.bm.f.469.5		16
240.197	even	4		720.2.bm.f.469.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.4	✓	16	5.2	odd	4
80.2.q.c.29.5	yes	16	5.3	odd	4
80.2.q.c.69.4	yes	16	80.53	odd	4
80.2.q.c.69.5	yes	16	80.37	odd	4
320.2.q.c.49.3		16	80.43	even	4
320.2.q.c.49.6		16	80.27	even	4
320.2.q.c.209.3		16	20.7	even	4
320.2.q.c.209.6		16	20.3	even	4
400.2.l.i.101.1		16	16.5	even	4	inner
400.2.l.i.101.8		16	80.69	even	4	inner
400.2.l.i.301.1		16	1.1	even	1	trivial
400.2.l.i.301.8		16	5.4	even	2	inner
640.2.q.e.289.3		16	40.37	odd	4
640.2.q.e.289.6		16	40.13	odd	4
640.2.q.e.609.3		16	80.13	odd	4
640.2.q.e.609.6		16	80.77	odd	4
640.2.q.f.289.3		16	40.3	even	4
640.2.q.f.289.6		16	40.27	even	4
640.2.q.f.609.3		16	80.67	even	4
640.2.q.f.609.6		16	80.3	even	4
720.2.bm.f.109.4		16	15.8	even	4
720.2.bm.f.109.5		16	15.2	even	4
720.2.bm.f.469.4		16	240.197	even	4
720.2.bm.f.469.5		16	240.53	even	4
1600.2.l.h.401.3		16	4.3	odd	2
1600.2.l.h.401.6		16	20.19	odd	2
1600.2.l.h.1201.3		16	16.11	odd	4
1600.2.l.h.1201.6		16	80.59	odd	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40501 + 0.161069i) q^{2} +(0.734294 + 0.734294i) q^{3} +(1.94811 - 0.452606i) q^{4} +(-1.14996 - 0.913419i) q^{6} -1.71452i q^{7} +(-2.66422 + 0.949697i) q^{8} -1.92163i q^{9} +(2.82684 - 2.82684i) q^{11} +(1.76283 + 1.09814i) q^{12} +(-2.59462 - 2.59462i) q^{13} +(0.276156 + 2.40893i) q^{14} +(3.59030 - 1.76346i) q^{16} +1.89939 q^{17} +(0.309513 + 2.69991i) q^{18} +(-2.89623 - 2.89623i) q^{19} +(1.25896 - 1.25896i) q^{21} +(-3.51643 + 4.42705i) q^{22} +2.00613i q^{23} +(-2.65368 - 1.25896i) q^{24} +(4.06338 + 3.22756i) q^{26} +(3.61392 - 3.61392i) q^{27} +(-0.776005 - 3.34009i) q^{28} +(6.72307 + 6.72307i) q^{29} -7.11778 q^{31} +(-4.76037 + 3.05596i) q^{32} +4.15146 q^{33} +(-2.66867 + 0.305932i) q^{34} +(-0.869740 - 3.74355i) q^{36} +(2.25207 - 2.25207i) q^{37} +(4.53572 + 3.60274i) q^{38} -3.81042i q^{39} +1.59630i q^{41} +(-1.56608 + 1.97164i) q^{42} +(8.06886 - 8.06886i) q^{43} +(4.22756 - 6.78645i) q^{44} +(-0.323124 - 2.81863i) q^{46} +4.43823 q^{47} +(3.93123 + 1.34144i) q^{48} +4.06040 q^{49} +(1.39471 + 1.39471i) q^{51} +(-6.22896 - 3.88027i) q^{52} +(-0.481758 + 0.481758i) q^{53} +(-4.49551 + 5.65968i) q^{54} +(1.62828 + 4.56787i) q^{56} -4.25336i q^{57} +(-10.5289 - 8.36311i) q^{58} +(-3.08580 + 3.08580i) q^{59} +(3.46410 + 3.46410i) q^{61} +(10.0006 - 1.14645i) q^{62} -3.29468 q^{63} +(6.19615 - 5.06040i) q^{64} +(-5.83285 + 0.668669i) q^{66} +(-1.80454 - 1.80454i) q^{67} +(3.70023 - 0.859677i) q^{68} +(-1.47309 + 1.47309i) q^{69} +0.379150i q^{71} +(1.82496 + 5.11964i) q^{72} +8.37718i q^{73} +(-2.80144 + 3.52691i) q^{74} +(-6.95303 - 4.33133i) q^{76} +(-4.84668 - 4.84668i) q^{77} +(0.613739 + 5.35369i) q^{78} -11.2566 q^{79} -0.457524 q^{81} +(-0.257114 - 2.24282i) q^{82} +(-8.24890 - 8.24890i) q^{83} +(1.88279 - 3.02242i) q^{84} +(-10.0372 + 12.6365i) q^{86} +9.87341i q^{87} +(-4.84668 + 10.2160i) q^{88} +11.9820i q^{89} +(-4.44854 + 4.44854i) q^{91} +(0.907986 + 3.90816i) q^{92} +(-5.22654 - 5.22654i) q^{93} +(-6.23577 + 0.714859i) q^{94} +(-5.73948 - 1.25154i) q^{96} +6.50543 q^{97} +(-5.70491 + 0.654003i) q^{98} +(-5.43213 - 5.43213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{6} + 8 q^{11} + 4 q^{14} + 16 q^{16} + 8 q^{19} - 16 q^{21} + 32 q^{24} + 32 q^{26} + 16 q^{29} + 16 q^{31} - 48 q^{34} + 60 q^{36} + 8 q^{44} - 28 q^{46} - 16 q^{49} - 16 q^{51} - 40 q^{54}+ \cdots - 88 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^6 + 8 * q^11 + 4 * q^14 + 16 * q^16 + 8 * q^19 - 16 * q^21 + 32 * q^24 + 32 * q^26 + 16 * q^29 + 16 * q^31 - 48 * q^34 + 60 * q^36 + 8 * q^44 - 28 * q^46 - 16 * q^49 - 16 * q^51 - 40 * q^54 - 56 * q^56 + 24 * q^59 + 16 * q^64 - 72 * q^66 - 32 * q^69 - 88 * q^76 - 16 * q^79 - 16 * q^81 + 80 * q^84 - 28 * q^86 - 16 * q^91 - 12 * q^94 + 56 * q^96 - 88 * q^99

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