LMFDB - Embedded newform 720.2.bm.f.469.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(109,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("720.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bm (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:	$5.74922894553$
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^{5} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			469.5
Root			$1.40501 - 0.161069i$ of defining polynomial
Character	$\chi$	$=$	720.469
Dual form			720.2.bm.f.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.161069 - 1.40501i) q^{2} +(-1.94811 - 0.452606i) q^{4} +(1.17216 - 1.90421i) q^{5} +1.71452 q^{7} +(-0.949697 + 2.66422i) q^{8} +(-2.48664 - 1.95361i) q^{10} +(-2.82684 - 2.82684i) q^{11} +(-2.59462 - 2.59462i) q^{13} +(0.276156 - 2.40893i) q^{14} +(3.59030 + 1.76346i) q^{16} +1.89939i q^{17} +(2.89623 - 2.89623i) q^{19} +(-3.14537 + 3.17910i) q^{20} +(-4.42705 + 3.51643i) q^{22} -2.00613 q^{23} +(-2.25207 - 4.46410i) q^{25} +(-4.06338 + 3.22756i) q^{26} +(-3.34009 - 0.776005i) q^{28} +(6.72307 - 6.72307i) q^{29} -7.11778 q^{31} +(3.05596 - 4.76037i) q^{32} +(2.66867 + 0.305932i) q^{34} +(2.00970 - 3.26482i) q^{35} +(2.25207 - 2.25207i) q^{37} +(-3.60274 - 4.53572i) q^{38} +(3.96005 + 4.93133i) q^{40} +1.59630i q^{41} +(-8.06886 + 8.06886i) q^{43} +(4.22756 + 6.78645i) q^{44} +(-0.323124 + 2.81863i) q^{46} +4.43823i q^{47} -4.06040 q^{49} +(-6.63485 + 2.44515i) q^{50} +(3.88027 + 6.22896i) q^{52} +(-0.481758 + 0.481758i) q^{53} +(-8.69642 + 2.06939i) q^{55} +(-1.62828 + 4.56787i) q^{56} +(-8.36311 - 10.5289i) q^{58} +(-3.08580 - 3.08580i) q^{59} +(3.46410 - 3.46410i) q^{61} +(-1.14645 + 10.0006i) q^{62} +(-6.19615 - 5.06040i) q^{64} +(-7.98203 + 1.89939i) q^{65} +(1.80454 + 1.80454i) q^{67} +(0.859677 - 3.70023i) q^{68} +(-4.26341 - 3.34952i) q^{70} +0.379150i q^{71} +8.37718 q^{73} +(-2.80144 - 3.52691i) q^{74} +(-6.95303 + 4.33133i) q^{76} +(-4.84668 - 4.84668i) q^{77} +11.2566 q^{79} +(7.56641 - 4.76963i) q^{80} +(2.24282 + 0.257114i) q^{82} +(8.24890 + 8.24890i) q^{83} +(3.61685 + 2.22640i) q^{85} +(10.0372 + 12.6365i) q^{86} +(10.2160 - 4.84668i) q^{88} -11.9820i q^{89} +(-4.44854 - 4.44854i) q^{91} +(3.90816 + 0.907986i) q^{92} +(6.23577 + 0.714859i) q^{94} +(-2.12019 - 8.90989i) q^{95} -6.50543i q^{97} +(-0.654003 + 5.70491i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 8 q^{5} - 12 q^{10} - 8 q^{11} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 4 q^{20} - 32 q^{26} + 16 q^{29} + 16 q^{31} + 48 q^{34} + 24 q^{35} + 24 q^{40} + 8 q^{44} - 28 q^{46} + 16 q^{49} - 24 q^{50}+ \cdots - 32 q^{95}+O(q^{100}) $ 16 * q - 4 * q^4 + 8 * q^5 - 12 * q^10 - 8 * q^11 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 4 * q^20 - 32 * q^26 + 16 * q^29 + 16 * q^31 + 48 * q^34 + 24 * q^35 + 24 * q^40 + 8 * q^44 - 28 * q^46 + 16 * q^49 - 24 * q^50 + 56 * q^56 + 24 * q^59 - 16 * q^64 + 20 * q^70 - 88 * q^76 + 16 * q^79 - 16 * q^80 + 28 * q^86 - 16 * q^91 + 12 * q^94 - 32 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.161069	−	1.40501i	0.113893	−	0.993493i
$2$	0.161069	−	1.40501i	0.113893	−	0.993493i
$3$		0			0
$3$		0			0
$4$	−1.94811	−	0.452606i	−0.974057	−	0.226303i
$5$	1.17216	−	1.90421i	0.524207	−	0.851591i
$5$	1.17216	−	1.90421i	0.524207	−	0.851591i
$6$		0			0
$7$	1.71452			0.648029			0.324015	−	0.946052i	$-0.394967\pi$
$7$	1.71452			0.648029			0.324015	+	0.946052i	$0.394967\pi$
$8$	−0.949697	+	2.66422i	−0.335768	+	0.941945i
$9$		0			0
$10$	−2.48664	−	1.95361i	−0.786346	−	0.617786i
$11$	−2.82684	−	2.82684i	−0.852324	−	0.852324i	0.138095	−	0.990419i	$-0.455902\pi$
$11$	−2.82684	−	2.82684i	−0.852324	−	0.852324i	−0.990419	+	0.138095i	$0.955902\pi$
$12$		0			0
$13$	−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
$17$			1.89939i			0.460671i	0.973111	+	0.230335i	$0.0739823\pi$
$17$			1.89939i			0.460671i	−0.973111	+	0.230335i	$0.926018\pi$
$18$		0			0
$19$	2.89623	−	2.89623i	0.664440	−	0.664440i	−0.291983	−	0.956423i	$-0.594315\pi$
$19$	2.89623	−	2.89623i	0.664440	−	0.664440i	0.956423	+	0.291983i	$0.0943151\pi$
$20$	−3.14537	+	3.17910i	−0.703326	+	0.710868i
$21$		0			0
$22$	−4.42705	+	3.51643i	−0.943851	+	0.749704i
$23$	−2.00613			−0.418306			−0.209153	−	0.977883i	$-0.567071\pi$
$23$	−2.00613			−0.418306			−0.209153	+	0.977883i	$0.567071\pi$
$24$		0			0
$25$	−2.25207	−	4.46410i	−0.450413	−	0.892820i
$26$	−4.06338	+	3.22756i	−0.796895	+	0.632976i
$27$		0			0
$28$	−3.34009	−	0.776005i	−0.631218	−	0.146651i
$29$	6.72307	−	6.72307i	1.24844	−	1.24844i	0.292034	−	0.956408i	$-0.405668\pi$
$29$	6.72307	−	6.72307i	1.24844	−	1.24844i	0.956408	−	0.292034i	$-0.0943321\pi$
$30$		0			0
$31$	−7.11778			−1.27839			−0.639195	−	0.769044i	$-0.720732\pi$
$31$	−7.11778			−1.27839			−0.639195	+	0.769044i	$0.720732\pi$
$32$	3.05596	−	4.76037i	0.540223	−	0.841522i
$33$		0			0
$34$	2.66867	+	0.305932i	0.457673	+	0.0524670i
$35$	2.00970	−	3.26482i	0.339702	−	0.551856i
$36$		0			0
$37$	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	$0.165685\pi$
$38$	−3.60274	−	4.53572i	−0.584442	−	0.735792i
$39$		0			0
$40$	3.96005	+	4.93133i	0.626139	+	0.779712i
$41$			1.59630i			0.249301i	0.992201	+	0.124650i	$0.0397809\pi$
$41$			1.59630i			0.249301i	−0.992201	+	0.124650i	$0.960219\pi$
$42$		0			0
$43$	−8.06886	+	8.06886i	−1.23049	+	1.23049i	−0.266715	+	0.963776i	$0.585938\pi$
$43$	−8.06886	+	8.06886i	−1.23049	+	1.23049i	−0.963776	+	0.266715i	$0.914062\pi$
$44$	4.22756	+	6.78645i	0.637328	+	1.02310i
$45$		0			0
$46$	−0.323124	+	2.81863i	−0.0476420	+	0.415585i
$47$			4.43823i			0.647383i	0.946163	+	0.323691i	$0.104924\pi$
$47$			4.43823i			0.647383i	−0.946163	+	0.323691i	$0.895076\pi$
$48$		0			0
$49$	−4.06040			−0.580058
$50$	−6.63485	+	2.44515i	−0.938310	+	0.345797i
$51$		0			0
$52$	3.88027	+	6.22896i	0.538097	+	0.863801i
$53$	−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	$0.264900\pi$
$54$		0			0
$55$	−8.69642	+	2.06939i	−1.17263	+	0.279036i
$56$	−1.62828	+	4.56787i	−0.217588	+	0.610408i
$57$		0			0
$58$	−8.36311	−	10.5289i	−1.09813	−	1.38251i
$59$	−3.08580	−	3.08580i	−0.401737	−	0.401737i	0.477108	−	0.878845i	$-0.341685\pi$
$59$	−3.08580	−	3.08580i	−0.401737	−	0.401737i	−0.878845	+	0.477108i	$0.841685\pi$
$60$		0			0
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	−0.449665	−	0.893197i	$-0.648457\pi$
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	0.893197	+	0.449665i	$0.148457\pi$
$62$	−1.14645	+	10.0006i	−0.145599	+	1.27007i
$63$		0			0
$64$	−6.19615	−	5.06040i	−0.774519	−	0.632551i
$65$	−7.98203	+	1.89939i	−0.990049	+	0.235591i
$66$		0			0
$67$	1.80454	+	1.80454i	0.220460	+	0.220460i	0.808692	−	0.588232i	$-0.200176\pi$
$67$	1.80454	+	1.80454i	0.220460	+	0.220460i	−0.588232	+	0.808692i	$0.700176\pi$
$68$	0.859677	−	3.70023i	0.104251	−	0.448719i
$69$		0			0
$70$	−4.26341	−	3.34952i	−0.509575	−	0.400344i
$71$			0.379150i			0.0449969i	0.999747	+	0.0224984i	$0.00716208\pi$
$71$			0.379150i			0.0449969i	−0.999747	+	0.0224984i	$0.992838\pi$
$72$		0			0
$73$	8.37718			0.980475			0.490237	−	0.871589i	$-0.336910\pi$
$73$	8.37718			0.980475			0.490237	+	0.871589i	$0.336910\pi$
$74$	−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			0
$79$	11.2566			1.26646			0.633231	−	0.773963i	$-0.281728\pi$
$79$	11.2566			1.26646			0.633231	+	0.773963i	$0.281728\pi$
$80$	7.56641	−	4.76963i	0.845951	−	0.533261i
$81$		0			0
$82$	2.24282	+	0.257114i	0.247678	+	0.0283935i
$83$	8.24890	+	8.24890i	0.905435	+	0.905435i	0.995900	−	0.0904649i	$-0.0288353\pi$
$83$	8.24890	+	8.24890i	0.905435	+	0.905435i	−0.0904649	+	0.995900i	$0.528835\pi$
$84$		0			0
$85$	3.61685	+	2.22640i	0.392303	+	0.241487i
$86$	10.0372	+	12.6365i	1.08234	+	1.36263i
$87$		0			0
$88$	10.2160	−	4.84668i	1.08903	−	0.516658i
$89$		−	11.9820i		−	1.27009i	−0.772474	−	0.635046i	$-0.780981\pi$
$89$		−	11.9820i		−	1.27009i	0.772474	−	0.635046i	$-0.219019\pi$
$90$		0			0
$91$	−4.44854	−	4.44854i	−0.466334	−	0.466334i
$92$	3.90816	+	0.907986i	0.407454	+	0.0946640i
$93$		0			0
$94$	6.23577	+	0.714859i	0.643170	+	0.0737321i
$95$	−2.12019	−	8.90989i	−0.217526	−	0.914136i
$96$		0			0
$97$		−	6.50543i		−	0.660526i	−0.943889	−	0.330263i	$-0.892863\pi$
$97$		−	6.50543i		−	0.660526i	0.943889	−	0.330263i	$-0.107137\pi$
$98$	−0.654003	+	5.70491i	−0.0660643	+	0.576283i
$99$		0			0
$100$	2.36680	+	9.71588i	0.236680	+	0.971588i
$101$	6.72307	+	6.72307i	0.668970	+	0.668970i	0.957478	−	0.288508i	$-0.0931590\pi$
$101$	6.72307	+	6.72307i	0.668970	+	0.668970i	−0.288508	+	0.957478i	$0.593159\pi$
$102$		0			0
$103$	15.1733			1.49506			0.747532	−	0.664225i	$-0.231238\pi$
$103$	15.1733			1.49506			0.747532	+	0.664225i	$0.231238\pi$
$104$	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	−0.620262	−	0.784395i	$-0.712974\pi$
$107$	1.69781	−	1.69781i	0.164134	−	0.164134i	0.784395	+	0.620262i	$0.212974\pi$
$108$		0			0
$109$	3.11120	−	3.11120i	0.297999	−	0.297999i	−0.542231	−	0.840230i	$-0.682420\pi$
$109$	3.11120	−	3.11120i	0.297999	−	0.297999i	0.840230	+	0.542231i	$0.182420\pi$
$110$	1.50680	+	12.5519i	0.143667	+	1.19678i
$111$		0			0
$112$	6.15565	+	3.02349i	0.581654	+	0.285693i
$113$		−	15.8259i		−	1.48877i	−0.667748	−	0.744387i	$-0.732742\pi$
$113$		−	15.8259i		−	1.48877i	0.667748	−	0.744387i	$-0.267258\pi$
$114$		0			0
$115$	−2.35151	+	3.82010i	−0.219279	+	0.356226i
$116$	−16.1402	+	10.0544i	−1.49858	+	0.933527i
$117$		0			0
$118$	−4.83261	+	3.83856i	−0.444878	+	0.353368i
$119$			3.25656i			0.298528i
$120$		0			0
$121$			4.98203i			0.452912i
$122$	−4.30914	−	5.42506i	−0.390132	−	0.491162i
$123$		0			0
$124$	13.8662	+	3.22155i	1.24523	+	0.289304i
$125$	−11.1404	−	0.944243i	−0.996427	−	0.0844556i
$126$		0			0
$127$			18.3239i			1.62598i	0.582276	+	0.812991i	$0.302162\pi$
$127$			18.3239i			1.62598i	−0.582276	+	0.812991i	$0.697838\pi$
$128$	−8.10793	+	7.89059i	−0.716647	+	0.697436i
$129$		0			0
$130$	1.38302	+	11.5208i	0.121298	+	1.01044i
$131$	10.2036	−	10.2036i	0.891491	−	0.891491i	−0.103172	−	0.994663i	$-0.532899\pi$
$131$	10.2036	−	10.2036i	0.891491	−	0.891491i	0.994663	+	0.103172i	$0.0328994\pi$
$132$		0			0
$133$	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
$137$	14.9845			1.28021			0.640107	−	0.768286i	$-0.278890\pi$
$137$	14.9845			1.28021			0.640107	+	0.768286i	$0.278890\pi$
$138$		0			0
$139$	−8.29094	−	8.29094i	−0.703228	−	0.703228i	0.261874	−	0.965102i	$-0.415660\pi$
$139$	−8.29094	−	8.29094i	−0.703228	−	0.703228i	−0.965102	+	0.261874i	$0.915660\pi$
$140$	−5.39281	+	5.45064i	−0.455776	+	0.460663i
$141$		0			0
$142$	0.532711	+	0.0610692i	0.0447041	+	0.00512481i
$143$			14.6691i			1.22670i
$144$		0			0
$145$	−4.92163	−	20.6827i	−0.408719	−	1.71760i
$146$	1.34930	−	11.7700i	0.111669	−	0.974095i
$147$		0			0
$148$	−5.40658	+	3.36798i	−0.444418	+	0.276846i
$149$	7.30735	+	7.30735i	0.598642	+	0.598642i	0.939951	−	0.341309i	$-0.110870\pi$
$149$	7.30735	+	7.30735i	0.598642	+	0.598642i	−0.341309	+	0.939951i	$0.610870\pi$
$150$		0			0
$151$			4.56873i			0.371798i	0.982569	+	0.185899i	$0.0595197\pi$
$151$			4.56873i			0.371798i	−0.982569	+	0.185899i	$0.940480\pi$
$152$	4.96565	+	10.4667i	0.402768	+	0.848964i
$153$		0			0
$154$	−7.59030	+	6.02900i	−0.611643	+	0.485831i
$155$	−8.34320	+	13.5538i	−0.670142	+	1.08867i
$156$		0			0
$157$	−1.52966	−	1.52966i	−0.122080	−	0.122080i	0.643427	−	0.765507i	$-0.277512\pi$
$157$	−1.52966	−	1.52966i	−0.122080	−	0.122080i	−0.765507	+	0.643427i	$0.777512\pi$
$158$	1.81308	−	15.8156i	0.144241	−	1.25822i
$159$		0			0
$160$	−5.48268	−	11.3991i	−0.433444	−	0.901181i
$161$	−3.43955			−0.271075
$162$		0			0
$163$	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
$167$	−2.57967			−0.199621			−0.0998105	−	0.995006i	$-0.531824\pi$
$167$	−2.57967			−0.199621			−0.0998105	+	0.995006i	$0.531824\pi$
$168$		0			0
$169$			0.464102i			0.0357001i
$170$	3.71068	−	4.72312i	0.284596	−	0.362246i
$171$		0			0
$172$	19.3711	−	12.0670i	1.47703	−	0.920104i
$173$	14.1773	+	14.1773i	1.07788	+	1.07788i	0.996700	+	0.0811779i	$0.0258682\pi$
$173$	14.1773	+	14.1773i	1.07788	+	1.07788i	0.0811779	+	0.996700i	$0.474132\pi$
$174$		0			0
$175$	−3.86122	−	7.65381i	−0.291881	−	0.578574i
$176$	−5.16418	−	15.1342i	−0.389264	−	1.14078i
$177$		0			0
$178$	−16.8349	−	1.92993i	−1.26183	−	0.144654i
$179$	9.88067	−	9.88067i	0.738516	−	0.738516i	−0.233775	−	0.972291i	$-0.575108\pi$
$179$	9.88067	−	9.88067i	0.738516	−	0.738516i	0.972291	+	0.233775i	$0.0751079\pi$
$180$		0			0
$181$	6.20514	+	6.20514i	0.461224	+	0.461224i	0.899057	−	0.437832i	$-0.144254\pi$
$181$	6.20514	+	6.20514i	0.461224	+	0.461224i	−0.437832	+	0.899057i	$0.644254\pi$
$182$	−6.96677	+	5.53373i	−0.516411	+	0.410187i
$183$		0			0
$184$	1.90521	−	5.34477i	0.140454	−	0.394021i
$185$	−1.64863	−	6.92820i	−0.121209	−	0.509372i
$186$		0			0
$187$	5.36928	−	5.36928i	0.392641	−	0.392641i
$188$	2.00877	−	8.64618i	0.146505	−	0.630587i
$189$		0			0
$190$	−12.8600	+	1.54378i	−0.932962	+	0.111998i
$191$	−18.9282			−1.36960			−0.684798	−	0.728733i	$-0.740110\pi$
$191$	−18.9282			−1.36960			−0.684798	+	0.728733i	$0.740110\pi$
$192$		0			0
$193$			4.42987i			0.318869i	0.987209	+	0.159434i	$0.0509670\pi$
$193$			4.42987i			0.318869i	−0.987209	+	0.159434i	$0.949033\pi$
$194$	−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	−0.441667	−	0.897179i	$-0.645613\pi$
$197$	6.39341	−	6.39341i	0.455511	−	0.455511i	0.897179	+	0.441667i	$0.145613\pi$
$198$		0			0
$199$			5.85641i			0.415150i	0.978219	+	0.207575i	$0.0665570\pi$
$199$			5.85641i			0.415150i	−0.978219	+	0.207575i	$0.933443\pi$
$200$	14.0321	−	1.76046i	0.992222	−	0.124483i
$201$		0			0
$202$	10.5289	−	8.36311i	0.740808	−	0.588426i
$203$	11.5269	−	11.5269i	0.809027	−	0.809027i
$204$		0			0
$205$	3.03970	+	1.87113i	0.212302	+	0.130685i
$206$	2.44393	−	21.3186i	0.170277	−	1.48534i
$207$		0			0
$208$	−4.73995	−	13.8910i	−0.328656	−	0.963164i
$209$	−16.3743			−1.13264
$210$		0			0
$211$	7.60373	−	7.60373i	0.523462	−	0.523462i	−0.395153	−	0.918615i	$-0.629308\pi$
$211$	7.60373	−	7.60373i	0.523462	−	0.523462i	0.918615	+	0.395153i	$0.129308\pi$
$212$	1.15657	−	0.720473i	0.0794334	−	0.0494823i
$213$		0			0
$214$	−2.11198	−	2.65891i	−0.144372	−	0.181759i
$215$	5.90682	+	24.8229i	0.402842	+	1.69291i
$216$		0			0
$217$	−12.2036			−0.828435
$218$	−3.87016	−	4.87239i	−0.262120	−	0.330000i
$219$		0			0
$220$	17.8782	−	0.0953508i	1.20535	−	0.00642855i
$221$	4.92820	−	4.92820i	0.331507	−	0.331507i
$222$		0			0
$223$			9.22430i			0.617705i	0.951110	+	0.308853i	$0.0999450\pi$
$223$			9.22430i			0.617705i	−0.951110	+	0.308853i	$0.900055\pi$
$224$	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	$0.892399\pi$
$228$		0			0
$229$	1.63811	+	1.63811i	0.108250	+	0.108250i	0.759157	−	0.650907i	$-0.225611\pi$
$229$	1.63811	+	1.63811i	0.108250	+	0.108250i	−0.650907	+	0.759157i	$0.725611\pi$
$230$	4.98852	+	3.91919i	0.328934	+	0.258424i
$231$		0			0
$232$	11.5269	+	24.2966i	0.756776	+	1.59515i
$233$	−12.3798			−0.811026			−0.405513	−	0.914089i	$-0.632907\pi$
$233$	−12.3798			−0.811026			−0.405513	+	0.914089i	$0.632907\pi$
$234$		0			0
$235$	8.45134	+	5.20233i	0.551305	+	0.339363i
$236$	4.61484	+	7.40815i	0.300401	+	0.482229i
$237$		0			0
$238$	4.57550	+	0.524529i	0.296586	+	0.0340002i
$239$	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	$0.535656\pi$
$242$	6.99981	+	0.802448i	0.449965	+	0.0515833i
$243$		0			0
$244$	−8.31634	+	5.18059i	−0.532399	+	0.331653i
$245$	−4.75946	+	7.73188i	−0.304071	+	0.493972i
$246$		0			0
$247$	−15.0292			−0.956286
$248$	6.75973	−	18.9633i	0.429243	−	1.20417i
$249$		0			0
$250$	−3.12104	+	15.5003i	−0.197392	+	0.980325i
$251$	−8.94765	−	8.94765i	−0.564771	−	0.564771i	0.365888	−	0.930659i	$-0.380765\pi$
$251$	−8.94765	−	8.94765i	−0.564771	−	0.564771i	−0.930659	+	0.365888i	$0.880765\pi$
$252$		0			0
$253$	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
$257$		−	3.62228i		−	0.225952i	−0.993598	−	0.112976i	$-0.963962\pi$
$257$		−	3.62228i		−	0.225952i	0.993598	−	0.112976i	$-0.0360383\pi$
$258$		0			0
$259$	3.86122	−	3.86122i	0.239925	−	0.239925i
$260$	16.4096	−	0.0875179i	1.01768	−	0.00542763i
$261$		0			0
$262$	−12.6927	−	15.9796i	−0.784156	−	0.987224i
$263$	−13.7416			−0.847345			−0.423673	−	0.905815i	$-0.639259\pi$
$263$	−13.7416			−0.847345			−0.423673	+	0.905815i	$0.639259\pi$
$264$		0			0
$265$	0.352672	+	1.48207i	0.0216644	+	0.0910429i
$266$	−6.17699	−	7.77661i	−0.378736	−	0.476815i
$267$		0			0
$268$	−2.69871	−	4.33221i	−0.164850	−	0.264632i
$269$	4.22240	−	4.22240i	0.257444	−	0.257444i	−0.566570	−	0.824014i	$-0.691730\pi$
$269$	4.22240	−	4.22240i	0.257444	−	0.257444i	0.824014	+	0.566570i	$0.191730\pi$
$270$		0			0
$271$	−5.40015			−0.328036			−0.164018	−	0.986457i	$-0.552445\pi$
$271$	−5.40015			−0.328036			−0.164018	+	0.986457i	$0.552445\pi$
$272$	−3.34950	+	6.81938i	−0.203093	+	0.413486i
$273$		0			0
$274$	2.41353	−	21.0534i	0.145807	−	1.27188i
$275$	−6.25307	+	18.9855i	−0.377074	+	1.14487i
$276$		0			0
$277$	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	$0.180653\pi$
$278$	−12.9843	+	10.3135i	−0.778745	+	0.618560i
$279$		0			0
$280$	6.78960	+	8.45489i	0.405756	+	0.505276i
$281$			21.2780i			1.26934i	0.772784	+	0.634669i	$0.218864\pi$
$281$			21.2780i			1.26934i	−0.772784	+	0.634669i	$0.781136\pi$
$282$		0			0
$283$	−4.08521	+	4.08521i	−0.242840	+	0.242840i	−0.818024	−	0.575184i	$-0.804931\pi$
$283$	−4.08521	+	4.08521i	−0.242840	+	0.242840i	0.575184	+	0.818024i	$0.304931\pi$
$284$	0.171606	−	0.738628i	0.0101829	−	0.0438295i
$285$		0			0
$286$	20.6103	+	2.36274i	1.21871	+	0.139712i
$287$			2.73690i			0.161554i
$288$		0			0
$289$	13.3923			0.787783
$290$	−29.8521	+	3.58361i	−1.75298	+	0.210437i
$291$		0			0
$292$	−16.3197	−	3.79156i	−0.955038	−	0.221884i
$293$	−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	$0.348943\pi$
$294$		0			0
$295$	−9.49310	+	2.25896i	−0.552709	+	0.131522i
$296$	3.86122	+	8.13878i	0.224429	+	0.473057i
$297$		0			0
$298$	11.4439	−	9.08993i	0.662927	−	0.526566i
$299$	5.20514	+	5.20514i	0.301021	+	0.301021i
$300$		0			0
$301$	−13.8343	+	13.8343i	−0.797394	+	0.797394i
$302$	6.41911	+	0.735878i	0.369378	+	0.0423450i
$303$		0			0
$304$	15.5057	−	5.29094i	0.889312	−	0.303456i
$305$	−2.53590	−	10.6569i	−0.145205	−	0.610212i
$306$		0			0
$307$	−16.6634	−	16.6634i	−0.951030	−	0.951030i	0.0478262	−	0.998856i	$-0.484771\pi$
$307$	−16.6634	−	16.6634i	−0.951030	−	0.951030i	−0.998856	+	0.0478262i	$0.984771\pi$
$308$	7.24825	+	11.6355i	0.413008	+	0.662996i
$309$		0			0
$310$	17.6994	+	13.9054i	1.00526	+	0.789772i
$311$			21.9072i			1.24224i	0.783714	+	0.621122i	$0.213323\pi$
$311$			21.9072i			1.24224i	−0.783714	+	0.621122i	$0.786677\pi$
$312$		0			0
$313$	12.4820			0.705525			0.352763	−	0.935713i	$-0.385242\pi$
$313$	12.4820			0.705525			0.352763	+	0.935713i	$0.385242\pi$
$314$	−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			0
$319$	−38.0100			−2.12815
$320$	−16.8990	+	5.86718i	−0.944683	+	0.327985i
$321$		0			0
$322$	−0.554004	+	4.83261i	−0.0308734	+	0.269311i
$323$	5.50108	+	5.50108i	0.306088	+	0.306088i
$324$		0			0
$325$	−5.73939	+	17.4259i	−0.318364	+	0.966615i
$326$	15.8739	−	12.6087i	0.879173	−	0.698330i
$327$		0			0
$328$	−4.25290	−	1.51600i	−0.234827	−	0.0837073i
$329$			7.60946i			0.419523i
$330$		0			0
$331$	1.10377	+	1.10377i	0.0606688	+	0.0606688i	0.736790	−	0.676121i	$-0.236341\pi$
$331$	1.10377	+	1.10377i	0.0606688	+	0.0606688i	−0.676121	+	0.736790i	$0.736341\pi$
$332$	−12.3363	−	19.8033i	−0.677042	−	1.08685i
$333$		0			0
$334$	−0.415504	+	3.62447i	−0.0227354	+	0.198322i
$335$	5.55146	−	1.32102i	0.303309	−	0.0721749i
$336$		0			0
$337$		−	7.47635i		−	0.407263i	−0.979048	−	0.203631i	$-0.934726\pi$
$337$		−	7.47635i		−	0.407263i	0.979048	−	0.203631i	$-0.0652744\pi$
$338$	0.652068	+	0.0747522i	0.0354678	+	0.00406598i
$339$		0			0
$340$	−6.03836	−	5.97429i	−0.327476	−	0.324001i
$341$	20.1208	+	20.1208i	1.08960	+	1.08960i
$342$		0			0
$343$	−18.9633			−1.02392
$344$	−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	−0.898512	−	0.438948i	$-0.855351\pi$
$347$	−8.56074	+	8.56074i	−0.459565	+	0.459565i	0.438948	+	0.898512i	$0.355351\pi$
$348$		0			0
$349$	7.91567	−	7.91567i	0.423716	−	0.423716i	−0.462765	−	0.886481i	$-0.653143\pi$
$349$	7.91567	−	7.91567i	0.423716	−	0.423716i	0.886481	+	0.462765i	$0.153143\pi$
$350$	−11.3756	+	4.19227i	−0.608052	+	0.224086i
$351$		0			0
$352$	−22.0955	+	4.81809i	−1.17769	+	0.256805i
$353$			9.67314i			0.514849i	0.966298	+	0.257425i	$0.0828739\pi$
$353$			9.67314i			0.514849i	−0.966298	+	0.257425i	$0.917126\pi$
$354$		0			0
$355$	0.721984	+	0.444426i	0.0383189	+	0.0235877i
$356$	−5.42314	+	23.3424i	−0.287426	+	1.23714i
$357$		0			0
$358$	−12.2910	−	15.4739i	−0.649599	−	0.817822i
$359$			17.0867i			0.901799i	0.892575	+	0.450900i	$0.148897\pi$
$359$			17.0867i			0.901799i	−0.892575	+	0.450900i	$0.851103\pi$
$360$		0			0
$361$			2.22373i			0.117038i
$362$	9.71774	−	7.71884i	0.510753	−	0.405693i
$363$		0			0
$364$	6.65283	+	10.6797i	0.348703	+	0.559768i
$365$	9.81943	−	15.9519i	0.513972	−	0.834963i
$366$		0			0
$367$		−	13.4500i		−	0.702086i	−0.936359	−	0.351043i	$-0.885827\pi$
$367$		−	13.4500i		−	0.702086i	0.936359	−	0.351043i	$-0.114173\pi$
$368$	−7.20259	−	3.53772i	−0.375461	−	0.184416i
$369$		0			0
$370$	−9.99975	+	1.20042i	−0.519862	+	0.0624070i
$371$	−0.825987	+	0.825987i	−0.0428831	+	0.0428831i
$372$		0			0
$373$	−12.0271	+	12.0271i	−0.622740	+	0.622740i	−0.946231	−	0.323491i	$-0.895143\pi$
$373$	−12.0271	+	12.0271i	−0.622740	+	0.622740i	0.323491	+	0.946231i	$0.395143\pi$
$374$	−6.67908	−	8.40872i	−0.345367	−	0.434804i
$375$		0			0
$376$	−11.8244	−	4.21497i	−0.609798	−	0.217371i
$377$	−34.8876			−1.79680
$378$		0			0
$379$	19.1552	+	19.1552i	0.983936	+	0.983936i	0.999873	−	0.0159369i	$-0.00507308\pi$
$379$	19.1552	+	19.1552i	0.983936	+	0.983936i	−0.0159369	+	0.999873i	$0.505073\pi$
$380$	0.0976914	+	18.3171i	0.00501146	+	0.939647i
$381$		0			0
$382$	−3.04874	+	26.5943i	−0.155987	+	1.36068i
$383$		−	17.7503i		−	0.907000i	−0.891256	−	0.453500i	$-0.850175\pi$
$383$		−	17.7503i		−	0.907000i	0.891256	−	0.453500i	$-0.149825\pi$
$384$		0			0
$385$	−14.9102	+	3.54802i	−0.759896	+	0.180824i
$386$	6.22401	+	0.713512i	0.316794	+	0.0363168i
$387$		0			0
$388$	−2.94440	+	12.6733i	−0.149479	+	0.643390i
$389$	1.18654	+	1.18654i	0.0601602	+	0.0601602i	0.736547	−	0.676387i	$-0.236455\pi$
$389$	1.18654	+	1.18654i	0.0601602	+	0.0601602i	−0.676387	+	0.736547i	$0.736455\pi$
$390$		0			0
$391$		−	3.81042i		−	0.192701i
$392$	3.85615	−	10.8178i	0.194765	−	0.546382i
$393$		0			0
$394$	−7.95303	−	10.0126i	−0.400668	−	0.504427i
$395$	13.1945	−	21.4349i	0.663889	−	1.07851i
$396$		0			0
$397$	−4.74478	−	4.74478i	−0.238134	−	0.238134i	0.577943	−	0.816077i	$-0.303855\pi$
$397$	−4.74478	−	4.74478i	−0.238134	−	0.238134i	−0.816077	+	0.577943i	$0.803855\pi$
$398$	8.22832	+	0.943283i	0.412448	+	0.0472825i
$399$		0			0
$400$	−0.213328	−	19.9989i	−0.0106664	−	0.999943i
$401$	−0.632677			−0.0315944			−0.0157972	−	0.999875i	$-0.505029\pi$
$401$	−0.632677			−0.0315944			−0.0157972	+	0.999875i	$0.505029\pi$
$402$		0			0
$403$	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
$407$	−12.7324			−0.631124
$408$		0			0
$409$		−	26.3809i		−	1.30445i	−0.758024	−	0.652226i	$-0.773835\pi$
$409$		−	26.3809i		−	1.30445i	0.758024	−	0.652226i	$-0.226165\pi$
$410$	3.11856	−	3.96944i	0.154015	−	0.196037i
$411$		0			0
$412$	−29.5592	−	6.86751i	−1.45628	−	0.338338i
$413$	−5.29069	−	5.29069i	−0.260338	−	0.260338i
$414$		0			0
$415$	25.3767	−	6.03862i	1.24570	−	0.296424i
$416$	−20.2804	+	4.42229i	−0.994328	+	0.216821i
$417$		0			0
$418$	−2.63739	+	23.0061i	−0.128999	+	1.12527i
$419$	1.37589	−	1.37589i	0.0672167	−	0.0672167i	−0.672699	−	0.739916i	$-0.734865\pi$
$419$	1.37589	−	1.37589i	0.0672167	−	0.0672167i	0.739916	+	0.672699i	$0.234865\pi$
$420$		0			0
$421$	6.65671	+	6.65671i	0.324428	+	0.324428i	0.850463	−	0.526035i	$-0.176322\pi$
$421$	6.65671	+	6.65671i	0.324428	+	0.324428i	−0.526035	+	0.850463i	$0.676322\pi$
$422$	−9.45861	−	11.9081i	−0.460438	−	0.579675i
$423$		0			0
$424$	−0.825987	−	1.74104i	−0.0401135	−	0.0845522i
$425$	8.47908	−	4.27756i	0.411296	−	0.207492i
$426$		0			0
$427$	5.93929	−	5.93929i	0.287422	−	0.287422i
$428$	−4.07597	+	2.53909i	−0.197019	+	0.122731i
$429$		0			0
$430$	35.8278	−	4.30096i	1.72777	−	0.207411i
$431$	−4.08798			−0.196911			−0.0984556	−	0.995141i	$-0.531390\pi$
$431$	−4.08798			−0.196911			−0.0984556	+	0.995141i	$0.531390\pi$
$432$		0			0
$433$			29.2913i			1.40765i	0.710373	+	0.703826i	$0.248526\pi$
$433$			29.2913i			1.40765i	−0.710373	+	0.703826i	$0.751474\pi$
$434$	−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
$438$		0			0
$439$			26.9790i			1.28764i	0.765178	+	0.643819i	$0.222651\pi$
$439$			26.9790i			1.28764i	−0.765178	+	0.643819i	$0.777349\pi$
$440$	2.74565	−	25.1345i	0.130894	−	1.19824i
$441$		0			0
$442$	−6.13040	−	7.71796i	−0.291594	−	0.367106i
$443$	−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	$0.412309\pi$
$444$		0			0
$445$	−22.8164	−	14.0449i	−1.08160	−	0.665792i
$446$	12.9603	+	1.48575i	0.613686	+	0.0703521i
$447$		0			0
$448$	−10.6235	−	8.67619i	−0.501911	−	0.409911i
$449$	−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
$452$	−7.16290	+	30.8306i	−0.336914	+	1.45015i
$453$		0			0
$454$	−14.4349	+	11.4657i	−0.677466	+	0.538113i
$455$	−13.6854	+	3.25656i	−0.641581	+	0.152670i
$456$		0			0
$457$	−37.7026			−1.76365			−0.881827	−	0.471572i	$-0.843687\pi$
$457$	−37.7026			−1.76365			−0.881827	+	0.471572i	$0.843687\pi$
$458$	2.56542	−	2.03772i	0.119874	−	0.0952165i
$459$		0			0
$460$	6.31001	−	6.37768i	0.294206	−	0.297361i
$461$	−11.3737	+	11.3737i	−0.529727	+	0.529727i	−0.920491	−	0.390764i	$-0.872211\pi$
$461$	−11.3737	+	11.3737i	−0.529727	+	0.529727i	0.390764	+	0.920491i	$0.372211\pi$
$462$		0			0
$463$		−	7.94895i		−	0.369419i	−0.982793	−	0.184710i	$-0.940866\pi$
$463$		−	7.94895i		−	0.369419i	0.982793	−	0.184710i	$-0.0591344\pi$
$464$	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	$0.806011\pi$
$468$		0			0
$469$	3.09394	+	3.09394i	0.142865	+	0.142865i
$470$	8.67058	−	11.0363i	0.399944	−	0.509067i
$471$		0			0
$472$	11.1518	−	5.29069i	0.513305	−	0.243524i
$473$	45.6187			2.09755
$474$		0			0
$475$	−19.4515	−	6.40656i	−0.892498	−	0.293953i
$476$	1.47394	−	6.34414i	0.0675578	−	0.290783i
$477$		0			0
$478$	1.25222	−	10.9232i	0.0572754	−	0.499617i
$479$	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
$482$	−0.559017	+	4.87634i	−0.0254625	+	0.222111i
$483$		0			0
$484$	2.25490	−	9.70556i	0.102495	−	0.441162i
$485$	−12.3877	−	7.62543i	−0.562498	−	0.346253i
$486$		0			0
$487$	36.6487			1.66071			0.830357	−	0.557232i	$-0.188137\pi$
$487$	36.6487			1.66071			0.830357	+	0.557232i	$0.188137\pi$
$488$	5.93929	+	12.5190i	0.268859	+	0.566708i
$489$		0			0
$490$	10.0968	+	7.93246i	0.456126	+	0.358352i
$491$	−23.4273	−	23.4273i	−1.05726	−	1.05726i	−0.998258	−	0.0590019i	$-0.981208\pi$
$491$	−23.4273	−	23.4273i	−1.05726	−	1.05726i	−0.0590019	−	0.998258i	$-0.518792\pi$
$492$		0			0
$493$	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
$497$			0.650063i			0.0291593i
$498$		0			0
$499$	−9.50152	+	9.50152i	−0.425346	+	0.425346i	−0.887040	−	0.461693i	$-0.847242\pi$
$499$	−9.50152	+	9.50152i	−0.425346	+	0.425346i	0.461693	+	0.887040i	$0.347242\pi$
$500$	21.2754	+	6.88170i	0.951464	+	0.307759i
$501$		0			0
$502$	−14.0127	+	11.1304i	−0.625419	+	0.496772i
$503$	20.6875			0.922411			0.461206	−	0.887293i	$-0.347417\pi$
$503$	20.6875			0.922411			0.461206	+	0.887293i	$0.347417\pi$
$504$		0			0
$505$	20.6827	−	4.92163i	0.920368	−	0.219009i
$506$	8.88124	−	7.05440i	0.394819	−	0.313606i
$507$		0			0
$508$	8.29351	−	35.6970i	0.367965	−	1.58380i
$509$	−11.6381	+	11.6381i	−0.515850	+	0.515850i	−0.916313	−	0.400463i	$-0.868849\pi$
$509$	−11.6381	+	11.6381i	−0.515850	+	0.515850i	0.400463	+	0.916313i	$0.368849\pi$
$510$		0			0
$511$	14.3629			0.635377
$512$	19.3665	−	11.7021i	0.855887	−	0.517163i
$513$		0			0
$514$	−5.08935	−	0.583436i	−0.224482	−	0.0257343i
$515$	17.7855	−	28.8931i	0.783724	−	1.27318i
$516$		0			0
$517$	12.5462	−	12.5462i	0.551780	−	0.551780i
$518$	−4.80314	−	6.04698i	−0.211038	−	0.265689i
$519$		0			0
$520$	2.52010	−	23.0697i	0.110514	−	1.01168i
$521$		−	5.18654i		−	0.227227i	−0.993525	−	0.113613i	$-0.963758\pi$
$521$		−	5.18654i		−	0.227227i	0.993525	−	0.113613i	$-0.0362425\pi$
$522$		0			0
$523$	26.9589	−	26.9589i	1.17883	−	1.17883i	0.198788	−	0.980043i	$-0.436300\pi$
$523$	26.9589	−	26.9589i	1.17883	−	1.17883i	0.980043	−	0.198788i	$-0.0637004\pi$
$524$	−24.4959	+	15.2595i	−1.07011	+	0.666616i
$525$		0			0
$526$	−2.21334	+	19.3071i	−0.0965064	+	0.841832i
$527$		−	13.5195i		−	0.588917i
$528$		0			0
$529$	−18.9755			−0.825020
$530$	2.13913	−	0.256793i	0.0929179	−	0.0111544i
$531$		0			0
$532$	−11.9211	+	7.42617i	−0.516847	+	0.321965i
$533$	4.14180	−	4.14180i	0.179401	−	0.179401i
$534$		0			0
$535$	−1.24288	−	5.22311i	−0.0537345	−	0.225815i
$536$	−6.52148	+	3.09394i	−0.281685	+	0.133638i
$537$		0			0
$538$	−5.25243	−	6.61262i	−0.226448	−	0.285090i
$539$	11.4781	+	11.4781i	0.494397	+	0.494397i
$540$		0			0
$541$	27.4945	−	27.4945i	1.18208	−	1.18208i	0.202878	−	0.979204i	$-0.434971\pi$
$541$	27.4945	−	27.4945i	1.18208	−	1.18208i	0.979204	−	0.202878i	$-0.0650294\pi$
$542$	−0.869794	+	7.58727i	−0.0373609	+	0.325901i
$543$		0			0
$544$	9.04181	+	5.80447i	0.387664	+	0.248865i
$545$	−2.27756	−	9.57123i	−0.0975598	−	0.409986i
$546$		0			0
$547$	−22.5197	−	22.5197i	−0.962873	−	0.962873i	0.0364619	−	0.999335i	$-0.488391\pi$
$547$	−22.5197	−	22.5197i	−0.962873	−	0.962873i	−0.999335	+	0.0364619i	$0.988391\pi$
$548$	−29.1915	−	6.78208i	−1.24700	−	0.289716i
$549$		0			0
$550$	25.6677	+	11.8436i	1.09447	+	0.505013i
$551$		−	38.9431i		−	1.65903i
$552$		0			0
$553$	19.2996			0.820704
$554$	−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	$0.615018\pi$
$558$		0			0
$559$	41.8713			1.77097
$560$	12.9728	−	8.17765i	0.548201	−	0.345569i
$561$		0			0
$562$	29.8958	+	3.42721i	1.26108	+	0.144568i
$563$	−0.229223	−	0.229223i	−0.00966061	−	0.00966061i	0.702260	−	0.711921i	$-0.252174\pi$
$563$	−0.229223	−	0.229223i	−0.00966061	−	0.00966061i	−0.711921	+	0.702260i	$0.752174\pi$
$564$		0			0
$565$	−30.1359	−	18.5505i	−1.26783	−	0.780427i
$566$	5.08177	+	6.39776i	0.213603	+	0.268918i
$567$		0			0
$568$	−1.01014	−	0.360078i	−0.0423846	−	0.0151085i
$569$		−	23.0376i		−	0.965787i	−0.875679	−	0.482894i	$-0.839586\pi$
$569$		−	23.0376i		−	0.965787i	0.875679	−	0.482894i	$-0.160414\pi$
$570$		0			0
$571$	−11.8610	−	11.8610i	−0.496367	−	0.496367i	0.413938	−	0.910305i	$-0.364153\pi$
$571$	−11.8610	−	11.8610i	−0.496367	−	0.496367i	−0.910305	+	0.413938i	$0.864153\pi$
$572$	6.63934	−	28.5772i	0.277605	−	1.19487i
$573$		0			0
$574$	3.84538	+	0.440829i	0.160503	+	0.0183998i
$575$	4.51793	+	8.95556i	0.188411	+	0.373473i
$576$		0			0
$577$			39.7168i			1.65343i	0.562621	+	0.826715i	$0.309793\pi$
$577$			39.7168i			1.65343i	−0.562621	+	0.826715i	$0.690207\pi$
$578$	2.15708	−	18.8163i	0.0897226	−	0.782657i
$579$		0			0
$580$	0.226773	+	42.5198i	0.00941622	+	1.76554i
$581$	14.1429	+	14.1429i	0.586748	+	0.586748i
$582$		0			0
$583$	2.72371			0.112804
$584$	−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	−0.505980	−	0.862545i	$-0.668869\pi$
$587$	8.63887	−	8.63887i	0.356564	−	0.356564i	0.862545	+	0.505980i	$0.168869\pi$
$588$		0			0
$589$	−20.6147	+	20.6147i	−0.849414	+	0.849414i
$590$	1.64483	+	13.7018i	0.0677167	+	0.564092i
$591$		0			0
$592$	12.0570	−	4.11416i	0.495540	−	0.169091i
$593$			45.8229i			1.88172i	0.338795	+	0.940860i	$0.389981\pi$
$593$			45.8229i			1.88172i	−0.338795	+	0.940860i	$0.610019\pi$
$594$		0			0
$595$	6.20118	+	3.81722i	0.254224	+	0.156491i
$596$	−10.9282	−	17.5429i	−0.447637	−	0.718586i
$597$		0			0
$598$	8.15166	−	6.47489i	0.333346	−	0.264778i
$599$		−	17.0609i		−	0.697090i	−0.937292	−	0.348545i	$-0.886676\pi$
$599$		−	17.0609i		−	0.697090i	0.937292	−	0.348545i	$-0.113324\pi$
$600$		0			0
$601$			38.0363i			1.55153i	0.631020	+	0.775766i	$0.282636\pi$
$601$			38.0363i			1.55153i	−0.631020	+	0.775766i	$0.717364\pi$
$602$	17.2090	+	21.6656i	0.701388	+	0.883023i
$603$		0			0
$604$	2.06783	−	8.90040i	0.0841390	−	0.362152i
$605$	9.48685	+	5.83975i	0.385695	+	0.237420i
$606$		0			0
$607$			8.67169i			0.351973i	0.984393	+	0.175987i	$0.0563115\pi$
$607$			8.67169i			0.351973i	−0.984393	+	0.175987i	$0.943688\pi$
$608$	−4.93635	−	22.6379i	−0.200196	−	0.918087i
$609$		0			0
$610$	−15.3815	+	1.84648i	−0.622779	+	0.0747617i
$611$	11.5155	−	11.5155i	0.465868	−	0.465868i
$612$		0			0
$613$	−13.9739	+	13.9739i	−0.564401	+	0.564401i	−0.930554	−	0.366153i	$-0.880675\pi$
$613$	−13.9739	+	13.9739i	−0.564401	+	0.564401i	0.366153	+	0.930554i	$0.380675\pi$
$614$	−26.0962	+	20.7283i	−1.05316	+	0.836526i
$615$		0			0
$616$	17.5155	−	8.30976i	0.705720	−	0.334810i
$617$	−37.3904			−1.50528			−0.752641	−	0.658431i	$-0.771220\pi$
$617$	−37.3904			−1.50528			−0.752641	+	0.658431i	$0.771220\pi$
$618$		0			0
$619$	−23.2754	−	23.2754i	−0.935516	−	0.935516i	0.0625269	−	0.998043i	$-0.480084\pi$
$619$	−23.2754	−	23.2754i	−0.935516	−	0.935516i	−0.998043	+	0.0625269i	$0.980084\pi$
$620$	22.3880	−	22.6281i	0.899125	−	0.908767i
$621$		0			0
$622$	30.7799	+	3.52856i	1.23416	+	0.141482i
$623$		−	20.5435i		−	0.823058i
$624$		0			0
$625$	−14.8564	+	20.1069i	−0.594256	+	0.804276i
$626$	2.01046	−	17.5374i	0.0803541	−	0.700934i
$627$		0			0
$628$	2.28761	+	3.67228i	0.0912857	+	0.146540i
$629$	4.27756	+	4.27756i	0.170557	+	0.170557i
$630$		0			0
$631$		−	19.1834i		−	0.763680i	−0.924228	−	0.381840i	$-0.875290\pi$
$631$		−	19.1834i		−	0.763680i	0.924228	−	0.381840i	$-0.124710\pi$
$632$	−10.6903	+	29.9900i	−0.425238	+	1.19294i
$633$		0			0
$634$	6.64526	−	5.27835i	0.263917	−	0.209630i
$635$	34.8926	+	21.4786i	1.38467	+	0.852352i
$636$		0			0
$637$	10.5352	+	10.5352i	0.417420	+	0.417420i
$638$	−6.12222	+	53.4045i	−0.242381	+	2.11431i
$639$		0			0
$640$	5.52156	+	24.6883i	0.218259	+	0.975891i
$641$	16.1765			0.638933			0.319466	−	0.947598i	$-0.396496\pi$
$641$	16.1765			0.638933			0.319466	+	0.947598i	$0.396496\pi$
$642$		0			0
$643$	−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
$647$	49.3812			1.94138			0.970688	−	0.240345i	$-0.0772606\pi$
$647$	49.3812			1.94138			0.970688	+	0.240345i	$0.0772606\pi$
$648$		0			0
$649$			17.4461i			0.684821i
$650$	23.5591	+	10.8707i	0.924066	+	0.426383i
$651$		0			0
$652$	−15.1586	−	24.3338i	−0.593655	−	0.952987i
$653$	−19.8685	−	19.8685i	−0.777514	−	0.777514i	0.201893	−	0.979408i	$-0.435291\pi$
$653$	−19.8685	−	19.8685i	−0.777514	−	0.777514i	−0.979408	+	0.201893i	$0.935291\pi$
$654$		0			0
$655$	−7.46954	−	31.3901i	−0.291859	−	1.22651i
$656$	−2.81501	+	5.73120i	−0.109908	+	0.223766i
$657$		0			0
$658$	10.6914	+	1.22564i	0.416793	+	0.0477806i
$659$	−4.94765	+	4.94765i	−0.192733	+	0.192733i	−0.796876	−	0.604143i	$-0.793516\pi$
$659$	−4.94765	+	4.94765i	−0.192733	+	0.192733i	0.604143	+	0.796876i	$0.293516\pi$
$660$		0			0
$661$	12.1602	+	12.1602i	0.472977	+	0.472977i	0.902877	−	0.429899i	$-0.141451\pi$
$661$	12.1602	+	12.1602i	0.472977	+	0.472977i	−0.429899	+	0.902877i	$0.641451\pi$
$662$	1.72860	−	1.37303i	0.0671838	−	0.0533643i
$663$		0			0
$664$	−29.8109	+	14.1429i	−1.15689	+	0.548853i
$665$	−3.63511	−	15.2762i	−0.140964	−	0.592387i
$666$		0			0
$667$	−13.4873	+	13.4873i	−0.522231	+	0.522231i
$668$	5.02550	+	1.16758i	0.194442	+	0.0451749i
$669$		0			0
$670$	−0.961880	−	8.01264i	−0.0371607	−	0.309555i
$671$	−19.5849			−0.756067
$672$		0			0
$673$		−	32.9882i		−	1.27160i	−0.771853	−	0.635801i	$-0.780670\pi$
$673$		−	32.9882i		−	1.27160i	0.771853	−	0.635801i	$-0.219330\pi$
$674$	−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	−0.256920	−	0.966433i	$-0.582708\pi$
$677$	18.4610	−	18.4610i	0.709513	−	0.709513i	0.966433	+	0.256920i	$0.0827076\pi$
$678$		0			0
$679$		−	11.1537i		−	0.428040i
$680$	−9.36653	+	7.52169i	−0.359190	+	0.288444i
$681$		0			0
$682$	31.5108	−	25.0291i	1.20661	−	0.958415i
$683$	−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	$0.357421\pi$
$684$		0			0
$685$	17.5643	−	28.5337i	0.671097	−	1.09022i
$686$	−3.05440	+	26.6437i	−0.116617	+	1.01726i
$687$		0			0
$688$	−43.1987	+	14.7405i	−1.64693	+	0.561977i
$689$	2.49996			0.0952409
$690$		0			0
$691$	−9.46014	+	9.46014i	−0.359881	+	0.359881i	−0.863769	−	0.503888i	$-0.831902\pi$
$691$	−9.46014	+	9.46014i	−0.359881	+	0.359881i	0.503888	+	0.863769i	$0.331902\pi$
$692$	−21.2022	−	34.0356i	−0.805987	−	1.29384i
$693$		0			0
$694$	10.6491	+	13.4068i	0.404233	+	0.508915i
$695$	−25.5061	+	6.06939i	−0.967500	+	0.230225i
$696$		0			0
$697$	−3.03201			−0.114845
$698$	−9.84664	−	12.3966i	−0.372701	−	0.469217i
$699$		0			0
$700$	4.05794	+	16.6581i	0.153376	+	0.629617i
$701$	5.14714	−	5.14714i	0.194405	−	0.194405i	−0.603192	−	0.797596i	$-0.706105\pi$
$701$	5.14714	−	5.14714i	0.194405	−	0.194405i	0.797596	+	0.603192i	$0.206105\pi$
$702$		0			0
$703$		−	13.0450i		−	0.492001i
$704$	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
$708$		0			0
$709$	−18.0125	−	18.0125i	−0.676472	−	0.676472i	0.282728	−	0.959200i	$-0.408761\pi$
$709$	−18.0125	−	18.0125i	−0.676472	−	0.676472i	−0.959200	+	0.282728i	$0.908761\pi$
$710$	0.740713	−	0.942812i	0.0277985	−	0.0353831i
$711$		0			0
$712$	31.9228	+	11.3793i	1.19636	+	0.426457i
$713$	14.2792			0.534759
$714$		0			0
$715$	27.9332	+	17.1946i	1.04464	+	0.643043i
$716$	−23.7207	+	14.7766i	−0.886485	+	0.552228i
$717$		0			0
$718$	24.0069	+	2.75212i	0.895931	+	0.102708i
$719$	−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
$722$	3.12437	+	0.358173i	0.116277	+	0.0133298i
$723$		0			0
$724$	−9.27983	−	14.8968i	−0.344882	−	0.553635i
$725$	−45.1532	−	14.8717i	−1.67695	−	0.552320i
$726$		0			0
$727$	12.8421			0.476288			0.238144	−	0.971230i	$-0.423461\pi$
$727$	12.8421			0.476288			0.238144	+	0.971230i	$0.423461\pi$
$728$	16.0767	−	7.62713i	0.595841	−	0.282680i
$729$		0			0
$730$	−20.8311	−	16.3658i	−0.770992	−	0.605724i
$731$	−15.3259	−	15.3259i	−0.566851	−	0.566851i
$732$		0			0
$733$	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
$737$		−	10.2023i		−	0.375807i
$738$		0			0
$739$	35.9398	−	35.9398i	1.32207	−	1.32207i	0.409966	−	0.912101i	$-0.365540\pi$
$739$	35.9398	−	35.9398i	1.32207	−	1.32207i	0.912101	−	0.409966i	$-0.134460\pi$
$740$	0.0759634	+	14.2431i	0.00279247	+	0.523587i
$741$		0			0
$742$	1.02748	+	1.29356i	0.0377200	+	0.0474881i
$743$	45.9502			1.68575			0.842875	−	0.538109i	$-0.180861\pi$
$743$	45.9502			1.68575			0.842875	+	0.538109i	$0.180861\pi$
$744$		0			0
$745$	22.4802	−	5.34935i	0.823610	−	0.195985i
$746$	14.9610	+	18.8354i	0.547762	+	0.689613i
$747$		0			0
$748$	−12.8901	+	8.02980i	−0.471310	+	0.293598i
$749$	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	$0.647394\pi$
$752$	−7.82663	+	15.9346i	−0.285408	+	0.581074i
$753$		0			0
$754$	−5.61929	+	49.0175i	−0.204643	+	1.78511i
$755$	8.69983	+	5.35529i	0.316619	+	0.194899i
$756$		0			0
$757$	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	$0.105777\pi$
$758$	29.9986	−	23.8280i	1.08960	−	0.865471i
$759$		0			0
$760$	25.7515	+	2.81305i	0.934104	+	0.102040i
$761$			8.53590i			0.309426i	0.987959	+	0.154713i	$0.0494453\pi$
$761$			8.53590i			0.309426i	−0.987959	+	0.154713i	$0.950555\pi$
$762$		0			0
$763$	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
$767$			16.0130i			0.578195i
$768$		0			0
$769$	−1.87438			−0.0675917			−0.0337959	−	0.999429i	$-0.510760\pi$
$769$	−1.87438			−0.0675917			−0.0337959	+	0.999429i	$0.510760\pi$
$770$	2.58344	+	21.5205i	0.0931007	+	0.775546i
$771$		0			0
$772$	2.00498	−	8.62988i	0.0721610	−	0.310596i
$773$	−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	$0.434518\pi$
$774$		0			0
$775$	16.0297	+	31.7745i	0.575804	+	1.14137i
$776$	17.3319	+	6.17818i	0.622179	+	0.221784i
$777$		0			0
$778$	1.85822	−	1.47599i	0.0666205	−	0.0529169i
$779$	4.62326	+	4.62326i	0.165645	+	0.165645i
$780$		0			0
$781$	1.07180	−	1.07180i	0.0383519	−	0.0383519i
$782$	−5.35369	−	0.613739i	−0.191448	−	0.0219473i
$783$		0			0
$784$	−14.5781	−	7.16035i	−0.520645	−	0.255727i
$785$	−4.70580	+	1.11979i	−0.167957	+	0.0399669i
$786$		0			0
$787$	−7.03687	−	7.03687i	−0.250837	−	0.250837i	0.570477	−	0.821314i	$-0.306759\pi$
$787$	−7.03687	−	7.03687i	−0.250837	−	0.250837i	−0.821314	+	0.570477i	$0.806759\pi$
$788$	−15.3488	+	9.56139i	−0.546778	+	0.340610i
$789$		0			0
$790$	−27.9911	−	21.9909i	−0.995877	−	0.782403i
$791$		−	27.1339i		−	0.964770i
$792$		0			0
$793$	−17.9761			−0.638348
$794$	−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	$0.685138\pi$
$798$		0			0
$799$	−8.42995			−0.298230
$800$	−28.1330	−	2.92146i	−0.994651	−	0.103289i
$801$		0			0
$802$	−0.101904	+	0.888918i	−0.00359837	+	0.0313888i
$803$	−23.6809	−	23.6809i	−0.835682	−	0.835682i
$804$		0			0
$805$	−4.03172	+	6.54965i	−0.142099	+	0.230845i
$806$	28.9222	−	22.9730i	1.01874	−	0.809191i
$807$		0			0
$808$	−24.2966	+	11.5269i	−0.854752	+	0.405514i
$809$			5.40185i			0.189919i	0.995481	+	0.0949595i	$0.0302722\pi$
$809$			5.40185i			0.189919i	−0.995481	+	0.0949595i	$0.969728\pi$
$810$		0			0
$811$	−10.3478	−	10.3478i	−0.363360	−	0.363360i	0.501688	−	0.865049i	$-0.332712\pi$
$811$	−10.3478	−	10.3478i	−0.363360	−	0.363360i	−0.865049	+	0.501688i	$0.832712\pi$
$812$	−27.6728	+	17.2385i	−0.971124	+	0.604953i
$813$		0			0
$814$	−2.05080	+	17.8892i	−0.0718804	+	0.627017i
$815$	31.1824	−	7.42011i	1.09227	−	0.259915i
$816$		0			0
$817$			46.7385i			1.63517i
$818$	−37.0655	−	4.24913i	−1.29596	−	0.148568i
$819$		0			0
$820$	−5.07480	−	5.02096i	−0.177220	−	0.175340i
$821$	−10.7321	−	10.7321i	−0.374551	−	0.374551i	0.494581	−	0.869132i	$-0.335322\pi$
$821$	−10.7321	−	10.7321i	−0.374551	−	0.374551i	−0.869132	+	0.494581i	$0.835322\pi$
$822$		0			0
$823$	−3.51588			−0.122556			−0.0612780	−	0.998121i	$-0.519518\pi$
$823$	−3.51588			−0.122556			−0.0612780	+	0.998121i	$0.519518\pi$
$824$	−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	−0.0348631	−	0.999392i	$-0.511100\pi$
$827$	27.7375	−	27.7375i	0.964529	−	0.964529i	0.999392	+	0.0348631i	$0.0110995\pi$
$828$		0			0
$829$	−19.5849	+	19.5849i	−0.680212	+	0.680212i	−0.960048	−	0.279836i	$-0.909720\pi$
$829$	−19.5849	+	19.5849i	−0.680212	+	0.680212i	0.279836	+	0.960048i	$0.409720\pi$
$830$	−4.39693	−	36.6272i	−0.152620	−	1.27135i
$831$		0			0
$832$	2.94683	+	29.2065i	0.102163	+	1.01255i
$833$		−	7.71231i		−	0.267216i
$834$		0			0
$835$	−3.02380	+	4.91225i	−0.104643	+	0.169995i
$836$	31.8991	+	7.41113i	1.10325	+	0.256319i
$837$		0			0
$838$	−1.71153	−	2.15476i	−0.0591238	−	0.0744348i
$839$			40.0520i			1.38275i	0.722496	+	0.691375i	$0.242995\pi$
$839$			40.0520i			1.38275i	−0.722496	+	0.691375i	$0.757005\pi$
$840$		0			0
$841$		−	61.3992i		−	2.11722i
$842$	10.4249	−	8.28056i	0.359267	−	0.285367i
$843$		0			0
$844$	−18.2544	+	11.3714i	−0.628343	+	0.391421i
$845$	0.883749	+	0.544003i	0.0304019	+	0.0187143i
$846$		0			0
$847$			8.54182i			0.293500i
$848$	−2.57922	+	0.880095i	−0.0885706	+	0.0302226i
$849$		0			0
$850$	−4.64430	−	12.6022i	−0.159298	−	0.432252i
$851$	−4.51793	+	4.51793i	−0.154873	+	0.154873i
$852$		0			0
$853$	−13.7328	+	13.7328i	−0.470202	+	0.470202i	−0.901980	−	0.431778i	$-0.857886\pi$
$853$	−13.7328	+	13.7328i	−0.470202	+	0.470202i	0.431778	+	0.901980i	$0.357886\pi$
$854$	−7.38814	−	9.30140i	−0.252817	−	0.318287i
$855$		0			0
$856$	2.91094	+	6.13575i	0.0994938	+	0.209716i
$857$	39.9485			1.36462			0.682308	−	0.731065i	$-0.260976\pi$
$857$	39.9485			1.36462			0.682308	+	0.731065i	$0.260976\pi$
$858$		0			0
$859$	33.6366	+	33.6366i	1.14766	+	1.14766i	0.987011	+	0.160654i	$0.0513602\pi$
$859$	33.6366	+	33.6366i	1.14766	+	1.14766i	0.160654	+	0.987011i	$0.448640\pi$
$860$	−0.272167	−	51.0312i	−0.00928082	−	1.74015i
$861$		0			0
$862$	−0.658445	+	5.74366i	−0.0224267	+	0.195630i
$863$			16.5303i			0.562697i	0.959606	+	0.281349i	$0.0907817\pi$
$863$			16.5303i			0.562697i	−0.959606	+	0.281349i	$0.909218\pi$
$864$		0			0
$865$	43.6146	−	10.3785i	1.48294	−	0.352879i
$866$	41.1546	+	4.71791i	1.39849	+	0.160321i
$867$		0			0
$868$	23.7740	+	5.52343i	0.806943	+	0.187477i
$869$	−31.8205	−	31.8205i	−1.07944	−	1.07944i
$870$		0			0
$871$		−	9.36421i		−	0.317294i
$872$	5.33423	+	11.2436i	0.180640	+	0.380757i
$873$		0			0
$874$	7.22756	+	9.09924i	0.244476	+	0.307786i
$875$	−19.1005	−	1.61893i	−0.645714	−	0.0547297i
$876$		0			0
$877$	9.66381	+	9.66381i	0.326324	+	0.326324i	0.851187	−	0.524863i	$-0.175883\pi$
$877$	9.66381	+	9.66381i	0.326324	+	0.326324i	−0.524863	+	0.851187i	$0.675883\pi$
$878$	37.9058	+	4.34547i	1.27926	+	0.146652i
$879$		0			0
$880$	−34.8720	−	7.90605i	−1.17554	−	0.266513i
$881$	43.4299			1.46319			0.731596	−	0.681739i	$-0.238776\pi$
$881$	43.4299			1.46319			0.731596	+	0.681739i	$0.238776\pi$
$882$		0			0
$883$	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
$887$	−31.6913			−1.06409			−0.532045	−	0.846716i	$-0.678576\pi$
$887$	−31.6913			−1.06409			−0.532045	+	0.846716i	$0.678576\pi$
$888$		0			0
$889$			31.4168i			1.05368i
$890$	−23.4082	+	29.7950i	−0.784646	+	0.998732i
$891$		0			0
$892$	4.17498	−	17.9700i	0.139789	−	0.601680i
$893$	12.8541	+	12.8541i	0.430147	+	0.430147i
$894$		0			0
$895$	−7.23315	−	30.3967i	−0.241778	−	1.01605i
$896$	−13.9012	+	13.5286i	−0.464408	+	0.451959i
$897$		0			0
$898$	−3.72989	+	32.5361i	−0.124468	+	1.08574i
$899$	−47.8533	+	47.8533i	−1.59600	+	1.59600i
$900$		0			0
$901$	−0.915049	−	0.915049i	−0.0304847	−	0.0304847i
$902$	−5.61328	−	7.06692i	−0.186902	−	0.235303i
$903$		0			0
$904$	42.1637	+	15.0298i	1.40234	+	0.499884i
$905$	19.0893	−	4.54248i	0.634551	−	0.150997i
$906$		0			0
$907$	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	$0.0510705\pi$
$908$	13.7845	+	22.1280i	0.457454	+	0.734345i
$909$		0			0
$910$	2.37121	+	19.7527i	0.0786050	+	0.654794i
$911$	47.0459			1.55870			0.779350	−	0.626589i	$-0.215549\pi$
$911$	47.0459			1.55870			0.779350	+	0.626589i	$0.215549\pi$
$912$		0			0
$913$		−	46.6366i		−	1.54345i
$914$	−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
$918$		0			0
$919$		−	12.5442i		−	0.413796i	−0.978362	−	0.206898i	$-0.933663\pi$
$919$		−	12.5442i		−	0.413796i	0.978362	−	0.206898i	$-0.0663369\pi$
$920$	−7.94436	−	9.89287i	−0.261918	−	0.326158i
$921$		0			0
$922$	14.1482	+	17.8121i	0.465948	+	0.586612i
$923$	0.983751	−	0.983751i	0.0323806	−	0.0323806i
$924$		0			0
$925$	−15.1252	−	4.98165i	−0.497315	−	0.163796i
$926$	−11.1684	−	1.28033i	−0.367015	−	0.0420741i
$927$		0			0
$928$	−11.4588	−	52.5497i	−0.376155	−	1.72503i
$929$	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
$932$	24.1172	+	5.60316i	0.789986	+	0.183538i
$933$		0			0
$934$	−8.37851	+	6.65508i	−0.274153	+	0.217761i
$935$	−3.93058	−	16.5179i	−0.128544	−	0.540194i
$936$		0			0
$937$	−3.06580			−0.100155			−0.0500777	−	0.998745i	$-0.515947\pi$
$937$	−3.06580			−0.100155			−0.0500777	+	0.998745i	$0.515947\pi$
$938$	4.84535	−	3.84868i	0.158206	−	0.125664i
$939$		0			0
$940$	−14.1096	−	13.9599i	−0.460203	−	0.455321i
$941$	14.6023	−	14.6023i	0.476020	−	0.476020i	−0.427836	−	0.903856i	$-0.640724\pi$
$941$	14.6023	−	14.6023i	0.476020	−	0.476020i	0.903856	+	0.427836i	$0.140724\pi$
$942$		0			0
$943$		−	3.20239i		−	0.104284i
$944$	−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	$0.986959\pi$
$948$		0			0
$949$	−21.7356	−	21.7356i	−0.705567	−	0.705567i
$950$	−12.1343	+	26.2978i	−0.393689	+	0.853212i
$951$		0			0
$952$	−8.67619	−	3.09274i	−0.281197	−	0.100236i
$953$	−33.6807			−1.09103			−0.545513	−	0.838103i	$-0.683665\pi$
$953$	−33.6807			−1.09103			−0.545513	+	0.838103i	$0.683665\pi$
$954$		0			0
$955$	−22.1870	+	36.0434i	−0.717953	+	1.16634i
$956$	−15.1456	−	3.51878i	−0.489843	−	0.113805i
$957$		0			0
$958$	1.54460	−	13.4737i	0.0499039	−	0.435315i
$959$	25.6913			0.829616
$960$		0			0
$961$	19.6628			0.634283
$962$	−1.88233	+	16.4197i	−0.0606887	+	0.529391i
$963$		0			0
$964$	6.76128	+	1.57085i	0.217766	+	0.0505937i
$965$	8.43541	+	5.19253i	0.271546	+	0.167153i
$966$		0			0
$967$	8.70089			0.279802			0.139901	−	0.990166i	$-0.455322\pi$
$967$	8.70089			0.279802			0.139901	+	0.990166i	$0.455322\pi$
$968$	−13.2732	−	4.73142i	−0.426618	−	0.152074i
$969$		0			0
$970$	−12.7091	+	16.1767i	−0.408064	+	0.519402i
$971$	5.87523	+	5.87523i	0.188545	+	0.188545i	0.795067	−	0.606522i	$-0.207436\pi$
$971$	5.87523	+	5.87523i	0.188545	+	0.188545i	−0.606522	+	0.795067i	$0.707436\pi$
$972$		0			0
$973$	−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
$977$			41.8541i			1.33903i	0.742798	+	0.669516i	$0.233498\pi$
$977$			41.8541i			1.33903i	−0.742798	+	0.669516i	$0.766502\pi$
$978$		0			0
$979$	−33.8713	+	33.8713i	−1.08253	+	1.08253i
$980$	12.7715	−	12.9084i	0.407969	−	0.412344i
$981$		0			0
$982$	−36.6890	+	29.1422i	−1.17079	+	0.929966i
$983$	−57.4539			−1.83250			−0.916248	−	0.400612i	$-0.868797\pi$
$983$	−57.4539			−1.83250			−0.916248	+	0.400612i	$0.868797\pi$
$984$		0			0
$985$	−4.68030	−	19.6685i	−0.149127	−	0.626692i
$986$	19.9984	−	15.8848i	0.636880	−	0.505876i
$987$		0			0
$988$	29.2786	+	6.80232i	0.931477	+	0.216411i
$989$	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	$0.434726\pi$
$992$	−21.7516	+	33.8832i	−0.690616	+	1.07579i
$993$		0			0
$994$	0.913345	+	0.104705i	0.0289696	+	0.00332103i
$995$	11.1519	+	6.86467i	0.353538	+	0.217625i
$996$		0			0
$997$	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	$0.140304\pi$
$998$	11.8193	+	14.8801i	0.374135	+	0.471022i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.f.469.5		16
3.2	odd	2		80.2.q.c.69.4	yes	16
5.4	even	2	inner	720.2.bm.f.469.4		16
12.11	even	2		320.2.q.c.49.3		16
15.2	even	4		400.2.l.i.101.1		16
15.8	even	4		400.2.l.i.101.8		16
15.14	odd	2		80.2.q.c.69.5	yes	16
16.13	even	4	inner	720.2.bm.f.109.4		16
24.5	odd	2		640.2.q.e.609.3		16
24.11	even	2		640.2.q.f.609.6		16
48.5	odd	4		640.2.q.e.289.6		16
48.11	even	4		640.2.q.f.289.3		16
48.29	odd	4		80.2.q.c.29.5	yes	16
48.35	even	4		320.2.q.c.209.6		16
60.23	odd	4		1600.2.l.h.1201.6		16
60.47	odd	4		1600.2.l.h.1201.3		16
60.59	even	2		320.2.q.c.49.6		16
80.29	even	4	inner	720.2.bm.f.109.5		16
120.29	odd	2		640.2.q.e.609.6		16
120.59	even	2		640.2.q.f.609.3		16
240.29	odd	4		80.2.q.c.29.4	✓	16
240.59	even	4		640.2.q.f.289.6		16
240.77	even	4		400.2.l.i.301.1		16
240.83	odd	4		1600.2.l.h.401.6		16
240.149	odd	4		640.2.q.e.289.3		16
240.173	even	4		400.2.l.i.301.8		16
240.179	even	4		320.2.q.c.209.3		16
240.227	odd	4		1600.2.l.h.401.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.4	✓	16	240.29	odd	4
80.2.q.c.29.5	yes	16	48.29	odd	4
80.2.q.c.69.4	yes	16	3.2	odd	2
80.2.q.c.69.5	yes	16	15.14	odd	2
320.2.q.c.49.3		16	12.11	even	2
320.2.q.c.49.6		16	60.59	even	2
320.2.q.c.209.3		16	240.179	even	4
320.2.q.c.209.6		16	48.35	even	4
400.2.l.i.101.1		16	15.2	even	4
400.2.l.i.101.8		16	15.8	even	4
400.2.l.i.301.1		16	240.77	even	4
400.2.l.i.301.8		16	240.173	even	4
640.2.q.e.289.3		16	240.149	odd	4
640.2.q.e.289.6		16	48.5	odd	4
640.2.q.e.609.3		16	24.5	odd	2
640.2.q.e.609.6		16	120.29	odd	2
640.2.q.f.289.3		16	48.11	even	4
640.2.q.f.289.6		16	240.59	even	4
640.2.q.f.609.3		16	120.59	even	2
640.2.q.f.609.6		16	24.11	even	2
720.2.bm.f.109.4		16	16.13	even	4	inner
720.2.bm.f.109.5		16	80.29	even	4	inner
720.2.bm.f.469.4		16	5.4	even	2	inner
720.2.bm.f.469.5		16	1.1	even	1	trivial
1600.2.l.h.401.3		16	240.227	odd	4
1600.2.l.h.401.6		16	240.83	odd	4
1600.2.l.h.1201.3		16	60.47	odd	4
1600.2.l.h.1201.6		16	60.23	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.161069 - 1.40501i) q^{2} +(-1.94811 - 0.452606i) q^{4} +(1.17216 - 1.90421i) q^{5} +1.71452 q^{7} +(-0.949697 + 2.66422i) q^{8} +(-2.48664 - 1.95361i) q^{10} +(-2.82684 - 2.82684i) q^{11} +(-2.59462 - 2.59462i) q^{13} +(0.276156 - 2.40893i) q^{14} +(3.59030 + 1.76346i) q^{16} +1.89939i q^{17} +(2.89623 - 2.89623i) q^{19} +(-3.14537 + 3.17910i) q^{20} +(-4.42705 + 3.51643i) q^{22} -2.00613 q^{23} +(-2.25207 - 4.46410i) q^{25} +(-4.06338 + 3.22756i) q^{26} +(-3.34009 - 0.776005i) q^{28} +(6.72307 - 6.72307i) q^{29} -7.11778 q^{31} +(3.05596 - 4.76037i) q^{32} +(2.66867 + 0.305932i) q^{34} +(2.00970 - 3.26482i) q^{35} +(2.25207 - 2.25207i) q^{37} +(-3.60274 - 4.53572i) q^{38} +(3.96005 + 4.93133i) q^{40} +1.59630i q^{41} +(-8.06886 + 8.06886i) q^{43} +(4.22756 + 6.78645i) q^{44} +(-0.323124 + 2.81863i) q^{46} +4.43823i q^{47} -4.06040 q^{49} +(-6.63485 + 2.44515i) q^{50} +(3.88027 + 6.22896i) q^{52} +(-0.481758 + 0.481758i) q^{53} +(-8.69642 + 2.06939i) q^{55} +(-1.62828 + 4.56787i) q^{56} +(-8.36311 - 10.5289i) q^{58} +(-3.08580 - 3.08580i) q^{59} +(3.46410 - 3.46410i) q^{61} +(-1.14645 + 10.0006i) q^{62} +(-6.19615 - 5.06040i) q^{64} +(-7.98203 + 1.89939i) q^{65} +(1.80454 + 1.80454i) q^{67} +(0.859677 - 3.70023i) q^{68} +(-4.26341 - 3.34952i) q^{70} +0.379150i q^{71} +8.37718 q^{73} +(-2.80144 - 3.52691i) q^{74} +(-6.95303 + 4.33133i) q^{76} +(-4.84668 - 4.84668i) q^{77} +11.2566 q^{79} +(7.56641 - 4.76963i) q^{80} +(2.24282 + 0.257114i) q^{82} +(8.24890 + 8.24890i) q^{83} +(3.61685 + 2.22640i) q^{85} +(10.0372 + 12.6365i) q^{86} +(10.2160 - 4.84668i) q^{88} -11.9820i q^{89} +(-4.44854 - 4.44854i) q^{91} +(3.90816 + 0.907986i) q^{92} +(6.23577 + 0.714859i) q^{94} +(-2.12019 - 8.90989i) q^{95} -6.50543i q^{97} +(-0.654003 + 5.70491i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 8 q^{5} - 12 q^{10} - 8 q^{11} + 4 q^{14} + 16 q^{16} - 8 q^{19} + 4 q^{20} - 32 q^{26} + 16 q^{29} + 16 q^{31} + 48 q^{34} + 24 q^{35} + 24 q^{40} + 8 q^{44} - 28 q^{46} + 16 q^{49} - 24 q^{50}+ \cdots - 32 q^{95}+O(q^{100}) \) 16 * q - 4 * q^4 + 8 * q^5 - 12 * q^10 - 8 * q^11 + 4 * q^14 + 16 * q^16 - 8 * q^19 + 4 * q^20 - 32 * q^26 + 16 * q^29 + 16 * q^31 + 48 * q^34 + 24 * q^35 + 24 * q^40 + 8 * q^44 - 28 * q^46 + 16 * q^49 - 24 * q^50 + 56 * q^56 + 24 * q^59 - 16 * q^64 + 20 * q^70 - 88 * q^76 + 16 * q^79 - 16 * q^80 + 28 * q^86 - 16 * q^91 + 12 * q^94 - 32 * q^95

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